基于BISQ高频极限方程的交错网格法数值模拟
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摘要
杨宽德 ,杨顶辉 ,王书强 .基于 BISQ高频极限方程的交错网格法数值模拟 .石油地球物理勘探 ,2 0 0 2 ,37(5 ) :4 6 3～ 4 6 8 BISQ方程是反映含流体多孔隙介质中 Biot流动和喷射流动共同作用下地震波和声波传播的最新研究成果。本文从多孔隙横向各向同性介质的 BISQ方程的高频极限方程出发 ,利用交错网格方法对横向各向同性孔隙介质中波的传播进行了数值模拟。结果表明 ,弹性波在横向各向同性多孔隙介质中传播时存在快拟 P波、慢拟 P波、拟 SH波和拟 SV波 ,同时出现横波分裂、波面尖角等现象 ,从而验证了 BISQ理论的正确性 ,并为进一步应用、研究奠定了基础。
BISQ equation is a latest studied result which describes the propagation of seismic and acoustic waves in porous medium with fluid under common action of Biot flow and squirt flow.Starting from the high frequency limited equation of BISQ equation in transversely isotropic porous medium,the paper numerically simulated the propagation in transversely isotropic porous medium by using staggered grid method.The results show that there exist fast quasi P wave,slow quasi P wave,quasi SH wave and quasi SV wave as well as also there appears the phenomenon of S wave splitting and acute wave plane when elastic wave propagates in the transversely isotropic porous medium,which show the correctness of BISQ theory and laid the foundation of further applied study.
BISQ equation is a latest studied result which describes the propagation of seismic and acoustic waves in porous medium with fluid under common action of Biot flow and squirt flow.Starting from the high frequency limited equation of BISQ equation in transversely isotropic porous medium,the paper numerically simulated the propagation in transversely isotropic porous medium by using staggered grid method.The results show that there exist fast quasi P wave,slow quasi P wave,quasi SH wave and quasi SV wave as well as also there appears the phenomenon of S wave splitting and acute wave plane when elastic wave propagates in the transversely isotropic porous medium,which show the correctness of BISQ theory and laid the foundation of further applied study.
引文
[1] BiotM A.Theory of propagation of elastic waves ina fluid- saturated porous solid:I L ow- frequencyrange;Higher frequency range.J AcoustSocAmer,1956,28:168～191
[2] BiotM A.Mechanics of deformation and acousticpropagation in porous m edia.J ApplPhys,1962,33(4):1482～1498
[3] BiotM A.Generalized theory of acoustic propaga-tion in porous dissipative m edia.J AcoustSocAmer,1962,34(9):1254～1264
[4] PlonaT J.Observation of a second bulk com press-ional wave in a porous media at ultrasonic frequen-cies.ApplPhysL ett,1980,36:259～261
[5] DvorkinJandNurA.Dynamic poroelasticity:a u-nified m odel with the squirt and theBiot mecha-nisms.Geophysics,1993,58(4):524～533
[6] ParraJ O.The transversely isotropic poroelasticwave equation including theBiot and the squirtmechanisms:theory and application.Geophysics,1997,62:309～318
[7] ParaJO.Poroelastic model to relate seism ic waveattenuation and dispersion to perm eabilityanisotropy.Geophysics,2000,65:201～210
[8] YangD H andZhangZ J.Effects of theBiot and thesquirt- flow coupling interaction on anisotropic elasticwaves.ChineseScienceBulletin,2000,45:2130～2138
[9] YangD H andZhangZ J.Poroelastic wave equationincluding theBiot/Squirt mechanism and the solid/fluid coupling anisotropy.WaveMotion,2002,35:223～245
[10] 杨顶辉,陈小宏.含流体多孔介质的BISQ模型.石油地球物理勘探,2001,36(2):146～159
[11] 杨顶辉.基于固—流耦合作用各向异性的弹性波方程.中国学术期刊文摘(科技快报),2000,6:733～735
[12] FornbergB.High- order finite differences and pseu-do- spectral method on staggered grids.SIMA J N u-merAnal,1990,27(4):904～918
[13] OzdenvarT andMcMechanG A.Causes and reduc-tion of numerical artifacts in pseudo- spectral wave-field extrapolation.GeophysJ Int,1996,126(3):819～828
[14] VirieuxJ.P-SV wave propagation in heterogeneousmedia:velocity- stress finite difference m ethod.Geo-physics,1986,51(4):889～901
[2] BiotM A.Mechanics of deformation and acousticpropagation in porous m edia.J ApplPhys,1962,33(4):1482～1498
[3] BiotM A.Generalized theory of acoustic propaga-tion in porous dissipative m edia.J AcoustSocAmer,1962,34(9):1254～1264
[4] PlonaT J.Observation of a second bulk com press-ional wave in a porous media at ultrasonic frequen-cies.ApplPhysL ett,1980,36:259～261
[5] DvorkinJandNurA.Dynamic poroelasticity:a u-nified m odel with the squirt and theBiot mecha-nisms.Geophysics,1993,58(4):524～533
[6] ParraJ O.The transversely isotropic poroelasticwave equation including theBiot and the squirtmechanisms:theory and application.Geophysics,1997,62:309～318
[7] ParaJO.Poroelastic model to relate seism ic waveattenuation and dispersion to perm eabilityanisotropy.Geophysics,2000,65:201～210
[8] YangD H andZhangZ J.Effects of theBiot and thesquirt- flow coupling interaction on anisotropic elasticwaves.ChineseScienceBulletin,2000,45:2130～2138
[9] YangD H andZhangZ J.Poroelastic wave equationincluding theBiot/Squirt mechanism and the solid/fluid coupling anisotropy.WaveMotion,2002,35:223～245
[10] 杨顶辉,陈小宏.含流体多孔介质的BISQ模型.石油地球物理勘探,2001,36(2):146～159
[11] 杨顶辉.基于固—流耦合作用各向异性的弹性波方程.中国学术期刊文摘(科技快报),2000,6:733～735
[12] FornbergB.High- order finite differences and pseu-do- spectral method on staggered grids.SIMA J N u-merAnal,1990,27(4):904～918
[13] OzdenvarT andMcMechanG A.Causes and reduc-tion of numerical artifacts in pseudo- spectral wave-field extrapolation.GeophysJ Int,1996,126(3):819～828
[14] VirieuxJ.P-SV wave propagation in heterogeneousmedia:velocity- stress finite difference m ethod.Geo-physics,1986,51(4):889～901
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