补偿吸收衰减的高角度叠前深度偏移方法(英文)
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摘要
实际介质的吸收衰减使地震波能量减弱,主频降低,影响分辨率。在偏移过程中,可以实现吸收衰减的补偿,提高地震资料的分辨率。本文基于高角度时间-空间域单程波方程,推导出能补偿介质吸收衰减的叠前深度偏移波场外推公式。设计了一个复杂构造的地质模型,用声波方程模拟了无吸收衰减和有吸收衰减介质存在时的两种地震炮集记录。用没有补偿吸收衰减和本文讨论的补偿吸收衰减的偏移方法分别处理了两种地震资料,得到无吸收衰减、吸收衰减未得到补偿和得到补偿的三个偏移叠加剖面。补偿后的偏移剖面与没有吸收衰减的地震记录的偏移剖面几乎相同,而有吸收衰减的地震记录用无吸收衰减补偿的偏移方法处理,由于介质的吸收衰减,使吸收衰减层下方的反射信号衰减,主频降低,能量减弱。实际资料的处理结果表明,补偿吸收的偏移剖面的分辨率得到了明显改善。
The absorption effect of actual subsurface media can weaken wavefield energy, decrease the dominating frequency,and further lead to reduced resolution.In migration,some actions can be taken to compensate for the absorption effect and enhance the resolution.In this paper,we derive a one-way wave equation with an attenuation term based on the timespace domain high angle one-way wave equation.A complicated geological model is then designed and synthetic shot gathers are simulated with acoustic wave equations without and with an absorbing term.The derived one-way wave equation is applied to the migration of the synthetic gathers without and with attenuation compensation for the simulated shot gathers. Three migration profiles are obtained.The first and second profiles are from the shot gathers without and with attenuation using the migration method without compensation,the third one is from the shot gathers with attenuation using the migration method with compensation.The first and third profiles are almost the same,and the second profile is different from the others below the absorptive layers.The amplitudes of the interfaces below the absorptive layers are weak because of their absorption.This method is also applied to field data.It is concluded from the migration examples that the migration method discussed in this paper is feasible.
The absorption effect of actual subsurface media can weaken wavefield energy, decrease the dominating frequency,and further lead to reduced resolution.In migration,some actions can be taken to compensate for the absorption effect and enhance the resolution.In this paper,we derive a one-way wave equation with an attenuation term based on the timespace domain high angle one-way wave equation.A complicated geological model is then designed and synthetic shot gathers are simulated with acoustic wave equations without and with an absorbing term.The derived one-way wave equation is applied to the migration of the synthetic gathers without and with attenuation compensation for the simulated shot gathers. Three migration profiles are obtained.The first and second profiles are from the shot gathers without and with attenuation using the migration method without compensation,the third one is from the shot gathers with attenuation using the migration method with compensation.The first and third profiles are almost the same,and the second profile is different from the others below the absorptive layers.The amplitudes of the interfaces below the absorptive layers are weak because of their absorption.This method is also applied to field data.It is concluded from the migration examples that the migration method discussed in this paper is feasible.
引文
Baysal,E.,Kosloff,S.D.D.,and Sherwood,J.W.C,1984, ??A two-way nonreflecting wave equation:Geophysics,49, 132-141.
Berenger,J.P.,1994,A perfectly matched layer for the absorption of electromagnetic waves:Journal of Computational Physics,114(1),185-200.
Biondi B.Stable wide-angle Fourier-finite difference downward extrapolation of 3-D wavefields.Stanford Exploration Project,2000,Report 103,63 - 86.
Cerjan,C,Kosloff,D.,Kosloff,R.,and Moshe,R.,1985,A non- reflection boundary condition for discrete acoustic and elastic wave equation:Geophysics,50(4),705 - 708.
Chen,K.Y.,2010,Review of seismic reverse time migration methods:Progress in Exploration Geophysics (in Chinese),33(3),153-159.
Chen,W.,and Fang,W.B.,2003,Migration and imaging techniques:Progress in Exploration Geophysics(in Chinese),26(5-6),451-462.
Chen,S.C,and Ma,Z.T.,2006,High order generalized screen propagator for wave equation prestack depth migration:Chinese J.Geophys.(in Chinese),49(5),1445 -1451.
Chen,S.C,Ma,Z.T.,Wu,R.S.,2006,Local split step Fourier propagator for wave equation depth migration: Chinese Journal of Computational Physics(in Chinese), 23(5),604-608.
Coruh,C,Ruhi,S.,Demirbag,E.,and Costain,J.,1990, Estimation of Q-factor for spectral whitening:60th Internat.Mtg.,Soc.Explor.Geophys.,Expanded Abstracts,1082-1085.
Gazdag,J.,1978,Wave equation migration with the phase shift method:Geophysics,43,1342 - 1351.
Gazdag,J.,1984,Wave equation migration with the phase shift plus interpolation:Geophysics,49,124 - 231.
Guddati,M.N.,and Heidari,A.H.,2005,Migration with arbitrarily wide-angle wave equations:Geophysics, 70(3),S61-S70.
Hale,D.,1991,Stable explicit depth extrapolation of seismic wavefields:Geophysics,56,1770 - 1777.
Hargreaves,N.D.,and Calvet,A.J.,1991,Inverse Q filtering by Fourier transform:Geophysics,56(4),519 - 527.
He,Q.D.,1988,Seismic wave theory:Geological Publishing House,Beijing,115-139.
Holberg,O.,1987,Computational aspects of the choice of operator and interval for numerical differentiation in large-scale simulation of wave phenomena:Geophysical Prospecting,35,629 - 655.
Li,Z.C,and Wang,Q.Z.,2007,A review of research on mechanism of seismic attenuation and energy compensation:Progress in Geophysics(in Chinese), 22(4),1147-1152.
Loewenthal,D.,Stoffa,P.L.,and Faria,E.L.,1987, Suppressing the unwanted reflections of the full wave equation:Geophysics,52(7),1007- 1012.
Ma,Z.T.,1989,Seismic imaging technique—finite difference migration:Petroleum Industry Press,Beijing, 61-84.
Ma Z T.A splitting-up method for solution of higher-order migration equation by finite-difference scheme.Chinese J.Geophys.(in Chinese),1983,26(4):377 - 388.
Ma,S.F,and Li,Z.C,2007,Review of wave equation prestack depth migration methods:Progress in Exploration Geophysics(in Chinese),30(3),153-161.
McMechan,G.A.,1983,Migration by extrapolation of time-dependent boundary values:Geophysical Prospecting,31,412- 420.
Mittet,R.,Sollie,R.and Hokstad,K.,1995,Prestack depth migration with compensation for absorption and dispersion:Geophysics,60(5),1485 - 1494.
Mittet,R.,2007,A simple design procedure for depth extrapolation operators that compensate for absorption and dispersion:Geophysics,72(2),S105 - S112.
Mou,Y.G.,and Pei,Z.L.,2005,Seismic numerical modeling for 3-D complex media:Petroleum Industry Press,Beijing,35 - 36.
Mufti,R.,Pita,J.A.,and Huntley,R.W.,1996,Finite-difference depth migration of exploration-scale 3-D seismic data:Geophysics,61(3),776 - 794.
Ristow,D.,and R(u|¨)hl T.,1994,Fourier finite-difference migration:Geophysics,59(12),1882 - 1893.
Stoffa,P.L.,Fokkema,J.T.,Freire,D.L.,et al.,1990, Split-step Fourier migration:Geophysics,55,410-421.
Wang,Y.H.,2002,A stable and efficient approach of inverse Q filtering:Geophysics,67(2),657-663.
Wang,Y.H.,2006,Inverse Q-filter for seismic resolution enhancement:Geophysics,71(3),V51-V60.
Wang,Y.H.,2008,Inverse-Q filtered migration: Geophysics,73(1),S1-S6.
Wang,Z.L.,Zhou,H.,and Li,G.F.,2007,Inversion of ground penetrating radar data for 2D electric parameters. Chinese J.Geophys.(in Chinese),50(3),897-904.
Wu,R.S.,and De Hoop,M.N.,1996,Accuracy analysis and numerical tests of screen propagators for wave extrapolation:Mathematical Methods in Geophysical Imaging IV,SPIE,2822,196-209.
Yoon,K.,and Marfurt,K.J.,2006,Reverse-time migration using the Poynting vector:Exploration Geophysics,37, 102-107.
Zhang,M.G.,and Wang,M.Y.,2001,Prestack finite element reverse-time migration for anisotropic elastic waves:Chinese J.Geophys.(in Chinese),44(5),711- 718.
Zhang,L.B.,and Wang,H.Z.,2010,A stable inverse Q migration method:Geophysical Prospecting for Petroleum(in Chinese),49(2),115-120.
Zhou,H.,Sato,M.,and Liu,H.,2005,Migration velocity analysis and prestack migration of common-transmitter ground-penetrating radar data:IEEE Transactions on Geoscience and Remote Sensing,43(1),86-91.
Berenger,J.P.,1994,A perfectly matched layer for the absorption of electromagnetic waves:Journal of Computational Physics,114(1),185-200.
Biondi B.Stable wide-angle Fourier-finite difference downward extrapolation of 3-D wavefields.Stanford Exploration Project,2000,Report 103,63 - 86.
Cerjan,C,Kosloff,D.,Kosloff,R.,and Moshe,R.,1985,A non- reflection boundary condition for discrete acoustic and elastic wave equation:Geophysics,50(4),705 - 708.
Chen,K.Y.,2010,Review of seismic reverse time migration methods:Progress in Exploration Geophysics (in Chinese),33(3),153-159.
Chen,W.,and Fang,W.B.,2003,Migration and imaging techniques:Progress in Exploration Geophysics(in Chinese),26(5-6),451-462.
Chen,S.C,and Ma,Z.T.,2006,High order generalized screen propagator for wave equation prestack depth migration:Chinese J.Geophys.(in Chinese),49(5),1445 -1451.
Chen,S.C,Ma,Z.T.,Wu,R.S.,2006,Local split step Fourier propagator for wave equation depth migration: Chinese Journal of Computational Physics(in Chinese), 23(5),604-608.
Coruh,C,Ruhi,S.,Demirbag,E.,and Costain,J.,1990, Estimation of Q-factor for spectral whitening:60th Internat.Mtg.,Soc.Explor.Geophys.,Expanded Abstracts,1082-1085.
Gazdag,J.,1978,Wave equation migration with the phase shift method:Geophysics,43,1342 - 1351.
Gazdag,J.,1984,Wave equation migration with the phase shift plus interpolation:Geophysics,49,124 - 231.
Guddati,M.N.,and Heidari,A.H.,2005,Migration with arbitrarily wide-angle wave equations:Geophysics, 70(3),S61-S70.
Hale,D.,1991,Stable explicit depth extrapolation of seismic wavefields:Geophysics,56,1770 - 1777.
Hargreaves,N.D.,and Calvet,A.J.,1991,Inverse Q filtering by Fourier transform:Geophysics,56(4),519 - 527.
He,Q.D.,1988,Seismic wave theory:Geological Publishing House,Beijing,115-139.
Holberg,O.,1987,Computational aspects of the choice of operator and interval for numerical differentiation in large-scale simulation of wave phenomena:Geophysical Prospecting,35,629 - 655.
Li,Z.C,and Wang,Q.Z.,2007,A review of research on mechanism of seismic attenuation and energy compensation:Progress in Geophysics(in Chinese), 22(4),1147-1152.
Loewenthal,D.,Stoffa,P.L.,and Faria,E.L.,1987, Suppressing the unwanted reflections of the full wave equation:Geophysics,52(7),1007- 1012.
Ma,Z.T.,1989,Seismic imaging technique—finite difference migration:Petroleum Industry Press,Beijing, 61-84.
Ma Z T.A splitting-up method for solution of higher-order migration equation by finite-difference scheme.Chinese J.Geophys.(in Chinese),1983,26(4):377 - 388.
Ma,S.F,and Li,Z.C,2007,Review of wave equation prestack depth migration methods:Progress in Exploration Geophysics(in Chinese),30(3),153-161.
McMechan,G.A.,1983,Migration by extrapolation of time-dependent boundary values:Geophysical Prospecting,31,412- 420.
Mittet,R.,Sollie,R.and Hokstad,K.,1995,Prestack depth migration with compensation for absorption and dispersion:Geophysics,60(5),1485 - 1494.
Mittet,R.,2007,A simple design procedure for depth extrapolation operators that compensate for absorption and dispersion:Geophysics,72(2),S105 - S112.
Mou,Y.G.,and Pei,Z.L.,2005,Seismic numerical modeling for 3-D complex media:Petroleum Industry Press,Beijing,35 - 36.
Mufti,R.,Pita,J.A.,and Huntley,R.W.,1996,Finite-difference depth migration of exploration-scale 3-D seismic data:Geophysics,61(3),776 - 794.
Ristow,D.,and R(u|¨)hl T.,1994,Fourier finite-difference migration:Geophysics,59(12),1882 - 1893.
Stoffa,P.L.,Fokkema,J.T.,Freire,D.L.,et al.,1990, Split-step Fourier migration:Geophysics,55,410-421.
Wang,Y.H.,2002,A stable and efficient approach of inverse Q filtering:Geophysics,67(2),657-663.
Wang,Y.H.,2006,Inverse Q-filter for seismic resolution enhancement:Geophysics,71(3),V51-V60.
Wang,Y.H.,2008,Inverse-Q filtered migration: Geophysics,73(1),S1-S6.
Wang,Z.L.,Zhou,H.,and Li,G.F.,2007,Inversion of ground penetrating radar data for 2D electric parameters. Chinese J.Geophys.(in Chinese),50(3),897-904.
Wu,R.S.,and De Hoop,M.N.,1996,Accuracy analysis and numerical tests of screen propagators for wave extrapolation:Mathematical Methods in Geophysical Imaging IV,SPIE,2822,196-209.
Yoon,K.,and Marfurt,K.J.,2006,Reverse-time migration using the Poynting vector:Exploration Geophysics,37, 102-107.
Zhang,M.G.,and Wang,M.Y.,2001,Prestack finite element reverse-time migration for anisotropic elastic waves:Chinese J.Geophys.(in Chinese),44(5),711- 718.
Zhang,L.B.,and Wang,H.Z.,2010,A stable inverse Q migration method:Geophysical Prospecting for Petroleum(in Chinese),49(2),115-120.
Zhou,H.,Sato,M.,and Liu,H.,2005,Migration velocity analysis and prestack migration of common-transmitter ground-penetrating radar data:IEEE Transactions on Geoscience and Remote Sensing,43(1),86-91.
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