各向异性介质地震波场的优化褶积微分算子法数值模拟
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摘要
在前人工作基础上,通过对窗函数参数进行优化实现了对基于Shannon奇异核理论的交错网格褶积微分算子的优化过程.应用这种优化褶积微分算子方法对各向异性介质进行了数值模拟,讨论了优化褶积微分算子法模拟的PML吸收边界条件以及稳定性条件,分析了弹性波在此类介质中的传播特征,并与高阶交错网格有限差分方法进行了对比.数值实验结果表明,该方法适用于各向异性介质中弹性波场模拟,精度高,稳定性好,是一种研究复杂介质中地震波传播的有效数值方法.
This paper optimizes the staggered-grid convolutional differentiator based on Shannon singular kernel theory on the window function parameters.We apply this numerical modeling method to anisotropic media modeling; and discuss the PML absorbing boundary and its stability conditions.Meanwhile,the elastic wave propagation characteristics in such media are also analyzed.The results are compared with high-order,staggered-grid finite difference technology.Numerical test shows that this method is suitable for wave field modeling in anisotropic media with high accuracy and robust stability,and proves that it s an effective numerical method of wave propagation modeling in complex media.
This paper optimizes the staggered-grid convolutional differentiator based on Shannon singular kernel theory on the window function parameters.We apply this numerical modeling method to anisotropic media modeling; and discuss the PML absorbing boundary and its stability conditions.Meanwhile,the elastic wave propagation characteristics in such media are also analyzed.The results are compared with high-order,staggered-grid finite difference technology.Numerical test shows that this method is suitable for wave field modeling in anisotropic media with high accuracy and robust stability,and proves that it s an effective numerical method of wave propagation modeling in complex media.
引文
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[3] 牛滨华,孙春岩.裂隙各向异性介质2． 5维弹性波场数值模拟[J].地球科学(中国地质大学学报),1995,20(1) :107～111． Niu B H,Sun C Y.Numerical simulation for 2． 5-D elastic wave fields in crack anisotropic media[J].Earth Science (Journal of the University of Geosciences,China) (in Chinese),1995,20(1) :107～111．
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[5] 侯安宁,何樵登.各向异性介质中弹性波传播特征的伪谱法模拟研究[J].石油物探,1995,34(2) :36～45． Hou A N,He Q D.Study on characteristics of elastic wave propagation in pseudo-spectral modeling[J].Geophysical Prospecting for Petroleum,1995,34(2) :36～45．
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[7] Igel H,Mora P,Rioll Et B.Anisotropic wave propagation through finite-difference grids[J].Geophysics,1995,60(4) :1203～1216．
[8] 张文生,宋海斌.三维正交各向异性介质三分量高精度有限差分正演模拟[J].石油地球物理勘探,2001,36(4) :422～432． Zhang W S,Song H B.Finite difference forward modeling of three-component records with high precision in 3-D orthorhombic anisotropic media[J].Oil Geophysical Prospecting,2001,36(4) :422～432．
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[10] 王童奎,李瑞华,李小凡,等.横向各向同性介质中地震波场谱元法数值模拟[J].地球物理学进展.2007,22(3) :778～784． Wang T K,Li R H,Li X F,et al.Numerical spectralelement modeling for seismic wave propagation in transversely isotropic medium[J].Progress in Geophys (in Chinese),2007,22(3) :778～784．
[11] Alterman Z,Karal Jr F C.Propagation of elastic waves in layered media by finite-difference methods[J].Bull.Seism.Soc.Am,1968,58:367～398．
[12] 张美根.各向异性弹性波正反问题研究[D].北京:中国科学院地质与地球物理研究所,2000． Zhang M G.The researches of forward modeling and inversion of anisotropic elastic wave[D].(in Chinese).Beijing:Institute of Geology and Geophysics,Chinese Academy of Sciences,2000．
[13] Fornberg B.The pseudospectral method:Comparisons with finite differences for elastic wave equation[J].Geophysics,1987,52(4) :483～501．
[14] Komatitsch D.Spectral and spectral-element methods for the 2D and 3D electrodynamics equations in heterogeneous media[D].Paris:Institute de Physique du Globe,1997．
[15] Mora P.Elastic finite difference with convolutional operaters[J].Staford Exploration Project Report,1986,48:277～289．
[16] Holgerg O.Computational aspects of the choice of operator and sampling interval for numerical differentiation in largescale simulation of wave phenomena[J].Geophys.Prosp,2006,35 (6) :629～655．
[17] Zhou B,Geeenhalgh S.Seismic scalar wave equation modeling by a convolutional differentiator[J].Bull.Seism.Am,1992,82(1) :289～303．
[18] 张中杰,滕吉文,杨顶辉.声波与弹性波场数值模拟中的褶积微分算子法[J].地震学报,1996,18(1) :63～69． Zhang Z J,Teng J W,Yang D H.The convolutional differentiator method for numerical modeling of acoustic and elastic wave-field[J].Acta Seismological Sinica(in Chinese),1996,18(1) :63～69．
[19] 戴志杨,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,2005,35(4) :520～524． Dai Z Y,Sun J G,Zha X J.Seismic wave field modeling with convolutional differentiator algorithm[J].Journal of Jilin University(in Chinese),2005,35(4) :520～524．
[20] 程冰洁,李小凡,龙桂华.基于广义正交多项式褶积微分算子的地震波场数值模拟方法[J].地球物理学报,2008,51(2) :531～537． Cheng B J,Li X F,Long G H.Seismic waves modeling by convolutional Forsyte polynomial differentiator method[J].Chinese J.Geophys(in Chinese),2008,51 (2) :531～537．
[21] 程冰洁,李小凡.2． 5维地震波场褶积微分算子法数值模拟[J].地球物理学进展,2008,23(4) :1099～1105． Cheng B J,Li X F.2． 5D modelling of elastic waves using the convolutional differentiator method[J].Progress in Geophys (in Chinese),2008,23(4) :1099～1105．
[22] 贺同江,刘红艳,李小凡.双向介质地震波常数值模拟的迭积微分算子及其PML边界条件,地球物理学进展[J].2010,24(4) :1180～1188． He T J,Liu H Y,Li X F.Two-phase media seismic wave simulation by the convolutional differentiator method and the PML absorbing boudary[J].Progress in Geophys.(in Chinese),2010,24(4) :1180～1188．
[23] 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场模拟中的应用[J].地球物理学报,2009,52(4) :1014～1024． Long G H,Li X F,Zhang M G.The application of convolutional differentiator in seismic modeling based on Shannon singular kernel theory[J].Chinese J.Geophys (in Chinese),2009,52(4) :1014～1024．
[24] 龙桂华.粘弹性介质中的地震波传播与波形反演研究[D].北京:中国科学院地质与地球物理研究所,2009． Long G H.The study of seismic wave propagation and waveform inversion in viscoelastic media[D](in Chinese).Beijing:Institute of Geology and Geophysics,Chinese Academy of Sciences,2009．
[25] 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[J].地球物理学报,2000,43(6) :856～864． DongLG,Ma Z T,Cao J Z.A study on stability of the staggered-grid high-order difference method of first-order difference method of first-order elastic wave equation[J].Chinese J.Geophys(in Chinese),2000,43(6) :856～864．
[2] 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[J].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[J].Chinese J.Geophys(in Chinese),2000,43(3) :411～419．
[3] 牛滨华,孙春岩.裂隙各向异性介质2． 5维弹性波场数值模拟[J].地球科学(中国地质大学学报),1995,20(1) :107～111． Niu B H,Sun C Y.Numerical simulation for 2． 5-D elastic wave fields in crack anisotropic media[J].Earth Science (Journal of the University of Geosciences,China) (in Chinese),1995,20(1) :107～111．
[4] 周辉,徐世浙,刘斌,等.各向异性介质中波动方程有限元模拟及其稳定性[J].地球物理学报,1997,40(6) :833～841． Zhou H,Xu S Z,Liu B,et al.Finite element simulation for wave equation in anisotropic media[J].Chinese J.Geophys,1997,40(6) :833～841．
[5] 侯安宁,何樵登.各向异性介质中弹性波传播特征的伪谱法模拟研究[J].石油物探,1995,34(2) :36～45． Hou A N,He Q D.Study on characteristics of elastic wave propagation in pseudo-spectral modeling[J].Geophysical Prospecting for Petroleum,1995,34(2) :36～45．
[6] Carcinoe J M,Kosloff D,Behl E A,et al.A spectral scheme for wave propagation simulation in 3-D elastic anisotropic media[J].Geophysics,1992,57(5) :1593～1607．
[7] Igel H,Mora P,Rioll Et B.Anisotropic wave propagation through finite-difference grids[J].Geophysics,1995,60(4) :1203～1216．
[8] 张文生,宋海斌.三维正交各向异性介质三分量高精度有限差分正演模拟[J].石油地球物理勘探,2001,36(4) :422～432． Zhang W S,Song H B.Finite difference forward modeling of three-component records with high precision in 3-D orthorhombic anisotropic media[J].Oil Geophysical Prospecting,2001,36(4) :422～432．
[9] 裴正林.三维各向异性介质中弹性波方程交错网格高阶有限差分法数值模拟[J].石油大学学报(自然科学版),2004,28(5) :23～29． Pei Z L.Three-dimensional numerical simulation of elastic wave propagation in 3-D anisotropic media with staggered-grid high-order difference method[J].Journal of the University of Petroleum of China(in Chinese),2004,28(5) :23～29．
[10] 王童奎,李瑞华,李小凡,等.横向各向同性介质中地震波场谱元法数值模拟[J].地球物理学进展.2007,22(3) :778～784． Wang T K,Li R H,Li X F,et al.Numerical spectralelement modeling for seismic wave propagation in transversely isotropic medium[J].Progress in Geophys (in Chinese),2007,22(3) :778～784．
[11] Alterman Z,Karal Jr F C.Propagation of elastic waves in layered media by finite-difference methods[J].Bull.Seism.Soc.Am,1968,58:367～398．
[12] 张美根.各向异性弹性波正反问题研究[D].北京:中国科学院地质与地球物理研究所,2000． Zhang M G.The researches of forward modeling and inversion of anisotropic elastic wave[D].(in Chinese).Beijing:Institute of Geology and Geophysics,Chinese Academy of Sciences,2000．
[13] Fornberg B.The pseudospectral method:Comparisons with finite differences for elastic wave equation[J].Geophysics,1987,52(4) :483～501．
[14] Komatitsch D.Spectral and spectral-element methods for the 2D and 3D electrodynamics equations in heterogeneous media[D].Paris:Institute de Physique du Globe,1997．
[15] Mora P.Elastic finite difference with convolutional operaters[J].Staford Exploration Project Report,1986,48:277～289．
[16] Holgerg O.Computational aspects of the choice of operator and sampling interval for numerical differentiation in largescale simulation of wave phenomena[J].Geophys.Prosp,2006,35 (6) :629～655．
[17] Zhou B,Geeenhalgh S.Seismic scalar wave equation modeling by a convolutional differentiator[J].Bull.Seism.Am,1992,82(1) :289～303．
[18] 张中杰,滕吉文,杨顶辉.声波与弹性波场数值模拟中的褶积微分算子法[J].地震学报,1996,18(1) :63～69． Zhang Z J,Teng J W,Yang D H.The convolutional differentiator method for numerical modeling of acoustic and elastic wave-field[J].Acta Seismological Sinica(in Chinese),1996,18(1) :63～69．
[19] 戴志杨,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,2005,35(4) :520～524． Dai Z Y,Sun J G,Zha X J.Seismic wave field modeling with convolutional differentiator algorithm[J].Journal of Jilin University(in Chinese),2005,35(4) :520～524．
[20] 程冰洁,李小凡,龙桂华.基于广义正交多项式褶积微分算子的地震波场数值模拟方法[J].地球物理学报,2008,51(2) :531～537． Cheng B J,Li X F,Long G H.Seismic waves modeling by convolutional Forsyte polynomial differentiator method[J].Chinese J.Geophys(in Chinese),2008,51 (2) :531～537．
[21] 程冰洁,李小凡.2． 5维地震波场褶积微分算子法数值模拟[J].地球物理学进展,2008,23(4) :1099～1105． Cheng B J,Li X F.2． 5D modelling of elastic waves using the convolutional differentiator method[J].Progress in Geophys (in Chinese),2008,23(4) :1099～1105．
[22] 贺同江,刘红艳,李小凡.双向介质地震波常数值模拟的迭积微分算子及其PML边界条件,地球物理学进展[J].2010,24(4) :1180～1188． He T J,Liu H Y,Li X F.Two-phase media seismic wave simulation by the convolutional differentiator method and the PML absorbing boudary[J].Progress in Geophys.(in Chinese),2010,24(4) :1180～1188．
[23] 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场模拟中的应用[J].地球物理学报,2009,52(4) :1014～1024． Long G H,Li X F,Zhang M G.The application of convolutional differentiator in seismic modeling based on Shannon singular kernel theory[J].Chinese J.Geophys (in Chinese),2009,52(4) :1014～1024．
[24] 龙桂华.粘弹性介质中的地震波传播与波形反演研究[D].北京:中国科学院地质与地球物理研究所,2009． Long G H.The study of seismic wave propagation and waveform inversion in viscoelastic media[D](in Chinese).Beijing:Institute of Geology and Geophysics,Chinese Academy of Sciences,2009．
[25] 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[J].地球物理学报,2000,43(6) :856～864． DongLG,Ma Z T,Cao J Z.A study on stability of the staggered-grid high-order difference method of first-order difference method of first-order elastic wave equation[J].Chinese J.Geophys(in Chinese),2000,43(6) :856～864．
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