改进的高精度拟谱微分方法及其在三维非均匀介质地震传播研究中的应用
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摘要
改进了用于模拟地震波场的傅里叶拟谱微分方法,改进后的方法精度是常规拟谱方法的4倍,称为改进的傅里叶拟谱方法.在较高数值精度的一阶应力-速度弹性波动方程的基础上,采用该方法和常规拟谱方法对Marmousi模型进行数值求解,结果表明,该方法的数值频散效应明显比常规拟谱方法弱.将该方法与有限元方法在各向异性介质中进行模拟比较,发现该方法的精度接近有限元方法,数值频散效应比有限元方法明显减小,而且可在较大空间网格间距下进行计算,从而提高计算效率.在3-D非均匀介质中的地震波传播数值模拟结果表明,该方法是一种研究复杂非均匀介质中地震波传播问题的高效方法.
A new fast differentiation operator,"pseudospectral time-staggered difference operator",is proposed in this paper.The accuracy of this method is four time of the normal pseudospectral method.It is confirmed that the numerical dispersion of this method is less than that of normal pseudospectral method by comparing the calculation result of Marmousi model.The new operation is applied to simulate seismic wave propagation in 3-D heterogeneous medium,and the results show that the time-staggered difference operator for the pseudospectral method is valid for the seismic wave simulation in the complex heterogeneous medium.
A new fast differentiation operator,"pseudospectral time-staggered difference operator",is proposed in this paper.The accuracy of this method is four time of the normal pseudospectral method.It is confirmed that the numerical dispersion of this method is less than that of normal pseudospectral method by comparing the calculation result of Marmousi model.The new operation is applied to simulate seismic wave propagation in 3-D heterogeneous medium,and the results show that the time-staggered difference operator for the pseudospectral method is valid for the seismic wave simulation in the complex heterogeneous medium.
引文
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[21]Cerjan C,Kosloff D,Kosloff R.A nonreflecting boundarycondition for discrete acoustic and elastic wave equation.Geophysics,1985,50(4):705~708
[22]Furunura T,Takenake H.A wrapapround eliminationtechnique for the pseudospectral wave synthesis using anantiperiodic extension of the wavefield.Geophysics,1995,60(1):302~307
[2]Igel H,Mora P,Riollet B,et al.Anisotropic wavepropagation through finite-difference grid.Geophysics,1995,60(4):1203~1216
[3]Carcione J M.Wave fields in real media:wave propagation inanisotropic anelastic and porous media.UK:Elsevier ScienceLtd.2001
[4]Carcione J M,Herman,Ten Kroode F P E,et al.SeismicModeling.Geophysics,2002,67(4):1304~1325
[5]王红落,常旭,陈传仁.基于波动方程有限差分算法的接收函数正演与偏移.地球物理学报,2005,48(2):415~422Wang H L,Chang X,Chen C R.Receiver function forwardmodeling and migration based on wave-equation finitedifference method.Chinese J.Geophys.(in Chinese),2005,48(2):415~422
[6]殷文,印兴耀,吴国忱等.高精度频率域弹性波方程有限差分方法及波场模拟.地球物理学报,2006,49(2):561~568Yin W,Yin X Y,Wu G C,et al.The method of finitedifference of high precision elastic wave equations in thefrequency domain and wave-field simulation.Chinese J.Geophys.(in Chinese),2006,49(2):561~568
[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.地球物理学报,2007,50(2):567~573Zhou Z S,Liu X L,Xiong X Y.Finite-difference modelling ofRayleigh surface wave in elastic media.Chinese J.Geophys.(in Chinese),2007,50(2):567~573
[8]Marfurt K J.Accuracy of finite difference and finite elementmodeling of the scalar and elastic wave equations.Geophysics,1984,49(5):533~549
[9]Lysmer.Shear waves in plane infinite structures.Journal ofthe Engineering Mechanics Division.1972,98(1):85~105
[10]陈少林,廖振鹏,陈进.两相介质近场波动模拟的一种解耦有限元方法.地球物理学报,2005,48(4):909~917Chen S L,Liao Z P,Chen J.A decoupling FEM forsimulating near-field wave motions in two-phase media.Chinese J.Geophys.(in Chinese),2005,48(4):909~917
[11]张新明,刘克安,刘家琦.流体饱和多孔隙介质二维弹性波方程正演模拟的小波有限元法.地球物理学报,2005,48(5):1156~1166Zhang X M,Liu K A,Liu J Q.A wavelet finite elementmethod for the 2-D wave equation in fluid-saturated porousmedia.Chinese J.Geophys.(in Chinese),2005,48(5):1156~1166
[12]Komatitsch D,et al.The spectral-element method,Beowulfcomputing and global seismology.Science,2002,298(29):1737~1742
[13]Fornberg B.The pseudo-spectral method:comparisons withfinite differences for the elastic wave equation.Geophysics,1987,52(4):483~501
[14]Dault C R,et al.A comparison of finite-difference and Fouriermethod calculations of synthetic seismograms:Bull.Seis.Soc.Am.,1989,79:1210~1230
[15]Fornberg B.Pseudospectral approximation of the elastic waveequation on a staggered grid.59thAnn.Internat.Mtg.,Soc.Expl.Geophys.Expandaed Abstracts,1989.SM2.1
[16]Kang I B,McMechan G A.Two-dimensional elasticpseudospectral modeling of wide-aperture seismic array datawith application to the Wichita Uplift-Anadarako Basin regionof southwestern Oklahoma:Bull.Seis.Soc.Am.1990,80:1677~1695
[17]Komatitsch D,Jeroen Ritsema,Jeroen Tromp.The spectral-element method,Beowulf computing and global seismology.Science,2002,298(29):1737~1742
[18]Virieux J.SH-wave propagation in heterogeneous media:velocity-stress finite-difference method.Geophysics,1984,49(11):1933~1957
[19]陆金甫,关治.偏微分方程数值解(第二版).北京:清华大学出版社,2003Lu J F,Guan Z.The Numerical Resolution of DifferentiationEquation.Beijing:Tsinghua University,2003
[20]赵志新,徐纪人,堀内茂人.错格实数傅立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.地球物理学报,2003,46(2):234~240Zhao Z X,Xu J R,Shigeki Horiuchi.Staggered grid realvalue FFT differentiation operator and its application on wavepropagation simulation in the heterogeneous medium.ChineseJ.Geophys.(in Chinese),2003,46(2):234~240
[21]Cerjan C,Kosloff D,Kosloff R.A nonreflecting boundarycondition for discrete acoustic and elastic wave equation.Geophysics,1985,50(4):705~708
[22]Furunura T,Takenake H.A wrapapround eliminationtechnique for the pseudospectral wave synthesis using anantiperiodic extension of the wavefield.Geophysics,1995,60(1):302~307
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