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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．
In this paper, we study the parameter inversion of transversely isotropic (TIV) media with layered and vertical axis as the axis of symmetry by using the characteristic theory of PDEs. Firstly, the plane wave coupling is derived from the relationship between elastic wave equation and stress-strain in TIV media. The characteristic type of the system of equations. According to the singularity analysis and the characteristic integral method, the boundary condition of the characteristic line under continuous condition is given. The wave field continuation equation under the continuous condition, that is to say, the characteristic and characteristic boundary conditions of the plane wave coupling equations, form the layered TIV smoothing medium , The basic equations of the weak discontinuous medium parameter inversion problem. The wave field continuation equation and the characteristic boundary condition are deduced in the discontinuous case. These equations can be used to inverse the parameters of the layered media (discontinuities). Based on these basic equations, the problem of retrieving multiple elastic parameters of layered TIV media using ground multi-component seismic data is discussed.