层状弹性介质的波阻抗反演

IMPEDANCE INVERSION FOR ELASTIC LAYERED MEDIA

讨论层状弹性介质的纵波阻抗和横波阻抗的同时反演问题．由纵波线源激发产生的弹性波场，通过倾斜叠加可以得到其平面波分解，分解出来的平面波场对应于以不同倾角斜入射激发所产生的波场，它们满足由二维弹性波基本方程派生出的一维偏微分方程组．利用在地面同时接收的位移速度的水平和垂直分量，可以由每个特定角度斜入射产生的平面波场所满足的一维方程组反演层状弹性介质的两个参数，在已知密度情况下，可以反演纵波阻抗和横波阻抗．本文给出了这个反演问题的提法，构造了求解此问题的特征线差分格式，并计算了一些数值例子．数值结果表明纵波阻抗的反演是成功的．

The simultaneous inversion of pressure wave impedance and sear wave impedance for the elastic layered media is discussed. The elastic wavefield excited by the line source of pressure wave can be decomposed into the plane waves, which correspond to the different angles of incidence. The propagation of the plane elastic waves is governed by the system of one-dimensional equations derived from the fundamental equations of elastic wave. From this system for a fixed angle of incidence two parameters of the elastic layered medium can be determined by using the surface data of the vertical and horizontal components of the displacement velocity. On the assumption that the density is known, then the impedance of pressure wave and the impedance of sear wave can be determined. In the paper the formulation of two-parameter inversion problem(IIP) is presented, the characteristic difference schemes for solving IIP are constructed and some numerical experiments are performed. The numerical results show that the impedance of pressure wave can be successfully determined.