基于双变网格算法的地震波正演模拟
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摘要
为了适应对局部复杂模型的精细模拟,本文实现了可变网格算法,对速度场进行局部加密,从空间上有效地提高模拟精度同时又降低计算机内存需求.但是在数值模拟中,由于稳定性条件的限制,当空间网格变化时,时间稳定性仍然必须满足最短波长的原则,从而增加了时间计算量.为了配合空间可变网格技术,本文对时间层计算也进行了局部变化,提出了双变网格有限差分算法.双变算法从根本上降低了整体的计算量和计算内存.本文还通过一系列的模型试算验证了双变网格算法的稳定性和正确性,并对双变算法进行了误差分析,证明了双变网格算法的精确性.
In order to adapt to fine simulation of locally complex models,we developed a variable grid method for partial densification in space.It can effectively raise the simulation accuracy while reducing computer memory requirements.However,in numerical simulation process because of stability condition limitation,when the spatial grid changes,the time stability must still meet the principle of the shortest wavelength,which would increase calculation time.So to cope with variable space grid,we made calculation time step change in local time scale,and proposed a dualvariable -grid finite difference method(variable space and variable time).Dual-variable algorithm can fundamentally reduce the overall amount of computation and computer memory.The paper also tested several models and made error analysis to show the stability and accuracy of dualvariable algorithm.
In order to adapt to fine simulation of locally complex models,we developed a variable grid method for partial densification in space.It can effectively raise the simulation accuracy while reducing computer memory requirements.However,in numerical simulation process because of stability condition limitation,when the spatial grid changes,the time stability must still meet the principle of the shortest wavelength,which would increase calculation time.So to cope with variable space grid,we made calculation time step change in local time scale,and proposed a dualvariable -grid finite difference method(variable space and variable time).Dual-variable algorithm can fundamentally reduce the overall amount of computation and computer memory.The paper also tested several models and made error analysis to show the stability and accuracy of dualvariable algorithm.
引文
[1] 杜世通.地震波动力学.山东东营:石油大学出版社,1999． 238 Du S T.Seismic Wave Dynamics (in Chinese).Shandong Dongying:China University of Petroleum Press,1999． 238
[2] Jastram C,Behle A.Acoustic modeling on a vertically varying grid.Geophys.Prosp.,1992 ,40:157～169
[3] Jastram C,Tessmer E.Elastic modeling on a grid of vertically varying spacing.Geophys.Prosp.,1994,42 :357～370
[4] Ivo Oprsal,Jiri Zahradnik.Elastic finite-difference method for irregular grids.Geophysics,1999 ,64 :240～250
[5] Pitarka A.3D elastic finite-difference modeling of seismic motion using staggered grids with nonuniform spacing.Bull.Seism.Soc.Am.,1999,89:54～68
[6] Wang Y,Xu J,Schuster G T.Viscoelastic wave simulation in basins by a variable-grid finite-difference method.Bull.Seism.Soc.Am.,2001,91 :1741～1749
[7] Falk J,Tessmer E,Gajewski D.Efficient finite-difference modelling of seismic waves using locally adjustable time steps.Geophys.Prosp.,1998,46 :603～616
[8] Tessmer E.Seismic finite-difference modeling with spatially varying time steps.Geophysics,2000,65 :1290～1293
[9] Hayashi K,Burns D R,Toksoz M N.Discontinuous-grid finite-difference seismic modeling including surface topography.Bull.Seism.Soc.Am.,2001,91:1750～1764
[10] Virieux J.P-SV wave propagation in heterogeneous media;velocity-stress finite-difference method.Geophysics,1986,51:88～901
[11] Graves R W.Simulating seismic wave propagation in 3D elastic media using staggered-grid finite-differences.Bull.Seism.Soc.Am.,1996b,86:1091～1107
[12] Igel H,Riollet B,Mora P.Accuracy of staggered 3-D finite-difference grids for anisotropic wave propagation.SEG Expanded Abstracts,1992． 1244～1246
[13] 董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分解法.地球物理学报,2000,43(3) :411～419 Dong L G,Ma Z T,Cao J Z.A staggered-grid high-order difference method of one-order elastic wave equation.Chinese J.Geophys.(in Chinese) ,2000,43(3) :411～419
[14] 李振春,张慧,张华.一阶弹性波方程的变网格高阶有限 差分数值模拟.石油地球物理勘探,2008,43(6) :711～716 Li Z C,Zhang H,Zhang H.Variable-grid high-order finite-difference numeric simulation of first-order elastic wave equation.Oil Geophysical Prospecting (in Chinese),2008,43(6) :711～716
[15] Sergio Adriano Moura Oliveira.A fourth-order finite-difference method for the acoustic wave equation on irregular grids.Geophysics,2003,68 :672～676
[16] 董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分解法稳定性分析.地球物理学报,2000,43(6) :856～864 Dong L G,Ma Z T,Cao J Z.A study of stability of the staggered-grid high-order difference method of one-order elastic wave equation.Chinese J.Geophys.(in Chinese),2000,43(6) :856～864
[2] Jastram C,Behle A.Acoustic modeling on a vertically varying grid.Geophys.Prosp.,1992 ,40:157～169
[3] Jastram C,Tessmer E.Elastic modeling on a grid of vertically varying spacing.Geophys.Prosp.,1994,42 :357～370
[4] Ivo Oprsal,Jiri Zahradnik.Elastic finite-difference method for irregular grids.Geophysics,1999 ,64 :240～250
[5] Pitarka A.3D elastic finite-difference modeling of seismic motion using staggered grids with nonuniform spacing.Bull.Seism.Soc.Am.,1999,89:54～68
[6] Wang Y,Xu J,Schuster G T.Viscoelastic wave simulation in basins by a variable-grid finite-difference method.Bull.Seism.Soc.Am.,2001,91 :1741～1749
[7] Falk J,Tessmer E,Gajewski D.Efficient finite-difference modelling of seismic waves using locally adjustable time steps.Geophys.Prosp.,1998,46 :603～616
[8] Tessmer E.Seismic finite-difference modeling with spatially varying time steps.Geophysics,2000,65 :1290～1293
[9] Hayashi K,Burns D R,Toksoz M N.Discontinuous-grid finite-difference seismic modeling including surface topography.Bull.Seism.Soc.Am.,2001,91:1750～1764
[10] Virieux J.P-SV wave propagation in heterogeneous media;velocity-stress finite-difference method.Geophysics,1986,51:88～901
[11] Graves R W.Simulating seismic wave propagation in 3D elastic media using staggered-grid finite-differences.Bull.Seism.Soc.Am.,1996b,86:1091～1107
[12] Igel H,Riollet B,Mora P.Accuracy of staggered 3-D finite-difference grids for anisotropic wave propagation.SEG Expanded Abstracts,1992． 1244～1246
[13] 董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分解法.地球物理学报,2000,43(3) :411～419 Dong L G,Ma Z T,Cao J Z.A staggered-grid high-order difference method of one-order elastic wave equation.Chinese J.Geophys.(in Chinese) ,2000,43(3) :411～419
[14] 李振春,张慧,张华.一阶弹性波方程的变网格高阶有限 差分数值模拟.石油地球物理勘探,2008,43(6) :711～716 Li Z C,Zhang H,Zhang H.Variable-grid high-order finite-difference numeric simulation of first-order elastic wave equation.Oil Geophysical Prospecting (in Chinese),2008,43(6) :711～716
[15] Sergio Adriano Moura Oliveira.A fourth-order finite-difference method for the acoustic wave equation on irregular grids.Geophysics,2003,68 :672～676
[16] 董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分解法稳定性分析.地球物理学报,2000,43(6) :856～864 Dong L G,Ma Z T,Cao J Z.A study of stability of the staggered-grid high-order difference method of one-order elastic wave equation.Chinese J.Geophys.(in Chinese),2000,43(6) :856～864
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