Bayesian Uncertainty Quantification for Subsurface Inversion Using a Multiscale Hierarchical Model

Handle URI:
http://hdl.handle.net/10754/597661
Title:
Bayesian Uncertainty Quantification for Subsurface Inversion Using a Multiscale Hierarchical Model
Authors:
Mondal, Anirban; Mallick, Bani; Efendiev, Yalchin; Datta-Gupta, Akhil
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.
Citation:
Mondal A, Mallick B, Efendiev Y, Datta-Gupta A (2014) Bayesian Uncertainty Quantification for Subsurface Inversion Using a Multiscale Hierarchical Model. Technometrics 56: 381–392. Available: http://dx.doi.org/10.1080/00401706.2013.838190.
Publisher:
Informa UK Limited
Journal:
Technometrics
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
3-Jul-2014
DOI:
10.1080/00401706.2013.838190
Type:
Article
ISSN:
0040-1706; 1537-2723
Sponsors:
The authors acknowledge NSF-CMG. This work is partly supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorMondal, Anirbanen
dc.contributor.authorMallick, Banien
dc.contributor.authorEfendiev, Yalchinen
dc.contributor.authorDatta-Gupta, Akhilen
dc.date.accessioned2016-02-25T12:43:56Zen
dc.date.available2016-02-25T12:43:56Zen
dc.date.issued2014-07-03en
dc.identifier.citationMondal A, Mallick B, Efendiev Y, Datta-Gupta A (2014) Bayesian Uncertainty Quantification for Subsurface Inversion Using a Multiscale Hierarchical Model. Technometrics 56: 381–392. Available: http://dx.doi.org/10.1080/00401706.2013.838190.en
dc.identifier.issn0040-1706en
dc.identifier.issn1537-2723en
dc.identifier.doi10.1080/00401706.2013.838190en
dc.identifier.urihttp://hdl.handle.net/10754/597661en
dc.description.abstractWe 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.en
dc.description.sponsorshipThe authors acknowledge NSF-CMG. This work is partly supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology.en
dc.publisherInforma UK Limiteden
dc.subjectBayesian hierarchical modelen
dc.subjectBayesian inverse problemsen
dc.subjectKarhunen-Loeve expansionen
dc.subjectTwo-stage reversible jump MCMCen
dc.titleBayesian Uncertainty Quantification for Subsurface Inversion Using a Multiscale Hierarchical Modelen
dc.typeArticleen
dc.identifier.journalTechnometricsen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-C1-016-04en
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