地震波反演方法研究的某些进展及其数学基础
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摘要
以地震波反演为背景 ,对非线性反演问题的某些最新进展做了系统的分析和介绍 ;着重对地震波反演理论中一些主要方法发展过程中的数学、物理的基本理论和基本假设做了分析、讨论和总结 ,而非面面俱到的阐述地震波反演理论本身的发展状况 .在此基础上 ,讨论了地震波反演问题的数学研究基础和所面临的问题及假设应注重的方面 ,并对较强烈地下介质物性异常所造成的非弱散射的反演问题做了分析和展望
On the background of research into the seismic inversion, new progress of the nonlinear inverse is introduced in this paper. Especially, the development, basic theories and assumptions on some major theories of seismic inversion are analyzed, discussed and summarized in mathematics and physics. Also, the problems faced by the mathematical basis of investigations of the seismic inversion are discussed, and inverse questions of strongly seismic scattering due to strong heterogeneous media in the Earth interior are analyzed and viewed.
On the background of research into the seismic inversion, new progress of the nonlinear inverse is introduced in this paper. Especially, the development, basic theories and assumptions on some major theories of seismic inversion are analyzed, discussed and summarized in mathematics and physics. Also, the problems faced by the mathematical basis of investigations of the seismic inversion are discussed, and inverse questions of strongly seismic scattering due to strong heterogeneous media in the Earth interior are analyzed and viewed.
引文
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[2] BackusGE ,GilbertJF .Theresolvingpowerofgrossearthdata[J].Geophys.J .R .astr.1968,16:169～205.
[3] BackusGE ,GilbertJF .Uniquenessintheinversionofinaccurategrossearthdata[J].Phil.TransRoy,1970,A266:123～192.
[4] AkiK ,RichardsPG .Quantativeseismologytheoryandmethods[J].FreemanandCompany,VolII ,Chapter12,
[5] OldenburgDW .Acomprehensivesolutiontothelineardeconvolutionproblem[J].Geophys.J.R .astr,1981,65:331～358.
[6] CookeDA ,SchneiderWA .Generalizedinversionofreflectionseismicdata[J].Geophys.,1983,48:665～676.
[7] HutsonV ,PymJS .Applicationoffunctionalanalysisandoperatortheory[M].AcademicPress,1980.
[8] TarentolaA ,ValatteB .Generalizednonlinearinverseproblemssolvedusongtheleastsquarescriterion[J].Reviewofgeophysicsspacephysics,1982,20:219～232.
[9] CohenJK ,etal.Three-dimensionalBorninversionwithanarbitraryreference[J].Geophys,Vol.51,1986,51:1552～1558.
[10] 杨文采.地球物理反演的理论与方法[M].北京:地质出版社,1997.
[11] ChernovLevA .Wavepropagationinarandommedium[M].IN :NewYork:McGRAW HillBookCompany,1960.
[12] WingginsRA .Thegeneralizedlinearinverseproblem:Implicationofsurfacewavesandfreeoscillationsforearthstructure[J].Rev.Geophys.SpacePhys.1972,10:251～285.
[13] JacksonDD .Interpretationofinaccurate,insufficient,andinconsistentdata[J].Geophys.J.R .astr,1972,28:97～109.
[14] 杨文采.非线性波动方程地震反演的方法及问题[J].地球物理学进展,1992,7(1):9～19.
[15] MoraP .Nonlineartwo-dimensionalelasticinversionofmulti-offsetseismicdata[J].Geophysics,1987,52:1211～1228.
[16] 黄联捷,杨文采.声波方程逆散射反演的近似方法[J].地球物理学报,1991,34(5):626～634.
[17] 杨文采.地震波场反演的BG 逆散射方法[J].地球物理学报,1995,38(5):358～361.
[18] MoraP .Inversion=migration+tomography[J].Geophysics,1989,54(12),1575～1586.
[19] 栾文贵,李幼铭.我国地球物理反演问题研究的某些进展[J].地球物理学报,1990,33:501～508.
[20] GubernatisJE ,DomanyE ,KrumhanslJA ,etal.TheBornapproximationintheoryofthescatteringofelasticwavesbyflaws[J].J .Appl.Phys.,1977,48(7),2812～2819.
[21] HudsonJA ,HeritageJR .TheuseoftheBornapproximationinseismicscatteringproblems[J].Geophys.J.R .astr.1981,66:221～240.
[22] RubramaniamDR ,GeorgeVF .AcomparisonbetweentheBornandRytovapproximationsfortheinversebackscatteringproblem[J].Geophysics,1989,54:864～871.
[23] ShenY ,YangWC .ApplicationofthegeneralizedRadontransformtoprestackseismicdataprotections[J].ChineseJ .Geophys.1992,35:97～110.
[24] 马兴瑞,陶良,黄文虎.弹性波反演方法及其应用[M].北京:科学出版社,1999.
[25] 杨文采,李幼铭.应用地震层析成像[M].北京:地震出版社,1993.
[26] LangenbergKJ.Introductiontothespecialissueoninverseproblems[J].WaveMotion,1989,11(4):99～112.
[27] ClaytonRW ,StoltRH .ABornWKBJinversionmethodforacousticreflectiondata[J].Geophysics,1981,46(11):1559～1567.
[28] ChapmanCH .Raytheoryanditsextensions:WKBJandMaslo vseimograms[J].JGeophys.,1985,58:27～43.
[29] FengK .DifferentialschemesforHamiltonianformalismandsymplecticgeometry[J].J.compu.Math.1986,4(3):279～289.
[30] 高 亮,李幼铭,陈旭容,杨孔庆.地震射线辛几何算法初探[J].地球物理学报,2000,43(3):402～409.
[31] BelykinG .TheinversionproblemandapplicationsofthegeneralizedRadentransform[J].Comm.Pure&AppliedMath.,1984,37:579～599.
[32] 王 云.非线性随即反演方法及其在地球物理联合反演中的应用[D].北京:中国科学院地球物理研究所博士学位论文,1998.
[33] 袁亚湘,孙文瑜.最优化理论与方法[M].北京:科学出版社,1997.
[34] PrattRG ,etal.GaussNewtonandfullNewtonmethodsinfrequency space[A].In:Seismicwaveforminversion[C].zhenlixiedebugou,1995.
[35] WangCS ,TangJ ,ZhaoB .AnimprovementonDdormdeconvolution:afastalgorithmandtherelatedprocedure[J].Geophys.1991,56(5):635～644.
[36] CryerCW .NumericalFunctionalanalysis[M].Iondon:ClarendonPressOxford,1982.
[37] SchechterM .Principlesoffunctionalanalysis[M].AcademicPress,1971.
[38] 李世雄,刘家琦.小波变换和反演数学基础[M].北京:地质出版社,1994.
[39] 侯遵译,杨文采.中国重力异常的小波变换与多尺度分析[J].地球物理学报,1997,40(1):122～132.
[40] MichelenaRJ ,HarrisJM .Tomographytraveltimeinversionusingnaturalpixels[J].Geophysics,1991:56(5):675～680.
[41] BartholomewBiggsMC .theestimationoftheHessianmatrixinnonlinearleastsquaresproblemswithnon zeroresiduals[J].Math.Prog.,1977,12(1):67～80.
[42] FletcherR .Anexactpenaltyfunctionfornonlinearforconstrainedoptimization[J].J .Inst.Math.Prog.,1973,(5):129～150.
[43] PowellMJD .Restartprocedurefortheconjugategradientmethod[J].Math.Prog.,1977:12:241～254.
[44] PhilipsDL .AtechniquefortheNumericalsolutionofcertainintegralequationofthefirstkind[J].J .ACM .1962,9:84～97.
[45] GroetchCW .ThetheoryofTikhonovRegularizationforFredholmintegralequationsofthefirstkind[M].PitmanBoston,1984.
[46] ScherzerO .ConvergenceratesofiteratedTikhonovRegularizedsolutionofnonlinearIII posedproblems[J].Numer.Math.,1993,66:259～279.
[47] HanB ,YouJH ,LiuJQ .Adesecrate typecontinuationregularizationmethodanditsapplication[J].J.HarbinInst,Tech.,1995,E 2(1):5～9&10～14.
[48] 陈开舟,党创寅,杨再福.不动点理论和算法[M].西安:西安电子科技大学出版社,1990.
[49] CowiePA .,VannesteC .&SornetteD .Statisticalphysicsmodelforthespatiotempralevolutionoffaults[J].J .Geophys.Res.,1993,98:21809～21821.
[50] RothmanD .H .Nonlinearinversion,statisticalmechanics,andresidualstaticsestimation[J].Geophysics,1985,50(12):2797～2807;2784～2796.
[51] TarantolaA ,ValetteB .Inverseproblems=questforinformation[J].J .Geophys.1982:50:159～170.
[52] TarantolaA .Linearizedinversionofseismicreflectiondata[J].Geophys.Prosp.1884,32:998～1015.
[53] TarantolaA .inversionofseismicreflectiondataintheacousticapproximation[J].Geophysics,1984,49:1259～1266.
[54] TarantolaA .Astrategyfornonlinearelasticinversionofseismicreflectiondata[J].Geophysics,1986,51:1893～1903.
[55] GauthierO ,VirieuxJ ,TarantolaA .Two dimensionalnonlinearinversionofseismicwaveforms:numericalresults[J].Geo physics,1986,51(7):1387～1403.
[56] MosegaardK ,TarantolaA .MonteCarlosamplingofsolutionstoinverseproblems[J].J .Geophys.Res.,1995,100(7):12431～12447.
[57] SzuH ,HartleyR .Fastsimulatedannealing[J].PhysicsLetterA ,1987,122(3):157～162.
[58] KirkpatrickS ,GelattJrCD ,VecchiMP .Optimizationbysimulatedannealing[J].Science,1983,220(4598):671～680.
[59] IngberL .Geneticalgorithmsandveryfastsimulatedreannealing:acomparison[J].MathlComputModeling,1992,16(3):87～100.
[60] DeanVB ,MichaelMM .TemporalInformationtransformedintoaspatialcodebyaNeuralNetworkwithrealisticproperties[J].Science,1995,267(17):1028～1031.
[61] DjurdjeC ,JacekK .Taboosearch:anapproachtotheMultipleminimaproblem[J].Science,1995,267(3):664～671.
[62] SambridgeMS .BraunandMcQueenH .Geophysicalparametrizationandinterpolationofirregulardatausingnaturalneighbours[J].Geophys.J.Int.,1995,122:837～857.
[63] KennettBLN ,SambridgeMS ,WilliamsonPR .Subspacemethodsforinverseproblemswithmultipleparameterclasses[J].Geo phys.J .Int.,1995,94:237～247.
[64] KennettBLN .OnthedensitydistributionwithintheEarth[J].Geophys.J.Int.,19 ,132:374～382.
[65] SambridgeMS ,GudmundssonO .Tomographicofequationswithirregularcells[J].J.Geophys.Res.,1998:103:773～781.
[66] SambridgeMS .Geophysicalinversionwithaneighbourhoodalgorithm—I .Searchingaparameterspace[J].Geophys.J .Int.,1999,138:479～494.
[67] SambridgeMS .Geophysicalinversionwithaneighbourhoodalgorithm—I .Appraisingtheensemble[J].Geophys.J .Int.,1999,138:727～746.
[68] VoronoiMG .Nouvellesapplicationsdesparameterscontinuesalatheoriedesformesquadratiques[J].JreineAngew.Math.,1998,134:198～287.
[69] WatsonDF .NaturalNeighbourSorting[J].AustralianComput.J .1985,17:189～193.
[70] KennettBLN ,SambridgeMS .Inversionformultipleparameterclasses[J].Geophys.J .Int.1998,135:304～306.
[71] MandelbrotBB .ThefractalGeometryofnature[M].NewYork,NY :W .H .Freeman&Co,1967.
[72] 陈.分形和分维在地球科学中的应用[M].北京:学术期刊出版社,1988.
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