Bayesian Gaussian Inversion of Time-Lapse Seismic AVO Data

Abstract

The goal of this study is to characterize an oil reservoir along a depth profile at two different points in time, based on seismic AVO data gathered at these times. We apply Bayesian methodology to the inversion problem. Gauss-linear likelihood models that establish a relationship between the porosity and water saturation in the reservoir and the seismic profiles are constructed, and combined with both standard Gaussian and selection Gauss prior models. We discuss and compare the different prior model. The solutions are represented as posterior distributions, and in the case of a Gaussian prior model, the solution is analytically tractable, whereas with a selection Gauss prior model, the posterior model is complicated to compute and evaluate, requiring computational approximation. From the posterior distributions, we make predictions with associated uncertainty assessments. The inversion models are tested and trained on synthetic data before we apply them on actual seismic observations supplied by Aker BP. We conclude that the method provides very encouraging results when a selection Gauss prior model is used.