复杂近地表三维初至波走时层析方法研究
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摘要
复杂起伏地表条件下三维初至波走时层析速度建模方法是我国西部山地、沙漠地区地震资料处理的关键技术之一.传统的三维走时层析反演在应用中存在诸多问题:一是射线追踪技术固有的计算效率低、对复杂模型计算不稳定;二是对于大规模三维模型,Tikhonov正则化难以对零空间和欠定分量进行有效约束,造成迭代收敛速度缓慢.本文首先在多模板快速推进算法(MSFM)走时计算的基础上,提出了一种新的射线追踪方法.整形正则化方法和共轭梯度法对反演方程进行了有效的约束,实现了初至波走时层析反演.三维理论模型实验和实际资料处理表明,该方法具有比传统射线走时层析方法更高的反演精度与迭代收敛速度.
Highly efficient and accurate ray-tracing method in complex near-surface media have continuously been the key technique in three dimensional travel-time tomography. However, traditional algorithms utilized for travel-time tomography usually encounter problems when handling large 3 D seismic data. First is the shortcomings inherited in the ray-tracing technique,such as the low computational efficiency and instability when strong velocity contrast exists in velocity model. Second,the disadvantages of traditional regularization algorithms lie in their low iterative convergence rate caused by the insufficient control on estimated model by the Tikhonov's regularization,which could be detrimental for large 3 D scale problems,when only few iterations are affordable. In this paper,we first develop the Multi-Stencils Fast Marching Method( MSFM) into 3 D travel-time computation for complex media with topography. We propose a new algorithm for calculating the Fréchet derivative matrix based on MSFM. Additionally,we incorporate a shaping regularization into conjugate gradient algorithm to minimize the data misfit iteratively. Finally,the numerical experiments on 3 D models and real data have demonstrated the higher accuracy and faster convergence of the proposed method compared to the classical algorithm.
Highly efficient and accurate ray-tracing method in complex near-surface media have continuously been the key technique in three dimensional travel-time tomography. However, traditional algorithms utilized for travel-time tomography usually encounter problems when handling large 3 D seismic data. First is the shortcomings inherited in the ray-tracing technique,such as the low computational efficiency and instability when strong velocity contrast exists in velocity model. Second,the disadvantages of traditional regularization algorithms lie in their low iterative convergence rate caused by the insufficient control on estimated model by the Tikhonov's regularization,which could be detrimental for large 3 D scale problems,when only few iterations are affordable. In this paper,we first develop the Multi-Stencils Fast Marching Method( MSFM) into 3 D travel-time computation for complex media with topography. We propose a new algorithm for calculating the Fréchet derivative matrix based on MSFM. Additionally,we incorporate a shaping regularization into conjugate gradient algorithm to minimize the data misfit iteratively. Finally,the numerical experiments on 3 D models and real data have demonstrated the higher accuracy and faster convergence of the proposed method compared to the classical algorithm.
引文
Alkhalifah T.2002.Traveltime computation with the linearized eikonal equation for anisotropic media[J].Geophysical Prospecting,50(4):373-382.
Dijkstra E W.1959.A note on two problems in connexion with graphs[J].Numerische Mathematik,1(1):269-271.
Fomel S.2007.Shaping regularization in geophysical-estimation problems[J].Geophysics,72(2):R29-R36.
Julian B R,Gubbins D.1997.Three-dimensional seismic ray tracing[J].Journal of Geophysics Research,43(1):95-113.
Klime2 L,Kvasni cˇka M.1994.3-D network ray tracing[J].Geophysical Journal International,116(3):726-738.
Li Z,Cheng D D.2014.Generalized approximation tomographic inversion method of complex near-surface velocity[J].Geophysical Prospecting for Petroleum(in Chinese),53(6):699-705.
Liu Y Z,Yang J Z.2014.Offset-weighted seismic tomography aimed at using the first arrival efficiently[J].Geophysical Prospecting for Petroleum,53(1):99-105.
Lu H Y,Liu Y K,Chang X.2013.MSFM-based travel-times calculation in complex near-surface model[J].Chinese J.Geophys.(in Chinese),2013,56(9):3100-3108,doi:10.6038/cjg20130922.
Moser T J.1991.Shortest path calculation of seismic rays[J].Geophysics,56(1):59-67.
Nakanishi L,Yamaguchi K.1986.A numerical experiment on nonlinear image reconstruction from first-arrival times for two-dimensional island arc structure[J].Journal of Physics of the Earth,34(2):195-201.
Prothero W A,Taylor W J,Eickemeyer J A.1988.A fast,two-point,three-dimensional raytracing algorithm using a simple step search method[J].Bulletin of the Seismological Society of America,78(3):1190-1198.
Qu Y M,Huang J P,Li Z C,et al.2014.A seismic ray tracing method based on irregular grids[J].Geophysical Prospecting for Petroleum(in Chinese),53(6):627-632.
Sang Y Y,Li Z C,Zhang K.2013.Shortest path ray tracing based on parabolic travel-time interpolation[J].Oil Geophysical Prospecting(in Chinese),48(3):403-409.
Sang Y Y,Sun J X,Jiao S P,et al.2014.Shortest path raytracing based on parabolic traveltime interpolation in irregular topography[J].Geophysical Prospecting for Petroleum(in Chinese),53(2):142-148.
Sethian J A.1999.Fast marching methods[J].Siam Review,41(2):199-235.
Sun Z Q,Sun J G,Han F X.2012a.Traveltime computation using the upwind finite difference method with nonuniform grid spacing in a 3Dundulating surface condition[J].Chinese J.Geophys.(in Chinese),55(7):2441-2449,doi:10.6038/j.issn.0001-5733.2012.07.028.
Sun Z Q,Sun J G,Han F X.2012b.The comparison of three schemes for computing seismic wave traveltimes in complex topographical conditions[J].Chinese J.Geophys.(in Chinese),55(2):560-568,doi:10.6038/j.issn.0001-5733.2012.02.018.
Tsai Y.R,Cheng L.T,Osher S,et al.2003.Fast sweeping algorithms for a class of Hamilton-Jacobi equation[J].SIAM Journal on Numerical Analysis,41(2):673-694.
Vidale J E.1990.Finite-difference calculation of traveltimes in three dimensions[J].Geophysics,55(5):521-526.
Wang F,Qu X Y,Liu S X,et al.2014.A new multistencils fast marching algorithm and raytracing method based on steepest descent method[J].Oil geophysical prospecting(in Chinese),49(6):1106-1114.
Wang H.Z.,Feng B,Wang X.W.et al.2015.Analysis of seismic inversion imaging and its technical core issues[J].Geophysical Prospecting for Petroleum(in Chinese),54(2):115-125.
Zelt C A,Barton P J.1998.Three-dimensional seismic refraction tomography:A comparison of two methods applied to data from the Faeroe Basin[J].Journal of Geophysical Research,103(B4):7187-7210.
Zhang J,Toks9z M N.1998.Nonlinear refraction traveltime tomography[J].Geophysics,63(5):1726-1737.
Zhang K,Li Z C.2013.Tomographic Velocity Inversion Method with Dual-complexity[J].Progress in Geophysics(in Chinese),vol.28(6):3001-3006.
Zhang K,Qin N,Li Z C.et al.2013.Progress in seismic tomography for unconventional marine carbonate reservoirs[J],Progress in Geophysics(in Chinese),vol.28(6),2993-3000.
Zhao F F,Ma T,Xu T.2014.A review of the travel-time calculation methods of seismic first break[J].Progress in Geophysics(in Chinese),29(3):1102-1113.
Zhao H K.2005.A fast sweeping method for eikonal equations[J].Journal of Math and Computing,74:603-627.
李哲,程丹丹.2014.复杂近地表速度广义近似反演方法研究[J].石油物探,53(6):699-705.
刘玉柱,杨积忠.2014.有效利用初至信息的偏移距加权地震层析成像方法[J].石油物探,53(1):99-105.
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.
曲英铭,黄建平,李振春,等.2014.一种基于非规则网格的地震波射线追踪方法[J].石油物探,53(6):627-632.
桑运云,李振春,张凯.2013.抛物旅行时插值最短路径射线追踪[J].石油地球物理勘探,48(3):403-409.
桑运云,孙军晓,焦淑萍,等.2014.起伏地表下基于抛物插值的最短路径射线追踪[J].石油物探,53(2):142-148.
孙章庆,孙建国,韩复兴.2012a.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,韩复兴.2012b.针对复杂地形的三种地震波走时算法及对比[J].地球物理学报,55(2):560-568,doi:10.6038/j.issn.0001-5733.2012.02.018.
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.
王华忠,冯波,王雄文,等.2015.地震波反演成像方法与技术核心问题分析[J].石油物探,54(2):115-125.
张凯,李振春.2013.双复杂条件下层析速度反演方法研究[J],地球物理学进展,vol.28(6):3001-3006.
张凯,秦宁,李振春,等.2013.非常规海相碳酸盐岩油气藏地震层析研究进展[J],地球物理学进展,vol.28(6),2993-3000.
赵烽帆,马婷,徐涛.2014.地震波初至走时的计算方法综述[J].地球物理学进展,29(3):1102-1113.
Dijkstra E W.1959.A note on two problems in connexion with graphs[J].Numerische Mathematik,1(1):269-271.
Fomel S.2007.Shaping regularization in geophysical-estimation problems[J].Geophysics,72(2):R29-R36.
Julian B R,Gubbins D.1997.Three-dimensional seismic ray tracing[J].Journal of Geophysics Research,43(1):95-113.
Klime2 L,Kvasni cˇka M.1994.3-D network ray tracing[J].Geophysical Journal International,116(3):726-738.
Li Z,Cheng D D.2014.Generalized approximation tomographic inversion method of complex near-surface velocity[J].Geophysical Prospecting for Petroleum(in Chinese),53(6):699-705.
Liu Y Z,Yang J Z.2014.Offset-weighted seismic tomography aimed at using the first arrival efficiently[J].Geophysical Prospecting for Petroleum,53(1):99-105.
Lu H Y,Liu Y K,Chang X.2013.MSFM-based travel-times calculation in complex near-surface model[J].Chinese J.Geophys.(in Chinese),2013,56(9):3100-3108,doi:10.6038/cjg20130922.
Moser T J.1991.Shortest path calculation of seismic rays[J].Geophysics,56(1):59-67.
Nakanishi L,Yamaguchi K.1986.A numerical experiment on nonlinear image reconstruction from first-arrival times for two-dimensional island arc structure[J].Journal of Physics of the Earth,34(2):195-201.
Prothero W A,Taylor W J,Eickemeyer J A.1988.A fast,two-point,three-dimensional raytracing algorithm using a simple step search method[J].Bulletin of the Seismological Society of America,78(3):1190-1198.
Qu Y M,Huang J P,Li Z C,et al.2014.A seismic ray tracing method based on irregular grids[J].Geophysical Prospecting for Petroleum(in Chinese),53(6):627-632.
Sang Y Y,Li Z C,Zhang K.2013.Shortest path ray tracing based on parabolic travel-time interpolation[J].Oil Geophysical Prospecting(in Chinese),48(3):403-409.
Sang Y Y,Sun J X,Jiao S P,et al.2014.Shortest path raytracing based on parabolic traveltime interpolation in irregular topography[J].Geophysical Prospecting for Petroleum(in Chinese),53(2):142-148.
Sethian J A.1999.Fast marching methods[J].Siam Review,41(2):199-235.
Sun Z Q,Sun J G,Han F X.2012a.Traveltime computation using the upwind finite difference method with nonuniform grid spacing in a 3Dundulating surface condition[J].Chinese J.Geophys.(in Chinese),55(7):2441-2449,doi:10.6038/j.issn.0001-5733.2012.07.028.
Sun Z Q,Sun J G,Han F X.2012b.The comparison of three schemes for computing seismic wave traveltimes in complex topographical conditions[J].Chinese J.Geophys.(in Chinese),55(2):560-568,doi:10.6038/j.issn.0001-5733.2012.02.018.
Tsai Y.R,Cheng L.T,Osher S,et al.2003.Fast sweeping algorithms for a class of Hamilton-Jacobi equation[J].SIAM Journal on Numerical Analysis,41(2):673-694.
Vidale J E.1990.Finite-difference calculation of traveltimes in three dimensions[J].Geophysics,55(5):521-526.
Wang F,Qu X Y,Liu S X,et al.2014.A new multistencils fast marching algorithm and raytracing method based on steepest descent method[J].Oil geophysical prospecting(in Chinese),49(6):1106-1114.
Wang H.Z.,Feng B,Wang X.W.et al.2015.Analysis of seismic inversion imaging and its technical core issues[J].Geophysical Prospecting for Petroleum(in Chinese),54(2):115-125.
Zelt C A,Barton P J.1998.Three-dimensional seismic refraction tomography:A comparison of two methods applied to data from the Faeroe Basin[J].Journal of Geophysical Research,103(B4):7187-7210.
Zhang J,Toks9z M N.1998.Nonlinear refraction traveltime tomography[J].Geophysics,63(5):1726-1737.
Zhang K,Li Z C.2013.Tomographic Velocity Inversion Method with Dual-complexity[J].Progress in Geophysics(in Chinese),vol.28(6):3001-3006.
Zhang K,Qin N,Li Z C.et al.2013.Progress in seismic tomography for unconventional marine carbonate reservoirs[J],Progress in Geophysics(in Chinese),vol.28(6),2993-3000.
Zhao F F,Ma T,Xu T.2014.A review of the travel-time calculation methods of seismic first break[J].Progress in Geophysics(in Chinese),29(3):1102-1113.
Zhao H K.2005.A fast sweeping method for eikonal equations[J].Journal of Math and Computing,74:603-627.
李哲,程丹丹.2014.复杂近地表速度广义近似反演方法研究[J].石油物探,53(6):699-705.
刘玉柱,杨积忠.2014.有效利用初至信息的偏移距加权地震层析成像方法[J].石油物探,53(1):99-105.
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.
曲英铭,黄建平,李振春,等.2014.一种基于非规则网格的地震波射线追踪方法[J].石油物探,53(6):627-632.
桑运云,李振春,张凯.2013.抛物旅行时插值最短路径射线追踪[J].石油地球物理勘探,48(3):403-409.
桑运云,孙军晓,焦淑萍,等.2014.起伏地表下基于抛物插值的最短路径射线追踪[J].石油物探,53(2):142-148.
孙章庆,孙建国,韩复兴.2012a.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,韩复兴.2012b.针对复杂地形的三种地震波走时算法及对比[J].地球物理学报,55(2):560-568,doi:10.6038/j.issn.0001-5733.2012.02.018.
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.
王华忠,冯波,王雄文,等.2015.地震波反演成像方法与技术核心问题分析[J].石油物探,54(2):115-125.
张凯,李振春.2013.双复杂条件下层析速度反演方法研究[J],地球物理学进展,vol.28(6):3001-3006.
张凯,秦宁,李振春,等.2013.非常规海相碳酸盐岩油气藏地震层析研究进展[J],地球物理学进展,vol.28(6),2993-3000.
赵烽帆,马婷,徐涛.2014.地震波初至走时的计算方法综述[J].地球物理学进展,29(3):1102-1113.