Magnetometric resistivity tomography using chaos polynomial expansion

Vu, Minh Tuan; Jardani, Abderrahim; Revil, A.; Jessop, Mike L.

doi:10.1093/gji/ggaa082

Cited by 3 publications

(1 citation statement)

References 44 publications

(48 reference statements)

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“…PCE can also be used as a compression tool. In a magnetometric resistivity tomography study, the logarithm of the electrical conductivity field is compressed using few tens of Hermite polynomials rather than tens of thousands of discretization parameters, resulting in important computational gains (Vu et al, 2020).…”

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confidence: 99%

Bayesian tomography with prior-knowledge-based parametrization and surrogate modeling

Meles,

Linde,

Marelli

2022

Preprint

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We present a Bayesian tomography framework operating with prior-knowledge-based parametrization that is accelerated by surrogate models. Standard high-fidelity forward solvers (e.g., Finite-Difference Time-Domain schemes) solve wave equations with natural spatial parametrizations based on fine discretization. Similar parametrizations, typically involving tens of thousand of variables, are usually employed to parameterize the subsurface in tomography applications. When the data do not allow to resolve details at such finely parameterized scales, it is often beneficial to instead rely on a priorknowledge-based parametrization defined on a lower dimension domain (or manifold). Due to the increased identifiability in the reduced domain, the concomitant inversion is better constrained and generally faster. We illustrate the potential of a prior-knowledge-based approach by considering ground penetrating radar (GPR) travel-time tomography in a crosshole configuration. An effective parametrization of the input (i.e., the permittivity distributions determining the slowness field) and compression in the output (i.e., the travel-time gathers) spaces are achieved via data-driven principal component decomposition based on random realizations of the prior Gaussian-process model with a truncation determined by the performances of the standard solver on the full and reduced model domains. To accelerate the inversion process, we employ a high-fidelity polynomial chaos expansion (PCE) surrogate model. We investigate the impact of the size of the training set on the performance of the PCE and show that a few hundreds design data sets is sufficient to provide reliable Markov chain Monte Carlo inversion at a fraction of the cost associated with a standard approach involving a fine discretization and physics-based forward solvers. Appropriate uncertainty quantification is achieved by reintroducing the truncated higher-order principle components in the original model space after inversion on the manifold and by adapting a likelihood function that accounts for the fact that the truncated higher-order components are not completely located in the null-space.

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confidence: 99%

Bayesian tomography with prior-knowledge-based parametrization and surrogate modeling

Meles,

Linde,

Marelli

2022

Preprint

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Bayesian tomography with prior-knowledge-based parametrization and surrogate modelling

Meles

Linde

Marelli

2022

Geophysical Journal International

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SUMMARY We present a Bayesian tomography framework operating with prior-knowledge-based parametrization that is accelerated by surrogate models. Standard high-fidelity forward solvers (e.g. finite-difference time-domain schemes) solve wave equations with natural spatial parametrizations based on fine discretization. Similar parametrizations, typically involving tens of thousand of variables, are usually employed to parametrize the subsurface in tomography applications. When the data do not allow to resolve details at such finely parametrized scales, it is often beneficial to instead rely on a prior-knowledge-based parametrization defined on a lower dimension domain (or manifold). Due to the increased identifiability in the reduced domain, the concomitant inversion is better constrained and generally faster. We illustrate the potential of a prior-knowledge-based approach by considering ground penetrating radar (GPR) traveltime tomography in a crosshole configuration with synthetic data. An effective parametrization of the input (i.e. the permittivity distributions determining the slowness field) and compression in the output (i.e. the traveltime gathers) spaces are achieved via data-driven principal component decomposition based on random realizations of the prior Gaussian-process model with a truncation determined by the performances of the standard solver on the full and reduced model domains. To accelerate the inversion process, we employ a high-fidelity polynomial chaos expansion (PCE) surrogate model. We investigate the impact of the size of the training set on the performance of the PCE and show that a few hundreds design data sets is sufficient to provide reliable Markov chain Monte Carlo inversion at a fraction of the cost associated with a standard approach involving a fine discretization and physics-based forward solvers. Appropriate uncertainty quantification is achieved by reintroducing the truncated higher order principle components in the original model space after inversion on the manifold and by adapting a likelihood function that accounts for the fact that the truncated higher order components are not completely located in the null space.

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Feasibility of induced magnetic gradient surveying for seepage detection in earth-filled dams: Insights from synthetic and field studies

Hu,

Wang,

Tang

et al. 2024

GEOPHYSICS

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Seepage is a common hydrogeological hazard in engineering. Determining the seepage paths is vital for de-risking the instability of embankment structures. With the improvement of the acquisition accuracy of magnetic sensors, the magnetometric resistivity method has become an emerging technology for detecting seepage paths through earth-filled dams. This technique is non-destructive and gives prominent signals. However, the resulting magnetic data have seen ambiguity in fully determining the targets. We propose an induced magnetic gradient surveying approach to monitor seepage paths in earth-filled dams. First, we briefly review the electromagnetic theory for the magnetic gradient tensor based on Maxwells equations. To match against the measurements, we present an accurate modeling framework using the third-order finite element method and a novel compact difference scheme. We verify our approach on both semi-analytical 1D and 3D models. Systematic modeling studies are then carried out to investigate the spatial distribution characteristics and sensitivities of the induced magnetic gradient to the seepage in typical dam scenarios. In addition, we conducted two field experiments in the Zhongmou experimental base and Xixiayuan Reservoir in Henan Province, China,respectively. The induced magnetic field vector and its gradient components were both acquired. Cross-validation with a-priori geological information shows that the seepage path can be spatially identified by the induced magnetic gradient components Byy, Byz, Bzy, and Bzz while the field components failed to locate the seepage pathways. This successful application indicates that the proposed approach could be a promising solution for seepage path discrimination in earth-filled dams with high resolution.

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Magnetometric resistivity tomography using chaos polynomial expansion

Cited by 3 publications

References 44 publications

Bayesian tomography with prior-knowledge-based parametrization and surrogate modeling

Bayesian tomography with prior-knowledge-based parametrization and surrogate modeling

Bayesian tomography with prior-knowledge-based parametrization and surrogate modelling

Feasibility of induced magnetic gradient surveying for seepage detection in earth-filled dams: Insights from synthetic and field studies

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