网格逐次剖分算法在三维地震射线追踪中的应用
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摘要
初至波走时计算与路径追踪是基于射线理论层析成像的关键,走时线性插值(LTI)算法具有较高的追踪精度和计算效率,在二维条件下应用广泛,但在三维情况下存在最小走时方程不能解析求解的问题。为此,在走时线性插值的基础上,提出了一种改进的网格逐次剖分方法。该方法基于原有的LTI网格界面剖分算法,在最小走时剖分点附近建立同样规格的剖分点阵列进行进一步的细分搜索,寻找最小走时,避免了增加剖分精度而进行的全局细化搜索,节约了计算时间。该方法解决了三维LTI最小走时求解问题,并且能够以较小的计算代价获得更高的计算精度。在给出算法原理与计算步骤的同时,通过模型及实例验证了新算法在计算精度与计算效率上的改进。
First arrival traveltime calculation and path tracing is the key of tomography based on ray theory.Linear traveltime interpolation(LTI) algorithm has high tracing accuracy and efficiency,which has been widely used in 2-D condition.However,for 3-D problem,minimum traveltime equation cannot obtain analytic solution.Therefore,on the basis of LTI,an improved grid successive subdivision method was proposed.The method is based on the original LTI network interface subdivision algorithm,which carry out further search by establishing same mode subdivision point array close to the minimum-traveltime subdivision point to obtain minimum-traveltime.The method avoids global search caused by the increase of subdivision accuracy and saves computation time.Meanwhile,the method solves 3-D LTI minimum-traveltime computation problem and can achieve higher calculation accuracy with less computation amount.Model testing and actual data application results proved the modification of computation accuracy and efficiency.
First arrival traveltime calculation and path tracing is the key of tomography based on ray theory.Linear traveltime interpolation(LTI) algorithm has high tracing accuracy and efficiency,which has been widely used in 2-D condition.However,for 3-D problem,minimum traveltime equation cannot obtain analytic solution.Therefore,on the basis of LTI,an improved grid successive subdivision method was proposed.The method is based on the original LTI network interface subdivision algorithm,which carry out further search by establishing same mode subdivision point array close to the minimum-traveltime subdivision point to obtain minimum-traveltime.The method avoids global search caused by the increase of subdivision accuracy and saves computation time.Meanwhile,the method solves 3-D LTI minimum-traveltime computation problem and can achieve higher calculation accuracy with less computation amount.Model testing and actual data application results proved the modification of computation accuracy and efficiency.
引文
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[17]梅胜全,邓飞,钟本善,等.基于改进的双线性旅行时插值的三维射线追踪[J].物探化探计算技术,2010,32(2):152-157Mei S Q,Deng F,Zhong B S,et al.The 3Dray trac-ing method based on the improved bilinear travetimeinterpolation[J].Computing Techniques for Geo-physical and Geochemical Exploration,2010,32(2):152-157
[18]Zhang J Z,Huang Y Q,Song L P,et al.Fast and ac-curate 3-D ray tracing using bilinear traveltime inter-polation and the wave front group marching[J].Ge-ophysical Journal International,2011,184(3):1327-1340
[19]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[J].地球物理学报,2009,52(9):2370-2376Zhang D,Fu X R,Yang Y,et al.3-D seismic raytracing algorithm based on LTI and partition of gridinterface[J].Chinese Journal of Geophysics,2009,52(9):2370-2376
[2]王祯祥,高尔根,徐果明,等.一种层状介质条件下射线的全路径迭代追踪法[J].煤田地质与勘探,2002,30(4):57-60Wang Z X,Gao E G,Xu G M,et al.The full path ofthe rays in a layered medium under the conditions ofiterative tracking method[J].Coal Geology&Ex-ploration,2002,30(4):57-60
[3]Nishi K.A three-dimensional robust seismic raytracer for volcanic regions[J].Earth Planets Space,2001,53(1):101-109
[4]Julian B R,Gubbins D.Three-dimensional seismicray tracing[J].Journal of Geophysics,1977,43(1):95-113
[5]赵连锋.井间地震波速与衰减联合层析成像方法研究[D].成都:成都理工大学,2002Zhao L F.Cross hole seismic velocity and attenua-tion of the joint tomographic imaging method[D].Chengdu:Chengdu University of Technology,2002
[6]Farra V.Ray tracing in complex media[J].Journalof Applied Geophysics,1993,30(1):55-73
[7]Um J,Thurber C H.A fast algorithm for two pointseismic ray tracing[J].Bulletin of the SeismologicalSociety of America,1987,77(3):972-986
[8]岳玉波,孙建国,杨昊,等.起伏地表下初值射线追踪的实现[J].勘探地球物理进展,2007,30(5):387-398Yue Y B,Sun J G,Yang H,et al.The implementa-tion of the ups and downs of the surface under theinitial value ray tracing[J].Progress in ExplorationGeophysics,2007,30(5):387-398
[9]张钋,刘洪,李幼铭.射线追踪方法的发展现状[J].地球物理学进展,2000,15(1):36-45Zhang P,Liu H,Li Y M.The development status ofthe ray tracing method[J].Progress in Geophysics,2000,15(1):36-45
[10]Hturber C H,Ellsworth W L.Rapid solution of raytracing problems in heterogeneous media[J].Bulle-tin of Seismological Society of America,1980,70(4):1137-1148
[11]Lees J M,Shalev E.On the stability of P-wavetomography at Loma Prieta:a comparison of param-eterizations,linear and nonlinear inversion[J].Bulle-tin of Seismological Society of America,1992,82(4):1821-1839
[12]Vidale J.Finite-difference calculation of traveltimes[J].Bulletin of Seismological Society of Ameri-ca,1988,78(6):2062-2076
[13]张建中,陈世军.复杂介质地震初至波数值模拟[J].计算物理,2003,20(5):429-433Zhang J Z,Chen S J.Complex medium earthquakeprimary wave numerical simulation[J].Computa-tional Physics,2003,20(5):429-433
[14]Moser T J.Shortest path calculation of seismic rays[J].Geophysics,1991,56(1):59-67
[15]Fischer R,Lees J M.Shortest path ray tracing withsparse graphs[J].Geophysics,1993,58(7):987-996
[16]Asakawa E,Kawanaka T.Seismic ray tracing usinglinear traveltime interpolation[J].Geophysical Pros-pecting,1993,41(1):99-112
[17]梅胜全,邓飞,钟本善,等.基于改进的双线性旅行时插值的三维射线追踪[J].物探化探计算技术,2010,32(2):152-157Mei S Q,Deng F,Zhong B S,et al.The 3Dray trac-ing method based on the improved bilinear travetimeinterpolation[J].Computing Techniques for Geo-physical and Geochemical Exploration,2010,32(2):152-157
[18]Zhang J Z,Huang Y Q,Song L P,et al.Fast and ac-curate 3-D ray tracing using bilinear traveltime inter-polation and the wave front group marching[J].Ge-ophysical Journal International,2011,184(3):1327-1340
[19]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[J].地球物理学报,2009,52(9):2370-2376Zhang D,Fu X R,Yang Y,et al.3-D seismic raytracing algorithm based on LTI and partition of gridinterface[J].Chinese Journal of Geophysics,2009,52(9):2370-2376
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