利用基于双平方根方程的局部谐波分解法提取角度道集
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摘要
本文在基于单平方根方程的局部谐波分解法提取角度道集方法基础上提出了一种利用双平方根方程的局部谐波分解法提取角度道集的新方法。文中推导了相关的理论计算公式。新方法使用高效滤波器直接从双平方根方程延拓后的叠前波场中求出反射系数的谐波分解,并由此获得角度道集。理论模型和实际资料的试算结果表明了方法的正确性和有效性。同基于单平方根方程的局部谐波分解方法相比,对于常规的海上地震资料,该方法具有较高的计算效率,而且成像质量相当。由于在实现叠前波场延拓时采用了炮检距域—有限差分延拓方法,使该方法增加了差分项,能适应剧烈的横向速度变化。
On the basis of the method detecting angle gathers by local harmonic wave decomposition based on single square root equation,the paper presented a new method for detecting angle gathers by local harmonic wave decomposition based on double square root equation.The paper deduced relevant theoretical computational formula.In implementation,the new method uses high-efficient filter to directly get the harmonic wave decomposition of reflectivity from prestack wavefield after continuation of double square root equation,and from which obtains angle gathers.The test results of theoretical model and practical data showed that the method has higher computational efficiency and equivalent imaging quality for common marine seismic data.Since the method adopts finite-difference continuation in offset domain for prestack wavefield continuation,increasing difference item,which is able to adapt to the violent lateral variation of velocity.
On the basis of the method detecting angle gathers by local harmonic wave decomposition based on single square root equation,the paper presented a new method for detecting angle gathers by local harmonic wave decomposition based on double square root equation.The paper deduced relevant theoretical computational formula.In implementation,the new method uses high-efficient filter to directly get the harmonic wave decomposition of reflectivity from prestack wavefield after continuation of double square root equation,and from which obtains angle gathers.The test results of theoretical model and practical data showed that the method has higher computational efficiency and equivalent imaging quality for common marine seismic data.Since the method adopts finite-difference continuation in offset domain for prestack wavefield continuation,increasing difference item,which is able to adapt to the violent lateral variation of velocity.
引文
[1]Xu S et al.Common angle image gather:Astrategy for imaging complex media.Expanded Abstracts of68th SEG Mtg,1998,1538～1541
[2]de Bruin C G Met al.Angle-dependent reflectivity by means of prestack migration.Geophysics,1990,55(9):1223～1234
[3]Prucha Met al.Angle-domain commonimage gathers by wave-equation migration.Expanded Abstracts of69th SEG Mtg,1999,824～827
[4]Mosher C and Foster D.Common angle imaging con-ditions for prestack depth migration.Expanded Ab-stracts of70th SEG Mtg,2000,830～833
[5]Soubaras R.Angle gathers for shot-record migration by local harmonic decomposition.Expanded Abstracts of73rd SEG Mtg,2003,889～892
[6]Rickett J and Sava P.Offset and angle-domain com-mon image-point gathers for shot-profile migration.Geophysics,2002,67(3):883～889
[7]Sava P and Fomel S.Angle-domain common-image gathers by wavefield continuation methods.Geophys-ics,2003,68(3):1065～1074
[8]Sava P and Fomel S.Time-shift imaging condition.Expanded Abstracts of75th SEG Mtg,2005,1850～1853
[9]Bevc D et al.Wave equation imaging comparisons:survey sinking vs shot profile methods.Expanded Abstracts of73rd SEG Mtg,2003,885～888
[10]Claerbout J F.Imagingthe Earth’s Interior.Black-well Scientific Publications Inc,1985
[11]Sun Het al.Globally optimized fourier finite-differ-ence migration in the offset domain.Expanded Ab-stracts of75th SEG Mtg,2005,1858～1861
[12]孙沛勇,张叔伦.双平方根叠前深度偏移的广义高阶屏方法.石油地球物理勘探,2001,36(4):398～407
[13]Popovici A M.Prestack migration by split-step DSR.Geophysics,1996,61(5):1412～1416
[14]Jin S and Wu R S.Common offset pseudo-screendepth migration.Expanded Abstracts of69th SEG Mtg,1999,1516～1519
[15]Sirovich L.Introductionto Applied Mathematics.Springer-Verlag World Publishing Corp,1988
[16]Thorbecke J W.Design of one-way wavefield extrap-olation operators,using smooth functions in WLSQ optimization.Geophysics,2004,69(4):1037～1045
[17]Golub G H.Matrixcomputations.The Johns Hop-kins University Press,1989
[18]Press W H.Numerical Recipes in C:The Art of Sci-entific Computing,Second Edition,Cambridge Uni-versity Press,1992
[2]de Bruin C G Met al.Angle-dependent reflectivity by means of prestack migration.Geophysics,1990,55(9):1223～1234
[3]Prucha Met al.Angle-domain commonimage gathers by wave-equation migration.Expanded Abstracts of69th SEG Mtg,1999,824～827
[4]Mosher C and Foster D.Common angle imaging con-ditions for prestack depth migration.Expanded Ab-stracts of70th SEG Mtg,2000,830～833
[5]Soubaras R.Angle gathers for shot-record migration by local harmonic decomposition.Expanded Abstracts of73rd SEG Mtg,2003,889～892
[6]Rickett J and Sava P.Offset and angle-domain com-mon image-point gathers for shot-profile migration.Geophysics,2002,67(3):883～889
[7]Sava P and Fomel S.Angle-domain common-image gathers by wavefield continuation methods.Geophys-ics,2003,68(3):1065～1074
[8]Sava P and Fomel S.Time-shift imaging condition.Expanded Abstracts of75th SEG Mtg,2005,1850～1853
[9]Bevc D et al.Wave equation imaging comparisons:survey sinking vs shot profile methods.Expanded Abstracts of73rd SEG Mtg,2003,885～888
[10]Claerbout J F.Imagingthe Earth’s Interior.Black-well Scientific Publications Inc,1985
[11]Sun Het al.Globally optimized fourier finite-differ-ence migration in the offset domain.Expanded Ab-stracts of75th SEG Mtg,2005,1858～1861
[12]孙沛勇,张叔伦.双平方根叠前深度偏移的广义高阶屏方法.石油地球物理勘探,2001,36(4):398～407
[13]Popovici A M.Prestack migration by split-step DSR.Geophysics,1996,61(5):1412～1416
[14]Jin S and Wu R S.Common offset pseudo-screendepth migration.Expanded Abstracts of69th SEG Mtg,1999,1516～1519
[15]Sirovich L.Introductionto Applied Mathematics.Springer-Verlag World Publishing Corp,1988
[16]Thorbecke J W.Design of one-way wavefield extrap-olation operators,using smooth functions in WLSQ optimization.Geophysics,2004,69(4):1037～1045
[17]Golub G H.Matrixcomputations.The Johns Hop-kins University Press,1989
[18]Press W H.Numerical Recipes in C:The Art of Sci-entific Computing,Second Edition,Cambridge Uni-versity Press,1992
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