大地电磁三维反演方法综述

201Vol.20No.120053(:214220)PROGRESSINGEOPHYSICSMarch20051,1,2(1.,430074;2.,100029)(MT),.MT,MT.,,,,,,P631A100422903(2005)0120214207ReviewofthreedimensionalmagnetotelluricinversionmethodsHUZu2zhi1,HUXiang2yun1,2(1.InstituteofGeophysics&GeomaticsChinaUniversityofGeosciences,Wuhan430074,China;2.InstituteofGeologyandGeophysics,ChineseAcademyofSciences,Beijing100029,China)AbstractTheforwardandinverseofthreedimensionalmagnetotelluricproblemshavebecometheissueinthefieldofInternationalEarth’sInteriorEMInduction.Severalmainmethodsofthreedimensionalmagnetotelluricinversionarebrieflyanalyzedthroughtheideasofeachalgorithminthispaper.Thenthedirectionsoffurtherresearchof32DMTinversionarediscussed.Keywordsmagnetotelluric,threedimensionalinversion,quasi2linearapproximation,conjugategradient,rapidrelax2ation,bayesianstatistics,artificialneuralnetwork2004207210;2004208220.,,1981,,,2002,,.(E2mail:[e-mail])0,(MT),[1].2070,[2].[35][69][1012][13,14],MT.,,,;,MT,,[15][16][17][18][19][20],,MT.11.1MackieMadden[21]1989..,,,.,Taylor,,,Mackie.,.(AHkR-1ddAk+R-1mm)mk=AHkR-1dd[d-g(mk)]+R-1mm(m0-mk),(1)1:.,A,d,m,gm,Rdd,Rmm,m0,m.,HHermitian.,m,,.k+1mk+1=mk+m.g,g(m).(1),Mackie,,.:.Mackie,.,,,,.,,,Spitzer[22];Zhang[23][24];RodiMackie[25](NLCG),,NewmanAlumbaugh.1.2NewmanAlumbaugh,NLCG,,.,.,NewmanAlumbaugh.,,.,,,.mM,=2Nn=1[(Zobsn-Zn)/n]2+mTWTWm,(2)ZobsnZn,N,N.W,..,.,.,,deGro2ot2Hedlin[26],,,.,(2).,.,Newmann.NLCG:(1)i=1,mi,ri=-ý(mi);(2)ui=M-1iri;(3)(mi+iui),i;(4)mi+1=mi+iui,ri+1=-ý(mi+1);(5)|ri+1|,(6);(6)i+1=(rTi+1M-1i+1ri+1-rTi+1M-1iri)/(rTiM-1iri);(7)ui+1=M-1i+1ri+1+i+1ui;(8)i=i+1,(3).iM-1iM-1i+1.NewmannMackieMaddenNLCG,,NLCG,(2),NLCG,(2),NLCG.NLCG,,.1.3Zhdanov,,,51220,.,.,.b,D=b+..,E=Eb+Ea,H=Hb+Ha.(3)bEb,Ea.DFa(rj)=mD^GF(rj|r)(r)[Eb(r)+Ea(r)]dv,(4)FaEaHa,^GF(rj|r)b.Ea(r)^(r)Eb(r),(5)(4)Fa(rj)=mD^GF(rj|r)(r)[^I+^(r)]Eb(r)dv,(6)^,^I.^m(r)=(r)[^I+^(r)],(7).(6)Fa(rj)=mD^GF(rj|r)^m(r)Eb(r)dv=GF(^m),(8)GF..^,^mEa(rj)=mD^GE(rj|r)^m(r)Eb(r)dv^Eb(rj),(9)^m^,(7).:(Born)^m,^,(Born).(8)F=GFm,(10)m^m,F,GF(8).,(9),Eb=GEm,(11),GE(8).(7)m=[I+],(12)(10)m,(11),(12).,.Zhdanov,KayabeMTVallesCalderaCSAMT,,,.1.4SmithBooker[27],,.[18]RRI,,dxy(xi,yi)=20[ESYx0(xi,yi,z)+(xi,yi,z)ESXx0(xi,yi,z)]2(ln(xi,yi,z))[ESYx0(xi,yi,0)+(xi,yi,0)ESXx0(xi,yi,0)][HSYy0(xi,yi,0)+(xi,yi,0)HSXy0(xi,yi,0)]dz,(13)dyx(xi,yi)=-20[ESXy0(xi,yi,z)+(xi,yi,z)ESYy0(xi,yi,z)]2(ln(xi,yi,z))[ESXy0(xi,yi,0)+(xi,yi,0)ESYy0(xi,yi,0)][HSXx0(xi,yi,0)+(xi,yi,0)HSYy0(xi,yi,0)]dz,(14),(xi,yi,z)=-HSYx0(xi,yi,z)HSXx0(xi,yi,z),(xi,yi,z)=-HSXy0(xi,yi,z)HSYy0(xi,yi,z),ESXx0(xi,yi,z)ESXy0(xi,yi,z)HSXx0(xi,yi,z)6121:HSXy0(xi,yi,z)=0SX;ESYx0(xi,yi,z)ESYx0(xi,yi,z)HSYx0(xi,yi,z)HSYy0(xi,yi,z)=0SY.Q(xi,yi)=zmax0(z+z0)352m(xi,yi,z)5z2+gx(z)52m(xi,yi,z)5x2x=xi+gy(z)52m(xi,yi,z)5y2y=yi2dz.(15),m,gx(z)gy(z)xy.RRI,.Mackie,RRI;,,RRI.,RRI.KayabeMT,.,,Zhdanov200,,16167,7,343447,17,9.RRI,.,RRI,,.1.5MT,.,,.,(,,,),.,,.Spichak[19].,,..MT,:MT.,.K{Dk,k=1,,K},=(k,k=1,,K).E(Mi,j,)H(Mi,j,){Mi;i=1,,I}{i;j=1,,J}.yijF(E,H).yij=F(E(Mi,j,),H(Mi,j,))+ij,(16){ij;i=1,,I;j=1,,J},,(PDFs)pij.,.SpichakPDFP(=a/Y=y)=f(y/a)q(a)bAf(y/b)q(b),(17)q(a)a,f(y/a)y=(yij,i=1,,I,j=1,J).a=(ak,k=1,,K),,f(y/a)=Ii=1Jj=1pij{yij-F[E(Mi,j,a),H(Mi,j,a)]},(18)pijij.pij,(ij)2,f(y/a)=Zexp-i,jyij-F[E(Mi,j,a),H(Mi,j,a)]2(ij)2,(19)Z.A(k,cj)cj,Dkkpkpk(cj)=P[A(k,cj)/Y=y]=aA(k,cj)f(y/a)q(a)bAf(y/b)q(b),(20)71220,:b,f(y/b)q(b)Lk,.,Spichak,.K.L.[(n)k;k=1,,K]n.k(n)n+1,,P((n+1)k(n))=cj=f(y/a((n),k(n),cj))q(a((n),k(n),cj))Lj=1f(y/a((n),k(n),cj))q(a((n),k(n),cj)),(21)a(,k,cj)Dk,Dkcj.(21)f(y/a((n),k(n),cj))q(a((n),k(n),cj))L.,LK.[(n),n0],.nkponk(cj)=f(y/a((k+nk),k,cj))q(a((k+nk),k,cj))Lj=1f(y/a((k+nk),k,cj))q(a((k+nk),k,cj)).(22)PDF,,pk(cj)=limN=1N+1pnk(cj).(23)k=Lj=1cjpok(cj)k=1,,K.(24).,.SpichakPC486,,5,,..1.6MT.,.,..,.Raiche[28](NN),NN,NN.,SpichakPopova[20](ANN).(BP),ANN.,ANN,ANN.ANN[2931].ANN:ANN;ANN;ANN;ANN,;ANN,ANN.SpichakPopova,,ANN,.,ANN:,.,,.2,,,..2.18121:,,,,.,,.,.2.2.,[8,32,33].,[34].,.2.3,,[35],;[36],;[37].,.[38],Tarantola[39]20,,.,,.[40][41],,,[42].,,,.(References):[1].[J].,2002,17(2):245254.[2]HohmannGW.There2dimensionalinducedpolarizationande2lectromagneticmodeling[J].Geophysics,1975,40(2):309324.[3]MackieRL,SmithJT,MaddenTR.There2dimensionale2lectromagneticmodelingusingdifferenceequations:Themag2netotelluricexample[J].RadioScience,1994,29(4):923935.[4]SmithJT.Conservativemodelingof32Delectromagneticfields,PartI:Propertiesanderroranalysis[J].Geophysics,1996,61(5):13081318.[5]SmithJT.Conservativemodelingof32Delectromagneticfields,PartII:Biconjugategradientsolutionandanaccelerator[J].Geophysics,1996,61(5):13191324.[6]RodiWL.Atechniqueforimprovetheaccuracyoffiniteele2mentsolutionformagnetotelluricdata[J].GeophyJRAstrSoc,1976,44:483506.[7].[J].,1981,20(3):8498.[8]WannamakerPE,StodtJA,RijoL.Two2dimensionaltopo2graphicresponsesinmagnetotelluricmodeledusingfiniteele2ments[J].Geophysics,1986,51(11):21312144.[9]MitsuhataY,UchidaT.3DmagnetotelluricmodelingusingtheT2finite2elementmethod[J].Geophysics,2004,69(1):108119.[10]WannamakerPE,HohmannGW,SanFilipoWA.Electro