A new methodology for Bayesian history matching using parallel interacting Markov chain Monte Carlo

Abstract

This paper presents an innovative application of a new class of parallel interacting Markov chains Monte Carlo to solve the Bayesian history matching (BHM) problem. BHM consists of sampling a posterior distribution given by the Bayesian theorem. Markov chain Monte Carlo (MCMC) is well suited for sampling, in principle, any type of distribution; however the number of iteration required by the traditional single-chain MCMC can be prohibitive in BHM applications. Furthermore, history matching is typically a highly nonlinear inverse problem, which leads in very complex posterior distributions, characterized by many separated modes. Therefore, single chain can be trapped into a local mode. Parallel interacting chains is an interesting way to overcome this problem, as shown in this paper. In addition, we presented new approaches to define starting points for the parallel chains. For validation purposes, the proposed methodology is firstly applied in a simple but challenging cross section reservoir model with many modes in the posterior distribution. Afterwards, the application to a realistic case integrated to geostatistical modelling is also presented. The results showed that the combination of parallel interacting chain with the capabilities of distributed computing commonly available nowadays is very promising to solve the BHM problem.