褶积微分算子法数值模拟的边界问题研究
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摘要
褶积微分算子法是一种全新的数值模拟方法,已被广泛应用于复杂介质的地震波场数值模拟,但是其边界反射问题一直没有解决。这里将最佳匹配层(PML)吸收边界条件引入到褶积微分算子法中,此方法是在研究区域的边界上加入吸收层,使边界上传入吸收层的波,随传播距离按指数规律衰减,不产生任何反射,以达到消除边界反射的目的。构造不同的模型,通过对比分析证明,PML吸收边界条件能比较好地解决褶积微分算子法的边界问题,从而验证了完全匹配层吸收效果的优越性。
The convolution differentiator method is a new numerical modeling method which is widely applied in complex media numerical modeling,but the boundary reflecting problem has not been resolved.This paper introduces perfect match layer(PML) absorbing boundary which was added on the boundary of the interesting region,no reflection is produced when wave propagates from boundary of studied region to absorbing layer and wave attenuates exponentially with propagation distance.By building different models and modeling,the numerical experiments demonstrate that the PML absorbing boundary can better resolve the boundary reflecting problems,Superiority of PML boundary condition was validated.
The convolution differentiator method is a new numerical modeling method which is widely applied in complex media numerical modeling,but the boundary reflecting problem has not been resolved.This paper introduces perfect match layer(PML) absorbing boundary which was added on the boundary of the interesting region,no reflection is produced when wave propagates from boundary of studied region to absorbing layer and wave attenuates exponentially with propagation distance.By building different models and modeling,the numerical experiments demonstrate that the PML absorbing boundary can better resolve the boundary reflecting problems,Superiority of PML boundary condition was validated.
引文
[1]程冰洁,李小凡,龙桂华.基于广义正交多项式褶积微分算子的地震波场数值模拟方法[J].地球物理学报,2008,51(2):531.
[2]程冰洁,李小凡.2.5维地震波场褶积微分算子法数值模拟[J].地球物理学进展,2008,23(4):1099.
[3]刘红艳,李小凡.非均匀介质中地震波传播的数值模拟[J].物探化探计算技术,2008,30(3):173.
[4]李信富,李小凡.复杂介质地震波传播的褶积微分算子数值模拟[J].地震学报,2008,30(4):377.
[5]CLAYTON R,ENGQUISTB.Absorbing boundary con-ditions for acoustic and elastic wave equations[J].Bull.Seis.Soc.Am.,1997,67:1529.
[6]CERJAN C,KOSLOFF D.A non-reflection boundarycondition for discrete acoustic and elastic wave equation[J].Geophysics,1985,50:705.
[7]BERENGER J P.Three-dimensional perfectly matchedlayer for the absorption electromagnetic waves[J].Comp.Phys,1996,127:363.
[8]CHWE W C,LIU Q H.Perfectly matched layers forelastodynamics:A new absorbing boundary condition[J].J.Comp.Acoust.,1996,4(4):72.
[9]FRANCIS COLLINO,CHRYSOULA TSOGKA.Appli-cation of the perfectly matched absorbing lamodel to thelinear elastodynamic problem in anisotropic heterogene-ous media[J].Geophysics,2001,66(1):294.
[10]FESTA G,NIELSEN S.PML Absorbing Boundaries[J].Bulletin of the Seismological Society America,2003,93(2):891.
[11]BECACHE E,FAUQUEUX S,JOLY P.Stability ofperfectly matched layers,group velocities and aniso-tropic waves[J].Journal of Computational Physics,2003,188:399.
[12]ZENG Y Q,HE J Q,LIU Q H.The application of theperfectly matched layer in numerical modeling of wavepropagation in poroelastic media[J].Geophysics,2001,66(4):1258.
[13]SONG RUOLONG,MA JUN,WANG KEXIE.The Appli-cation of the nonsplitting perfectly matched layer in nu-merical modeling of wave propagation in poroelasticmedia[J].Applied Geophysics,2005,2(4):216.
[14]SHUO MA,PENGCHENG LIU.Modeling of the Per-fectly Matched Layer absorbing boundary and intrinsicattenuation in explicit Finite-Element methods[J].Bulletin of the Seismological Society of America,2006,96(5):1779.
[15]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[J].地球物理学报,2007,50(2):581.
[2]程冰洁,李小凡.2.5维地震波场褶积微分算子法数值模拟[J].地球物理学进展,2008,23(4):1099.
[3]刘红艳,李小凡.非均匀介质中地震波传播的数值模拟[J].物探化探计算技术,2008,30(3):173.
[4]李信富,李小凡.复杂介质地震波传播的褶积微分算子数值模拟[J].地震学报,2008,30(4):377.
[5]CLAYTON R,ENGQUISTB.Absorbing boundary con-ditions for acoustic and elastic wave equations[J].Bull.Seis.Soc.Am.,1997,67:1529.
[6]CERJAN C,KOSLOFF D.A non-reflection boundarycondition for discrete acoustic and elastic wave equation[J].Geophysics,1985,50:705.
[7]BERENGER J P.Three-dimensional perfectly matchedlayer for the absorption electromagnetic waves[J].Comp.Phys,1996,127:363.
[8]CHWE W C,LIU Q H.Perfectly matched layers forelastodynamics:A new absorbing boundary condition[J].J.Comp.Acoust.,1996,4(4):72.
[9]FRANCIS COLLINO,CHRYSOULA TSOGKA.Appli-cation of the perfectly matched absorbing lamodel to thelinear elastodynamic problem in anisotropic heterogene-ous media[J].Geophysics,2001,66(1):294.
[10]FESTA G,NIELSEN S.PML Absorbing Boundaries[J].Bulletin of the Seismological Society America,2003,93(2):891.
[11]BECACHE E,FAUQUEUX S,JOLY P.Stability ofperfectly matched layers,group velocities and aniso-tropic waves[J].Journal of Computational Physics,2003,188:399.
[12]ZENG Y Q,HE J Q,LIU Q H.The application of theperfectly matched layer in numerical modeling of wavepropagation in poroelastic media[J].Geophysics,2001,66(4):1258.
[13]SONG RUOLONG,MA JUN,WANG KEXIE.The Appli-cation of the nonsplitting perfectly matched layer in nu-merical modeling of wave propagation in poroelasticmedia[J].Applied Geophysics,2005,2(4):216.
[14]SHUO MA,PENGCHENG LIU.Modeling of the Per-fectly Matched Layer absorbing boundary and intrinsicattenuation in explicit Finite-Element methods[J].Bulletin of the Seismological Society of America,2006,96(5):1779.
[15]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[J].地球物理学报,2007,50(2):581.
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