TY - JOUR

T1 - Efficient multiscale imaging of subsurface resistivity with uncertainty quantification using ensemble Kalman inversion

AU - Tso, C.-H.M.

AU - Iglesias, M.

AU - Wilkinson, P.

AU - Kuras, O.

AU - Chambers, J.

AU - Binley, A.

N1 - This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Geophysical Journal International following peer review. The definitive publisher-authenticated version Chak-Hau Michael Tso, Marco Iglesias, Paul Wilkinson, Oliver Kuras, Jonathan Chambers, Andrew Binley, Efficient multiscale imaging of subsurface resistivity with uncertainty quantification using ensemble Kalman inversion, Geophysical Journal International, Volume 225, Issue 2, May 2021, Pages 887–905, https://doi.org/10.1093/gji/ggab013 is available online at: https://academic.oup.com/gji/article-abstract/225/2/887/6081097

PY - 2021/5/31

Y1 - 2021/5/31

N2 - Electrical resistivity tomography (ERT) is widely used to image the Earth's subsurface and has proven to be an extremely useful tool in application to hydrological problems. Conventional smoothness-constrained inversion of ERT data is efficient and robust, and consequently very popular. However, it does not resolve well sharp interfaces of a resistivity field and tends to reduce and smooth resistivity variations. These issues can be problematic in a range of hydrological or near-surface studies, for example mapping regolith-bedrock interfaces. While fully Bayesian approaches, such as those using Markov chain Monte Carlo sampling, can address the above issues, their very high computation cost makes them impractical for many applications. Ensemble Kalman inversion (EKI) offers a computationally efficient alternative by approximating the Bayesian posterior distribution in a derivative-free manner, which means only a relatively small number of 'black-box' model runs are required. Although common limitations for ensemble Kalman filter-type methods apply to EKI, it is both efficient and generally captures uncertainty patterns correctly. We propose the use of a new EKI-based framework for ERT which estimates a resistivity model and its uncertainty at a modest computational cost. Our EKI framework uses a level-set parametrization of the unknown resistivity to allow efficient estimation of discontinuous resistivity fields. Instead of estimating level-set parameters directly, we introduce a second step to characterize the spatial variability of the resistivity field and infer length scale hyperparameters directly. We demonstrate these features by applying the method to a series of synthetic and field examples. We also benchmark our results by comparing them to those obtained from standard smoothness-constrained inversion. Resultant resistivity images from EKI successfully capture arbitrarily shaped interfaces between resistivity zones and the inverted resistivities are close to the true values in synthetic cases. We highlight its readiness and applicability to similar problems in geophysics.

AB - Electrical resistivity tomography (ERT) is widely used to image the Earth's subsurface and has proven to be an extremely useful tool in application to hydrological problems. Conventional smoothness-constrained inversion of ERT data is efficient and robust, and consequently very popular. However, it does not resolve well sharp interfaces of a resistivity field and tends to reduce and smooth resistivity variations. These issues can be problematic in a range of hydrological or near-surface studies, for example mapping regolith-bedrock interfaces. While fully Bayesian approaches, such as those using Markov chain Monte Carlo sampling, can address the above issues, their very high computation cost makes them impractical for many applications. Ensemble Kalman inversion (EKI) offers a computationally efficient alternative by approximating the Bayesian posterior distribution in a derivative-free manner, which means only a relatively small number of 'black-box' model runs are required. Although common limitations for ensemble Kalman filter-type methods apply to EKI, it is both efficient and generally captures uncertainty patterns correctly. We propose the use of a new EKI-based framework for ERT which estimates a resistivity model and its uncertainty at a modest computational cost. Our EKI framework uses a level-set parametrization of the unknown resistivity to allow efficient estimation of discontinuous resistivity fields. Instead of estimating level-set parameters directly, we introduce a second step to characterize the spatial variability of the resistivity field and infer length scale hyperparameters directly. We demonstrate these features by applying the method to a series of synthetic and field examples. We also benchmark our results by comparing them to those obtained from standard smoothness-constrained inversion. Resultant resistivity images from EKI successfully capture arbitrarily shaped interfaces between resistivity zones and the inverted resistivities are close to the true values in synthetic cases. We highlight its readiness and applicability to similar problems in geophysics.

KW - Electrical resistivity tomography (ERT)

KW - Hydrogeophysics

KW - Inverse theory

KW - Tomography

KW - Bayesian networks

KW - Cost benefit analysis

KW - Markov chains

KW - Monte Carlo methods

KW - Computationally efficient

KW - Constrained inversions

KW - Electrical resistivity tomography

KW - Ensemble Kalman Filter

KW - Fully bayesian approaches

KW - Markov chain monte carlo samplings

KW - Posterior distributions

KW - Uncertainty quantifications

KW - Uncertainty analysis

U2 - 10.1093/gji/ggab013

DO - 10.1093/gji/ggab013

M3 - Journal article

VL - 225

SP - 887

EP - 905

JO - Geophysical Journal International

JF - Geophysical Journal International

SN - 0956-540X

IS - 2

ER -