波动方程深度偏移的频率相关变步长延拓方法
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摘要
发展了波动方程深度延拓的频率相关变步长深度延拓方法和表驱动的单点波场插值技术.前者通过减少深度延拓的次数减少了波动方程深度偏移的计算量,而后者用很少的计算量实现了等间距、理想采样的深度成像.就同一偏移方法,采用频率相关变步长深度延拓加单点插值,其计算量大约是常规的等间距采样延拓方法的三分之一,但两者的成像效果基本相同.文中以最优分裂Fourier方法为例,用二维理论数据(Marmousi模型)和三维实际地震资料验证了这一方法,但这一方法可适用于各类频率域波动方程深度偏移方法.
We propose a frequency-dependent varying-step depth extrapolation scheme and a table-driven, one-point wavefield interpolation technique for the wave equation based migration methods. The former reduces the computational cost of wavefield depth extrapolation, and the latter reconstructs the extrapolated wavefield with an equal,desired vertical step with high computational efficiency. The proposed varying-step depth extrapolation plus one-point interpolation scheme results in 2/3 reduction in computational cost when compared to the conventional equal-step depth extrapolation of wavefield, but gives the almost same imaging. We present the scheme using the optimum split-step Fourier method on the 2-D Marmousi dataset and 3-D field dataset. The results demonstrate the high computational efficiency of the scheme in the absence of loss of accuracy. The proposed scheme can also be used by other wave equation based migration methods of the frequency domain.
We propose a frequency-dependent varying-step depth extrapolation scheme and a table-driven, one-point wavefield interpolation technique for the wave equation based migration methods. The former reduces the computational cost of wavefield depth extrapolation, and the latter reconstructs the extrapolated wavefield with an equal,desired vertical step with high computational efficiency. The proposed varying-step depth extrapolation plus one-point interpolation scheme results in 2/3 reduction in computational cost when compared to the conventional equal-step depth extrapolation of wavefield, but gives the almost same imaging. We present the scheme using the optimum split-step Fourier method on the 2-D Marmousi dataset and 3-D field dataset. The results demonstrate the high computational efficiency of the scheme in the absence of loss of accuracy. The proposed scheme can also be used by other wave equation based migration methods of the frequency domain.
引文
[1]Sbastien G,Jean Brac.Can we image complexstructures withfirst-arrival traveltime?Geophysics,1993,58(4):564~575
[2]Stoffa P L,Fokkema J T,de Luna Freire R M,et al.Split-step Fourier migration.Geophysics,1990,55(4):410~421
[3]Fu L Y.Wavefield interpolation in the Fourier wavefield extrapolation.Geophysics,2004,69(1):257~264
[4]刘洪,袁江华,陈景波等.大步长波场深度延拓的理论.地球物理学报,2006,49(6):1779~1793Liu H,Yuan J H,Chen J B,et al.Theory of large step wavefield depth extrapolation.Chinese J.Geophys.,2006,49(6):1779~1793
[5]Liu Linong,Zhang Jianfeng.3D wavefield extrapolation with optimumsplit-step Fourier method.Geophysics,2006,71(3):T95~T108
[6]Liu Linong,Zhang Jianfeng.Optimum split-step Fourier one-way operators for seismic modeling and imaging in3D VTI media.Geophysical Research Letters,2006,33:L09308
[7]Zhang Jianfeng,Liu Linong.Optimum split-step Fourier3D depth migration:Developments and practical aspects.Geophysics,2007,72(3):S167~S175
[8]Claerbout J F.Imaging the Earth’s Interior.Blackwell Scientific Publications.1985
[9]Zhang Yu,Sun J C,Gray S H.Aliasing in wavefield extrapolation prestack migration.Geophysics,2003,68(2):629~633
[10]Le Rousseau J H,de Hoop M V.Modeling and imaging with the scalar generalized-screen algorithms in isotropic media.Geophysics,2001,66(5):1551~1568
[11]RistowD,Ruhl T.Fourier finite-difference migration.Geophysics,1994,59(12):1882~1893
[12]RistowD,Ruhl T.Optimized operators for3-D Fourier finite-difference migration.J.Seis.Expl.,1997,6:367~383
[2]Stoffa P L,Fokkema J T,de Luna Freire R M,et al.Split-step Fourier migration.Geophysics,1990,55(4):410~421
[3]Fu L Y.Wavefield interpolation in the Fourier wavefield extrapolation.Geophysics,2004,69(1):257~264
[4]刘洪,袁江华,陈景波等.大步长波场深度延拓的理论.地球物理学报,2006,49(6):1779~1793Liu H,Yuan J H,Chen J B,et al.Theory of large step wavefield depth extrapolation.Chinese J.Geophys.,2006,49(6):1779~1793
[5]Liu Linong,Zhang Jianfeng.3D wavefield extrapolation with optimumsplit-step Fourier method.Geophysics,2006,71(3):T95~T108
[6]Liu Linong,Zhang Jianfeng.Optimum split-step Fourier one-way operators for seismic modeling and imaging in3D VTI media.Geophysical Research Letters,2006,33:L09308
[7]Zhang Jianfeng,Liu Linong.Optimum split-step Fourier3D depth migration:Developments and practical aspects.Geophysics,2007,72(3):S167~S175
[8]Claerbout J F.Imaging the Earth’s Interior.Blackwell Scientific Publications.1985
[9]Zhang Yu,Sun J C,Gray S H.Aliasing in wavefield extrapolation prestack migration.Geophysics,2003,68(2):629~633
[10]Le Rousseau J H,de Hoop M V.Modeling and imaging with the scalar generalized-screen algorithms in isotropic media.Geophysics,2001,66(5):1551~1568
[11]RistowD,Ruhl T.Fourier finite-difference migration.Geophysics,1994,59(12):1882~1893
[12]RistowD,Ruhl T.Optimized operators for3-D Fourier finite-difference migration.J.Seis.Expl.,1997,6:367~383
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