高精度屏算子地震偏移成像方法研究
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摘要
从波场延拓的非稳态相移公式出发,基于反问题求解中常用的摄动理论,利用单平方根算子的渐进展开,推导出了波动方程广义屏叠前深度偏移算子方程的高阶形式;针对散射波场计算项对于横向变速介质的不稳定性问题,通过数学近似提出了有效提高稳定性的策略并应用到波场递归外推过程中,从而得到一种稳定的高精度屏算子地震偏移成像方法。数值试验和实际资料处理表明,该方法具有更高的精度,对宽角度信息成像更好,是对传统广义屏算子的有效补充和发展。
Starting from unstable phase-shift formula of wavefield continuation and based on the perturbation theory which is usually used in the solving of inverse question,we derived a high-order form of wave equation generalized screen pre-stack depth migration operator equation by utilizing gradual spreading of single square root operators. Aiming at the instability for the calculation items of scattered wavefield in lateral variable-velocity media,we proposed an effective way to improve the stability by math approximation,and applied it to the wavefield recursion extrapolation.Then a stable seismic migration imaging method of high precision screen operators was obtained.The numerical testing and actual data processing results show that the method has higher precision,which is better for the imaging of wide-angle information,and is the effective supplement and development of traditional generalized screen operators.
Starting from unstable phase-shift formula of wavefield continuation and based on the perturbation theory which is usually used in the solving of inverse question,we derived a high-order form of wave equation generalized screen pre-stack depth migration operator equation by utilizing gradual spreading of single square root operators. Aiming at the instability for the calculation items of scattered wavefield in lateral variable-velocity media,we proposed an effective way to improve the stability by math approximation,and applied it to the wavefield recursion extrapolation.Then a stable seismic migration imaging method of high precision screen operators was obtained.The numerical testing and actual data processing results show that the method has higher precision,which is better for the imaging of wide-angle information,and is the effective supplement and development of traditional generalized screen operators.
引文
[1]Gazdag J.Wave equation migration with the phase-shift method[J].Geophysics,1978,43(10):1342-1351
[2]Gazdag J,Sguazzero P.Migration of seismic data by phase-shift plus interpolation[J].Geophysics,1984, 49(2):.124-131
[3]Stolt R H.Migration by Fourier transform[J].Geophysics, 1978,43(1):23-48
[4]Ristow D,Ruhl T.3-D implicit finite difference migration by multiway splitting[J].Geophysics,1997, 62(5):554-567
[5]程玖兵,王华忠,马在田.带误差补偿的有限差分叠前深度偏移算法[J].石油地球物理勘探,2001,36 (4):408-413
[6]程玖兵,王华忠,马在田.频率-空间域有限差分法叠前深度偏移[J].地球物理学报,2001,44(3):389-395
[7]Stoffa P L,Fokkema J,Luna F,et al.Split step Fourier migration[J].Geophysics,1990,55(4):410-421
[8]张文生,张关泉.SEG/EAEG盐丘模型的三维分步傅里叶炮集叠前深度偏移[J].石油物探,2002,41(4): 396-399
[9]Wu R S,Huang L J.Scattered field calculation in heterogeneous media using phase-screen propagator[J].Expanded Abstracts of 62~(nd) Annual Internat SEG Mtg, 1992,1289-1292
[10]Ristow D,Ruhl T.Fourier finite-difference migration [J].Geophysics,1994,59(12):1882-1893
[11]Huang L J,Fehler M.Quasi-Born Fourier migration [J].Geophysical Journal International,2000,140 (3):521-534
[12]Huang L J,Fehler M,Wu R S.Extended local Born Fourier migration[J].Geophysics,1999,64(5):1524-1534
[13]Huang L J,Fehler M,Roberts P,et al.Extended local Rytov Fourier migration method[J].Geophysics, 1999,64(5 ):1535-1545
[14]Jin S,Wu R S,Peng C.Prestack depth migration using a hybrid pseudo-screen propagator[J].Expanded Abstracts of 68~(th) Annual Internat SEG Mtg, 1998,1819-1822
[15]Wu R S,de Hoop M V.Accuracy analysis and numerical tests of screen propagators for wave extrapolation [C]//Mathematical Methods in Geophysical Imaging IV.Denver,USA:SPIE,1996:196-209
[16]陈生昌,曹景忠,马在田.基于Rytov近似的叠前深度偏移方法[J].石油地球物理勘探,2001,36(6): 690-697
[17]陈生昌,曹景忠,马在田.基于拟线性Born近似的叠前深度偏移方法[J].地球物理学报,2001,44(5): 704-709
[18]丁伟,李振春,刘玉莲.基于Born/Rytov近似的联合叠前深度偏移方法[J].石油物探,2003,42(1):29-34
[19]李振春,刘玉莲,丁伟,等.基于最优Born近似的叠前深度偏移方法[J].石油大学学报(自然科学版), 2002,26(5):32-36
[20]李振春,叶月明,仝兆岐.起伏地表下基于高阶广义屏算子的叠前深度偏移[J].勘探地球物理进展, 2007,30(5):377-381
[21]石建新,王华忠,徐兆涛,等.三维Born近似波动方程炮域叠前深度偏移[J].勘探地球物理进展,2002, 25(3):32-36
[22]张文生,张关泉,郝现军.Marmousi模型单炮叠前深度偏移的广义相位屏法及其并行实现[J].石油物探,2000,39(3):1-7
[23]陈生昌,曹景忠,马在田.稳定的Born近似叠前深度偏移方法[J].石油地球物理勘探,2001,36(3): 291-296
[2]Gazdag J,Sguazzero P.Migration of seismic data by phase-shift plus interpolation[J].Geophysics,1984, 49(2):.124-131
[3]Stolt R H.Migration by Fourier transform[J].Geophysics, 1978,43(1):23-48
[4]Ristow D,Ruhl T.3-D implicit finite difference migration by multiway splitting[J].Geophysics,1997, 62(5):554-567
[5]程玖兵,王华忠,马在田.带误差补偿的有限差分叠前深度偏移算法[J].石油地球物理勘探,2001,36 (4):408-413
[6]程玖兵,王华忠,马在田.频率-空间域有限差分法叠前深度偏移[J].地球物理学报,2001,44(3):389-395
[7]Stoffa P L,Fokkema J,Luna F,et al.Split step Fourier migration[J].Geophysics,1990,55(4):410-421
[8]张文生,张关泉.SEG/EAEG盐丘模型的三维分步傅里叶炮集叠前深度偏移[J].石油物探,2002,41(4): 396-399
[9]Wu R S,Huang L J.Scattered field calculation in heterogeneous media using phase-screen propagator[J].Expanded Abstracts of 62~(nd) Annual Internat SEG Mtg, 1992,1289-1292
[10]Ristow D,Ruhl T.Fourier finite-difference migration [J].Geophysics,1994,59(12):1882-1893
[11]Huang L J,Fehler M.Quasi-Born Fourier migration [J].Geophysical Journal International,2000,140 (3):521-534
[12]Huang L J,Fehler M,Wu R S.Extended local Born Fourier migration[J].Geophysics,1999,64(5):1524-1534
[13]Huang L J,Fehler M,Roberts P,et al.Extended local Rytov Fourier migration method[J].Geophysics, 1999,64(5 ):1535-1545
[14]Jin S,Wu R S,Peng C.Prestack depth migration using a hybrid pseudo-screen propagator[J].Expanded Abstracts of 68~(th) Annual Internat SEG Mtg, 1998,1819-1822
[15]Wu R S,de Hoop M V.Accuracy analysis and numerical tests of screen propagators for wave extrapolation [C]//Mathematical Methods in Geophysical Imaging IV.Denver,USA:SPIE,1996:196-209
[16]陈生昌,曹景忠,马在田.基于Rytov近似的叠前深度偏移方法[J].石油地球物理勘探,2001,36(6): 690-697
[17]陈生昌,曹景忠,马在田.基于拟线性Born近似的叠前深度偏移方法[J].地球物理学报,2001,44(5): 704-709
[18]丁伟,李振春,刘玉莲.基于Born/Rytov近似的联合叠前深度偏移方法[J].石油物探,2003,42(1):29-34
[19]李振春,刘玉莲,丁伟,等.基于最优Born近似的叠前深度偏移方法[J].石油大学学报(自然科学版), 2002,26(5):32-36
[20]李振春,叶月明,仝兆岐.起伏地表下基于高阶广义屏算子的叠前深度偏移[J].勘探地球物理进展, 2007,30(5):377-381
[21]石建新,王华忠,徐兆涛,等.三维Born近似波动方程炮域叠前深度偏移[J].勘探地球物理进展,2002, 25(3):32-36
[22]张文生,张关泉,郝现军.Marmousi模型单炮叠前深度偏移的广义相位屏法及其并行实现[J].石油物探,2000,39(3):1-7
[23]陈生昌,曹景忠,马在田.稳定的Born近似叠前深度偏移方法[J].石油地球物理勘探,2001,36(3): 291-296
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