相空间中的保真振幅偏移
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摘要
在三维地震资料叠前偏移中,平面波偏移的成像效果可以等价于共炮点偏移,但计算效率却能成倍提高。此外,保真振幅偏移可以得到地下反射层的相对强度,获得品质更好的地下结构图像,为储层分析提供定量信息。基于这种考虑,针对平面波的保真振幅偏移进行了系统的研究。引人Maslov理论,利用τ-ρ变换将数据从空间(s,r,t)分别变换到(P~s,r,τ)和(s,p~r,τ)及(p~s,p~r,τ)空间中,并将其结合到Born反演中,推导出了相空间偏移算子振幅的高频渐近解。基于Marmousi复杂地质模型的模拟计算结果表明,平面波的保真振幅偏移在合理的计算量条件下可以得到高品质的地下结构图像。
In 3D pre-stack depth migration of seismic data,the imaging effect of plane wave is equal to that of common shot migration; however,the computational efficiency has been significantly im- proved.In addition,the true amplitude scheme in migration can provide relative intensity for reflectors,which can further improve the imaging quality of subsurface structures and offer quantitative information for reservoir analysis.For the consideration,the true amplitude migration for plane wave was systematically studied.In this paper,the Maslov theory was introduced.Byτ-p transform, seismic data is transformed from(s,γ,τ)space to(p~s,γ,τ),(s,p~r,τ)and phase(p~s,p~r,τ)space.Then it is combined with Born in- version,and deduce the high-frequency asymptotic solution of mi- gration operator amplitude in phase domain.The numerical compu- tation results based on complex geologic model show that the true amplitude migration can obtain high-quality subsurface structure maps with reasonable computation amount.
In 3D pre-stack depth migration of seismic data,the imaging effect of plane wave is equal to that of common shot migration; however,the computational efficiency has been significantly im- proved.In addition,the true amplitude scheme in migration can provide relative intensity for reflectors,which can further improve the imaging quality of subsurface structures and offer quantitative information for reservoir analysis.For the consideration,the true amplitude migration for plane wave was systematically studied.In this paper,the Maslov theory was introduced.Byτ-p transform, seismic data is transformed from(s,γ,τ)space to(p~s,γ,τ),(s,p~r,τ)and phase(p~s,p~r,τ)space.Then it is combined with Born in- version,and deduce the high-frequency asymptotic solution of mi- gration operator amplitude in phase domain.The numerical compu- tation results based on complex geologic model show that the true amplitude migration can obtain high-quality subsurface structure maps with reasonable computation amount.
引文
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3 Beylkin G.Imaging of discontinuities in the inverse scaterring problem by inversion of a causal generalized Radon transform[J].Journal of Mathematical Physics, 1985,26:99～108
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6 Duquet B,Lailly P,Ehinger A.3D Plane wave migra- tion of streamer data[J].Expanded Abstracts of 71~(st) Annual Internat SEG Mtg,2001,1033
7 Liu Faqi,Hanson D W,Whitmore N D,et al.Toward a unified analysis for source plane-wave migration[J]. Geophysics,2006,71(4):S129～S139
8 Maslov V P.Théroie des perturbations et methods as- ymptotiques[M].Paris:Dunod,1972.1～384
9 Karvtsov Y,Orlov Y.Caustics,catastrophes and wave- fields[M].Berlin:Springer-Verlag,1993.1～216
10 Xu S,Lambare G.Maslov+Born migration/inversion in complex media[J].Expanded Abstracts of 68~(th)An- nual Internat SEG Mtg,1998,1704～1707
11 Chapman C H.Ray theory and its extension:WKBJ and maslov seismogram[J].Journal of Geophysics, 1985,58(1):27～43
12 Jin S,Madariaga R,Virieux J,et al.Two dimensional asymptotic iterative elastic inversion[J].Geophysical Journal International,1992,108(2):575～588
13 Bourgeois A,Bourget M,Lailly P,et al.Marmousi model and data[A].In:Versteeg R,Grau G,Eds.The Marmousi experience[C].Proceedings of the 1990 EAEG Workshop on Practical,1991,5～16
2 Zhang Yu,Sun J,Notfors C,et al.Delayed-shot 3-D prestack depth migration[J].Geophysics,2005,70(5): E21～E28
3 Beylkin G.Imaging of discontinuities in the inverse scaterring problem by inversion of a causal generalized Radon transform[J].Journal of Mathematical Physics, 1985,26:99～108
4 ten Kroode A P E,Smit D J,Verdel A R.A microlocal analysis of migration[J].Wave Motion,1998,28(2): ??149～172
5 Xu S,Chauris H,LambaréG,et al.Common angle mi- gration:a strategy for imaging complex media[J].Geo- physics,2001,66(6):1877～1894
6 Duquet B,Lailly P,Ehinger A.3D Plane wave migra- tion of streamer data[J].Expanded Abstracts of 71~(st) Annual Internat SEG Mtg,2001,1033
7 Liu Faqi,Hanson D W,Whitmore N D,et al.Toward a unified analysis for source plane-wave migration[J]. Geophysics,2006,71(4):S129～S139
8 Maslov V P.Théroie des perturbations et methods as- ymptotiques[M].Paris:Dunod,1972.1～384
9 Karvtsov Y,Orlov Y.Caustics,catastrophes and wave- fields[M].Berlin:Springer-Verlag,1993.1～216
10 Xu S,Lambare G.Maslov+Born migration/inversion in complex media[J].Expanded Abstracts of 68~(th)An- nual Internat SEG Mtg,1998,1704～1707
11 Chapman C H.Ray theory and its extension:WKBJ and maslov seismogram[J].Journal of Geophysics, 1985,58(1):27～43
12 Jin S,Madariaga R,Virieux J,et al.Two dimensional asymptotic iterative elastic inversion[J].Geophysical Journal International,1992,108(2):575～588
13 Bourgeois A,Bourget M,Lailly P,et al.Marmousi model and data[A].In:Versteeg R,Grau G,Eds.The Marmousi experience[C].Proceedings of the 1990 EAEG Workshop on Practical,1991,5～16
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