地震波数值模拟的非规则网格PML吸收边界
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摘要
以格子法为基础,以声波方程为例研究非规则网格PML(Perfectly Matched Layer)方法.本方法的核心是建立局部坐标系下的分裂方程和基于积分近似的微分方程弱形式.该非规则网格模拟方法允许在计算域内设置任意形状的人工边界.对于二维半空间问题,与采用矩形人工边界相比,采用半圆形人工边界可减少计算量20%以上.采用光滑的曲边界,不仅可减少计算区域,还可避免常规的PML吸收边界在吸收带角点区域的特殊处理.本方法事先计算和存储边界单元的局部几何参数,在计算的每一时间步查表调用这些参数,与常规的直边界PML方法相比,不增加任何计算量.
The perfectly matched layer(PML)absorbing boundary condition is incorporated into the acoustic grid method,thus resulting in an irregular-grid PML method.The proposed scheme is developed using the local coordinate system based PML splitting equations and integral approaches of the PML equations under a discretization of triangular grid cells.The irregular-grid PML method allows the artificial boundaries to be constructed with arbitrary geometries only if the interested zones are enclosed.We can take a semi-circle rather than a rectangle as the artificial boundary in simulating the 2-D half-space using the proposed scheme.This results in an over 20% reduction of the nodes in the numerical discretization.By using a smoothed artificial boundary,the irregular-grid PML method can also avoid the special treatments for the corners,which lead to complex computer implementations in the conventional PML method.Owing to that the local geometrical coefficients are computed and stored in a table in advance,no extra computational costs arise when we use the irregular-grid PML method rather than the conventional PML method.The 2-D acoustic cases are considered here.
The perfectly matched layer(PML)absorbing boundary condition is incorporated into the acoustic grid method,thus resulting in an irregular-grid PML method.The proposed scheme is developed using the local coordinate system based PML splitting equations and integral approaches of the PML equations under a discretization of triangular grid cells.The irregular-grid PML method allows the artificial boundaries to be constructed with arbitrary geometries only if the interested zones are enclosed.We can take a semi-circle rather than a rectangle as the artificial boundary in simulating the 2-D half-space using the proposed scheme.This results in an over 20% reduction of the nodes in the numerical discretization.By using a smoothed artificial boundary,the irregular-grid PML method can also avoid the special treatments for the corners,which lead to complex computer implementations in the conventional PML method.Owing to that the local geometrical coefficients are computed and stored in a table in advance,no extra computational costs arise when we use the irregular-grid PML method rather than the conventional PML method.The 2-D acoustic cases are considered here.
引文
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[2]周竹生,刘喜亮,熊孝雨.弹性介质中瑞雷面波有限差分法正演模拟.地球物理学报,2007,50(2):567～573Zhou Z S,Liu X L,Xiong X Y.Finite-difference modelling of Rayleigh surface wave in elastic media.Chinese J.Geophys.(in Chinese),2007,50(2):567～573
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[8]薛东川,王尚旭,焦淑静.起伏地表复杂介质波动方程有限元数值模拟方法.地球物理学进展,2007,22(2):522～529Xue D C,Wang S X,Jiao S J.Wave equation finite-element modeling including rugged topography and complicated medium.Progress in Geophysics(in Chinese),2007,22(2):522～529
[9]Komatitsch D,Tromp J.Introduction to the spectral element method for three-dimensional seismic wave propagation.Geophysical Journal International,1999,139(3):806～822
[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.地球物理学进展,2007,22(3):778～784Wang T K,Li R H,Li X F,et al.Numerical spectral-element modeling for seismic wave propagation in transversely isotropic medium.Progress in Geophysics(in Chinese),2007,22(3):778～784
[11]张金海,王卫民,赵连锋等.傅里叶有限差分法三维波动方程正演模拟.地球物理学报,2007,50(6):1854～1862Zhang J H,Wang W M,Zhao L F,et al.Modeling3-D scalar waves using the Fourier finite-difference method.Chinese J.Geophys.(in Chinese),2007,50(6):1854～1862
[12]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.地球物理学报,2008,51(2):531～537Cheng B J,Li X F,Long G H.Seismic waves modeling by convolutional Forsyte polynomial differentiator method.Chinese J.Geophys.(in Chinese),2008,51(2):531～537
[13]殷文,印兴耀,吴国忱等.高精度频率域弹性波方程有限差分方法及波场模拟.地球物理学报,2006,49(2):561～568Yin W,Yin X Y,Wu G C,et al.The method of finite difference of high precision elastic wave equations in the frequency domain and wave-field simulation.Chinese J.Geophys.(in Chinese),2006,49(2):561～568
[14]Zhang J,Liu T.P-SV-wave propagation in heterogeneous media:grid method.Geophysical Journal International,1999,136:431～438
[15]Zhang J,Liu T.Elastic wave modellingin3D heterogeneous media:3D grid method.Geophysical Journal International,2002,150(3):780～799
[16]Zhang J.Elastic wave modellingin heterogeneous media with high velocity contrasts.Geophysical Journal International,2004,159(1):223～239
[17]Zhang J.Wave propagation across fluid-solid interfaces:a grid method approach.Geophysical Journal International,2004,159(1):240～252
[18]Zhang J.Elastic wave modeling in fractured media with an explicit approach.Geophysics,2005,70(5):75～85
[19]Zhang J.Triangle-quadrangle grid method for poroelastic,elastic,and acoustic wave equations.Journal of Computational Acoustics,2001,9:681～702
[20]廖振鹏,黄孔亮,杨柏坡等.暂态波透射边界.中国科学(A辑),1984,26(6):556～564Liao Z P,Huang K L,Yang B P,et al.Transient wave transmitting boundary condition.Sciencein China(Ser.A),1984,26(6):556～564
[21]Clayton R,Engquist B.Absorbing boundary conditions for acoustic and elastic wave equations.Bulletin of the Seismological Society of America,1977,67(6):1529～1540
[22]Peng C,Toksoz M N.An optimal absorbing boundary condition for elastic wave modeling.Geophysics,1995,60(1):296～301
[23]Berenger J P.Aperfectly matchedlayer for the absorption of electromagnetic waves.Journal of Computational Physics,1994,114(2):185～200
[24]Lysmer J,Kuhlemeyer R L.Finite dynamic model forinfinite media.Journal of Engineering Mechanics.ASCE,1969,95(1):759～877
[25]Berenger J P.Three-dimensional perfectly matched layer for the absorption of electromagnetic waves.Journal of Computational Physics,1996,127(2):363～379
[26]Quan Q,Thomas L G.Evaluation of the perfectly matched layer for computational acoustics.Journal of Computational Physics,1998,139(1):166～183
[27]Collino F,Tsogka C.Application of the perfectly matched absorbing layer model to the linear elastodynamic problemin anisotropic heterogeneous media.Geophysics,2001,66(1):294～307
[28]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):581～591Zhao HB,Wang X M,Wang D,et al.Applications of the boundary absorption using a perfectly matched layer for elastic wave simulation in poroelastic media.Chinese J.Geophys.(in Chinese),2007,50(2):581～591
[2]周竹生,刘喜亮,熊孝雨.弹性介质中瑞雷面波有限差分法正演模拟.地球物理学报,2007,50(2):567～573Zhou Z S,Liu X L,Xiong X Y.Finite-difference modelling of Rayleigh surface wave in elastic media.Chinese J.Geophys.(in Chinese),2007,50(2):567～573
[3]刘恩儒,岳建华,刘彦.具有离散裂缝空间分布的二维固体中地震波传播的有限差分模拟.地球物理学报,2006,49(1):180～188Liu E R,Yue J H,Liu Y.Finite difference simulation of seismic wave propagation in2-D solids with spatial distribution of discrete fractures.Chinese J.Geophys.(in Chinese),2006,49(1):180～188
[4]Carcione J M,Kosloff D,Behle A,Seriani G.A spectral scheme for wave propagation simulation in3-D elastic-anisotropic media.Geophysics,1992,57(12):1593～1607
[5]谢桂生,刘洪,赵连功.伪谱法地震波正演模拟的多线程并行计算.地球物理学进展,2005,20(1):17～23Xie G S,Liu H,Zhao L G.Parallel Algorithmbased on the multithread technique for pseudospectal modeling of seismic wave.Progress in Geophysics(in Chinese),2005,20(1):17～23
[6]刘财,张智,邵志刚等.线性粘弹体中地震波场伪谱法模拟技术.地球物理学进展,2005,20(3):640～652Liu C,Zhang Z,Shao Z G,et al.Pseudospectral forward modeling of seismic wave in linear viscoelasic solid.Progress in Geophysics(in Chinese),2005,20(3):640～652
[7]Smith WD.The application of finite element analysis to body wave propagation problems.Geophysical Journal International,1975,42(2):747～768
[8]薛东川,王尚旭,焦淑静.起伏地表复杂介质波动方程有限元数值模拟方法.地球物理学进展,2007,22(2):522～529Xue D C,Wang S X,Jiao S J.Wave equation finite-element modeling including rugged topography and complicated medium.Progress in Geophysics(in Chinese),2007,22(2):522～529
[9]Komatitsch D,Tromp J.Introduction to the spectral element method for three-dimensional seismic wave propagation.Geophysical Journal International,1999,139(3):806～822
[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.地球物理学进展,2007,22(3):778～784Wang T K,Li R H,Li X F,et al.Numerical spectral-element modeling for seismic wave propagation in transversely isotropic medium.Progress in Geophysics(in Chinese),2007,22(3):778～784
[11]张金海,王卫民,赵连锋等.傅里叶有限差分法三维波动方程正演模拟.地球物理学报,2007,50(6):1854～1862Zhang J H,Wang W M,Zhao L F,et al.Modeling3-D scalar waves using the Fourier finite-difference method.Chinese J.Geophys.(in Chinese),2007,50(6):1854～1862
[12]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.地球物理学报,2008,51(2):531～537Cheng B J,Li X F,Long G H.Seismic waves modeling by convolutional Forsyte polynomial differentiator method.Chinese J.Geophys.(in Chinese),2008,51(2):531～537
[13]殷文,印兴耀,吴国忱等.高精度频率域弹性波方程有限差分方法及波场模拟.地球物理学报,2006,49(2):561～568Yin W,Yin X Y,Wu G C,et al.The method of finite difference of high precision elastic wave equations in the frequency domain and wave-field simulation.Chinese J.Geophys.(in Chinese),2006,49(2):561～568
[14]Zhang J,Liu T.P-SV-wave propagation in heterogeneous media:grid method.Geophysical Journal International,1999,136:431～438
[15]Zhang J,Liu T.Elastic wave modellingin3D heterogeneous media:3D grid method.Geophysical Journal International,2002,150(3):780～799
[16]Zhang J.Elastic wave modellingin heterogeneous media with high velocity contrasts.Geophysical Journal International,2004,159(1):223～239
[17]Zhang J.Wave propagation across fluid-solid interfaces:a grid method approach.Geophysical Journal International,2004,159(1):240～252
[18]Zhang J.Elastic wave modeling in fractured media with an explicit approach.Geophysics,2005,70(5):75～85
[19]Zhang J.Triangle-quadrangle grid method for poroelastic,elastic,and acoustic wave equations.Journal of Computational Acoustics,2001,9:681～702
[20]廖振鹏,黄孔亮,杨柏坡等.暂态波透射边界.中国科学(A辑),1984,26(6):556～564Liao Z P,Huang K L,Yang B P,et al.Transient wave transmitting boundary condition.Sciencein China(Ser.A),1984,26(6):556～564
[21]Clayton R,Engquist B.Absorbing boundary conditions for acoustic and elastic wave equations.Bulletin of the Seismological Society of America,1977,67(6):1529～1540
[22]Peng C,Toksoz M N.An optimal absorbing boundary condition for elastic wave modeling.Geophysics,1995,60(1):296～301
[23]Berenger J P.Aperfectly matchedlayer for the absorption of electromagnetic waves.Journal of Computational Physics,1994,114(2):185～200
[24]Lysmer J,Kuhlemeyer R L.Finite dynamic model forinfinite media.Journal of Engineering Mechanics.ASCE,1969,95(1):759～877
[25]Berenger J P.Three-dimensional perfectly matched layer for the absorption of electromagnetic waves.Journal of Computational Physics,1996,127(2):363～379
[26]Quan Q,Thomas L G.Evaluation of the perfectly matched layer for computational acoustics.Journal of Computational Physics,1998,139(1):166～183
[27]Collino F,Tsogka C.Application of the perfectly matched absorbing layer model to the linear elastodynamic problemin anisotropic heterogeneous media.Geophysics,2001,66(1):294～307
[28]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):581～591Zhao HB,Wang X M,Wang D,et al.Applications of the boundary absorption using a perfectly matched layer for elastic wave simulation in poroelastic media.Chinese J.Geophys.(in Chinese),2007,50(2):581～591
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