Bayesian Uncertainty Quantification for Subsurface Inversion Using a Multiscale Hierarchical Model

Anirban Mondal, Bani Mallick, Yalchin R. Efendiev, Akhil Datta-Gupta

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We consider a Bayesian approach to nonlinear inverse problems in which the unknown quantity is a random field (spatial or temporal). The Bayesian approach contains a natural mechanism for regularization in the form of prior information, can incorporate information from heterogeneous sources and provide a quantitative assessment of uncertainty in the inverse solution. The Bayesian setting casts the inverse solution as a posterior probability distribution over the model parameters. The Karhunen-Loeve expansion is used for dimension reduction of the random field. Furthermore, we use a hierarchical Bayes model to inject multiscale data in the modeling framework. In this Bayesian framework, we show that this inverse problem is well-posed by proving that the posterior measure is Lipschitz continuous with respect to the data in total variation norm. Computational challenges in this construction arise from the need for repeated evaluations of the forward model (e.g., in the context of MCMC) and are compounded by high dimensionality of the posterior. We develop two-stage reversible jump MCMC that has the ability to screen the bad proposals in the first inexpensive stage. Numerical results are presented by analyzing simulated as well as real data from hydrocarbon reservoir. This article has supplementary material available online. © 2014 American Statistical Association and the American Society for Quality.
Original languageEnglish (US)
Pages (from-to)381-392
Number of pages12
JournalTechnometrics
Volume56
Issue number3
DOIs
StatePublished - Jul 24 2014
Externally publishedYes

Fingerprint Dive into the research topics of 'Bayesian Uncertainty Quantification for Subsurface Inversion Using a Multiscale Hierarchical Model'. Together they form a unique fingerprint.

Cite this