一种基于非规则网格的地震波射线追踪方法
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摘要
地震波走时计算对地震资料层析速度建模、偏移成像及地震定位等研究都具有非常重要的意义。有限差分法计算地震波走时具有计算效率高、易于实现、准确性高的优点,因而得到广泛应用。针对规则网格有限差分方法处理尖锐速度界面时存在不足的问题,提出了一种非规则网格的有限差分走时计算方法,即在Vidale差分算式的基础上推导出不规则网格差分算式,使其适用于不同的网格剖分方式。对均匀介质模型、复杂模型和Marmousi模型试算的结果表明,改进的方法能较好地解决尖锐速度界面和首波走时计算问题,且对复杂速度模型具有较好的适应性。
The calculation of seismic wave traveltime is very important for the study of velocity modeling by seismic data tomography,migration imaging and seismic positioning.Finite difference method is widely used to calculate seismic traveltime due to its advantages of high computational efficiency,easy to achieve and high accuracy.Finite difference method based on regular grids is no good at treating sharp velocity interface and in view of this problem,a finite difference method based on irregular grids is proposed to calculate traveltime.The results show that the improved method can solve the problem of treating sharp velocity interface and calculating head wave traveltime,with a better adaptability for complex velocity models.
The calculation of seismic wave traveltime is very important for the study of velocity modeling by seismic data tomography,migration imaging and seismic positioning.Finite difference method is widely used to calculate seismic traveltime due to its advantages of high computational efficiency,easy to achieve and high accuracy.Finite difference method based on regular grids is no good at treating sharp velocity interface and in view of this problem,a finite difference method based on irregular grids is proposed to calculate traveltime.The results show that the improved method can solve the problem of treating sharp velocity interface and calculating head wave traveltime,with a better adaptability for complex velocity models.
引文
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[20]张慧,李振春.基于双变网格算法的地震波正演模拟[J].地球物理学报,2011,54(1):77-86Zhang H,Li Z C.Seismic wave simulation method based on dual-variable grid[J].Chinese Journal of Geophysics(in Chinese),2011,54(1):77-86
[21]褚春雷,王修田.非规则三角网格有限差分法地震正演模拟[J].中国海洋大学学报,2005,35(1):43-48Chu C L,Wang X T.Seismic modeling with a finitedifference method on irregular triangular grids[J].Periodical of Ocean University of China,2005,35(1):43-48
[22]尧德中.六角形网格波动方程数值模拟德傅氏变换算法[J].计算物理,1994,11(1):101-106Yao D Z.Wave equation numerical modeling of hexagonal sample by Fourier method[J].Chinese Journal of Computational Physics,1994,11(1):101-106
[23]Chu W H.Development of a general finite difference approximation for a general domain[J].Journal of Computational Physics,1971,8(3):392-408
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[25]Hole J A,Zelt B C.3-d finite difference reflection travel times[J].Geophysical Journal International,1995,121(2):427-434
[26]Brackbill J U,Saltzman J S.Adaptive zoning for singular problems in two dimensions[J].Journal of Computational Physics.1982,46(3):342-368
[27]于明.二维自适应结构网格的变分生成方法[J].计算物理,2004,21(1):27-34Yu M.Generation of 2-D adaptive structured grids by variational methods[J].Chinese Journal of Computational Physics,2004,21(1):27-34
[2]Langan R T,Lerche I,Cutler R T.Tracing of rays through heterogeneous media:An accurate and efficient procedure[J].Geophysics,1985,50(9):1456-1465
[3]Julian B R,Gubbins D.Three-dimensional seismic ray tracing[J].Journal of Geophysics,1977,43(1):95-114
[4]Um J,Thurber C.A fast algorithm for two-points seismic ray tracing[J].Bulletin of the Seismological Society of America.1987,77(3):972-986
[5]Pereyra V.Two-point ray tracing in general 3-D media[J].Geophysical Prospecting,1992,40(3):267-287
[6]Thurber C H,Ellsworth W L.Rapid solution of ray tracing problems in heterogeneous media[J].Bulletin of the Seismological Society of America,1980,70(4):1137-1148
[7]Lees J M,Shalev E.On the stability of P-wave tomography at Loma Prieta:a comparision of parameterizations,linear and nonlinear inversion[J].Bulletin of the Seismological Society of America,1992,82(4):1821-1839
[8]Vidale J E.Finite difference calculation of travel times[J].Bulletin of the Seismological Society of America,1988,78(6):2062-2076
[9]Trier van J,Symes W W.Upwind finite-difference calculation of traveltimes[J].Geophycics,1991,56(6):812-821
[10]Podvin P,Lecomte I.Finite difference computation of traveltimes in very contrasted velocity models:a massively parallel approach and its associated tools[J].Geophysics,1991,105:271-284
[11]Schneider W A,Ranzinger K A,Balch A H,et al.A dynamic programming approach to first arrival traveltimes computation in media with arbitarily distributed velocities[J].Geophysics,1992,57(1):39-50
[12]Qin F H,Luo Y,Olsen K B,et al.Finite-difference solution of the eikonal equation along expanding wavefronts[J].Geophysics,1992,57(3):478-487
[13]Moser T.Shortest path calculation of seismicrays[J].Geophysics,1991,56(1):59-67
[14]Fornberg B.The pseudospectral method:comparisons with finite differences for the elastic wave equation[J].Geophysics,1987,52(4):483-501
[15]Nielsen P,If F,Berg P,et al.Using the pseudospectral technique on curved grids for 2Dacoustic forward modelling[J].Geophysical Prospecting,1994,42(4):321-341
[16]Tessmer E,Kosloff D,Behle A.Elastic wave propagation simulation in the presence of surface topography[J].Geophysical Journal International,1992,108(2):621-632
[17]Jastram C,Behle A.Acoustic modeling on a vertically varying grid[J].Geophysical Prospecting,1992,40(2):157-169
[18]Jastram C,Tessmer E.Elastic modeling on a grid with vertically varying spacing[J].Geophysical Prospecting,1994,42(4):357-370
[19]Oprsal I,Zahradnik J.Elastic finite-difference method for irregular grids[J].Geophysics,1999,64(1):240-250
[20]张慧,李振春.基于双变网格算法的地震波正演模拟[J].地球物理学报,2011,54(1):77-86Zhang H,Li Z C.Seismic wave simulation method based on dual-variable grid[J].Chinese Journal of Geophysics(in Chinese),2011,54(1):77-86
[21]褚春雷,王修田.非规则三角网格有限差分法地震正演模拟[J].中国海洋大学学报,2005,35(1):43-48Chu C L,Wang X T.Seismic modeling with a finitedifference method on irregular triangular grids[J].Periodical of Ocean University of China,2005,35(1):43-48
[22]尧德中.六角形网格波动方程数值模拟德傅氏变换算法[J].计算物理,1994,11(1):101-106Yao D Z.Wave equation numerical modeling of hexagonal sample by Fourier method[J].Chinese Journal of Computational Physics,1994,11(1):101-106
[23]Chu W H.Development of a general finite difference approximation for a general domain[J].Journal of Computational Physics,1971,8(3):392-408
[24]Thomas P D,Middlecoff J F.Direct control of the grid point distribution in meshes generated by elliptic equations[J].AIAA Journal,1980,18(6):652-660
[25]Hole J A,Zelt B C.3-d finite difference reflection travel times[J].Geophysical Journal International,1995,121(2):427-434
[26]Brackbill J U,Saltzman J S.Adaptive zoning for singular problems in two dimensions[J].Journal of Computational Physics.1982,46(3):342-368
[27]于明.二维自适应结构网格的变分生成方法[J].计算物理,2004,21(1):27-34Yu M.Generation of 2-D adaptive structured grids by variational methods[J].Chinese Journal of Computational Physics,2004,21(1):27-34
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