组合吸收边界条件下VTI介质地震波场模拟
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摘要
针对横向各向同性(VTI)介质P-SV波和SH波一阶速度—应力波动方程,本文应用交错网格法进行了地震波场数值模拟。其模拟效果在很大程度上取决于边界条件的处理。针对特征分析法吸收边界条件存在的边界处差分精度低、吸收效果差等问题,本文采用特征分析法和扩边衰减法形成组合边界条件对人工边界进行吸收处理,较显著地削弱数值频散,提高了差分精度;同时还提出了改进的衰减函数及其应用原则,可以更好地模拟复杂介质波场传播机理。
One-order P-SV and SH wave velocity-stress wave equation in transversely isotropic(VTI)medium is able to be used for numeric simulation of seismic wavefield with the aid of staggering grid method,which depends on the treatment of boundary condition to a very degree.Facing the issue that the absorption boundary condition of characteristic analysis method characterized by lower differential precision at boundary and poorer absorption effect,the paper presented using characteristic analysis method and boundary-enlarged attenuation method to form combined boundary condition to carry out absorption processing of manual boundary,which remarkably weakens numeric dispersion and improves differential precision;at the same time,the paper also presented the improved damping function and application principle,which is able to better simulate the propagation mechanism of wavefield in complex medium.
One-order P-SV and SH wave velocity-stress wave equation in transversely isotropic(VTI)medium is able to be used for numeric simulation of seismic wavefield with the aid of staggering grid method,which depends on the treatment of boundary condition to a very degree.Facing the issue that the absorption boundary condition of characteristic analysis method characterized by lower differential precision at boundary and poorer absorption effect,the paper presented using characteristic analysis method and boundary-enlarged attenuation method to form combined boundary condition to carry out absorption processing of manual boundary,which remarkably weakens numeric dispersion and improves differential precision;at the same time,the paper also presented the improved damping function and application principle,which is able to better simulate the propagation mechanism of wavefield in complex medium.
引文
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[4]Levander L R.Fourth-order finite-difference P-SV seismograms.Geophysics,1988,3(11):1425～1435
[5]Crase E.High-order(space and time)finite-difference and modeling of elastic wave equation.Expanded Ab-stracts of60th SEG Mtg,1990,987～991
[6]董良国,马在田,曹景忠等.一阶弹性波方程交错网格高阶差分解法.地球物理学报,2000,43(3):411～419
[7]Saenger E H,Gold N,Shapiro S A.Modeling the propagation of elastic waves using a modified finite-difference grid.Wave Motion,2000,31:77～92
[8]Clayton R,Engquiste B.Absorbing boundary condi-tions for acoustic and elastic wave equat-ions.BSSA,1977,67:1529～1540
[9]廖振鹏,周正华,张艳红.波动数值模拟中透射边界的稳定实现.地球物理学报,2002,45(4):533～543
[10]Cerjan C,Kosloff D.A none reflection boundary con-dition for discrete acoustic and elastic wave equation.Geophysics,1985,50(4):705～708
[11]Berenger J.A perfectly matched layer for the absorp-tion of electro-magnetic waves.Jcomput Phys,1994,114:185～200
[12]武晔,李小凡,赵玉莲等.2.5维各向异性介质中地震波场数值模拟.物探化探计算技术,2006,28(4):290～295
[13]董良国.弹性波数值模拟中的吸收边界条件.石油地球物理勘探,1999,34(1):45～56
[14]吴国忱,梁锴.VTI介质准P波频率空间域组合边界条件研究.石油物探,2005,44(4):301～307
[15]周竹生,刘喜亮,熊孝雨.弹性介质中瑞雷面波有限差分法正演模拟.地球物理学报,2007,50(2):567～573
[16]牟永光,裴正林.三维复杂介质地震数值模拟.北京:石油工业出版社,2005,45～51
[2]Virieux J.SH-wave propagationin heterogeneous media:Velocity-stress finite difference method.Geophysics,1984,49(11):33～1941
[3]Virieux J.P-SV wave propagation in heterogeneous media:Velocity-stress finite difference method.Geo-physics,1986,5(4):889～893
[4]Levander L R.Fourth-order finite-difference P-SV seismograms.Geophysics,1988,3(11):1425～1435
[5]Crase E.High-order(space and time)finite-difference and modeling of elastic wave equation.Expanded Ab-stracts of60th SEG Mtg,1990,987～991
[6]董良国,马在田,曹景忠等.一阶弹性波方程交错网格高阶差分解法.地球物理学报,2000,43(3):411～419
[7]Saenger E H,Gold N,Shapiro S A.Modeling the propagation of elastic waves using a modified finite-difference grid.Wave Motion,2000,31:77～92
[8]Clayton R,Engquiste B.Absorbing boundary condi-tions for acoustic and elastic wave equat-ions.BSSA,1977,67:1529～1540
[9]廖振鹏,周正华,张艳红.波动数值模拟中透射边界的稳定实现.地球物理学报,2002,45(4):533～543
[10]Cerjan C,Kosloff D.A none reflection boundary con-dition for discrete acoustic and elastic wave equation.Geophysics,1985,50(4):705～708
[11]Berenger J.A perfectly matched layer for the absorp-tion of electro-magnetic waves.Jcomput Phys,1994,114:185～200
[12]武晔,李小凡,赵玉莲等.2.5维各向异性介质中地震波场数值模拟.物探化探计算技术,2006,28(4):290～295
[13]董良国.弹性波数值模拟中的吸收边界条件.石油地球物理勘探,1999,34(1):45～56
[14]吴国忱,梁锴.VTI介质准P波频率空间域组合边界条件研究.石油物探,2005,44(4):301～307
[15]周竹生,刘喜亮,熊孝雨.弹性介质中瑞雷面波有限差分法正演模拟.地球物理学报,2007,50(2):567～573
[16]牟永光,裴正林.三维复杂介质地震数值模拟.北京:石油工业出版社,2005,45～51
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