二维频率空间域25点优化系数差分格式弹性波数值模拟(英文)
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摘要
频率空间域地震波数值模拟具有独特的优势:可以同时模拟多源的波传播、每个频率之间独立并行地计算、计算频带选择灵活、不存在累计误差、容易模拟粘弹性介质中地震波传播。但是该方法的最大瓶颈是对于计算机内存的巨大需求。我们使用压缩存储系数矩阵的方法,极大地减少了计算机内存的需求量。同时为了减少短差分算子的数值频散,引用了频率空间域25点弹性波波动方程的差分格式,并使用了最小二乘意义下求出的优化差分系数。为了克服边界反射,采用了最佳匹配层吸收边界条件。数值模拟试验证明:用压缩存储系数矩阵及优化差分系数的频率空间域25点差分格式进行弹性波正演模拟,可以减少数值频散,提高计算精度。使用较大的网格间距,降低计算机内存需求,并保持较高的计算效率。该正演方法为后续弹性波偏移和弹性参数反演提供较好的基础。
Numerical simulation in the frequency-space domain has inherent advantages,such as:it is possible to simulate wave propagation from multiple sources simultaneously;there are no cumulative errors;only the interesting frequencies can be selected;and it is more suitable for wave propagation in viscoelastic media.The only obstacle to using the method is the requirement of huge computer storage.We extend the compressed format for storing the coefficient matrix.It can reduce the required computer storage dramatically.We get the optimal coefficients by least-squares method to suppress the numerical dispersion and adopt the perfectly matched layer(PML) boundary conditions to eliminate the artificial boundary reflections.Using larger grid intervals decreases computer storage requirements and provides high computational efficiency.Numerical experiments demonstrate that these means are economic and effective,providing a good basis for elastic wave imaging and inversion.
Numerical simulation in the frequency-space domain has inherent advantages,such as:it is possible to simulate wave propagation from multiple sources simultaneously;there are no cumulative errors;only the interesting frequencies can be selected;and it is more suitable for wave propagation in viscoelastic media.The only obstacle to using the method is the requirement of huge computer storage.We extend the compressed format for storing the coefficient matrix.It can reduce the required computer storage dramatically.We get the optimal coefficients by least-squares method to suppress the numerical dispersion and adopt the perfectly matched layer(PML) boundary conditions to eliminate the artificial boundary reflections.Using larger grid intervals decreases computer storage requirements and provides high computational efficiency.Numerical experiments demonstrate that these means are economic and effective,providing a good basis for elastic wave imaging and inversion.
引文
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Jo,C. H.,Shin,C. S.,and Suh,J. H.,1996,An optimal 9-point,finite-difference frequency- space 2-D scalar wave extrapolator: Geophysics,61(2),529 - 537.
Liao,J. P.,Wang,H. Z.,and Ma,Z. T.,2009,Frequency-space domain two dimension elastic wave model using compressed storage format:. SEG-CPS Annual Meeting,Beijing.
Lysmer,J.,and Drake,L. A.,1972,A finite element method for seismology: in Bolt,B. A.,Ed.,Methods in Computational Physics,Volume 11: Seismology: Surface Waves and Earth Oscillations,Academic Press,America.
Marmousi2: An elastic upgrade for Marmousi: The Leading Edge,25(2),156 - 166.
Min,D. J.,Shin,C. S.,Kwon,B. D.,and Chung,S. W.,2000,Improved frequency- domain elastic wave modeling using weighted-averaging difference operators: Geophysics,65(3),884 - 895.
Plessix,R. E.,2007,A Helmholtz iterative solver for 3D seismic-imaging problems: Geophysics,72(5),SM185 - SM194.
Pratt,R. G.,and Worthington,M. H.,1990,Inverse theory applied to multi-source cross-hole tomography,Part: I Acoustic wave-equation method: Geophysical Prospecting,38,287 - 310.
Pratt,R. G.,1990,Frequency-domain elastic wave modeling by finite differences. A tool for crosshole seismic imaging: Geophysics,55(5),626 - 632.
Ren,H. R.,Wang,H. Z.,and Gong,T.,2009,Numericalmodeling of scalar seismic wave propagation with nite-difference scheme and in the frequency-space domain:Geophysical Prospecting for Petroleum (in Chinese),48(1),20 - 26.
Shan,G. J.,and Zhang,L.,2008,Velocity sensitivity of reverse-time migration: 78th Ann. Internat. Mtg.,Soc. Expl. Geophys.,Expanded Abstracts.
Sheriff,R. E.,and Geldart,L. P.,1999,Exploration seismology (second edition): (Translated by Chu,Y.,Li,C. C.,and Wang H. W.),Petroleum Industry Press,Beijing.
Shin,C. S.,and Sohn,H. J.,1998,A frequency-space 2-D scalar wave extrapolator using extended 25-point nite-difference operator: Geophysics,63(1),289 - 296.
Stekl,I.,and Pratt,R. G.,1998,Accurate viscoelastic modeling by frequency-domain finite differences using rotated operators: Geophysics,63(5),1779 - 1794.
Jo,C. H.,Shin,C. S.,and Suh,J. H.,1996,An optimal 9-point,finite-difference frequency- space 2-D scalar wave extrapolator: Geophysics,61(2),529 - 537.
Liao,J. P.,Wang,H. Z.,and Ma,Z. T.,2009,Frequency-space domain two dimension elastic wave model using compressed storage format:. SEG-CPS Annual Meeting,Beijing.
Lysmer,J.,and Drake,L. A.,1972,A finite element method for seismology: in Bolt,B. A.,Ed.,Methods in Computational Physics,Volume 11: Seismology: Surface Waves and Earth Oscillations,Academic Press,America.
Marmousi2: An elastic upgrade for Marmousi: The Leading Edge,25(2),156 - 166.
Min,D. J.,Shin,C. S.,Kwon,B. D.,and Chung,S. W.,2000,Improved frequency- domain elastic wave modeling using weighted-averaging difference operators: Geophysics,65(3),884 - 895.
Plessix,R. E.,2007,A Helmholtz iterative solver for 3D seismic-imaging problems: Geophysics,72(5),SM185 - SM194.
Pratt,R. G.,and Worthington,M. H.,1990,Inverse theory applied to multi-source cross-hole tomography,Part: I Acoustic wave-equation method: Geophysical Prospecting,38,287 - 310.
Pratt,R. G.,1990,Frequency-domain elastic wave modeling by finite differences. A tool for crosshole seismic imaging: Geophysics,55(5),626 - 632.
Ren,H. R.,Wang,H. Z.,and Gong,T.,2009,Numericalmodeling of scalar seismic wave propagation with nite-difference scheme and in the frequency-space domain:Geophysical Prospecting for Petroleum (in Chinese),48(1),20 - 26.
Shan,G. J.,and Zhang,L.,2008,Velocity sensitivity of reverse-time migration: 78th Ann. Internat. Mtg.,Soc. Expl. Geophys.,Expanded Abstracts.
Sheriff,R. E.,and Geldart,L. P.,1999,Exploration seismology (second edition): (Translated by Chu,Y.,Li,C. C.,and Wang H. W.),Petroleum Industry Press,Beijing.
Shin,C. S.,and Sohn,H. J.,1998,A frequency-space 2-D scalar wave extrapolator using extended 25-point nite-difference operator: Geophysics,63(1),289 - 296.
Stekl,I.,and Pratt,R. G.,1998,Accurate viscoelastic modeling by frequency-domain finite differences using rotated operators: Geophysics,63(5),1779 - 1794.
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