基于CFS-CPML边界处理的LOVE面波有限差分模拟
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摘要
建立近地表横波速度模型时通常需要用到面波分析的方法.Love面波是在低速层分界面附近传播的一种SH型不均匀平面波,本文利用高阶有限差分算子、合理的自由地表边界条件以及CFS-CPML吸收边界条件,获得了高精度的Love面波波场记录,并与传统的分裂式完全匹配层得到的波场记录作对比,体现了CFS-CPML吸收边界条件的优越性.在此基础上将数值模拟提取的频散特征与理论的频散特征进行对比,证明二者非常吻合,验证了Love面波有限差分模拟的精度很高,可以用来研究复杂情形下的Love面波频散特征,并分析了Love面波位移应力等一系列正演特征.
Surface wave analysis is usually used to build the shear-wave velocity model of near surface.Love wave is a kind of inhomogeneous plane waves of SH type which propagates near interface with low velocity layer.The thesis obtains highresolution Love wave field records replying high order finite difference operator,proper free surface boundary condition and CFS-CPML absorbing boundary condition.It reflects the superiority of CFS-CPML absorbing boundary condition after comparing with wave field records obtained by traditional split perfectly matched layer.On this basis it proves that the dispersion characteristics extracted by numerical simulation fit well with theoretical ones.So the high precision of Love wave finite difference simulation can be confirmed and the method can be used to study the dispersion characteristics of Love wave in complex cases.This paper also analyses a series of forward modeling characteristics of Love wave,like displacement,stress and so forth.
Surface wave analysis is usually used to build the shear-wave velocity model of near surface.Love wave is a kind of inhomogeneous plane waves of SH type which propagates near interface with low velocity layer.The thesis obtains highresolution Love wave field records replying high order finite difference operator,proper free surface boundary condition and CFS-CPML absorbing boundary condition.It reflects the superiority of CFS-CPML absorbing boundary condition after comparing with wave field records obtained by traditional split perfectly matched layer.On this basis it proves that the dispersion characteristics extracted by numerical simulation fit well with theoretical ones.So the high precision of Love wave finite difference simulation can be confirmed and the method can be used to study the dispersion characteristics of Love wave in complex cases.This paper also analyses a series of forward modeling characteristics of Love wave,like displacement,stress and so forth.
引文
Berenger J P.1994.A perfectly matched layer for the absorption of electromagnetic waves[J].J.Comp.Phys.,114(2):185-200.
Chen X F.1993.A systematic and efficient method of computing normal modes for multilayered half-space[J].Geophysical Journal International,115(2):391-409.
Chew W C,Liu Q H.1996.Perfectly matched layers for elastodynamics:a new absorbing boundary condition[J].J.Comp.Acous.,4(4):341.
Collino F,Tsogka C.2001.Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media[J].Geophysics,68(1):294-307.
Drossaert F H,Giannopoulos A.2007.Complex frequency shifted convolution PML for FDTD modelling of elastic waves[J].Wave Motion,44(7-8):593-604.
Drossaert F H,Giannopoulos A.2007.A nonsplit complex frequency-shifted PML based on recursive integration for FDTDmodeling of elastic waves[J].Geophysics,72(2):T9-T17.
Du S T.1996.Seismic Waves Dynamics Theory and Methods(in Chinese)[M].Dongying:University of Petroleum Press,108-110.
Fang G,Fomel S,Du Q Z.2014.Lowrank finite difference on a staggered grid and its application on reverse time migration[J].Journal of China University of Petroleum(in Chinese),38(2):44-51.
Hastings F D,Schneider J B,Broschat S L.1996.Application of the perfectly matched layer(PML)absorbing boundary condition to elastic wave propagation[J].J.Acoust.Soc.Am.,100(5):3061-3069.
Kuzuoglu M,Mittra R.1996.Frequency dependence of the constitutive parameters of causal perfectly matched anisotropic absorbers[J].IEEE Microwave and Guided Wave Letters,6(12):447-449.
Lu J M,Wang Y G.2011.The Principle of Seismic Exploration(in Chinese)[M].Dongying:China University of Petroleum Press,77-83.
Luo Y H,Xia J H,Xu Y X,et al.2010.Finite-difference modeling and dispersion analysis of high-frequency Love waves for nearsurface applications[J].Pure and Applied Geophysics,167(12):1525-1536.
Pei Z L.2006.A staggered-grid high-order finite difference method for modeling elastic wave equation in 3-D dual-phase anisotropic media[J].Journal of China University of Petroleum(in Chinese),30(2):16-20.
Qin Z,Zhang C,Zheng X D,et al.2010.High precision finite difference Rayleigh wave simulation and frequency dispersion characteristics extraction[J].Oil Geophysical Prospecting(in Chinese),45(1):40-46.
Sun C Y,Zhang L.2012.An exact solution for 2-D Lamb problem of arbitrary direction source[J].Chinese Journal of Geophysics(in Chinese),55(10):3370-3378,doi:10.6038/j.issn.0001-5733.2012.10.019.
Virieux J.1984.SH-wave propagation in heterogeneous media:velocity-stress finite-difference method[J].Geophysics,49(11):1933-1942.
Wang T,Tang X M.2003.Finite-difference modeling of elastic wave propagation:a nonsplitting perfectly matched layer approach[J].Geophysics,68(5):1749-1755.
Xiao Y F.2010.Wavefield analysis-oriented wave equation finite difference forward modeling(in Chinese)[Master thesis].Qingdao:China University of Petroleum.
Yang Y.2009.The research on two-dimensional finite-difference seismic wave field numerical simulation(in Chinese)[Master thesis].Beijing:China University of Geosciences(Beijing).
Zhou X H,Chen Z B,Zeng X X,et al.2012.Simulation of microtremor using staggered-grid finite difference method[J].Journal of Jilin University(Earth Science Edition)(in Chinese),42(3):852-857.
杜世通.1996.地震波动力学[M].东营:石油大学出版社,108-110.
方刚,Fomel S,杜启振.2014.交错网格Lowrank有限差分及其在逆时偏移中的应用[J].中国石油大学学报(自然科学版),38(2):44-51.
陆基孟,王永刚.2011.地震勘探原理[M].东营:中国石油大学出版社,77-83.
裴正林.2006.三维双相各向异性介质弹性波方程交错网格高阶有限差分法模拟[J].中国石油大学学报(自然科学版),30(2):16-20.
秦臻,张才,郑晓东,等.2010.高精度有限差分瑞雷面波模拟及频散特征提取[J].石油地球物理勘探,45(1):40-46.
孙成禹,张立.2012.任意方向震源二维兰姆问题的一个精确解[J].地球物理学报,55(10):3370-3378,doi:10.6038/j.issn.0001-5733.2012.10.019.
肖云飞.2010.面向波场分析的波动方程有限差分正演方法[硕士论文].青岛:中国石油大学.
杨莹.2009.二维地震波场有限差分法数值模拟研究[硕士论文].北京:中国地质大学(北京).
周晓华,陈祖斌,曾晓献等.2012.交错网格有限差分法模拟微动信号[J].吉林大学学报(地球科学版),42(3):852-857.
Chen X F.1993.A systematic and efficient method of computing normal modes for multilayered half-space[J].Geophysical Journal International,115(2):391-409.
Chew W C,Liu Q H.1996.Perfectly matched layers for elastodynamics:a new absorbing boundary condition[J].J.Comp.Acous.,4(4):341.
Collino F,Tsogka C.2001.Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media[J].Geophysics,68(1):294-307.
Drossaert F H,Giannopoulos A.2007.Complex frequency shifted convolution PML for FDTD modelling of elastic waves[J].Wave Motion,44(7-8):593-604.
Drossaert F H,Giannopoulos A.2007.A nonsplit complex frequency-shifted PML based on recursive integration for FDTDmodeling of elastic waves[J].Geophysics,72(2):T9-T17.
Du S T.1996.Seismic Waves Dynamics Theory and Methods(in Chinese)[M].Dongying:University of Petroleum Press,108-110.
Fang G,Fomel S,Du Q Z.2014.Lowrank finite difference on a staggered grid and its application on reverse time migration[J].Journal of China University of Petroleum(in Chinese),38(2):44-51.
Hastings F D,Schneider J B,Broschat S L.1996.Application of the perfectly matched layer(PML)absorbing boundary condition to elastic wave propagation[J].J.Acoust.Soc.Am.,100(5):3061-3069.
Kuzuoglu M,Mittra R.1996.Frequency dependence of the constitutive parameters of causal perfectly matched anisotropic absorbers[J].IEEE Microwave and Guided Wave Letters,6(12):447-449.
Lu J M,Wang Y G.2011.The Principle of Seismic Exploration(in Chinese)[M].Dongying:China University of Petroleum Press,77-83.
Luo Y H,Xia J H,Xu Y X,et al.2010.Finite-difference modeling and dispersion analysis of high-frequency Love waves for nearsurface applications[J].Pure and Applied Geophysics,167(12):1525-1536.
Pei Z L.2006.A staggered-grid high-order finite difference method for modeling elastic wave equation in 3-D dual-phase anisotropic media[J].Journal of China University of Petroleum(in Chinese),30(2):16-20.
Qin Z,Zhang C,Zheng X D,et al.2010.High precision finite difference Rayleigh wave simulation and frequency dispersion characteristics extraction[J].Oil Geophysical Prospecting(in Chinese),45(1):40-46.
Sun C Y,Zhang L.2012.An exact solution for 2-D Lamb problem of arbitrary direction source[J].Chinese Journal of Geophysics(in Chinese),55(10):3370-3378,doi:10.6038/j.issn.0001-5733.2012.10.019.
Virieux J.1984.SH-wave propagation in heterogeneous media:velocity-stress finite-difference method[J].Geophysics,49(11):1933-1942.
Wang T,Tang X M.2003.Finite-difference modeling of elastic wave propagation:a nonsplitting perfectly matched layer approach[J].Geophysics,68(5):1749-1755.
Xiao Y F.2010.Wavefield analysis-oriented wave equation finite difference forward modeling(in Chinese)[Master thesis].Qingdao:China University of Petroleum.
Yang Y.2009.The research on two-dimensional finite-difference seismic wave field numerical simulation(in Chinese)[Master thesis].Beijing:China University of Geosciences(Beijing).
Zhou X H,Chen Z B,Zeng X X,et al.2012.Simulation of microtremor using staggered-grid finite difference method[J].Journal of Jilin University(Earth Science Edition)(in Chinese),42(3):852-857.
杜世通.1996.地震波动力学[M].东营:石油大学出版社,108-110.
方刚,Fomel S,杜启振.2014.交错网格Lowrank有限差分及其在逆时偏移中的应用[J].中国石油大学学报(自然科学版),38(2):44-51.
陆基孟,王永刚.2011.地震勘探原理[M].东营:中国石油大学出版社,77-83.
裴正林.2006.三维双相各向异性介质弹性波方程交错网格高阶有限差分法模拟[J].中国石油大学学报(自然科学版),30(2):16-20.
秦臻,张才,郑晓东,等.2010.高精度有限差分瑞雷面波模拟及频散特征提取[J].石油地球物理勘探,45(1):40-46.
孙成禹,张立.2012.任意方向震源二维兰姆问题的一个精确解[J].地球物理学报,55(10):3370-3378,doi:10.6038/j.issn.0001-5733.2012.10.019.
肖云飞.2010.面向波场分析的波动方程有限差分正演方法[硕士论文].青岛:中国石油大学.
杨莹.2009.二维地震波场有限差分法数值模拟研究[硕士论文].北京:中国地质大学(北京).
周晓华,陈祖斌,曾晓献等.2012.交错网格有限差分法模拟微动信号[J].吉林大学学报(地球科学版),42(3):852-857.