VTI介质起伏界面混合网格旅行时线性插值计算方法
|
摘要
为了计算起伏地表(界面)VTI介质中地震波旅行时,采用矩形网格与不规则四边形网格组成的混合网格对模型进行剖分,以提高网格对起伏地表(界面)的拟合程度。在混合网格中把群速度与群角的关系式转换成群速度与插值点坐标的关系式,进而结合分区多步计算技术,将旅行时线性插值射线追踪算法推广到VTI介质中,实现了VTI介质中多种类型(初至、反射、多次反射、多次透射转换以及多次反射转换)地震波旅行时的计算。通过与有限差分算法、分区多步快速步进算法和分区多步不规则网格最短路径算法的计算结果对比,以及复杂构造模型的试算,说明方法比较精确,且对复杂构造模型有良好的适应能力。
In order to calculate seismic wave traveltime in VTI medium under rugged interface conditions,we divide a model with a hybrid mesh composed by rectangular meshes and irregular quadrilateral meshes to better fit rugged interface conditions.In the hybrid mesh,the relationship between group velocity and group angle is transformed into the relationship between group velocity and interpolated point coordinates to find the local traveltime.Thenwith the multi-step partitioning technique,the ray tracing algorithm is extended to VTI medium to realize the traveltime calculation of seismic waves(first arrival,reflection,multiple reflection,multiple transmission conversion,and multiple reflection conversion)in VTI medium.Comparedand irregular cell shortest path method,numerical simulations show that the proposed algorithm is more accurate and can better adapt complex-structure models.
In order to calculate seismic wave traveltime in VTI medium under rugged interface conditions,we divide a model with a hybrid mesh composed by rectangular meshes and irregular quadrilateral meshes to better fit rugged interface conditions.In the hybrid mesh,the relationship between group velocity and group angle is transformed into the relationship between group velocity and interpolated point coordinates to find the local traveltime.Thenwith the multi-step partitioning technique,the ray tracing algorithm is extended to VTI medium to realize the traveltime calculation of seismic waves(first arrival,reflection,multiple reflection,multiple transmission conversion,and multiple reflection conversion)in VTI medium.Comparedand irregular cell shortest path method,numerical simulations show that the proposed algorithm is more accurate and can better adapt complex-structure models.
引文
[1] Tsvankin I.Seismic Signatures and Analysis of Re-flection Data in Anisotropic Media.Elsevier,2001.
[2] Charles S.Data-driven tomographic velocity analysisin tilted transversely isotropic media:A 3D case history from the Canadian Foothills.Geophysics,2008,73(5):VE261-VE268.
[3] Thomsen L.Weak elastic anisotropy.Geophysics,1986,51(10):1954-1966.
[4] Sena A G.Seismic traveltime equations for azimutha-lly anisotropic and isotropic media:Estimation of interval elastic properties.Geophysics,1991,56(12):2090-2101.
[5] Faria E L and Stoffa P L.Traveltime computation in transversely isotropic media.Geophysics,1994,59(2):272-281.
[6] 邓怀群,刘雯林.横向各向同性介质中地震波旅行时的计算.石油地球物理勘探,2000,35(4):508-516.Deng Huaiqun,Liu Wenlin.Computation of seismic travel times in transversely isotropic medium.OGP,2000,35(4):508-516.
[7] Alkhalifah T.Traveltime computation with the linea-rized eikonal equation for anisotropic media.Geophy-sical Prospecting,2002,50(4):373-382.
[8] Zhou B,Greenhalgh S A.“Shortest path” ray tracing for most general 2D/3D anisotropic media.Journal of Geophysics & Engineering,2005,2(1):54-63.
[9] 赵爱华,张美根,丁志峰.横向各向同性介质中地震波旅行时模拟.地球物理学报,2006,49(6):1762-1769.Zhao Aihua,Zhang Meigen,Ding Zhifeng.Seismic traveltime computation for transversely isotropy media.Chinese Journal of Geophysics,2006,49(6):1762-1769.
[10] 马德堂,朱光明.横向各项同性介质中的初至波旅行时计算.石油地球物理勘探,2006,41(1):26-31.Ma Detang,Zhu Guangming.Computation of traveltimes of seismic first breaks in transversely isotropic medium.OGP,2006,41(1):26-31.
[11] 李建国,李彦鹏,郭晓玲.VTI介质试射射线追踪.石油地球物理勘探,2010,45(4):491-496.Li Jianguo,Li Yanpeng,Guo Xiaoling.VTI media test-firing ray tracing.OGP,2010,45(4):491-496.
[12] 马德堂,朱光明,范延恩.二维TTI介质中初至波旅行时的搜索算法.石油地球物理勘探,2011,46(5):710-714.Ma Detang,Zhu Guangming,Fan Tingen.A search algorithm for first break traveltime in 2D TTI medium.OGP,2011,46(5):710-714.
[13] 白海军,孙赞东,王学军.基于波前构建法的TTI介质射线追踪.石油地球物理勘探,2011,46(增刊1):1-6.Bai Haijun,Sun Zandong,Wang Xuejun.Ray tracing in TTI media using wavefront construction.OGP,2011,46(S1):1-6.
[14] 李晓玲,白超英,胡光义.起伏层状TI介质中多次波射线追踪.石油地球物理勘探,2013,48(6):924-931. Li Xiaoling,Bai Chaoying,Hu Guangyi.Multiple ray tracing in an undulated layered TI media.OGP,2013,48(6):924-931.
[15] Farra V.Ray tracing in complex media.Journal of Applied Geophysics,1993,30(1-2):55-73.
[16] Berryman J G.Long-wave elastic anisotropy in transversely isotropy media.Geophysics,1979,44(5):896-917.
[17] 李庆春,叶佩.初至波与反射波旅行时多尺度渐进联合层析成像.石油地球物理勘探,2013,48(4):536-544.Li Qingchun,Ye Pei.Joint tomography of first break and reflection traveltime with multi-scale netsize method.OGP,2013,48(4):536-544.
[18] 李永博,李庆春,吴琼等.快速行进法射线追踪提高旅行时计算精度和效率的改进措施.石油地球物理勘探,2016,51(3):467-473.Li Yongbo,Li Qingchun,Wu Qiong et al.Improved fast marching method for higher calculation accuracy and efficiency of traveltime.OGP,2016,51(3):467-473.
[19] 叶佩,李庆春.旅行时线性插值射线追踪提高计算精度和效率的改进方法.吉林大学学报(地球科学版),2013,43(1):291-298.Ye Pei,Li Qingchun.Improvements of linear traveltime interpolation ray tracing for the accuracy and efficiency.Journal of Jilin University(Earth Science Edition),2013,43(1):291-298.
[20] 秦宁,王延光,杨晓东等.非水平地表高斯束叠前深度偏移及山前带应用实例.石油地球物理勘探,2017,52(1):81-86.Qin Ning,Wang Yanguang,Yang Xiaodong et al.Gaussian bean prestack depth migration for undulating-surface area in piedmont zone.OGP,2017,52(1):81-86.
[21] 黄国娇,白超英.二维复杂层状介质中地震多波旅行时联合反演成像.地球物理学报,2010,53(12):2972-2981.Huang Guojiao,Bai Chaoying.Simultaneous inversion with multiple traveltimes within 2-D complex layered media.Chinese Journal of Geophysics,2010,53(12):2972-2981.
[22] Asakawa E,Kawanaka T.Seismic ray tracing using linear traveltime interpolation.Geophysics Prospecting,1993,41(4):99-111.
[23] Li X G,Uirych T J.LTI formulations and application to curved wavefronts.Journal of Seismic Exploration,1993,2(1):239-246.
[24] 赵改善,郝守玲.基于旅行时线性插值的地震射线追踪算法.石油物探,1998,32(2):14-24.Zhao Gaishan,Hao Shouling.Seismic ray tracing algorithm based on the linear traveltime interpolation.GPP,1998,32(2):14-24.
[25] Cardarelli E and Cerreto A.Ray tracing in elliptical anisotropic media using the linear traveltime interpolation (LTI) method applied to traveltime seismic tomography.Geophysical Prospecting,2002,50(1):55-72.
[26] 聂建新,杨慧珠.地震波旅行时二次/线性联合插值法.清华大学学报,2003,43(11):1495-1498.Nie Jianxin,Yang Huizhu.Quadrarical linear travel time interpolation of seismic ray-tracing.Journal of Tsinghua University,2003,43(11):1495-1498.
[27] Kumar D,Sen M K,Ferguson R J.Traveltime calculation and prestack depth migration in tilted transversely isotropic media.Geophysics,2004,69(1):37-44.
[28] 张赛民,周竹生,陈灵君等.对旅行时进行抛物型插值的地震射线追踪方法.地球物理学进展,2007,22(1):43-48.Zhang Saimin,Zhou Zhusheng,Chen Lingjun et al.Seismic ray tracing method of applying parabolic interpolation to travel time.Progress in Geophysics,2007,22(1):43-48.
[29] 张东,谢宝莲,杨艳等.一种改进的线性旅行时插值射线追踪算法.地球物理学报,2009,52(1):200-205.Zhang Dong,Xie Baolian,Yang Yan et al.A ray tra-cing method based on improved linear traveltime interpolation.Chinese Journal of Geophysics,2009,52(1):200-205.
[30] 张东,傅相如,杨艳等.基于LTI和网格界面剖分的三维地震射线追踪算法.地球物理学报,2009,52(9):2370-2376.Zhang Dong,Fu Xiangru,Yang Yan et al.3-D seismic ray tracing algorithm based on LTI and partition of grid interface.Chinese Journal of Geophysics,2009,52(9):2370-2376.
[31] Byun B S,Corrigan D and Gaiser J E.Anisotropicvelocity analysis for lithology discrimination.Geophy-sics,1989,54(12):1564-1574.
[32] 赵爱华,丁志峰.一种弱各向异性介质地震波群速度的近似表示新方法.地球物理学进展,2005,20(4):916-919.Zhao Aihua,Ding Zhifeng.New approximate expressions of seismic group velocities for weakly anisotro-pic media.Progress in Geophysics,2005,20(4):916-919.
[33] 吴国忱,梁锴,戚艳平.三维TTI介质相速度和群速度.地球物理学进展,2009,24(6):2097-2105.Wu Guochen,Liang Kai,Qi Yanping.Phase velocity and group velocity in 3D TTI media.Progress in Geophysics,2009,24(6):2097-2105.
[34] 赵瑞,白超英.复杂层状模型中多次波快速追踪——一种基于非规则网格的最短路径算法.地震学报,2010,32(4):433-444.Zhao Rui,Bai Chaoying.Fast multiple ray tracing within complex layered media:the shortest path me-thod based on irregular grid cells.Acta Seismologica Sinica,2010,32(4):433-444.
[2] Charles S.Data-driven tomographic velocity analysisin tilted transversely isotropic media:A 3D case history from the Canadian Foothills.Geophysics,2008,73(5):VE261-VE268.
[3] Thomsen L.Weak elastic anisotropy.Geophysics,1986,51(10):1954-1966.
[4] Sena A G.Seismic traveltime equations for azimutha-lly anisotropic and isotropic media:Estimation of interval elastic properties.Geophysics,1991,56(12):2090-2101.
[5] Faria E L and Stoffa P L.Traveltime computation in transversely isotropic media.Geophysics,1994,59(2):272-281.
[6] 邓怀群,刘雯林.横向各向同性介质中地震波旅行时的计算.石油地球物理勘探,2000,35(4):508-516.Deng Huaiqun,Liu Wenlin.Computation of seismic travel times in transversely isotropic medium.OGP,2000,35(4):508-516.
[7] Alkhalifah T.Traveltime computation with the linea-rized eikonal equation for anisotropic media.Geophy-sical Prospecting,2002,50(4):373-382.
[8] Zhou B,Greenhalgh S A.“Shortest path” ray tracing for most general 2D/3D anisotropic media.Journal of Geophysics & Engineering,2005,2(1):54-63.
[9] 赵爱华,张美根,丁志峰.横向各向同性介质中地震波旅行时模拟.地球物理学报,2006,49(6):1762-1769.Zhao Aihua,Zhang Meigen,Ding Zhifeng.Seismic traveltime computation for transversely isotropy media.Chinese Journal of Geophysics,2006,49(6):1762-1769.
[10] 马德堂,朱光明.横向各项同性介质中的初至波旅行时计算.石油地球物理勘探,2006,41(1):26-31.Ma Detang,Zhu Guangming.Computation of traveltimes of seismic first breaks in transversely isotropic medium.OGP,2006,41(1):26-31.
[11] 李建国,李彦鹏,郭晓玲.VTI介质试射射线追踪.石油地球物理勘探,2010,45(4):491-496.Li Jianguo,Li Yanpeng,Guo Xiaoling.VTI media test-firing ray tracing.OGP,2010,45(4):491-496.
[12] 马德堂,朱光明,范延恩.二维TTI介质中初至波旅行时的搜索算法.石油地球物理勘探,2011,46(5):710-714.Ma Detang,Zhu Guangming,Fan Tingen.A search algorithm for first break traveltime in 2D TTI medium.OGP,2011,46(5):710-714.
[13] 白海军,孙赞东,王学军.基于波前构建法的TTI介质射线追踪.石油地球物理勘探,2011,46(增刊1):1-6.Bai Haijun,Sun Zandong,Wang Xuejun.Ray tracing in TTI media using wavefront construction.OGP,2011,46(S1):1-6.
[14] 李晓玲,白超英,胡光义.起伏层状TI介质中多次波射线追踪.石油地球物理勘探,2013,48(6):924-931. Li Xiaoling,Bai Chaoying,Hu Guangyi.Multiple ray tracing in an undulated layered TI media.OGP,2013,48(6):924-931.
[15] Farra V.Ray tracing in complex media.Journal of Applied Geophysics,1993,30(1-2):55-73.
[16] Berryman J G.Long-wave elastic anisotropy in transversely isotropy media.Geophysics,1979,44(5):896-917.
[17] 李庆春,叶佩.初至波与反射波旅行时多尺度渐进联合层析成像.石油地球物理勘探,2013,48(4):536-544.Li Qingchun,Ye Pei.Joint tomography of first break and reflection traveltime with multi-scale netsize method.OGP,2013,48(4):536-544.
[18] 李永博,李庆春,吴琼等.快速行进法射线追踪提高旅行时计算精度和效率的改进措施.石油地球物理勘探,2016,51(3):467-473.Li Yongbo,Li Qingchun,Wu Qiong et al.Improved fast marching method for higher calculation accuracy and efficiency of traveltime.OGP,2016,51(3):467-473.
[19] 叶佩,李庆春.旅行时线性插值射线追踪提高计算精度和效率的改进方法.吉林大学学报(地球科学版),2013,43(1):291-298.Ye Pei,Li Qingchun.Improvements of linear traveltime interpolation ray tracing for the accuracy and efficiency.Journal of Jilin University(Earth Science Edition),2013,43(1):291-298.
[20] 秦宁,王延光,杨晓东等.非水平地表高斯束叠前深度偏移及山前带应用实例.石油地球物理勘探,2017,52(1):81-86.Qin Ning,Wang Yanguang,Yang Xiaodong et al.Gaussian bean prestack depth migration for undulating-surface area in piedmont zone.OGP,2017,52(1):81-86.
[21] 黄国娇,白超英.二维复杂层状介质中地震多波旅行时联合反演成像.地球物理学报,2010,53(12):2972-2981.Huang Guojiao,Bai Chaoying.Simultaneous inversion with multiple traveltimes within 2-D complex layered media.Chinese Journal of Geophysics,2010,53(12):2972-2981.
[22] Asakawa E,Kawanaka T.Seismic ray tracing using linear traveltime interpolation.Geophysics Prospecting,1993,41(4):99-111.
[23] Li X G,Uirych T J.LTI formulations and application to curved wavefronts.Journal of Seismic Exploration,1993,2(1):239-246.
[24] 赵改善,郝守玲.基于旅行时线性插值的地震射线追踪算法.石油物探,1998,32(2):14-24.Zhao Gaishan,Hao Shouling.Seismic ray tracing algorithm based on the linear traveltime interpolation.GPP,1998,32(2):14-24.
[25] Cardarelli E and Cerreto A.Ray tracing in elliptical anisotropic media using the linear traveltime interpolation (LTI) method applied to traveltime seismic tomography.Geophysical Prospecting,2002,50(1):55-72.
[26] 聂建新,杨慧珠.地震波旅行时二次/线性联合插值法.清华大学学报,2003,43(11):1495-1498.Nie Jianxin,Yang Huizhu.Quadrarical linear travel time interpolation of seismic ray-tracing.Journal of Tsinghua University,2003,43(11):1495-1498.
[27] Kumar D,Sen M K,Ferguson R J.Traveltime calculation and prestack depth migration in tilted transversely isotropic media.Geophysics,2004,69(1):37-44.
[28] 张赛民,周竹生,陈灵君等.对旅行时进行抛物型插值的地震射线追踪方法.地球物理学进展,2007,22(1):43-48.Zhang Saimin,Zhou Zhusheng,Chen Lingjun et al.Seismic ray tracing method of applying parabolic interpolation to travel time.Progress in Geophysics,2007,22(1):43-48.
[29] 张东,谢宝莲,杨艳等.一种改进的线性旅行时插值射线追踪算法.地球物理学报,2009,52(1):200-205.Zhang Dong,Xie Baolian,Yang Yan et al.A ray tra-cing method based on improved linear traveltime interpolation.Chinese Journal of Geophysics,2009,52(1):200-205.
[30] 张东,傅相如,杨艳等.基于LTI和网格界面剖分的三维地震射线追踪算法.地球物理学报,2009,52(9):2370-2376.Zhang Dong,Fu Xiangru,Yang Yan et al.3-D seismic ray tracing algorithm based on LTI and partition of grid interface.Chinese Journal of Geophysics,2009,52(9):2370-2376.
[31] Byun B S,Corrigan D and Gaiser J E.Anisotropicvelocity analysis for lithology discrimination.Geophy-sics,1989,54(12):1564-1574.
[32] 赵爱华,丁志峰.一种弱各向异性介质地震波群速度的近似表示新方法.地球物理学进展,2005,20(4):916-919.Zhao Aihua,Ding Zhifeng.New approximate expressions of seismic group velocities for weakly anisotro-pic media.Progress in Geophysics,2005,20(4):916-919.
[33] 吴国忱,梁锴,戚艳平.三维TTI介质相速度和群速度.地球物理学进展,2009,24(6):2097-2105.Wu Guochen,Liang Kai,Qi Yanping.Phase velocity and group velocity in 3D TTI media.Progress in Geophysics,2009,24(6):2097-2105.
[34] 赵瑞,白超英.复杂层状模型中多次波快速追踪——一种基于非规则网格的最短路径算法.地震学报,2010,32(4):433-444.Zhao Rui,Bai Chaoying.Fast multiple ray tracing within complex layered media:the shortest path me-thod based on irregular grid cells.Acta Seismologica Sinica,2010,32(4):433-444.