基于MPI的三维瑞雷面波有限差分并行模拟
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摘要
三维地震波动方程数值求解对计算机的内存大小和运算速度都有很高的要求。采用基于消息传递接口(Message Passing Interface,MPI)的并行算法对三维空间的瑞雷面波进行了交错网格有限差分正演模拟。该算法将待模拟区域划分为若干个子区域,各个进程互相协同,并行完成各个子区域的数值模拟过程,从而达到扩大模型规模、加快模拟速度的目的。数值模拟过程中,采用声学-弹性界面法处理自由地表边界。利用均匀各向同性介质模型模拟所得的单道地震记录与解析解的对比结果和波场快照验证了算法的可行性和正确性;通过3层速度递增模型数值模拟所得波场记录的频散曲线与解析解对比,进一步验证了算法的有效性。
Numerical simulation of three-dimensional wave equation requires large computer memory and high calculation speed.Parallel algorithm based on Message Passing Interface(MPI) was adopted to simulate Rayleigh wave by using staggered-grid finite difference method.The model region to be simulated was divided into several sub-regions.Then all processors collaborate each other and the simulation in sub-regions is completed by each processor in parallel.Accordingly,the purposes of accelerate the computing speed and expand the scale of the model are achieved.Acoustic-elastic boundary approach was adopted to implement the traction-free boundary in the simulation.Feasibility and correctness of the simulation method were certificated by comparing the single-channel seismic records from the heterogeneous isotropic medium model obtained by numerical simulation with the results of analytical solution and the snapshots.The method is further verified by the comparison of dispersion curves derived from wave records and analytical solution of a three-layer velocity incremented model.
Numerical simulation of three-dimensional wave equation requires large computer memory and high calculation speed.Parallel algorithm based on Message Passing Interface(MPI) was adopted to simulate Rayleigh wave by using staggered-grid finite difference method.The model region to be simulated was divided into several sub-regions.Then all processors collaborate each other and the simulation in sub-regions is completed by each processor in parallel.Accordingly,the purposes of accelerate the computing speed and expand the scale of the model are achieved.Acoustic-elastic boundary approach was adopted to implement the traction-free boundary in the simulation.Feasibility and correctness of the simulation method were certificated by comparing the single-channel seismic records from the heterogeneous isotropic medium model obtained by numerical simulation with the results of analytical solution and the snapshots.The method is further verified by the comparison of dispersion curves derived from wave records and analytical solution of a three-layer velocity incremented model.
引文
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[17]巴特.地震学的数学问题[M].郑治真,译.北京:科学出版社,1976:229-234Bart M.Mathematical problem of seismology[M].Zhen Z Z,translator.Beijing:Science Press,1976:229-234
[18]凡友华,肖柏勋,刘家琦.计算层状介质中轴对称柱面瑞雷面波频散函数的δ矩阵法[J].物探与化探,2001,25(2):109-116Fan Y Y,Xiao B X,Liu J Q.Theδmatrix methodfor the dispersion function computation of axis sym-metrical cylindrical Rayleigh wave in multilayeredmedia[J].Geophysics&Geochemical Exploration,2001,25(2):109-116
[2]董良国,马在田,曹景忠,等.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):411-419Dong L G,Ma Z T,Cao J Z,et al.A staggered-gridhigh-order difference method of one-order elasticwave equation[J].Chinese Journal Geophysics,2000,43(3):411-419
[3]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问题[J].地球物理学报,2000,43(6):856-864Dong L G,Ma Z T,Cao J Z.A study on stability ofthe staggered-grid high-order difference method offirst-order elastic wave equation[J].Chinese JournalGeophysics,2000,43(6):856-864
[4]Igel H,Nissen-Meyer T,Jahnke G.Wave propaga-tion in 3Dspherical sections:effects of subductionzones[J].Physics of the Earth and Planetary Interi-ors,2002,132(1):219-234
[5]Peter M,Jozef K,Ladislav H.3Dfourth-order stag-gered-grid finite-difference schemes:stability andgrid dispersion[J].Bulletin of the Seismological So-ciety of America,2000,90(3):587-603
[6]熊章强.复杂介质中瑞雷面波的正演模拟及传播特征研究[D].武汉:中国地质大学(武汉),2006Xiong Z Q.Forward modeling and propagation char-acteristics research of Rayleigh wave in complexmedia[D].Wuhan:China University of Geosciences(Wuhan),2006
[7]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[J].地球物理学报,2007,50(2):567-573Zhou Z S,Liu X L,Xiong X Y.Finite-differencemodeling of Rayleigh surface wave in elastic media[J].Chinese Journal Geophysics,2007,50(2):567-573
[8]裴正林.三维各向同性介质弹性波方程交错网格高阶有限差分法模拟[J].石油物探,2005,44(4):308-315Pei Z L.Numerical simulation of elastic wave equa-tion in 3-D isotropic media with staggered-grid high-order difference method[J].Geophysical Prospectingfor Petroleum,2005,44(4):308-315
[9]Zahradník J,Priolo E.Heterogeneous formulationsof elastodynamic equations and finite-differenceschemes[J].Geophysical Journal International,1995,120:663-676
[10]Graves R W.Simulating seismic wave propagation in3Delastic media using staggered-grid finite differ-ences[J].Bulletin of the Seismological Society of A-merica,1996,86(4):1091-1106
[11]Mittet R.Free-surface boundary conditions for elas-tic staggered-grid modeling schemes[J].Geophys-ics,2002,67(5):1616-1623
[12]Xu Y X,Xia J H,Miller R D.Numerical investiga-tion of implementation of air-earth boundary by a-coustic-elastic boundary approach[J].Geophysics,2007,72(5):147-153
[13]王月英.基于MPI的的三维波动方程有限元法并行正演模拟[J].石油物探,2009,48(3):221-225Wang Y Y.3Dwave-equation finite-element forwardmodeling based on message passing interface parallelcomputing[J].Geophysical Prospecting for Petrole-um,2009,48(3):221-225
[14]Minkoff S E.Spatial parallelism of a 3Dfinite differ-ence velocity-stress elastic wave propagation code[J].SIAM Journal on Scientific Computing,2002,24(1):1-19
[15]何兵寿,张会星,韩令贺.弹性波方程正演的粗粒度并行算法[J].地球物理学进展,2010,25(2):650-656He B S,Zhang H X,Han L H.Forward modeling ofelastic wave equation with coarse-grained parallel al-gorithm[J].Progress in Geophysics,2010,25(2):650-656
[16]张林波,迟学斌,莫则尧,等.并行计算导论[M].北京:清华大学出版社,2006:175-182Zhang L B,Chi X B,Mo Z Y,et al.Introduction toparallel computing[M].Beijing:Tsinghua UniversityPress,2006:175-182
[17]巴特.地震学的数学问题[M].郑治真,译.北京:科学出版社,1976:229-234Bart M.Mathematical problem of seismology[M].Zhen Z Z,translator.Beijing:Science Press,1976:229-234
[18]凡友华,肖柏勋,刘家琦.计算层状介质中轴对称柱面瑞雷面波频散函数的δ矩阵法[J].物探与化探,2001,25(2):109-116Fan Y Y,Xiao B X,Liu J Q.Theδmatrix methodfor the dispersion function computation of axis sym-metrical cylindrical Rayleigh wave in multilayeredmedia[J].Geophysics&Geochemical Exploration,2001,25(2):109-116
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