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Well-posed Bayesian geometric inverse problems arising in subsurface flow

Iglesias, Marco A. and Lin, Kui and Stuart, Andrew M. (2014) Well-posed Bayesian geometric inverse problems arising in subsurface flow. Inverse Problems, 30 (11). Art. No. 114001. ISSN 0266-5611.

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In this paper, we consider the inverse problem of determining the permeability of the subsurface from hydraulic head measurements, within the framework of a steady Darcy model of groundwater flow. We study geometrically defined prior permeability fields, which admit layered, fault and channel structures, in order to mimic realistic subsurface features; within each layer we adopt either a constant or continuous function representation of the permeability. This prior model leads to a parameter identification problem for a finite number of unknown parameters determining the geometry, together with either a finite number of permeability values (in the constant case) or a finite number of fields (in the continuous function case). We adopt a Bayesian framework showing the existence and well-posedness of the posterior distribution. We also introduce novel Markov chain Monte Carlo (MCMC) methods, which exploit the different character of the geometric and permeability parameters, and build on recent advances in function space MCMC. These algorithms provide rigorous estimates of the permeability, as well as the uncertainty associated with it, and only require forward model evaluations. No adjoint solvers are required and hence the methodology is applicable to black-box forward models. We then use these methods to explore the posterior and to illustrate the methodology with numerical experiments.

Item Type:Article
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URLURL TypeDescription Paper
Iglesias, Marco A.0000-0002-8952-717X
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Additional Information:© 2014 IOP Publishing. Received 22 January 2014, revised 2 June 2014; Accepted for publication 10 June 2014; Published 28 October 2014. KL is partially supported by National Natural Science Foundation of China grant no. 11101093. AMS and MI are grateful to ERC and EPSRC for support.
Funding AgencyGrant Number
National Natural Science Foundation of China11101093
European Research Council (ERC)UNSPECIFIED
Engineering and Physical Sciences Research Council (EPSRC)UNSPECIFIED
Subject Keywords:Bayesian inverse problems, geometric priors, subsurface flow
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Other Numbering System NameOther Numbering System ID
Andrew StuartJ115
Issue or Number:11
Record Number:CaltechAUTHORS:20160719-114834043
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Official Citation:Marco A Iglesias et al 2014 Inverse Problems 30 114001
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:69112
Deposited By: Linda Taddeo
Deposited On:19 Jul 2016 21:36
Last Modified:09 Mar 2020 13:18

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