共炮检距道集波动方程保幅叠前深度偏移方法
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摘要
本文提出了一种基于双平方根算子的共炮检距道集波动方程保幅叠前深度偏移方法,将振幅误差补偿作为偏移的一部分与“运动学偏移”一起在偏移过程中实现.其基本内容包括:(1)从保幅的单平方根算子方程出发,推导出由双平方根算子定义的保幅单程波方程;(2)根据地震波摄动理论把速度场分裂为层内常速背景和变速扰动,分别在频率-波数域和频率-空间域求得波场深度延拓的偏移时移量及振幅校正系数,从而得到最终的DSR保幅波场延拓算子;(3)在高频假设条件下,把DSR保幅波场延拓公式中的积分运算进行稳相近似,得到保幅波场延拓的相移公式.理论分析和模型数值试验表明,该方法不但可以使散射能量聚焦、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,为后续的地震属性分析(如AVO/AVA)提供更真实的地震信息.
This article proposes a wave equation preserved-amplitude prestack depth migration method for common offset gathers based on double-square-root equation.In this method,amplitude errors compensation is regarded as one part of migration and can be accomplished with "kinematics migration" during the migration.Its basic theory is as follows.(1) We can derive preserved-amplitude one-way wave equation defined by double-square-root(DSR) operator from the equation of preserved-amplitude single-square-root operator;(2) According to the perturbation theory of seismic wave,we split the velocity field into intraformational constant velocity background and variable velocity disturbance.Then we calculate time-shift quantity of migration and amplitude correction coefficients for wavefield continuation in frequency-wave number domain and frequency-spatial domain,respectively.So we obtain the final DSR preserved-amplitude field continuation operation.(3) The phase-shift formulae for preserved-amplitude wave field continuation can be obtained by stationary phase approximation for integral operation of DSR preserved-amplitude wave field continuation formulae in a condition of high-frequence hypothesis.The theoretic analysis and models on synthetic datasets show that the proposed method not only can focus scattering energy,turn over to the correct position and improve the imaging fidelity,but also can output the correct amplitude information which exactly reflects underground reflection factor.So this method can provide more real seismic information for the following attribute analysis,such as AVO/AVA.
This article proposes a wave equation preserved-amplitude prestack depth migration method for common offset gathers based on double-square-root equation.In this method,amplitude errors compensation is regarded as one part of migration and can be accomplished with "kinematics migration" during the migration.Its basic theory is as follows.(1) We can derive preserved-amplitude one-way wave equation defined by double-square-root(DSR) operator from the equation of preserved-amplitude single-square-root operator;(2) According to the perturbation theory of seismic wave,we split the velocity field into intraformational constant velocity background and variable velocity disturbance.Then we calculate time-shift quantity of migration and amplitude correction coefficients for wavefield continuation in frequency-wave number domain and frequency-spatial domain,respectively.So we obtain the final DSR preserved-amplitude field continuation operation.(3) The phase-shift formulae for preserved-amplitude wave field continuation can be obtained by stationary phase approximation for integral operation of DSR preserved-amplitude wave field continuation formulae in a condition of high-frequence hypothesis.The theoretic analysis and models on synthetic datasets show that the proposed method not only can focus scattering energy,turn over to the correct position and improve the imaging fidelity,but also can output the correct amplitude information which exactly reflects underground reflection factor.So this method can provide more real seismic information for the following attribute analysis,such as AVO/AVA.
引文
[1]刘礼农,陈树民,张剑锋.稀疏采样下陡角度构造的波动方程深度偏移成像[J].地球物理学报,2006,49(5):1452~1459.
[2]吕小林,刘洪.波动方程深度波场延拓算子的快速重建[J].地球物理学进展,2005,20(1):24~28.
[3]刘喜武,刘洪.波动方程地震偏移成像方法的现状与进展[J].地球物理学进展.2002,17(4):582~591.
[4]刘伊克,常旭,卢孟夏.目标函数叠前保幅偏移方法与应用[J].地球物理学报,2006,49(4):1150~1154.
[5]李振春.地震成像理论与方法[D].东营:石油大学研究生院,2004.
[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]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.
[8]Gazdag J.Wave equation migration with the phase-shift meth-od[J].Geophysics,1978,43(10):1342~1351.
[9]Gazdag J,Sguazzero P.Migration of seismic data by phase-shift plus interpolation[J].Geophysics,1984,49(2):124~131.
[10]陈生昌,曹景忠,马在田.混合域单程波传播算子及其在偏移成像中的应用[J].地球物理学进展,2003,18(2):210~217.
[11]陈生昌,马在田.波动方程的高阶广义屏叠前深度偏移[J].地球物理学报,2006,49(5):1445~1451.
[12]金胜汶,许士勇,吴如山.基于波动方程的广义屏叠前深度偏移[J].地球物理学报,2002,45(5):684~690.
[13]Stoffa P L,Fokkema J,Luna Freire,et al.Split step Fouriermigration[J].Geophysics,1990,55(4):410~421.
[14]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[J].地球物理学报,2004,47(3):509~513.
[15]刘定进,印兴耀.傅里叶有限差分法保幅叠前深度偏移方法[J].地球物理学报(待发表).
[16]徐升,Gilles Lambaré.复杂介质下保真振幅Kirchhoff深度偏移[J].地球物理学报,2006,49(5):1431~1444.
[17]张平平,常旭.保幅偏移中的权函数[J].地球物理学进展,2006,21(1):203~207.
[18]张宇.振幅保真的单程波方程偏移理论[J].地球物理学报,2006,49(5):1410~1430.
[19]Ekren B O,Ursin B.True-amplitude frequency-wavenumberconstant-offset migration[J].Geophysics,1999,64:915~924.
[20]Gray S.True-amplitude seismic migration:A comparison ofthree approaches[J].Geophysics,1997,62:629~38.
[21]Operto S,LambaréG,Podvin P and Thierry P.3-D pre-served amplitude prestack imaging of the Overthrust model[J].59th Ann.Mtg.,Eur.Assn.Geoscientists Eng.,Ex-panded Abstracts,1997a:A043.
[22]Zhang Y,Sun J,et al.Towards accurate amplitudes for one-way wavefield extrapolation of 3-d common shot records[J].2001,71th Ann.Mtg.,Soc.Expl.Geophys.
[23]Zhang Y,Zhang G.Theory of true amplitude common-shotmigration[J],2002,72th Ann.Mtg.,Soc.Expl.Geophys.
[24]程玖兵,王华忠,马在田.窄方位地震数据双平方根方程偏移方法探讨[J].地球物理学报,2000,48(2):399~405.
[25]程玖兵,王华忠,马在田.双平方根方程三维叠前深度偏移[J].地球物理学报,2003,46(5):676~683.
[26]陈湛文,陈小宏.用共方位角偏移实现叠前二维资料三维化成像[J].地球物理学进展,2005,20(4):1021~1026.
[27]孙沛勇,张叔伦.双平方根叠前深度偏移的广义高阶屏方法[J].石油地球物理勘探,2001,36(4):398~407.
[28]Deregowski S M,Rocca F.Geometric optics and wave theoryof constant offset section in layered meadia[J].GeophysicsalProspecting,1981,29:374~406.
[29]Jin S W,Wu R S.Common offset pseudo-screen depth migra-tion[J].Expanded Abstracts of 69th SEG Mtg,1999,1516~1519
[30]Popovici A M.Prestack migration by split-step DSR[J].Ge-ophysics,1996,61(5):1412~1416.
[31]Wapenaar C P A,Berkhout A J.Fullprestack versus shot re-cord migration[J].57th Annual Internat.Mtg.,Soc.Expl.Geophys.,Expanded Abstracts,Π:1999:1110~1113.
[32]印兴耀.基于HAMILTON方法的波场变换[D].北京:中国科学院地球物理研究所,1998.
[2]吕小林,刘洪.波动方程深度波场延拓算子的快速重建[J].地球物理学进展,2005,20(1):24~28.
[3]刘喜武,刘洪.波动方程地震偏移成像方法的现状与进展[J].地球物理学进展.2002,17(4):582~591.
[4]刘伊克,常旭,卢孟夏.目标函数叠前保幅偏移方法与应用[J].地球物理学报,2006,49(4):1150~1154.
[5]李振春.地震成像理论与方法[D].东营:石油大学研究生院,2004.
[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]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.
[8]Gazdag J.Wave equation migration with the phase-shift meth-od[J].Geophysics,1978,43(10):1342~1351.
[9]Gazdag J,Sguazzero P.Migration of seismic data by phase-shift plus interpolation[J].Geophysics,1984,49(2):124~131.
[10]陈生昌,曹景忠,马在田.混合域单程波传播算子及其在偏移成像中的应用[J].地球物理学进展,2003,18(2):210~217.
[11]陈生昌,马在田.波动方程的高阶广义屏叠前深度偏移[J].地球物理学报,2006,49(5):1445~1451.
[12]金胜汶,许士勇,吴如山.基于波动方程的广义屏叠前深度偏移[J].地球物理学报,2002,45(5):684~690.
[13]Stoffa P L,Fokkema J,Luna Freire,et al.Split step Fouriermigration[J].Geophysics,1990,55(4):410~421.
[14]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[J].地球物理学报,2004,47(3):509~513.
[15]刘定进,印兴耀.傅里叶有限差分法保幅叠前深度偏移方法[J].地球物理学报(待发表).
[16]徐升,Gilles Lambaré.复杂介质下保真振幅Kirchhoff深度偏移[J].地球物理学报,2006,49(5):1431~1444.
[17]张平平,常旭.保幅偏移中的权函数[J].地球物理学进展,2006,21(1):203~207.
[18]张宇.振幅保真的单程波方程偏移理论[J].地球物理学报,2006,49(5):1410~1430.
[19]Ekren B O,Ursin B.True-amplitude frequency-wavenumberconstant-offset migration[J].Geophysics,1999,64:915~924.
[20]Gray S.True-amplitude seismic migration:A comparison ofthree approaches[J].Geophysics,1997,62:629~38.
[21]Operto S,LambaréG,Podvin P and Thierry P.3-D pre-served amplitude prestack imaging of the Overthrust model[J].59th Ann.Mtg.,Eur.Assn.Geoscientists Eng.,Ex-panded Abstracts,1997a:A043.
[22]Zhang Y,Sun J,et al.Towards accurate amplitudes for one-way wavefield extrapolation of 3-d common shot records[J].2001,71th Ann.Mtg.,Soc.Expl.Geophys.
[23]Zhang Y,Zhang G.Theory of true amplitude common-shotmigration[J],2002,72th Ann.Mtg.,Soc.Expl.Geophys.
[24]程玖兵,王华忠,马在田.窄方位地震数据双平方根方程偏移方法探讨[J].地球物理学报,2000,48(2):399~405.
[25]程玖兵,王华忠,马在田.双平方根方程三维叠前深度偏移[J].地球物理学报,2003,46(5):676~683.
[26]陈湛文,陈小宏.用共方位角偏移实现叠前二维资料三维化成像[J].地球物理学进展,2005,20(4):1021~1026.
[27]孙沛勇,张叔伦.双平方根叠前深度偏移的广义高阶屏方法[J].石油地球物理勘探,2001,36(4):398~407.
[28]Deregowski S M,Rocca F.Geometric optics and wave theoryof constant offset section in layered meadia[J].GeophysicsalProspecting,1981,29:374~406.
[29]Jin S W,Wu R S.Common offset pseudo-screen depth migra-tion[J].Expanded Abstracts of 69th SEG Mtg,1999,1516~1519
[30]Popovici A M.Prestack migration by split-step DSR[J].Ge-ophysics,1996,61(5):1412~1416.
[31]Wapenaar C P A,Berkhout A J.Fullprestack versus shot re-cord migration[J].57th Annual Internat.Mtg.,Soc.Expl.Geophys.,Expanded Abstracts,Π:1999:1110~1113.
[32]印兴耀.基于HAMILTON方法的波场变换[D].北京:中国科学院地球物理研究所,1998.
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