复杂介质中地震波前及射线追踪综述
|
摘要
本文较为系统综述了国内外在不均匀介质中各种主要和实用的射线追踪方法,例如:基于射线理论的打靶法、弯曲法(伪弯曲法)、高斯射线束算法等;基于网格单元扩展的有限差分解程函方程法(FD)、最短路径算法(SPM);以及结合射线和网格单元扩展的波前构造法等.同时对目前出现的多次波射线追踪技术、以及多值波前追踪技术(如:相空间算法、水平集算法)也进行了分析讨论.同时对基于网格单元扩展算法的优缺点进行了评述,其基本结论是:基于单元模型的SPM要优于FD算法,而基于网格的SPM算法则次之.就传统的射线追踪算法(如:打靶法和弯曲法)而言,其未来的发展方向是实现完全非线性的相应算法,而基于网格单元的算法则主要是扩展功能(如:后续波、多值波前的追踪).射线追踪方法技术未来需要解决的问题主要有:块状模型中多次波的追踪;多值波前及多值射线追踪;走时与振幅的同时追踪计算;以及其它领域新方法的引入.
In this paper we focus on the review of main and practical seismic ray tracing algorithms in complex media,which includes the ray based method,such as the shooting method,the bending method(or pseudo bending method)and the Gaussian beam method;the grid-cell based method,such as the finite-difference Eikonal equation solver(FD)and the shortest-path method(SPM);the combined method,such as the wavefront construction method.Meanwhile,we also discuss some current algorithms for multiple arrival tracking and multi-valued wavefront tracing(e g,the level set method and the phase space method).Based on the previous researches,we compare the grid-cell based methods and conclude that the cell-based SPM is superior to the FD algorithm,and the grid-based SPM is less favorable choice in term of computational efficiency.For the traditional ray-based algorithm(e g,shooting and bending method),it will concentrate on the full non-linear algorithm;while for the grid-cell based algorithms,they will focus on the extension of the functional(such as,later arrival tracking and multi-valued wavefront tracing).The future emphases in seismic ray tracing may include:multiple arrival tracking methods in block model,efficient multi-valued wavefront tracing algorithms;methodologies for simultaneous calculation of the traveltime and amplitude information and introduction of model algorithms from other fields(for example,computing mathematics).
In this paper we focus on the review of main and practical seismic ray tracing algorithms in complex media,which includes the ray based method,such as the shooting method,the bending method(or pseudo bending method)and the Gaussian beam method;the grid-cell based method,such as the finite-difference Eikonal equation solver(FD)and the shortest-path method(SPM);the combined method,such as the wavefront construction method.Meanwhile,we also discuss some current algorithms for multiple arrival tracking and multi-valued wavefront tracing(e g,the level set method and the phase space method).Based on the previous researches,we compare the grid-cell based methods and conclude that the cell-based SPM is superior to the FD algorithm,and the grid-based SPM is less favorable choice in term of computational efficiency.For the traditional ray-based algorithm(e g,shooting and bending method),it will concentrate on the full non-linear algorithm;while for the grid-cell based algorithms,they will focus on the extension of the functional(such as,later arrival tracking and multi-valued wavefront tracing).The future emphases in seismic ray tracing may include:multiple arrival tracking methods in block model,efficient multi-valued wavefront tracing algorithms;methodologies for simultaneous calculation of the traveltime and amplitude information and introduction of model algorithms from other fields(for example,computing mathematics).
引文
[1]Julian B R,Gubbins D.Three dimensional seismic ray tracingJ.J Geophys,1977,43:95-119.
[2]CervenV.Seismic Ray Theory.Cambridge:Cambridge UniversityPress,2001.
[3]Um J,Thurber C.A fast algorithm for two-point seismic raytracing J.Bull Seism Soc Am,1987,77:972-986.
[4]CervenV,Psencik I.Gaussian beams and paraxial ray approximationin three dimensional elastic inhomogeneous media.J Geophys,1983,53:1-15.
[5]Vidale J E.Finite-difference calculations of traveltimes.BullSeism Soc Am,1988,78:2062-2076.
[6]Moser T J.Shortest path calculation of seismic rays.Geophysics,1991,56:59-67.
[7]Rawlinson N,Sambridge M.Multiple reflection and transmissionphases in complex layered media using a multistage fastmarching method.Geophysics,2004,69:1338-1350.
[8]Cao S,Greenhalgh S.Calculation of the seismic first-break timefield and its ray path distribution using a minimum traveltimetree algorithm.Geophys J Int,1993,114:593-600.
[9]Bai C Y,Greenhalgh S A,Zhou B.3-D ray tracing by using amodified shortest-path method.Geophysics,2007,72:T27-T36.
[10]Vinje V,Iversen E,Gjystdal H.Traveltime and amplitudeestimation using wavefront construction.Geophysics,1993,58:1157-1166.
[11]De Kool M,Rawlinson N,Sambridge M.A practical gridbased method for tracking multiple refraction and reflectionphases in 3dheterogeneous media.Geophys J Int,2006,167:253-270.
[12]唐小平,白超英.最短路径算法下二维层状介质中的多次波追踪.地球物理学进展,2009,24(6):2087-2096.Tang X P,Bai C Y.Multiple ray tracing in 2-D layered mediawith the shortest path method.Progress in Geophys.(inChinese),2009,24(6):2087-2096.
[13]唐小平,白超英.最短路径算法下三维层状介质中的多次波追踪.地球物理学报,2009,52(10):2635-2643.Tang X P,Bai C Y.Multiple ray tracing within 3-D layeredmedia with the shortest path method.Chinese J.Geophys.(inChinese),2009,52(10):2635-2643.
[14]Bai C Y,Tang X P,Zhao R.2-D/3-D multiply transmitted,converted and reflected arrivals in complex layered mediawith the modified shortest path method.Geophys J Int,2009,179:201-214.
[15]赵瑞,白超英.复杂层状模型中多次波跟踪:一种基于非规则网格的最短路径快速算法.地震学报,2010,32(4):433-444.Zhao R,Bai C Y.Fast multiple ray tracing within complexlayered media:The shortest path method based on irregulargrid cells.Acta Seismologica Sinica.(in Chinese),2010,32(4):433-444.
[16]Bai C Y,Huang G J,Zhao R.2D/3DIrregular shortest-pathraytracing for multiple arrivals and its applications.Geophys JInt,2010,in press.
[17]Vinje V,Iversen E,Astebl K,et al.Estimation ofmultivalued arrivals in 3D models using wavefrontconstruction-Part I.Geophys Prosp,1996,44:819-842.
[18]Symes W W,Qian J.A slowness matching eulerian methodfor multivalued solutions of eikonal equaions.SIAM J SciComput,2003,19:501-526.
[19]Sethian J A.Level set methods and fast marching methods.Cambridge:Cambridge University Press,1999.
[20]Hauser J,Sambridge M,Rawlinson N.Multiarrival wavefronttracking and its applications.Geochem Geophys Geosyst,2008,9,Q11001,doi:10.1029/2008GC002069.
[21]Chapman C.Fundamentals of seismic wave propagation.Cambridge:Cambridge University Press,2004.
[22]Rawlinson N,Hauser J,Sambridge M.Seismic ray tracing andwavefront tracking in laterally heterogeneous media.Advances in Geophysics,2007,49:203-267.
[23]Williamson P R.Tomographic inversion in reflection seismology.Geophys J Int,1990,100:255-274.
[24]Rawlinson N,Houseman G A,Collins C D.Inversion ofseismic refraction and wide-angle reflection traveltimes for 3-D layered crustal structure.Geophys J Int,2001,145:381-401.
[25]Sambridge M S,Kennett B L N.Boundary value ray tracing ina heterogeneous medium:A simple and versatile algorithm.Geophys J Int,1990,101:157-168.
[26]Virieux J,Farra F.Ray tracing in 3-d complex isotropic media:Ananalysis of the problem.Geophysics,1991,56:2057-2069.
[27]Slawinski M A,Slawinski R A,Brown R J,et al.A generalizedform of snell’s law in anisotropic media.Geophysics,2000,65:632-637.
[28]马争鸣,李衍达.二步法射线追踪.地球物理学报,1991,34(4):501-508.Ma Z M,Li Y D.Two-step ray tracing method.Chinese J.Geophys.(in Chinese),1991,34(4):501-508.
[29]高尔根,徐果明.二维速度随机分布逐步迭代射线追踪方法.地球物理学报,1996,39(增刊):302-308.Gao E G,Xu G M.A new kind of step by step iterative ray-tracing method.Chinese J.Geophys.(in Chinese),1996,39(Supplement):302-308.
[30]高尔根,徐果明,蒋先艺,等.三维结构下逐段迭代射线追踪方法.石油地球物理勘探,2002,37(1):11-16.Gao E G,Xu G M,Jiang X Y,et al.Iterative ray-tracingmethod segment by segment under 3-D construction.OilGeophysical Prospecting.(in Chinese),2002,37(1):11-16.
[31]陈裕明,李晶,唐湘蓉,等.最小时间两点射线追踪.石油地球物理勘探,2002,37(5):455-459.Chen Y M,Li J,Tang X R,et al.Two point ray tracing withminimum time.Oil Geophysical Prospecting.(in Chinese),2002,37(5):455-459.
[32]徐涛,徐果明,高尔根,等.三维复杂介质的块状建模和试射射线追踪.地球物理学报,2004,47(6):1118-1126.Xu T,Xu G M,Gao E G,et al.Block modeling and shootingray tracing in complex 3-D media.Chinese J.Geophys.(inChinese),2004,47(6):1118-1126.
[33]朱光明,曹建章.高斯射线束合成地震记录.西安:西北工业大学出版社,2003.Zhu G M,Cao J Z.Gaussian beam synthetic seismograms.Xi’an:Northwestern Polytechnical University press,2003.
[34]吴立明,许云,乌达巴拉.高斯束射线法在二维非均匀介质复杂构造中的应用.地球物理学报,1995,38(增刊):144-152.Wu L M,Xu Y,Wu D B L.Applied study of gaussian beammethod in 2-D inhomogeneous media and laterally varyinglayered stauctures.Chinese J.Geophys.(in Chinese),1995,38(Supplement):144-152.
[35]邓飞,刘超颖.三维射线快速追踪及高斯射线束正演.石油地球物理勘探,2009,44(2):158-165.Deng F,Liu C Y.Fast ray tracing in 3-D and Gaussian BeamForward.Oil Geophysical Prospecting.(in Chinese),2009,44(2):158-165.
[36]Velis D R,Ulrych T J.Simulated annealing two-point raytracing.Geophys Res Lett,1996,23:201-204.
[37]Velis D R,Ulrych T J.Simulated annealing ray tracing incomplex three dimensional media.Geophys J Int,2001,145:447-459.
[38]Zhao D,Hasegawa A,Horiuchi S.Tomographic imaging of Pand S wave velocity structure beneath Northeastern Japan.JGeophys Res,1992,97:19,909-19,928.
[39]Koketsu K,Sekine S.Pseudo-bending method for three-dimensional seismic ray tracing in a spherical earth withdiscontinuities.Geophys J Int,1998,132:339-346.
[40]Xu T,Zhang Z J,Gao E G,et al.Segmentally iterative raytracing in complex 2Dand 3Dheterogeneous block models.Bull Seism Soc Am,2010,100:841-850.
[41]黄中玉,赵金州.矩形网格三点Fermat射线追踪技术.地球物理学进展,2004,19(1):201-204.Huang Z Y,Zhao J Z.Three points Fermat ray tracingtechnique.Progress in Geophys.(in Chinese),2004,19(1):201-204.
[42]田玥,陈晓非.水平层状介质中的快速两点间射线追踪方法.地震学报,2005,27(2):147-154.Tian Y,Chen X F.A rapid and accurate two-point ray tracingmethod in horizontally layered velocity model.ActaSeismologica Sinica.(in Chinese),2005,27(2):147-154.
[43]Thurber C H.Hypocenter-velocity structure coupling in localearthquake tomography.Phys Earth Planet Inter,1992,75:55-62.
[44]Thurber C,Eberhart-Phillips D.Local earthquake tomographywith flexible gridding.Comput Geosci,1999,25:809-818.
[45]Zhao D,Hasegawa A,Kanamori H.Deep structure of Japansubduction zone as derived from local,regional,andteleseismic events.J Geophys Res,1994,99:22313-22329.
[46]Zhao D,Todo S,Lei S.Local earthquake reflection tomography ofthe Landers aftershock area.Earth Planet Sci Lett,2005,235:623-631.
[47]Farra V,Madariaga R.Seismic waveform modelling inheterogeneous media by ray perturbation theory.J GeophysRes,1987,92:2697-2712.
[48]Snieder R,Sambridge M.Ray perturbation theory for traveltimesand ray paths in 3-d heterogeneous media.Geophys J Int,1992,109:294-322.
[49]Pulliam J,Snieder R.Fast,efficient calculation of rays andtravel times with ray perturbation theory.J Acoust Soc Am,1996,99:383-391.
[50]Snieder R,Spencer C.A unified approach to ray bending,rayperturbation and paraxial ray theories.Geophys J Int,1993,115:456-470.
[51]Sadeghi H,Suzuki S,Takenaka H.A two-point,three-dimensionalseismic ray tracing using genetic Algorithms.Phys EarthPlanet Inter,1999,113:355-365.
[52]Vidale J E.Finite-difference calculations of traveltimes in threedimensions.Geophysics,1990,55:521-526.
[53]Cao S,Greenhalgh S.Finite difference solution of the eikonalequation using an efficient,first arrival wavefront tracingscheme.Geophysics,1994,59:632-643.
[54]Podvin P,Lecomte I.Finite difference computation of traveltimes invery contrasted velocity models:a massively parallel approachand its associated tools.Geophys J Int,1991,105:271-284.
[55]Qin F,Luo Y,Olsen K B,et al.Finite-difference solution ofthe eikonal equation along expanding wavefronts.Geophysics,1992,57:478-487.
[56]Trier J,Symes W W.Upwind finite-difference calculation oftraveltimes.Geophysics,1991,56:812-821.
[57]Schneider Jr W A.Robust and efficient upwind finite-differencetraveltime calculations in three dimensions.Geophysics,1995,60:1108-1117.
[58]Afnimar,Koketsu K.Finite difference traveltime calculationfor head waves travelling along an irregular interface.Geophys J Int,2000,143:729-734.
[59]张霖斌,许云,乌达巴拉,等.地震反射波波前法射线追踪.石油地球物理勘探,1995,30(1):50-55.Zhang L B,Xu Y,Wu D B L,et al.Ray tracing for seismicreflection wave.Oil Geophysical Prospecting.(in Chinese),1995,30(1):50-55.
[60]徐广民,王华忠,范华,等.复杂介质常梯度射线追踪方法研究.石油地球物理勘探,2004,39(3):265-270.Xu G M,Wang H Z,Fan H,et al.Study of constant gradientray-tracing method in complex media.Oil GeophysicalProspecting.(in Chinese),2004,39(3):265-270.
[61]李文杰,魏修成,宁俊瑞,等.一种改进的利用程函方程计算旅行时的方法.石油地球物理勘探,2008,43(5):589-594.Li W J,Wei X C,Ning J R,et al.A improved traveltimescalculation method by eikonal equation.Oil GeophysicalProspecting.(in Chinese),2008,43(5):589-594.
[62]范桃园,杨长春,王真理,等.复杂地质层面的网格化模型及两点射线追踪方法.地球物理学进展,2009,24(1):118-123.Fan T Y,Yang C C,Wang Z L,et al.Surface meshing and 3-Dtwo-point ray tracing in complex geology structure.Progressin Geophys.(in Chinese),2009,24(1):118-123.
[63]张风雪,吴庆举,李永华,等.FMM射线追踪方法在地震学正演和反演中的应用.地球物理学进展,2010,25(4):1197-1205.Zhang F X,Wu Q J,Li Y H,et al.Application of FMM raytracing to forward and inverse problems of seismology.Progress in Geophys.(in Chinese),2010,25(4):1197-1205.
[64]Nakanishi I,Yamaguchi K.A numerical experiment on nonlinearimage reconstruction from first-arrival times for two-dimensional island arc structure.J Phys Earth,1986,34:195-201.
[65]Fischer R,Lees J M.Shortest path ray tracing with sparsegraphs.Geophysics,1993,58:987-996.
[66]KlimeˇsL,Kvasniˇcka M.3-D network ray tracing.Geophys JInt,1994,116:726-738.
[67]Cheng N,House L.Minimum traveltime calculations in 3-Dgraph theory.Geophysics,1996,61:1895-1898.
[68]Zhao A,Zhongjie Z,Teng J.Minimum travel time tree algorithmfor seismic ray tracing:improvement in efficiency.J GeophysEng,2004,1:245-251.
[69]许昇,杨长春,刘洪,等.射线追踪的微变网格方法.地球物理学报,1996,39(1):97-102.Xu S,Yang C C,Liu H,et al.A grid-changeable method forray tracing.Chinese J.Geophys.(in Chinese),1996,39(1):97-102.
[70]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 D,Fu X R,Yang Y,et al.3-D Seismic ray tracingalgorithm based on LTI and partition of grid interface.Chinese J.Geophys.(in Chinese),2009,52(9):2370-2376.
[71]刘洪,孟凡林,李幼铭.计算最小走时和射线路径的界面网全局方法.地球物理学报,1995,38(6):823-832.Liu H,Meng F L,Li Y M.The interface grid method forseeking global minimum travel-time and the correspondentraypath.Chinese J.Geophys.(in Chinese),1995,38(6):823-832.
[72]赵改善,郝守玲,杨尔皓,等.基于旅行时线性插值的地震射线追踪方法.石油物探,1998,37(2):14-24.Zhao G S,Hao S L,Yang E H,et al.Seismic ray tracingalgorithm based on linear traveltime Interpolation.Geophysical Prospecting for Petroleum.(in Chinese),1998,37(2):14-24.
[73]张东,谢宝莲,杨艳,等.一种改进的线性走时插值射线追踪算法.地球物理学报,2009,52(1):200-205.Zhang D,Xie B L,Yang Y,et al.A ray tracing method basedon improved linear traveltime interpolation.Chinese J.Geophys.(in Chinese),2009,52(1):200-205.
[74]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 S M,Zhou Z S,Chen L J,et al.Seismic ray-tracingmethod of applying parabolic Interpolation to travel-time.Progress in Geophysics.(in Chinese),2007,22(1):43-48.
[75]Bai C Y.Three-dimensional seismic kinematic inversion withapplication to reconstruction of the velocity structure of Rabaulvolcano.PhD thesis,The University of Adelaide,2004.
[76]许琨,吴律,王妙月.改进Moser法射线追踪.地球物理学进展,1998,13(4):60-66.Xu K,Wu L,Wang M Y.Improved Moser ray trace.Progressin Geophysics.(in Chinese),1998,13(4):60-66.
[77]王辉,常旭.基于图形结构的三维射线追踪方法.地球物理学报,2000,43(4):534-541.Wang H,Chang X.3-D ray tracing method based on graphicstructure.Chinese J.Geophys.(in Chinese),2000,43(4):534-541.
[78]王汪根,刘盛东,张平松.弯曲射线追踪中Dijkstra算法的改进与实现.地球物理学进展,2006,21(4):1120-1126.Wang W G,Liu S D,Zhang P S.The improvement andimplementation of the Dijkstra algorithm in bending raytracing.Progress in Geophysics.(in Chinese),2006,21(4):1120-1126.
[79]杜增利,施泽进,尹成,等.折射初至波射线追踪方法研究.石油地球物理勘探,2008,43(4):401-404.Du Z L,Shi Z J,Yin C,et al.Study on approach of ray-tracingof refraction first breaks.Oil Geophysical Prospecting.(inChinese),2008,43(4):401-404.
[80]郝奇,何樵登,王德利,等.二维层状VTI介质的梯形块状建模及qP/pSV反射波运动学射线追踪.石油地球物理勘探,2009,44(6):662-670.Hao Q,He Q D,Wang D L,et al.2-D layered VTI media withtrapezoidal block model construction and qP/pSV kinematicreflection ray-tracing.Oil Geophysical Prospecting.(inChinese),2009,44(6):662-670.
[81]赵爱华,张中杰,王光杰,等.非均匀介质中地震波走时与射线路径快速计算技术.地震学报,2000,22(2):151-157.Zhao A H,Zhang Z J,Wang G J,et al.A new scheme for fastcalculation of seismic traveltines and ray paths ininhomogeneous media.Acta Seismologica Sinica.(inChinese),2000,22(2):151-157.
[82]赵爱华,张中杰.三维复杂介质中转换波走时快速计算.地球物理学报,2004,47(4):702-707.Zhao A H,Zhang Z J.Fast calculation of converted wavetravel time in 3-d complex media.Chinese J.Geophys.(inChinese),2004,47(4):702-707.
[83]赵爱华,丁志峰,孙为国,等.复杂介质地震定位中震源轨迹的计算.地球物理学报,2008,51(4):1188-1195.Zhao A H,Ding Z F,Sun W G,et al.Calculation of focal locifor earthquake location in complex media.Chinese J.Geophys.(in Chinese),2008,51(4):1188-1195.
[84]张建中,陈世军,余大祥.最短路径射线追踪方法及其改进.地球物理学进展,2003,18(1):146-150.Zhang J Z,Chen S J,Yu D X.Improvement of shortest pathray tracing method.Progress in Geophysics.(in Chinese),2003,18(1):146-150.
[85]张建中,陈世军,徐初伟.动态网络最短路径射线追踪.地球物理学报,2004,47(5):899-904.Zhang J Z,Chen S J,Xu C W.A method of shortest pathraytracing with dynamic networks.Chinese J.Geophys.(inChinese),2004,47(5):899-904.
[86]张美根,程冰洁,李小凡,等.一种最短路径射线追踪的快速算法.地球物理学报,2006,49(5):1467-1474.Zhang M G,Cheng B J,Li X F,et al.A fast algorithm ofshortest path ray tracing.Chinese J.Geophys.(in Chinese),2006,49(5):1467-1474.
[87]张美根,贾豫葛,王妙月,等.界面二次源波前扩展法全局最小走时射线追踪技术.地球物理学报,2006,49(4):1169-1175.Zhang M G,Jia Y G,Wang M Y,et al.A global minimumtraveltime raytracing algorithm of wavefront expanding withinterface points as secondary sources.Chinese J.Geophys.(inChinese),2006,49(4):1169-1175.
[88]王童奎,张美根,李小凡,等.PS转换波界面二次源法射线追踪.地球物理学进展,2007,22(1):165-170.Wang T K,Zhang M G,Li X F,et al.Interface points assecondary sources method raytracing PS converted waves.Progress in Geophysics(in Chinese),2007,22(1):165-170.
[89]鲁彬,周立发,孔省吾,等.迭代优化的网络最短路径射线追踪方法研究.地球物理学进展,2009,24(3):1420-1425.Lu B,Zhou L F,Kong X W,et al.A method of shortest pathraytracing by iterative optimization.Progress in Geophys.(inChinese),2009,24(3):1420-1425.
[90]鲁彬,周立发,王兴春,等.迭代法在三维网络模型最短路径射线追踪中的应用.地球物理学进展,2010,25(2):533-537.Lu B,Zhou L F,Wang X C,et al.A method of shortest pathraytracing using iterative optimization in a 3-D grid model.Progress in Geophys.(in Chinese),2010,25(2):533-537.
[91]黄国娇,白超英.最短路径算法下二维复杂层状介质中地震多波走时的联合反演成像.地球物理学报,2010,53(12):2972-2981.Huang G J,Bai C Y.Simultaneous inversion with multipletraveltimes within 2-D complex layered media.Chinese J.Geophys.(in Chinese),2010,53(12):2972-2981.
[92]Bai C Y,Zhao R,Greenhalgh S.Rapid 3-D earthquake locationusing a hybrid global-local inversion approach.Pure ApplGeophys,2010,167:1377-1387.
[93]唐巍,李磊.多层垂直对称轴横向各向同性介质精确走时计算.地震学报,2008,30(4):367-376.Tang W,Li L.Exact traveltime computation in multi-layeredtransversely isotropic media with vertical symmetry axis.ActaSeismologica Sinica(in Chinese),2008,30(4):367-376.
[94]Vinje V,Astebl K,Iversen E,Gjystdal H.3-D ray modelling bywavefront construction in open models.GeophysicalProspecting,1999,64:1912-1919.
[95]赵连锋,朱介寿,曹俊兴,等.有序波前重建法的射线追踪.地球物理学报,2003,46(3):415-420.Zhao L F,Zhu J S,Cao J X,et al.Ray Tracing using ordinalwavefront reconstruction method.Chinese J.Geophys.(inChinese),2003,46(3):415-420.
[96]张钋,杨长春,李幼铭.三维多值走时地震波场重建及格林函数计算.地球物理学报,2000,43(2):241-250.Zhang P,Yang C C,Li Youming.3-D multi-valued seismicwavefield reconstruction and Green’s function computation.Chinese J.Geophys.(in Chinese),2000,43(2):241-250.
[97]韩复兴,孙建国,杨昊.基于C++语言实现波前构建射线追踪.石油地球物理勘探,2007,42(4):474-481.Han F X,Sun J G,Yang H.Ray tracing by implementing C++language-based wavefront construction approach.Oil GeophysicalProspecting.(in Chinese),2007,42(4):474-481.
[98]李波涛,杨长春,陈雨红,等.基于波前面三角形网格剖分的波前重建法三维射线追踪.地球物理学进展,2009,24(2):507-512.Li B T,Yang C C,Chen Y H,et al.3Dwavefront constructionmethod ray tracing based on triangular grids layout onwavefront.Progress in Geophys.(in Chinese),2009,24(2):507-512.
[99]Benamou J D.Direct computation of multivalued phase spacesolutions for Hamilton-Jacobi equations.Comm Pure ApplMath,1999,52:1443-1475.
[100]Hauser J,Sambridge M,Rawlinson N.Phase space methodsfor multi-arrival wavefronts.ExplorationGeophysics,2006,37:331-339.
[101]Osher S,Sethian J.Fronts propagating with curvature dependentspeed:Algorithms based on hamilton-jacobi formulations.JComp Phys,1988,79:12-49.
[102]Osher S,Cheng L T,Kang M,Shim H,Tsai Y H.Geometricoptics in a phase-space-based level set and Eulerianframework.J Comp Phys,2002,179:622-648.
[103]唐小平,白超英.分区多步最短路径极值法多值多次反射波追踪.地球物理学报,2011,已投稿.Tang X P,Bai C Y.Multivalued and multiple reflectedraytracing with extreme value based on the multistagemodified shortest-path method.Progress in Geophys.(inChinese),2011,in press.
[104]Leidenfrost A,Ettrich N,Gajewski D,et al.Comparison ofsix different methods for calculating traveltimes.GeophysProspect,1999,47:269-297.
[105]Bai C Y,Greenhalgh S.3-D local earthquake hypocenterdetermination with an‘irregular’shortest path method.Bull Seism Soc Am,2006,96:2257-2268.
[106]Bai C Y,Greenhalgh S.3-D multi-step travel time tomography:Imaging the local,deep velocity structure of Rabaul volcano,Papua New Guinea.Phys Earth Planet Inter,2005a,151:259-275.
[107]Bai C Y,Greenhalgh S.3-D non-linear travel time tomography:Imaging high contrast velocity anomalies.Pure ApplGeophys,2005b,162:2029-2049.
[108]Bai C Y,Peng J B,Grenhalgh S.3-D P-wave velocity structure ofthe crust beneath the Loess Plateau and surroundingregions of China.Tectonophysics,2008,460:278-287.
[109]白超英,黄国娇,李忠生.分区多步最短路径算法下三维复杂层状介质中地震多波走时联合反演成像.地球物理学报,2011,54(1):182-192.Bai C Y,Huang G J,Li Z S.Simultaneous inversion withmultiple-phase traveltimes within 3-D complex layeredmedia.Chinese J.Geophys.(in Chinese),2011,54(1):182-192.
[110]Moser T J,Van Eck T,Nolet G.Hypocenter Determinationin strongly heterogeneous earth models using the shortestpath method.J Geophys Res,1992,97:6563-6572.
[111]Moser T J.Migration using the shortest-path method.Geophysics,1994,59:1110-1120.
[112]Tang X P,Bai C Y.Multiple ray tracing within 3Dlayeredmedia with the shortest path method.Chinese J Geophys,2009,52(5):1130-1138.
[113]El-Mageed M A.3Dfirst arrival traveltime and amplitudesvia Eikonal and Transport finite difference solvers[D].Houston:Rice University,1996.
[2]CervenV.Seismic Ray Theory.Cambridge:Cambridge UniversityPress,2001.
[3]Um J,Thurber C.A fast algorithm for two-point seismic raytracing J.Bull Seism Soc Am,1987,77:972-986.
[4]CervenV,Psencik I.Gaussian beams and paraxial ray approximationin three dimensional elastic inhomogeneous media.J Geophys,1983,53:1-15.
[5]Vidale J E.Finite-difference calculations of traveltimes.BullSeism Soc Am,1988,78:2062-2076.
[6]Moser T J.Shortest path calculation of seismic rays.Geophysics,1991,56:59-67.
[7]Rawlinson N,Sambridge M.Multiple reflection and transmissionphases in complex layered media using a multistage fastmarching method.Geophysics,2004,69:1338-1350.
[8]Cao S,Greenhalgh S.Calculation of the seismic first-break timefield and its ray path distribution using a minimum traveltimetree algorithm.Geophys J Int,1993,114:593-600.
[9]Bai C Y,Greenhalgh S A,Zhou B.3-D ray tracing by using amodified shortest-path method.Geophysics,2007,72:T27-T36.
[10]Vinje V,Iversen E,Gjystdal H.Traveltime and amplitudeestimation using wavefront construction.Geophysics,1993,58:1157-1166.
[11]De Kool M,Rawlinson N,Sambridge M.A practical gridbased method for tracking multiple refraction and reflectionphases in 3dheterogeneous media.Geophys J Int,2006,167:253-270.
[12]唐小平,白超英.最短路径算法下二维层状介质中的多次波追踪.地球物理学进展,2009,24(6):2087-2096.Tang X P,Bai C Y.Multiple ray tracing in 2-D layered mediawith the shortest path method.Progress in Geophys.(inChinese),2009,24(6):2087-2096.
[13]唐小平,白超英.最短路径算法下三维层状介质中的多次波追踪.地球物理学报,2009,52(10):2635-2643.Tang X P,Bai C Y.Multiple ray tracing within 3-D layeredmedia with the shortest path method.Chinese J.Geophys.(inChinese),2009,52(10):2635-2643.
[14]Bai C Y,Tang X P,Zhao R.2-D/3-D multiply transmitted,converted and reflected arrivals in complex layered mediawith the modified shortest path method.Geophys J Int,2009,179:201-214.
[15]赵瑞,白超英.复杂层状模型中多次波跟踪:一种基于非规则网格的最短路径快速算法.地震学报,2010,32(4):433-444.Zhao R,Bai C Y.Fast multiple ray tracing within complexlayered media:The shortest path method based on irregulargrid cells.Acta Seismologica Sinica.(in Chinese),2010,32(4):433-444.
[16]Bai C Y,Huang G J,Zhao R.2D/3DIrregular shortest-pathraytracing for multiple arrivals and its applications.Geophys JInt,2010,in press.
[17]Vinje V,Iversen E,Astebl K,et al.Estimation ofmultivalued arrivals in 3D models using wavefrontconstruction-Part I.Geophys Prosp,1996,44:819-842.
[18]Symes W W,Qian J.A slowness matching eulerian methodfor multivalued solutions of eikonal equaions.SIAM J SciComput,2003,19:501-526.
[19]Sethian J A.Level set methods and fast marching methods.Cambridge:Cambridge University Press,1999.
[20]Hauser J,Sambridge M,Rawlinson N.Multiarrival wavefronttracking and its applications.Geochem Geophys Geosyst,2008,9,Q11001,doi:10.1029/2008GC002069.
[21]Chapman C.Fundamentals of seismic wave propagation.Cambridge:Cambridge University Press,2004.
[22]Rawlinson N,Hauser J,Sambridge M.Seismic ray tracing andwavefront tracking in laterally heterogeneous media.Advances in Geophysics,2007,49:203-267.
[23]Williamson P R.Tomographic inversion in reflection seismology.Geophys J Int,1990,100:255-274.
[24]Rawlinson N,Houseman G A,Collins C D.Inversion ofseismic refraction and wide-angle reflection traveltimes for 3-D layered crustal structure.Geophys J Int,2001,145:381-401.
[25]Sambridge M S,Kennett B L N.Boundary value ray tracing ina heterogeneous medium:A simple and versatile algorithm.Geophys J Int,1990,101:157-168.
[26]Virieux J,Farra F.Ray tracing in 3-d complex isotropic media:Ananalysis of the problem.Geophysics,1991,56:2057-2069.
[27]Slawinski M A,Slawinski R A,Brown R J,et al.A generalizedform of snell’s law in anisotropic media.Geophysics,2000,65:632-637.
[28]马争鸣,李衍达.二步法射线追踪.地球物理学报,1991,34(4):501-508.Ma Z M,Li Y D.Two-step ray tracing method.Chinese J.Geophys.(in Chinese),1991,34(4):501-508.
[29]高尔根,徐果明.二维速度随机分布逐步迭代射线追踪方法.地球物理学报,1996,39(增刊):302-308.Gao E G,Xu G M.A new kind of step by step iterative ray-tracing method.Chinese J.Geophys.(in Chinese),1996,39(Supplement):302-308.
[30]高尔根,徐果明,蒋先艺,等.三维结构下逐段迭代射线追踪方法.石油地球物理勘探,2002,37(1):11-16.Gao E G,Xu G M,Jiang X Y,et al.Iterative ray-tracingmethod segment by segment under 3-D construction.OilGeophysical Prospecting.(in Chinese),2002,37(1):11-16.
[31]陈裕明,李晶,唐湘蓉,等.最小时间两点射线追踪.石油地球物理勘探,2002,37(5):455-459.Chen Y M,Li J,Tang X R,et al.Two point ray tracing withminimum time.Oil Geophysical Prospecting.(in Chinese),2002,37(5):455-459.
[32]徐涛,徐果明,高尔根,等.三维复杂介质的块状建模和试射射线追踪.地球物理学报,2004,47(6):1118-1126.Xu T,Xu G M,Gao E G,et al.Block modeling and shootingray tracing in complex 3-D media.Chinese J.Geophys.(inChinese),2004,47(6):1118-1126.
[33]朱光明,曹建章.高斯射线束合成地震记录.西安:西北工业大学出版社,2003.Zhu G M,Cao J Z.Gaussian beam synthetic seismograms.Xi’an:Northwestern Polytechnical University press,2003.
[34]吴立明,许云,乌达巴拉.高斯束射线法在二维非均匀介质复杂构造中的应用.地球物理学报,1995,38(增刊):144-152.Wu L M,Xu Y,Wu D B L.Applied study of gaussian beammethod in 2-D inhomogeneous media and laterally varyinglayered stauctures.Chinese J.Geophys.(in Chinese),1995,38(Supplement):144-152.
[35]邓飞,刘超颖.三维射线快速追踪及高斯射线束正演.石油地球物理勘探,2009,44(2):158-165.Deng F,Liu C Y.Fast ray tracing in 3-D and Gaussian BeamForward.Oil Geophysical Prospecting.(in Chinese),2009,44(2):158-165.
[36]Velis D R,Ulrych T J.Simulated annealing two-point raytracing.Geophys Res Lett,1996,23:201-204.
[37]Velis D R,Ulrych T J.Simulated annealing ray tracing incomplex three dimensional media.Geophys J Int,2001,145:447-459.
[38]Zhao D,Hasegawa A,Horiuchi S.Tomographic imaging of Pand S wave velocity structure beneath Northeastern Japan.JGeophys Res,1992,97:19,909-19,928.
[39]Koketsu K,Sekine S.Pseudo-bending method for three-dimensional seismic ray tracing in a spherical earth withdiscontinuities.Geophys J Int,1998,132:339-346.
[40]Xu T,Zhang Z J,Gao E G,et al.Segmentally iterative raytracing in complex 2Dand 3Dheterogeneous block models.Bull Seism Soc Am,2010,100:841-850.
[41]黄中玉,赵金州.矩形网格三点Fermat射线追踪技术.地球物理学进展,2004,19(1):201-204.Huang Z Y,Zhao J Z.Three points Fermat ray tracingtechnique.Progress in Geophys.(in Chinese),2004,19(1):201-204.
[42]田玥,陈晓非.水平层状介质中的快速两点间射线追踪方法.地震学报,2005,27(2):147-154.Tian Y,Chen X F.A rapid and accurate two-point ray tracingmethod in horizontally layered velocity model.ActaSeismologica Sinica.(in Chinese),2005,27(2):147-154.
[43]Thurber C H.Hypocenter-velocity structure coupling in localearthquake tomography.Phys Earth Planet Inter,1992,75:55-62.
[44]Thurber C,Eberhart-Phillips D.Local earthquake tomographywith flexible gridding.Comput Geosci,1999,25:809-818.
[45]Zhao D,Hasegawa A,Kanamori H.Deep structure of Japansubduction zone as derived from local,regional,andteleseismic events.J Geophys Res,1994,99:22313-22329.
[46]Zhao D,Todo S,Lei S.Local earthquake reflection tomography ofthe Landers aftershock area.Earth Planet Sci Lett,2005,235:623-631.
[47]Farra V,Madariaga R.Seismic waveform modelling inheterogeneous media by ray perturbation theory.J GeophysRes,1987,92:2697-2712.
[48]Snieder R,Sambridge M.Ray perturbation theory for traveltimesand ray paths in 3-d heterogeneous media.Geophys J Int,1992,109:294-322.
[49]Pulliam J,Snieder R.Fast,efficient calculation of rays andtravel times with ray perturbation theory.J Acoust Soc Am,1996,99:383-391.
[50]Snieder R,Spencer C.A unified approach to ray bending,rayperturbation and paraxial ray theories.Geophys J Int,1993,115:456-470.
[51]Sadeghi H,Suzuki S,Takenaka H.A two-point,three-dimensionalseismic ray tracing using genetic Algorithms.Phys EarthPlanet Inter,1999,113:355-365.
[52]Vidale J E.Finite-difference calculations of traveltimes in threedimensions.Geophysics,1990,55:521-526.
[53]Cao S,Greenhalgh S.Finite difference solution of the eikonalequation using an efficient,first arrival wavefront tracingscheme.Geophysics,1994,59:632-643.
[54]Podvin P,Lecomte I.Finite difference computation of traveltimes invery contrasted velocity models:a massively parallel approachand its associated tools.Geophys J Int,1991,105:271-284.
[55]Qin F,Luo Y,Olsen K B,et al.Finite-difference solution ofthe eikonal equation along expanding wavefronts.Geophysics,1992,57:478-487.
[56]Trier J,Symes W W.Upwind finite-difference calculation oftraveltimes.Geophysics,1991,56:812-821.
[57]Schneider Jr W A.Robust and efficient upwind finite-differencetraveltime calculations in three dimensions.Geophysics,1995,60:1108-1117.
[58]Afnimar,Koketsu K.Finite difference traveltime calculationfor head waves travelling along an irregular interface.Geophys J Int,2000,143:729-734.
[59]张霖斌,许云,乌达巴拉,等.地震反射波波前法射线追踪.石油地球物理勘探,1995,30(1):50-55.Zhang L B,Xu Y,Wu D B L,et al.Ray tracing for seismicreflection wave.Oil Geophysical Prospecting.(in Chinese),1995,30(1):50-55.
[60]徐广民,王华忠,范华,等.复杂介质常梯度射线追踪方法研究.石油地球物理勘探,2004,39(3):265-270.Xu G M,Wang H Z,Fan H,et al.Study of constant gradientray-tracing method in complex media.Oil GeophysicalProspecting.(in Chinese),2004,39(3):265-270.
[61]李文杰,魏修成,宁俊瑞,等.一种改进的利用程函方程计算旅行时的方法.石油地球物理勘探,2008,43(5):589-594.Li W J,Wei X C,Ning J R,et al.A improved traveltimescalculation method by eikonal equation.Oil GeophysicalProspecting.(in Chinese),2008,43(5):589-594.
[62]范桃园,杨长春,王真理,等.复杂地质层面的网格化模型及两点射线追踪方法.地球物理学进展,2009,24(1):118-123.Fan T Y,Yang C C,Wang Z L,et al.Surface meshing and 3-Dtwo-point ray tracing in complex geology structure.Progressin Geophys.(in Chinese),2009,24(1):118-123.
[63]张风雪,吴庆举,李永华,等.FMM射线追踪方法在地震学正演和反演中的应用.地球物理学进展,2010,25(4):1197-1205.Zhang F X,Wu Q J,Li Y H,et al.Application of FMM raytracing to forward and inverse problems of seismology.Progress in Geophys.(in Chinese),2010,25(4):1197-1205.
[64]Nakanishi I,Yamaguchi K.A numerical experiment on nonlinearimage reconstruction from first-arrival times for two-dimensional island arc structure.J Phys Earth,1986,34:195-201.
[65]Fischer R,Lees J M.Shortest path ray tracing with sparsegraphs.Geophysics,1993,58:987-996.
[66]KlimeˇsL,Kvasniˇcka M.3-D network ray tracing.Geophys JInt,1994,116:726-738.
[67]Cheng N,House L.Minimum traveltime calculations in 3-Dgraph theory.Geophysics,1996,61:1895-1898.
[68]Zhao A,Zhongjie Z,Teng J.Minimum travel time tree algorithmfor seismic ray tracing:improvement in efficiency.J GeophysEng,2004,1:245-251.
[69]许昇,杨长春,刘洪,等.射线追踪的微变网格方法.地球物理学报,1996,39(1):97-102.Xu S,Yang C C,Liu H,et al.A grid-changeable method forray tracing.Chinese J.Geophys.(in Chinese),1996,39(1):97-102.
[70]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 D,Fu X R,Yang Y,et al.3-D Seismic ray tracingalgorithm based on LTI and partition of grid interface.Chinese J.Geophys.(in Chinese),2009,52(9):2370-2376.
[71]刘洪,孟凡林,李幼铭.计算最小走时和射线路径的界面网全局方法.地球物理学报,1995,38(6):823-832.Liu H,Meng F L,Li Y M.The interface grid method forseeking global minimum travel-time and the correspondentraypath.Chinese J.Geophys.(in Chinese),1995,38(6):823-832.
[72]赵改善,郝守玲,杨尔皓,等.基于旅行时线性插值的地震射线追踪方法.石油物探,1998,37(2):14-24.Zhao G S,Hao S L,Yang E H,et al.Seismic ray tracingalgorithm based on linear traveltime Interpolation.Geophysical Prospecting for Petroleum.(in Chinese),1998,37(2):14-24.
[73]张东,谢宝莲,杨艳,等.一种改进的线性走时插值射线追踪算法.地球物理学报,2009,52(1):200-205.Zhang D,Xie B L,Yang Y,et al.A ray tracing method basedon improved linear traveltime interpolation.Chinese J.Geophys.(in Chinese),2009,52(1):200-205.
[74]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 S M,Zhou Z S,Chen L J,et al.Seismic ray-tracingmethod of applying parabolic Interpolation to travel-time.Progress in Geophysics.(in Chinese),2007,22(1):43-48.
[75]Bai C Y.Three-dimensional seismic kinematic inversion withapplication to reconstruction of the velocity structure of Rabaulvolcano.PhD thesis,The University of Adelaide,2004.
[76]许琨,吴律,王妙月.改进Moser法射线追踪.地球物理学进展,1998,13(4):60-66.Xu K,Wu L,Wang M Y.Improved Moser ray trace.Progressin Geophysics.(in Chinese),1998,13(4):60-66.
[77]王辉,常旭.基于图形结构的三维射线追踪方法.地球物理学报,2000,43(4):534-541.Wang H,Chang X.3-D ray tracing method based on graphicstructure.Chinese J.Geophys.(in Chinese),2000,43(4):534-541.
[78]王汪根,刘盛东,张平松.弯曲射线追踪中Dijkstra算法的改进与实现.地球物理学进展,2006,21(4):1120-1126.Wang W G,Liu S D,Zhang P S.The improvement andimplementation of the Dijkstra algorithm in bending raytracing.Progress in Geophysics.(in Chinese),2006,21(4):1120-1126.
[79]杜增利,施泽进,尹成,等.折射初至波射线追踪方法研究.石油地球物理勘探,2008,43(4):401-404.Du Z L,Shi Z J,Yin C,et al.Study on approach of ray-tracingof refraction first breaks.Oil Geophysical Prospecting.(inChinese),2008,43(4):401-404.
[80]郝奇,何樵登,王德利,等.二维层状VTI介质的梯形块状建模及qP/pSV反射波运动学射线追踪.石油地球物理勘探,2009,44(6):662-670.Hao Q,He Q D,Wang D L,et al.2-D layered VTI media withtrapezoidal block model construction and qP/pSV kinematicreflection ray-tracing.Oil Geophysical Prospecting.(inChinese),2009,44(6):662-670.
[81]赵爱华,张中杰,王光杰,等.非均匀介质中地震波走时与射线路径快速计算技术.地震学报,2000,22(2):151-157.Zhao A H,Zhang Z J,Wang G J,et al.A new scheme for fastcalculation of seismic traveltines and ray paths ininhomogeneous media.Acta Seismologica Sinica.(inChinese),2000,22(2):151-157.
[82]赵爱华,张中杰.三维复杂介质中转换波走时快速计算.地球物理学报,2004,47(4):702-707.Zhao A H,Zhang Z J.Fast calculation of converted wavetravel time in 3-d complex media.Chinese J.Geophys.(inChinese),2004,47(4):702-707.
[83]赵爱华,丁志峰,孙为国,等.复杂介质地震定位中震源轨迹的计算.地球物理学报,2008,51(4):1188-1195.Zhao A H,Ding Z F,Sun W G,et al.Calculation of focal locifor earthquake location in complex media.Chinese J.Geophys.(in Chinese),2008,51(4):1188-1195.
[84]张建中,陈世军,余大祥.最短路径射线追踪方法及其改进.地球物理学进展,2003,18(1):146-150.Zhang J Z,Chen S J,Yu D X.Improvement of shortest pathray tracing method.Progress in Geophysics.(in Chinese),2003,18(1):146-150.
[85]张建中,陈世军,徐初伟.动态网络最短路径射线追踪.地球物理学报,2004,47(5):899-904.Zhang J Z,Chen S J,Xu C W.A method of shortest pathraytracing with dynamic networks.Chinese J.Geophys.(inChinese),2004,47(5):899-904.
[86]张美根,程冰洁,李小凡,等.一种最短路径射线追踪的快速算法.地球物理学报,2006,49(5):1467-1474.Zhang M G,Cheng B J,Li X F,et al.A fast algorithm ofshortest path ray tracing.Chinese J.Geophys.(in Chinese),2006,49(5):1467-1474.
[87]张美根,贾豫葛,王妙月,等.界面二次源波前扩展法全局最小走时射线追踪技术.地球物理学报,2006,49(4):1169-1175.Zhang M G,Jia Y G,Wang M Y,et al.A global minimumtraveltime raytracing algorithm of wavefront expanding withinterface points as secondary sources.Chinese J.Geophys.(inChinese),2006,49(4):1169-1175.
[88]王童奎,张美根,李小凡,等.PS转换波界面二次源法射线追踪.地球物理学进展,2007,22(1):165-170.Wang T K,Zhang M G,Li X F,et al.Interface points assecondary sources method raytracing PS converted waves.Progress in Geophysics(in Chinese),2007,22(1):165-170.
[89]鲁彬,周立发,孔省吾,等.迭代优化的网络最短路径射线追踪方法研究.地球物理学进展,2009,24(3):1420-1425.Lu B,Zhou L F,Kong X W,et al.A method of shortest pathraytracing by iterative optimization.Progress in Geophys.(inChinese),2009,24(3):1420-1425.
[90]鲁彬,周立发,王兴春,等.迭代法在三维网络模型最短路径射线追踪中的应用.地球物理学进展,2010,25(2):533-537.Lu B,Zhou L F,Wang X C,et al.A method of shortest pathraytracing using iterative optimization in a 3-D grid model.Progress in Geophys.(in Chinese),2010,25(2):533-537.
[91]黄国娇,白超英.最短路径算法下二维复杂层状介质中地震多波走时的联合反演成像.地球物理学报,2010,53(12):2972-2981.Huang G J,Bai C Y.Simultaneous inversion with multipletraveltimes within 2-D complex layered media.Chinese J.Geophys.(in Chinese),2010,53(12):2972-2981.
[92]Bai C Y,Zhao R,Greenhalgh S.Rapid 3-D earthquake locationusing a hybrid global-local inversion approach.Pure ApplGeophys,2010,167:1377-1387.
[93]唐巍,李磊.多层垂直对称轴横向各向同性介质精确走时计算.地震学报,2008,30(4):367-376.Tang W,Li L.Exact traveltime computation in multi-layeredtransversely isotropic media with vertical symmetry axis.ActaSeismologica Sinica(in Chinese),2008,30(4):367-376.
[94]Vinje V,Astebl K,Iversen E,Gjystdal H.3-D ray modelling bywavefront construction in open models.GeophysicalProspecting,1999,64:1912-1919.
[95]赵连锋,朱介寿,曹俊兴,等.有序波前重建法的射线追踪.地球物理学报,2003,46(3):415-420.Zhao L F,Zhu J S,Cao J X,et al.Ray Tracing using ordinalwavefront reconstruction method.Chinese J.Geophys.(inChinese),2003,46(3):415-420.
[96]张钋,杨长春,李幼铭.三维多值走时地震波场重建及格林函数计算.地球物理学报,2000,43(2):241-250.Zhang P,Yang C C,Li Youming.3-D multi-valued seismicwavefield reconstruction and Green’s function computation.Chinese J.Geophys.(in Chinese),2000,43(2):241-250.
[97]韩复兴,孙建国,杨昊.基于C++语言实现波前构建射线追踪.石油地球物理勘探,2007,42(4):474-481.Han F X,Sun J G,Yang H.Ray tracing by implementing C++language-based wavefront construction approach.Oil GeophysicalProspecting.(in Chinese),2007,42(4):474-481.
[98]李波涛,杨长春,陈雨红,等.基于波前面三角形网格剖分的波前重建法三维射线追踪.地球物理学进展,2009,24(2):507-512.Li B T,Yang C C,Chen Y H,et al.3Dwavefront constructionmethod ray tracing based on triangular grids layout onwavefront.Progress in Geophys.(in Chinese),2009,24(2):507-512.
[99]Benamou J D.Direct computation of multivalued phase spacesolutions for Hamilton-Jacobi equations.Comm Pure ApplMath,1999,52:1443-1475.
[100]Hauser J,Sambridge M,Rawlinson N.Phase space methodsfor multi-arrival wavefronts.ExplorationGeophysics,2006,37:331-339.
[101]Osher S,Sethian J.Fronts propagating with curvature dependentspeed:Algorithms based on hamilton-jacobi formulations.JComp Phys,1988,79:12-49.
[102]Osher S,Cheng L T,Kang M,Shim H,Tsai Y H.Geometricoptics in a phase-space-based level set and Eulerianframework.J Comp Phys,2002,179:622-648.
[103]唐小平,白超英.分区多步最短路径极值法多值多次反射波追踪.地球物理学报,2011,已投稿.Tang X P,Bai C Y.Multivalued and multiple reflectedraytracing with extreme value based on the multistagemodified shortest-path method.Progress in Geophys.(inChinese),2011,in press.
[104]Leidenfrost A,Ettrich N,Gajewski D,et al.Comparison ofsix different methods for calculating traveltimes.GeophysProspect,1999,47:269-297.
[105]Bai C Y,Greenhalgh S.3-D local earthquake hypocenterdetermination with an‘irregular’shortest path method.Bull Seism Soc Am,2006,96:2257-2268.
[106]Bai C Y,Greenhalgh S.3-D multi-step travel time tomography:Imaging the local,deep velocity structure of Rabaul volcano,Papua New Guinea.Phys Earth Planet Inter,2005a,151:259-275.
[107]Bai C Y,Greenhalgh S.3-D non-linear travel time tomography:Imaging high contrast velocity anomalies.Pure ApplGeophys,2005b,162:2029-2049.
[108]Bai C Y,Peng J B,Grenhalgh S.3-D P-wave velocity structure ofthe crust beneath the Loess Plateau and surroundingregions of China.Tectonophysics,2008,460:278-287.
[109]白超英,黄国娇,李忠生.分区多步最短路径算法下三维复杂层状介质中地震多波走时联合反演成像.地球物理学报,2011,54(1):182-192.Bai C Y,Huang G J,Li Z S.Simultaneous inversion withmultiple-phase traveltimes within 3-D complex layeredmedia.Chinese J.Geophys.(in Chinese),2011,54(1):182-192.
[110]Moser T J,Van Eck T,Nolet G.Hypocenter Determinationin strongly heterogeneous earth models using the shortestpath method.J Geophys Res,1992,97:6563-6572.
[111]Moser T J.Migration using the shortest-path method.Geophysics,1994,59:1110-1120.
[112]Tang X P,Bai C Y.Multiple ray tracing within 3Dlayeredmedia with the shortest path method.Chinese J Geophys,2009,52(5):1130-1138.
[113]El-Mageed M A.3Dfirst arrival traveltime and amplitudesvia Eikonal and Transport finite difference solvers[D].Houston:Rice University,1996.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心