转换波反射系数近似公式及精度分析

Approximate formula of PS-wave reflection coefficient and its precision analysis

(1.中国石油勘探开发研究院物探技术研究所，北京100083；2.中国地质大学，北京100083)

Research Institute of Petroleum Exploration and Development, PetroChina, Beijing 100083, China

为便于研究，在转换波AVO分析和叠前反演中经常用到由Zoeppritz方程衍生出的各种转换波(PS波)反射系数近似公式，但对这些研究结果尚没有进行过系统的分析和归纳，应用时存在着适用性问题。为此，在详细推导各种近似公式的基础上，对其假设条件、参数类型、适用范围进行了总结，并利用Ostrander和Goodway含气砂岩模型，分别对各近似公式的相对误差随入射角的变化进行了分析。结果表明，各近似公式在入射角较小时普遍适用，在大角度入射时，各近似公式的精度与上、下界面弹性参数的组合密切相关。

For convenience of studying, various approximate formulas of PS-wave reflection coefficient derived from Zoeppritz equation are often used in AVO analysis and pre-stack inversion. These research results have not been systematically analyzed and summarized and so there exist some problems in practical application. Based on the detailed derivation of various approximate formulas, the assumptions, parameters, and applicability were summarized. Meanwhile, Ostrander and Goodway gas-bearing sandstone models were adopted to analyze the relative error of various approximate formulas with the change of incident angle. The results show that all the approximate formulas are suitable for small incident angle situation and the accuracy of formulas are closely linked with elastic parameters of up and down boundaries in big incident angle situation.