三维大地电磁数据的二维反演举例.docx
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三维大地电磁数据的二维反演举例.docx
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三维大地电磁数据的二维反演举例
Two-dimensionalinterpretationofthree-dimensionalmagnetotelluricdata:
anexampleoflimitationsandresolution
SUMMARY
Interpretationofmagnetotelluric(MT)dataforthree-dimensional(3-D)regionalconductivitystructuresremainsuncommon,andtwo-dimensional(2-D)modelsareoftenconsideredanadequateapproach.Inthispaperweexamine2-Dinterpretationof3-Ddatabyconsideringthesyntheticresponsesofa3-Dstructurechosenspecificallytohighlighttheadvantagesandlimitationsof2-Dinterpretation.2-Dmodelswereobtainedfrominversionofthesynthetic3-Ddatasetwithdifferentconditions(noiseanddistortion)appliedtothedata.Wedemonstratetheimportanceofunderstandinggalvanicdistortionofthedataandshowhow2-Dinversionisimprovedwhentheregionaldataarecorrectedpriortomodelling.Whenthe3-Dconductivestructureislocatedbelowtheprofile,themodelsobtainedsuggestthattheeffectsoffinitestrikearenotsignificantifthestructurehasastrikeextentgreaterthanaboutone-halfofaskindepth.InthiscasetheuseofonlyTM-modedatadeterminedbetterthehorizontalextentofthe3-Danomaly.Whentheprofilesarelocatedawayfromthe3-DconductivestructuretheuseofonlyTM-modedatacanimaginephantomconductivestructuresbelowtheprofile,inthiscasetheuseofbothpolarizationsproducedabetterdeterminationofthesubsurfacestructures.
Itisimportanttonotethatthemainstructuresareidentifiedinallthecasesconsideredhere,althoughinsomecasesthelargedatamisfitwouldcausescepticismaboutfeaturesofthemodels.
Keywords:
electromagneticinduction,electromagneticmodelling,magnetotellurics,tensordecomposition.
INTRODUCTION
Inrecentyearsadvancesincomputertechnologyhaveenabledthedevelopmentoffasterandmorereliablealgorithmstocalculatethethree-dimensional(3-D)electromagneticresponseofearthmodels.Consequently,thecurrentstate-of-the-artformagnetotelluric(MT)datainterpretationisthat3-Dtrial-and-errorforwardmodelfittingisbeingusedmorefrequentlyforhypothesistesting,and3-Dinversionswillbecomeavailableinthenearfuture.Dataacquisitionondense2-Dgridshasbeenundertakentostudygeothermal(e.g.Takasugietal.1992)andmining-scaleproblems(e.g.Zhangetal.1998),butregional-scalefieldexperimentsona2-Dgridareoftenimpracticalduetohighcostandinaccessibility.Accordingly,regionalscalesurveysareoftenrestrictedtoasingleprofileorwidelyseparatedprofiles(e.g.southernBritishColumbia,Jones&Gough1995;Ledo&Jones2001).Insuchcases,researchershavetoextractthemaximuminformationpossiblefromadatasetthatmaybespatiallyundersampled.Theuseofadditionalgeophysicalinformationmayallow3-DmodellingofMTdataevenwherethedatawerecollectedalongaprofile(Pousetal.1995;Park&Mackie2000;Ledoetal.2000).
Dependingontheinductiveandgeologicallengthscalesofthetarget,2-Dinterpretationofthedatamaybeappropriateforalimitednumberofsitesandoveralimitedperiodband.However,interpretationof3-Ddatawith2-Dtechniquesmaynotbeabletoreproducethesignificantfeaturesofthesubsurface;anexampleofthiscanbefoundinthe2-DinterpretationoftheKayabedataset(Jones&Schultz1997)byGarc´ıaetal.(1999).
Inthispaper,weexploresomeofthelimitationsof2-Dinterpretationof3-DMTdatathroughtheanalysisofsynthetic3-DMTdatawiththecurrentlyavailable2-Dtools.Moreover,wedemonstratetheimportanceofremovingnear-surfacegalvanicdistortionon3-Ddata,notonlytoreducetheerrorsourcesina2-Dinterpretation
butalsobecauseofitsimportancein3-Dinterpretation.Whilstthistestisnotaimedatreproducingallpossible3-Dsituations,weneverthelessfollowproceduresthatwewouldundertakeifthesewereactualfielddatatogaininsightintothevalidityof2-Dmodellingandinterpretationof3-Ddata.
SYNTHETICDATA:
3-DMODEL
Wehavechosenasimple3-Dmodeltorepresenttheregionalstructureforexploringthemainproblemsarisingfrom2-Dinterpretationof3-Ddata(Fig.1).Themodelconsistsofaregional-scale2-Ddippingcontrastbeneathconductiveoverburden.Wehaveembeddeda3-Delongatedconductivebodyatanangleof−45degreeswith
respecttothemain2-Dstructure.Withthismodel,wecanstudytwoofthemainproblemsassociatedwith2-Dinterpretationof3-Ddata:
thepresenceofstructureswithdifferentstrikesandtheeffectsoffinitebodylength.Thismodelcouldrepresentasubhorizontal,kilometre-scalesillintrusion(i.e.mineralisedlayeredintrusionssuchastheBushveldortheStillwatercomplex;Philpotts1990)crosscuttingatamediumangleanolder2-Dregionalstructure.Inanothergeologicalenvironment,Marquisetal.(1995)proposedastrike-depthvariationtoexplaintherelationshipbetweentheallochtonousandautochtonousterranesacrosstheboundaryoftheIntermontaneandOminecamorphogeologicalbeltsintheSouthernCanadianCordillera.
Thesurfaceresponseofthe3-Dmodelat31periods,between0.01and1000s,wascalculatedusingthecodeofMackieetal.(1994)withmodificationsbyMackie&Booker(2000,pers.comm.).Toensurereliabilityoftheresponses,themeshwasrefineduntilconvergenceintheresponseswasobtained.Thefinalmeshconsisted
of99×99horizontalelementsand50verticalelements.Threeprofilescrossingthemodelwerechosen,retrievingthedataateverythirdnodeofthemeshforatotalof30sitesperprofile.ThedatafromprofileIareinfluencedbythedirectionandfinitestrikeofthe3-Dconductivestructurebelowit,whereasthedatafromprofilesIIandIIIareinfluencedbythenearby,off-profilepresenceofthe3-D
conductivebody.
Inordertoshowthe3-Dnatureoftheresponses,weappliedGroom–Bailey(G–B)decomposition(Groom&Bailey1989)tothesyntheticdatafromProfileI.Fig.2showstheunconstrainedG–BgalvanicdistortionparameterstwistandshearrecoveredfromthedataofprofileIatfourdifferentperiodswithfixedstrikedirection(0◦,alongxdirectiononFig.1).Exceptattheshortestperiod(0.1s),thevaluesoftheseparametersarehigh,especiallytheshear.Giventhatthereisnonear-surfacegalvanicdistortionaffectingthedata,thesevaluesdescribetheeffectsofthe3-Dbody.Atshortperiods,between0.1–10s,theGroom–Baileydecompositionmodelisinappropriate;theperioddependenceofthetwistsandshearsindicatesthereareinductiveeffectsassociatedwiththe3-Dbody.Atlongerperiods,10and100s,inductionisweakandtheresponseofthebodycanbevalidlydescribedbyamodelwhichincludesperiodindependentgalvaniceffects.AmoreexhaustiveanalysisofthedimensionalityofthedatausingtheG–Btechniquewillbepresentedbelow.
Fig.3showsthereversedrealinductionarrowsfollowingParkinson’scriteria(pointingtowardscurrentconcentrations)forthethreeprofilesatthesamefourperiodsdiscussedabove.OnprofileI,theeffectofthe3-Dbodyalonecanbeobservedforperiodsbelow1s,andatlongerperiodsthereisacombinationofeffectsduetothe3-Dbodyandtheregional2-Dstructure.OnprofilesIIandIII,inductionarrowsforperiodsof1sand10sarealsostronglyaffectedbythe3-Danomaly.TakentogethertheverticalmagneticfieldsandMTresponsesindicatethatthemodelyieldscharacteristicsofa3-Ddatasetandfacilitatesourstudyoftypicalproblemsinvolvedin2-Dinterpretationof3-Ddata.
Fig.4showsthephasesobtainedatprofileIandtheresponseofa2-DmodelreproducingthestructuresbelowprofileI.Thedifferencebetweentheresponsesofbothmodelsisreadilyapparent,reachingamaximumof−22◦inthecentreoftheprofile.
3-DDATAAFFECTEDBYGALVANICDISTORTION
Thenear-surfacegalvanicdistortionsconsideredinthispaperrepresentsmall-scalelocalscatterersoveraregionalstructure(1-D,2-Dor3-D).FollowingG–B,wecandescribetheeffectsbyZ=CZR,whereZistheobserved2×2compleximpedance,Cisareal2×2matrixperiodindependentandZRisthe2×2complexresponseoftheregionalstructure.
Toanalysetheeffectsofnear-surfacegalvanicdistortiononregional3-Dresponses,weappliedgalvanicdistortionsCtothesyntheticimpedancetensorsfromeachsiteonprofileI.Thedistortionmatriceshadtheunresolvablestaticshiftparameters(gainandanisotropyinG–B’sdescription)settounity,thustherearenounrecoverableamplitudescalingeffects.Twistandshearparameterswereassignedatrandom,(Fig.5).Toensuredistortionconsistentwithgalvaniceffects,
periodindependenttwistswereboundedbetween−60◦and60◦andperiodindependentshearsbetween−45◦and45◦,exceptforfivesiteswhereshearsbetween−60◦and60◦werepermitted.Fig.6showstheapparentresistivitiesandphasesforsite14onprofileIbeforeandafterdistortionwasapplied.Inthiscase,thevaluesof
thetwistandshearparameterswere40◦and5◦respectively.Foroffdiagonal
elementsatshortperiods(Fig.6a),thedifferencebetweenthemconsistsofonlyaperiodindependentmagnitudeshiftintheapparentresistivities(staticshift,Jones1988)andthephasesarecoincident.However,atperiodslongerthan0.1sthereisanimportantchangeintheshapeofthecurvesbecauseofthenon-negligible
valuesoftheregionaldiagonalimpedancetensorcomponents.Forthediagonalelements(Fig.6b)theshortperiodbehaviourcorrespondsto2-Dintheprincipaldirection(strikeequalto0◦);theregionalcomponentsarenegligibleandthedistortedapparentresistivitycurvesareproportionaltotheregionalρxyandρyxdata.
InordertosimulaterealdatabeingacquiredalongprofileI,weaddednoiseandscatte
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