转换波和非转换波与射线参数p的关系

本文对Aki固体-固体分界面的反射和透射公式进行适当变换,使之成为一组适合不同坐标系下,固体、液体、气体和真空之间所有可能形成的分界面上,入射P、SV和SH波所形成的反射和透射公式,从而把不同边界条件的反射和透射方程统一起来,并且阐明了转换波和非转换波动力学特征的差异.指出:在不同弹性介质分界面上入射平面弹性波,转换波的反射系数和透射系数是射线参数p的奇函数;非转换波的反射系数和透射系数是射线参数p的偶函数.根据奇函数和偶函数的性质可见:垂直入射时不存在转换波.同时也为简化Zoeppricz方程,开展AVO分析打开新思路.

RELATIONSHIPS BETWEEN CONVERTED AND NON-CONVERTED WAVES AND PARAMETER p

In this paper, a set of analytic solutions to reflection and transmission is derived, which are suitable for P, SV and SH waves incidence on any possible interfaces composed of solid, liquid, gas and vaccum, such as solid-solid, solid-liquid, liquid-liquid and free interfaces etc. So the reflection and transmission equations, which were established by their boundary conditions and were regarded as no relation to each other are integrated. The difference of dynamics between converted wave and non-converted wave is illustrated with the solutions, and the conclusion is that for elastic plane waves incidence on different boundary conditions, the coefficients of reflection and transmission are the odd function of raypath parameter p for converted wave; and the even function of raypath parameter p for non-converted wave. Theoretical investigation has shown that amplitude versus angle of incidence (AVA) is comprised in reflected, transmitted and converted waves. Based on the properties of odd and even functions, no wave conversion occurs at normal incidence, and the conclusion offers a new way for the simplification of Zoeppritz equations and for the extension of AVA analysis in seismic exploration.