最优化广义离散Shannon奇异核交错网格褶积微分算子地震波场模拟
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摘要
笔者基于离散Shannon奇异核褶积微分算子(GDSCD)计算地震波速度应力方程的空间导数,推导了一阶GDSCD的具体形式,并提出了优化方法,即在频率域逼近平面波的真实导数,得到了不同半径和采样下限的最优窗函数系数,通过滤波响应分析算子精度,与多种数值方法对比以及模型测试表明,笔者构造的最优化GDSCD模拟地震波具有较高的计算效率和精度。
This paper deals with the generalized discrete Shannon convolutional differentiator(GDSCD) for solving seismic velocitystress equation.The first-order convolution differentiators are provided.An efficient method is proposed to optimize the coefficients of the convolution differentiator.A series of optimal coefficients are obtained for various operator lengths and sampling rates per shortest wave length.The operator accuracy is discussed through filter response.A comparison with various numerical methods and numerical experiments show that the new designed staggered grid convolution differentiator has high accuracy and efficiency for seismic wave modeling.
This paper deals with the generalized discrete Shannon convolutional differentiator(GDSCD) for solving seismic velocitystress equation.The first-order convolution differentiators are provided.An efficient method is proposed to optimize the coefficients of the convolution differentiator.A series of optimal coefficients are obtained for various operator lengths and sampling rates per shortest wave length.The operator accuracy is discussed through filter response.A comparison with various numerical methods and numerical experiments show that the new designed staggered grid convolution differentiator has high accuracy and efficiency for seismic wave modeling.
引文
[1]陈景波,秦孟兆.辛几何算法在射线追踪中的应用[J].数值计算与计算机应用,2000,21(4):254-265.
[2]Cerveny V.Seismic ray theory[M].Cambridge:Cambridge Univ Press,2001.
[3]Pao Y H,Varatharajulu V.Huygen's principle,radiation condi-tions,and intergral formulas for the scattering of elastic wave[J].J.Acoust.Soc.Am.,1976,59(6):1361-1371.
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[6]董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分法稳定性研究[J].地球物理学报,2000,43(6):856-864.
[7]张美根,王妙月,李小凡,等.各向异性弹性波场的有限元数值模拟[J].地球物理学进展,2002,17(3):384-389.
[8]Gazdag J.Modeling of the acoustic wave equation with transform methods[J].Geophysics,1981,46(5):854-859.
[9]Komatitsch D.Spetctal and spectral-element methods for the2D and3D elastodynamics equations in heterogeneous media[D].Par-is:Institute de Physique du Globe,1997.
[10]Wang Y B,Takenaka H,Furumura T.Modelling seismic wave prop-agation in a two-dimensional cylindrical whole-earth model using the pseudospectral method[J].Geophys.J.Int.,2001,145(3):689-708.
[11]Yang D H,Song G J,Lu M.Optimally accurate nearly analyti dis-crete scheme for wave-field simulation in3D anisotropic media[J].Bull.Seism.Soc.Am.,2007,97(5):1557-569.
[12]Li X F,Zhu T,Zhang M G,et al.Seismic scalar wave equation with variable coefficient modeling by a new convolutional differentiator[J].Computer Physics Communications,2010,181:1850-858.
[13]Bayliss A,Jordan K E,Lemesurier B J.A fourth-order accurate fi-nite-difference scheme for the computation of elastic wave[J].Bull.Seism.Soc.Am.,1986,76(4):1115-1132.
[14]吴国忱,王华忠.波场模拟中的数值频散分析与校正策略.地球物理学进展,2005,20(1):58-65.
[15]Fornberg B.The Pseudospectral method:Comparison with finite differences for the elastic wave equation[J].Geophysics,1987,52(4):483-501.
[16]Fornberg B.The Pseudospectral method:Accurate representation of interfaces in elastic wave calculations[J].Geophysics,1988,53(5):625-637.
[17]Li X F,Wang W S,Lu M W,et al.Structure-preserving modeling of elastic wave:a symplectic discrete singular convolution differetiator method[J].Geophys.J.Int.,2012,188(3):1382-1392.
[18]龙桂华,李小凡,张美根.错格傅立叶伪谱微分算子在波场模拟中的运用[J].地球物理学报,2009,52(1):193-199.
[19]龙桂华,李小凡,江东辉.基于交错网格Fourier伪谱微分矩阵算子的地震波场模拟GPU加速方案[J].地球物理学报,2010,53(13):2934-2971.
[20]Mora P.Elastic Fininte Difference with Convolutional Operatrors[R].California:Stanford Exploration Project Report,1986:277-290.
[21]Holberg O.Comutational aspects of the choice of operator and sam-pling interval for numerical differentiation in large-scale simulation of wave phenomena[J].Geophysical Prospecting,1987,35(6):629-655.
[22]Zhou B,Greenhalgh S.Seismic scalar wave equation modeling by a convolutonal differentiator[J].Bull.Seism.Soc.Amer.,1992,82(1):289-303.
[23]滕吉文,张中杰,杨顶辉,等.各向异性介质中褶积微分算子法三分量地震资料的数值仿真[J].石油物探,1995,34(3):15-22.
[24]张中杰,滕吉文,杨顶辉.声波与弹性波数值模拟中的褶积微分算子法[J].地震学报,1996,18(1):63-69.
[25]戴志阳,孙建国,查显杰.地震波场模拟中的褶积微分算子法[J].吉林大学学报:地球科学版,2005,35(4):520-524.
[26]龙桂华,赵宇波,赵家福.地震波数值模拟中的最优Shannnon奇异核褶积微分算子[J].地震学报,2011,33(5):650-662.
[27]Wei G W.Quasi wavelets and quasi interpolating wavelets[J].Chemical Physics Letters,1998,296:215-222.
[28]Qian L W.On the Regularized whittaker-kotel'nikov Shannon sham-pling formula[J].Proceedings of the American Mathematical Soci-ety,2002,131(4):1169-1176.
[29]Feng B F,Wei G W.A comparison of the spectral and the discrete singular convolution schemes for the KdV-type equations[J].Jour-nal of Computational and Applied Mathematics,2002,145(1):183-188.
[30]Li X F,Li Y Q,Zhang M G.Scalar seismic wave equation modeling by a multisymplectic discrete singular convolution differentiator method[J].Bull.Seis.Soc.Am.,2011,101(4):1710-1718.
[31]龙桂华,李小凡,张美根.基于Shannon奇异核理论的褶积微分算子在地震波模拟中的应用[J].地球物理学报,2009,52(4):1014-1024.
[32]Jean Virieux.P-SV wave propagation in heterogeneous media Veloc-ity-stress finite-difference method[J].Geophysics,1986,51(4):889-901.
[33]李一琼,李小凡,朱童.基于辛格式奇异核褶积微分算子的地震标量波场模拟[J].地球物理学报,2011,54(7):1827-1834.
[34]Aki K,Richards P G.Quantitative seismology theory and methods[R].San Franciso:W H Freeman and Company,1980.
[35]Berenger J.A perfectly match layer for the absorption of electromag-netic waves[J].J Comput Phys,1994,114(2):185-220.
[36]李信富,李小凡.地震波传播的褶积微分算子法数值模拟[J].地球科学:中国地质大学学报,2008,33(6):861-866.
[2]Cerveny V.Seismic ray theory[M].Cambridge:Cambridge Univ Press,2001.
[3]Pao Y H,Varatharajulu V.Huygen's principle,radiation condi-tions,and intergral formulas for the scattering of elastic wave[J].J.Acoust.Soc.Am.,1976,59(6):1361-1371.
[4]Ursin B.Review of elastic and electromagnetic wave propagation in horizontally layered media[J].Geophysics,1983,44(8):1063-1081.
[5]Alterman Z,Karal F C.Propagation of elastic waves in layered media by finite-difference methods[J].Bull.Seism.Soc.Am.,1968,58(1):367-398.
[6]董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分法稳定性研究[J].地球物理学报,2000,43(6):856-864.
[7]张美根,王妙月,李小凡,等.各向异性弹性波场的有限元数值模拟[J].地球物理学进展,2002,17(3):384-389.
[8]Gazdag J.Modeling of the acoustic wave equation with transform methods[J].Geophysics,1981,46(5):854-859.
[9]Komatitsch D.Spetctal and spectral-element methods for the2D and3D elastodynamics equations in heterogeneous media[D].Par-is:Institute de Physique du Globe,1997.
[10]Wang Y B,Takenaka H,Furumura T.Modelling seismic wave prop-agation in a two-dimensional cylindrical whole-earth model using the pseudospectral method[J].Geophys.J.Int.,2001,145(3):689-708.
[11]Yang D H,Song G J,Lu M.Optimally accurate nearly analyti dis-crete scheme for wave-field simulation in3D anisotropic media[J].Bull.Seism.Soc.Am.,2007,97(5):1557-569.
[12]Li X F,Zhu T,Zhang M G,et al.Seismic scalar wave equation with variable coefficient modeling by a new convolutional differentiator[J].Computer Physics Communications,2010,181:1850-858.
[13]Bayliss A,Jordan K E,Lemesurier B J.A fourth-order accurate fi-nite-difference scheme for the computation of elastic wave[J].Bull.Seism.Soc.Am.,1986,76(4):1115-1132.
[14]吴国忱,王华忠.波场模拟中的数值频散分析与校正策略.地球物理学进展,2005,20(1):58-65.
[15]Fornberg B.The Pseudospectral method:Comparison with finite differences for the elastic wave equation[J].Geophysics,1987,52(4):483-501.
[16]Fornberg B.The Pseudospectral method:Accurate representation of interfaces in elastic wave calculations[J].Geophysics,1988,53(5):625-637.
[17]Li X F,Wang W S,Lu M W,et al.Structure-preserving modeling of elastic wave:a symplectic discrete singular convolution differetiator method[J].Geophys.J.Int.,2012,188(3):1382-1392.
[18]龙桂华,李小凡,张美根.错格傅立叶伪谱微分算子在波场模拟中的运用[J].地球物理学报,2009,52(1):193-199.
[19]龙桂华,李小凡,江东辉.基于交错网格Fourier伪谱微分矩阵算子的地震波场模拟GPU加速方案[J].地球物理学报,2010,53(13):2934-2971.
[20]Mora P.Elastic Fininte Difference with Convolutional Operatrors[R].California:Stanford Exploration Project Report,1986:277-290.
[21]Holberg O.Comutational aspects of the choice of operator and sam-pling interval for numerical differentiation in large-scale simulation of wave phenomena[J].Geophysical Prospecting,1987,35(6):629-655.
[22]Zhou B,Greenhalgh S.Seismic scalar wave equation modeling by a convolutonal differentiator[J].Bull.Seism.Soc.Amer.,1992,82(1):289-303.
[23]滕吉文,张中杰,杨顶辉,等.各向异性介质中褶积微分算子法三分量地震资料的数值仿真[J].石油物探,1995,34(3):15-22.
[24]张中杰,滕吉文,杨顶辉.声波与弹性波数值模拟中的褶积微分算子法[J].地震学报,1996,18(1):63-69.
[25]戴志阳,孙建国,查显杰.地震波场模拟中的褶积微分算子法[J].吉林大学学报:地球科学版,2005,35(4):520-524.
[26]龙桂华,赵宇波,赵家福.地震波数值模拟中的最优Shannnon奇异核褶积微分算子[J].地震学报,2011,33(5):650-662.
[27]Wei G W.Quasi wavelets and quasi interpolating wavelets[J].Chemical Physics Letters,1998,296:215-222.
[28]Qian L W.On the Regularized whittaker-kotel'nikov Shannon sham-pling formula[J].Proceedings of the American Mathematical Soci-ety,2002,131(4):1169-1176.
[29]Feng B F,Wei G W.A comparison of the spectral and the discrete singular convolution schemes for the KdV-type equations[J].Jour-nal of Computational and Applied Mathematics,2002,145(1):183-188.
[30]Li X F,Li Y Q,Zhang M G.Scalar seismic wave equation modeling by a multisymplectic discrete singular convolution differentiator method[J].Bull.Seis.Soc.Am.,2011,101(4):1710-1718.
[31]龙桂华,李小凡,张美根.基于Shannon奇异核理论的褶积微分算子在地震波模拟中的应用[J].地球物理学报,2009,52(4):1014-1024.
[32]Jean Virieux.P-SV wave propagation in heterogeneous media Veloc-ity-stress finite-difference method[J].Geophysics,1986,51(4):889-901.
[33]李一琼,李小凡,朱童.基于辛格式奇异核褶积微分算子的地震标量波场模拟[J].地球物理学报,2011,54(7):1827-1834.
[34]Aki K,Richards P G.Quantitative seismology theory and methods[R].San Franciso:W H Freeman and Company,1980.
[35]Berenger J.A perfectly match layer for the absorption of electromag-netic waves[J].J Comput Phys,1994,114(2):185-220.
[36]李信富,李小凡.地震波传播的褶积微分算子法数值模拟[J].地球科学:中国地质大学学报,2008,33(6):861-866.
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