基于佐普里兹方程的高精度叠前反演方法

本文利用佐普里兹方程及其近似公式计算了四类具典型AVO特征地层模型的反射系数曲线,计算结果表明:在小角度(小于30°)入射时,利用Aki-Richards、Shuey近似公式计算的反射系数精度较高,与佐普里兹方程计算的反射系数非常接近;当入射角大于30°时,利用近似公式计算的反射系数与佐普里兹方程计算的反射系数的差别较大。为此,本文提出了直接利用佐普里兹方程进行叠前反演,并通过引入广义线性反演理论和贝叶斯方法详细推导了叠前反演算法。理论模型试算结果表明,基于佐普里兹方程的叠前反演能够获得精度较高的反演结果。

High precision prestack inversion algorithm based on Zoeppritz equations

The article uses Zoeppritz equations and its approximate formula to calculate reflection coefficient curves of four type formation models which have different AVO typical characteristics.The calculation results show that the reflection coefficients calculated by Aki-Richard and Shuey approximate formula have a high accuracy,and they are similar to reflection coefficient calculated by Zoeppritz equations when the incident angle is less than 30 degrees.However,the reflection coefficients calculated by Aki-Richard and Shuey approximate formula have a low precision and a big error compared with reflection coefficient calculated by Zoeppritz equations when the incident angle is greater than 30 degrees.Therefore,this paper proposes to directly carry out prestack inversion by use of Zoeppritz equation,and the prestack inversion algorithm is particularly derived based on the generalized linear inversion theory and Bayesian method.Test results of theoretical models show that our prestack inversion based on Zoeppritz equation can obtain inversion results with hiqher accuracy.