Inference Networks in Earth Models with Multiple Components and Data

Bosch, Miguel

doi:10.1002/9781118929063.ch3

Cited by 8 publications

(7 citation statements)

References 57 publications

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“…Our coupled Bayesian hydrogeophysical inversion approach with explicit inference of spatially-correlated petrophysical prediction uncertainty leads to less bias (e.g., in the inferred variance of the inferred hydrogeological property field), more realistic uncertainty quantification and less over confident model selection compared to the common choice of ignoring this type of uncertainty. Even if our approach to infer petrophysical prediction uncertainty doubles the number of parameters in the inversion problem, we observe dramatic gains in sampling efficiency compared to MC-within-MCMC (e.g., Bosch (1999Bosch ( , 2016). Moreover, DREAM (ZS) allows for parallel evaluation of the different Markov chains and, therefore, enables feasible computational times even in high (e.g., in our case, more than 200) model dimensions.…”

Section: Discussionmentioning

confidence: 85%

“…Petrophysical prediction uncertainty has received less attention in coupled inversion. In the rare circumstances it is included at all, it is commonly conceptualized with a multivariate Gaussian distribution with known mean and covariance matrix (Bosch, 2004;Bosch et al, 2009;Bosch, 2016;Chen & Dickens, 2009). The petrophysical prediction uncertainty is then typically sampled using the brute force Monte Carlo method by adding random multivariate Gaussian realizations to the petrophysical model outputs at each iteration of the MCMC inversion.…”

Section: Introductionmentioning

confidence: 99%

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Impact of petrophysical uncertainty on Bayesian hydrogeophysical inversion and model selection

Brunetti

Linde

2018

Advances in Water Resources

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Quantitative hydrogeophysical studies rely heavily on petrophysical relationships that link geophysical properties to hydrogeological properties and state variables. Coupled inversion studies are frequently based on the questionable assumption that these relationships are perfect (i.e., no scatter). Using synthetic examples and crosshole ground-penetrating radar (GPR) data from the South Oyster Bacterial Transport Site in Virginia, USA, we investigate the impact of spatially-correlated petrophysical uncertainty on inferred posterior porosity and hydraulic conductivity distributions and on Bayes factors used in Bayesian model selection. Our study shows that accounting for petrophysical uncertainty in the inversion (I) decreases bias of the inferred variance of hydrogeological subsurface properties, (II) provides more realistic uncertainty assessment and (III) reduces the overconfidence in the ability of geophysical data to falsify conceptual hydrogeological models.

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Section: Discussionmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

Impact of petrophysical uncertainty on Bayesian hydrogeophysical inversion and model selection

Brunetti

Linde

2018

Advances in Water Resources

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“…In geophysics, inference of the joint conditional distribution of (u, v) given geophysical data y is referred to as lithological tomography [183]. A recent tutorial [184] describes how to formulate Bayesian networks (using direct acyclic graphs) for arbitrarily complicated situations involving multiple data and parameter types, as well as a hierarchy of hidden variables. For simplicity, we focus our discussion on a single hidden variable v. The standard approach (notably advocated by [184]) for posterior simulations of u consists in applying (variations of) the Metropolis-Hastings algorithm to (u, v), where at each iteration the model perturbation consist in (i) drawing u, and then (ii) drawing v conditionally on u.…”

Section: Hydrogeophysics and Uncertain Petrophysical Relationshipsmentioning

confidence: 99%

“…A recent tutorial [184] describes how to formulate Bayesian networks (using direct acyclic graphs) for arbitrarily complicated situations involving multiple data and parameter types, as well as a hierarchy of hidden variables. For simplicity, we focus our discussion on a single hidden variable v. The standard approach (notably advocated by [184]) for posterior simulations of u consists in applying (variations of) the Metropolis-Hastings algorithm to (u, v), where at each iteration the model perturbation consist in (i) drawing u, and then (ii) drawing v conditionally on u. Unfortunately, such a sampling strategy can be very inefficient when confronted with high parameter dimensions, large data sets with small errors , and uncertain petrophysical relationships.…”

Section: Hydrogeophysics and Uncertain Petrophysical Relationshipsmentioning

confidence: 99%

On uncertainty quantification in hydrogeology and hydrogeophysics

Linde

Ginsbourger

Irving

et al. 2017

Advances in Water Resources

105

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Recent advances in sensor technologies, field methodologies, numerical modeling, and inversion approaches have contributed to unprecedented imaging of hydrogeological properties and detailed predictions at multiple temporal and spatial scales. Nevertheless, imaging results and predictions will always remain imprecise, which calls for appropriate uncertainty quantification (UQ). In this paper, we outline selected methodological developments together with pioneering UQ applications in hydrogeology and hydrogeophysics. The applied mathematics and statistics literature is not easy to penetrate and this review aims at helping hydrogeologists and hydrogeophysicists to identify suitable approaches for UQ that can be applied and further developed to their specific needs. To bypass the tremendous computational costs associated with forward UQ based on full-physics simulations, we discuss proxy-modeling strategies and multi-resolution (Multi-level Monte Carlo) methods. We consider Bayesian inversion for non-linear and non-Gaussian state-space problems and discuss how Sequential Monte Carlo may become a practical alternative. We also describe

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“…Others include mutual information (Mandolesi and Jones 2014), or geostatistical methods in a probabilistic inversion (e.g., Zahner et al 2016). Bosch (2016) and Hansen et al (2016) discuss the theoretical basis of using geological prior information in more detail.…”

Section: Cooperative and Constrained Inversionmentioning

confidence: 99%

Integrating Electromagnetic Data with Other Geophysical Observations for Enhanced Imaging of the Earth: A Tutorial and Review

Moorkamp

2017

Surv Geophys

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In this review, I discuss the basic principles of joint inversion and constrained inversion approaches and show a few instructive examples of applications of these approaches in the literature. Starting with some basic definitions of the terms joint inversion and constrained inversion, I use a simple three-layered model as a tutorial example that demonstrates the general properties of joint inversion with different coupling methods. In particular, I investigate to which extent combining different geophysical methods can restrict the set of acceptable models and under which circumstances the results can be biased. Some ideas on how to identify such biased results and how negative results can be interpreted conclude the tutorial part. The case studies in the second part have been selected to highlight specific issues such as choosing an appropriate parameter relationship to couple seismic and electromagnetic data and demonstrate the most commonly used approaches, e.g., the cross-gradient constraint and direct parameter coupling. Throughout the discussion, I try to identify topics for future work. Overall, it appears that integrating electromagnetic data with other observations has reached a level of maturity and is starting to move away from fundamental proof-of-concept studies to answering questions about the structure of the subsurface. With a wide selection of coupling methods suited to different geological scenarios, integrated approaches can be applied on all scales and have the potential to deliver new answers to important geological questions.

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Inference Networks in Earth Models with Multiple Components and Data

Cited by 8 publications

References 57 publications

Impact of petrophysical uncertainty on Bayesian hydrogeophysical inversion and model selection

Impact of petrophysical uncertainty on Bayesian hydrogeophysical inversion and model selection

On uncertainty quantification in hydrogeology and hydrogeophysics

Integrating Electromagnetic Data with Other Geophysical Observations for Enhanced Imaging of the Earth: A Tutorial and Review

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