TTI介质Low-rank有限差分法高效正演模拟及逆时偏移
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摘要
计算效率是制约各向异性逆时偏移实用化的关键因素,此外,伪横波假象、数值频散以及不稳定问题也是TTI介质qP波正演模拟及逆时偏移的固有难题。Low-rank波场延拓算法虽能解决上述三方面问题,但其运算速度受模型参数限制,计算效率较低。为此,本文基于混合网格有限差分思想,给出一种新的紧致差分模板,并借助Low-rank分解求取与模型匹配的自适应差分系数,进而实现一种针对TTI介质的Low-rank有限差分法高效正演模拟及逆时偏移成像策略。数值模型测试结果表明:本文方法既继承了有限差分法高效灵活的特点,又拥有Low-rank波场延拓方法准确计算纯qP波波场的优势,即在提高计算效率的同时避免了伪横波假象和数值不稳定,是一种兼顾成像精度与计算效率的各向异性逆时偏移实用方法。
The computation efficiency is the key factor torestrict the practicality of anisotropic reverse time numerical dispersion,and instability are also inherent problems of TTI medium qP-wave forward modeling and reverse time migration.The low-rankwavefield extrapolation algorithm is basically free sion,and instability.However,this method is a time-consuming and inefficient because its compu-ting speed is controlled by model parameters.To differential template is proposed based on the idea of mixed-grid finite-difference,and the adaptive difference coefficient matched with the model is obtained by means of low-rank decomposition.Then,a low-rank finite-difference forward modeling and reverse time migration for TTI media are implemented.Numerical tests show that the proposed scheme is an anisotropic reverse time migration practical approach which combines high imaging accuracy and high calculation efficiency.The proposed scheme possesses the flexibility and efficiency of finite-difference method and pure-qP-wave precise calculation of low-rank wavefield extrapolation algorithm.So it can remove the pseudo shearwave artifacts and numerical instability while improving the computation efficiency.
The computation efficiency is the key factor torestrict the practicality of anisotropic reverse time numerical dispersion,and instability are also inherent problems of TTI medium qP-wave forward modeling and reverse time migration.The low-rankwavefield extrapolation algorithm is basically free sion,and instability.However,this method is a time-consuming and inefficient because its compu-ting speed is controlled by model parameters.To differential template is proposed based on the idea of mixed-grid finite-difference,and the adaptive difference coefficient matched with the model is obtained by means of low-rank decomposition.Then,a low-rank finite-difference forward modeling and reverse time migration for TTI media are implemented.Numerical tests show that the proposed scheme is an anisotropic reverse time migration practical approach which combines high imaging accuracy and high calculation efficiency.The proposed scheme possesses the flexibility and efficiency of finite-difference method and pure-qP-wave precise calculation of low-rank wavefield extrapolation algorithm.So it can remove the pseudo shearwave artifacts and numerical instability while improving the computation efficiency.
引文
[1] 孙伟家,符力耘,管西竹等.页岩气地震勘探中页岩各向异性的地震模拟研究.地球物理学报,2013,56(3):961-970.Sun Weijia,Fu Liyun,Guan Xizhu et al.A study on anisotropy of shale using seismic forward modeling in shale gas exploration.Chinese Journal of Geophysics,2013,56(3):961-970.
[2] 张广智,陈怀震,王琪等.基于碳酸盐岩裂缝岩石物理模型的横波速度和各向异性参数预测.地球物理学报,2013,56(5):1707-1715.Zhang Guangzhi,Chen Huaizhen,Wang Qi et al.Estimation of S-wave velocity and anisotropic parameters using fractured carbonate rock physics model.Chinese Journal of Geophysics,2013,56(5):1707-1715.
[3] 李振春,黄金强,黄建平等.基于平面波加速的VTI介质最小二乘逆时偏移.地球物理学报,2017,60(1):240-257.Li Zhenchun,Huang Jinqiang,Huang Jianping et al.Fast least-squares reverse time migration based on plane-wave encoding for VTI media.Chinese Journal of Geophysics,2017,60(1):240-257.
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[7] 张洪宙,王彦飞.VTI介质迭代正则化偏移反演算法.石油地球物理勘探,2014,49(6):1083-1090.Zhang Hongzhou and Wang Yanfei.Iterative regularization migration inversion in VTI media.OGP,2014,49(6):1083-1090.
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[11] 段鹏飞,程玖兵,陈爱萍等.TI介质局部角度域高斯束叠前深度偏移成像.地球物理学报,2013,56(12):4206-4214.Duan Pengfei,Cheng Jiubing,Chen Aiping et al.Local angle-domain Gaussian beam prestack depth migration in a TI media.Chinese Journal of Geophysics,2013,56(12):4206-4214.
[12] 韩建光,王赟,张晓波等.VTI介质高斯束叠前深度偏移.石油地球物理勘探,2015,50(2):267-273.Han Jianguang,Wang Yun,Zhang Xiaobo et al.Gaussian beam prestack depth migration in VTI media.OGP,2015,50(2):267-273.
[13] 段新意,李振春,黄建平等.各向异性介质共炮域高斯束叠前深度偏移.石油物探,2014,53(5):579-586.Duan Xinyi,Li Zhenchun,Huang Jianping et al.A prestack Gaussian beam depth migration in common-shot domain for anisotropic media.GPP,2014,53(5):579-586.
[14] 张凯,段新意,李振春等.角度域各向异性高斯束逆时偏移.石油地球物理勘探,2015,50(5):912-918.Zhang Kai,Duan Xinyi,Li Zhenchun et al.Angle domain reverse time migration with Gaussian beams in anisotropic media.OGP,2015,50(5):912-918.
[15] Thomsen L.Weak elastic anisotropy.Geophysics,1986,51(10):1954-1966.
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[18] Zhou H B,Zhang G Q,Bloor R.An anisotropic acoustic wave equation for modeling and migration in 2D TTI media.SEG Technical Program Expanded Abstracts,2006,25:194-198.
[19] Fletcher R P,Du X,Fowler P J.Reverse time migration in tilted transversely isotropic (TTI) media.Geophysics,2009,74(6):WCA179-WCA187.
[20] Duveneck E,Milcik P,Bakker P M et al.Acoustic VTI wave equations and their application for anisotropic reverse-time migration.SEG Technical Program Expanded Abstracts,2008,27:2186-2190.
[21] Zhang Y,Zhang H,Zhang G Q.A stable TTI reverse time migration and its implementation.Geophysics,2011,76(3):WA3-WA11.
[22] 程玖兵,康玮,王腾飞.各向异性介质qP波传播描述Ⅰ:伪纯模式波动方程.地球物理学报,2013,56(10):3474-3486.Cheng Jiubing,Kang Wei,Wang Tengfei.Description of qP-wave propagation in anisotropic media,Part Ⅰ:Pseudo-pure-mode wave equations.Chinese Journal of Geophysics,2013,56(10):3474-3486.
[23] Yoon K,Suh S,Ji J et al.Stability and speedup issues in TTI RTM implementation.SEG Technical Program Expanded Abstracts,2010,29:3221-3225.
[24] Muir F,Dellinger J.A practical anisotropic system.SEP,1985,44:55-58.
[25] Du X,Bancroft J C,Lines L R.Reverse-time migration for tilted TI media.SEG Technical Program Expanded Abstracts,2005,24:1930-1934.
[26] Zhang Y,Zhang H.A stable TTI reverse time migration and its implementation.SEG Technical Program Expanded Abstracts,2009,28:2794-2798.
[27] Zhan G,Pestana R C,Stoffa P L.Decoupled equations for reverse time migration in tilted transversely isotropic media.Geophysics,2012,77(2):T37-T45.
[28] Zhan G,Pestana R C,Stoffa P L.An efficient hybrid pseudo spectral/finite-difference scheme for solving the TTI pure P-wave equation.Journal of Geophysics and Engineering,2013,10(2):025004.
[29] Sheng X,Zhou H B.Accurate simulations of pure quasi-P-waves in complex anisotropic media.Geophysics,2014,79(6):T341-T348.
[30] Alkhalifah T,Ma X X,Waheed U B et al.Efficient anisotropic wavefield extrapolation using effective isotropic models.//13th International Congress of the Brazilian Geophysical Society & EXPOGEF.Rio de Janeiro,Brazil,2013,1540-1543.
[31] Chu C L,Macy B K,Anno P D.Pure acoustic wave propagation in transversely isotropic media by the pseudospectral method.Geophysical Prospecting,2013,61(3):556-567.
[32] 黄金强,李振春.基于Low-rank分解的复杂TI介质纯qP波正演模拟与逆时偏移.地球物理学报,2017,60(2):704-721.Huang Jinqiang,Li Zhenchun.Modeling and reverse time migration of pure quasi-P-waves in complex TI media with a low-rank decomposition.Chinese Journal of Geophysics,2017,60(2):704-721.
[33] Fomel S,Ying L X,Song X L.Seismic wave extrapolation using lowrank symbol approximation.SEG Technical Program Expanded Abstracts,2010,29:3092-3096.
[34] Song X L,Alkhalifah T.Modeling of pseudo-acoustic P-waves in orthorhombic media with a low-rank approximation.Geophysics,2013,78(4):C33-C40.
[35] Song X L,Fomel S,Ying L X.Lowrank finite-differences and lowrank Fourier finite-differences for seismic wave extrapolation in the acoustic approximation.Geophysical Journal International,2013,193(2):960-969.
[36] Sun J Z,Zhu T,Fomel S.Viscoacoustic modeling and imaging using low-rank approximation.Geophysics,2015,80(5):A103-A108.
[37] Zhang Y,Zhang G Q.One-step extrapolation method for reverse time migration.Geophysics,2009,74(4):A29-A33.
[38] Liu H F,Dai N X,Niu F et al.An explicit time evolution method for acoustic wave propagation.Geophy-sics,2014,79(3):T117-T124.
[39] Fang G,Fomel S,Du Q Z et al.Lowrank seismic-wave extrapolation on a staggered grid.Geophysics,2014,79(3):T157-T168.
[40] Song X L,Fomel S,Ying L X et al.Lowrank finite-differences for wave extrapolation.SEG Technical Program Expanded Abstracts,2011,30:3372-3376.
[41] Wu Z D,Alkhalifah T.The optimized expansion based low-rank method for wavefield extrapolation.Geophysics,2014,79(2):T51-T60.
[42] Xue Z G,Chen Y K,Fomel S et al. Seismic imaging of incomplete data and simultaneous-source data using least-squares reverse time migration with shaping re-gularization.Geophysics,2016,81(1):S11-S20.
[43] Cheng J B,Fomel S.Fast algorithms for elastic-wave-mode separation and vector decomposition using low-rank approximation for anisotropic media.Geophy-sics,2014,79(4):C97-C110.
[44] Charles C,Dan K,Ronnie K et al.A nonreflecting boundary condition for discrete acoustic and elastic wave equations.Geophysics,1985,50(4):705-708.
[45] 胡自多,贺振华,刘威等.旋转网格和常规网格混合的时空域声波有限差分正演.地球物理学报,2016,59(10):3829-3846.Hu Ziduo,He Zhenhua,Liu Wei et al.Scalar wave equation modeling using the mixed-grid finite-diffe-rence method in the time-space domain.Chinese Journal of Geophysics,2016,59(10):3829-3846.
[46] 李娜,黄建平,李振春等.Lebedev网格改进差分系数TTI介质正演模拟方法研究.地球物理学报,2014,57(1):261-269.Li Na,Huang Jianping,Li Zhenchun et al.The study on numerical simulation method of Lebedev Grid with dispersion improvement coefficients in TTI media.Chinese Journal of Geophysics,2014,57(1):261-269.
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[48] 黄建平,朱峰,李振春等.VTI介质FFD叠前深度偏移成像方法.石油地球物理勘探,2017,52(3):491-501.Huang Jianping,Zhu Feng,Li Zhenchun et al.FFD prestack depth migration for VTI media.OGP,2017,52(3):491-501.
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[50] 吴玉,符力耘,陈高祥.基于分数阶拉普拉斯算子解耦的黏声介质地震正演模拟与逆时偏移.地球物理学报,2017,60(4):1527-1537.Wu Yu,Fu Liyun,Chen Gaoxiang.Forward modeling and reverse time migration of viscoacoustic media using decoupled fractional Laplacians.Chinese Journal of Geophysics,2017,60(4):1527-1537.
[2] 张广智,陈怀震,王琪等.基于碳酸盐岩裂缝岩石物理模型的横波速度和各向异性参数预测.地球物理学报,2013,56(5):1707-1715.Zhang Guangzhi,Chen Huaizhen,Wang Qi et al.Estimation of S-wave velocity and anisotropic parameters using fractured carbonate rock physics model.Chinese Journal of Geophysics,2013,56(5):1707-1715.
[3] 李振春,黄金强,黄建平等.基于平面波加速的VTI介质最小二乘逆时偏移.地球物理学报,2017,60(1):240-257.Li Zhenchun,Huang Jinqiang,Huang Jianping et al.Fast least-squares reverse time migration based on plane-wave encoding for VTI media.Chinese Journal of Geophysics,2017,60(1):240-257.
[4] 黄建平,黄金强,李振春等.TTI介质一阶qP波方程交错网格伪谱法正演模拟.石油地球物理勘探,2016,51(3):487-496.Huang Jianping,Huang Jinqiang,Li Zhenchun et al.Staggered grid pseudo-spectral numerical simulation of first-order quasi P-wave equation for TTI media.OGP,2016,51(3):487-496.
[5] 黄金强,李振春,黄建平等.TTI介质Lebedev网格高阶有限差分正演模拟及波型分离.石油地球物理勘探,2017,52(5):915-927.Huang Jinqiang,Li Zhenchun,Huang Jianping et al.Lebedev grid high-order finite-difference modeling and elastic-wave-mode separation for TTI media.OGP,2017,52(5):915-927.
[6] 刘立彬.VTI介质角度域Kirchhoff叠前时问偏移方法.中国石油大学学报(自然科学版),2012,36(5):51-55.Liu Libin.Angle-domain Kirchhoff prestack time migration approach in VTI media.Journal of China University of Petroleum (Natural Science Edition),2012,36(5):51-55.
[7] 张洪宙,王彦飞.VTI介质迭代正则化偏移反演算法.石油地球物理勘探,2014,49(6):1083-1090.Zhang Hongzhou and Wang Yanfei.Iterative regularization migration inversion in VTI media.OGP,2014,49(6):1083-1090.
[8] Alkhalifah T.Gaussian beam depth migration for anisotropic media.Geophysics,1995,60(5):1474-1484.
[9] Zhu T,Gray S H,Wang D L.Prestack Gaussian-beam depth migration in anisotropic media.Geophysics,2007,72(3):S133-S138.
[10] 刘鹏,杨长春,王彦飞.三维TTI介质格林函数的高斯束计算方法.地球物理学进展,2013,28(5):2547-2553.Liu Peng,Yang Changchun,Wang Yanfei.Three-dimensional Green’s Function Calculation in TTI media using the Gaussian beam method.Progress in Geophysics,2013,28(5):2547-2553.
[11] 段鹏飞,程玖兵,陈爱萍等.TI介质局部角度域高斯束叠前深度偏移成像.地球物理学报,2013,56(12):4206-4214.Duan Pengfei,Cheng Jiubing,Chen Aiping et al.Local angle-domain Gaussian beam prestack depth migration in a TI media.Chinese Journal of Geophysics,2013,56(12):4206-4214.
[12] 韩建光,王赟,张晓波等.VTI介质高斯束叠前深度偏移.石油地球物理勘探,2015,50(2):267-273.Han Jianguang,Wang Yun,Zhang Xiaobo et al.Gaussian beam prestack depth migration in VTI media.OGP,2015,50(2):267-273.
[13] 段新意,李振春,黄建平等.各向异性介质共炮域高斯束叠前深度偏移.石油物探,2014,53(5):579-586.Duan Xinyi,Li Zhenchun,Huang Jianping et al.A prestack Gaussian beam depth migration in common-shot domain for anisotropic media.GPP,2014,53(5):579-586.
[14] 张凯,段新意,李振春等.角度域各向异性高斯束逆时偏移.石油地球物理勘探,2015,50(5):912-918.Zhang Kai,Duan Xinyi,Li Zhenchun et al.Angle domain reverse time migration with Gaussian beams in anisotropic media.OGP,2015,50(5):912-918.
[15] Thomsen L.Weak elastic anisotropy.Geophysics,1986,51(10):1954-1966.
[16] Alkhalifah T.An acoustic wave equation for aniso-tropic media.Geophysics,2000,65(4):1239-1250.
[17] Zhou H B,Zhang G Q,Bloor R.An anisotropic acoustic wave equation for VTI media.Extended Abstracts of 68th EAGE Conference and Exhibition,2006.
[18] Zhou H B,Zhang G Q,Bloor R.An anisotropic acoustic wave equation for modeling and migration in 2D TTI media.SEG Technical Program Expanded Abstracts,2006,25:194-198.
[19] Fletcher R P,Du X,Fowler P J.Reverse time migration in tilted transversely isotropic (TTI) media.Geophysics,2009,74(6):WCA179-WCA187.
[20] Duveneck E,Milcik P,Bakker P M et al.Acoustic VTI wave equations and their application for anisotropic reverse-time migration.SEG Technical Program Expanded Abstracts,2008,27:2186-2190.
[21] Zhang Y,Zhang H,Zhang G Q.A stable TTI reverse time migration and its implementation.Geophysics,2011,76(3):WA3-WA11.
[22] 程玖兵,康玮,王腾飞.各向异性介质qP波传播描述Ⅰ:伪纯模式波动方程.地球物理学报,2013,56(10):3474-3486.Cheng Jiubing,Kang Wei,Wang Tengfei.Description of qP-wave propagation in anisotropic media,Part Ⅰ:Pseudo-pure-mode wave equations.Chinese Journal of Geophysics,2013,56(10):3474-3486.
[23] Yoon K,Suh S,Ji J et al.Stability and speedup issues in TTI RTM implementation.SEG Technical Program Expanded Abstracts,2010,29:3221-3225.
[24] Muir F,Dellinger J.A practical anisotropic system.SEP,1985,44:55-58.
[25] Du X,Bancroft J C,Lines L R.Reverse-time migration for tilted TI media.SEG Technical Program Expanded Abstracts,2005,24:1930-1934.
[26] Zhang Y,Zhang H.A stable TTI reverse time migration and its implementation.SEG Technical Program Expanded Abstracts,2009,28:2794-2798.
[27] Zhan G,Pestana R C,Stoffa P L.Decoupled equations for reverse time migration in tilted transversely isotropic media.Geophysics,2012,77(2):T37-T45.
[28] Zhan G,Pestana R C,Stoffa P L.An efficient hybrid pseudo spectral/finite-difference scheme for solving the TTI pure P-wave equation.Journal of Geophysics and Engineering,2013,10(2):025004.
[29] Sheng X,Zhou H B.Accurate simulations of pure quasi-P-waves in complex anisotropic media.Geophysics,2014,79(6):T341-T348.
[30] Alkhalifah T,Ma X X,Waheed U B et al.Efficient anisotropic wavefield extrapolation using effective isotropic models.//13th International Congress of the Brazilian Geophysical Society & EXPOGEF.Rio de Janeiro,Brazil,2013,1540-1543.
[31] Chu C L,Macy B K,Anno P D.Pure acoustic wave propagation in transversely isotropic media by the pseudospectral method.Geophysical Prospecting,2013,61(3):556-567.
[32] 黄金强,李振春.基于Low-rank分解的复杂TI介质纯qP波正演模拟与逆时偏移.地球物理学报,2017,60(2):704-721.Huang Jinqiang,Li Zhenchun.Modeling and reverse time migration of pure quasi-P-waves in complex TI media with a low-rank decomposition.Chinese Journal of Geophysics,2017,60(2):704-721.
[33] Fomel S,Ying L X,Song X L.Seismic wave extrapolation using lowrank symbol approximation.SEG Technical Program Expanded Abstracts,2010,29:3092-3096.
[34] Song X L,Alkhalifah T.Modeling of pseudo-acoustic P-waves in orthorhombic media with a low-rank approximation.Geophysics,2013,78(4):C33-C40.
[35] Song X L,Fomel S,Ying L X.Lowrank finite-differences and lowrank Fourier finite-differences for seismic wave extrapolation in the acoustic approximation.Geophysical Journal International,2013,193(2):960-969.
[36] Sun J Z,Zhu T,Fomel S.Viscoacoustic modeling and imaging using low-rank approximation.Geophysics,2015,80(5):A103-A108.
[37] Zhang Y,Zhang G Q.One-step extrapolation method for reverse time migration.Geophysics,2009,74(4):A29-A33.
[38] Liu H F,Dai N X,Niu F et al.An explicit time evolution method for acoustic wave propagation.Geophy-sics,2014,79(3):T117-T124.
[39] Fang G,Fomel S,Du Q Z et al.Lowrank seismic-wave extrapolation on a staggered grid.Geophysics,2014,79(3):T157-T168.
[40] Song X L,Fomel S,Ying L X et al.Lowrank finite-differences for wave extrapolation.SEG Technical Program Expanded Abstracts,2011,30:3372-3376.
[41] Wu Z D,Alkhalifah T.The optimized expansion based low-rank method for wavefield extrapolation.Geophysics,2014,79(2):T51-T60.
[42] Xue Z G,Chen Y K,Fomel S et al. Seismic imaging of incomplete data and simultaneous-source data using least-squares reverse time migration with shaping re-gularization.Geophysics,2016,81(1):S11-S20.
[43] Cheng J B,Fomel S.Fast algorithms for elastic-wave-mode separation and vector decomposition using low-rank approximation for anisotropic media.Geophy-sics,2014,79(4):C97-C110.
[44] Charles C,Dan K,Ronnie K et al.A nonreflecting boundary condition for discrete acoustic and elastic wave equations.Geophysics,1985,50(4):705-708.
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