EVALUATING THE EFFECTS OF MAGNETIC SUSCEPTIBILITY IN UXODISCRIMINATION PROBLEMS

LeonardR. Pasion,StephenD. Billings, andDouglas W. OldenburgUBC - Geophysical Inversion Facility

Departmentof EarthandOceanSciences,University of British ColumbiaVancouver, B.C., V6T 1Z4,CANADA

email: pasion@geop.ubc.ca

Abstract

Pastunexploded ordnance(UXO) clearanceprojects have demonstratedthat the ability to detectUXO canbe seriously hinderedby the presenceof magnetic rocks andsoils. In particular, magneticmaterial affects thedecay curve characteristics in electromagnetic surveys andthis canadverselyaffectinversioncalculationsthat try to estimateparameters of the UXO or answerthe question of whetherthe item is UXO or scrap. Our research is in two parts. Firstly, we carry out numerical 1D forwardmodelling to evaluate thedistortionsof signalsdueto laterally uniform magnetic material. In thesecondpart of the talk we examine how the distortions in the signal affect our inversionalgorithms usedforUXO discrimination.

Introduction

The taskof discriminating UXO from non-UXO itemsis moredifficult whensensor datais con-taminated with geological noiseoriginating from magnetic soils. The magnetic properties of soils aremainly dueto the presenceof iron. Hydrated iron oxidessuchasmuscovite, dolomite, lepidocrocite,andgeothite areweakly paramagnetic, andplay a minor role in determiningthe magnetic character ofthesoil. Themagnetic characterof thesoil is dominatedby thepresenceof ferrimagneticmineralssuchasmaghaemite( � Fe� O� ) andmagnetite (Fe� O� ). Maghaemite is considered themostimportant of theminerals within archaeological remotesensing circles(for example[Scollaret al., 1990]). Magnetite isthemostmagnetic of theiron oxides,andis themostimportantmineralwhenconsidering theeffects ofmagnetic soilson EM measurements.

Electromagneticsensorsaresensitive to thepresenceof magnetite dueto thephenomenonof mag-netic viscosity. Electromagnetic sensors illuminate the subsurfacewith a time or frequency varyingprimary field. Suppose that we apply a magnetic field

�to an areacontaining magneticsoil. The

magnetization vector of the soils will try to adjustto align itself with the exciting field. At the instantthemagnetic field is applied there is an immediatechange in magnetizationand,possibly, anadditionaltime dependentchange in magnetization. This time dependentphenomenonis referred to asmagneticviscosity or magnetic after-effect. A time constant � is usedto characterize the time for the magne-tization vector to rotate from its minimum energy orientation prior to application of the field, to itsnew orientation. For a sampleof magnetic grains which hasa large range of relaxation timesthat are

1

distributed uniformly over their spectrum, themagnetic momentof thesoil samplewill decay logarith-mically [Chikazumi,1997]. Consequently, the time derivative of the decaying magneticfield producedby the magnetization decays as ��� . This ��� decayhave beenobserved in archaeological prospect-ing [Colani andAitken, 1996], time domainelectromagnetic (TEM) surveys carried out over laeteriticsoilsfor mineral exploration [Buselli, 1982], andalsoin TEM surveyscarried outonKaho’olaweIsland,Hawaii [Ware,2001].

This talk focuseson the effectsof magnetic soils andmagnetic viscosity on time domainandfre-quency domain electromagnetic sensor data. By forward modelling of a1-D layeredearth modelwehopeto obtain somesenseof how sensitivesurveys areto magnetic soils,andthestrengthof themagnetic soilresponserelativeto buriedmetallic objects. Wethenseehow perturbationsin signal dueto magnetic soilaffect theability to recover parametersof thedipole modelpresentedin PasionandOldenburg [2001a].

Electromagnetic Response of Magnetic Soils

Frequency Dependent Susceptibility Models

Lee[1983] showedfor thatasamplecontainingacollection of particleswith auniform distributionof decay timeshasa magnetic susceptibility of�� ���� ����� ������ � ��� � �� ��� �"!$# � �"%

�!$# � % �'&)( (1)

This modelof susceptibil ity is expressedasa function of two time constants( � and � � ) thatdeterminethe limits of the uniform distribution of time constants, and the static ( # +* ) susceptibility � � . Thequadratureand inphasecomponentsdescribed by this model areplotted in Figure 1(a). Betweenthefrequencies # � � � � and # � � � thequadrature componentof susceptibility is nearlyconstant,butthereis a peakat #-, � � �.� � � . The inphasecomponent decreaseslinearly with the logarithm offrequency.

TheCole-Colemodelhasalsobeenused to representthemagnetic susceptibility (for example [Ol-hoeft andStrangway, 1974]and[Dabaset al., 1992]). Figure1(b) contains plotsof theCole-Coledistri-bution for a range of distributions.TheCole-Colemodelfor magnetic susceptibility is:�� ��0/ % �0� � � /� % � !$# � � 1�32 (2)

where � / is therealsusceptibility asfrequency approaches infinity ( #5476 ) and �8� is therealsuscep-tibil ity asfrequency approacheszero( #54 * ). Weassumethat �9/: ;* andthatthemodelfor magneticsusceptibility canbewritten as�� �0�� % � !$# � � 1�32 (3)

2

The parameter � is related to the distribution of relaxation times. The limits of � are �< 7* for asingle Debyerelaxation mechanism [Olhoeft andStrangway, 1974] and �= � for an infinitely broaddistribution of relaxation times. A plot of Cole-Coledistributionsfor a rangeof � valuesis shown inFigure1. For the broadrangeof distribution of relaxation timesthatwe areassuming in this study, we

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(a) SusceptibilityModel from Lee(1983).

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(b) Cole-Colemodelof susceptibilityasa functionof > . Thetime constant?�@BA .

Figure 1: Differentfrequency dependentsusceptibilitymodels.

would expect to model susceptibility with � values approaching1. The time constant � controls thelocation of thepeakof theimaginary partof thesusceptibility , with thepeakoccurring at # � � � . Forlarge � theCole-Cole modelyieldsa straight line for therealpartanda constantnegative value for theimaginary part. This is thesameasLee’s representation andis a key characteristic for determining thebehaviourof theelectromagnetic response.

Constructing a Magnetic Susceptibility Model from Kaho’olawe Soil Measurements

The problems of magnetic soils at Kaho’olawe have beenwell documented [Cespedes,2001]. Amodelfor thefrequency dependent susceptibility of Kaho’olawesoilsis required to investigatemagneticnoise problemsthrough forwardmodelling. Kaho’olawe is a single volcanicdomemadeof thin beddedpahoehoe(smooth, very fastmoving lava) and’a’a (rugged,slow moving lava) basalt [Stearns,1940].The baserock is tholeiitic basalt, containing up to 20% magnetite [Butler, personal communication,2001]. Thebaserock is coveredby a number of differentsoil typeswith variable geophysical character-istics [Parsons-UXB, 1998].

Table1 listsmeasurementsof themagneticsusceptibility for soil samplesatSeagullandLuaKakikasiteson Kaho’Olawe. Thesemeasurementsprovide us with the real part of the complex susceptibil ityat two frequencies. Given this limited information of the soil’s magnetic characteristics, we needtomake someassumptionsin generating a susceptibility model. First, we assumethat the two measuring

3

(a)SeagullSite- MagneticSusceptibility( CED�F'GIH SI)Low Frequency High Frequency % Frequency

Sample (0.46kHz) (4.6kHz) Effect

7462-2728A-6” 3554 3311 7.07462-2728A-24” 3022 2771 8.27462-2728B-6” 1046 1001 4.37468-2734AP-6” 1726 1630 5.67468-2734AP-18” 1529 1448 5.37468-2734BP-12” 2807 2634 6.27468-2734BP-24” 1920 1807 5.97468-2734AB-6” 845 805 4.67468-2734BB-8” 1795 1707 4.9

(b) LuaKakikaSite- Magnetic Susceptibility( CED8F GJH SI)Low Frequency High Frequency % Frequency

Sample (0.46kHz) (4.6kHz) Effect

7537-2754AP-6” 2355 2249 4.57537-2754AP-18” 2227 2134 4.27537-2754BP-12” 1461 1383 5.47537-2754BP-24” 1497 1411 5.87537-2754AB-6” 2475 2431 1.87537-2754B-12” 1394 1334 4.3

Table1: Threeseparatesamplesweremeasuredfrom eachbagof soil. Themeanof themeasurementsis listed.

frequencies are within the frequency range wherethe inphasecomponent decreaseslinearly with thelogarithm of frequency ( � �� K # K � � ). Second, we assumethat all the frequencies of interestfall within this rangeof frequencies. With thesetwo assumptions, we canmodel the real part of thesusceptibility asa straight line. By manipulatingequation 1 we canshow that for � �ML � theslope oftheinphasecomponentis relatedto thequadraturecomponentby

Slope �.N Re� � �N ��� # ( POQ Im

� � � # �1� � � ����R� � �S� � �� (4)

This relationship hasalsobeenderivedwithout theuseof equation (1) [Mulli nsandTite, 1974], andhasbeenobserved in complex susceptibili ty measurementsby Dabaset al. [Dabaset al., 1992]. Therefore,by determining theslopeof theinphasecomponentfrom thesusceptibility measurements,wecanimme-diately estimatethequadrature component. Thesusceptibil ity modelof Figure2 wasconstructedusingsusceptibility measurementsof sample7462-2728A-6 (Table 1). In 1D earthmodelling that foll ows,oneof the layered earthmodelsconsidered will usethis magnetic susceptibility modelto representthesusceptibility for thetop layer of soil.

Electromagnetic Response of a 1-D Layered Magnetic Earth

Forward modelling in 1D is solved in the frequency domainin the standard propagationmatrixformalism[Farquharsonet al., 2001]. Let usconsidera circular transmitter loop of radius T , carrying acurrent U , andat a height V above a 1-D layered earth.At anobservation point W above theground and

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Figure2: A magneticsusceptibilitymodel constructed for soil sample7463-2726A-6 from the SeagullSite atKaho’olawe,Hawaii.

a radial distance X from the axis of circular transmitter loop, the vertical component�-Y

andthe radialcomponent

�MZof the [ -field are� Z � # � U\TO^] /_ �a` �'b�ced YgfihSj �^k � k 1 ` bSced Y � hlj (nmo � m T � o � m X �Ip m (5)�qY � # � U\TO ] /_ � ` �'b c d YgfihSj % k � k 1 ` b c d Y � hlj ( m �r � o � m T � o � � m X �Jp m (6)

where r � Ps m � �ut �� , t � is the wave numberof the air, ando � and

o arethe zeroth andfirst orderBesselfunctions,respectively.

k � andk 1 areelements of thematrix v :v xw ,yz�{ � w z (7)

where w }|~ ��� � %��l� b��� �$b ��� ��� ��� �l� b��� �$b ���� � ��� �l� b��� �$b � � � � � % �l� b��� �$b � ���

(8)

w z |~ ��� � % �8��� � b ��8� b �1� � � ��� ��� �8��� � b ��8� b �1� � ���� ��� �8��� � b ��8� b �1� � � ` � � b ��� ��� �1� � ��� � % �8��� � b ��8� b �1� � � ` � � b �1� �$� �1� ���

(9)

Thethicknessof the � � h layer is � z , and � z is themagnetic permeability of thelayer.

To determine the fields at the center of the transmitter loop, we can simply set X �* and setW � V . Thesesubstitutionsgive� Z � # � ;* (10)

5

��Y � # � U\TO^] /_ � � % k � k 1 ` � � b c h ( m �r � o � m T ��p m (11)

Therefore, asthesymmetryof the1-D would alsosuggest, there is no horizontalcomponentto the [ -field responseat the centerof the transmitter loop. This is an important point becauseit shows, forthe situation wherethe fields are measured along the axis of the transmitter loop, that the effects ofmagnetic susceptibili ty will appearonly in the vertical component. This feature will be exploited laterwhenprocessingelectromagnetic data.

The time domainsolution is obtainedby calculating Fourier transformations of the frequency re-sponsefor a causal stepturn-off [Newmanet al., 1986]:N V � � �N � � OQ ] /_ Re � � � # ���S�e��� � # � �Ip # (12)N V � � �N � OQ ] /_ Im � � � # ���S��� ��� # � �Ip # (13)V � � � � OQ ] /_ Im � � � # ���# �e��� � # � �Ip # (14)

Theseintegralsareevaluatedusingthedigital filters of Anderson[1975].

Let us consider a pair of two-layer models. The first, shownin Figure 3(a), consistsof a 1 mthick top layer with a conductivity of � :*J��* � S/manda frequency dependentcomplex susceptibil itydefinedby Figure2. Thesecond two-layer model,shown in Figure3(b), hasa static real susceptibil ityof �^ �*J��*�  SI in the top layer. Both models have a basement conductivity of � ¡*J��*�* � S/m andastatic susceptibili ty of �¢ £*J��*�¤ SI. Thecalculatedresponsesof this two-layer modelwill becomparedto the responseof a conductive andpermeable sphere with theapproximatematerialpropertiesof steel( � �  ¥* � � , � ¡¤I�¦ 9§ ¨ � *�© S/m),a diameter of 25 cm, andburied at a depth of 30 cm. The sphereresponsewill beapproximatedusing thesolution outlinedby Ward[1959] for aspherein auniform fieldin a whole-space.

1 mσ = 0.01 S/m

σ = 0.001 S/m

χª χ ωlayer = ( )

χª = 0.03 SI

h

(a) Two layer modelwith frequencydependent magnetic susceptibility«­¬¯®i° in thetop layer.

1 mσ = 0.01 S/m

σ = 0.001 S/m

χ± layer = 0.05 SI

χ± = 0.03 SI

h

(b) Two layermodelwith staticmag-neticsusceptibility.

P²

H³

oσ = 3.54x10 S/m

6s

µ µs = 150 o

25cm

30cm

h´

(c) A conductive and permeablemetal sphere. Material parametersarechosento matchsteel.

Figure3: Threeexample models.

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(a) Thesolid linesrepresenttheresponseof thetwolayermodelwith frequency dependentsusceptibility(Fig. 3(a)) anddashedlines representthe two layermodelwith real,staticsusceptibility(Fig. 3(b)).

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layer = 0.05

(b) Frequency domain responseof the two layer

model betweenA1µ ��¶ and A�µ8· Hz.

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(c) The imaginarypart of ¸ -field for the two layermodelwith frequency dependent susceptibilityandwith realstaticsusceptibility.

Figure4: Forwardmodelledfrequency domainelectromagneticresponsesfor thetwo layermodel.

Figure4(a) shows the modelled frequency responsefor the two-layer models. Whenplotting theresponsesat thechosen axis ranges, theresults for thestatic,realsusceptible modelandthemodelwithcomplex susceptibili ty look similar. Subtle,but important, differencesbecomeapparentwhenfocusingthe plot on the lower frequency range. Figure 4(b) shows that the real part of the [ -field hasa lineof negative slope. The effect of the frequency dependent layer on the quadraturecomponentbecomesevident whenplotting thelogarithm of thequadrature component(Figure 4(c)).

Theeffectof thesedifferencesonthetimedomainsignatureis shownin Figure5(a). Weseethatthe

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(a) Time domainresponsesof thetwo layermodels.The modelwith frequency dependentsusceptibilityfollows the ¹�� � responsewhile themodelwith onlystatic,realsusceptibilityfollows a ¹���ºa»�¼ decay.

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(b) Time domainresponsesof the the steelsphereandthe two-layermodelwith frequency dependentsusceptibility.

Figure5: Forward modelledelectromagneticresponsesfor thetwo layermodel andthespheremodel.

two layer modelwith complex, frequency dependentsusceptibil ity producesa � � response,while thetwo-layer modelwith static realsusceptibility follows a � �3½�¾ � decay. For the time range of theGeonicsEM63 (approximately 0.1 ms to 25 ms) it is clear that the responseof the real, static susceptibil itydistribution producesa muchweaker responsethanwhen the model contains the complex, frequencydependentsusceptibility layer. Figure4(d) shows the responseof thesphere modelis muchlarger thantheTEM responseof themodelwith only static, realsusceptibil ity. However theTEM responsefor themodelwith complex susceptibil ity becomescomparableat early andlatetimes.

The ��� responseonly occursfor astepfunction primaryfield. To take into accountthefinite lengthof the inducing field we canconvolve the solution with the transmitter current [Asten, 1987]. The fullwaveform convolution isV-¿ � � � ] /_ VÁÀa�ÃÂ�Ä�VJÅBÀ$� � ��ÂÆÄ p �� (15)

wherethe V�¿ � � � is the receiver waveform and VSÅ � � � is the transmitterwaveform. Figure6(a) demon-strateshow, asthepulselength increases,the

N � � N � responseapproaches the � � behaviour of thestepoff response.FromFigure6(a),we seethatto observe the � � responseat 10 msafterturn-off, thepulselength would needto begreaterthan10ms.

The Effect of Susceptibility on Dipole Discrimination Algorithms

In this section we consider theeffect of magneticsoils on the ability to recover the representativedipole parametersof a buriedtarget. Weconsider datafrom a 3-componenttime domain sensors.

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(a)Two layermodel

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Figure6: Comparisonof thethe ÇIÈ�É.ÇIÊ responsesfor different transmitterloopheights andpulselengths.

Generation of Synthetic TEM Data

Although 3-component sensorshave beendevelopedby GeonicsInc. (EM61-3D) andZongeEngi-neering(NanoTEM),testing of either sensorhasbeenlimited. Fielddata,in particulardataacquiredovermagnetic soils, arenot readily available. Therefore, to investigatethe effectsof the magnetic soils wemustgeneratesynthetic datasets. We generatesynthetic field datasetsby assuming that thesecondaryfield is a linear sumof the responseof theburied metallic target, the responseof the magnetic soil andGaussian noise:p\Ë ;Ì�ÍË �ÏÎ � %ÑÐ.Ò p�Ó ;Ì�ÍÓ ��Î � %ÑÐ.Ò p Y ;Ì�ÍY �ÏÎ � % ÌMÔ ��ÕÆÖ %×Ð (16)

where p Ë , p Ó , and p Y arethe threecomponentsof secondaryfield recordedby the sensor, Ì Ë , Ì Ó , andÌ Y arecomponentsof the buried metaltarget responsein the absenceof the magnetic soil, Ì Ô �ÃÕØÖ is theresponseof the magnetic soils and Ð is the Gaussian noise. We have usedthe conclusion, arrived atearlier, that themagnetic soils affect only theverifiedcomponentof thereceiver if thereceiver is on theaxisof thetransmitter.

The buried target response Ù Í �ÏÎ � is calculatedby using the decaying two-dipole approximationoutlinein PasionandOldenburg [2001a]. Theresponseof a compactburied target canbeapproximatedby a 13 element modelvector:Î � Ú Ò�ÛÜÒ p Ò�Ý'Ò�ÞßÒ t Ò � Ò1à Ò�á Ò t �¥Ò � �¥Ò1à-�¥Ò�áI� � (17)

where� Ú Ò�Û � is thetarget location, p is thedepthbelow thesurface, Ý and Þ definethetarget orientation,t Ò � Ò1à Ò�á definethedecaycharacteristic of a dipole orientedparallel to theaxisof symmetryof the

target, and

t � Ò � � Ò1à � Ò�á � definethedecaycharacteristic of a dipole orientedperpendicular to theaxisofsymmetryof the target. The validity of this modelhasverified, aswell asappropriateparameters fordifferentUXO andscraptargets,arereportedin PasionandOldenburg [2001b]. For theexamples in thisreport, we will forwardmodeltheresponsefor thestokesmortarof Figure7(a). Thestokesmortarwill

9

(a)Photosof aStokesmortar(top)anda60mmmor-tar.

Decay Stokes 60mmParameter Mortar Mortarâ¥ã

43.9 3.38ä ã 0.02 0.019å ã0.73 0.9æ ã 9.1 2.55âlç4.9 0.79ä ç 0.001 0.02å ç1.09 1.19æ ç 10.8 3.59

(b) Characteristicdecayconstantsfor theStokesand60 mm mortar.

Figure 7: PhotosandDecayConstantsfor a Stokesmortaranda 60mmmortar.

beplacedat� Ú Ò�Û � (2m,2m)andatadepth of 40cm. Thetargetwill beorientedsuchthat

� Ý�Ò�Þ � (30degrees,70 degrees).

Wealsoshowedthatanappropriate representation for themagnetic soil responseisÌMÔ �ÃÕÆÖ �è � � (18)

Themagnitudeof thesoil signal is varied throughout thesurvey areaby adding a random componenttoè at eachstation location, that isÌ Ô �ÃÕÆÖ À0éè %êÐgë Ä � � (19)

where éè controls the overall level of the soil signal and Ð ë is Gaussian distributedrandom noise thathasa standarddeviationequal to 25%of éè . Two differentsoil signal distributionsareconsideredin thisreport. For thefirst distribution éè is chosensuchthatat thefirst timechannel of theEM63response(180�íì ) themeansoil signal over thesurvey areais 50 mV. For thesecond distribution themeansoil signalis setto 100mV. Figures8(a)and(b) plots thedistribution of decay curve for the two differentchoicesof éè (labelled éè= îè ½ _ ,ðï and éè= £è _1_ ,)ï , respectively). Figure8(c) comparesthemeansoil signalè ½ _ ,)ï ��� and è _1_ ,)ï ��� with theresponseof theStokesmortarmeasured directly over thetarget (i.e.at� Ú Ò�Û � (2m, 2m)). Figure8(c) shows that the responseof the Stokes mortarhasa portion of its

curve that is simlarto the �$� responseof themagnetic soil. This similarity makesthesubtractionof themagnetic soil responsefrom survey datamoredifficult.

Finally somenoiseÐ is addedto thesumof thebasalt responseandthedipole response. Theamountof noisehasa standarddeviation of 5% of thedataplus 0.5mV.

Pre-processing of Data Using Horizontal Components of Field

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(b) Distribution of basalt models ñ ò c�ó¦ô @¬�õ � �a�aö÷ øqú$û ° ¹ � � .

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Stokes MortarBasalt 50mVBasalt 100 mV

(c) Comparisonof thedecayresponsedirectlyabove

a Stokes mortar buried 40 cm deep, ñ ò c�óüô @õ º �aöi÷3¹ � � and ñ ò c�óüô @ õ � �a�aöi÷3¹ � � .Figure8: DifferentBasaltmodels.

As our modelling suggests,thepresenceof magnetic soils will producea � � signal in theverticalcomponentof themeasured secondaryfield. Thedifficulty in removing this signal lies in identifying ifthemeasuredresponseis only from thesoil or if theresponseis partly dueto thepresenceof a metallictarget. Theabsenceof thesoil signal in thehorizontalcomponentssuggest that they canbeusedaspartof a pre-processing stepto helpdeterminewhereandhow weshould attempt to remove thesoil signal inthevertical component.Onepossible (andsimple)way of doing this would beto

1. Calculatethehorizontal componentof thedataatthefirst timechannel: p h � � �� =ý p �Ë � � �� % p �Ó � � �� .2. At eachsounding, if p h is lessthansomethreshold value(e.g. p h�þ O mV) thenidentify thisstation

asnot likely containing signalfrom a target. We canproceedto fit è �Ï� to thedataat this station

11

50mV Basalt 100mV BasaltModel,Basalt Model, Basalt

Real 50mV Basalt Response 100mV Basalt ResponseParameters No Basalt Model subtracted Model subtractedÿ

2 2 2 1.98 1.78 1.7�2 2 2.02 1.99 1.84 1.77

depth 0.4 0.4 0.37 0.39 0.35 0.35�30 30.1 31.9 29.9 26.2 51.8�70 69.9 72.5 65.9 164.6 180â¥ã

43.9 45.113 47.455 39.866 11.243 11.239ä ã 0.02 0.001 0.019 0.019 0.001 0.018å ã0.73 0.664 0.667 0.638 0.744 0.76æ ã 9.1 6.442 5.998 7.379 12.924 10.869â ç4.9 5.309 6.201 4.358 24.574 5.991ä ç 0.001 0.001 0.019 0.019 0.001 0.018å ç1.09 1.038 1.03 1.073 0.657 0.904æ ç 10.8 5.566 6.549 5.361 25.101 19.769

Table2: InversionResultsfor a StokesMortarburiedin a background of magneticsoils.

andsubtractfrom thedata.

3. At soundings where p h is greater than the threshold, we can then subtract è�� �g� where è�� isdeterminedfrom the fitting of stationsin the previous step. For example, è � could be the meanvalue of all the previously obtained è values, or we could interpolate valuesfor è�� from the èvalues.

In theexamplesof thefinal section, è � is calculatedby taking themeanvalueof the è valuesobtainedfrom data wherep h þ O mV.

Inversion Results

The synthetic datawereinvertedfor the 13 parameterslisted in equation (17). Theseparameterswereobtainedby minimizing a leastsquaresobjective function in two steps. Thefirst stepwasto mini-mizetheobjective function using aglobal optimizationalgorithm, andthesecond stepwasto takethere-sult from theglobal algorithm anduseit asastarting point for a local algorithm. Weused theneighbour-hoodalgorithm [Sambridge,1999] for theglobal search, andaProjectedBFGSalgorithm [Kelley, 1999]for thelocal search.

The synthetic datawasgeneratedfor a StokesMortar buried at a depth of 40 cm and located at� Ú Ò�Û � (2 m, 2 m). Threedifferentmagnetic soil modelswereused: éèx ;* Ò è ½ _ ,)ï Ò and è _1_ ,)ï . Theresults of inverting the datasetsare found in table2. Table2 show that the inversionwasreasonablysuccessful in recovering the location, orientation, anddipole parameters in all cases except for whenthe basalt signal was Ì Ô �ÃÕÆÖ � è _1_ ,ðï %^Ðgë � ��� . Figure9 examinesthe datafit whenthe magnetic

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soil responseis Ì Ô ��ÕÆÖ � è ½ _ ,ðï % Ð�ë � ��� . Eventhough thebasalt wasnot removedfor this inversion,thealgorithm wasvery successful in recovering themodelparametersdueto presenceof thehorizontalcomponents.

Conclusions

Electromagneticsensor dataacquired in thepresenceof magneticsoils hasa characteristicN � � N �

decay of � � . This � � decaycanbecanbederivedby assuming thesoil consistsof magnetic particleswith a uniform distribution of decay times. This assumption leads to a representation of the magneticsusceptibility asa frequency dependent, complex quantity. The1D forward modelling of this suscepti-bilit y modelreveal that thehorizontalcomponentsof datameasured along theaxisof a transmitterloopis not sensitive to magnetic soils provided that thesubsurfacepropertiescanbeadequatelyrepresentedby a 1D layered model. As a consequence, wheninverting the threecomponentsensor data collectedover a target buried magnetic soil, the informationprovidedby thehorizontal componentsof datamay:(1) improve detection, (2) be exploited in developing processingroutinesto aid in the removal of themagnetic soil responsein the vertical component of data, and(3) help constrainthe inversionto morereliably recover dipole modelparameters.

Acknowledgments

Wewould like to thankDwain Butler from theEngineer ResearchandDevelopment Centerfor themagnetic susceptibility measurementsof Kaho’olawe,Hawaii soils.

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(a) Plan view of observed and predicteddata andresidualfor thefirst time channel( ¹3@BA��8µ s).

(b) Decaycurve comparisonat ¬��� ��)° @ (2.5,1.3)m.

(c) Profileof observedandpredicteddataandresidualfor theline � @A�� � m.

Figure9: Inversion resultsfor a datasetwith a basaltbackgroundof ����������� � H"!$#&% Ê G ã . The bias in the ' -componentindicatestheinability to fit thebasaltbackground dueto thepresence of thehorizontalcomponentsofthedata.

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