波阻抗反演正则参数估计
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摘要
为了解决用正则化方法能够将波阻抗反演的病态问题转为良态问题 ,通过统计方法合理地选择正则参数的初值 ,在反演过程中用极大似然 (ML)方法实时进行正则参数值估计 ,提高反演收敛速度 ,改善反演结果 .同时 ,在具体反演中将正则化方法与快速模拟退火算法相结合 ,充分发挥正则参数作用 ,可以获得全局最优解 ,取得了好的实际应用效果 .
Using the regularization method,we can turn the ill-posed inverse problem into good-posed one. Through selecting reasonable initial regular parameter values by the statistic method and estimating regular parameter values by the maximum likelihood(ML)in the inverse procedure,the inverse result and convergent speed would be improved. Meanwhile,we combine the regularization and the fast simulated annealing algorithms,and make the regular parameters play its full role. This method can acquire a global optimum result and gain good applied effect.
Using the regularization method,we can turn the ill-posed inverse problem into good-posed one. Through selecting reasonable initial regular parameter values by the statistic method and estimating regular parameter values by the maximum likelihood(ML)in the inverse procedure,the inverse result and convergent speed would be improved. Meanwhile,we combine the regularization and the fast simulated annealing algorithms,and make the regular parameters play its full role. This method can acquire a global optimum result and gain good applied effect.
引文
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[15]刘 展,潘作枢.磁性下界面的正则化反演方法.物探与化探,1995,19(6):439～447LiuZ ,PanZS .Regularizedinversionofmagneticlowerinterface.Geophysical&GeochemicalExploration(inChinese),1995,19(6):439～447
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[19]DescombesX ,MorrisRD ,ZerubiaJ,etal.EstimationofMarkovrandomfieldpriorparametersusingMarkovchainMonteCarlomaximumlikelihood.IEEETransactionsonImageProcessing,1999,8(7):954～963
[20]Mohammad_DjafariA .OntheestimationofhyperparametersinBayesianapproachofsolvinginverseproblems.ProceedingofIEEEICASSP ,1993,2(4):567～571
[2]宋海斌,张关泉.层状介质弹性参数反演问题研究综述.地球物理学进展,1998,13(4):67～72SongHB ,ZhangGQ .Asummaryofinverseproblemresearchonelasticparametersstratifiedmedia.ProgressinGeophysics(inChinese),1998,13(4):67～72
[3]姚 姚.地球物理非线性反演模拟退火法的改进.地球物理学报,1995,38(5):643～650YaoY .Improvementonnonlineargeophysicalinversionsimulatedannealing.ChineseJ .Geophys.(ActaGeophysicaSinica)(inChinese),1995,38(5):643～650
[4]王山山,李灿平,李青仁等.快速模拟退火地震反演.地球物理报,1995,38(增1):123～134WangSS ,LiCP ,LiQR ,etal.Theseismicinversionusingthefastsimulatedannealingalgorithm.ChineseJ.Geophys.(ActaGeophysicaSinica)(inChinese),1995,38(Suppl.1):123～134
[5]王 ,王妙月,彭苏萍.地球物理随机联合反演.地球物理学报,1999,42(增1):142～151WangY ,WangMY ,PengSP .Stochasticjointinversioningeophysics.ChineseJ .Geophys.(inChinese),1999,42(Suppl.1):142～151
[6]尹 成,谢桂生,吕中育等.地震反演与非线性随机优化方法.物探化探计算技术,2001,23(1):6～10YinC ,XieGS ,LuZY ,etal.Seismicinversionandnon_linearstochasticoptimisticalgorithms.ComputingTechforGeophysical&GeochemicalExploration(inChinese),2001,23(1):6～10
[7]АН吉洪诺夫,ВЯ阿尔先宁著.不适定问题的解法.王秉忱译.北京:地质出版社,1979AHTиXOHOB ,BяAPCEHиH .Solutionsofill_posedproblems.WangBC ,Translation.Beijing:GeologicalPublishingHouse,1979
[8]张宏兵.超参数控制下的波阻抗约束反演[博士论文].北京:中国科学院地质与地球物理研究所,2002ZhangHB .Theimpedanceconstrainedinversemethodcontrollingbyregularizedparameters.[Ph.D .Thesis](inChinese).Beijing:InstituteofGeologyandGeophysics,ChineseAcademyofSciences,2002
[9]张宏兵,杨长春.正则参数控制下的波阻抗约束反演.地球物理学报,2003,46(6):827～834ZhangHB ,YangCC .Aimpedanceconstrainedinversionmethodcontrollingbyregularparameters.ChineseJ .Geophys.(inChinese),2003,46(6):827～834
[10]GemanD ,ReynoldsG .Constrainedrestorationandtherecoveryofdiscontinuities.IEEETransactionsonPatternAnalysisandMachineIntelligence,1992,14(3):367～383
[11]CharbonnierP ,F啨raudLB,AubertG ,etal.Deterministicedge_preservingregularizationincomputedimaging.IEEETransactionsonImageProcessing,1997,6(2):298～311
[12]王守东,刘家琦,黄文虎等.二维声波方程速度反演的一种方法.地球物理学报,1995,38(6):833～839 WangSD ,LiuJQ ,HuangWH ,etal.Amethodofvelocityinversionoftwodimensionacousticwaveequation.ChineseJ .Geophys.(ActaGeophysicaSinica)(inChinese),1995,38(6):833～839
[13]张文飞,李晓江.多参数反演的分步正则化法.石油地球物理勘探,1997,32(3):338～344ZhangWF ,LiXJ .Themulti_parametersinversionofsteppedregularization.OilGeophysicalProspecting(inChinese),1997,32(3):338～344
[14]刘 展,王万银.曲面位场的正则化线性规划法直接反演技术.地质与勘探,1999,35(6):62～66LiuZ ,WangWY .Amethodofregularizedlinearprogrammingapplyingtodirectlyinversionofpotentialfieldsonacurvedsurface.GeologyandProspecting(inChinese),1999,35(6):62～66
[15]刘 展,潘作枢.磁性下界面的正则化反演方法.物探与化探,1995,19(6):439～447LiuZ ,PanZS .Regularizedinversionofmagneticlowerinterface.Geophysical&GeochemicalExploration(inChinese),1995,19(6):439～447
[16]陆 璇编著.应用统计.北京:清华大学出版社,1999LuX .AppliedStatistics(inChinese).Beijing:TsinghuaUniversityPress,1999
[17]JalobeanuA ,Blanc_F啨raudL,ZerubiaJ .HyperparameterestimationforsatelliteimagerestorationbyaMCMCMLmethod.RapportdeRechercheINRIANo3469,1998
[18]GeyerCJ .MarkovchainMonteCarlomaximumlikelihood.SchoolofStatisticsUniv.ofMinnesotaMinneapolis,1993,MN55455
[19]DescombesX ,MorrisRD ,ZerubiaJ,etal.EstimationofMarkovrandomfieldpriorparametersusingMarkovchainMonteCarlomaximumlikelihood.IEEETransactionsonImageProcessing,1999,8(7):954～963
[20]Mohammad_DjafariA .OntheestimationofhyperparametersinBayesianapproachofsolvinginverseproblems.ProceedingofIEEEICASSP ,1993,2(4):567～571
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