弹性波方程正演的粗粒度并行算法
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摘要
波动方程正演在地震资料采集、处理、解释与反演中均能发挥重要作用,但现有的基于求解地震波动方程的正演算法由于受庞大计算量的制约而难于大规模应用于工业生产.本文从二维弹性波动方程出发,研究了利用有限差分法并行求解该方程的基本思路与方法,给出了适于并行求解的计算空间划分方法与通信方案,分析了不同参数条件下并行程序的运行时间、加速比与效率.引入消息传递接口(MPI)实现了弹性波方程的并行求解,极大地提高了数值求解弹性波方程的计算效率.
Wave equation forward modelling plays a significant role in seismic data acquisition,processing, interpretation and inversion.At present,however,forward modelling algorithms based on the seismic wave-equation are restrained in large-scale industrial application because of their massive computational cost.This article studies the basic methods for solving the 2D elastic wave-equation with finite difference and parallel algorithms,and gives the computation domain division method and communication scheme that are suitable for the parallel algorithm.Also,the article analyzes the difference of the computation time cost,the speedup ratio and efficiency of the parallel programs under different parameters.Numerical experiments realized the parallel solution of elastic wave-equation with Message Passing Interface (MPI),and show that the introduction of MPI greatly improves the computation efficiency.
Wave equation forward modelling plays a significant role in seismic data acquisition,processing, interpretation and inversion.At present,however,forward modelling algorithms based on the seismic wave-equation are restrained in large-scale industrial application because of their massive computational cost.This article studies the basic methods for solving the 2D elastic wave-equation with finite difference and parallel algorithms,and gives the computation domain division method and communication scheme that are suitable for the parallel algorithm.Also,the article analyzes the difference of the computation time cost,the speedup ratio and efficiency of the parallel programs under different parameters.Numerical experiments realized the parallel solution of elastic wave-equation with Message Passing Interface (MPI),and show that the introduction of MPI greatly improves the computation efficiency.
引文
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[15] 都志辉.高性能计算并行编程技术--MEI并行程序设计[M].北京:清华大学出版社,2001． Du Z H.High-performance computing parallel programming technology-MPI parallel programming [M].Beijing:Tsinghua University Press,2001．
[16] Berfenger J P.A perfectly matched layer for the absorption of electromagnetics waves [J].Journal Computation Physics,1994,114(2) : 185～200．
[17] 张剑锋,刘书.弹性波混合差分解法的透射边界条件[J].固体力学学报,1997,18(4) :341～346． Zhang J F,Liu S.Transmission boundary condition for mixed variable finite-difference method[J].Chinese Journal of Solid Mechanics,1997,18(4) :341～346．
[18] 董良国.弹性波数值模拟中的吸收边界条件[J].石油地球物理勘探,1999,34(1) :45～56． Dong L G.Absorptive boundary condition in elastic-wave numerical modeling[J].OGP,1999,34(1) :45～56．
[19] 徐义,张剑锋.地震波数值模拟的非规则网格PML吸收边界[J].地球物理学报,2008,51(5) :1520～1526Xu Y,Zhang J F.An irregular-grid perfectly matched layer absorbing boundary for seismic wave modeling[J].Chinese J.Geophys.(in Chinese),2008,51(5) :1520～1526
[20] Martin G S.Marmousi2． An elastic upgrade for Marmousi[J].The leading edge,2006,156～166．
[2] 井西利,杨长春,王世清.一种改进的地震反射层析成像方法 [J].地球物理学报,2007,50(6) :1831～1836． Jing X L,Yang C C,Wang S Q.A improved seismic reflection tomographic method[J].Chinese J.Geophys.(in Chinese),2007,50(6) : 1831～1836．
[3] 曹志勇,杨德义.陷落柱的高斯射线束法模拟[J].中国煤炭地质,2008,20(6) :63～65,69． Cao Z Y,Yang D Y.Modeling of subsided column with Gaussian beam method[J].Coal Geology of China,2008,20 (6) :63～65,69．
[4] 张赛民,周竹生,陈灵君,等.对旅行时进行抛物型插值的地震射线追踪方法[J].地球物理学进展,2007,22(1) :43～48． Zhang S M,Zhou Z S,Chen L J,etal.Seismic ray-tracing method of applying parabolic Interpolation to travel-time[J].Progress in Geophysics(in Chinese),2007,22(1) :43～48．
[5] 王童奎,张美根,李小凡,等.PS转换波界面二次源法射线追踪[J].地球物理学进展,2007,22(1) :165～170． Wang T K,Zhang M G,Li X F,et al.Interface points as secondary sources method raytracing PS converted waves[J].Progress in Geophysics(in Chinese),2007,22(1) :165～170．
[6] 井涌泉,高红伟,王续红.二维各向同性介质P波和S波分离方法研究[J].地球物理学进展,2008,23(5) :1412～1416． Jing Y Q,Gao H W,Wang W H.The study of P-waves and S-waves separation in two-dimensional isotropic media [J].Progress in Geophysics(in Chinese),2008,23(5) : 1412～1416．
[7] 孙卫涛,杨慧珠.各向异性介质弹性波传播的三维不规则网格有限差分方法[J].地球物理学报,2004,47(2) :332～337． Sun W T,Yang H Z.A 3-D finite difference method using irregular grids for elastic wave propagation in anisotropic media [J].Chinese J.Geophys.(in Chinese),2004,47(2) : 332～337．
[8] 张会星,何兵寿,张晶,等.复杂各向异性介质中的地震波场有限差分模拟[J].煤炭学报,2008,33(11) :1257～1262。ZhangH X,He B S,Zhang J,etal.Forward modeling of seismic wave fields in complex anisotropic media using finite difference method[J].Journal of China Coal Society,2008,33(11) :1257～1262．
[9] 孙银行.弱各向异性介质弹性波的准各向同性近似正演模拟[J].地球物理学进展,2008,23(4) :1118～1123． Sun Y H.Elastic wave forward modeling with quasi-isotropic approximation in weakly anisotropic medium[J].Progress in Geophysics(in Chinese),2008,23(4) :1118～1123．
[10] 郭桂红,石双虎,剡慧君,等.基于二维三分量伪谱法模拟数据的EDA介质中横波分裂研究[J].地球物理学报,2008,51(2) :469～478． Guo G H,Shi S H,Yan H J,etal.Azimuth-dependence of shear-wave splitting in EDA media: Two-dimensional three-component pseudo-spectral modeling [J].Chinese J.Geophys.(in Chinese),2008,51(2) :469～478．
[11] 董良国,马在田,曹景钟,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) :411～419． Dong L G,Ma Z T,Cao J Z,et al.A staggered high-order difference method of one-order elastic wave equation [J].Chinese J.Geophys.(in Chinese),2000,43(3) :411～419．
[12] 牟永光,裴正林.三维复杂介质地震数值模拟[M].北京:石工业出版社,2005． Mu Y G,Pei Z L.Seismic numerical modeling for 3-D complex media [M].Beijing: Petroleum Industry Press,2005．
[13] 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[J].地球物理学进展,2007,22(2) :522～529． Xue D C,Wang S X,Jiao S J.Wave equation finite-element modeling including rugged topography and complicated medium[J].Progress in Geophysics(in Chinese),2007,22(2) :522～529．
[14] 王若,王妙月,卢元林.三维三分量CSAMT法有限元正演模拟研究初探[J].地球物理学进展,2007,22(2) :579～585． Wang R,Wang M Y,Lu Y L.Preliminary study on 3D3C CSAMT method modeling using finite element method [J].Progress in Geophysics(in Chinese),2007,22(2) :579～585．
[15] 都志辉.高性能计算并行编程技术--MEI并行程序设计[M].北京:清华大学出版社,2001． Du Z H.High-performance computing parallel programming technology-MPI parallel programming [M].Beijing:Tsinghua University Press,2001．
[16] Berfenger J P.A perfectly matched layer for the absorption of electromagnetics waves [J].Journal Computation Physics,1994,114(2) : 185～200．
[17] 张剑锋,刘书.弹性波混合差分解法的透射边界条件[J].固体力学学报,1997,18(4) :341～346． Zhang J F,Liu S.Transmission boundary condition for mixed variable finite-difference method[J].Chinese Journal of Solid Mechanics,1997,18(4) :341～346．
[18] 董良国.弹性波数值模拟中的吸收边界条件[J].石油地球物理勘探,1999,34(1) :45～56． Dong L G.Absorptive boundary condition in elastic-wave numerical modeling[J].OGP,1999,34(1) :45～56．
[19] 徐义,张剑锋.地震波数值模拟的非规则网格PML吸收边界[J].地球物理学报,2008,51(5) :1520～1526Xu Y,Zhang J F.An irregular-grid perfectly matched layer absorbing boundary for seismic wave modeling[J].Chinese J.Geophys.(in Chinese),2008,51(5) :1520～1526
[20] Martin G S.Marmousi2． An elastic upgrade for Marmousi[J].The leading edge,2006,156～166．