利用广义反射-透射系数方法求解含低速层水平层状介质模型中面波频散曲线问题

Normal mode computation by the generalized reflection-transmission coefficient method in planar layered half space

在计算面波频散问题的广义反射-透射系数方法基础上研究了含有低速层的均匀平层固体地球模型的面波的频散曲线以及简正振型的计算问题.当不存在低速层时,仅利用陈晓非1993年提出的单一的久期函数对求解这两个问题已经足够.但是当模型中存在低速层时,该单一久期函数在数值求解较低阶模式很困难.本文提出用久期函数族代替该单一久期函数、对不同的简正振型模式采用对应的久期函数来求解的方法,从而更加容易有效地求解较低阶的模式,完善了利用广义反射-透射系数方法求解面波频散问题的理论和算法.

We present a new approach to calculation of dispersion curves and normal mode solutions of multilayered solid earth model with low velocity layers based on the generalized reflection-transmission coefficient method. It is efficient to tackle these two problems by utilizing the single top-layer secular function proposed by Chen in 1993. However, some lower order modes are difficult to be obtain by merely using the single top-layer secular function due to numerical singularity while the earth model contains low velocity layers. In this paper, we propose using the secular function set, instead of the single secular function, to solve this problem. With the secular function set, different modes can be calculated respectively through corresponding secular functions. Numerical experiments show that the new approach is efficient, stable and reliable, thus it makes the generalized reflection-transmission coefficient method applicable to computation of normal modes in various stratified earth models.