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Well-posed Bayesian geometric inverse problems arising in subsurface flow
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Iglesias, Marco A., Lin, Kui and Stuart, A. M. (2014) Well-posed Bayesian geometric inverse problems arising in subsurface flow. Inverse Problems, 30 (11). 114001. doi:10.1088/0266-5611/30/11/114001 ISSN 0266-5611.
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Official URL: http://dx.doi.org/10.1088/0266-5611/30/11/114001
Abstract
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 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 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: | Journal Article | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Journal or Publication Title: | Inverse Problems | ||||||||
| Publisher: | Institute of Physics Publishing Ltd. | ||||||||
| ISSN: | 0266-5611 | ||||||||
| Official Date: | 28 October 2014 | ||||||||
| Dates: |
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| Volume: | 30 | ||||||||
| Number: | 11 | ||||||||
| Article Number: | 114001 | ||||||||
| DOI: | 10.1088/0266-5611/30/11/114001 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 3 March 2017 |
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