双相各向异性介质中偶数阶精度有限差分数值模拟(英文)
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摘要
采用任意偶数阶精度有限差分数值模拟方法,可以提高传统有限差分方法的精度。本文首先介绍了由泰勒级数展开得到的计算任意阶导数的任意偶数阶精度有限差分方法;然后,将此方法应用于双相各向异性介质中地震波传播数值模拟中。数值模拟结果表明,模拟精度随着差分精度阶数的提高而提高;为了平衡计算精度和计算效率之间的关系,得到合适的阶数、网格大小和时间步长是比较重要的;通过模拟观测到了四类波、震源点的静态模式、SV波波面尖角、反射波和透射波等。
To improve the accuracy of the conventional finite-difference method,finite- difference numerical modeling methods of any even-order accuracy are recommended.We introduce any even-order accuracy difference schemes of any-order derivatives derived from Taylor series expansion.Then,a finite-difference numerical modeling method with any even- order accuracy is utilized to simulate seismic wave propagation in two-phase anisotropic media.Results indicate that modeling accuracy improves with the increase of difference accuracy order number.It is essential to find the optimal order number,grid size,and time step to balance modeling precision and computational complexity.Four kinds of waves,static mode in the source point,SV wave cusps,reflection and transmission waves are observed in two-phase anisotropic media through modeling.
To improve the accuracy of the conventional finite-difference method,finite- difference numerical modeling methods of any even-order accuracy are recommended.We introduce any even-order accuracy difference schemes of any-order derivatives derived from Taylor series expansion.Then,a finite-difference numerical modeling method with any even- order accuracy is utilized to simulate seismic wave propagation in two-phase anisotropic media.Results indicate that modeling accuracy improves with the increase of difference accuracy order number.It is essential to find the optimal order number,grid size,and time step to balance modeling precision and computational complexity.Four kinds of waves,static mode in the source point,SV wave cusps,reflection and transmission waves are observed in two-phase anisotropic media through modeling.
引文
Biot,M.A.,1955,Theory of elasticity and consolidation for a porous anisotropic solid:Journal of Applied Physics,26,182-185.
Biot,M.A.,1956,Theory of propagation of elastic waves in fluid-saturated porous solidⅠ:Low- frequency range:Journal of the Acoustical Society of America,28, 168-178.
Dai,N.,Vafidis,A.,and Kanasewich, E.R.,1995,Wave propagation in heterogeneous,porous media:A velocity-stress,finite-difference method:Geophysics,60,327-340.
Deresiewicz,H.,and Rice,J.T., 1962,The effect of boundaries on wave propagation in a liquid filled porous-solid,Ⅲ-reflection of plane waves at a free plane boundary (general case):Bulletin of the Seismological Society of America, 52,505-525.
Deresiewicz,H.,and Rice,J.T., 1964,The effect of boundaries on wave propagation in a liquid filled porous-solid,Ⅴ-transmission across a plane interface:Bulletin of the Seismological Society of America, 54,409-416.
Fornberg,B.,1987,The pseudospectral method- comparisons with finite differences for the elastic wave equation: Geophysics,52,483-501
Geerstma,J.,and Smit,D.C.,1961, Some aspects of elastic wave propagation in fluid-saturated porous solids:Geophysics,26,169 -181.
Korneev,V.,2008,Slow waves in fractures filled with viscous fluid: Geophysics,73(1),N1-N7.
Li,Z.S.,2008,Physical mechanism of seismic attenuation in a two-phase medium:Applied Geophysics,5(1),9-17.
Liu,Y.,and Li,C.C.,1999,Research on propagation properties of elastic waves in two-phase anisotropic media:Acta Seismologica Sinica, 12(4),405-412.
——,2000,Study of elastic wave propagation in two-phase anisotropic media by numerical modeling of pseudospectral method:Acta Seismologica Sinica,13 (2),143-150.
Liu,Y.B.,Li,Y.M.,and Wu,R.S.,1994,Seismic wave propagation in transversely isotropic porous media: Acta Geophysica Sinica(in Chinese),37,499-514.
Liu,Y.,Li,C.C.,and Mou,Y.G.,2000,Reflections and transmissions of plane wave on an interface between dissimilar two-phase,transversely isotropic media: Chinese Journal of Geophysics(in Chinese),43(5), 731-739.
Liu,Y.,and Wei,X.C.,2003,Finite element equations and numerical simulation of elastic wave propagation in two-phase anisotropic media:Acta Seismologica Sinica(English Edition),16(2),166-174.
——,2004,Fast P-wave AVO in fluid-saturated porous media with aligned fractures:Journal of Geophysics and Engineering,1,307-311.
Liu,Y.,Li,C.C.,and Mou,Y.G.,1998,Finite-difference numerical modeling of any even-order accuracy:Oil Geophysical Prospecting(in Chinese),33,1-10.
Pei,Z.L.,2006,Staggering grid high-order finite- difference modeling of elastic wave transmission in biphase anisotropic medium:Oil Geophysical Prospecting(in Chinese),41(2),137-143.
Ren,J.X.,and Gangi,A.F.,1994,Reflections and transmissions of plane waves on an interface between dissimilar fluid-saturated porous media:64th Ann. Internat.Mtg.,Soc.Expl.Geophys.,Expanded Abstracts,1167-1170.
Sharma,M.D.,2007,Wave propagation in a general anisotropic poroelastic medium:Blot's theories and homogenisation theory:Journal of Earth System Science,116(4),357-367.
Wang,Z.J.,He,Q.D.,and Wang,D L.,2008,The numerical simulation for a 3D two-phase anisotropic medium based on BISQ model:Applied Geophysics, 5(1),24-34.
Wei,X.C.,1995,Research on seismic wave field in two- phase anisotropic media:PhD Thesis,University of Petroleum,Beijing.
White,J.E.,1982,Computed waveforms in transversely isotropic media:Geophysics,47,771-783.
Zhang,Y.W.,Liu,X.W.,and Yao,C.L.,2005, Recognition of gas hydrate using AVO-attribute crossplots based on the porous medium theory: Applied Geophysics,2(1),7-13.
Zhu,X.H.,and McMechan,G.A.,1991,Numerical simulation of seismic responses of poroelastic reservoirs using Biot theory:Geophysics,56,328- 339.
Biot,M.A.,1956,Theory of propagation of elastic waves in fluid-saturated porous solidⅠ:Low- frequency range:Journal of the Acoustical Society of America,28, 168-178.
Dai,N.,Vafidis,A.,and Kanasewich, E.R.,1995,Wave propagation in heterogeneous,porous media:A velocity-stress,finite-difference method:Geophysics,60,327-340.
Deresiewicz,H.,and Rice,J.T., 1962,The effect of boundaries on wave propagation in a liquid filled porous-solid,Ⅲ-reflection of plane waves at a free plane boundary (general case):Bulletin of the Seismological Society of America, 52,505-525.
Deresiewicz,H.,and Rice,J.T., 1964,The effect of boundaries on wave propagation in a liquid filled porous-solid,Ⅴ-transmission across a plane interface:Bulletin of the Seismological Society of America, 54,409-416.
Fornberg,B.,1987,The pseudospectral method- comparisons with finite differences for the elastic wave equation: Geophysics,52,483-501
Geerstma,J.,and Smit,D.C.,1961, Some aspects of elastic wave propagation in fluid-saturated porous solids:Geophysics,26,169 -181.
Korneev,V.,2008,Slow waves in fractures filled with viscous fluid: Geophysics,73(1),N1-N7.
Li,Z.S.,2008,Physical mechanism of seismic attenuation in a two-phase medium:Applied Geophysics,5(1),9-17.
Liu,Y.,and Li,C.C.,1999,Research on propagation properties of elastic waves in two-phase anisotropic media:Acta Seismologica Sinica, 12(4),405-412.
——,2000,Study of elastic wave propagation in two-phase anisotropic media by numerical modeling of pseudospectral method:Acta Seismologica Sinica,13 (2),143-150.
Liu,Y.B.,Li,Y.M.,and Wu,R.S.,1994,Seismic wave propagation in transversely isotropic porous media: Acta Geophysica Sinica(in Chinese),37,499-514.
Liu,Y.,Li,C.C.,and Mou,Y.G.,2000,Reflections and transmissions of plane wave on an interface between dissimilar two-phase,transversely isotropic media: Chinese Journal of Geophysics(in Chinese),43(5), 731-739.
Liu,Y.,and Wei,X.C.,2003,Finite element equations and numerical simulation of elastic wave propagation in two-phase anisotropic media:Acta Seismologica Sinica(English Edition),16(2),166-174.
——,2004,Fast P-wave AVO in fluid-saturated porous media with aligned fractures:Journal of Geophysics and Engineering,1,307-311.
Liu,Y.,Li,C.C.,and Mou,Y.G.,1998,Finite-difference numerical modeling of any even-order accuracy:Oil Geophysical Prospecting(in Chinese),33,1-10.
Pei,Z.L.,2006,Staggering grid high-order finite- difference modeling of elastic wave transmission in biphase anisotropic medium:Oil Geophysical Prospecting(in Chinese),41(2),137-143.
Ren,J.X.,and Gangi,A.F.,1994,Reflections and transmissions of plane waves on an interface between dissimilar fluid-saturated porous media:64th Ann. Internat.Mtg.,Soc.Expl.Geophys.,Expanded Abstracts,1167-1170.
Sharma,M.D.,2007,Wave propagation in a general anisotropic poroelastic medium:Blot's theories and homogenisation theory:Journal of Earth System Science,116(4),357-367.
Wang,Z.J.,He,Q.D.,and Wang,D L.,2008,The numerical simulation for a 3D two-phase anisotropic medium based on BISQ model:Applied Geophysics, 5(1),24-34.
Wei,X.C.,1995,Research on seismic wave field in two- phase anisotropic media:PhD Thesis,University of Petroleum,Beijing.
White,J.E.,1982,Computed waveforms in transversely isotropic media:Geophysics,47,771-783.
Zhang,Y.W.,Liu,X.W.,and Yao,C.L.,2005, Recognition of gas hydrate using AVO-attribute crossplots based on the porous medium theory: Applied Geophysics,2(1),7-13.
Zhu,X.H.,and McMechan,G.A.,1991,Numerical simulation of seismic responses of poroelastic reservoirs using Biot theory:Geophysics,56,328- 339.
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