层状横向各向同性介质反问题初探

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 PRIMARY STUDY ON AN INVERSE PROBLEM FOR STRATIFIED TRANSVERSELY ISOTROPIC MEDIA

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.