模拟地震波场的伪谱和高阶有限差分混合方法
|
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方法,但是由于它的微分算子的全局性,使得该方法不适用于分散内存的并行计算.本文将有限差分算子的局部性和伪谱法算子的高效、高精度相结合,发展基于两种方法的伪谱/有限差分混合方法.该方法在一个空间坐标方向上利用交错网格高阶有限差分算子,在另外的空间坐标方向上利用交错网格伪谱法算子,既保留了后者的高效、高精度优势,又便于在PC集群上实现并行计算.对二维模型的计算显示,混合方法能有效处理介质不连续面,在保证伪谱法计算精度的情况下,提供了一种并行计算的可能途径.
The pseudospectral approach is an efficient and accurate numerical method for seismic wave modeling in heterogeneous medium.However,due to the global nature of its spatial derivative operator,it is difficult to implement this method in parallel computation on distributed memory cluster system.In this paper,we propose a hybrid scheme based on the pseudospectral method (PSM) and finite difference method (FDM),which combines the local nature of the FDM operator and the high accuracy and efficiency of PSM.In the hybrid method,the spatial derivative in one of the space coordinates is approximated using the high-order staggered grid FDM,while in other coordinates are approximated by staggered PSM.This method retains the advantages of the PSM and can be easily implemented on a parallel PC cluster for large scale parallel computation.Numerical tests for 2D models showed that the hybrid method can be used to effectively calculate seismic wavefield in heterogeneous medium,and it provides a possible parallel scheme without loosing accuracy of the results.
The pseudospectral approach is an efficient and accurate numerical method for seismic wave modeling in heterogeneous medium.However,due to the global nature of its spatial derivative operator,it is difficult to implement this method in parallel computation on distributed memory cluster system.In this paper,we propose a hybrid scheme based on the pseudospectral method (PSM) and finite difference method (FDM),which combines the local nature of the FDM operator and the high accuracy and efficiency of PSM.In the hybrid method,the spatial derivative in one of the space coordinates is approximated using the high-order staggered grid FDM,while in other coordinates are approximated by staggered PSM.This method retains the advantages of the PSM and can be easily implemented on a parallel PC cluster for large scale parallel computation.Numerical tests for 2D models showed that the hybrid method can be used to effectively calculate seismic wavefield in heterogeneous medium,and it provides a possible parallel scheme without loosing accuracy of the results.
引文
马德堂,朱光明.2004.有限元法与伪谱法混合求解弹性波动方程[J].地球科学与环境学报,26(1):61--64.
严九鹏,王彦宾.2008.重叠区域伪谱法计算非均匀地球介质地震波传播[J].地震学报,30(1):47--58.
赵志新,徐纪人,堀内茂木.2003.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.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(4):705--708.
Daudt C R,Braille L W,Nowack R L,Chiang C S.1989.Acomparison of finite-difference and Fourier method calculations of synthetic seismograms[J].Bull Seis Soc Amer,79(4):1210--1230.
Fornberg B.1996.A Practical Guide to Pseudospectral Method[M].Cambridge,UK:Cambridge University Press:15--34.
Furumura T,Kennett B L N.1998.On the nature of regional seismic phases-Ⅲ.The influence of crustal heterogeneityon the wavefield for subduction earthquakes:the1985Michoacan and1995Copala,Guerrero,Mexico earthquakes[J].Geophys J Int,135(3):1060--1084.
Furumura T,Koketsu K,Wen K L.2002.Parallel PSM/FDMhybrid si mulation of ground motions fromthe1999ChChi,Tai wan,earthquake[J],Pure Appl Geophys,159(9):2133--2146.
Herrmann R B.1979.SH-wave generation by dislocation source-a numerical study[J].Bull Seis Soc Amer,69(1):1--15
Komatitsch D,Vilotte J P.1998.The spectral element method:An efficient tool to si mulate the seismic response of2Dand3D geological structures[J].Bull Seis Soc Amer,88(2):368--392.
Kosloff D,Baysal E.1982.Forward modeling by a Fourier method[J].Geophysics,47(10):1402--1412.
Mikhailenko B G.2000.Seismic modeling by the spectral-finite difference method[J].Phys Earth Planet Interi,119(1--2):133--147.
Mittet R.2002.Free-surface boundary conditions for elastic staggered-grid modeling schemes[J].Geophysics,67(5):1616--1623.
zdenvar T,Mc Mechan G A.1996.Causes and reduction of numerical artefacts in pseudo-spectral wavefield extrapola-tion[J].Geophys J Int,126(3):819--828.
Virieux J.1986.P-SV wave propagationin heterogeneous media:Velocity-stress finite-difference method[J].Geophys-ics,51(4):889--901.
Wang Y B,Takenaka H,Furumura T.2001.Modeling seismic wave propagationin a two-di mensional cylindrical whole-earth model using the pseudospectral method[J].Geophys J Int,145(3):689--708.
Witte D C,Richards P G.1990.The pseudospectral method for si mulating wave propagation[C]∥Lee D,Cakmak R,Vichnevetsky R eds.Computational Acoustics:Proceedings of the2nd IMACS Symposium on ComputationalAcoustics.North-Holland,New York:1--18.
严九鹏,王彦宾.2008.重叠区域伪谱法计算非均匀地球介质地震波传播[J].地震学报,30(1):47--58.
赵志新,徐纪人,堀内茂木.2003.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.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(4):705--708.
Daudt C R,Braille L W,Nowack R L,Chiang C S.1989.Acomparison of finite-difference and Fourier method calculations of synthetic seismograms[J].Bull Seis Soc Amer,79(4):1210--1230.
Fornberg B.1996.A Practical Guide to Pseudospectral Method[M].Cambridge,UK:Cambridge University Press:15--34.
Furumura T,Kennett B L N.1998.On the nature of regional seismic phases-Ⅲ.The influence of crustal heterogeneityon the wavefield for subduction earthquakes:the1985Michoacan and1995Copala,Guerrero,Mexico earthquakes[J].Geophys J Int,135(3):1060--1084.
Furumura T,Koketsu K,Wen K L.2002.Parallel PSM/FDMhybrid si mulation of ground motions fromthe1999ChChi,Tai wan,earthquake[J],Pure Appl Geophys,159(9):2133--2146.
Herrmann R B.1979.SH-wave generation by dislocation source-a numerical study[J].Bull Seis Soc Amer,69(1):1--15
Komatitsch D,Vilotte J P.1998.The spectral element method:An efficient tool to si mulate the seismic response of2Dand3D geological structures[J].Bull Seis Soc Amer,88(2):368--392.
Kosloff D,Baysal E.1982.Forward modeling by a Fourier method[J].Geophysics,47(10):1402--1412.
Mikhailenko B G.2000.Seismic modeling by the spectral-finite difference method[J].Phys Earth Planet Interi,119(1--2):133--147.
Mittet R.2002.Free-surface boundary conditions for elastic staggered-grid modeling schemes[J].Geophysics,67(5):1616--1623.
zdenvar T,Mc Mechan G A.1996.Causes and reduction of numerical artefacts in pseudo-spectral wavefield extrapola-tion[J].Geophys J Int,126(3):819--828.
Virieux J.1986.P-SV wave propagationin heterogeneous media:Velocity-stress finite-difference method[J].Geophys-ics,51(4):889--901.
Wang Y B,Takenaka H,Furumura T.2001.Modeling seismic wave propagationin a two-di mensional cylindrical whole-earth model using the pseudospectral method[J].Geophys J Int,145(3):689--708.
Witte D C,Richards P G.1990.The pseudospectral method for si mulating wave propagation[C]∥Lee D,Cakmak R,Vichnevetsky R eds.Computational Acoustics:Proceedings of the2nd IMACS Symposium on ComputationalAcoustics.North-Holland,New York:1--18.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心