Deutsche Geophysikalische Gesellschaft e.V. ... - Bibliothek - GFZ

Deutsche 

Geophysikalische 

Gesellschaft e.V. 

Protokoll über das 

23. Schmucker-Weidelt-Kolloquium für 

Elektromagnetische Tiefenforschung, 

Heimvolkshochschule am Seddiner See, 

Oliver Ritter 

GeoForschungsZentrum 

Telegrafenberg 

14473 Potsdam 

28. September - 2. Oktober 2009 

ISSN 0946-7467 

herausgegeben von 

Ute Weckmann 

GeoForschungsZentrum 

Telegrafenberg 

14473 Potsdam

Widmung 

Wir wollen unser Kolloquium Ulrich Schmucker (1930 -2008) und Peter 

Weidelt (1938 – 2009) widmen und ihm den Namen „Schmucker-Weidelt- 

Kolloquium für Elektromagnetische Tiefenforschung“ geben. 

Unser Kolloquium soll Gespräche zwischen allen fördern, die mit 

elektromagnetischen Methoden das Innere der Erde erforschen wollen. 

Ulrich Schmucker und Peter Weidelt haben in diesem Kolloquium seit 

seiner Gründung neue und anspruchsvolle Methoden entwickelt, dort 

vorgestellt, oft sogar nur in diesem Kolloquium. Sie haben damit den 

internationalen Ruf dieses Kolloquiums begründet und das hohe 

intellektuelle Niveau dieser Forschungsrichtung weltweit bestimmt. 

Wenn wir dieses Kolloquium, das eigentlich auch ungenannt schon immer 

das Schmucker-Weidelt-Kolloquium war, nun auch so nennen wollen, dann 

hat das drei tiefe Gründe: 

Es sollen diese beiden Wurzeln unseres Kolloquiums und unserer 

Forschungsrichtung im Gedächtnis bleiben. 

Das Kolloquium soll uns Teilnehmer erinnern, auch in Zukunft die 

methodenorientierte Grundlagenforschung und ihre praktische Erprobung 

auf hohem Niveau als Ideal und Ziel dieses Kolloquiums anzustreben. 

Eine besondere Botschaft von Ulrich Schmucker und Peter Weidelt war es, 

gerade junge Studierende der elektromagnetischen Tiefenforschung von 

Anfang an in einen ernsthaften und lebhaften Kontakt mit allen 

Teilnehmern einzubinden, ihnen zuzuhören und zu helfen, sie zu kritisieren 

und Neues von ihnen zu lernen. Wenn wir diese Botschaft auch in Zukunft 

zum Arbeitsstil unseres Kolloquiums machen werden, wird die Entwicklung 

der elektromagnetischen Tiefenforschung so voller Dynamik bleiben, wie 

sie es bisher war.

I 

Vorwort 

Mit Erscheinen dieses Bandes und im Einvernehmen mit den Hinterbliebenen wollen wir von nun an 

das Kolloquium Prof. Ulrich Schmucker (1930 -2008) und Prof. Peter Weidelt (1938 – 2009) widmen. 

Den Wortlaut der Widmung haben wir an den Beginn des Bandes gestellt. Beide waren für die 

Entwicklung der elektromagnetischen Tiefenforschung weltweit von herausragender Bedeutung. Ihre 

Persönlichkeit und Schaffenskraft hatten aber vor allem in Deutschland einen maßgeblichen Anteil an 

der überaus positiven Entwicklung, die die Elektromagnetische Tiefenforschung genommen hat. 

Veranstalter des 23. Kolloquiums war das Deutsche GeoForschungsZentrum - GFZ. Der Tagungsort, 

die Heimvolkshochschule am Seddiner See, befand sich in unmittelbarer Nähe zur 

brandenburgischen Landeshauptstadt Potsdam, direkt am Großen Seddiner See, in einer für 

Brandenburg typischen Umgebung mit vielen Seen, Laub- und Kiefernwäldern. Am Kolloquium hatten 

sich 88 Teilnehmer angemeldet, größtenteils aus dem deutschsprachigen Raum, aber wie auch schon 

in den Jahren zuvor gab es auch diesmal eine ganze Reihe von Anmeldungen aus dem europäischen 

Ausland. Insgesamt waren 15 deutsche und 8 europäische Institutionen vertreten. 

Im Gedenken an Ulrich Schmucker hatten seine ehemaligen Schüler bereits ein Kolloquium vom 26 - 

28 Juni 2009 im Herz-Jesu Kloster in Neustadt ausgerichtet. Peter Weidelt wurde in einer Reihe von 

Beiträgen im Rahmen des 23. Kolloquiums gedacht und besonders gefreut hat uns, dass auch Heidi, 

Anne und Jan Weidelt anwesend waren. Im vorliegenden Tagungsband sind die meisten dieser 

Beiträge protokolliert. Allerdings haben wir uns entschlossen, sie nicht besonders hervorzuheben, 

sondern sie wie immer thematisch einzuordnen. 

Ulrich Schmucker und Peter Weidelt hatten von Beginn an in diesem Kolloquiumsband publiziert, oft 

sogar nur in diesem. Der diesjährige Band enthält 32 Beiträge. Es gab die übliche große Bandbreite an

Beiträgen die theoretisch- methodische Aspekte und experimentelle Untersuchungen im Hinblick auf 

geodynamische und angewandte Fragestellungen abdeckten. Generell war vielleicht eine Zunahme 

der mehr angewandten Arbeiten festzustellen, was sicherlich auch darauf zurückzuführen ist, dass 

die elektromagnetischen Verfahren mittlerweile fester Bestandteil der Exploration im off-shore aber 

auch on-shore Bereich geworden sind. 

Quicklebendige Debatten gab es auch im Rahmen unserer neuen Rubrik „Was Sie schon immer über 

die Elektromagnetik wissen wollten, sich bisher aber nicht zu fragen trauten.“, die Ute Weckmann 

angeregt hatte. Insbesondere sollten damit die jüngeren Teilnehmer angesprochen werden, jedoch 

hatten offensichtlich besonders viele der Ü40 Teilnehmer noch jahrelang unbeantwortet gebliebene 

Fragen. Manchmal war für die Beantwortung der Fragen auch etwas mehr Zeit zum Nachdenken 

nötig, weshalb wir eine nach dem Kolloquium entstandene Antwort in diesen Band ebenfalls 

aufgenommen haben. 

Für die finanzielle Unterstützung danken wir auch unseren Sponsoren: den Firmen KMS und 

Metronix. Herzlich bedanken möchten wir uns bei Frau Hannelore Gendt (GFZ) für die Hilfe bei 

administrativen und finanziellen Aufgaben. Herrn Palm und dem Daten- und Rechenzentrum sei für 

die Einrichtung des Internetportals gedankt. Roxana Barth und Gregor Willkommen haben für den 

reibungslosen Ablauf während des Kolloquiums gesorgt und auch tatkräftig bei der 

Zusammenstellung dieses Bandes geholfen. Natürlich ließ sich ein solches Kolloquium nur mit der 

Unterstützung der gesamten MT Arbeitsgruppe des GFZ durchführen. Ein herzliches Dankeschön 

dafür; ebenso an Herrn Bertelmann von der Bibliothek für das Hosting der Protokollbände. 

Oliver Ritter und Ute Weckmann 

Potsdam, 6. Juni 2010

II 

Inhaltsverzeichnis / table of contents 

Rita Streich & Michael Becken, EM fields generated by finite-length wire sources in 1D media: 

comparison with point dipole solutions ............................................................................................1 

M. Afanasjew, R.-U. Börner, M. Eiermann, O. G. Ernst, S. Güttel & K. Spitzer, 2D Time Domain TEM 

Simulation Using Finite Elements, an Exact Boundary Condition, and Krylov Subspace Methods 16 

Tilman Hanstein, TEM with anomalous diffusion in fractal conductive media. .................................... 25 

K. M. Bhatt, A. Hördt & T. Hanstein, Analysis of seafloor marine EM data with respect to motioninduced 

noise ................................................................................................................................ 33 

K. M. Bhatt, A. Hördt, P.Weidelt & T. Hanstein, Motionally Induced Electromagnetic Field within the 

Ocean................... .......................................................................................................................... 46 

S. Kütter, A. Franke-Börner, R.-U. Börner & K. Spitzer, Three-dimensional finite element simulation of 

magnetotelluric fields incorporating digital elevation models ...................................................... 60 

M. Becken, R. Streich & O. Ritter, Establishing Controlled Source MT at GFZ ...................................... 71 

Johannes Kenkel, Andreas Hördt & Andreas Kemna, 2D-SIP-Modellierung mit anisotropen 

Widerständen. ................................................................................................................................ 77 

Xiaoming Chen, Ute Weckmann, Kristina Tietze, Towards a 2D anisotropic inversion. ....................... 88 

Kristina Tietze, Oliver Ritter & Ute Weckmann, Substitute models for static shift in 2D. ..................... 97 

Andreas Hördt, Peter Weidelt & Anita Przyklenk, Die Übergangsimpedanz einer kapazitiv 

angekoppelten Elektrode ............................................................................................................. 102 

Häuserer & Junge, Eine Methode gegen auslaufende Ag/AgCl//KCl(H2O) Elektroden ...................... 115 

Johannes B. Stoll, Celle, Christopher Virgil, Attitude Algorithm Utilised in Mobile Geophysical 

Measuring Systems ...................................................................................................................... 120 

G. Muñoz, K. Bauer, I. Moeck, O. Ritter, Joint Interpretation of Magnetotelluric and Seismic Models 

for Exploration of the Gross Schoenebeck Geothermal Site ......................................................... 126 

Ulrich Kalberkamp, Magnetotelluric measurements to explore for deeper structures of the Tendaho 

geothermal field, Afar, NE Ethiopia.. ............................................................................................ 131 

J. H. Börner, V. Herdegen, R.-U. Börner, K. Spitzer, Electromagnetic Monitoring of CO2 Storage in Deep 

Saline Aquifers - Numerical Simulations and Laboratory Experiments. ....................................... 137 

K. Lippert, B. Tezkan, R. Bergers, M. Gurk, M. v. Papen, P. Yogeshwar, Erkundung eines Aquifers unter 

dem Mittelmeer vor der israelischen Küste mit LOTEM. .............................................................. 143 

M. von Papen, B. Tezkan, On the analysis of LOTEM time series from Israel and the preliminary 1D 

inversion of data ........................................................................................................................... 149 

P. Yogeshwar, B. Tezkan, M. Israil, Grundwasserkontamination bei Roorkee/Indien: 2D Joint Inversion 

von Radiomagnetotellurik und Gleichstromgeoelektrik Daten .................................................... 153 

Widodo, Marcus Gurk, Bülent Tezkan, Site Effect Assessment in the Mygdonian Basin (EUROSEISTEST 

area, Northern Greece) using RMT and TEM Soundings .............................................................. 164 

Gerlinde Schaumann, Annika Steuer, Bernhard Siemon, Helga Wiederhold & Franz Binot, Die 

deutsche Nordseeküste im Fokus von aeroelektromagnetischen Untersuchungen Teilgebiete 

Langeoog mit Wattenmeer und Elbemündung ............................................................................ 177

Annika Steuer, Bernhard Siemon and Michael Grinat, The German North Sea Coast in Focus of 

Airborne Electromagnetic Investigations: The Freshwater Lenses of Borkum ............................. 188 

Gerhard Kapinos & Heinrich Brasse, Some notes on bathymetric effects in marine magnetotellurics, 

motivated by an amphibious experiment at the South Chilean margin ...................................... 198 

Dirk Brändlein, Oliver Ritter, Ute Weckmann, A permanent array of magnetotelluric stations located 

at the South American subduction zone in Northern Chile. ......................................................... 210 

D. Eydam & H. Brasse, Discussion on backarc mantle melting in the central Andean subduction zone, 

based on results of magnetotelluric studies ................................................................................. 216 

Václav Červ, Světlana Kováčiková, Michel Menvielle and Josef Pek, Thin Sheet Conductance Models 

from Geomagnetic Induction Data: Application to Induction Anomalies at the Transition from the 

Bohemian Massif to the West Carpathians .................................................................................. 232 

Anne Neska, Subsurface Conductivity Obtained from DC Railway Signal Propagation with a Dipole 

Model ........................................................................................................................................... 244 

Anja Schäfer, Heinrich Brasse, Norbert Hoffmann and EMTESZ working group, Magnetotelluric 

investigation of the Sorgenfrei-Tornquist Zone and the NE German Basin ................................. 252 

P. Sass, O. Ritter, A. Rybin, G. Muñoz, V. Batalev and M. Gil, Magnetotelluric data from the Tien Shan 

and Pamir continental collision zones, Central Asia ..................................................................... 263 

Alexander Löwer, Audiomagnetotellurik im Hohen Vogelsberg ......................................................... 269 

Ute Weckmann, Carsten Scholl, Dumme Fragen ................................................................................ 277

III 

Teilnehmerverzeichnis 

YassineAbdelfettah LaboratoiredeGéothermie,Neuchâtel,Suisse 

FilipeAdão CentrodeGeofísicadaUniversidadedeLisboa,Lisboa,Portugal 

JulianeAdrian UniversitätzuKöln,InstitutfürGeophysikundMeteorologie 

MartinAfanasjew TUBergakademieFreiberg 

KatharinaBairlein TUBraunschweig 

RoxanaBarth UniversitätPotsdam 

MichaelBecken DeutschesGeoForschungsZentrumPotsdamGFZ 

K.MangalBhatt TUBraunschweig 

DirkBrändlein DeutschesGeoForschungsZentrumPotsdamGFZ 

AnneBublitz J.W.GoetheUniversität,FrankfurtamMain 

MatthiasBücker TUBraunschweig 

XiaomingChen DeutschesGeoForschungsZentrumPotsdamGFZ 

JinChen IFMGEOMAR,Kiel 

DanielDiaz FUBerlin 

SebastianEhmann TUBraunschweig 

DianeEydam DeutschesGeoForschungsZentrumPotsdamGFZ 

JohannesGeiermann igem,Bingen 

MichaelGrinat LeibnizInstitutfürAngewandteGeophysik,Hannover(LIAG) 

HannahGroßbach UniversitätzuKöln,InstitutfürGeophysikundMeteorologie 

MarkusGurk UniversitätzuKöln,InstitutfürGeophysikundMeteorologie 

VolkerHaak Blankenfelde 

TilmanHanstein KMSTechnologiesGmbH,Köln 

MichaelHäuserer J.W.GoetheUniversität,FrankfurtamMain 

BjörnHenningHeincke IFMGEOMAR,Kiel 

WiebkeHeise CentrodeGeofísicadaUniversidadedeLisboa,Lisboa,Portugal 

StefanHendricks AlfredWegenerInstitut,Bremerhaven 

PaulHofmeister TUBraunschweig 

SebastianHölz IFMGEOMAR,Kiel

AndreasHördt TUBraunschweig 

AndreasJunge J.W.GoetheUniversität,FrankfurtamMain 

UlrichKalberkamp FederalInstituteforGeosciencesandNaturalResources,Hannover(BGR) 

ThomasKalscheuer ETHZurich,Zurich,Switzerland 

JochenKamm UppsalaUniversity,DepartmentofEarthSciences,Uppsala,Sweden 

GerhardKapinos FUBerlin 

JohannesKenkel TUBraunschweig 

JudithKirchner TUBergakademieFreiberg 

FlorianLePape DIAS,Dublin,Ireland 

JochenLehmannHorn ETHZurich,Zurich,Switzerland 

MartinLeven InstitutfürGeophysik,UniversitätGöttingen 

ShengjunLiang TUBergakademieFreiberg 

MaikLinke TUBergakademieFreiberg 

KlausLippert UniversitätzuKöln,InstitutfürGeophysikundMeteorologie 

AlexanderLöwer J.W.GoetheUniversität,FrankfurtamMain 

StephanMalecki TUBergakademieFreiberg 

EricMandolesi DIAS,Dublin,Ireland 

NaserMeqbel DeutschesGeoForschungsZentrumPotsdamGFZ 

MarionMiensopust DIAS,Dublin,Ireland 

MaxMoorkamp IFMGEOMAR,Kiel 

DanaMoritz TUBergakademieFreiberg 

GerardMuñoz DeutschesGeoForschungsZentrumPotsdamGFZ 

LutzMütschard FUBerlin 

AnneNeska InstituteofGeophysics,PolishAcad.Sci.,CentralneObserwatorium 

Geofizyczne,BelskDuzy,Poland 

LaustB.Pedersen UppsalaUniversity,DepartmentofEarthSciences,Uppsala,Sweden 

JosefPek InstituteofGeophysics,Acad.Sci.CzechRep.,Prague,CzechRepublic 

AnitaPrzyklenk TUBraunschweig 

LasseRabenstein AWIBremerhaven 

TinoRadic RadicResearch,Berlin 

ZhengyongRen ETHZurich,Zurich,Switzerland 

OliverRitter DeutschesGeoForschungsZentrumPotsdamGFZ

AnnikaRödder UniversitätzuKöln,InstitutfürGeophysikundMeteorologie 

EstelleRoux DIAS,Dublin,Ireland 

AnjaSchäfer FUBerlin 

GerlindeSchaumann LeibnizInstitutfürAngewandteGeophysik,Hannover(LIAG) 

CarstenScholl FugroElectroMagnetic,Berlin 

KatrinSchwalenberg FederalInstituteforGeosciencesandNaturalResources,Hannover(BGR) 

KlausSpitzer TUFreibergTUBergakademieFreiberg 

AnnikaSteuer LeibnizInstitutfürAngewandteGeophysik,Hannover(LIAG) 

JohannesStoll Celle 

KurtStrack KMSTechnologies,HoustonTX,USA 

RitaStreich DeutschesGeoForschungsZentrumPotsdamGFZ 

BülentTezkan UniversitätzuKöln,InstitutfürGeophysikundMeteorologie 

KristinaTietze DeutschesGeoForschungsZentrumPotsdamGFZ 

AndreaTreichel WestfälischeWilhelmsUniversität,Münster 

ChristopherVirgil TUBraunschweig 

MichaelvonPapen UniversitätzuKöln,InstitutfürGeophysikundMeteorologie 

UteWeckmann DeutschesGeoForschungsZentrumPotsdamGFZ 

JuliaWeißflog TUBergakademieFreiberg 

Widodo UniversitätzuKöln,InstitutfürGeophysikundMeteorologie 

GregorWillkommen UniversitätPotsdam 

HelmuthWinter J.W.GoetheUniversität,FrankfurtamMain 

TamaraWorzewski IFMGEOMAR,Kiel 

PritamYogeshwar UniversitätzuKöln,InstitutfürGeophysikundMeteorologie 

FanZhang TUBergakademieFreiberg

EM fields generated by finite-length wire sources in 1D 

media: comparison with point dipole solutions 

Rita Streich ∗† and Michael Becken ∗† , 

∗ Potsdam University, Institute of Geosciences, 

Karl-Liebknecht-Str. 24, 14476 Potsdam-Golm, Germany 

† GFZ German Research Centre for Geosciences, 

Telegrafenberg, 14473 Potsdam, Germany 

ABSTRACT 

In present-day land and marine controlled-source electromagnetic (CSEM) surveys, EM 

fields are commonly generated using wires that are hundreds of meters long. Nevertheless, 

simulations of CSEM data often approximate these sources as point dipoles. 

Although this is justified for sufficiently large source-receiver distances, many real surveys 

include frequencies and distances at which the dipole approximation is inaccurate. 

For 1D layered media, EM fields for point dipole sources can be computed using 

well-known quasi-analytical solutions, and fields for sources of finite lengths can be 

synthesized by superposing point dipole fields. However, the calculation of numerous 

point dipole fields is computationally expensive, requiring a large number of numerical 

integral evaluations. We combine a more efficient representation of finite-length sources 

in terms of components related to the wire and its end points with very general expressions 

for EM fields in 1D layered media. We thus obtain a formulation that requires 

fewer numerical integrations than the superposition of dipole fields and permits source 

and receiver placement at any depth within the layer stack. Complex source geometries, 

such as wires bent due to surface obstructions, can be simulated by segmenting 

the wire and computing the responses for each segment separately. We first describe 

our finite-length wire expressions, and then present examples of EM fields due to finitelength 

wires for typical land and marine survey geometries and discuss differences to 

point dipole fields. 

INTRODUCTION 

Controlled-source electromagnetic (CSEM) surveys are a useful exploration tool, applicable, 

e.g., for exploring hydrocarbon reservoirs, geothermal reservoirs, or for characterizing 

and potentially monitoring sites considered for carbon sequestration. A multitude of active 

electromagnetic sources are available, including magnetic loops (Frischknecht et al., 1991; 

Spies and Frischknecht, 1991) and long wires, grounded in land-based surveys (Strack, 1992; 

Wright et al., 2002; Ziolkowski et al., 2007) and deployed at the seafloor (Edwards, 2005) or 

towed through the water (e.g., Constable and Srnka, 2007) in marine surveys. Wire sources 

with lengths of several 100 m are most commonly used in commercial hydrocarbon exploration 

because of their capability to generate three-dimensional electrical current systems 

sensitive to both resistive and conductive, relatively deep targets (Spies and Frischknecht, 

1991; Constable and Srnka, 2007). 

23. Schmucker-Weidelt-Kolloquium für Elektromagnetische Tiefenforschung, 

Heimvolkshochschule am Seddiner See, 28 September - 2 Oktober 2009 

1

In processing, inversion and interpretation of CSEM data, the sources are commonly 

approximated as point dipoles (e.g., Edwards, 1997; Johansen et al., 2005; Ziolkowski et al., 

2007). This is adequate for sufficiently large source-receiver distances. However, real surveys 

targeting increasingly deep and small structures may include distances and frequencies at 

which the inaccuracy of the dipole approximation is on the order of (or larger than) the 

target-related anomalies. In such cases, it is vital to consider the actual source geometry. 

For horizontally layered media, EM fields can be computed using well-known quasianalytical 

solutions that involve numerical evaluations of Bessel function integrals (e.g., 

Weidelt, 2007; Løseth and Ursin, 2007). Using such point dipole solutions, EM fields due 

to finite-length wire sources can be synthesized by representing the wire as a line of point 

dipoles and summing the dipole fields. However, this procedure is computationally expensive, 

requiring many numerical integrations to calculate all of the point dipole contributions. 

To improve the efficiency of long-wire source simulations, Soerensen and Christensen 

(1994) derived integrated Hankel integral expressions for finite-length wires that barely 

require more integral evaluations than the computation of point dipole fields. However, their 

approach includes elaborate computations of filter coefficients for every source-receiver pair. 

Another approach that reduces the number of integrations from that required for summing 

dipole fields is the separation of EM fields due to long wires into contributions from the wire 

and its end points (Ward and Hohmann, 1987). This technique works with standard Hankel 

filters. Whereas previous application of this approach considered subsurface receivers and 

sources located at the air-ground interface (Ward and Hohmann, 1987), we have applied 

it to a more general 1D field formulation that permits source and receiver positions at 

arbitrary depths within the layer stack (Løseth and Ursin, 2007). This allows simulations 

of finite marine sources in addition to land sources. 

In this contribution, we first describe our finite-length wire representation. We then show 

examples of EM fields due to finite-length wires in representative land and marine settings 

over the frequency and distance ranges of typical CSEM surveys, and discuss differences to 

the fields due to infinitesimal dipoles. 

EM FIELD EXPRESSIONS FOR FINITE-LENGTH WIRES 

Expressions for the electromagnetic field due to a finite-length wire can be obtained by 

representing the wire as a line of infinitesimal dipoles and integrating the dipole expressions 

along the length of the wire. Using the nomenclature of Løseth and Ursin (2007), the EM 

fields for an x-directed point dipole embedded in a 1D layered medium can be expressed in 



2

a form convenient for later integration as (see Appendix A) 

Ex = Idx 

⎛ 

∞ 

−μ0 ⎝ √ 

4π pr zp 0 

s R 

z 

A ⎧ 

⎨ 

x 

11κJ0(κr)dκ+∂x 

⎩ 

r−xs∞ 

μ0 

√ 

r pr zp 0 

s R 

z 

A 

pr zp 11− 

s z 

˜ε r ˜ε s RA ⎫⎞ 

⎬ 

22 J1(κr)dκ ⎠, (1a) 

⎭ 

Ey = Idx 

4π ∂x 

⎧ 

⎨ 

y 

⎩ 

r − ys∞ 

μ0 

√ 

r pr zp 

0 

s R 

z 

A 

pr zp 11 − 

s z 

˜ε r ˜ε s RA ⎫ 

⎬ 

22 J1(κr)dκ , (1b) 

⎭ 

Ez = jIdx 

⎧ 

⎨∞ 

˜ε 

∂x 

4πω˜ε r ⎩ 

0 

r ˜ε s 

pr zps R 

z 

D 22κJ0(κr)dκ ⎫ 

⎬ 

, (1c) 

⎭ 

Hx = Idx 

4π ∂x 

⎧ 

⎨ 

y 

⎩ 

r − ys ∞ 

 

p 

r 

0 

r z 

ps R 

z 

D 11 − 

 

˜ε rps z 

˜ε spr R 

z 

D ⎫ 

⎬ 

22 J1(κr)dκ , (1d) 

⎭ 

Hy = Idx 

⎛ 

∞ 

⎝ 

p 

4π 

r z 

ps R 

z 

D 11κJ0(κr)dκ ⎧ 

⎨ 

x 

− ∂x 

⎩ 

r−x s ∞ 

p 

r 

r z 

ps R 

z 

D 11− 

˜ε rps z 

˜ε spr R 

z 

D ⎫⎞ 

⎬ 

22 J1(κr)dκ ⎠, (1e) 

⎭ 

Hz = jIdx 

4πωμ0 

0 

yr − ys 

r 

0 

∞ 

0 

μ0 

√ 

pr zps R 

z 

A 11κ2J1(κr)dκ, (1f) 

where I is the source current, dx is the length of the source dipole, κ is the horizontal 

wavenumber, ω is the angular frequency, μ0 is the vacuum magnetic permeability, 

˜ε {s,r} = ε {s,r} + jσ {s,r} /ω are the dielectric permittivity and electric conductivity of the 

source and receiver layer, respectively, p {s,r} 

z 

= μ0˜ε {s,r} − κ 2 /ω 2 are frequency-normalized 

vertical wavenumbers, r = (x r − x s ) 2 +(y r − y s ) 2 is the horizontal source-receiver distance, 

and J0 and J1 are the zero- and first-order Bessel functions. R A 11 , RA 22 , RD 11 and RD 22 

are the reflection responses of the layered medium as given by Løseth and Ursin (2007, their 

Equation 134). These quantities are computed recursively using the properties and thicknesses 

of all layers and the source and receiver depths. Subscripts 11 denote the TE-mode 

and subscripts 22 the TM-mode responses. Slightly different expressions apply for receivers 

below (Equations 134a and b) and above the source (Equations 134c and d of Løseth and 

Ursin, 2007). In Equations (1), a spatial derivative ∂x has been retained wherever possible. 

To obtain electromagnetic fields for a finite-length wire, we integrate Equations (1) over 

thewirelength. Assumingthatthewireisparalleltothex-axis, we express the integrals as 

discrete sums over N wire elements of length Δx, located at (xn,y s ,z s ). The derivatives ∂x 

are replaced by −∂/∂Δx (Ward and Hohmann, 1987). Then the fields at receiver location 



3

(x r ,y r ,z r )are 

Ex = I 

4π 

− I 

4π 

Ey = − I 

4π 

N 

 

Δx 

n=1 

2 

m=1 

0 

∞ 

−κμ0 

√ 

pr zps R 

z 

A 11J0(κrn)dκ 

(−1) m x r − xm 

rm 

∞ 

0 

∞ 

2 

(−1) m yr − ys 

m=1 

Ez = − jI 

4πω˜ε r 

Hx = − I 

4π 

Hy = I 

4π 

+ I 

4π 

rm 

2 

(−1) m 

 

m=1 

0 

∞ 

 

2 

(−1) m yr − ys m=1 

N 

 

Δx 

n=1 

2 

m=1 

Hz = jI(yr − y s ) 

4πμ0ω 

0 

∞ 

 

pr z 

ps z 

rm 

(−1) m x r − xm 

rm 

N Δx 

n=1 

rn 

0 

 

 

μ0 

√ 

pr zps R 

z 

A 11 − 

μ0 

√ 

pr zps R 

z 

A 11 − 

p r zp s z 

˜ε r ˜ε r RA 22 

p r zp s z 

˜ε r ˜ε r RA 22 

 

J1(κrm)dκ, (2a) 

 

J1(κrm)dκ, (2b) 

˜ε rps z 

˜ε spr R 

z 

D 22κJ0(κrm)dκ, (2c) 

∞ 

0 

 

pr z 

ps z 

R D 11κJ0(κrn)dκ 

∞ 

0 

∞ 

0 

 

pr z 

ps z 

R D 11 − 

 

˜ε rps z 

˜ε spr R 

z 

D 

22 J1(κrm)dκ, (2d) 

R D 

11 − 

˜ε rps z 

˜ε spr R 

z 

D 

22 J1(κrm)dκ, (2e) 

μ0 

√ 

pr zps R 

z 

A 11κ 2 J1(κrn)dκ. (2f) 

For Ex, Hy and Hz, we obtain a contribution from each wire element. This contribution 

is described by the first sum in Equations 2a, 2e and 2f, with the distance between the 

receiver and the n th wire element given by rn = (x r − xn) 2 +(y r − y s ) 2 .Uponintegrating 

those terms of Equations (1) that contain derivatives ∂x, the derivatives disappear, and we 

obtain explicit contributions from the integration limits, i.e., the end points of the wire. In 

Equations (2), the end point contributions are given by the summation over m (m ∈{1, 2}), 

with the distances between the receiver and the wire ends denoted rm. 

To compute all EM field components for a finite-length wire using Equation (2), we 

have to evaluate three different integrals over the entire wire length. Accordingly, for a 

wire discretized into N elements, the number of numerical integral evaluations is approximately 

3N. In contrast, Equation (A-7) shows that two different integrals are required 

for computing only Ex for an infinitesimal dipole. The computation of all electromagnetic 

field components for a horizontal electric point dipole source requires numerical evaluations 

of eight different integrals (Løseth and Ursin, 2007). This would result in 8N numerical 

integrations when calculating finite-length wire fields from the contributions of N dipole 

elements. Compared to the simple summation of dipole fields, the separate computation of 

wire and end point contributions thus reduces the computational effort by more than 60%. 



4

EXAMPLES 

We use the expressions of EM fields due to finite-length wires given in Equation (2) to assess 

differences between the fields of finite sources and point dipoles for different representative 

experimental settings of land and marine surveys. 

Land survey: straight grounded wire 

We have simulated a land survey using the setup depicted in Figure 1. The electric conductivity 

model is based on the situation at the CO2 sequestration pilot site in Ketzin, 

Germany, using measured conductivity values and the actual depth and thickness of the 

layer into which CO2 is being injected (Giese et al., 2009). To simulate a realistic survey, 

in which sensors would typically be buried just below the surface, we placed electric and 

magnetic field receivers at a depth of 0.15 m. EM fields were computed for an infinitesimal 

dipole source at (x, y) =(0, 0) and a 1-km long finite-length wire centered at (x, y) =(0, 0). 

Both sources were located at a depth of 0.1 m. 

surface 

source, 

centered 

at (0,0) 

air 

1/3 

0.1 

1 S/m 

10 km 

surface 

receivers 

15 km 

0 

635 

650 

z (m) 

Figure 1: The 1D conductivity model and survey geometry used for simulating a land CSEM 

survey. The red arrow indicates the point dipole or 1000-m long wire source, centered at 

(x, y) =(0, 0) and located 0.1 m below the surface. Receivers are located 0.15 m below the 

surface. 

For convenience in the numerical simulations, we place the entire wire at a constant 

depth, either above or below the air-ground interface, although in real field surveys, grounded 

wires would typically be used, with the wire laid out on the surface and the end points coupled 

into the ground, e.g., via metal electrodes. The contribution from the wire body is 

typically smaller than that from the grounding points, and varies slowly as the wire depth 

crosses interfaces. Therefore, this simplification does not cause noticeable errors. 

In Figure 2, we display the electric field component Ex at a frequency of 0.1 Hz for 

the model depicted in Figure 1. The finite-wire and point dipole fields differ significantly 

withinaradiusof∼ 4 km from the source. Large relative differences also occur in the 

lowest-amplitude regions at oblique angles to the source; however, these are insignificant, 

because in these regions, Ex would not be measurable. 

For comparison, we show in Figure 3 the electric field for the reservoir model of Fig- 



5

y (km) 

−6 

−3 

0 

3 

6 

(a) 

0 3 6 9 

x (km) 

y (km) 

−6 

−3 

−14 −12 −10 −8 

log10( | Ex [V/m] |) 

0 

3 

6 

(b) 

0 3 6 9 

x (km) 

y (km) 

−6 

−3 

0 

3 

6 

(c) 

0 3 6 9 

x (km) 

| Ex wire / Ex dipole 0.8 1 1.2 

| 

Figure 2: Electric field Ex for the configuration shown in Figure 1, a frequency of 0.1 Hz 

and (a) a point dipole source at (0, 0, 0.1) m and (b) a 1000-m long grounded wire extending 

from (−500, 0, 0.1) to (500, 0, 0.1) m. (c) shows the ratio between the finite-length wire and 

point dipole fields. 

ure 1 relative to the electric field for a model that does not contain a resistive layer. This 

demonstrates the size of the anomaly we would attempt to detect in the CSEM survey. The 

reservoir-related anomaly is smaller than the relative differences between finite-length wire 

and dipole fields, and overlaps spatially with the region in which the response is significantly 

influenced by the source geometry. This clearly indicates the importance of considering the 

true source geometry. 

Similar observations can be made over a wide frequency range. In Figure 4, we compare 

the electric field Ex for finite-length and point dipole sources, and for the reservoir and 

background models, at frequencies of 0.001 Hz and 1 Hz. Significant differences between 

finite-length and point dipole sources occur in a similar region as for f =0.1 Hz(compare 

Figures 4a and b to Figure 2c). The reservoir-related anomalies are somewhat smaller than 

for f =0.1 Hz, underlining again that it is vital to consider the actual source length when 

searching for such relatively small anomalies. 

In Figure 5, we display the finite-length wire fields for the Ey and Ez components, 

and their ratios to the respective point dipole fields. Here, the relative differences between 

the finite-length wire and point dipole fields are of similar size as for Ex. The regions in 

which the responses of finite-length wires and point dipoles differ significantly are similar, 

or slightly larger, in extent than for Ex. However, the amplitudes of Ez are considerably 

smaller than those of Ex and Ey, such that nearly the entire region in which Ez would 

be measurable (assuming instrument detection thresholds of ∼ 10 −14 − 10 −15 , and possible 

measurement of Ez in shallow boreholes) is strongly influenced by the source geometry. 



6

y (km) 

−6 

−3 

0 

3 

6 

0 3 6 9 

x (km) 

Figure 3: Electric field Ex for the configuration shown in Figure 1, a 1000-m long wire source 

and f =0.1 Hz, normalized by the electric field for a background model not containing a 

resistive layer. 

Required wire discretization 

To minimize the computational effort, we have empirically investigated the effects of wire 

discretization on the resulting electromagnetic field values. In Figure 6, we display differences 

between a reference field Ex computed for a 1000-m long wire discretized using an 

element length of 0.1 m, and more coarsely discretized wires with element lengths varying 

between 1 m and 50 m. As expected, differences between the reference field and fields computed 

using coarser discretizations increase as the element length increases. Nevertheless, 

at the lower frequency of 0.1 Hz (Figure 6a), differences are small for all tested element 

lengths. As expected, differences are larger at f = 100 Hz, with maximum differences 

occurring in the vicinity of the end point of the wire at x = 500 m. 

From this test, we conclude that for the lower frequency, a coarse discretization of ∼ 

20−50 m would be sufficient, whereas for the higher frequency, the wire should be discretized 

using elements no longer than ∼ 2 − 5 m. These results may serve as rough guidelines for 

further simulation studies, but actual required discretizations are likely to depend on the 

total wire length and the resistivity model. To exclude any discretization-related error, 

all results presented here were computed using somewhat too careful discretizations with 

element lengths of 1 m. 

Non-straight grounded wire 

In real field surveys, surface obstacles may preclude laying out the source wire in a straight 

line. We have therefore studied differences between the EM fields for straight and nonstraight 

wire sources. EM fields for non-straight wires are calculated by segmenting the 

wire into straight sections, and computing the responses for each segment separately using 

1.2 

1.1 

1 

0.9 

0.8 



7 

|Ex reservoir / Ex background |

y (km) 

y (km) 

−6 

−3 

0 

3 

6 

−6 

−3 

(a) 

0 3 6 9 

x (km) 

0 

3 

6 

(c) 

0 3 6 9 

x (km) 

y (km) 

y (km) 

−6 

−3 

0 

3 

6 

−6 

−3 

(b) 

0 3 6 9 

x (km) 

0 

3 

6 

0 3 6 9 

x (km) 

Figure 4: Ratio of Ex for a 1000-m long wire source to Ex for a point dipole for frequencies 

of (a) 0.001 Hz and (b) 1 Hz, and ratio of Ex for a 1000-m long wire source and the reservoir 

model shown in Figure 1 relative to Ex for a background model not containing the resistive 

layer for frequencies of (c) 0.001 Hz and (d) 1 Hz. 

Equations (2) with appropriate rotations. As an example, we have computed the responses 

for a wire that consists of two segments arranged at a 120 ◦ angle. This wire has the same 

grounding points as the 1000-m long straight wire used previously. Figure 7 shows the wire 

geometry and the electric field Ex for the bent wire relative to Ex for a straight wire at 

frequencies of 0.001 Hz, 0.1 Hz and 1 Hz. 

As expected, the Ex amplitudes for the bent wire are increased relative to the straight 

wire field at the side to which the wire is deviated (y >0), and decreased at y

y (km) 

y (km) 

−6 

−3 

0 

3 

6 

−6 

−3 

(a) 

0 3 6 9 

x (km) 

0 

3 

6 

(c) 

0 3 6 9 

x (km) 

−6 

−8 

−10 

−12 

−14 

−10 

−12 

−14 

−16 

−18 

log10(Ey [V/m]) 

log10(Ez [V/m]) 

y (km) 

−6 

−3 

0 

3 

6 

(b) 

0 3 6 9 

x (km) 

0 3 6 9 

x (km) 

Figure 5: Electric field components (a) Ey and (c) Ez for the model shown in Figure 1 and 

a 1000-m long wire source at f =0.1 Hz, and (b, d) the ratios of the finite-source Ey and 

Ez to the respective point dipole fields. 

pare Figure 7b to 3), and larger than the reservoir-related anomaly for f =1Hz(compare 

Figure 7c to 4d). These results demonstrate that at these frequencies, the EM fields are 

significantly influenced not only by the grounding point locations, but also by the entire 

wire layout. In contrast, at f =0.001 Hz, differences between bent and straight wire fields 

are barely visible (Figure 7a). At this low frequency, the electric field is similar to the potential 

field occurring in the DC limit (i.e., for f = 0). Here, the electric field is practically 

determined by the grounding point locations alone. 



9 

y (km) 

−6 

−3 

0 

3 

6 

(d) 

1.2 

1.1 

1 

0.9 

0.8 

1.2 

1.1 

1 

0.9 

0.8 

| Ey wire / Ey dipole | 

| Ez wire / Ez dipole |

log 10(| (E x coarse - Ex fine ) / Ex fine |) 

−2 

−4 

−6 

−8 

(a) 

Element length (m) 

1 

2 

5 

10 

20 

50 

0 5 10 

x (km) 

Figure 6: Relative differences between E coarse 

x 

−2 

−4 

−6 

−8 

(b) 

0 5 10 

x (km) 

computed for a 1000-m long wire using wire 

element lengths between 1 m and 50 m, and a reference field E fine 

x for a wire discretized 

using 0.1-m long elements, for frequencies of (a) 0.1 Hz and (b) 100 Hz. The resistivity 

model shown in Figure 1 was used, and field values were extracted along a line parallel to 

the source wire at a lateral offset of 50 m. 

Marine survey: floating wire 

Finite electric dipole sources used in marine CSEM surveys for commercial hydrocarbon 

exploration are typically ∼ 100 − 300 m long (Constable and Srnka, 2007). Accordingly, 

differences between the EM fields due to such finite-length sources and point dipole fields 

are expected to be somewhat smaller than those observed for the 1-km long wire considered 

in the land survey examples. 

We have computed marine EM responses for the model shown in Figure 8, which contains 

a 200-m water column and a stack of sedimentary layers, into which a 100-m thick resistive 

layer, representing a hydrocarbon reservoir, is embedded at a depth of 800–900 m below 

the seafloor. We simulated a point dipole source located at (x, y) =(0, 0) and a 300-m long 

wire source, also centered at (0, 0). Both sources were located 50 m above the seafloor, and 

receivers were placed 0.01 m above the seafloor. 

Electric field Ex data for this configuration due to the finite-length wire and point dipole 

sources are shown in Figures 9a and b, and finite-source Ex data for the reservoir model 

relative to Ex for a model not containing the resistive layer are displayed in Figure 9c. The 

finite-length wire and point dipole fields are nearly identical at radii larger than ∼ 1km 

from the source center. The anomaly due to the resistive layer is several times larger 

than the relative differences between the finite-length wire and point dipole fields, and is 

largest at distances well beyond the region significantly influenced by the source geometry. 

Therefore, the point dipole approximation may be adequate in this case. However, taking 

into account the exact source geometry may again become important when searching for 

smaller anomalies caused, e.g., by thinner reservoirs or relatively small 3D structures. 



10

y (km) 

−6 

−3 

3 

6 

(a) 

-500 0 500 

120° x (m) 

287 

y (m) 

0 3 6 9 

x (km) 

y (km) 

−6 

−3 

0 

3 

6 

(b) 

0 3 6 9 

x (km) 

y (km) 

| Ex bent / Ex straight 0.8 0.9 1 1.1 1.2 

| 

−6 

−3 

0 

3 

6 

(c) 

0 3 6 9 

x (km) 

Figure 7: Electric field Ex for a bent wire. The inset in (a) shows the geometry of a wire 

that consists of two segments and has the same grounding points as the straight wire used 

previously. Shown is the ratio of Ebent x for the bent wire to E straight 

x for the straight wire at 

depth z =0.15 m and frequencies of (a) 0.001 Hz, (b) 0.1 Hz and (c) 1 Hz. Gray shades in 

(b) and (c) roughly mark very low-amplitude regions in which Ex would not be measurable. 

σ (S/m) 

0 

3.6 

0.5 

0.01 

1 

10 km 

seafloor 

receivers 

15 km 

0 

200 

1000 

1100 

z (m) 

Figure 8: The 1D conductivity model and survey geometry used for simulating a marine 

CSEM survey. The red arrow indicates the point dipole or 300-m long wire source, centered 

at (x, y) =(0, 0) and located 50 m above the seafloor. Receivers are located 0.01 m above 

the seafloor. 

CONCLUSIONS 

We have presented a formulation for computing electromagnetic fields due to electric dipole 

sources of finite extent by splitting the responses into contributions from the wire body 

and its end points. Being derived from a quite general representation of point dipole fields, 

our finite-length wire formulation allows us to compute EM fields in 1D layered media for 



11

y (km) 

−4 

−2 

0 

2 

(a) 

4 

0 2 

x (km) 

4 

log10(Ex wire −12 −11 −10 −9 −8 

[V/m]) 

y (km) 

−4 

−2 

0 

2 

(b) 

4 

0 2 

x (km) 

4 

y (km) 

| Ex wire / Ex dipole 0.9 0.95 1 1.05 1.1 

| 

−4 

−2 

0 

2 

(c) 

4 

0 2 

x (km) 

4 

| Ex reservoir / Ex background 0.5 0.75 1 1.25 1.5 

| 

Figure 9: (a) Electric field Ex for a 300-m long wire source and the marine survey configurationshowninFigure8atf 

=0.1 Hz. (b) The ratio between the finite-length wire field 

shown in (a) and the field due to a point dipole source. (c) The finite-length wire field for 

the reservoir model of Figure 8 relative to the background field for a model not containing 

the 100-m thick resistive layer. Note the different color scales in (b) and (c). 

sources and receivers located at any depth. Compared to direct summation of dipole fields, 

we gain ∼ 60% efficiency. Implementation is straightforward, as we only require integral 

evaluations via standard fast Hankel transforms, for which precomputed sets of coefficients 

are available. 

The utility of the finite-length wire formulation has been demonstrated by presenting 

EM fields for several representative CSEM survey configurations. Our tests confirm that 

finite-length wire and point dipole fields can differ significantly over distance ranges reaching 

several times the wire length. For a simulated land CSEM survey targeting a thin resistive 

anomaly, comparison of the responses for a 1000-m long grounded wire source to point dipole 

responses shows that in this case, it is crucial to consider the actual source geometry. The 

anomalous response of the target structure is smaller than the relative differences between 

finite-length wire and point dipole fields, and overlaps spatially with the region in which 

the response is strongly influenced by the source geometry. Qualitatively similar deviations 

between finite-length wire and point dipole fields are observed over relatively wide frequency 

ranges and for different EM field components. At frequencies above the ‘effective’ DC limit, 

it is also important to consider the actual wire layout; knowledge of the grounding point 

positions is not sufficient for computing accurate responses. 

In contrast, for the marine survey simulated, using a shorter wire and thicker target layer, 

the wire geometry only had a relatively small impact on the responses, and anomalies due 

to the target layer were spatially well separated from the region significantly influenced by 



12

the source geometry. This indicates that the actual source geometry is of minor importance 

for the survey considered. Nevertheless, this cannot be generalized to other surveys aiming 

at detecting smaller target structures that generate weaker EM field anomalies. 

Our 1D solution for finite-length wire sources can easily be incorporated into higherdimensional 

CSEM modeling and inversion algorithms. Most 2D and 3D modeling schemes 

use a secondary field approach, in which primary fields for a simple (e.g., homogeneous or 

1D) model are computed analytically, and secondary fields arising from deviations of the 

2D or 3D resistivity model from the background model are computed numerically. Here, 

finite-length sources can be included into the background field computations. 

ACKNOWLEDGMENTS 

This work was funded by the German Federal Ministry of Education and Research within 

the framework of the GeoEn project. 

APPENDIX A 

EM FIELD EXPRESSIONS FOR POINT DIPOLES 

We show the derivation of expressions for dipole EM fields in a form convenient for integration 

over the length of a source wire using the example of the Ex component. Analogous 

considerations apply for the other EM field components. 

Using the nomenclature of Løseth and Ursin (2007), the space-frequency domain electric 

field Ex for an isotropic layered medium, with source and receiver embedded at arbitrary 

depth, is given by the double Fourier integral 

Ex = − Idx 

8π2 ∞ 

∞ 

1− k2 x 

κ2 

μ0 

√ 

pr zps R 

z 

A 11 + 

−∞ −∞ 

 

pr zps z 

˜ε r ˜ε s 

k2 x 

κ2 RA22 

exp {j (kxx+kyy)}dkxdky, (A-1) 

where kx and ky are horizontal wavenumbers with κ2 = k2 x + k2 y , and the other symbols are 

the same as those explained for Equation (1). 

Transformation to cylindrical coordinates using kx = κ cos α, ky = κ sin α, x = r cos β, 

y = r sin β, ξ = α − β + π/2, k2 x →−∂2 x , and substituting the zero-order Bessel function, 

results in 

Ex = Idx 

4π 

⎛ 

 

⎝ 

0 

∞ 

−μ0 

√ p r z p s z 

J0 (κr) = 1 

2π 

2π 

R A 11κJ0(κr)dκ−∂ 2 ⎧ 

⎨∞ 

 

μ0 

x √ 

⎩ pr zps R 

z 

A 11− 

0 

0 

e jκr sin ξ dξ, (A-2) 

p r zp s z 

˜ε r ˜ε s RA 22 

κ J0(κr)dκ 

⎫⎞ 

⎬ 

⎠. 

⎭ 

(A-3) 

After evaluating one of the spatial derivatives using (Ward and Hohmann, 1987) 

∂xJ0 (κr) =− κx 

r J1 (κr) , (A-4) 



13 

 

1

we obtain 

Ex = Idx 

4π 

⎛ 

 

⎝ 

0 

∞ 

−μ0 

√ 

pr zps R 

z 

A 11κJ0 (κr)dκ + ∂x 

⎧ 

⎨ 

x 

⎩ r 

0 

∞ 

 

μ0 

√ 

pr zps R 

z 

A 11 − 

p r zp s z 

˜ε r ˜ε s RA 22 

⎫⎞ 

⎬ 

dκ ⎠ . (A-5) 

⎭ 

Equation (A-5) is used as the basis for deriving the expressions for finite-length wire fields. 

Further evaluation of the second spatial derivative using 

∂xJ1 (κr) =− x 

r2 J1 (κr)+ κx 

r J0 (κr) (A-6) 

results in an explicit expression for the point dipole field in terms of two different Hankel 

integrals: 

Ex = Idx 

4π 

+ 

⎛ 

 

⎝ 

0 

∞ 

x 2 

 

1 2x2 

− 

r r3 ∞ 

− 1 

r2 0 

 

μ0 

√ 

pr zps R 

z 

A x2 

11 − 

r2 μ0 

√ 

pr zps R 

z 

A 11 − 

p r z p s z 

˜ε r ˜ε r RA 22 

REFERENCES 

p r zp s z 

˜ε r ˜ε r RA 22 

 

κJ0 (κr)dκ 

⎞ 

J1 (κr)dκ⎠ 

. (A-7) 

Constable, S., and L. J. Srnka, 2007, An introduction to marine controlled-source electromagnetic 

methods for hydrocarbon exploration: Geophysics, 72, WA3–WA12. 

Edwards, N., 2005, Marine controlled source electromagnetics: Principles, methodologies, 

future commercial applications: Surveys in Geophysics, 26, 675–700. 

Edwards, R. N., 1997, On the resource evaluation of marine gas hydrate deposits using 

sea-floor transient electric dipole-dipole methods: Geophysics, 62, 63–74. 

Frischknecht, F. C., V. F. Labson, B. R. Spies, and W. L. Anderson, 1991, Profiling methods 

using small sources, in Electromagnetic Methods in Applied Geophysics: Society of 

Exploration Geophysicists, 2, 105–270. 

Giese, R., J. Henninges, S. Lüth, D. Morozova, C. Schmidt-Hattenberger, H. Würdemann, 

M. Zimmer, C. Cosma, C. Juhlin, and CO2SINK Group, 2009, Monitoring at the 

CO2SINK site: A concept integrating geophysics, geochemistry and microbiology: Energy 

Procedia, 1, 2251–2259. 

Johansen, S. E., H. E. F. Amundsen, T. Røsten, S. Ellingsrud, T. Eidesmo, and A. H. 

Bhuyian, 2005, Subsurface hydrocarbons detected by electromagnetic sounding: First 

Break, 23, 3136. 

Løseth, L. O., and B. Ursin, 2007, Electromagnetic fields in planarly layered anisotropic 

media: Geophysical Journal International, 170, 44–80. 

Soerensen, K. I., and N. B. Christensen, 1994, The fields from a finite electrical dipole - A 

new computational approach: Geophysics, 59, 864–880. 

Spies, B. R., and F. C. Frischknecht, 1991, Electromagnetic sounding, in Electromagnetic 

Methods in Applied Geophysics: Society of Exploration Geophysicists, 2, 285–425. 

Strack, K. M., 1992, Exploration with deep transient electromagnetics: Elsevier. 

Ward, S. H., and G. W. Hohmann, 1987, Electromagnetic theory for geophysical applications, 

in Electromagnetic Methods in Applied Geophysics: Society of Exploration Geophysicists, 

131–311. 



14

Weidelt, P., 2007, Guided waves in marine CSEM: Geophysical Journal International, 171, 

153–176. 

Wright, D., A. Ziolkowski, and B. Hobbs, 2002, Hydrocarbon detection and monitoring 

with a multicomponent transient electromagnetic (MTEM) survey: The Leading Edge, 

21, 852–864. 

Ziolkowski, A., B. A. Hobbs, and D. Wright, 2007, Multitransient electromagnetic demonstration 

survey in france: Geophysics, 72, F197–F209. 



15

2D Time Domain TEM Simulation Using Finite Elements, an 

Exact Boundary Condition, and Krylov Subspace Methods 

M. Afanasjew 1,2 ,R.-U.Börner 1 ,M.Eiermann 2 ,O.G.Ernst 2 ,S.Güttel 2,3 , and K. Spitzer 1 

1 Institute of Geophysics, TU Bergakademie Freiberg, Germany, 2 Institute of Numerical 

Analysis and Optimization, TU Bergakademie Freiberg, Germany, 3 now at: Section of 

Mathematics, Université deGenève, Switzerland 

1 Summary 

In this report we present a numerical method for solving Maxwell’s equations in the time domain 

assuming an arbitrary two-dimensional conductivity distribution including an isolating air half-space. 

The method allows to carry out the computations for the subsurface only, because the air-earth interface 

is handled by an exact boundary condition. The spatial discretization is done with the finite element 

method, leading to a linear system of ordinary differential equations (ODE). We use state-of-the-art 

Krylov subspace methods for this ODE to advance a given initial electric field to selected times of 

interest. The presented theory is tested with some standard models and compared to a traditional 

finite difference time stepping implementation with respect to accuracy and efficiency. The results 

clearly demonstrate the superiority of the presented method in terms of run time given a comparable 

accuracy. 

Keywords: Analytic boundary condition, finite element method, Krylov subspace, time domain, transient 

EM 

2 Introduction 

The transient electromagnetic (TEM) method has become a standard technique in geophysical prospecting 

during the past years. It is already in wide use, e. g., for the exploration of important resources like 

hydrocarbons, groundwater and minerals. One important aspect here is a reliable and computationally 

efficient simulation of the decaying electromagnetic field, which can be leveraged to get a better understanding 

of field behavior in complicated real-world settings as well as a building block in inversion 

schemes, that ultimately aim at resolving arbitrary conductivity structures from only a few well-placed 

measurements. 

The predominant forward modeling technique in the literature is the finite difference time domain 

(FDTD) method, that was already introduced by Yee (1966). An explicit time-stepping technique, that 

already dealt with an isolating air half-space, was developed by Oristaglio and Hohmann (1984) for the 

two-dimensional case and later refined by Wang and Hohmann (1993) for three dimensions. Like for 

other explicit time-stepping methods, the size of the time steps, that the described Du Fort-Frankel 

scheme can stably perform, depends on the grid spacing and the lowest conductivity. Although the 

resistive air is already eliminated, thousands of time steps have to be performed although only a few 

dozen solutions are necessary to describe the decaying field. 

The approach taken here is based on a finite element discretization, which allows for greater flexibility 

when modeling complicated conductivity structures. High accuracy is obtained with less effort compared 

to graded tensor product grids used with finite differences. It also helps in the construction of an 

analytic boundary condition, avoiding a few drawbacks the implementation by Oristaglio and Hohmann 

(1984) has. Contrary to the finite difference approach, the matrices resulting from the discretization are 

symmetric and, thus, allow for a wide range of efficient and state-of-the-art time integration techniques, 

which can exploit this property. One such family of time integrators is based on building a Krylov 



16

subspace and extracting approximations to the matrix exponential function from said space, thus 

evaluating the sought electric field directly at a given time. 

3 Theory 

3.1 Governing Equations 

Our governing equation derives from Maxwell’s equations in the diffusive limit, with the constitutive 

relations used and the magnetic field already eliminated. Thus, we write 

with 

∇× μ −1 ∇× e + ∂tσe = −∂tj e 

e = e(x,t) the electric field, 

μ = μ(x) the magnetic permeability, 

σ = σ(x) the electric conductivity, and 

j e = j e (x,t) the impressed source current density. 

We now restrict ourselves to the two-dimensional case (xz-plane) with infinitely long line sources 

perpendicular to this plane. Given these assumptions, we can express the electric field as 

e(x, y, z, t) =e(x, z, t) y (2) 

where y is the unit vector along the y-axis and e a scalar function. Equation (1) then reduces to 

−∇ 2 e + σμ∂te = −μ∂tj e . (3) 

Γ0 

Ω 

z =0 

Figure 1: Computational domain with an arbitrary conductivity structure. On top is the air-earth interface 

(bold), the remaining boundaries are subsurface boundaries. 

Our computational domain Ω (cf. Figure 1) is a rectangle and its top edge is aligned with the airearth 

interface Γ0 = {(x, z) :z =0} on which we impose an explicit boundary condition and perfect 

conductor boundary conditions on all other domain boundaries. It is important for these boundaries to 

be sufficiently far away from the sources, so that they don’t distort the propagating field. 

Our objective will be to compute the configuration of the electric field ei at times ti for i ∈{1, 2,...,n} 

givenaninitialfielde0 at t0. We use sources that are switched off at t = 0 and therefore the right hand 

side of (3) vanishes for t>0. 



17 

(1)

3.2 Air-Earth Interface 

We assume that e satisfies Laplace’s equation in the isolating air half-space (z 0} denotes the lower half-space. 

By using the exact boundary condition (6) we can write 

∂ta(e, ψ) σ + c(e, ψ)+ 

+∞ 

−∞ 

Te(x, t) ψ(x, 0) dx = −μ 

+∞ 

−∞ 

∂tj e (x, t) ψ(x, 0) dx. (10) 

To be able to discretize this equation we need a computable expression for the following bilinear form 

b(φ, ψ) = 

+∞ 

−∞ 

Tφ(x) ψ(x) dx (11) 

and indeed, after some rearrangement in the Fourier domain, one obtains (Goldman et al. 1986) 

+∞ +∞ 

b(φ, ψ) =− 1 

log(|x − y|) φ 

π −∞ −∞ 

′ (x) ψ ′ (y) dxdy. (12) 

The discretization of this integral on the boundary of a triangulation can now be easily computed. 

The continuity of e allows us to use standard linear Lagrange elements on a triangulation of the 

computational domain. After discretizing the variational formulation we arrive at 

M∂te = Ke. (13) 



18

Finite Differences For comparison, we also perform a finite difference discretization and get the ODE 

∂te = Ae where A is a large sparse matrix representing the discrete curl-curl operator. 

The following procedure, that has to be repeated in every time step, outlines the implementation of an 

exact boundary condition in this setting: Take the field data at the air-earth interface, interpolate it to 

an equidistant grid, perform an FFT to transform the data into the wave number domain, multiply 

every wave number with a constant (this would be a convolution in the space domain), revert the 

FFT and finally interpolate back to the graded grid to get the field values at a negative z, thus, inside 

the air half-space. Use the data resulting from this classical upward continuation in the usual finite 

difference stencil to compute the top layer in the next step. 

A variation of this approach was also implemented for the numerical examples. It combines all of the 

above steps into a single (dense) matrix that has the same effect but can be evaluated more efficiently. 

This is called matrix upward continuation later on. 

Details about the finite difference discretization can be found in Oristaglio and Hohmann (1984). 

3.4 Time Integration Techniques 

Krylov Subspace Methods Krylov subspace methods cover a big range of applications and are in 

use for several decades. What we want to focus on are Krylov subspace methods for the evaluation 

of matrix functions, like we can see in (13), where the function is the matrix exponential and the 

matrices come from the spatial discretization using finite elements. A nice side effect of the origin of 

those matrices is, that they are usually symmetric which many algorithms can benefit from. 

Given a square matrix A of size n × n, a vector b of length n and a suitable scalar function f, wecan 

write 

f(A) b = p(A) b. (14) 

with p a polynomial that Hermite-interpolates in the eigenvalues of A. We will be focusing on the 

exponential function and on rational Krylov subspaces, that are defined as follows 

with Km(A, b) = b,Ab,A 2 b,...,A m−1 b and 

Q(A, b) := qm−1(A) −1 Km(A, b) (15) 

qm−1(z) = 

m−1 

j=1 

ξj=∞ 

(z − ξj) . (16) 

Such subspaces are constructed, e. g., with the rational Arnoldi method to obtain an orthonormal 

basis of Qm from which approximations to f(A) b can be computed with several procedures. We have 

to choose the poles ξj of the rational Krylov subspace. Their number and choice highly impact the 

quality of the approximations that can be extracted from the subspace. Luckily, there is a heuristic to 

determine good poles for the approximation of the exponential function, given a certain parameter 

interval (in our case the times we want to advance to) and accuracy requirements. These, and many 

more things concerning rational Krylov subspaces, are tackled in Güttel (2010), which is also a good 

starting place to dig deeper into the literature. 

Looking more closely at (13) we see, that in order to apply a Krylov subspace method we need to 

remove the matrix M in front of the time derivative, e. g. by moving it to the right 

∂te = M −1 Ke. (17) 

The inverse of the matrix doesn’t have to be explicitly computed, but we have to solve a system of 

linear equations in every iteration step. This might be considered too expensive, so there is a technique 



19

termed mass lumping which converts M into a diagonal matrix that can be easily inverted without 

distorting the solution too much. 

However, even if we don’t have to solve linear systems with the matrix M, wedohavetosolveshifted 

systems with the matrix K during the construction of the rational Krylov subspace. Therefore, an 

efficient solver is also an important ingredient. We will see in the numerical examples what options we 

have. 

Time Stepping On the other hand there are simple, yet relatively efficient explicit time stepping 

techniques. One of them is the well-known Du Fort-Frankel method which is implemented here to 

perform the intergration in time for the finite difference discretization. 

4 Numerical Examples 

All computations were carried out on a machine with four AMD Opteron 8380 quad cores, running 

at 2.5 GHz with a total of 128 GiB of RAM. The algorithms were implemented in pure MATLAB 

code running under MATLAB 2008b, with some finite element related tasks (nothing time-critical) 

performed by COMSOL 3.5a, both running in a 64-bit Linux environment. To generate reproducible 

timing we restricted ourselves to one computational thread that was explicitly pinned to one of the 

cores. 

4.1 Model 

The considered models are basically those from Oristaglio and Hohmann (1984), all based on graded 

tensor product grids. We extended the mesh slightly so as not to get a distortion from the boundaries 

for late times. The resulting grid has 236 × 88 cells, is 12800 m wide and 5255 m deep, with grid spacings 

ranging between 10 m and 240 m. To make the computations comparable with the finite difference code 

we decided to use exactly the same grid for the finite element code. We simply subdivided each cell 

into two triangles, however, the number of unknowns or degrees of freedom and their locations are 

identical. Technically, this is of course not necessary and a properly adapted unstructured grid would 

certainly yield even better results at lower cost. 

The initial field e0 at t0 =10 −6 s is due to two line sources at positions (x, z) = (−500 m, 0m) and 

(x, z) = (0 m, 0m), the former being negative while the latter is positive with a unit source current 

strength. It is computed analytically for a homogeneous half-space that corresponds to the background 

conductivity of the model. 

We have looked at two models with different conductivity structures. See Figure 2 to get an approximate 

idea of their location inside the grid. The background has a resistivity of 300 Ωm and the conductor 

(red) 0.3 Ωm. 

Γ0 

Ω 

z =0 

Figure 2: Schematic view of the computed models. The models are the homogeneous half-space and a conductor 

(red) inside a homogeneous half-space. The conductor is located at the position 290 m ≤ x ≤ 310 m, 

100 m ≤ z ≤ 400 m in the grid. 



20

4.2 Methods and Setup 

Independently of the method of choice we start at the time t0 =10 −6 s and integrate from there till 

we reach tn =10 −2 s. We seek to compute the configuration of the electric field at 10 logarithmically 

equidistant times per decade. 

For the finite difference code we mostly stick to the implementation by Oristaglio and Hohmann 

(1984), with the only option to perform the upward continuation in the traditional way, which is a 

significant expense per time step, or we can decide to precompute the matrix formulation of this 

upward continuation and to apply it in every time step. 

For the finite element method we have no choice regarding the exact boundary condition. However, we 

can choose between different variants of the rational Krylov method. For all of them we have a total 

of 25 poles, which should be close to optimal for this application. For the first 24 poles we alternate 

between 2.7826 · 10 5 and 0.0242 · 10 5 . The last pole is set to infinity. 

We have four implementations, that we included in this test. Two of them use mass lumping to reduce 

the mass matrix to a diagonal matrix. Furthermore, for each group we can either call the standard 

MATLAB solver or we can exploit the fact that we have multiple identical poles for which we have to 

solve with different right hand sides, but identical matrices. We do this by computing a sparse LU 

factorization (we use UMFPACK for this) for every unique pole and then leverage that factorization to 

speed up the solves during the construction of the rational Krylov subspace. 

4.3 Results 

We first look at the computation times that are pictured in Figure 3 and listed in Table 1. The times 

shown here are for the homogeneous half-space model, but aren’t significantly different for the other 

models since the grid and the minimal conductivity are identical. Thus, we can use these numbers to 

judge the acceleration we can get by using our method. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3: Computation times split into solve and setup/post-processing step, cf. also Table 1. On the left 

are the computation times for the default grid and on the right for the regularly refined version 

of this grid with approximately four times as many nodes and degrees of freedom. The following 

abbreviations were used: classical upward continuation (cUC), matrix upward continuation (mUC), 

rational Krylov (rK), mass lumping (ML), UMFPACK solver (UMF). 

As is clearly visible, all FE-based methods are significantly faster than their finite difference counterparts, 

sometimes even 22 times faster. 

Looking at the transients (cf. Figure 4) at some select points inside the mesh, we see that although 

these newer methods are so much faster, we don’t really sacrifice accuracy. In fact, in many cases the 

finite element solution is more accurate than the one obtained by finite differences. 

We conclude our numerical examples with showing some cross-sections (cf. Figure 5), that are nothing 

but a few snapshots of an animation that is just not suitable for this medium, but nevertheless gives a 

coarse idea of how the electric field propagates with time. 



21

Figure 4: Transients of the homogeneous half-space model with relative errors (left) and the model with a 

conductor (right). Negative field values are denoted by dashed lines while positive values are drawn 

with a solid line. We can see that we have a very good agreement between the FD and FE solution. 

When comparing against an analytical solution in the homogeneous half-space, we see that the relative 

errors are often lower than those of the FD solution, despite the lower numerical effort. 



22

Figure 5: Cross-sections of a homogeneous half-space model (left) and the model with a conductor (right). 

These cross-sections were plotted to give a visual idea of how the fields advance in time. The common 

initial configuration was omitted. We decided to plot the results of the FE simulation, but there was 

hardly any visible difference compared to the FD solution. On the right we can nicely see how the 

field gets captured inside the high conductivity structure and creates an anomaly compared to the 

homogeneous case. 



23

Default grid Refined grid 

Method Solve Other Solve Other 

FD, time stepping, classical upward continuation 31.7s < 0.1 s 171.8s < 0.1s 

FD, time stepping, matrix upward continuation 8.6s 0.9s 98.4s 2.7s 

FE, rational Krylov 3.6s 0.6s 19.4s 1.9s 

FE, rational Krylov, mass lumping 3.1s 0.6s 17.7s 1.9s 

FE, rational Krylov, UMFPACK 1.9s 0.6s 10.4s 1.9s 

FE, rational Krylov, mass lumping, UMFPACK 1.4s 0.6s 7.7s 1.9s 

Table 1: Computation times for the default grid and one, that was obtained from this with regular refinement. 

The column Solve denotes the time spent for performing the integration in time, while the column 

Other lists the time spent in setting up the boundary condition and the computation of field values 

from the solution vectors in case of the FE method. Other setup times are not shown. The advantage 

of FE-based methods can be clearly seen. 

5 Conclusions 

We were able to leverage several state-of-the-art techniques to create a combined efficient forward 

modeling code that is significantly faster than traditional codes. We have also seen that we don’t have 

to make sacrifices regarding the accuracy of those computations. This was already achieved by using 

the mesh from the finite difference discretization, which was helpful for comparison, but which also 

has many limitations due to its regular structure. An unstructured grid—properly adapted to the 

problem—could be used to further increase accuracy or speed. 

We are working on creating a similar framework for the three-dimensional time domain TEM problem. 

All of the methods and tools are already existing or have a straightforward extension to 3D. Given the 

results from 2D we expect an even greater speed-up when applying this to three dimensions. 

6 Acknowledgments 

This work was supported by the German Research Foundation (DFG) under signature Spi 356/9. 

References 

Goldman, Y., C. Hubans, S. Nicoletis, and S. Spitz (1986). A finite-element solution for the transient electromagnetic 

response of an arbitrary two-dimensional resistivity distribution. Geophysics 51(7): 1450–1461. 

Goldman, Y., P. Joly, and M. Kern (1989). The Electric Field in the Conductive Half Space as a Model in Mining and 

Petroleum Prospecting. Mathematical Methods in the Applied Sciences 11: 373–401. 

Güttel, S. (2010). Rational Krylov Methods for Operator Functions. PhD thesis. TU Bergakademie Freiberg. 

Oristaglio, M. L. and G. W. Hohmann (1984). Diffusion of Electromagnetic Fields into a Two-Dimensional Earth: A 

Finite-Difference Approach. Geophysics 49(7): 870–894. 

Wang, T. and G. W. Hohmann (1993). A Finite-Difference, Time-Domain Solution for Three-Dimensional Electromagnetic 

Modeling. Geophysics 58(6): 797–809. 

Yee, K. S. (1966). Numerical Solution of Initial Boundary Problems Involving Maxwell’s Equations in Isotropic Media. 

IEEE Trans. Ant. Propag. 14: 302–309. 



24

Abstract 

TEM with anomalous diffusion in fractal conductive media 

Tilman Hanstein 

KMS Technologies GmbH, Köln 

The transient electromagnetic response of an inductive loop source over a half-space with 

fractal characteristics is simulated. The conductivity of the ground has a spatial distribution, 

which is described by a roughness parameter. The roughness can be related to the fractal 

dimension and controls the transient decay of the signal. Asymptotic limits are observed for 

the early and late time behaviour. 

The work is based on a paper by Everett (2009), which has been reviewed and the aspect of 

asymptotic limits in time has been further investigated. Contrary to that paper, here a 

relationship between roughness and the electromagnetic decay at early and late time has been 

deduced. The transient decay for normal diffusion is t -5/2 and for anomalous diffusion the 

decay is slower. The new power law for anomalous diffusion has been proven by theoretical 

analysis and has been verified by numerical experiments. 

The numerical evaluation of the inverse Laplace transform with the method of the fast Hankel 

transform are excellent in numerical accuracy and the method with the Gaver-Stehfest 

algorithm is not sufficient to estimate the power law decay at late times. 

Anomalous Diffusion 

The concept of anomalous diffusion is a useful approach for the description of diffusion 

process and transport dynamics in complex systems. The fractional equations are derived 

asymptotically from basic random walk models and become a complementary tool for 

handling non-exponential relaxation patterns. 

For transient electromagnetic diffusion Everett starts this concept with a generalized Ohm’s 

law (Everett 2009, Weiss and Everett 2007) 

j 

E 

1 t t 

E j E 

0 

the parameter ~t - describes the generalized electrical conductivity and is appropriate for 

the anomalous diffusion coefficient. The Ohm’s law becomes a convolution between the 

generalized conductivity and the electric field E. The roughness parameter can vary 0 1. 

d 



25

After applying Ampere‘s and Faraday‘s law to the generalized current density, we get the 

fractional diffusion equation 

 

E 0 

* E 0 

0Dt 

t 

2 1 

where now the fractional derivative or Riemann-Louiville operator is introduced (Metzler and 

Klafter 2000) 

t 

1 

1 E 

 

0 Dt 

E t 

d 

1 

t 

t 

0 

 

and is the Gamma function which serves as normalization constant. 

The fractional diffusion equation will be solved in the Laplace domain and the transformation 

of the operator yield to 

1 

1 

~ 

D E 

t s E 

s 

L 0 t 

with the complex Laplace variable s=i (Abramowitz & Stegun 1964). 

The fractional diffusion equation becomes now a simple expression 

2 ~ 

E s 

1 

0 

 

This differential equation can be solved straightforward with the standard methods as used for 

the electromagnetic 1-D formulation in a layered medium. 

~ 

E 

s 

Electromagnetic responese of a loop over rough half-space 

Everett (2009) has used a separate horizontal loop configuration for transmitter and receiver 

as it is typically used for TEM. The transmitter loops usually a square loop can be represented 

by a circular loop whith equivalent area. For the separate loop configuration the time 

derivative of the vertical magnetic field is measured outside the transmitter loop. 

In frequency domain the vertical magnetic field is presentated as Hankel Integrals 

~ 

h z 

s Ia 

J aJr 

0 

 

2 

 

2 

k 

2 

 

1 

0 

E 

t 

d 

. 

The integration is over the spatial wavenumber and I is the current in the transmiter, a the 

transmitter loop radius, r the distance to the receiver point, J0 and J1 are Bessel functions of 

order 0 and 1 and k the fractional wavenumber. The integral can be solved analytically for an 

infinitessimally magnetic dipole, therefore the limit of the first order Bessel function for small 

radius is taken into account (Abramowitz & Stegun 9.1.10) 



26

a 

J1 a . 

a 

0 

2 

The response of a vertical magnetic dipole in frequency domain over a rough conductive 

media is 

m 1 

2 

u 

s 999u4uue ~ 3 

z 

3 2 

H 

2 

r 

with the fractional induction number u = k r = (s 1- 0 ) 1/2 r. 

Asymptotic limits in frequency and time domain 

u 

For normal diffusion with roughness equal zero the transient response can be also given in 

analytical expression but for a general fractional induction number with the roughness 

parameter the transformation to time domain has to be done by numerical techniques. Only 

the asymptotic limits for the high and low frequency limit can be calculated in closed form. 

For high frequency and early time we get 

~ 

H 

h. 

f . 

z 

m 9 

m 9 1 

 

t 

2 2 

z 

3 2 

2 

r u 

2 

r r 

e. 

t. 

s 

H t 

The low frequency can be developed in a series 

n1n3 

2 

~ m 1 

n 

H z s 1 

2 

3 

2 

r 2 n4 

n! 

The first 3 terms are important for the late time behavior 

~ 

H z 

m 

2 

r 

1 

2 

 

0 

2 

u 

 

2 

3 

s 1 

u u 

3 

1 

2 

4 

15 

 

 

 

. 

1 In time domain the first term is a -function without influence on late time decay. The second 

term is responsible for the late time behavior in a rough medium 

L 

1 

1 

s 

 

 

t 

 

 

 

 

t 

1 

2 

for 0 

for 0 

The third term describes the classical -5/2 decay response in a non-fractional medium and for 

a fractional medium this term decays faster than the previous second term. 

 

. 



27 

 

.

The late time response for the magnetic field can be summarized 

 

. 

H t l 

z 

t 

m 

 

2 

r 

3 

3 2 

5 

0 

2 

t 

10 

 

 

0 

 

 

t 

 

2 1 

2 

for 0 

for 0 

The cause for the heavy tailed decay response in rough geological media can be explained by 

the additive second term which yield to a continuous transition from non-fractional to 

fractional diffusion as is shown in figure 1 and 2. 

Numerical inverse Laplace transform 

Numerical methods are applied for the transformation to time domain. Since the transient is a 

real and causal function, the inverse Fourier or Laplace transform can be calculated by a sinetransform. 

 

2 

h z 

z 

0 

t Im h ~ sint In this expression I have already considered that the current step in the transmitter decribed by 

1/i and the time derivative of the receiver coil by a multiplication with i cancel each other. 

Since for diffusion processes the kernel function is a smooth function, the technique of the 

Fast Hankel Transform can be applied. The sine function is experessed by Bessel function 

with fractional order ½ 

2 

J 1 x sinx. 

2 x 

The fast Hankel transform is a well know technique for calculating the transient response, I 

used 250 filter coefficients, 15 /decade, calculated with the program by Christensen (1990). 

Everett (2009) has chosen the Gaver-Stehfest algorthim for his investigation. This method is 

also good for diffusion processes and has been succesfully applied. It is a favourized method 

in hydrology, because it needs only real arithmetic and the Laplace variable s is considered as 

a real variable. Knight and Raiche (1982) introduced this technique to the electromagnetic 

community. Stehfest (1970) published an Algol routine, which can be straight forward 

translated to other computer languages and Everett (2009) has tabled the coefficients for 

several total number of coefficients. 

d 



28

Figure 1: Transient loop-loop response with early and late time approximation over halfspace 

with different roughness in conductivity, the offset is 100 m, = 0.1 S/m. 



29

The disadvantage of the Gaver-Stehfest algorithm is that the numerical accurracy cannot 

generally be increased by increasing the number of coeffcients. The accuracy is depending on 

the accurracy in number of digits of the kernel function and the number of digits of the 

maschine precision. Stehfest recommended 8 coefficients for single precision and 18 

coeffcients for double precision. Everett used 18 coefficients. In my experiments I have found 

out that 12 is an optimal number for electromagnetic application. 

Figure 2: Numerical evaluation of the exponent in the transient decay and theoretical 

asymptotic limit for different roughness 



30

Results 

For the numerical experiment I used the same model as Everett, beside that here a vertical 

magnetic dipole instead of a horizontal circular loop is used. The base conductivity of the 

half-space is 0.1 S/m with combination of various roughness parameter has been applied. 

Figure 1 shows the transient as induced voltage due to an step response of the transmitter 

current for different roughness paramters. The large time range has been chosen to 

demonstrate the early and late time behavior in comparison with the asymptotic limits. For 

real measurements the time range will be much smaller. All transients - shown here - are 

calculated with the fast Hankel transform. As reference the transient of homogenous halfspace 

with normal diffusion is also shown with grey lines. For separate loop configuration the 

transient shows a sign change. The negative values are shown with dashed lines and positive 

with solid lines. The asymptotic limits agree very well with theoretical prediced limits at eary 

and late times shown here as straight lines. The early time behaviour is for practical pupose of 

minor relevance, because in real meausrements the early time is influenced by system 

response of the system as the ramp for the current step off. So that in the data the straight line 

will not be visible. But the late time behaviour will be visible if the late time data can be 

measured and the data quatlity is sufficient. 

To analyze how accurate the power law decay can be estimated from the calculated transients 

especialle for low roughness numbers, the transients are calculated up to extrem late times and 

the power law is determined by taking the numerical derivative d ln H(t) / d ln t. The result is 

shown in figure 2. 

Figure 3: Numerical evaluation of the exponent in the transient decay and theoretical 

asymptotic limit for different roughness calculated with Gaver-Stehfest alogorithm 



31

The graphs show the exellent accuracy of the fast Hankel transform, even for small roughness 

numbers, and indicates the smooth transition, when the roughness approaches zero. The 

influence of the anomalous diffusion moves to later times for decreasing roughness. 

For very low roughness there will be a time range showing almost normal decay t -5/2 and then 

goint to the predicted power law decay at extrem late time – approaching infinity. Responsible 

for this behavior is the second term of the low frequency approximation which is added. 

The Gaver-Stehfest algorithm is not sufficient to estimate the power law decay. I tried 

different ways of programming, e.g to consider numerical accuracy the Laplace transform is 

done before the Hankel transform over the spatial wave number as recommended by Knight 

and Raiche (1982). The best results are shown in figure 3, achieved with 12 coefficients and 

using the analytical response for a vertical magnetic dipole in Lapace domain. Notice that the 

time range is shorter but still 3 decades more than in Everett’s paper. 

Reference: 

Abramowitz, M. & Stegun, I. A., 1966. Handbook of Mathematical Functions with Formulas, 

Graphs and Mathematical Tables. National Bureau of Standards, Applied Mathematics Series 

55. 

Christensen, N. B., 1990. Optimized Fast Hankel Transform Filters, Geophys. Prosp., 38, 

545-568. 

Everett, M., 2009. Transient electromagnetic response of a loop source over a rough 

geological medium, Geophys. J. Int., 177, 421-429. 

Knight, J. H. & Raiche, A. P., 1982. Transient electromagnetic calculation using Gaver- 

Stehfest inverse Laplace transform method, Geophysics, 47, 47-50. 

Metzler, R. & Klafter, J., 2000. The random walk’s guide to anomalous diffusion: a fractional 

dynamics approach, Phys. Rep.,339, 1-77. 

Stehfest, H., 1970. Numerical inversion of Laplace transforms, Comm. A.C.M.,13,47-49 (see 

also remark p.624). 

Weiss, C. J. & Everett, M. E., 2007. Anomalous diffusion of electromagnetic eddy currents in 

geological formations, J. geophys. Res. 112, B08102, doi:10.1029/2006JB004475. 



32

Analysis of seafloor marine EM data with respect to motion-induced noise 

K. M. Bhatt 1 , A. Hördt 1 and T. Hanstein 2 

1 

Inst. f. Geophysik u. Extraterrestrische Physik, TU Braunschweig 

2 KMS Technologies - KJT Enterprises Inc. 

Abstract 

Any appreciable movement of sea water induces an electromagnetic field, which acts as 

noise for marine controlled source electromagnetic (mCSEM) data. Noise in seafloor 

mCSEM data is considered small, but since the characteristic reservoir signal is also small, 

the understanding and possible removal of noise may be essential to increase the number 

of possible target reservoirs. 

A power spectral density plot of the time-series extracts the power of each frequency 

contribution, but the shortcoming is that the time information is lost. To get time 

information corresponding to each frequency, we plotted a spectrogram which shows how 

the spectral density of a signal varies with time. The collective use of these three plots, i.e. 

time series, power spectral density and spectrogram, helps to analyse the information 

concealed in the time-series. In a measured signal-free mCSEM data, we are able to 

identify various oceanic features like microseisms, swell etc, which play a significant role 

in inducing an electric field. 

Key words: mCSEM, Swell, Microseisms 

____________________________________________________________________________ 

1. Introduction 

Marine controlled source electromagnetic (mCSEM) data is generally contaminated by 

some unwanted electromagnetic (EM) signals ambient at the seafloor. Understanding and 

possible removal of the noise is essential as technology is advancing from deep ocean to 

shallow ocean, where the noise is much more effective. 

In general, there could be two possible sources of oceanic noise production. 

Internal oceanic processes or any other external influences like ionospheric and 

magnetospheric current systems. Faraday (1832) reported that any appreciable 

movement of seafloor and sea water by induction generates electromagnetic signals with 

in the ocean. Motional induction got more attention after world war II, with the detailed 

oceanic induction study by many authors like Sanford (1971), Podney (1975), Chave and 

Cox (1982), Chave and Luther (1990). Similarity in all these studies is that they all 



33

studied the theoretical aspect of motional induction occurring due to various movements 

in the ocean. Experimental evidence was provided by Webb and Cox (1986), who made a 

nice comprehensive study about the seafloor microseisms by observing pressure and 

electric field spectra at the seafloor. 

Wave progressions and oceanic processes are, usually, a function of the regional 

and local conditions. A variety of motional processes like swell, ripples, internal waves, 

microseisms, hum etc generate a range of EM noise at the seafloor, which varies from 

place to place. External, ionospheric and magnetospheric, current systems also 

contribute EM noise, but they are limited to the lower frequency range due to the 

conductive filtering of the ocean. Characteristics of the noise are poorly known till now, 

as only few studies are made. The present study is dedicated to the understanding of the 

noise characteristics at the sea floor. 

For the study, a marine EM data set recorded at the seafloor in the absence of a 

transmitter, is used. Recording is made for two horizontal components of electric fields 

i.e. Ex and Ey, which are perpendicular to each other. Visibly, Ex and Ey time series data 

appears different in their pattern and amplitudes despite the same oceanic environment. 

This suggests that a comprehensive study on the directional characteristics of the 

events/sources of noise could play a decisive role in identifying the noise sources. 

The oscillatory occurrence, due to a disturbance, can be comfortably visualised in 

frequency domain. The power spectral density (PSD) of each frequency contribution 

helps in marking the power of the individual sources. But the shortcoming of the PSD 

calculation is that if the source of the characteristic frequency is not known a priori, it is 

difficult to conclude about the source environment with the frequency information only. 

In this case, time information together with the PSD may help at least to distinguish 

between localised and ambient sources, which itself is of significant use. To overcome the 

PSD shortcoming to retain time information corresponding to each frequency, 

spectrograms are plotted, which show how the spectral density of a signal varies with 

time. 

In the signal-free mCSEM data, we have observed many features which are new 

for mCSEM studies. The spectrogram presents clear prints of oceanic features like 

microseisms and swell, which play a significant role in inducing an electric field at the 

seafloor. 

2. Marine Controlled Source Electromagnetism (mCSEM) 

A mCSEM data acquisition methodology is shown in Figure 1. In practice, an EM 

transmitter is towed close to the seafloor to maximize the coupling of electric and 



34

magnetic fields with seafloor rocks. These fields are recorded by instruments deployed on 

the seafloor at some distance from the transmitter. Details about the data acquisition 

practice in both time and frequency domain of mCSEM is well documented in the article 

by Constable and Srnka, (2007). 

Figure 1: Schematic diagram showing field layout for mCSEM sounding. 

3. Sources of mCSEM noise 

The noise convolved in mCSEM data is capable of masking significant marine 

information. Broadly, two origins are expected as noise sources in mCSEM data:- 

a) External origin: The magnetospheric and ionospheric current system induces 

natural electric and magnetic (EM) fields in the conductive formations. The 

induced fields are signal for the magnetotelluric (MT) technique but noise for 

mCSEM data. The conductive ocean filters the higher frequencies. The skin depth 

() is given by 

This implies, f 76,000 / 2 

503 

1 

f 

for =3.3 S/m 

Therefore, at the ocean floor the external origin fields effectively contribute 

frequencies less than or equal to f = (76,000/ D 2 ), where D is the depth of ocean 

floor in meters and f is given in (1/s). As example for an ocean of depth 500 m, the 

external field will contribute frequencies less than 0.3 Hz at the sea floor. This 



35

suggests that the frequencies higher than 0.3 Hz could be by internal oceanic 

origin. 

b) Internal origin: The dynamics of oceanic water with in the ambient geomagnetic 

field induces electric and magnetic field in the ocean. A frequency range of the 

fields is generally 0.3 < f (Hz) < 16 (Dahm et. al., 2006) excluding long period 

waves like tidal waves, tsunami, seiches and storm surge etc. 

Other than these noise sources, there are processes like earthquakes, volcanoes, 

manmade explosions etc occurring at the vibrant ocean floor, which add noise in 

mCSEM data. 

4. Motional induction 

The ocean is an electrically conducting fluid containing the ionic charge particles. 

Moving charge particles in the ambient geomagnetic field experience a deflective Lorentz 

force. If v is the velocity of charge particle q moving in the geomagnetic field B , then the 

Lorentz force is- 

 

q( 

v B) 

(1) 

F L 

The charge q experiences the deflecting force FL because of the action of an electric field 

which we call Lorentz electric field ( EL ), 

 

FL 

 

qEL 

(1-a) 

 

v B 

(2) 

E L 

The field EL generates a secondary electric field E , mainly by two processes: i) Galvanic 

process, ii) Inductive process (Bhatt et al, 2010). For a stationary frame of reference, the 

current density in the Ohms law is given by 

 

( 

E E ) ( 

E v B) 

(3) 

J L 

Here, is the conductivity of the ocean, E is the current term generated by both a 

 

galvanic and an inductive process and ( 

v B) 

is the source current term for the motional 

induction case. Under the quasi-static approximation, the set of Maxwell’s equation to be 

solved for the motional induction case is 

 

H ( 

E v B0) 

 

(4-a,b) 

E 

H 

0 

t 



36

Simplification of the source ( 

v B) 

in terms of component Jx, Jy and Jz can be written as, 

J 

J 

J 

x 

y 

z 

( 

E 

 

( 

E 

( 

E 

x 

y 

z 

v 

v 

v 

y 

z 

x 

B 

B 

B 

z 

x 

y 

The non-divergent requirement condition of the current (i.e. . J 0 

 

) suggests that the 

current will close its loop with in the earth rather than closing in the ocean. Therefore, 

the horizontal electric currents (i.e. Jx and Jy) in the ocean are more effective than the 

vertical currents (i.e. Jz) as the horizontal extent of ocean is much larger than the vertical 

depth. In mCSEM, the data is recorded at the seafloor, where normally the vertical 

velocity component (i.e. vz) is very small. Therefore, terms vzBBy and vzBx B is negligible. 

Above argument simplifies (4), 

Jx 

( 

Ex 

v yBz 

) 

(6) 

J ( 

E v B ) 

Using (6), simplification of (4-a) gives 

E 

E 

y 

x 

y 

x 

x 

1 

 

( zH 

 

1 

 

( zH 

 

y 

x 

z 

v 

v 

v 

 

 

y 

x 

z 

x 

y 

B 

B 

B 

z 

z 

y 

z 

x 

) 

) 

) 

H ) v B 

y 

H ) v B 

Where the first term is the induced field and second term is the source term. Normally, 

the area used for mCSEM data acquisition is very small to observe horizontal variation in 

the vertical magnetic field Hz. Therefore, term y z H and xH z are negligible. Finally, we 

have a simplified equation, 

E 

E 

x 

y 

1 

 

zH 

 

1 

 

zH 

 

y 

x 

v B 

y 

v B 

Noticeably, the horizontal particle motion (i.e. vx and vy) is source for the induction of the 

horizontal electric field (i.e. Ex and Ey). 

5. The Data 

We have analysed horizontal component electric field (i.e. Ex and Ey) data recorded at 

500 m depth on the ocean floor. The recording is made in the absence of transmitter 

current to understand the oceanic background noise. Time series is shown in Figure 2. It 

is evident that the strength and pattern of Ex and Ey are different. 



37 

x 

z 

z 

 

 

 

 

 

 

x 

z 

z 

 

 

 

 

 

 

(5) 

(7) 

(8)

In equation (8), the first term is much smaller than the second term (i.e. 

( 1/ 

) 

H v B ), suggesting x-and y- component of velocity principally controls the 

z 

y| 

x 

y| 

x 

z 

strength of the Ey and Ex component of the electric field respectively. Evidently, the 

strength of Ex is higher than Ey (Figure 2). This suggests that the wave velocity in the ydirection 

will be higher than the x-direction (i.e. vy > vx). Further, as normally the surface 

wave moves towards the coast. Accordingly, the velocity component pointing towards the 

coast has higher velocity than the other horizontal component. The present data is 

recorded with a setting that the y-component of the receiver points towards the cost and 

constructs an angle of approx. 55 with it. Thus, the data acquisition setting as well 

favours for vy > vx. In general, electric field measurements characterize an average 

motion over the length of the antenna. Therefore electric field components can be used to 

derive information about the average velocity of the movements. 

Electric field (nV/m) 

Electric field (nV/m) 

200 

100 

0 

-100 

-200 

100 

50 

0 

-50 

-100 

Time series for E x 

50 100 150 200 250 300 

Time (minute) 

Time series for E 

y 

50 100 150 200 250 300 

Time (minute) 

Figure 2: Five hour times-series of two horizontal components of electric fields. Ex (top) and Ey 

(bottom). The recording is made at the seafloor, 500 m below the sea surface. 

6. Power Spectral Density (PSD) and Spectrogram 

Power spectral density is calculated to study the power content of the frequencies. For 

the PSD calculation, steps followed are as follows: 

I. Inspection of time series (Figure 2): Inspection is done to recognize glitches or 

other outliers in the data that are not consistent with the rest of the time series. 



38

II. Detrending: Detrending ensures that the first Fourier coefficient does not 

dominate the PSD. 

III. Windowing: A Hanning window is applied to minimise the leakage of spectral 

density. 

IV. Calculation of discrete Fourier transform (DFT): 

V. Calculation of PSD: PSD is calculated by segment averaging method (Welch, 

1967). 

The PSD for Ex and Ey is shown in Figure 3. Over all spectral power is decreasing with 

increase in frequency. Four different slopes can be seen in the both PSD’s (Ex and Ey). 

Let the slope containing frequencies between 0.001 – 0.1 Hz, 0.1 - 2 Hz, 2 – 10 Hz and 10 

- 25 Hz represent respectively low, intermediate, sub-high and high frequency range. 

Evidently, in the low frequency range the power of the electric field rises sharply. 

Generally, external origin field mainly affects the low frequency range, as higher 

frequencies are filtered out by the ocean resulting in passage for low frequencies only 

(i.e. less than 0.3 Hz for a 500 m deep ocean) to the ocean bottom due to skin depth. The 

oceanic eddies (very long wavelength oceanic feature) are another low frequency source 

(Chave and Filloux, 1984). Here, these two sources are presumed for the sharp rise in 

power in the low frequency range (0.001 – 0.1 Hz). In the range of intermediate 

frequency, four peaks are evident, at 0.2, 0.3, 0.4 and 1 Hz, in the PSD representing that 

this frequency range is receptive for the various oceanic flows close to seafloor. The subhigh 

frequency range is nearly flat. A flat PSD, generally, corresponds to a field which 

contains equal power within a fixed bandwidth which resembles noise. In the high 

frequency range a sharp rise is evidenced which is presumed due to digitisation noise. 

The frequency and power information of a PSD is insufficient to characterise the 

source process corresponding to the frequencies. Time preservation may help in this 

subject. Together with the frequency and power, information about time may help in 

identifying and characterising the source nature of process. The localised time process 

may represent a source progressing in an interval of time while an ambient time process 

reflects a continuous process. For the purpose therefore spectrograms are plotted which 

preserve the time information together with frequency and power. The spectrogram is 

the discrete-time Fourier transform for a sequence, computed using a sliding window. 

For a spectrogram calculation, the time series is divided in to segments equal to the 

length of the hamming window. Each segment overlaps 50% of the samples with the 

adjacent segment and then PSD is calculated for a defined frequency length. Again and 

again PSD is calculated by sliding the window to build a spectrogram. The Spectrograms 

corresponding to time series shown in Figure 2 is shown in Figure 5. There are three 



39

distinct anomalous features evident in spectrograms. One feature is corresponding to 

time approx. 165 min (like spike) and other two are at frequencies 1, 0.3 Hz. It is difficult 

to confidently propose a source nature for the spiky feature at approx. 165 min. This 

could be due to either by a regional earthquake or by a volcano like feature. In general, 

regional earthquakes are found in band frequencies of 0.1 to 1 Hz and here the spiky 

feature correspond the same range. The other two features at frequencies 1 and 0.3 Hz 

are respectively by the microseisms and swell, that will be discussed in the next section. 

E x (nV/m) 2 /Hz 

10 5 

10 4 

10 3 

10 2 

10 1 

10 0 

10 -1 

10 -2 

10 -2 

Power Spectral Density (E x ) 

10 -1 

Frequency (Hz) 

0.2 & 0.4 Hz 

0.3 Hz 

10 0 

1 Hz 

10 1 

E y (nV/m) 2 /Hz 

10 5 

10 4 

10 3 

10 2 

10 1 

10 0 

10 -1 

10 -2 

10 -2 

Power Spectral Density (E y ) 

0.2 & 0.4 Hz 

10 -1 

Frequency (Hz) 

Figure 3: Spectra of the two horizontal electric components Ex and Ey corresponding to time series 

shown in Figure 2. The graphs show the PSD vs. frequency. The anomalous peaks are visible at 0.2, 0.4 and 

1 Hz. There is also a weaker peak at 0.3 Hz. Four slopes can be observed in the spectra (pink dashed lines). 

7. Microseisms and swell 

Microseisms are like a soft earth tremor originating with in the ocean by non linear 

interaction of oceanic waves, which causes a continuing oscillation of the ocean floor. The 

broad frequency range for microseisms is between 0.05 to 1 Hz, which mainly depends 

on the ocean depth and oceanic conditions. 

Languet-Higgins (1950) proposed a mechanism for microseisms (0.05 -2.0 Hz) and 

showed that if two identical progressive waves travelling in opposite directions interact 

with each other, there is a second order pressure term effect which does not vanish with 

depth and can thus reach the deep ocean bottom (Figure 4). Consider two surface waves 

of frequencies f1 and f2 (f1f2), moving with approx. same velocity in opposite direction. 

Let the wave number of frequencies are respectively k1 and -k2, and then k1-k2. 

Interaction of these waves will leave behind a wave with very small wave number {i.e. 

k1+ (-k2) = diminutive} and very large wavelength. The large wavelength is capable of 

creating a pressure disturbance effectively at the ocean floor. The amplitude of the 



40 

0.3 Hz 

1 Hz 

10 0 

10 1

pressure disturbance is proportional to the product of the interacting wave heights and 

the frequency. These pressure fluctuations in the water column might then excite 

Rayleigh waves in the solid earth and be observed as microseisms. 

In short, the favourable oceanic conditions for microseisms generation are: 

1. Shoreline geological setting creating grounds for nonlinear interaction of 

surface waves. 

2. Near shore reflection of high frequency surface waves and thereafter head 

on interaction. 

3. A fast moving storm creating a sequence of wave in different directions. 

4. High frequency wave interaction may generate whitecaps (a wind blown 

wave whose crest is broken and appears white), which leads in acoustic 

energy transmission to ocean bottom. 

The depth of the ocean is another important factor in microseisms generation. The wave 

generation in the ocean depends on the wind velocity, which become efficient when the 

wave velocity is close to the phase 

velocity of the ocean waves. Velocity of 

ocean wave (V) is, roughly speaking, 

(gD), where D is ocean depth and g is 

acceleration due to gravity. Therefore, 

for a 4 km deep ocean and a 500 m 

shallow ocean, the velocity V is 

Figure 4: Microseisms mechanism (from Elgar approximately 200 m/s and 70 m/s 

(2008)). Nonlinear interaction of short opposing respectively. A typical wind velocity 

waves leads to a long wavelength wave generation, rarely exceeds few tens of m/s. This 

which reaches the seafloor and generates 

suggests wind velocities are quite close 

i i 

to the oceanic velocities especially in the shallow oceans. Therefore the generation of 

microseisms is likely to be efficient in shallow oceans (Tanimoto, 2005). 

Swells are a kind of oceanic surface waves. They are often created by the 

breaking of storms thousands of kilometres away from the seashore. The distance allows 

the waves comprising the swells to become more stable, clean, and continuous as they 

travel toward the coast. For microseisms generation, in general, higher frequency waves 

are more efficient than the lower frequency waves like swells. Swells are more 

directional and therefore chances for non linear interaction is not as much as of higher 

frequency gravity waves (Webb and Cox, 1986), which are generated with in the ocean by 

the influence of gravity at the interface involving the density contrast. In Figure 3 and 5, 



41

the anomalous feature close to 1 Hz is likely due to a microseism. A microseism is a time 

localised feature, the duration of which depends on the time of effective nonlinear wave 

interaction. It is evident from Figure 5 that close to 1 Hz, there are four time localised 

features (Ey component has more clear appearance than Ex), corresponding to time 8, 40, 

90 and 250 min approx. Further evidence in support of microseisms is the observed 

frequency (i.e. 1 Hz). 

The acquired electric field data was recorded in a shallow ocean (500 m depth). 

Normally, a shallow ocean may contribute the microseisms in high frequency range (i.e 

close to 1 Hz) as analogous to high frequency even a comparable wavelength (not 

necessary a huge wavelength) may reach ocean bottom to produce microseisms. The 

mechanism of microseisms generation suggests that maximum electric field power will be 

experienced in the component perpendicular to the direction of wave propagation. Here, 

the velocity component Vy > Vx as amplitude of Ex > Ey. The strong power of microseisms 

in the Ey component compared to the Ex component further supports to interpret 1 Hz 

frequency as microseisms. 

Figure 5: Spectrogram for Ex & Ey. Electric field power is colour coded in dB and displayed as function of 

time and frequency. Two anomalous features are visible, one at 1 Hz and the other covering a broad 

frequency range, having max. power at 0.2 & 0.4 Hz. 

The individual feature ambient in time at 0.3 Hz (Figure 3 & 5) is interpreted here 

as a swell. A swell consists of long-wavelength surface waves which are more stable in 

their directions and frequency than normal wind waves. Swells are dispersive in nature 

and their frequency is given by 2 gs tanh(sD), where g is acceleration of gravity; s = 

2/ is wave number, is the wavelength of the swell and D is the depth of ocean. A 

calculation suggests that a swell of frequency 0.3 Hz corresponds to a wavelength of 18 

m for 500 m deep oceanic water. The obtained wavelength is well in range for the 



42

wavelengths of swells. As 0.3 Hz frequency is evident throughout the time in 

spectrogram (Figure 5), this is another strong support for 0.3 Hz to stand for a swell. 

7. Microseisms during mCSEM data recording 

Microseisms are a powerful feature to effectively generate EM signal at the ocean floor. 

They are quite capable of masking the mCSEM signals. We have an example comparing 

the power of microseism and mCSEM transmitter current. In Figure 5, we have seen the 

spectrograms of mCSEM the time-series recorded in the absence of transmitter current. 

On the other hand, Figure 6 represents spectrograms of the mCSEM data when 

transmitter was transmitting signals. Systematic decay in the power is evident in Figure 

6, representing transmitter is moving away from the receiver. A gathering of high power 

(yellow colour) patch is evident corresponding to frequency 0.1 Hz and time 200 min, 

may be representing a microseism. Clearly, the power of a microseism is significant 

enough to contaminate the mCSEM data. It is as well evident that the effect of swell is 

feeble in the presence of a transmitter current. For a larger transmitter receiver distance 

this effect may be significant. 

Microseisms Microseisms 

Figure 6: Presence of a microseism during mCSEM data recording. Electric field power is colour coded 

in dB and displayed as function of time and frequency. Corresponding to frequency 0.1 Hz and time 200 min 

(approx), a yellow coloured high power patch is evident, which may be is by a microseism. The other efficient 

high power patches in the spectrogram is by the transmitter current 

8. Conclusions 

By the analysis seafloor electric field data, we provide evidence for the observation of 

microseisms and swell in mCSEM data. Power spectral density (Figure 3) and 



43

spectrogram (Figure 5) clearly present the evidence for the possible presence of 

microseism and swell corresponding to the frequencies 1 Hz and 0.3 Hz respectively. 

Swells are time ambient oceanic feature, which can be clearly marked in the 

spectrograms. The stability of 0.3 Hz in spectrograms indicates that oceanic conditions 

were quite stable during the recording of present mCSEM data. 

Figure 6 shows that the power of a microseism is significant even when the 

transmitter current is ‘on’. Overall, the time series analysis suggests that features like 

microseism and swell induce a significant electric field at the seafloor to contaminate the 

mCSEM data. Proper measures for removal of the noise are essential for a better 

interpretation of mCSEM data. 

Acknowledgement 

We thank KMS Technologies –KJT Enterprises Inc. for sponsoring the work. 

References 

1. Bhatt, K. M., A. Hördt, P.Weidelt, T. Hanstein, 2009. Motionally induced 

electromagnetic field within the ocean, 23. Kolloquium Electromagnetische 

Tiefenforschung (EMTF), Brandenburg, Germany, September-October, this issue. 

2. Chave, A.D., and C.S. Cox, 1982. Controlled electromagnetic sources for measuring 

electrical conductivity beneath the oceans, 1, forward problem and model study, J. 

Geophys. Res., 87, 5327-5338. 

3. Chave, A.D., and D.S. Luther, 1990. Low-frequency, motionally induced 

electromagnetic fields in the ocean, 1, theory, J. Geophys. Res., 95, 7185-7200. 

4. Chave, A.D., and J.H. Filloux, 1984. Electromagnetic induction fields in the deep 

ocean off California: oceanic and ionospheric sources, Geophys. J. R. astr. Soc., 77, 

143-171. 

5. Constable, Steven and Leonard J. Srnka, 2007. An introduction to marine controlledsource 

electromagnetic methods for hydrocarbon exploration, Geophysics, vol. 72, no. 

2, p. wa3–wa12. 

6. Crews, A., and J. Futterman, 1962. Geomagnetic micropulsation due to the motion of 

ocean waves, J. Geophys. Res., 67, 299-306. 



44

7. Dahm T, F. Tilmann, J. P. Morgan, 2006. Seismic broadband ocean-bottom data and 

noise observed with free-fall stations: experiences from long-term deployments in the 

North Atlantic and the Tyrrhenian Sea, Bull. Seismol. Soc. Am, 96, 647–664, doi: 

10.1785/0120040064. 

8. Elgar, S. ,2008. Ripples run deep, Nature, Vol 455, Page 888. 

9. Longuet-Higgins, M.S., E. Stern, H. Stommel, 1954. The electrical field induced by 

ocean currents and waves with application to the method of towed electrodes, Pap. 

Phys. Oceanog. Meteorol., 13(1),1-37. 

10. Longuet-Higgins, M.S., 1950. A theory of the origin of microseisms, Philos.Trans. R. 

Soc. London, Ser. A, 243, 1–35. 

11. Podney, W., 1975. Electromagnetic fields generated by ocean waves, J. Geophys. Res., 

80, 2977-2990. 

12. Sanford, T.B., 1971. Motionally induced electric and magnetic fields in the sea, J. 

Geophys. Res., 76, 3476-3492. 

13. Tanimoto, T., 2005. The oceanic excitation hypothesis for the continuous oscillations 

of the Earth, Geophy. J. Int., 160, 276-288. 

14. Webb, S.S. and C.S. Cox, 1985. Observation and modelling of seafloor microseisms, J. 

Geophys. Res., 91, B-7, 7343-7358. 

15. Welch, P. D. 1967. The use of fast-Fourier transform for the estimation of power 

spectra: A short method based on time averaging over short, modified periodograms, 

IEEE Transactions of the Audio and Electroacoustics, AUlS, 70-13. 



45

Motionally Induced Electromagnetic Field within the Ocean 

K. M. Bhatt 1 , A. Hördt 1 , P.Weidelt 1,* and T. Hanstein 2 

1 

Inst. f. Geophysik u. Extraterrestrische Physik, TU Braunschweig 

2 

KMS Technologies - KJT Enterprises Inc 

Abstract 

The contribution of motionally induced electromagnetic (EM) fields at the seafloor is generally 

considered small, but since the characteristic reservoir signal in marine controlled source 

electromagnetic (mCSEM) data is also small, the inclusion of the motional induction 

contribution in modelling the signal will enhance the probability of reservoir detection. Here, 

we have studied the electromagnetic induction caused by ocean water flow with in earth’s 

magnetic field. 

When a charge particle moves with certain velocity in earth’s magnetic field, it 

experiences a Lorentz force. The action of Lorentz force generates a secondary electric field 

through galvanic and inductive processes. For the mathematical formulation, we considered 

Lorentz electric field as a source in the corresponding set of Maxwell’s equations. We solved 

these Maxwell's equations for a 1D model and velocity structure using two different Green’s 

function i.e. a two half space Green’s function and a layered Green’s function. The layered 

Green’s function is especially useful in studying the sensitivity of electric and magnetic field for 

different conductivity structures in the earth. Further, the signal variation with the conductivity 

of ocean, depth of ocean and wave velocity is studied to profoundly understand the effect of 

these parameters. 

________________________________________________________________________________ 

* Deceased 

1. Introduction 

Oceanic water movements in the earth’s magnetic field induce electric and magnetic 

fields in the ocean. The induced fields are signal for oceanographic and seismological 

applications but noise for magnetotelluric (MT) and marine controlled source 

electromagnetic (mCSEM) applications. Oceanographers and seismologists use the fields 

respectively to study the velocity structure and the seismic background noise. The MT 

and mCSEM signals, which are generally used for lithospheric and hydrocarbon 

exploration studies, are contaminated by the induced field and act as noise. Our prime 

focus of motional induction study here is on mCSEM problems; nevertheless the results 

are also applicable for other scientific applications. 

Generally, motionally induced noise in seafloor mCSEM data is considered small, 

but since the characteristic reservoir signal is also small, the understanding and possible 

removal of noise may be essential to increase the number of possible target reservoirs. 



46

The electromagnetic induction investigation has a long history. Initially, by an 

observation of deflection in the galvanometer by stream waves Faraday (1832) concluded 

that flow of water will induce electric currents, which was afterwards measured 

experimentally by Young et al (1920). Later it was almost neglected and got re-attention 

after World War II. Longuet-Higgins et al., (1954) initiated the investigation of electric 

field induction by surface waves. Crews and Futterman (1962) investigated the magnetic 

field induction by oceanic movement. Further, Sanford, (1971) extended the theory of 

motional induction by considering three-dimensional water flows. A comprehensive study 

of the theory has been made by Podney (1975), who generalised and extended the 

previous work by removing the restrictive assumptions imposed on ocean-water velocity 

field. Chave (1983) generalised the EM induction process by considering driving electric 

 

field term (i.e. v B ) and further, Chave and Luther (1990) re-examined the motional 

induction problem. 

A primary purpose of this paper is to present a generalised simple illustrative 

theory for the problems of motional induction. For the purpose, we have formulated a set 

of Maxwell’s equation for our problem. These equations are simplified for electric and 

magnetic field components by considering a horizontally progressing ocean wave and 

then solved by using the Green’s function, with appropriate boundary conditions. Here, 

we solved the problem with two different Green’s functions. For a uniformly conductive 

earth, a two half space Green’s function is utilised and for a layered earth, a layered 

Green’s function is utilised. A two half space Green’s function doesn’t offer reflections 

because of homogeneous conductivity consideration and thus expresses only the case of 

downward progressive diffusive waves. The layered Green’s function includes both 

downward and upward propagating diffusive waves offered by the layered boundaries. 

2. Problem formulation in terms of Maxwell’s equation 

2.1 Basics 

An electrically conducting fluid like ocean consists of charged particles. The particles in 

the ambient geomagnetic field experience a deflective Lorentz force. If ‘ v ’is the velocity 

of charge particle ‘q’ moving in the geomagnetic field ‘ B0 ’, then the Lorentz force is: 

 

q( 

v B ) 

(1) 

FL 0 

The charge ‘q’ experiences the deflecting force ‘ FL ’ because of the action of an electric 

field which we call as Lorentz electric field ( EL ), 



47

Therefore, L 0 

 

FL 

 

qEL 

(1-a) 

 

E 

 

v B 

(2) 

The field ‘ EL ’ generates a secondary electric field ‘ E ’, mainly by two processes- 

(1) Galvanic process: At locations, where ‘ EL ’ has a component parallel to the 

conductivity gradient ' 

' 

( is conductivity in S/m), space/surface charges are 

accumulated. The accumulated charges galvanically create a secondary field ‘ E ’, 

even if the wave velocity is constant. 

(2) Inductive process: The magnetic field ‘ HL 

’ is created by the current density 

 

’ i.e. 

‘ JL 

 

JL 

( 

v B0 

) 

 

H J 

L 

L 

when the velocity ‘ v ’ changes with time. This induces a secondary electric field E 

via the law of induction. 

We assume that all the hydrodynamics, including Coriolis force, is included in the given 

‘ v ’. We do not care about the sources of forces. Finally, for a stationary frame of 

reference, the current density in the Ohms law is given by 

 

( E E ) ( E v B ) 

(3) 

J L 

0 

Here, ‘ ’ is the conductivity of the fluid, ‘ E ’ is the current term generated by both a 

galvanic and an inductive process and ‘ 

 

( v B ) ’ is the source current term for motional 

0 

induction case. Under the quasi-static approximation, the set of Maxwell’s equation to be 

solved for the motional induction case is 

 

H ( 

E v B0 

) 

 

(4- a, b) 

E 

H 

0 

t 

In an exact formulation, the ambient magnetic field is the sum of geomagnetic field ‘ B0 ’, 

the external magnetic field by ionospheric currents ‘ Bext 

’, the field generated by small 

local anomalies 

 

‘ B lano 

’ and the motionally induced field ‘ Bmi 

’ i.e. 

 

( B 

 

B 

 

B 

 

B ) . In general, the last three terms are orders of magnitude 

B 0 ext l ano mi 

smaller than the geomagnetic field B0 . Therefore, for computations, the local value of 

earth’s magnetic field would be a good choice. 



48

3. A halfspace model 

Let the north, east and positive downward directional depth in Cartesian coordinate 

system be represented by xˆ , yˆ and zˆ . Consider a two halfspace model with the boundary 

at the earth surface (i.e. z 0 ). Let the insulating air halfspace extend in the negative 

vertical upward direction while the earth halfspace extends in positive vertical downward 

direction from the boundary surface (Fig 1). The conductivity of the earth’s half space is 

=3.33 S/m, which contains an ocean and sediments below. In general, the conductivity 

of the ocean depends on dissolved ions content and their mobility, which is primarily a 

function of temperature and pressure. The conductivity in warm, top shallow water is 

normally high (5 S/m) compared to cold, deep water (2.5 S/m). For simplicity, oceans 

can be considered homogeneous as the range of conductivity difference (i.e. 2.5–5 S/m) is 

small. Consider with depth d=1000 m ocean moving with a velocity v in the x-direction 

(Fig 1). Below the ocean, a subsurface of stationary sediments (i.e. v = 0, motionless) 

exists. 

z=0 

+z 

z=d 

V x 

Ocean (v0) (v0) (v0) 

, , 0 

Sediments (v = 0) 

, , 0 

Air Half-Space 

x 

Earth Half-Space 

Fig 1. The two halfspace model. z = 0 is the 

boundary between earth and air halfspace. Depth is 

considered positive in the downward direction. The 

earth halfspace consists of two layers. The top layer 

represents the ocean having non-zero velocity in 

the x-direction. The depth of the ocean is d. Below 

the ocean, a second layer of static (i.e. velocity 

zero) sediments extends. The conductivity and 

magnetic permeability of earth halfspace is and 

0 respectively. 

 

 

Let B0 B0 

zˆ and v v x ( z, 

t) 

xˆ 

This will generate a horizontal electric field perpendicular to the velocity direction and a 

horizontal magnetic field perpendicular to the electric field, and thus we can write: 

 

 

E ( z, 

t) 

yˆ and H ( z, 

t) 

xˆ 

From eq. (4), we have 

E y 

2 

H x 

EBv Assume a harmonic time dependence for simplicity, 

~ it 

Then E ( z, 

t) 

E ( z) 

e , H 

y 

y 

z Ey 0 

t y 0 t x 

(5) 

x 

( z, 

t) 

x 

v 

x 

( z, 

t) 

~ it 

v ( z) 

e , 

it 

H ( z) 

e 

~ 

and eq. (5) reduces to 

2~ 

2 ~ 

E k (z) E (z) - g(z) 

(6) 

z 

y 

y 



49 

x

where, 

2 

g(z) k (z) 

~ 

v x(z) 

B0 

is the source term, k( 

z) 

i0( 

z) 

represents the 

electromagnetic damping phenomenon. It is complex such that amplitude decay is 

associated with a phase shift with respect to the field at the surface. The Green’s function 

G( z | z0 

) corresponding to equation (6) is defined by 

2 

2 

G 0 

0 

0 

( z | z ) k (z)G(z | z ) - (z 

- z ) 

(7) 

Crosswise multiplication with G and y E 

~ 

and subtraction yields 

 

~ 

G 

E 

~ 

E 

~ 

G) 

- g(z) G E ( 

z z ) (8) 

z ( z y y z 

y 0 

The integration of (8) over depths z yields the solution 

d 

~ 

E y(z0) 

g(z) G(z | z0 

) dz , for - z0 

(9) 

0 

i.e. a convolution of the source term with the Green’s function. The integration, which 

formally must be carried out from minus to plus infinity, reduces to 0 to d, because that is 

~ 

y 0 

where the source is nonzero. For the horizontal electric field E (z ) calculation at any 

desired depth, knowledge of the Green’s function is required. 

3.1 Green’s function 

3.1.1. Half space 

The Green's function is commonly used to solve inhomogeneous boundary value 

problems. The solution by means of Green’s function gives a special advantage because 

of its reciprocity property, which states ‘relationship between a oscillating source and the 

resulting field at some point of observation is unchanged even if the observation and 

source points are interchanged’. Using the boundary conditions, the Green’s function is 

calculated for the halfspace. Calculation is as follows: 

For an arbitrary small , equation (7) follows, 

( z | z ) G( 

z | z ) 1 

(10) 

zG 

0 0 z 0 0 

The second boundary condition is that G( z | z0) 

is continuous at z z0 

i.e. 

G( z0 

| z0 

) G( 

z0 

| z0 

) 0 

(11) 

For the uniform halfspace, 

 

A e 

kz 

G ( z | z0 

) 

Be 

kz 

for z z0 

for z z0 

(12-a,b) 

A and B are determined from (10) and (11) which yields the Green’s function for the half 

space 



50

3.1.2 Two halfspaces 

G( 

z | z 

0 

) 

1 

2k 

k| 

zz 

| 

0 

e 

(13) 

In order to consider the diffusive reflection and transmission effects due to boundaries, 

let us consider two uniform half spaces with k( z) 

k 0 in the air (i.e. z0). The Green’s function, for z0>0, can be written as 

G( 

z | z 

1 k | z z 

e 

) 

2k 

k z 

T e 0 

 

0 

| 

R e 

kz 

for z 0 

0 (14) 

for z 0 

where, T and R are respectively transmission and reflection coefficients. The continuity of 

G and zG 

at z 0 yields 

1 k | z z | k - k k( 

z z ) 

e 

0 

0 e 

0 

 

2k 

 

k k0 

G( 

z | z ) 

 

1 

 

k z kz 

e 0 0 

k k 

0 

for z 

0, 

z 

for z 0, 

z 

0 

0 

0 (15) 

In particular, for the insulating air halfspace k 0 0 , the two halfspace Green’s functions 

take the form 

1 k | z z | k( 

z z ) 

 

e 

0 e 

0 

 

G( 

z | z ) 2k 

1 

 

kz 

e 0 

 

k 

for z 0, 

z 

for z 0, 

z 

0 

0 

0 

0 

0 

0 (16) 

3.1.3. A simple model and field expression 

Equation (9) includes the source term g(z), which depends on conductivity and velocity, 

both are depth dependent. For simplicity, consider a uniform horizontal velocity i.e. 

v(z) v0 

, 0 z d . Let the depth dependent conductivity be zero in the air and 

3. 

33 S / m for the earth i.e. 

(z) 

 

 

, z 0 

0 , z 0 

The equation (9), (16) and (4), yields the horizontal electric and magnetic field expression 

for the full space. 



51 

0

Electric field in full space: 

~ 

Ey 

( z0 

) v 

~ 

Ey 

( z0 

) v 

~ 

E ( z ) v 

Magnetic field in full space: 

H ~ 

H ~ 

H ~ 

y 

x 

x 

x 

0 

( z 

( z 

( z 

0 

0 

0 

0 

0 

0 

) 0 

B ( 1 e 

B ( 1 e 

B 

0 

0 

0 

e 

kv0 

B 

) 

i 

kv0 

B 

) 

i 

kz 

0 

0 

0 

0 

kd 

kd 

) 

cosh( kz 

)) 

, z 

0 

,0 z 

0 sinh( kd) 

, z d 

e 

e 

kd 

kz 

sinh( kz 

0 

0 

) 

, z 

0 sinh( kd) 

, z d 

0 

0 

0 

0 

,0 z 

0 

0 

0 

d 

d 

(17-a, b, c) 

(18-a, b, c) 

The graphical response of (17) and (18) is shown in Fig (2). The response is calculated for 

a halfspace model (Fig 1) of a conductivity of 3.33 S/m containing 1000 m thick layers of 

ocean and sediments. The magnetic permeability is kept constant for both halfspace and 

is equal to free space permeability i.e. 0 =410 -7 Vs/Am. The ocean has a homogeneous 

velocity of 10 cm/s in an ambient geomagnetic field of 510 -5 T. The responses are 

studied for frequencies 0.001, 0.01, 0.1, and 1 Hz. In general, the electric field becomes 

gradually weaker with depth (Fig 2). For 1 Hz, rather than weakening gradually, the 

electric field amplitude increases and becomes strongest with in the ocean (at 400 m 

depth). Further, the field Bx is zero at the surface and progressively becomes stronger 

with respect to depth. At the ocean bottom, it offers strongest amplitude. The zilch of Bx 

~ 

at the earth surface is for the reason that in air halfspace field Ey 

is constant and 

~ 

z y 

therefore E 0 in particular, which is BBx (eq. 4-b). Further, as far as frequency based 

variation are concerned, the smallest frequency Bx produces the strongest amplitude at 

the ocean bottom. The field Ey shows a contrary behaviour. Here the smallest frequency 

offers the weakest amplitude at the ocean floor. At large frequencies the field Ey can not 

reach to the ocean floor, because of the shallow skin depth, offers constant amplitude 

(Fig 3). 

The important result in Fig 2 & 3 is that the field Ey is smooth over the boundary 

between the ocean and sediment. On the other hand, the field Bx offers a sharp change in 

pattern there (at boundary). Note that the conductivity of the ocean and subsurface 

(sediments) are identical. They differ only in their velocity state (subsurface is static and 



52

ocean is dynamic). Therefore the sensitivity of the field Bx at the boundary is interpreted 

as result of velocity change. 

Depth, (m) 

0 

-1000 

-2000 

0 1 2 3 4 5 6 

E (V/m) 

y 

0.001 Hz 0.01 Hz 0.1 Hz 1 Hz 

0 

Depth, (m) 

-1000 

-2000 

0 5 10 

B (nT) 

x 

15 20 

Fig 2. Variation of the horizontal comp. electric 

(Ey) and magnetic (Bx) field with respect to 

depth. Variation is shown for four frequencies viz. 

0.001, 0.01, 0.1 and 1 Hz. An ocean of conductivity 

=3.33 S/m extends from surface to 1000 m depth 

(i.e. 0 z 1000 m). Below the ocean (i.e. below 

1000 m depth) there is a sediment layer with the 

same conductivity as the ocean (i.e. =3.33 S/m). 

The horizontal line at 1000 m is to show the 

separation of these two boundaries. 

Depth, (m) 

0 

-1000 

-2000 

0 1 2 3 4 5 6 

E (V/m) 

y 

2 Hz 10 Hz 50 Hz 

Depth, (m) 

0 

-1000 

-2000 

0 0.5 

B (nT) 

x 

1 1.5 

Fig 3. Variation of the horizontal component 

electric (Ey) and magnetic (BBx) field with 

respect to depth. Variation is shown for three 

frequencies viz. 2, 10 and 50 Hz. Other information 

is the same as in Fig 2. It is evident thet at the ocean 

floor, the field Ey offers almost same amplitude for 

all the three frequencies. Bx is strongest and 

weakest respectively for the smallest and largest 

frequency. 

The field Ey (17-b) with in the ocean (i.e. 0 z0 

d ) consists of two terms. The first 

term is the kernel for the motional induction, while the second governs the depth 

dependent frequency based EM damping. From the expressions (17-b & 18-b), it is clear 

that the strength of both the fields Ey and BBx depends on the ocean depth (i.e. ocean 

-kd 

deepening) because of the factor e . Effect of the ocean deepening is studied for oceans 

of thickness (depth) varying from 1000 m to 9000 m. Observation depth is constant for all 

practical cases and is 1000 m (i.e. z0 

= 1000 m). Results are shown in Fig (4). Ey is 

strongest for the thickest ocean and weakens down gradually as ocean shallows up. The 

reverse is observed for the Bx case with weakest strength in the deepest ocean which 

progressively becomes stronger as the ocean gradually shallows up. The sensitivity for 

the deepening effect depends on frequency and therefore on skin depths. For that reason, 

the deepening effect is more effective at smaller frequencies. The skin depths, for a 

halfspace of 3.33 S/m, at frequencies 0.001, 0.01, 0.1, 1 and 10 Hz are approximately 

8664, 2739, 866, 273 and 86 m, respectively. 



53

The factor which may significantly influence the motional induction is the 

conductivity of the ocean. The results of the conductivity variation are shown in Fig 5. 

The field strength is observed at 1000 m depth for conductivities varying from 3 to 5 S/m. 

Observations are made for five different frequencies (i.e. 0.001, 0.01, 0.1, 1 and 10 Hz). 

The results suggest that the field Bx is more sensitive to conductivity variation than the 

field Ey. Further, lower frequencies are more responsive to conductivity variation than 

high ones because of the thicker skin-depth. 

Various Ocean Depths (m) 

9000 

8000 

7000 

6000 

5000 

4000 

3000 

2000 

1000 

10 0 

0.001 Hz 0.01 Hz 0.1 Hz 1 Hz 10 Hz 

E y (V/m) 

Various Ocean Depths (m) 

9000 

8000 

7000 

6000 

5000 

4000 

3000 

2000 

1000 

10 -5 

B x (nT) 

Fig 4. Deepening effect of an ocean: Conductivity 

of ocean kept constant (i.e. 3.33 S/m). For 1000 to 

9000 m deep ocean the field strengths are calculated 

at frequencies 0.001, 0.01, 0.1, 1 & 10 Hz. The y- and 

x-axis represents ocean depths and field strength 

respectively. The observation depth is constant and is 

1000 m. The magnetic component for 1 and 10 Hz is 

truncated for depths greater than 5000 and 2000 m 

respectively to save the Figure from masking and 

cluttering. 

10 0 

Conductivity (S/m) 

5 

4.8 

4.6 

4.4 

4.2 

4 

3.8 

3.6 

3.4 

3.2 

0.001 Hz 0.01 Hz 0.1 Hz 1 Hz 10 Hz 

3 

0.5 1 1.5 2 2.5 3 

E (V/m) 

y 

Conductivity (S/m) 

5 

4.8 

4.6 

4.4 

4.2 

4 

3.8 

3.6 

3.4 

3.2 

3 

0 5 10 15 

B (nT) 

x 

20 25 30 

Fig 5. Conductivity variation effect: The 

conductivity of the ocean is varied from 3 to 5 S/m 

and the effect is studies for frequencies 0.001, 

0.01, 0.1, 1 & 10 Hz. The horizontal component 

electric and magnetic field strength, observed at 

1000 m ocean depth is shown w.r.t. conductivities 

for the chosen frequencies. Electric and magnetic 

components both are sensitive to the conductivity 

of the ocean. Sensitivity increases with the 

decreasing frequency. 

Equation (17) and (18) indicate that the field BBx is more sensitive to conductivity 

variation in vertical direction, as conductivity is effectively convolved, than the field Ey. 

But it would not be appropriate to discuss conductivity variation in vertical direction 

using a halfspace model. Therefore, we will be back on this issue with a justified layered 

model and a layered Green’s function. 

Moreover, the equation (17) and (18) implies that the increase in the wave 

velocity v0 will cause a constant shift in the Ey 

and Bx field. Three experiments are 

conducted for wave velocities of 10, 1 and 0.1 cm/s to study the effects. The results are 

shown in the Fig 5. A log scale is used for x-axis plotting for clarity reasons. As at the 



54

surface Bx=0, therefore the log scale plot starts from 100 m depth as 100 m is the 2 nd 

discretized layer of the ocean. The selection of velocities is such that the 1 st selection 

exceeds the 2 nd by factor of 10 and same is true for 3 rd and 2 nd . Evidently, response for 

the field Ey and Bx also exceeds by a static shift of factors of 10. The graph clearly 

illustrates that the velocity is an important parameter for practical simulation, any bias in 

velocity leads to the same bias in EM field. 

D epth, (m ) 

0 

-1000 

10 -2 

-2000 

10 -1 

E y (V/m) 

0.1 m/s 0.01 m/s 0.001 m/s 

10 0 

10 1 

D epth, (m ) 

0 

-1000 

10 -2 

-2000 

10 0 

B x (nT) 

Fig 6. Wave Velocity effect. Semi-log plot of 

horizontal electric and magnetic field component 

illustrating the effect of velocity change. The 

strongest velocity generates the strongest EM field. 

The Bx plots starts from 100 m depth as the strength 

of Bx at z=0 is zero and at z=100 m the next layer 

starts. 

4. Layered model 

4.1. Layered Green’s function 

10 2 

Depth (m ) 

-0 

-1.000 

-2.000 

Let us consider a layered Green’s function defined as 

f=0.001 Hz f=0.01 Hz f=0.1 Hz f=1 Hz 

-3.100 

0 2 4 6 

Ey (Volt/meter) 

Depth (m ) 

-0 

-1.000 

-2.000 

Ocean 

Sediments 

Reservoir 

Sediments 

-3.100 

0 5 10 

Bx (nT) 

15 20 

Fig 7. Variation of the horizontal component 

electric (Ey) and magnetic (Bx) field with 

respect to depth for a layered model. Variation is 

shown for four frequencies viz. 0.001, 0.01, 0.1 and 

1 Hz. An ocean of conductivity =3.33 S/m extends 

from the surface to 1000 m depth (i.e. 0 z 1000 

m). Below the ocean there, is a 1000 m thick 

sediments layer with conductivity =1 S/m. A 100 

m thick reservoir of conductivity 0.01 S/m is 

embedded at 2000 m depth. The horizontal line 

marks the boundary of different formation. 

1 k | z z | k z k z 

G( z | z ) 

 

e 1 0 

R e 1 

R e 1 

0 

 

0 

d ; 0 z d, 

0 z0 

d 

2k 

 

 

 

 

1 



55

where, k1 i0 

is the electromagnetic damping in the ocean, R 0 describes the field 

1 

diffusing downward by reflection from the air-earth interface and R d describes the field 

diffusing upward by reflection from the seafloor (i.e. z d ). In this particular case the 

constants R 0 and R d are determined from boundary conditions:- 

a) 

( 0 | z ) 0 , Since ( z | z ) is constant in the air halfspace 

zG 

0 

G 0 

b) ( d | z ) b ( d) 

G( 

d | z ) 0 , where, b2 ( d) 

is determined via continuous 

transfer function. 

They yield, 

R 

0 

with 

zG 

0 0 2 

0 

1 R ce 

 

1 R e 

R 

c 

2k 

( d z 

) 

c 

0b 

 

b 

0 

2k 

d 

2 

2 

1 

1 

1 1 

k 

k 

0 

1 

1 

e 

k 

z 

1 0 

4.2 Layered model and Response 

; 

R 

d 

R c ( 1 e 

 

1 R e 

c 

2k 

z 

1 0 

2k 

d 

1 1 

) 

e 

k 

( 2d 

z 

) 

EM field responses calculated for a layered model are shown in Fig (6). The parameters 

of the model are tabled in table 1. The magnetic permeability of the each layer is equal to 

free space permeability (0). The response is computed for four frequencies viz. 0.001, 

0.01, 0.1 and 1 Hz. It is evident that the field Ey varies smoothly over layer boundaries, 

indicating its sensitivity to the vertically averaged conductivity rather than conductivity 

variation at layered boundaries. However, the field Bx senses each layer and offers a 

change in field strength at each layer boundary. Evidently, the magnetic field and its 

sensitivity for conductivity variation is frequency dependent. At a small frequency the 

field is strong and vice versa. 

Table 1: Layered Model 

Layers 

Thickness 

(m) 

Conductivity 

(S/m) 

Ocean 1000 3.33 

Sediments 1000 1 

Reservoir 100 0.01 

Below 1000 1 

1 

Other Parameters 

Wave Velocity=0.1 m/s 

Ext. Magnetic Field=510 -5 T 

Magnetic Permeability of each layer 

1 

=410 -7 



56 

0

5. Discussion and Conclusion 

No doubt, the actual earth is 3D and therefore the electromagnetic response of the earth 

will always be more complex than the response of any simplified model. However, a 

simplified model, roughly representing actual earth layers can be used to validate results. 

The choice of the model dimension (i.e. 1D, 2D or 3D) sometimes has a large impact on 

the result. In particular, for mCSEM surveys, generally 2D data acquisition methodology 

is followed and therefore a 2D/3D modelling may lead to a better interpretation. 

However, 1D model formulations are simple and give good insight into the physics of the 

problems. 

Field strength depends on their components (depending on the physical process 

involved), whose production mainly depends on the involvement of the source 

components. For example, a 1D model in motional induction study results in Ey and Bx 

(two) components when a 1D source (i.e. wave-velocity in x-direction) is considered. 

However, a 2D source (i.e. wave-velocity in x-direction and a wave wavelength in ydirection) 

consideration results in Ey, Bx and Ez (three) components. This suggests, even a 

1D model, with a proper source formulation offers significant insight to the problems. 

Further, the simplicity of a 1D model is an important advantage. In this paper we 

thoroughly looked for the sources of the motional induction in the ocean, which is 

incorporated in 1D model for theoretical development. The horizontal (x-direction) wave 

motion and a vertical (z-direction) geomagnetic field consideration lead to the excitation 

of the field components ‘Ey’ and ‘Bx’. These fields illustrate some of important results and 

effects of the ocean dynamics in varying oceanic conditions. 

In general, for a uniform halfspace, there is gradual reduction and increase 

respectively in the strength of Ey and Bx. w.r.t. ocean depth (Fig 2). This conclusion is 

valid for frequencies with skin depth ‘’ greater than the ocean depth ‘d’. For the case 

when < d, Ey may show maximum amplitude somewhere in the ocean, rather than at 

the ocean surface. On the other hand in the ocean the field Bx always offers maximum 

strength at the floor and minimum (i.e Bx = 0) at the surface. Since Bx vanishes at the 

surface, the mCSEM surface measurement may offer significant noise-free signals there, 

if MT field is avoided. At the ocean floor as Bx always has maximum strength therefore it 

is necessary to correct mCSEM data for motionally induced field. It is evident from Fig 

(2), even in a halfspace where the conductivity of ocean and subsurface is same, Bx 

senses the boundary of the ocean and subsurface (i.e. sediments) though Ey does not see 

it. Still, an important question left to answer is ‘which field is/are sensitive to layer 

demarcation, either Ey or Bx or both?’ This issue will be conferred below later, in the 

paragraph with layered earth discussion. 



57

The fields Bx and Ey both are sensitive (Fig 5) to the conductivity variation of the 

oceans. The observations with several oceans differing in their conductivity suggests that 

at frequencies with < d, in general, the variation of ocean conductivity is negligible but 

at frequencies with > d, the more conductive ocean increases the strength of Ey and Bx 

field. 

The average depth of Atlantic, Pacific and Indian Ocean is respectively 3926 m, 

4282 m and 3963 m. Moreover, from place to place the oceanic depths are quite diverse 

and therefore the significance of deepening of the ocean is studied (Fig 4). For a fixed 

observation depth in ocean, the gradual increase in the strength of Ey and decrease in the 

strength of Bx is the consequence of deepening of the ocean. The component Ey and Bx 

show strongest and weakest strength respectively for the deepest ocean and vice-versa. 

For frequencies for which the skin depth is smaller than the ocean depth (i.e. < d), the 

further deepening of the ocean (greater than skin depth) is ineffective and therefore the 

field value may saturate with further deepening. 

Another important parameter is the ocean wave velocity. The study suggests (Fig 

5) that any bias in velocity value may cause same bias in field strength. The change in 

velocity does not modify the pattern with depth, but causes a static shift in the field. 

Expression for layered Green’s function has allowed us to study the EM field 

variation for different layers with in the earth. The layered model involves both resistive 

and conductive layers. Clearly, electric field Ey does not see the layered boundaries (Fig 

6) although the magnetic field clearly sees it by offering a change in the slope of Bx at the 

boundaries. 


We thank KMS Technologies - KJT Enterprises for sponsoring the work. 

References 

1. Chave, A.D., and C.S. Cox, Controlled electromagnetic sources for measuring 

electrical conductivity beneath the oceans, 1, forward problem and model study, J. 

Geophys. Res., 87, 5327-5338, 1983. 

2. Chave, A.D., and D.S. Luther, Low-frequency, motionally induced electromagnetic 

fields in the ocean, 1, theory, J. Geophys. Res., 95, 7185-7200, 1990. 



58

3. Crews, A., and J . Futterman, Geomagnetic micropulsation due to the motion of ocean 

waves, J. Geophys. Res., 67, 299-306, 1962. 

4. Faraday, M., Bakerian Lecture-Experimental researches in electricity, Phil. Trans. 

Roy. Soc. London, Part 1, 163-177, 1832. 

5. Longuet-Higgins, M.S., E. Stern, H. Stommel, The electrical field induced by ocean 

currents and waves with application to the method of towed electrodes, Pap. Phys. 

Oceanog. Meteorol., 13(1),1-37, 1954. 

6. Podney, W., Electromagnetic fields generated by ocean waves, J. Geophys. Res., 80, 

2977-2990, 1975. 

7. Sanford, T.B., Motionally induced electric and magnetic fields in the sea, J. Geophys. 

Res., 76, 3476-3492, 1971. 

8. Young, F.B., H. Gerrard and W. Jevons, On electrical disturbances due to tides and 

waves, Phil. Mag. Ser. 6, 40,149-159. 



59

Three-dimensional finite element simulation of 

magnetotelluric fields incorporating digital elevation models 

S. Kütter, A. Franke-Börner, R.-U. Börner, K. Spitzer 

Institut für Geophysik, TU Bergakademie Freiberg, Gustav-Zeuner-Str. 12, 09599 Freiberg 


Pronounced topography may have an important impact on the magnetotelluric (MT) response and its 

neglect may lead to severe misinterpretations. Common simulation techniques based on rectangular 

grids are generally not well suited to deal with arbitrary geometry. We therefore use vector finite 

element (FE) schemes formulated on unstructured grids to cope with realistic topography and/or 

bathymetry. As an example, we have chosen the volcanic island of Stromboli which is located in the 

Mediterranean Sea off the west coast of Italy. Stromboli is an extreme electric environment with very 

conductive sea water surrounding the steep topography of the resistive volcanic edifice. Moreover, the 

varying bathymetry and the topography of the other islands of the Liparian archipelago cause distinct 

effects on the magnetotelluric response. Due to the large conductivity contrast and these extraordinary 

features it can be expected that the magnetotelluric apparent resistivities as well as the phases show a 

very complex behaviour. The objective of this work is to incorporate digital elevation models of this area 

into our numerical MT simulations allowing for a realistic look at the electromagnetic (EM) induction 

phenomena in such a complicated environment. On top of its challenge for numerical simulation 

methods this volcano has always fascinated geoscientists (Fig. 1) and future interdisciplinary studies 

aim at investigating the inner structure and the processes that lead to the continuous mild eruptions 

recorded over the last 2 000 years (the so called ’Strombolian activity’). 

Figure 1: Map of the Aeolian Islands (left, Wikipedia (2010)) and Stromboli (right, SwissEduc (2010)) 

2 Physical and numerical basics 

Based on Maxwell’s equations and assuming a harmonic time dependency e iωt of the incoming plane 

wave, the equation of induction in terms of the vector potential A reads as 

∇×μ −1 (∇×A)+(iωσ − ω 2 ε)A = 0, (1) 

where μ, σ, ε, ω and i are the magnetic permeability, the electric conductivity, the permittivity, the 

angular frequency and the imaginary unit, respectively. The magnetic field H and the electric field E 

are obtained by 

H = μ −1 (∇×A) and E = −iωA −∇V . (2) 

The scalar potential V was eliminated from eq. (1) by the gauge condition ψ = −iV/ω and substituting 

A for A −∇ψ which leaves H and E unchanged. 



60

To calculate A in a bounded domain Ω ⊂ R 3 , electric and magnetic insulation are required for all outer 

boundaries parallel (Γ ||) and perpendicular (Γ⊥) to the current flow, respectively: 

n × H = 0 on Γ ||, 

n × A = 0 on Γ⊥. 

Depending on whether the condition of electric insulation is applied to the boundaries parallel to the 

x- ory-direction, xy- oryx-polarisation data are obtained, respectively. At the top (Γtop) and bottom 

boundaries (Γbottom) we impose boundary values in terms of the magnetic field induced in a horizontally 

layered half-space (Wait (1953)): 

H⊥ =1Am −1 

on Γtop, 

H⊥ = Hj(z), j = x, y on Γbottom. 

For the construction of the full 3-D MT impedance tensor, both xy- andyx-polarization data are 

required. Arranging the x- andy-components of the electric and magnetic fields obtained for xy- and 

yx-polarization such that 

 

Ex(xy) Ex(yx) 

E = 

(5) 

H = 

Ey(xy) Ey(yx) 

Hx(xy) Hx(yx) 

Hy(xy) Hy(yx) 

 

, (6) 

the impedance tensor Z can the be obtained by Z = EH −1 . The off-diagonal elements of the impedance 

tensor are therefore 

Zxy = Ex(yx)Hx(xy) − Ex(xy)Hx(yx) 

Hx(xy)Hy(yx) − Hx(yx)Hy(xy) 

(3) 

(4) 

, Zyx = Ey(xy)Hy(yx) − Ey(yx)Hy(xy) 

. (7) 

Hx(xy)Hy(yx) − Hx(yx)Hy(xy) 

For any period T =2π/ω, the apparent resistivity ρa and phase φ can then be calculated by 

ρxy = 1 

ωμ |Zxy| 2 , ρyx = 1 2 

|Zyx| 

ωμ 

and φxy = arg(Zxy), φyx = arg(Zyx). (8) 

Inthefollowing,weusethetermsZxy mode or Zyx mode to distinguish xy- andyx-polarization 

from quantities derived by a combination of both (Nam et al. (2007)). An important property of 

time-harmonic EM field is the skin depth δ ≈ 503 ρ/f, whereδ, the resistivity ρ and the frequency 

f are given in [m], [Ω m] and [Hz], respectively. is determined, whereas δ, the resistivity ρ and the 

frequency f are given in [m], [Ω m] and [Hz], respectively. 

To solve the boundary value problem (1) - (4), the finite element method (FEM) is applied on unstructured 

tetrahedral meshes (see Börner (2010); Schwarzbach (2009)). Tetrahedral meshes are well 

suited for the spatial discretization of arbitrary 3-D geometries which occur when digital elevation 

models have to be incorporated into numerical simulations. In the 3-D simulations presented here, 

curl-conforming Nédélec elements with second-order basis functions are employed. In all experiments the 

FE discretization has been carried out using the Electromagnetics Module of the COMSOL Multiphysics 

package. 

3 Description of the digital elevation model 

The area used in the simulations extends from 38.4° to 39.2° N and 14.7° to 15.7° E. At 39° N, the 

distance between two degrees of latitude is 110.95 km, whereas the distance between two degrees of 

longitude is 86.51 km. Hence, the model area has a length of 86.51 km in the east-west (x) and 88.76 km 

in the north-south (y) direction. 

We have used two sets of digital terrain data. The ETOPO1 data set is a 1 arc-minute model and 

provides elevation values for both land and sea. It is available online at the National Geophysical Data 

Center (http://www.ngdc.noaa.gov) and gives a good approximation for the regional bathymetry. Since, 



61

however, its spatial data density is not sufficient to describe Stromboli’s topography, a second data set 

has been used. These data are available from the Shuttle Radar Topography Mission (SRTM), a project 

to obtain high-resolution topographic data (http://srtm.csi.cgiar.org/). The horizontal resolution of 

the two data sets are listed in the following table. The digital elevation model for the area considered 

here has been obtained by blending both ETOPO1 and SRTM data sets. 

resolution x-direction resolution y-direction 

SRTM 0.0721 km 0.0925 km 

ETOPO1 1.4419 km 1.8491 km 

Interpolating the bathymetry data and fitting the two data sets along the coastlines leads to a digital 

elevation model as depicted in Fig. 2. 

φ [ o ] 

39.1 

39 

38.9 

38.8 

38.7 

38.6 

38.5 

38.4 

14.8 14.9 15 15.1 15.2 

λ [ 

15.3 15.4 15.5 15.6 15.7 

o ] 

Figure 2: Data points obtained from ETOPO1 (coarse grid) and SRTM (fine grid resembling the islands) for 

bathymetry and topography (left), digital elevation model obtained by smooth interpolation onto the 

SRTM grid (right). Stromboli island is located at the centre of both images. 

4 Numerical studies 

The geometry of the volcanic island of Stromboli is incorporated into the simulation models in three 

different levels of increasing complexity. This approach enables us to better differentiate which part of 

the model has an influence on the electromagnetic fields and how distinct this influence is. The first 

model uses a frustum as the volcanic edifice embedded in a layered background consisting of an air 

layer, a sea layer and a substratum. In the second model the frustum is replaced with the topography 

of Stromboli. The edges of this topographic surface have been adjusted to the sea-floor. The third, 

most complex model uses both topography and bathymetry data. 

For the numerical computations three different computer architectures have been used: 

computer name architecture RAM 

klio 4Intel(R)Xeon(R)@3GHz 16 GB 

erato 4 Quad-Core AMD Opteron @ 2.5 GHz 128 GB 

RM 56 nodes based on Intel Xeon (E5450 @ 3 GHz) 16 GB per 8-core blade 

For each of the three models, apparent resistivities ρa and phases φ were calculated along profiles 

running along the sea-floor and over the slopes of the volcano for a period of T =10 3 s. Furthermore, 

sounding curves were determined for selected sites on the sea-floor and on the volcano to demonstrate 

the dependency of ρa and φ on frequency. 

4.1 Frustum model 

The geometry and appropriate conductivities of the frustum model as well as a map of the locations 

of the sounding sites are depicted in Fig. 3. Since there are large conductivity contrasts between the 



62

frustum, the sea and the air layer, a non-trivial behaviour of the electromagnetic fields is to be expected. 

The electric currents are mainly induced in the conductive sea layer and are compressed above the 

slopes. Moreover, the currents tend to concentrate below the sea surface due to the skin effect. 

Due to horizontal conductivity contrasts, electric charges accumulate at the interfaces between the 

volcano and the sea layer. Their surface density is proportional to −E ·∇σ. Therefore, an additional 

electric field is generated which leads to an increase of the total electric field towards the top of the 

volcano (around x = ±0.5 km in the profile, Fig. 4) and to a decrease towards the sea-floor (around 

x = ±5.6 km in the profile). This static shift effect results in discontinuities of the apparent resistivity 

at the base points of the frustum on the sea-floor, at the coastline points and at the top of the volcano. 

Unlike the apparent resistivity, the phase has a more continuous behaviour and appears to be a 

rather robust parameter even for pronounced topography. 40 km away from the center of the volcano 

(x, y = ± 40 km), both phase and apparent resistivity reach their values expected for the half-space 

(45°, 100 Ω m). 

-20 

[km] 0 

2 

air: 10 −14 Sm −1 

volcano: 0.02 Sm −1 

half-space: 0.01 Sm −1 

sea: 5 Sm −1 

32 

-40 -5.6 0 

[km] 

5.6 40 

 

 

 

 

Figure 3: Vertical cross-section through the frustum model (left) and plan view of the model domain (right) 

showing the locations of the sounding curves (T, N40, E40). 

To verify our results, two independent numerical codes have been used to provide reference datasets 

for the frustum model. More precisely, data have been obtained using a finite element package (FEP) 

by Schwarzbach (2009), and a finite difference package (FD) by Mackie et al. (1994). 

A comparison of the apparent resistivities with those obtained by FEP reveals that they slightly differ 

near the boundaries of the model and at the lower part of the volcano slopes (Fig. 4, left), where ρa is 

lower for FEP. Moreover, the peaks at the base of the frustum, at the coastline points and at the edges 

of the plateau are even more pronounced for FEP. Here, we assume an influence of the different spatial 

discretization of the model. The curves of the phase are nearly congruent for both FE codes. 

Apparent resistivities and phases obtained by FD (Fig. 4, right) show similar features in general. 

However, there are significant differences along the slopes of the volcano. We attribute this to the 

fact that in the FD code considered here electric field components are located perpendicular to cell 

faces of a rectangular cartesian grid. Problems in interpolating the discrete electric field components at 

the desired positions along the volcano slopes are thus to be expected. Finite element techniques on 

unstructured grids clearly show their superiority in this respect. 



63

[km] 

ρ a [Ω m] 

φ [ o ] 

−2 

0 

2 

4 

10 2 

10 1 

10 0 

50 

COMSOL 

FEP 

0 

−40 −30 −20 −10 0 

x [km] 

10 20 30 40 

Figure 4: Comparison of the profile curves of the frustum model, T =10 3 s. 

ρ a [Ω m] 

φ [ o ] 

10 2 

10 1 

10 0 

50 

COMSOL 

FD 

0 

−40 −30 −20 −10 0 

[km] 

10 20 30 40 

Fig. 5 depicts three sounding curves for the sites on top (point T in Fig. 3) and 40 km away from the 

volcano (E40, N40 in Fig. 3). 

Sounding curves for the volcano site T are displayed for periods between 10 −3 and 10 3 s (Fig. 5, left). 

For short periods, where the skin depth is small (δ ≈ 355 m for 50 Ω m and 10 −2 s), the resistivity of the 

volcano is reproduced and the phase reaches values around 45°. For periods between 10 −1 sand10 2 s, 

the influence of the conductive sea layer is dominant and therefore, the apparent resistivity decreases 

whereas the phase increases. For longer periods the resistive half-space dominates the curves (δ ≈ 16 km 

for 100 Ω m and 10 3 s). The sounding curves for the two sites on the sea-floor are displayed for a subset 

of the full period range (between 10 1 and 10 3 s) because of the strong attenuation within the very 

conductive sea water (Fig. 5). High frequencies generally require a much finer spatial discretization in 

regions where the skin depth is small. However, the computational experiments have been carried out 

on a mesh well suited for mid to low frequencies. Results for high frequencies were not satisfactory for 

the coarse meshes used here, and thus have not been included in the comparison. 

The long period ends of the sounding curves nicely approach the values of the lower half-space, i.e. 

100 Ωm for ρa and about 45° for φ. For short periods there are deviations from these values, which are 

larger for the points on the profiles oriented perpendicular to the component of the driving electric 

field, i.e. for point E40 at y =40kmforρxy and the point at x =40kmforρyx (cross markers in Fig. 5, 

cf. Fig. 3, right). As mentioned above, these deviations are due to the insufficient spatial discretization 

for short periods in regions of strong attenuation. 

ρ a [Ω m] 

φ [ o ] 

10 2 

10 1 

10 0 

100 

50 

10 −3 

0 

10 −2 

10 −1 

10 0 

T [s] 

10 1 

xy−polarisation 

yx−polarisarion 

10 2 

10 3 

ρ a [Ω m] 

10 3 

10 2 

10 1 

10 0 

100 

50 

10 1 

0 

10 2 

T [s] 

xy−pol. (x) 

xy−pol. (y) 

yx−pol. (x) 

yx−pol. (y) 

Figure 5: Sounding curves for the volcano site T (left) and the sea-floor sites E40 and N40 (right) for the 

frustum model. Here, xy-pol. and yx-pol. refer to ρxy and ρyx, resp. 

The following table summarizes important computational parameters for the three different codes, 

such as polynomial degree of the basis functions (BFD) for the FE method and degrees of freedom 

(DOF). The overall CPU time required to obtain the result for one frequency was in the order of two 

minutes. The total time required to compute all field components for one polarization sums up to 



64 

φ [ o ] 

10 3

about two hours for all 49 frequencies for the FE codes and 30 minutes for the FD code. Note that the 

3-D impedance requires the calculation of both polarizations (see eq. (7)). 

computer CPUs BFD elements DOFs time [min] 

COMSOL Multiphysics 

xy-pol. klio 4 quadratic 82 661 523 580 119,56 

FEP 

xy-pol. erato 8 quadratic 57 666 434 456 119,07 

FD code 

FD code 131 x 131 x 154 grid cells + 15 air layers ≈ 30 

4.2 Stromboli-Topography model 

In the second level of complexity, a realistic topography of Stromboli is incorporated. Since this 

topography is smoothly adjusted to the flat sea-floor, the edifice is larger in this model than in reality. 

Furthermore, the conductivity of the volcano has been reduced to 0.01 Sm −1 . 

Figs 6 and 7 illustrate the model with the positions of the profiles and the locations for which sounding 

curves have been calculated. Sounding curves are shown for sites a, N and E only. 

Figure 6: Flat sea-floor model including the real topography of Stromboli island. Red and blue lines indicate 

the x- and y-profiles, respectively. 

Figure 7: Locations for which sounding curves are computed are denoted by a, b, c, d on the island (left) and 

N,E,S,W on the sea-floor (right). 

Fig. 8 displays the apparent resistivities ρxy and phase Φxy for T =10 3 s along two profiles aligned with 

the x-axis (x-profile) and the y-axis (y-profile). The apparent resitivity for the x-profile is associated 



65

with the xy-impedance tensor elements (Zxy mode) while the apparent resistivity for the y-profile 

is derived from the yx-elements (Zyx mode). The curves for both Zxy and Zyx modes show similar 

features. This can be explained by the similar topography along the two different profiles. Nevertheless, 

the extent of the volcano’s edifice in y-direction is larger than in x-direction. Hence, the corresponding 

minima and maxima of the curves are shifted relative to each other. 

Due to the smoother transition of the topography from the sea-floor to the volcano slopes the peaks at 

the base points of the edifice are not as pronounced as for the frustum model. Since there is no volcano 

plateau in the x-profile, there is just one minimum at x ≈ 44 km for ρxy. 

As for the frustum model, the sounding curves for the volcano (e.g. for site a in Fig. 9, left) reflect 

the layering of the earth with regard to the electrical conductivity whereas long periods correspond 

to large skin depths. Since the same conductivity is assigned to the volcano and the half-space the 

sounding curves reach values around 100 Ω m for short periods. 

Due to the asymmetry of the model, offsets occur between the curves derived from Zxy and Zyx that 

are higher for ρa than for φ. Hence, it can be assumed that the phase is less affected by these two 

aspects. 

The sounding curves for the sea-floor are displayed in Fig. 9 (right). Since the edifice is larger than the 

one represented by the frustum the long period apparent resitvities deviate more significantly from the 

undisturbed half-space values. 

z [km] 

ρ a [Ω m] 

φ [°] 

−5 

0 

5 

10 4 

10 2 

10 0 

40 

20 

xy−pol. x profile 

yx−pol. y profile 

0 10 20 30 40 50 60 70 80 

[km] 

Figure 8: Topography (top), apparent resistivity (center), phase (bottom), derived from Zxy and Zyx (xy- and 

yx-pol., resp.) along the x- andthey-profile for T =10 3 s. 

The differences in the short period range may again be attributed to the insufficient spatial discretization. 

ρ a [Ω m] 

φ [°] 

10 3 

10 2 

10 1 

10 0 

10 −1 

100 

50 

10 −3 

0 

10 −2 

10 −1 

10 0 

T [s] 

10 1 

10 2 

xy−pol. a 

yx−pol. a 

10 3 

ρ a [Ω m] 

φ [°] 

10 3 

10 2 

10 1 

80 

60 

40 

10 1 

20 

10 2 

T [s] 

xy−pol. N 

yx−pol. N 

xy−pol. E 

yx−pol. E 

Figure 9: Sounding curves for the island site a (left) and for the sea-floor sites N and E (right). xy-pol. and 

yx-pol. refer to Zxy and Zyx, resp. 

The incorporation of the detailed Strombolian topography leads to a massively increasing number of 

mesh points. In order to keep computational costs low the meshes for computing the full sounding 



66 

10 3

curves were coarsened. 

Computer CPUs BFD No. of elements DOFs Time [min] 

profile curves 

xy-pol. erato 8 quadratic 443 563 2 823 488 114.78 

sounding curves 

xy-pol. erato 8 quadratic 164 662 1 048 116 ≈ 721 

4.3 Bathymetry-Topography model 

In the third level of complexity, the topography of the island is incorporated as well as the regional 

bathymetry including the other Liparian islands. This allows to analyse the effect on the electromagnetic 

fields not only due to the volcano itself but also due to the variable thickness of the sea layer. 

Figs 10 and 11 illustrate the model and the locations of the profiles and points for which sounding 

curves have been calculated. As an example, apparent resistivities and phases for a period of 1000 s 

are shown for the xN- and xS-profiles as well as the full sounding curves for points a, c, N and S. 

Figure 10: Model including the regional bathymetry and the topography of Stromboli and the Liparian Islands. 

Figure 11: Left: Elevation map inferred from digital terrain data showing the locations of seafloor sounding 

points N, E, S, W and the profile lines xN, xS in the EW-direction and yE, yW in the NS-direction. 

Right: Coast line of Stromboli and locations of sounding points a, b, c, d. 

The xN and xS profiles running East-West in parallel (Fig. 12) are close to each other. Hence, the 

features of the respective apparent resistivity and phase curves are similar. As for the previous models, 

peaks at the coastline and at the top of the volcano can be observed. However, serious perturbations 

are provoked by the regional bathymetry. Induced currents are vertically compressed in the shallow 

parts of the ocean yielding higher apparent resistivities. Vice versa, apparent resistivites are decreased 

in deep water areas. The soundings at site c (Fig. 13, right) again show the influence of the volcano, 



67

z [km] 

ρ a [Ω m] 

φ [°] 

−5 

0 

5 

10 4 

10 2 

10 0 

200 

100 

0 

xy−pol. xN profile 

xy−pol. xS profile 

0 20 40 

x [km] 

60 80 

Figure 12: Topography (top), apparent resistivity (center) and phase (bottom) for T = 10 3 satprofilesxS and 

xS. xy-pol. and yx-pol. refer to Zxy and Zyx, resp. 

ρ a [Ω m] 

φ [°] 

10 3 

10 2 

10 1 

10 0 

400 

200 

10 −3 

0 

10 −2 

10 −1 

10 0 

T [s] 

10 1 

10 2 

xy−pol. a 

yx−pol. a 

10 3 

Figure 13: Sounding curves for the island sites a (left) and c (right). xy-pol. and yx-pol. refer to Zxy and Zyx, 

resp. 

the sea layer and the half-space for the appropriate period ranges. However, at site a, which is located 

directly at the coastline, the sea layer affects the curves already for shorter periods, especially for the 

Zyx mode. Still, for periods longer than T =10 −1 s the shapes of the curves are similar to those at 

point c (although shifted to higher ρa-values). 

All curves derived from Zxy and Zyx show an offset which can be attributed to the asymmetric elevation 

data used in the MT simulations. 

For the two sea-floor sites N and S the topography effect varies for the two cases considered (Fig. 14). 

Site N (Fig. 14, left) is located at greatest distance from the islands. Therefore, the curves are similar to 

those obtained using the simpler models and for longer periods they are almost assume the corresponding 

half-space values. 

The sounding curves at site S (Fig. 14, right) seem to be affected by two different facts. For ρxy the 

graben-like structure in this area (cf. Fig. 11, left) leads to lower apparent resistivities. On the other 

hand, the more resistive islands affect the ρyx-curves. 

We note that the out-of-quadrant phases in Fig. 14 occur mainly at the high frequencies, which indicates 

that the mesh used for the numerical computations is still not fine enough to obtain results with the 

desired accuracy. 

The following table summarizes the mesh properties and CPU times associated with the bathymetrytopography 

model. 

ρ a [Ω m] 

10 3 

10 2 

10 1 

10 0 

100 

50 

10 −3 

0 

10 −2 

10 −1 

10 0 

T [s] 



68 

φ [°] 

10 1 

10 2 

xy−pol. c 

yx−pol. c 

10 3

ρ a [Ω m] 

φ [°] 

10 4 

10 3 

10 2 

10 1 

400 

200 

0 

10 1 

−200 

10 2 

T [s] 

xy−pol. N 

yx−pol. N 

10 3 

Figure 14: Sounding curves for the sea-floor sites N (left) and S (right). xy-pol. and yx-pol. refer to Zxy and 

Zyx, resp. 

ρ a [Ω m] 

φ [°] 

10 4 

10 3 

10 2 

10 1 

400 

200 

10 1 

0 

10 2 

T [s] 

xy−pol. S 

yx−pol. S 

Computer CPUs BFD No. of elements DOFs Time [min] 

profile curves 

xy-pol. erato 16 quadratic 546 759 3 479 830 44.41 

sounding curves 

xy-pol. erato 16 quadratic 312 721 1 987 514 ≈ 1103 

5 Conclusions 

In this work, distortion effects on MT data caused by topography and bathymetry are examined for 

the area around Stromboli. The geometry of Stromboli has been incorporated into FE simulations 

applying three different levels of increasing complexity. 

In the first model, a frustum representing the volcano has been embedded in a layered background. 

This model yields a non-trivial apparent resistivity profile curve which is mainly dominated by peaks at 

the base points of the frustum, at the coastline points and at the edges of the volcano plateau. These 

are caused by static shift effects and the high conductivity contrast between the volcano and the sea 

layer. The results of the frustum model have been verified by a finite element code by Schwarzbach 

(2009) and a finite difference code by Mackie et al. (1994). 

For the second model of Stromboli digital elevation data of the island have been included in the model 

geometry. Compared to the frustum model, the apparent resistivity and phase curves along the profiles 

and the sounding curves for the volcano show similar features. 

Finally, digital bathymetry data have been added to the third, most complex Stromboli model to 

take into account realistic topography and bathymetry features of the region. The apparent resistivity 

still shows the characteristic peaks at the coastline points for most of the profiles. The effects of 

the bathymetry and topography of the surrounding islands are superposed, which results in very 

complicated profile and sounding curves. 

These results clearly point out that topography and bathymetry can heavily distort MT data and thus 

need to be considered for an accurate numerical interpretation of MT measurements. 

Finally, we emphasize that FE methods on unstructured grids provide a sophisticated tool for treating 

problems associated with complex geometry. 

Acknowledgements 

We would like to thank Randall L. Mackie for providing the results for the FD simulations. Furthermore, 

we are thankful to Christoph Schwarzbach for providing his FE code and for his useful help. We are 

grateful to the German Research Foundation DFG for funding our numerical research work (Spi 356-9). 



69 

10 3

References 

Börner, R.-U. (2010). Numerical Modelling in Geo-Electromagnetics: Advances and Challenges. Surveys in Geophysics 

31(2): 225–245. 

Mackie, R. L., J. T. Smith, and T. R. Madden (1994). Three-dimensional electromagnetic modeling using finite difference 

equations: The magnetotelluric example. Radio Science 29(4): 923–935. 

Nam, M. J., H. J. Kim, Y. Song, T. J. Lee, J.-S. Son, and J. H. Suh (2007). 3D magnetotelluric modelling including 

surface topography. Geophysical Prospecting (55): 277–287. 

Schwarzbach, C. (2009). Stability of Finite Element Solutions to Maxwell’s Equations in Frequency Domain. PhDthesis. 

TU Bergakademie Freiberg. 

SwissEduc (2010). SwissEduc: Stromboli Online - Die Insel. url: http://www.swisseduc.ch/stromboli/volcano/geogr/ 

aerial-de.html. 

Wait, J. R. (1953). Propagation of radio waves over a stratified ground. Geophysics 18(2): 416–422. 

Wikipedia (2010). Liparische Inseln. url: http://de.wikipedia.org/wiki/Liparische_Inseln. 



70

Establishing Controlled Source MT at GFZ 

M. Becken 1,2 , R. Streich 1,2 , O. Ritter 2 

1 Potsdam University, Department of Geosciences, Karl-Liebknecht-Strasse 24, 14476 Potsdam, Germany 

2 Helmholtz Centre Potsdam GFZ German Research Centre for Geosciences, Telegrafenberg, 14473 Potsdam, Germany 

Summary 

The multidisciplinary GeoEn project (the Brandenburg pilot project in the BMBF program 

„Spitzenforschung und Innovation in den Neuen Ländern“) integrates research in the fields of 

geothermal energy, carbon dioxide capture, transport and storage (CCTS) as well as the exploration of 

unconventional gas reserves (shale gas). The electrical conductivity is one key parameter to characterize 

reservoirs and to monitor changes due to circulation or injection of fluids at reservoir depth. Bulk 

electrical conductivity is highly sensitive to fluids within interconnected pores, and therefore EM 

techniques are powerful tools for exploring and monitoring geothermal reservoirs, CO2 storage sites and 

shale gas reservoirs. In the framework of the GeoEn project, we establish Controlled Source MT (CSMT) 

at GFZ Potsdam. We aim at combining active and passive MT to image the electrical conductivity 

structure within the Earth, ultimately in 3D. 

For CSMT, we intend to use grounded electrodes to inject a frequency-dependent current into the Earth 

and measure the induced electric and magnetic fields at near-field to far-field distances. We will use 

novel transmitter systems from Metronix (Braunschweig) which are presently under development. 

Standard MT receivers will be utilized to measure the induced electric and magnetic fields. In the scope 

of the project, we will (i) assemble the transmitter system and the source dipole, (ii) optimize and design 

CSMT field procedures for geothermal exploration, carbon dioxide reservoir characterization and shale 

gas exploration (Streich et al., 2010a), (iii) develop and implement time-series processing, (iv) develop 

and implement 1D modeling (Streich and Becken, 2009) and inversion software and 3D modeling codes 

(Streich, 2009; Streich et al., 2010b). 

In this contribution, we describe a test of long steel electrodes as the current electrodes of the source 

dipole, and we examine the resolution power of CSMT using 1D inversion of synthetic data. 

Current electrodes of CSMT source dipole 

Low grounding resistances of the current electrodes are crucial for injecting strong currents into the 

subsurface. The Metronix 22 kVA transmitter generates currents of max. 40 A (560 V), which can, 

however, only be achieved if the total resistance of the dipole (1-km long cable and grounding 

electrodes) is less than 14 . We use a thick cable that has a resistance of 2 /km. Accordingly, to 

achieve maximum currents, the electrode grounding resistances should be less than 12 . At high 

frequencies, the maximum current will be further limited by the inductance of the cable. 

The grounding resistance depends primarily on the surface of the electrode that is in contact with the 

ground, and the surrounding resistivity within the Earth. For a homogenous earth, the grounding 

resistance R of a steel rod is 

R 

4L 

ln 

2 L 

a 

1 

, (1) 



71

Figure 1: Electrode test. We measured the ground resistance of a steel electrode (diameter 32 mm) vs. depth of 

the rod at two different locations, which may represent typical conditions in northern Germany. Ground resistance 

measurements were taken against two reference electrodes at ~30 m distance to the left and right. DC Wenner 

spreads were measured at the same locations (left panels). The panels to the right show the measured resistances 

(red and blue lines), compared to theoretical predictions (dashed black lines) based on the resistivity-depth 

profiles at the electrode locations shown in the rightmost plots. The sudden drop in resistance at

greater depths, we penetrate conductive glacial till at test location 1 (upper panel in Figure 1) and a 

groundwater layer at test location 2 (lower panel). The measured grounding resistance values are 

roughly consistent with predictions (dashed lines) based on the geometry and the subsurface resistivity 

distribution. For resistance predictions, we approximated the resistance R from a parallel circuit of steel 

rod segments of length L embedded into a medium with piecewise constant resistivity i . 

Approximate i values were extracted from the 2D DC resistivity-depth sections. Let the individual rod 

pieces have resistance 

R 

i 

i 4 L 

ln 

2 L a 

then the resistance of the entire rod to a depth L is given by 

1 

R 

1 

i i R 

1 

, (3) 

. (4) 

Equations 3 and 4 were used to estimate grounding resistances from the 2D resistivity models (Figure 1). 

This test shows that long steel rods may be suitable electrodes for CSMT source dipoles. At one test 

location with favorable geology (glacial till), we achieved a ground resistance of ~10 with electrodes 

penetrating 7.5 m deep; the second test location, a sandy soil with a freshwater layer at ~3 m depth, 

may require deeper electrodes. Our predictions suggest that the ground resistance of the steel rod may 

drop at this location to values of ~10 at ~15 m depth. The simple model used to predict grounding 

resistance has proven to be useful for practical purposes. Before installing electrodes, it may be 

advisable to investigate potential locations with DC resistivity soundings in order to predict expectable 

resistances and required electrode lengths. 

1D CSMT Inversion 

Vertical currents, galvanically injected into the subsurface with a grounded dipole source, exhibit 

sensitivity to buried resistors at depth. This makes the CSMT technique suitable for imaging resistive 

layers, whereas both passive MT and CSMT are sensitive to conductive layers. The effect of anomalously 

resistive subsurface structures on surface CSMT data is typically smaller in land applications than in 

deep-water marine applications. Land applications of frequency-domain CSMT suffer from energy 

travelling through the air even more than marine applications, which obscures the response from 

deeper targets. Nevertheless, forward modeling studies suggest that in many cases, the e.m. response 

of thin resistive layers is above noise level (see Streich and Becken, this issue). 

A practical question is to what extent the resistivity models giving rise to these anomalies can be 

recovered from measured data. We ran 1D Occam-type inversions to investigate the resolution power of 

CSMT data. To infer the resistivity structure from 1D inversion, we can exploit the spatial decay of CSMT 

fields with increasing distance to the source, and the frequency dependency of the fields. In land-based 

applications, we will typically have only few source locations combined with a relatively large number of 

receivers (say, 100), and potentially long transmitting times that allow us to cover a broad frequency 

range. In contrast, marine applications use a source towed continuously over a number of receivers, 

effectively yielding many source point locations, but only short transmitting times and thus a narrow 

frequency band for a given source location. Hence, land applications will primarily utilize the frequency 



73

Figure 2: 1D Occam inversion of synthetic CSMT data. The data are the real and imaginary parts of the inline 

electric field, contaminated with white noise with 1% of the signal amplitude. In addition, white noise with a 

standard deviation of 10 -9 V/m was added. a) Inversion of the spatial decay of the field for a single frequency (1 

Hz), using an unconstrained Occam inversion and using an Occam variant where the deviation from an a priori 

model is penalized outside of the depth of interest. b) Inversion of the frequency spectrum recorded at 5 km 

distance from the transmitter. 

Figure 3: Comparison of single and joint 1D inversion models for passive MT and CSMT data. In (a), the left panel 

shows passive MT data (apparent resistivity and phase) for the true model and MT inversion result displayed in the 

right panel. In (b), CSMT data (real and imaginary part of the inline electric field) are displayed for the true 

resistivity model and CSMT inversion result. (c) shows the resistivity model resulting from joint MT and CSMT 

inversion. In this example, the MT data add information only at greater depths, where the sensitivity of CSMT 

sounding is low. In practice, we anticipate that MT data will help construct a (2D/3D) regional background model, 

and CSMT data will help refine the model at reservoir scale (1D/3D). 

dependency of the fields, whereas marine applications will primarily exploit spatial variations of the 

fields. 

We have implemented a 1D CSMT inversion based on Weidelt’s formulation of the forward problem 

(Weidelt, 2007), and analytically derived expressions for the Jacobian matrix required in the inversion. 

Finite source dipoles (Streich and Becken, this issue) have been incorporated into the inversion; 

however, in the present form of the inversion scheme, the source and receivers are placed at the 

surface. Here, we only consider horizontal electric point dipole sources. The inversion is similar to 



74

Occam inversion (Constable et al., 1987); however, Occam’s second phase (i.e., the determination of the 

regularization parameter that yields optimal trade-off between data residuals and model norm) has not 

been implemented. Instead, we fix the regularization parameter for one entire inversion run. 

Using this inversion scheme, we found that both the inversion of multi-offset data at a single frequency 

and multi-frequency data at a single receiver location have the power to yield comparable inversion 

models, if the frequency range and the distance to the transmitter are appropriate for imaging the 

target depth (Figure 2). The left panels in Figure 2a and b depict the inline electric field as a function of 

distance from the transmitter for the frequency f = 1 Hz and as a function of frequency at 5 km distance, 

respectively, for a model containing a resistive layer embedded into a homogeneous half-space. 

Random noise of 1% of the field amplitudes and a noise floor of 10 -9 V/m were added to the data prior to 

inversion. The central panel in Figure 2a shows the inversion model obtained from smooth inversion 

using a standard Laplacian penalty on the logarithmic model resistivities (red line). A similar result (not 

shown) was obtained from inversion of the multi-frequency electric field data shown in Figure 2b. In 

both cases, the recovered 1D model contains a resistive zone that is smeared over a wide depth range, 

because regularization penalizes thin model layers. 

For monitoring applications (e.g., CO2 injection), the depth of interest is known. A focused inversion that 

searches for deviations from an a priori model primarily at reservoir depth may help improve the model. 

We have therefore incorporated a term into the Occam inversion that allows us to weight the penalty 

depending on the difference of every inversion model parameter to an a priori model (Key, 2009). The 

right panels in Figure 2a and b show the result of this variant of regularized inversion. The hashed areas 

correspond to depth levels where the inversion model is constrained to deviate minimally from the a 

priori model (which is the true model in this case), whereas the rest of the model was permitted to vary 

freely (in the sense of a Laplacian regularization). This approach clearly helps focusing the resistive 

anomaly at the true depth and may thus be adequate for a focused model search. 

The penetration depth of CSMT data is limited by the lowest frequencies used and the greatest offsets 

providing reasonable signal quality. Combing CSMT with passive MT may prove helpful to expand the 

model scale. Furthermore, both techniques exhibit different sensitivities to resistive and conductive 

structures (and to deviations from 1D media) and thus provide complementary information. We have 

therefore implemented a joint 1D inversion for both data types. In Figure 3, we compare the 1D 

inversion models for a multi-layered structure obtained from MT data and CSMT data alone and from 

joint CSMT and MT inversion. Here, the CSMT data are the frequency-dependent inline electric field 

data, measured at 5 km offset from the transmitter. The individual inversion models show that (i) both 

techniques resolve shallow conductive layers, (ii) the CSMT data resolve a resistive layer at 1 km depth, 

and (iii) the MT data resolve the conductivity of the basal layer that is too deep to be sensed with CSMT. 

All of these model features are revealed by joint inversion, suggesting increased resolution capabilities 

from combined applications of both techniques. 


This work is funded by the German Federal Ministry of Education and Research (BMBF) within the 

framework of the GeoEn project. S. Costabel, TU Berlin, made the DC measurements and provided the 

2D inversion models. 



75

References: 

Constable, S. C., Parker, R. L. and Constable, C. G., 1987, Occam's inversion: A practical algorithm for 

generating smooth models from electromagnetic sounding data, Geophysics 75(3), 289-300. 

Key, K., 2009, 1D inversion of multicomponent, multifrequency marine CSEM data: Methodology and 

synthetic studies for resolving thin resistive layers, Geophysics 74(2), F9-F20. 

Streich, R., 2009, 3D finite-difference frequency-domain modeling of controlled-source electromagnetic 

data: direct solution and optimization for high accuracy, Geophysics 74(5), F95-F105. 

Streich, R., Becken, M. and Ritter, O., 2010a, Imaging of CO2 storage sites, geothermal reservoirs, and 

gas shales using controlled-source magnetotellurics: modeling studies, Chemie der Erde, submitted. 

Streich, R. and Becken, M., 2010, EM fields generated by finite-length wire sources in 1D media: 

comparison with point dipole solutions, Protokoll zum Kolloquium “Elektromagnetische Tiefenforschung”, 

Seddiner See, 28.09.-02.10.2009. 

Streich, R., Schwarzbach, C., Becken, M. and Spitzer, K., 2010b, Controlled-source electromagnetic 

modelling studies: utility of auxiliary potentials for low-frequency stabilization, EAGE 70 th Conference 

and Exhibition, Barcelona, Spain, submitted. 

Weidelt, P., 2007, Guided waves in marine CSEM: Geophysical Journal International, 171, 153–176. 



76

2D-SIP-Modellierung mit anisotropen 

Widerständen 

Johannes Kenkel a∗ , Andreas Hördt a , Andreas Kemna b 

a Institut für Geophysik und extraterrestrische Physik, TU Braunschweig 

b Fachbereich Angewandte Geophysik, Universität Bonn 

1 Einleitung 

Die Modellierung von Messdaten der spektralen induzierten Polarisation (SIP) geschieht 

üblicherweise unter der Annahme makroskopisch, also in der Größenordnung einer Zelle 

der Modellrechnung, isotroper komplexer Widerstände im Untergrund. Für diese Art der 

Modellierung von Daten der SIP wurde von A. Kemna das Finite-Elemente-Programm 

CRMod entwickelt ([1], [2]). Mit der Annahme isotroper Widerstände lassen sich viele 

Messdaten hinreichend erklären. Nguyen et al. ([3]) zeigten jedoch für den reellwertigen 

gleichstromgeoelektrischen Fall, dass, wenn der Untergrund aus vielen abwechselnd gelagerten 

Schichten besteht, die eine geringe räumliche Ausdehnung gegenüber der bei der 

Inversion benutzen Gitterzellen haben, die Annahme isotroper Leitfähigkeiten zu Fehlinterpretationen 

führen kann. Hier kann die Erweiterung auf anisotrope Widerstände 

Abhilfe schaffen, weil diese auf makroskopischer Skala, also Zellenebene, Schichtlagerungen 

beschreiben können. Das Auftreten von Anisotropieeffekten auch bei SIP wurde 

von Winchen et al. ([4]) demonstriert. Das Programm CRMod wurde zum Zweck der 

Modellierung anisotroper komplexer Widerstände erweitert. In diesem Artikel sollen anhand 

von verschiedenen modellierten Beispielen verschiedene Effekte eines Untergrund 

mit anisotropen komplexen Widerständen gezeigt werden. 

2 Methodik 

2.1 Spektrale Induzierte Polarisation (SIP) 

Die spektrale induzierte Polarisation (SIP) ist ein elektrisches Verfahren, das wie die Geoelektrik 

aus dem Messen von Potentialverläufen künstlicher elektrischer Quellen Rückschlüsse 

auf die Leitfähigkeitsverteilung im Untergrund zieht. 

∗ Adresse: Mendelssohnstraße 3, D-38106 Braunschweig, E-Mail: j.kenkel@tu-bs.de 



77

Das Aufnehmen der Messwerte geschieht in einem wiederum der Geoelektrik sehr 

ähnlichen Aufbau, jedoch werden zusätzlich Phasenbeziehungen zwischen Sende- und 

Empfangssignal aufgezeichnet. Als Quellsignal werden Wechselströme unterschiedlicher 

Frequenzen gewählt. Die Messdaten sind dann Spannungswerte und deren Phasenverschiebungen 

zum Quellsignal. Aus diesen Daten und den Positionen der Elektroden ergeben 

sich mit den Geometriefaktoren die Messwerte als scheinbare spezifische Widerstände 

(Amplituden) und deren Phasen. Diese lassen sich zur Abschätzung der Eigenschaften 

des Profils als Pseudosektion auftragen. 

Das physikalische Problem der spektralen induzierten Polarisation und der Geoelektrik 

lässt sich für den Fall anisotroper komplexer Widerstände in x-, y- und z-Richtung in 

Form der Poisson-Gleichung 

∂x(σx∂xφ)+∂y(σy∂yφ)+∂z(σz∂zφ)+Iδ(x − xs)δ(y − ys)δ(z − zs) =0 (1) 

mit dem Potential φ = φ(x, y, z), dem Strom I und der Diracschen Delta-Funktion δ 

schreiben. Die Anisotropie beschränke sich dabei auf die Diagonalelemente des Leitfähigkeitstensors 

⎛ 

σx 

σ = ⎝ 0 

0 

σy 

⎞ 

0 

0 ⎠ . (2) 

0 0 σz 

Die Stromeinspeisung findet an den Koordinaten (xs,ys,zs) statt. 

2.2 Modellierung 

Für die Modellierung wird das oben aufgeführte Problem der Potentialverteilung durch 

einen 2D-Finite-Elemente-Algorithmus gelöst (vgl. [2]). Die Ergebnisse sind Potentialverläufe 

und zugehörige Phasen an jedem Gitterpunkt. Aus diesen Informationen und 

den Messelektrodenpositionen lassen sich damit die zum Modell gehörigen synthetischen 

Messdaten - Amplituden und Phasen der scheinbaren spezifischen Widerstände - berechnen 

und in Pseudosektionen auftragen. Das hier benutzte Finite-Elemente-Programm 

CRMod ist von einer bereits bestehenden Version für die Modellierung isotroper spezifischer 

Widerstände und Phasen ([2]) um die Möglichkeit der Modellierung von Anisotropie 

erweitert worden. 

Die Poisson-Gleichung 1 wird unter der Annahme eines konstanten Leitfähigkeitstensors 

in y-Richtung durch die Fourier-Transformation in den Wellenzahlbereich mit 

∞ 

F (k) = f(y)e 

−∞ 

iky dy 

∞ 

∞ 

= f(y) cos(ky)dy + i f(y) sin(ky)dy 

−∞ 

und der Wellenzahl k transformiert. Bei Reduktion auf Funktionen, die in y-Richtung 

zum Nullpunkt symmetrisch sind, fällt das zum Nullpunkt y = 0 antisymmetrische 

Teilintegral weg, so dass sich die Fourier-Kosinus-Transformation 

∞ 

F (k) = f(y) cos(ky)dy (3) 

−∞ 

−∞ 



78

ergibt. Das Ergebnis der Transformation der Gleichung 1 in den Wellenzahlbereich entlang 

der y-Achse ist dann 

∂x(σx∂x ˜ φ) − σyk 2 ˜ φ + ∂z(σz ˜ φ)+ I 

2 δ(x − x0)δ(z − z0) =0 (4) 

mit ˜ φ = ˜ φ(x, k, z). Diese Gleichung wird von dem hier verwendeten Finite-Elemente- 

Programm auf einem zweidimensionalen Gitter in x- und z-Richtung gelöst. Aus den 

erhaltenen Werten für ˜ φ, bzw. nach Fourier-Kosinus-Rücktransformation φ lassen sich 

mit den Geometriefaktoren der Elektrodenkonfiguration die synthetischen Messwerte für 

Amplitude und Phase der scheinbaren spezifischen Widerstände angeben. 

2.3 Bewertung der Genauigkeit 

Das Programm muss auf seine Gültigkeit und Genauigkeit in Bezug sowohl auf analytisch 

berechenbare Probleme als auch auf verschiedene, mit dem bisherigen Programm zum 

Modellieren isotroper spezifischer Widerstandsverteilungen berechnete Modelle geprüft 

werden. Für einen homogenen Halbraum mit spezifischem Widerstand ρh und Phase 

φh erwartet man eine Pseudosektion mit dem konstanten Wert ρ = ρh des scheinbaren 

spezifischen Widerstands und φ = φh für die scheinbare Phase. Die Messwerte werden 

mit einer simulierten Dipol-Dipol-Anordnung mit Elektrodenabstand 1 m berechnet. Die 

Abweichungen der Modellierungsergebnisse zum analytischen Ergebnis betragen weniger 

als 10 % in den scheinbaren spezifischen Widerständen und weniger als 1 % in den scheinbaren 

Phasen. Ein homogener Halbraum mit anisotropen spezifischen Widerständen in 

Horizontal- und Vertikalrichtung, ρhorizontal und ρvertikal, weist nach analytischen Berechnungen 

einen scheinbaren spezifischen Widerstand von 

ρ = √ ρhori. · ρvert. 

(nach z.B. [5, S. 95]) auf. In Abb. 1 ist ein Modellierungsergebnis für diesen Fall dargestellt. 

Der spezifische Widerstand des Halbraums beträgt 100 Ωm in horizontaler Richtung 

(x- und y-Richtung) und 25 Ωm in z-Richtung. Dies entspricht einem scheinbaren 

spezifischen Widerstand von 50 Ωm in der Pseudosektion. Die Phase des Halbraums 

beträgt gleichmäßig (homogen und isotrop) −5 mrad. Die Abweichung des Modellierungsergebnisses 

zu diesem analytischen Wert beträgt an keiner Stelle mehr als 3 % 

sowohl für den scheinbaren spezifischen Widerstand als auch für die scheinbare Phase. 

3 Modellparameter 

Unter der Annahme einer horizontalen Wechsellagerung unterschiedlich leitfähiger Schichten 

wurde ein Modell mit isotropen spezifischen Widerständen erstellt und mit einem 

entsprechenden Modell mit anisotropen spezifischen Widerständen verglichen. Zur 

Abschätzung der Stärke der Anomalien wird ein Hintergrundmodell mit homogenem und 



79 

(5)

(a) (b) 

Abbildung 1: Dipol-Dipol-Pseudosektion von spezifischem Widerstand und Phase eines 

homogenen Halbraums mit den anisotropen spezifischen Widerständen 

(Amplituden) 100 Ωm in x- und y-Richtung und 25 Ωm in z-Richtung und 

der isotropen Phase −5 mrad. 

isotropem spezifischen Widerstand angegeben. Abb. 2 zeigt die Diskretisierung des Modellraumes 

in 233 Zellen in x-Richtung und 114 Zellen in z-Richtung mit variablem Gitterlinienabstand 

in den Außenbereichen und konstantem Gitterlinienabstand von 0, 5m 

m in einem Bereich von 0 m bis 100 m in x-Richtung. 

Abbildung 2: Gittermodell des Profils mit 233x114 Gitterzellen und einem Gitterlinienabstand 

von 0, 5 m im linearen Bereich. 

Für das Hintergrundmodell wurde wie im vorherigen Abschnitt ein homogener und 



80

isotroper spezifischer Widerstand mit Amplitude 100 Ωm und Phase −5 mrad gewählt. 

3.1 Wechsellagerungen mit unterschiedlichen spezifischen Widerständen 

Im ersten Beispiel wird eine Wechsellagerung von unterschiedlich resistiven, isotropen 

Schichten (100 Ωm und 1 Ωm) in einem Hintergrund mit spezifischem Widerstand von 

100 Ωm betrachtet. Die Phase des spezifischen Widerstands beträgt überall −5 mrad. 

Eine Skizze der Anordnung findet sich in Abb. 3(a). Die Schichtung beginnt 1 m unter 

(a) (b) 

Abbildung 3: Schema des Untergrundmodells: a) vertikale Schichtung mit den spezifischen 

Widerständen 100 Ωm in hellgrau und 1 Ωm in dunkelgrau. b) Vertikale 

Schichtung mit spezifischem Widerstand 1, 98 Ωm in x- und y- sowie 

50, 5 Ωm in z-Richtung. Der spezifische Hintergrundwiderstand beträgt 

100Ωm in x-, y- und z-Richtung. Die Phase beträgt überall −5 mrad. 

der Oberfläche und reicht bis zu einer Tiefe von 7, 5 m. Die Ausdehnung in x-Richtung 

beträgt 40 m. 

Die gleiche Schichtung wird in Abb. 3(b) durch einen Block mit anisotropem spezifischen 

Widerstand beschrieben. Die anisotropen spezifischen Widerstandswerte berechnen 

sich nach 

ρ = R A 

l 

⇔ R = ρ l 

(6) 

A 

mit dem Widerstand R eines Blocks der Länge l und der Querschnittsfläche A. Bei 

Reihenschaltung von zwei Schichten mit den Widerständen R1 und R2 mit je der Querschnittsfläche 

A und der Länge l ergibt sich aus dem Gesamtwiderstand R, der die 

Querschnittsfläche A und die Länge 2 · l hat: 

RSerie = R1 + R2 

2 · l l l 

⇔ ρSerie = ρ1 + ρ2 

A A A 

⇔ ρSerie = ρ1 + ρ2 

. 

2 



81 

(7)

Bei Parallelschaltung von zwei Schichten gleicher Querschnittsfläche A und gleicher 

Länge l und den Widerständen R1 und R2 ergibt sich der Gesamtwiderstand R, der 

die Querschnittsfläche 2 · A und die Länge l hat: 

⇔ 

2 · A 

l 

1 

RSerie 

1 

ρSerie 

⇔ ρP arallel =2· 

= 1 

+ 

R1 

1 

R2 

= A 

l ρ1 + A 

l ρ2 

1 

1 1 + ρ1 ρ2 

Mit diesen Beziehungen folgt für die äquivalenten anisotropen spezifischen Widerstände 

50, 5Ωminx-und1, 98 Ωm in z-Richtung. In y-Richtung beträgt der spezifische Widerstand 

wie in x-Richtung 1, 98 Ωm. Die Phasen der spezifischen Widerstände betragen 

homogen und isotrop −5 mrad. Die Modellierungsergebnisse sind als Pseudosektionen 

einer Dipol-Dipol-Anordnung in den Abb. 4(a) bis 5(b) jeweils für Betrag und Phase des 

spezifischen Widerstands dargestellt. 

(a) (b) 

Abbildung 4: Pseudosektion des Betrags des scheinbaren spezifischen Widerstands. a) 

Vertikale Wechsellagerung isotroper Schichten mit 1 Ωm und 100 Ωm. b) 

Anisotrope Beschreibung der Wechsellagerung durch spez. Widerstände 

50, 5 Ωm in x- und 1, 98 Ωm in y- und z-Richtung. Die Phase beträgt in 

beiden Modellen überall −5 mrad. 



82 

. 

(8)

(a) (b) 

Abbildung 5: Pseudosektion der scheinbaren Phase. a) Vertikale Wechsellagerung isotroper 

Schichten mit 1 Ωm und 100 Ωm. b) Anisotrope Beschreibung der 

Wechsellagerung durch spez. Widerstände 50, 5Ωminx-und1, 98 Ωm in 

y- und z-Richtung. Die Phase beträgt in beiden Modellen überall −5 mrad. 

Beide Modelle - isotropes mit Schichten und anisotropes mit Block - zeigen nahezu 

gleiche Ergebnisse in den Pseudosektionen. Sehr deutlich ist die durch die Schichtlagerung 

bzw. durch den Block anisotroper spezifischer Widerstände erzeugte Anomalie 

sichtbar. Der maximale Wert für den scheinbaren spezifischen Widerstand ρa ist etwa 

100 Ωm, was dem Hintergrundmodell entspricht. Der minimale Wert für ρa beträgt etwa 

10 0,5 Ωm = 3 Ωm. Der erwartete minimale scheinbare spezifische Widerstand beträgt im 

Fall des anisotropen Modells gemäß Gleichung 5 etwa 10 Ωm. Dieser Wert wird im Bereich 

des Blocks und darunter erreicht und sogar unterschritten. Der bis in 7, 5 m Tiefe 

ausgedehnte Block führt einen ”Schatten” mit, der in Form eines nach unten gerichteten 

Dreiecks bis in ca. 20 m Tiefe reicht. An beiden Flanken des Dreiecks zeigen schräge 

”Schatten” nach außen, die ebenfalls einen relativ niedrigen spezifischen Widerstand von 

etwa 10 Ωm aufweisen. Die scheinbaren Phasen betragen gleichmäßig −5 mrad, entsprechend 

den Vorgaben der beiden Modelle. 

3.2 Wechsellagerungen mit unterschiedlichen Phasen des spezifischen 

Widerstandes 

In diesem Abschnitt soll die Schichtlagerung mit Schichten unterschiedlicher Phasen betrachtet 

werden. Dazu wird das Schichtmodell aus Abb. 3(a) für Schichten mit isotropen 

Phasen und das Blockmodell aus Abb. 3(b) als entsprechendes Modell mit anisotropen 

Phasen betrachtet. Die spezifischen Widerstände ρ sind in allen Schichten gleich 

und entsprechend auch im anisotropen Fall in allen Richtungen gleich. Die Reihenschaltung 

von Elementen mit unterschiedlichen Phasen - also komplexen Impedanzen 

X = R(cos φ1 + i sin φ1) - ergibt sich mit Realteil ℜ(X) und Imaginärteil ℑ(X) zu 

XSerie = X1 + X2 

= ℜ(X1 + X2)+iℑ(X1 + X2) 

=(Rcos φ1 + R cos φ2)+i(R sin φ1 + R sin φ2). 



83 

(9)

Für kleine Winkel von φ1 und φ2 kann man die Kosinus-Terme über eine Taylor-Entwicklung 

in erster Ordnung um 0 mit 

cos φ ≈ 1 (10) 

und die Sinus-Terme mit 

annähern. Es ergibt sich dann für die Reihenschaltung 

sin φ ≈ φ (11) 

XSerie ≈ 2 · R + iR(φ1 + φ2) (12) 

Diese Beziehung lässt sich zur Berechnung des komplexen spezifischen Widerstandes 

heranziehen. Zwei Elemente mit den Impedanzen X1 und X2 und je der Querschnittsfläche 

A und der Länge l ergeben in Reihenschaltung eine Impedanz X mit der gleichen 

Querschnittsfläche und der doppelten Länge 2 · l: 

ρ = X A 

l 

A 

= XSerie 

2l 

≈ (R + iR φ1 + φ2 

) 

2 

A 

l 

≈ R(cos φ1 + φ2 

+ i sin 

2 

φ1 + φ2 

) 

2 

A 

l . 

Die Reihenschaltung zweier gleich mächtiger Schichten mit gleichem spezifischen Widerstand 

und unterschiedlicher Phase bedeutet folglich näherungsweise eine Mittelung der 

Phasen, also 

φSerie ≈ φ1 + φ2 

. (14) 

2 

Die Parallelschaltung unterschiedlicher Phasen bei gleichem Betrag des spezifischen Widerstands 

ergibt sich mit den obigen Näherungen und φ ≪ 1zu 

XP arallel = 

≈ R 

1 

1 1 + X1 X2 

1 

1+iφ1 

1 

+ 1 

1+iφ2 

≈ R( 1 i 

+ 

2 2 (φ1 + φ2 

)). 

2 

Werden zwei Elemente mit gleichem spezifischen Widerstand und unterschiedlicher Phase 

und je der Querschnittsfläche A und der Länge l parallel geschaltet, ergibt sich die 

Impedanz XP arallel mit der doppelten Querschnittsfläche 2 · A und der gleichen Länge. 



84 

(13) 

(15)

Der komplexe spezifische Widerstand ergibt sich damit zu 

ρ = X A 

l 

= XP arallel 

≈ R( 1 i 

+ 

2 

2A 

l 

2 (φ1 + φ2 

2 

)) 2A 

l 

= R(1 + i( φ1 + φ2 

)) 

2 

A 

l 

≈ R(cos φ1 + φ2 

2 

+ i sin φ1 + φ2 

) 

2 

A 

l , 

und für die Phasen wie schon bei der Reihenschaltung näherungsweise: 

(16) 

φP arallel ≈ φ1 + φ2 

. (17) 

2 

Dieses Ergebnis macht klar, dass bei konstantem spezifischen Widerstand eine Wechsellagerung 

von Schichten unterschiedlicher Phasen wohl in ihrer Stärke im Mittel, nicht 

jedoch in ihrer Richtung erkannt werden kann. Nur in Verbindung mit unterschiedlich 

spezifischen Widerständen der einzelnen Schichten können auch die Phasenwerte der 

abwechselnden Schichten unterschieden werden. 

Ein Schichtmodell mit den Phasen der einzelnen Schichten von −15 mrad bzw. −5 mrad 

(Hintergrund) hat demnach die anisotropen Phasen −10 Ωm in x-,y- und z-Richtung. 

Die Ergebnisse sind in den Abb. 6(a) bis 7(b) als scheinbare spezifische Widerstände und 

scheinbare Phasen in Pseudosektionen dargestellt. 

(a) (b) 

Abbildung 6: Dipol-Dipol-Pseudosektion der Amplitude des scheinbaren spezifischen 

Widerstands. a) Vertikale Wechsellagerung isotroper Schichten mit 

−15 mrad und −5 mrad. b) Anisotrope Beschreibung der Wechsellagerung 

durch Phasen −10 mrad in x-, y- und z-Richtung 



85

(a) (b) 

Abbildung 7: Dipol-Dipol-Pseudosektion der scheinbaren Phase. a) Vertikale Wechsellagerung 

isotroper Schichten mit −15 mrad und −5 mrad. b) Anisotrope 

Beschreibung der Wechsellagerung durch Phasen −10 mrad in x-, y- und 

z-Richtung 

Wie erwartet zeigt sich in den Pseudosektionen des scheinbaren spezifischen Widerstandes 

keine Variation mit der eingestellten Phase. Dadurch wird der in Gl. 14 und 17 

aufgestellte Zusammenhang bekräftigt. Die Pseudosektionen der Phasen weisen wie die 

Pseudosektionen im Abschnitt 3.1 starke ”Schatten” unterhalb der unteren Störkörpergrenze 

auf. Auch die seitlichen Flanken sind sichtbar. 

4 Schlussfolgerungen 

Es ist mit dem auf anisotrope spezifische Widerstände und Phasen erweiterten Programm 

CRMod nun möglich, Effekte von Anisotropie, z.B. bei Wechsellagerungen von Sedimenten, 

zu berücksichtigen. Die vorliegenden Ergebnisse zeigen in den möglichen Vergleichen 

zu analytischen Berechnungen die Gültigkeit des Programms. Es wurde hierbei insbesondere 

Wert auf die Vorschrift zur Berechnung des spezifischen Widerstands im Fall eines 

homogenen Halbraums mit anisotropen spezifischen Widerständen (vgl. Gleichung 5) 

gelegt. Im Zusammenhang mit der Wechsellagerung von Phasen wurde mittels der Gleichungen 

14 und 17 gezeigt, dass horizontale und vertikale Wechsellagerungen gleicher 

Mächtigkeit und gleichen spezifischen Widerstands nicht unterschieden werden können. 

Im Zusammenhang mit dieser Arbeit ist eine Messkampagne geplant, die auf stark 

anisotropem Untergrund stattfinden soll. Die Messdaten sollen mit entsprechenden Modellen 

mit anisotropen spezifischen Widerständen des vorliegenden Modellierungsprogramms 

erklärt werden. Zusätzlich zu dieser Anwendung besteht die Möglichkeit, auch 

das auf dem Modellierungsprogramm CRMod basierende Inversionsprogramm CRTomo 

([2]) auf Anisotropie zu erweitern. 



86

5 Danksagungen 

Diese Arbeiten werden im Rahmen des Forschungsverbunds Geothermie und Hochleistungsbohrtechnik 

(GEBO) vom Niedersächsischen Ministerium für Wissenschaft und 

Kultur und von Baker Hughes/ Celle gefördert 

Literatur 

[1] A. Kemna, ”Tomographic Inversion of Complex Resistivity - Theroy and Application”, 

Berichte des Instituts für Geophysik der Ruhr-Universität Bochum, Reihe A, Nr. 

56, Der Andere Verlag, 2000, ISBN-13: 978-3934366923. 

[2] A. Kemna, ”Tomographische Inversion des spezifischen Widerstandes in der Geoelektrik”, 

Diplomarbeit, Institut für Geophysik und Meteorologie der Universität zu 

Köln, 1995. 

[3] F. Nguyen, S. Garambois, D. Chardon, D. Hermitte, O. Bellier, D. Jongmans, ”Subsurface 

electrical imaging of anisotropic formations affected by a slow active reverse 

fault, Provence, France”, Journal of Applied Geophysics 62, Seiten 338 - 353, 2007. 

[4] T. Winchen, A. Kemna, H. Vereecken und J.A. Huisman, ”Characterization of bimodal 

facies distributions using effective anisotropic complex resistvity: A 2D numerical 

study based on Cole-Cole models”, Geophysics 74, Seiten A19 - A22, 2009. 

[5] K. Knödel, H. Krummel, G. Lange, ”Geophysik”, 2. überarbeitete Auflage, Springer- 

Verlag, Berlin, 2005, ISBN 3-540-22275-8. 



87

From forward modelling of MT phases over 90 ◦ towards 

2D anisotropic inversion 

X. Chen 1,2 , U. Weckmann 1 , K. Tietze 1,3 

1 Helmholtz Centre Potsdam - German Research Center for Geosciences,Germany 

2 University of Potsdam, Institute of Geosciences, Germany 

3Free University of Berlin, Institute of Geological Sciences, Germany 

xiaoming@gfz-potsdam.de, uweck@gfz-potsdam.de, ktietze@gfz-potsdam.de 

Abstract 

Within the framework of the German - South African geo-scientific research initiative Inkaba 

yeAfrica several magnetotelluric (MT) field experiments were conducted along the Agulhas- 

Karoo Transect in South Africa. This transect crosses several continental collision zones between 

the Cape Fold Belt, the Namaqua Natal Mobile Belt and Kaapvaal Craton. Along the profile 

we can identify areas (> 10km) with phases over 90 ◦ . This phenomenon usually occurs in presence 

of electrical anisotropy. Due to the dense site spacing we are able to observe this behaviour 

consistently at several sites. 

In this presentation we focus on the profile section between Prince Albert and Mosselbay. With 

isotropic 2D inversion we are able to explain most features in the MT data but not the abnormal 

phase behavior. With several anisotropic forward modelling studies we have tested the influence 

of anisotropy parameters on the MT responses. In a first step we use simple 2D models with 

embedded zones of electrical anisotropy to get a basic understanding of anisotropic responses. In 

a second step isotropic 2D inversion results serve as background models in which we included 

anisotropic zones, e.g. to fit the abnormal phase curves. These resolution tests are necessary and 

important for the future development of a 2D inversion with spatially constraint anisotropy. 


For a 2D geoelectric model with a finite system of homogeneous, but generaly anisotropic blocks the 

electrical conductivity is a tensor instead of a scalar quantity. It is symmetric and positive-definite. 

Due to its symmetry the conductivity tensor σ within each layer of model can be diagonalized and expressed 

by three principal conductivities σ1, σ2, σ3 and a rotation matrix, which can be decomposed 

into three elementary Euler’s rotations αS, αD, αL respectively. 

⎛ 

⎞ 

σ = 

⎝ 

σxx σxy σxz 

σyx σyy σyz 

σzx σzy σzz 

⎠ 

⎛ 

= Rz(−αS)Rx(−αD)Rz(−αL) ⎝ 

σ1 0 0 

0 σ2 0 

0 0 σ3 

⎞ 

⎠Rz(αL)Rx(αD)Rz(αS) 

where Rx and Rz are elementary rotation matrices around the coordinate axis x and z, respectively.The 

angles αS, αD, αL are typically called anisotropy strike, dip and slant, respectively. 

In this work we investigate the feasibility of use of 2D forward anisotropy modelling to simulate 

phases over 90 ◦ which we observed in field data from the MT survey in South Africa. Using the 2D 

anisotropy forward modelling algorithm of Pek and Verner (1997) we vary the model parameters in 



88

order to gain a basic understanding of the MT transfer function in presence of anisotropy. First we 

will give a brief introduction of the survey area and then we will show the results of 2D isotropic 

inversion and 2D anisotropic forward modelling. 

2 Survey area 

Within the framework of the German - South African geo-scientific research initiative Inkaba yeAfrica 

four magnetotelluric (MT) field experiments were conducted along the Agulhas-Karoo Transect in 

South Africa (Weckmann et al., 2007, Stankiewicz et al., 2008). These transects cross several continental 

collision zones and their respective units, such as the Cape Fold Belt, the Namaqua Natal 

Mobile Belt and the Kaapvaal Craton. The MT profile on which we focus in this paper is located in 

CFB 

NNMB 

MT2 profile 

SCCB 

BMA 

MT 

NVR 

WRR 

Offshore seismics 

Kaapvaal 

Craton 

Karoo 

Agulhas-Falkland Fracture Zone 

Agulhas 

Plateau 

Transkei 

Basin 

Figure 1: Left: Map of the Agulhas-Karoo Geoscience Transect with MT Profiles (red lines) across 

Cape Fold Belt , the Namaqua Natal Mobile Belt and the Kaapvaal Craton. Right: The profile MT2 

contains 46 broad band MT sites and 8 broad band / long period MT sites. It extends 120 km from 

Prince Albert in the North to Mosselbay in the South and covers the entire Cape Fold Belt. 

the Cape Fold Belt. In total, 54 MT sites were deployed along this 120 km long profile MT 2 (Fig. 1). 

It extends from Prince Albert in the North to Mosselbay in the South and covers the entire Cape Fold 

Belt (CFB), its inliers, the Oudtshoorn and the Kaaimans Basins, the Swartberg and the Outeniequa 

Mountain ranges and several major thrusts and faults. 

3 Data and isotropic 2D inversion 

Along the profile MT2 we acquired 5-component MT data at all stations in a period range from 

0.001s to 1000s using GPS synchronized S.P.A.M. MkIII (Ritter et al., 1998) and CASTLE broadband 

instrument. Metronix MFS06/06 induction coil magnetometer and non-polarizable Ag/AgCl telluric 

electrodes were used to record natural magnetic and electric field variations. The data were processed 

with the EMERALD software package (Ritter et al., 1998) using both robust single site and remote 

reference techniques. At some sites, for which a suitable reference site was not available and the 

data were affected by cultural noise (extensive farming), we applied the frequency domain selection 

scheme after Weckmann et al. (2005) to improve data quality. 

Mozambique Ridge 

SCCB 



89

Figure 2: Pseudo-sections of TE and TM mode apparent resistivity and phase (x direction pointing 

west).We can observe phase values over 90 degrees in the middle of the profile in both TE and TM 

component (marked with black ellipses in the upper panel). Two exemplary sites (site 121 and site 

116) are displayed as apparent resistivity, phase and induction arrows (Wiese convention) over period. 

The red arrows in the pseudo-sections show the location of the selected sites. We can identify that the 

phases, (especially in the TE component) leave the first quadrant at a minimum period of 10 s, but 

typically at longer periods of 100-1000 s. 



90

After data processing, we applied different strike and dimensionality analyses, e.g. the ellipticity 

analysis after Becken & Burkhardt (2004), obtaining an electromagnetic strike direction of −90 ◦ , i.e. 

East-West direction. This is in general compatible with the tectonic grain of the CFB. Furthermore, 

most of the data seem to be compatible with a 2D interpretation approach. However, in a limited area 

we observe impedance phases exceeding 90 degrees at long periods. They typically appear in both, 

TE and TM mode, and persit in either component even if we rotate the coordinate system (Fig. 2). 

Figure 3: TE and TM mode data used for isotropic 2D inversion. Prior to inversion they were rotated 

into a common coordinate system according to the geoelectric strike direction of ≈ 90 ◦ (obtained by 

strike and phase tensor analysis). Data with phases over 90 ◦ are discarded from the data base. 

For an isotropic 2D inversion approach we use RLM2D (Rodi & Mackie, 2001, implemented in 

the WinGlink software package). Before starting a 2D inversion we have to make sure that large phase 

values over 90 ◦ are excluded as they cannot be fitted by a 2D inversion approach. Figure 3 shows 

the data which were finally used for 2D inversion. Figure 4 displays our preferred 2D conductivity 

image of the upper 35 km together with a section of the geological map after Hälbich et al. (1993). 

The inversion was started from a homogeneous half-space of 100Ωm with τ = 10 using TE and 

TM component, with intermediate inclusion of the vertical magnetic transfer function. Within the 

framework of this work, we refrain from interpreting conductivity anomalies in a geological context, 

but focus on the area where phases over 90 ◦ occur. One of the most prominent conductivity anomalies 

is a triangular shaped, highly conductive structure in the middle of the profile. In this area we also 

observe phases leaving the quadrant. This conductivity anomaly is required by the data which is 

compatible with a 2D interpretation approach; however, we believe that the phases over 90 ◦ are caused 

by some electrically anisotropic structures in this area (in Fig. 4 between black dashed lines). We 

should also note that the deep part of this area only possesses a very limited resolution (in Fig. 4 

marked with semitransparent mask) because most of the data which relates to this part are excluded 

in order to satisfy the 2D isotropic procedure (see Fig. 3). Similar phase behaviour was explained 

with crustal anisotropy by Weckmann et al. (2003) and Heise & Pous (2003), where data within old 

continental collision zones in Namibia and on the Iberian Peninsula, respectively. In both cases the 

data could be fit by using a shallow and a deeper electrically anisotropic zone with different anisotropy 

strike. 

4 Anisotropic forward modelling 

Isotropic 2D inversion is adequate to explain the data in most parts along the profile but it is very 

unsatisfactory not being able to include phases greater than 90 degrees and thus neglect a substantial 

amount of data. In order to develop a 2D inversion with spatially constraint anisotropy, resolution 

tests and synthetic modelling studies are necessary. In a first step towards the constraint anisotropic 



91

Figure 4: 2D inversion model together with a section from the geological map after Hälbich et al. 

(1993). The area where we observe phases over 90 ◦ is located where the inversion puts a triangular 

shaped high conductivity anomaly (area between black dashed lines). Zones of limited resolution are 

also in this area and marked with a semitransparent mask. 

inversion we included zones with electrical anisotropy in a 2D isotropic model and calculated its 

forward responses which aim to understand the anisotropy effect. 

4.1 Lateral extension 

Pek & Verner (1997) have suggested that a combination of two azimuthal anisotropies with anisotropy 

strikes perpendicular to each other could produce phases that exceed 90 ◦ . Based on the suggestion 

we study at first a combination of two different anisotropic blocks. The initial model (Fig. 5, left) 

consists of a 300m isotropic surface layer with a resistivity of 30Ωm and an anisotropic block starting 

at a depth of 300m embedded in a medium of 100Ωm. The principal resistivities of the block 

are σ1/σ2/σ3 = 50/0.5/50Ωm and the anisotropy strike αS is 120 ◦ . The block is underlain by an 

isotropic layer with a resistivity of 15Ωm. Beneath the isotropic layer a second anisotropic block 

with σ1/σ2/σ3 = 30/0.3/30Ωm and αS = 30 ◦ (perpendicular to αS of the first block) is embedded in 

an isotropic half-space with 100Ωm. The second, deeper anisotropic block has a lateral extension of 

15km in the first (Fig. 5, left upper panel), and 80km in the second (Fig. 5, left lower panel) model, 

respectively. 

The forward responses are displayed in figure 5 (right) as apparent resistivities and phases in xy 

and yx component, respectively. Comparing the responses of both models we see that the phases of 

yx component (Φyx) for the second model (Fig. 5, left lower panel) at sites above the first anisotropy 

block leave the quadrant at a period of ≈ 100s (Fig. 5, right lower panel), while they are smaller than 

90 ◦ (Fig. 5, right upper panel) for the first model (Fig. 5, left upper panel) with the narrower deep 

anisotropic block. 



92

Figure 5: Models (left) and their forward responses (right). The models differ only in lateral extension 

of anisotropy block. The lateral extension of the second block is about 15km in the first model (left 

upper panel) and 80km (left lower panel) in the second model. The major difference in the responses 

appears in the yx component. Phases over 90 ◦ occur if the lateral extension of the deeper anisotropy 

block is greater than it of the shallower anisotropy block. 

4.2 Depth 

In a second step, we used the same anisotropy parameters as described above. The initial model 

consists of a 300m isotropic surface layer and a isotropic half-space with resisitivity of 100Ωm. Two 

anisotropy blocks are embedded in the half-space. The first block started at depth of 300m and shaped 

as a trapezoid. In this attempt we vary the depth of the second block. In the first model (Fig. 6, left 

upper panel) the second block started at a depth of 1.8km and in the second model (Fig. 6, left lower 

panel) started at a depth of 6.8km. 

In the forward responses (Fig. 6, right) we see that the phases Φyx for the second model become 

larger than 90 ◦ at periods > 10s at sites above the first block, while they for the first model are 

all smaller than 90 ◦ . In this attempt the second anisotropy block has always sufficiently greater 

lateral extension than the first anisotropy block, but we only see the phase anomalies by model with 

anisotropy block in adequate depth. Besides the lateral extension of the anisotropy block, also the 

depth is one of those key conditions under which phase anomalies appear. 

4.3 Rotation angle 

In a third test we use a similar model as described above for step two. The model contains a 300m 

isotropic surface layer and an isotropic half-space with resisitivity of 100Ωm. Two anisotropic blocks 

are embedded in the half-space. The first block starts directly beneath the surface layer and the 

second block in a depth of 6km. They have the principal resistivities σ1/σ2/σ3 = 50/0.5/50Ωm and 

σ1/σ2/σ3 = 30/0.3/30Ωm, respectively. In this attempt we vary the anisotropy strike angle αS1 and 

αS2 for both blocks. 

The forward response for the model with αS1 = αS2 = 0 ◦ is displayed in the right upper panel 

of figure 7. The phases of the yx component approach 90 ◦ for long periods. For αS1 = 60 ◦ and 

αS2 = 120 ◦ (Fig. 7, left lower panel) the yx component phases become larger than 90 ◦ for periods 

> 10s, while they stay below 90 ◦ for αS1 = 90 ◦ and αS2 = 120 ◦ (Fig. 7, right lower panel). Comparing 

the three examples, we see that model with different combination of strike angle in both shallow and 



93

Figure 6: Models (left) and their forward responses (right). The models differ by depth of the second 

anisotropy block. In the first model (left upper panel) the second block starts in a depth of 1.8km 

and in the second model (left lower panel) the block starts in a depth of 6.8km. The phases of yx 

component for the model with the deeper anisotropic block become larger than 90 ◦ at periods > 10s 

at sites above the first block. For the model with the shallower block all phases are smaller than 90 ◦ . 

αS1 and αS2 

αS1 = 0 ◦ and αS2 = 0 ◦ 

αS1 = 60 ◦ and αS2 = 120 ◦ αS1 = 90 ◦ and αS2 = 120 ◦ 

Figure 7: Model (left upper panel) and its forward responses with different anisotropy strike angles. 

The model contains the same surface layer, background medium and resistivities for both anisotropic 

blocks as the models in fig. 6. We vary the strike angles αS1 and αS2 for the shallow and the deep 

block (left upper panel). The forward responses are displayed as apparent resistivities and phases in 

xy and yx component. 



94

deep blocks produce forward responses with pronounced difference. This can be observed not only in 

yx component (ρa(yx) and Φyx ) but also in xy component (ρa(xy) and Φxy ). A possible explanation is 

that a change of strike angle forces the current flow to change its preferred direction from the shallow 

to the deep block. According to this fact we may conclude that the anisotropy strike angle influences 

forward responses significantly and phase greater than 90 ◦ will appear if the strike angle of both 

blocks differ by an adequate amount. 

5 Conclusions 

Phases greater than 90 ◦ can only be modelled by a combination of a deep and a shallow anisotropic 

block. We varied several model parameters to study the changes in forward responses. For our models 

we can conclude that phases out of the first quadrant occur when: (i) the anisotropy ratio (σmax/σmin) 

is high (for both blocks); (ii) the deep anisotropic block has a much larger lateral extension than the 

shallow block; (iii) the deep anisotropic block is located in greater depth; (iv) the angles of anisotropy 

of both blocks differ by a considerable amount. In our models the difference should be at least 45 ◦ so 

that the preferred direction of current flow changes significantly from the shallow to the deep block. 

References 

Becken, M., & Burkhardt, H. (2004). An ellipticity criterion in magnetotelluric tensor analysis. 

Geophys. J. Int., 159, 69–82. 

Eisel, M., & Haak, V. (1999). Macro-anisotropy os the electrical conductivity of the crust: a magnetotelluric 

study from the German continental Deep Drilling site (KTB). Geophys. J. Int., 136, 109– 

122. 

Hälbich, I. (1993). Cape Fold Belt – Agulhas Bank Transect across Gondwana suture, southern 

Africa. Geosci. Transect, 9, 18 pp. AGU, Washington, D. C. 

Heise, W., & Pous, J. (2003). Anomalous phases exceeding 90 ◦ in magnetotellurics: anisotropic 

model studies and a field example. Geophys. J. Int., 155, 308–318. 

Kellett, R. L., Mareschal, M., & Kurtz, R. D. (1992). A model of lower crustal electrical anisotropy 

for the Pontiac Subprovince of the Canadian Shield. Geophys. J. Int., 111, 141–150. 

Mareschal, M., Kellett, R. L., Kurtz, R. D., Ludden, J. N., Ji, S., & Bailey, R. C. (1995). Archaean 

cratonic roots, mantle shear zones and deep electrical anisotropy. Nature, 375, 134–137. 

O’Brien, D. P., & Morrison, H. F. (1967). Electromagnetic fields in an N-layer anisotropic half space. 

Geophysics, 32, 668–677. 

Pek, J., & Verner, T. (1997). Finite-difference modelling of magneto-telluric fields in two-dimensional 

anisotropic media. Geophys. J. Int., 128, 505–521. 

Reddy, I. K., & Rankin, D. (1975). Magnetotelluric response of lateerally inhomogeneous and 

anisotropic media. Geophysics, 40, 1035–1045. 

Ritter, O., Junge, A., & Dawes, G. J. K. (1998). New equipment and processing for magnetotelluric 

remote reference observations. Geophys. J. Int., 132, 535–548. 

Rodi, W., & Mackie, R. L. (2001). Nonlinear conjugate gradients algorithm for 2-d magnetotelluric 

inversion. Geophysics, 66, 174–187. 



95

Stankiewicz, J., Ryberg, T., Schulzw, A., Lindeque, A., Weber, M., & de Wit, M. (2007). Initial 

results from wide-angle seismic refraction lines in the southern Cape. South African Journal of 

Geology, 110, 407–418. 

Weckmann, U., Jung, A., Branch, T., & Ritter, O. (2007). Comparison of electrical conductivity 

structures and 2D magnetic modelling along two profiles crossing the Beattie Magnetic Anomaly, 

South Africa. South African Journal of Geology, 110, 449–464. 

Weckmann, U., Magunia, A., & Ritter, O. (2005). Effective noise separation for magnetic single site 

data processing using a frequency domain selection scheme. Geophys. J. Int., 161, 635–652. 

Weckmann, U., Ritter, O., & Haak, V. (2003). A magnetotelluric study of the damara belt in namibia 

– 2. MT phases over 90 ◦ reveal the internal structure of the Waterberg Fault/Omaruru Lineament. 

Phys. Earth Planet. Inter., 138(2), 91–112. 



96

Substitute models for static shift in 2D 

Kristina Tietze 1,2 , Oliver Ritter 1,2 , Ute Weckmann 1,3 

1 Helmholtz Centre Potsdam - German Research Centre For Geosciences GFZ, Department 2, Section 2.2, Telegrafenberg, 14473 Potsdam 

2 Free University Berlin, Department of Earth Sciences, Malteserstr. 74-100, 12249 Berlin 

3 University of Potsdam, Department of Geosciences, Karl-Liebknecht-Str. 24, 14476 Potsdam 

Contact: kristina.tietze@gfz-potsdam.de 

Introduction 

MT practitioners often down-weight apparent resistivity TE mode data prior to 2D inversion to avoid 

problems with static shift, obviously assuming that static shift of the TM mode is handled automatically 

by the inversion. Static shift is caused by conservation of charges at local conductivity discontinuities 

which are small with respect to the inductive scale length. 

Here we present a class of shallow conductivity anomalies which can produce significant up- or 

downwards shifted TM mode apparent resistivity curves (static shift in the TE mode cannot be 

simulated with 2D modeling). We examine how this static shift is reproduced by 2D inversion and show 

that the results are strongly influenced by grid design and regularization. We conclude that modern 2D 

inversion packages are not optimized to handle static shift. Our results also indicate that it is no good 

reason to assume that static shift cancels out on average. 

2D substitute structures for static shift 

As 2D models only allow for conductivity changes in one of the horizontal directions, static shift can only 

be accounted for in one component (TM) and re-produced by forward modeling. 

Fig. 1 (right): Starting from a 1D layered halfspace 

(LH) model (Fig. 1a) 2D inhomogeneities 

were added to the resistivity model just 

below/at the surface (Figs 1b-g, left panel). TE 

and TM model responses were calculated for 

frequencies between 10 3 Hz and 10 -3 Hz directly 

above the center of the inhomogeneities. The 

2D forward computations are compared to the 

1D LH results indicated by crosses (Figs 1b-g, 

right panel). 



97

Fig. 1b (left): A 15 m wide 10 m conductor with a 

thickness varying from 1 m to 5 m causes downward shift 

of the TM resistivity curves. The shift increases in 

dependence of the block thickness, i.e. the extent of the 

horizontal resistivity contrast. The amount of static shift 

which can be generated by extending the conductive inset 

downwards is limited. At some point the structure is 

becoming inductively effective. 

Fig. 1d (left): Enhancing the conductivity contrast by 

padding the conductor with resistive (10 3 m) cells TM 

downward shift is increased. Structures of this type can be 

observed in inversion models below static shift affected 

sites when static shift is not taken into account during 

inversion (cf. pane view in Fig. 2c (2)). 



98 

Fig. 1c (left): For a fixed thickness of 

3 m the lateral dimensions of the 10 

m-block were altered between 15 

m and 65 m. With increasing block 

width, the static shift effect becomes 

smaller as the lateral resistivity 

contrast which is responsible for the 

distortion of the electrical field 

moves away from the site location. 

Fig. 1e (left): Placing a highly 

resistive block (10 4 m) with a width 

of 15 m and varying thicknesses 

between 5 m and 110 m beneath the 

site results in upward shift of the TM 

mode. Static shift increases with 

increasing vertical block dimensions.

Fig. 1f (left): For a fixed thickness of 

55m the lateral extent of the 10 4 mblock 

was altered between 15 m and 65 

m. As seen for the 10 m-block, the 

static shift effect becomes smaller with 

increasing block width as the resistivity 

contrast distorting the electrical field 

moves away from the site location. 

Fig. 1g (left): Padding the resistive block 

with a thin column of conductive (10 

m) cells increases the upward shift of 

the TM resistivity curve slightly. The 

horizontal padding cells must be very 

small horizontally to prevent inductive 

effects. 

As expected, the TE resistivity curves and the phase curves of both, TM and TE, modes are mostly 

unaffected by these very small scale structures. 

Fig. 1h (left): Distortion of the TM 

apparent resistivities is due to static 

shift as the skin depth exceeds 15 km 

for =10 m and f=0.01 Hz. The 

downward shifting effect above the 

good conductor is significantly stronger 

than the upward shift above the 

resistive block, although resistivity 

contrasts of the two blocks to the 

background are the same. Static shift 

values along this profile do not sum up 

to zero. The figures above indicate that 

structures causing upwards shift have to 

have a larger vertical extent to produce 

the same amount of shift. 

So, it is at least questionable if a zero sum/average assumption for static shift values, which is often 

applied in inversion schemes, is appropriate. 



99

2D Inversion 

Fig. 2a (left): A 2D resistivity model was 

created by adding a low and a high 

resistive block to the layered half-space 

model (cf. Fig. 1a). Data were calculated 

for 50 sites along a 50km long profile with 

1 km site spacing adding 2.5% Gaussian 

noise. 

Fig. 2b (above): Right: Synthetic shift values c were generated obeying a modified logarithmic Gammadistribution: 

log10(c) = -(0.5,2)+0.5 and shift=c. The maximum of the modified distribution is at 10 0 , 

the expected value is 10 -0.5 . Left: Shift was applied randomly to 2/3 of the sites, independently for TE 

and TM. The left panel shows the applied shift values for each site along the profile. 

Fig. 2c (below): Inversion results for un-shifted (1) and shifted (2)-(4) data for 100 iterations starting 

from a 100m homogeneous half space, applying a uniform smoothing with =10. Error floors were 2% 

(0.6°) for the phases and 5% and 500% for TM and TE apparent resistivities, respectively. 



100

Fig. 2c (above, continued): The model grid was created setting the column widths to 0.5 times of the 

minimum skin depth pmin, for (1) and (2), and was refined to 0.1*pmin for (3) and (4) (cf. pane views). 

(2) & (3): As smoothing (regularization) is working against sharp resistivity contrasts, the inversion 

introduces complex and wide-stretched structures below the sites affected by static shift. The refined 

grid in (3) reduces smoothing lengths for uniform regularization. As a consequence, introduced 

compensatory structures appear simpler or diminish. 

(4) Inversion result after introducing a so-called “tear zone” (feature of WinGLink) at site 114 (red 

outline). Tear zone inversion does not penalize sharp conductivity contrasts at the outline of the tear 

zone. Now, the inversion can properly model static shift. The model can account for TM static shift 

within this zone while obtaining surrounding resistivity values close to the original ones. 

Fig. 2d (right) shows un-shifted data, 

shifted data as symbols and the inversion 

results (cf. Fig. 2c) for sites 114 and 133 as 

lines. For periods longer than 10 -2 s shifted 

data are fitted well by all inversions. For 

shorter periods, the inversion struggles to 

fit the data, especially at site 114 where 

TM resistivities were shifted downwards by 

two decades. TM phase responses below 

10 -2 s deviating from forward data clearly 

show the inductive effects of the near 

surface structures. Static shift effects 

decrease with the refined grid (3) and 

introduction of a tear zone (4). 

Summary 

Static shift for the TM mode can easily be produced by a range of simple structures at surface being 

introduced to the regional resistivity models as substitutes for natural structures causing static shift in 

field data. 

To account for TM static shift within 2D inversion, model grids have to be very fine in the vicinity of sites 

with column widths and thicknesses much smaller than the induction volume of the highest frequency 

to be analyzed. 

Smoothing routinely applied in minimum structure inversions does not allow for the sharp conductivity 

contrasts required to produce sensible static shift. It would therefore be desirable to be able to apply 

different smoothing factors to a static shift compensating top layer and the remaining model. 



101

Die Übergangsimpedanz einer kapazitiv angekoppelten Elektrode 

Andreas Hördt, Peter Weidelt, Anita Przyklenk 

Institut für Geophysik und extraterrestrische Physik, TU Braunschweig 

Vorwort von A. Hördt 

Die in diesem Artikel vorgestellte Theorie beruht auf einer unveröffentlichen Arbeit von Prof. 

Peter Weidelt, der am 1.7.2009 unerwartet verstorben ist. Die Arbeit ist ein typisches Beispiel 

für seine außerordentliche Hilfsbereitschaft, für die er unter Kollegen in aller Welt bekannt 

war. Im Jahr 2007 hatte ich ihn um Unterstützung bei der Berechnung der 

Übergangsimpedanz einer kapazitiven Elektrode gebeten. Einige Wochen später hatte er die 

vollständige Lösung hergeleitet und in ein Programm umgesetzt. Er selbst hat die Aufgabe als 

nicht allzu schwierig oder wichtig empfunden, und hätte die Ergebnisse vermutlich nie 

veröffentlicht. 

1 Zusammenfassung 

Es wird eine Möglichkeit vorgestellt, die Impedanz einer Kreisscheibe zu berechnen, die an 

einen Halbraum mit endlicher Leitfähigkeit angekoppelt ist. Basierend auf den 

Maxwellgleichungen wird eine Integralgleichung für die Ladungsdichte q auf der 

Kreisscheibe aufgestellt. Mit der Randbedingung, dass das Potential auf der Scheibe konstant 

ist, kann die Ladungsdichte gender zu angehobener Platte stetig aund damit die Gesamtladung 

bestimmt werden. Es zeigt sich, dass der Übergang von aufliels Funktion des Abstandes 

verläuft. Zudem nimmt die Impedanz als Funktion des Abstandes zu, d.h. die Ankopplung 

einer kapazitiv angekoppelten Elektrode kann niemals geringer sein, als die einer 

aufliegenden mit gleicher Fläche. Je nach Modellparametern kann die Impedanz jedoch 

innerhalb weniger Nanometer über Größenordnungen variieren, so dass es dennoch günstig 

sein kann, die Elektrode zu isolieren, um starke Schwankungen der Impedanz zu vermeiden. 

2 Einleitung 

Bei geoelektrischen Messungen über sehr schlecht leitendem Untergrund kann es von Vorteil 

sein, den Strom kapazitiv anzukoppeln (Kuras et al., 2006). Dabei wird ein hochfrequentes 

Wechselfeld an eine Elektrode angelegt, die keinen direkten Kontakt mit dem Untergrund hat. 

Eine genaue Berechnung der Übergangsimpedanz einer solchen Elektrode ist notwendig, um 

zu beurteilen, unter welchen Bedingungen eine kapazitive Ankopplung einer galvanischen 

überlegen ist. Für die praktische Umsetzung ist die Frage von Bedeutung, ob es günstig ist, 

eine kapazitive Elektrode zu isolieren und einen galvanischen Kontakt auszuschließen. Die 

Standardformeln für die Ankopplung kapazitiver Elektroden sind allerdings nur für hohe 

Leitfähigkeiten des Untergrundes gültig. Hördt (2007) hat analytische Gleichungen für eine 

Kugelelektrode im sphärisch geschichteten Vollraum hergeleitet und diskutiert. Hier wird nun 

eine Lösung für eine zylindrische Scheibe über einem Halbraum hergeleitet. 



102

3 Modellbeschreibung 

Abbildung 1 illustriert das zu lösende Problem. Zu berechnen ist, welcher Strom I bei einer 

vorgegebenen Spannung U zwischen zwei zylindrischen Scheiben über einem homogenen 

Halbraum fließt. 

Abbildung 1: Skizze der kapazitiv angekoppelten Stromquelle: Zwei zylindrische Scheiben 

sind kapazitiv an einen homogenen Halbraum mit Leitfähigkeit und Permittivität 

angekoppelt, es fließt ein Strom I bei vorgegebener Spannung U. 

Wenn der Untergrund ein idealer Leiter ist, gilt bei kleinem Abstand zwischen Elektrode und 

Untergrund für die komplexe Übergangsimpedanz (Smythe, 1968): 

1 

Z (1) 

iC 

wobei die Kreisfrequenz ist und C die Kapazität, mit 

A 

0 

C (2) 

d 

Dabei ist A die Fläche der Elektrode, d der Abstand zum Untergrund, und 0 die 

Dielektrizitätszahl des Vakuums zwischen den Elektroden. diese Formeln stellen allerdings 

eine Näherung für einen idealen Leiter dar. Je nach Frequenz und Leitfähigkeit gilt die 

Näherung nicht mehr, und die elektrischen Parameter des Untergrundes müssen explizit 

berücksichtigt werden. Dies erfordert eine vollständige Lösung der Maxwellgleichungen. 

Die geometrischen Parameter des Modelles sind in Abbildung 2 illustriert. Die ideal leitende 

Kreisscheibe mit Radius a befindet sich im Abstand d über dem Untergrund. Der Mittelpunkt 

der Scheibe ist der Ursprung des zylindrischen Koordinatensystemes. Es wird angenommen, 

dass alle zeitlichen Variationen harmonisch sind, die zeitliche Abhängigkeit sich also durch 

e it darstellen lässt. Die Leitfähigkeit des Untergrundes lässt sich dann als komplexe Größe 

darstellen: 1 1 i 

1, 

wobei 1 die Gleichstromleitfähigkeit ist. Das Medium zwischen 

Untergrund und Scheibe hat die rein imaginäre Leitfähigkeit 0 i 

0 . 

Wenn an die Scheibe ein Potential U angelegt wird, stellt sich eine radialsymmetrische 

Ladungsverteilung q(r) ein. Die Gesamtladung Q erhält man dann aus 

a 

 

Q 2 qds 

s 

(3) 

0 

U 

~ 

, 



103 

I

Abbildung 2: Parameter des Modelles der ideal leitenden Kreisscheibe über homogenem 

Halbraum. 

Es muss also die Flächenladungsdichte q(r) gefunden werden, aus der dann Q und mit 

Q 

C (4) 

U 

die komplexe Kapazität, bzw. mit Gl. (1) die komplexe Impedanz der Kreisscheibe berechnet 

werden kann. 

Aus der Forderung, dass die Leitfähigkeit auf der Scheibe unendlich ist, ergibt sich, dass das 

elektrische Feld auf der Scheibe verschwindet. Die Lösungsstrategie besteht darin, eine 

Gleichung für das elektrische Feld im gesamten Raum als Funktion von q(r) zu berechnen 

und dann q(r) so zu bestimmen, dass die Radialkomponente Er auf der Scheibe verschwindet. 

4 Theorie 

4.1 Grundgleichungen 

Um das elektrische Feld zu berechnen, müssen die Maxwellgleichungen in 

Zylinderkoordinaten gelöst werden. Aus dem Amperegesetz folgt unter der Berücksichtigung 

der harmonischen Zeitabhängigkeit: 

 

E 

E iEErot H 

(5) 

t 

mit dem elektrischen Feld E und dem Magnetfeld H. Die Leitfähigkeit und die 

Dielektrizitätszahl hängen von z ab. Aus Symmetriegründen besitzt das elektrische Feld nur 

eine Vertikal- und eine Radialkomponente, die nur von z und r abhängen. Das Magnetfeld 

besitzt nur eine von r und z abhängige -Komponente. 

Damit folgt aus Gl. (5): 



104

H 

 

Er 

(6a,b) 

z 

1 r 

H 

E z 

r r 

Aus dem Induktionsgesetz: 

B 

rotE 

t 

folgt: 

(7) 

E 

z E 

r 

i 

0 H 

(8) 

r 

z 

 

Durch Einsetzen von (6a) und (6b) in (8) erhält man eine entkoppelte Gleichung für H: 

1 

rHzzH i 

H 

1 

r r 

0 

(9) 

r 

 

 

wobei die Schreibweise r angewandt wurde. 

r 

Der erste Term in Gl. 9 legt eine Trennung der Variablen mit Hilfe der Besselfunktion 1. 

Ordnung mit der Wellenzahl u nahe: 

r, zfz, 

uJur 

H 1 

(10) 

denn die Besselfunktion erfüllt die Bessel’sche Differentialgleichung: 

ur r J1 

r 

2 

r J1 

1 

2 

r 

so dass mit (10) folgt: 

2 

ur J uru J ur 2 

rHuH 1 

1 

r r r 

1 

 

(12) 

 

Bei dieser Strategie besteht eine Analogie zur Fouriertransformation, bei welcher z.B. eine 

zweifache zeitliche Ableitung nach Transformation in den Frequenzbereich mit der Funktion 

e it zu einer Multiplikation mit – 2 führt. Entsprechend führt hier der Differentialoperator im 

1. Term in Gl. (9) zu einer Multiplikation mit –u 2 . Die Lösung von (9) lässt sich folglich 

darstellen als: 

z, uJurdu 

H r, 

z) 

f 1 

 

( 

(11) 

(13) 

0 

Die Wahl der Besselfunktion 1. Ordnung ergibt sich daraus, dass aus Symmetriegründen H 

bei r=0 verschwinden muss, was von J1 erfüllt wird, aber nicht von J0. Aus dem 

Amperegesetz (6a und 6b) ergeben sich damit direkt die Gleichungen für die Komponenten 

des elektrischen Feldes: 



105

z, u 

1 

f 

Er ( r, 

z) 

J1 

z 

1 

E z ( r, 

z) 

u 

f 0 

 

 

0 

 

0 

urdu z, uJurdu 

Zur Bestimmung von f(z,u) wird zunächst Gl. (13) herangezogen. Durch Einsetzen in (9) sieht 

man unter Benutzung von (12), dass die Funktion f(z,u) die Gleichung 

(14) 

(15) 

1 2 

z z f f 

 

 

erfüllen muss, mit 

(16) 

2 

2 

i 0 

u 

(17) 

4.2 Bestimmung von f(z,u) 

Gleichung (14) muss unter der Berücksichtigung der Randbedingungen an den 

Schichtgrenzen und der Quellbedingung gelöst werden. Die Quelle wird durch einen Sprung 

der Vertikalkomponente des elektrischen Feldes an der Scheibe beschrieben: 

r 

E z 

wobei 

 

q 

r 

 

 

(18) 

 

0 

die Differenz der Werte unmittelbar oberhalb und unterhalb der Scheibe, also den 

Sprung des Funktionswertes, kennzeichnet. 

 

 

 

Ez0Ez0 

E (18a) 

 

Um aus (18) eine Bedingung für f(r,z) abzuleiten, transformien wir sie in den 

Wellenzahlbereich mittels Gl. (15), aus der folgt: 

 

1 

 

 

0 

 

 

( r, 

z) 

ufz, 

u 

J ur E z 

 

0 

r 

q 

, 0 r a 

0 

du 

0, 

r a 

 

 

Die Ladungsdichte q(r) läßt sich mittels der Hankeltransformation in den Wellenzahlbereich 

transformieren: 

q~ 

 

0 

0 

u uqrJurdr 

(19) 

(20) 

Mit q u ~ als der Ladungsdichte im Wellenzahlbereich. 

Dementsprechend ist q(r) ist darstellbar als: 

q 

 

 

0 

0 

r uq~ 

u J urdu (21) 

Durch Einsetzen von (21) in (19) wird klar, dass 



106

0 

f z, u 

q~ 

u (22) 

0 

d.h.die im Raumbereich formulierte Randbedingung (18) transformiert sich gemäß (22) in den 

Wellenzahlbereich. 

Nach der Formulierung der Randbedingungen wird nun die Differenzialgleichung für f gelöst. 

Aus der Form von Gleichung (16) ergibt sich direkt, dass die Lösungen Funktionen der Form 

z 

e 

sind, wobei berücksichtigt werden muss, dass im unteren Halbraum und in der Luft 

unterschiedlich sind. Daraus ergibt sich folgender Ansatz für die Funktion f(z,u): 

f 

z, u 

wobei 

0 Ae 

 

0z 

 

Ae 

 

 

Ce 

 

z 

 

 

Be 

 

z 

1 

Be 

, 

 

z 

 

z 

0 

, 

0 

, 

0 z d 

z d 

z 0 

(23a,b,c) 

2 

2 

2 

2 

0 i0 0 

u und 1 i 0 

1 

u 

(24a,b) 

die Parameter in Luft und im unteren Halbraum sind. 

Die Vorzeichen der Exponenten in den Ansatzfunktionen in (23) ergeben sich jeweils aus der 

Forderung, dass f(z,u) im Unendlichen sowohl für z0 verschwinden muss. 

Die Randbedingungen an Schichtgrenzen ergeben sich aus den Stetigkeitsbedingungen für die 

elektromagnetischen Felder. Da die Horizontalkomponenten von E und H an Schichtgrenzen 

1 f 

stetig sind, folgt mittels (13) und (14), dass f und stetig sein müssen. 

z 

Damit und mit der Sprungbedingung für f (Gl. (22)) lassen sich nun die Konstanten A,B und C 

in Gl. (23) berechnen. Beispielsweise folgt aus (23a,b), dass 

f 

z 0 

_ B A 

z0 A B 

f 

 

und damit für den Sprung von f bei z=0: 

 

 

 

fz, u 

f z0fz02A (25a,b) 

(26) 

und mit (22) erhält man hieraus für A: 

0 

A q~ 

u (27) 

2 0 

Die Bestimmung von B und C aus den Stetigkeitsbedingungen erfolgt analog, ist aber 

komplexer und wird hier nicht im Einzelnen ausgeführt. Man erhält folgendes Endergebnis 

für f: 

f 

 

2 

0 z, u 

q~ 

u 0 

 

 

e 

 

 

e 

 

T 

 

0 z 

0 z 2 

d 

Rue 

0 z 

0 z2d Rue 

, 

1 

zd 

0d 

ue e , 

mit Reflektions-und Tranmissionsfaktor 

, 

z 0 

0 z d 

z d 



107 

(28a,b,c)

R 

T 

u u 

 

0 

u11u0 u11u0 2 

0u1 

u11u0 0 (29) 

(30) 

 

0 

Mit (28-30) und (13-15) lassen sich dann alle Feldkomponenten berechnen, wobei für die 

Bestimmung der Ladungsdichte nur die Gleichung für Er im Bereich zwischen Halbraum und 

Scheibe benötigt wird. Im Folgenden wird die Näherung 0=u verwendet. Im Vakuum ist 

nämlich 

2 

2 2 2 

2 2 

0 u 

0 

0 u u 

(24c) 

2 

c 

Die relevanten Wellenzahlen u ergeben sich aus der Dimension des Messystemes, welches bei 

den hier berücksichtigten Frequenzen in jedem Fall klein ist gegen die elektromagnetische 

Wellenänge im Vakuum. Es ist also u c und damit der 1. Term auf der rechten Seite 

vernachlässigbar. 

Die Gleichung für Er ergibt sich aus (28b) und (14), wobei die Ableitung von f nach z einen 

Faktor u unter dem Integral ergibt: 

E 

u 

z 

uz2d 

ueRueJurdu 0 z d 

 

1 

r ( r, 

z) 

uq~ 

1 

2 

0 0 

4.3 Bestimmung der Ladungsdichteverteilung 

Zur Bestimmung der Ladungsdichteverteilung wird wir oben erläutert gefordert, dass die 

Radialkomponente des elektrischen Feldes auf der Scheibe verschwindet. Benötigt wird also 

das Feld bei z=0: 

E 

1 

 

rz0uq~ u1Ru , 

2u 

d 

e Jurdu r 1 

2 

0 0 

Die Idee ist nun, eine Ladungsverteilung q(r) zu suchen, so dass Er überall verschwindet. 

Damit lässt sich Gleichung (32) im Prinzip in ein Gleichungssystem überführen. Setzt man 

die Transformation der Ladungsdichte (Gl. 20) in (32) ein, so erhält man: 

1 

2 

a 

 

0 0 0 

sq 

2u 

d 

s J s u1R 

u e Jurduds 0 

0 

1 

Dabei wurde die neue Variable s eingeführt, die ebenso wie r von 0 bis a läuft, allerdings 

verschieden von r sein muss, da ja das elektrische Feld bei r von der gesamten 

Ladungsdichteverteilung abhängt. Definiert man nun die Funktion: 

F 

 

sr u 1 

Ru 

, 

0 

2u 

d 

e JusJurdu 0 

1 

(31) 

(32) 

(33) 

(34) 

so kann man Gl. (33) schreiben als: 

1 

2 

0 

a 

 

0 

s q 

s Fs, 

r 

ds 0 



108 

(35)

Die Funktion F(s,r) lässt sich nach Gl. (34) für jedes s und r direkt durch Integration über u 

berechnen. Die Scheibe wird also geeignet diskretisiert, und mit den diskreten Werten für s 

und r erhält man eine Matrix F . Gleichung 35 wird dann zur linearen Gleichung 

F q 0 

(36) 

in der die Einträge von q die unbekannte Ladungsdichteverteilung darstellen. Durch 

Gleichung (36) ist q allerdings noch nicht vollständig bestimmt, da sie die triviale Lösung 

q 0 besitzt. 

Um eine endliche Ladungsdichte zu erhalten, benötigt man eine Gleichung für das Potential 

der Scheibe. Eine Möglichkeit besteht darin, ein aus 2 identischen Scheiben bestehendes 

System zu betrachten (Abb. 3). 

Abbildung 3: Geometrie des aus zwei identischen Scheiben aufgebauten Sendesytemes. Der 

Abstand der Mittelpunkte ist L, der Radius der Scheiben a. 

Die Integration von Er entlang der Verbindungslinie der beiden Scheibenmittelpunkte ergibt 

die angelegte Spannung U. Da Er=0 auf den Scheiben, gilt: 

LaLa 

Er0ELr, 0dr 

2 E r, 

r 

r 

U , 0 dr 

(37) 

a 

a 

r 

Er(r,0) wurde in Gl. (32) berechnet und lässt sich direkt einsetzen. Die Integration über r kann 

man ausführen, und man erhält: 

U 2 

1 

 

 

1 

 

 

La 

 

 

0 0 

 

 

0 0 

 

a 

uq~ 

q~ 

1 

2 

0 0 

uq~ 

u1Ru 2u 

d 

e Jur u1Ru L 

a 

2u 

d 

e J1ur 2u 

d 

e J uaJuLa u1Ru 

 

a 

 

drdu 

 

du dr 

du 

0 

1 

0 

Um eine explizite Diskretisierung definieren zu können, wird die Ladungsdichte wieder 

mittels Gl. (20) im Raumbereich aufgeschrieben. Fasst man alle Terme mit u zusammen, so 

erhält man: 

1 

U 

 

1 

 

 

mit 

a 

 

0 0 

a 

 

0 0 0 

sq 

s J usds 1 

R 

u 

0 

sq 

s Gds 

s 

2u 

d 

e J uaJuLa 

0 



109 

0 

du 

(38) 

(39)

G 

 

 

0 

2u 

d 

e JusJuaJuLa s R 

u 

0 

du 

1 (40) 

0 

0 

Gleichungen (39) und (40) werden wiederum durch Diskretisierung der Scheibe in eine 

Gleichung der Form 

q G U 

(41) 

umgesetzt. 

Gleichung (41) ist die inhomogene Bedingung, die nötig ist, um die triviale Lösung q 0 

auszuschließen und eine vom Potential abbhängige Ladungsdichte zu erhalten. Man wählt 

also ein beliebiges U und erhält aus der Lösung von (36) unter der Bedingung (41) eine 

Ladungsdichteverteilung q(r). Die Gesamtladung erhält man mit Gl. (3), und die Kapazität 

aus Gl. (4). 

Für ein aus zwei Scheiben bestehendes System gilt die Lösung nur in hinreichendem Abstand 

der Scheiben zueinander, da die gegenseitige Beeinflussung der Ladung auf den beiden 

Scheiben hier nicht berücksichtigt wurde. Eine quantitative Abschätzung dieses Effektes 

wurde bisher nicht vorgenommen. Betrachtungen mit halbkugelförmigen Elektroden im 

Gleichstromfall legen nahe, dass die vernachlässigten Terme von der Ordnung (a/L) 4 sind, so 

dass die Näherung schon bei geringen Elektrodenabständen gut funktioniert. 

Die berechnete Kapazität C der Elektrode ist komplex, da der Reflektionsfaktor (Gl. 29) 

komplex ist. Aus ihr lässt sich mit 

1 

Z 

iC 

die komplexe Impedanz der Elektrode, bzw. deren Betrag und Phase berechnen. 

5 Ergebnisse 

Um die Genauigkeit der Lösung zu bewerten, wurden die Ergebnisse mit einer analytischen 

Lösung für eine Kugelelektrode verglichen, die von Hördt (2007) vorgestellt wurde. 

Abbildung 4 zeigt die Geometrie und die Parametrisierung. Für die mittlere Schale mit Radius 

r1 wird hier Vakuum gewählt werden, mit 1=0 und 1=0 (Permitticität des Vakuums). 

Abbildung 4: Geometrie der Kugelelektrode. Eine ideal leitende Elektrode mit Potential V 

und Radius r0 ist in eine Kugelschale mit Radius r1 eingebettet. 



110

Die Impedanz der Elektrode ergibt sich dann zu: 

* * 

2 2 r1 

1 

* * 

1 

 

1 1 r0 

Z 

* * 

4 

r0 

1 2 r1 

* 

1 r0 

wobei 

* 

i 

 

 

 

 

 

 

In Abbildung 5 wird der Betrag der Impedanz der Scheibenelektrode mit der einer 

Kugelelektrode verglichen. Die Radien wurden so gewählt, dass die Oberfläche der Kugel 

gleich der einseitigen Fläche der Scheibe ist. Bei der Kugelelektrode wurde für die mittlere 

Schale die Werte für Vakuum eingesetzt, der Abstand entspricht der Dicke der mittleren 

Schale. 

Für mittlere Abstände stimmen die Impedanzen der Kugelelektrode und der 

Scheibenelektrode überein, bei großen und kleinen Abständen sind die Impedanzen 

unterschiedlich, was auch so zu erwarten ist. Der Grenzwert großer Abstände entspricht der 

Impedanz der Elektrode im Vakuum. Die Impedanzen beider Elektroden in Abb. 5 

konvergieren gegen den jeweiligen Grenzwert. 

Abbildung 5: Impedanzbetrag der kapazitiven Elektrode gegen Abstand der Elektrode zum 

Medium für verschiedene Leitfähigkeiten des Mediums. Durchgezogene Linie: 

Kugelelektrode mit Radius 0.05m. Gestrichelte Linie: Scheibenelektrode mit Radius 0.1m. 

Die Frequenz ist f=10 kHz, die relative Permittivität des Untergrundes ist in beiden Fällen 

r=4. 

Für die Kugel mit Radius r0 beträgt dieser (Smythe, 1968): 

(42) 

(43) 

1 

Z 

4 

i 

0 r0 

(44) 

und für eine Scheibe mit Radius a: 



111

1 

Z (45) 

8i 

0 a 

Wenn a=2r0, wie für die Rechnung aus Abb. 5 der Fall, entspricht die Gesamtfläche der 

Kugel der einseitigen Fläche der Scheibe. Dann ist die Vakuumimpedanz der Scheibe etwas 

kleiner, weil im Vakuum beide Seiten der Scheibe gleich wirksam sind. 

Für kleine Abstände ist der Vergleich von der Leitfähigkeit des Untergrundes abhängig. Bei 

moderaten Leitfähigkeiten (rote und grüne Kurve) konvergiert der Impedanzbetrag gegen den 

Grenzwert der galvanischen Ankopplung, also den Fall, dass die Scheibe aufliegt, bzw. die 

Kugel direkten Kontakt zum leitenden Medium hat. Der Grenzwert ist für die Kugel 

1 

Z (46) 

4 

r0 

und für die kreisförmige Scheibe 

1 

Z (47) 

4 

a 

wobei die Gleichstromleitfähigkeit ist. 

In diesem Fall liefert die Scheibe bei gleicher Oberfläche (mit a=2r0) die etwas größere 

Impedanz. Eine Gleichheit ist hier nicht zu erwarten, da nicht nur die Fläche wichtig ist, 

sondern auch die Stromverteilung im Medium. Bei sehr hohen Leitfähigkeiten in der 

Größenordnung von Metallen (blaue Kurve) wird der Grenzwert auch für extrem kleine 

Abstände noch nicht erreicht. Bei =0 (schwarze Kurve) sind nur die Verschiebungsströme 

(mit r=4) zur Ankopplung wirksam. Die Scheibe hat eine etwas höhere Impedanz verglichen 

mit der Kugel. 

Insgesamt verhalten sich die Kurven wie erwartet. Im mittleren Abstandsbereich ist nur die 

Ankopplungsfläche relevant und die Impedanzen von Kugel und Scheibe stimmen überein. 

Bei sehr großen und sehr kleinen Abständen werden jeweils die analytischen Grenzwerte 

erreicht, die für Kugel und Scheibe unterschiedlich sind. 

Der Verlauf der Impedanz in Abbildung 5 hat zwei wichtige Konsequenzen. Zum Einen 

nimmt die Impedanz stetig als Funktion der Höhe zu. Dies schließt den Grenzwert einer 

galvanisch gekoppelten Elektrode ein. Das bedeutet, dass eine kapazitiv gekoppelte Elektrode 

niemals eine geringere Impedanz haben kann, als eine galvanisch gekoppelte, aufliegende. 

Zum Anderen ist der Übergang von der aufliegenden zur abgehobenen Elektrode stetig. Dies 

könnte der Intuition widersprechen; man würde evtl. einen Sprung der Impedanz zwischen 

aufliegender und abgehobener Impedanz erwarten. 

Um das beobachtete Verhalten zu verstehen, ist in Abb. 6 die Impedanz in Real-und 

Imaginärteil aufgespalten dargestellt, mit anderem Abstandsbereich. Der Realteil (Mitte) der 

Impedanz ist für sehr große und sehr kleine Leitfähigkeiten verschwindend gering bzw. 

identisch null und wird nicht mit dargestellt. Bei moderaten Leitfähigkeiten (grüne und rote 

Kurve) wird die Impedanz durch den Realteil dominiert. Bei extrem niedriger und bei extrem 

hoher Leitfähigkeit überwiegt der Imaginärteil. 

Dieses Verhalten lässt sich verstehen, wenn man die Gesamtimpedanz näherungsweise als 

Reihenschaltung zwischen einem kapazitiven Anteil und einem Erdungswiderstand betrachtet. 

Der kapazitive Anteil Zc entspricht der Überwindung des Raumes zwischen Boden und Luft 

und ist rein imaginär, der Erdungswiderstand Ze ist komplex und entspricht dem 

Ankopplungswiderstand der aufliegenden Platte. Man kann daher näherungsweise schreiben: 



112

d 

1 

Z Z c Z e 

(48) 

2 

i 

0 

a 4ai01 

Zunächst einmal erklärt das Modell, warum der Übergang zwischen aufliegender und 

abgehobener Platte stetig ist und kein Sprung auftritt. Wenn der Abstand d0, beginnt der 2. 

Term zu dominieren und „übernimmt“ stetig die Ankopplung. Allerdings ist in der Abbildung 

zu erkennen, dass der Übergang bei extrem kleinen Abständen erfolgt, die sogar unterhalb 

eines Atomdurchmessers liegen können. In der Praxis wird der stetige Übergang in der Regel 

also nicht zu sehen sein, sondern als Sprung erscheinen. 

Abbildung 6: Betrag der Impedanz (oben), Realteil (mitte) und Imaginärteil (unten) für die 

Scheibe für dasselbe Modell wie in Abb. 5. Der Realteil der Impedanz (mitte) für =0 ist 

identlisch null und nicht darstellbar, der Realteil für die sehr gut leitende Platte ist extrem 

klein und wird nicht dargestellt. 



113

Das Modell aus Gl. (48) erklärt auch die Zerlegung der Impedanz in Real-und Imaginärteil. 

Bei sehr kleiner Leitfähigkeit und kleinem Abstand dominiert der Imaginärteil der Impedanz, 

bei moderater und hoher Leitfähigkeit dominiert der Realteil. Bei sehr hoher Leitfähigkeit 

wird der Abstand, in dem der 1.Term vernachlässigbar ist, in der Abbildung nicht erreicht und 

es dominiert immer noch der rein imaginäre 1. Term die Gesamtimpedanz. 

6 Schlussfolgerungen 

Es wurde ein Programm entwickelt, um die Impedanz einer kreisförmigen Scheibe über einem 

homogenen Halbraum zu berechnen. Das Verfahren beruht auf einer vollständigen Lösung 

der Maxwellgleichungen. Es verwendet eine Näherung, bei der angemommen wird, dass der 

Radius der Scheibe klein ist gegen die elektromagnetische Wellenlänge. Die Näherung 

verliert bei sehr hohen Frequenzen ihre Gültigkeit, ist jedoch beispielsweise für einen Radius 

0.1m und eine Frequenz von 1 MHz vollkommen unproblematisch. Das Programm wurde 

durch Vergleich mit einer analytischen Lösung für eine Kugelelektrode und durch analytische 

Grenzwerte für große und kleine Abstände verifizert. 

Der Übergang zur Impedanz einer aufliegenden Elektrode erfolgt stetig als Funktion des 

Abstandes zwischen Elektrode und Halbraum. Die Impedanz der aufliegenden Scheibe ist 

immer kleiner als die der angehobenen. Dies bedeutet, dass die Übergangsimpedanz nicht 

durch eine kapazitive Elektrode gegenüber einer gleich gebauten, galvanischen verringert 

werden kann. Der galvanische Anteil der Impedanz ist auch bei kapazitiver Ankopplung mit 

enthalten. 

In der Praxis kann es dennoch sinnvoll sein, kapazitive Elektroden statt galvanische zu 

verwenden, also den galvanischen Kontakt durch Isolierung oder Anheben zu verhindern. Bei 

Aufliegenden Elektroden ist die Impedanz sehr schwer zu kontrollieren, da die Auflagefläche 

stark variieren kann. Dies kann dazu führen, dass die Impedanz um Größenordnungen 

schwankt, da sie sehr stark als Funktion des Abstandes variiert und die aufliegenden Teile die 

Ankopplung dominieren können. Eine Isolierung stabilisiert die Impedanz und verhindert 

starke Schwankungen, was für die Messung von Vorteil sein kann. 

7 Referenzen 

Hördt, A., 2007, Contact impedance of grounded and capacitive electrodes, in: Ritter, O., 

Brasse, H., Protokoll zum 22. Kolloquium „Elektromagnetische Tiefenforschung“, 164-173. 

Kuras, O., Beamish, D., Meldrum, P.I., and Ogilvy, R.D., 2006, Fundamentals of the 

capacitive resistivity technique. Geophysics, 71, G135-G152. 

Smythe, W., 1968. Static and dynamic electricity, McGRaw-Hill. 



114

H2O 

 

 

 

 

 

 

H2O 

 

H2O 

 

 

 

 

 

 

 

H2O 

 

 

 

 

 

 

 

 

 

 

 

H2O 

 

 

 



115

5mm 

 

 

 

 

 

 

±0.5mm 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



116

EG EB 

EN EB 

dx =50m 

 

By 

 

 

 

 

 

(EG) 

(EN) 

 

 

(EB) 

 

 

EGel 

Enorm 

 

(BY ) 

 

EGel Enorm BY 

 

 

 

16 2/3Hz 50Hz 

 

 

 

 

 

 

 

 

 

0 − 250Hz 

 

 

 



117

EGel Enorm EnormEGel 

EGel/BY 

Enorm/BY EGel Enorm 

 

0 − 250Hz 

EGel Enorm 

 

Txy = 

< |Y | > 

X, Y EGel, Enorm, BY 

EGel = TxyEnorm 

Enorm = TxyEGel 



118

204Hz 

8Hz 

 

 

EGel = TxyBy Enorm = 

TxyBy 

ρa 

EGel/BY Enorm/BY 

 

204Hz 1Hz 

 

 

 

H2O 

 

 

 

 

 

• 

• 

 

 



119

Attitude Algorithm Utilised in Mobile Geophysical 

Measuring Systems 

Johannes B. Stoll, Celle 

Christopher Virgil, Institut für Geophysik und extraterrestrische Physik, TU-Braunschweig 


Accurate real-time tracking of orientation or attitude of rigid bodies has wide applications in robotics, 

aerospace, on-land and underwater vehicles, automotive industry, and virtual reality. A quite recent 

application in geophysics is the analysis of the attitude effect of geophysical sensors such as coil 

arrays or magnetometers attached to mobile measuring platforms e.g. helicopters and fixed wing 

airplanes and the correction with respect to the Earth’s reference coordinate frame (Reid etal, 2003, 

Yin and Fraser, 2004). Another field of application is wireline logging with a borehole tool. While 

measuring, the tool spins about its vertical body axis due to the torsion force of the logging cable, 

which results in a disorientation of geophysical sensors. 

In the borehole industry, it is essential to accurately monitor and guide the direction of the drill bit. It is 

also necessary for an oil rig to log the location of its boreholes at a regular frequency such that the oil 

rig can be properly monitored. To determine the location of a drill bit in a borehole, it is necessary to 

know the position and the attitude, which includes the vertical orientation and the North direction. 

In prior art systems, a magnetometer is used to determine the magnetic field direction from which the 

direction of North is approximated. Triple component magnetometers were widely used to sense the 

tool rotation during a log run. However orientation via magnetometers is subject to restrictions. The 

employing of magnetometers in boreholes drilled into strongly magnetized formations such as oceanic 

crust, volcanoes and ore deposits, make it very difficult to utilize the Earth’s magnetic field as a 

reference (Steveling et al, 2003). First, these systems must make corrections for magnetic 

interference and use of magnetic materials for the drill pipe. Second, systems that rely only on 

magnetometers to determine North can suffer accuracy degradation due to the Earth's magnetic field 

variations. Third, a magnetometer alone cannot give an unequivocal measurement of a set of sensor 

attitude. Measurements made with such a sensor define the angle between the Earth’s magnetic field 

and a particular axis of the sensor. However, this axis can lie anywhere on the surface of a cone of 

semi-angle equal to that angle about the magnetic vector. Hence, an additional measurement is 

required to determine attitude with respect to another fixed reference frame. 

In order to determine the direction of a spinning borehole tool another type of sensor technology 

must be utilised to provide orientation that is independent from the Earth’s magnetic field as a 

reference (Galliot et al, 2004, Stoll and Leven, 2002). 

The problem to be solved consists of a way to sense the attitude of a borehole tool, which are free to 

rotate about any direction. A good compromise between accuracy and sensor size are the fibre optical 

gyros. These devices measure the turning rate about the sensor axis in the tool frame. In this paper an 

algorithm is presented that approaches the attitude determination based on this discrete data. 

2 Principle of Fibre Optical Gyro (FOG) 

Gyroscopes are used in various applications to sense the angular rate of turn about some defined 

axis. The most basic and the original form of gyroscopes make use of the inertial properties of a 

wheel, or rotor, spinning at high speed. The wheel tends to maintain the direction of its spinning axis in 

space due to conservation of the angular momentum vector. These devices are susceptible to 

damage from shock and vibration, exhibit cross-axis acceleration sensitivity and, for the lower cost 

versions, have reliability problems. 

Another type is the vibratory gyroscope. The basic principle of operation of such sensors is that the 

vibratory motion of part of the instrument creates an oscillatory linear velocity. If the sensor is rotated 

about an axis orthogonal to this velocity, a Coriolis acceleration is induced. The acceleration modifies 

the motion of the vibrating element which is an indication of the magnitude of the applied rotation. 

However, this type of sensor tends to produce biases in the region of 1°/s. 



120

Optical gyroscopes use an interferometer to sense angular motion. An optical gyroscope, laser or 

fibre, measures the interference pattern generated by two light beams, traveling in opposite directions 

within a mirrored ring or fibre loop, in order to detect very small changes in motion. This type of 

gyroscope can be subdivided into fibre optical gyro (FOG), ring laser gyro (RLG), and ring resonator 

gyro (PARR). 

In order to keep track on the orientation of the geophysical sensors the utilisation of fibre optical 

gyroscopes are now common in navigation and replace prior art systems like mechanical gyros. 

Important attributes of this new technology are no moving parts, high reliability, stable performance 

and low costs. Many of its components are based on proven technology from the fiber optical 

telecommunications industry. Using optical gyros, inertial navigation is accomplished by integrating the 

output of a set of angular rate sensors to compute the attitude. 

In figure 1 a FOG manufactured by LITEF is shown exemplary. The gyro operates at an optical 

wavelength of 820 nanometers, with a 110 meter coil of elliptical-core polarization maintaining fiber. 

The low coherence reduces unwanted interference between waves reflected from the fusion splices 

used to join the components. 

Fig. 1: Example of the FORS -family (LITEF, Freiburg) (here FORS-6U) 

3 Attitude Computation 

Inertial orientation tracking of borehole tools is based upon the same methods and algorithm as 

those used for aircrafts, ships, and missiles. There is a large quantity of technical literature that 

describes the fundamentals of inertial navigation technology in great detail, e.g., Grewal et al. (2001), 

v. Hinüber (1993), Savage (1998a, b), Stovall (1997). If angular rates of a tool are measured 

constantly with depth, the orientation of the sensors of the tool with respect to inertial space can be 

determined by applying a suitable coordinate transformation. 

A transformation from one coordinate frame to another can be carried out as three successive 

rotations about different axes. The transformation matrix is given by the product of these three 

separate transformations as follows: 

C n 

b 

C C 

C 

(1) 

3 

Various mathematical representations can be used to define the attitude of a body with respect to a 

coordinate reference frame. One of the most common ways of parameterizing the transformation 

matrix is by use of direction cosine matrix (DCM). Other methods of describing rotations are the use of 

Euler Angles and Quaternions. 

The DCM is a 3x3 matrix, the columns of which represent unit vectors in body axes projected along 

n 

the reference axes. Matrix Cb 

describes the transformation from coordinate frame “b” to the frame “n” 

and is written here in component form as follows: 



121 

2 

1

c 

 

c 

 

c 

31 

c 

32 

33 

 

 

 

 

 

11 12 13 

C 21 c22 

c23 

n 

b (2) 

c 

The element in the i th row and the j th column represent the cosine of the angle between the i th axis of 

the reference frame “n” and the j th axis of the body frame “b”. 

When designing a navigation system it is necessary to relate the information from the sensors to a 

navigation coordinate. The coordinate choice for borehole applications is a geographic or navigation 

frame “n” with axes {N, E, D}, (North, East and Down). The inertial measurement unit is mounted on 

the borehole tool constituting a new frame. This is called the body frame “b”, and has axes {X, Y, Z}. 

This frame will be in rotation with respect to the geographic frame. The velocity of this rotation is 

measured by three orthogonal gyros. The transformation matrix that relates “b” and “n” coordinate 

frames propagates with time in accordance with the following equation: 

0 

z y 

 

 

 

n n b 

C b 

b Cb 

nb 

, where nb 

z 

0 

x (3) 

 

 

 

y 

x 

0 

b 

n 

nb is the skew symmetric matrix formed from the elements of the vector b x y z , which 

th th 

represents the turn rate of the body between the i -frame and the (i+1) -frame as measured by the 

gyroscopes in the body frame. In real time applications the integration is implemented with the 

following approximation 

t 

C 

n 

b 

c 

c 

n t t 

C t A 

t 

(4) 

b 

T , 

, 

A t 

A t 

where is the DCM which relates the b-frame at time t to the b-frame at time t . For small 

angle rotations, may be written as follows: 

 

where I is the 3×3 identity matrix and 

0 

 

 

 

 

 

t I A (5) 

 

0 

 

 

 

 

0 

 

in which , and are small rotation angles through which the body-frame has rotated over the 

time interval t about its yaw, pitch and roll axes respectively. If the limit t approaches zero, small 

angle approximations are valid and the order of the rotation becomes unimportant. 

Hence, the minimum sampling time of the gyros is important for obtaining the transformation matrix 

with reasonable accuracy. This interval will be a function of the severity of manoeuvres expected from 

the borehole tool. In many applications the rotation velocity expected is usually less than 25 

degrees/sec. With a sampling time of 100 Hz the maximum angle variation will be less than 0.25 

degree satisfying the small angle approximation. Rotations with faster dynamics will require smaller 

sampling time to compute the transformation matrix appropriately. 

n 

In order to update the DCM Cb 

, it is necessary to solve a matrix differential equation (3). Over a 

single computer cycle, from time tk 

to tk+1, the solution of the equation may be written as: 

k 1 

(6) 

C C exp dt (7) 

k 1 

k 

Provided that the orientation of the turn rate vector remains fixed in space over the update interval, 

we may define: 



122 

t 

t 

k

and 

t 

k 1 

t 

k 

dt 

(8) 

CkAk C C exp 

k 1 

k 

(9) 

Where Ck represents the direction cosine matrix which relates body to reference axes at the k th 

computer cycle, and Ak the direction cosine matrix which transforms a vector from body co-ordinates 

at the k th computer cycle to body co-ordinates at the (k+1) th computer cycle. 

The variable is an angle vector with direction and magnitude such that a rotation of the body frame 

about through an angle equal to the magnitude of will rotate the body frame from its orientation at 

computer cycle k to its position at the computer cycle k+1. The components of are denoted by x, 

y, and z and its magnitude given by: 

and 

 

 

(10) 

2 

x 

2 

y 

2 

z 

0 

z y 

 

 

z 0 

x (11) 

 

 

 

y x 0 

Expanding the matrix exponential function in a power series gives: 

where 

Thus we may write 

A 

k 

2 

3 

4 

 

Ak I 

(12) 

2! 

3! 

4! 

2 

2 2 

y 

x 

 

x 

y 

z 

and which may be written as follows: 

 

 

z 

 

 

2 2 

x 

x 

y 

 

 

3 2 

 

2 2 

4 

 

 

y 

z 

z 

 

 

 

x 

 

 

 

2 2 

 

(14) 

(15) 

I 

2! 

 

2 4 

I 

1 

... 

 

3! 

5! 

 

 

 

 

2 2 

3! 

2 

 

1 

 

2! 

2 

 

4! 

x 

y 

z 

z 

4! 

4 

 

6! 

y 

 

(13) 

2 

... 

 

 

1cos 2 

sin 

Ak I 

(17) 

2 

 

Equation (17) is input in equation (9) that updates the frame at time t to the frame at time t+t. To 

compute the attitude of the tool, first the measured rotation rates are input in equation 17. Then, 

beginning with C0 = I the rotation matrices Ck+1 for each computer cycle k+1 are successively 

computed by equation (9). The tool attitude r in the external frame at the k th cycle results to 

n 

k 

2 

... 



123 

 

 

 

(16)

n 

with the starting orientation . 

r 0 

 

 

(18) 

n 

n 

rk Ck 

r0 

4 Attitude Computation allied to the Göttingen Borehole Magnetometer (GBM) 

The Göttingen Borehole Magnetometer (GBM) contains a triple of FORS-36M sensors, which are 

attached rigidly to the borehole tool. The rotation axes of the sensors are aligned with the body axes of 

the tool, and thereby sense the rotation rate about the vertical axis and the tilting movement about the 

two horizontal axes. Angular rates are output with a sample rate of 1 second. The salient 

specifications of the FORS-36m are the maximum input rotation rate of ±720°/s that allows sensing a 

maximum rotation rate of 2 revolutions per second with a resolution of 9·10 -5 °. Moreover, the 

dimensions of the sensor (53mm x 58mm x 19mm) are small enough to fit to the inner diameter of 

65mm of the GBM. This is important to reduce the overall diameter of the tool and make it applicable 

in narrower boreholes. The bias drift is 6/h (1) and is reduced to

Steveling, E., J.B. Stoll, and M. Leven, 2003. Paleomagnetic age dating from magnetisation and 

inclination studies of the Mauna Kea/Hawaii, Geochem.Geophys. Geosystems 

Stoll, J.B., and M. Leven, 2002. Results of the oriented magnetic logging at Detroit Seamount. In: 

Tarduno, J.A., Duncan, R.A., Scholl, D.W., Proc. ODP, Initial Reports, Vol. 197. Available from 

http://www-odp.tamu.edu/publications/197_IR/197ir.htm. 

Stovall, S.H., 1997. Basic Inertial Navigation, Naval Air Warefare Center Weapons Division, 

http://www.fas.org/spp/military/program/nav/basicnav.pdf 



125

Joint Interpretation of Magnetotelluric and Seismic Models for Exploration of 

the Gross Schoenebeck Geothermal Site 

G. Muñoz, K. Bauer, I. Moeck, O. Ritter 

GFZ Deutsches GeoForschungsZentrum 

Introduction 

Due to the non-uniqueness of the inverse problem, the interpretation of geophysical models in 

terms of geological units is not always straightforward. It is common to use a combination of 

different geophysical methods to obtain the distribution of independent physical properties 

over the area of interest in order to discriminate between the different lithologies or geologic 

units. This kind of studies is usually limited to qualitative comparisons of the different 

models, which may – or may not –support a relation between the parameters in certain areas. 

Quantitative approaches are in general based on empirical relations between physical 

parameters, which often are not of universal applicability. 

The magnetotelluric (MT) and seismic methods resolve the physical parameters electric 

resistivity (ρ) and (seismic) velocity (Vp, Vs) respectively with similar spatial resolution and 

are often used in combination to derive earth models. By looking at both resistivity and 

velocity simultaneously, we can keep the strengths of both methods while avoiding their 

weaknesses. The problem with a joint interpretation is that there is no unique universal law 

linking electrical and acoustic properties. While electrical resistivity in deep sedimentary 

basins is mostly sensitive to the pore geometry and contents , seismic velocity is mostly 

imaging rock matrix properties. However, with a statistical analysis of the distributions of 

both resistivity and velocity, we can find certain areas of the models space where a particular 

relation between the physical parameters holds locally, thus allowing us to characterize this 

region as a particular lithology. In the present work, we use a statistical analysis, as described 

by Bedrosian et al. (2007) in order to correlate two independently obtained models of the 

Groß Schönebeck geothermal test site in the Northeast German Basin. 

Methodology description 

The methodology used in the present paper was described by Bedrosian et al. (2007) and is 

based on a probabilistic approach developed by Bosch (1999), in a sense that diverse 

geophysical parameters are represented as a probability density function (pdf) in the joint 

parameter space. The coincident velocity and resistivity models are first interpolated onto a 

common grid. Therefore, a joint parameter space is built, where each point in the modelled 

area is associated with a velocity – resistivity pair. By plotting one parameter against the other 

in a cross-plot and including the error estimates we can then construct a joint pdf in the 

parameter space. The areas of enhanced probability can be identified with classes represented 

by a certain range of values in both resistivity and velocity. By mapping back these classes 

onto the spatial domain they can be related to certain lithologies and/or geological units. 

In the present work, the resistivity model was interpolated onto the seismic mesh, given that it 

is uniformly spaced and finer than the magnetotelluric mesh. An inverse distance weighted 

interpolation scheme was used, which forms estimates from a weighted average of many 

samples found within a pre-defined area around the point, with decreasing weights with 

distance. 

Each element of this distribution can be interpreted as the outcome of a process defined by a 

probability density function (pdf). Assuming normal error distribution and independence of 

the data, the joint pdf is expressed as the sum of the individual pdfs (pdfi) for each data point, 



126

according to the following expression, with the errors of the resistivity and velocity (δlog(ρi) 

and δVp,i) estimated from the sensitivity matrix and the hit count distribution respectively: 

 

 

 

 

 

 

 

 

 

 

 

The different classes are identified as zones of enhanced probability in the joint pdf crossplot. 

Assuming that the geological units are characterized by uniform physical properties 

normally distributed, each class is defined by a mean point and a covariance matrix 

(representing the ~60 per cent confidence interval ellipse for the peak) in the joint parameter 

space. 

Geophysical models 

The Groß Schönebeck low enthalpy geothermal site, with the well doublet GrSk 3/90 and 

GrSk 4/05, is located in the Northeast German Basin (NEGB). MT data was collected along a 

40 km-long profile centred on the well doublet. The profile consists of 55 stations with a site 

spacing of 400 m in the central part (close to the borehole) of the profile, increasing to 800 m 

towards both profile ends. The period range of the observations was 0,001 to 1000 s. This 

profile is spatially coincident with the seismic tomography profile and most of the stations 

were located at the same places as the seismic shot points. At all sites, we recorded horizontal 

electric and magnetic field components and the vertical magnetic field. 

The resistivity model for the MT profile (Figure 1a) shows a shallow conductive layer 

extending from the surface down to depths of about 4 km, with an antiform-type shape below 

the central part of the profile. At a depth range of 4-5 km two conductive bodies are found, 

separated by a region of moderate conductivity. According to the seismic tomography, which 

shows high velocity values for depths greater than 4 km, a resistive basement was introduced 

a priori in the resistivity model (Muñoz et al., 2010). 

A 40 km long seismic profile was measured coincident with the MT experiment (Figure 1b). 

The objective was to derive a regional 2-D seismic model, which can be combined with the 

electrical conductivity model from the MT data analysis to study the potential reservoir layers 

and overlying sediments. The experimental setup was designed to provide data suitable for 

refraction tomography. 45 explosion shots were fired from 20 m deep boreholes with charge 

sizes of 30 kg. The shot spacing was 800 m on average. The recording instrumentation 

consisted of 4.5 Hz 3-component geophones. These were deployed as a 40 km long receiver 

spread with spacings of 200 m. Each shot was recorded by all receivers. 

The velocity model (Figure 1b) can be divided into three major sequences: The upper section 

(depth range 0-2 km) is characterized by low velocities (2-3.5 km/s) and a strong increase of 

velocity with depth. The section between 2 and 4 km depth shows velocities between 4 and 

4.5 km/s and is characterized by a strong topography on top which is related with salt 

mobility. The third, deepest section is bounded on top by a subhorizontal interface at 4.2 km 

depth and reveals velocities of more than 5 km/s (Bauer et al., 2010). 



127

a) 

b) 

Figure 1: Electrical resistivity model obtained from inversion of the magnetotelluric data 

using a priori information from the seismic velocity model for the deeper part of the model (> 

5 km) (a) and seismic velocity model obtained from (Vp) travel time inversion (b). 

Joint analysis 

In the cross-plot of the probability density function (Figure 2a) we can identify five more or 

less clear peaks, or areas of enhanced probability with respect to the neighbouring region. The 

coloured ellipses in Figure 2a represent the ~60 per cent confidence intervals of the Gaussian 

peaks best fitting the pdf. The clusters were mapped back to the cross section providing a 

depth distribution of the classes along the profile (Fig. 2c). In order to interpret the nature of 

these litho-types, the model is superimposed on the stratigraphy derived from pre-existing 

reflection seismic data and borehole information (Moeck et al., 2008). 

Class 1, the shallowest, is characterised by low velocity (1.8 – 2.7 km/s) and moderate 

resistivity (5 – 70 Ωm) and comprises of unconsolidated sediments. Class 2, with higher 

velocities (2.7 – 3.9 km/s) and lower resistivities (0.5 – 3.5 Ωm) encompasses weak or soft 

rocks with high porosity, which are more conductive because they provide storage for a 

greater volumes of fluids. Class 3 coincides with successions of Middle Triassic to Lower 

Permian. Significantly these successions represent harder brittle rock of limestone and 

sandstone as indicated by increasingly higher velocities (4 – 5 km/s) and resistivities (2 – 15 

Ωm). This class includes also thick salt rock layers (Zechstein) which, however, yield no 

significant variation of resistivity or velocity within the class. Class 4, the deepest one, is 

characterized by the highest velocity and resistivity values (4.7 – 5.5 km/s and around 3000 - 

30000 Ωm). It represents the basin floor, comprising volcanic rock, quartzite and slate. This 



128

class reflects the fact that the magnetotelluric model used seismic a priori information to 

introduce a resistive basin floor. Obviously this causes the very high correlation between 

velocity and resistivity of class 4 in Fig. 2b. Class 5 is characterized by high velocities (4.7 – 

5.5 km/s) but extremely low resistivities (0.1 – 0.7 Ωm). 

Figure 2: Cross-plot of the probability density function in gray-scale plan view (a) and threedimensional 

view (b). Spatial distribution of classes (c). Colours correspond with the ellipses 

in (a) defining the class boundaries. 

It is remarkable that Class 5 is restricted to salt lows where presumably anhydrites of Upper 

Permian age remain after salt movement. These anhydrites have a brittle behaviour and are 

expected to be highly fractured. In this case, an estimation of the resistivity by using Archie’s 

Law (Archie, 1942) for fracture-controlled porosity and assuming a formation fluid salinity of 

260 g/l (Giese et al., 2001), and a reasonable range of porosities and temperatures (15% and 

130ºC) the modelled resistivities of 0.1 – 0.7 Ωm can be explained. High velocities can be 

explained by the high density of anhydrite (2.9 g/cm 3 ). The classes are summarized in the 

Table 1, below. 

Table 1: Resistivity and P velocity of the classes from figure 9. Also included are lithology 

and stratigraphic units. 



129

Conclusions 

MT and seismic data were used to derive independent 2-D models of the electrical 

conductivity and the seismic P velocity around the geothermal research well GrSk 3/90. The 

resulting models were combined in a statistical analysis to determine correlating features in 

both models. The classification method used in this analysis revealed 5 distinct litho-types 

which show up as separate clusters in the underlying geophysical parameter space of Pa and 

VP. 

This study demonstrates the concert of MT, seismic and structural geologic models. Therefore 

the combination of different geophysical methods (MT and seismic) combined with structural 

geological information revealed information which was previously unknown and which could 

not be determined with the individual methods. Clearly, this approach is applicable in other 

areas too and could represent a promising new approach for geothermal exploration. 


This work was funded within the 6 th Framework Program of the European Union (I-GET 

Project, Contract nº 518378). The instruments for the geophysical experiments were provided 

by the Geophysical Instrument Pool Potsdam (GIPP). We wish to thank Paul Bedrosian for 

making his statistical analysis code available to us. 

References 

Archie, G. [1942] The electrical resistivity log as an aid in determining some reservoir 

characteristics. Trans. Am. Inst. Min. Metall. Pet. Eng., 146, 54–62. 

Bauer, K., Moeck, I., Norden, B., Schulze, A., Weber, M. [2010] . Tomographic P velocity 

and gradient structure across the geothermal site Gross Schoenebeck (NE German Basin): 

Relationship to lithology, salt tectonics, and thermal regime. J. Geophys. Res., Submitted. 

Bedrosian, P.A., Maercklin, N., Weckmann, U., Bartov, Y., Ryberg, T., Ritter, O. [2007] 

Lithology-derived structure classification from the joint interpretation of magnetotelluric and 

seismic models. Geophysical Journal International, 170 170, 170 

737-748. 

Bosch, M. [1999] Lithologic tomography: from plural geophysical data to lithology 

estimation. Journal of Geophysical Research, 104, 749-766. 

Giese, L., Seibt A., Wiersberg T., Zimmer M., Erzinger J., Niedermann S. and Pekdeger A. 

[2001] Geochemistry of the formation fluids, in: 7. Report der Geothermie Projekte, In situ- 

Geothermielabor Groß Schönebeck 2000/2001 Bohrarbeiten, Bohrlochmessungen, Hydraulik, 

Formationsfluide, Tonminerale. GeoForschunsZentrum Potsdam. 

Moeck, I., Schandelmeier, H., Holl, H.G. [2008] The stress regime in Rotliegend reservoir 

reservoir of the Northeast German Basin. International Journal of Earth Sciences (Geol. 

Rundsch.), doi:10.1007/s00531-008-0316-1. 

Muñoz. G., Ritter, O., Moeck, I. [2010] A target-oriented magnetotelluric inversion scheme 

for characterizing the low enthalpy Groß Schönebeck geothermal reservoir. Geophysical 

Journal International, submitted. 



130

Magnetotelluric measurements to explore for deeper structures of the Tendaho 

geothermal field, Afar, NE Ethiopia 

Ulrich Kalberkamp 

Bundesanstalt für Geowissenschaften und Rohstoffe (BGR), Hannover, Germany 

Email: ulrich.kalberkamp@bgr.de 

Introduction 

In regions with high heat flow, like at volcanically active plate margins, high total 

thermodynamic energy is accumulated in the so called high enthalpy resources. The East 

African Rift System is one of the privileged areas to yield numerous sites for potential 

geothermal energy extraction including power generation. Along the Ethiopian part of the rift 

high temperature geothermal resources are associated with zones of quaternary tectonic and 

magmatic activity. Including the Afar depression at least 120 independent geothermal systems 

have been identified since the 1970s (UNEP 1973) about 24 of them are judged to have high 

enthalpy potential. To explore for these resources up to a pre feasibility stage a range of 

geoscientific methods is used in a defined sequence starting with regional reviews and remote 

sensing followed by geologic, hydrologic, geochemical and geophysical surveys. 

The applied geophysical methods usually comprise temperature measurements (gradient 

boreholes), seismology, magnetics and resistivity methods, including Magnetotellurics (MT). 

Geothermal surface manifestations like hot springs, fumaroles, geysers and the associated 

geological and geochemical settings are indicating the presence of a geothermal reservoir. 

Particularly resistivity methods 

may be used for delineating the 

lateral and depth extensions of 

such potential reservoirs. The 

MT method is frequently used 

for this purpose since it easily 

covers the necessary 

exploration depth down to 

approximately 10 km. 

In the following paper MT data 

and interpretation is presented, 

showing the already known 

shallow reservoir of the 

Tendaho geothermal field and 

its so far unknown deep 

structure, possibly feeding the 

shallow reservoir. 

Figure 1: Survey area at the SE end of the Hararo and Dabbahu 

magmatic segments. TGD = Tendaho-Goba’ad Discontinuity 

(after Ebinger et al. 2008). 

Survey area and tectonic 

setting 

The Tendaho geothermal field 

is located in the Afar 

depression (NE Ethiopia), at or 

very close to the assumed triple 

junction formed by the Red Sea, 

Gulf of Aden and East African 

rift arms. The extension of the Manda-Hararo axial rift zone in its south-easterly strike 

direction ends up at the Tendaho geothermal system (figure 1). The Red Sea and Aden rifts 



131

are characterised by oceanic crust. The Afar triple junction is therefore a zone where thinned 

continental crust of the Main Ethiopian rift joins with crust of oceanic character (Barberi et al. 

1972). 

Within this area of active extensional tectonics several geothermal manifestations can be 

observed. Quaternary faulting and volcanism formed chains of fissural flows, basaltic cones 

and stratovolcanoes, usually accompanied by shallow seismicity and positive gravity 

anomalies. These active magmatic segments are comparable to slow spreading mid oceanic 

ridge segments and are thought to form new igneous crust by dyke like intrusions as 

demonstrated in the recent Dabbahu rift events (since 2005 up to now) just 80 km NW of the 

survey area. A previously mapped magmatic segment within the Manda-Hararo rift zone had 

been ruptured. Earthquake recordings indicated a 60 km long and about 8 m wide dyke 

intrusion (Ebinger et al. 2008, figures 8 & 9). 

Tendaho geothermal field 

The Tendaho geothermal field has been 

investigated in detail since the 1980s. 

Geological, geochemical as well as magnetic, 

seismological and resistivity data (DC 

soundings) were acquired by an extensive 

Ethiopian-Italian cooperation (Aquater, 1996). 

Based on this results, six exploratory wells had 

been drilled, three of them hitting a production 

horizon at approx. 300 m depth yielding steam 

temperatures above 250 °C (figure 2). Additional 

gravity and magnetic data had been acquired 

recently by Lemma and Hailu (2006) to delineate 

fractured zones which could serve as potential 

pathways for hydrothermal 

fluid flow from a deeper 

reservoir. 

To further investigate the 

proposed deep reservoir 

and/or heat source, deep 

reaching resistivity 

methods had to be applied. 

Due to the generally low 

resistivities the penetration 

depths of the DC 

soundings were limited to a 

few hundred meters. To 

extend this depth of 

exploration the MT method 

has been applied by BGR 

in collaboration with the 

Geological Survey of 

Ethiopia (GSE) during a 

field survey in 2007 (figure 

3). To reach the desired 

exploration depth of about 5 

km a frequency range from 

Figure 2: Production test of well TD5 (at well 

head: T >250 °C, p > 18 bar). The well is located 

inside the MT survey area. 

L1 

L2 

Kurub 

Figure 3: Survey area Tendaho geothermal field (red frame) projected onto 

satellite images (google earth). Red triangles = MT stations, blue squares = 

TEM stations. Line nos. L1, L2, L3 and L97 refer to MT lines in SE-NW 

bearing. TD5 = productive exploratory well. Yellow line = main road to 

Djibouti. 



132 

TD5 

 

L97 

L3

10 kHz to 0.01 Hz (100 s) has been acquired. 

MT resistivity signature 

Due to alluvial and lacustrine infill of the Tendaho graben apparent resistivity curves show 

generally values below 10 Ohm*m, even at high frequencies. A typical sounding curve is 

shown in figure 4. 

The minimum is 

reached at approximately 

4 Hz with 

apparent resistivities 

just below 1 Ohm*m. 

With decreasing 

frequency the 

apparent resistivity 

rises again. Source 

signal was generally 

quite low, especially 

within the dead band 

region ranging from 

approximately 1 to 

0.1 Hz (1 to 10 sec.). 

Figure 4: Typical sounding curve. Apparent resistivities (top) and phases Nonetheless 16 hrs 

(bottom). Due to low signal strength in the dead band from about 1 to 0.1 Hz of recording time 

unstable estimation especially of phase values, resulting in increased error bars. 

proved to be 

sufficient to yield 

acceptable estimates 

of the impedance 

tensor, using mainly 

single site processing. 

This apparent resistivity pattern, which is also reflected in the resistivity models (see below), 

is indicative for high temperature geothermal reservoirs (figure 5, see also e.g. Kalberkamp 

2007) where the resistivity low is interpreted as the clay cap while the increasing resistivities 

below the clay cap point to the core of the reservoir and represent a possible drilling target. 

In the 2d inverted resistivity sections, exemplarily 

shown for profile L1 in figure 6, this resistivity 

pattern can be seen quite clearly. Although 

resistivities are generally low, they show signatures 

typical for hydrothermal alteration halos (see e.g. 

Johnston et al. 1992, Kalberkamp 2007) and (partly) 

molten magma intrusions at depth below 4 km. 

Taking the Dabbahu rift events into account it seems 

to be likely that the heat source for the geothermal 

reservoir is formed by magma intrusions along dyke 

like fracture zones as it is suggested by our 

interpretation of the MT data. Areas with high 

resistivities (>300 Ohm*m) may be associated with 

basalts from the Afar Stratoid Series, constituting the 

borders of the Tendaho graben structure. 

Figure 5: Schema of a generalised 

geothermal system. The smectite cap 

formed exhibits resistivities in the 

range of 2 Ohm*m, the mixed layer 

around 10 Ohm*m (modified after 

Johnston et al. 1992). 



133

Figure 6: 2 d inverted resistivity section (L1). Lateral extension is 27 km; vertical depth covers 8 km. 

Interpretation and recommendations 

As has been shown for profile L1 exemplarily the magnetotelluric soundings show in their 2dimensional 

inverted resistivity sections regions with resistivities as low as 2 Ohm*m, 

especially in near surface layers along profiles L1, 2, and 3 as well as at greater depth (below 

5 km) in profiles P1, 3, and 97. When using the 2d MT sections to compile resistivity maps 

for constant elevations each, thus based on the inverted resistivities, we get a general view of 

the lateral resistivity structure as presented in figure 7 for selected elevations. 

Figure 7: Resistivity maps of survey area as covered by red frame in figure 3, resistivity range 2 (red) – 2048 

(blue) Ohm*m. Left: at 200 masl (150 m below surface). Shallow low resistive layer (red) due to sedimentary 

infill. The sediments are up to 1 km thick. Centre: at 1000 mbsl (1350 m below surface). Slight increase of 

resistivity (> 10 Ohm*m) possibly due to mixed layer clays and advancement towards deeper reservoir (blue 

circle). Right: at 9000 mbsl (9350 m below surface). Resistivity drop below 2 Ohm*m along NW-SE 

trending feature (partly molten magma dyke?). This may form the deep heat source feeding the shallow 

geothermal reservoir. 

At greater depth of around 7 km a 

resistivity anomaly below 2 Ohm*m 

appears elongating in NW-SE direction. 

This direction coincides with the strike 

direction of the Tendaho graben and rift 

structures further to the NW, up to the 

Dabbahu rift and Boina vent, where lava 

ascended along a fault system, almost 

reaching the surface (figure 8). Therefore 

it seems likely, that the low resistive 

structures at greater depth are caused by 

lava filled fracture zones. (figure 7 right). 

Ebinger et al. (2008) have presented a 

working model of the Dabbahu magmatic 

Figure 8: Volcanic vent, created during 2006 eruption 

event (Photo by J. Rowland). 



134

Figure 9: Working model of the Dabbahu magmatic system as 

presented by Ebinger et al. (2008). Pink ellipses = shallow magma 

chambers, connected to assumed lower crust/upper mantle feeding 

zones. 

system (figure 9) based 

mainly on seismological, 

radar interferometric and 

structural data. They suggest 

that lower crustal/upper 

mantle source zones are 

feeding the basaltic dyke 

and shallow magma 

chambers at a few kilometres 

depth. 

Magnetotelluric measurements 

by the Afar Rift 

Consortium / University of 

Edinburgh (Scotland, U.K.) 

are ongoing in that area and 

results thereof may help to 

refine the interpretation of 

the Tendaho geothermal 

field data. 

With the current data therefore the following preliminary conclusions may be drawn: 

The deep heat source feeding the currently drilled reservoir at 300 m depth is most likely 

(partly) molten magma along NW-SE trending dykes or faults. In the Tendaho geothermal 

field these structures may be as shallow as 4 km depth. 

A deep reservoir may be expected below 1300 m. 

An up flow zone could be present at the S end of the survey area indicated by low 

resistivities throughout the acquired depth range. 

To identify the proposed up flow zone at the S end of the current survey area it is 

recommended to apply additional TEM soundings which could enhance the resolution at 

shallow depth. 

Additional MT sounding profiles are recommended further towards the Hararo and Dabbahu 

magmatic segments NW of the survey area. Since rift events including ascending magma are 

evident further to the NW it may be assumed that high temperature reservoirs could be 

reached at comparatively shallow depth there. First MT results from the research work within 

the Afar Rift Consortium do support this assumption (Desissa et al., 2009). 

Also additional MT soundings beyond the Awash river up to the geothermal manifestations of 

Alalobad in the south would be helpful to establish either the extension of one large reservoir 

or the existence of a separate second geothermal system. 


The MT survey in Ethiopia has been carried out as part of a cooperation project between the 

Geological Survey of Ethiopia (GSE) and BGR as part of the GEOTHERM Programme. We 

gratefully acknowledge the cooperation with Mohammednur Desissa, Yohannes Lemma and 

the Geothermal Working Group within the GSE. We also appreciate helpful communications 

and cooperation with Kathy Whaler and the Afar Rift Consortium. 

GEOTHERM (www.bgr.de/geotherm/) is a technical cooperation programme to promote the 

use of geothermal energy in partner countries, implemented by the BGR on behalf of the 

German Federal Ministry for Economic Cooperation and Development (BMZ) under contract 

no. 2002.2061.6. 



135

References 

Aquater; 1996. Tendaho geothermal project, final report. Ministry of Mines of Ethiopia and 

Ministry of Foreign Affairs of Italy, San Lorenzo in Campo, Italy (unpublished). 

Barberi, F., Tazieff, H. & Varet, J., 1972. Volcanism in the Afar depression: its tectonic and 

magmatic significance. Tectonophysics, 15, 19-29. 

Desissa; M., Whaler, K., Hautot, S., Dawes, G., Fisseha, S., Johnson, N., 2009. A 

Magnetotelluric study of continental lithosphere in the final stages of break-up: Afar, 

Ethiopia. Abstract I.06-1158, 11th IAGA Scientific Assembly, Sopron, Hungary. 

Ebinger, C.J., Keir, D., Ayele, A., Calais, E., Wright, T.J., Belachew, M., Hammond, J.O.S., 

Campbell, E. & Buck, W.R., 2008. Capturing magma intrusion and faulting processes 

during continental rupture: seismicity of the Dabbahu (Afar) rift, Geophys. J. Int. 

Johnston, J.M., Pellerin, L. & Hohmann, G.W. (1992): Evaluation of Electromagnetic 

Methods for Geothermal Reservoir Detection, Geothermal Resources Council 

Transactions, 16, 241-245. 

Kalberkamp, U., 2007. Exploration of geothermal high enthalpy resources using 

Magnetotellurics – an Example from Chile, in: Ritter, O., Brasse, H. (eds.): Protokoll 

22. Kolloquium Elektromagnetische Tiefenforschung, Hotel Maxiky. Dín, Czech 

Republic, 1.-5. Oktober 2007, DGG, 194-198. 

Lemma, Y., Hailu, A., 2006. Gravity and magnetics survey at the Tendaho geothermal field. 

GSE, Addis Ababa, Ethiopia, 23pp (unpublished),. 

UNEP (ed.), 1973. Ethiopia: Investigation of geothermal resources for power development – 

Geology, geochemistry and hydrology of hot springs of the East African Rift System 

within Ethiopia, Technical Report DP/SF/UN/116, United Nations, New York. 



136

Electromagnetic Monitoring of CO2 Storage in Deep Saline 

Aquifers - Numerical Simulations and Laboratory 

Experiments 

J. H. Börner, V. Herdegen, R.-U. Börner, K. Spitzer 

Institut für Geophysik, TU Bergakademie Freiberg, Gustav-Zeuner-Str. 12, 09599 Freiberg 


The knowledge of petrophysical parameters and their contrasts is crucial to reliably monitoring CO2 

storage processes. The electrical conductivity appears to be a sensitive indicator for a resistive gaseous 

or supercritical CO2 phase replacing a conductive pore fluid in a porous medium like a saline sandstone 

aquifer. However, detailed knowledge on the influence of supercritical CO2 on the electrical resistivity 

of a formation is not sufficiently available yet. 

Therefore, we have carried out laboratory experiments to predict the contrast in electrical resistivity due 

to the presence of CO2 in an initially water-saturated sand sample resembling the petrophysical situation 

typical for a reservoir. Furthermore, the expected parameter contrasts were estimated according to 

empirical equations and numerical simulations (Fig. 1). 

On a middle- to long-term perspective, we aim at developing an electromagnetic monitoring technique 

using a borehole transient electromagnetic sensor which offers a unique opportunity to generate 

enhanced sensitivity at depth with respect to detecting migrating CO2 in a reservoir. This work is 

therefore integrated into national CCS research programs with an interdisciplinary variety of partners. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 1: Workflow of the numerical simulation steps necessary for the transformation of water saturation into 

electrical resistivity. 

2 Theory 

Two-phase flow is governed by two equations simultaneously enforcing continuity of the water (w) and 

the CO2 (co2) phase flow (Busch et al. 1993). Both equations are linked by retention curves Se(pc) and 

relative permeabilities kr(S), such that 

∇·d w [− κkw r 

ηw (∇pw + d w g∇D)] = −Φ ∂(dwS w e ) 

+ d 

∂t 

w w0 

∇·d co2 [− κkco2 r 

ηco2 (∇pco2 + d co2 g∇D)] = −Φ ∂(dco2Sco2 e ) 

+ d 

∂t 

co2 w0 

with d as density, κ as intrinsic permeability, η as viscosity, Φ as porosity and g as gravitational acceleration. 

The link between both phases has been established by experimental data or parameterization, 

23 . Schmucker-Weidelt-Kolloquium für Elektromagnetische Tiefenforschung, 


137 

(1)

e.g., by van Genuchten (1980) or Mualem (1976) (with effective saturation Se, capillary pressure height 

Hc and parameters α, n,m,L): 

1 

S w e = 

(1 + |αHc| n ) m 

k w r =(S w e ) L · 

 

1 − 

 

1 − (S w e ) 1/m m 2 

S co2 

e =1− S w e (2) 

k co2 

r 

=(1− S w e ) L · 

 

1 − (S w e ) 1/m 2m 

The resulting distribution of water saturation S(x, y, z, t) can be transformed into electrical formation 

resistivity ρ using empirical resistivity models, e.g., Archie’s law (Archie 1942): 

ρ = a1 · Φ −a2 −a3 1 

· S · (4) 

σw 

with σw denoting pore water conductivity. Archie’s empirical parameters a1, a2 and a3 strongly depend 

on rock formation characteristics and can be combined with porosity and water saturation yielding the 

formation factor F , such that 

ρ = F · ρw. (5) 

For sands and sandstones with considerable clay content Waxman and Smits (1968) expanded Archie’s 

law to account for both electrolytic conductance and interfacial conductance: 

ρ = 

F ∗ 

S n · (σw + B·Qv 

S )−1 (6) 

with a unique formation factor F ∗ , the counterion mobility B describing the weak dependance of the 

interface conductivity on pore water salinity and the shalyness parameter Qv being the cation exchange 

capacity normalized to the pore volume. 

3 Numerical simulation studies 

The process of CO2 sequestration as well as the indication of a successful storage by observation of 

changes in electrical resistivity has been simulated following the steps indicated by the workflow shown 

in Fig. 1. 

Figure 2: CO2 saturation after 6 months of constant injection of 1000 m 3 per day into a 25 m thick reservoir. 

The injection well is located at the geometric center. These results were obtained using the FD 

simulation code Mod2PhaseThermo. 



138 

(3)



139



140

Final experiments have demonstrated that an increase in resistivity may also be achieved under 

supercritical conditions. However, the sample was not homogeneously infiltrated by the CO2 and 

preferential flow paths were built up during the experiment. The pore water has been pressed out only 

partially, leaving behind tube-shaped flow channels and a very heterogeneous water distribution with 

average residual water contents of more than 70 %. 

pressure height in m 

500 

400 

300 

200 

100 

van Genuchten 

measured data 

0 

0 0.2 0.4 0.6 0.8 1 

water saturation 

Figure 6: Relation between CO2 pressure and water saturation derived from data obtained by the initial 

pressure build-up for an experiment with a projected maximum pressure of 50 bar. The reference 

data have been calculated according to van Genuchten (1980) with α = 0.02 and n =3.9 (cf. eqs. 

(2)-(3)). 

The complications are due to the density of supercritical CO2 which is large compared to the density 

of CO2 in its gaseous state. Consequently, the current experimental assembly causes the high density 

to result in low flow velocities within the measuring cell. In addition to the flow channels, this effect 

prevents an effective replacement of the pore water by supercritical CO2. 

The experiments have shown that theoretical pressure-saturation relations can generally be verified in 

practice using our set-up (Fig. 6). All experimental data sufficiently agree with Archie’s law. However, 

we have to carry out further investigations on the effects of CO2 dissolving in the pore water. There 

are indications that this has an important impact on the pore water resistivity depending on pressure, 

temperature, and brine salinity. 

6 Conclusions 

Numerical simulation studies and laboratory experiments show that the electrical resistivity of a 

fluid-saturated porous medium is highly sensitive to the presence of CO2. Geo-electromagnetic methods 

are therefore considered as a promising approach for monitoring CO2 storage. 

Still, the laboratory set-up has to be improved further to provide reliable results at high pressures. 

Subject to these prerequisites, well-founded simulations of electromagnetic monitoring scenarios can be 

carried out. 

Further laboratory experiments will also aim at quantifying the influence of dissolved CO2 on pore 

water and formation resistivity. A feasibility study could show whether electromagnetic methods are 

able to monitor, e.g., an expanding plume of CO2-rich formation water during CO2 injection. Finally, 

the applicability of the laboratory assembly for measuring reliable retention curves of unconsolidated 

sedimentary rocks will be further tested in the near future. 



141

References 

Archie, G. E. (1942). The electrical resistivity log as an aid in determining some reservoir characteristics. Trans. Americ. 

Inst. Mineral. Met. (146): 54–62. 

Busch, K.-F., L. Luckner, and K. Tiemer (1993). Geohydraulik. Edited by G. Matthess. 3rd edition. Volume 3. Lehrbuch 

der Hydrogeologie. Gebrüder Borntraeger. isbn: 3-443-01004-0. 

Häfner, F. and S. Boy (2009). Mod2PhaseThermo Nutzermanual. IBeWa. 

Mualem, Y. (1976). A new Model for predicting the hydraulic condyctivity of unsaturated porous media. Water Resour. 

Res. 12: 283–291. 

Schön, J. (1996). Physical Properties of Rocks - Fundamentals and Principles of Petrophysics. 1st edition. Volume 18. 

Handbook of Geophysical Exploration. Section I, Seismic Exploration. Pergamon. 

van Genuchten, M. (1980). A Closed-form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils. Soil 

Science Society of America Journal 44(5): 892–898. 

Waxman, M. H. and L. J. M. Smits (1968). Electrical conductivities in oil-bearing shaly sands. Society of Petroleum 

Engineers Journal 8: 107–122. 



142

Erkundung eines Aquifers unter dem Mittelmeer 

vor der israelischen Küste mit LOTEM. 

K. Lippert 1 , B. Tezkan, R. Bergers, M. Gurk, M. v. Papen, P. Yogeshwar 

Institut für Geophysik und Meteorologie, Universität zu Köln 

Abstract 

Im Rahmen dieses BMBF-geförderten Projektes 2 kommt die Long-Offset Transient 

Elektromagnetik (LOTEM) Methode zum ersten Mal in mariner Umgebung zur Erkundung 

von Grundwasseraquiferen zum Einsatz. Hauptziel des Projektes ist die Detektion 

der Süßwassergrenze unter dem Mittelmeer an der Küste Israels. Zu diesem Zweck wurden 

Hardware-Modifikationen durchgeführt und bereits in einer ersten Testmessung in Israel 

erprobt. Des weiteren werden die Interpretationen der ersten Testmessung sowie die Modellierungsergebnisse 

des Küstenabschnitts vorgestellt, welche zur Planung der Hauptmessung 

wichtig sind. 

Einleitung 

Die Bedeutung von Offshore-Süßwasserleitern 

für das Grundwassermanagment nahm in den 

letzten Jahren stark zu. Das Vorhandensein 

dieser Aquifere, die sich bis zu mehreren 

Kilometern unter dem Meeresboden erstrecken 

können, wurde in der Fachliteratur beschrieben: 

z.B. an der Küste von Guyana [Arad, 1983] 

oder vor den Niederlanden [Groen et al., 

2005]. Der israelische Küstenaquifer ist eine 

der Hauptgrundwasserresourcen des Landes 

(vgl. Fig. 1). Aufgrund der intensiven 

Nutzung verschlechtert sich allerdings die 

Wasserqualität zumehmend. Die Gründe hierfür 

liegen sowohl in der anthropogenen Verschmutzung 

vom Land aus, als auch im Eindringen 

von Salzwasser. 

1 E-mail: lippert@geo.uni-koeln.de 

2 BMBF-Förderkennzeichen: 02WT0987 

Figure 1: Die großen Aquifere der Region. 



143

Geologie und Fragestellung 

Der Küstenaquifer besteht hauptsächlich aus 

kalkhaltigem Sandstein und Sanden und ist 

selbst noch in vier Sub-Aquifere unterteilt 

(vgl. Fig.2). Die oberen zwei grundwasserführenden 

Schichten werden vom Land 

aus anthropogen und vom Meer aus durch 

Salzwassereindringen verunreinigt. Bisher 

wurde davon ausgegangen, daß die unteren Sub- 

Aquifere stellenweise vom Meerwasser getrennt 

sind und dort keine Salzwasserintrusion stattfindet. 

Neuere Untersuchungen ([Kafri, U., 

Goldman, M., 2006],[Yechieli et. al, 2009]) 

hingegen deuten jedoch auf das Fortsetzen des 

Aquifers unter dem Meer hin. So zeigen 

z.B. TDEM-Messungen auf Land, nahe der 

Küste, einen schlechteren elektrischen Leiter 

10 (Ωm) eingebetet zwischen zwei guten elektrischen 

Leitern (∼ 2 Ωm). Diese Schicht, 

in der Tiefe der unteren Sub-Aquifere, wird 

als Grundwasserführenden Schicht interpretiert 

(vgl. Fig.3). Die Fragestellung an die LOTEM- 

Methode ist nun 1. die Prüfung der Existenz 

des unteren Sub-Aquifers in etwa 100m Tiefe 

und 2. dessen Ausbreitung unter dem Mittelmeer. 

Figure 2: Möglicher Verlauf des unteren Subaquifers an der Küste [Yechieli et. al, 2009]: a) 

Der untere Subaquifer (CD) hat keine Verbindung zum Meer, b): Das Salzwasser dringt in den 

unteren Aquifer ein. 

Figure 3: Onshore SHOTEM-Ergebnisse [Kafri, U., Goldman, M., 2006]. 



144

Hardwaremodifikationen 

Das Kölner LOTEM-Equipement ist für 

Landmessungen konzipiert. Deswegen waren 

einige Hardware-Modifikationen für die Offshoremessung 

nötig. Als Sender konnte aus 

logistischen Gründen nur der kleinere Kölner 

Sender 3 verwendet werden. Da dieser bei 

verwendeten Stromstärken von ∼ 9A zuviel 

Wärme entwickelt, war es nötig eine zusätzliche 

Wasserkühlung einzubauen. Für die Einspeisung 

des Sendesignals wurden neue Elektroden 

entwickelt (vgl. Fig.4), deren Form, 

durch Maximierung des angekoppelten Wasservolumes, 

elektrochemische Vorgänge minimiert. 

Zusätzlich kann das Sendesignal Stromgeregelt 

werden, um einen konstanten Stromverlauf zu 

erreichen. In Fig.5 sind Sendesignale gezeigt. 

Links wird mit konstanter Spannung gesendet. 

Bei sich verändernder Ankopplung ergibt sich 

kein konstanter Stromverlauf. Deswegen wurde 

der Sendestrom nachträglich auf einen konstan- 

Figure 5: Aufgezeichnete Sendesignale bei 

einem Test in Wilhelmshaven. 

ten Wert heruntergeregelt (Fig.5 rechts). 

Die verwendeten Magnetfeldsensoren 4 wurden 

in Druck- und Salzwasserbeständige Behälter 

verpackt (Fig.6). 

Figure 4: Neuentwickelte Elektroden für die 

Einspeisung des Sendesignals. 

Figure 6: Seewasserfestes Gehäuse für die 

Magnetfeld-Sensoren. 

3 NT-20 von Zonge Engineering & Research Organization, Inc., Tucson AZ, USA 

4 TEM/3-Spulen von Zonge Engineering & Research Organization, Inc., Tucson AZ, USA 



145

Ergebnisse Messung 2008 

Anfang November 2008 wurden die ersten Messung 

vor Ort durchgeführt. Hierbei wurden verschiedene 

Messkonfigurationen gestestet: 

• BroadSide: Sender an der Küstenlinie, 

Empfänger an Land. Offset 200m. vgl. 

Fig.7: Tx2 und Rx3. 

• BroadSide: Sender an der Küstenlinie, 

Empfänger im Wasser. Offset 300m. vgl. 


• BroadSide: Sender im Wasser, 

Empfänger an Land. Offset 500m. vgl. 


Figure 7: Setups der Messung 2008. 

Das Setup “Sender an der Küstenlinie, 

Empfänger an Land” ist das einzige, welches 

annehmbar 1D interpretiert werden konnte. 

Als Beispiel ist hier die dHz/dt - Komponente 

gezeigt. Das Endmodell einer Marquardt- 

Inversion ist in Fig.9, die zugehörige Datenanpassung 

in Fig.8 zu sehen. Das Startmodell 

wurde anhand der Vorinformationen und 

dem Ergebnis einer Occam-Inversion gewählt 5 . 

Figure 8: Datenanpassung des “besten” Modells 

(rot) in Fig. 9. 

Figure 9: 1D-Inversionsergebnis mit 

Äquivalenzmodellen. 

Das Ergebnis ist gut mit den SHOTEM- 

Ergebnissen (Fig. 3) vergleichbar. Der gesuchte 

Aquifer ist deutlich in einer Tiefe ab ca. 90m 

zu erkennen. Sowohl die Schichtdicke mit ca. 

100m als auch viele 

Äquivalenzmodelle mit 

einem Widerstand von ∼ 10 Ωm sind vergleichbar 

und glaubwürdig. 

Die anderen beiden Messkonfigurationen 

5Vgl. M.v.Papen, B.Tezkan: “On the analysis of LOTEM time series from Israel and preliminary 1D 

inversion of data.”, Poster EMTF 2009. 



146

können nicht als eindimensionales Problem 

angesehen und somit auch nicht 1D ausgewertet 

werden. Die gemessenen Transienten 

wurden mit synthetischen Daten verglichen. 

Das 2D Leitfähigkeitsmodell ist in Fig. 11 

dargestellt. Mit diesem synthetischen Modell 

war eine qualitative Anpassung möglich. Exemplarisch 

ist in Fig.10 die Datenanpassung für 

die Ex-Komponente gezeigt. 

Figure 10: Setup Tx2 - Rx3 (vgl.Fig.7): Anpassung 

der Messdaten der Ex-Komponente mit 

modellierten Daten. 

Vorab-Modellierungen 

Für die Messung im November 2009 sind die 

Empfängerlokationen von Bedeutung. Eine 

Frage hierbei ist u.a. ob das Target auch mit 

einem Sender auf dem Meer und Empfängern 

auf dem Land auflösbar ist. Diese Konfiguration 

ist logistisch relativ einfach durchführbar. 

Es wurde also ein 2D-Küstenmodell erstellt, 

mit welchem synthetische Daten mittels 

SLDMEM3T [Druskin, Knizhnermann, 1988] 

erzeugt wurde. Als Datenbeispiel sind in Fig.12 

die Ex-Komponenten dargestellt. Hierfür werden 

im Modell (Fig.11) Daten mit Targetlayer 

und einmal ohne Targetlayer unter dem Meeresboden 

verglichen. “Ohne Targetlayer” bedeutet 

in diesem Fall, daß der Targetlayer 300m im 

Landesinneren endet (nicht dargestellt). Die 

darüberliegende Schicht (1.2 Ωm, gelb) wurde 

nach unten erweitert. 

Modelliert wurden verschiedene Senderpositionen 

in unterschiedlichen Entfernungen zur 

Küstenlinie. Im Beispiel beträgt die Entfernung 

1500m. Betrachtet werden nun 2 

Empängerpositionen: einmal 275m von der 

Küstenlinie entfernt auf dem Meeresboden und 

einmal 95m im Landesinneren. Modelliert 

wurde die BroadSide Konfiguration (Senderrichtung 

und Profilrichtung senkrecht zueinander) 

und die InLine Konfiguration (Senderrichtung 

und Profilrichtung auf einer Linie). Die 

System-Antwort wurde für diese Modellierungen 

nicht berücksichtigt. 

Figure 11: Verwendetes Küstenmodell. Das 

gesuchte Target ist die 15 Ωm-Schicht (rot). 

Blau = Wasser. 



147

Sowohl bei der InLine als auch bei der Broad- 

Side Konfiguration ist in dieser Komponente 

der Targetlayer klar auflösbar: die Transienten 

unterscheiden sich deutlich in den Amplituden 

von den Transienten ohne Targetlayer. Bei 

der BroadSide Konfiguration verschiebt sich der 

auftretende Vorzeichenwechsel durch das Target 

zu späten Zeiten. Ein Vorzeichenwechsel ist 

bei der Auswertung immer schwer interpretierbar. 

Aufgrund der Unterscheidbarkeit der Transienten 

sind Empfänger auf dem Land für diese 

Fragestellung sinnvoll. 

Figure 12: Modellierte Transienten der Ex- 

Komponente an den Positionen, die in Fig.11 

als Kreise markiert sind. 

Zusammenfassung und Ausblick 

Aufgrund der Ergebnisse und der Erfahrungen 

der ersten Messung (2008) und der Modellierungen 

sind die Setups für die erste Hauptmessung 

im November 2009 festgelegt worden. Die Messung 

ist inzwischen durchgeführt worden. Es 

wurden die Konfigurationen InLine und Broad- 

Side gemessen. Der Sender befand sich dabei 

immer auf dem Meer in verschiedenen Abständen 

zur Küste. Pro Senderposition gab es mehrere 

Empfängerpositionen, sowohl auf dem Wasser 

als auch auf Land. 

Literatur 



148 

Arad, A.: “ A summary of artesian coastal 

basin of Guyana.”, J.Hydrol. 63:299-313, 1983. 

Druskin, V.L., Knizhnermann, L.A.: ”A 

spektral semi-discrete method for the numerical 

solution of 3d nonstationary problems in electrical 

prospecting.”, Phys. Solid Earth, 24:641- 

648, 1988. 

Groen J., Groen M., Post V., Kooi H., 

Mendizabal I. and Groot S.M.: ” Seaward 

continuation of groundwater flow systems along 

the coast of the Netherlands.”, GSA Salt Lake 

Ann.Meet. Abstract Paper No.211-9., 2005. 

Kafri U. and Goldman M.: “ Are the lower 

subaquifers of the Mediterranean coastal aquifer 

blocked to seawater intrusion? Results of a TDEM 

(time domain electromagnetic) study.”, Isr.J.Earth 

Sci., 2006. 

Yechieli et. al: “ The inter-relationship between 

coastal sub-aquifers and the Mediterranean 

Sea, deduced from radioactive isotopes analysis.” 

Hydrogeology Journal Vol 17 Num 2 / 

2009.

On the analysis of LOTEM time series from Israel and the preliminary 1D inversion of 

data 

M. von Papen, B. Tezkan 

Institute of Geophysics and Meteorology, University of Cologne, Germany 

Abbildung 1: Overview of measurement setups (A,B,C from left to 

right) 

1. Data Processing of TEM time series from the 

first Israel survey 

Abbildung 2: Power spectrum of Ex at station A/B before (blue 

asterisks) and after application of different filters 

The measurement took place at the coast near Ashdod, 

Israel (fig.1), where the task is the detection of fresh 

groundwater bodies within the mediterranean submarine 

aquifers [3]. For that matter a 380 m long dipole emitting 

in a 50% duty cycle was used, located on the shoreline for 

stations A and C and at -300m offshore on the seabottom 

for station B. Receiver stations recorded four components 

of the EM field (Ex,Ey, ˙ Hy, ˙ Hz) with Summit receivers. Receivers 

at station C were set up 5mbeneath the water on 

the sea bottom. 

• The measured transients consist of 4096 data points 

(DP) with a sample rate of 1/16 ms and 256 DP as 

onset. Switch time of Tx is t0 = 1500ms. 

Abbildung 3: Parts of transient [5] 

Noise measurements showed a dominant 50 Hz noise 

together with multiples (fig.2). The average noise 

power for each component is: PN,Ex = 0.2V 2 ,PN,Ey = 

0.02V 2 ,P N, ˙ Hy = 4.8V 2 ,P N, ˙ Hz = 0.2V 2 (measured on 

land). Due to relative short offsets of 200-500 m between 

receiver and transmitter the signal is - except for Ey component 

- clearly visible in the raw transients. 

Abbildung 4: Stacked transients of only on-switches and only offswitches 

2. Application of a segmented lockin filter 

First step of the processing was to filter out the 50 Hz 

noise. This was done using a segmented lockin filter (LOF) 



149

Abbildung 5: Quantiles of normal distribution for stations A,B,C 

from top to bottom 

[1]. It fits harmonics in segments of 60 ms to the data and 

subtracts them. Amplitude and phase are computed with 

Fourier series expansion. Regarding the high dynamic of 

the transient at the time of the switch (e.g. switch on in 

part B of fig.3) the fitting is being done in parts A and 

C only [5]. In addition a 3rd degree polynomial is fitted 

in part C to simulate the descent of the transient. Other 

filters like Delay Lower Nyquist frequency (DLN), Delay 

filter or (not segmented) Lockin-Filter [1, 5] remove the 

noise less efficient for this dataset (fig.2). 

• Application of the filter reduced the noise power, computed 

at the end of the time series, to PN,Ex = 

0.2nV 2 ,P N, ˙ Hy =0.2V 2 and P N, ˙ Hz =1.4nV 2 . 

• The DC bias is removed by levelling the data in the 

onset after filtering. 

Due to the short onset and the resulting error in determining 

the DC bias the inverted conductivities will exhibit 

a slight shift [4]. Higher accuracy can be achieved by averaging 

over a complete transmitter period. 

3. Analysis of data distribution 

The data measured with 50% duty cycle consists of two 

different sets of transients. One set is created when switching 

the current off and another when switching on. Because 

the given transmitter system shows a much shorter 

ramp time for off-switches, these transients are generally 

less broad and have a higher peak than those created by 

switch-on (fig.4). Cluster analysis [2] in the blue area of 

fig.4 resulted in two equally populated groups identified as 

on and off switches by cross checking the Ex component. 

The distribution of the data in terms of probability can 

be visualized with quantiles of gauss distribution (fig.5). 

The mean values of all transients in a certain time segment 

are sorted by ascending value and are then plotted 

against an axis, which is scaled in such a way that normal 

distributed data will show as a line of slope 1. This has 

been done for each component over a 62 ms window at the 

end of each switch-off time series, which have been filtered 

and levelled beforehand. 

The top graph shows that the distribution of Hz (and 

- to a smaller extent - Ex) at station A is dominated by 

a step. However, cluster analysis could not sort out these 

time series. The other stations show a much better result 

with normal distributed data for all components. 

4. Stacking and 1D Occam inversion 

After the data is analysed and if it needs no further 

editing (like correction of the right switch moment) it is 

ready to be stacked and smoothed. 



150 

• The data was stacked selectively omitting the highest 

and lowest 5% of the values per DP.

Abbildung 6: Normalized stacked transients sorted by component 

Abbildung 7: Normalized system responses measured broadside 

Abbildung 8: Result of Occam inversion of data at station A for 1st 

and 2nd order roughness 

• Afterwards it was smoothed with a dynamic Hanning 

window function. 

Fig.6 shows the normalized transients of the stations 

sorted by components. Field setup is according to fig. 1. 

Ex shows a noticeable “bump” in early times at receiver 

station C, which could be a 2D effect of the water-land 

interface. More on interpretation of this data can be found 

in Lippert et al., 2010 . 

System responses measured on land are shown in fig.7 

and are used for convolution in forward calculation. Fig.8 

shows the Occam inversion results for station A. All components 

show a good conductor at about 80 m depth between 

two more resistive layers at approximately 10 m and 

150 m depth, which represent the sought fresh water bodies. 

Hz ˙ could resolve a second good conductor, which is 

not visible in ˙ Hy and only indicated in Ex. These results 

are in good agreement with the SHOTEM measurements 

of this area. 



151

5. Future research 

Some system responses measured broadside include negative 

values. This is supposed to be a geometric phenomenom 

related to the ’air wave’. Future measurements of 

the system response will therefore be conducted in the laboratory. 

For the geometries of stations B and C there are at the 

moment no inversion codes available, therefore they will be 

interpreted using 2D forward modelling. Joint inversions 

using different LOTEM components will be realized. 

6. References 

Literatur 

[1] T. Hanstein. Digitale Optimalfilter für LOTEM Daten. Protokoll 

über das 16. Kolloquium EMTF, pages 320–328, 1996. 

[2] S. Helwig. Clusteranalyse als Tool zur Selektion und Verarbeitung 

elektromagnetischer Daten. Protokoll über das 16. Kolloquium 

EMTF, pages 156–161, 1996. 

[3] K. Lippert et al. Erkundung eines Aquifers unter dem Mittelmeer 

vor der israelischen Küste mit LOTEM. Protokoll über das 23. 

Kolloquium EMTF, 2010. 

[4] A. Osman. Interpretation der LOTEM-Daten in näherer Umgebung 

von den Bohrungen des KTB. Diploma Thesis, Institute 

for Geophysics, University of Cologne, 1995. 

[5] C. Scholl. Die Periodizität von Sendesignalen bei LOTEM. Diploma 

Thesis, Institute for Geophysics, University of Cologne, 

2001. 



152

Grundwasserkontamination bei Roorkee/Indien: 

2D Joint Inversion von Radiomagnetotellurik und Gleichstromgeoelektrik 

Daten 

P. Yogeshwar 1 , B. Tezkan 1 , M. Israil 2 

1: Institut für Geophysik und Meteorologie, Universität zu Köln, Email: yogeshwar@geo.uni-koeln.de 

2: Earth Science Departement, Indian Institute of Technology, Roorkee 

In der landwirtschaftlich geprägten Region um Roorkee in Nordindien ist der Einsatz von Düngemittel 

sowie die Bewässerung der Felder mit Abwasser gängige Praxis, wobei das Abwasser durch 

offene, teilweise unbefestigte Kanäle transportiert wird. Die umliegende Landbevölkerung bezieht 

ihr Frischwasser oftmals aus Brunnen, die aus einem oberflächennahen Aquifer gespeist werden. 

Eine Gefährdung dieser oberflächennahen Aquifersysteme durch den praktizierten Umgang mit 

Abwasser und Düngemittel ist nicht auszuschließen. 

Im Rahmen der hier durchgeführten Untersuchungen wurden ein landwirtschaftlich genutztes und 

stark mit Abwasser bewässertes Gebiet nahe einer Mülldeponie und ein als kontaminationsfrei 

angenommenes Referenzprofil mit den Methoden der Gleichstromgeolelektrik (DC) und der Radiomagnetotellurik 

(RMT) vermessen. 

Die einzelnen Profile wurden neben Benutzung von gängiger 1D und 2D Auswertesoftware mittels 

eines neu entwickelten 2D Joint Inversionsprogrammes invertiert und interpretiert. 

Verglichen mit den Ergebnissen des Referenzprofils zeigen die Ergebnisse auf dem kontaminierten 

Gebiet nahe der Deponie deutlich erhöhte Leitfähigkeitswerte bis zu einer Tiefe von ca. 15 m. Der 

Tiefenbereich von 5 m bis ungefähr 15 m konnte mit dem oberflächennahen Aquifer identifiziert 

werden. Darüber hinaus ergibt sich eine Abnahme der Leitfähigkeitswerte mit dem Abstand von 

der Mülldeponie und den Abwasserauslässen. 

Durch die Anwendung einer 2D Joint Inversion konnten die Datensätze beider Methoden durch 

einheitliche Untergrundmodelle angepasst werden. 

Einleitung 

Roorkee befindet sich in den Vorläufern des Himalaja 

am rechten Ufer des Solani Flusses im Distrikt Haridwar 

des nordindischen Staates Uttharakand (Geographische 

Breite: 29 ◦ 50 ′ bis 29 ◦ 56 ′ N, Geographische 

Länge: 77 ◦ 48 ′ bis 77 ◦ 56 ′ E). Der Solani ist ein Nebenfluss 

des Ganges. Der Ganges ist in dem Gebiet 

kanalisiert und teilt Roorkee in „Old“- und „New“- 

Roorkee. Die Stadt hat ca. 100000 Einwohner, mit 

einer jedoch wachsenden Bevölkerung. Die Region ist 

stark landwirtschaftlich geprägt, wobei sich dort vermehrt 

Industrie entwickelt. 

Die Untersuchungen fanden in Zusammenarbeit 

mit dem Indian Institute of Technology in Roorkee/Nordindien 

(IIT-Roorkee) im Rahmen eines 

deutsch-indischen Partnerprojektes statt. Das Hauptanliegen 

dieses Projektes besteht in der Anwendung 

geophysikalischer Methoden zur Abschätzung der 

Gefährdung der Aquifersysteme der Region um Roorkee. 

In der landwirtschaftlich geprägten Region um Roorkee 

ist der Einsatz von Düngemittel sowie die Bewässerung 

der Felder mit Abwasser gängige Praxis, 

wobei das Abwasser durch offene, teilweise nicht befestigte, 

Kanäle transportiert wird. Gleichzeitig bezieht 

die umliegende Landbevölkerung ihr Frischwasser 

oftmals aus Brunnen, die aus oberflächennahen 

Aquiferen gespeist werden. Eine Gefährdung dieser 

oberflächennahen Aquifersysteme durch den praktizierten 

Umgang mit Abwasser und Düngemittel ist 

nicht auszuschließen. 

Ein weiteres Risiko geht von Mülldeponien aus, die 

zu Grundwasserkontamination in deren unmittelbaren 

Umgebung führen können und deren schädlicher 

Einfluss auf die Aquifersysteme der Region ebenfalls 

nicht auszuschließen ist. Die Grundwasserproblematik 

wird, durch den Frischwasserbedarf der zunehmenden 

Bevölkerung und der wachsenden Industrie, 

verschärft. 

Geophysikalische Erkundungsmethoden haben sich 

in ihrer Anwendung auf hydrogeologische Fragestellungen, 

sowie zur Untersuchung von Altlasten mehrfach 

bewährt ([Tezkan, 1999], [Recher, 2002] und [Seher, 

2005]). Insbesondere eignet sich die Kombination 

von DC und RMT, da sich beide Methoden in ihrem 

Erkundungstiefenbereich und ihrer Sensitivität 

gegenüber leitfähigen Strukturen ergänzen. 

Im Rahmen des Projektes wurde das umliegende Gebiet 

einer Mülldeponie nahe dem Dorf Saliyar mit diesen 

Methoden profilweise vermessen. Seit 1975 wird 

dieses Gebiet zur landwirtschaftlichen Nutzung an 

Kleinbauern verpachtet und intensiv mit Abwasser 

bewässert, welches von Roorkee durch Rohrleitungen 

auf die Felder transportiert wird. 

In Abbildung 1 ist eine Übersichtskarte der Region 

dargestellt. Das Messgebiet bei Saliyar befindet sich 

ca. 6 km nordwestlich von Roorkee auf der rechten 

Uferseite des Solani. Das ungeklärte Abwasser der 

Stadt wird von der Mahingram Pumpstation über 

eine Kanalleitung zur Mülldeponie geleitet. Das vermessene 

Referenzgebiet befindet sich auf der linken 

Uferseite des Solani und ist ca 10 km von Saliyar entfernt. 

Das ganze Gelände hat ein leichtes Gefälle in 

Richtung Südosten. 

Der Einfluss von Abwassernutzung auf die Grund- 



153

googlemaps 

Abbildung 1: Übersicht der Region um Roorkee. Das Messgebiet Saliyar ist rot, das Referenzgebiet grün 

umrandet. Weitere wichtige Plätze sind farblich hervorgehoben und beschriftet. Brunnen, die überwacht und 

untersucht wurden sind als weiße Kringel mit roten Punkten dargestellt (Rechte Abbildung: [Singhal et al., 

2003]). 

wasserqualität wurde bisher überwiegend unter Berücksichtigung 

von hydrochemischen Daten untersucht. 

Die chemischen und bakteriellen Analysen des 

Grundwassers zeigen bisher nur erhöhte Werte für die 

Proben aus der unmittelbarem Umgebung von Saliyar, 

wo sich die Mülldeponie befindet. Singhal et al. 

[2003] schließen eine Gefährdung der Aquifersysteme 

weiter flussabwärts in Richtung Roorkee auf Grund 

der angenommenen Grundwasserfließrichtung. Sudha 

et al. [2010] haben bereits in den Gebieten nördlich 

von Roorkee, in Saliyar und in Khanjapur, eine Vielzahl 

von DC-Profilen und „Time Domain Electromagnetic“ 

(TEM) Stationen vermessen, um den Einfluss 

des Abwassers auf das oberflächennahe Aquifer zu detektieren 

und die Ausmaße des kontaminierten Bereichs 

zu bestimmen. 

Ziel dieser Arbeit ist es ebenfalls, den Einfluss der 

Kontamination auf die Leitfähigkeitsverteilung der 

oberen 20 − 25 m zu bestimmen. Hierzu wurden die 

auf dem kontaminierten Gebiet vermessenen Profile 

mit dem Referenzprofil verglichen, auf dem keine 

Kontamination erwartet wird. Durch die Vielzahl der 

vermessenen Profile soll auch eine Aussage über die 

laterale Verbreitung des kontaminierten Bereichs, sowie 

die Ausbreitung von Kontaminationsfahnen getroffen 

werden. 

Zusätzlich wurden die Datensätze beider Methoden 

mittels des 2D Joint Inversionsprogrammes 

RMTDC2D von Candansayar und Tezkan [2008] einzeln 

und gemeinsam invertiert. Es soll dabei untersucht 

werden, inwiefern die Anwendung der 2D 

Joint Inversion verlässlichere und einheitlichere Untergrundmodelle 

zu liefern vermag. 

Geologie des Messgebiet 

Der indische Subkontinent lässt sich geologisch in drei 

Bereiche unterteilen: den Himalaja im Norden, die 

Gangesebene und die indische Halbinsel im Süden. 

Die Gangesebene stellt dabei das Entwässerungsbecken 

der großen indischen Flüsse Ganges, Indus, 

Brahmaputra und Yamuna dar. Das Messgebiet befindet 

sich im nördlichen Teil der Gangesebene (Abbildung 

1). Da es sich um Schwemmland des Ganges 

und des Solani handelt, weist der Boden überwiegend 

ungehärtete alluviale Sedimente jüngeren Alters 

mit einer einfachen eindimensionalen Schichtung auf. 

Diese Sedimente bestehen aus abwechselnden Schichten 

von Ton, Sand, Kunkur und in manchen Gebieten 

Kies, wobei Kunkur ein nodulares Kalziumkarbonat 

ist, welches sich häufig in Semi-ariden Regionen 

bildet. Lithologische Diagramme bei [Singhal et al., 

Bohrlochinformation DC Ergebnisse 

Lithologie z (m) ρ (Ωm) z (m) 

Sandiger Lehm 0-4 >100 0-7 

Sand 4-32 40-100 7-38 

Ton + Kies 32-45 30-50 38-45 

Sand 45-105 — — 

Tabelle 1: Bohrlochinformationen verglichen mit den 

DC Ergebnissen in Sherpur von Sudha et al. [2010]. 

2003] zeigen eine oberflächennahe Schicht aus sehr 

feinem bis sandigem Lehm von 3 − 6 m Mächtigkeit. 

Die darunterliegende Sandschicht in 3 − 27 m Tiefe 

bezeichnet den ersten unbegrenzten, oberflächennahen 

Aquifer. Darunter befindet sich eine nichtpermeable 

Ton-Kies-Schicht von ca. 13 m Mächtigkeit 



154

googlemaps 

Abbildung 2: Die vermessenen Profile sind rot dargestellt und tragen die Bezeichnung der Profilnummer 

(PR1 bis PR13) sowie den Zusatz RMT oder RMT-DC, je nachdem ob nur RMT oder zusätzlich DC gemessen 

wurde. (Ab-)Wasserkanäle sind blau und Hochspannungsleitungen schwarz gestrichelt dargestellt. Der 

Hauptabwasserkanal verläuft von 1 nach 2. Auslässe für das Abwasser befinden sich entlang des Hauptabwasserkanals 

ca. alle 50m. An den Orten S1, S2 und S3 wurden Wasserproben entnommen. 

und trennt den oberen Grundwasserleiter von dem 

tieferen, der überwiegend aus Sand und Kies besteht. 

In der Tabelle 1 sind die DC-Inversionsergebnisse von 

Sudha et al. [2010] mit den Bohrlochdaten verglichen. 

Die Bohrlochdaten wurden von einem Litholog auf 

dem Referenzprofil bei Sherpur abgeleitet und zeigen 

gute Übereinstimmung mit den DC-Ergebnissen. 

Messung bei Roorkee 

Insgesamt wurden 13 RMT und 8 DC Profile bei einer 

zweiwöchigen Kampagne im Februar 2009 vermessen 

(Abbildung 2). Zu dieser Jahreszeit war das Messgebiet 

nur teilweise kultiviert und daher gut zugänglich. 

Die Profile sind, ausgehend von der Mülldeponie 

am südlichen Bildrand bis zum Flussbett des Solani, 

überwiegend parallel angeordnet. Der Abstand der 

Profile betrug ca. 50 m, je nach verfügbarem Platz. 

Damit wurde eine ca. 200 × 600 m 2 große Fläche abgedeckt. 

Das ganze Gebiet nordwestlich vom Hauptabwasserkanal 

hat ein leichtes Gefälle in Richtung 

Nordosten zum Solani hin. Die Mülldeponie im unteren 

Bildteil umfasst eine Fläche von 170 × 100 m 2 . 

Eine Messung direkt auf der Mülldeponie war nicht 

möglich, deswegen wurden Profil 8 und Profil 10 seitlich 

positioniert um einen etwaigen Einfluss der Mülldeponie 

durch z.B. Sickerwasser zu ermitteln. 

Der Hauptabwasserkanal verläuft von der Mülldepo- 

nie nordöstlich in Richtung des Solani. Ungefähr alle 

50 m befinden sich Wasserauslässe, um die Felder 

zu fluten. Der kleinere offene Kanal (hellblau dargestellt) 

im linken Bildbereich verläuft parallel zum 

großen und wurde von den Profilen gekreuzt. Der Bereich 

oberhalb von Profil 6 war stark bewachsen und 

konnte nicht vermessen werden. Das oberste Profil 

(Profil 7) verläuft im trockenen Flussbett des Solani 

und ist ca. 600 m von der Kontaminationsquelle entfernt, 

weswegen hier eine Abnahme der Kontamination 

zu erwarten ist. Der Bereich zwischen Profil 3 und 

Profil 6 war stark bewässert, konnte aber dennoch 

vermessen werden. Profil 1, welches im Folgenden explizit 

vorgestellt wird, wurde am ersten Tag mit einer 

Länge von 710 m und einem Stationsabstand von 

10 − 50 m vermessen, um den Einfluss der Kontamination 

mit der Entfernung von der Quelle abzuschätzen. 

Die RMT-Messung wurde mit dem RMT-F 

Gerät der Universität zu Köln durchgeführt. Es arbeitet 

im erweiterten Frequenzbereich von 10 kHz bis 

1 MHz und ermöglicht dadurch ein verbessertes Auflösungsvermögen 

oberflächennaher Schichten [Wiebe, 

2007]. Der Messpunktabstand für die RMT-Stationen 

betrug bei allen anderen Profilen 10 m und die Anzahl 

in der Regel 21 Stationen. Gemessen wurden beide 

horizontalen Komponenten des elektrischen und 

des magnetischen Feldes zur Bestimmung der spezifischen 

Widerstands- und Phasenwerte der TE- und 



155

(a) (b) 

(c) (d) 

Abbildung 3: Inversionsmodelle des Referenzprofils 11 bei Sherpur der Daten der Wennerauslage (a), der 

Daten der TM-Mode (b), der der TE-Mode (c), sowie beider Datensätze (TE+TM) gemeinsam invertiert 

(d). Die RMT Stationen sind als schwarze Dreiecke dargestellt. Die 0.2 Isolinie des DOI ist als schwarz 

gestrichelte Linie geplottet und stellt die maximale Erkundungstiefe dar. 

der TM-Mode. Für die DC wurde eine ABEM Terrameter 

SAS 1000 benutzt. Als Messauslage wurde 

eine Wenner und eine Schlumberger „Short-Long“- 

Auslage gewählt. Durch den geringeren Elektrodenabstand 

im mittleren Bereich der Auslage ist eine 

oberflächennah bessere Auflösung gewährleistet. 

Eine geologische Streichrichtung zur Ausrichtung der 

Profile lässt sich anhand der Kontaminationsausbreitung 

nur ungenügend festlegen. Zu erwarten wäre 

eine Ausbreitung der Kontamination von den Abwasserauslässen 

Richtung Nordwesten oder auch eine 

Verbreitung der Kontamination von der Mülldeponie 

ausgehend. 

Demzufolge und in Anbetracht der nahezu eindimensionalen 

Struktur des Untergrundes wurden die Profile 

anhand der verfügbaren Sender für die RMT und 

der Verfügbarkeit von Platz ausgerichtet. 

Inversionsergebnisse Referenzprofils 11 bei 

Sherpur 

In den Abbildungen 3 sind die Inversionsmodelle der 

einzelnen 2D Inversionen für die Wennerauslage und 

für die RMT Daten mit DC2DINVRES [Günther, 

2004] bzw. RUND2_NLCG2_FAST (RUND2) [Rodi 

und Mackie, 2001] dargestellt. Die nicht-sensitiven 

Bereiche sind in den Inversionsergebnissen ausgeblendet 

und der „Depth Of Investigation“-Index (DOI) 

nach Oldenburg und Li [1998] ist zur Abschätzung der 

maximalen Erkundungstiefe in den RMT-Modellen 

dargestellt. 

Das DC Inversionsergebnis zeigt wie erwartet eine 

hochohmige Deckschicht mit einem spezifischen Widerstand 

von ρ>200 Ωm und einer Mächtigkeit von 

5 − 7 m, welche als sandige Lehmschicht identifiziert 

werden kann. Im Bereich von 0 − 60 m war das Profil 

sehr trocken, da dieser Bereich nicht als landwirtschaftliche 

Nutzfläche diente. Der Bereich von 60- 

120 m war kultiviert und wurde wahrscheinlich regelmäßig 

künstlich bewässert, wodurch sich der erniedrigte 

Widerstand der Deckschicht bis zu einer 

Tiefe von ungefähr 2 m erklären lässt. Der Bereich 

danach zeigt wieder eine durchgehende hochohmige 

Deckschicht, obwohl dieser ebenfalls kultiviert war. 

Entsprechend den lithologischen Informationen aus 

Tabelle 1 und den DC Ergebnissen von Sudha et al. 

[2010] zeigt das Inversionsmodell unter der Deckschicht 

eine leitfähige Schicht mit einem spezifischen 

Widerstand von 30−50 Ωm, welches das oberflächennahe 

Aquifer, also eine wassergesättigte Sandschicht, 

darstellt und als die aufzulösende Zielstruktur aufgefasst 

wird. 

Die Inversionsmodelle der Daten der TM-Mode, der 

TE- Mode und der Joint Inversion beider Datensätze 

zeigen qualitativ eine identische Leitfähigkeitsstruktur. 

Auch die Abnahme des Widerstands im mittleren 

Teil des Profils ist identisch zum DC Inversionsmodell. 

Die hochohmige Deckschicht wird allerdings mit einem 

spezifischen Widerstand von 100 − 200 Ωm rekonstruiert, 

welcher verglichen mit dem DC-Ergebnis 

zu gering ist. Die darunterliegende Zielstruktur wird 

wiederum mit einem spezifischen Widerstand von 

20 − 40 Ωm aufgelöst und ist vergleichbar mit dem 

DC-Ergebnis. Zusätzlich wurde ein zweites RMT Profil 

in ca. 200 m Entfernung von Profil 11 vermessen. 

Die geologische Struktur ist hier identisch und der 

spezifische Widerstand der Zielstruktur wird ebenfalls 

mit einem Wert von 20 − 40 Ωm gut aufgelöst 

Yogeshwar [2010]. 

Eine Erklärung für den verminderten Widerstand der 

Deckschicht ist die geringe Sensitivität der RMT für 

hochohmige Bereiche. Desweiteren könnte ein statischer 

Versatz der ρa-Daten den geringen Widerstand 

der Deckschicht erklären. Oberflächennahe Inhomogenitäten 

in der Nähe der Empfängerelektroden kön- 



156

nen z.B. einen zusätzlichen Versatz auf die ρa-Daten 

bewirken. 

Die Unterkante des Aquifers wird in den Inversionsmodellen 

nicht aufgelöst. Zum einen hängt das 

mit der maximalen Erkundungstiefe zusammen, zum 

anderen ergibt sich wahrscheinlich kein entscheidender 

Leitfähigkeitskontrast zwischen dem oberflächennahen 

Aquifer und der darunterliegenden nichtpermeablen 

Ton-Kies-Schicht, deren spezifischer Widerstand 

ebenfalls ungefähr 40 − 50 Ωm beträgt. 

Um die maximale Erkundungstiefe abzuschätzen 

wurde der DOI nach Oldenburg und Li [1998] berechnet. 

Für die Wennerauslage ergibt sich bei [Yogeshwar, 

2010] eine maximale Erkundungstiefe von 20 m 

bis 25 m für den mittleren Bereich des Profils. 

Für die RMT-Modelle ist der DOI als schwarz gestrichelte 

Linie in den Modellen dargestellt. Für das 

Inversionsmodell der Daten der TM-Mode ist die Erkundungstiefe 

ungefähr 15 − 20 m, wobei im Bereich 

von x = 100 − 200 m der DOI, auf Grund der erhöhten 

Leitfähigkeit, etwas abnimmt. Für die beiden 

anderen RMT-Inversionsmodelle in Abbildung 3 ergibt 

sich eine ähnliche Erkundungstiefe von ca. 15 m. 

Inversionsergebnisse des kontaminierten Profils 1 

bei Saliyar 

Das Profil 1 befindet sich in ca 100 m Entfernung 

zur Mülldeponie und wurde am ersten Messtag vermessen 

(Abbildung 2). Es war nicht bewässert und 

kaum kultiviert. Benutzt wurde eine Wenner Long- 

Auslage mit einer Länge von 120 m, im Gegensatz zu 

den anderen DC Profilen, die ausschließlich eine Profillänge 

von 200 m haben. Das RMT-Profil wurde bis 

zu einer Entfernung von 710 m vom Hauptabwasserkanal 

(Abbildung 2) fortgesetzt um den Einfluss der 

Kontamination mit dem Abstand zur Quelle zu bestimmen, 

wobei der Stationsabstand im Bereich von 

x =0− 200 m zehn Meter betrug und dann bis zu 

50 m vergrößert wurde. Ausgewertet wurden nur die 

Daten der TE-Mode, da die der TM-Mode viele Senderlücken 

und teilweise negative Phasenwerte aufwiesen. 

In den Abbildungen 4(a) und 4(b) sind die Inversionsmodelle 

der einzelnen 2D Inversionen für die Wennerauslage 

und für die Daten der TE- Mode dargestellt. 

Das DC-Modell zeigt eine einfache, eindimensionale 

geologische Schichtung, wobei die Deckschicht im 

Vergleich zum Referenzprofil in Abbildung 3 wesentlich 

weniger mächtig ist und einen geringeren Widerstand 

von ca. 30 Ωm aufweist. Eine mögliche Ursache 

für die insgesamt weniger hochohmige Deckschicht 

mit ca. 2-3 m Mächtigkeit ist wahrscheinlich die sonst 

häufige Bewässerung mit Abwasser. Im rechten Bereich 

nahe des Hauptabwasserkanals befindet sich ein 

hochohmiger Bereich der Deckschicht, welcher von einer 

Erdaufschüttung herrühren könnte, und der in 

dem RMT Inversionsmodell identisch rekonstruiert 

ist. Darunter folgt das kontaminierte Aquifer, bzw., 

verglichen mit dem Ergebnis für das Referenzprofil, 

ein Bereich stark erhöhter Leitfähigkeit bis zu 

einer Tiefe von ungefähr 12 m. Dies ist im RMT- 

(a) 

(b) 

Abbildung 4: Inversionsergebnis des Profils 1 bei Saliyar 

der Daten der Wennerauslage (a) und der Daten 

der TE-Mode (b). Die RMT Stationen sind als 

schwarze Dreiecke dargestellt, der DOI als schwarz 

gestrichelte Linie. 

Profil ebenfalls identisch wiedergegeben. Der spezifische 

Widerstand fällt im DC-Modell mit 6 − 15 Ωm 

etwas höher aus als der des RMT-Modells. Die Anpassung 

beider Datensätze ist mit einem RMS < 2.5 

gut. 

Die maximale Erkundungstiefe für das DC-Modell ergibt 

sich mit dem DOI-Index bei Yogeshwar [2010] 

zu 15 − 20 m im mittleren Bereich des Profils. Die 

schwarze Linie in Abbildung 4 stellt die maximale 

Erkundungstiefe von 10 − 15 m für das RMT-Modell 

dar. Mit dieser Erkundungstiefe für die RMT wird 

die Unterkante des kontaminierten Bereichs nur mit 

der DC aufgelöst. 

Auf den vermessenen Profilen in Saliyar wurde mit 

dem Programm EMUPLUS [Wiebe, 2007] eine 1D 

RMT-DC und eine 1D RMT-DC Joint Inversion im 

jeweiligen Mittelpunkt des Profils durchgeführt um 

die Leitfähigkeit des kontaminierten Aquifers genauer 

zu bestimmen. Die 1D Marquardt Inversionen für 

Profil 1 (Abbildung 5) entsprechen sehr gut den 2D 

Ergebnissen im Mittelpunkt des Profils. Das Modell 

der Geoelektrik zeigt einen Dreischichtfall mit gut 

aufgelösten Schichtgrenzen und spezifischen Widerständen, 

außer für den der obersten Schicht. Die äquivalenten 

Modelle in Abbildung 5 unterscheiden sich 

also kaum. Ebenso zeigt das Ergebnis für die RMT- 

Daten nahezu identische äquivalente Modelle, was auf 

eine gute Auflösung beider Schichten schließen lässt. 

Beide Inversionsergebnisse stimmen gut überein, wobei 

die RMT die Unterkante des Aquifers nicht auflösen 

kann. 

Das Modell der 1D Joint Inversion passt die Datensätze 

beider Methoden mit einem RMS von 1.65 gut 

an und löst die Unterkante der zweiten Schicht durch 

Hinzunahme der DC Daten auf. Der Widerstand des 



157

z (m) 

0 

5 

10 

15 

Profile 1, Schlumberger, VES at x=60m 

equi. models 

RMS=1.39 

20 

0 10 20 30 40 50 60 70 

ρ (Ωm) 

(a) 

z (m) 

0 

5 

10 

15 

Profile 1, te, sounding at x=60m 

equi. models 

RMS=1.75 

20 

0 10 20 30 40 50 60 70 

ρ (Ωm) 

(b) 

z (m) 

Profile 1, x=60m, Joint Inversion RMT/DC 

0 

5 

10 

15 

RMS all =1.65, 

RMS dc =1.4, 

RMS rmt =2.1, cf=0.82 

20 

0 10 20 30 40 50 60 70 

ρ (Ωm) 

Abbildung 5: 1D Marquardt Inversionsmodelle für die Sondierungskurve der Schlumbergerauslage (a) und 

der Daten der TE-Mode (b), sowie der Joint Inversion beider Datensätze (c) bei x =60m in der Mitte des 

Profils 1 bei Saliyar. Aufgetragen ist der spezifische Widerstand gegen die Tiefe. Äquivalente Modelle sind 

grün und der Mittelwert der äquivalenten Modelle sind rot dargestellt. 

kontaminierten Bereichs ist mit ρ ≈ 10 Ωm ziemlich 

genau bestimmt. Da weitaus mehr DC-Daten vorhanden 

sind, stellt das Inversionsergebnis zwar einen Informationsgewinn 

für die RMT dar, entspricht aber 

ziemlich genau dem 1D Modell der DC Inversion. 

Nur oberflächennah liefern die hochfrequenten RMT- 

Daten Zusatzinformation zur Verbesserung der Auflösung 

der obersten Schicht. 

2d Joint Inversion 

In der Abbildung 6 sind die Inversionsmodelle der 

Wenner Long Auslage, der Daten der TE-Mode und 

das Ergebnis der 2D Joint Inversion beider Datensätze 

mit RMTDC2D dargestellt. Die Leitfähigkeitsstruktur 

der Endmodelle ist gut vergleichbar mit den 

Inversionsmodellen der einzelnen 2D Inversionen mit 

DC2DINVRES und RUND2. 

Die Modelle der einzelnen Inversionen sind bis zu einer 

Tiefe von ungefähr 10 m gut vergleichbar, wobei 

die Anpassung der RMT-Daten mit einem RMS von 

1.9 besser ist als die der DC-Daten. Der kontaminierte 

Bereich wird im RMT Inversionsmodell etwas leitfähiger 

rekonstruiert. Eine Aussage über die Unterkante 

des Aquifers lässt sich auf Grund der mangelnden 

Eindringtiefe der RMT nicht treffen, wohingegen 

die Unterkante im DC-Modell aufgelöst wird. Die 2D 

Joint Inversion in Abbildung 6 passt beide Datensätze 

mit einem RMS von 5.0 zufriedenstellend an. Die 

Unterkante und der Widerstand des Aquifers sind gut 

aufgelöst. 

Die mit dem mittleren Tiefenbereich korrespondierenden 

DC-Daten in Abbildung 7(b) sind über die 

ganze Profillänge relativ gleichmäßig, 

z (m) 

z (m) 

−5 

0 

5 

10 

15 

(c) 

Profile 1/Saliyar, Wenner long, ρ 0 =9 Ω m, It.=9 Alpha=5 RMS=3.0816 

20 

0 10 20 30 40 50 

x (m) 

60 70 80 90 100 

5 

−5 

0 

5 

10 

15 

(a) 

Profile 1/Saliyar, TE, ρ 0 =9 Ω m, It.=30 Alpha=5 RMS=1.9128 

20 

0 10 20 30 40 50 

x (m) 

60 70 80 90 100 

5 

(b) 

Profile 1/Saliyar, TE/Wenner long, ρ =9 Ω m, It.=12 Alpha=10 RMS=5.0686 

0 

−5 

100 

z (m) 

0 

5 

10 

15 

20 

0 10 20 30 40 50 

x (m) 

60 70 80 90 100 

5 

(c) 

Abbildung 6: Inversionsergebnis der Wenner Long- 

Auslage (a), der TE-Mode (b) und der 2D Joint Inversion 

(c) des Profils 1. Die RMT-Stationen sind als 

schwarze Dreiecke dargestellt. 



158 

100 

65 

42 

28 

18 

12 

8 

65 

42 

28 

18 

12 

8 

ρ (Ω m) 

100 

65 

42 

28 

18 

12 

8 

ρ (Ω m) 

ρ (Ω m)

ρ a (Ωm) 

ρ a (Ωm) 

100 

80 

60 

40 

20 

0 

100 

80 

60 

40 

20 

0 

45 ° 

Profile 1, TE−mode,RMS=6.52, f=18000 Hz 

ρ a,mess 

ρ a,calc 

φ mess 

φ calc 

20 

0 20 40 60 

x (m) 

80 100 120 

Profile 1, TE−mode,RMS=6.52, f=666000 Hz 

ρ 

a,mess 

ρ 

a,calc φ 

mess 

φ 

calc 

80 

45 ° 

0 20 40 60 

x (m) 

(a) 

80 100 120 

80 

70 

60 

50 

40 

30 

70 

60 

50 

40 

30 

20 

φ (°) 

φ (°) 

n−level 

n−level 

n−level 

1 

3 

6 

8 

10 

12 

1 

3 

6 

8 

10 

12 

1 

3 

6 

8 

10 

12 

Meas. Pseudo−section:Wenner 

Calc. Pseudo−section: Wenner 

0 20 40 60 

x (m) 

(b) 

80 100 120 

ρ a (Ω m) 

50 

40 

30 

20 

10 

ρ a (Ω m) 

50 

40 

30 

20 

10 

%Misfit Section: Wenner (RMS=4.0584) %MISFIT 

10 

Abbildung 7: Daten und Datenanpassung der Daten der TE-Mode (a) und der Wenner Long Auslage (b) für 

das Ergebnis der 2D Joint Inversion mit RMTDC2D. Die gemessenen ρa und ϕ Werte sind als schwarze, 

bzw. rote Punkte und die Modellantwort als schwarze, bzw. rote Kreuze für f =18kHz, 666 kHz gegen die 

Station aufgetragen. Die DC-Daten und die Modellantwort sind als Pseudosektionen dargestellt, wobei die 

untere Abbildung (b) die relative Differenz beider zeigt. 

wohingegen die RMT Daten der 18 kHz Frequenz in 

Abbildung 7(a) und das Inversionsmodell der einzelnen 

2D RMT Inversion in Abbildung 6(b) auch Bereiche 

erhöhter Leitfähigkeit zeigen. Bei der 2D Joint 

Inversion werden die RMT-Daten daher nicht so gut 

wie die DC-Daten angepasst. Die Modellantwort der 

RMT ist durch die Regularisierung und dem Einfluss 

der insgesamt gleichmäßigeren DC-Daten sehr glatt. 

Der RMS für die RMT-Daten ergibt sich zu 6.5. Die 

Hinzunahme der RMT-Daten führt zu einer besseren 

Bestimmung der Deckschicht vor allem im etwas 

hochohmigeren Bereich von x =80− 100 m. Die DC- 

Daten in diesem Bereich sind nicht so gut angepasst, 

wie in der Darstellung der relativen Differenz der Daten 

und der Modellantwort in Abbildung 7(b) erkennbar 

ist. Eine Verringerung des Glättungsparameters 

passt diese zwar besser an, führt allerdings zu Inversionsartefakten 

für die tieferen Bereiche. 

Qualitativ zeigen die Auflösungsmatrizen der 2D 

Joint Inversion bei Yogeshwar [2010] eine verbesserte 

Auflösung im Vergleich zur RMT-Einzelinversion, 

wobei die Randbereiche im Vergleich zur DC- 

Einzelinversion besser aufgelöst sind, da die DC dort 

keine Tiefeninformation liefert. Die maximale Erkundungstiefe 

wird durch die DC-Daten bestimmt, weswegen 

keine erhöhte Sensitivität der tieferen Strukturen 

durch Hinzunahme der RMT-Daten erreicht wird. 

Abschätzung der Kontaminationsverbreitung 

Um die lateralen Ausmaße des kontaminierten Bereichs 

abzuschätzen, wurden insgesamt 9 parallele 

RMT und 5 parallele DC Profile auf einem ca 200 × 

600 m 2 großen Gebiet vermessen (Abbildung 2). Die 

pr6 

pr5 

pr4 

pr3 

pr2 

pr1 

pr9 

pr10 

pr7 

Waste 

Solani 

Kanal 

0 

−10 

Abbildung 8: Ansicht aller RMT-Profile von der 

Mülldeponie bis zum Solani. Der Hauptabwasserkanal 

verläuft von der Mülldeponie in Richtung des Solani 

und ist rot dargestellt. 

RMT-Profile sind in Abbildung 8 als Flächenschnitte 

der xz-Ebene dargestellt. Die Profile verlaufen parallel 

zwischen der Mülldeponie und dem Solani. Die 

RMT-Modelle liefern auf Grund der teilweise mäßigen 

Datenqualität nicht so glatte und gleichmäßige 

Modelle wie die DC-Modelle bei Yogeshwar [2010]. 

In der Darstellungen 8 ist eine leichte Abnahme der 

Leitfähigkeit zum Solani hin zu beobachten. Das Profil 

7 am Solani in Abbildung 8 zeigt insgesamt hochohmigere 

Bereiche im Inversionsmodell für die RMT. 

Die Inversionsergebnisse der DC-Daten sind bei Yo- 



159

z (m) 

0 

5 

10 

15 

20 

Profile 1/3/5/11, Joint Inversion model 

1D Joint Pr11 

1D Joint Pr1 

1D Joint Pr3 

1D Joint Pr5 

reference site ρ=50 Ωm 

10 100 

(a) 

ρ (Ωm) 

z (m) 

0 

5 

10 

15 

20 

Profile 7/8/9/13/11, Joint Inversion model 

1D Joint Pr11 

1D Joint Pr7 

1D Joint Pr8 

1D Joint Pr9 

1D Joint Pr13 


10 100 

(b) 

ρ (Ωm) 

z (m) 

Profile 2/4/6/10/11, RMT Inversion modells 

0 

5 

10 

15 

20 

1D Joint Pr11 

1D RMT Pr2 

1D RMT Pr4 

1D RMT Pr6 

1D RMT Pr10 


10 100 

Abbildung 10: 1D Marquardt Joint Inversionsmodelle der DC- und RMT-Daten im jeweiligen Mittelpunkt 

der Auslage für Profil 1,3,5 (a) und Profil 7,8,9,13 (b), sowie einzelne RMT 1D Inversionsmodelle für Profil 

2,4,6,10 (c). Das 1D Joint Inversionsmodell des Referenzprofils (Profil 11) ist rot dargestellt. 

geshwar [2010] mit denen der RMT sehr gut vergleichbar, 

wobei die Unterkante des Aquifers jedoch mit der 

DC aufgelöst wird. Um eine genauere Vorstellung 

z (m) 

z (m) 

Relative difference between model result of pr11 and pr1: Wenner ρ 01 =120 Ωm, ρ 02 =15 Ωm 

−5 

0 

5 

10 

15 

0.81 

0.64 

0.46 

0.29 

0.11 

−0.06 

20 

−0.24 

−0.41 

25 

−0.59 

30 

0 20 40 60 

x (m) 

80 100 

−0.76 

120 

−5 

0 

5 

10 

15 

20 

25 

(a) 

Relative difference between model results of pr11 and pr1: ρ 01 =50 Ωm, ρ 02 =10 Ωm 

30 

0 20 40 60 80 100 120 

x (m) 

(b) 

0.99 

0.79 

0.63 

0.47 

0.31 

−0.51 

relative difference 

relative difference 

0.14 

−0.02 

−0.18 

−0.34 

Abbildung 9: Dargestellt ist die relative Differenz 

der RMT- (a) und der DC-Inversionsmodelle (a) des 

Referenzprofils 11 und des kontaminierten Profils 1 

(Relative Differenz > 0 ⇒ ρref >ρpr1). 

des Leitfähigkeitsunterschiedes zwischen dem Inversionsmodell 

des Referenzprofils und den Profilen auf 

dem kontaminierten Bereich zu erhalten, wurde für 

(c) 

ρ (Ωm) 

jedes Profil die relative Differenz beider Modelle berechnet. 

Die relative Differenz des Profils 1 mit dem 

Referenzprofil 11 in Abbildung 9(a) zeigt für die Geoelektrik 

über die gesamte Auslagenlänge einen wesentlich 

geringeren spezifischen Widerstand. In einer 

Tiefe von ca. 15 m befindet sich die Unterkante des 

kontaminierten Aquifers und die Widerstände werden 

vergleichbar, bzw. der des Profils 1 wird größer. Für 

die RMT zeigt die Abbildung 9(b) ein identisches Ergebnis. 

Auch hier ist der spezifische Widerstand des 

Inversionsmodells für das Referenzprofil weitaus höher. 

Bei beiden Ergebnisses zeigen nur kleine oberflächennahe 

Bereiche der Deckschicht ein anderes Verhalten. 

In der Darstellung der relativen Differenz bei 

Yogeshwar [2010] zeigen die vermessenen Profile auf 

dem kontaminierten Gebiet in Saliyar im Vergleich 

mit dem Referenzprofil ausschließlich erhöhte Leitfähigkeitswerte 

bis zu einer Tiefe von ca. 15 − 20 m, bis 

auf das Profil 7, welches sich am Ufer des Solani befand 

und am weitesten von der Kontaminationsquelle 

entfernt war. 

In Abbildung 10(a) und 10(b) sind die 1D Joint Inversionsmodelle 

der Daten aller Profilmittelpunkte in 

Saliyar mit dem des Referenzprofils verglichen. Insgesamt 

zeigen alle Profile unterhalb einer etwas hochohmigeren 

Deckschicht einen spezifischen Widerstand 

von ρ ≈ 10 Ωm für das kontaminierte Aquifer, wiederum 

gefolgt von einer Schicht mit einen erhöhten spezifischen 

Widerstand. Das in grün geplottete Modell im 

rechten Teil der Abbildung 10 entstammt dem Pro- 



160

y (m) 

y (m) 

600 

300 

250 

200 

150 

100 

50 

0 

600 

300 

250 

200 

150 

100 

50 

0 

xy−planeview of RMT profiles at the depth of z=1m 

0 50 100 

x (m) 

150 200 

(a) 


0 50 100 

x (m) 

150 200 

(c) 

y (m) 

y (m) 

600 

300 

250 

200 

150 

100 

50 

0 

600 

300 

250 

200 

150 

100 

50 

0 


0 50 100 

x (m) 

150 200 

(b) 


pr7 

pr6 

pr5 

pr4 

pr3 

pr2 

pr1 

pr9 

pr10 

canal 

waste 

0 50 100 

x (m) 

150 200 

2 

Abbildung 11: xy-Schnitte der RMT Inversionsmodelle von RUND2 für verschiedene Tiefen: 1 m (a), 5 m 

(b),10 m (c) und 15 m (d). Die Kreuze bezeichnen die RMT-Stationen. 

fil 7 am Solani und zeigt eine etwas andere Struktur 

mit höheren Widerständen, wie schon in Abbildung 

8 ersichtlich war. Die Modelle der 1D RMT Inversionen 

in Abbildung 10(c) zeigen ebenfalls geringere 

spezifische Widerstände für das Aquifer. Das Ergebnis 

von Profil 4 in Abbildung 5(c) zeigt den Beginn 

einer hochohmige Schicht in ca. 8 m Tiefe, die auch im 

2D Modell der TM-Mode zu finden ist, aber nicht in 

dem der TE-Mode, und auf mangelnde Datenqualität 

oder die Streichrichtung zurückzuführen ist [Yogeshwar, 

2010]. Die Ergebnisse der einzelnen 2D Inversionsmodelle 

wurden für beide Methoden linear auf ein 

dreidimensionales Gitter interpoliert. Um eine Aussage 

über die laterale Verbreitung der Kontamination 

mit der Tiefe zu treffen, sind in Abbildung 11, am 

Beispiel der RMT, Flächenschnitte in der xy-Ebene 

für vier verschiedene Tiefen, z=1 m, 5 m, 10 m und 

1 5m, dargestellt. 

In einer Tiefe von einem Meter erkennt einen sehr 

hochohmigen Bereich direkt in der Umgebung der 

(d) 

ρ(Ωm) 

300 

172 

Mülldeponie. Das gesamte Profil 10, Profil 9 und die 

ersten 50 m direkt am Kanal von Profil 1 zeigen diese 

hochohmige Deckschicht. Dies könnte von einer Erdaufschüttung 

im Zusammenhang mit der Mülldeponie 

herrühren. Genaueres ist jedoch nicht bekannt. 

Für z = 5 m zeigt die Flächendarstellung spezifischen 

Widerstände um die 10 Ωm im Bereich von y =0m 

bis 300 m. Die Leitfähigkeit ist in der Nähe der Mülldeponie 

erhöht und nimmt dann in Richtung des Solani 

etwas ab. Das Profil 7 am Solani ist wie bereits 

gesagt über den gesamten Tiefenbereich hochohmiger 

als die anderen Profile. 

In einer Tiefe von 10 m und 15 m lässt die Kontamination 

etwas nach und es zeichnet sich die Unterkante 

des Aquifers ab, wobei der Bereich nahe der Mülldeponie 

im Vergleich zum Rest leitfähiger ist. Dies lässt 

wieder auf einen Einfluss der Mülldeponie schließen, 

vor allem da die Leitfähigkeit der Profile in der unmittelbaren 

Nähe der Deponie bis zu einer größeren 

Tiefe erhöht ist. So ist für Profil 9 in 15 m keine Un- 



161 

99 

56 

32 

19 

11 

6 

3

terkante des kontaminierten Aquifers erkennbar. Die 

DC-Ergebnisse bei Yogeshwar [2010] bestätigen die 

der RMT, wobei die Unterkante des kontaminierten 

Bereichs sich in 15 m wesentlich deutlicher bei den 

DC-Ergebnissen abzeichnet. 

Eine solche flächenhafte Darstellung ist auf Grund 

der Interpolation zwischen den Profilen kritisch zu 

bewerten. Zwischen dem letzten Profil und dem Ufer 

des Solani lässt sich keine verlässliche Aussage treffen, 

da sich die Entfernung auf ca. 300 m beläuft. Problematisch 

sind auch Inversionsartefakte, die bei der 

Interpolation zwischen den Profilen überakzentuiert 

werden. Trotzdem eignet sich die Flächendarstellung 

zur Visualisierung der lateralen Leitfähigkeitsverteilung 

und insbesondere, um ein räumliches Bild des 

Untergrundes zu gewinnen. 

Diskussion und Ausblick 

Die Inversionsmodelle, der bei der Mülldeponie aufgenommenen 

Datensätze, haben in der Regel einander 

ähnliche Strukturen. Unterhalb einer etwas hochohmigeren 

Deckschicht zeigen diese, im Vergleich zu 

dem Inversionsmodell des Referenzprofils, Werte des 

spezifischen Widerstands kleiner als 10 Ωm bis zu einer 

Tiefe von ungefähr 15 m. Dieser Bereich konnte 

mit dem oberflächennahen Grundwasserleiter identifiziert 

werden und der im Vergleich geringere Wert 

des spezifischen Widerstands kann auf den Einfluss 

des Abwassers zurückgeführt werden. 

Aus der flächenhaften Darstellung der Inversionsmodelle 

konnte die laterale Verbreitung der Kontamination 

abgeleitet werden. Erkennbar ist eine Zunahme 

des spezifischen Widerstands mit der Entfernung 

von der Mülldeponie, so dass diese vermutlich auch 

als Kontaminationsquelle angenommen werden kann. 

Auch reichen die Werte verringerter spezifischer Widerstände 

nahe der Deponie vergleichsweise tief. 

Darüber hinaus sind die spezifischen Widerstände der 

RMT-Inversionsmodelle in der Nähe des Hauptabwasserkanals, 

wo sich die Wasserauslässe befinden, 

ebenfalls verringert. In ungefähr 600 m Entfernung 

von der Mülldeponie im Flussbett des Solani sind die 

Werte des spezifischen Widerstands wiederum deutlich 

höher und vergleichbar mit denen des Referenzprofils. 

Insgesamt lassen sich die Mülldeponie und das Abwasser 

als Kontaminationsquellen bestätigen und es 

kann eine Systematik der Kontaminationsverbreitung 

mit dem Abstand von den Quellen abgeleitet werden. 

Das Programm RMTDC2D [Candansayar und Tezkan, 

2008] lieferte vergleichbare Inversionsmodelle 

wie die einzelnen Inversionen der Datensätze mit 

DC2DINVRES [Günther, 2004] und RUND2 [Rodi 

und Mackie, 2001]. Insbesondere die Inversionsmodelle 

der einzelnen Inversionen mit RMTDC2D waren 

den Inversionsmodellen der anderen Programmen 

sehr ähnlich. 

Bei Inversionsmodellen, die in ihrer Struktur starke 

Unterschiede zeigten, war die Joint Inversion schwierig, 

da beide Datensätze nicht gleichzeitig anzupassen 

waren. Trotzdem konnte mit der Jointinversion 

ein einheitliches Modell beider Datensätze gefunden 

werden, was eine nützliche Hilfe bei der Interpretation 

der Ergebnisse darstellt. 

Vor allem konnte die Unterkante des kontaminierten 

Bereichs durch Hinzunahme der DC-Daten aufgelöst 

werden und gleichzeitig lieferten die RMT-Daten 

Zusatzinformation an den Rändern der Profile, wo 

mit der DC keine Tiefenaussage zu treffen möglich 

war. Die Joint Inversion führte unter diesem Gesichtspunkt 

zu verbesserten Endmodellen. 

Problematisch gestaltete sich allerdings die Auswirkung 

des Regularisierungsparameters. Bei einem zu 

geringen Wert ergaben sich stark überstrukturierte 

Inversionsmodelle und Inversionsartefakte. 

Schwierig war auch die Bewertung der Inversionsmodelle 

anhand der Auflösungsmatrizen. Die Auflösungsmatrizen 

der Joint Inversion waren mit denen 

der einzelnen Inversionen von RMTDC2D nicht 

vergleichbar und eine quantitative Aussage über das 

verbesserte Auflösungsvermögen der Joint Inversion 

konnte daher nicht getroffen werden. 

Im Rahmen des DFG-DST Projektes, welches diese 

Arbeit ermöglicht hat, ist eine weitere Messung auf 

dem selben Gebiet vorgesehen. Hierbei soll die „Transient 

Electromagnetic“ Methode (TEM) zum Einsatz 

kommen. Mit dieser Methode besteht die Möglichkeit 

tiefer liegende Strukturen aufzulösen. Wünschenswert 

wäre mit dieser Methode den Einfluss der 

Kontamination auf den tiefer liegenden Grundwasserleiter 

zu untersuchen, da sich die hier vorliegende 

Arbeit auf die Erkundung des oberen Grundwasserleiter 

konzentriert hat. 

Des Weiteren eignen sich die verwendeten Methoden 

gut für die Erkundung von kontaminierten Böden 

und könnten gerade in Indien vermehrt zum Einsatz 

kommen um damit zur Verbesserung der Grundwasserversorgung 

beizutragen. 

Interessant wäre auch die Einbeziehung der geophysikalischen 

Ergebnisse in eine hydrogeologische Interpretation, 

um die Auswirkung der Kontamination auf 

größeren räumlichen und auch zeitlichen Skalen abzuschätzen. 

Die 2D Joint Inversion stellt ein zusätzliches Hilfsmittel 

zur Interpretation von RMT- und DC- 

Inversionsmodellen dar. Die einzeln erhaltenen Inversionsmodelle 

lassen sich durch die Hinzunahme der 

Joint Inversionsmodelle leichter qualitativ und quantitativ 

bewerten. Eine weitere Anwendung dieses Programmes 

ist daher wünschenswert. 

Literatur 

Candansayar, M. und B. Tezkan, Two-dimensional 

joint inversion of radiomagnetotelluric and direct current 

resistivity data, Geophysical Prospecting, 56, 737– 

749, 2008. 

Günther, T., Inversion Methods and Resolution Analysis 

for the 2D/3D Reconstruction of Resistivity Structures 

from DC Measurements, Dissertation, Technischen 

Universität Bergakademie Freiberg, 2004. 



162

Oldenburg, D. W. und Y. Li, Estimating the depth 

of investigation in DC resistivity and IP surveys, Geophysics, 

64, 403–416, 1998. 

Recher, S., Dreidimesionale Erkundung von Altlasten 

mit Radiomagnetotellurik - Vergleiche mit geophysikalischen, 

geochemischen und geologischen Analysen an 

Bodenproben aus Rammkernsondierungen, Dissertation, 

Universität zu Köln, Institut für Geophysik und 

Meteorologie, 2002. 

Rodi, W. und R. L. Mackie, Nonlinear conjugate gradients 

algorithm for 2D magnetotelluric inversion, Geophysics, 

66, (1), 174–187, 2001. 

Seher, T., Untersuchung von Feuchtbiotopen in Ostfriesland: 

Gefährdungsabschätzung mit Multielektroden- 

Geoelektrik und Radiomagnetotellurik, Diplomarbeit, 

Universität zu Köln, Institut für Geophysik und Meteorologie, 

2005. 

Singhal, D., T. Roy, H. Joshi und A. Seth, Evaluation 

of Groundwater Pollution in Roorkee Toen, Uttaranchal, 

Journal Geological Society of India, 62, 465– 

477, 2003. 

Sudha, B.Tezkan, M.Israil, D. Singhal und J.Rai, 

Geoelektrical mapping of aquifer contamination: a case 

study from Roorkee, India, Near Surface Geophysics, 8, 

33–42, 2010. 

Tezkan, B., A review of environmental applications of 

quasi-stationary electromagnetic techniques, Surveys 

in Geophysics, 20, 279–308, 1999. 

Wiebe, H., 1D-Joint-Inversion von Geoelektrik und Radiomagnetotellurik, 

Diplomarbeit, Universität zu Köln, 

Institut für Geophysik und Meteorologie, 2007. 

Yogeshwar, P., Grundwasserkontamination bei Roorkee/Indien: 

2D Joint Inversion von Radiomagnetotellurik 

und Gleichstromgeoelektrik Daten, Diplomarbeit, 

Universität zu Köln, Institut für Geophysik und Meteorologie, 

2010. 



163

Site Effect Assessment in the Mygdonian Basin (EUROSEISTEST area, Northern Greece) 

using RMT and TEM Soundings 

Widodo 1,2) , Marcus Gurk 2) , Bülent Tezkan 2) 

1) Adhi Tama Institute of Technology Surabaya (ITATS), Indonesia 

2) Institute of Geophysics and Meteorology, University of Cologne, Germany 

Abstract 

During the project “Euroseistest Volvi-Thessaloniki”, a strong-motion test site 

(EUROSEISTEST) for Engineering Seismology was installed in the Mygdonian Basin between the 

two lakes Volvi and Lagada ca. 45 km northeast of Thessaloniki (Northern Greece). The basin itself 

is a neotectonic graben structure (5 km wide) with increased seismic activity along distinct normal 

fault patterns. Fluvioterrestrial and lacustrien sediments (approximately 350-400 m thick) are 

overlying the basement consisting of gneiss with schist. To improve the seismic wave propagation 

model it is vital to know about site effects, e.g. the geotectonic properties of the area such as the topof-basement, 

vertical tectonic boundaries (faults and basement fracturation) and the geothermal 

regime. Therefore, we carried out near surface EM studies to understand the distribution of the 

active faulting and the top of basement structure of this particular area. 

The RMT (Radiomagnetotelluric) and TEM (Transient electromagnetic) measurements were 

carried out on three profiles and thirty sounding. The inverted RMT and TEM data show generally a 

four layer model. The layers are indicated as metamorphic and sediment rocks, which are in detail: 

marly silty sand with gravel (>> 100 Ωm), marly silty sand with clay (50 - 100 Ωm), sandy clay 

(30 – 50 Ωm) and silty sand (10 - 30 Ωm). Due to the high resistivity of the top layer, the skin depths 

of the RMT soundings are around 35 m. The TEM data gives detail information of the lower structure 

down to a depth of 200 m. According to our analysis, a normal fault next to the Euroseistest could be 

located having a strike direction of N 60 E. The joint interpretation of RMT and TEM data proves to 

be an effective tool to investigate complex geology structures. 

Introduction 

This study refers to the Thessaloniki area, which has recently been affected by the 1978 

destructive earthquake sequence [Papazachos and Papazachou, 1997]. It has been well established 

that the strong ground motion of such a seismic event causes irregularly distributed modification to 

the local geology [Tranos and Mountrakis, 1998], [Raptakis, et. al., 1999]. Different geophysical 

methods have been applied in this area [Thanassoulas, et.al.,1987], [Raptakis,et.al.,1999], 

[Savvaidis,et.al.,1999], [Tranos, et.al, 2003], [Gurk, et.al., 2007], however detail information of fault 

structures has not been verified so far. Ambient noise measurements from the area east of the 

Euroseistest experiment give strong implication for a complex 3-D tectonic setting. Therefore we 

carried out near surface EM studies to understand the distribution of the active faulting and the top of 

basement structure of this particular area. 

Joint TEM and RMT inversion has been successfully applied to geological and engineering 

problems in the past [Tezkan et.al., 1995], [Schwinn, 1999], [Steuer, 2002]. The RMT method has 

low penetration depth and therefore gives information of the surface layers, whereas the TEM 

method gives detail information of the lower structure of the investigated area. Hence, a joint 

interpretation of RMT and TEM data will produce a good resolution of resistivities and thicknesses, in 

shallow and in deeper parts of the subsurface. 



164

Test Area and Geological Setting 

The investigated sites are located between the Lagada and the Volvi Lake in Northern Greece. The 

area is now covered with alluvial deposits as shown in (Fig.1). The local geological mapping in this 

area was done by the Geology Institute the University of Cologne [Maith, 2009]. The Mygdonian 

system corresponds to various types of sediments that were deposited in a quaternary graben 

structure. Due to its hydrothermal activity, the top was intensively covered with travertine/tufa 

deposits, now mostly removed by erosion [Jongmans, et.al. 1998]. The local geological map of the 

area is shown in Fig.1. We find four major units: metamorphic basement formed by schist and 

gneisses in the deeper depths, lower terrace deposit was deposited on the top of the basement 

metamorphic, lacustrine and deltaic sediments including conglomerate, gravel and sand. Fans 

comprise of soil and silt are located between lower terrace deposit and the Holocene deposit is 

composed of sand, silt and clay which are deposited on the top of these sediments. To obtain detail 

information of the geology in this area, TEM and RMT data were observed on all various types of the 

sediments (Fig.1). 

Lower 

Terrace Dep. 

Fans 

Holocene 

Deposit 

Profile Direction of RMT 

Profile 1 of RMT 

Gneiss-Schist 

Fig. 1. Site Location, geology of the study area, location of RMT station ( ), TEM station ( ) and 

location of boreholes ( ) are also displayed in the figure GTEM-1 at the location of TEM-1 

sounding. 

RMT Measurements and Interpretation 

GTEM-1 

S-1 



The RMT measurements were carried out on three profiles as indicated in Figure 1. Parameter of 

the survey design is listed in Table 1. The RMT of profile 1 is along 1600 m with direction N 0 S, 

whereas the direction of profile 2 is located N60 E, which are parallel with transmitters. The direction 

of profile 3 in this area is N60W with length of 1400 m, which are perpendicular with transmitter. Due 

to partial inaccessibility of the area the profiles could not be set up in a straight line. The RMT-F 

system consists out of two magnetic sensors (induction coils, 30 cm length), a preamplifier for the 



165

electrical channels, two electrical antennae and a recorder. It is a four channel instrument (Ex, Ey, 

Hx, Hy) with the capability of estimating the full impedance tensor [Tezkan and Saraev, 2008]. 

Table1. Parameter of RMT survey design 

RMT Length Site distance [m] Orientation Transmitter 

Profile [m] 

azimuth 

Profile 1 1600 25 N0oS N60oE Profile 2 1000 25 N60oE N60oE Profile 3 1400 25 N60oW N60oE A special feature is the way how the electric field is sampled. Instead of grounded dipoles, 

the device uses symmetrical electrical dipoles (e.g. two arms of 20 m length) that are capacitively 

coupled to the ground. The system records time series in two bands: D2 band (10-100 kHz) and D4 

band (100 kHz—1 MHz). The coherency level is important to prevent signals with high noise level, 

generally we used for this study a coherency value of 0.8. 

N S 

Silty Sand 

Marly Salty Sand 

Fault structure 

(????) 

Sandy clay 

Silty Sand 

Fig 2. The RMT 2-D inversion model of profile 2 indicates metamorphic rock (marly salty 

sand) in a depth of 0 -5 m. Stations 1 – 16 and stations 25 – 38 show a very low resistivity (

Fault Structure 

(???) 

Fig.3. The Fault structure direction (black arrow) derived from 2-D RMT inversions 

ρ (Ωm) 

Fig.4. Correlation between the 1-D inversion of the TEM data (GTEM1) at the reference site and 

borehole S-1 information 



167

In order to calibrate the geophysical measurements with the lithology, TEM data at our 

reference site was correlated with borehole data in S-1 (Fig.1). This analysis allows identifying 

characteristic strata based on the electrical conductivity. The modeling of RMT data was done by 

using 2-D inversion techniques (Fig. 2 and Fig.3). The 2-D inversion was performed with the 2-D 

Mackie code [Mackie, et.al, 1997], the 1-D inversion was done with the Marquardt [Cerv and Pek, 

1979] and Occam algorithm [Constable, 1978]. Prior to any 2-D modeling, the penetration depth 

have been estimated using the ρ* (z*) transformation [Schmucker, 1979]. Penetration depths are 

found to be around 35 m. 

As an example, we explain the RMT model of profile 2 in detail. This model (Fig.2) shows 

high resistivities on the top layer (more than 100 Ω m) which correlates to the marly silty with clay of 

the borehole data (Fig.4). For stations 1 -16 and stations 25-38 there is a low resistive structure 

beneath the surface layer. Between stations 17-24 there is a high resistive structure with the same 

resistivities as the surface layer. This region is interpreted as a fault structure (Fig.2), which is filled 

with sedimentary rock (sandy clay). 

The data quality and the consistency between ρa and φ could be checked in the apparent 

resistivity curves, which are shown in Fig.5. RMT station 8 on profile 2 show that the resistivity 

values decrease from highest resistivity (> 80 Ωm) to low resistivity (30 Ωm) with phase values less 

than 50 °. The sounding curves of station 8 and 13 (figure 5) and station 16 (figure 5) on profile 2 

shows that the phases exceeds value more than 45° indicating a low resistive (sediment) structure 

at larger depths, meanwhile the good conductive metamorphic series is indicated by the phase 

values lower than 45. Fig. 6 shows a comparison between measured and calculated data at 

selected frequencies (79 kHz, 387 kHz and 784 kHz). Measured and synthetic data fit well together 

keeping in mind the geological complexity and inhomogeneous in this survey area, however some 

misfits which are associated as 3-D effect. 

The direction of the fault can be constructed using the 2-D inversion models of profile 1-3 as 

shown in Fig.3. The direction of the fault structure is found to be N60E. 



168

N60E 

N60E 

N60E 

Fig.5. Comparison of measured and calculated RMT data of stations 8, 13 and 16 on profile 2 



169

Fig.6. Comparison of measured and calculated RMT data at frequencies 79, 387 and 784 kHz 



170

TEM soundings 

In order to overcome the resolution problem of TEM soundings for near surface structures, 

we carried out RMT soundings at each TEM location to use this additional information in the 

following joint inversion. The distance between the TEM stations is depending on the accessibility of 

the area. Thirty loop-loop measurements (Tx: 50 m x 50 m and Rx: 10 m x 10 m) were performed 

during this campaign. TEM data were obtained using the Zonge NT 20 transmitter and the Zonge 

GDP32 receiver. 

c 

a b 

Time (s) 

Time (s) 

0.01 

0.0001 

1e-06 

1e-08 

1e-10 

e 

Fig.7. The segmentation recording scheme for the in-loop Zonge manufactured TEM system; 

low-gain Nano TEM (a), high-gain Nano TEM (b), automatic-gain Zero TEM (c), combination of alltransient 

(d), TEM sounding of station 1 was processed with deconvulation and inversion (e). 

The circle indicate unreliable decay curves for very late times that we address to be an A/D 

conversion problem of the Zonge device. 

d 

Time (s) 

Time (s) 



171

The system allows to measure TEM data in two distinct modes, according to different 

investigation depths: Nano TEM with low and high gain and Zero TEM measurements (Fig.7). Both 

modes give unreliable decay curves for very late times that we address to be an A/D conversion 

problem of the Zonge device. To cope with this problem we simply changed polarity of the receiver 

loop. Consequently a time consuming data acquisition procedure was required. 

The first measurement for shallow investigation was done in NANO TEM low gain mode. 

This mode uses low currents (about 0.3 A) which is switched of quickly. Moreover, the ramp time 

were taken from 0.3 μs to 2.5 ms with manual low-gain settings. Whereas, Nano TEM high-gain uses 

a higher transmitter current (about 3 A), which gives a higher penetration depth with a saturation for 

earlier time. Nano TEM low-gain and high-gain uses 12 Volt power supply. To obtain higher 

penetration depths, Zero TEM measurements were carried out from 31 μs to 6 ms time window with 

accompanying automatic-gain settings. It uses a relatively high transmitter current (10 A) at 24 Volts 

and 50-55 μs turn-off ramp time. 

The penetration depth of TEM methods depends on the time after the transmitters current is 

switched off [Parasnis, 1986]. The diffusion process of the transient electromagnetic induction field 

can be visualized using the smoke ring concept [Nabighian, 1979]. Due to the low conductivity 

(metamorphic rock), the maximal penetration depth (δT) of TEM sounding is approximately 200-300 

meter. The next step is a deconvolution of the data that was done by the EADEC algorithm (Lange, 

2002) followed by a 1-D inversion with EMUPLUS (e.g. Scholl, 2005) (Fig.7 (e)). The 1-D 

interpretation of the TEM data also shows the lateral boundary of the fault structure at stations 12- 17 

on profile 1 (Fig.8). 

Fig.8. One-dimensional TEM model on profile 1 



172

Joint Interpretation of RMT and TEM data 

A joint interpretation can be used to get a better resolution of the model parameter and this 

will enhance the possibility to detect the active fault structure. Generally we conducted RMT 

soundings at each TEM site location so that we can estimate a jointly inverted model at each TEM 

location (Fig.9). 

a). 

b). 

c). 

Table2. The importance parameter of station 10 

RMT Imp TEM Imp Joint Imp 

ρ1[Ωm] 322.46 0.99 367.98 0.57 247.99 0.99 

ρ2[Ωm] 158.17 0.99 367.98 0.88 344.23 0.27 

h1[m] 5.56 0.97 9.75 0.97 9.15 0.84 

RMS[%] 4.90 3.10 3.20 

Table 3. Model resistivies obtained from the 

RMT and TEM data for the selected stations 

Station RMT TEM Joint 

10 322.46 367.98 344.23 

11 332.20 273.45 303.06 

12 450.73 372.20 616.36 

13 562.36 271.88 531.33 

14 363.93 420.46 865.49 

17 199.91 260.49 208.14 

26 4.47 23.48 26.93 

25 28.71 15.83 32.98 

Fig. 9. (a) One-dimensional model section derived by RMT data (b). One-dimensional model 

section of TEM data (c) Joint interpretation of TEM and RMT data. The comparison between 

TEM, RMT and Joint on station 10, 11,12,14,17 and 25 are shown with ellipses. 



173

The 2-D model of the RMT data (Fig.2) gives information about the top structure of this area, 

but the deeper structures and the fault system cannot be resolved in detail solely based on RMT 

soundings. On the other hand, TEM shows a good resolution of deeper structure. The joint 

interpretation/inversion process was done using the Marquardt algorithm. The interpretation of the 1- 

D RMT model between station 13 – 25 resolves of the top layer (Fig 9 (a)) and the TEM 1-D model 

(Fig.9b) shows the bottom of boundary layers of fault structure (Fig.8) in this area more distinctly, 

however the top layers of TEM stations 13-25 could not be resolved well because the top layer has 

high resistivity value (> 80 Ω m) addressed as metamorphic rock from our reference borehole. 

Joint inversion can increase the number of model parameter that includes some of which the 

methods cannot resolve separately (Fig.9c). The importance parameters were calculated for the 

model resistivities and thickness [Jupp and Vozoff, 1975] [Tezkan et.al., 1995], [Schwinn, 1999], 

which are plotted in Table 2. It shows the parameter (ρ1, ρ2, h1) as a result of the individual 

single/joint inversions. Values between 0 (unimportant) and 1 (important) are calculated. From this 

analysis we conclude that the resistivity values and thicknesses of the fault structure (Fig.9) is well 

resolved at station 10, 11,12,14,17 and 25; however, at station 13, it is hardly resolved (importance 

0.65). The resistivity value at station 26 is weakly resolved with importance parameter 0.12. The 

model resistivities of the second layer (between 5-20 m) obtained from 1-D models of TEM and RMT 

data are in good agreement with the joint inversion models (Table 3). 

Conclusion 

The Inversion of RMT and TEM data indicates a normal fault structure with a strike direction 

of approximately N 60 E. The RMT and TEM models generally show four layers that can be 

separated according to their resistivity values. We address them as to be metamorphic and sediment 

rocks, which are marly silty sand with gravel (>> 100 Ω m), marly silty sand with clay (50 - 100 Ω m), 

sandy clay (30 – 50 Ω m) and silty sand (10-30 Ω m). The RMT data was interpreted using 2-D 

inversions technique that results in a good fitting between observed and calculated data. Due to the 

high resistivity of the top layer, the skin depths of the RMT soundings are around 35 m. The TEM 

data gives detail information of the lower structure down to a depth of 200 m. 

This study was financed by the Marie Curie project: IGSEA – Integrated Nonseismic 

Geophysical Studies to Assess the Site Effect of the EUROSEISTEST Area in Northern Greece – 

PERG03-GA-2008-230915 {REF RTD REG/T.2 (2008)D/596232}. 

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inferred from MT and gravity data, Tectonophysics, 317, 171-1886, 2000. 

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176

Die deutsche Nordseeküste im Fokus von aeroelektromagnetischen 

Untersuchungen 

Teilgebiete Langeoog mit Wattenmeer und Elbemündung 

Gerlinde Schaumann 1 , Annika Steuer 2 , Bernhard Siemon 2 , Helga Wiederhold 1 & Franz Binot 1 

1. Einleitung 

1 Leibniz-Institut für Angewandte Geophysik (LIAG), Hannover 

2 Bundesanstalt für Geowissenschaften und Rohstoffe (BGR), Hannover 

gerlinde.schaumann@liag-hannover.de 

Hubschrauberelektromagnetische (HEM) Untersuchungen bieten ein großes Potential für die flächendeckende 

Kartierung der Sedimente der ersten hundert Meter des Untergrundes (Siemon et al., 2009). 

Sie sind für hydrogeologische Fragestellungen von großer Bedeutung, da mit Hilfe des spezifischen 

Widerstands die Verteilung sandiger und tonhaltiger Sedimente im Untergrund sowie Versalzungszonen 

und Süßwasserbereiche ermittelt werden können. 

In den Jahren 2008 und 2009 wurden in Kooperation von LIAG und BGR im Rahmen des LIAG- 

Projektes zur „Flächenhaften Befliegung“ und des „D-AERO“-Projektes der BGR gemeinsam aerogeophysikalische 

Erkundungen zu Salz-/Süßwasserfragestellungen in insgesamt fünf Messgebieten 

im Bereich der deutschen Nordseeküste durchgeführt (Wiederhold et al. 2008, Steuer et al. 2009). 

Das Messgebiet Langeoog umfaßt die Ostfriesischen Inseln Langeoog und Spiekeroog und das angrenzende 

Wattenmeer, das Messgebiet Glückstadt umfaßt den Bereich der Elbemündung nordwestlich 

von Hamburg (Abb. 1). 

Abbildung 1: Lage der Messgebiete Langeoog und Glückstadt (nordwestlich von Hamburg). 



177

Für die Insel Langeoog waren die Lage und die Ausdehnung der Süßwasserlinse zu ermitteln. Im küstennahen 

Bereich erhoffte man im Wattenmeer mutmaßliche Süßwasseraustritte zu finden. Im Bereich 

der Elbemündung sollten die grundwasserführenden Schichten und mögliche Versalzungszonen 

kartiert werden. 

Die Daten dienen als Grundlage für die Planung und Arbeit in vielfältigen ökonomischen und ökologischen 

Bereichen, wie z.B. Raumplanungen und der Entwicklung von Wassernutzungs- und Wasserschutzkonzepten. 

Sie werden über das Fachinformationssystem (FIS) Geophysik des LIAG nutzbar 

sein. 

Das eingesetzte Messsystem wird bei Steuer et al. (2010) beschrieben. Die Karten des scheinbaren 

spezifischen Widerstands a und der Schwerpunktstiefe z* (Siemon, 2009) für die verschiedenen 

Messfrequenzen geben einen ersten Überblick über die Leitfähigkeitsstrukturen in den Messgebieten. 

Die Erkundungstiefe nimmt dabei mit abnehmender Frequenz und Leitfähigkeit zu. Die HEM- 

Messungen liefern die Verteilung der elektrischen Leitfähigkeit bis maximal 150 m Tiefe. Dabei können 

Salzwasser und Süßwasser oder ton- und sandhaltige Sedimente unterschieden werden. Hier dargestellt 

sind erste Ergebnisse in Form von Karten auf dem Bearbeitungsstand nach der Grundprozessierung, 

bei der Korrekturfaktoren und Filtereinstellungen für jeden Flug gleich angesetzt werden. Die 

darauf folgende Feinprozessierung behandelt jeden Flug und jede Frequenz individuell. Die Prozessierung 

der Daten beinhaltet: Filterung, Sprungkorrektur, Nullniveaukorrektur, Feinjustierung der Kalibrierfaktoren 

und Berechnung der Halbraumparameter. 

2. Messgebiet Langeoog 

Langeoog und Spiekeroog sind zwei der Ostfriesischen Inseln im Wattenmeer der Nordsee, die sich 

wenige Kilometer vor der Küste befinden. Sie bestehen aus quartären Sedimenten wie Sanden, Tonen 

und Schluffen (Abb. 3). Durch Versickerung der Niederschläge in den Dünengürteln werden dort 

Grundwasserreservoire mit Süßwasser aufgefüllt, die die Versorgung der Inseln mit Frischwasser sicherstellen. 

Weil Süßwasser ein geringeres spezifisches Gewicht als das versalzte Grundwasser hat, 

schwimmt es als „Linse“ auf dem Salzwasser. Verändert sich der Wasserstand des dichteren Salzwassers, 

ändert sich das Druckniveau und entsprechend auch Stand und Ausdehnung der Süßwasserlinse. 

Durch Stürme können Salzwassereinbrüche bis an den Rand des inneren Dünengürtels der 

Inseln gelangen und dort versickern. Solche Ereignisse, aber auch der erhöhte Wasserbedarf für den 

Tourismus in den Sommermonaten gefährden das Süßwasserreservoir. Noch erfolgt die gesamte 

Trinkwasserversorgung mit inseleigenem Grundwasser, welches in den Wintermonaten allein durch 

Regenfälle wieder aufgefüllt wird. Unterhalb wasserundurchlässiger Bodenschichten kann Süßwasser 

darüber hinaus vom Festland aus unterschiedlich weit in das Wattenmeer vordringen, um dann unter 

gewissen Bedingungen an die Oberfläche zu treten. Die Befliegungen wurden bei Niedrigwasser 

durchgeführt, um vergleichbare Bedingungen für jeden Flug zu haben und insbesondere auch, um 

den Untergrund des Wattenmeeres ohne die bei Flut vorhandene Meerwasserschicht besser erkun- 



178

den zu können. Aufgrund der Berücksichtigung von Naturschutzauflagen konnte die aerogeophysikalische 

Erkundung nur in den Wintermonaten durchgeführt werden. Das Messgebiet umfasst die gesamte 

Insel Langeoog, den westlichen Teil der Insel Spiekeroog und das Wattenmeer zwischen Langeoog 

und dem Festland (Abb. 2). Einen Überblick über die Messkampagne gibt Tabelle 1. 

Abbildung 2: Insel Spiekeroog mit Wattenmeer während der Befliegung im März 2009 und westlicher Teil von 

Langeoog mit der Dünenlandschaft, unter der sich Süßwasserlinsen verbergen (Fotos: W. Voß). 

Tabelle 1: 

Größe des Messgebietes: 259 km² 

Gesamtprofillänge: 1200 km 

Linienabstand: 67 Mess-Linien mit 250 m (N-S), 7 Kontroll-Linien mit 2000 m (W-O) 

Messzeitraum: Februar und November 2008, Februar und März 2009; nur bei Niedrigwasser 

Abbildung 3: Geologische Karte des Messgebietes aus dem FIS Geophysik des LIAG. 



179

Abbildung 4 zeigt die vorläufigen Karten des scheinbaren spezifischen Widerstands (mit a bis maxi- 

mal 2000 m) der verschiedenen Messfrequenzen (133400 Hz, 41520 Hz, 8390 Hz, 5345 Hz, 1823 Hz und 

387 Hz) für das Messgebiet. Jeder Frequenz wird dabei zu den einzelnen Messpunkten eine Schwerpunktstiefe 

z* zugeordnet, die in Abbildung 5 dargestellt ist. Für die höchsten Frequenzen sind dies 

einige wenige Meter unter der Erdoberfläche, die tiefsten Frequenzen erreichen eine Erkundungstiefe 

bis etwa 100 m. Diese Erkundungstiefen sind neben der Frequenz auch von den spezifischen Widerständen 

der Untergrundstrukturen abhängig und können somit von Messpunkt zu Messpunkt variieren. 

Die Abfolge einer Auswahl von Karten des scheinbaren spezifischen Widerstands in einer 3D- 

Darstellung gibt daher eine Abbildung der Leitfähigkeitsstrukturen mit Bezug zur Tiefe nur bedingt 

wieder (Abb. 7). Die tiefste Frequenz bildet die Basis der Süßwasserlinse ab. 

Deutlich sind die den Süßwasserlinsen zugeordneten Strukturen auf der Insel und die mit salzhaltigem 

Nordseewasser gefüllten Priele zu erkennen. Im Bereich vor der Festlandküste kann man Gebiete mit 

für Süßwasser typischen Werten der scheinbaren Widerstände erkennen. Hier ist zu klären, ob dies 

Austritten von Süßwasser im Watt entspricht. 

Abbildung 4: Vorläufige Karten des scheinbaren spezifischen Widerstands a für die Messfrequenzen 

133400 Hz, 41520 Hz, 8390 Hz, 5345 Hz, 1823 Hz und 387 Hz (a bis maximal 2000 m). 



180

Abbildung 5: Vorläufige Karten der Schwerpunktstiefe z* für die Messfrequenzen133400 Hz, 41520 Hz, 

8390 Hz, 5345 Hz, 1823 Hz und 387 Hz. 

Benutzt man einen anderen Farbkeil für die Darstellung der scheinbaren spezifischen Widerstände 

(mit a bis maximal 200 m), kann man beispielsweise die Priele noch viel deutlicher erkennen, siehe 

Abbildung 6. Auch die mutmaßlichen Austritte von Süßwasser im Bereich vor der Festlandküste sind 

wesentlich besser aufgelöst. 

Abbildung 6: Vorläufige Karten des scheinbaren spezifischen Widerstands a für drei ausgewählte Frequenzen 

(41520 Hz, 8390 Hz und 387 Hz), dargestellt mit einem anderen Farbkeil (a bis maximal 

200 m). 

In Abbildung 8 wird die topographische Karte mittels des digitalen Höhenmodells (digital elevation model, 

DEM) aus dem FIS Geophysik des LIAG gezeigt. Dabei wurden die Daten des Höhenmodells auf 

die Fluglinien übertragen. Die topographische Karte kann auch aus GPS- und Laseraltimeterdaten des 

Hubschraubermesssystems abgeleitet werden. 



181

Abbildung 7: 3D-Darstellung der Karten des scheinbaren spezifischen Widerstands a für die Frequenzen 

41520 Hz, 8350 Hz und 387 Hz. Bild aus Google-Earth, September 2009. 

Abbildung 8: Topographische Karte mittels des digitalen Höhenmodells (digital elevation model, DEM) aus 

dem FIS Geophysik des LIAG. Dabei wurden die Daten des Höhenmodells auf die Fluglinien 

übertragen. 



182

3. Messgebiet Glückstadt 

Das Messgebiet Glückstadt umfasst große Teile des Elbemündungsbereichs (Abb. 9). Teile der Ergebnisse 

der HEM-Befliegung werden in das Projekt KLIMZUG-NORD (www.klimzug-nord.de) einfließen, 

bei dem unter anderem die Auswirkungen des Klimawandels auf das Ästuar der Elbe erforscht 

werden. Es ist davon auszugehen, dass sich der Elbwasserstand in diesem Gebiet erhöht, was eine 

Intrusion von Brackwasser in den Süßwasseraquifer nach sich ziehen würde. Mit hydraulischen Strömungsmodellen 

können solche Fragestellungen untersucht werden. Bereits vorhandene geologische 

Informationen sollen mit Hilfe von elektrischen Leitfähigkeitsmodellen der HEM flächenhaft zu einem 

geologischen Strukturmodell ergänzt werden. Dieses wird mit hydraulischen Parametern belegt und 

dient damit als Grundlage für eine hydraulische Modellierung. 

10 km 

Abbildung 9: Flugplan für das Messgebiet Glückstadt, welches große Teile des Elbemündungsbereichs 

umfasst. 



183

Einen Überblick über den Umfang der Messkampagne gibt Tabelle 2. 

Tabelle 2: 

Größe des Messgebietes: 1949 km² 

Gesamtprofillänge: 8500 km 

Linienabstand: 209 Mess-Linien mit 250 m (W-O), 19 Kontroll-Linien mit 2500 m (N-S) 

Messzeitraum: Juli und Oktober 2008, März-Mai 2009 

Aus den GPS- und den Laseraltimeterdaten des Hubschraubermesssystems kann ein digitales Höhenmodell 

abgeleitet werden (Abb. 10). Hier wird besonders der Verlauf der Geest (Höhenzug bestehend 

aus pleistozänen Sandablagerungen von Moränen) und der Marsch (flaches holozänes 

Schwemmland) deutlich. 

10 km 

Abbildung 10: Digitales Höhenmodell des Elbemündungsgebietes, abgeleitet aus GPS- und Laseraltimeterdaten 

des Hubschraubermesssystems. 

Erste Ergebnisse in Form von vorläufigen Karten des scheinbaren spezifischen Widerstands und der 

Schwerpunktstiefe sind in Abbildung 11 dargestellt. Die Datenlücken sind teilweise auf Hochspannungsleitungen 

und entlang der Elbe auf Radarstationen bzw. Sperrzonen um die Atomkraftwerke 

herum zurückzuführen. 



184

Elbe 

3 2 

1 

3 

4 

41 520 Hz 

6 

8 390 Hz 

1 823 Hz 

387 Hz 

5 

2 

a 

[m] 

10 km 

a 

[m] 

a 

[m] 

a 

[m] 

a 

[m] 

41 520 Hz 

8 390 Hz 

1 823 Hz 

Abbildung 11: Vorläufige Karten des scheinbaren spezifischen Widerstands a und der Schwerpunktstiefe z* 

für vier ausgewählte Messfrequenzen. 

387 Hz 



185 

z* 

[m] 

z* 

[m] 

z* 

[m] 

z* 

[m] 

10 km 

z* 

[m]

Mit Hilfe der geologische Karte vom Mündungsbereich der Elbe (Abb. 12a) können z.B. in der Karte 

des scheinbaren spezifischen Widerstands zu der Frequenz 41 kHz (Abb. 12b) folgende Leitfähigkeitsstrukturen 

identifiziert werden: 1. Brackwasser der Elbe, 2. Perimarine Ablagerungen: Ton, schluffig, 

3. Brackische Ablagerungen: Ton bis Schluff, feinsandig, 4. Moor: Torfe, 5. Rotschlammdeponie: 

Eisen- und Titanoxide, 6. Glazifluviatile Ablagerungen: Sand und Kies. 

Elbe 

4. Zusammenfassung und Ausblick 

3 

2 

3 

4 

a) b) 

2 

41 520 Hz 

Abbildung 12: a) Geologische Karte und b) Karte des scheinbaren spezifischen Widerstands der Frequenz 

41 kHz. Im Mündungsbereich der Elbe können folgende Leitfähigkeitsstrukturen identifiziert 

werden: 1. Brackwasser der Elbe, 2. Perimarine Ablagerungen: Ton, schluffig, 3. Brackische 

Ablagerungen: Ton bis Schluff, feinsandig, 4. Moor: Torfe, 5. Rotschlammdeponie: Eisen- 

und Titanoxide, 6. Glazifluviatile Ablagerungen: Sand und Kies. 

In beiden Messgebieten wurde die HEM zur Erkundung von Grundwasserstrukturen erfolgreich eingesetzt. 

Die hier gezeigten Karten dokumentieren die vorläufigen Ergebnisse. Nach Abschluss der Prozessierung 

werden die HEM-Daten in Schichtmodelle des spezifischen Widerstands invertiert. 

Auf den Ostfriesischen Inseln Langeoog und Spiekeroog konnten die Lage und Ausdehnung der 

Süßwasserlinsen erfasst werden. Daneben zeigten sich insbesondere in den Daten der tiefsten Messfrequenz 

Bereiche veränderter scheinbarer spezifischer Widerstände im Wattenmeer vor der Festlandküste, 

die die Vermutung nahe legen, dass hier Süßwasser austritt. 

Im Gebiet Glückstadt werden als Fragestellung mögliche Intrusionen von Brackwasser in den Süßwasseraquifer 

untersucht. Die bereits vorhandenen geologischen Informationen werden mit Hilfe der 

HEM-Modelle flächenhaft zu einem geologischen Strukturmodell ergänzt. Nach einer Belegung mit 

hydraulischen Parametern kann es damit als Grundlage für eine Interpretation mit Strömungsmodellen 

dienen. 

Elbe 

3 2 



186 

1 

3 

4 

6 

5 

2 

a 

[Ohm*m] 

a 

[m] 

10 km

Danksagung 

Die hier vorgestellten Teilgebiete des BGR/LIAG-Projektes wurden in Zusammenarbeit mit dem Institut 

für Chemie und Biologie des Meeres (ICBM), der Universität Oldenburg sowie der Behörde für 

Stadtentwicklung und Umwelt Hamburg durchgeführt. 

Referenzen 

Siemon, B. [2009] Electromagnetic methods – frequency domain: Airborne techniques, In: Kirsch, R. 

(Ed.), Groundwater Geophysics – A Tool for Hydrogeology. 2nd Edition, Springer-Verlag, Berlin, 

Heidelberg, 155-170. 

Siemon, B., Christiansen, A.V. & Auken, E. [2009] A review of helicopter-borne electromagnetic 

methods for groundwater exploration. Near Surface Geophysics, 7, 629-646. 

Steuer, A., Siemon, B., Schaumann, G., Wiederhold, H., Meyer, U., Pielawa, J., Binot, F. & Kühne, K. 

[2009] The German North Sea Coast in Focus of Airborne Geophysical Investigations, AGU Fall 

Meeting 2009, San Francisco, USA. 

Steuer, A., Siemon, B. & Grinat, M. [2010] The German North Sea Coast in Focus of Airborne 

Electromagnetic Investigations: The Freshwater Lenses of Borkum, EMTF, this volume. 

Wiederhold, H., Binot, F., Kühne, K., Meyer, U., Siemon, B. & Steuer, A. [2008] Airborne geophysical 

investigation of the German North Sea Coastal Area, 20th Salt Water Intrusion Meeting 2008, Naples, 

USA. 

http://www.liag-hannover.de/forschungsschwerpunkte/grundwassersysteme-hydrogeophysik/salz- 

suesswassersysteme/flaechenhafte-befliegung.html 

http://www.bgr.bund.de/cln_101/nn_328750/DE/Themen/GG__Geophysik/Aerogeophysik/Projektbeitr 

aege/D-AERO/deutschlandweite__aerogeophysik__befliegung__D-AERO.html 

http://www.fis-geophysik.de/ 



187

The German North Sea Coast in Focus of Airborne Electromagnetic 

Investigations: The Freshwater Lenses of Borkum 

Annika Steuer 1 , Bernhard Siemon 1 and Michael Grinat 2 

1 

Federal Institute for Geosciences and Natural Resources (BGR), Hannover, Germany 

2 

Leibniz Institute for Applied Geophysics (LIAG), Hannover, Germany 

annika.steuer@bgr.de 

Abstract 

Helicopter-borne electromagnetic (HEM) measurements were conducted over the North Sea island of 

Borkum to determine the size of the freshwater lenses. Additionally, geoelectrical measurements were 

carried out at locations where data of 13–17 years old Schlumberger soundings exist. HEM 

successfully revealed the lateral extension as well as the thickness of the freshwater lenses of the 

island of Borkum. At several locations the depth of the freshwater/saltwater boundary determined by 

HEM was confirmed by the results of the Schlumberger soundings. No significant changes of the 

freshwater/saltwater boundary were found at the locations where old and new Schlumberger 

soundings exist. Regarding the results of direct-push and borehole measurements, the HEM related 

resistivity structure could be determined more precisely and additional to the freshwater/saltwater 

boundary thin clay layers were revealed. Based on the HEM inversion results the volume of the 

freshwater resource was estimated. 

North Sea 

Germany 

Figure 1: The location of the island of Borkum in the North Sea 

and a Google-Earth map with the flight-lines. 



188

Introduction 

Since 2008, the German North Sea Coast has been in the focus of airborne geophysical investigations 

carried out by the Federal Institute for Geosciences and Natural Resources (BGR) and the Leibniz 

Institute for Applied Geophysics (LIAG). Especially electromagnetics is the most versatile of the 

airborne geophysical methods and widely applied in hydrogeological investigations as the 

measurements respond to both lithologic and water-chemistry variations. The applications comprise 

geologic mapping and aquifer structure, delineation of soil and groundwater salinization, saltwater 

intrusion into coastal aquifers etc. 

Here, we present the HEM results for the North Sea island of Borkum, which was the first of the five 

HEM project areas investigated in 2008-2009, and compare them with DC Schlumberger soundings, 

lithological logs and direct-push measurements. These data will be used for a hydraulic modelling of 

the freshwater lenses of the island of Borkum in the CLIWAT project (http://cliwat.eu, EU Interreg IVB 

North Sea Region). Additionally we show an estimation of the volume of the freshwater lenses 

calculated by Siemon et al. (2009b). 

Other HEM results for the Wadden Sea, the North Sea islands of Langeoog and Spiekeroog, and the 

Elbe estuary are shown by Schaumann et al. (2010) in this volume. Wiederhold et al. (2009) presented 

the results of two SkyTEM surveys at the North Sea island of Föhr and the saltdome Bad Segeberg, 

which were conducted in 2008 by SkyTEM Aps by order of LIAG. 

HEM Survey 

The Borkum survey covers an area of 88 km² and was flown within two days in March 2008. The flightline 

spacing was 250 m and the tie-line spacing was 500 m, totalling to about 412 line-kilometres 

(Figure 1). The BGR helicopter-borne geophysical system simultaneously uses frequency-domain EM, 

magnetics and radiometrics (Figure 2). 

The HEM system, a RESOLVE bird manufactured by Fugro Airborne Surveys, operates at six 

frequencies ranging from 386 Hz to 133 kHz. 



189

Figure 2: BGR helicopter-borne geophysical system: 

Electromagnetics: 

RESOLVE (Fugro Airborne Surveys) 

Frequencies: 386, 1 823, 5 495, 8 338, 

41 430 and 133 300 Hz 

Coil separations: ~8 m 

Coil orientation: 5× horizontal coplanar 

1× vertical coaxial 

Investigation depth: 1–70 m (at Borkum) 

Magnetics: Cs magnetometer 

Radiometrics: 256 channel gamma-ray 

spectrometer 

Navigation/Positioning: 

GPS / radar and laser altimeter 

Bird altitude: ~ 34 m 

Flight speed: ~140 km/h 

Sampling distance: ~4 m 

The investigation depth increases with decreasing frequency. The EM fields of the lowest frequency 

penetrate the freshwater lenses nearly completely as seen in the apparent resistivity maps (Figure 3). 

Here, higher resistivities are represented by green and blue colours (freshwater) and lower resistivities 

by red colours (saltwater). The apparent resistivity maps, which are based on the half-space 

approximation, provide a first insight into the subsurface conductivity distribution. 

133 kHz 41 kHz 1.8 kHz 0.4 kHz 

Figure 3: Apparent resistivity maps: The investigation depth increases with decreasing frequency. The 

freshwater lenses – represented by higher resistivities (green & blue) – are nearly completely 

penetrated by the EM fields of lowest frequency. 

The HEM data were also inverted using Marquardt-Levenberg 1-D inversion technique based on a 

layered half-space model (Siemon et al., 2009a). Starting models required were derived automatically 

from the apparent resistivities vs. centroid depth sounding curves. Resistivity maps at selected depths 

and stitched together vertical resistivity sections were derived from these 1-D inversion models. The 

lateral extensions as well as the thicknesses of the freshwater lenses were mapped successfully with 

HEM, as shown in the resistivity maps and the vertical resistivity sections of Figure 4. 



190

Figure 4: Resistivity maps at 5 and 40 m bsl and vertical resistivity sections along the tie lines T13.9 

and T6.9. 

The first layer represents the resistive dry dune sands above the groundwater table (dark blue) and 

the bottom layer the conductive saltwater-filled sediments (red) below the freshwater lenses (blue). 

The two layers in-between are associated with sediments filled with fresh or brackish water. The 

freshwater/saltwater boundary was detected down to about 60 m depth. 



191

DC survey: Comparison of measurements 16 years apart 

In 2008, 36 Schlumberger soundings were 

carried out at sites already measured 

between 1991 and 1995 (Worzyk, 1995a 

and 1995b). 

All the sounding curves at Borkum have a 

Q-type shape with three or more layers (e.g. 

Figure 5). Higher resistivities are due to dry 

and freshwater filled sediments, whereas the 

lower resistivities at the end of the sounding 

curves are due to saltwater-filled sediments 

underlying the freshwater lenses. 

apparent resistivity [m] 

10000 

1000 

1 10 100 1000 

current electrode separation AB / 2 [m] 

In 1992, the freshwater filled sediments 

were associated with resistivities between 

Figure 5: DC sounding curve of site GTS 60. 

70 and 110 m in the water catchment area 

Ostland; these resistivities were almost reproduced in 2008. The underlying saltwater-filled sediments 

showed resistivities below 10 m, but these values were not determined exactly. Taking equivalent 

models into consideration the thickness of the freshwater lens can be determined with an accuracy of 

about 6–8 m. 

No significant changes of the freshwater/saltwater boundary were found at the locations where old and 

new Schlumberger soundings exist. 

100 

10 

GTS 60 (5/1992): Data + model (-) 

GTS 60 (10/2008): Data + model (-) 



192

Combined analysis 

At several locations the depth of the freshwater/saltwater boundary determined by HEM was 

confirmed by the results of the Schlumberger soundings (e.g., Figure 6). 

a) 

c) 

BR40 

T 7.9 

NE SW 

HEM T 7.9 

GTS 60 

BR 40 

HF510S3L5 D2 SF075 200 

The elevation map in Figure 6b shows the location of the Schlumberger sounding GTS 60 (blue circle), 

the drilling BR 40 (orange circle) and a part of flight-line T 7.9 (red line). The flight-line crosses a dune 

and the Schlumberger sounding is located about 80 m apart from the flight-line in a dune valley. The 

vertical resistivity section of this part in Figure 6c shows that the saltwater/freshwater boundary was 

determined by the HEM 1-D inversions at about 60 m depth. This is confirmed by the 1-D inversion 

result of the Schlumberger sounding of 2008 which has not changed significantly since 1992 (Figure 

6d). 

Regarding the results of direct-push (Winter, 2008) and borehole measurements, the HEM related 

resistivity structure could be determined more precisely. A more detailed 6-layer approach revealed 

additionally to the freshwater/saltwater boundary thin conductive layers at about 10 m depth, not seen 

in the 4-layer models of the standard inversion procedure (Figure 7b). Partly, they were identified as 

clay layers by lithological logs; and also the result of a direct-push measurement shows an increasing 

conductivity at 10 m depth (Figure 7c). The depth of the freshwater/saltwater boundary remains nearly 

constant and has a layer with little higher resistivity above, which could be interpreted as transition 

b) 

d) 

1 

2 

3 

4 

5 

6 

7 

0 

8 

depth [m] 

HEM 

GTS 60 (10/2008) GTS 60 (5/1992) BR 40 

4560 2578 m 

Br unnen 40 

2181 m 

Feinsand, 

z.T. schluffig 

76 

Filter I 

69 

1.05 

92 

1.1 

87 

1.1* 

M itt elsand 

Mittelsand, 

fein- bis 

grobsandig 

Geschiebelehm, 

Schluff, tonig 

Filter II 

ET 

Figure 6: a) Resistivity map (5 mbsl) with the location of a part of flight-line T7.9 (red line), the lithological log 

BR40 (orange circle) and the DC site GTS 60 (blue circle). b) Digital elevation model revealed 

from laser scan data of NLWKN. c) Vertical resistivity section T7.9 as result of a 5-layer 1-D 

inversion (every 5 th model is shown). d) Comparison of 1-D inversion results of HEM and DC 

reveals the freshwater/saltwater boundary at a similar depth of about 60 mbsl. 



193 

BR40 

T 7.9

zone of brackish water. The data misfit q [%] of the 6-layer inversion is smaller than the misfit of the 4layer 

inversion, especially in the south-eastern part of the section. 

a) 

b) 

c) 

NW HEM L16.1 

SE 

DP 06 

DirectPush 06 

GTS 8 

m/min mS/m Ohmm 

10-12 m 

L16.1 

WWBO 1026 BORK II 811 

H_F5_10_S3_L4_D2_SF100_ 

0 

10 

20 

30 

40 

50 

60 

70 

78 

37 

2.0 

80 

depth [m] 

HEM GTS 8 

9890 

80 

18 

103 

9.3 

2.0 

9883 

NW HEM L16.1 

SE 

Figure 7: a) Apparent resistivity map (41 kHz) with the location of the vertical resistivity section 

L16.1, the lithological logs and the direct-push measurement. b) Comparison of HEM 1-D 

inversion results (4- and 6-layer models) along L16.1 with c) lithological logs (WWBO 1016 and 

BORK II 811) (LBEG), direct-push results (DP 06) (Winter, 2008) and DC 1-D inversion results 

(GTS8). 

118 

61 

2.3 

DP 06 

1035 m 

GTS 8 

WWBO 1026 

WWBO 1026 BORK II 811 

> 8.9 m clay 



194 

H_F5_10_S3_L6_D2_SF100_200 

BORK II 811 

6.3-9.5 m clay 

9.5-12 m peat

Estimation of the aquifer thickness 

The aquifer thickness was estimated using Archie’s law with the following approach: The resistivity of 

freshwater is assumed to be higher than 5.6 m (180 mS/m) and thereby the resistivity of freshwater 

saturated sediment with 33% porosity and a formation factor of 4 should be above 23 m (Siemon et 

al., 2009b). Based on that, the accumulated layer thickness with resistivities of 30–500 m is defined 

as aquifer thickness and is shown in Figure 8. From that, the freshwater volume was estimated to 175 

x 10 6 m³. 

Conclusions 

Figure 8: Aquifer thickness derived from DC and HEM. 

(1991/92) 

(based on 4-layer model) 

At several locations the depth of the freshwater/saltwater boundary as derived by the HEM inversion 

was confirmed by Schlumberger soundings. The DC measurements were carried out at the same sites 

as 16 years before, no significant changes of the freshwater/saltwater boundary were found. 

Regarding direct-push and borehole data, the HEM inversion provided more information about 

resistivity structure. A 6-layer approach revealed additionally to the freshwater/saltwater structure thin 

clay layers. 

Based on the HEM inversion results the volume of the freshwater resource was estimated. 



195

Acknowledgments 

The HEM survey was funded by LIAG/BGR project “Airborne Geophysical Investigation of the German 

North Sea Coastal Area” (Wiederhold et al., 2008): 

http://www.liag-hannover.de/forschungsschwerpunkte/grundwassersysteme- 

hydrogeophysik/salz-suesswassersysteme/flaechenhafte-befliegung.html 

http://www.bgr.bund.de/cln_101/nn_328750/DE/Themen/GG__Geophysik/Aerogeophysik/Proj 

ektbeitraege/D-AERO/deutschlandweite__aerogeophysik__befliegung__D-AERO.html 

The lithological logs were taken from the LBEG Map Server (http://www.geophysics-database.de/) of 

the Niedersächsisches Landesamt für Bergbau, Energie und Geologie (LBEG). 

The direct-push results were provided by the Ingenieurbüro für Hydrogeologie, Sedimentologie und 

Wasserwirtschaft (HSW) (Winter, 2008). 

The digital elevation model was provided by the Niedersächsischer Landesbetrieb für 

Wasserwirtschaft, Küsten- und Naturschutz (NLWKN), Forschungsstelle Küste, An der Mühle 5, 26548 

Norderney. 

References 

Schaumann, G., Steuer, A., Siemon, B., Wiederhold, H. & Binot, F. [2010] Die deutsche Nordseeküste 

im Fokus von aeroelektromagnetischen Untersuchungen, Teilgebiete Langeoog mit Wattenmeer und 

Elbemündung, EMTF, this volume. 

Siemon B. [2006] Electromagnetic methods – frequency domain: Airborne techniques, In: Kirsch, R. 

(Ed.), Groundwater Geophysics – A Tool for Hydrogeology. Springer-Verlag, Berlin, Heidelberg, 155- 

170. 

Siemon B., Auken E. & Christiansen A.V. [2009a] Laterally constrained inversion of frequency-domain 

helicopter-borne electromagnetic data, Journal of Applied Geophysics, 67, 259-268. 

Siemon, B., Christiansen, A.V. & Auken, E. [2009b] A review of helicopter-borne electromagnetic 

methods for groundwater exploration. Near Surface Geophysics, 7, 629-646. 

Wiederhold, H., Binot, F., Kühne, K., Meyer, U., Siemon, B. & Steuer, A. [2008] Airborne geophysical 

investigation of the German North Sea Coastal Area, 20th Salt Water Intrusion Meeting 2008, Naples, 

USA. 



196

Wiederhold, H., Kirsch, R., Schaumann, G., Scheer, W. & Steuer, A. [2009] Airborne geophysical 

investigations for hydrogeological purposes in Northern Germany. Extended Abstracts Book of the 

15th European Meeting of Environmental and Engineering Geophysics – Near Surface 2009, Dublin, 

Ireland, 7.-9.9.2009. 

Winter, S. [2008] Erkundung und Bewertung von Grundwasserbelastungen im Bereich der 

Süßwasserlinsen Borkum, Teilprojekt Direct-Push-Sondierungen, Ergebnisbericht, HSW, Leer. 

Worzyk P. [1995a] Geoelektrische Tiefensondierungen auf der Insel Borkum – Untersuchungen zur 

Veränderung der Süßwasserlinse im Ostland. NLfB Archives no 111751, Hannover. 

Worzyk P. [1995b] Geoelektrische Tiefensondierungen auf der Insel Borkum – Untersuchungen zur 

Struktur der Süßwasserlinse im Einzugsbereich des Gewinnungsgebietes Waterdelle. NLfB Archives 

no 114088, Hannover. 



197

Some notes on bathymetric effects in marine 

magnetotellurics, motivated by an amphibious 

experiment at the South Chilean margin 

Gerhard Kapinos, Heinrich Brasse 1 

Freie Universität Berlin, Fachrichtung Geophysik, Malteserstr. 74-100, 12249 Berlin, 

Germany 


Whilst the onshore magnetotelluric method is established as a useful method for imaging 

electrical conductivity structures in the deep earth’s interior, electromagnetic investigation 

in marine environment has attracted until recently much less attention, although 

the oceans cover the most part of the Earth’s surface. Beside of logistical challenges, 

high technical demands on the instruments and involved higher costs, physical conditions 

in marine environments make the acquisition and interpretation of offshore data 

by far more difficult than onshore data. The broad period range of usable signals utilized 

in the terrestrial MT is substantially limited on the seafloor. The ionospheric and 

magnetospheric primary source field recorded on the seafloor is at short periods strongly 

attenuated by the covering highly conductive ocean layer and at long periods contaminated 

by motionally induced secondary electromagnetic fields. Additionally, attention 

has to be payed to the shape of the ocean bottom, which can massively distort the 

electromagnetic fields particularly in coast region. 

2 Decay of electromagnetic fields in the ocean 

The decay of the electromagnetic amplitude in a high conductive homogeneous half space 

like ocean water (ρ =0.3Ωm) and a less conductive medium like earth (ρ = 100Ωm) 

shows Fig. 1. In a homogeneous half space without boundary in vertical direction the 

field behaviour in both media can be estimated according to the simple formula used for 

the calculation of the skin depth 

F = F0e −kz , (1) 

1 kapinosg@geophysik.fu-berlin.de, h.brasse@geophysik.fu-berlin.de 



198

z/δ 

0 

1 

2 

3 

4 

Re 

Im 

magnitude 

land 

ocean 

5 

-0.5 0 0.5 1 

E(z)/E(0) 

Figure 1: Decay of the of magnitude of electromagnetic field F (green) and its real 

(red) and imaginary part (blue) as function of depth in a highly conductive (i.e. ocean 

water, dashed line) and a less conductive homogeneous half space (solid line). The 

decay is scaled to the surface value F0. 

where k = √ iμσω. At a depth of 4000 m, which corresponds to the average ocean 

depth, the amplitude of a field propagating in the ocean at a period of 10 s is attenuated 

hundredfold, i.e. the field on the ocean bottom would be approximately 1% of the surface 

value. 

This simple relationship becomes more complicated when taking into account real 

conditions with a highly conductive ocean layer which is limited downward by a relatively 

resistive basement. Analog to the N-layered half space the solution has to be upgraded 

by a further term according to the reflection on the ocean bottom at depth h. The 

solution for the x-component of the electric field in the first and second layer is 

E1,x = E11e −k1z + E12e k1z 

E2,x = E22e −k2z 

where E11 is the amplitude of the downgoing and E12 of the upgoing wave in the first 

medium and E22 the amplitude of the downgoing wave in the second medium. For the 

y−component of the magnetic field follows from Faraday’s law in a 1-D case 

B1,y = − 1 ∂E1x 

iω ∂z 

B2,y = − 1 ∂E2x 

iω ∂z 

= k1 

iω 

 

E11e −k1z k1z 

− E12e 

(2) 

(3) 

(4) 

= k2 

iω E22e −k2z . (5) 



199

A similar relation can be derived for the pair Ey and Bx. Using the continuity of the 

fields at z = h resulting from the boundary conditions 

and introducing the admittances 

ζ1 = k1 

iω = 

E1,x(h) =E2,x(h), B1,y(h) =B2,y(h) (6) 

 

iωμσ1 

iω = 

 

μσ1 

iω 

and ζ2 = k2 

iω = 

 

μσ2 

iω 

the ratio of amplitudes of the downgoing and upgoing fields in the ocean is 

where ζ12 = ζ1−ζ2 

ζ1+ζ2 

E12 

E11 

(7) 

= ζ1 − ζ2 

e 

ζ1 + ζ2 

−2k1h 

= ζ12e −2k1h 

, (8) 

is the reflection coefficient. Its value is estimated according to eq. 7 by 

the conductivity contrast at the boundary between layers. For instance, in case of sharp 

contrast like ocean water (σ1 =3.2 S/m) and basement (σ2 =0.001 S/m) ζ12 =0.965. 

Note, that using as solution in eq. 2 and 3 the magnetic field instead of electric field, the 

reflection coefficient has to be expressed by reciprocal impedances instead of admittance 

and yields: η12 = η1−η2 

η1+η2 ,withη1,2 = k1 

μσ1,2 = 

iω 

μσ1,2 . 

Combining the equations 8 and 2 the electric field at depth z ≤ h becomes 

E1,x(z) = 

−k1z 

E11 e + ζ12e −2k1h k1z 

e 

and at the surface z =0 

 

E1,x(0) = E11 1+ζ12e −2k1h . (10) 

The ratio of the equations 9 and 10 gives the attenuation of the electric field in the ocean 

for 0 ≤ z ≤ h normalized in terms of the total field at the surface 

|VE| = E1,x(z) 

E1,x(0) = e−k1z + ζ12e−2k1h 1+ζ12e−2k1h −2k1(h−z) 

1+ζ12e 

= e−k1z 

1+ζ12e−2k1h This applies accordingly for the ratio of magnetic fields 

B1,y(z) = 

−k1z 

B11ζ1 e − ζ12e −2k1h k1z 

e 

B1,y(0) = 

−2k1h 

B11ζ1 1 − ζ12e 

(12) 

(13) 

|VB| = B1,y(z) 

B1,y(0) = e−k1z − ζ12e−2k1h 1 − ζ12e−2k1h −2k1(h−z) 

1 − ζ12e 

= 

1 − ζ12e−2k1h e−k1z . (14) 

The behaviour of the electric and magnetic fields as function of depth in a 5 km deep 

ocean for two selected and representative periods (100 s and 10000 s) and realistic conductivities 

in the ocean (σ1 = 3.2 S/m) and basement (σ1 = 0.001 S/m) is illustrated in 

Fig. 2(left). The fields are normalized to their surface magnitude according to relations 



200 

(9) 

(11)

z [km] 

0 

1 

2 

3 

4 

5 

3200 

B 

E 

E,B (hs) 

T=100s 

T=10000s 

0 0.2 0.4 0.6 0.8 1 

|V | , |V | 

B E 

T=10000s 

B 

E 

E,B (hs) 

=3.2 

3200 

0 0.2 0.4 0.6 0.8 1 

|V B | , |V E | 

Figure 2: The decay of electromagnetic fields in an ocean shows a deviation from simple 

half space attenuation due to boundary conditions on the seafloor and depends beside 

period length and ocean depth also on resistivity contrast between ocean water and 

basement. Attenuation of electric (blue) and magnetic (red) fields for two periods 

T1 = 100 s (solid line) and T1 = 10000 s (dashed line) in a 5 km deep ocean with a sea 

water resistivity of 0.3Ωm and seafloor resistivity of 1000 Ωm(right). Attenuation of the 

fields at a period of 10000 s for two different conductivities of the basement (0.001 S/m 

and 1 S/m) (left). See also (Brasse, 2009). 

11 and 14. They show different decay in dependence of period. At short periods (solid 

line) both the electric (blue) and magnetic (red) fields experience strong attenuation and 

the curve shape is determined by exponential decay. Large differences in attenuation 

are observed at long periods (dashed line). While the electric field penetrates the ocean 

layer from surface to the seafloor nearly unchanged, the magnetic field is attenuated 

about fifteen-fold and reaches on the ocean bottom just about 7% of its surface value. 

However, both fields would behave identically in an infinitely extended ocean, that would 

be regarded as a homogeneous half space. 

At first sight of the equations 11 and 14 one would think that the behaviour of the 

fields depends rather on the ocean thickness than on period. However, actually both 

is true. The decay of the fields is determined by both period T and thickness h of the 

ocean layer. That becomes evident considering the exponential and crucial term in the 

equations as function of skin depth according to the relations of skin depth δ = 

and complex wave number k =(1+i) ωσμ 

2 : 

2 

ωσμ 

e −2k1h = e − 2h 

δ 1 (i+1) . (15) 

The quantity h 

δ1 is the electrical layer thickness and via δ ∼ √ T also directly associated 

with the period length of the penetrating wave (McNeill and Labson, 1986). The fields 

behave identically if the exponent remains constant, regardless if high frequency fields 

propagate in a shallow ocean or low frequency fields in a deep ocean. The behaviour 

of the fields replicates, similar to a self-similarity principle by stimulating the exponent 



201

h , i.e. by appropriate and simultaneous increasing or decreasing the frequency and 

δ1 

the ocean thickness and thus creating either electrical thick h >> 1 or thin conditions 

δ1 

h > 1andbothe−2k1h 

δ1 

and e−2k1(h−z) → 0 (Brasse, 2009). Thus the effect of the basement on the fields is only 

marginal and the behaviour in a thick electrical layer is governed by exponential decay 

E1,x(z) 

E1,x(0) 

≈ e−k1z 

respectively B1,y(z) 

B1,y(0) ≈ e−k1z . (16) 

The decay of both fields becomes more alike the more the ocean depth or the frequency 

increases until finally approaching the decay curve of a homogeneous half space. 

For low frequencies or for an electrically thin ocean, where the skin depth is significantly 

greater than ocean depth, h

would imply that the currents only flow in the ocean, inducing a secondary magnetic 

field which removes entirely the opposite primary field in agreement with the above 

mentioned result. In real conditions with high but not infinite basement resistivity 

the currents diffuse also to the seafloor, so that the the secondary magnetic field of 

the diminished currents in the ocean can in fact reduce but not completely cancel the 

primary magnetic field. Thus the ratio B1,y(z) 

B1,y(z) 

doesn’t become zero rather 0 < < 1 

B1,y(0) B1,y(0) 

depending on ζ12 and electrical conditions of the ocean layer. In other words the reflection 

coefficient regularizes the conditions for distribution of electrical currents in sea bottom 

and estimates in this manner the damping behaviour of the fields (Chave et al., 1991). 

The decay of the electric field in the ocean is against intuition, and negligible compared 

to the magnetic field. In the theoretical case with infinite conductivity contrast, (ζ12 =1) 

the ocean represents for long periods an electrical thin layer that the electric field passes 

almost intact. In real condition mentioned above ζ12 is still high and the low frequency 

field decays gently, in terms of an electrical thin layer. That would change assuming 

a layer of highly conductive sediments on the ocean bottom. Since the layer becomes 

thicker, the electric field decays more strongly, the magnetic field in contrast much less 

since a part of currents now flows in the sediments. Thus both fields would approximate 

the curve of attenuation in a homogeneous half space, what for short periods corresponds 

to exponential decay Fig. 2(right). 

Similar effects would be observed considering the fields at a fixed point z1, within the 

ocean (0

It is also instructive to consider the electric and magnetic fields in the ocean as function 

of periods. Fig. 3 illustrates graphically the ratio |VB| = B1,y(z) 

B1,y(0) and |VE| = E1,x(z) 

E1,x(0) 

for various thicknesses of the ocean layer. It becomes clear immediately that in the 

real ocean environment attenuation of the fields differs fundamentally over a total period 

range. While the electric field remains nearly unchanged in electric thin layer 

( h

ocean depends on pressure, salinity and temperature. While the effect of pressure and 

salinity is marginally, the temperature variations in ocean change resistivity of oceanic 

water from 0.16 Ωm at 30 ◦ C to 0.33 Ωm at 1.0 ◦ C. The estimated resistivity values about 

0.3Ωm corresponds very well to literature values (Filloux, 1987) 

3 Offshore magnetotelluric and magnetic transfer 

functions in presence of bathymetry 

The discussions about magnetotellurics on the seafloor are often dominated by attenuation 

of electromagnetic fields by high conductive ocean and secondary induction by 

sea tides. Fewer studies refer to distorting effects on electromagnetic fields caused by 

changes in seafloor bathymetry in presence of overlaying high conductive environment 

(Constable et al., 2009). 

For a model incorporating a homogeneous half space with resistivity of 100Ωm and 

conductive ocean with bathymetry that is observed at the South Chilean continental 

margin (Fig. 5, top), magnetotelluric transfer function were calculated with the algorithm 

of Mackie et al. (1994). At least two clear findings can be derived from the model 

0 

2 

4 

6 

10 0 

10 1 

10 2 

10 3 

104 100 10 1 

10 2 

10 3 

10 4 

ocean 

ρ= 0.3Ωm ρ=100Ωm TM 

TM 

0 50 100 150 200 250 300 350 400 

distance [km] 

0 50 100 150 200 250 300 350 400 

distance [km] 

Figure 5: Responses of a synthetic amphibious model shown on the top. Middle: resistivity 

of TM and TE mode. Bottom: phase of TM and TE mode. Dashed line separates 

the profile into offshore and onshore part. 



205 

TE 

TE 

4 

3 

2 

1 

0 

90 

75 

60 

45 

30 

15 

0

esponses (Fig. 5, middle and bottom). Firstly the ocean has rather a marginal effect 

on the onshore magnetotelluric transfer function (right of the dashed line). Actually 

only in TM mode of onshore stations close to the ocean slightly decreasing phases and 

enhanced apparent resistivity on the edge between offshore- and onshore profile marked 

by a dashed line, can be observed. Secondly the bathymetry produces dramatic anomalous 

effects in the ocean, which can be observed in both modes as well as in phases and 

resistivities. The resistivity in TE mode rises and falls dramatically producing cusps in 

the image and phases even exceed −180 ◦ and 180 ◦ . 

Similar anomalous features can be observed in the magnetic transfer functions (Fig. 

6). Slight changes in the shape of the seafloor, adumbrated by a dotted line, are overdrawn 

reproduced by dramatic variations in the magnitude of the induction arrows (note 

the smooth bathymetry change between stations A09 and A13 and their huge impact on 

the magnitude of the induction arrows). On the other hand, the ocean effect on onshore 

station is limited to long-periods and to near-coastal region, again. 

10 0 

10 1 

10 2 

10 3 

10 4 

tipper M r 

0 50 100 150 200 250 300 350 400 

distance [km] 

tipper Mag 

0 50 100 150 200 250 300 350 400 

distance [km] 

Figure 6: Real part (left) and the magnitude (right) of the tipper calculated for synthetic 

and amphibious model shown on the top of figure 5. The dotted line indicates 

the shape of the bathymetry of the model. 

Comparing these synthetic responses with the real induction vectors observed at the 

only station at the continental slope, ob7, shows that the bathymetry indeed affects the 

measured data, as shown in Fig. 7. The huge induction vectors (over 1) at middle 

and long periods correspond roughly with magnitude values calculated from the simple 

amphibious model. For short periods (until 100 s) a comparison is impossible due to 

Re 

1.0 

0.5 

0.0 

10 2 

ob7 

10 3 

Figure 7: Real part of the observed induction vectors at station ob7, deployed on the 

continental margin off Southern Chile. Induction vectors observed land-side are presented 

by Brasse (2009). 

10 4 

10 5 



206 

1.2 

1.0 

0.8 

0.6 

0.4 

0.2 

0.0

unavailable data (note the different period range of the images). 

The anomalous responses can be elucidated considering electric and magnetic fields in 

presence of changing seafloor shape. An enhanced concentration of electrical currents at 

the continental slope produces anomalous strong vertical magnetic field, that is known 

also on the land-side as coast effect (e.g., Fischer, 1979). Due to the high sea water 

conductivity the induced electric currents concentrate primarily in the ocean avoiding 

the much more resistive subsurface and generate a secondary magnetic field which compensates 

the primary opposite field, so that the magnetic field diminish considerably or 

disappears completely in case of insulating substrate as mentioned in 2 and shown in 

Fig. 2. At the continental margin, where the seafloor shallows towards land, the density 

of electric currents flowing in the ocean along the coast (i.e. in the TE mode) and above 

(instead below) measurement points increase inducing an anomalous and opposite magnetic 

field. This opposite, secondary field becomes predominant on the ocean bottom, 

where the primary field is strongly damped whereas the electric field is by the coast effect 

only marginally affected, and causes jumps in the phase (Weidelt, 1994). Moreover the 

resistivities in TE mode rise steeply generating upward cusps and the tipper gets very 

large as presented in Fig. 6 and 5. 

The periods at which the effects occur depend on position of the probe in relation to 

the slope and corresponds to lateral distance to which a transfer function is sensitive 

to bathymetry. However, at high frequencies the field is generally unaffected by the 

bathymetry and the results are MT-like because the fields still behave like plane waves. 

At low frequencies, the currents are below the ocean. At the middle frequencies, the 

currents are in the ocean and this causes the responses looking like those due to infinite 

line currents right above the station. Note that if the MT responses were recorded 

on the top of the sea, the responses would be perfectly fine as expected in an usual 

2-D case, since all the currents pass below the sounding surface instead above like in 

the presented marine model. This behavior is overcome or reduced by introducing a 

very conductive layer below the ocean bottom (e.g., sediments), which has to be at least 

several kilometers thick. However, the assumption of an oceanic crust being entirely well 

conductive seems unrealistic; this is even more the case for the continental crust below 

the slope: every aquiclude would prohibit the intrusion of sea water into deeper layers. 

Another class of models makes the effect described above disappear too: the association 

of the upper part of the downgoing plate with a good conductor, in accordance with 

standard models of subduction. 

4 Summary 

Offshore magnetotellurics is an useful method for exploration of seafloor and oceancontinent 

subduction zones, where fluids and melts are known to control the subduction 

process. A combined on- and offshore magnetotelluric transect across subduction zone 

is assumed to be able to resolve high conductive structures associated with dehydration 

processes, water migration and melts building. 

However special conditions on the ocean floor not allow to interpret and to deal 



207

with the marine records in the same manner as with onshore data. The presence of 

bathymetry distorts the magnetic and magnetotelluric transfer functions, particularly 

in the TE mode. Even a gently changing seafloor shape generates an enhanced concentrations 

of electric currents flowing above instead below measurement station and 

inducing on the ocean bottom a predominant anomalous opposite magnetic field. This 

results in phases exceeding the quadrant and cusps in the apparent resistivity. 

The high conductive sea water causes a strong attenuation of electric and magnetic 

field at short periods. Towards long periods the decay differs clearly for both fields. The 

electric field penetrates the ocean layer from surface to the seafloor, counterintuitive, 

nearly unchanged, while the magnetic field experiences a strong decay and reaches the 

ocean bottom just with a fraction of its surface value. Moreover the decay depends 

strongly from the resistivity contrast between ocean and seafloor. Reducing the resistivity 

of the basement the electrical thickness of layer increases and both fields approximate 

a field decay like in a homogeneous half space. 

References 

Brasse, H., G. Kapinos, Y. Li, L. Mütschard, W. Soyer, D. Eydam (2009): Structural 

electrical anisotropy in the crust at the South-Central Chilean continental margin as 

inferred from geomagnetic transfer functions, Phys. Earth Planet. Inter., 173, 7-16. 

Brasse, H. (2009): Methods of geoelectric and electromagnetic deep sounding, Lecture 

Notes, Free University of Berlin. 

Chave, A.D., S.C. Constable, and R.N. Edwards (1991): Electrical Exploration Methods 

for the Seafloor, in: Electromagnetic Methods in Applied Geophysics, Vol. 2 (Ed. M.N. 

Nabighian), Soc. Expl. Geophys., Tulsa, 931-966. 

Constable, S.C., K. Key, and, L. Lewis (2009): Mapping offshore sedimentary structure 

using electromagnetic methods and terrain effects in marine magnetotelluric data, 

Geophys. J. Int., 176, 431-442. 

Filloux, J.H. (1987):Instrumentation and experimental methods for oceanic studies, in: 

Geomagnetism, (Eds. J.A. Jacob), Academic Press,1987,143–248. 

Fischer, G. (1979): Electromagnetic induction effects on the ocean coast, Proc. IEEE, 

67, 1050-1060 

McNeill, J.D., and V. Labson (1986), Geological mapping using VLF radio fields. Electromagnetic 

Methods in Applied Geophysics. Volume 2, Appliction, Parts A and B, 

(Ed. M.N. Nabighian), SEG, Tulsa, 521-639. 

Mackie, R., J. Smith, and T.R. Madden (1994), Three-dimensional modeling using finite 

difference equations: The magnetotelluric example, Radio Science, 29, 923-935. 



208

Weidelt, P. (1994), Phasenbeziehungen für die B-Polarisation, in: Protokoll über das 

Kolloquium ”Elektromagnetische Tiefenforschung” (Eds. K. Bahr and A. Junge), 

Höchst, Odenwald, 60-65. 



209

A permanent array of magnetotelluric stations located at the 

South American subduction zone in Northern Chile. 

Introduction 

Dirk Brändlein 1,2 , Oliver Ritter 1,2 , Ute Weckmann 1,3 

1 GFZ German Research Centre for Geosciences, Potsdam, Germany 

2 Freie Universität Berlin, Fachrichtung Geophysik, Berlin, Germany 

3 University of Potsdam, Institute of Geosciences, Potsdam, Germany 

Monitoring the dynamic behavior of an active deep 

subduction system is focus of the Integrated Plate Boundary 

Observatory Chile (IPOC), a permanent array of combined 

geophysical and geodetic stations in Northern Chile which is 

operated since 2006 by the GFZ German Research Centre for 

Geosciences. Magnetotelluric (MT) data is gathered at seven 

out of a total of eleven observation sites. 

The MT set up consists of three component long period 

fluxgate magnetometers (GeoMagnet) and non-polarizing 

Ag/AgCl electrodes to measure all three components of the 

magnetic field and both horizontal components of the 

electric field. The signals of the electromagnetic fields are 

continuously sampled at a rate of 20 Hz and at four sites 

transferred via satellite link to the GFZ in Germany. The 

objective of the project is to monitor and analyze 

electromagnetic data to decipher possible changes in the 

subsurface resistivity distribution, e.g. as a consequence of 

large scale fluid relocation. 

Here, we present vertical magnetic transfer functions as time 

series over a time span of more than two years for the 

period range from 10 -1 to 10 4 seconds 1 . These vertical 

magnetic transfer functions are sensitive to lateral changes 

of electric conductivity in the subsurface. Some components 

of these transfer functions show frequency dependent 

variations with a periodicity of roughly one year. These 

effects are observed at all sites of the array. 

Figure 1: The IPOC-MT array in 

Northern Chile showing sites PB01 

to PB07 (red symbols). Blue stars 

indicate major earthquakes. 

Due to the extreme dry ground of the Atacama desert 

continuous monitoring the electric field is difficult. Contact 

resistances are on the order of MΩ and electrolyte is leaking. Different types of electrodes are 

currently being tested. 

1 Periods shorter than 10 seconds are not considered since this is the shortest period fluxgate magnetometers are able to resolve. 



210

Periodic variations in the MT monitoring data 

To identify changes in the subsurface we examine time series of vertical magnetic transfer functions 

Tx(ω) and Ty(ω): 

Bz(ω) = Tx(ω) Bx(ω) + Ty(ω) By(ω). 

These quantities are sensitive to lateral changes of electric conductivity in the subsurface. 

The value of each day and component of the transfer function time series is obtained by processing 

magnetic field time series of 3 days (using the day before and after). Subsequently the 3 day time 

window is forwarded by one day and the procedure is repeated until the entire time series is 

processed. The geomagnetic transfer functions were obtained using the robust processing described 

in Ritter el al. (1998), Weckmann et al. (2005), and Krings (2007). 

Figure 2: Time series showing the differences between daily values of Ty and the median of the 

entire data section of 730 days at each period for site PB03. For monitoring purposes it is 

desirable to amplify variations in the vertical magnetic transfer function components. Therefore, 

the median is calculated for each period and component and subtracted from the value of each 

day. The median of each frequency band is plotted on the right hand side. The median is more 

robust against outliers than the arithmetic average. Vertical red lines indicate major earthquakes 

(see Fig. 1), vertical blue lines indicate turn of the year. Interestingly, the ocean effect, which 

would be indicated by a large positive value of the median of Re[Ty], is rather small at site PB03. 

The time series of the real and imaginary parts of the Ty (east-west) component at PB03 show a 

remarkable frequency dependent feature (Fig. 2). At periods between approximately 40 and 1000 s 

the observed Re[Ty] values show a continuous variation of the amplitudes with a periodicity of 

roughly one year. The amplitudes vary in the range ± 0.1 and reach maximum values in the austral 



211

winter before the winter solstice. In the austral summer, the minimum occurs before the summer 

solstice. Similar effects can be observed consistently at all sites of the array (Fig. 3). 

Figure 3: Time series of real (blue) and imaginary (red) parts of vertical magnetic transfer 

functions Tx and Ty of around 600 days at a period of 1000 seconds of sites PB01, PB02, PB03 

and PB05. 

Possible causes for the periodic variations of Ty 

Possible causes for this periodic variation of the Ty component could be source field 

inhomogeneities. The sources for the MT-method are the natural variations of the earth's magnetic 

field which are assumed to be far away from the observer so that electromagnetic waves penetrate 



212 

Figure 4: Time series 

of the magnetic auto 

spectra of PB03, 

extracted from the 3day-average 

processing described 

in section 2. The 

ByBy * spectra show 

the same variations 

with a periodicity of 

one year as Ty.

the subsurface as plane waves. 

To examine if the variations in the time series of vertical magnetic transfer functions are caused by 

seasonal alterations of source fields we plotted the time series of magnetic auto spectra of PB03 (Fig. 

7) for the same time window as in Figure 2. These magnetic auto spectra show a clear correlation 

between the By-auto spectrum (east-west direction) and the Ty data (Fig. 8). This would support the 

idea that the results are influenced by source field effects. 

Sq variations and equatorial electrojet 

There exist several effects on the geomagnetic field 

which have a wide spectrum of variations 

(Onwumechili, 1997). Annual variations of the 

geomagnetic solar quiet daily variation (Sq) show the 

same periodicity as the measured variations of the 

magnetic auto spectra at PB03. The geomagnetic Sq 

field has a variation with a dominant periodicity of 1 

day. Solar radiation generates ionized molecules in 

parts of the ionosphere (around 80 to 300 km height) 

which produces variable charged particles and, 

consequently, conducting air. Additionally, the solar 

radiation causes thermo-tidal winds which move the 

conducting ionosphere through the geomagnetic field. 

The result is a system of electric currents depending 

on the position of the sun. Horizontal and vertical 

components of Sq tend to be predominantly semiannual 

in the zone of Equatorial Electrojet (EEJ) but 

predominantly annual at other latitudes (Onwumechili, 

1997). 

The IPOC MT array (21 - 23° south) in 

Northern Chile is located near the 

tropic of Capricorn (23° 26' south). This 

means, it is influenced by the 

Equatorial Electrojet (EEJ), a varying 

electric current flowing eastward in the 

ionosphere at a height of 100 - 130 km. 

Over South America the EEJ is warped 

to the south because it follows the 

magnetic dip equator (Fig. 8). The 

amplitudes are aligned to the north 

and to the south by return currents 

(Lühr et al.,2004) with peak values at 

latitudes some 5° away from the 

magnetic dip equator. 

Figure 5: Exemplary electric currents in 

the ionosphere cause Sq variations in 

the northern summer. 

http://geomag.usgs.gov/images/ionosp 

heric_current.jpg (10.02.2010) 

Figure 6: Electrojet current densities inferred from 2600 

passes of the CHAMP satellite over the magnetic 

equator between 11:00 and 13:00 local time. 

http://www.geomag.us/info/equatorial_electrojet.html 

(10.02.2010) 

Annual Sq variations are most likely the cause of the variations of the Y-component of the vertical 

magnetic transfer functions at the MT-array in Northern Chile. 



213

Non-periodic variations in the MT monitoring data 

No periodic long term variations can be identified in the Tx component of the vertical magnetic 

transfer function time series (Fig. 7). A continuous variation at a period of approximately 20 s can be 

observed in the Re[Tx] component. It has a high amplitude variation between -0.2 and +0.2. 

Figure 7: Time series of differences between daily values of Tx and median of the entire data 

section at each period at site PB03. Vertical red lines indicate major earthquakes, vertical blue 

lines indicate turn of the year. Values of median versus period are plotted on the right hand side. 



214 

Figure 8: Time series of 

differences between daily 

values of vertical magnetic 

transfer functions and 

median at site PB03 versus 

period. Length and period 

range correspond to the 

black box in figure 6. 

Vertical red lines indicate 

major earthquakes (Fig. 1), 

vertical blue lines indicate 

turn of the year.

Figure 9: Time series of differences between daily values of 

vertical magnetic transfer functions and median at site PB05 

versus period. Length and period range correspond to the black 

box of Fig. 6. Vertical red lines indicate major earthquakes (Fig. 

1), vertical blue lines indicate turn of the year. 

Note that the curve of the 

median, which represents the 

average transfer function, 

varies smoothly and 

consistently in this period 

range. 

A remarkable feature can be 

observed between two major 

earthquakes in December 

2007 (Fig. 7, black box). The 

area of interest shows a 

sudden rise in amplitudes up 

to ±0.25 (Fig. 8), which 

corresponds to 100% of the 

median value of Tx (Fig. 7, 

right hand side). A similar but 

less pronounced effect is 

observed at site PB05 (Fig. 9). 

More modeling is necessary 

to quantify the scale and location of structural changes of the electrical conductivity in the 

subsurface which could explain these non-periodic variations in the vertical magnetic transfer 

function time series. Calculation and modeling of inter station transfer function time series should 

also give more detailed information about changes in the conductivity structure of the underground. 


We acknowledge funding from the GFZ German Research Centre for Geosciences. For continuous 

logistic help in Chile we want to thank Prof. Guillermo Chong and the people from the Universidad 

Catolica del Norte in Antofagasta. We are grateful to Günter Asch for his cooperation and help to 

install and maintain the technical infrastructure in the Atacama desert. We are very thankful for 

support in the field by Kristina Tietze and Thomas Krings. 

References 

Krings, T., 2007. The influence of Robust Statistics, Remote Reference, and Horizontal Magnetic Transfer 

Functions on data processing in Magnetotellurics. Diploma Thesis, WWU Münster ― GFZ Potsdam. 

Lühr, H., S. Maus, and M. Rother, 2004. Noon-time equatorial electrojet: Its spatial features as determined by 

the CHAMP satellite, Journal of Geophysical Research, 109, A01306, doi:10.1029/2002JA009656. 

Onwumechili, C. A., 1997. The Equatorial Electrojet, Gordon and Breach, Newark, N. J. 

Ritter, O., Junge, A. and Dawes, G., 1998. New equipment and processing for magnetotelluric remote 

reference observations. Geophysical Journal International, 132, 535-548. 

Weckmann, U., Magunia, A. and Ritter, O., 2005. Effective noise separation for magnetotelluric single site 

data processing using a frequency domain selection scheme. Geophysical Journal International, 161, 

635-652. 



215

Discussion on backarc mantle melting in the central Andean 

subduction zone, based on results of magnetotelluric studies 

D. Eydam ∗ & H. Brasse 

Free University of Berlin, Malteserstr. 74-100, 12249 Berlin 

Abstract 

Long-period magnetotelluric measurements in the Bolivian orocline revealed a large 

conductor in the backarc upper mantle of the central Andean subduction zone at 18◦S. Data analysis and interpretation by 2-D inversion has already been described by Brasse 

& Eydam (2008a) who interpreted this conductor as an image of partial melt triggered 

by fluid influx from the subducting slab. 

Remarkable are its high conductivities ranging up to above 1 S/m and implying high 

melting rates of more than 6vol%. However, regarding the distribution of intermediate 

depths seismicity which marks dehydration reactions in the subducting slab, one has 

to note the large distance of more than 60 km between fluid source and the assumed 

fluid-triggered partial melting of mantle peridotite. How do actual concepts of subduction 

zone dynamics fit to this resistivity image? 

There are at least two approaches which are both followed by in the subsequent discussion: 

first is to study the mobility of deep fluids in subduction zones, second is to 

study the mobility of the slab itself. 

Introduction 

Ocean-continent subduction zones are earth regions of major raw material recyclings. 

Hot magmas erupt nearby where cold oceanic lithosphere subducts. This apparently 

contradictory observation is explainable by consumption of deep slab-derived fluids for 

flux melting of the peridotitic mantle in the asthenospheric wedge: 

Hydrous minerals in the oceanic lithosphere are progressively dehydrating during subduction. 

The hereby released water may trigger partial melting of the overlying asthenospheric 

wedge by lowering mantle solidus generally at depths below 80 km. Melts 

and fluids ascent with some intermediate storage at density contrasts at the Moho 

or intra-crustal boundaries and give rise to arc and backarc volcanism. Due to their 

∗ now at GFZ Potsdam, Telegraphenberg, 14437 Potsdam 



216

Eydam & Brasse: Discussion on backarc mantle melting 

enhanced conductivities, saline fluids and (hydrous) melt should principally be detectable 

by deep electromagnetic sounding methods, as was demonstrated, e.g., in the 

Cascadia/Juan de Fuca subduction zones (Kurtz et al., 1986; Wannamaker et al., 1989; 

Varentsov et al., 1996). 

Hydrous phases in the oceanic crust relevant for sub-arc water release are amphibole 

and lawsonite. Amphibole is abundant in the basaltic oceanic crust and decays only 

slightly pressure-dependent at 65-80 km depths, marking the transition from blueschist 

to eclogite facies. In contrast, lawsonite can be stable up to high pressures of 8.4 GPa 

(z ≈ 250 km) and dehydrates when temperatures exceed 700-800◦C. Mantle water release 

is mainly controlled by serpentinite dehydration between 500-700◦C. Serpentinite 

can be stable up to high pressures of 6 GPa where it transforms through a waterconserving 

reaction to the hydrous DHMS (Dense Hydrous Magnesium Silicat) -phase 

A. 

The amount of released water thus strongly depends on the thermal structure as well 

as on subduction geometry. Young and slowly subducting slabs may dehydrate completely 

whereas old and rapidly subducting lithospheres may import large amounts of 

mantle water into the deeper mantle, making them crucial for the global water cycle. 

The definitive amount of deep fluids in subduction zones is still uncertain because 

of the dependency of dehydrations from slab heating via mantle convection which in 

turn, strongly depends on water content in the wedge, besides other mostly poorly 

constrained parameters. 

Geological setting 

The central Andean subduction zone 

Along 7000 km length the oceanic Nazca plate subducts beneath the South American 

continental margin where the Andes evolved as a Neogene volcanic chain embedded in 

a compressive backarc tectonic setting. Holocene volcanism is seperated in four active 

segments, the austral, southern, central and northern volcanic zone (fig. 1). 

Characteristic for the whole subduction system are low slab dips of less than 30◦ and inactive volcanism in regions where aseismic ridges subduct. Those hot oceanic 

lithospheres probably flatten at main depths of sub-arc water release due to a retard 

of dehydration and thus density increase of the slab which may lead to ’horizontal subduction’ 

over several hundreds of kilometres (Gutscher et al., 2000). Therefore, slab 

pull and buoyancy forces should be quite equilibrated probably making the slab mobile 

in geological time scales. 

The Bolivian orocline (13-28◦S) encompasses the central volcanic zone (CVZ) where 

the oldest part of the Nazca plate (55 Ma) subducts obliquely with an angle of N77◦E and with a current velocity of 6.5 cm/a (Klotz et al., 2006). Convergence rate has 

continuously slowed down from high 15 cm/a since the breakup of the oceanic Farallon 

plate in Nazca and Cocos plate 26 Ma ago (Somoza, 1998). 

During the highly compressive Miocene regime, stresses are mainly relaxed by extreme 



217


10°S 

20°S 

30°S 

40°S 

Nazca Rise 

Iquique Rise 

Juan-Fernández Ridge 

Chile Rise 

7.8 cm/a 

SVZ 

Easte 

Altiplano 

CVZ 

Puna 

80°W 75°W 70°W 65°W 

Figure 1: South American subduction zone with structural units of the central volcanic zone (CVZ) 

backarc and foreland. Hachures: Altiplano-Puna transition between 22-24 ◦ S; SB, SP - thick-skinned 

folding and thrusting in the Santa-Bárbara system and Sierras Pampeanas; P - Pica-Gap of Holocene 

volcanism (19.2-20.7 ◦ S) where Iquique Rise subducts (Wörner et al., 2000); SVZ - southern volcanic 

zone. Convergence rate after Somoza (1998). 

crustal shortening, thickening and uplift of the entire Andean arc and backarc region 

(e.g., Allmendinger et al., 1997; Scheuber et al., 1994; Elger et al., 2005). As a consequence 

the Altiplano-Puna high plateau developed, encompassing the highest volcanoes 

of the world (e.g., 6500 m for Sajama volcano) in the Western Cordillera to the west, 

rough mountain ranges in the Eastern Cordillera at the eastern boundary and the intramontanous 

drained Altiplano and Puna basins with thick Miocene stratas in-between. 

The up to 1800 km long and 350 km wide Altiplano-Puna plateau is the worldwide 

greatest high plateau in a subduction context. Crustal thickness is enormous (up to 

75 km; e.g., Wigger et al., 1994) and decreases beyond the plateau extension to normal 

values for continental lithosphere of 35-40 km. Likewise volcanism in the CVZ is highly 

crustally contaminated against more island-arc denoted lavas in the SVZ. 

Altiplano and Puna form an unique tectonomorphic entity within the orogen although 

their morphology differs. While the Altiplano in the north is rather flat and tectonically 

quiet, the Puna in the south is pervaded by many deep reaching, active horst- and 

graben structures. Average elevations are around 3700 m in the Altiplano and 4500 m 

in the Puna. 

Actual compressive tectonics are mainly restricted to the Andean foreland, where 

westvergent thin-skinned thrusting in the Subandean to the north change to thickskinned 

thrusting in the Santa Bárbara system and Sierras Pampeanas to the south 

(Allmendinger et al., 1997). At Altiplano latitudes, the comparatively fast westward 

subduction of the Brazilian Shield enhances the compressive backarc regime. 

P 

rn 

Cordi 

llera 

SP 

Suba 

SB 

nde 

an 

Chaco 



218


50 km 

75 km 

Pacific Ocean 

100 km 

125 km 

Argentina 

100 km 

CC 

LV 

150 km 

175 km 

125 km 

PC 

200 km 

Western Cordillera 

San Andrés fault 

P S 

225 km 

Coniri 

fault 

system 

Corque Basin 

Altiplano 

Rio Desaguadero 

Chuquichambi 

Eastern Cordillera 

Laurani fault 

Figure 2: Survey area with locations of the 30 MT sites in the Bolivian orocline. Profile trends roughly 

perpendicular to the strike of main morphological units and to the contour lines of the Wadati-Benioff 

zone (dotted lines). CC denotes Coastal Cordillera, LV Longitudinal Valley and PC Precordillera; P, 

S are Parinacota, Sajama volcanoes; mN is magnetic north. 

The survey area 

The magnetotelluric profile transverses the central Bolivian orocline from the Coastal 

Cordillera in northermost Chile, to the active volcanic arc and the Altiplano in central 

Bolivia and ends in the Eastern Cordillera. The profile follows a general trend of N48◦S which is roughly perpendicular to main structural units as well as to contour lines of 

the Wadati-Benioff zone (fig. 2). 

Main morphological units in the forearc are paralleling the trench and correspond to an 

ancient magmatic arc which shifted eastward through time, recordable since the Jurassic 

in the Coastal Cordillera, afterwards in the Longitudinal Valley, in the Precordillera 

and until the Neogene in the Western Cordillera (Scheuber et al., 1994). The exposure 

of the forearc crust to periods of extensive and long-lived magmatism gave rise to the 

formation of deep, long and wide fault zones (sub-)paralleling the trench among which 

some are still active like the Precordillera Fault System at 19.2-21◦S. Here, large copper 

deposits evidence strong fluid circulation and mineralisation after the eastward shift of 

the arc 32 Ma ago. 

In the closer survey area, the forearc is incised by deep, E-W running valleys which 

open to the ocean and may have served as Miocene drainage systems. Some of them 

may be associated with active faults (Wörner et al., 2000). A system of west vergent, 

steeply dipping thrust faults in the eastern Precordillera, the West-Vergent-Thrust- 

System, marks the transition to the high plateau and is thought to be the location of 

major plateau uplift (Muñoz & Charrier, 1996). 

The smooth monoclinal western slope of the high plateau is locally shaped by huge 

land slides, e.g., the Oxaya collaps 12 Ma ago (Wörner et al., 2002). In the West- 



219 

thrust 

275 km 

250 km 

mN N


ern Cordillera, Plio-Pleistocene to recent, andesitic to rhyodacitic stratovolcanoes are 

build on thick layers of ignimbrites which are widespread throughout the entire forearc 

and are dated between 22-19 Ma (Oxaya Ignimbrites) and to 2.7 Ma (Lauca-Pérez 

Ignimbrite) (Wörner et al., 2000). 

The Altiplano can be separated into the volcanic Mauri region to the west and in huge 

sedimentary basins easterly. The San-Andrés fault marks the boundary in-between and 

limits the Arequipa terrane to the east, a component of the Arequipa-Antofalla massif 

which comprises up to 2 Ga old rocks and underpins the volcanic arc probably along 

the whole plateau (see in James & Sacks, 1999). The most prominent feature in the 

Altiplano is the 80 km wide Corque basin, a deep asymmetric sedimentary basin with 

thick and folded tertiary strata, exceeding 10 km thickness (Hérail et al., 1997) and 

evidencing orogeny dynamics during Miocene’s pronounced compressive regime. 

To the east the basin is controlled by the Chuquichambi thrust system. The Coniri- 

Laurani fault system marks the transition to the Eastern Cordillera, the rough eastern 

flank of the plateau. Farther to the east the Interandean Zone and Main Andean Thrust 

separate the Altiplano plateau from the actual deformation front in the Subandean, 

with thin-skinned folding and thrusting holding the record of shortening rates within 

the study area (Allmendinger et al., 1997). 

After the Oligocene eastward shift of the magmatic arc, Neogene volcanism first relived 

in the Eastern Cordillera 27 Ma ago and afterwards encompassed the whole plateau region. 

Neogene volcanism of the Altiplano plateau is composed of three main units: 

Pliocene to recent stratovolcanoes are erupting in the main arc and Miocene to recent 

backarc calderas and mafic mongenetic pulses are distributed in the arc and backarc. 

Intensive ignimbritic volcanism erupted 10-4 Ma ago at the Altiplano-Puna transition 

between 21-24◦S and formed one of the greatest ignimbrite provinces of the earth, the 

Altiplano-Puna-Volcanic-Complex. Recent ignimbrite eruptions are older than 1 Ma. 

The high water, phenocrystal and silicate content signify long storage in huge crustal 

magma chambers with pronounced fluidal circulation. 

Holocene volcanic activity is less than in the Puna where the lithosphere probably is 

50 km thinner (Whitman et al., 1996). Volcanism in the closer survey area is categorised 

from dormant (Parinacota) to solfataras state with intensive fumarolic activity 

at Guallatiri volcano. The profile volcano Parinacota may possess a stable magma 

chamber with only minor magmatic input. 

Glance on data analysis and 2-D inversion 

We measured horizontal components of the electromagnetic field as well as the vertical 

magnetic field for long periods between 10 and 20 000 s. Data analysis and its interpretation 

by 2-D inversion has already been described by Brasse & Eydam (2008a) and 

will not be replicated in this article. 

Some important results are just mentioned: We could not resolve subduction-related 

features near the slab, like fluid curtains or fluid and melt pathways, due to significant 



220

Re 

Period: 993 s 


Figure 3: Real part induction arrows in 

Wiese convention for one chosen period 

demonstrating the remarkable good alignement 

of arrows in profile direction. Arrows 

in the forearc are deflected; they are pointing 

parallel to the coast. 

3-D effects in the forearc. This can easily be seen in the behavior of real part induction 

arrows pointing parallel to the coast (fig. 3) which is also observed in other coastal regions 

in Chile so that one might call them ’Chile arrows’. Brasse et al. (2008b) showed 

that they can be explained by anisotropy in the forearc crust. Seven forearc station 

data were thus discarded from further interpretation by 2-D inversion. 

Induction arrows as well as the analysis of impedance data, which reveals phasesensitive 

skew values below 0.3 for plateau sites, suggest fairly good electrical 2-D 

approximation for the plateau region. We observe a remarkable good alignement of 

middle to long period real part induction arrows in profile direction, as seen in figure 3. 

Correspondingly, electrical strike derived by impedance data is fairly perpendicular 

to the profile. Real arrows disappear in the central Altiplano where resistivities are 

signifcantly reduced for all sites and rotation angles and follow a well marked downward 

trend for longer periods indicating assumably well conducting features at greater 

depths. 

2-D inversions were performed with the inversion program of Rodi & Mackie (2001). 

Accounting for the consistency of induction arrows in the Altiplano, tipper weight was 

set high by assigning a small (absolute) error floor of 0.02. Error floors for resistivities 

and phases were set to 20% and 5% in order to overcome the static shift problem. 

Reliable models are achieved after numerous experiments inculding tests of starting 

models, specifying the regularisation term and further resolution tests (see Eydam, 

2008). 

Discussion on backarc mantle melting 

The final model, shown in figure 4, is obtained by jointly inverting tippers, TE and 

TM mode apparent resistivities and phases. Static effects were accounted for by using 

the program internal adjustment. Fair regularisation parameters lie around 20. Model 

RMS is 1.80, with larger misfits at the electrically less 2-D plateau borders (see Brasse 

& Eydam, 2008a). 



221

depth (km) 


SW NE 

Moho 

600°C 

W. Cordillera Altiplano 

E. Cordillera 

fluids 

& 

melt 

A1 A2 A3 

C1 

B C2 

MASH - zone 

D 

mantle convection 

6-7vol% melt 

WB-zone 

San-Andrés 

Fault 

lithospheric 

mantle layer? 

not 

resolved 

distance (km) 

Coniri-Laurani 

Fault 

fluids & melt? 

Figure 4: Final resistivity model with suspectable fluid & melt dynamics - Ai: Corque and minor 

basins, B: Arequipa block(?), Ci: structures beneath the Eastern Cordillera, D: backarc mantle magma 

reservoir plus rise of fluids and melts. Circles indicate location of mayor earthquakes (M > 4.5, Engdahl 

& Villaseñor, 2002). WB denotes Wadati-Benioff zone. MASH-zone stands for melting, assimilation, 

storage and homogenisation zone of arc magmas. Below: RMS for the inverted station data. 

The large upper mantle conductor D is interpreted as an image of partial melts triggered 

by fluid influx from the slab. Conductivities range up to above 1 S/m and are 

definitely required by data down to 115 km depth, particularly to fit the downward 

trends in long period app. resistivities; they are consistent with data down to slab 

depths. This implies high melting rates of more than 6vol% (Eydam, 2008). 

Lithospheric mantle material should stabilise magma and trap hot fluids which otherwise 

would rapidly trigger wide scale crustal melting like this is the case in the southern 

Altiplano (e.g., ANCORP Working Group, 2003). This is consistent with seismic data 

from Dorbath & Granet (1996) who resolve lithospheric characteristics just beneath 

the Altiplano Moho. 

The source region of subduction related magmatism is offset from the arc by almost 

100 km, implying fluid and melt storage near the Moho (in so called MASH-zones) and 

non-vertical rise of only few fluidal and molten material towards the volcanoes. This 

accords to low volcanic productivity in the closer survey area, while lavas are bearing 

highly modified mantle signatures (Wörner et al., 1992). Magma and fluid lateral motion 

should be enforced by internal convections. 

This ’scenario’ implies a widely hydrated crust and upper mantle beneath the high 

plateau which is consistent with other geophysical anomalies, like high heat flow densities 

(e.g., Springer & Förster, 1998), neagtive Bouguer anomalies (Tassara et al., 2006), 

slow seismic velocities in a thick and highly absorbing crust (e.g., Beck & Zandt, 2002) 



222 

? 

C3 

 

4 

3 

lg m 2 

1 

0

component of 

oceanic plate 

sediments 

crust 

mantle 

total 


water import 

per m 

Nazca plate [kg] 

2 

1 700 

170 000 

250 000 

1 000 000 

421 700 

1 171 700 

in percentage of 

imported water 

20 

55 

60 

water release in 80-180 km depth 

per subducted 

meter [kg] 

340 

93 500 

150 000 

600 000 

243 840 

693 840 

per Ma [10 kg] 2) 6 

32 

8 883 

14 250 

57 000 

23 165 

65 915 

3) 

in neogene cycle, 

6 

WC = VA [10 kg] 

832 

230 958 

1) 1) 1) 1) 

2) 2) 2) 2) 

370 500 

1 482 000 

602 290 

1 713 790 

Table 1: Water budget for main dehydration depths in the central Andean subduction zone calculated 

by using 1) a standardised mantle hydration model after Rüpke et al. (2004), 2) a mantle hydration 

model deduced from local data after Ranero & Sallarès (2004) and 3) by using averaged subduction 

rates after Somoza (1998). WC - Western Cordillera, VA - main volcanic arc. 

and a strong mantle signature of geothermal fluids (Hoke et al., 1994). 

Estimation of arc and backarc water release 

A critical mind might state that the ability of water import is probably not sufficient 

to nurture such wide scale melting of mantle material. Table 1 shows the water balance 

for slab dewatering at main dehydration depths between 80-180 km, deduced from intermediate 

depths microseismicity published in David (2007) and seen in figure 7. 

For the calculation we used hydration estimates after Rüpke et al. (2004) modified by local 

data (fig. 5). Mantle hydration is poorly definable and depends on depth and density 

of bending related faults as well as on the thermal structure of the oceanic lithosphere. 

Therefore estimates based on regional seismic and gravimetric data evaluated by Ranero 

& Sallarès (2004) are four times higher than those assumed by Rüpke et al. (2004) who 

standardised hydration levels with regards to the age of the lithosphere. Water balances 

are presented for both models. 

The presented water releases are based on results of chemo-thermo-mechanical modellings 

performed by Rüpke et al. (2004) who solved for slab dehydration during sub- 

moho 

fault 

pelagic 

sediments 

sheeted dykes 

& pillow lavas 

1) 

100 m 7.3wt% H2O gabbro intrusions 4 km ~ dry 

serpentinized 

peridotite 

1 km 2.7wt% H O 

2km 1wt%HO 

2 

2) 

~23 km 

2 

2.5wt% H O 

Figure 5: Oceanic lithosphere with estimated water content in sediments, crust and mantle after 

Rüpke et al. (2004) modified by local data: 1) the thickness of sedimentary deposits after von Huene 

et al. (1999) and 2) mantle hydration after Ranero & Sallarès (2004). 



223 

2 

2)


duction regarding latent heat consumption and neglecting shear heating1 (fig. 6). 

Thereafter, one column of one square metre Nazca lithosphere releases 700 t water at 

main dehydration depths (80-180 km) which sums up to 1.7 Gt water regarding the entire 

Neogene cycle of Nazca plate subduction starting 26 Ma ago (Sempere et al., 1990). 

Using the molar volume of water at 120 km depths, this mass fills a cross-section of 

more than 1500 km2 which finally lies in the dimension of the mantle magma reservoir. 

Phases of oroclinal bending might have been important for the water budget, because 

bending related faults should have opened parallel as well as perpendicular to the trench 

so that large amounts of water could have been fixed in the mantle. 

Slab-derived water in the mantle wedge should thus be sufficient to trigger a wide 

scale melting of mantle material, well noticing the presumably prior hydration of the 

Western Cordillera as pre-Neogene backarc. If the residual water, retained in the 

oceanic lithosphere, is released as well, the cross-section will expand for additional 

170 km 2 in case of complete crustal dehydration resp. 880 km 2 for complete mantle 

depth [km] 

retained water [%] 

100 

200 

100 

50 

T(°C) 

1300 

1100 

900 

700 

500 

300 

100 

100 200 300 400 

distance [km] 

crust 

sediments 

mantle 

50 100 150 200 250 

depth [km] 

Figure 6: Dehydration of oceanic lithosphere 

during subduction, presented above) as main 

depths’ water release of sediments, crust and 

mantle and below) as percentage of retained water 

respectively; after Rüpke et al. (2004). 

a water-conserving reaction to mantle phase A (Eydam, 2008). 

dehydration which points out the role 

of oceanic mantle for subduction zone 

dynamics. 

The double seismic layer shown in figure 

7 allows allocating the events to stability 

limits of mayor hydrous minerals in the 

oceanic lithosphere which can be used to 

predict slab temperatures at depths. 

Crustal seismicity stops around 140 km 

depth, whereas seismicity in the oceanic 

mantle is ongoing until the stability limit 

of serpentine in 180 km. Lawsonite is the 

only hydrous mineral in the crust which is 

stable down to 140 km depth. Lawsonite 

decay starts at the hot interplate boundary 

at shallower dephts and proceeds during 

subduction to deeper slab layers where temperatures 

at 140 km depth should exceed 

730◦C. Serpentine as the main hydrous 

mantle phase should still be present at 

180 km depth where it transforms through 

These estimates correspond to a fairly warm subduction system although the Nazca 

plate is quite old (55 Ma). Shear heating at the interplate boundary may elevate 

temperatures in the oceanic crust, because lubricates like sediments are sparse in the 

1 Modifying the mantle hydration model to higher estimates after Ranero & Sallarès (2004) will change 

the modelling results to even larger water releases than calculated in table 1, considering that dehydrations 

are mostly exothermic reactions. 



224


central Andean subduction zone as a consequence of its arid climate (Lamb & Davis, 

2003). Thus more water than listed in table 1 may be released into the mantle wedge. 

Dehydrations finish below 200 km depth, suggesting that slab-derived fluids supply 

partial melting of mantle peridotite more than 60 km laterally away from their source 

region. Might this be possible? 

Discussion on fluid mobility 

There are several models describing fluid mobility in subduction zones like fluid channeling 

along cracks opened by dehydration induced hydrofracturing, lateral transports 

in the coupled mantle wedge, porous flows and thermally induced convections in the 

asthenospheric wedge. 

At considered depths hydrofractured faults shouldn’t reach far into the mantle and 

a coupled mantle wegde should be unrealistically thick to explain the requested 

transportation lengths. Porous flows start when interstitial fluids or melts interconnect 

depending on temperature, fluid salinity and melt viscosity. Deep slab-derived fluids 

are highly saline (Scambelluri & Philippot, 2001) and temperatures below 140 km 

depth definitively exceed 620◦C (see above), the minimum temperature of pure water 

interconnection in an olivine matrix (Mibe et al., 1999). 

Water enhances mantle convection via lowering the peridotitic solidus in the mantle 

wedge. This effect may be more pronounced than expected so far, considering the 

very slow reaction kinetics of olivine melting in laboratory experiments (Grove et al., 

2006). The correction of peridotitic solidus to much lower temperatures, e.g. to 860◦C at 100 km depth, implies that first water-enriched melts may be generated just above 

the slab. The melt fraction should be minor due to fast segregation of the low-viscous 

melts into lower and hotter mantle regions. 

Additionally, water import in the central Bolivian orocline might have been temporarily 

elevated in phases of its oroclinal bending leading to a significant reduction of 

mantle viscosity and enabling effective material transports via thermal convections, 

like it is modelled for some general case studies by Gerya et al. (2006). Saline 

fluids and melts may be transported far into the hotter backarc mantle where melt 

fractions rise and segregation rates decrease and fluids and melts become detectable 

by magnetotellurics. 

Models of mantle convection deal with numerous low constrainted parameters, like 

the degree of mantle hydration, shear heating at the interplate boundary, latent 

heat produced by mineral reactions or advective heat transports by fluids and melts. 

Therefore mantle rheology is only poorly definable and viscosity values may differ over 

several magnitudes. 

Water release at intermediate depths plays thus an important role in subduction zone 

dynamics. Currie & Hyndman (2006) even postulate that hot backarc mantles are a 

fundamental characteristic of an ocean-continent subduction zone. And indeed, other 

magnetotelluric images from the central Andean backarc mantle seem to concur with 

this: Schwarz & Krüger (1997) modelled 0.02 S/m conductive mantle features at the 



225


Profil 

E4 

E5 

Depth [km] 

Depth [km] 

0 

100 

Amp 

Ser 

600°C 

< 40° 

Law 

730°C 

E4 

200 

0 200 400 

0 

100 

E5 

200 

0 200 

Distance [km] 

400 

Figure 7: Local microseismic events (M > 1) after David (2007) with map of projection lines E4, E5 

and MT profile. Above: Events allocated to decay temperatures of hydrous minerals, this are in the 

crust: Amp - amphibole and Law - lawsonite and in the oceanic mantle: Ser - serpentine. Note the 

double seismic layer. 

transition to the Puna around 23 ◦ S and northwards at 20-21 ◦ S upper mantle material 

seems to be quite conductive as well with values over 0.05 S/m (Lezaeta, 2001), though 

electromagnetic fields are severely attenuated by a crustal high conductivity zone here 

(Brasse et al., 2002). 

Discussion on the mobility of the slab itself 

The Nazca plate subducts along the whole margin with small dip angles between 25-30 ◦ 

or even horizontally in greater depths at some segments (so called ’flat subduction’) 

where volcanism above is inactive. 

Depth [km] 

0 

100 

Nazca Plate 

A (25-20 Ma) 

Flat to normal slab transition (25-20 Ma) 

uplifting 

volcanic front 

migration 

hydrated lithosphere 

200 

0 200 400 

Distance [km] 

Eastern 

Cordillera 

melt 

asthenospheric 

influx & slab - 

steepening 

600 

Figure 8: ’Mobile slab model’ for the central Andes after 

James & Sacks (1999). Due to retarded dehydration at 

intermediate depths, slab flattens and dewaters sparsely, 

insufficient to melt but to hydrate the base of the overlying 

lithosphere. Slab compacts and steepens again when 

hot asthenospheric material influx and triggers effective 

dehydrations; magmatism and volcanism above develop. 



226 

Thus, slab pull and buoyancy 

forces are fairly equilibrated and 

the slab may react sensible to density 

changes due to retarded dehydrations; 

it gets mobile in geological 

time scales. 

Such ’chemically controlled slab 

mobility’ was already discussed by 

James & Sacks (1999) and applied 

on central Andean history by supposing 

a period of flat subduction 

35-25 Ma ago, basically due to 

absent lava dates for this period 

(fig. 8). 

Remarkable is the slight slab steepening 

in the central orocline (fig. 7).

Depth [km] 

Depth [km] 

Depth [km] 

0 

100 

A 


Nazca Plate 

Western 

Cordillera 

melt 

200 

oroclinal bending (16-10 Ma) 

0 200 400 

0 

100 

B 

formation of backarc 

melt reservoire (< 10-6 Ma) 

huge mantle 

water release 

200 

0 200 400 

0 

100 

C 

Altipano 

pulse of mafic 

volcanism 

melt thermal weakening 

melt 

fluid-melt-path 

melt 

200 

isolation of backarc 

melt reservoire (< 6 Ma) 

slab steepening 

0 200 

Distance [km] 

400 

Figure 9: Attempt to reconstruct Neogene Nazca 

plate subduction in the Bolivian orocline: 

A) Increased hydration of oceanic Nazca plate 

mantle due to significant oroclinal bending. 

B) 2-4 Ma later, highly hydrated mantle reaches 

dehydration depths of serpentine (100-180 km) where 

the released fluids trigger high-grade partial melting 

in the backarc. Backarc melts rise vertically as well as 

non-vertically to the arc via internal convections. 

C) Slab steepens during dehydration. The voluminous 

backarc reservoir persists but is maintained by 

less fluids. Volcanic productivity decreases. 

Tracing the regression line of shallow Wadati-Benioff events (z < 100 km) to greater 

depths, this line cuts the mantle conductor at dehydration depths of serpentine 

(z = 180 km), the most important hydrous mantle mineral which may bound huge 

amounts of water. Therefore backarc peridotitic melting may have been triggered 

just above the slab by enormous fluid influx whereby the slab was compacting and 

steepening slowly to its actual position (fig. 9). Today, the magma reservoir should be 

maintained by much less fluidal material and probably cools down. 

This scenario implies a prior period of extensive oceanic mantle hydration which might 

have occured during phases of oroclinal bending. Bending dates are hard to fix, probably 

block rotations in the closer survey area give a hint, they were dated at 12 Ma 

(Wörner et al., 2000). 

Using an average for ancient subduction rates of 10 cm/a, evaluated by Somoza (1998), 

and a constant slab dip of 25◦ , those huge amounts of fixed water will have started 

to deliberate after 2.4 Ma of subduction (z ≈ 100 km) and will have reached depths 

of high-grade partial backarc melting (z ≈ 180 km) further 1.9 Ma later. Surficial expression 

of high-grade mantle melting are Pliocene to recent pulses of mafic andesites 

erupting in the Bolivian Altiplano backarc (Davidson & de Silva, 1994). Furthermore 

backarc mantle magma might have been transported via internal convections to the 

sub-arc region and have also erupted at the main volcanic arc. However, the basal input 

into the deep magma system of the recent strato-volcanoes is only minor (Wörner 

et al., 2000). 



227


Conclusion 

The huge backarc mantle conductor imaged by 2-D inversion of magnetotelluric data 

from the central Bolivian orocline inspired reflections about fluid and melt dynamics 

in the central Andean subduction zone. Among the two approaches considered here 

to explain the remarkable offset between intermediate depths mircoseismic events and 

the imaged magma reservoir, sub-arc and -backarc water release plays a key role for 

subduction zone dynamics. 

In the central Bolivian orocline huge amounts of water might have been released at 

main slab dehydration depths some million years after oroclinal bending occurred where 

faults should have opened not only parallel but also perpendicular to the trench allowing 

deep water infiltration and fixation in the oceanic mantle. This implies on the one hand 

that mantle viscosity is definitely lowered and leads to significant material transports 

due to thermal convections, whereby fluids and melts may be widespreaded in the 

arc and backarc mantle. On the other hand, enhanced slab dehydration and slab 

compacting may have been followed by slab steepening and the imaged mantle melting 

process isn’t supplied by much fluidal material anymore and therefore probably cools 

down. 

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231

Thin Sheet Conductance Models from 

Geomagnetic Induction Data: 

Application to Induction Anomalies at the Transition from 

the Bohemian Massif to the West Carpathians 

VclavČerv a (vcv@ig.cas.cz), Světlana Kov čikov a , Michel Menvielle b and Josef Pek a 

a Inst. Geophys., Acad. Sci. Czech Rep., v.v.i., Prague, Czech Rep. 

b CEETP CNRS, Saint Maur des Fosses, France 

Abstract 

Thin sheet approximation of Earth’s conductive structures made it possible to quantitatively estimate effects of 

lateral conductivity variations in the Earth long before full 3-D electromagnetic modeling was practicable. The 

thin sheet approach is still useful when induction data with limited vertical resolution are to be interpreted on a 

surface. It especially refers to collections of long period induction arrows across large areas and geological units. 

For this purpose, inverse procedures, both linearized and stochatic, for a conductance distribution in a thin sheet have 

been suggested recently. We present a stochastic Monte Carlo inversion of geomagnetic induction data based on 

the bayesian formulation of the inverse problem. An example of the inversion of practical induction data from the 

transition zone between the Bohemian Massif and the West Carpathians suggests that an SW-NE anomalous induction 

zone observed above the eastern slopes of the Bohemian Massif admits explanation in terms of a phantom effect due 

to the superposition of fields of the strong SE-NW Carpathian conductivity anomaly to the east with NW-SE to W-E 

trending conductivity zones to the west that conform with the fault pattern of the eastern Bohemian Massif. 


Regional geoelectrical information on the contact zone between the Variscean Bohemian Massif and the Alpine Western 

Carpathians is mainly available from long-period geomagnetic transfer functions. Magnetotelluric data and broadband 

electromagnetic induction experiments are scarce in the region, mainly because of high level of the civilization 

noise all over the area, and also because of the lack of instrumentation in the past. Only recently, magnetotelluric 

experiments have been carried out in some subareas of the region, mainly for commercial targets (e.g., Voz r, 2005). 

Long-period geomagnetic induction data covering a period band of about one decade in the range of thousands 

of seconds cannot provide detailed geoelectrical information on structures beneath the region of interest. They are, 

however, suitable characteristics to be used to model large-scale horizontal conductivity distribution in the Earth’s 

crust or lithosphere, and thus to indicate regional lateral conductivity anomalies that are responsible for the observed 

induction pattern over the area under study. With data at periods of the order of thousands of seconds, with penetration 

depths starting at several tens of km for standard conditions of the continental lithosphere, a quasi 3-D thin sheet 

approximation of crustal conductivity structures is a reasonable induction model (e.g., Vasseur and Weidelt, 1977). 

The thin sheet approximation largely reduces the computational demands of the modeling procedure as compared with 

a full 3-D treatment and, moreover, bypasses some intrinsic difficulties of dealing with the geomagnetic induction data 

alone, especially their low sensitivity with respect to the normal layered background of the model. 

Recently, two methods of inversion of geomagnetic induction data for conductances in a thin sheet have been 

developed, one based on the non-linear conjugate gradient technique (Wang and Lilley, 2002) and the other on a 

Bayesian approach with Markov chain Monte Carlo (MCMC) method used for a stochastic sampling process (Grandis, 

2002). In this contribution, we are using the latter approach to analyze conductance distributions which are compatible 

with the geomagnetic induction data in the West Carpathians region and at its transition to the Bohemian Massif on 

the territories of the Czech Republic, Slovakia and Poland. 

More specifically, the data base of this study are induction response data at 150 field stations that were published 

earlier (Praus and Pěčov , 1991) covering the Bohemian Massif (BM), the Brunovistulicum (BV), and the West 

Carpathian region (WCP) and re-analyzed in (Pěčov and Praus, 1996). Spatial distribution of both the in-phase and 

the out-of phase induction vectors, contour maps of individual transfer functions (TF) and contour maps of anomalous 



232

Latitude (deg) 

54 

53 

52 

51 

50 

49 

48 

47 

Mid-G 

Saxo-Thuringian 

Rheno-Hercynian 

Moldanubian region 

North-German-Polish Caledonides 

ine 

erma n C rystall R 

ise 

BM 

it of Alpi atio 

Alpine Front 

ne deform 

o r li 

ute 

outer limn 

mit of Varisceandefor tion 

East European 

Platform 

Holy Cross 

Mts 

8 10 12 14 16 18 20 22 

Longitude (deg) 

T 

eisseyre rnquist Line 

Vienna 

Basin 

ma 

-To 

Midmountains 

Pannonian 

Basin 

Bohemian Massif (BM ) with uni ts: 

Moldanubicum 

Teplá-Barrandian region 

Krušné hory-Thuringian 

region 

Bohemian Cretaceous 

basin 

West-Sudetic region 

Brunovistulicum (BV) 

including Silesicum, Moravicum 

and Brno Massif 

West Carpathians (WCP) with units: 

Tertiary basins 

(Carpathian foredeep, 

Pannonian basin) 

Outer (Flysch) Carpathians 

Klippen Belt 

Central (Inner) Carpathians 

Neovolcanites 

Figure 1: Geological scheme of the region of Central Europe relevant to our modeling study. The dashed-line rectangle 

shows the region in which the inversion for a laterally variable conductance distribution in a thin sheet is carried out. 

vertical field that were generated from the TF’s by the hypothetical field of different polarizations and systems of internal 

anomalous currents indicate the existence of two zones of anomalous induction at the eastern margin of the BM 

and near the boundary of the Carpathian plate (Kov čikov et al., 1997). The previous analyses, and the recent one 

performed by a new approach to imaging the induction data of the Wiese vectors at almost 1800 localities covering 

mainly the Central European area (Wybraniec et al., 1999) suggest that these anomalies might be connected with the 

North-German-Polish anomalous zone, representing an important part of the Trans-European Suture Zone (TESZ). 

The analysis of certain models of electrical conductivity distribution is performed to fit the anomalous features of 

the induction response data over the Central European area, specifically zones of anomalous induction in the eastern 

margin of the BM, across the entire block of the BV and near the margin of the Carpathian tectonic plate. 

The structure of the article is as follows: In Section 2, we give a short overview of the principal geological units of 

the region under study. Section 3 briefly summarizes the geoelectrical features of the region previously inferred from 

the geomagnetic induction data in the region. In Section 4, we formulate the thin sheet model used in the inversion. 

The principles of the Bayesian inversion of the geomagnetic induction data for the conductance distribution in the 

thin sheet are presented in Section 5. Section 6 then summarizes outputs of the Bayesian inversion for the induction 

data over the BM/BV/WCP region with indications on possible correlations of the conductance model with regional 

geological structures. 

2 Geological context of the induction studies 

Fundamental elements of the central European geological structure that are relevant to our modeling experiment are 

schematically displayed in Fig. 1 together with the major geological units over the Czech and Slovak Republics covered 

by induction response data involved in the modeling process. 

(i) The Tornquist-Teisseyre tectonic zone (TTZ) constitutes one substantial part of a number of fault zones and 

sutures found within the Trans-European Suture Zone (TESZ) that represents the most important geological boundary 

in Europe separating mobile Phanerozoic western terranes (Meso-Europe) from the Precambrian east European Craton. 

It is as clearly defined in the deep lithosphere as in the upper crust, Moho depths increase across this zone from 30 km 

beneath Variscan Europe to 45 km beneath the East European Craton. In contrast to the relatively cold eastern craton 

relatively high heat flow characterises Western Europe. 

(ii) The Bohemian Massif (BM) represents the easternmost consolidated block of the Variscan branch of the European 

Hercynides (Meso-Europe) that builds up Bohemia and the western part of Moravia. The major elements of 



233

the BM are several SW-NE trending zones separated usually by deep-seated faults, which are reflected in the results 

of the deep seismic profiling, in the gravity, geomagnetic and heat flow maps (Suk et al.,1984). The fault structures 

are essentially parallel with the boundaries of individual Hercynian zones. The intersection of these zones with the 

second order system of NW-SE trending faults is responsible for the complicated block structure of the BM. 

(iii) The Carpathians belong to the young Tertiary Alpine-orogenic belt and they constitute the NE branch of the 

Alpides. Their boundary with the Eastern Alps runs along the Danube Valley. The northern boundary with the East 

European Platform is defined by the erosive margin of the flysch nappes. Our model covers the West Carpathians 

(WCP) and we distinguish here the inner (central) Carpathians, the Klippen zone, the outer (Flysch) Carpathians and 

the Carpathian foredeep (Fig. 1, dashed-line rectangle). 

(iv) The Brno unit, termed recently the Brunovistulicum (BV) (Dudek, 1980; Suk, 1995) lies in between those 

previously mentioned structural elements. The BV unit is assumed to be an independent geological structure forming 

the Precambrian (Cadomian) basement (Palaeo-Europe) of both the eastern part of the Hercynides (Variscides) of the 

BM and the Alpides, i.e. of the WCP in Moravia. Recent geophysical and geological data have shown that the BV 

and the whole Moravian block occupy a highly independent position and form a separate geological unit belonging 

probably to the Fenno-Sarmatian Platform (Dudek, 1980). 

3 Geoelectrical data and features of the region 

3.1 The data 

The experimental data were collected in 1970’s and 1980’s in a series of field experiments organized in co-operation 

with Czech, Slovak and Polish colleagues. The field measurements consisted in analogue recordings of magnetic 

transient variations at alltogether 150 temporary field sites over an area of about 500 × 250 km 2 . They were analysed 

in terms of induction arrows (Wiese, 1962). At each station, in-phase and out-of phase induction arrows have been 

estimated for periods in the range of 1200 to 5840 s. They correspond to the real and imaginary components of singlestation 

transfer functions between the horizontal and vertical components of the transient magnetic field at the station. 

A sample of the real and imaginary induction arrows at a particular period of T = 3860 s is presented in Fig. 2. 

3.2 Major conductivity anomalies 

As the magnetic Z-component is known to be highly sensitive to laterally inhomogeneous distribution of the internal 

electrical conductivity, maps of these vectors provide us with a view of the changing anomalous behaviour of the 

Z-variation as function of frequency and location. Reversals of the arrows distinguish zones of anomalous induction, 

which often mark important geological features such as contacts between blocks with different geological histories of 

development, zones of past and recent tectonic activities, collision zones and etc. A qualitative analysis of the maps 

of induction arrows led to evidence two major conductivity anomalies in the area under study. Quantitative modeling 

allowed to characterize the conductivity distribution in the lithosphere that accounts for the observed induction arrows. 

The Carpathian anomaly, WCA The induction vectors across the WCP region show a clear perpendicular orientation 

with respect to a general trend of the anomalous induction zone localized along the external margin of the 

Carpathians Mts. chain (see WCA in Fig. 2. They show almost a perfect 180 o reversals of their azimuths above the 

anomalous induction zone. In the WCP, modules of the induction vectors situated to the south from the zero line are 

by about 25-50% larger than the corresponding induction vectors located to the north of the anomaly. The Carpathian 

14˚ 15˚ 16˚ 17˚ 18˚ 19˚ 20˚ 21˚ 22˚ 23˚ 

51˚ 51˚ 

Real arrow 0.5 

50˚ 50˚ 

49˚ 

WCA 

49˚ 

EBMA 

48˚ 48˚ 

14˚ 

15˚ 

16˚ 

? 

17˚ 

18˚ 

19˚ 

20˚ 

21˚ 

22˚ 

23˚ 

14˚ 15˚ 16˚ 17˚ 18˚ 19˚ 20˚ 21˚ 22˚ 23˚ 

51˚ 51˚ 

Imag arrow 0.5 

50˚ 50˚ 

49˚ 49˚ 

48˚ 48˚ 

Figure 2: Sample of experimental real and imaginary induction arrows in the BM/BV/WCP region for the period of 

3860 s, with two main regional conductivity anomalies indicated, the West Carpathian conductity anomaly (WCA) 

and the conductivity anomaly on the eastern margin of the Bohemian Massif (EBMA). 

14˚ 

15˚ 

16˚ 

17˚ 

18˚ 



234 

? 

19˚ 

20˚ 

21˚ 

22˚ 

23˚

geoelectrical anomaly is constrained by the presence of high-conductivity rock series at depth of 10-25 km in different 

segments of the orogen. Different geological models explaining the presence of highly conductive rocks or solutions 

as sources of the anomalies have been suggested. The role of altered and/or fractured rocks, saturated with hot mineral 

waters, as well as the proximity of anomaly sources to boundaries of different crustal blocks, including those between 

the Carpathians and adjacent platforms, have been taken into account ( d m and Posp il, 1984; Jankowski et al., 

1984; 1991; 2008; Hvo dara and Voz r, 2004). Other authors discuss possible connection between the Carpathian 

anomaly and the presence of metamorphosed coal bearing Carboniferous strata beneath the orogen or relation to the 

graphitized rocks occurring close to the boundaries of crustal blocks (Glover and Vine, 1992; Glover and Vine, 1995; 

´Zytko, 1997). 

The EBMA anomaly The induction vectors on the eastern margin of the BM are distinguished by the vectors 

oriented predominantly parallel to the general SW-NE trend of the anomalous zone. Also the reversal of the azimuths 

at the anomalous zone is rather poorly developed, only sudden changes of azimuths are observed at individual profiles. 

These facts are clear indications of a 3-D character of the conductivity distribution. The EBMA has been generally 

attributed to processes in the the subduction of the eastern margin of the BM beneath the WCP plate, but precise 

induction processes for generating the peculiar 3-D features of this anomaly are still unknown (e.g. Kov čikov et al., 

2005). Speculating on the physical/geological sources of the anomaly may thus be premature. 

3.3 Results from numerical modeling 

From the equivalent current systems (Červ et al., 1997) it was concluded that the source depth of the induction 

anomalies can be about 18 km in the WCP region and about 10 km in the EBM/BV. These estimates are suggesting the 

source of the anomalies at shallower depth than those obtained previously by separating the magnetic field variations 

into internal and external parts (Pěčov and Praus, 1996) and applying the line current approximation (Jankowski et 

al., 1985). 

2-D models for induction vectors along the profiles crossing the WCP are summarized in (Jankowski et al., 1985). 

The models featured anomalous bodies with a cross-section× conductivity parameter of the order of 10 7 to 10 8 Sm, 

with the top of the bodies at depths beneath 12-15 km. In (Jankowski et al., 1991) the 2-D modeling was used for 

simultaneous modeling of the induction vectors and apparent resistivities, collected in a series of sites in the Polish 

section of the Carpathian Foredeep. In the latter models, the source of the WCA was situated at shallower depths, less 

than about 10 km, and hypothesized to be related to deep sediments of the Carpathian Foredeep. The 2-D inversion on 

the Carpathian data was firstly used in (Červ and Pek, 1981). The geoelectrical structural model along the DSS profile 

No VI, crossing the BM, BV and WCP, based on the MT and MV results was presented in (Červ et al., 1984). 

3.4 Depth of the asthenosphere 

The electrical asthenosphere, if present, is an additional structural feature that can affect the induction data especially 

at long periods. In the model derived from the P-wave residuals for the Bohemian Massif the depth of the lithosphereasthenosphere 

transition zone are between 90 and 140 km (Babu ka et al., 1988). From MT sounding a layer of 

increased electrical conductivity attributable to the asthenosphere was interpreted at depth between 100 and 150 km 

(Červ et al., 1984). 

The most likely depth of the conducting layer in the upper mantle in the Pannonian Basin region are between 

60 and 85 km in the central part of the depression. The depths seem to increase towards the flanks of the basin to 

about 100 km ( d m, 1976). In some parts (R ba-Ro nava tectonic line) the thickness of the litosphere reduces to 

even less than 60km ( d m, 1988). The regions of lithosphere thinning penetrate from the Pannonian Basin into 

inner parts of the WCP in several promontories. In the thinned part of the lithosphere in the West Carpathians the 

lithosphere-asthenosphere transition zone is at the depth 90-120 km (Červ et al., 1984). 

A gradual increase of the lithosphere thickness to 140-180 km occurs in the Outer Carpathians and father towards 

the margin of the East European Platform (Praus et al., 1990). In the Alps the depth of the asthenosphere varies from 

100 to 200 km (Praus et al., 1990). 

4 A possible thin sheet model 

In the subsequent inversion for a laterally non-uniform conductance, we will use a thin sheet model formally defined 

as follows: 

Let us consider a model consisting in a heterogeneous thin sheet at the surface of or embedded in a 1-D medium, 

hereafter called normal model. The normal model is defined by the conductivities σn(r) at any point r. In the thin 

sheet, the actual conductivity σ(r) differs from the normal one in a domain of interest Ω. InsideΩ, σa(r) denotes the 



235

difference σ(r) − σn(r): σa(r) is the anomalous conductivity that is zero outside Ω. Solutions of the forward and 

inverse problems have already been published for such a model. They are briefly recalled in the next section. 

With regard to the experimental geomagnetic TF’s available, several aspects of the thin sheet model must be 

considered. First, the validity of the thin sheet hypothesis must be assessed. We assume that the anomalous electrical 

targets are localized mainly in the crust. Penetration depths for typical continental crustal sections should not be less 

than about 50 km in the period range of thousands of seconds (corresponds to the resistivity of 10 Ωm and period 

of 1000 s). Thus, the anomalous zone of 20-30 km below the Earth’s surface can be reasonably (though, may be, 

not completely unquestionably for highly conductive anomalous zones) approximated by a thin sheet. According to 

Bruton (1994), the size of the square tiles a used to discretize the anomalous subdomain Ω of the sheet should meet 

the condition aωμSmax ≪ 1. For the most extreme parameters in our models, say Tmin = 1200 sandSmax = 

5000 siemens, the size of the tiles should be much less than about 30 km. We typically use tiles with a =20to 25 km 

in our models, which meets the Bruton’s condition for most of the model situations. 

The second aspect is the depth of the thin sheet. As we are not able to employ a multiple sheet model in the 

inversion at present, we use a single thin sheet that integrates all the conductivity anomalies from the surface down to 

the crust. Thus, the sheet is situated on the surface of the Earth in our experiments. This may result in increased misfit, 

especially in imaginary induction arrows, if the anomalous current flow deep in the crust. 

The third aspect is the embedding normal structure. Due to large differences of the depth vs. resistivity sections 

of the two main region of our study, the BM and the WCP with the adjacent Pannonian Basin, we cannot suggest 

any single 1-D normal model down to the asthenospheric depths for the whole region. Therefore, we simplified the 

normal model into a two-layer structure with a poor conductor resistivity of several hundreds of Ωm up to 1000 Ωm) 

underlaid by a more conductive asthenosphere with resistivity within the range of 100-500 Ωm. The effect of the 

topography of the asthenospheric layer was checked independently by a 3-D modeling experiment with seismic data 

(Praus et al., 1990) taken to approximate the top of the asthenosphere. The checks showed that the effect of the 

asthenosphere is negligible in induction arrows for periods of the order of thousands of seconds unless the resistivity 

of the asthenosphere is less than about 10 Ωm. 

5 Bayesian Monte Carlo Markov Chain thin sheet inversion 

We present in this section the Bayesian Monte Carlo Markov Chain (MCMC) method we used to solve the inverse 

problem. For the sake of self-completeness, let us first briefly recall basic notions concerning Bayesian inversion and 

Markov chains behaviour. The readers are referred to Roussignol et al. (1993), Menvielle and Roussignol (1995), and 

Grandis et al. (1999; 2002), and references therein for more details. 

5.1 The Bayesian approach 

Let the a priori knowledge be the information available on the model before processing the data, and the a posteriori 

knowledge the information available after processing the data. A priori and a posteriori distributions account in a 

probabilistic way for the a priori and a posteriori knowledge respectively. In the Bayesian context, solving the inverse 

problem thus comes down to determining the a posteriori knowledge by updating the a priori knowledge with the 

information gleaned from the data (Box et Tiao, 1973; Berger, 1985; Press et al., 1989). 

Solving the inverse problem first requires the direct problem to be solved. Let F be the direct problem function 

which enables computation of the observations d for a model m. Assuming that the error δd is only related to the 

data acquisition, it becomes 

d = F (m)+δd 

The a priori knowledge is given by a probability distribution function (pdf ) P0(M = m | M ∈M) defined on 

the set of possible models M. The a posteriori probability for the parameter vector M to take the value m given the 

observations d is given by Bayes’ formula (Bayes, 1763; also see, e.g., Bolstad, 2004, for a more modern treatment). 

Noting P (M = m | D = d, M ∈M) the conditional probability of M given D, and assuming that the error δd is 

gaussian with standard deviation τ, it becomes 

 

 

||F (m) − d)||2 

exp − P0(m) 

P (M = m|D = d, M ∈M)= 

 

m∈M 

exp 

 

− 

2τ 2 

||F (m) − d)||2 

2τ 2 

 

P0(m) 

The value d of the random vector D corresponds to the observed data. Since d is not modified during the inversion 

process, we will from now on omit D in the expression of the probability distributions and denote the a posteriori pdf 

P (M = m|D = d, M ∈M) simply by Π(m). 



236 

(1)

The normalization constant, which appears in the denominator of eq. (1) is a sum over the set of possible models, 

the dimension of which is very large: for instance, it is equal to M × L for models with M parameters that can each 

take on L different values. It is actually very difficult, if not impossible to estimate directly. We choose to use a Monte 

Carlo Markov Chain (MCMC) simulation method to achieve this estimation. 

5.2 Markov chains 

In order to estimate the pdf Π(m), let us define a Markov Chain on the set M of possible models that have Π(m) 

as invariant probability. The marginal pdf ’s of Π(m) will be estimated by empirical averages from simulations of the 

Markov Chain. 

Consider a system which can take a certain number of states and evolves at random with time. At a given time, 

the state of the system can be described as a random variable M, the values of which, m, belong to M. The system is 

a Markovian process if, at any time, its future evolution depends only on its present state. It means that a Markovian 

system depends only on its past through its present state. Markov chains are a particular class of Markovian processes 

such that (i) the set M is finite or countable, and (ii) the successive times for the evolution are denoted by integers. 

Aseries{M(n),n =0, 1, 2,...,N} of random variables with values in a finite or countable space is then a Markov 

chain if the state of the system at the time n +1, M(n +1), depends only on its past through the state of the system 

at time n, M(n). The behaviour of a Markov chain is defined by the set of its transition probabilities, 

Pn(m, m ′ )=P (M(n +1)=m ′ | M(n) =m) , 

where m and m ′ belong to M. If (i) the transition probabilities do not depend on time n, (ii) M is finite, and (iii) each 

possible state can be reached from any other, the chain is a homogeneous ergodic aperiodic Markov chain, and there 

exists one, and only one probability density function Π on M which is invariant for the Markov chain. When n 

increases towards infinity, the behavior of ergodic Markov chains is such that the average fraction of time at which the 

chain is at a state m (m ∈M) tends towards the invariant probability of m,i.e.Π(m). 

Methods for Bayesian inversion with Markov chains has been proposed for the 1-D magnetotelluric (Grandis et 

al., 1999) and DC problems (Schott et al., 1999) with the a priori of smooth variation of resistivity with depth, and for 

the thin sheet approximation (Roussignol et al. 1993; Grandis, 1994; Grandis et al., 2002). The present analysis of 

crustal conductivity over the transition from the Bohemian Massif to the West Carpathians relies on the inversion of 

induction arrows using the latter method, which is briefly described in the following sections. 

5.3 The thin sheet forward problem 

Let us consider a model consisting of a heterogeneous thin sheet at the surface of or embedded in a 1-D medium, 

specified in detail in the first two paragraphs of Section 4 above. Let E(r,ω,σ) and H(r,ω,σ) be the time Fourier 

transforms of the electric and magnetic field at point r and circular frequency ω, ω =2π/T, T period, for the actual 

conductivity structure σ. Using the Green kernel method, we can rewrite basic equations of electromagnetism as 

(Weidelt, 1975) 

 

E(r,ω,σ) = En(r,ω) − iωμ σa(r 

Ω 

′ ) G(r, r ′ ,ω) E(r ′ ,ω,σ(r ′ )) d 3 r ′ , (2) 

 

H(r,ω,σ) = Hn(r,ω)+ σa(r ′ )curl(G(r, r ′ ,ω)) E(r ′ ,ω,σ(r ′ ) d 3 r ′ , (3) 

Ω 

at any point r and any frequency ω. The quantity μ is the magnetic permeability of the vacuum in our models. 

G(r, r ′ ,ω) is a 3 × 3 complex matrix, named Green kernel, and represents the Fourier transform at frequency ω of the 

electric field created at point r by a unit dipole δ(r ′ ) located at point r ′ (Morse and Feshbach, 1953), curl(G(r, r ′ ,ω)) 

is a 3 × 3 complex matrix obtained by taking the curl at point r of the field of the column vectors of the matrix 

G(r, r ′ ,ω). 

A numerical solution of the forward problem has been first proposed by Vasseur and Weidelt (1977) for a superficial 

thin sheet. The Vasseur and Weidelt’s (1977) approach can be extended to a thin sheet at any depth below the surface. 

The code was made operational by Tarits (1989). These solutions are based upon a digitization of Ω in K small square 

cells Pk, k = 1,...,K, in which conductivities, Green kernels, electric and magnetic fields are nearly constant. 

Let S(Pk) and Sn(Pk) be the actual and normal integrated conductivities (i.e. conductances) of the cell Pk, and 

Sak = S(Pk) − Sn(Pk), k =1,...,K, the anomalous conductance of Pk. Then basic equations become, using the 



237

same notations for the sake of simplicity, 

E(r,ω,S) = En(r,ω) − iωμ 

H(r,ω,S) = Hn(r,ω)+ 

k 

k 

Sak G(r,Pk,ω) E(Pk,ω,S(r ′ )) |Pk|, (4) 

Sak curl(G(r,Pk,ω)) E(Pk,ω,S(r ′ )) |Pk| (5) 

at any point r and any frequency ω. 

Let us consider the linear system made up of equation (4) written at each point Pk of Ω, k =1,...,K.Given 

the distribution of anomalous conductances Sak, k =1,...,K, the quantities E(Pk,ω,S(r ′ )) are solutions of this 

system. For each frequency, the system has 6 × K equations and 6 × K real unknowns in the general case. Solving 

this system allows us to compute the electric field E(r,ω,S(r)) at any point r and frequency ω. The magnetic field 

H(r,ω,S(r)) is then derived using (5) written at any point r and frequency ω. 

5.4 The inverse problem 

The structure of the embedding 1-D model, i.e., Sn(r), the depth of the heterogeneous thin sheet, the domain Ω, and 

the cells Pk are first defined, and remain fixed during the inversion. Their values are to be deduced from previous 

investigations in the studied area (geology, other geophysical methods, ...) and from laboratory measurements of 

rock conductivity. The conductances Sk, k =1,...,K, are the parameters, and solving the inverse problem consists 

in estimating their a posteriori pdf given the data d =(dij), i =1,...,I, j =1,...,J, and the a priori pdf P0. 

The data d are actually estimates of a function T [ E(r,ω,S(r)), H(r,ω,S(r)) ] at points ri, i =1,...,I,ofthe 

surface and frequencies ωj, j =1,...,J, plus an experimental noise δd, 

dij = T [ E(ri,ωj,S(r)), H(ri,ωj,S(r)) ] + δdij. (6) 

The δdij, and therefore the dij are assumed to be independent gaussian random variables with zero mean value and 

standard deviation τ. 

In situations for which no particular information is available, we choose as a priori distribution the product of a 

uniform pdf on each layer. In this case P0 is a uniform distribution over all the possible models and where the different 

parameters are independent. P0 is digitised over a set of conductance values, hereafter called possible conductance 

values, the choice of which depends on the a priori knowledge of the considered medium. There is no constraint on 

this choice, but it is clear that the larger this number the better the determination of the a posteriori distribution, but 

the greater the computer time. The possible conductance values may depend on the cell. We will only consider here 

situations with the same number L of possible values Sl, l =1,...,L, for each cell. The a posteriori distribution will 

accordingly be expressed as the a posteriori probability of these possible conductance values. 

The a posteriori pdf of the parameters S is estimated by means of a Markov chain. Let an algorithm that considers 

each cell Pk successively and updates the value of the parameter for this cell with a transition probability equal to the 

conditional probability distribution of Sl, l =1,...,L, given the actual values of the parameters for the other cells, 

the data d and the a priori pdf P0(S). The sequence of images thus obtained after each scanning of the whole set of 

K cells is a homogeneous Markov chain, because the probability of an image depends only on the previous image, 

and does not change with step n. This process is a Markov chain on M called the Gibbs sampler (Robert, 1996). 

It is ergodic, and its invariant probability Π is the a posteriori probability is the conditional probability Π(S) of the 

parameters given the data d and the a priori pdf P0(S) (Roussignol et al., 1993; Roussignol and Menvielle, 1995; 

Robert, 1996; Grandis et al., 1999; 2002). 

In the present case, the required L × K solutions of the forward problem that are necessary for computing the 

transition probability of the Markov chain (in the present case, the K conditional pdf ’s corresponding to the whole set 

of cells) requires a very long CPU time. In order to limit the CPU time, the forward problem is not fully solved at each 

scanning, and the electric field is estimated by the Markov chain. The Markov chain is then a two-dimensional one, 

which estimates a quantity (the conductance) distributed over a finite set of real values and another one (the electric 

field) distributed over a continuous set of real vectors. 

The asymptotic behavior of such a Markov chain has first been studied empirically by Jouanne (1991), then Grandis 

(1994) for situations representatives of those encountered in geophysics. Using synthetic models, Grandis (1994) 

evidenced that the empirical average of the transition pdf of this Markov chain tends towards an invariant pdf that corresponds 

to the a posteriori pdf of the parameters, provided the estimate of the electric field at each scanning is precise 

enough for the transition probabilities to be reasonably estimated. Later on, Touijar (1994) gave the first demonstration 

that such a chain converges under given conditions. The physical interpretation of Touijar’s mathematical results 

suggests that the empirical results established by Jouanne (1991) and Grandis (1994) are likely to be valid for most of 

geophysical situations (Menvielle and Roussignol, 1995). 



238

6 The inversion 

6.1 The description of the model and data 

In accord with the above discussion, we chose the following particular parameters for the thin sheet model used in the 

MCMC inversion of the long-period geomagnetic induction data over the BM/BV/WCP region: 

(i) The anomalous domain of the superficial thin sheet is divided into 21(N)×29(E) square cells, each 25×25 km 2 

in size, covering thus a region of about 500(N)×750(E) km 2 . This gives in total 609 variable parameters (cell conductances) 

for the inversion. 

(ii) The normal model was composed of a two-layer background model with the first layer of 100 km/1000 Ωmand 

a uniform basement of 300 Ωm. The basement was used to simulate the asthenospheric layer. The topography of the 

asthenosphere was neglected. The layered model was overlain by a uniform infinite thin sheet with the conductance 

of 300 siemens. 

(iii) For the inversion purposes, the 150 experimental geomagnetic TF’s available were interpolated into the centers 

of the sheet cells. As reliable data variances were not available for the experimental TF’s, we assumed the data to be 

contamined with Gaussian errors with the standard deviation of 0.03. 

(iv) For the MCMC run, data for only one period, T = 3860 s, were used to keep the computation times in 

reasonable limits. Fit of the data and model arrows for further periods available were only checked by direct modeling 

tests. 

6.2 The MCMC procedure, convergence, output models, post-processing 

For the MCMC procedure (Gibbs sampler), the conductance of each of the 609 variable cells could take on one of 

12 predefined values from the interval of 3 to 5000 siemens. The Markov chains were typically running for 1000 cycles 

of the Gibbs sampler, which took about 10 hours of the CPU time on a standard PC station (Intel Xeon 3 GHz, 1 MB 

RAM). Repeated MCMC runs were carried out to simulate parallel chains and check the convergence of the MCMC 

process. First 500 cycles of each of the MCMC chains were discarded as a burn-in period during which the chain 

approaches a vicinity of the solution and stabilizes. In our runs, the chains did not change substantially after the burnin 

period, and simulated parallel chains converged to similar conductance distributions for the same cells. From this 

rough diagnostics, we can conclude that the chains converged and can provide reasonable estimates of the means of 

the cell conductances within the selected model class M. As the number of MCMC iteration cycles is relatively small 

in our experiments, it is not realistic to obtain reasonably accurate estimates of higher moments of the aposteriori pdf ’s 

for the cell conductances. In fact, only highly qualitative conclusions may be made as regards the uncertainties of the 

variables. 

The MCMC procedure gives a series of models which should be probabilistically distributed in accord with the 

experimental data. We obtain a whole histogram of conductance values for each cell, which shows how much likely 

are the particular conductance values in the cell considered. After long enough iteration process, the histograms 

approximate the marginal aposteriori probabilities of the discrete conductance values in the individual sheet cells. We 

can estimate the mean values of the cell conductances by integrating over the histogram, as well as the most probable 

cell conductances (maximum aposteriori probabability, or MAP estimates) by taking the most frequent value from the 

histogram. 

Fig. 3 displays sheet models over the BM/BV/WCP region set together from the mean values of the conductance 

in the individual sheet cells and from the MAP estimates of the cell conductances. These models do not represent 

the average or MAP models from the chain, which would both require integration of the multi-dimensional empirical 

posterior pdf over the whole parameter space. The presented models are put together from estimates based on individual 

marginal pdf ’s for the individual sheet cells. It is clear that these models may differ considerably from each 

other, especially in regions where the cell conductances are poorly constrained by the data. Nevertheless, the models 

in Fig. 3 represent simple integrated information on the conductance structure projected from a 3-D probabilistic (histogram) 

image of the cell conductances provided by the whole underlying Markov chain. Fit of the model data from 

the ‘average’ model in Fig. 3 (left) and the experimental induction arrows is shown in Fig. 4 for the inverted period 

of 3860 s. Model vs. experiment fit for longer periods (not shown) is very similar, larger discrepancies are observed 

for the period T = 1200 s with model induction arrows substantially smaller than the experimental data. This is most 

likely due to a misspecified depth of the sheet in our model (superficial sheet). 

Qualitatively, we can also estimate the uncertainty of the conductance by simply observing the ‘flatness’ or ‘peakiness’ 

of the histograms for the cell conductances. In Fig. 5 (left), we show the ‘average’ model from Fig. 3 (left) 

modified by keeping in it only those cells for which 90% of the cell conductance values in the MCMC histograms fall 

within an interval of a width of 2/3 of a decade. All remaining cells, with flatter conductance histograms, have been 

discarded. The cells in Fig. 5 (left) thus indicate regions of the model in which the conductance is reasonably well constrained 

by the data. More precise, quantitative uncertainty estimation would be perhaps possible from longer MCMC 



239

chains which would allow us to integrate directly for variance-covariance functions estimates for the parameters. 

Because of high computational demands, thin sheet models for the MCMC inversion are mostly designed with 

only a coarse tiling. In the model post-processing stage, spatial smoothing often results in a more realistic image of 

the conductance distribution. The smoothed image has to be checked by an additional direct modeling test. We show 

a smoothed version of the ‘average’ conductance model from Fig. 3 (left) in the right-hand side panel of Fig. 5. 

Figure 3: Left: Conductance model over the BM/BV/WCP region designed from average cell conductances obtained 

form the stabilized part of the Markov chain. Right: Conductance model designed from maximum aposteriori conductances 

in the individual sheet cells. The color scale corresponds to the logarithm of the conductances. Period of 

inverted data was 3860 s. 

14˚ 15˚ 16˚ 17˚ 18˚ 19˚ 20˚ 21˚ 22˚ 23˚ 

51˚ 51˚ 

50˚ 50˚ 

49˚ 49˚ 

48˚ 48˚ 

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15˚ 

16˚ 

17˚ 

18˚ 

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21˚ 

22˚ 

23˚ 

14˚ 15˚ 16˚ 17˚ 18˚ 19˚ 20˚ 21˚ 22˚ 23˚ 

51˚ 51˚ 

50˚ 50˚ 

49˚ 49˚ 

48˚ 48˚ 

Figure 4: Fit of the real (left) and imaginary (right) induction arrows for the period of 3860 s. White arrors show the 

input data obtained by interpolating the experimental TF’s into the centers of the sheet cells. Orange-yellow arrows 

were generated by the thin sheet model designed from average cell conductivities from the MCMC chain (model to 

the left in Fig. 3). 

7 Tectonic correlation 

Interpretation of narow-band long-period geomagnetic data by the MCMC sampling can only provide a large-scale 

image of the conductance distribution which conforms with the observed TF’s. The conductance pattern restored from 

the induction arrows collected above the eastern slopes of the BM and its transition to the WCP gives a geologically 

plausible image of the region. The Carpathian conductivity anomaly is reconstructed in detail, suggesting possible 

weakening/local interruption at the crossing with the Central Slovakia fault zone (near 19.2 o E in Fig. 5 right) where 

other geophysical fields and geological indicators show discontinuous features on a presumably strike-slip fault (e.g., 

Kov č and H t, 1993). Though in coarse mesh, the high conductance anomaly well fits the position of a low resistivity 

layer from the magnetotelluric data collected in the esternmost sector of the model, close 22 o E (Voz r, 2005). 

The induction anomaly at the eastern margin of the Bohemian Massif seems to have a more complex explanation 

than that of a quasi-linear conductor along the SW-NE zone of a rapid change of direction of the induction arrows 

(see Fig. 2). Two features may be observed in the model in Fig. 5 (right), which were already discussed earlier by 

Kov čikov et al. (2005). First, it is a conductive zone in the NE of the BM, which may generate induction arrows 

directed towards the SW, as clearly observed all across the area to the west of the EBMA. Second, it is an alteration 

of conductive and resistive E-W zones in the eastern part of the BM. Though still not clear how much of this effect 

14˚ 

15˚ 

16˚ 

17˚ 

18˚ 



240 

19˚ 

20˚ 

21˚ 

22˚ 

23˚

14˚ 15˚ 16˚ 17˚ 18˚ 19˚ 20˚ 21˚ 22˚ 23˚ 

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48˚ 48˚ 

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21˚ 

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23˚ 

14˚ 15˚ 16˚ 17˚ 18˚ 19˚ 20˚ 21˚ 22˚ 23˚ 

51˚ 51˚ 

50˚ 50˚ 

49˚ 49˚ 

48˚ 48˚ 

14˚ 

15˚ 

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4 

3 

2 

1 

0 

log10(S) 

Figure 5: Left: Model from Fig 3 (left) with only those cells of the original ‘average’ model shown that have 90% of 

all conductance values within 2/3 of a decade. Cells with flat histograms are eliminated. Right: Spatially smoothed 

‘average’ conductance model. The dashed lines indicate main regional fault zones. 

may be caused by the profile arrangement of the data, this quasi-anisotropic domain is actually required by the data. It 

helps in feeding the induction process all across the Moravia region and in keeping the relatively large modules of the 

induction arrows in that region. If these induction sources could be verified, the regional induction in the eastern part 

of the BM would be mainly driven by the NW-SE to W-E pattern of tectonic zones (Elbe fault zone, Sudety faults, 

Poˇr č -Hronov fault zone, Odra fault zone, etc.) rather than by the SW-NE zones which conform with the tectonics of 

the transition to the WCP. 

8 Conclusion 

From the experience accumulated with the MCMC inversion we can conclude that for moderately sized thin sheet 

models (tens of cells in each direction), the MCMC inverse procedure is practicable with standard computer facilities. 

Speeding-up the forward solutions by using a 2-D Markov chain derived from the integral equation numerical approach 

by Vasseur and Weidelt (1977) is essential for the algorithm. 

Though computationally still demanding, the advantage of the MCMC is that it provides a probabilistic output 

for the inverse solution. Parameters can be assessed with respect to their values and uncertainty ranges, though true 

uncertainties (variance-covariance matrices) are hard to obtain in problems with demanding direct solutions. Effective 

visualization of complete probabilistic outputs from the MCMC algorithm may still be one of its weak points. 

The conductance pattern restored by the MCMC sampling from the induction arrows collected above the eastern 

slopes of the BM and its transition to the WCP gives a geologically plausible image of the region. The Carpathian 

conductivity anomaly is reconstructed in detail. The induction anomaly suggested at the eastern margin of the BM 

admits an alternative explanation in terms of a NW-SE to W-E conductance patterns, hypothetically coinciding with 

the fault pattern of the eastern Bohemian Massif. A detailed verification of the structural hypotheses in this region is, 

however, hardly possible by employing the long period geomagnetic induction data alone. 


Financial assistance of the Czech Sci. Found., contract No. 205/07/0292, and of the Grant Agency Acad. Sci. Czech 

Rep., contract No. IAA300120703, is highly acknowledged. 

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243

Subsurface Conductivity Obtained from DC Railway 

Signal Propagation with a Dipole Model 

Anne Neska 

Institute of Geophysics PAS, Ul. Ks. Janusza 64, 01-452 Warszawa, Poland, email: anne@igf.edu.pl 

Abstract 

In the presented study, an attempt is made to model the propagation behavior of signals 

emitted by a Polish DC railway line with a number of grounded horizontal electric dipoles on 

the surface of a homogeneous half-space. The signals were measured on a magnetotelluric 

profile perpendicular to the railway line mainly in its near-field and transition zone, and they 

were separated from the natural electromagnetic variations by means of a reference site. 

Fitting the DC signals to the dipole model yields the conductivity of the homogeneous halfspace. 

Its value for the vertical and for the perpendicular horizontal magnetic component is 

confirmed by the usual 2D MT model obtained from the profile. 

Introduction 

The electrified part of the Polish railway network (fig. 1) is run by DC current. This makes 

magnetotelluric (MT) studies in this country difficult. On the other hand, the “disturbing” (in 

terms of MT) signals emitted by this system propagate according to a dipole model (Oettinger et 

al. 2001 and citations therein) which contains, like MT, the electrical conductivity of the 

subsurface as a parameter. So, after designing and performing a MT field experiment 

comprehending railway signals in an appropriate way, it should be possible to obtain information 

about the subsurface conductivity by both the dipole model and the MT approach. By this idea 

the present study has been motivated. 

The methodology of this study lies somewhere in-between two other domains encountered in 

geophysics. One is certainly the electromagnetic methods of the controlled-source near-field 

branch. The difference to our case is that the source is more under control there, but in return not 

free of experimental effort. The second related domain is techniques for modeling the 

propagation behavior of disturbances from DC railways and cables, applied especially to 

investigate their influence on magnetic measurements run at observatories (e.g. Pirjola et al. 

2007, Lowes 2009, Maule et al. 2009). However, the induction character of this propagation 

including phenomena like frequency-dependent damping, phase shift, and the electric 

conductivity as a propagation parameter is almost completely omitted there in contrast to the 

approach presented here. 

In the following, there will be considered the data processing including the separation of the 

natural electromagnetic variations from the railway signals and the estimation of the transfer 

functions between different stations. The dipole model will be described and the data be inverted 

according to it. The conductivity result will be compared to the output of a usual 2D MT model. 



244

Fig. 1 The electrified part of the Polish railway network (red lines) with a profile of MT sites for 

investigation of one line (zoomed-in part). Green squares denote positions of reference stations. 

Measurement and data processing 

As shown in fig. 1, a profile of six MT sites has been installed perpendicular to an isolated railway 

line. The distances of sites to the line were 0.8, 7, 16, 25, 50, and 75 km. Two remote reference 

sites were set up at relatively noise-free places, and the whole array was running synchronously. 

The obtained data were processed with codes by Neska 2006, but not only for MT purposes. 

By means of its correlation to the reference sites, the natural part of the electromagnetic 



245

signal could be removed from the measured data using a method by Larsen et al. 1996 (fig. 2). In 

this way a dataset for analysis of the railway signals was established (cf. fig. 3). It has to be emphasized 

that it can be problematic to work with such “deduced” data, since distortions introduced 

to it during the separation, e.g. due to uncorrelated noise in the reference site, can bias the 

subsequent results. It proved useful to separate the data of the station closest to the railway which 

plays a special role in the following with one reference site and the rest with the second one. 

Fig. 2 Separation of time series into a “natural” and a “railway” part (site s02, see fig. 1). 

Fig. 3 The propagation/decay of railway signals (component Bx) over the profile. Note that a rest of 

natural variations remained in the time series in spite of separation. 



246

All following considerations refer to “railway data” separated from natural signals in the way 

indicated above. 

The formulas for the dipole response are given in frequency domain, so our calculation has to 

take place there. Furthermore, in these formulas there occur factors like current I and dipole 

length L (see table 1), i.e. technical parameters of railway traction which we cannot measure 

immediately. So it appeared reasonable to remove these factors by normalizing each field 

component to that of the railway-nearest site which represents the strongest, most pronounced, or 

least attenuated railway signal, respectively. 

To perform this normalization in a convenient way, the algorithm for calculation of the interstation 

transfer function or Horizontal Magnetic Tensor (HMT) was used, which played an 

essential role during the separation already. The site nearest to the railway takes the function of 

the reference, i.e. its data are input channels, and the data of the remaining sites are the output 

channels. So Bx and By data of “local” and “reference” sites lead to normalized values for both 

horizontal magnetic components, Ex and Ey to those for the electric components (even if the 

analogy to the HMT is overstretched here since it refers to magnetic data only, the formalism is 

the same), and Bz and some other, uncorrelated channel (e.g. of one of the real, off-profile 

references, just to fit the requirement of the HMT formalism that there must be two input 

channels) to the normalized value for the vertical magnetic component. This description remains 

a bit vague because it cannot be recommended for imitation for the following reason: 

For this study, it has been noticed too late that this approach is not quite correct. The problem is 

that the HMT formalism bases on bivariate statistics (i.e. there are two independent variables or 

input channels, respectively), whereas the railway provides only one independent source 

polarization (pers. comm. K. Nowożyński). A similar problem occurs in Controlled-Source MT, 

where only one scalar transfer function instead of the usual 2x2 impedance tensor can be 

obtained if only one transmitter is used (pers. comm. M. Becken). So it has to be expected that 

our normalized values are influenced in an unfavorable way. This impact is expected to be very 

small in the case of Bz, since the warranted uncorrelatedness of the second input channel should 

make the difference between the univariate and the bivariate result vanish. This will be 

confirmed in the following section (cf. fig. 4: better result for Bz). However, the direction of the 

railway line under investigation is almost East-West (fig. 1), so its signal has a polarization 

almost coinciding with one of the directions we measure and calculate in with the MT or HMT 

approach. So there is hope that the error introduced due to this wrong statistic approach is 

somehow bearable if the diagonal elements of the “HMT” are used. 

Finally, the normalized values are displayed over period and distance in 3D-plots (red lines in 

fig. 4). The decay of amplitudes with distance as well as their period-dependency (stronger 

damping at low periods) becomes clearly visible for Bx and Bz components. Bx has partly 

unsystematic and, especially at long periods, rather high values that make the impression to be 

distortions, maybe due to incomplete separation or the wrong statistic approach mentioned. 



247

Hence the possibility to include data errors to the business was provided, since they have an 

important meaning as weights during the inversion. 

The dipole model and its application 

The railway line was simulated by a chain of horizontal grounded electric dipoles following its 

(not constant) bearing within a distance of some dozens of km around the profile. The distance 

between single dipole centers was 250 m. The solutions for the electromagnetic field components 

for the quasi-static approximation are taken from Zonge & Hughes 1987 and hold for one dipole 

on the surface of a homogeneous half-space (see table 1). These values are transformed from 

cylindrical to Cartesian coordinates to match the measuring system of MT and summarized over 

all dipoles subsequently. Then the values for each component and station were divided by the 

value of the corresponding component of the station closest to the railway. Since we look only 

for one model parameter (i.e. the conductivity σ), the inversion consists just of testing the whole 

model space and selecting the value with minimum RMS. The relevant software related to the 

dipole model was created by K. Nowożyński. 

The components behaving best in our study were Bx and Bz. The inversion of Bx alone gave a 

resistivity of 5 Ωm, that of Bz alone 14 Ωm, and the joint inversion 10 Ωm. The model response 

for the latter is shown in fig. 4 as blue lines. 

Table 1 

Solution for horizontal grounded electric dipole on HH surface 

according to Zonge & Hughes, 1987 

Where I/K_0/1 - modified Bessel functions and 



248

Fig. 4 Railway signal data (red) and dipole model response for a 10 Ωm homogeneous half-space (blue) 

over period and distance. Upper part for Bx, lower part for Bz component amplitude. The values on the 

vertical axis are normalized to that of site s01 nearest to the railway line (cf. fig. 1). 



249

Fig. 5 2D MT model (TE and TM mode) of the profile on fig. 1 obtained with the REBOCC code 

(Siripunvaraporn & Egbert 2000). The shallow cells beneath the northernmost sites have resistivity values 

between 9 and 80 Ωm. 

Discussion and conclusions 

The MT model yields resistivities of 9-80 Ωm beneath the northernmost sites close to the railway 

(fig. 5). This is consistent with the dipole model result, so there is evidence that the dipole 

approach is not unreasonable. 

Nevertheless, there are unexplained features in this model and one has to be critical with it. Not 

shown here is the behavior of phases and of electric components, where a similarity between data 

and model response is much harder to find for reasons still unclear. 

However, taking into account first, the similarity of data and model response (fig. 4), and second, 

the compatibility of MT and dipole modeling results in spite of some quite principal problems in 

this implementation (i.e. input data biased during separation, errors due to application of 

bivariate instead of univariate statistics, limitation to the oversimplified case of a homogeneous 

half-space), there can be stated that the dipole model is not only a valid approach to model the 

propagation of DC railway signals, but even a relatively robust one. 



250


This work would not exist without the help of Paweł Czubak, Tomasz Ernst, Jerzy Jankowski, Waldemar 

Jóźwiak, Krzysztof Kucharski, Janusz Marianiuk, Mariusz Neska, Krzysztof Nowożyński, Jan Reda, 

Michał Sawicki, and Józef Skowroński. 

The project is funded by the Ministry of Science and Higher Education of the Republic of Poland (grant 

number N N307 2496 33). 

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251

Magnetotelluric investigation of the 

Sorgenfrei-Tornquist Zone and the NE German Basin 

Anja Schäfer 1∗ , Heinrich Brasse 1 , Norbert Hoffmann 2 

and EMTESZ working group 

1 Freie Universität Berlin, Fachrichtung Geophysik, Malteserstr. 74-100, 12249 Berlin, Germany 

2 Wilhelm-Külz-Straße 70, 14532 Stahnsdorf, Germany 

Abstract 

The Sorgenfrei-Tornquist Zone (STZ) is the northwestern branch of the Trans-European Suture 

Zone (TESZ). The TESZ runs along more than 2 000 km through the North Sea, South Scandinavia, 

the Baltic Sea, and Poland into the Black Sea. It divides old Precambrian lithosphere in 

the northeast from younger, Caledonian and Variscan one in the southwest. Data, dimensionality 

analysis and 2D models of a long-period magnetotelluric (LMT) profile crossing this prominent 

tectonic border in South Scandinavia are presented and a possible interpretation of conductivity 

anomalies below Rügen Island and south of Strelasund Basin is given. Furthermore these models 

map the saline aquifer of the Northeast German Basin. The ”North German Conductivity 

Anomaly” is perhaps mainly due to the effect of the basin edges. 

Introduction 

The EMTESZ project (Electromagnetic Study of the Trans-European Suture Zone) was a multinational 

research project to study the electrical conductivity of the Trans-European Suture Zone 

(TESZ), which is one of the largest tectonic boundaries in Europe. It separates the East European 

Platform from the Paleozoic mobile belt of central and western Europe and is traced from the 

Black Sea through Poland and Southern Scandinavia into the North Sea (Gee (1996); Pharaoh 

(1999)). In the northeast the margin is marked by the lineaments of the Sorgenfrei-Tornquist 

Zone (STZ) and the Teisseyere-Tornquist Zone (TTZ, which runs in a SE-NW direction through 

Poland and the Baltic Sea, fig. 1). Several seismic refraction and reflection experiments have been 

carried out (BABEL and BASIN 9601 in Northeast Germany, POLONAISE and the LT surveys 

in Poland). Major results include a sedimentary thickness in the Northeast German Basin and 

below the TTZ of 4 to more than 11 km. Also sharp lateral boundaries, a Moho from 32-35 km 

in the SW to 40-45 km in the NE and a reflector below the STZ/TTZ at depth of 50-55 km are 

known. Most of the earlier EMTESZ measurements were carried out in 2003 to 2005 (e.g., Brasse 

et al. (2006), Ernst et al. (2008)). Profiles MVB and MVS were conducted in 2006 and 2009. 

The long period magnetotelluric profile shown here is one of these EMTESZ profiles. The direction 

of this profile was chosen because of earlier measurements by the Bundesanstalt für Geowissenschaften 

und Rohstoffe (BGR) in the 1990ies. Due to tipper data along this profile and of site 

MAT deployed in 2005 on Rügen Island (MT working group Free University of Berlin) a direction 

∗ e-mail: schaefer@geophysik.fu-berlin.de 



252

OST 

DAB 

BAK 

MIR 

SWI 

NIE 

KOC 

SCZ WIA 

DRE 

PIE 

GAT 

WIE 

ZAR 

ZAL 

GRA 

KUS 

KNY 

PRZ 

KUZ 

SIE 

SLA 

B010 

ZOL ZOL 

B020 

POM 

GLE 

B030 

A010 END 

REC 

B040 

A020 

RAD 

B050 

A030 CRI 

LUB 

KUK 

B060 

TEE 

LYS 

B070 

A040 LOE 

MOC 

LES 

LAW 

B080 

A050 OLE 

CHO 

WAR 

B090 

A060 

LAK 

B100 

PAS 

MOS 

A070 

STO 

SAR 

B110 

A080 

B120 

NKU BLE 

GOR 

B130 

VEV 

A090 

FRI 

B140 

A100 

HOB FAL 

B150 

A110 

MAR MAD 

B160 

B170 

AGO KUN 

B180 

A120 

B190 

DAM 

BRI 

B200 

A130 

GLI 

B210 

A140 

B220 

BUS 

A150 

TOR 

B230 A160 

B240 

HBO 

A170 

B250 A180 

B260 

B270 

B280 

56°N 

55°N 

54°N 

53°N 

52°N 

VDF 

TEF 

Rostock 

AAF 

STZ 

BGR-B 

KIS 

ROH 

TET 

WIL 

BRE 

DOL 

Magdeburg 

Trelleborg 

CDF 

IBI 

DAR 

LEL 

WEN 

ROT 

JAB 

MVS 

NGK 

KRU 

PAP 

k31 

MAT 

PAR 

TAN 

BAR 

Germany 

BGR-A 

LOV 

TOM 

BOO 

k25 

Berlin 

KOP 

NYT 

HOR 

AND 

Rügen 

KRI 

BER 

REG 

BLU 

MVB 

BS1 

DZI 

FEL 

BS3 

Odra R. 

Bornholm 

Baltic Sea 

Poland 

0 50 

11°E 12°E 13°E 14°E 15°E 16°E 17°E 18°E 19°E 

BOR 

Szczecin 

Kostrzyn 

Frankfurt 

CYB 

NIN 

Koszalin 

KAR 

WLO 

ROT 

TAC 

BLA 

MAS 

BS2 

ZAS 

JAN 

Poznan 

LT-7 

VDF 

km 

study area 

Figure 1: Measured profiles of the EMTESZ project and profile B from the Bundesanstalt für Geowissenschaften 

und Rohstoffe (BGR-B). Location of MT sites in Poland, Germany, Sweden and Bornholm 

(Denmark); STZ-Sorgenfrei-Tornquist-Zone; TTZ-Tornquist-Teiseyre-Zone; TEF-Trans European Fault; 

CDF-Caledonian Deformation Front; VDF-Variscan Deformation Front; AAF-Amorica Avalonia Fault. 

perpendicular to the assumed strike-direction of the Sorgenfrei-Tornquist Zone (see fig. 1) was 

chosen. It runs over about 370 km with a site spacing from 6 to 12 km. 

Data examples 

Stable transfer functions result from remote reference analysis according to Egbert & Booker 

(1986). The remote data is from the observatories of Belsk and Niemegk and simultaneous measuring 

sites. In figure 2 three representative data examples for sites of profile MVS are shown. 

Site ROT, which is located in the southern part of the profile, shows the characteristic curves for 

the North German Basin. Apparent resistivities at short periods are very low until 100 s (1 to 

3 Ωm), pointing to a very good conductor near the surface. With increasing periods app. resistivity 

is growing, accompanied by a splitting of impedance components Zxy and Zyx, reflecting 



253 

STZ 

P2 

Gdansk 

P08 

TTZ 

TTZ 

Wisła R. 

HLP 

E

ρ a [Ωm] 

10 4 

10 3 

10 2 

10 1 10 1 

rot 

Zxy 

Zyx 

10 0 

10 1 10 2 10 2 10 3 10 4 10 5 

10 

90 

0 

10 1 10 2 10 2 10 3 10 4 10 5 

10 

90 

0 

10 1 10 2 10 2 10 3 10 4 10 5 

90 

φ ο 

Re 

Im 

45 

10 4 

10 3 

10 2 

10 1 10 1 

45 

boo 

0 

10 1 10 2 10 2 10 3 10 4 10 5 

1.0 

0.5 

0.0 

-0.5 

-1.0 

10 1 10 2 10 2 10 3 10 4 10 5 

↑Ν 

1.0 

0.5 

0.0 

-0.5 

-1.0 

10 1 10 2 10 2 10 3 10 4 10 5 

0 

10 

T [s] 

1 10 2 10 2 10 3 10 4 10 5 

1.0 

0.5 

0.0 

-0.5 

-1.0 

10 1 10 2 10 2 10 3 10 4 10 5 

↑Ν 

1.0 

0.5 

0.0 

-0.5 

-1.0 

10 1 10 2 10 2 10 3 10 4 10 5 

0 

10 

T [s] 

1 10 2 10 2 10 3 10 4 10 5 

1.0 

0.5 

0.0 

-0.5 

-1.0 

10 1 10 2 10 2 10 3 10 4 10 5 

↑Ν 

1.0 

0.5 

0.0 

-0.5 

-1.0 

10 1 10 2 10 2 10 3 10 4 10 5 

T [s] 

Figure 2: Examples of transfer functions for sites of the profile (ρa-apperent resistivity, φ-Phase and Re- 

Real part, Im- imaginary part of induction arrows as function of period). Site ROT as an example for the 

southern part of the profile shows low resitivity in short periods, which shows the thick sedimentary covers 

of North German Basin (ρa at low periods around 1-3 Ωm), for longer periods it shows higher resitivity. 

BOO is the site at the most southern part of the swedish part and shows the margin of the sedimentary 

basin. NYT is an example for the northern part of the profile in Southscandinavia. There the profile 

reaches the crystalline basement (ρa has higher values even for low periods). 

multidimensional structures at greater depths. Induction arrows are very small. For sites in the 

southern part of the profile a change of direction for induction arrows is observed. Site BOO is 

located at the edge of the East European Craton. Here real parts of induction arrows are very 

large (up to an absolute value greater than 0.8) and are perpendicular to the strike direction of the 

Sorgenfrei-Tornquist Zone. They point to a very good conductor in southeastern direction. Apparent 

resistivities for this site are even for short periods much higher than in the North German 

part of the profile and increase rapidly for large periods, which points to the resistive basement of 

the East European Craton. NYT is an example for the northernmost part of the profile and shows 

high apparent resistivity even for the lowest periods (about 1 000 Ωm), reflecting the crystalline 

basement of Baltica. 

Magnetic transfer functions 

Induction arrows at long periods increase from south to the north, hinting at well-conductive 

structures in the south, i.e., below the Baltic Sea. The apparent resistivities ρa in the north of 

the profile are relatively high and get lower at the southern sites, which agrees with the geological 

structure. The high resistivities in the north are caused by the crystalline basement and the low 

resistivities in the south by the sedimentary cover. 

Figure 3 shows a map of the real part of induction arrows at a period 1 820 s for the EMTESZ 

profiles LT-7, MVB and the discussed profile MVS, according to Wiese-Convention (Wiese, 1962). 



254 

Zxy 

Zyx 

10 4 

10 3 

10 2 

10 1 10 1 

45 

nyt 

Zxy 

Zyx

For profile MVS arrows are mainly perpendicular to the NW-SE striking direction. With values 

greater than 0.8, the unusually large induction arrows in the northern part of the profile indicate 

a good conductor below Rügen Island. Real induction arrows at the southernmost station of 

Sweden, the sites in the Baltic Sea and at the northernmost point of Rügen Island are largest. 

The ”flip-around” of induction arrows in Northern Germany and Poland was already recognized 

in the initial days of electromagnetic deep sounding. The underlying cause – a large conductivity 

anomaly at depth – was termed the North German-Polish Conductivity Anomaly (e.g., 

Schmucker (1959); Untiedt (1970); Jankowski (1967)). Until today, however, the depth extent 

of this anomaly is controversially discussed and models range from an upper mantle high 

conductivity zone to the simple effect of the basin edges. The magnitude of the inductive effect 

at the basin margins and their rapid decrease seem to favor the second explanation, which will 

also become evident from 2-D inversion (see later). 

56°N 

55°N 

54°N 

53°N 

52°N 

12°E 13°E 14°E 15°E 16°E 17°E 18°E 19°E 

km 

0 50 

1820 sec 

Figure 3: Induction arrows for profiles MVS, MVB and LT-7 (real part) at a period of 1 820 s. In South 

Sweden and north of Rügen Island induction arrows are very large. They obviously result from the edge 

of the Baltic Shield (STZ). The change of direction of the real parts in the center of the NE German and 

Polish Basins shows the effect of the so-called ”North German-Polish Conductivity Anomaly”. It can be 

seen in all profiles. Profile MVS shows this effect (sign reversal of real part) approximately at the location 

of the Stralsund-Anklam-Fault (SAF). In the northern part of profile MVS the induction arrows are very 

large. The highest absolute value with more then 0.8 is reached in the southern part of Sweden and 0.7 in 

the northernmost part of Rügen Island. 



255

Dimensionality analysis 

Strike angles were calculated for single and multi sites after Smith (1995), which allows to sort 

out bad data with a weighting matrix (see figure 4). The strike angle for profile MVS has a strong 

variation especially in the northern part; the average for the profile is around N67 ◦ W. 

WEST 

NORTH 

SOUTH 

EAST 

Figure 4: Average strike angle after Smith (1995) for profile MVS: N67 ◦ W. 

Figure 5 shows the phase tensor (Caldwell et al., 2004) for each site of the profile for two 

different periods. The orientation of the ellipses point to the strike direction of the conductive 

structures. The northwest-pointing direction of the main axis of the ellipse corresponds with the 

calculated strike direction. 

a) b) 

56˚ 

55˚ 

54˚ 

53˚ 

PAP 

IBI 

DAR 

LEL 

WEN 

ROT 

JAB 

KIS 

ROH 

TET 

WIL 

BRE 

DOL 

MAT 

PAR 

TAN 

BAR 

KRU 

KOP 

NYT 

HOR 

BER 

REG 

LOV 

TOM 

BOO 

KRI 

0 50 

12˚ 13˚ 14˚ 15˚ 12˚ 13˚ 14˚ 15˚ 

-16 -12 -8 -4 0 4 8 12 16 

β [ o ] 

PAP 

IBI 

DAR 

LEL 

WEN 

ROT 

JAB 

KIS 

ROH 

TET 

WIL 

BRE 

DOL 

MAT 

PAR 

TAN 

BAR 

KRU 

KOP 

NYT 

HOR 

BER 

REG 

LOV 

TOM 

BOO 

KRI 

0 50 

Figure 5: Phase tensor plot for periods of 992 s and 1 820 s calculated after Caldwell et al. (2004). 



256

Skew angle β is small throughout the study area with the exception of the northernmost sites in 

Sweden. Summarizing, it suffices to carry out a 2-D modeling of the data. 

2-D modeling 

All presented 2-D inversion models were calculated with the CG-FD inversion algorithm of Rodi 

&Mackie(2001). First the data were rotated by -67 ◦ . A homogeneous halfspace of 100 Ωm 

and a fine grid for the start model was chosen. The smoothing factor was set to τ=15, which is 

the best trade-off between model roughness and data misfit (Hansen & O’Leary, 1993). For 

the inversion of the 2D-models in fig. 6 all components (TE-, TM-mode and tipper) were used. 

In these models all resolved structures can be seen; these models have the best fitting model 

response to the data (see examples in fig. 7). For a better overview of the modeled features, the 

profile intersecting geological structures in the respective locations are marked. Furthermore, the 

location of the basement is shown. Figure 6a shows the result of inversion of TE-, TM-mode and 

tipper data after 200 iterations. The resulting RMS is 2.27. The model shown in figure 6b also 

results from inversion of all components (TE-, TM-mode and tipper), furthermore a horizontal 

weighting function was used (β=1). The resulting RMS of this inversion after 200 iterations is 

with 2.67 worse then the RMS of the model without weighting function, but the model is more 

consistent with geological assumptions (Hoffmann & Franke, 2008). 

a) 

b) 

z [km] 

z [km] 

0 

20 

40 

60 

80 

0 

20 

40 

60 

80 

S 

VDF 

dol 

bre 

wil 

tet 

roh 

kis 

jab 

rot 

wen 

lel 

dar 

ibi 

pap 

kru 

OA 

OA 

A 

A 

East-Avalonia 

Paleozoic Platform 

SAF CDF 

Strelasund 

-Basin 

D 

D 

bar 

Wiek 

trough 

tan 

par 

mat 

k31 

C 

Baltica 

Baltica 

k25 

boo 

STZ 

tom 

lov 

reg 

and 

ber 

hor 

nyt 

kop 

Baltica 

0 50 100 150 200 250 300 350 

distance [km] 

C 

Baltica 

Baltica 

East European Craton 

Figure 6: 2-D models for profile MVS inverted by applying Rodi and Mackie’s algorithm starting from 

a homogeneous halfspace. a) For this model all components were inverted (TE-, TM-mode and tipper 

data). The resulting RMS after 200 iterations was 2.27. b) For inversion of this model all components 

were used (TE-, TM-mode and Tipper). A horizontal weighting function was used. Resulting RMS after 

200 iterations was 2.67. For both models the smoothing factor was set to τ=15. Letters sign resolved 

conductivity structures: A-saline aquifer in Northeast Germany, Baltica-basement of the Baltic Continent, 

OA-basement, associated with the basement of the East-Avalonian plate. Also the assumed location of 

plates and fault zones is marked. 

In both models one can see the underlying plate of Baltica in the north as a poor conductor, the 

sediments in Northeast Germany as a very good conductor (structure A) and two conductivity 

anomalies below Rügen Island (structure C) and south of Stralsund (structure D) in depths from 

8 to 30 km. Figure 7 shows examples of model response of the inversion shown in figure 6a. 



257 

kri 

N 

4 

3 

log ρ [Ωm] 

2 

1 

0

Rho App. (ohm.m) 

Phase (deg) 

Tip Mag 

10 4 

10 3 

10 2 

10 1 

10 0 

90 

60 

30 

0 

1,0 

,5 

,0 

dol 

10 1 

TE measured 

TE model response 

rms= 1.2261 

10 4 

10 3 

10 2 

10 1 

10 0 

90 

60 

30 

0 

1,0 

,5 

lel rms= 1.2746 

10 2 

10 3 

10 4 

10 1 

10 2 

10 3 

,0 

10 4 10 1 

10 2 

10 3 

10 4 

,0 

4 

10 

Period(sec) 

1 

10 2 

,0 

Period(sec) Period(sec) 

Period(sec) 

TM measured 

TM model response 

Hz measured 

Hz model response 

10 4 

10 3 

10 2 

10 1 

10 0 

90 

60 

30 

0 

1,0 

,5 

mat rms= 1.6917 

10 4 

10 3 

10 2 

10 1 

10 0 

90 

60 

30 

0 

1,0 

,5 

boo rms= 2.1131 

Figure 7: Examples of model responses for the 2-D inversion result as shown in fig. 6a. 

Geological Interpretation 

Structure A seen in the models of fig. 6 is characteristic for the North German Basin; it represents 

the saline aquifer and is already known from previous measurements. This structure is resolved in 

all inversions of this profile and could be seen in all components (TE-, TM-mode and tipper) and 

with its vertical elongation and extension to depths of 3 to 4 km it is consistent with simulations 

of Magri et al. (2007) and models of the BGR-profiles in Hoffmann et al. (1997). This 

structure is resolved as a surface conductor in all other sections of the EMTESZ project (e.g., 

Brasse et al. (2006), Ernstetal.(2008)) and in the models of Houpt (2008) as well. It is 

caused by huge deposits of Zechstein salt, which is dissolved by deeper ground water. Through 

thermal and hydraulic transport mechanisms it reaches in some cases up to the surface (Magri 

et al., 2005). In some parts of the North German Basin salinities up to 350 g/l are observed 

(Hoth et al., 1997). The conductivity of such layers depends on the salinity of the fluid, the 

size and connection of the pore spaces. High salt contents and pore sizes of sediment layers in 

North Germany may cause conductivities well above 1 S/m. 

Structure ”Baltica” is also resolved in all inversions of profile MVS - a very poor conductor in the 

north of the profile. It represents the crystalline Precambrian basement of Baltica. This basement 

of Baltica is with an age of 1.9 billion years one of the oldest rocks in Europe. Its high resistivity 

is due to the strong compression of rocks at depth with almost no interconnected fluid inclusions 

left. 

Extension and value of the conductivity of the good conductor below Rügen Island (structure 

C) can also be regarded as assured due to its shallow depth and the sensitivity tests carried out 

(Schäfer, 2010). Its boundary to the north is indicated by the size of the induction arrows at 

MAT, the northernmost station on Rügen Island. Structure C is located at about 8 to 20 km 

depth. This good conductor is depicted in all inversions as a structure separated from the surface 

conductor (structure A). 

Also structure D, with a depth of 10 to 30 km is resolved in all models of the joint inversion of TE-, 

TM-mode and tipper, and also proofed by sensitivity tests as a separate structure from the surface 

conductor. Conductors in these depths were explained with the occurrence of highly-carbonated 

paleozoic black shales, the so-called Scandinavian alum shales (e.g., Hoffmann et al. (1998); 

Hengesbach (2006)). 

These alum shales crop out at the Andrarum quarry in the southern Swedish province of Scania, 

near MT sites AND and REG, where they have been mined since centuries. In order to test 

the hypothesis of high conductivity, several DC-geoelectric array measurements were conducted 

in this area during a student field trip of the Free University of Berlin (Field Report Scania, 



258 

10 3 

10 4

2006). Fig. 8 displays an example. It clearly shows the black shale (blue colors) as an intermediate 

conductor only, with resistivities in the range of 100 to 150 Ωm. Nevertheless, this does not exclude 

high conductivities of deeply buried shales; at or near the surface, the relatively high resistivity 

may be due to strong weathering, destroying the conductive paths, which are otherwise continuous 

in deeper layers. 

Figure 8: Geoelectric section near the Andrarum black shale quarry (South Sweden). Note the reverse 

color scale. 

From laboratory studies and drilling black or alum shale at greater depths and without weathering 

it is obtained with conductivities of less than 1 Ωm (Duba et al., 1988). Black shale has been 

investigated by drilling in the well of G14 (north of Rügen Island) and Rügen 5, where it reaches 

thicknesses of 50 to 70 m. In the well Pröttlin I further south, black shales were found, too, but 

could not be fully intersected. In addition, studies demonstrated that the necessary pore size for 

an electrolytic conduction mechanism not exists in deeper sediment layers (Jödicke, 1991). This 

would exclude the interpretation of structure D as a deep sedimentary trough. 

Thus, the conductive ”layer” in the model of figure 6b can be seen as a reference to alum shale occurrence. 

However, this layer can be even more conductive because of hydrothermal waters, which 

are often rising in geological fault zones. Under high pressure and special temperature conditions 

in highly-carbonated black shales also graphite-structures may form, according to estimates from 

Duba et al. (1988) and Raab et al. (1998). With a layer of mostly continuous black shale 

or graphite surface, a relatively low-friction thrust faulting with little deformation of the plate 

boundaries in the collision of Eastern Avalonia and Baltica at the time of the Ordovician could 

be explained. 

Furthermore, Raab et al. (1998) could demonstrate in laboratory experiments that pyrite inclusions 

(which often occur in black shale layers) may convert to much more conductive pyrrhotite 

at temperature and pressure conditions as encountered in the middle crust. Pyrrhotite usually 

occurs in dendritic form and increases conductivity even through small volumes. 

Model experiments and sensitivity tests show that a 70 m thick alum shale layer at such depths is 

not sufficient, even if modeled with bulk resistivities as low 0.1 Ωm. Another possible explanation 

is the occurrence of intrusive bodies, which rose in the time of Rotliegend (Upper Carboniferous 

to Middle Permian). Their contact aureoles usually consist of highly conductive material (such as 

ilmenite or even graphite), and can extend over larger areas. So the high conductive structures C 

and D might be explained by a combination of highly conductive layers of black shales and such 

dykes. Motivation for this hypothesis emerged from the well Greifswald I, where intrusive granite 

bodies from the Rotliegend with apophyses could be found. This granite body is also known as 

Südrügen Pluton (Hoth et al., 1993) and is possibly extending to the south of Rügen Island. 

In fact, the combination of these two interpretations, seems to be the best explanation of the high 

conductivities of structures C and D at depth. Thus, it is very likely a combination of graphitized 

black shale and intrusive bodies (e.g., Südrügen Pluton) with the accompanying conductive material 

and the associated apophyses. This interpretation would explain the very good conductivity 

in such depths and the resolution of the structures as an almost vertical body in the mid crust. 

Unfortunately no better resolution of these structures is possible due to the strong shielding effect 

of the saline aquifer. 



259

The good conductor of model 6b ends in the south of the Stralsund Anklam Fault (SAF). The trend 

of the SAF, which is also indicated by magnetic transfer functions and their graphic presentation 

in fig. 3 fits very well to the results of Houpt (2008) and Ernst et al. (2008), which were 

obtained further east. According to these models and the induction arrows shown in fig. 3, the 

SAF appears to be a fundamental crustal boundary of Northeastern Europe which can be traced 

to the southeast of Szczecin in Poland. 

Figure 9 shows a comparison with an interpretation of the BASIN 9601 project and 2 prolonging 

profiles in the Baltic Sea from McCann & Krawczyk (2001). There we observe a good correlation 

with underlying Baltica and the Zechstein base (strong reflector), and the well-conducting 

sediments in the upper layers of the Northeast German Basin. 

z [km] 

0 

20 

40 

60 

80 

S VDF 

SAF CDF 

dol 

bre 

wil 

tet 

roh 

kis 

jab 

A 

OA 

Moho 

Baltica 

Baltica 

0 50 100 150 200 250 300 350 

distance [km] 

STZ 

Grimmen High Baltic Sea 

G14 

ber 

hor 

nyt 

kop 

Figure 9: 2-D models for profile MVS with an overlayed interpretation of the seismic reflection/refraction 

profile BASIN 9601 and 2 prolonging profiles in the Baltic Sea from McCann & Krawczyk (2001). 

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Duba, A., Huenges, E., Nover, G., Will, G. & Jödicke, H. (1988). Impedance of black 

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Other members of the EMTESZ Working Group include T. Ernst, V. Červ, J. Jankowski, W. 

Jó´zwiak, A. Kreutzmann, A. Neska, N. Palshin, L. Pedersen, M. Smirnov, E. Sokolova and I. 

Varentsov. We thank Belsk and Niemegk Observatories for supplying data and German Science 

Foundation (DFG) for funding. 



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Magnetotelluric data from the Tien Shan and Pamir 

continental collision zones, Central Asia 

P. Sass*, O. Ritter*, A. Rybin**, G. Muñoz*, V. Batalev** and M. Gil* 

*Helmholtz Centre Potsdam GFZ, German Research Centre for Geosciences 

**Research Station of the Russian Academy of Sciences, Bishkek, Kyrgyzstan 

1 Intoduction 

We present magnetotelluic (MT) data obtained within the framework of the multidisciplinary 

Tien Shan - Pamir Geodynamic Program (TIPAGE). The dynamics of the 

Tien Shan and Pamir orogenic belts are dominated by the collision of the Indian and 

Eurasian continental plates. With the geophysical components, we intend to image the 

deepest active intra-continental subduction zones on Earth (the N-dipping Hindu Kush 

and the S-dipping Pamir zones) and to establish how the highest strain over the shortest 

distance that is manifested in the India-Asia collision zone is accommodated structurally. 

The Tien Shan-Pamirs mountain knot forms the northwestern corner of the India-Asia 

Figure 1: Central and eastern Asia orogens. TIPAGE and INDEPTH surveys are 

marked on the map. TIPAGE investigation area lies inside the blue circle. 

collision zone and the Pamir-Tibet Plateau (Fig. 1). Note that N - S shortening in 

the Pamir and western Tien Shan is absorbed in less than 50% of the distance than 

further east. Basins denote areas little affected by intra-continental shortening. The 

Pamir excels over the adjacent Tibet by including the most active areas of intermediatedepth 

seismicity in the world and by far the most active one not associated with oceanic 



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subduction, three coevally active, thick-skinned, high-strain contractional belts and four 

distinct intra-continental magmatic belts. 

2 Measurements 

The MT data were recorded in summer 2008 at 80 stations in the Pamir mountain 

ranges in Tajikistan and in summer 2009 at 98 stations in the Pamir and the southern 

Tien Shan in Kyrgyzstan and Tajikistan(Fig. 2). A typical spacing was approximately 

2 km between BB-only sites and 14 km for the combined BB+LMT sites. The stations 

form an approximately 340 km long profile from Osh in Kyrgyzstan via Sarytash, the 

Kyrgyz-Tajik border, Karakul and Murgab to Zorkul in southern Tajikistan. 

72˚ 

73˚ 

74˚ 

75˚ 

41˚ 41˚ 

Uzbekistan 

Osh 

Kyrgyzstan 

40˚ 40˚ 

39˚ 

Kara-Kul 

Lake 186L 

39˚ 

Tajikistan 

Sary-Tash 

Afganistan 

China 

7000 

Sarez 

Lake 

6000 

Murghab 

38˚ 

5000 

38˚ 

m 

134 

116L 

102L 

088L 

074L 

km 

356 

354L 

340L 

326L 

312L 

298L 

270L 

256L 

242L 

228L 

214L 

284L 

4000 

3000 

2000 

1000 

37˚ 

0 50 

0 

37˚ 

72˚ 

73˚ 

74˚ 

75˚ 

200L 

172L 

158L 

144L 

130L 

060L 

046L 

000 

032L 

018L 

004L 



264 

Figure 2: Topographic map with 

stations and profile of the TIPAGE 

survey. Numbers of stations with 

broad band and long period measurements 

(L) are marked. The station 

alignement follows the a single 

road in that remote area with rough 

terrain.

3 Preliminary Data Analysis 

Data examples 

Some representative graphs of apparent resistivities and phases are shown in Fig. 3. 

The curves were obtained after a recording time of three days, using robust single site 

processing. Varying shapes of the curves indicate considerable changes in the underlying 

conductivity structure. The distances between the shown stations are approximately 

50 km. For station locations, see Fig. 2. The overall data quality is superb, especially 

in the very remote southern parts of the profile. 

Figure 3: Exemplary apparent resistivity and phase curves of four broad-band stations 

from the Pamir. For station locations, see Fig. 2. 

Pseudosections 

Apparent resistivities and impendance phases of all TIPAGE stations are plotted as 

pseudo sections in Fig. 4. In the southern part of the profile, the TE and TM modes 

apparent resistivities show values below 10 Ωm at higher periodes and high phase values 

reaching 90 ◦ . There are more low-resistivity features further north at middle to high 

periods, which are more present in the TE mode. This hints at a deep conducting 

structure in the southern profile part and a complex distribution of conducting features 

in the northern segment of the profile. 



265

Figure 4: Pseudosections of apparent resistivity and phase data, in TE and TM modes. 

In the left part of each pseudosection the southern profile stations are plotted, in the 

right part the northern stations. For stations location, see Fig. 2. 

Induction arrows 

The presence or absense of lateral variation in conductivity can be inferred from induction 

arrow maps. In Fig. 5 induction arrows are plotted using the Wiese convention for 

periods of 1, 32, 128, and 1024 s. The arrow distribution indicates several ’reversals’, 

which suggest the presence of elongated good conductors below the profile. Alltogether 

the induction arrow plots exhibit a complex distribution of the subsurface conductivity 

structure. 

Strike analysis 

Regional strike analysis (Becken & Burkhard, 2003) of sites recorded in the Pamir and 

Tien Shan is displayed in Fig. 6. The analysis of surface sensitive higher frequencies (Fig. 

6 left) shows a E - W (N - S) strike direction. This is consistent with the predominant 

E - W distribution of geological structures. The lower frequencies (Fig. 6 right) reveal a 

pronounced geoelectric strike of approximately −17 ◦ to −20 ◦ . This strike direction may 

be in agreement with structures of the India-Asian collision zone. 



266

Figure 5: Maps of induction vectors (Wiese convention) for periods of 1, 32, 128, and 

1024 s. Each arrow starts at one station location, compare Fig. 2. 

Figure 6: Regional strike analysis (Becken & Burkhard, 2003) of all sites recorded in 

the years 2008 and 2009. Left for the period range 0.001 s - 10 s, right for the period 

range 10 s - 10000 s. 



267

Figure 7: The Kyrgyz/Russian - Tajik - German MT team of 2008 (left image) and 

2009 (right image). The Research station of the Russian Academy of Sciences in Bishkek 

provided most of the field logistics, including 4WD vans and 4WD trucks. 

Figure 8: The amazing hospitality of local people during the field campaigns was a 

memorable experience. 

4 Acknowledgments 

The MT field team: Employees and students of the international Research Center, 

Russian Academy of Sciences, Bishkek and from Germany: D. Brändlein, X. Chen, 

T. Krings, A. Nube, M. Schüler, K. Tietze, C. Twardzik and G. Willkommen. 

Dr. V. E. Minaev, Dr. N. Radjabov, Dr. I. Oimahmadov, Prof. A. R. Faiziev: Institute 

of Geology, Academy of Sciences of the Republic of Tajikistan, Dushanbe. 

Dr. B. Moldobekov, Prof. H. Echtler, Dr. A. Mikolaichuk: Central Asian Institute for 

Applied Geosciences, Bishkek. 

Dr. S. K. Negmatullaev: PMP International / Seismic Monitoring Network in Tajikistan, 

Dushanbe. 

All other German colleagues participating in the TIPAGE collaborative research project. 

We very gratefully acknowledge substantial funding which we received from the GFZ 

and the DFG. The magnetotelluric instruments were provided by the GFZ Geophysical 

Instrument Pool (GIPP). 



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269



270 

16 2/ 3



271 

E x 

E y 

= Z xx 

Z yx 

Z xy 

Z yy 

B x 

B y



272

Z B =0.5· (Z xy − Z yx ) 



273



274

· 

· 



275



276

In our session "What I always wanted to know ..." we had the question 

How would you choose the period for LOTEM? 

Carsten Scholl continued thinking about it even after the colloquium and send an email with some 

additional thoughts. Here is his email: 

Well, in the discussion I said that it is not necessary to wait until the signal is decayed into the noise 

level before switching again, which is totally true. Actually, this would be to some extent a circular 

argument, because the noise level depends on the number of stacks, and the number of stacks 

depends on the period. 

So, one should check before with synthetic models, which time range is required to resolve a certain 

feature. Note, the time range to RESOLVE a feature, is not the same (and typically significantly larger) 

than the time range up to the point where deviations between the “target” and “no target” curves 

appear. I recommend doing 1D inversions with reasonable noise estimates for resolution studies… . 

Further, it is advisable to increase this time, because the true background resistivity might deviate 

from the synthetic und thus delay the features representing the target. 

The time saved by using a higher period and thus collecting the required number of stacks faster can 

be used by measuring at more sites. 

Often, in academic LOTEM campaigns, the target depth is not well defined but you’d like to get as 

deep as possible. Further, setting up LOTEM stations is tedious and the number of stations is limited 

anyways because of limited equipment. Often, the time spent on deploying and packing up the 

sensors exceeds the actual measurement time. So, in this case, there is not really the option to 

measure more sites on the same day (well, I always envision a roll-along scheme, where you start to 

measure at one station while building up the next site. When the final site is set up, the first site is 

redeployed, while the TX is still running…). 

In this case, I recommend to take some generous period the first day. In the evening the data for the 

day should be processed to see what the latest usable time is (this should be done with either a 

switch-off E-field or a magnetic component). For the subsequent days, the period should be set to 

something slightly longer (say, a factor of 2) longer than this time. 

Another aspect of this question: You should check, whether your time domain forward solver actually 

can handle higher switching times by taking into account previous transients. Otherwise, it might be 

better to stick to a more conservative period as well. 



277

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