大地电磁法反演方法回顾-胡祥云

Inversion-historicaldevelopments•Startsfrom1-DinversionbyWu(1968)•1970s:from1-Dto2-D–Bostickinversion–Variouslocaloptimizationmethods,Generalizedinversion,JuppandVozoff(1975)–anisotropy•1980s:2-Dinversion–Jointinversion:Apparentresistivityandphase,TE+TMmode–Smoothnessconstrainedinversion-Occam,SmithandBooker(1988)andConstable(1987)–Seismicanalogyinversion(migration,Wang,Oldenburg,1988)•1990s:from2-Dto3-D–RRIinversion:bySmithandBooker(1991),isoneofthebestapproximatemethods,providesreasonablesolutions,withlesscomputingresources,becausepartialderivativesareobtainedfromaperturbationanalysiswhichusesonlythecrosstermsofthehorizontalgradient.–MackieandMadden(1993)implementedaniterated,linearizedinversionalgorithmfor3-DMTdata,–forwardmodellingandFrechetderivativesbyQuasilinearApproximation–Electromagneticmigration–Globaloptimization–Rebocc•2000s:3-Dinversion–Non-linearconjugategradient,W.Rodi,2001,R.L.Mackie,T.R.Madden,G.A.Newman,D.L.Alumbaugh,–Dataspacemethod,WeerachaiSiripunvaraporn,2007–BBIinversion(Constable(2004))–JointInversion(conductivity,magneticpermitivity,polarization,density,velocityOutlineofthissection•Nonlinearconjugategradients•Dataspacealgorithm•RRI(RapidRelaxationInversion)•ApproximatedcalculationofFrechetderivatives•M.S.ZhdanovfromMTtoMagnetic•D.W.OldenburgfromMTtoGravity•ConsideringStaticshift•BoundaryBasedinversion•ApplicationofANN•CombinationofSVDafterCGBayesianinversionwithMarkovchains-I.TheMT1-Dcase,H.Grandis,1999•Toassesstheuncertainty,theinversionprocessshouldbecastintoastatisticalsetting.ABayesiansettingisanaturalchoiceformanygeophysicalinverseproblems,whereitispossibletocombineavailablepriorknowledgewiththeinformationcontainedinthemeasureddata(Bayesiantime-lapseinversion,ArildBuland,2006)•TheMT1-Dinverseproblemisaclassicalproblem,andithasalreadybeenaddressedbymanyauthors.Variousalgorithmsbasedondeterministicorprobabilisticapproachsareatpresentavailable•However,itisstillofgreatimportancenotonlyfor2-Dand3-DinversionbutalsoespeciallyforEarthdeepsoundingNonlinearconjugategradientsalgorithmfor2-DMTinversion,W.Rodi,2001•Minimizeanobjectivefunctionthatpenalizesdataresidualsandsecondspatialderivativesofresistivity•MoreefficientthantheGauss-NewtonalgorithmintermsofbothcomputermemoryrequirementsandCPUtimeThree-dimensionalmagnetotelluricinversionusingnon-linearconjugategradientsGregoryA.Newman,2000FromModelspacetoDataspaceThree-dimensionalmagnetotelluricinversion:data-spacemethod,WeerachaiSiripunvaraporna,2005•Computationalcostsassociatedwithconstructionandinversionofmodel-spacematricesmakeamodel-spaceOccamapproachto3DMTinversionimpractical•Withthetransformationtodataspaceitbecomesfeasibletoinvertmodest3DMTdatasetsonaPCDataspaceconjugategradientinversionfor2-DMTdata,WeerachaiSiripunvaraporn,2007•AdataspaceapproachtoMTinversionreducesthesizeofthesystemofequationsthatmustbesolvedfromM×M,asrequiredforamodelspaceapproach,toonlyN×N,whereMisthenumberofmodelparameterandNisthenumberofdata.•ThedataspaceOccam’s(DASOCC)inversionhasbeensuccessfullyappliedto2-D(2000)and3-D(2004)MTinversion.•ComputationalefficiencyisassessedandcomparedtotheDASOCCinversionbycountingthenumberofforwardmodelingcalls.•ExperimentswithsyntheticdatashowthatalthoughDCGrequiressignificantlylessmemory,itgenerallyrequiresmoreforwardproblemsolutionsthanaschemesuchasDASOCC,whichisbasedonafullcomputationofJ.GeneralizedRRImethod,KazunobuYamane,1996Advantages:Highspeed,acceptableaccuracy•RRIstartsbyJ.T.Smith,J.R.Booker(1991),applicableto2Dand3DMTinversion,developedtoGRRI(1996),usedtoCSAMT,whichapproximateshorizontalderivativeswiththeirvaluescalculatedfromthefieldsofpreviousiteration•TheGRRIalgorithmoffersanewwaytodirectlyconvertMTdataacquiredoverroughterrainwithvariabletopographyintosubsurfaceimages.Itispossibletoreconstructtheseresistivityimageswitharelativelysmallamountofcomputerresources.•WhencomparedwiththeoriginalRRImethod,theGRRImethoddoesnotrequireadditionalcomputationtime,andtheinvertedimagehashigherresolutionbecausethenewschemeisbasedonalocally2-Danalysis.ComputingJacobian:importantinclusionofInversion•Twocomputationalroadblocksencounteredwhensolvinganinverseproblem:(Oldenburg,1994)(1)calculationofthesensitivitymatrixand(2)solutionoftheresultantlargesystemofequations.•Reciprocalprinciple-usingvaluesobtainedformforwardmodeling(PhilipE.Wannamaker,1996)•Approximationbyusingofhalfspaceanalyticformula•Approximatesensitivitiesfortheelectromagneticinverseproblem(C.G.Farquharson,D.W.Oldenburg,1996)•NothingisaattemptcorrespondingtoApproximatedupdatingofJacobianinDCresistivityinversion(Loke,Barker,1996)EandEJxdenotetheelectricfieldsduetoaMTplanewavesourceandanx-directedunitelectricdipolesourceJx,locatedatthemeasurementsite,respectively.VJxmxdVEEERapid3-Dinversionalgorithm,basedonthequasi-linearapproximationofGreen’sfunctionbyM.S.Zhdanov•Zhdanov,M.S.,Fang,S.&Hursan,G.,2000.Electromagneticinversionusingquasi-linearapproximation,Geophysics,65,1501–1513.•3-Dmagneticinversionwithdatacompressionandimagefocusing,OlegPortniaguine,andMichaelS.Zhdanov