各向异性介质中三分量地震记录的FCT有限差分模拟
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摘要
基于声波或弹性波方程的有限差分方法是数值模拟地震波场或合成VSP地震记录的有力工具。然而传统的有限差分方法在每一波长内采样太少时，会存在严重的数值频微，降低数位结果的分辨率。本文将流体动力学方法中的通量校正传输技术（FCT）与求解各向异性波动方程组的有限差分方法结合，获得了一种适用于求解各向异性介质中二阶声波和弹性波方程的FCT有限差分算法，有效地压制了传统有限差分数值模拟中的数值频微。横向各向同性介质中的波场快照和VSP三分量地震记录合成均表明这种FCT技术和有限差分法的结合不仅能消除粗网格条件下数值频微而引起的伪波动，而且还能有效地压制大梯度变化、间断等所引起的数位解的不稳定。
The finite difference methods based on acoustic or elastic wave equation are very useful tools for wave-field numerical modeling or VSP data synthesizing. However,usual finite difference methods for solving these equations cause severe numerical dispersion to reduce the resolution of resultant wave field when insufficient samplings are taken in one wavelength- FCT finite difference method for easy solving the second-order acoustic and elastic wave equations in anisotropic medium has been formed by combining the flux-corrected transport (FCT) technique in hydrodynamics with the finite difference method that is used to solve wave equation system in anisotropic medium j and it suppresses effectively the numerical dispersion which occurs in usual finite-difference numerical modeling. The wave field snapshotand three-component VSP data synthesizing in transversely isotropic medium show that the good combination of FCT technique with finite difference method can eliminate the false ripples due to numerical dispersion in coarse grid,and suppress satisfactorily the numerical solution unstability caused by big gradient change,discontinuity and so on.
The finite difference methods based on acoustic or elastic wave equation are very useful tools for wave-field numerical modeling or VSP data synthesizing. However,usual finite difference methods for solving these equations cause severe numerical dispersion to reduce the resolution of resultant wave field when insufficient samplings are taken in one wavelength- FCT finite difference method for easy solving the second-order acoustic and elastic wave equations in anisotropic medium has been formed by combining the flux-corrected transport (FCT) technique in hydrodynamics with the finite difference method that is used to solve wave equation system in anisotropic medium j and it suppresses effectively the numerical dispersion which occurs in usual finite-difference numerical modeling. The wave field snapshotand three-component VSP data synthesizing in transversely isotropic medium show that the good combination of FCT technique with finite difference method can eliminate the false ripples due to numerical dispersion in coarse grid,and suppress satisfactorily the numerical solution unstability caused by big gradient change,discontinuity and so on.
引文
1 Keith C M and Crampin S.Seismic body Waves in anisotropic media:Propagation through a layer,Syn- thetic seismic Seismograms,Geophys J Roy Astr Soc, 1977, 49: 209～224, 225～243
2 Aminzadeh F. Application of elastic modelling in processing and interpretation of VSP data: A case histo- ry.Geophy ProsP,1989,37:893～906
3 Igel H,Peter M and Domin R B.Hook’s law in a staggered finite difference grid. Journal of Canadian Explorational Geophysics,1993,29:45～50
4 Chen K H. Simulation of seismic propagation in anisotropic media:Finite elemmedia: Finite element methods. The 54th SEG Annual Meeting Expanded Abstracts,1984, 631～632
5 朱培民,詹亚彬.任意各向异性介质中波传播的有限元数值模拟及其结果分析.中国地球物理学会年刊, 1993
6 Zhang Z J,He Q D,Teng J W et al.The simulation of 3-component seismic records in 2-D homogeneous tranversely isotropic media.Journal Canadian Expltional Geophysics, 1993,29: 51～58
7 Reshef M and D D Kosloff.Applications of elastic forward modelling to seismic interpretation. Geo physics,1985,50(8):1266～1272
8 Kosloff D,Carcione J M et al.Three-dimension wave Propagation simulation in elastic anisotropy media. The 59th SEG Annual Meeting Expanded Abstracts,1989,1016～1018
9 张中杰.各向异性介质中地震波动理论研究,中国科学院地球物理研究所博士后研究报告,1993
1O Chspman C H and Shearer P M.Ray tracing in azimuthally anisotropic media : quasi-shear-wave cou pling. Geophys J Int, 1989,96:65～83
11 Alford R,Kelly K and Boore D.Accuracy of finite-difference modelling of the acoustic wave equation. GeophysiCC,1974,39(6):834～842
12 Kelly K,Ward K,Treitel R and Alford R.synthetic seismograms:A finite-difference approach.Geophysics,1976,41(1):2～27
13 Dablain M A. The application Of high-order differencing to the Scalar wave equation.Geophysics,1986,51 (1):54～66
14 王才经.波动方程模拟和偏移的频效分析.计算地球物理研究文集,1990,33:521～528
15 Boris J P and Book D L.Flux-corrected transPort, 1. SHASTA, A fluid transPortalgorlthm that works. J Cmput Phys,1973,11:38～69
16 Book D L,Boris J P and Hain K.Flux-corrected transport : generalization of the method.J Comput Phys,1975,18:248～283
17 杨顶辉.各向导性介质中弹性波方程的正反演方法研究.中国科学院地球物理研究所博士学位论文,1996
18 Erveny V and Firbas P.Numerical modellingand inversion of travel-times ofselsmic body waves in inho mogeneous anisotropic media.Geophys J Roy Astr Soc,1984,76:41～51
2 Aminzadeh F. Application of elastic modelling in processing and interpretation of VSP data: A case histo- ry.Geophy ProsP,1989,37:893～906
3 Igel H,Peter M and Domin R B.Hook’s law in a staggered finite difference grid. Journal of Canadian Explorational Geophysics,1993,29:45～50
4 Chen K H. Simulation of seismic propagation in anisotropic media:Finite elemmedia: Finite element methods. The 54th SEG Annual Meeting Expanded Abstracts,1984, 631～632
5 朱培民,詹亚彬.任意各向异性介质中波传播的有限元数值模拟及其结果分析.中国地球物理学会年刊, 1993
6 Zhang Z J,He Q D,Teng J W et al.The simulation of 3-component seismic records in 2-D homogeneous tranversely isotropic media.Journal Canadian Expltional Geophysics, 1993,29: 51～58
7 Reshef M and D D Kosloff.Applications of elastic forward modelling to seismic interpretation. Geo physics,1985,50(8):1266～1272
8 Kosloff D,Carcione J M et al.Three-dimension wave Propagation simulation in elastic anisotropy media. The 59th SEG Annual Meeting Expanded Abstracts,1989,1016～1018
9 张中杰.各向异性介质中地震波动理论研究,中国科学院地球物理研究所博士后研究报告,1993
1O Chspman C H and Shearer P M.Ray tracing in azimuthally anisotropic media : quasi-shear-wave cou pling. Geophys J Int, 1989,96:65～83
11 Alford R,Kelly K and Boore D.Accuracy of finite-difference modelling of the acoustic wave equation. GeophysiCC,1974,39(6):834～842
12 Kelly K,Ward K,Treitel R and Alford R.synthetic seismograms:A finite-difference approach.Geophysics,1976,41(1):2～27
13 Dablain M A. The application Of high-order differencing to the Scalar wave equation.Geophysics,1986,51 (1):54～66
14 王才经.波动方程模拟和偏移的频效分析.计算地球物理研究文集,1990,33:521～528
15 Boris J P and Book D L.Flux-corrected transPort, 1. SHASTA, A fluid transPortalgorlthm that works. J Cmput Phys,1973,11:38～69
16 Book D L,Boris J P and Hain K.Flux-corrected transport : generalization of the method.J Comput Phys,1975,18:248～283
17 杨顶辉.各向导性介质中弹性波方程的正反演方法研究.中国科学院地球物理研究所博士学位论文,1996
18 Erveny V and Firbas P.Numerical modellingand inversion of travel-times ofselsmic body waves in inho mogeneous anisotropic media.Geophys J Roy Astr Soc,1984,76:41～51
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