A Bayesian Inversion Approach to Filtering and Decision Making with Applications to Reservoir Characterization

Abstract

The main objectives of this thesis are the estimation/filtering and decision making problems with a Bayesian inversion point of view, and in geophysical systems. In addition, determining the information content in the measured data is also a challenge in estimation problems, and we use the dimension reduction techniques to deal with this problem. The main applications of the proposed algorithms are for reservoir characterization, and the seismic amplitude versus offset (AVO) data is the most used measurement.

The first part of this thesis tries to address some of the existing problems in the state estimation of high dimensional and complex systems. Our first proposal is a robustified Gaussian mixture filter. Simulations show promising results and the performance of the proposed filter is at least as good as the ensemble Kalman filter (EnKF) and particle filter (PF). In addition, we extend the traditional KF and EnKF for capturing the skewness of the distributions. They automatically converge to the KF or EnKF if there is no skewness in the probability density function (pdf). Simulation results confirm our claim, and they seem to have better performance in the presence of skewness. Furthermore, we investigate the nature of geophysical observations from a filtering point of view by testing several data reduction techniques. We show how to assess the information content in the data, compress the data, and use this compressed data in a reservoir conditioning setting. The methods we present are generic; they apply equally well to all geophysical attributes regardless of representation and can be applied with any filtering algorithm. The last part of this thesis relates to the value of information (VOI) analysis and decision making. We extend the previous method for computing the VOI of seismic AVO data by using a closed skew normal pdf model instead of the Gaussian. The previous method is an special case of the proposed method, and simulation results seems to result in more reliable decisions.