起伏层状介质中曲线交错网格有限差分弹性波逆时偏移成像
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摘要
采用曲线网格有限差分法描述复杂起伏地形(或不规则波阻抗界面)时,波场正演中可以避免因阶梯近似导致的虚假散射,进而波场逆时偏移可对起伏地表模型进行准确成像.文中以弹性波逆时偏移理论为基础,求解一阶速度-应力方程,推导出了弹性波正向传播和逆时传播的曲线网格差分格式,使用完全匹配吸收边界压制边界反射,采用互相关成像条件,实现了起伏层状介质中的波场逆时偏移.三层起伏、尖灭模型,以及起伏地表条件下的部分盐丘模型结果表明:曲线网格有限差分法逆时偏移法是一种高效、准确的逆时偏移法.
When describing complex and undulating terrain(or irregular wave impedance interface) by using curvilinear-grid finite difference method, the forward wavefield simulation can avoid of false scattering caused by the ladder approximation. Therefore, the reverse time migration can accurately image the undulating subsurface structure. We in this article solve a one-order velocity-stress equation based on the theory of elastic wave reverse time migration, and deduce the curvilinear-grid finite difference scheme of elastic wave forward modeling and reverse time migration, using perfect match layer absorbing boundary, apply cross-correlation imaging conditions, and finally realize wavefield reverse time migration in the presentation of the undulating layer medium. The results of the undulated three-layer, interface merger model and the undulated part of salt mode show that the curvilinear-grid finite difference method is an efficient and accurate reverse time migration method.
When describing complex and undulating terrain(or irregular wave impedance interface) by using curvilinear-grid finite difference method, the forward wavefield simulation can avoid of false scattering caused by the ladder approximation. Therefore, the reverse time migration can accurately image the undulating subsurface structure. We in this article solve a one-order velocity-stress equation based on the theory of elastic wave reverse time migration, and deduce the curvilinear-grid finite difference scheme of elastic wave forward modeling and reverse time migration, using perfect match layer absorbing boundary, apply cross-correlation imaging conditions, and finally realize wavefield reverse time migration in the presentation of the undulating layer medium. The results of the undulated three-layer, interface merger model and the undulated part of salt mode show that the curvilinear-grid finite difference method is an efficient and accurate reverse time migration method.
引文
Appel? D, Petersson N. 2009. A stable finite difference method for the elastic wave equation on complex geometries with free surface [J]. Communications in Computational Physics, 5(1): 84-107.
Baysal E, Kosloff D D, Sherwood J W C. 1983. Reverse time migration [J], Geophysics, 48(11): 1514-1524.
Cai X H, Liu Y, Wang J M, et al. 2015. Full-wavefield VSP reverse-time migration based on the adaptive optimal finite-difference scheme [J].Chinese J. Geophys (in Chinese), 58(9): 3317-3334, doi: 10.6038/cig20150925.
Chen C. 2011. Prestack Reverse-time Migration and Imaging(in Chinese) [Master’s thesis]. Beijing:China University of Geosciences.
Chen K Y. 2010. Study on perfectly matched layer absorbing boundary condition [J]. Geophysical Prospecting for Petroleum (in Chinese), 49(5): 472- 477.
Chun C L, Wang X T. 2005. Seismic Modeling with a Finite-Difference method on Irregular Triangular grids [J]. College of Marine Geosciences, Ocean University of China (in Chinese). 35(1): 43- 48.
Claerbout J F. 1971. Toward a unified theory of reflector mapping [J]. Geophysics, 36(3): 467- 481.
Clayton R, Enquist B. 1977. Absorbing boundary conditions for acoustic and elastic wave equations [J]. Bull. Seism Soc. Amer., 67(6): 1529-1540.
Guo N M, Wu G C. 2012. High-order finite difference method in reverse-time migration with variable grids based on PML boundary condition [J]. Oil Geophysical Prospecting (in Chinese), 47(2): 256-265.
Guo Q. 2012 .Common-imagine gathers extraction based on reverse-time migration and amplitude fidelity analysis (in Chinese) [Master’s thesis]. Qingdao: China University of Petroleum.
Hole J A. 1992. Nonlinear high-resolution three-dimensional seismic travel time tomography [J]. J. Geophys Res. (Solid Earth), 97(B5): 6553-6562.
Hou J, Liu Y S, Lan H Q, et al. 2018. Elastic reverse time migration using a topography flattening scheme [J].Chinese J. Geophys (in Chinese), 61(4): 1434-1446, doi: 10.6038/cjg2018L0624.
Jiang L L. 2010. Body-fitted grid generation for the Geological conditions(in Chinese)[Ph.D. thesis]. Changchun: Jilin University.
Jiang L L, Sun J G. 2008. Source terms of elliptic system in grid generation [J]. Global Geology (in Chinese), 27(3): 298-305.
Kristek J, Moczo P, Galis M. 2010. Stable discontinuous staggered grid in the finite-difference modelling of seismic motion [J]. Geophys J. Int., 183(3): 1401-1407.
Li Z C. 2014. Research status and development trend of seismic migration imaging technology [J]. Oil Geophysical Prospecting (in Chinese), 49(1): 1-21.
Liao Z P. 1982. Finite model of transient scalar wave problem in an infinite elastic medium [J]. Journal of Earthquake engineering and engineering vibration (in Chinese), 2(4): 40-55.
Lisekin V. 2010. Grid generation methods [M]. New York, Springer.
Liu Z Q, Sun J G, Sun H, et al. 2017. A perfectly matched layer absorbing boundary condition under the curvilinear coordinate system [J]. Journal of Jilin University (Earth Science Edition) (in Chinese, 47(6): 1875-1884.
Qiu L. 2012. Study on seismic wave simulations in orthogonally curvilinear coordinate system (in Chinese) [Ph.D. thesis]. HangZhou: Zhejiang University.
Wei C L. 2013. Seismic data reverse-time migration and GPU parallel algorithm (in Chinese) [Master’s thesis]. Qingdao: Ocean University of China.
Whitmore N D. 1983. Iterative depth migration by backward time propagation [J]. Expanded Abstracts of 53 Annual International SEG Meeting, 382-385.
Xue D C. 2013 .Imaging condition comparison of prestack reverse-time migration [J]. Oil Geophysical Prospecting (in Chinese), 48(2): 222-227.
Yang S B, Bai C Y, He L Y. 2016. Comparison of seismic wave-field simulation between the curvilinear-grid finite difference method and ray method in undulated layered medium [J]. Acta Seismological Sinica, 38(6): 854-868, doi: 10.11939/jass.2016.06.005.
Zhang W, Chen X F. 2006. Traction image method for irregular free surface boundaries in finite difference seismic wave simulation [J]. Geophys J. Int., 167(1): 337-353.
Zhang W, Shen Y. 2010. Unsplit complex frequency-shifted PML implementation using auxiliary differential equations for seismic wave modeling [J]. Geophysics, 75(4): T141-T154.
Zhang W, Zhang Z G, Chen X F. 2012. Three-dimensional elastic wave numerical modelling in the presence of surface topography by a collocated-grid finite-difference method on curvilinear grids [J]. Geophys J. Int., 190(1): 358-378.
Zhang Z, Liu Y S, Xu T, et al. 2013. A stable excitation amplitude imaging condition for reverse time migration in elastic wave equation [J]. Chinese Journal of Geophys (in Chinese), 56(10): 3523-3533, doi: 10.6038/cjg20131027.
Zhou X M. 2010. Staggered-grid high-order finite-difference numerical simulation and prestack reverse-time migration (in Chinese) [Master’s thesis]. Xi’an: Chang an University.
蔡晓慧, 刘洋, 王建民, 等. 2015. 基于自适应优化有限差分方法的全波VSP逆时偏移[J]. 地球物理学报, 58(9): 3317-3334, doi: 10.6038/cig20150925.
陈聪. 2011. 叠前逆时偏移及成像[硕士论文]. 北京:中国地质大学.
陈可洋. 2010. 完全匹配层吸收边界条件研究[J]. 石油物探, 49(5): 472- 477.
褚春雷, 王修田. 2005. 非规则三角网格有限差分法地震正演模拟[J]. 中国海洋大学学报(自然科学版), 35(1): 43- 48.
Claerbout J F著, 许云译. 1991. 地震成像理论及方法[M]. 北京: 石油工业出版社.
郭念民, 吴国忱. 2012. 基于PML边界的变网格高阶有限差分声波方程逆时偏移[J]. 石油地球物理勘探, 47(2): 256-265.
郭倩. 2012 .基于逆时偏移的共成像点道集提取与保幅性分析[硕士论文]. 青岛: 中国石油大学.
侯爵, 刘有山, 兰海强, 等. 2018. 基于起伏地形平化策略的弹性波逆时偏移成像方法[J]. 地球物理学报, 61(4): 1434-1446, doi: 10.6038/cjg2018L0624.
蒋丽丽. 2010. 面向地质条件的贴体网格生成技术[博士论文]. 长春: 吉林大学.
蒋丽丽, 孙建国. 2008. 基于Poisson方程的曲网格生成技术[J]. 世界地质, 27(3): 298-305.
李振春. 2014. 地震偏移成像技术研究现状与发展趋势[J]. 石油地球物理勘探, 49(1): 1-21.
廖振鹏. 1982. 无限弹性介质中,暂态标量波问题的有限模型[J]. 地震工程与工程震动, 2(4): 40-55.
刘志强, 孙建国, 孙辉, 等. 2017. 曲线坐标系下的完全匹配吸收边界条件[J]. 吉林大学学报(地球科学版), 47(6): 1875-1884.
丘磊. 2012. 正交曲坐标系下地震波场数值模拟技术研究[博士论文]. 杭州: 浙江大学.
孙耀充. 2017. 曲线网格有限差分模拟地震波在各向异性介质和固-液耦合介质中的传播[博士论文]. 合肥: 中国科学技术大学.
魏程霖. 2013. 地震资料逆时偏移的关键技术及GPU并行算法[硕士论文]. 青岛: 中国海洋大学.
薛东川. 2013. 几种叠前逆时偏移成像条件的比较[J]. 石油地球物理勘探, 48(2): 222-227.
杨尚倍, 白超英, 何雷宇. 2016. 起伏层状介质中曲线网格有限差分方法与射线法波场模拟对比研究 [J]. 地震学报, 38(6): 854-868, doi: 10.11939/jass.2016.06.005.
张敬秋. 2015. 交错网格有限差分法地震资料逆时偏移[硕士论文] 成都: 成都理工大学.
张智, 刘有山, 徐涛, 等. 2013. 弹性波逆时偏移中的稳定激发振幅成像条件[J]. 地球物理学报, 56(10): 3523-3533, doi: 10.6038/cjg20131027.
周学明. 2010. 交错网格高阶差分数值模拟及叠前逆时偏移[硕士论文]. 西安: 长安大学.
Baysal E, Kosloff D D, Sherwood J W C. 1983. Reverse time migration [J], Geophysics, 48(11): 1514-1524.
Cai X H, Liu Y, Wang J M, et al. 2015. Full-wavefield VSP reverse-time migration based on the adaptive optimal finite-difference scheme [J].Chinese J. Geophys (in Chinese), 58(9): 3317-3334, doi: 10.6038/cig20150925.
Chen C. 2011. Prestack Reverse-time Migration and Imaging(in Chinese) [Master’s thesis]. Beijing:China University of Geosciences.
Chen K Y. 2010. Study on perfectly matched layer absorbing boundary condition [J]. Geophysical Prospecting for Petroleum (in Chinese), 49(5): 472- 477.
Chun C L, Wang X T. 2005. Seismic Modeling with a Finite-Difference method on Irregular Triangular grids [J]. College of Marine Geosciences, Ocean University of China (in Chinese). 35(1): 43- 48.
Claerbout J F. 1971. Toward a unified theory of reflector mapping [J]. Geophysics, 36(3): 467- 481.
Clayton R, Enquist B. 1977. Absorbing boundary conditions for acoustic and elastic wave equations [J]. Bull. Seism Soc. Amer., 67(6): 1529-1540.
Guo N M, Wu G C. 2012. High-order finite difference method in reverse-time migration with variable grids based on PML boundary condition [J]. Oil Geophysical Prospecting (in Chinese), 47(2): 256-265.
Guo Q. 2012 .Common-imagine gathers extraction based on reverse-time migration and amplitude fidelity analysis (in Chinese) [Master’s thesis]. Qingdao: China University of Petroleum.
Hole J A. 1992. Nonlinear high-resolution three-dimensional seismic travel time tomography [J]. J. Geophys Res. (Solid Earth), 97(B5): 6553-6562.
Hou J, Liu Y S, Lan H Q, et al. 2018. Elastic reverse time migration using a topography flattening scheme [J].Chinese J. Geophys (in Chinese), 61(4): 1434-1446, doi: 10.6038/cjg2018L0624.
Jiang L L. 2010. Body-fitted grid generation for the Geological conditions(in Chinese)[Ph.D. thesis]. Changchun: Jilin University.
Jiang L L, Sun J G. 2008. Source terms of elliptic system in grid generation [J]. Global Geology (in Chinese), 27(3): 298-305.
Kristek J, Moczo P, Galis M. 2010. Stable discontinuous staggered grid in the finite-difference modelling of seismic motion [J]. Geophys J. Int., 183(3): 1401-1407.
Li Z C. 2014. Research status and development trend of seismic migration imaging technology [J]. Oil Geophysical Prospecting (in Chinese), 49(1): 1-21.
Liao Z P. 1982. Finite model of transient scalar wave problem in an infinite elastic medium [J]. Journal of Earthquake engineering and engineering vibration (in Chinese), 2(4): 40-55.
Lisekin V. 2010. Grid generation methods [M]. New York, Springer.
Liu Z Q, Sun J G, Sun H, et al. 2017. A perfectly matched layer absorbing boundary condition under the curvilinear coordinate system [J]. Journal of Jilin University (Earth Science Edition) (in Chinese, 47(6): 1875-1884.
Qiu L. 2012. Study on seismic wave simulations in orthogonally curvilinear coordinate system (in Chinese) [Ph.D. thesis]. HangZhou: Zhejiang University.
Wei C L. 2013. Seismic data reverse-time migration and GPU parallel algorithm (in Chinese) [Master’s thesis]. Qingdao: Ocean University of China.
Whitmore N D. 1983. Iterative depth migration by backward time propagation [J]. Expanded Abstracts of 53 Annual International SEG Meeting, 382-385.
Xue D C. 2013 .Imaging condition comparison of prestack reverse-time migration [J]. Oil Geophysical Prospecting (in Chinese), 48(2): 222-227.
Yang S B, Bai C Y, He L Y. 2016. Comparison of seismic wave-field simulation between the curvilinear-grid finite difference method and ray method in undulated layered medium [J]. Acta Seismological Sinica, 38(6): 854-868, doi: 10.11939/jass.2016.06.005.
Zhang W, Chen X F. 2006. Traction image method for irregular free surface boundaries in finite difference seismic wave simulation [J]. Geophys J. Int., 167(1): 337-353.
Zhang W, Shen Y. 2010. Unsplit complex frequency-shifted PML implementation using auxiliary differential equations for seismic wave modeling [J]. Geophysics, 75(4): T141-T154.
Zhang W, Zhang Z G, Chen X F. 2012. Three-dimensional elastic wave numerical modelling in the presence of surface topography by a collocated-grid finite-difference method on curvilinear grids [J]. Geophys J. Int., 190(1): 358-378.
Zhang Z, Liu Y S, Xu T, et al. 2013. A stable excitation amplitude imaging condition for reverse time migration in elastic wave equation [J]. Chinese Journal of Geophys (in Chinese), 56(10): 3523-3533, doi: 10.6038/cjg20131027.
Zhou X M. 2010. Staggered-grid high-order finite-difference numerical simulation and prestack reverse-time migration (in Chinese) [Master’s thesis]. Xi’an: Chang an University.
蔡晓慧, 刘洋, 王建民, 等. 2015. 基于自适应优化有限差分方法的全波VSP逆时偏移[J]. 地球物理学报, 58(9): 3317-3334, doi: 10.6038/cig20150925.
陈聪. 2011. 叠前逆时偏移及成像[硕士论文]. 北京:中国地质大学.
陈可洋. 2010. 完全匹配层吸收边界条件研究[J]. 石油物探, 49(5): 472- 477.
褚春雷, 王修田. 2005. 非规则三角网格有限差分法地震正演模拟[J]. 中国海洋大学学报(自然科学版), 35(1): 43- 48.
Claerbout J F著, 许云译. 1991. 地震成像理论及方法[M]. 北京: 石油工业出版社.
郭念民, 吴国忱. 2012. 基于PML边界的变网格高阶有限差分声波方程逆时偏移[J]. 石油地球物理勘探, 47(2): 256-265.
郭倩. 2012 .基于逆时偏移的共成像点道集提取与保幅性分析[硕士论文]. 青岛: 中国石油大学.
侯爵, 刘有山, 兰海强, 等. 2018. 基于起伏地形平化策略的弹性波逆时偏移成像方法[J]. 地球物理学报, 61(4): 1434-1446, doi: 10.6038/cjg2018L0624.
蒋丽丽. 2010. 面向地质条件的贴体网格生成技术[博士论文]. 长春: 吉林大学.
蒋丽丽, 孙建国. 2008. 基于Poisson方程的曲网格生成技术[J]. 世界地质, 27(3): 298-305.
李振春. 2014. 地震偏移成像技术研究现状与发展趋势[J]. 石油地球物理勘探, 49(1): 1-21.
廖振鹏. 1982. 无限弹性介质中,暂态标量波问题的有限模型[J]. 地震工程与工程震动, 2(4): 40-55.
刘志强, 孙建国, 孙辉, 等. 2017. 曲线坐标系下的完全匹配吸收边界条件[J]. 吉林大学学报(地球科学版), 47(6): 1875-1884.
丘磊. 2012. 正交曲坐标系下地震波场数值模拟技术研究[博士论文]. 杭州: 浙江大学.
孙耀充. 2017. 曲线网格有限差分模拟地震波在各向异性介质和固-液耦合介质中的传播[博士论文]. 合肥: 中国科学技术大学.
魏程霖. 2013. 地震资料逆时偏移的关键技术及GPU并行算法[硕士论文]. 青岛: 中国海洋大学.
薛东川. 2013. 几种叠前逆时偏移成像条件的比较[J]. 石油地球物理勘探, 48(2): 222-227.
杨尚倍, 白超英, 何雷宇. 2016. 起伏层状介质中曲线网格有限差分方法与射线法波场模拟对比研究 [J]. 地震学报, 38(6): 854-868, doi: 10.11939/jass.2016.06.005.
张敬秋. 2015. 交错网格有限差分法地震资料逆时偏移[硕士论文] 成都: 成都理工大学.
张智, 刘有山, 徐涛, 等. 2013. 弹性波逆时偏移中的稳定激发振幅成像条件[J]. 地球物理学报, 56(10): 3523-3533, doi: 10.6038/cjg20131027.
周学明. 2010. 交错网格高阶差分数值模拟及叠前逆时偏移[硕士论文]. 西安: 长安大学.