Using deep generative neural networks to account for model errors in Markov chain Monte Carlo inversion
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Version: Author's accepted manuscript
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State: Public
Version: Author's accepted manuscript
License: Not specified
Serval ID
serval:BIB_F9EB4B2A2188
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
Using deep generative neural networks to account for model errors in Markov chain Monte Carlo inversion
Journal
Geophysical Journal International
ISSN
0956-540X
Publication state
Published
Issued date
2022
Peer-reviewed
Oui
Volume
228
Number
2
Pages
1098-1118
Language
english
Abstract
Most geophysical inverse problems are non-linear and rely upon numerical forward solvers involving discretization and simplified representations of the underlying physics. As a result, forward modelling errors are inevitable. In practice, such model errors tend to be either completely ignored, which leads to biased and over-confident inversion results, or only partly taken into account using restrictive Gaussian assumptions. Here, we rely on deep generative neural networks to learn problem-specific low-dimensional probabilistic representations of the discrepancy between high-fidelity and low-fidelity forward solvers. These representations are then used to probabilistically invert for the model error jointly with the target geophysical property field, using the computationally cheap, low-fidelity forward solver. To this end, we combine a Markov chain Monte Carlo (MCMC) inversion algorithm with a trained convolutional neural network of the spatial generative adversarial network (SGAN) type, whereby at each MCMC step, the simulated low-fidelity forward response is corrected using a proposed model-error realization. Considering the crosshole ground-penetrating radar traveltime tomography inverse problem, we train SGAN networks on traveltime discrepancy images between: (1) curved-ray (high fidelity) and straight-ray (low fidelity) forward solvers; and (2) finite-difference-time-domain (high fidelity) and straight-ray (low fidelity) forward solvers. We demonstrate that the SGAN is able to learn the spatial statistics of the model error and that suitable representations of both the subsurface model and model error can be recovered by MCMC. In comparison with inversion results obtained when model errors are either ignored or approximated by a Gaussian distribution, we find that our method has lower posterior parameter bias and better explains the observed traveltime data. Our method is most advantageous when high-fidelity forward solvers involve heavy computational costs and the Gaussian assumption of model errors is inappropriate. Unstable MCMC convergence due to non-linearities introduced by our method remain a challenge to be addressed in future work.
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Create date
30/06/2023 10:20
Last modification date
14/08/2024 6:17