应力诱导各向异性介质中地震波的传播
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摘要
主要讨论了应力变化如何影响各向异性介质中波速度的问题。推导了一般各向异性介质在初始应力下的Christoffel方程,得到介质中3种波的相速度和初始应力的关系表达式;通过实验数据验证了单轴应力能够诱导各向异性,当施加单轴应力时,速度在沿应力的方向增加最大,在垂直应力的方向增加最小,实验结果与理论推导一致;用Christoffel方程的数值解模拟在3种对称情况下的弹性各向异性介质中初始应力对波速度的影响。数值结果表明:初始应力对各向异性介质中波传播速度的影响,随着各向异性强度的增加而增大,而且速度越慢,影响越大。
In this paper,the problem that how stress change inference the wave velocity of anisotropic media is discussed.Firstly,the Christoffel function about general anisotropic medium under initial stress is derived and the expression between phase velocity of three modeled wave and initial stress in the media is obtained.Experiment shows that uniaxial stress can induce anisotropy.When the media is loaded under uniaxial stress,wave velocity along the direction of the stress increase maximally,while increased minimally in the direction perpendicular to the stress,the experimental results coincide with the theory.Finally,under the condition of three kinds of symmetries,the inference caused by the initial stress to the wave velocity in elastic anisotropic media is modeled by the numerical solution of the Christoffel equation.The numerical results show that: the inference caused by the initial stress to the wave velocity in anisotropic media increase with the degree of anisotropy and slower the velocity is,the greater the inference will be.
In this paper,the problem that how stress change inference the wave velocity of anisotropic media is discussed.Firstly,the Christoffel function about general anisotropic medium under initial stress is derived and the expression between phase velocity of three modeled wave and initial stress in the media is obtained.Experiment shows that uniaxial stress can induce anisotropy.When the media is loaded under uniaxial stress,wave velocity along the direction of the stress increase maximally,while increased minimally in the direction perpendicular to the stress,the experimental results coincide with the theory.Finally,under the condition of three kinds of symmetries,the inference caused by the initial stress to the wave velocity in elastic anisotropic media is modeled by the numerical solution of the Christoffel equation.The numerical results show that: the inference caused by the initial stress to the wave velocity in anisotropic media increase with the degree of anisotropy and slower the velocity is,the greater the inference will be.
引文
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[9]Nur,Amos and Gene Simmons.Stress-induced velocity anisotropy in rock:An experimental study,J.Geophys.Res.,1969,74(27):6667-6674.
[10]Tolstoy,I.On elastic waves in prestressed solid.J.Geophys.Res.,1982,87:6823-6827.
[11]Degtyar,A.D.,and Rokhlin,S.I.Absolute stress determination in orthotropic materials from angular dependence of ultrasonic veloci-ties.J.Appl.Phys.,1995,78:1547-1556..
[12]Degtyar,A.,D.and Rokhlin.S.I.Stress effect on ultrasonic wave propagation through the solid-solid and liquid-solid plane interface.Reviewsof Progress in Quantitative NDE Vol.16B(eds)D O Thompson and D E Chimenti(New York:Plenum),1997,pp.1699-1706.
[13]Degtyar,A.D.,and Rokhlin,S.I.Stress effect on boundary conditions and elastic wave propagation through an interface between ani-sotropic media.J.Acoust.Soc.Am.,1998,104:1992-2003.
[14]Man,C.S.,and Lu,W.Y.Towards an acoustoelastic theory for measurements of residual stress.J.Elast.,1987,17:159-182.
[15]Chai,J.F.,and Wu,T.T.Determination of surface wave velocities in a prestressed anisotropic solid.NDT&E Int,1996,29:281-292.
[16]Prikazchikov,D.A.,and Rogerson,G.A.Some comments on the dynamic properties of anisotropic and strongly anisotropic pre-stressed elastic solids.Int.J.Engg.Sci.,2003,41:149-171.
[17]曾融生.固体地球物理学导论[M].北京:科学出版社,1980:156.
[18]Nikitin,L.V.,and Chesnokov,E.M.Wave propagation in elastic media with stress-induced anisotropy.Geophys.J.R.Astr.Soc,1984,76:129-133.
[19]Johnson,P.A.,and Rasolofosaon,P.Nonlinear elasticity and stress-induced anisotropy in rock.J.Geophys.Res.,1996,100(B2):3113-3124.
[20]Sharma,M.D.,and Garg,Neetu.Wave velocities in a pre-stressed anisotropic elastic medium.J.Earth.Syst.Sci.,2006,115(2):257-265.
[21]Rasolofosaon,P.N.J.,and Zinszner,B.E.Comparison between permeability anisotropy and elasticity anisotropy of reservoir rocks.Geophysics,2002,67:230-240.
[2]Anderson,D.L.Theory of the Earth.Blackwell Scientific Publications,Oxford,UK,1989.
[3]Thill,R.E.,Willard,R.J.,and Bur T R.Correlation of longitudinal velocity variation with rock fabric.J.Geophys.Res.,1969,74(20):4897-4909.
[4]Cauchy,A.L.Exercise de Mathematique.Paris:Bure Feres,1827.
[5]Biot,M.A.Non-linear theory of elasticity and the linearized case for a body under initial stress.Phil.Mag,1939,27(7):468-489.
[6]Biot,M.A.Influence of initial stress on elastic waves.J.Appl.Phys.,1940,11:522-530.
[7]Hayes,M.Wave propagation and uniqueness in prestressed elastic solids.Proc.Roy.Soc,London,1963,A274:500-506.
[8]Biot,M.A.Mechanics of Incremental Deformation.New York:John Wiley,1965,p.214..
[9]Nur,Amos and Gene Simmons.Stress-induced velocity anisotropy in rock:An experimental study,J.Geophys.Res.,1969,74(27):6667-6674.
[10]Tolstoy,I.On elastic waves in prestressed solid.J.Geophys.Res.,1982,87:6823-6827.
[11]Degtyar,A.D.,and Rokhlin,S.I.Absolute stress determination in orthotropic materials from angular dependence of ultrasonic veloci-ties.J.Appl.Phys.,1995,78:1547-1556..
[12]Degtyar,A.,D.and Rokhlin.S.I.Stress effect on ultrasonic wave propagation through the solid-solid and liquid-solid plane interface.Reviewsof Progress in Quantitative NDE Vol.16B(eds)D O Thompson and D E Chimenti(New York:Plenum),1997,pp.1699-1706.
[13]Degtyar,A.D.,and Rokhlin,S.I.Stress effect on boundary conditions and elastic wave propagation through an interface between ani-sotropic media.J.Acoust.Soc.Am.,1998,104:1992-2003.
[14]Man,C.S.,and Lu,W.Y.Towards an acoustoelastic theory for measurements of residual stress.J.Elast.,1987,17:159-182.
[15]Chai,J.F.,and Wu,T.T.Determination of surface wave velocities in a prestressed anisotropic solid.NDT&E Int,1996,29:281-292.
[16]Prikazchikov,D.A.,and Rogerson,G.A.Some comments on the dynamic properties of anisotropic and strongly anisotropic pre-stressed elastic solids.Int.J.Engg.Sci.,2003,41:149-171.
[17]曾融生.固体地球物理学导论[M].北京:科学出版社,1980:156.
[18]Nikitin,L.V.,and Chesnokov,E.M.Wave propagation in elastic media with stress-induced anisotropy.Geophys.J.R.Astr.Soc,1984,76:129-133.
[19]Johnson,P.A.,and Rasolofosaon,P.Nonlinear elasticity and stress-induced anisotropy in rock.J.Geophys.Res.,1996,100(B2):3113-3124.
[20]Sharma,M.D.,and Garg,Neetu.Wave velocities in a pre-stressed anisotropic elastic medium.J.Earth.Syst.Sci.,2006,115(2):257-265.
[21]Rasolofosaon,P.N.J.,and Zinszner,B.E.Comparison between permeability anisotropy and elasticity anisotropy of reservoir rocks.Geophysics,2002,67:230-240.
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