Fisher-Bayesian inversion for estimating shale gas facies

Abstract

The classification of shale gas facies from seismic properties is critical for shale gas reservoir characterization. Shale gas facies are affected by many petrophysical properties. Therefore, the characterization of shale facies should be carried out by multiple parameters, which is more reasonable and accurate. However, multi-parameter inversion often leads to unstable results, and coupled properties are generally a way of solving this problem. A Fisher-Bayesian inversion method for estimating shale gas facies is developed in this paper by combining the Fisher projection and Bayesian inversion method. The mathematical method adopted for the inversion is the Bayesian framework. The link between different facies and coupled properties is given by a joint prior distribution. We derive the analytical formulation of the Bayesian inversion under the Gaussian mixture assumption for coupled attributes and different shale gas facies. The proposed approach realizes the fusion of multi-dimensional petrophysical parameters and establishes a shale gas facies prediction method based on coupled properties. The application to real data sets delivers accurate and stable results, where shale gas facies and coupled attributes are accurately predicted and inversed.