地震波散射非线性反演的不动点理论研究
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摘要
本文的工作聚焦于构造一种新的地震波散射非线性反演方法.文中将不动点理论引入到地震波散射非线性反演中,并具体的构造出了波的相空间里的一系列关于速度参数具体的压缩映射算子,从而从理论上保证了速度参数不动点的存在性和寻找途径.在此基础上文中还证明了利用此速度参数的不动点和正演所得到的相应的波的值也是波函数本身的不动点,并利用不动点的稳定属性得出此不动点是一个全局最优的点.
The paper gathers all ours attention to make a new method of nonlinear seismic scattering inversion. The paper provides a theory and method of how to introduce the fixed-point theory into the nonlinear seismic scattering inversion and how to obtain the solution, and gives the actually method to create a serials of contractive mappings of velocity parameter's in the mapping space of wave. Therefore, the results testify the existence of fixed point of velocity parameter and give the method the find it. Furthermore, the paper proves the conclusion that the value obtained by taking the fixed point of velocity parameter into wave equation is the fixed point of the wave of the contractive mapping. Thence, the fixed point is the global minima since the stabilities quality of the fixed point.
The paper gathers all ours attention to make a new method of nonlinear seismic scattering inversion. The paper provides a theory and method of how to introduce the fixed-point theory into the nonlinear seismic scattering inversion and how to obtain the solution, and gives the actually method to create a serials of contractive mappings of velocity parameter's in the mapping space of wave. Therefore, the results testify the existence of fixed point of velocity parameter and give the method the find it. Furthermore, the paper proves the conclusion that the value obtained by taking the fixed point of velocity parameter into wave equation is the fixed point of the wave of the contractive mapping. Thence, the fixed point is the global minima since the stabilities quality of the fixed point.
引文
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[3]杨文采.地球物理反演的理论与方法[M].北京:地质出版社,1997.YangWencai.Inversetheoryandmethodofgeophysics(In Chinese)[M].Geologypublishhouse,Beijing,1997.
[4]TarentolaA,ValatteB.Generalizednonlinearinverseprob lemssolvedusingtheleastsquarescriterion[J].Reviewof geophysicsspacephysics,1982,20:219～232.
[5]TarantolaA,ValetteB.Inverseproblems=questforinforma tion[J].JGeophys.1984,50:59～170.
[6]MoraP.Inversion=migration+tomography[J].Geophysics,1989,54(12),1575～1586.
[7]杨晓春,李小凡,张美根.地震波反演方法研究的某些进展及其数学基础[J].地球物理学进展,2001,16(4):96～109.YangXiaochun,LiXiaofan,ZhangMeigeng.Progressand mathematicsbasisofinvestigationsofseismicinversion[J].ProgressinGeophysics(InChinese),2001,16(4):96～109.
[8]IngberL.Geneticalgorithmsandveryfastsimulatedreanneal ing[A]:acomparison[C].MathlComputModeling.1992,16:87～100.
[9]DjurdjeC,JacekK.Taboosearch:anapproachtotheMulti pleminimaproblem[J].Science,1995,267(3):664～671.
[10]DeanVB,MichaelMM.TemporalInformationtransformed intoaspatialcodebyaNeuralNetworkwithrealisticproper ties[J].Science,1995,267(17):1028～1031.
[11]SambridgeMS.Geophysicalinversionwithaneighbourhood algorithm———I.Searchingaparameterspace[J].GeophysJ Int.,1999,138:479～494.
[12]SambridgeMS.Geophysicalinversionwithaneighbourhood algorithm———I.Appraisingtheensemble[J].GeophysJInt,1999,138:727～746.
[13]VoronoiMG.Nouvellesapplicationsdesparameterscontinue alatheoriedesformesquadratiques[J].JReineAngew.Math,1908,134:198～287.
[14]杨文采.波方程的逆散射与迭代线性化反演[J].石油物探,1995,34(3):114～122.YangWencai.Inversescatteringanditerativelinearinversion ofwaveequation[J].PetroleumandSubstanceProbation(in Chinese),1995,34(3):114～122.
[15]杨文采.非线性地震道反演方法的补充及比较[J].石油物探,1995,34(4):110～116.YangWencai.ComplementarityandCompareoftheNonlinear inversionmethodofseismictracks[J].PetroleumandSub stanceProbation(inChinese),1995,34(3):110～116.
[16]杨磊,张向君,李幼铭.地震到非线性反演的参数反馈控制及效果[J].地球物理学报,1999,42(5):677～684.YangLei,ZhangXiangjun,andLiYouming.Controlnonlin earinversionofseismictracks[J].ChineseJournalofGeo physics(InChinese),1999,42(5):677～684.
[17]SmartDR.FixedPointTheorems[M].London:Cambridge University,1980.
[18]SchechterM.Principlesoffunctionalanalysis[M].Academic Press,1971.
[19]顾本立.主编:杨文采,李幼铭.地球物理衍射CT[M].应用地震层析成像,北京:地震出版社,1993,70～110.GuBenli.Edt:YangWencai,LiYouming(InChinese).Dif fractionCTingeophysics[J].Appliedseismictomography.Beijing:Geologypublishhouse,1993,70～110.
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