基于分区多步快速行进法下3D起伏层状介质中多震相射线追踪
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摘要
快速行进法(FMM)是一种求解程函方程数值解计算网格节点走时,然后向后处理进行射线追踪的方法.为了求取任意起伏界面下高精度多震相的地震走时与相应的射线路径,本文采用任意起伏地表条件下的的三维不等距上行差分公式结合分区多步计算技术实现了三维复杂层状起伏介质中多震相(透射、反射、转换波)地震走时的计算,利用上行有限差分公式逐次进行射线路径的追踪,并且通过与较为成熟的不规则最短路径法(ISPM)对比,验证了本算法的计算精度和有效性.数值模拟实例和对比结果表明该算法具有较高的计算精度,数值计算稳健,能灵活处理含任意三维起伏界面模型中多震相地震走时及相应射线路径的追踪问题.
Fast Marching Method(FMM) for ray tracing is a method using numerical solutions of Eikonal equation to calculate the traveltime of all gridded points, and applying backward processing ray tracing for obtaining raypath information. To obtain a high accurate traveltimes in 3D complex media with undulated topography,we in this paper calculate the traveltime and tracking arrivals composed of any kind of combinations of transmissions,conversions and reflections by integrating upwind finite difference method and multistage computation technique in complex 3D complex media. In addition, the accuracy and efficiency of proposed algorithm are compared with the well developed Irregular Shortest-path Method(ISPM). We use an uneven differential format to compute the traveltimes at the irregular grids near the subsurface interface, and establish a upwind finite-difference formula for tracking raypaths. Finally,the traveltime computation and the corresponding raypaths finding for multi-phase arrivals are solved flexibly by multistage computation technique. The simulation and comparison tests show that the proposed algorithm has a high computational accuracy,numerical stability and flexible adaptability in traveltime computation and raypath finding for multi-phase seismic arrivals in any 3D complex media.
Fast Marching Method(FMM) for ray tracing is a method using numerical solutions of Eikonal equation to calculate the traveltime of all gridded points, and applying backward processing ray tracing for obtaining raypath information. To obtain a high accurate traveltimes in 3D complex media with undulated topography,we in this paper calculate the traveltime and tracking arrivals composed of any kind of combinations of transmissions,conversions and reflections by integrating upwind finite difference method and multistage computation technique in complex 3D complex media. In addition, the accuracy and efficiency of proposed algorithm are compared with the well developed Irregular Shortest-path Method(ISPM). We use an uneven differential format to compute the traveltimes at the irregular grids near the subsurface interface, and establish a upwind finite-difference formula for tracking raypaths. Finally,the traveltime computation and the corresponding raypaths finding for multi-phase arrivals are solved flexibly by multistage computation technique. The simulation and comparison tests show that the proposed algorithm has a high computational accuracy,numerical stability and flexible adaptability in traveltime computation and raypath finding for multi-phase seismic arrivals in any 3D complex media.
引文
Bai C Y,Greenhalgh S,Zhou B.2007.3D ray tracing using a modified shortest-path method[J].Geophysics,72(4):T27.
Bai C Y,Huang G J,Li X L,et al.2013.Ray tracing of multiple transmitted/reflected/converted waves in 2-D/3-D layered anisotropic TTI media and application to crosswell traveltime tomography[J].Eophysical Journal International,195(2):1068-1087.
Bai C Y,Huang G J,Zhao R.2010.2-D/3-D irregular shortest-path ray tracing for multiple arrivals and its applications[J].Geophysical Journal International,183(3):1596-1612.
Bai C Y,Li X L,Tang X P.2011.Seismic wavefront evolution of multiply reflected,transmitted,and converted phases in 2D/3Dtriangular cell model[J].Journal of Seismology,15(4):637-652.
Bai C Y,Tang X P,Zhao R.2009.2-D/3-D multiply transmitted,converted and reflected arrivals in complex layered media with the modified shortest path method[J].Geophysical Journal International,179(1):201-214.
Cerveny V,Psencik I.1983.Gaussian beams and paraxial ray approximation in three-dimensional elastic inhomogeneous media[J].Journal of Geophysics,53:1-15.
de Kool M D,Rawlinson N,Sambridge M.2006.A practical grid-based method for tracking multiple refraction and reflection phases in threedimensional heterogeneous media[J].Geophysical Journal International,167(1):253-270.
Huang G J,Bai C Y,Greenhalgh S.2013.Fast and accurate global multiphase arrival tracking:the irregular shortest-path method in a3-D spherical earth model[J].Geophysical Journal International,194(3):1878-1892.
Huang X G,Sun J G,Sun Z Q,et al.2016.A method for complex traveltime calculation based on the complex eikonal equation and the modified fast marching[J].Oil Geophysical Prospecting(in Chinese),51(6):1109-1118,1147.
Julian B R,Gubbins D.1977.Three-dimensional seismic ray tracing[J].Journal of Geophysics,43(1):95-113.
Kim S,Folie D.2000.The group marching method:an O(N)level set eikonal solver[C]//70th Annual International Meeting,SEG.Expanded Abstracts,2297-2300.
Lan H Q,Zhang Z,Xu T,et al.2012.A comparative study on the fast marching and fast sweeping methods in the calculation of first-arrival traveltime field[J].Progress in Geophysics(in Chinese),27(5):1863-1870,doi:10.6038/j.issn.1004-2903.2012.05.005.
Li X W,Bai C Y.2017.Multiple-phase seismic ray tracing in ellipsoidal coordinates[J].Chinese Journal of Geophysics(in Chinese),60(9):3368-3377,doi:10.6038/cjg20170908.
Lu H Y,Liu Y K,Chang X.2013.MSFM-based travel-times calculation in complex near-surface model[J].Chinese Journal of Geophysics(in Chinese),56(9):3100-3108,doi:10.6038/cjg20130922.
Moser T.1991.Shortest path calculation of seismic rays[J].Geophysics,56(1):59-67.
Rawlinson N.Sambridge M.2004.Multiple reflection and transmission phases in complex layered media using a multistage fast marching method[J].Geophysics,69(5):1338-1350.
Sethian J A,Popovici A M.1999.3-D traveltime computation using the fast marching method[J].Geophysics,64(2):516-523.
Sun Z Q,Sun J G,Han F X.2012.Traveltime computation using the upwind finite difference method with nonuniform grid spacing in a 3Dundulating surface condition[J].Chinese Journal of Geophysics(in Chinese),55(7):2441-2449,doi:10.6038/j.issn.0001-5733.2012.07.028.
Sun Z Q,Sun J G,Wang X Q,et al.2017.Computation of multiple seismic traveltime in mountainous areas with complex 3D conditions using the multistage group marching upwind hybrid method[J].Chinese Journal of Geophysics(in Chinese),60(5):1861-1873,doi:10.6038/cjg20170521.
Um J,Thurber C.1987.A fast algorithm for two-point seismic ray tracing[J].Bulletin of the Seismological Society of America,77(3):972-986.
Vinje V,Iversen E,Gjystdal H.1993.Traveltime and amplitude estimation using wavefront construction[J].Geophysics,58(8):1157-1166.
Vinje V,stebl K,Iversen E,et al.1999.3-D ray modelling by wavefront construction in open models[J].Geophysics,64(6):1912-1919.
Wang F,Qu X X,Liu S X,et al.2014.A new ray tracing approach based on both multi-stencils fast marching and the steepest descent[J].Oil Geophysical Prospecting(in Chinese),49(6):1106-1114.
Zhang F X,Wu Q J,Li Y H,et al.2010.Application of FMM ray tracing to forward and inverse problems of seismology[J].Progress in Geophysics(in Chinese),25(4):1197-1205,doi:10.3969/j.issn.1004-2903.2010.04.008.
黄兴国,孙建国,孙章庆,等.2016.基于复程函方程和改进的快速推进法的复旅行时计算方法[J].石油地球物理勘探,51(6):1109-1118,1147.
兰海强,张智,徐涛,等.2012.地震波走时场模拟的快速推进法和快速扫描法比较研究[J].地球物理学进展,27(5):1863-1870,doi:10.6038/j.issn.1004-2903.2012.05.005.
李兴旺,白超英.2017.椭球坐标系下多震相地震射线追踪[J].地球物理学报,60(9):3368-3377,doi:10.6038/cjg20170908.
卢回忆,刘伊克,常旭.2013.基于MSFM的复杂近地表模型走时计算[J].地球物理学报,56(9):3100-3108,doi:10.6038/cjg20130922.
孙章庆,孙建国,韩复兴.2012.三维起伏地表条件下地震波走时计算的不等距迎风差分法[J].地球物理学报,55(7):2441-2449,doi:10.6038/j.issn.0001-5733.2012.07.028.
孙章庆,孙建国,王雪秋,等.2017.三维复杂山地多级次群推进迎风混合法多波型走时计算[J].地球物理学报,60(5):1861-1873,doi:10.6038/cjg20170521.
王飞,曲昕馨,刘四新,等.2014.一种新的基于多模板快速推进算法和最速下降法的射线追踪方法[J].石油地球物理勘探,49(6):1106-1114.
张风雪,吴庆举,李永华,等.2010.FMM射线追踪方法在地震学正演和反演中的应用[J].地球物理学进展,25(4):1197-1205,doi:10.3969/j.issn.1004-2903.2010.04.008.
Bai C Y,Huang G J,Li X L,et al.2013.Ray tracing of multiple transmitted/reflected/converted waves in 2-D/3-D layered anisotropic TTI media and application to crosswell traveltime tomography[J].Eophysical Journal International,195(2):1068-1087.
Bai C Y,Huang G J,Zhao R.2010.2-D/3-D irregular shortest-path ray tracing for multiple arrivals and its applications[J].Geophysical Journal International,183(3):1596-1612.
Bai C Y,Li X L,Tang X P.2011.Seismic wavefront evolution of multiply reflected,transmitted,and converted phases in 2D/3Dtriangular cell model[J].Journal of Seismology,15(4):637-652.
Bai C Y,Tang X P,Zhao R.2009.2-D/3-D multiply transmitted,converted and reflected arrivals in complex layered media with the modified shortest path method[J].Geophysical Journal International,179(1):201-214.
Cerveny V,Psencik I.1983.Gaussian beams and paraxial ray approximation in three-dimensional elastic inhomogeneous media[J].Journal of Geophysics,53:1-15.
de Kool M D,Rawlinson N,Sambridge M.2006.A practical grid-based method for tracking multiple refraction and reflection phases in threedimensional heterogeneous media[J].Geophysical Journal International,167(1):253-270.
Huang G J,Bai C Y,Greenhalgh S.2013.Fast and accurate global multiphase arrival tracking:the irregular shortest-path method in a3-D spherical earth model[J].Geophysical Journal International,194(3):1878-1892.
Huang X G,Sun J G,Sun Z Q,et al.2016.A method for complex traveltime calculation based on the complex eikonal equation and the modified fast marching[J].Oil Geophysical Prospecting(in Chinese),51(6):1109-1118,1147.
Julian B R,Gubbins D.1977.Three-dimensional seismic ray tracing[J].Journal of Geophysics,43(1):95-113.
Kim S,Folie D.2000.The group marching method:an O(N)level set eikonal solver[C]//70th Annual International Meeting,SEG.Expanded Abstracts,2297-2300.
Lan H Q,Zhang Z,Xu T,et al.2012.A comparative study on the fast marching and fast sweeping methods in the calculation of first-arrival traveltime field[J].Progress in Geophysics(in Chinese),27(5):1863-1870,doi:10.6038/j.issn.1004-2903.2012.05.005.
Li X W,Bai C Y.2017.Multiple-phase seismic ray tracing in ellipsoidal coordinates[J].Chinese Journal of Geophysics(in Chinese),60(9):3368-3377,doi:10.6038/cjg20170908.
Lu H Y,Liu Y K,Chang X.2013.MSFM-based travel-times calculation in complex near-surface model[J].Chinese Journal of Geophysics(in Chinese),56(9):3100-3108,doi:10.6038/cjg20130922.
Moser T.1991.Shortest path calculation of seismic rays[J].Geophysics,56(1):59-67.
Rawlinson N.Sambridge M.2004.Multiple reflection and transmission phases in complex layered media using a multistage fast marching method[J].Geophysics,69(5):1338-1350.
Sethian J A,Popovici A M.1999.3-D traveltime computation using the fast marching method[J].Geophysics,64(2):516-523.
Sun Z Q,Sun J G,Han F X.2012.Traveltime computation using the upwind finite difference method with nonuniform grid spacing in a 3Dundulating surface condition[J].Chinese Journal of Geophysics(in Chinese),55(7):2441-2449,doi:10.6038/j.issn.0001-5733.2012.07.028.
Sun Z Q,Sun J G,Wang X Q,et al.2017.Computation of multiple seismic traveltime in mountainous areas with complex 3D conditions using the multistage group marching upwind hybrid method[J].Chinese Journal of Geophysics(in Chinese),60(5):1861-1873,doi:10.6038/cjg20170521.
Um J,Thurber C.1987.A fast algorithm for two-point seismic ray tracing[J].Bulletin of the Seismological Society of America,77(3):972-986.
Vinje V,Iversen E,Gjystdal H.1993.Traveltime and amplitude estimation using wavefront construction[J].Geophysics,58(8):1157-1166.
Vinje V,stebl K,Iversen E,et al.1999.3-D ray modelling by wavefront construction in open models[J].Geophysics,64(6):1912-1919.
Wang F,Qu X X,Liu S X,et al.2014.A new ray tracing approach based on both multi-stencils fast marching and the steepest descent[J].Oil Geophysical Prospecting(in Chinese),49(6):1106-1114.
Zhang F X,Wu Q J,Li Y H,et al.2010.Application of FMM ray tracing to forward and inverse problems of seismology[J].Progress in Geophysics(in Chinese),25(4):1197-1205,doi:10.3969/j.issn.1004-2903.2010.04.008.
黄兴国,孙建国,孙章庆,等.2016.基于复程函方程和改进的快速推进法的复旅行时计算方法[J].石油地球物理勘探,51(6):1109-1118,1147.
兰海强,张智,徐涛,等.2012.地震波走时场模拟的快速推进法和快速扫描法比较研究[J].地球物理学进展,27(5):1863-1870,doi:10.6038/j.issn.1004-2903.2012.05.005.
李兴旺,白超英.2017.椭球坐标系下多震相地震射线追踪[J].地球物理学报,60(9):3368-3377,doi:10.6038/cjg20170908.
卢回忆,刘伊克,常旭.2013.基于MSFM的复杂近地表模型走时计算[J].地球物理学报,56(9):3100-3108,doi:10.6038/cjg20130922.
孙章庆,孙建国,韩复兴.2012.三维起伏地表条件下地震波走时计算的不等距迎风差分法[J].地球物理学报,55(7):2441-2449,doi:10.6038/j.issn.0001-5733.2012.07.028.
孙章庆,孙建国,王雪秋,等.2017.三维复杂山地多级次群推进迎风混合法多波型走时计算[J].地球物理学报,60(5):1861-1873,doi:10.6038/cjg20170521.
王飞,曲昕馨,刘四新,等.2014.一种新的基于多模板快速推进算法和最速下降法的射线追踪方法[J].石油地球物理勘探,49(6):1106-1114.
张风雪,吴庆举,李永华,等.2010.FMM射线追踪方法在地震学正演和反演中的应用[J].地球物理学进展,25(4):1197-1205,doi:10.3969/j.issn.1004-2903.2010.04.008.
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