地震波传播的三维伪谱和高阶有限差分混合方法并行模拟
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摘要
基于交错网格伪谱法和高阶精度有限差分方法,发展了模拟非均匀介质地震波传播的三维伪谱和有限差分混合算法.该方法在两个水平方向利用交错网格伪谱算子计算空间微分,保留了该方法高效、高精度的优势,在垂直方向采用交错网格高阶精度有限差分算子实现空间微分计算.利用有限差分方法的局部性特征,将三维计算区域在垂直方向上划分为一系列子区域,并分配给不同的处理器,实现了在并行计算机集群上的三维并行计算.通过模拟算例,与离散波数法比较,检验了该算法的精度.为了检验该方法的实用性,在64个处理器上,对三维沉积盆地模型进行了67108864个网格点的并行计算,模拟的波场主频率为1.25Hz,讨论了沉积盆地深度对三维沉积盆地地面运动的影响.
Based on the pseudospectral method(PSM) and higher-order finite difference method(FDM) for staggered grid,this paper presents a 3D parallel hybrid PSM/FDM scheme to simulate seismic wave propagation in heterogeneous medium.The spatial derivatives in the wave equations for the two horizontal directions are calculated with the efficient and high accuracy PSM operator,while the vertical derivatives are calculated with a high-order FDM operator.The localized FDM operation in vertical direction enables us to divide the 3D model into subregions,which are assigned to different processors of a PC cluster for 3D parallel computation.The accuracy of this scheme was verified by comparing our result with that of using discrete wave number method.To show the feasibility of the parallel scheme,we performed parallel simulation for a 3D sedimentary basin to show the effect of basin depth on ground motion.The simulation is carried out on PC cluster with 64 processors for a 67108864 grids model.The dominated frequency for the simulated seismic wavefield is 1.25 Hz.
Based on the pseudospectral method(PSM) and higher-order finite difference method(FDM) for staggered grid,this paper presents a 3D parallel hybrid PSM/FDM scheme to simulate seismic wave propagation in heterogeneous medium.The spatial derivatives in the wave equations for the two horizontal directions are calculated with the efficient and high accuracy PSM operator,while the vertical derivatives are calculated with a high-order FDM operator.The localized FDM operation in vertical direction enables us to divide the 3D model into subregions,which are assigned to different processors of a PC cluster for 3D parallel computation.The accuracy of this scheme was verified by comparing our result with that of using discrete wave number method.To show the feasibility of the parallel scheme,we performed parallel simulation for a 3D sedimentary basin to show the effect of basin depth on ground motion.The simulation is carried out on PC cluster with 64 processors for a 67108864 grids model.The dominated frequency for the simulated seismic wavefield is 1.25 Hz.
引文
高孟潭,俞言祥,张晓梅,吴健,胡平,丁彦慧.2002.北京地区地震动的三维有限差分模拟[J].中国地震,18(4):356-364.
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.
魏星,王彦宾,陈晓非.2010.模拟地震波场的伪谱和高阶有限差分混合方法[J].地震学报,32(4):392-400.
严九鹏,王彦宾.2008.重叠区域伪谱法计算非均匀介质地震波传播[J].地震学报,30(1):47-58.
严珍珍,张怀,杨长春,石耀霖.2009.汶川大地震地震波传播的谱元法数值模拟研究[J].中国科学:D辑,39(4):393-402.
张冬丽,张伟,徐锡伟,柴炽章,张献兵.2009.断层破裂方式对银川盆地强地面运动的影响[J].地震工程与工程振动,29(4):1-8.
张怀,周元泽,吴忠良,严珍珍,陈石,景惠敏,徐锡伟,石耀霖.2009.福州盆地强地面运动特征的有限元数值模拟[J].地球物理学报,52(5):1270-1279.
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,廊坂安彦,棍川昌三.2003b.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(4):705-708.
Daudt C R,Braile L W,Nowack R L,Chiang C S.1989.A comparison of finite-difference and Fourier method calcula-tions of synthetic seismograms[J].Bull Seism Soc Amer,79(4):1210-1230.
Frankel A,Stephenson W,Carver D.2009.Sedimentary basin effects in Seattle,Washington:Ground-motion observa-tions and3Dsimulations[J].Bull Seism Soc Amer,99(3):1579-1611.
Fornberg B.1987.The pseudospectral method:Comparisons with finite-differences for the elastic wave equations[J].Geophysics,52(4):483-501.
Furumura T,Koketsu K,Wen K L.2002.Parallel PSM/FDM hybrid simulation of ground motions from the1999Chi-Chi,Taiwan,earthquake[J].Pure Appl Geophys,159(9):2133-2146.
Ge Z X.2010.Simulation of the seismic response of sedimentary basins with constant-gradient velocity along arbitrary di-rection using boundary element method:SH case[J].Earthq Sci,23(2):149-155.
Hartzell S,Harmsen S,Williams R A,Carver D,Frankel A,Choy G,Liu P C,Jachens R C,Brocher T M,WentworthC M.2006.Modeling and validation of a3Dvelocity structure for the Santa Clara Valley,California,for seismic-wave simulations[J].Bull Seis Soc Amer,96(5):1851-1881.
Herrmann R B.1979.SH-wave generation by dislocation source:A numerical study[J].Bull Seism Soc Amer,69(1):1-15.
Koketsu K,Hatayama K,Furumura T,Ikegami Y,Akiyama S.2005.Damaging long-period ground motions from the2003MW8.3Tokachi-oki,Japan earthquake[J].Seismological Research Letters,76(1):67-73.
Kosloff D,Reshef M,Loewenthal D.1984.Elastic wave calculation by the Fourier method[J].Bull Seism Soc Amer,74:875-891.
Levander A R.1988.Fourth-order finite-difference P-5Vseismograms[J].Geophysics,53(11):1425-1436.
zdenva T,McMechan G A.1996.Causes and reduction of numerical artifacts in pseudo spectral wavefield extrapolation[J].Geophys J Int,126(3):819-828.
Sánches-Sesma F J,Pérez-Rocha L E,Reinoso E.1993.Ground motion in Mexico city during the April25,1989,Guer-rero earthquake[J].Tectonophysics,218(1-3):127-140.
Tromp J.2007.Forward modeling and synthetic seismograms:3Dnumerical methods∥Romanowicz B,Dziewonski Aeds.Treatise on Geophysicseditors.Elsevier:191-217.
Virieux J.1986.P-SV wave propagation in heterogeneous media:Velocity-stress finite-difference method[J].Geophys-ics,51(4):889-901.
Wang Y,Takenaka H,Furumura T.2000.Effect of vertical velocity gradient on ground motion in a sediment-filled basindue to incident SV wave[J].Earth Planets Space,52(1):13-24.
Witte D C,Richards P G.1990.The pseudospectral method for simulating wave propagation[J].Computational Acous-tics,3:1-18.
Zhang W,Shen Y,Chen X F.2008.Numerical simulation of strong ground motion for the MS8.0Wenchuan earthquakeof12May2008[J].Science in China:Series D,51(12):1673-1682.
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.
魏星,王彦宾,陈晓非.2010.模拟地震波场的伪谱和高阶有限差分混合方法[J].地震学报,32(4):392-400.
严九鹏,王彦宾.2008.重叠区域伪谱法计算非均匀介质地震波传播[J].地震学报,30(1):47-58.
严珍珍,张怀,杨长春,石耀霖.2009.汶川大地震地震波传播的谱元法数值模拟研究[J].中国科学:D辑,39(4):393-402.
张冬丽,张伟,徐锡伟,柴炽章,张献兵.2009.断层破裂方式对银川盆地强地面运动的影响[J].地震工程与工程振动,29(4):1-8.
张怀,周元泽,吴忠良,严珍珍,陈石,景惠敏,徐锡伟,石耀霖.2009.福州盆地强地面运动特征的有限元数值模拟[J].地球物理学报,52(5):1270-1279.
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,廊坂安彦,棍川昌三.2003b.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(4):705-708.
Daudt C R,Braile L W,Nowack R L,Chiang C S.1989.A comparison of finite-difference and Fourier method calcula-tions of synthetic seismograms[J].Bull Seism Soc Amer,79(4):1210-1230.
Frankel A,Stephenson W,Carver D.2009.Sedimentary basin effects in Seattle,Washington:Ground-motion observa-tions and3Dsimulations[J].Bull Seism Soc Amer,99(3):1579-1611.
Fornberg B.1987.The pseudospectral method:Comparisons with finite-differences for the elastic wave equations[J].Geophysics,52(4):483-501.
Furumura T,Koketsu K,Wen K L.2002.Parallel PSM/FDM hybrid simulation of ground motions from the1999Chi-Chi,Taiwan,earthquake[J].Pure Appl Geophys,159(9):2133-2146.
Ge Z X.2010.Simulation of the seismic response of sedimentary basins with constant-gradient velocity along arbitrary di-rection using boundary element method:SH case[J].Earthq Sci,23(2):149-155.
Hartzell S,Harmsen S,Williams R A,Carver D,Frankel A,Choy G,Liu P C,Jachens R C,Brocher T M,WentworthC M.2006.Modeling and validation of a3Dvelocity structure for the Santa Clara Valley,California,for seismic-wave simulations[J].Bull Seis Soc Amer,96(5):1851-1881.
Herrmann R B.1979.SH-wave generation by dislocation source:A numerical study[J].Bull Seism Soc Amer,69(1):1-15.
Koketsu K,Hatayama K,Furumura T,Ikegami Y,Akiyama S.2005.Damaging long-period ground motions from the2003MW8.3Tokachi-oki,Japan earthquake[J].Seismological Research Letters,76(1):67-73.
Kosloff D,Reshef M,Loewenthal D.1984.Elastic wave calculation by the Fourier method[J].Bull Seism Soc Amer,74:875-891.
Levander A R.1988.Fourth-order finite-difference P-5Vseismograms[J].Geophysics,53(11):1425-1436.
zdenva T,McMechan G A.1996.Causes and reduction of numerical artifacts in pseudo spectral wavefield extrapolation[J].Geophys J Int,126(3):819-828.
Sánches-Sesma F J,Pérez-Rocha L E,Reinoso E.1993.Ground motion in Mexico city during the April25,1989,Guer-rero earthquake[J].Tectonophysics,218(1-3):127-140.
Tromp J.2007.Forward modeling and synthetic seismograms:3Dnumerical methods∥Romanowicz B,Dziewonski Aeds.Treatise on Geophysicseditors.Elsevier:191-217.
Virieux J.1986.P-SV wave propagation in heterogeneous media:Velocity-stress finite-difference method[J].Geophys-ics,51(4):889-901.
Wang Y,Takenaka H,Furumura T.2000.Effect of vertical velocity gradient on ground motion in a sediment-filled basindue to incident SV wave[J].Earth Planets Space,52(1):13-24.
Witte D C,Richards P G.1990.The pseudospectral method for simulating wave propagation[J].Computational Acous-tics,3:1-18.
Zhang W,Shen Y,Chen X F.2008.Numerical simulation of strong ground motion for the MS8.0Wenchuan earthquakeof12May2008[J].Science in China:Series D,51(12):1673-1682.
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