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A new Bayesian framework for the interpretation of geophysical data

Hadrien Michel
(2023)
Author
Promoter
Frédéric Nguyen and (UGent)
Organization
Abstract
Providing images of the subsurface from ground-based datasets is at the heart of the geophysicist's work. Multiple approaches have been applied to tackle this task. Most of the time, this task is performed in a deterministic framework, meaning that for a given dataset, a single model is provided to explain the data. However, those deterministic approaches lack the ability to provide reasonable uncertainty estimations, that take into account the non-unicity of the solution, noise in the data and modelling error. To provide precise and accurate models of the subsurface along with uncertainty, geophysicists use probabilistic approaches. Those approaches are able to sample the ensemble of a priori possible models (the prior) in order to extract models that can reasonably explain the datasets (the posterior). Such approaches, even though superior in terms of the reliability of their results, are rarely applied in practice due to their significant computational requirements. In this manuscript, the aim is to propose a new Bayesian framework to interpret those geophysical datasets. This new framework, called Bayesian Evidential Learning, promises to enable a fast, precise and accurate estimation of the uncertainty. This framework is applied and adapted for 1D geophysical datasets (BEL1D). The new and adapted framework presents several advantages when compared to classical probabilistic approaches: from fast computations due to the limited number of forward runs needed, to providing insight about the experiment sensitivity and the validity of the prior. Moreover, it benefits from its construction as a Machine Learning algorithm, leading to quasi-instantaneous models of uncertainty.
Fournir des images du sous-sol à partir d'ensembles de données terrestres est au cœur du travail du géophysicien. De multiples approches ont été appliquées pour s'attaquer à cette tâche. La plupart du temps, cette tâche est réalisée dans un cadre déterministe, ce qui signifie que pour un ensemble de données déterminé, un modèle unique est fourni pour expliquer les données. Cependant, ces approches déterministes ne permettent pas de fournir des estimations raisonnables de l'incertitude, qui tiennent compte de la non-unicité de la solution, du bruit dans les données et des erreurs de modélisation. Pour fournir des modèles précis et exacts du sous-sol tout en tenant compte de l'incertitude, les géophysiciens utilisent des approches probabilistes. Ces approches sont capables d'échantillonner l'ensemble des modèles a priori possibles (le prior) afin d'extraire les modèles qui peuvent raisonnablement expliquer l'ensemble des données (le posterior). De telles approches, bien que supérieures en termes de fiabilité des résultats, sont rarement appliquées en pratique en raison de leurs importantes exigences en termes de temps de calcul. Dans ce manuscrit, l'objectif est de proposer un nouveau processus bayésien pour interpréter ces données géophysiques. Ce nouveau système, appelé Bayesian Evidential Learning, promet de permettre une estimation rapide, précise et exacte de l'incertitude. Ce processus est appliqué et adapté aux jeux de données géophysiques 1D (BEL1D). Ce système présente plusieurs avantages par rapport aux approches probabilistes classiques : il permet des calculs rapides grâce au nombre limité d'exécutions nécessaires, et donne un aperçu de la sensibilité de l'expérience et de la validité de l'antériorité. De plus, il bénéficie de sa construction en tant qu'algorithme de Machine Learning, conduisant à la construction de modèles d'incertitude quasi-instantanés.
Het maken van beelden van de ondergrond op basis van grondgegevens is essentieel voor het werk van de geofysicus. Er zijn verschillende manieren om deze taak uit te voeren. Meestal wordt deze taak binnen een deterministisch kader uitgevoerd, wat betekent dat voor een bepaalde dataset één enkel model wordt verstrekt om de gegevens te verklaren. Deze deterministische benaderingen zijn echter niet geschikt om redelijke onzekerheidsanalyses te maken, die rekening houden met gegevensruis, modeleringsfouten, enz. Om precieze en nauwkeurige modellen van de ondergrond te berekenen, samen met onzekerheid, gebruiken geofysici probabilistische methoden. Die benaderingen mogen het ensemble van alle mogelijke modellen (de prior) bemonsteren om er modellen uit te halen die de datasets redelijkerwijs kunnen verklaren (de posterior). Deze benaderingen, hoewel superieur door de betrouwbaarheid van hun resultaten, worden in praktijk bijna nooit toegepast omdat ze veel computerwerk vergen. In dit manuscript wordt een nieuw Bayesiaans raamwerk voorgesteld om die geofysische gegevenssets te interpreteren. Aan de hand van dit nieuwe systeem, genaamd Bayesian Evidential Learning, kan de onzekerheid snel, nauwkeurig en accuraat worden ingeschat. Dit kader wordt toegepast en aangepast voor 1D geofysische gegevenssets (BEL1D). Het nieuwe en aangepaste raamwerk biedt verschillende voordelen in vergelijking met klassieke probabilistische strategieën: van snelle berekeningen door het beperkte aantal forward runs die nodig zijn, tot inzicht in de sensitiviteit van het experiment en de validiteit van de prior. Bovendien profiteert het van zijn constructie als Machine Learning-algoritme, wat leidt tot quasi-onmiddellijk modellenren van onzekerheid.
Keywords
Geophysics, Inversion, Bayesian Evidential Learning, Uncertainty Quantification, Bayesian, Machine Learning

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Citation

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MLA
Michel, Hadrien. A New Bayesian Framework for the Interpretation of Geophysical Data. University of Liège ; Ghent University. Faculty of Sciences, 2023.
APA
Michel, H. (2023). A new Bayesian framework for the interpretation of geophysical data. University of Liège ; Ghent University. Faculty of Sciences, Ghent, Belgium.
Chicago author-date
Michel, Hadrien. 2023. “A New Bayesian Framework for the Interpretation of Geophysical Data.” Ghent, Belgium: University of Liège ; Ghent University. Faculty of Sciences.
Chicago author-date (all authors)
Michel, Hadrien. 2023. “A New Bayesian Framework for the Interpretation of Geophysical Data.” Ghent, Belgium: University of Liège ; Ghent University. Faculty of Sciences.
Vancouver
1.
Michel H. A new Bayesian framework for the interpretation of geophysical data. [Ghent, Belgium]: University of Liège ; Ghent University. Faculty of Sciences; 2023.
IEEE
[1]
H. Michel, “A new Bayesian framework for the interpretation of geophysical data,” University of Liège ; Ghent University. Faculty of Sciences, Ghent, Belgium, 2023.
@phdthesis{01GQ7BT9B7TN8MHXSA0CEQENAG,
  abstract     = {{Providing images of the subsurface from ground-based datasets  is at the heart of the geophysicist's work. Multiple approaches have been applied to tackle this task. Most of the time, this task is performed in a deterministic framework, meaning that for a given dataset, a single model is provided to explain the data. However, those deterministic approaches lack the ability to provide reasonable uncertainty estimations, that take into account the non-unicity of the solution, noise in the data and modelling error. To provide precise and accurate models of the subsurface along with uncertainty, geophysicists use probabilistic approaches. Those approaches are able to sample the ensemble of a priori possible models (the prior) in order to extract models that can reasonably explain the datasets (the posterior). Such approaches, even though superior in terms of the reliability of their results, are rarely applied in practice due to their significant computational requirements. 

In this manuscript, the aim is to propose a new Bayesian framework to interpret those geophysical datasets. This new framework, called Bayesian Evidential Learning, promises to enable a fast, precise and accurate estimation of the uncertainty. This framework is applied and adapted for 1D geophysical datasets (BEL1D). The new and adapted framework presents several advantages when compared to classical probabilistic approaches: from fast computations due to the limited number of forward runs needed, to providing insight about the experiment sensitivity and the validity of the prior. Moreover, it benefits from its construction as a Machine Learning algorithm, leading to quasi-instantaneous models of uncertainty.}},
  author       = {{Michel, Hadrien}},
  keywords     = {{Geophysics,Inversion,Bayesian Evidential Learning,Uncertainty Quantification,Bayesian,Machine Learning}},
  language     = {{eng}},
  pages        = {{XX, 178}},
  publisher    = {{University of Liège ; Ghent University. Faculty of Sciences}},
  school       = {{Ghent University}},
  title        = {{A new Bayesian framework for the interpretation of geophysical data}},
  year         = {{2023}},
}