VTI介质迭代正则化偏移反演算法
|
摘要
VTI介质地震数据成像的关键问题之一是解决反问题的不适定性,特别是当正演算子的伴随算子无法对其逆算子充分逼近时,可以采用迭代偏移反演方法求取更精确的逆算子。本文研究了VTI介质地震偏移反演成像的计算方法,导出了偏移成像算子方程,并提出了固定点迭代正则化算法。该方法是一种改进的迭代正则化算法,与一般的迭代正则化方法相比,无需矩阵分解,具有更高的计算效率。本文对典型模型数据进行了数值模拟,并对实际数据进行了试验性处理,结果表明,该偏移反演成像方法在地震成像领域具有一定的应用前景。
One of the key issues of seismic imaging in VTI media is to solve ill-posed inverse problems,especially when the inverse operator of a modelingoperator cannot be approximated sufficiently by its adjoint.We first discuss in this paper algorithms of migration inversion imaging,which is based on a different strategy from the conventional seismic migration,in VTI media.Then we derive an operator equation of migration,and propose the fixpoint iterative(F PI)regularization migration inversion algorithm.FPI is more computational efficient than conventionally regularization methods,because matrix decompositions are no longer needed in the algorithm.In order to verify the feasibility of our new method,we perform tests on both synthetic and field seismic data.The results show that applications of the fixpoint iteration migration inversion obtain higher data S/N ratio and higher accuracy of seismic imaging than conventional approaches.
One of the key issues of seismic imaging in VTI media is to solve ill-posed inverse problems,especially when the inverse operator of a modelingoperator cannot be approximated sufficiently by its adjoint.We first discuss in this paper algorithms of migration inversion imaging,which is based on a different strategy from the conventional seismic migration,in VTI media.Then we derive an operator equation of migration,and propose the fixpoint iterative(F PI)regularization migration inversion algorithm.FPI is more computational efficient than conventionally regularization methods,because matrix decompositions are no longer needed in the algorithm.In order to verify the feasibility of our new method,we perform tests on both synthetic and field seismic data.The results show that applications of the fixpoint iteration migration inversion obtain higher data S/N ratio and higher accuracy of seismic imaging than conventional approaches.
引文
[1]Tsvankin I.Seismic Signatures and Analysis of Reflection Data in Anisotropic Media.Oxford:PERGAMON,2001.
[2]Tsvankin I,Gaiser J,Grechka V et al.Seismic anisotropy in exploration and reservoir characterization:An overview.Geophysics,2010,75(5):75A15-75A29.
[3]Sarkar D and Tsvankin I.Migration velocity analysisin factorized VTI media.Geophysics,2004,69(3):708-718.
[4]Tarantola A.Inversion of seismic reflection data inthe acoustic approximation.Geophysics,1984,49(8):1259-1266.
[5]Cole S and Karrenbach M.Least squares Kirchhoffmigration.SEP,1992,75:101-110.
[6]Schuster G T.Least-squares crosswell migration.SEG Technical Program Expanded Abstracts,1993,12:110-113.
[7]Nemeth T,Wu C J and Schuster G T.Least-squaresmigration of incomplete reflection data.Geophysics,1999,64(1):208-221.
[8]Ronen S,Nichols D,Bale R et al.Dealiasing DMO:good-pass,bad-pass and unconstrained.SEG Technical Program Expanded Abstracts,1995,14:743-746.
[9]Duquet B.Improving seismic imaging in complex geologic structures[D].Univ of Paris XIII,1996.
[10]Mittet R,Hokstad K,Helgesen J et al.Imaging offset VSP data with an elastic iterative migrationscheme.Geophysical Prospecting,1997,45(2):247-268.
[11]Sevink A and Herman G.Fast iterative solution ofsparsely sampled seismic inverse problems.InverseProblems,1994,10(4):937-948.
[12]Lecomte I and Gelius L J.Have a look at the resolution of prestack depth migration for any model,survey and wavefields.SEG Technical Program Expanded Abstracts,1998,17:1112-1115.
[13]Gelius L J,Lecomte I and Tabti H.Analysis of theresolution function in seismic prestack depth imaging.Geophysical Prospecting,2002,50(5):505-515.
[14]Hu J X,Schuster G T and Valasek P A.Poststackmigration deconvolution.Geophysics,2001,66(3):939-952.
[15]Yu J H,Hu J X and Schuster G T.Prestack migrationdeconvolution.Geophysics,2006,71(2):S53-S62.
[16]Sacchi M D et al.Regularized migration/inversion:New generation of seismic imaging algorithm.CSEGRecorder,2006,Special Edition:54-59.
[17]王彦飞,杨长春,段秋梁.地震偏移反演成像的迭代正则化方法研究.地球物理学报,2009,52(6):1615-1624.Wang Yanfei,Yang Changchun and Duan Qiuliang.On iterative regulation methods for migration deconvolution and inversion in seismic imaging.ChineseJournal of Geophysics,2009,52(6):1615-1624.
[18]Wang Y F and Yang C C.Accelerating migration deconvolution using a nonmonotone gradient method.Geophysics,2010,75(4):131-137.
[19]Cerven■ V.Seismic Ray Theory.Cambridge:Cambridge University Press,2001.
[20]Thomsen L.Weak elastic anisotropy.Geophysics,1986,51(10):1954-1966.
[21]孙成禹.地震波理论与方法.山东东营:中国石油大学出版社,2007.
[22]Alkhalifah T.Acoustic approximations for processingin transversely isotropic media.Geophysics,1998,63(2):623-631.
[23]Alkhalifah T.An acoustic wave equation for anisotropic media.Geophysics,2000,65(4):1239-1250.
[24]Alkhalifah T.Traveltime computation with the linearized eikonal equation for anisotropic media.Geophysical Prospecting,2002,50(4):373-382.
[25]王彦飞等.地球物理数值反演问题.北京:高等教育出版社,2011.
[26]Bleistein N,Cohen J K and Stockwell J W.Mathematics of Multidimensional Seismic Imaging,Migration,and Inversion.New York:Springer,2000.
[27]王彦飞.反演问题的计算方法及其应用.北京:高等教育出版社,2007.
[28]马在田.论反射地震偏移成像.勘探地球物理进展,2002,25(3):631~635.Ma Zaitian.On reflection seismic migration imaging.Progress in Exploration Geophysics,2002,25(3):631-635.
[29]王彦飞.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.地球物理学报,2013,56(1):230-238.Wang Y F.Comparison of interferometric migrationand preconditioned regularizing least squares migration inversion methods in seismic imaging.ChineseJournal of Geophysics,2013,56(1):230-238.
[30]Dai W,Fowler P and Schuster G T.Multi-sourceleast-squares reverse time migration.GeophysicalProspecting,2012,60(4):681-695.
[31]Wang Y F,Li Z H and Yang C C.Seismic Migrationand Inversion,in Computational Methods for AppliedInverse Problems(Inverse and Ill-Posed Problems Series 56).De Gruyter,2012,439-474.
[32]Wang Y F,Yagola A G and Yang C C eds.Optimization and Regularization for Computational InverseProblems and Applications(1st Edition).Berlin-Heidelberg:Springer,2011.
[33]Schoenberg M and Helbig K.Orthorhombic media:Modeling elastic wave behavior in a vertically fractured earth.Geophysics,1997,62(6):1954-1974.
[34]Psencik I and Farra V.First-order P-wave ray synthetic seismograms in inhomogeneous weakly anistropic media.Geophysical Journal International,2007,170(3):1243-1252.
[2]Tsvankin I,Gaiser J,Grechka V et al.Seismic anisotropy in exploration and reservoir characterization:An overview.Geophysics,2010,75(5):75A15-75A29.
[3]Sarkar D and Tsvankin I.Migration velocity analysisin factorized VTI media.Geophysics,2004,69(3):708-718.
[4]Tarantola A.Inversion of seismic reflection data inthe acoustic approximation.Geophysics,1984,49(8):1259-1266.
[5]Cole S and Karrenbach M.Least squares Kirchhoffmigration.SEP,1992,75:101-110.
[6]Schuster G T.Least-squares crosswell migration.SEG Technical Program Expanded Abstracts,1993,12:110-113.
[7]Nemeth T,Wu C J and Schuster G T.Least-squaresmigration of incomplete reflection data.Geophysics,1999,64(1):208-221.
[8]Ronen S,Nichols D,Bale R et al.Dealiasing DMO:good-pass,bad-pass and unconstrained.SEG Technical Program Expanded Abstracts,1995,14:743-746.
[9]Duquet B.Improving seismic imaging in complex geologic structures[D].Univ of Paris XIII,1996.
[10]Mittet R,Hokstad K,Helgesen J et al.Imaging offset VSP data with an elastic iterative migrationscheme.Geophysical Prospecting,1997,45(2):247-268.
[11]Sevink A and Herman G.Fast iterative solution ofsparsely sampled seismic inverse problems.InverseProblems,1994,10(4):937-948.
[12]Lecomte I and Gelius L J.Have a look at the resolution of prestack depth migration for any model,survey and wavefields.SEG Technical Program Expanded Abstracts,1998,17:1112-1115.
[13]Gelius L J,Lecomte I and Tabti H.Analysis of theresolution function in seismic prestack depth imaging.Geophysical Prospecting,2002,50(5):505-515.
[14]Hu J X,Schuster G T and Valasek P A.Poststackmigration deconvolution.Geophysics,2001,66(3):939-952.
[15]Yu J H,Hu J X and Schuster G T.Prestack migrationdeconvolution.Geophysics,2006,71(2):S53-S62.
[16]Sacchi M D et al.Regularized migration/inversion:New generation of seismic imaging algorithm.CSEGRecorder,2006,Special Edition:54-59.
[17]王彦飞,杨长春,段秋梁.地震偏移反演成像的迭代正则化方法研究.地球物理学报,2009,52(6):1615-1624.Wang Yanfei,Yang Changchun and Duan Qiuliang.On iterative regulation methods for migration deconvolution and inversion in seismic imaging.ChineseJournal of Geophysics,2009,52(6):1615-1624.
[18]Wang Y F and Yang C C.Accelerating migration deconvolution using a nonmonotone gradient method.Geophysics,2010,75(4):131-137.
[19]Cerven■ V.Seismic Ray Theory.Cambridge:Cambridge University Press,2001.
[20]Thomsen L.Weak elastic anisotropy.Geophysics,1986,51(10):1954-1966.
[21]孙成禹.地震波理论与方法.山东东营:中国石油大学出版社,2007.
[22]Alkhalifah T.Acoustic approximations for processingin transversely isotropic media.Geophysics,1998,63(2):623-631.
[23]Alkhalifah T.An acoustic wave equation for anisotropic media.Geophysics,2000,65(4):1239-1250.
[24]Alkhalifah T.Traveltime computation with the linearized eikonal equation for anisotropic media.Geophysical Prospecting,2002,50(4):373-382.
[25]王彦飞等.地球物理数值反演问题.北京:高等教育出版社,2011.
[26]Bleistein N,Cohen J K and Stockwell J W.Mathematics of Multidimensional Seismic Imaging,Migration,and Inversion.New York:Springer,2000.
[27]王彦飞.反演问题的计算方法及其应用.北京:高等教育出版社,2007.
[28]马在田.论反射地震偏移成像.勘探地球物理进展,2002,25(3):631~635.Ma Zaitian.On reflection seismic migration imaging.Progress in Exploration Geophysics,2002,25(3):631-635.
[29]王彦飞.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.地球物理学报,2013,56(1):230-238.Wang Y F.Comparison of interferometric migrationand preconditioned regularizing least squares migration inversion methods in seismic imaging.ChineseJournal of Geophysics,2013,56(1):230-238.
[30]Dai W,Fowler P and Schuster G T.Multi-sourceleast-squares reverse time migration.GeophysicalProspecting,2012,60(4):681-695.
[31]Wang Y F,Li Z H and Yang C C.Seismic Migrationand Inversion,in Computational Methods for AppliedInverse Problems(Inverse and Ill-Posed Problems Series 56).De Gruyter,2012,439-474.
[32]Wang Y F,Yagola A G and Yang C C eds.Optimization and Regularization for Computational InverseProblems and Applications(1st Edition).Berlin-Heidelberg:Springer,2011.
[33]Schoenberg M and Helbig K.Orthorhombic media:Modeling elastic wave behavior in a vertically fractured earth.Geophysics,1997,62(6):1954-1974.
[34]Psencik I and Farra V.First-order P-wave ray synthetic seismograms in inhomogeneous weakly anistropic media.Geophysical Journal International,2007,170(3):1243-1252.
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