正则参数控制下的波阻抗约束反演
|
摘要
通过势函数方式将波阻抗反演的病态问题转为良态问题 ,并且给出了边界保护势函数所具备的条件 .在反演过程中 ,通过改变正则参数数值以及合理地选择正则参数的初值 ,改善反演结果 ,提高反演收敛速度 .同时 ,在具体反演中使用快速模拟退火算法 ,可以克服目标函数局部极值的限制 ,从而获得全局最优解 .通过理论模型试算和实际资料处理 ,说明本文方法具有精度高、实用性强的特点 .
Using the potential function method,we turn the ill-posed inversion problem into good-posed one,and provide the conditions of the edge-preserving potential function. Through changing regularized parameter values and selecting a reasonable initial regularized parameter value in inversion procedure,the inversion result and convergent speed are improved. Meanwhile,we use a fast simulation annealing algorithm in the inversion,which can overcome the limitation of the local extremum of objective function,and acquire a global optimum result. Through calculating in theoretic model and applying to the field data,it is proved that this method has the advantage of high precision and practicability.
Using the potential function method,we turn the ill-posed inversion problem into good-posed one,and provide the conditions of the edge-preserving potential function. Through changing regularized parameter values and selecting a reasonable initial regularized parameter value in inversion procedure,the inversion result and convergent speed are improved. Meanwhile,we use a fast simulation annealing algorithm in the inversion,which can overcome the limitation of the local extremum of objective function,and acquire a global optimum result. Through calculating in theoretic model and applying to the field data,it is proved that this method has the advantage of high precision and practicability.
引文
[1] 杨文采.地球物理反演的理论与方法.北京:地质出版社,1997YANGWencai.TheTheoryandMethodofGeophysicalInversion.Beijing:GeologicalPublishingHouse,1997
[2] Tarantola.InverseProblemTheory.Amsterdam:Elsevier,1987
[3] 张宏彬,何樵登.宽带约束反演.石油物探,1995,34(1):1～10ZHANGHongbin,HEQiaodeng.Thebroad bandconstrainedinver sion.GeophysicalProspectingforPetroleum(inChinese),1995,34(1):1～10
[4] 纪 晨,姚振兴.用于地球物理反演的均匀设计优化算法.地球物理学报,1996,39(2):233～241JIChen,YAOZhenxing.Theuniformdesignoptimizedmethodforgeophysicsinversionproblem.ChineseJ.Geophys.(ActaGeophysicaSinica),1996,39(2):233～241
[5] 艾印双,刘鹏程,郑天愉等.自适应全局混合反演.中国科学(D辑),1998,28(2):105～110AIYinshuang,LIUPengcheng,ZHENGTianyu,etal.Theglobalself accommodatecompoundinversion.ScienceinChina(SeriesD ),1998,28(2):105～110
[6] 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,1979АНТихонов,ВЯАрсенин.Solutionsofill posedproblems.Bytrans.WANGBingchen.Beijing:GeologicalPublishingHouse,1979
[7] 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):833～839WANGShoudong,LIUJiaqi,HUANGWenhu,etal.Amethodofve locityinversionoftwodimensionacousticwaveequation.ChineseJ .Geophys.(ActaGeophysicaSinica),1995,38(6):833～839
[8] 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):338～344ZHANGWenfei,LIXiaojiang.Themulti parametersinversionofsteppedregularization.OilGeophysicalProspecting(inChinese),1997,32(3):338～344
[9] DemomentG .Imagereconstructionandrestoration:overviewofcom monestimationstructuresandproblems.IEEETrans.Acoust.,Speech,SignalProcessing,1989,37(11)
[10] GemanD ,ReynoldsG .Constrainedrestorationandtherecoveryofdiscontinuities.IEEETransactionsonPatternAnalysisandMachineIntelligence,1992,14(3)
[11] BoumanC ,SauerK .AgeneralizedGaussianimagemodelforedge pr eservingMAPestimation.IEEETrans.ImageProcessing,1993,2(7):296～310
[12] HebertT ,LeahyR .AgeneralizedEMalgorithmfor3DBayesianre constructionfrompoissondatausingGibbspriors.IEEETrans.Med.Image.,1990,MI 8(6):194～202
[13] CharbonnierP ,F啨raudLB,AubertG ,etal.Deterministicedge pre servingregularizationincomputedimaging.IEEETransactionsonIm ageProcessing,1997,6(2)
[14] MetropolisN ,RosenbluthAW ,RosenbluthMN ,etal.Equationofstatecalculationsbyfastcomputermachines.JournalofChemicalPhysics,1953,21:1087～1091
[15] KirkpatrickS ,GelattCD ,JrVecchiMP ,etal.Optimizationbysimu latedannealing.Science,1983,220:671～680
[16] RothmanDH .Automaticestimationoflargeresidualstaticcorrec tions.Geophysics,1986,50:2784～2796
[17] 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):643～650YAOYao.Improvementonnonlineargeophysicalinversionsimulatedannealing.ChineseJ .Geophys.(ActaGeophysicaSinica),1995,38(5):643～650
[18] 王山山,李灿平,李青仁等.快速模拟退火地震反演.地球物理学报,1995,38(Suppl.1):123～134WANGShanshan,LICanping,LIQingren,etal.Theseismicinversionusingthefastsimulatedannealingalgorithm.ChineseJ.Geophys.(ActaGeophysicaSinica),1995,38(Suppl.1):123～134
[19] 张霖斌,姚振兴,纪 晨等.快速模拟退火算法及应用.石油地球物理勘探,1997,32(5):654～659ZHANGLinbin,YAOZhenxing,JIChen,etal.Thefastsimulatedan nealingalgorithmanditsapplication.OilGeophysicalProspecting(inChinese),1997,32(5):654～659
[20] 伊 成,周熙襄,钟本善等.热槽法模拟退火分析及其改进.石油物探,1998,37(1):63～70YINCheng,ZHOUXixiang,ZHONGBenshan,etal.Theanalysisandimprovementofthesimulatedannealingabouttheheatbathmethod.GeophysicalProspectingforPetroleum(inChinese),1998,37(1):63～70
[21] 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,2002ZHANGHongbing.Theimpedanceconstrainedinversemethodcon trollingbyregularizedparameters[Ph.D .thesis].Beijing:InstituteofGeologyandGeophysics,ChineseAcademyofSciences,2002
[2] Tarantola.InverseProblemTheory.Amsterdam:Elsevier,1987
[3] 张宏彬,何樵登.宽带约束反演.石油物探,1995,34(1):1～10ZHANGHongbin,HEQiaodeng.Thebroad bandconstrainedinver sion.GeophysicalProspectingforPetroleum(inChinese),1995,34(1):1～10
[4] 纪 晨,姚振兴.用于地球物理反演的均匀设计优化算法.地球物理学报,1996,39(2):233～241JIChen,YAOZhenxing.Theuniformdesignoptimizedmethodforgeophysicsinversionproblem.ChineseJ.Geophys.(ActaGeophysicaSinica),1996,39(2):233～241
[5] 艾印双,刘鹏程,郑天愉等.自适应全局混合反演.中国科学(D辑),1998,28(2):105～110AIYinshuang,LIUPengcheng,ZHENGTianyu,etal.Theglobalself accommodatecompoundinversion.ScienceinChina(SeriesD ),1998,28(2):105～110
[6] 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,1979АНТихонов,ВЯАрсенин.Solutionsofill posedproblems.Bytrans.WANGBingchen.Beijing:GeologicalPublishingHouse,1979
[7] 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):833～839WANGShoudong,LIUJiaqi,HUANGWenhu,etal.Amethodofve locityinversionoftwodimensionacousticwaveequation.ChineseJ .Geophys.(ActaGeophysicaSinica),1995,38(6):833～839
[8] 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):338～344ZHANGWenfei,LIXiaojiang.Themulti parametersinversionofsteppedregularization.OilGeophysicalProspecting(inChinese),1997,32(3):338～344
[9] DemomentG .Imagereconstructionandrestoration:overviewofcom monestimationstructuresandproblems.IEEETrans.Acoust.,Speech,SignalProcessing,1989,37(11)
[10] GemanD ,ReynoldsG .Constrainedrestorationandtherecoveryofdiscontinuities.IEEETransactionsonPatternAnalysisandMachineIntelligence,1992,14(3)
[11] BoumanC ,SauerK .AgeneralizedGaussianimagemodelforedge pr eservingMAPestimation.IEEETrans.ImageProcessing,1993,2(7):296～310
[12] HebertT ,LeahyR .AgeneralizedEMalgorithmfor3DBayesianre constructionfrompoissondatausingGibbspriors.IEEETrans.Med.Image.,1990,MI 8(6):194～202
[13] CharbonnierP ,F啨raudLB,AubertG ,etal.Deterministicedge pre servingregularizationincomputedimaging.IEEETransactionsonIm ageProcessing,1997,6(2)
[14] MetropolisN ,RosenbluthAW ,RosenbluthMN ,etal.Equationofstatecalculationsbyfastcomputermachines.JournalofChemicalPhysics,1953,21:1087～1091
[15] KirkpatrickS ,GelattCD ,JrVecchiMP ,etal.Optimizationbysimu latedannealing.Science,1983,220:671～680
[16] RothmanDH .Automaticestimationoflargeresidualstaticcorrec tions.Geophysics,1986,50:2784～2796
[17] 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):643～650YAOYao.Improvementonnonlineargeophysicalinversionsimulatedannealing.ChineseJ .Geophys.(ActaGeophysicaSinica),1995,38(5):643～650
[18] 王山山,李灿平,李青仁等.快速模拟退火地震反演.地球物理学报,1995,38(Suppl.1):123～134WANGShanshan,LICanping,LIQingren,etal.Theseismicinversionusingthefastsimulatedannealingalgorithm.ChineseJ.Geophys.(ActaGeophysicaSinica),1995,38(Suppl.1):123～134
[19] 张霖斌,姚振兴,纪 晨等.快速模拟退火算法及应用.石油地球物理勘探,1997,32(5):654～659ZHANGLinbin,YAOZhenxing,JIChen,etal.Thefastsimulatedan nealingalgorithmanditsapplication.OilGeophysicalProspecting(inChinese),1997,32(5):654～659
[20] 伊 成,周熙襄,钟本善等.热槽法模拟退火分析及其改进.石油物探,1998,37(1):63～70YINCheng,ZHOUXixiang,ZHONGBenshan,etal.Theanalysisandimprovementofthesimulatedannealingabouttheheatbathmethod.GeophysicalProspectingforPetroleum(inChinese),1998,37(1):63～70
[21] 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,2002ZHANGHongbing.Theimpedanceconstrainedinversemethodcon trollingbyregularizedparameters[Ph.D .thesis].Beijing:InstituteofGeologyandGeophysics,ChineseAcademyofSciences,2002
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心