单程波算子地震波入射角计算
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摘要
基于单程波深度延拓方法,发展了一种地震波入射角度计算方法.入射角度的计算仅利用简谐波场,可得到整个成像区域内所有点的入射波波前面方向.该方法具有较高的计算效率,可服务于合成角道集等深度偏移方法;与偏移算法相比,其计算量几乎可以忽略.与射线法或基于走时梯度的入射角度计算方法相比,本文方法更稳健,避免了速度场的微小变化导致的入射角较大变化,因此更适用于实际偏移速度模型,也与波动方程深度偏移方法更匹配.数值算例表明,本文方法既有较高的计算效率又有很好的精度,且有很好的稳定性.
We present a robust method to estimate the incident angle field based on the one-way propagator.The employment of monochromatic wave field is to reduce the extrapolation time dramatically and ensure the generation of the incident angle field in the whole imaging space.This incident angle field estimation method has high computational efficiency and can be applied in getting angle gather in one-way wave equation depth migration scheme.Comparison with depth migration,the cost of incident angle field estimation can be omitted.The proposed algorithm is free of smoothness of velocity model and hence can avoid large incident angle variation with small velocity perturbation compared to the traditional ray tracing or travel-time gradient picking method.This means the proposed angle field estimation method is more suitable for real velocity model and match well with the one-way wave equation prestack depth migration scheme.Computation of incident angle fields of the 2-D,3-D layered and complicated structured models show the high computational efficiency,stability and precision of the proposed algorithm.
We present a robust method to estimate the incident angle field based on the one-way propagator.The employment of monochromatic wave field is to reduce the extrapolation time dramatically and ensure the generation of the incident angle field in the whole imaging space.This incident angle field estimation method has high computational efficiency and can be applied in getting angle gather in one-way wave equation depth migration scheme.Comparison with depth migration,the cost of incident angle field estimation can be omitted.The proposed algorithm is free of smoothness of velocity model and hence can avoid large incident angle variation with small velocity perturbation compared to the traditional ray tracing or travel-time gradient picking method.This means the proposed angle field estimation method is more suitable for real velocity model and match well with the one-way wave equation prestack depth migration scheme.Computation of incident angle fields of the 2-D,3-D layered and complicated structured models show the high computational efficiency,stability and precision of the proposed algorithm.
引文
[1]Wapenaar K,Goudswaard J,van Wijngaarden A J.Multi-angle,multi-scale inversion of migrated seismic data.TheLeading Edge,1999,18(8):928-932.
[2]Berkhout A J,Ongkeihong L,Volker A W F,et al.Comprehensive assessment of seismic acquisition geometriesby focal beams—Part 1:Theoretical considerations.Geophysics,2001,66(3):911-917.
[3]张辉,王成祥,张剑锋.基于单程波方程的角度域照明分析.地球物理学报,2009,52(6):1606-1614.Zhang H,Wang C X,Zhang J F.One-way wave equationbased illumination analysis in angle domain.Chinese J.Geophys.(in Chinese),2009,52(6):1606-1614.
[4]de Bruin C G M,Wapenaar C P A,Berkhout A J.Angle-dependent reflectivity by means of prestack migration.Geophysics,1990,55(9):1223-1234.
[5]Zhang Y,Xu S,Bleistein N,et al.True-amplitude,angle-domain,common-image gathers from one-way wave-equationmigrations.Geophysics,2007,72(1):S49-S58.
[6]Biondi B,Symes W W.Angle-domain common-image gathersfor migration velocity analysis by wavefield-continuation imaging.Geophysics,2004,69(5):1283-1298.图8不同深度水平切片上理论角度与计算角度的等值线对比分析图中实线为理论值,虚线为本文方法计算值.Fig.8 Comparisons between the contour lines at different depth slices of theoretical(illustrated by the solid line)and estimated(illustrated by the dashed line)angles(a)Slice at the depth of 1km;(b)Slice at the depth of 3km;(c)Slice at the depth of 5km.
[7]Kuhl H,Sacchi M D.Least-squares wave-equation migration for AVP/AVA inversion.Geophysics,2003,68(1):262-273.
[8]Cˇerveny V.Seismic Ray Theory.Cambridge:Cambridge University Press,2001.
[9]Claerbout J F.Toward a unified theory of reflector mapping.Geophysics,1971,36(3):467-481.
[10]Liu L N,Zhang J F.3Dwavefield extrapolation with optimum split-step Fourier method.Geophysics,2006,71(3):T95-T108.
[11]Zhang J F,Liu L N.Optimum split-step Fourier3Ddepth migration:Developments and practical aspects.Geophysics,2007,72(3):S167-S175.
[12]张剑锋,卢宝坤,刘礼农.波动方程深度偏移的频率相关变步长延拓方法.地球物理学报,2008,51(1):222-228.Zhang J F,Lu B K,Liu L N.Frequency-dependent varying-step depth extrapolation scheme for wave equation based migration.Chinese J.Geophys.(in Chinese),2008,51(1):222-228.
[2]Berkhout A J,Ongkeihong L,Volker A W F,et al.Comprehensive assessment of seismic acquisition geometriesby focal beams—Part 1:Theoretical considerations.Geophysics,2001,66(3):911-917.
[3]张辉,王成祥,张剑锋.基于单程波方程的角度域照明分析.地球物理学报,2009,52(6):1606-1614.Zhang H,Wang C X,Zhang J F.One-way wave equationbased illumination analysis in angle domain.Chinese J.Geophys.(in Chinese),2009,52(6):1606-1614.
[4]de Bruin C G M,Wapenaar C P A,Berkhout A J.Angle-dependent reflectivity by means of prestack migration.Geophysics,1990,55(9):1223-1234.
[5]Zhang Y,Xu S,Bleistein N,et al.True-amplitude,angle-domain,common-image gathers from one-way wave-equationmigrations.Geophysics,2007,72(1):S49-S58.
[6]Biondi B,Symes W W.Angle-domain common-image gathersfor migration velocity analysis by wavefield-continuation imaging.Geophysics,2004,69(5):1283-1298.图8不同深度水平切片上理论角度与计算角度的等值线对比分析图中实线为理论值,虚线为本文方法计算值.Fig.8 Comparisons between the contour lines at different depth slices of theoretical(illustrated by the solid line)and estimated(illustrated by the dashed line)angles(a)Slice at the depth of 1km;(b)Slice at the depth of 3km;(c)Slice at the depth of 5km.
[7]Kuhl H,Sacchi M D.Least-squares wave-equation migration for AVP/AVA inversion.Geophysics,2003,68(1):262-273.
[8]Cˇerveny V.Seismic Ray Theory.Cambridge:Cambridge University Press,2001.
[9]Claerbout J F.Toward a unified theory of reflector mapping.Geophysics,1971,36(3):467-481.
[10]Liu L N,Zhang J F.3Dwavefield extrapolation with optimum split-step Fourier method.Geophysics,2006,71(3):T95-T108.
[11]Zhang J F,Liu L N.Optimum split-step Fourier3Ddepth migration:Developments and practical aspects.Geophysics,2007,72(3):S167-S175.
[12]张剑锋,卢宝坤,刘礼农.波动方程深度偏移的频率相关变步长延拓方法.地球物理学报,2008,51(1):222-228.Zhang J F,Lu B K,Liu L N.Frequency-dependent varying-step depth extrapolation scheme for wave equation based migration.Chinese J.Geophys.(in Chinese),2008,51(1):222-228.
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