声波方程数值模拟中的任意广角单程波吸收边界
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摘要
地震数值模拟需要使用稳定有效的吸收边界条件,以达到衰减人工截断边界反射的目的。本文将一种高精度单程波方程,即任意广角波动方程(AWWE)用作二阶声波方程的吸收边界条件,采用有限差分法给出边界的计算公式,并对角点进行了特殊处理。均匀模型与解析分析法结果的对比及Marmousi模型波场模拟证实:AWWE用作吸收边界能适用于较大入射角情况,其吸收效果明显优于传统的二阶傍轴近似吸收边界条件(CE2);AWWE吸收边界几乎不增加额外计算量,并且不影响内部区域数值计算的稳定性。
To attenuate artificial edge reflections arising at truncation boundary,stable and effective absorbing boundary conditions(ABC) should be applied in seismic numerical simulation.In this paper,we use a high accurate one-way wave equation,named arbitrarily wide-angle wave equation(AWWE),as ABC in second-order acoustic wave equation simulation.We give out the corresponding discrete formulation of the boundary condition using the finite-difference method.Meanwhile,the corner regions are carefully treated.The numerical simulations of a homogeneous medium and 2D Marmousi model show that AWWE boundary condition can adapt to a wide range of incident angle and has a better absorption effect than second-order paraxial approximations(CE2 in short).The computation efficiency of the AWWE boundary condition is almostidentical to CE2.In addition,such an ABC has noinfluence to the interior stability.
To attenuate artificial edge reflections arising at truncation boundary,stable and effective absorbing boundary conditions(ABC) should be applied in seismic numerical simulation.In this paper,we use a high accurate one-way wave equation,named arbitrarily wide-angle wave equation(AWWE),as ABC in second-order acoustic wave equation simulation.We give out the corresponding discrete formulation of the boundary condition using the finite-difference method.Meanwhile,the corner regions are carefully treated.The numerical simulations of a homogeneous medium and 2D Marmousi model show that AWWE boundary condition can adapt to a wide range of incident angle and has a better absorption effect than second-order paraxial approximations(CE2 in short).The computation efficiency of the AWWE boundary condition is almostidentical to CE2.In addition,such an ABC has noinfluence to the interior stability.
引文
[1]Cerjan C,Kosloff D,Kosloff R et al.A nonreflectingboundary condition for discrete acoustic and elasticwave equations.Geophysics,1985,50(4):705～708
[2]Bérenger J P.Three-dimensional perfectly matchedlayer for the absorption of electromagnetic waves.JComput Phys,1996,127(2):363～379
[3]赵海波,王秀明,王东等.完全匹配层吸收边界在孔隙介质弹性波模拟中的应用.地球物理学报,2007,50(2):581～591Zhao Haibo,Wang Xiuming,Wang Dong et al.Ap-plications of the boundary absorption using aperfectlymatched layer for elastic wave simulation in poroelas-tic media.Chinese J Geophys,2007,50(2):581～591
[4]徐义,张剑锋.地震波数值模拟的非规则网格PML吸收边界.地球物理学报,2008,51(5):1520～1526Xu Yi,Zhang Jianfeng.An irregular-grid perfectlymatched layer absorbing boundary for seismic wavemodeling.Chinese J Geophys,2008,51(5):1520～1526
[5]王守东.声波方程完全匹配层吸收边界.石油地球物理勘探,2003,38(1):31～34Wang Shoudong.Absorbing boundary condition foracoustic wave equation by perfectly matched layer.OGP,2003,38(1):31～34
[6]熊章强,毛承英.声波数值模拟中改进的非分裂式PML边界条件.石油地球物理勘探,2011,46(1):35～39Xiong Zhangqiang,Mao Chengying.Improved un-split PML boundary conditions in acoustic wave nu-merical simulation.OGP,2011,46(1):35～39
[7]韩令贺,何兵寿.VTI介质一阶准P波方程正演模拟及边界条件.石油地球物理勘探,2010,45(6):819～825Han Linghe,He Bingshou.First-order Quasi-P waveequation forward modeling and boundary conditions inVTI medium.OGP,2010,45(6):819～825
[8]杜启振,孙瑞艳,张强.组合边界条件下二维三分量TTI介质波场数值模拟.石油地球物理勘探,2011,46(2):187～195Du Qizhen,Sun Ruiyan,Zhang Qiang.Numericalsimulation of three-component elastic wavefield in 2DTTI media in the condition of the combined bounda-ry.OGP,2011,46(2):187～195
[9]Clayton R,Engquist B.Absorbing boundary condi-tions for acoustic and elastic wave equations.Bulletinof the Seismological Society of America,1977,67(6):1529～1540
[10]Clayton R,Engquist B.Absorbing boundary condi-tions for wave equations migration.Geophysics,1980,45(3):895～904
[11]夏凡,董良国,马在田.三维弹性波数值模拟中的吸收边界条件.地球物理学报,2004,47(1):132～136Xia Fan,Dong Liangguo,Ma Zaitian.Absorbingboundary conditions in 3D elastic-wave numericalmodeling.Chinese J Geophys,2004,47(1):132～136
[12]杜启振,李宾.组合吸收边界条件下VTI介质地震波场模拟.石油地球物理勘探,2009,44(2):173～178Du Qizhen,Li Bin.Seismic wavefield simulation ofVTI medium under combined absorption condition.OGP,2009,44(2):173～178
[13]李文杰,魏修成,宁俊瑞.一种新的弹性波数值模拟吸收边界条件.石油地球物理勘探,2009,44(4):501～507Li Wenjie,Wei Xiucheng,Ning Junrui.A new nu-meric simulating absorbing boundary condition of e-lastic wave.OGP,2009,44(4):501～507
[14]Guddati M N,Heidari A H.Migration with arbitrar-ily wide-angle wave equations.Geophysics,2005,70(3):61～70
[15]Guddati M N,Heidari A H.Application of arbitrari-ly wide-angle wave equations to subsurface imagingand nondestructive evaluation.Proceedings of the16th Engineering Mechanics Conference,AmericanSociety of Civil Engineers,2003,794～804
[16]Guddati M N,Tassoulas J L.Continued-fractionsabsorbing boundary conditions for the wave equation.Journal of Computational Acoustics,2000,8(1):139～156
[17]Guddati M N.Arbitrarily wide-angle wave equationsfor complex media.Computer Methods in AppliedMechanics and Engineering,2006,195(3):65～93
[18]孙歧峰,杜启振.任意广角波动方程频率—空间域叠前深度偏移成像.石油地球物理勘探,2011,46(6):890～896Sun Qifeng,Du Qizhen.The frequency-space domainprestack depth migration with arbitrarily wide-anglewave equation.OGP,2011,46(6):890～896
[19]孙歧峰.基于任意广角波动方程的频率—空间域深度偏移方法研究.CT理论与应用研究,2010,19(2):17～24Sun Qifeng.The frequency-space domain depth mi-gration based on arbitrarily wide-angle wave equation.CT Theory and Applications,2010,19(2):17～24
[20]何兵寿,张会星,张晶.任意广角波动方程叠前逆时深度偏移.地震学报,2008,30(5):491～499He Bingshou,Zhang Huixing,Zhang Jing.Prestackreverse-time depth migration of arbitrarily wide-anglewave equations.Acta Seismologica Sinica,30(5):491～499
[21]周辉,谢春临,王尚旭等.复杂地表地震资料叠前深度偏移成像.吉林大学学报(地球科学版),2012,42(1):262～268Zhou Hui,Xie Chunlin,Wang Shangxu et al.Pre-stack depth migration for geological structures withcomplicated surface.Journal of Jilin University(Earth Science Edition),2012,42(1):262～268
[22]Claerbout J F.Fundamentals of Geophysical DataProcessing.New York:McGraw-Hill,1976
[2]Bérenger J P.Three-dimensional perfectly matchedlayer for the absorption of electromagnetic waves.JComput Phys,1996,127(2):363～379
[3]赵海波,王秀明,王东等.完全匹配层吸收边界在孔隙介质弹性波模拟中的应用.地球物理学报,2007,50(2):581～591Zhao Haibo,Wang Xiuming,Wang Dong et al.Ap-plications of the boundary absorption using aperfectlymatched layer for elastic wave simulation in poroelas-tic media.Chinese J Geophys,2007,50(2):581～591
[4]徐义,张剑锋.地震波数值模拟的非规则网格PML吸收边界.地球物理学报,2008,51(5):1520～1526Xu Yi,Zhang Jianfeng.An irregular-grid perfectlymatched layer absorbing boundary for seismic wavemodeling.Chinese J Geophys,2008,51(5):1520～1526
[5]王守东.声波方程完全匹配层吸收边界.石油地球物理勘探,2003,38(1):31～34Wang Shoudong.Absorbing boundary condition foracoustic wave equation by perfectly matched layer.OGP,2003,38(1):31～34
[6]熊章强,毛承英.声波数值模拟中改进的非分裂式PML边界条件.石油地球物理勘探,2011,46(1):35～39Xiong Zhangqiang,Mao Chengying.Improved un-split PML boundary conditions in acoustic wave nu-merical simulation.OGP,2011,46(1):35～39
[7]韩令贺,何兵寿.VTI介质一阶准P波方程正演模拟及边界条件.石油地球物理勘探,2010,45(6):819～825Han Linghe,He Bingshou.First-order Quasi-P waveequation forward modeling and boundary conditions inVTI medium.OGP,2010,45(6):819～825
[8]杜启振,孙瑞艳,张强.组合边界条件下二维三分量TTI介质波场数值模拟.石油地球物理勘探,2011,46(2):187～195Du Qizhen,Sun Ruiyan,Zhang Qiang.Numericalsimulation of three-component elastic wavefield in 2DTTI media in the condition of the combined bounda-ry.OGP,2011,46(2):187～195
[9]Clayton R,Engquist B.Absorbing boundary condi-tions for acoustic and elastic wave equations.Bulletinof the Seismological Society of America,1977,67(6):1529～1540
[10]Clayton R,Engquist B.Absorbing boundary condi-tions for wave equations migration.Geophysics,1980,45(3):895～904
[11]夏凡,董良国,马在田.三维弹性波数值模拟中的吸收边界条件.地球物理学报,2004,47(1):132～136Xia Fan,Dong Liangguo,Ma Zaitian.Absorbingboundary conditions in 3D elastic-wave numericalmodeling.Chinese J Geophys,2004,47(1):132～136
[12]杜启振,李宾.组合吸收边界条件下VTI介质地震波场模拟.石油地球物理勘探,2009,44(2):173～178Du Qizhen,Li Bin.Seismic wavefield simulation ofVTI medium under combined absorption condition.OGP,2009,44(2):173～178
[13]李文杰,魏修成,宁俊瑞.一种新的弹性波数值模拟吸收边界条件.石油地球物理勘探,2009,44(4):501～507Li Wenjie,Wei Xiucheng,Ning Junrui.A new nu-meric simulating absorbing boundary condition of e-lastic wave.OGP,2009,44(4):501～507
[14]Guddati M N,Heidari A H.Migration with arbitrar-ily wide-angle wave equations.Geophysics,2005,70(3):61～70
[15]Guddati M N,Heidari A H.Application of arbitrari-ly wide-angle wave equations to subsurface imagingand nondestructive evaluation.Proceedings of the16th Engineering Mechanics Conference,AmericanSociety of Civil Engineers,2003,794～804
[16]Guddati M N,Tassoulas J L.Continued-fractionsabsorbing boundary conditions for the wave equation.Journal of Computational Acoustics,2000,8(1):139～156
[17]Guddati M N.Arbitrarily wide-angle wave equationsfor complex media.Computer Methods in AppliedMechanics and Engineering,2006,195(3):65～93
[18]孙歧峰,杜启振.任意广角波动方程频率—空间域叠前深度偏移成像.石油地球物理勘探,2011,46(6):890～896Sun Qifeng,Du Qizhen.The frequency-space domainprestack depth migration with arbitrarily wide-anglewave equation.OGP,2011,46(6):890～896
[19]孙歧峰.基于任意广角波动方程的频率—空间域深度偏移方法研究.CT理论与应用研究,2010,19(2):17～24Sun Qifeng.The frequency-space domain depth mi-gration based on arbitrarily wide-angle wave equation.CT Theory and Applications,2010,19(2):17～24
[20]何兵寿,张会星,张晶.任意广角波动方程叠前逆时深度偏移.地震学报,2008,30(5):491～499He Bingshou,Zhang Huixing,Zhang Jing.Prestackreverse-time depth migration of arbitrarily wide-anglewave equations.Acta Seismologica Sinica,30(5):491～499
[21]周辉,谢春临,王尚旭等.复杂地表地震资料叠前深度偏移成像.吉林大学学报(地球科学版),2012,42(1):262～268Zhou Hui,Xie Chunlin,Wang Shangxu et al.Pre-stack depth migration for geological structures withcomplicated surface.Journal of Jilin University(Earth Science Edition),2012,42(1):262～268
[22]Claerbout J F.Fundamentals of Geophysical DataProcessing.New York:McGraw-Hill,1976
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