傅里叶有限差分法保幅叠前深度偏移方法
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摘要
地震数据中饱含有丰富的走时信息和振幅信息.为解决传统偏移方法中几何扩散和入射角变化引起的振幅误差问题,本文提出了一种实用的波动方程保幅地震偏移方法.该方法从全声波方程出发进行单程波保幅分解,得到直观、高效率的直接面对地震波传播波场的压力分量进行延拓的保幅偏移单程波方程,进而推导出一个含有6项的傅里叶有限差分法保幅偏移的算子方程;修改边界条件和成像条件,使修改后的边界条件和成像方程中考虑振幅补偿,从而从三方面补偿几何扩散损失和入射角变化对振幅的影响.脉冲响应测试、单炮记录的数值试验以及SEG/EAGE盐丘模型的叠前偏移结果表明,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.
Seismic data contain rich travel-time and amplitude information.In order to solve the problem of amplitude errors caused by geometric spreading and incidence angle variations,we propose a practical wave equation preserved-amplitude migration method.In this method,we derive the high efficiency direct-viewing one-way wave equation for preserved-amplitude migration from full acoustic wave equation using one-way wave's preserved-amplitude decomposition,which is extrapolated while facing the pressure component of the seismic wavefield.Then we derive a 6-item operator equation based on the method of Fourier finite-difference preserved-amplitude migration,and modify boundary conditions and imaging conditions to take amplitude compensation into account in modified boundary conditions and imaging equations.So we compensate for amplitudes affected by geometric spreading loss and incidence angle variations from three aspects above.Theoretical model testing and real data processing indicate that this method not only can make scattering energy be focused and migrated to the correct position to improve imaging accuracy,but also can output the amplitude information which reflects the correct subsurface reflection coefficients.So this method can provide more real seismic information for following attribute analysis,such as AVO/AVA.
Seismic data contain rich travel-time and amplitude information.In order to solve the problem of amplitude errors caused by geometric spreading and incidence angle variations,we propose a practical wave equation preserved-amplitude migration method.In this method,we derive the high efficiency direct-viewing one-way wave equation for preserved-amplitude migration from full acoustic wave equation using one-way wave's preserved-amplitude decomposition,which is extrapolated while facing the pressure component of the seismic wavefield.Then we derive a 6-item operator equation based on the method of Fourier finite-difference preserved-amplitude migration,and modify boundary conditions and imaging conditions to take amplitude compensation into account in modified boundary conditions and imaging equations.So we compensate for amplitudes affected by geometric spreading loss and incidence angle variations from three aspects above.Theoretical model testing and real data processing indicate that this method not only can make scattering energy be focused and migrated to the correct position to improve imaging accuracy,but also can output the amplitude information which reflects the correct subsurface reflection coefficients.So this method can provide more real seismic information for following attribute analysis,such as AVO/AVA.
引文
[1]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.石油地球物理勘探,2001,36(4):408-413Cheng J B,Wang H Z,Ma Z T.Finite-difference pre-stack depthmigration with errors compensation.Oil Geophysical Prospecting(inChinese),2001,36(4):408-413
[2]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.地球物理学报,2001,44(3):389-395Cheng J B,Wang H Z,Ma Z T.Pre-stack depth migration withfinite-difference method in frequency-space domain.Chinese J.Geophys.(in Chinese),2001,44(3):389-395
[3]Ristow D,Rühl T.3-D implicit finite difference migration bymultiway splitting.Geophysics,1997,62(5):554-567
[4]Gazdag J.Wave equation migration with the phase-shift method.Geophysics,1978,43(10):1342-1351
[5]Gazdag J,Sguazzero P.Migration of seismic data by phase-shift plusinterpolation.Geophysics,1984,49(2):124-131
[6]Stoffa P L,Fokkema J,Luna Freire,et al.Split step Fouriermigration.Geophysics,1990,55(4):410-421
[7]Ristow D,Rühl T.Fourier finite-difference migration.Geophysics,1994,59(12):1882-1893
[8]吴如山,金胜汶,谢小碧.广义屏传播算子及其在地震波偏移成像方面的应用.石油地球物理勘探,2001,36(6):655-664Wu R S,Jin S W,Xie X B.Generalized screen propagator and itsapplication in seismic wave migration imaging.Oil GeophysicalProspecting(in Chinese),2001,36(6):655-664
[9]Gray S.True-amplitude seismic migration:A comparison of threeapproaches.Geophysics,1997,62(3):629-638
[10]Ekren B O,Ursin B.True-amplitude frequency-wavenumberconstant-offset migration.Geophysics,1999,64(3):915-924
[11]Thierry P,Lambar?G,Podvin P,et al.3D prestack preservedamplitude migration:Application to real data.66th Ann.Internat.Mtg.,Soc.Expl.Geophys..Expanded Abstracts,1995.555-558
[12]Operto S,Lambar?G,Podvin P,et al.3-D preserved amplitudeprestack imaging of the Overthrust model.59th Ann.Mtg.,Eur.Assn.Geoscientists Eng.,Expanded Abstracts,1997.A043
[13]Baina R,Thierry P,Calandra H.3D preserved-amplitude prestackdepth migration and amplitude versus angle relevance.The LeadingEdge,2002,21(12):1237-1241
[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.地球物理学报,2004,47(3):509-513Cui X F,Zhang G Q,Wu Y L.True amplitude seismic migrationoperator in 3-D heterogeneous medium.Chinese J.Geophys.(inChinese),2004,47(3):509-513
[15]刘东奇,崔兴福,张关泉.波动方程混合法真振幅偏移.石油地球物理勘探,2004,39(3):283-286Liu D Q,Cui X F,Zhang G Q.True-amplitude migration of wave-equation hybrid method.Oil Geophysical Prospecting(in Chinese),2004,39(3):283-286
[16]杨午阳,Houzhu Zhang,茅金根等.F-X域弹性波动方程保幅偏移.石油物探,2003,42(3):285-288Yang W Y,Zhang H Z,Mao J G,et al.Finite-difference migrationwith compensation for absorption,dispersion and transmission lossesin seismic data.Geophysical Prospecting for Petroleum(in Chinese),2003,42(3):285-288
[17]孙建国.Kirchhoff型真振幅偏移与反偏移.勘探地球物理进展,2002,25(6):1-5Sun J G.Kirchhoff-type true-amplitude migration and demigration.Progress in Exploration Geophysics(in Chinese),2002,25(6):1-5
[18]徐升,Gilles Lambaré.复杂介质下保真振幅Kirchhoff深度偏移.地球物理学报,2006,49(5):1431-1444Xu S,Gilles Lambaré.True amplitude Kirchhoff prestack migrationin complex media.Chinese J.Geophys.(in Chinese),2006,49(5):1431-1444
[19]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):251-263Zhang G Q.System of coupled equations for downgoing and upcomingwaves.Acta Math.Appl.Sinica(in Chinese),1993,16(2):251-263
[20]张关泉.波场分裂、平方根算子与偏移.反射地震学论文集.上海:同济大学出版社,2000.6-20Zhang G Q.Wavefield Decomposition,Square Root Operator andMigration.Refection Seismology Symposium(in Chinese).Shanghai:Tongji University Press,2000.6-20
[21]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):1410-1430Zhang Y.The theory of true amplitude one-way wave equationmigration.Chinese J.Geophys.(in Chinese),2006,49(5):1410-1430
[22]Zhang Y,Sun J,Gray S,et al.Towards accurate amplitudes for one-way wavefield extrapolation of 3-D common shot records.71st Ann.Internat.Mtg.,Soc.Expl.Geophys..Workshop,2001
[2]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.地球物理学报,2001,44(3):389-395Cheng J B,Wang H Z,Ma Z T.Pre-stack depth migration withfinite-difference method in frequency-space domain.Chinese J.Geophys.(in Chinese),2001,44(3):389-395
[3]Ristow D,Rühl T.3-D implicit finite difference migration bymultiway splitting.Geophysics,1997,62(5):554-567
[4]Gazdag J.Wave equation migration with the phase-shift method.Geophysics,1978,43(10):1342-1351
[5]Gazdag J,Sguazzero P.Migration of seismic data by phase-shift plusinterpolation.Geophysics,1984,49(2):124-131
[6]Stoffa P L,Fokkema J,Luna Freire,et al.Split step Fouriermigration.Geophysics,1990,55(4):410-421
[7]Ristow D,Rühl T.Fourier finite-difference migration.Geophysics,1994,59(12):1882-1893
[8]吴如山,金胜汶,谢小碧.广义屏传播算子及其在地震波偏移成像方面的应用.石油地球物理勘探,2001,36(6):655-664Wu R S,Jin S W,Xie X B.Generalized screen propagator and itsapplication in seismic wave migration imaging.Oil GeophysicalProspecting(in Chinese),2001,36(6):655-664
[9]Gray S.True-amplitude seismic migration:A comparison of threeapproaches.Geophysics,1997,62(3):629-638
[10]Ekren B O,Ursin B.True-amplitude frequency-wavenumberconstant-offset migration.Geophysics,1999,64(3):915-924
[11]Thierry P,Lambar?G,Podvin P,et al.3D prestack preservedamplitude migration:Application to real data.66th Ann.Internat.Mtg.,Soc.Expl.Geophys..Expanded Abstracts,1995.555-558
[12]Operto S,Lambar?G,Podvin P,et al.3-D preserved amplitudeprestack imaging of the Overthrust model.59th Ann.Mtg.,Eur.Assn.Geoscientists Eng.,Expanded Abstracts,1997.A043
[13]Baina R,Thierry P,Calandra H.3D preserved-amplitude prestackdepth migration and amplitude versus angle relevance.The LeadingEdge,2002,21(12):1237-1241
[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.地球物理学报,2004,47(3):509-513Cui X F,Zhang G Q,Wu Y L.True amplitude seismic migrationoperator in 3-D heterogeneous medium.Chinese J.Geophys.(inChinese),2004,47(3):509-513
[15]刘东奇,崔兴福,张关泉.波动方程混合法真振幅偏移.石油地球物理勘探,2004,39(3):283-286Liu D Q,Cui X F,Zhang G Q.True-amplitude migration of wave-equation hybrid method.Oil Geophysical Prospecting(in Chinese),2004,39(3):283-286
[16]杨午阳,Houzhu Zhang,茅金根等.F-X域弹性波动方程保幅偏移.石油物探,2003,42(3):285-288Yang W Y,Zhang H Z,Mao J G,et al.Finite-difference migrationwith compensation for absorption,dispersion and transmission lossesin seismic data.Geophysical Prospecting for Petroleum(in Chinese),2003,42(3):285-288
[17]孙建国.Kirchhoff型真振幅偏移与反偏移.勘探地球物理进展,2002,25(6):1-5Sun J G.Kirchhoff-type true-amplitude migration and demigration.Progress in Exploration Geophysics(in Chinese),2002,25(6):1-5
[18]徐升,Gilles Lambaré.复杂介质下保真振幅Kirchhoff深度偏移.地球物理学报,2006,49(5):1431-1444Xu S,Gilles Lambaré.True amplitude Kirchhoff prestack migrationin complex media.Chinese J.Geophys.(in Chinese),2006,49(5):1431-1444
[19]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):251-263Zhang G Q.System of coupled equations for downgoing and upcomingwaves.Acta Math.Appl.Sinica(in Chinese),1993,16(2):251-263
[20]张关泉.波场分裂、平方根算子与偏移.反射地震学论文集.上海:同济大学出版社,2000.6-20Zhang G Q.Wavefield Decomposition,Square Root Operator andMigration.Refection Seismology Symposium(in Chinese).Shanghai:Tongji University Press,2000.6-20
[21]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):1410-1430Zhang Y.The theory of true amplitude one-way wave equationmigration.Chinese J.Geophys.(in Chinese),2006,49(5):1410-1430
[22]Zhang Y,Sun J,Gray S,et al.Towards accurate amplitudes for one-way wavefield extrapolation of 3-D common shot records.71st Ann.Internat.Mtg.,Soc.Expl.Geophys..Workshop,2001
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