快速精确的二维频率空间域弹性波数值模拟
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摘要
二维频率空间域的数值模拟方法具有以下的优势:多炮模拟时,计算成本比时间域方法低;无累计误差;在地震反演中处理多震源模拟时,只需要有限的几个频率就可以得到好的反演结果.差分离散化形成的稀疏系数矩阵,需要求解一个巨大规模的线性方程组,最大瓶颈是需要海量的计算机内存,导致计算量庞大.本文在前人研究的基础上,采用嵌套剖分网格排序法,极大限度减少对计算机内存的需求,从而减少了计算量.针对弹性波数值模拟的特征,提出二维频率空间域弹性波多炮模拟的快速计算流程.数值模拟试验证明使用嵌套剖分排序法的弹性波多炮数值模拟比压缩存储法具有节省存储量、计算效率高等优势,为后续的二维频率空间域弹性波全波形反演奠定了很好的基础.
There are many advantages of the two dimensional numerical simulation on seismic waves in frequency space domain:the calculating cost of a large number of sources in frequency space domain is much lower than that of time domain methods.Without accumulative errors,it is very useful in dealing with the multiple source simulation in seismic inversion,it can get good inversion results only with several frequencies.Once the frequency domain equations are discretized to form matrix equation.The coefficient matrix is a very huge and sparse band matrix equation.We need solve a large number of linear equations,the biggest bottleneck of frequency domain simulation method is the huge demand for computer's memory and computing amount.We adopt the nested-dissection method which can decrease the requiring of computer capacity greatly and decrease the computing cost based on the former's paper.For multi-shot forward modeling's charactering,This paper presents a fast computational procedure of numerical simulation elastic wave in frequency space domain.Numerical results demonstrate that nested-dissection has many advantages comparing to compressed storage format,such as saving a huge storage and computing time as well as high computing efficiency,which provides a good base for the 2-D elastic wave full waveform inversion.
There are many advantages of the two dimensional numerical simulation on seismic waves in frequency space domain:the calculating cost of a large number of sources in frequency space domain is much lower than that of time domain methods.Without accumulative errors,it is very useful in dealing with the multiple source simulation in seismic inversion,it can get good inversion results only with several frequencies.Once the frequency domain equations are discretized to form matrix equation.The coefficient matrix is a very huge and sparse band matrix equation.We need solve a large number of linear equations,the biggest bottleneck of frequency domain simulation method is the huge demand for computer's memory and computing amount.We adopt the nested-dissection method which can decrease the requiring of computer capacity greatly and decrease the computing cost based on the former's paper.For multi-shot forward modeling's charactering,This paper presents a fast computational procedure of numerical simulation elastic wave in frequency space domain.Numerical results demonstrate that nested-dissection has many advantages comparing to compressed storage format,such as saving a huge storage and computing time as well as high computing efficiency,which provides a good base for the 2-D elastic wave full waveform inversion.
引文
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[2]Marfurt K J.Accuracy of finite-difference and finite-elementmodeling of the scalar and elastic wave equations.Geophysics,1984,49(5):533-549.
[3]Pratt R G.Frequency-domain elastic wave modeling by finitedifferences.A tool for crosshole seismic imaging.Geophysics,1990,55(5):626-632.
[4]Gerhard P.Inverse theory applied to multi-source cross-holetomography.Part 2:elastic wave-equation method.GeophysicalProspecting,1990,38(3):311-329.
[5]Shin C.Sponge boundary condition for frequency-domain modeling.Geophysics,1995,60(6):1870-1874.
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[8]tekl I,Pratt R G.Accurate viscoelastic modeling byfrequency-domain finite differences using rotated operators.Geophysics,1998,63(5):1779-1794.
[9]Pratt R G,Shin C,Hicks.Gauss-Newton and full Newton methodsin frequency-space seismic waveform inversion.Geophys.J.Int,1998,133(2):341-362.
[10]Pratt R G.Seismic waveform inversion in the frequency domain,Part 1:Theory and verification in a physical scale model.Geophysics,1999,64(3):888-901.
[11]Pratt R G,Shipp R M.Seismic waveform inversion in thefrequency domain,Part 2:Fault delineation in sedimentsusing crosshole data.Geophysics,1999,64(3):902-914.
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[14]廖建平,王华忠,刘和秀等.精确的频率空间域黏声波有限差分数值模拟.物探与化探,2011,35(4):541-545.Liao J P,Wang H Z,Liu H X,et al.Accurate visco-acousticwave finite difference numerical simulation in frequency spacedomain.Geophysical&Geochemical Exploration(inChinese),2011,35(4):541-545.
[15]廖建平,刘和秀,王华忠等.二维频率空间域粘声波正演模拟研究.地球物理学进展,2011,26(6):2075-2081.Liao J P,Liu H X,Wang H Z,et al.Two dimensional visco-acoustic wave modeling research in Frequency-space Domain.Progress in Geophys.(in Chinese),2011,26(6):2075-2081.
[16]Liao J P,Wang H Z,Ma Z T.Frequency-space domain twodimension elastic wave model using compressed storageformat.//SEG-CPS Annual Meeting.Beijing,2009:1180.
[17]Liao J P,Wang H Z,Ma Z T.2-D elastic wave modeling withfrequency-space 25-point finite-difference operators.AppliedGeophysics,2009,6(3):259-266.
[18]廖建平,王华忠,杨天春等.二维频率空间域声波数值模拟及其应用.新疆石油地质,2011,32(6):651-653.Liao J P,Wang H Z,Yang T C,et al.2-D acoustic wavenumerical simulation and its application in frequency spacedomain.Xinjiang Petroleum Geology(in Chinese),2011,32(6):651-653.
[19]廖建平.频率空间域地震波数值模拟方法研究.上海:同济大学,2009.Liao J P.Research on Seismic Wave Numerical ModelingMethod in Frequency-space Domain(in Chinese).Shanghai:Tongji University,2009.
[20]廖建平,刘和秀,王华忠等.高分辨率的频率空间域声波全波形速度反演-理论模型.地球物理学进展,2011,26(5):1690-1695.Liao J P,Liu H X,Wang H Z,et al.High resolution acousticwave full waveform velocity inversion in frequency spacedomain-theoretical model.Progress in Geophys.(in Chinese),2011,26(5):1690-1695.
[21]廖建平,刘和秀,王华忠等.快速高精度的频率空间域声波数值模拟方法研究.地球物理学进展,2011,26(4):1359-1363.Liao J P,Liu H X,Wang H Z,et al.Study on rapid highlyaccurate acoustic wave numerical simulation in frequencyspace domain.Progress in Geophys.(in Chinese),2011,26(4):1359-1363.
[22]George A,Liu J W H.Computer Solution of Large SparsePositive Definite Systems.New York:Prentice Hall,1981.
[23]刘长学.超大规模稀疏矩阵计算方法.上海:上海科技出版社,1991.Liu C X.Calculation of Large Scale Sparse Matrix(inChinese).Shanghai:Shanghai Science and Technology Press,1991.
[24]Martin G S,Wiley R,Marfurt K J.Marmousi2:An elasticupgrade for Marmousi.The Leading Edge,2006,25(2):156-166.
[25]Stockwell J W Jr,Cohen J K.The New SU User’s Manual(Version 4.0).Golden,USA,2008.
[2]Marfurt K J.Accuracy of finite-difference and finite-elementmodeling of the scalar and elastic wave equations.Geophysics,1984,49(5):533-549.
[3]Pratt R G.Frequency-domain elastic wave modeling by finitedifferences.A tool for crosshole seismic imaging.Geophysics,1990,55(5):626-632.
[4]Gerhard P.Inverse theory applied to multi-source cross-holetomography.Part 2:elastic wave-equation method.GeophysicalProspecting,1990,38(3):311-329.
[5]Shin C.Sponge boundary condition for frequency-domain modeling.Geophysics,1995,60(6):1870-1874.
[6]Jo C H,Shin C,Suh J H.An optimal 9-point,finite-difference,frequency-space,2-D scalar wave extrapolator.Geophysics,1996,61(2):529-537.
[7]Shin C,Sohn H.A frequency-space 2-D scalar waveextrapolator using extended 25-point finite-difference operator.Geophysics,1998,63(1):289-296.
[8]tekl I,Pratt R G.Accurate viscoelastic modeling byfrequency-domain finite differences using rotated operators.Geophysics,1998,63(5):1779-1794.
[9]Pratt R G,Shin C,Hicks.Gauss-Newton and full Newton methodsin frequency-space seismic waveform inversion.Geophys.J.Int,1998,133(2):341-362.
[10]Pratt R G.Seismic waveform inversion in the frequency domain,Part 1:Theory and verification in a physical scale model.Geophysics,1999,64(3):888-901.
[11]Pratt R G,Shipp R M.Seismic waveform inversion in thefrequency domain,Part 2:Fault delineation in sedimentsusing crosshole data.Geophysics,1999,64(3):902-914.
[12]Min M J,Shin C,Kwon B D,et al.Improved frequency-domain elastic wave modeling using weighted-averagingdifference operators.Geophysics,2000,65(3):884-895.
[13]Min D J,Yoo H S,Shin C,et al.Weighted-averaging finite-element method for scalar wave equation in the frequencydomain.J.Seism.Explor.,2002,11:197-222.
[14]廖建平,王华忠,刘和秀等.精确的频率空间域黏声波有限差分数值模拟.物探与化探,2011,35(4):541-545.Liao J P,Wang H Z,Liu H X,et al.Accurate visco-acousticwave finite difference numerical simulation in frequency spacedomain.Geophysical&Geochemical Exploration(inChinese),2011,35(4):541-545.
[15]廖建平,刘和秀,王华忠等.二维频率空间域粘声波正演模拟研究.地球物理学进展,2011,26(6):2075-2081.Liao J P,Liu H X,Wang H Z,et al.Two dimensional visco-acoustic wave modeling research in Frequency-space Domain.Progress in Geophys.(in Chinese),2011,26(6):2075-2081.
[16]Liao J P,Wang H Z,Ma Z T.Frequency-space domain twodimension elastic wave model using compressed storageformat.//SEG-CPS Annual Meeting.Beijing,2009:1180.
[17]Liao J P,Wang H Z,Ma Z T.2-D elastic wave modeling withfrequency-space 25-point finite-difference operators.AppliedGeophysics,2009,6(3):259-266.
[18]廖建平,王华忠,杨天春等.二维频率空间域声波数值模拟及其应用.新疆石油地质,2011,32(6):651-653.Liao J P,Wang H Z,Yang T C,et al.2-D acoustic wavenumerical simulation and its application in frequency spacedomain.Xinjiang Petroleum Geology(in Chinese),2011,32(6):651-653.
[19]廖建平.频率空间域地震波数值模拟方法研究.上海:同济大学,2009.Liao J P.Research on Seismic Wave Numerical ModelingMethod in Frequency-space Domain(in Chinese).Shanghai:Tongji University,2009.
[20]廖建平,刘和秀,王华忠等.高分辨率的频率空间域声波全波形速度反演-理论模型.地球物理学进展,2011,26(5):1690-1695.Liao J P,Liu H X,Wang H Z,et al.High resolution acousticwave full waveform velocity inversion in frequency spacedomain-theoretical model.Progress in Geophys.(in Chinese),2011,26(5):1690-1695.
[21]廖建平,刘和秀,王华忠等.快速高精度的频率空间域声波数值模拟方法研究.地球物理学进展,2011,26(4):1359-1363.Liao J P,Liu H X,Wang H Z,et al.Study on rapid highlyaccurate acoustic wave numerical simulation in frequencyspace domain.Progress in Geophys.(in Chinese),2011,26(4):1359-1363.
[22]George A,Liu J W H.Computer Solution of Large SparsePositive Definite Systems.New York:Prentice Hall,1981.
[23]刘长学.超大规模稀疏矩阵计算方法.上海:上海科技出版社,1991.Liu C X.Calculation of Large Scale Sparse Matrix(inChinese).Shanghai:Shanghai Science and Technology Press,1991.
[24]Martin G S,Wiley R,Marfurt K J.Marmousi2:An elasticupgrade for Marmousi.The Leading Edge,2006,25(2):156-166.
[25]Stockwell J W Jr,Cohen J K.The New SU User’s Manual(Version 4.0).Golden,USA,2008.
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