基于离散粒子理论地震波传播数值模拟网格剖分计算方法
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摘要
介绍一种基于离散粒子理论地震波传播数值模拟的网格剖分计算方法.根据离散粒子理论,将研究区域划分为由一系列相互作用的粒子组成的正六边形网格,这些粒子在它们的接触点处发生相互作用,并用Hooke定律和Newton定律描述.为解决六边形网格带来的网格交错而难以计算以及波场输出问题,将横向网格进行加密,加密处赋予假想的粒子,输出波场时选取偶数行偶数列点或奇数行奇数列点的波场值.均匀介质和层状介质模型的数值模拟结果表明,该网格剖分计算方法能够将离散粒子理论用于模拟弹性波在非均匀各向同性介质中地震波的传播.
A mesh generation calculation method based on discrete particle scheme for numerical modeling seismic waves is presented.According to the discrete particle theory,the study area can be divided into regular hexagon grid composed of a series of interacting particles.These particles interact at their contact points and the motion of particles in space is described by Hook's Law and Newton's Law.To solve the problem of the grid crisscross brought by hexagon grids which may lead to difficulty in calculation and output wave field's value,we encrypt the imaginary particles at the horizontal grids and output the wave field value of the even lines' points in the even column or odd lines' points in odd column.The numerical simulation results of homogeneous model and layer model proved that this mesh generation calculation method based on discrete particle theory is capable of modeling the propagation of elastic waves through heterogeneous isotropic media.
A mesh generation calculation method based on discrete particle scheme for numerical modeling seismic waves is presented.According to the discrete particle theory,the study area can be divided into regular hexagon grid composed of a series of interacting particles.These particles interact at their contact points and the motion of particles in space is described by Hook's Law and Newton's Law.To solve the problem of the grid crisscross brought by hexagon grids which may lead to difficulty in calculation and output wave field's value,we encrypt the imaginary particles at the horizontal grids and output the wave field value of the even lines' points in the even column or odd lines' points in odd column.The numerical simulation results of homogeneous model and layer model proved that this mesh generation calculation method based on discrete particle theory is capable of modeling the propagation of elastic waves through heterogeneous isotropic media.
引文
[1]裴正林,牟永光.地震波传播数值模拟[J].地球物理学进展,2004,19(4):933-941.Pei Z L,Mu Y G.Numerical simulation of seismic wavepropagation[J].Progress in Geophysics(in Chinese),2004,19(4):933-941.
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[3]Toomey A,Bean C J.Numerical simulation of seismic wavesusing a discrete particle scheme[J].Geophys.J.Int.,2002,141(3):595-604.
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[5]姚姚.细胞自动机方法地震正演模拟[J].石油地球物理勘探,1995,30(2):216-223.Yao Y.Forward seismic modeling by cellular automatonmethod[J].OGP(in Chinese),1995,30(2):216-223.
[6]李幼铭,胡健行.细胞自动机在地震波传播研究中的应用[J].地球物理学报,1995,38(5):651-661.Li Y M,Hu J X.Application of cellular automata approach tothe study of seismic wave propagation[J].Chinese J.Geophys.(in Chinese),1995,38(5):651-661.
[7]胡健行,李幼铭.模拟固体中波动过程的细胞自动机建模研究[J].地球物理学报,1997,40(1):120-126.Hu J X,Li Y M.A study of the cellular automata modellingfor P wave propagation in complex media[J].Chinese J.Geophys.(in Chinese),1997,40(1):120-126.
[8]赵雪平,杨宝俊.固体介质中弹性波传播机制的细胞自动机有限深势阱模型[J].地球物理学进展,2002,17(3):390-398,405.Zhao X P,Yang B J.CA’s finite deep potential trough modelof the elastic wave propagational mechanism in solid medium[J].Progress in Geophysics(in Chinese),2002,17(3):390-398,405.
[9]刘劲松,许云,乌达巴拉,等.细胞自动机用于地震偏移:数值模拟试验[J].地球物理学进展,2004,19(3):621-624.Liu J S,Xu Y,Wudabala,et al.Numerical experiment ofseismic migration using cellular automata[J].Progress inGeophysics(in Chinese),2004,19(3):621-624.
[10]Rothman D H.Modeling seismic P-waves with cellullar automata[J].Geophys.Res.Lett.,1987,14(1):17-20.
[11]Huang T I,Chu Y H,Yin C S.Lattice-gas automata formodeling acoustic wave propagation in inhomogeneous media[J].Geophys.Res Lett.,1988,15(11):1239-1241.
[12]刘舒考,刘雯林,郑晓东.格子气自动机模型—一种地震数据正演研究的新方法[J].石油地球物理勘探,1998,33(5):658-663.Liu S K,Liu W L,Zheng X D.Lattice gas automata model-A new method for seismic data forward simulation[J].OGP(in Chinese),1998,33(5):658-663.
[13]Mora P.The lattice boltzmann phononic lattice solid[J].Journal of Statistical Physics,1992,68(3-4):591-609.
[14]Huang L J,Mora P.The phononic lattice solid by interpolationfor modeling P-waves in heterogeneous media[J].Geophys.J.Internat.,1994,119(2):766-778.
[15]刘劲松,许云,乌达巴拉.用于地震波场模拟的变网格边长声格固体模型[J].地球物理学报,1999,42(4):536-542.Liu J S,Xu Y,Wudababla.Phononic lattice solid withvarious grid length for modeling seismic waves[J].ChineseJ.Geophys.(in Chinese),1999,42(4):536-542.
[16]刘劲松,许云,乌达巴拉.声格固体模型地震波场模拟[J].石油地球物理勘探,1997,32(3):370-376.Liu J S,Xu Y,Wudabala.Seismic wave field simulationusing phononic lattice solid model[J].OGP(in Chinese),1997,32(3):370-376.
[17]刘劲松,许云,乌达巴拉.声格固体模型插值算法的稳定性研究[J].物探与化探,1997,21(2):99-103.Liu J S,Xu Y,Wudabala.A study of the stability ofphononic lattics solid interpolation method[J].Geophysicaland Geochemical Exploration(in Chinese),1997,21(2):99-103.
[18]刘劲松,许云,乌达巴拉.用于地震波场模拟的变网格边长声格固体模型[J].地球物理学报,1999,42(4):536-542.Liu J S,Xu Y,Wudabala.Phononic lattice solid with variousgrid length for modeling seismic waves[J].Chinese J.Geophys.(in Chinese),1999,42(4):536-542.
[19]董桥梁,周玉冰,姚姚.格子Boltzmann方法地震波场模拟[J].中国科学—中国地质大学学报,1997,22(6):638-642.Dong Q L,Zhou Y B,Yao Y.Seismic simulating by usinglattice Boltzmann method[J].Earth Science-Journal of ChinaUniversity of Geosciences(in Chinese),1997,22(6):638-642.
[20]Hoover W G,Arhurst W T,Olness R J.Two-dimensionalcomputer studies of crystal stability and fluid viscosity[J].J.Chem.Phys.,1974,60(10):4043-4047.
[21]王真理,李幼铭.细胞自动机地震波模拟的并行化算法[J].地球物理学报,1999,42(3):410-415.Wang Z L,Li Y M.Parallel algorithm for simulating seismicwave propagation by cellular automata[J].Chinese J.Geophys.(in Chinese),1999,42(3):410-415.
[2]张永刚.地震波场数值模拟方法[J].石油物探,2003,42(2):143-148.Zhang Y G.On numerical simulations of seismic wavefield[J].Geophysical Prospecting for Petroleum(in Chinese),2003,42(2):143-148.
[3]Toomey A,Bean C J.Numerical simulation of seismic wavesusing a discrete particle scheme[J].Geophys.J.Int.,2002,141(3):595-604.
[4]Wolfram S.Theory and Applications of Cellular Automata[M].Singapore:World Scientific Publishing Co.Pte.Ltd,1986.
[5]姚姚.细胞自动机方法地震正演模拟[J].石油地球物理勘探,1995,30(2):216-223.Yao Y.Forward seismic modeling by cellular automatonmethod[J].OGP(in Chinese),1995,30(2):216-223.
[6]李幼铭,胡健行.细胞自动机在地震波传播研究中的应用[J].地球物理学报,1995,38(5):651-661.Li Y M,Hu J X.Application of cellular automata approach tothe study of seismic wave propagation[J].Chinese J.Geophys.(in Chinese),1995,38(5):651-661.
[7]胡健行,李幼铭.模拟固体中波动过程的细胞自动机建模研究[J].地球物理学报,1997,40(1):120-126.Hu J X,Li Y M.A study of the cellular automata modellingfor P wave propagation in complex media[J].Chinese J.Geophys.(in Chinese),1997,40(1):120-126.
[8]赵雪平,杨宝俊.固体介质中弹性波传播机制的细胞自动机有限深势阱模型[J].地球物理学进展,2002,17(3):390-398,405.Zhao X P,Yang B J.CA’s finite deep potential trough modelof the elastic wave propagational mechanism in solid medium[J].Progress in Geophysics(in Chinese),2002,17(3):390-398,405.
[9]刘劲松,许云,乌达巴拉,等.细胞自动机用于地震偏移:数值模拟试验[J].地球物理学进展,2004,19(3):621-624.Liu J S,Xu Y,Wudabala,et al.Numerical experiment ofseismic migration using cellular automata[J].Progress inGeophysics(in Chinese),2004,19(3):621-624.
[10]Rothman D H.Modeling seismic P-waves with cellullar automata[J].Geophys.Res.Lett.,1987,14(1):17-20.
[11]Huang T I,Chu Y H,Yin C S.Lattice-gas automata formodeling acoustic wave propagation in inhomogeneous media[J].Geophys.Res Lett.,1988,15(11):1239-1241.
[12]刘舒考,刘雯林,郑晓东.格子气自动机模型—一种地震数据正演研究的新方法[J].石油地球物理勘探,1998,33(5):658-663.Liu S K,Liu W L,Zheng X D.Lattice gas automata model-A new method for seismic data forward simulation[J].OGP(in Chinese),1998,33(5):658-663.
[13]Mora P.The lattice boltzmann phononic lattice solid[J].Journal of Statistical Physics,1992,68(3-4):591-609.
[14]Huang L J,Mora P.The phononic lattice solid by interpolationfor modeling P-waves in heterogeneous media[J].Geophys.J.Internat.,1994,119(2):766-778.
[15]刘劲松,许云,乌达巴拉.用于地震波场模拟的变网格边长声格固体模型[J].地球物理学报,1999,42(4):536-542.Liu J S,Xu Y,Wudababla.Phononic lattice solid withvarious grid length for modeling seismic waves[J].ChineseJ.Geophys.(in Chinese),1999,42(4):536-542.
[16]刘劲松,许云,乌达巴拉.声格固体模型地震波场模拟[J].石油地球物理勘探,1997,32(3):370-376.Liu J S,Xu Y,Wudabala.Seismic wave field simulationusing phononic lattice solid model[J].OGP(in Chinese),1997,32(3):370-376.
[17]刘劲松,许云,乌达巴拉.声格固体模型插值算法的稳定性研究[J].物探与化探,1997,21(2):99-103.Liu J S,Xu Y,Wudabala.A study of the stability ofphononic lattics solid interpolation method[J].Geophysicaland Geochemical Exploration(in Chinese),1997,21(2):99-103.
[18]刘劲松,许云,乌达巴拉.用于地震波场模拟的变网格边长声格固体模型[J].地球物理学报,1999,42(4):536-542.Liu J S,Xu Y,Wudabala.Phononic lattice solid with variousgrid length for modeling seismic waves[J].Chinese J.Geophys.(in Chinese),1999,42(4):536-542.
[19]董桥梁,周玉冰,姚姚.格子Boltzmann方法地震波场模拟[J].中国科学—中国地质大学学报,1997,22(6):638-642.Dong Q L,Zhou Y B,Yao Y.Seismic simulating by usinglattice Boltzmann method[J].Earth Science-Journal of ChinaUniversity of Geosciences(in Chinese),1997,22(6):638-642.
[20]Hoover W G,Arhurst W T,Olness R J.Two-dimensionalcomputer studies of crystal stability and fluid viscosity[J].J.Chem.Phys.,1974,60(10):4043-4047.
[21]王真理,李幼铭.细胞自动机地震波模拟的并行化算法[J].地球物理学报,1999,42(3):410-415.Wang Z L,Li Y M.Parallel algorithm for simulating seismicwave propagation by cellular automata[J].Chinese J.Geophys.(in Chinese),1999,42(3):410-415.
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