基于贝叶斯理论的VTI介质多波叠前联合反演

Multi-wave prestack joint inversion in VTI media based on Bayesian theory

以VTI介质Ruger近似反射系数公式为基础,研究了多波叠前多参数联合反演方法。该方法以VTI介质Ruger近似公式为AVO正演方程,联合应用转换波和纵波数据,利用最小二乘原理构建目标函数来反演密度比、速度比、各向异性参数差等5个参数。在反演过程中引入贝叶斯理论,假定先验信息服从高斯分布,待求参数服从改进的Cauchy分布,并对待求参数去除相关性。对某地区地层模型正演的多波数据和含噪声数据分别采用本文方法进行了反演,与单独利用纵波数据反演的结果相比,联合反演的结果精度更高、抗噪能力更强、稳定性更好。模型数据测试结果验证了本文方法的可行性和有效性。

Based on the Ruger approximation equation in VTI media,mutli wave and mutli parameter prestack joint inversion is studied.In this article,we use the Ruger approximation equation in VTI media as AVO forward equcation,based on the principle of least square,and construct an objective function to invert density contrast,Pwave and S-wave velocity contrast and anisotropic parameter difference through combining PP wave and PS wave.This method is based on Bayesian parameter estimation theory.The assumptions of Gaussian distribution is used for prior information and modified Cauchy distribution is used for unknown distribution.The correlation of the known data is got rid of.Joint inversion is carried out both on mutli wave data and noised data from forward modeling with above method.Compared with the conventional inversion method only using PP wave,the joint inversion is more accurate,antinoise and stable,which demonstrates the feasibility and validity of this method.