三维层状地质结构下整体迭代射线追踪法
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摘要
作者在文中对三维任意界面情况下的两点间射线追踪问题进行了研究 ,从 Fermat原理出发 ,对射线路径上的旅行时 ,采用一阶 Taylor不完全展开等办法 ,推出了三维情况下计算射线路径的整体迭代算法。并通过模型计算证明了本方法的稳健性以及计算的高精确度和高效率。为三维结构下地震偏移和层析成像提供了一种可行的射线追踪方法。
In this paper, two point ray tracing is studied for three-dimensional arbitrary interface. from Fermat's principle, traveltime is expanded in the initial ray path according to one order Taylor's incompletion expansion. Then, the algorithm of total iterative ray tracing in three dimension is derived. Numerical tests based on this method in three dimensional media show that this algorithm is fast, well-posed and high efficient. It offers a new kind of efficient ray tracing method for three dimensional seismic migration and tomography.
In this paper, two point ray tracing is studied for three-dimensional arbitrary interface. from Fermat's principle, traveltime is expanded in the initial ray path according to one order Taylor's incompletion expansion. Then, the algorithm of total iterative ray tracing in three dimension is derived. Numerical tests based on this method in three dimensional media show that this algorithm is fast, well-posed and high efficient. It offers a new kind of efficient ray tracing method for three dimensional seismic migration and tomography.
引文
[1] Aki K,Christoffersson A,Husebye E S.Determination of the three-dim ensional seismic structure of the lithosphere[J] .Geophys,1977,82 :2 77.
[2 ] Cassell B R.A method for calculating synthetic seismograms in laterally varying media[J] .Geophys,Astron,1982 ,6 9:339.
[3] Cerveny V,Molotkov I A,Psencik I. Ray method in seismology[M] . Charles Univ,Press,1977.
[4] Chander R. On tracing seism ic rays with specified end points in layersof constant velocity and plane interface[J] . Geophys,1997,2 5 :12 0 .
[5 ] Chapman C H.A new method for computing synthetic seismograms[J] .Geophys,1978,5 4,481.
[6 ] Farra V.Amplitude computation in heterogeneous m edia by ray pertubation theory:a finite element method approach[J] .Geophys.J.Int.,1990 ,10 3:341.
[7] Farra V. Bending method revisited:a Hamiltonian approach[J] . Geophys,1992 ,10 9:138.
[8] Farra V. Ray tracing in complex m edia[J] . Geophys,1993,30 :5 5 .
[9 ] Hanyga A. U nmerical methods for tracing rays and wavefronts[A] .In:D. J. Doornbos(Editor) ,Seismological Algorithm:Computational methods and com puter programs[M] .L ondon,Academic Press,1988.
[10 ] 高尔根 ,徐果明 ,赵炎 .一种任意界面的逐段迭代射线追踪方法 [J] .石油地球物理勘探 ,1998,33(1) :5 4.
[11] 高尔根 ,徐果明 .二维速度随机分布逐步迭代射线追踪方法 [J] .地球物理学报 ,1996 ,39(Suppl.) :30 2 .
[12 ] Kakal F C,Keller JB. Elastic wave propagation in hom ogeneous and inhomogeneous media[J] . Accoust,195 9,31:6 94.
[13] Langan R T,Lerche I,Cutler R T.Tracing of rays through heterogeneous media:an accurate and efficient procedure[J] .Geophysics,1985 ,5 0 :14 5 6 .
[14 ] 刘学才 ,周熙襄 .二维非均匀介质移动网格的射线追踪算法 [J] .物探化探计算技术 ,1994,16 (1) :34.
[15 ] Pereyra V,L ee W H K,Keller H B. Solving two-point seismic ray-tracing problem s in a heterogeneous medium,Part :A generaladaptative finite difference method[J] . Bull. Seis. Sec. Am .,1980 ,70 :79.
[16 ] Podvin P,L ecomte I.Finite difference computation of traveltim e in very contrasted velocity models:A massively parallel approach and itsassociated tools[J] .Geophys,1991,10 5 :2 71.
[17] Sam bridge M S,Kennett B L N. Boundary value ray tracing in heterogeneous medium:a simple and versatile algorithm[J] . Geophys,1990 ,10 1:15 7.
[18] Um J,Thurber C H. A fast algorithm for two-point seismic ray tracing[J] . Bull. Seis. Sec. Am .,1987,77:972 .
[19] Vidale JE.Finite different calculation of traveltime in three dim ensions[J] .Geophysics,1990 ,5 5 :5 2 1.
[2 0 ] Vidale JE.Finite difference calculation of traveltime[J] .Bull.Seis.Sec.Am.,1988,78:2 0 6 2 .
[2 1] 张文生 ,何樵登 .有限差分法精确计算地震走时 [J] .物探化探计算技术 ,1996 ,18(4) :331.
[2 ] Cassell B R.A method for calculating synthetic seismograms in laterally varying media[J] .Geophys,Astron,1982 ,6 9:339.
[3] Cerveny V,Molotkov I A,Psencik I. Ray method in seismology[M] . Charles Univ,Press,1977.
[4] Chander R. On tracing seism ic rays with specified end points in layersof constant velocity and plane interface[J] . Geophys,1997,2 5 :12 0 .
[5 ] Chapman C H.A new method for computing synthetic seismograms[J] .Geophys,1978,5 4,481.
[6 ] Farra V.Amplitude computation in heterogeneous m edia by ray pertubation theory:a finite element method approach[J] .Geophys.J.Int.,1990 ,10 3:341.
[7] Farra V. Bending method revisited:a Hamiltonian approach[J] . Geophys,1992 ,10 9:138.
[8] Farra V. Ray tracing in complex m edia[J] . Geophys,1993,30 :5 5 .
[9 ] Hanyga A. U nmerical methods for tracing rays and wavefronts[A] .In:D. J. Doornbos(Editor) ,Seismological Algorithm:Computational methods and com puter programs[M] .L ondon,Academic Press,1988.
[10 ] 高尔根 ,徐果明 ,赵炎 .一种任意界面的逐段迭代射线追踪方法 [J] .石油地球物理勘探 ,1998,33(1) :5 4.
[11] 高尔根 ,徐果明 .二维速度随机分布逐步迭代射线追踪方法 [J] .地球物理学报 ,1996 ,39(Suppl.) :30 2 .
[12 ] Kakal F C,Keller JB. Elastic wave propagation in hom ogeneous and inhomogeneous media[J] . Accoust,195 9,31:6 94.
[13] Langan R T,Lerche I,Cutler R T.Tracing of rays through heterogeneous media:an accurate and efficient procedure[J] .Geophysics,1985 ,5 0 :14 5 6 .
[14 ] 刘学才 ,周熙襄 .二维非均匀介质移动网格的射线追踪算法 [J] .物探化探计算技术 ,1994,16 (1) :34.
[15 ] Pereyra V,L ee W H K,Keller H B. Solving two-point seismic ray-tracing problem s in a heterogeneous medium,Part :A generaladaptative finite difference method[J] . Bull. Seis. Sec. Am .,1980 ,70 :79.
[16 ] Podvin P,L ecomte I.Finite difference computation of traveltim e in very contrasted velocity models:A massively parallel approach and itsassociated tools[J] .Geophys,1991,10 5 :2 71.
[17] Sam bridge M S,Kennett B L N. Boundary value ray tracing in heterogeneous medium:a simple and versatile algorithm[J] . Geophys,1990 ,10 1:15 7.
[18] Um J,Thurber C H. A fast algorithm for two-point seismic ray tracing[J] . Bull. Seis. Sec. Am .,1987,77:972 .
[19] Vidale JE.Finite different calculation of traveltime in three dim ensions[J] .Geophysics,1990 ,5 5 :5 2 1.
[2 0 ] Vidale JE.Finite difference calculation of traveltime[J] .Bull.Seis.Sec.Am.,1988,78:2 0 6 2 .
[2 1] 张文生 ,何樵登 .有限差分法精确计算地震走时 [J] .物探化探计算技术 ,1996 ,18(4) :331.
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