重叠区域伪谱法计算非均匀地球介质地震波传播
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摘要
伪谱法是一种高效、高精度计算非均匀介质地震波传播的数值算法,由于它的微分算子的全局性,一般认为该方法不适于并行计算.本文介绍了并行计算非均匀介质中地震波传播的重叠区域分解算法,给出了一种基于傅里叶伪谱法的并行算法.文中给出的算法将介质划分为相互重叠的若干区域,在各个子域上单独求解,利用重叠部分的解的传递,将各个子域连接起来,实现了伪谱法在分布式并行处理机上的计算.文中给出了一个将二维区域分解的算例,比较了并行算法和整体算法的结果,分析了并行算法的计算精度.结果表明,并行算法会有效降低计算时间,并且保证计算精度.该方法在大规模三维非均匀介质的地震波场模拟方面有应用价值.
Pseudospectral method is an efficient and highly precise numerical method for simulating seismic wave propagation in heterogeneous earth medium. Since its derivative operator is global, this method is commonly considered unsuitable for parallel computation. In this paper, we introduce the parallel overlap domain decomposition scheme and give a parallel pseudospectral method implemented on distributed memory PC cluster system for modeling seismic wave propagation in heterogeneous medium. In this parallel method, the medium is decomposed into several subdomains and the wave equations for each subdomain are solved simultaneously. The solutions in each subdomain are connected through the transferring at the overlapped region. Using 2D model, we compared the parallel and traditional pseudospectral method, analyzed the accuracy of the parallel method. The result shows that the parallel method can efficiently reduce computation time for the same accuracy as the traditional method. It is possible to apply this method to the large scale modeling of seismic wave propagation in 3D heterogeneous medium.
Pseudospectral method is an efficient and highly precise numerical method for simulating seismic wave propagation in heterogeneous earth medium. Since its derivative operator is global, this method is commonly considered unsuitable for parallel computation. In this paper, we introduce the parallel overlap domain decomposition scheme and give a parallel pseudospectral method implemented on distributed memory PC cluster system for modeling seismic wave propagation in heterogeneous medium. In this parallel method, the medium is decomposed into several subdomains and the wave equations for each subdomain are solved simultaneously. The solutions in each subdomain are connected through the transferring at the overlapped region. Using 2D model, we compared the parallel and traditional pseudospectral method, analyzed the accuracy of the parallel method. The result shows that the parallel method can efficiently reduce computation time for the same accuracy as the traditional method. It is possible to apply this method to the large scale modeling of seismic wave propagation in 3D heterogeneous medium.
引文
刘鲁波,陈晓非,王彦宾.2007.切比雪夫伪谱法模拟地震波场[J].西北地震学报,[1]:20--27.
刘洋,李承楚.2000.双相各向异性介质中弹性波传播伪谱法数值模拟研究[J].地震学报,22[2]:132--138.
谢桂生,刘洪,赵连功.2005.伪谱法地震波正演模拟的多线程并行计算[J].地球物理学进展,20[1]:17--23.
赵志新,徐纪人,堀内茂木.2003a.错格实数傅里叶变换微分算子及其在非均匀介质波动传播研究中的应用[J].地球物理学报,46[2]:234--240.
赵志新,徐纪人,久保田隆二,脇坂安彦,梶川昌三.2003b.1995年日本神户地震建筑物倒塌与S波和盆地边缘次生面波干涉的研究[J].科学通报,48[24]:2566--2571.
赵志新,徐纪人.2005.盆地构造地震地面运动速度和加速度分布特征的数值模拟[J].地球物理学报,48[5]:1085--1091.
Cerjan C,Kosloff D,Kosloff R,Reshef M.1985.A nonreflecting boundary condition for discrete acoustic and elasticwave equation[J].Geophysics,50:705--708.
Daudt C R,Braile L W,Nowack R L,Chiang C S.1989.Acomparison of finite-difference and Fourier method calcula-tions of synthetic seismograms[J].Bull Seism Soc Amer,79:1210--1230.
Fan J,Nihei K T,Myers L R,Cook N G W.1997.Overlap domain decomposition methodfor wave propagation[C/OL]∥67th Annual Internat Mtg,Soc Expl Geophys,Expanded Abstracts.[2007-05-04].http:∥appliedgeophysics.berkeley.edu:7057/geoengineering/appliedgeophysics/papers/fr97.pdf.
Fornberg B.1996.A Practical Guide to Pesudospectral Methods[M].Cambridge,UK:Cambridge University Press:15--34.
Fornberg B.1987.The pseudospectral method:Comparisons with finite-differences for the elastic wave equations[J].Geophysics,52:483--501.
Furumura T,Kennett B L N,Takenaka H.1998.Parallel3-D pseudospectral si mulation of seismic wave propagation[J].Geophysics,63:279--288.
Furumura T,Koketsu K,Wen K L.2002.Parallel PSM/FDMhybrid si mulation of ground motions fromthe1999Chi-Chi,Tai wan,earthquake[J].Pure Appl Geophys,159:2133--2146.
Kosloff D,Baysal E.1982.Forward modeling by a Fourier method[J].Geophysics,47:1402--1412.
Kosloff D,Reshef M,Loewenthal D.1984.Elastic wave calculation by the Fourier method[J].Bull Seism Soc Amer,74:875--891.
Lacave C,Hollender F.2006.2Dsi mulationinthe Grenoble basin usingthe Aki-Larner method combined with an equiv-alent linear approach[C]∥Bard P Y,Chaljub E,Cornou C,et aleds.Proceedings,ThirdInternational Symposiumonthe Effects of Surface Geology on Seismic Motion.Paris:Laboratoire Central des Ponts et Chausses:14--24.
Liao Q B,Mc Mechan G A.1993.2-D pseudo-spectral viscoacoustic modeling in a distributed-memory multi-processorcomputer[J].Bull Seism Soc Amer,83:1345--1354.
Wang Y B,Takenaka H,Furumura T.2001.Modelling seismic wave propagationin a two-di mensional cylindrical whole-earth model using the pesudospectral method[J].Geophys J Int,145:689--708.
Wang Y B,Takenaka H.2001.A multidomain approach of the Fourier pseudospectral method using discontinuous gridfor elastic wave modeling[J].Earth Planets and Space,53:149--158.
Zhao Z,Xu J,Horiuchi S.2001.Differentiation operation in the wave equation for the pseudospectral method with astaggered mesh[J].Earth Planets and Space,53:327--332.
刘洋,李承楚.2000.双相各向异性介质中弹性波传播伪谱法数值模拟研究[J].地震学报,22[2]:132--138.
谢桂生,刘洪,赵连功.2005.伪谱法地震波正演模拟的多线程并行计算[J].地球物理学进展,20[1]:17--23.
赵志新,徐纪人,堀内茂木.2003a.错格实数傅里叶变换微分算子及其在非均匀介质波动传播研究中的应用[J].地球物理学报,46[2]:234--240.
赵志新,徐纪人,久保田隆二,脇坂安彦,梶川昌三.2003b.1995年日本神户地震建筑物倒塌与S波和盆地边缘次生面波干涉的研究[J].科学通报,48[24]:2566--2571.
赵志新,徐纪人.2005.盆地构造地震地面运动速度和加速度分布特征的数值模拟[J].地球物理学报,48[5]:1085--1091.
Cerjan C,Kosloff D,Kosloff R,Reshef M.1985.A nonreflecting boundary condition for discrete acoustic and elasticwave equation[J].Geophysics,50:705--708.
Daudt C R,Braile L W,Nowack R L,Chiang C S.1989.Acomparison of finite-difference and Fourier method calcula-tions of synthetic seismograms[J].Bull Seism Soc Amer,79:1210--1230.
Fan J,Nihei K T,Myers L R,Cook N G W.1997.Overlap domain decomposition methodfor wave propagation[C/OL]∥67th Annual Internat Mtg,Soc Expl Geophys,Expanded Abstracts.[2007-05-04].http:∥appliedgeophysics.berkeley.edu:7057/geoengineering/appliedgeophysics/papers/fr97.pdf.
Fornberg B.1996.A Practical Guide to Pesudospectral Methods[M].Cambridge,UK:Cambridge University Press:15--34.
Fornberg B.1987.The pseudospectral method:Comparisons with finite-differences for the elastic wave equations[J].Geophysics,52:483--501.
Furumura T,Kennett B L N,Takenaka H.1998.Parallel3-D pseudospectral si mulation of seismic wave propagation[J].Geophysics,63:279--288.
Furumura T,Koketsu K,Wen K L.2002.Parallel PSM/FDMhybrid si mulation of ground motions fromthe1999Chi-Chi,Tai wan,earthquake[J].Pure Appl Geophys,159:2133--2146.
Kosloff D,Baysal E.1982.Forward modeling by a Fourier method[J].Geophysics,47:1402--1412.
Kosloff D,Reshef M,Loewenthal D.1984.Elastic wave calculation by the Fourier method[J].Bull Seism Soc Amer,74:875--891.
Lacave C,Hollender F.2006.2Dsi mulationinthe Grenoble basin usingthe Aki-Larner method combined with an equiv-alent linear approach[C]∥Bard P Y,Chaljub E,Cornou C,et aleds.Proceedings,ThirdInternational Symposiumonthe Effects of Surface Geology on Seismic Motion.Paris:Laboratoire Central des Ponts et Chausses:14--24.
Liao Q B,Mc Mechan G A.1993.2-D pseudo-spectral viscoacoustic modeling in a distributed-memory multi-processorcomputer[J].Bull Seism Soc Amer,83:1345--1354.
Wang Y B,Takenaka H,Furumura T.2001.Modelling seismic wave propagationin a two-di mensional cylindrical whole-earth model using the pesudospectral method[J].Geophys J Int,145:689--708.
Wang Y B,Takenaka H.2001.A multidomain approach of the Fourier pseudospectral method using discontinuous gridfor elastic wave modeling[J].Earth Planets and Space,53:149--158.
Zhao Z,Xu J,Horiuchi S.2001.Differentiation operation in the wave equation for the pseudospectral method with astaggered mesh[J].Earth Planets and Space,53:327--332.
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