地表反射弹性波多参数反演
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摘要
在Born近似条件下,文中讨论了地震反射式弹性波三参数（密度和二个接梅参数）的衍射CT问题,给出了地表反射条件下的散射场积分表达式,和在单一频率的情况下,充分利用各类波型所包含的信息,从散射波场中分离出4种不同类型的散射波的数学表达式。最后,推导了多参数在变换域内解耦的衍射CT反传播公式。本文仅作公式推导,理论模型的数值计算将另文发表。
on the condition of Born approximation,the diffraction CT problem for the three parameters (density and two Lame's constants )of seismic reflcetion elastic wave is discussed. Thc integral expression of the scattered field is given on the surface rcflection condition. Moreover,in the case of single frcauency,the mathematical expressions for four different types of scattcred wave are seperated from the scattered wave by means of information contained in cvery mode. Finally, the invcrse-propogating farmula of diffraction CT is dorivcd. This paper shows only the formula dcrivation,and the numerical computation of theorctica] modols will be present in next paper.
on the condition of Born approximation,the diffraction CT problem for the three parameters (density and two Lame's constants )of seismic reflcetion elastic wave is discussed. Thc integral expression of the scattered field is given on the surface rcflection condition. Moreover,in the case of single frcauency,the mathematical expressions for four different types of scattcred wave are seperated from the scattered wave by means of information contained in cvery mode. Finally, the invcrse-propogating farmula of diffraction CT is dorivcd. This paper shows only the formula dcrivation,and the numerical computation of theorctica] modols will be present in next paper.
引文
[1]S.J. Norton and M. Limer,Ultrasonic reflcctivity imaging in three dimensions:Exact invcrsescattering solutions for plane,cylinderical and spherical apertures,IEEE Trans.Bionled.Eng,BME-28,(198),202～220.
[2] A.J.Devaneyand G.B Beylkin,Diffraction tomography using arbitrary source-recciver sur.faces ,Ultrason Inag ,6,(1984),181～193.
[3] D.Nahamoo,S.X.Pan and A.C.Kak,Synthetic aperturc diffraction tomography and its in-terpolation-froe computer implementation,IEEE.Trans.Sonics Ultrason,SU-31,(1984),218～229.
[4] A.J.Devaney,Geophysical diffraction tomography,IEEE Trans.Geosci Remote Sensing GE-22,(198),3～13.
[5]黄联捷、杨文采,声波方程逆散射反演的近似方法,《地球物理学报》,34,(199),626～634.
[6]J.M.Blacklcdge, et al,Quantitative diffraction tomosraphy,J.phys,D:Appl.phys,20,(1987),11～20.
[7] G.BeylkinandR.Burridgc,Linearizcd invcrse scattering problems inacoustics and elasticity,Wave Motion,12,(1990),15～22
[8] W. H. Zhu,Inverse scattcring of the three-dimensional elastic wave equation ofr three pa.rametors,J.Acoust.Soc Am,87(1990),2371～2375
[9]何樵登等,地震波衍射层析成象,《石油物探》,第31卷,第 2期,P, 76～86,1992年。
[10]W. H.Zhu,Three—parameter Born invrsion of elastic wave scatterins in a 3-D Solid,Proc·of 14th Int. Conf. on Acoustics,China, 1992.
[11] A.C.Erinsen and E.S.Suhubi,Elastodynamics, Vol,2,Academic Press,1975·
[2] A.J.Devaneyand G.B Beylkin,Diffraction tomography using arbitrary source-recciver sur.faces ,Ultrason Inag ,6,(1984),181～193.
[3] D.Nahamoo,S.X.Pan and A.C.Kak,Synthetic aperturc diffraction tomography and its in-terpolation-froe computer implementation,IEEE.Trans.Sonics Ultrason,SU-31,(1984),218～229.
[4] A.J.Devaney,Geophysical diffraction tomography,IEEE Trans.Geosci Remote Sensing GE-22,(198),3～13.
[5]黄联捷、杨文采,声波方程逆散射反演的近似方法,《地球物理学报》,34,(199),626～634.
[6]J.M.Blacklcdge, et al,Quantitative diffraction tomosraphy,J.phys,D:Appl.phys,20,(1987),11～20.
[7] G.BeylkinandR.Burridgc,Linearizcd invcrse scattering problems inacoustics and elasticity,Wave Motion,12,(1990),15～22
[8] W. H. Zhu,Inverse scattcring of the three-dimensional elastic wave equation ofr three pa.rametors,J.Acoust.Soc Am,87(1990),2371～2375
[9]何樵登等,地震波衍射层析成象,《石油物探》,第31卷,第 2期,P, 76～86,1992年。
[10]W. H.Zhu,Three—parameter Born invrsion of elastic wave scatterins in a 3-D Solid,Proc·of 14th Int. Conf. on Acoustics,China, 1992.
[11] A.C.Erinsen and E.S.Suhubi,Elastodynamics, Vol,2,Academic Press,1975·
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