组合边界条件下二维三分量TTI介质波场数值模拟
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摘要
从TTI介质一阶应力—速度方程出发,利用旋转交错网格高阶有限差分方法,将非分裂完全匹配层(Non-spliting Perfect Match Layer,简称NPML)边界吸收条件和自由边界条件相结合形成组合边界条件,进行了二维三分量TTI介质弹性波场数值模拟。波场快照和炮记录表明:①采用非分裂式边界条件能较好地消除近地表大角度入射波和瞬逝波;②组合边界条件与NPML边界吸收条件相比,不仅有效地压制了边界反射,同时实现了对自由地表的模拟,获得了丰富的全波场信息,其中在地表产生的PS转换横波作为一种特殊的横波现象,可为近地表结构调查以及多波波场分析等提供有益信息;③自由地表引起的面波以及多次波对偏移结果有着重要影响,因此在实际地震资料处理中应当充分考虑自由地表条件对波场的影响效应。数值模拟结果证实了组合边界条件下二维三分量TTI介质波场数值模拟方法的可行性和正确性。
In this work,based on the rotated staggered grid high-order finite-difference schemes of the first-order velocity-stress elastic wave equation,three-component elastic wavefield in the 2D TTI(Tilted Transverse Isotropy) media is simulated after combining NPML(Non-splitting Perfect Match Layers) absorption condition and the free-surface boundary condition.The snapshot and synthetic records illustrate: 1.The NPML absorption condition can efficiently attenuate near-surface incidence waves and evanescent waves;2.Comparison with the NPML absorption condition,the combined boundary conditions not only attenuate boundary reflections,but also accurately simulate free-surface situation and obtain full waves seismic data.Among these waves,PS converted wave as a special phenomenon provide useful information for the near surface structure investigation and multi-wave wavefield analysis;3.Rayleigh surface wave and surface multiples generated in the free-surface boundary have an important influence on seismic imaging,thus the free surface condition should be taken account in seismic data processing.The simulation results indicate the numerical simulation of elastic wavefield in the 2D TTI media based on the combined boundary conditions is feasible and valid.
In this work,based on the rotated staggered grid high-order finite-difference schemes of the first-order velocity-stress elastic wave equation,three-component elastic wavefield in the 2D TTI(Tilted Transverse Isotropy) media is simulated after combining NPML(Non-splitting Perfect Match Layers) absorption condition and the free-surface boundary condition.The snapshot and synthetic records illustrate: 1.The NPML absorption condition can efficiently attenuate near-surface incidence waves and evanescent waves;2.Comparison with the NPML absorption condition,the combined boundary conditions not only attenuate boundary reflections,but also accurately simulate free-surface situation and obtain full waves seismic data.Among these waves,PS converted wave as a special phenomenon provide useful information for the near surface structure investigation and multi-wave wavefield analysis;3.Rayleigh surface wave and surface multiples generated in the free-surface boundary have an important influence on seismic imaging,thus the free surface condition should be taken account in seismic data processing.The simulation results indicate the numerical simulation of elastic wavefield in the 2D TTI media based on the combined boundary conditions is feasible and valid.
引文
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[12]Du Qi-zhen,Li Bin and Hou bo.Numerical modelingof seismic wavefields in transversely isotropic mediawith a compact staggered-grid finite differencescheme.Applied Geophysics,2009,6(1):42~49
[13]Engquist B,Majda A.Absorbing boundary conditionsfor the numerical si mulation of waves.Mathematicsof Computation,1977,31:629~651
[14]Cerjan C,Kosloff D,Kosloff Rand Reshef M.A non-reflecting boundary condition for discrete acoustic andelastic wave equation.Geophysics,1985,50(4):705~708
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[16]Collino F and Tsogka C.Application of the perfectlymatched absorbing layer model to the linear elastody-namic problem in anisotropic heterogeneous media.Geophisics,2001,66(1):294~307
[17]Drossaert H F and Giannopoulos A.A nonsplit com-plex frequency-shifted PML based on recursive inte-gration for FDTD modeling of elastic waves.Geo-physics,2007,72(2):T9~T17
[18]Kuzuoglu Mand Mittra R.Frequency dependence ofthe constitutive parameters of causal perfectlymatched anisotropic absorbers.IEEE Microwave andGuided Wave Letters,1996,6:447~449
[19]Levander A R.Fourth-order finite-difference P-SVseismograms.Geophysics,1988,53(11):1425~1436
[20]Robertsson O AJ.A numerical free-surface conditionfor elastic/viscoelastic finite difference modeling inthe presence of topography.Geophisics,1996,61(6):1921~1934
[21]Bohlen Tand Saenger H E.Accuracy of heterogene-ous staggered-grid finite-difference modeling of Ray-leigh waves.Geophisics,2006,71(4):T109~T115
[22]吴国忱,罗彩明,梁锴.TTI介质弹性波频率—空间域有限差分数值模拟.吉林大学学报.2007,37(5):1023~1033Wu Guo-chen,Luo Cai-ming and Liang Kai.Fre-quency-space domain finite difference numerical si mu-lation of elastic wave in TTI media.Journal of JilinUniversity(Earth Science Edition),2007,37(5):1023~1033
[23]裴正林,王尚旭.任意倾斜各向异性介质中弹性波波场交错网格高阶有限差分法模拟.地震学报.2005.27(4),441~451Pei Zheng-lin and Wang Shang-xu.A Staggered-gridhigh-order finite-difference modeling for elastic wave-field in arbitry titlt anisotropic media.Acta Seis-mologica Sinica,2005,27(4):441~451
[24]吴国忱.各向异性介质地震波传播与成像.山东东营:中国石油大学出版社,2006
[25]Mittet R.Free-surface boundary conditions for elasticstaggered-grid modeling schemes.Geophysics,2002,67(5):1616~1623
[26]Gutowski P R,Hron F,Wagner D E and Treitel S.S*.Bulletin of the Seismological Society of Ameri-ca,1984,74(1):61~78
[27]杜启振,秦童.横向各向同性介质弹性波多分量叠前逆时偏移.地球物理学报,2009,52(3):801~807Du Qi-zhen,Qin Tong.Wavefield propagation char-acteristics in the fracture induced anisotropic doubleporosity medium.Chinese Journal of Geophysics,2009,52(3):801~807
[2]Madariaga R.Dynamics of an expanding circular fault.Bulletin of the Seismological Society of America,1976,66(3):639~666
[3]Virieux J.SH wave propagation in heterogeneousmedia:velocity-stress finite difference method.Geo-physics,1984,49(11):1933~1957
[4]Virieux J.P-SV wave propagation in heterogeneousmedia:velocity-stress finite difference method.Geo-physics,1986,51(4):889~901
[5]Robbert van Vossen,Robertsson J O A,Chapman CH.Finite-difference modeling of wave propagation ina fluid-solid configuration.Geophysics,2002,67(2):618~624
[6]Moczo P,Kristek J et al.3D heterogeneous stag-gered-grid finite-difference modeling of seismic mo-tion with volume harmonic and arithmetic averagingof elastic moduli and densities.Bulletin of the Seis-mological Society of America,2002,92(8):3042~3066
[7]Saenger E H,Gold N,Shapiro S A.Modeling thepropagation of elastic waves using a modified finite-difference grid.Wave Motion,2000,31(1):77~92
[8]Saenger E H,Bohlen T.Finite-difference modeling ofviscoelastic and anisotropic wave propagation usingthe rotated staggered grid.Geophysics,2004,69(2):583~591
[9]Li Z.Compensating finite-difference errors in 3-D mi-gration and modeling.Geophysics,1995,56(10):1650~1660
[10]Boris J P,Book D L.Flux-corrected transport:I.SHASTA,a fluid transport algorithm that works.Journal of Computational Physics,1973,11(1):38~69
[11]Book D L,Boris J P,Hain K.Flux-corrected transportII:generalization of the method.Journal of Computa-tional Physics,1975,18:248~283
[12]Du Qi-zhen,Li Bin and Hou bo.Numerical modelingof seismic wavefields in transversely isotropic mediawith a compact staggered-grid finite differencescheme.Applied Geophysics,2009,6(1):42~49
[13]Engquist B,Majda A.Absorbing boundary conditionsfor the numerical si mulation of waves.Mathematicsof Computation,1977,31:629~651
[14]Cerjan C,Kosloff D,Kosloff Rand Reshef M.A non-reflecting boundary condition for discrete acoustic andelastic wave equation.Geophysics,1985,50(4):705~708
[15]Berenger J.Aperfectly matched layer for the absorp-tionofelectromagneticwaves.JournalofComputationalPhysics,1994,114:185~200
[16]Collino F and Tsogka C.Application of the perfectlymatched absorbing layer model to the linear elastody-namic problem in anisotropic heterogeneous media.Geophisics,2001,66(1):294~307
[17]Drossaert H F and Giannopoulos A.A nonsplit com-plex frequency-shifted PML based on recursive inte-gration for FDTD modeling of elastic waves.Geo-physics,2007,72(2):T9~T17
[18]Kuzuoglu Mand Mittra R.Frequency dependence ofthe constitutive parameters of causal perfectlymatched anisotropic absorbers.IEEE Microwave andGuided Wave Letters,1996,6:447~449
[19]Levander A R.Fourth-order finite-difference P-SVseismograms.Geophysics,1988,53(11):1425~1436
[20]Robertsson O AJ.A numerical free-surface conditionfor elastic/viscoelastic finite difference modeling inthe presence of topography.Geophisics,1996,61(6):1921~1934
[21]Bohlen Tand Saenger H E.Accuracy of heterogene-ous staggered-grid finite-difference modeling of Ray-leigh waves.Geophisics,2006,71(4):T109~T115
[22]吴国忱,罗彩明,梁锴.TTI介质弹性波频率—空间域有限差分数值模拟.吉林大学学报.2007,37(5):1023~1033Wu Guo-chen,Luo Cai-ming and Liang Kai.Fre-quency-space domain finite difference numerical si mu-lation of elastic wave in TTI media.Journal of JilinUniversity(Earth Science Edition),2007,37(5):1023~1033
[23]裴正林,王尚旭.任意倾斜各向异性介质中弹性波波场交错网格高阶有限差分法模拟.地震学报.2005.27(4),441~451Pei Zheng-lin and Wang Shang-xu.A Staggered-gridhigh-order finite-difference modeling for elastic wave-field in arbitry titlt anisotropic media.Acta Seis-mologica Sinica,2005,27(4):441~451
[24]吴国忱.各向异性介质地震波传播与成像.山东东营:中国石油大学出版社,2006
[25]Mittet R.Free-surface boundary conditions for elasticstaggered-grid modeling schemes.Geophysics,2002,67(5):1616~1623
[26]Gutowski P R,Hron F,Wagner D E and Treitel S.S*.Bulletin of the Seismological Society of Ameri-ca,1984,74(1):61~78
[27]杜启振,秦童.横向各向同性介质弹性波多分量叠前逆时偏移.地球物理学报,2009,52(3):801~807Du Qi-zhen,Qin Tong.Wavefield propagation char-acteristics in the fracture induced anisotropic doubleporosity medium.Chinese Journal of Geophysics,2009,52(3):801~807
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