稳定的保幅高阶广义屏地震偏移成像方法研究
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摘要
以先进的波动理论为基础的波动方程保幅地震偏移成像是在给出正确位置的同时也给出真实振幅的一种特殊完善.作者从保幅单程波动方程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,从而推导出保幅叠前深度偏移方程的高阶广义屏形式;针对散射波场计算项对于横向变速介质的不稳定性,通过数学近似提出一个有效提高稳定性的策略,应用到波场递归外推过程中,从而得到一种稳定的保幅高阶广义屏叠前深度偏移算子.理论模型试算和实际资料处理表明,该方法不但可以更精确地使散射能量聚焦、归位,提高成像精度;而且可以输出正确反映地下反射系数的振幅信息,使AVO响应更加清晰,提高了AVO资料的分析精度.
Wave equation preserved-amplitude seismic migration imaging has a special function that can give true amplitudes as well as the correct locations based on advanced wave theories.The author first starts from the unstable phase shift expression of preserved-amplitude one way wave equation.Based on perturbation theory which is often used in reversed question solution,the author uses the progressive expansion of single square root operator to drive a high-order generalized screen form of preserved-amplitude prestack depth migration equation.To solve the unstable problem in lateral variable speed media caused by computation items of the scattering wavefield,the author proposes a strategy which can effectively improve the stability by math approximation.Then this strategy is applied to the wavefield recursion extrapolation,so a kind of stable preserved-amplitude prestack depth migration operators of high-order generalized screen are obtained.Theoretical model testing and real data processing indicate that this method can not only make scattering energy be focused and migrated to the correct position to improve imaging accuracy but also output the amplitude information which reflects the correct subsurface reflection coefficients.So this method has clearer AVO response and can enhance analytic precision for AVO data.
Wave equation preserved-amplitude seismic migration imaging has a special function that can give true amplitudes as well as the correct locations based on advanced wave theories.The author first starts from the unstable phase shift expression of preserved-amplitude one way wave equation.Based on perturbation theory which is often used in reversed question solution,the author uses the progressive expansion of single square root operator to drive a high-order generalized screen form of preserved-amplitude prestack depth migration equation.To solve the unstable problem in lateral variable speed media caused by computation items of the scattering wavefield,the author proposes a strategy which can effectively improve the stability by math approximation.Then this strategy is applied to the wavefield recursion extrapolation,so a kind of stable preserved-amplitude prestack depth migration operators of high-order generalized screen are obtained.Theoretical model testing and real data processing indicate that this method can not only make scattering energy be focused and migrated to the correct position to improve imaging accuracy but also output the amplitude information which reflects the correct subsurface reflection coefficients.So this method has clearer AVO response and can enhance analytic precision for AVO data.
引文
[1]Bevc D.Imaging complex structures with semirecursive Kirchhoff migration.Geophysics,1997,62:577-588.
[2]Sun H,Gerard S.Wavepath migration versus Kirchhoff migration.69th Annul Internat.Mtg.Soc.Expl.Geophys.,Expanded Abstracts,1999.
[3]张廉萍,刘洪.适于Kirchhoff叠前深度偏移的地震走时李代数积分算法.地球物理学报,2010,53(8):1893-1901.Zhang L P,Liu H.Lie algebra integral algorithm of travel-time calculation for pre-stack Kirchhoff depth migration.Chinese J.Geophys(in Chinese),2010,53(8):1893-1901.
[4]王华忠,蔡杰雄,孔祥宁.适于大规模数据的三维Kirchhoff积分法体偏移实现方案.地球物理学报,2010,53(7):1699-1709.Wang H Z,Cai J X,Kong X N.An implementation of Kirchhoff integral prestack migration for large-scale data.Chinese J.Geophys(in Chinese),2010,53(7):1699-1709.
[5]Stolt R H.Migration by Fourier transform.Geophysics,1978,43:23-48
[6]Ober C C,Oldfield R A,Womble D E.Practical aspects of prestack depth migration with finite-difference.67th Ann.Mtg.,Soc.Expl.Geophys.,Expanded Abstracts,1997.
[7]Stoffa P L,Fokkema J,Luna Freire,et al.Split step Fourier migration.Geophysics,1990,55(4):410-421.
[8]符力耘,孙伟家,李东平.退化的Fourier偏移算子及其在复杂断块成像中的应用.地球物理学报,2007,50(4):1241-1250.Fu L Y,Sun W J,Li D P.Degenerate migrators for imaging fault-related complex structures.Chinese J.Geophys(in Chinese),2007,50(4):1241-1250.
[9]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):221-227.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):221-227.
[10]Thierry P,LambaréG,Podvin P.3D prestack preserved amplitude migration:Application to real data.66th Ann.Internat.Mtg.Soc.Expl.Geophys.,Expanded Abstracts,1996:555-558.
[11]Hanitzsch C.Comparison of weights in prestack amplitude-preserving depth Migration.Geophysics,1997,62:1812-1816.
[12]Gray S.True-amplitude seismic migration:A comparison of three approaches.Geophysics,1997,62:629-638.
[13]Ekren B O,Ursin B.True-amplitude frequency-wavenumber constant-offset Migration.Geophysics,1999,64:915-924.
[14]张平平,常旭.保幅偏移中的权函数.地球物理学进展,2006,21(1):203-207.Zhang P P,Chang X.The weight functions of amplitude-preserving migration.Progress in Geophysics,2006,21(1):203-207.
[15]刘伊克,常旭,卢孟夏.目标函数叠前保幅偏移方法与应用.地球物理学报,2006,49(4):1150-1154.Liu Y K,Chang X,Lu M X.Objective function prestack amplitude preserving migration and its application.Chinese J.Geophys(in Chinese),2006,49(4):1150-1154.
[16]徐升,Gilles Lambaré.复杂介质下保真振幅Kirchhoff深度偏移振幅.地球物理学报,2006,49(5):1431-1444.Xu S,Gilles Lambaré.True amplitude Kirchhoff prestack depth migration in complex media.Chinese J.Geophys(in Chinese),2006,49(5):1431-1444.
[17]张关泉.波动方程的上行波和下行波的耦合方程组.应用数学学报,1993,16(2):251-263.Zhang G Q.System of coupled equations for down going and upcoming waves.Acta Math.Appl.Sin.(in Chinese),1993,16(2):251-263.
[18]Zhang Y,Zhang G.Theory of true amplitude common-shot migration.72nd Ann.Internat.Mtg.,Soc.Expl.Geophys.Expanded Abstracts,2002:2471-2474.
[19]Zhang Y,Sun J,Gray S,et al.Towards accurate amplitudes for one-way wavefield extrapolation of3-D common shot records.71st Ann.Internat.Mtg.,Soc.Expl.Geophys.Workshop,2001.
[20]张宇.振幅保真的单程波方程偏移理论.地球物理学报,2006,49(5):1410-1430.Zhang Y.The theory of true amplitude one-way wave equation migration.Chinese J.Geophys(in Chinese),2006,49(5):1410-1430.
[21]吕彬,王宇超,李斐.保幅型裂步傅里叶叠前深度偏移方法探讨.岩性油气藏,2007,19(3):101-105.LüB,Wang Y C,Li F.Research and application of amplitude-preserved split-step Fourier prestack depth migration.Lithologic Reservoirs(in Chinese),2007,19(3):101-105.
[22]刘定进,印兴耀.傅里叶有限差分法保幅叠前深度偏移方法.地球物理学报,2007,50(1):269-277.Liu D J,Yin X Y.A method of Fourier finite-difference preserved-amplitude prestack depth migration.Chinese J.Geophys.(in Chinese),2007,50(1):269-277.
[23]叶月明,李振春,仝兆岐.双复杂介质条件下频率空间域有限差分法保幅偏移.地球物理学报,2008,51(5):1511-1519.Ye Y M,Li Z C,Tong Z Q.Preserved-amplitude migration with dual-complexity.Chinese J.Geophys(in Chinese),2008,51(5):1511-1519.
[24]崔兴福,张关泉,吴雅丽.三维非均匀介质中真振幅地震偏移算子研究.地球物理学报,2004,47(3):509-513.Cui X F,Zhang G Q,Wu Y L.True amplitude seismic migration operator in3-D heterogeneous medium.Chinese J.Geophys.(in Chinese),2004,47(3):509-513.
[25]Zhang Y,Xu S,Zhang G Q,et al.How to obtain true amplitude common-angle gathers from one-way wave equation migration.74th Ann.Internat,Mtg:Soc.of Expl.Geophys.1021-1024.
[26]陈生昌,曹景忠,马在田.稳定的Born近似叠前深度偏移方法.石油地球物理勘探,2001,36(3):291-296.Chen S C,Cao J Z,Ma Z T.Stable pre-stack depth migration method with Born approximation.OGP(in Chinese),2001,36(3):291-296.
[2]Sun H,Gerard S.Wavepath migration versus Kirchhoff migration.69th Annul Internat.Mtg.Soc.Expl.Geophys.,Expanded Abstracts,1999.
[3]张廉萍,刘洪.适于Kirchhoff叠前深度偏移的地震走时李代数积分算法.地球物理学报,2010,53(8):1893-1901.Zhang L P,Liu H.Lie algebra integral algorithm of travel-time calculation for pre-stack Kirchhoff depth migration.Chinese J.Geophys(in Chinese),2010,53(8):1893-1901.
[4]王华忠,蔡杰雄,孔祥宁.适于大规模数据的三维Kirchhoff积分法体偏移实现方案.地球物理学报,2010,53(7):1699-1709.Wang H Z,Cai J X,Kong X N.An implementation of Kirchhoff integral prestack migration for large-scale data.Chinese J.Geophys(in Chinese),2010,53(7):1699-1709.
[5]Stolt R H.Migration by Fourier transform.Geophysics,1978,43:23-48
[6]Ober C C,Oldfield R A,Womble D E.Practical aspects of prestack depth migration with finite-difference.67th Ann.Mtg.,Soc.Expl.Geophys.,Expanded Abstracts,1997.
[7]Stoffa P L,Fokkema J,Luna Freire,et al.Split step Fourier migration.Geophysics,1990,55(4):410-421.
[8]符力耘,孙伟家,李东平.退化的Fourier偏移算子及其在复杂断块成像中的应用.地球物理学报,2007,50(4):1241-1250.Fu L Y,Sun W J,Li D P.Degenerate migrators for imaging fault-related complex structures.Chinese J.Geophys(in Chinese),2007,50(4):1241-1250.
[9]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):221-227.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):221-227.
[10]Thierry P,LambaréG,Podvin P.3D prestack preserved amplitude migration:Application to real data.66th Ann.Internat.Mtg.Soc.Expl.Geophys.,Expanded Abstracts,1996:555-558.
[11]Hanitzsch C.Comparison of weights in prestack amplitude-preserving depth Migration.Geophysics,1997,62:1812-1816.
[12]Gray S.True-amplitude seismic migration:A comparison of three approaches.Geophysics,1997,62:629-638.
[13]Ekren B O,Ursin B.True-amplitude frequency-wavenumber constant-offset Migration.Geophysics,1999,64:915-924.
[14]张平平,常旭.保幅偏移中的权函数.地球物理学进展,2006,21(1):203-207.Zhang P P,Chang X.The weight functions of amplitude-preserving migration.Progress in Geophysics,2006,21(1):203-207.
[15]刘伊克,常旭,卢孟夏.目标函数叠前保幅偏移方法与应用.地球物理学报,2006,49(4):1150-1154.Liu Y K,Chang X,Lu M X.Objective function prestack amplitude preserving migration and its application.Chinese J.Geophys(in Chinese),2006,49(4):1150-1154.
[16]徐升,Gilles Lambaré.复杂介质下保真振幅Kirchhoff深度偏移振幅.地球物理学报,2006,49(5):1431-1444.Xu S,Gilles Lambaré.True amplitude Kirchhoff prestack depth migration in complex media.Chinese J.Geophys(in Chinese),2006,49(5):1431-1444.
[17]张关泉.波动方程的上行波和下行波的耦合方程组.应用数学学报,1993,16(2):251-263.Zhang G Q.System of coupled equations for down going and upcoming waves.Acta Math.Appl.Sin.(in Chinese),1993,16(2):251-263.
[18]Zhang Y,Zhang G.Theory of true amplitude common-shot migration.72nd Ann.Internat.Mtg.,Soc.Expl.Geophys.Expanded Abstracts,2002:2471-2474.
[19]Zhang Y,Sun J,Gray S,et al.Towards accurate amplitudes for one-way wavefield extrapolation of3-D common shot records.71st Ann.Internat.Mtg.,Soc.Expl.Geophys.Workshop,2001.
[20]张宇.振幅保真的单程波方程偏移理论.地球物理学报,2006,49(5):1410-1430.Zhang Y.The theory of true amplitude one-way wave equation migration.Chinese J.Geophys(in Chinese),2006,49(5):1410-1430.
[21]吕彬,王宇超,李斐.保幅型裂步傅里叶叠前深度偏移方法探讨.岩性油气藏,2007,19(3):101-105.LüB,Wang Y C,Li F.Research and application of amplitude-preserved split-step Fourier prestack depth migration.Lithologic Reservoirs(in Chinese),2007,19(3):101-105.
[22]刘定进,印兴耀.傅里叶有限差分法保幅叠前深度偏移方法.地球物理学报,2007,50(1):269-277.Liu D J,Yin X Y.A method of Fourier finite-difference preserved-amplitude prestack depth migration.Chinese J.Geophys.(in Chinese),2007,50(1):269-277.
[23]叶月明,李振春,仝兆岐.双复杂介质条件下频率空间域有限差分法保幅偏移.地球物理学报,2008,51(5):1511-1519.Ye Y M,Li Z C,Tong Z Q.Preserved-amplitude migration with dual-complexity.Chinese J.Geophys(in Chinese),2008,51(5):1511-1519.
[24]崔兴福,张关泉,吴雅丽.三维非均匀介质中真振幅地震偏移算子研究.地球物理学报,2004,47(3):509-513.Cui X F,Zhang G Q,Wu Y L.True amplitude seismic migration operator in3-D heterogeneous medium.Chinese J.Geophys.(in Chinese),2004,47(3):509-513.
[25]Zhang Y,Xu S,Zhang G Q,et al.How to obtain true amplitude common-angle gathers from one-way wave equation migration.74th Ann.Internat,Mtg:Soc.of Expl.Geophys.1021-1024.
[26]陈生昌,曹景忠,马在田.稳定的Born近似叠前深度偏移方法.石油地球物理勘探,2001,36(3):291-296.Chen S C,Cao J Z,Ma Z T.Stable pre-stack depth migration method with Born approximation.OGP(in Chinese),2001,36(3):291-296.
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