共偏移距可分表示法叠前深度偏移
摘要
基于双平方根方程的共偏移距可分表示法叠前深度偏移用于复杂介质成像,该方法在中点-偏移距坐标中同时向下延拓炮点和检波点波场,实现方式采用正反傅立叶变换.构造的双平方根方程波场延拓算子能够使波数域变量与空间(速度)域变量分离,波数域内进行相移计算,在空间域对因介质横向变速引起的时移作修正.地震数据偏移不需要逐炮计算,具有较高的效率.对Marmousi模型数据的偏移成像结果显示,该方法较好地成像强横向变速介质中的复杂构造.
The offset-domain prestack depth migration with optimal separable approximation, based on the double square root equation, is applied to image complex media with large and rapid velocity variations. The method downward continues the source and the receiver wavefields simultaneously. The mixed domain algorithm with forward Fourier and inverse Fourier transform is used to construct the double square root equation wavefield extrapolation operator. This operator separates variables in the wave number domain and variables in the space domain. The phase operation is implemented in the wave number domain, while the time delay for lateral velocity variation is corrected in the space domain. The migration algorithm is efficient for the seismic data and it is not computed shot by shot. The data set test of the Marmousi model indicates that the offset-domain migration provides a satisfactory seismic migration section on which complex geologic structures are imaged in media with large and rapid lateral velocity variations.
The offset-domain prestack depth migration with optimal separable approximation, based on the double square root equation, is applied to image complex media with large and rapid velocity variations. The method downward continues the source and the receiver wavefields simultaneously. The mixed domain algorithm with forward Fourier and inverse Fourier transform is used to construct the double square root equation wavefield extrapolation operator. This operator separates variables in the wave number domain and variables in the space domain. The phase operation is implemented in the wave number domain, while the time delay for lateral velocity variation is corrected in the space domain. The migration algorithm is efficient for the seismic data and it is not computed shot by shot. The data set test of the Marmousi model indicates that the offset-domain migration provides a satisfactory seismic migration section on which complex geologic structures are imaged in media with large and rapid lateral velocity variations.
引文
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Chen,J.B.,Liu,H.,2004.Opti mization approxi mation withseparable variables for the one-way wave operator.Geo-physical Research Letters,31:L06613.
Chen,J.B.,Liu,H.,Zhang,Z.F.,2007.A separable-kerneldecomposition method for approxi mating the DSR con-tinuation operator.Geophysics,72:S25-S31.
Claerbout,J.F.,1985.I maging the earth's interior.BlackwellScientific publication,Oxford.
Gazdag,J.,1978.Wave-equation migration with the phaseshift method.Geophysics,43:1342-1351.
Jin,S.W.,Mosher,C.C.,Wu,R.S.,2002.Offset-domainpseudoscreen prestack depth migration.Geophysics,67:1895-1902.
Le Rousseau,J.H.,De Hoop,M.V.,2001.Modeling andi maging with the scalar generalized-screen algorithms inisotropic media.Geophysics,66:1551-1568.
Liu,L.N.,Zhang,J.F.,2006.3-D wavefield extrapolation with opti mum split-step Fourier method.Geophysics,71:T95-108.
Popovici,A.M.,1996.Prestack migration by split-step DSR.Geophysics,61:1412-1416.
Ristow,D.,Ruhl,T.,1994.Fourier finite-difference migra-tion.Geophysics,59:1882-1893.
Ristow,D.,Ruhl,T.,1997.3-Di mplicit finite-difference mi-gration by multi way-splitting.Geophysics,62:554-567.
Song,J.,2001.The opti mization expression of functions andmanifolds in high di mensions by ones in low di men-sions.Chin.Sci.Bull.,46:977-984(in Chinese)
Stoffa,P.L.,Fokkema,J.T.,Freire,R.M.,et al.,1990.Split-step Fourier migration.Geophysics,55:410-421.
Zhang,G.Q.,Zhang,Y.,Zhou,H.B.,2000.Helical finite-difference schemes for3-D depth migration.70th Ann.Internat.Mtg.Geophys.,Expanded Abstract,19:862-865.
Zhang,Z.F.,Liu,H.,Chen,J.B.,2005.I mplement of opti-mal separable approxi mation in seismic migration.Chi-nese Journal of Geophysics,48:1422-1427(in Chinesewith English abstract).
宋健,2001.高维函数和流形在低维可视空间中的最优表达.科学通报,46:977-984.
张致付,刘洪,陈景波,等,2005.地震偏移的最优可分近似算法实现.地球物理学报,48:1422-1427.
Chen,J.B.,Liu,H.,2004.Opti mization approxi mation withseparable variables for the one-way wave operator.Geo-physical Research Letters,31:L06613.
Chen,J.B.,Liu,H.,Zhang,Z.F.,2007.A separable-kerneldecomposition method for approxi mating the DSR con-tinuation operator.Geophysics,72:S25-S31.
Claerbout,J.F.,1985.I maging the earth's interior.BlackwellScientific publication,Oxford.
Gazdag,J.,1978.Wave-equation migration with the phaseshift method.Geophysics,43:1342-1351.
Jin,S.W.,Mosher,C.C.,Wu,R.S.,2002.Offset-domainpseudoscreen prestack depth migration.Geophysics,67:1895-1902.
Le Rousseau,J.H.,De Hoop,M.V.,2001.Modeling andi maging with the scalar generalized-screen algorithms inisotropic media.Geophysics,66:1551-1568.
Liu,L.N.,Zhang,J.F.,2006.3-D wavefield extrapolation with opti mum split-step Fourier method.Geophysics,71:T95-108.
Popovici,A.M.,1996.Prestack migration by split-step DSR.Geophysics,61:1412-1416.
Ristow,D.,Ruhl,T.,1994.Fourier finite-difference migra-tion.Geophysics,59:1882-1893.
Ristow,D.,Ruhl,T.,1997.3-Di mplicit finite-difference mi-gration by multi way-splitting.Geophysics,62:554-567.
Song,J.,2001.The opti mization expression of functions andmanifolds in high di mensions by ones in low di men-sions.Chin.Sci.Bull.,46:977-984(in Chinese)
Stoffa,P.L.,Fokkema,J.T.,Freire,R.M.,et al.,1990.Split-step Fourier migration.Geophysics,55:410-421.
Zhang,G.Q.,Zhang,Y.,Zhou,H.B.,2000.Helical finite-difference schemes for3-D depth migration.70th Ann.Internat.Mtg.Geophys.,Expanded Abstract,19:862-865.
Zhang,Z.F.,Liu,H.,Chen,J.B.,2005.I mplement of opti-mal separable approxi mation in seismic migration.Chi-nese Journal of Geophysics,48:1422-1427(in Chinesewith English abstract).
宋健,2001.高维函数和流形在低维可视空间中的最优表达.科学通报,46:977-984.
张致付,刘洪,陈景波,等,2005.地震偏移的最优可分近似算法实现.地球物理学报,48:1422-1427.
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