Bayesian calibration of geothermal reservoir models via Markov Chain Monte Carlo

Abstract

The aim of the research described in this thesis is the development of methods for solving computationally intensive computer model calibration problems by sample based inference. Although our primary focus is calibrating computer models of geothermal reservoirs, the methodology we have developed can be applied to a wide range of computer model calibration problems. In this study, the Bayesian framework is employed to construct the posterior distribution over all model parameters consistent with the measured data, accounting for various uncertainties in the calibration process. To construct the posterior distribution for computer model calibration problems, several methods such as the additive bias framework of Kennedy and O'Hagan (2001) and the enhanced error model (Kaipio and Somersalo, 2007) are investigated. Then, the solutions of computer model calibration problems are given by estimating the expected value of statistics of interest over the posterior distribution. Markov chain Monte Carlo (MCMC) sampling, Metropolis-Hastings (MH) algorithm (Metropolis et al., 1953; Hastings, 1970) in particular, is empoyed to explore the posterior distribution, and Monte Carlo integration is used to calculating the expected values.