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    Bayesian Uncertainty Quantification for Subsurface Inversion Using a Multiscale Hierarchical Model

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    Type
    Article
    Authors
    Mondal, Anirban
    Mallick, Bani
    Efendiev, Yalchin R. cc
    Datta-Gupta, Akhil
    KAUST Grant Number
    KUS-C1-016-04
    Date
    2014-07-24
    Online Publication Date
    2014-07-24
    Print Publication Date
    2014-07-03
    Permanent link to this record
    http://hdl.handle.net/10754/597661
    
    Metadata
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    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.
    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.
    Publisher
    Informa UK Limited
    Journal
    Technometrics
    DOI
    10.1080/00401706.2013.838190
    ae974a485f413a2113503eed53cd6c53
    10.1080/00401706.2013.838190
    Scopus Count
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