1D geological imaging of the subsurface from geophysical data with Bayesian Evidential Learning

Michel, Hadrien; Nguyen, Frédéric; Kremer, Thomas; Elen, Ann; Hermans, Thomas

doi:10.1016/j.cageo.2020.104456

Cited by 25 publications

(55 citation statements)

References 38 publications

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“…However, the threshold might be approximated using synthetic benchmarking, as presented here. A similar observation has been made for other approximate Bayesian methods (e.g., [13]).…”

Section: Multi-layer Inversionsupporting

confidence: 80%

“…Highly-parametrized models result in computationally expensive forward model runs that limit the applicability of MCMC methods [11]. Only recently, efficient approximations of the posterior distribution have been proposed for geophysical problems, while using innovative methods, such as the Kalman ensemble generator (KEG, [12]) or Bayesian Evidential Learning [13]. Those techniques rely on a smaller number of forward model runs and are, thus, less expensive.…”

Section: Introductionmentioning

confidence: 99%

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Efficient Probabilistic Joint Inversion of Direct Current Resistivity and Small-Loop Electromagnetic Data

et al. 2020

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Often, multiple geophysical measurements are sensitive to the same subsurface parameters. In this case, joint inversions are mostly preferred over two (or more) separate inversions of the geophysical data sets due to the expected reduction of the non-uniqueness in the joint inverse solution. This reduction can be quantified using Bayesian inversions. However, standard Markov chain Monte Carlo (MCMC) approaches are computationally expensive for most geophysical inverse problems. We present the Kalman ensemble generator (KEG) method as an efficient alternative to the standard MCMC inversion approaches. As proof of concept, we provide two synthetic studies of joint inversion of frequency domain electromagnetic (FDEM) and direct current (DC) resistivity data for a parameter model with vertical variation in electrical conductivity. For both studies, joint results show a considerable improvement for the joint framework over the separate inversions. This improvement consists of (1) an uncertainty reduction in the posterior probability density function and (2) an ensemble mean that is closer to the synthetic true electrical conductivities. Finally, we apply the KEG joint inversion to FDEM and DC resistivity field data. Joint field data inversions improve in the same way seen for the synthetic studies.

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“…However, the threshold might be approximated using synthetic benchmarking, as presented here. A similar observation has been made for other approximate Bayesian methods (e.g., [13]).…”

Section: Multi-layer Inversionsupporting

confidence: 80%

Section: Introductionmentioning

confidence: 99%

Efficient Probabilistic Joint Inversion of Direct Current Resistivity and Small-Loop Electromagnetic Data

et al. 2020

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“…In addition, heterodox transients can be generated for a dipole potential measurement by subtracting two pole measurements (two P1 potentials). In the examples shown so far, only 2D anomalies that produce heterodox transients have been presented, but anomalies in a 1D model space can generate any kind of heterodox types as well (Michel et al, 2020). Furthermore, similar reasoning with comparable results applies to frequency-domain responses, where the phase of the apparent complex resistivity can change the sign or present heterodox shapes, or both.…”

Section: The Basic Mechanism For Heterodox (And Orthodox) Transientsmentioning

confidence: 76%

Heterodox transients in time-domain-induced polarization

et al. 2021

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Negative induced polarization (IP) time-domain transients, sign-changing or non-monotonically decaying transients are currently often considered as measurement errors and removed in the data processing. These transients, here named heterodox in the sense of other than generally accepted signals, might originate from measurement errors, inductive effects, or poor signal processing, but synthetic modelling and field measurements show that these transients are physically possible. A simple theoretical explanation of the basic mechanism for their origin can be found through the superposition of contributions from regions with different sensitivities and such heterodox transients can be identified through the processing of full-waveform IP data. A mathematical classification of orthodox and heterodox IP transients into six different types is introduced based on the temporal development of the sign of their amplitude and derivative. The basic mechanism for IP transients with heterodox shapes is further investigated by considering the subsurface Cole-Cole parameter sensitivities and time-varying IP potential for 2D synthetic models. The time-domain forward response and sensitivities are computed through a time transformation that accounts for the current waveform. This approach allows for quantitative unbiased estimates of the time-domain transients and sensitivities, different from the estimates obtained when using multiple direct-current forward computations, as often done in the inversion of time-domain IP data. Time-domain IP transients may differ from the traditionally expected decaying-like transients when the electrode geometry has IP potential sensitivities with different signs for areas with different IP parameters. Hence, previously disregarded IP transients containing valuable information of the subsurface can be kept for inversion and contribute to the final parameter distribution. Increased understanding of theoretically possible IP transients makes way for more accurate processing of data in the future, reducing the time and resources needed for spectral inversion of time-domain data.

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“…Such direct forecasting is possible because predictions often have a much-lower dimensionality than models. Nevertheless, when the data-prediction relationship is complex and highly nonlinear, BEL might overestimate uncertainty (Michel et al, 2020a), for instance when the prior uncertainty is large (Hermans et al, 2019). In such a case, classical inversion might still be needed (Scheidt et al, 2018).…”

Section: Numerical Methods Development For 4d Data Integration and In...mentioning

confidence: 99%

“…In such a case, classical inversion might still be needed (Scheidt et al, 2018). Recent advances have shown that BEL can also estimate the model parameter distributions and be used as a more traditional inversion technique (Yin et al, 2020;Michel et al, 2020a). However, such more advanced applications require further development of appropriate tools to identify highly non-linear relationships (Park and Caers, 2020) which will inevitably come at a larger computational cost (Michel et al, 2020b).…”

Section: Numerical Methods Development For 4d Data Integration and In...mentioning

confidence: 99%

Advancing measurements and representations of subsurface heterogeneity and dynamic processes: towards 4D hydrogeology

Hermans

Goderniaux

Jougnot

et al. 2022

Preprint

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Abstract. Essentially all hydrogeological processes are strongly influenced by the subsurface spatial heterogeneity and the temporal variation of environmental conditions, hydraulic properties, and solute concentrations. This spatial and temporal variability needs to be considered when studying hydrogeological processes in order to employ adequate mechanistic models or perform upscaling. The scale at which a hydrogeological system should be characterized in terms of its spatial heterogeneity and temporal dynamics depends on the studied process and it is not always necessary to consider the full complexity. In this paper, we identify a series of hydrogeological processes for which an approach coupling the monitoring of spatial and temporal variability, including 4D imaging, is often necessary: (1) groundwater fluxes that control (2) solute transport, mixing and reaction processes, (3) vadose zone dynamics, and (4) surface-subsurface water interaction occurring at the interface between different subsurface compartments. We first identify the main challenges related to the coupling of spatial and temporal fluctuations for these processes. Then, we highlight some recent innovations that have led to significant breakthroughs in this domain. We finally discuss how spatial and temporal fluctuations affect our ability to accurately model them and predict their behavior. We thus advocate a more systematic characterization of the dynamic nature of subsurface processes, and the harmonization of open databases to store hydrogeological data sets in their four-dimensional components, for answering emerging scientific question and addressing key societal issues.

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1D geological imaging of the subsurface from geophysical data with Bayesian Evidential Learning

Cited by 25 publications

References 38 publications

Efficient Probabilistic Joint Inversion of Direct Current Resistivity and Small-Loop Electromagnetic Data

Efficient Probabilistic Joint Inversion of Direct Current Resistivity and Small-Loop Electromagnetic Data

Heterodox transients in time-domain-induced polarization

Advancing measurements and representations of subsurface heterogeneity and dynamic processes: towards 4D hydrogeology

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