目标函数叠前保幅偏移方法与应用
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摘要
将理论反射率与偏移反射率的差作为目标函数,给出一种迭代振幅补偿保幅偏移方法.把偏移看作一个反问题,寻找反问题中的最优解.偏移算子是正演算子的伴随共轭,其伴随矩阵非对角占优.通过预条件优化伴随矩阵,使Hessian矩阵准对角化.依据地震波传播稳定相位理论,计算反射点,以反射点为中心、菲涅耳带为半径偏移.考虑振幅几何扩散补偿、散射角度补偿,在迭代反演过程求出最优解,即保幅偏移解.本文给出了一个保幅数值模拟结果和一个实际地震数据实例.
An iterative migrated method is developed by building a misfit function between the observed seismic data and forward modeling synthetic data.A weight function is used to compensate the amplitude attenuation for seismic wave transmitting in the earth.We consider migration as an inversion problem and find an optimal solution in the inversion.The migrated operator is the adjoint of forward modeling operator,and the transpose matrix is not dominant diagonal matrix.A preconditioning matrix is applied to make the Hessian matrix a diagonal approximation.Take-off and incidence angles are estimated for locating at the reflected points by applying stationary phase,which decreases greatly computing costs.An optimal solution,which is a true amplitude,is obtained in the process of iteration by considering the weighted factors to compensate the amplitude spreading and the angle effects with offset.Two numerical examples effectively illustrate the results of amplitude preserved and a case of field data is presented.
An iterative migrated method is developed by building a misfit function between the observed seismic data and forward modeling synthetic data.A weight function is used to compensate the amplitude attenuation for seismic wave transmitting in the earth.We consider migration as an inversion problem and find an optimal solution in the inversion.The migrated operator is the adjoint of forward modeling operator,and the transpose matrix is not dominant diagonal matrix.A preconditioning matrix is applied to make the Hessian matrix a diagonal approximation.Take-off and incidence angles are estimated for locating at the reflected points by applying stationary phase,which decreases greatly computing costs.An optimal solution,which is a true amplitude,is obtained in the process of iteration by considering the weighted factors to compensate the amplitude spreading and the angle effects with offset.Two numerical examples effectively illustrate the results of amplitude preserved and a case of field data is presented.
引文
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[2]Clayton R W,Stolt R H.A Born-WKBJ inversion method foracoustic reflection data.Geophysics,1981,46:1559~1567
[3]Cohen J K,Hagin F G,Bleistein N.Three dimensional Borninversion with an arbitrary reference.Geophysics,1986,51:1552~1558
[4]Bleistein N.On the imaging of reflectors in the earth.Geophysics,1987,52:931~942
[5]Miller D,Oristaglio M,Beylkin G.A new slant on seismic imaging:Migration and integral geometry.Geophysics,1987,52:943~964
[6]Beylkin G,Burridge R.Linearized inverse scattering problem inacoustics and elasticity.Wave Motion,1990,12:15~52
[7]Tarantola A.Linearized inversion of seismic reflection data.Geophys.Prosp.,1984,32:998~1005
[8]Nemeth T,Wu C,Schuster G T.Least-squares migration ofincomplete reflection data.Geophysics,1999,64(1):208~221
[9]Chavent G,Plessix R.An optimal true-amplitude least-squaresprestack depth-migration operator.Geophysics,1999,64(2):508~515
[10]Kuhl H,Saachi M D.Least-squares wave-equation migration forAVP/AVA inversion.Geophysics,2003,68(1):262~273
[11]Liu Y,Sun H,Chang X.Least-squares wave-path migration.Geophysical Prospecting,2005,53:811~816
[12]Claerbout J.Processing and Inversion.Blackwell Publ.,D F.1992
[13]Paige C C,Saunders M A.LSQR:Sparse linear equations and leastsquares problems.ACM Transactions Mathematics,1982,8:195~209
[14]Cerveny V,Molotkov I A,Psencik I.Ray Method in Seismology,Iniverzita Karlova,Praha.1977
[2]Clayton R W,Stolt R H.A Born-WKBJ inversion method foracoustic reflection data.Geophysics,1981,46:1559~1567
[3]Cohen J K,Hagin F G,Bleistein N.Three dimensional Borninversion with an arbitrary reference.Geophysics,1986,51:1552~1558
[4]Bleistein N.On the imaging of reflectors in the earth.Geophysics,1987,52:931~942
[5]Miller D,Oristaglio M,Beylkin G.A new slant on seismic imaging:Migration and integral geometry.Geophysics,1987,52:943~964
[6]Beylkin G,Burridge R.Linearized inverse scattering problem inacoustics and elasticity.Wave Motion,1990,12:15~52
[7]Tarantola A.Linearized inversion of seismic reflection data.Geophys.Prosp.,1984,32:998~1005
[8]Nemeth T,Wu C,Schuster G T.Least-squares migration ofincomplete reflection data.Geophysics,1999,64(1):208~221
[9]Chavent G,Plessix R.An optimal true-amplitude least-squaresprestack depth-migration operator.Geophysics,1999,64(2):508~515
[10]Kuhl H,Saachi M D.Least-squares wave-equation migration forAVP/AVA inversion.Geophysics,2003,68(1):262~273
[11]Liu Y,Sun H,Chang X.Least-squares wave-path migration.Geophysical Prospecting,2005,53:811~816
[12]Claerbout J.Processing and Inversion.Blackwell Publ.,D F.1992
[13]Paige C C,Saunders M A.LSQR:Sparse linear equations and leastsquares problems.ACM Transactions Mathematics,1982,8:195~209
[14]Cerveny V,Molotkov I A,Psencik I.Ray Method in Seismology,Iniverzita Karlova,Praha.1977
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