2D声波频率域数值模拟中几种有限差分方法的对比分析
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摘要
频率域数值模拟是频率域全波形反演的基础,在地震波场数值模拟中占有重要地位.相对于时间域数值模拟,频率域数值模拟具有两个明显的优势:没有时间累计误差,适合于并行计算.然而,严重的数值频散和巨大的内存损耗是阻碍其应用的两大瓶颈.为解决这两个问题,基于有限差分方法,学者提出了多种差分格式,如优化9点、15点、17点以及25点差分格式.本文从频散关系、计算效率和存储量三个方面,对比、分析了以上四种差分方法.基于2D声波方程,通过在均匀模型、层状模型以及Marmousi模型上的应用效果,对每种方法的优缺点进行了总结,为高精度数值模拟和声波频率域全波形反演提供方法选择上的参考.
Frequency-domain numerical modeling is the basis of full waveform inversion,which is very important in seismic wave modeling.Compared with conventional time domain forward modeling,frequency-space domain forward modeling has two advantages:no time accumulated error;suitable for parallel cmputation.However,there are two problems with this modeling method;severe grid dispersion and huge memory consumption which have restricted its application to a large extent.Finite-differencing method is effective to achieve the simulation in the frequency-domain.To overcome the disadvantages,based on the finite-differencing,scholars proposed optimal 9-point,15-point,17-point and 25-point scheme.Based on the frequency domain 2D acoustic equation,these methods are applied in the homogeneous model,the single layer model and Marmousi model,then the results are compared and analyzed.By the comparisons of above methods from the point of dispersion,efficiency and computer memory of numerical simulation,we summarize the advantages and disadvantages of the methods,which gives the selection and reference to the following high precision numerical simulation and frequency domain full waveform inversion,
引文
Alford R M,Kelly K R,Boore D M.1974.Accuracy of finitedifference modeling of the acoustic wave equation[J].Geophysics,39(6):834-842,doi:10.1190/1.1440470.
    Berenger J-P.1994.A perfectly matched layer for the absorption of electromagnetic waves[J].Journal of Computational Physics,114(2):185-200,doi:10.1006/jcph.1994.1159.
    Bian A F,Yu W H,Zhou H W.Progress in the frequency-domain full waveform inversion method[J],Progress in Geophys.(in Chinese).25(3):982-993,doi:10.3969/j.issn.1004-2903.2010.03.037.
    Cao S H,Chen J B.2012.A 17-point scheme and its numerical implementation for high-accuracy modeling of frequency-domain acoustic equation[J].Chinese J.Geophys.(in Chinese),55(10):3440-3449,doi:10.6038/j.issn.0001-5733.2012.10.27.
    Chen J B.2012.An average-derivative optimal scheme for frequency-domain scalar wave equation[J].Geophysics,77(6):T201-T210,doi:10.1190/Geo2011-0389.1.
    Chen J B.2013.A generalized optimal 9-point scheme for frequencydomain scalar wave equation[J].Journal of Applied Geophysics,92:1-7,doi:10.1016/j.jappgeo.2013.02.008.
    Chen J B.2014.A 27-point scheme for a 3D frequency-domain scalar wave equation based on an average-derivative method[J].Geophysical Prospecting,62(2):258-277,doi:10.1111/1365-2478.12090.
    Clapp R G.2009.Reverse time migration with random boundaries[C].//79th Annual International Meeting,SEG,Expanded Abstracts,2809-2813.
    Ding J C,Chang X,Liu Y K,et al.2007.Layer by layer waveform inversion of seismic reflection data[J].Chinese J.Geophys.(in Chinese),50(2):574-580,doi:10.3321/j.issn;0001-5733.2007.02.031.
    Dong L G,Chi B X,Tao J X,et al.2013.Objective function behavior in acoustic full-waveform inversion[J].Chinese J.Geophys.(in Chinese),56(10):3445-3460,doi:10.6038/cjg20131020.
    GAO Feng-Xia.LIU Cai,FENG Xuan,et al.2013.Comparisons and analyses of several optimization methods in the application of frequency-domain full waveform inversion[J].Progress in Geophys.(in Chinese),28(4):2060-2068,doi:10.6038/pg20130450.
    Gu B L,Liang G H,Li Z Y.2012.A 21-point finite difference scheme for 2D frequency-domain elastic wave modelling[J].Exploration Geophysics,44(3):156-166.
    Husted B,Operto S,Virieux J.2004.Mixed-grid and staggered grid finite-difference methods for frequency-domain acoustic wave modelling[J].Geophysical Journal International,157(3):1269-1296,doi:10.1111/j.1365-264X.2004.02289..
    Jo C-H,Shin C S,Suh J H.1996.An optimal 9-point,finitedifference,frequency-space,2-D scalar wave extrapolator[J].Geophysics,61(2):529-537,doi:10.1190/1.1443979.
    Liao J P,Liu H X,Wang H Z,et al.2011.Study on rapid highly accurate acoustic wave numerical simulation in frequency space domain[J].Progress in Geophysics(in Chinese),26(4):1359-1363,doi:10.3969/j.issn.1004-2903.2011.04.029.
    Liu G F,Liu H,Meng X H,et al.2012.Frequency-related factors analysis in frequency domain waveform inversion[J].Chinese J.Geophys.(in Chinese),55(4):1345-1353,doi:10.6038/j.issn.0001-5733.2012.04.030.
    Liu H W,Li B,Liu H,et al.2010.The algorithm of high order finite difference pre-stack reverse time migration and GPU implementation[J].Chinese J.Geophys.(in Chinese),53(7):1725-1733,doi:10.3969/j.issn.0001-5733.2010.07.024.
    Liu L,Liu H,Liu H W.2013.Optimal 15-point finite difference forward modeling in frequency-space domain[J].Chinese J.Geophys.(in Chinese),56(2):644-652,doi:10.6038/cjg20130228.
    Liu Y.2014.An optimal 5-point scheme for frequency-domain scalar wave equation[J].Journal of Applied Geophysics,108(3):19-24,doi:10.1016/j.jappgeo.2014.06.006.
    LIU You-Shan,TENG Ji-Wen,Xu Tao,et al.2014.Numerical modeling of seismic wavefield with the SEM based on Triangles[J].Progress in Geophysics(in Chinese),29(4):1715-1726,doi:10.6038/pg20140430.
    Lysmer J,Drake L A.1972.A finite-element method for seismology[A].//Bolt B A ed.Methods in Computational Physics,Volume 11:Seismology:Surface Waves and Earth Oscillations[M].New York:Academic Press Inc.,181-216.
    Mallick S,Frazer L N.1987.Practical aspects of reflectivity modeling[J].Geophysics,52(10):1355-1364,doi:10.1190/1.1442248.
    Marfurt K,Shin C.1989.The future of iterative modelling in geophysical exploration[A].//Eisner E ed.Handbook of Geophysical Exploration:I-Seismic Exploration,21-Supercomputers in Seismic Exploration[M].Pergamon Press,203-228.
    Marfurt K J.1984.Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equations[]].Geophysics,49(5):533-549,doi:10.1190/1.1441689.
    Operto S,Virieux J,Amestoy P,et al.2007.3D finite-difference frequency-domain modeling of visco-acoustic wave propagation using a massively parallel direct solver:A feasibility study[J].Geophysics,72(5):SM195-SM211,doi:10.1190/1.2759835.
    Pratt R G.1990a.Frequency-domain elastic wave modeling by finite differences:A tool for cross-hole seismic imaging[J].Geophysics,55(5):626-632.
    Pratt R G.1990b.Inverse theory applied to multi-source cross-hole tomography,Part 2:Elastic wave-equation method[J].Geophysical Prospecting,38(3):311-329.
    Pratt R G,Worthington M H.1990.Inverse theory applied to multi-source cross-hole tomography,Part 1:Acoustic wave equation method[J].Geophysical Prospecting,38(3):287-310.
    Pratt R G,Shin C,Hicks G J.1998.Gauss-Newton and full Newton methods in frequency-space seismic waveform inversion[J].Geophysics,133(2):341-362.
    Ren H R,Wang H Z,Gong T.2009.Seismic modeling of scalar seismic wave propagation with finite-difference scheme in frequency-space domain[J].Geophysical Prospecting for Petroleum(in Chinese),48(1):20-26.
    Ren H R,Huang G H,Wang H Z,et al.2013.A research on the Hessian operator in seismic inversion imaging[J].Chinese J.Geophys.(in Chinese),56(7):2429-2436,doi:10.6038/cjg20130728.
    Shi Y M,Zhang Y,Yao F C,et al.2014.Methodology of seismic imaging for hydrocarbon reservoirs based on acoustic full waveform inversion[J].Chinese J.Geophys.,57(5):1599-1611,doi:10.6038/cjg20140523.
    Shin C,Sohn H.1998.A frequency-space 2-D scalar wave extrapolator using extended 25-point finite-difference operator[J].Geophysics,63(1):289-296.doi:10.1190/1.1444323.
    Stekl I,Pratt R.1998.Accurate viscoelastic modeling by frequencydomain finite differences using rotated operators[J].Geophysics,63(5):1779-1794,doi:10.1190/1.1444472.
    Symes W M.2007.Reverse time migration with optimal chekpointing[J].Geophysics,72(5):SM213-SM-221,doi:10.1190/1.2742686.
    Tarantola A.1984.Inversion of seismic reflection data in the acoustic approximation[J].Geophysics,49(8):1259-1266.
    Virieux J,Operto S.2009.An overview of full-waveform inversion in exploration geophysics[J].Geophysics,74(6):WCC1-WCC26,doi:10.1190/1.3238367.
    Wei Z F,Gao H W,Zhang J F.2014.Time-domain full waveform inversion based on an irregular-grid acoustic modeling method[J],Chinese].Geophys.(in Chinese),57(2):586-594,doi:10.6038/cjg20140222.
    Wu G C,Luo C M,Liang K.2007.Frequency-space domain finite difference numerical simulation of elastic wave in TTI media[J].Journal of Jilin University(Earth Science Edition)(in Chinese),37(5):1023-1033,doi:10.3969/j.issn.1671-5888.2007.05.030.
    Zhang H,Liu H,Liu L,et al.2014.Frequency domain acoustic equation high-order modeling based on an average-derivative method[J].Chinese J.Geophys.(in Chinese),57(5):1599-1611,doi:10.6038/cjg20140523.
    卞爱飞,於文辉,周华伟.2010.频率域全波形反演方法研究进展.地球物理学进展[J].25(3):982-993,doi:10.3969/j.issn.1004-2903.2010.03.037.
    曹书红,陈景波.2012.声波方程频率域高精度正演的17点格式及数值实现[J].地球物理学报,55(10):3440-3449,doi:10.6038/j.issn.0001-5733.2012.10.027.
    丁继才,常旭,刘伊克,等.2007.反射地震数据的逐层波形反演[J].地球物理学报,50(2):574-580,doi:10.3321/j.issn:0001-5733.2007.02.031。
    董良国,迟本鑫,陶纪霞,等.2013.声波全波形反演目标函数性态[J].地球物理学报,56(10):3445-3460,doi:10.6038/cjg20131020.
    高凤霞,刘财,冯晅等.2013.几种优化方法在频率域全波形反演中的应用效果及对比分析研究[J].地球物理学进展,28(4):2060-2068,doi:10.6038/pg20130450.
    廖建平,刘和秀,王华忠,等.2011.快速高精度的频率空间域声波数值模拟方法研究[J].地球物理学进展,26(4):1359-1363,doi:10.3969/j.issn.1004-2903.2011.04.029.
    刘国峰,刘洪,孟小红,等.2012.频率域波形反演中与频率相关的影响因素分析[J].地球物理学报,2012,55(4):1345-1353,doi:10.6038/j.issn.0001-5733.2012.04.030.
    刘红伟,李博,刘洪,等.2010.地震叠前逆时偏移高阶有限差分算法及GPU实现[J].地球物理学报,53(7):1725-1733,doi:10.3969/j.issn.0001-5733.2010.07.024.
    刘璐,刘洪,刘红伟.2013.优化15点频率一空间域有限差分正演模拟[J].地球物理学报,56(2):644-652,doi:10.6038/cjg20130228.
    刘有山,滕吉文,徐涛,等.2014.三角网格谱元法地震波场数值模拟[J].地球物理学进展,29(4):1715-1726,doi:10.6038/pg20140430.
    任浩然,王华忠,龚婷.2009.标量地震波频率一空间域有限差分法数值模拟[J].石油物探,48(1):20-26.
    任浩然,黄光辉,王华忠,等.2013.地震反演成像中的Hessian算子研究[J].地球物理学报,56(7):2429-2436,doi:10.6038/qg20130728.
    石玉梅,张研,姚逢昌,等.2014.基于声学全波形反演的油气藏地震成像方法[J].地球物理学报,57(2):607-617,doi:10.6038/cjg20140224.
    魏哲枫,高红伟,张剑锋.2014.基于非规则网格声波正演的时间域全波形反演[J].地球物理学报,57(2):586-594,doi:10.6038/cjg20140222.
    吴国忱,罗彩明,梁楷.2007.TTI介质弹性波频率一空间域有限差分数值模拟[J].吉林大学学报(地球科学版),37(5):1023-1033.
    张衡,刘洪,刘璐,等.2014.基于平均导数方法的声波方程频率域高阶正演[J].地球物理学报,57(5):1599-1611,doi:10.6038/cjg20140523.

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