TI介质弹性波传播特征及qP波深度偏移方法研究
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摘要
地震各向异性研究已经成为地震学研究领域中的前沿课题之一,开展地震各向异性研究对认知地球介质结构、勘探开发复杂油气藏和预报地质灾害均具有理论意义和实用价值。针对沉积岩普遍存在的各向异性介质,深入研究了TTI介质弹性波传播特征、弹性波波动方程分解和VTI介质Born近似qP波深度偏移成像方法。
相速度、群速度是弹性波传播的重要特征。从TTI介质弹性波Christoffel方程出发,研究了TTI介质弹性波传播的相速度、群速度和偏振方向。在此基础上,进一步讨论了TTI介质弹性波反射、透射特征,为各向异性介质AVO研究奠定了理论基础。
波动方程分解在地震偏移成像和多分量地震学理论研究中具有非常重要的作用。从Thomsen弱各向异性理论与声学假设条件两个途径对TTI介质弹性波波动方程进行了分解,获得了TTI介质中描述qP波传播具有较高精度的波动方程,为研究VTI介质单程双域传播算子和建立VTI介质深度偏移算法奠定了理论基础。
在波动方程深度偏移成像过程中,波场延拓算子和算法流程是地震偏移成像的核心。从VTI介质qP波波动方程出发,建立了VTI介质Born近似qP波单程双域传播算子,由各向同性介质qP波扩展局部Born近似传播算子和各向异性扰动项组成。在该算子研究的基础上,建立了VTI介质qP波深度偏移算法流程,并实现了叠前和叠后深度偏移。叠前深度偏移和叠后深度偏移均获得了较好的成像效果,证明了VTI介质深度偏移成像算子的正确性、有效性和适应性。
Seismic anisotropy has been one of the latest scientific research topics in seismology, and also it is a great challenge for seismology theory study and application. Carrying out seismic anisotropy research has great academic significance and applied value for the cognition of earth media configuration, the exploration and development of complex oil gas reservoir, the forecast of the geological disaster. For the ubiquitous anisotropic media in the sedimentary rock, the elastic wave propagation characteristics in the TI media, the decomposition of elastic wave equation, one-way dual-domain propagation operator for qP wave and the wave equation depth migration imaging method in VTI media are systematically studied.
Phase velocity and group velocity are important characteristics of elastic wave propagation. According to the elastic wave Christoffel equation in TTI media, we have a research on phase velocity, group velocity and polarization direction for elastic wave propagation in TTI media. Based on them, elastic reflection characteristic and transmission characteristic in TTI media are discussed, which provides a basis for anisotropy AVO study.
Wave equation decomposition plays a very important role in the research of seismic migration imaging and multi-component seismology. The decomposition of elastic wave equation in TTI media is carried out on the base of Thomsen weak anisotropy theory and acoustic assumption condition. The result shows that high accuracy wave equation describing qP wave propagation in the TTI media can be obtained through wave equation decomposition, which plays a foundation for studying one-way dual-domain propagation operator in VTI media and establishing depth migration algorithm in VTI media.
In the process of wave equation depth migration imaging, the core things of seismic migration imaging are the wave field propagation operator and the algorithm flow. On the basis of qP Wave equation in VTI media, we thoroughly studies Born one-way dual-domain propagator for qP wave in VTI media. The operator consists of the extended local Born approximate operator in isotropic media and anisotropic perturbation operator. Basing on one-way dual-domain propagator in VTI media, the qP wave depth migration algorithm flow in anisotropic media is established, and prestack and poststack depth migration are carried out. Not only prestack depth migration but also poststack depth migration has obtained good imaging results, and these results validate the accuracy, validity and compatibility of depth migration imaging operator in VTI media.
相速度、群速度是弹性波传播的重要特征。从TTI介质弹性波Christoffel方程出发,研究了TTI介质弹性波传播的相速度、群速度和偏振方向。在此基础上,进一步讨论了TTI介质弹性波反射、透射特征,为各向异性介质AVO研究奠定了理论基础。
波动方程分解在地震偏移成像和多分量地震学理论研究中具有非常重要的作用。从Thomsen弱各向异性理论与声学假设条件两个途径对TTI介质弹性波波动方程进行了分解,获得了TTI介质中描述qP波传播具有较高精度的波动方程,为研究VTI介质单程双域传播算子和建立VTI介质深度偏移算法奠定了理论基础。
在波动方程深度偏移成像过程中,波场延拓算子和算法流程是地震偏移成像的核心。从VTI介质qP波波动方程出发,建立了VTI介质Born近似qP波单程双域传播算子,由各向同性介质qP波扩展局部Born近似传播算子和各向异性扰动项组成。在该算子研究的基础上,建立了VTI介质qP波深度偏移算法流程,并实现了叠前和叠后深度偏移。叠前深度偏移和叠后深度偏移均获得了较好的成像效果,证明了VTI介质深度偏移成像算子的正确性、有效性和适应性。
Seismic anisotropy has been one of the latest scientific research topics in seismology, and also it is a great challenge for seismology theory study and application. Carrying out seismic anisotropy research has great academic significance and applied value for the cognition of earth media configuration, the exploration and development of complex oil gas reservoir, the forecast of the geological disaster. For the ubiquitous anisotropic media in the sedimentary rock, the elastic wave propagation characteristics in the TI media, the decomposition of elastic wave equation, one-way dual-domain propagation operator for qP wave and the wave equation depth migration imaging method in VTI media are systematically studied.
Phase velocity and group velocity are important characteristics of elastic wave propagation. According to the elastic wave Christoffel equation in TTI media, we have a research on phase velocity, group velocity and polarization direction for elastic wave propagation in TTI media. Based on them, elastic reflection characteristic and transmission characteristic in TTI media are discussed, which provides a basis for anisotropy AVO study.
Wave equation decomposition plays a very important role in the research of seismic migration imaging and multi-component seismology. The decomposition of elastic wave equation in TTI media is carried out on the base of Thomsen weak anisotropy theory and acoustic assumption condition. The result shows that high accuracy wave equation describing qP wave propagation in the TTI media can be obtained through wave equation decomposition, which plays a foundation for studying one-way dual-domain propagation operator in VTI media and establishing depth migration algorithm in VTI media.
In the process of wave equation depth migration imaging, the core things of seismic migration imaging are the wave field propagation operator and the algorithm flow. On the basis of qP Wave equation in VTI media, we thoroughly studies Born one-way dual-domain propagator for qP wave in VTI media. The operator consists of the extended local Born approximate operator in isotropic media and anisotropic perturbation operator. Basing on one-way dual-domain propagator in VTI media, the qP wave depth migration algorithm flow in anisotropic media is established, and prestack and poststack depth migration are carried out. Not only prestack depth migration but also poststack depth migration has obtained good imaging results, and these results validate the accuracy, validity and compatibility of depth migration imaging operator in VTI media.
引文
[1] Aki K., Richards P.G.. Quantitative seismology: Theory and methods. W. H. Freeman and Company, 1980, volumes 1 and 2
[2] Alkhalifah T., Larner K.. Migration error in transversely isotropic media: Geophysics, 1994; 59(9): 1405～1418
[3] Alkhalifah T.. Gaussian beam depth migration for anisotropic media. Geophysics, 1995; 60(5): 1474～1484
[4] Alkhalifah T.. Acoustic approximation for processing in transversely isotropic media. Geophysics, 1998; 63(2): 623～631
[5] Alkhalifah T.. Prestack phase-shift migration of separate offsets. Geophysics, 2000; 65(4): 1179～1194
[6] Alkhalifah T.. An acoustic wave equation for anisotropic media. Geophysics, 2000; 65(4): 1239～1250
[7] Alkhalifah T.. An acoustic wave equation for orthorhombic media. Geophysics, 2003; 68(4): 1169～1172
[8] Cheadle S.P., Brown R. J., Lawton D. C.. Orthorhombic anisotropy: A physical modeling study. Geophysics, 1991; 56(10), 1603～1613
[9] Crampin S.. A review of wave motion in anisotropic and cracked elastic-media. Wave Motion, 1981; 3: 343～391
[10] Crampin S.. Effective anisotropic elastic constants for wave propagation through cracked solids. Geophys. J. R. astr. Soc., 1984; 76: 135～145
[11] Daley P.F., Hron F.. Reflection and transmission coefficients for seismic waves in ellipsoidally anisotropic media. Geophysics, 1979; 44(1): 27～38
[12] Ferguson Robert J., Margrave Gary F.. Depth imaging in anisotropic media by symmetric non-stationary phase shift. Geophysical Prospecting, 2002; 50: 281～288
[13] Gajewski, D., Psencik I.. qP wave phase velocities in weakly anisotropic media–perturbation approach. 66th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded abstracts, 1996: 1507～1510
[14] Gonzalez A., Lynn W., Robinson W.. Prestack frequency-wave number (f-k) migration in a transversely isotropic medium. 61st Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1991: 1155～1157
[15] Hawkins K., Leggott R., Gareth Williams. An integrated geoscience approach to reservoir imaging using anisotropic pre-SDM 72nd Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 2002: 472～475
[16] Hokstad K., Sollie R.. Multi-component elastic anisotropic Kirchhoff migration. 68th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1998: 121～124
[17] Issac J.H., Lawton D.C.. Image mispositioning duo to dipping TI media: A physical seismic modeling study. Geophysics, 1999; 64(4): 1230～1238
[18] Kitchenside P.. Phase shift-based migration for transverse anisotropy. 61st Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1991: 993～996
[19] Larner K., Cohen J.K.. Migration error in transversely isotropic media with linear velocity variation in depth: Geophysics, 1993; 58(10): 1454～1467
[20] Le Rousseau. Depth migration in heterogeneous, transversely isotropic media with the phase-shift-plus-interpolation method. 67th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1997: 1703～1706
[21] Le Rousseau J. H., De Hoop M.V.. Scalar generalized-screen algorithms in transversely isotropic media with a vertical symmetry axis. Geophysics, 2001; 66(5): 1538～1550
[22] Lian-jie H., Michael C., Ru-shan Wu. Extended local Born Fourier migration method. Geophysics, 1999; 64(5): 1524～1534
[23] Lian-jie H., Michael C., Ru-shan Wu. Extended local Rytov Fourier migration method. Geophysics, 1999; 64(5): 1535～1545
[24] Linbin Zhang et al. An acoustic wave equation for modeling in tilted TI media. 73nd Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts,Expanded Abstracts, 2003: 153～156
[25] Meadows M.A., Abriel W.L.. 3-D poststack phase-shift migration in transversely isotropic media. 64th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts,Expanded Abstracts, 1994: 1205～1208
[26] Postma G.W.. Wave propagation in a stratified medium. Geophysics, 1955; 20(4): 780～806.
[27] Qiyu Han, Ru-shan Wu. Depth imaging in strongly heterogeneous VTI media. 74th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 2004: 1061～1064
[28] Qiyu Han, Ru-shan Wu. A one-way dual-domain propagator for scalar qP-waves in VTI media. Geophysics, 2005; 70(2): D9～D17
[29] Ristow D.. 3-D finite difference migration in azimuthally anisotropic media: 68th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1998: 1823～1826
[30] Clayton R.W., Stolt R. H.. A Born-WKBJ inversion method for acoustic reflection data. Geophysics, 1981; 46(11): 1559～1567
[31] Schoenberg M., de Hoop M.V.. Approximate dispersion relations for qP-qSV-waves in transversely isotropic media. Geophysics, 2000; 65(3): 919～933
[32] Sena A.G., Toksoz M.N.. Kirchhoff migration and velocity analysis for converted and nonconverted waves in anisotropic media. Geophysics, 1993; 58(2): 265～276
[33] Thomsen L.. Weak elastic anisotropy. Geophysics, 1986; 51(10): 1954～1966
[34] Uren N.F., Gardner G. H., McDonald J. A.. The migrator’s equation for anisotropic media. Geophysics, 1990; 55(11): 1429～1434
[35] Uzcategui O.. 2-D depth migration in transversely isotropic media using explicit operators. Geophysics, 1995; 60(6): 1819～1829
[36] Zhang J., Verschuur D.J., Wapenaar C.P.A.. Depth migration of shot records in heterogeneous transversely isotropic media using optimum explicit operators. Geophysical Prospecting, 2001; 49: 287～299
[37] 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.地球物理学报,2001;44(5):704～709
[38] 程玖兵,王华忠,于富文等.波动方程共炮检距道集叠前深度偏移.石油地球物理勘探,2001;36(5):526～532
[39] 杜世通.地震波动力学.山东东营:石油大学出版社,1996
[40] 贺振华,王才经,李建朝.反射地震资料偏移处理与反演方法.重庆:重庆大学出版社,1989
[41] 马在田等编著.计算地球物理学概论.上海:同济大学出版社, 1997
[42] 马在田.地震成像技术—有限差分法偏移.北京:石油工业出版社, 1989
[43] 宋海滨,马在田,张关泉.层状横向各向同性介质反问题初探.地球物理学报,1997;40(1):105～118
[44] 吴国忱,梁锴.VTI 介质准 P 波频率空间域组合边界条件研究.石油物探,2005;44(4):302～307
[45] 吴国忱,梁锴.VTI 介质频率空间域准 P 波正演模拟.石油地球物理勘探,2005;40(5):535～545
[46] 阴可,杨慧珠.各向异性介质中的 AVO.地球物理学报,1998;41(3):382～391
[2] Alkhalifah T., Larner K.. Migration error in transversely isotropic media: Geophysics, 1994; 59(9): 1405～1418
[3] Alkhalifah T.. Gaussian beam depth migration for anisotropic media. Geophysics, 1995; 60(5): 1474～1484
[4] Alkhalifah T.. Acoustic approximation for processing in transversely isotropic media. Geophysics, 1998; 63(2): 623～631
[5] Alkhalifah T.. Prestack phase-shift migration of separate offsets. Geophysics, 2000; 65(4): 1179～1194
[6] Alkhalifah T.. An acoustic wave equation for anisotropic media. Geophysics, 2000; 65(4): 1239～1250
[7] Alkhalifah T.. An acoustic wave equation for orthorhombic media. Geophysics, 2003; 68(4): 1169～1172
[8] Cheadle S.P., Brown R. J., Lawton D. C.. Orthorhombic anisotropy: A physical modeling study. Geophysics, 1991; 56(10), 1603～1613
[9] Crampin S.. A review of wave motion in anisotropic and cracked elastic-media. Wave Motion, 1981; 3: 343～391
[10] Crampin S.. Effective anisotropic elastic constants for wave propagation through cracked solids. Geophys. J. R. astr. Soc., 1984; 76: 135～145
[11] Daley P.F., Hron F.. Reflection and transmission coefficients for seismic waves in ellipsoidally anisotropic media. Geophysics, 1979; 44(1): 27～38
[12] Ferguson Robert J., Margrave Gary F.. Depth imaging in anisotropic media by symmetric non-stationary phase shift. Geophysical Prospecting, 2002; 50: 281～288
[13] Gajewski, D., Psencik I.. qP wave phase velocities in weakly anisotropic media–perturbation approach. 66th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded abstracts, 1996: 1507～1510
[14] Gonzalez A., Lynn W., Robinson W.. Prestack frequency-wave number (f-k) migration in a transversely isotropic medium. 61st Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1991: 1155～1157
[15] Hawkins K., Leggott R., Gareth Williams. An integrated geoscience approach to reservoir imaging using anisotropic pre-SDM 72nd Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 2002: 472～475
[16] Hokstad K., Sollie R.. Multi-component elastic anisotropic Kirchhoff migration. 68th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1998: 121～124
[17] Issac J.H., Lawton D.C.. Image mispositioning duo to dipping TI media: A physical seismic modeling study. Geophysics, 1999; 64(4): 1230～1238
[18] Kitchenside P.. Phase shift-based migration for transverse anisotropy. 61st Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1991: 993～996
[19] Larner K., Cohen J.K.. Migration error in transversely isotropic media with linear velocity variation in depth: Geophysics, 1993; 58(10): 1454～1467
[20] Le Rousseau. Depth migration in heterogeneous, transversely isotropic media with the phase-shift-plus-interpolation method. 67th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1997: 1703～1706
[21] Le Rousseau J. H., De Hoop M.V.. Scalar generalized-screen algorithms in transversely isotropic media with a vertical symmetry axis. Geophysics, 2001; 66(5): 1538～1550
[22] Lian-jie H., Michael C., Ru-shan Wu. Extended local Born Fourier migration method. Geophysics, 1999; 64(5): 1524～1534
[23] Lian-jie H., Michael C., Ru-shan Wu. Extended local Rytov Fourier migration method. Geophysics, 1999; 64(5): 1535～1545
[24] Linbin Zhang et al. An acoustic wave equation for modeling in tilted TI media. 73nd Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts,Expanded Abstracts, 2003: 153～156
[25] Meadows M.A., Abriel W.L.. 3-D poststack phase-shift migration in transversely isotropic media. 64th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts,Expanded Abstracts, 1994: 1205～1208
[26] Postma G.W.. Wave propagation in a stratified medium. Geophysics, 1955; 20(4): 780～806.
[27] Qiyu Han, Ru-shan Wu. Depth imaging in strongly heterogeneous VTI media. 74th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 2004: 1061～1064
[28] Qiyu Han, Ru-shan Wu. A one-way dual-domain propagator for scalar qP-waves in VTI media. Geophysics, 2005; 70(2): D9～D17
[29] Ristow D.. 3-D finite difference migration in azimuthally anisotropic media: 68th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1998: 1823～1826
[30] Clayton R.W., Stolt R. H.. A Born-WKBJ inversion method for acoustic reflection data. Geophysics, 1981; 46(11): 1559～1567
[31] Schoenberg M., de Hoop M.V.. Approximate dispersion relations for qP-qSV-waves in transversely isotropic media. Geophysics, 2000; 65(3): 919～933
[32] Sena A.G., Toksoz M.N.. Kirchhoff migration and velocity analysis for converted and nonconverted waves in anisotropic media. Geophysics, 1993; 58(2): 265～276
[33] Thomsen L.. Weak elastic anisotropy. Geophysics, 1986; 51(10): 1954～1966
[34] Uren N.F., Gardner G. H., McDonald J. A.. The migrator’s equation for anisotropic media. Geophysics, 1990; 55(11): 1429～1434
[35] Uzcategui O.. 2-D depth migration in transversely isotropic media using explicit operators. Geophysics, 1995; 60(6): 1819～1829
[36] Zhang J., Verschuur D.J., Wapenaar C.P.A.. Depth migration of shot records in heterogeneous transversely isotropic media using optimum explicit operators. Geophysical Prospecting, 2001; 49: 287～299
[37] 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.地球物理学报,2001;44(5):704～709
[38] 程玖兵,王华忠,于富文等.波动方程共炮检距道集叠前深度偏移.石油地球物理勘探,2001;36(5):526～532
[39] 杜世通.地震波动力学.山东东营:石油大学出版社,1996
[40] 贺振华,王才经,李建朝.反射地震资料偏移处理与反演方法.重庆:重庆大学出版社,1989
[41] 马在田等编著.计算地球物理学概论.上海:同济大学出版社, 1997
[42] 马在田.地震成像技术—有限差分法偏移.北京:石油工业出版社, 1989
[43] 宋海滨,马在田,张关泉.层状横向各向同性介质反问题初探.地球物理学报,1997;40(1):105～118
[44] 吴国忱,梁锴.VTI 介质准 P 波频率空间域组合边界条件研究.石油物探,2005;44(4):302～307
[45] 吴国忱,梁锴.VTI 介质频率空间域准 P 波正演模拟.石油地球物理勘探,2005;40(5):535～545
[46] 阴可,杨慧珠.各向异性介质中的 AVO.地球物理学报,1998;41(3):382～391