层状横向各向同性介质反问题初探
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摘要
用偏微分方程组特征理论研究层状并以垂直轴为对称轴的横向各向同性（TIV）介质的参数反演问题，首先从弹性波运动方程与TIV介质的应力－应变关系导出了平面波耦合方程组的特征型．根据奇性分析与特征积分法给出了连续情形下的特征线边界条件，连续清形下的波场延拓方程即平面波耦合方程组的特征型与特征线边界条件组成了层状TIV平滑介质、弱间断介质参数反演问题的基本方程组．并导出了间断情形下的波场延拓方程与特征线边界条件，这些方程组可用于层状介质（间断情况）的参数反演．基于这些基本方程组，探讨了利用地面多分量地震资料反演层状TIV介质多个弹性参数的问题．
A study is conducted of inversion of elastic parameters in stratified transverselyisotropic media with a vertical axis of symmetry (TIV media) by using partial differentialsystem characteristic theory. At first, the characteristic type of plane wave coupledequations are derived from equation of motion and stress-strain relation. Thencharacteristic line boundary condition expressions (continued situation) are given throughmethods of singularity analysis and characteristic line integral. These two systems arebasic equations for inversion of elastic parameters in stratified smooth media or weaklydiscontinued TIV media, Besides, wavefield extrapolation formulae and characteristicline boundary condition expressions corresponding to discontinued situation are also attained and can be used for inversion of elastic parameters in stratified TIV media(discontinued situation). At last, it is considered how to reconstruct simultaneouslyseveral or six elastic parameters (density and five dependent stiffness coefficients)from multi-wave multi-component seismic data at the surface through analysis ofthese basic systems.
A study is conducted of inversion of elastic parameters in stratified transverselyisotropic media with a vertical axis of symmetry (TIV media) by using partial differentialsystem characteristic theory. At first, the characteristic type of plane wave coupledequations are derived from equation of motion and stress-strain relation. Thencharacteristic line boundary condition expressions (continued situation) are given throughmethods of singularity analysis and characteristic line integral. These two systems arebasic equations for inversion of elastic parameters in stratified smooth media or weaklydiscontinued TIV media, Besides, wavefield extrapolation formulae and characteristicline boundary condition expressions corresponding to discontinued situation are also attained and can be used for inversion of elastic parameters in stratified TIV media(discontinued situation). At last, it is considered how to reconstruct simultaneouslyseveral or six elastic parameters (density and five dependent stiffness coefficients)from multi-wave multi-component seismic data at the surface through analysis ofthese basic systems.
引文
[1]滕吉文、张中杰、王爱武等,弹性介质各向异性研究沿革、现状与问题,地球物理学进展,7,14-28,1992
[2] Takeuchi, H., Saito, M., Seismic surface waves, In: Methods of Computational Physics, 11, ed. By Bolt, B.A., New York: Academic Press, 1972.
[3] Auld, B. A.. Acoustic Fields and Waves in Solids, New York: John Wiley & Sons, Inc., 1973.
[4] Fryer, G. J., Frazer, L. N., Seismic waves in stratified anisotropic media, Geophys.J. Roy.Astr.Soc., 78,691-710, 1984.
[5] Fryer, G. J., Frazer, L N., Seismic waves in stratified edsotropic media-Ⅱ elastodynamic eigensolutionsfor some anisotropic systems, Geophys. J Roy. Astr. Soc., 81, 73-101, 1987.
[6] Graebner, M.. Plane-wave reflection and transmission coefficients for a transversely isotropic solid, Geophysics,57, 1512-1519, 1992.
[7] Amundsen, L.. Reitan, A., Extraction of P-and S-waves from the vertical component of the partical velocityat the sea floor, Geophysics, 60, 231-240, 1995.
[8] Byun. B. S., Corrigan, D., Seimic traveltime inversion for traveltime inversion for transverse isotropy, Geophysics,55, 192-200, 1990.
[9]张关泉,一维波动方程的反演问题,中国科学(A辑), 18,707-721, 1988
[10]王天禧,用平面波延拓方程进行地震数据的叠前速度及演,地球物理学报,36, 388-394, 1993.
[11]刘家琦、刘克安,微分方程反演波阻抗剖面,地球物理学报,101,101—107、1994.
[12]李幼铭,从矢量波动方程出发反演层状地球结构的方法,地球物理学报,33(专辑Ⅱ),19-29,1990
[13] Yagle, A. E., Levy, B. C., A layer-stripping solution of the inverse problem for one-dimensional elasticmediurn, Geophysics, 50, 425-433, 1985.
[14] Liu, P.. Tsai-C.. Wu, T., Inversion of the elastic parameters of a layered medium, J Acoust. Soc. Am., 97,1687-1693, 1995.
[15] Song Hai-bin,Ma Zai-tian, Zhang Guan-quan,Finite bandwidth simultanous inversion of three parametersin stratified elastic media, 65th Ann. Internat. Mtg., Soc. Expl. Geophys., Expandd Abetracts, 643-646,1995.
[16]李世雄,一维波动方程的奇性及演与小波,地球物理学报,38,93对-104,1995.
[17]杨文采,地震道的非线性混浊反演(Ⅰ),地球物理学报,36,222-232,1993
[18]杨文采,非线性地震道的混饨反演(Ⅱ),地球物理学报,36,376-387,1993.
[19] Aki, K, Richards,P, G, Quantitative Seismology,San Fraciscisco:W.H.Freeman and Company,1980.
[20]Courant,R.Hilbert,D,Methods of Mathematical Physics,Vol.Ⅱ,New York:John Wiley,1962.
[2] Takeuchi, H., Saito, M., Seismic surface waves, In: Methods of Computational Physics, 11, ed. By Bolt, B.A., New York: Academic Press, 1972.
[3] Auld, B. A.. Acoustic Fields and Waves in Solids, New York: John Wiley & Sons, Inc., 1973.
[4] Fryer, G. J., Frazer, L. N., Seismic waves in stratified anisotropic media, Geophys.J. Roy.Astr.Soc., 78,691-710, 1984.
[5] Fryer, G. J., Frazer, L N., Seismic waves in stratified edsotropic media-Ⅱ elastodynamic eigensolutionsfor some anisotropic systems, Geophys. J Roy. Astr. Soc., 81, 73-101, 1987.
[6] Graebner, M.. Plane-wave reflection and transmission coefficients for a transversely isotropic solid, Geophysics,57, 1512-1519, 1992.
[7] Amundsen, L.. Reitan, A., Extraction of P-and S-waves from the vertical component of the partical velocityat the sea floor, Geophysics, 60, 231-240, 1995.
[8] Byun. B. S., Corrigan, D., Seimic traveltime inversion for traveltime inversion for transverse isotropy, Geophysics,55, 192-200, 1990.
[9]张关泉,一维波动方程的反演问题,中国科学(A辑), 18,707-721, 1988
[10]王天禧,用平面波延拓方程进行地震数据的叠前速度及演,地球物理学报,36, 388-394, 1993.
[11]刘家琦、刘克安,微分方程反演波阻抗剖面,地球物理学报,101,101—107、1994.
[12]李幼铭,从矢量波动方程出发反演层状地球结构的方法,地球物理学报,33(专辑Ⅱ),19-29,1990
[13] Yagle, A. E., Levy, B. C., A layer-stripping solution of the inverse problem for one-dimensional elasticmediurn, Geophysics, 50, 425-433, 1985.
[14] Liu, P.. Tsai-C.. Wu, T., Inversion of the elastic parameters of a layered medium, J Acoust. Soc. Am., 97,1687-1693, 1995.
[15] Song Hai-bin,Ma Zai-tian, Zhang Guan-quan,Finite bandwidth simultanous inversion of three parametersin stratified elastic media, 65th Ann. Internat. Mtg., Soc. Expl. Geophys., Expandd Abetracts, 643-646,1995.
[16]李世雄,一维波动方程的奇性及演与小波,地球物理学报,38,93对-104,1995.
[17]杨文采,地震道的非线性混浊反演(Ⅰ),地球物理学报,36,222-232,1993
[18]杨文采,非线性地震道的混饨反演(Ⅱ),地球物理学报,36,376-387,1993.
[19] Aki, K, Richards,P, G, Quantitative Seismology,San Fraciscisco:W.H.Freeman and Company,1980.
[20]Courant,R.Hilbert,D,Methods of Mathematical Physics,Vol.Ⅱ,New York:John Wiley,1962.
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