基于修正柯西分布的弹性参数反演方法

The elastic parameters inversion based on modified Cauchy distribution

岩石弹性参数能够直接反映储层流体的变化,因而在含油气储层流体识别中应用十分广泛。传统的弹性参数反演方法通常是基于不同角度的弹性阻抗体进行线性求解,对噪声较为敏感,稳健性较差。其主要原因在于传统方法所采用的最小平方线性回归的应用前提是噪声扰动服从高斯分布,而实际上,在地球物理勘探领域,观测资料中噪声的分布特征更接近于修正柯西分布。在传统的弹性参数反演方法原理的基础上,从最大似然估计理论出发,分析了最小平方线性回归的应用局限,并基于修正柯西概率密度分布函数,推导出了一种高稳健性的线性回归方法,将其应用到弹性参数反演中,取得了较好的应用效果。

Elastic parameters which can directly indicate the changes in the reservoir fluid are widely used in the hydrocarbon reservoir prediction.The conventional elastic parameters inversion methods based on the different angles of the elastic impedance body solved by Least Square regression are sensitive to noise with poor robustness.Application premise of the conventional methods using Least Square regression is mainly due to Gaussian disturbance of noise.In fact,the distribution characteristics of noise in geophysical survey data are closer to the modified Cauchy distribution.On the basis of the conventional elastic parameter inversion method,from the maximum likelihood estimation theory,and analysis on the limitations of the least squares linear regression,a high robust regression method is deduced based on modified Cauchy distribution,which achieves a good result in elastic parameters inversion.