优化近似解析离散化方法的二维弹性波波场分离模拟
|
摘要
近似解析离散化方法是近年来出现的一种数值模拟方法,其特点是在高阶有限差分中引入了位移梯度,与四阶Lax-Wendroff修正格式数值模拟方法相比,该方法能够在大网格条件下有效地压制频散、提高计算效率和精度。本文首次将优化的近似解析离散化方法应用于弹性波场纵横波分离模拟,建立了波场分离的差分格式。通过模型试算分离出来的纵横波特征更加清晰,说明了该方法的有效性和实用性,对于认识地震波在复杂介质中的传播规律有着重要的意义。
The optimal nearly-analytic discretization(ONAD),a newly developed numerical simulation,is characterized by the use of the displacement gradient in the high-order finite difference.Comparing with the Lax-Wendroff numerical simulation,the ONAD method can effectively restrain the dispersion in a large grid,thus improve the computational efficiency and accuracy.In this paper,we apply the ONAD method to an elastic wave field separation simulation,and set up difference formats of the wave field separation simulation.Based on our model tests,characteristics of P-and S-waves are clearly extracted by the proposed method,which proves its validity and applicability in the analysis of seismic wave propagation in complex media.
The optimal nearly-analytic discretization(ONAD),a newly developed numerical simulation,is characterized by the use of the displacement gradient in the high-order finite difference.Comparing with the Lax-Wendroff numerical simulation,the ONAD method can effectively restrain the dispersion in a large grid,thus improve the computational efficiency and accuracy.In this paper,we apply the ONAD method to an elastic wave field separation simulation,and set up difference formats of the wave field separation simulation.Based on our model tests,characteristics of P-and S-waves are clearly extracted by the proposed method,which proves its validity and applicability in the analysis of seismic wave propagation in complex media.
引文
[1]Cerveny V.Seismic rays and ray intensities in inhomogeneous anisotropic media.Geophysical Journal International,1972,29(1):1-33.
[2]Kosloff D D,Baysal E.Forward modeling by a Fourier method.Geophysics,1982,47(10):1402-1412.
[3]Reshef M,Kosloff D,Edwards M et al.Three dimensional elastic modeling by the Fourier method.Geophysics,1988,53(9):1184-1193.
[4]Drake L A.Rayleigh waves at a continental boundary by the finite element method.Bulletin of the Seismological Society of America,1972,62(5):1259-1268.
[5]Bouchon M,Coutant O.Calculation of synthetic seismograms in a laterally varying medium by the boundary element-discrete wavenumber method.Bulletin of the Seismological Society of America,1994,84(6):1869-1881.
[6]Komatissch D,Barnes C,Tromp J.Simulation of anisotropic wave propagation based upon a spectral element method.Geophysics,2000,65(4):1251-1260.
[7]Alterman Z,Karal F C.Propagation of seismic wave in layered media by finite difference methods.Bulletin of the Seismological Society of America,1968,58(1):367-398.
[8]Kelly K R,Ward R W,Treitel S et al.Synthetic seismograms:a finite-difference approach.Geophysics,1976,41(1):2-27.
[9]Virieux J.P-SV wave propagation in heterogeneous media:Velocity-stress finite-difference method.Geophysics,1986,51(4):889-901.
[10]Graves R W.Simulation seismic wave propagation in3D elastic media using staggered-grid finite differences.Bulletin of the Seismological Society of America,1996,86(4):1091-1106.
[11]董良国,马在田,曹景忠等.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 Liangguo,Ma Zaitian,Cao Jingzhong et al.The staggered-grid high-order difference method of oneorder elastic equation.Chinese Journal of Geophysics,2000,43(3):411-419.
[12]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研究.地球物理学报,2000,43(6):856-864.Dong Liangguo,Ma Zaitian,Cao Jingzhong.A study on stability of the staggered-grid high-order difference method of first-order elastic wave equation.Chinese Journal of Geophysics,2000,43(6):856-864.
[13]董良国.弹性波数值模拟中的吸收边界条件.石油地球物理勘探,1999,34(1):46-56.Dong Liangguo.Absorptive boundary condition in elastic-wave numerical modeling.OGP,1999,34(1):46-56.
[14]王书强,杨顶辉,杨宽德.弹性波方程的紧致差分方法.清华大学学报(自然科学版),2002,42(8):1128-1131.Wang Shuqiang,Yang Dinghui,Yang Kuande.Compact finite difference scheme for elastic equations.Journal of Tsinghua University(Science and Technique),2002,42(8):1128-1131.
[15]Saenger E H,Gold N,Shapiro S A.Modeling the propagation of elastic waves using a modified finitedifference grid.Wave Motion,2000,31(1):77-92.
[16]Saenger E H,Bohlen T.Finite-difference modeling of viscoelastic and anisotropic wave propagation using the rotated staggered grid.Geophysics,2004,69(2):583-591
[17]Kondoh Y,Hosaka Y,Ishii K.Kerrel optimum nearly analytical discrimination algorithm applied to parabolic and hyperbolic equations.Computers&Mathematics with Applications,1994,27(3):59-90.
[18]杨顶辉,滕吉文,张中杰.三分量地震波场的近似解析离散模拟技术.地球物理学报,1996,39(增刊):283-291.Yang Dinghui,Teng Jiwen,Zhang Zhongjie.A nearly-analytical discretization modelling technique of 3-component seismic wave-fields.Acta Geophysica Sinica.1996,39(S):283-291.
[19]Yang D H,Teng J W,Zhang Z J et al.A nearly-analytic discrete method for acoustic and elastic wave equation.Bulletin of the Seismological Society of A-merica,2003,93(2):882-890
[20]Yang D H,Lu M,Wu R S et al.An optimal nearlyanalytic discrete method for 2Dacoustic and elastic wave equations.Bulletin of the Seismological Society of America,2004,94(5):1982-1992.
[21]Yang D H,Song G J,Lu M.Optimally accurate nearly analytic discrete scheme for wave-field simulation in 3Danisotropic media.Bulletin of the Seismological Society of America,2007,97(5):1557-1569.
[22]Yang D H,Song G J,Chen S et al.An improved nearly analytical discrete method:an efficient tool to simulate the seismic response of 2-D porous structures.Journal of Geophysics and Engineering,2007,4(1):40-52.
[23]卢明.改进的近似解析离散化方法及弹性波波场模拟[学位论文].北京:清华大学数学科学系,2004.
[24]宋国杰.三维弹性波方程的改进近似解析离散化方法及波场模拟[学位论文].北京:清华大学数学科学系,2008.
[25]Tong P,Yang D H,Hua B L.High accuracy wave simulation-revised derivation,numerical analysis and testing of a nearly analytic integration discrete method for solving acoustic equation.International Journal of Solids&Structures,2011,48(1):56-70.
[26]陈伟明,聂勋碧.慢度-频率域纵横波分离.石油地球物理勘探,1994,29(3):348-356.Chen Weiming,Nie Xunbi.Separating compressional wave from shear wave in slowness-frequency domain.OGP,1994,29(3):348-356.
[27]马德堂,朱光明.弹性波波场P波和S波分解的数值模拟.石油地球物理勘探,2003,38(5):482-486.Ma Detang,Zhu Guangming.Numerical modeling of P-wave and S-wave separation in elastic wavefield.OGP,2003,38(5):482-486.
[28]李振春,张华,刘庆敏等.弹性波交错网格高阶有限差分法波场分离数值模拟.石油地球物理勘探,2007,42(5):510-515.Li Zhenchun,Zhang Hua,Liu Qingmin.Numeric simulation of elastic wavefield separation by staggering grid high-order finite-difference algorithm.OGP,2007,42(5):510-515.
[29]陈可洋,杨微,刘洪林等.二阶弹性波动方程高精度交错网格波场分离数值模拟.物探与化探,2009,33(6):700-704.Chen Keyang,Yang Wei,Liu Honglin et al.Wave field separation numerical modeling of second order elastic wave equation by high-precision staggered-grid finite difference scheme.Geophysical&Geochemical Exploration.2009,33(6):700-704.
[30]唐小平,白超英,刘宽厚.伪谱法分离波动方程弹性波模拟.石油地球物理勘探,2012,47(1):19-26.Tang Xiaoping,Bai Chaoying,Liu Kuanhou.Elastic wavefield simulation using separated equations through pseudo-spectral method.OGP,2012,47(1):19-26.
[31]Medvidova L M,Warnecke G.Lax-Wendroff type second order evolution Galerkin methods for multidimensional hyperbolic systems.East-West Journal of Numerical Mathematics,2000,8(2):127-152.
[32]赵海波,王秀明,王东等.完全匹配层吸收边界在孔隙介质弹性波模拟中的应用.地球物理学报,2007,50(2):581-591.Zhao Haibo,Wang Xiuming,Wang Dong et al.Applications of the boundary absorption using aperfectly matched layer for elastic wave simulation in poroelastic media.Chinese Journal of Geophysics,2007,50(2):581-591.
[2]Kosloff D D,Baysal E.Forward modeling by a Fourier method.Geophysics,1982,47(10):1402-1412.
[3]Reshef M,Kosloff D,Edwards M et al.Three dimensional elastic modeling by the Fourier method.Geophysics,1988,53(9):1184-1193.
[4]Drake L A.Rayleigh waves at a continental boundary by the finite element method.Bulletin of the Seismological Society of America,1972,62(5):1259-1268.
[5]Bouchon M,Coutant O.Calculation of synthetic seismograms in a laterally varying medium by the boundary element-discrete wavenumber method.Bulletin of the Seismological Society of America,1994,84(6):1869-1881.
[6]Komatissch D,Barnes C,Tromp J.Simulation of anisotropic wave propagation based upon a spectral element method.Geophysics,2000,65(4):1251-1260.
[7]Alterman Z,Karal F C.Propagation of seismic wave in layered media by finite difference methods.Bulletin of the Seismological Society of America,1968,58(1):367-398.
[8]Kelly K R,Ward R W,Treitel S et al.Synthetic seismograms:a finite-difference approach.Geophysics,1976,41(1):2-27.
[9]Virieux J.P-SV wave propagation in heterogeneous media:Velocity-stress finite-difference method.Geophysics,1986,51(4):889-901.
[10]Graves R W.Simulation seismic wave propagation in3D elastic media using staggered-grid finite differences.Bulletin of the Seismological Society of America,1996,86(4):1091-1106.
[11]董良国,马在田,曹景忠等.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 Liangguo,Ma Zaitian,Cao Jingzhong et al.The staggered-grid high-order difference method of oneorder elastic equation.Chinese Journal of Geophysics,2000,43(3):411-419.
[12]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研究.地球物理学报,2000,43(6):856-864.Dong Liangguo,Ma Zaitian,Cao Jingzhong.A study on stability of the staggered-grid high-order difference method of first-order elastic wave equation.Chinese Journal of Geophysics,2000,43(6):856-864.
[13]董良国.弹性波数值模拟中的吸收边界条件.石油地球物理勘探,1999,34(1):46-56.Dong Liangguo.Absorptive boundary condition in elastic-wave numerical modeling.OGP,1999,34(1):46-56.
[14]王书强,杨顶辉,杨宽德.弹性波方程的紧致差分方法.清华大学学报(自然科学版),2002,42(8):1128-1131.Wang Shuqiang,Yang Dinghui,Yang Kuande.Compact finite difference scheme for elastic equations.Journal of Tsinghua University(Science and Technique),2002,42(8):1128-1131.
[15]Saenger E H,Gold N,Shapiro S A.Modeling the propagation of elastic waves using a modified finitedifference grid.Wave Motion,2000,31(1):77-92.
[16]Saenger E H,Bohlen T.Finite-difference modeling of viscoelastic and anisotropic wave propagation using the rotated staggered grid.Geophysics,2004,69(2):583-591
[17]Kondoh Y,Hosaka Y,Ishii K.Kerrel optimum nearly analytical discrimination algorithm applied to parabolic and hyperbolic equations.Computers&Mathematics with Applications,1994,27(3):59-90.
[18]杨顶辉,滕吉文,张中杰.三分量地震波场的近似解析离散模拟技术.地球物理学报,1996,39(增刊):283-291.Yang Dinghui,Teng Jiwen,Zhang Zhongjie.A nearly-analytical discretization modelling technique of 3-component seismic wave-fields.Acta Geophysica Sinica.1996,39(S):283-291.
[19]Yang D H,Teng J W,Zhang Z J et al.A nearly-analytic discrete method for acoustic and elastic wave equation.Bulletin of the Seismological Society of A-merica,2003,93(2):882-890
[20]Yang D H,Lu M,Wu R S et al.An optimal nearlyanalytic discrete method for 2Dacoustic and elastic wave equations.Bulletin of the Seismological Society of America,2004,94(5):1982-1992.
[21]Yang D H,Song G J,Lu M.Optimally accurate nearly analytic discrete scheme for wave-field simulation in 3Danisotropic media.Bulletin of the Seismological Society of America,2007,97(5):1557-1569.
[22]Yang D H,Song G J,Chen S et al.An improved nearly analytical discrete method:an efficient tool to simulate the seismic response of 2-D porous structures.Journal of Geophysics and Engineering,2007,4(1):40-52.
[23]卢明.改进的近似解析离散化方法及弹性波波场模拟[学位论文].北京:清华大学数学科学系,2004.
[24]宋国杰.三维弹性波方程的改进近似解析离散化方法及波场模拟[学位论文].北京:清华大学数学科学系,2008.
[25]Tong P,Yang D H,Hua B L.High accuracy wave simulation-revised derivation,numerical analysis and testing of a nearly analytic integration discrete method for solving acoustic equation.International Journal of Solids&Structures,2011,48(1):56-70.
[26]陈伟明,聂勋碧.慢度-频率域纵横波分离.石油地球物理勘探,1994,29(3):348-356.Chen Weiming,Nie Xunbi.Separating compressional wave from shear wave in slowness-frequency domain.OGP,1994,29(3):348-356.
[27]马德堂,朱光明.弹性波波场P波和S波分解的数值模拟.石油地球物理勘探,2003,38(5):482-486.Ma Detang,Zhu Guangming.Numerical modeling of P-wave and S-wave separation in elastic wavefield.OGP,2003,38(5):482-486.
[28]李振春,张华,刘庆敏等.弹性波交错网格高阶有限差分法波场分离数值模拟.石油地球物理勘探,2007,42(5):510-515.Li Zhenchun,Zhang Hua,Liu Qingmin.Numeric simulation of elastic wavefield separation by staggering grid high-order finite-difference algorithm.OGP,2007,42(5):510-515.
[29]陈可洋,杨微,刘洪林等.二阶弹性波动方程高精度交错网格波场分离数值模拟.物探与化探,2009,33(6):700-704.Chen Keyang,Yang Wei,Liu Honglin et al.Wave field separation numerical modeling of second order elastic wave equation by high-precision staggered-grid finite difference scheme.Geophysical&Geochemical Exploration.2009,33(6):700-704.
[30]唐小平,白超英,刘宽厚.伪谱法分离波动方程弹性波模拟.石油地球物理勘探,2012,47(1):19-26.Tang Xiaoping,Bai Chaoying,Liu Kuanhou.Elastic wavefield simulation using separated equations through pseudo-spectral method.OGP,2012,47(1):19-26.
[31]Medvidova L M,Warnecke G.Lax-Wendroff type second order evolution Galerkin methods for multidimensional hyperbolic systems.East-West Journal of Numerical Mathematics,2000,8(2):127-152.
[32]赵海波,王秀明,王东等.完全匹配层吸收边界在孔隙介质弹性波模拟中的应用.地球物理学报,2007,50(2):581-591.Zhao Haibo,Wang Xiuming,Wang Dong et al.Applications of the boundary absorption using aperfectly matched layer for elastic wave simulation in poroelastic media.Chinese Journal of Geophysics,2007,50(2):581-591.