地震波干涉偏移及预条件正则化最小二乘偏移成像方法对比
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摘要
地震波干涉偏移和偏移反演成像是近年来十分活跃的两个研究领域.干涉偏移提供了一个新的地震波数据成像工具,而偏移反演则提供了高逼近度地震成像.二者的共同目的是改善传统直接偏移方法的成像效果,展宽成像区域并提高成像的分辨率.本文研究干涉偏移方法和偏移反演方法对于地震成像效果的影响,探讨二者在提高成像分辨率上的异同.对于偏移反演,通过建立正则化模型,研究了预条件共轭梯度迭代正则化方法及改进措施,并通过绕射点模型数值模拟验证了该方法比直接偏移能够提高振幅的保真度和成像的分辨率.对于干涉偏移和偏移反演这两种方法,对层速度地震模型进行了数值模拟.结果表明干涉偏移和偏移反演成像方法比传统的偏移方法在成像效果上是更加有效的,因而对于实际的地震成像问题很有应用前景.
Interferometric migration and migration inversion are two active research fields in seismic imaging.The interferometric migration supplies us a new tool for seismic data imaging,while the migration inversion supplies us an improved resolution of imaging of seismic data.Both methods aim to improve the performance of the traditional migration imaging tool.In this paper,we consider comparison of the interferometric migration with the migration inversion.For migration inversion,we consider regularization techniques and propose a preconditioning regularized conjugate gradient method,numerical simulations on diffraction point models verify that the regularization method could yield higher resolution and more accurate amplitude than the traditional migration technique.To show the potential for application of these methods,we perform synthetic seismic data imaging.Numerical experiments based on layered velocity model are developed.The numerical results indicate that both methods are useful for seismic migration imaging and may be used for practice in the future.
Interferometric migration and migration inversion are two active research fields in seismic imaging.The interferometric migration supplies us a new tool for seismic data imaging,while the migration inversion supplies us an improved resolution of imaging of seismic data.Both methods aim to improve the performance of the traditional migration imaging tool.In this paper,we consider comparison of the interferometric migration with the migration inversion.For migration inversion,we consider regularization techniques and propose a preconditioning regularized conjugate gradient method,numerical simulations on diffraction point models verify that the regularization method could yield higher resolution and more accurate amplitude than the traditional migration technique.To show the potential for application of these methods,we perform synthetic seismic data imaging.Numerical experiments based on layered velocity model are developed.The numerical results indicate that both methods are useful for seismic migration imaging and may be used for practice in the future.
引文
[1]Claerbout J.Synthesis of a layered medium from its acoustictransmission response.Geophysics,1968,33(2):264-269.
[2]Bakulin A,Calvert R.Virtual source:New method forimaging and 4D below complex overburden.74th AnnualInternational Meeting,SEG,Expanded Abstracts,2004:2477-2480.
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[6]Schuster G T,Katz L,Followill F,et al.Autocorrelogrammigration:Theory.Geophysics,2003,68(5):1685-1694.
[7]Snieder R,Grêt A,Douma H,et al.Coda wave interferometryfor estimating nonlinear behavior in seismic velocity.Science,2002,295(5563):2253-2255.
[8]Wang Y B,Luo Y,Schuster G T.Interferometric interpolationof missing seismic data.Geophysics,2009,74(3):SI37-SI45.
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[11]Wapenaar K,Fokkema J.Green′s function representationsfor seismic interferometry.Geophysics,2006,71(4):SI33-SI46.
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[14]Hu J X,Schuster G T,Valasek P A.Poststack migrationdeconvolution.Geophysics,2001,66(3):939-952.
[15]Nemeth T,Wu C J,Schuster G T.Least-squares migrationof incomplete reflection data.Geophysics,1999,64(1):208-221.
[16]Sjberg T A,Gelius L J,Lecomte I.2Ddeconvolution ofseismic image blur.Expanded Abstracts,SEG 73th AnnualMeeting,Dallas,2003.
[17]王彦飞,斯捷潘诺娃I E,提塔连科V N等.地球物理数值反演问题[全球变化与地球系统科学系列].北京:高等教育出版社,2011.Wang Y F,Stepanova I E,Titarenko V N,et al.InverseProblems in Geophysics and Solution Methods[Series inGlobal Change and Earth System Science].Beijing:HigherEducation Press,2011.
[18]Wang Y F,Yang C C.Accelerating migration deconvolutionusing a non-monotone gradient method.Geophysics,2010,75(4):S131-S137.
[19]Aki K,Richards P G.Quantitative Seismology:Theory andMethods.San Francisco:W H Freeman and Company,1980.
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[22]Lecomte I.Resolution and illumination analyses in PSDM:Aray-based approach.The Leading Edge,2008,27(5):650-663.
[23]Guitton A.Amplitude and kinematic corrections of migratedimages for nonunitary imaging operators.Geophysics,2004,69(4):1017-1024.
[24]Sacchi M D,Wang J,Kuehl H.Regularized migration/inversion:new generation of imaging algorithms.CSEGRecorder,2006,31(S1):54-59.
[25]Wang Y F.Preconditioning non-monotone gradient methodfor retrieval of seismic reflection signals.Advances inComputational Mathematics,2012,36(2):353-376.
[26]Marquardt D W.An algorithm for least-squares estimation ofnonlinear parameters.SIAM J.Appl.Math.,1963,11(2):431-441.
[27]Levenberg K.A method for the solution of certain nonlinearproblems in least squares.Quart.Appl.Math.,1944,2:164-166.
[28]崔岩,王彦飞,杨长春.带先验知识的波阻抗反演正则化方法研究.地球物理学报,2009,52(8):2135-2141.Cui Y,Wang Y F,Yang C C.Regularizing method with apriori knowledge for seismic impedance inversion.Chinese J.Geophys.(in Chinese),2009,52(8):2135-2141.
[29]李振华,王彦飞,杨长春.正则化偏移成像的全局优化快速算法.地球物理学报,2011,54(3):828-834.Li Z H,Wang Y F,Yang C C.A fast global optimizationalgorithm for regularized migration imaging.Chinese J.Geophys.(in Chinese),2011,54(3):828-834.
[30]Wang Y F,Yuan Y X.Convergence and regularity of trustregion methods for nonlinear ill-posed inverse problems.Inverse Problems,2005,21(3):821-838.
[31]Tarantola A.Inverse Problems Theory:Methods for DataFitting and Model Parameter Estimation.Amsterdam:Elsevier,1987.
[32]Ulrych T J,Sacchi M D,Woodbury A.A Bayesian tour toinversion.Geophysics,2000,66:55-69.
[33]杨文采.地球物理反演和地震层析成像.北京:地质出版社,1989.Yang W C.Geophysical Inversion and Seismic Tomography(in Chinese).Beijing:Geological Publishing House,1989.
[34]王彦飞.反演问题的计算方法及其应用[当代科学前沿论丛].北京:高等教育出版社,2007.Wang Y F.Computational Methods for Inverse Problems andTheir Applications[New Frontiers of Sciences](in Chinese).Beijing:Higher Education Press,2007.
[35]Nolet G.Solving or resolving inadequate and noisytomographic systems.J.Comp.Phys.,1985,61(3):463-482.
[36]Nolet G,Snieder R.Solving large linear inverse problems byprojection.Geophys.J.Int.,1990,103(2):565-568.
[37]VanDecar J C,Snieder R.Obtaining smooth solutions tolarge,linear,inverse problems.Geophysics,1994,59(5):818-829.
[38]Trampert J,Leveque J J.Simultaneous iterative reconstructiontechnique:physical interpretation based on the generalizedleast squares solution.Journal of Geophysical Research,1990,95(B9):12553-12559.
[39]陶毅,符力耘,孙伟家等.地震波干涉法研究进展综述.地球物理学进展,2010,25(5):1775-1784.Tao Y,Fu L Y,Sun W J,et al.A review of seismicinterferometry.Progress in Geophysics(in Chinese),2010,25(5):1775-1784.
[40]Yilmaz O.Seismic Data Analysis.Investigations in GeophysicsNo.10.Society of Exploration Geophysicists,Tulsa,Okla,2001.
[41]Chen J,Schuster G T.Resolution limits of migrated images.Geophysics,1999,64(4):1046-1053.
[42]Schuster G T.Green′s functions for migration.Abstracts ofExpanded Abstracts 67th SEG meeting,1997:1754-1758.
[43]Schuster G T,Hu J X.Green′s function for migration:Continuous recording geometry.Geophysics,2000,65(1):167-175.
[44]Yu J H,Hu J X,Schuster G T,Estill R.Prestack migrationdeconvolution.Geophysics,2006,71(2):S53-S62.
[45]Tikhonov A N,Arsenin V Y.Solutions of Ill-posedProblems.New York:John Wiley and Sons,1977.
[46]Engl H W,Hanke M,Neubauer A.Regularization ofInverse Problems.Dorcrecht:Kluwer Academic Publishers,1996.
[47]袁亚湘.非线性规划数值方法.上海:上海科学与技术出版社,1993.Yuan Y X.Numerical Methods for Nonlinear Programming(in Chinese).Shanghai:Shanghai Science and TechnologyPress,1993.
[48]肖庭延,于慎根,王彦飞.反问题的数值解法[计算方法丛书].北京:科学出版社,2003.Xiao Y F,Yu S G,Wang Y F.Numerical Methods for theSolution of Inverse Problems[Series in Numerical Methods](in Chinese).Beijing:Science Press,2003.
[2]Bakulin A,Calvert R.Virtual source:New method forimaging and 4D below complex overburden.74th AnnualInternational Meeting,SEG,Expanded Abstracts,2004:2477-2480.
[3]常旭,刘伊克,王辉等.地震相干偏移与数据自参照偏移的关系.地球物理学报,2009,52(11):2840-2845.Chang X,Liu Y K,Wang H,et al.Seismic interferometricmigration and data-referenced-only migration.Chinese J.Geophys.(in Chinese),2009,52(11):2840-2845.
[4]He R Q,Hornby B,Schuster G.3D wave-equationinterferometric migration of VSP free-surface multiples.Geophysics,2007,72(5):S195-S203.
[5]Schuster G T,Yu J,Sheng J,Rickett J.Interferometric/daylight seismic imaging.Geophysical Journal International,2004,157(2):838-852.
[6]Schuster G T,Katz L,Followill F,et al.Autocorrelogrammigration:Theory.Geophysics,2003,68(5):1685-1694.
[7]Snieder R,Grêt A,Douma H,et al.Coda wave interferometryfor estimating nonlinear behavior in seismic velocity.Science,2002,295(5563):2253-2255.
[8]Wang Y B,Luo Y,Schuster G T.Interferometric interpolationof missing seismic data.Geophysics,2009,74(3):SI37-SI45.
[9]Wapenaar K.Retrieving the elastodynamic Green′s functionof an arbitrary inhomogeneous medium by cross correlation.Physics Review Letters,2004,93(25):254301-1-254301-4.
[10]Wapenaar K,Draganov D,Robertsson J O A,et al.SeismicInterferometry:History and Present Status.GeophysicsReprint Series No.26,Society of Exploration Geophysicists,2008.
[11]Wapenaar K,Fokkema J.Green′s function representationsfor seismic interferometry.Geophysics,2006,71(4):SI33-SI46.
[12]Yu J H,Katz L,Followill F,et al.Autocorrelogrammigration:IVSPWD test.Geophysics,2003,68(1):297-307.
[13]Yu J H,Schuster G T.Crosscorrelogram migration ofinverse vertical seismic profile data.Geophysics,2006,71(1):S1-S11.
[14]Hu J X,Schuster G T,Valasek P A.Poststack migrationdeconvolution.Geophysics,2001,66(3):939-952.
[15]Nemeth T,Wu C J,Schuster G T.Least-squares migrationof incomplete reflection data.Geophysics,1999,64(1):208-221.
[16]Sjberg T A,Gelius L J,Lecomte I.2Ddeconvolution ofseismic image blur.Expanded Abstracts,SEG 73th AnnualMeeting,Dallas,2003.
[17]王彦飞,斯捷潘诺娃I E,提塔连科V N等.地球物理数值反演问题[全球变化与地球系统科学系列].北京:高等教育出版社,2011.Wang Y F,Stepanova I E,Titarenko V N,et al.InverseProblems in Geophysics and Solution Methods[Series inGlobal Change and Earth System Science].Beijing:HigherEducation Press,2011.
[18]Wang Y F,Yang C C.Accelerating migration deconvolutionusing a non-monotone gradient method.Geophysics,2010,75(4):S131-S137.
[19]Aki K,Richards P G.Quantitative Seismology:Theory andMethods.San Francisco:W H Freeman and Company,1980.
[20]Claerbout J F.Imaging the Earth′s Interior.Oxford:Blackwell,1985.
[21]Stolt R H,Benson A K.Seismic Migration:Theory andPractice,Vol.5,Handbook of Geophysical Exploration,Section I.Seismic Exploration.London:Geophysical Press,1986.
[22]Lecomte I.Resolution and illumination analyses in PSDM:Aray-based approach.The Leading Edge,2008,27(5):650-663.
[23]Guitton A.Amplitude and kinematic corrections of migratedimages for nonunitary imaging operators.Geophysics,2004,69(4):1017-1024.
[24]Sacchi M D,Wang J,Kuehl H.Regularized migration/inversion:new generation of imaging algorithms.CSEGRecorder,2006,31(S1):54-59.
[25]Wang Y F.Preconditioning non-monotone gradient methodfor retrieval of seismic reflection signals.Advances inComputational Mathematics,2012,36(2):353-376.
[26]Marquardt D W.An algorithm for least-squares estimation ofnonlinear parameters.SIAM J.Appl.Math.,1963,11(2):431-441.
[27]Levenberg K.A method for the solution of certain nonlinearproblems in least squares.Quart.Appl.Math.,1944,2:164-166.
[28]崔岩,王彦飞,杨长春.带先验知识的波阻抗反演正则化方法研究.地球物理学报,2009,52(8):2135-2141.Cui Y,Wang Y F,Yang C C.Regularizing method with apriori knowledge for seismic impedance inversion.Chinese J.Geophys.(in Chinese),2009,52(8):2135-2141.
[29]李振华,王彦飞,杨长春.正则化偏移成像的全局优化快速算法.地球物理学报,2011,54(3):828-834.Li Z H,Wang Y F,Yang C C.A fast global optimizationalgorithm for regularized migration imaging.Chinese J.Geophys.(in Chinese),2011,54(3):828-834.
[30]Wang Y F,Yuan Y X.Convergence and regularity of trustregion methods for nonlinear ill-posed inverse problems.Inverse Problems,2005,21(3):821-838.
[31]Tarantola A.Inverse Problems Theory:Methods for DataFitting and Model Parameter Estimation.Amsterdam:Elsevier,1987.
[32]Ulrych T J,Sacchi M D,Woodbury A.A Bayesian tour toinversion.Geophysics,2000,66:55-69.
[33]杨文采.地球物理反演和地震层析成像.北京:地质出版社,1989.Yang W C.Geophysical Inversion and Seismic Tomography(in Chinese).Beijing:Geological Publishing House,1989.
[34]王彦飞.反演问题的计算方法及其应用[当代科学前沿论丛].北京:高等教育出版社,2007.Wang Y F.Computational Methods for Inverse Problems andTheir Applications[New Frontiers of Sciences](in Chinese).Beijing:Higher Education Press,2007.
[35]Nolet G.Solving or resolving inadequate and noisytomographic systems.J.Comp.Phys.,1985,61(3):463-482.
[36]Nolet G,Snieder R.Solving large linear inverse problems byprojection.Geophys.J.Int.,1990,103(2):565-568.
[37]VanDecar J C,Snieder R.Obtaining smooth solutions tolarge,linear,inverse problems.Geophysics,1994,59(5):818-829.
[38]Trampert J,Leveque J J.Simultaneous iterative reconstructiontechnique:physical interpretation based on the generalizedleast squares solution.Journal of Geophysical Research,1990,95(B9):12553-12559.
[39]陶毅,符力耘,孙伟家等.地震波干涉法研究进展综述.地球物理学进展,2010,25(5):1775-1784.Tao Y,Fu L Y,Sun W J,et al.A review of seismicinterferometry.Progress in Geophysics(in Chinese),2010,25(5):1775-1784.
[40]Yilmaz O.Seismic Data Analysis.Investigations in GeophysicsNo.10.Society of Exploration Geophysicists,Tulsa,Okla,2001.
[41]Chen J,Schuster G T.Resolution limits of migrated images.Geophysics,1999,64(4):1046-1053.
[42]Schuster G T.Green′s functions for migration.Abstracts ofExpanded Abstracts 67th SEG meeting,1997:1754-1758.
[43]Schuster G T,Hu J X.Green′s function for migration:Continuous recording geometry.Geophysics,2000,65(1):167-175.
[44]Yu J H,Hu J X,Schuster G T,Estill R.Prestack migrationdeconvolution.Geophysics,2006,71(2):S53-S62.
[45]Tikhonov A N,Arsenin V Y.Solutions of Ill-posedProblems.New York:John Wiley and Sons,1977.
[46]Engl H W,Hanke M,Neubauer A.Regularization ofInverse Problems.Dorcrecht:Kluwer Academic Publishers,1996.
[47]袁亚湘.非线性规划数值方法.上海:上海科学与技术出版社,1993.Yuan Y X.Numerical Methods for Nonlinear Programming(in Chinese).Shanghai:Shanghai Science and TechnologyPress,1993.
[48]肖庭延,于慎根,王彦飞.反问题的数值解法[计算方法丛书].北京:科学出版社,2003.Xiao Y F,Yu S G,Wang Y F.Numerical Methods for theSolution of Inverse Problems[Series in Numerical Methods](in Chinese).Beijing:Science Press,2003.
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