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Summary statistics and model selection in Hydrogeophysics

English title Summary statistics and model selection in Hydrogeophysics
Applicant Linde Niklas
Number 155924
Funding scheme Project funding (Div. I-III)
Research institution Institut de géographie et de durabilité Faculté des géosciences et environnement Université de Lausanne
Institution of higher education University of Lausanne - LA
Main discipline Geophysics
Start/End 01.02.2015 - 31.01.2019
Approved amount 474'928.00
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All Disciplines (2)

Discipline
Geophysics
Hydrology, Limnology, Glaciology

Keywords (9)

Inverse theory; Hydrogeophysics; Sub-resolution effects; Hydrogeology; Approximate Bayesian computation; Conceptual models; Lithological tomography; Markov chain Monte Carlo; Model selection

Lay Summary (French)

Lead
Il est relativement facile de déterminer des modèles du sous-sol permettant d'expliquer des milliers de mesures indirects de ses propriétés (p. ex. des données géophysiques). Il est beaucoup plus difficile de répondre à des questions telles que: quelle est l'incertitude d'un paramètre du modèle en particulier ou quel est l'environnement géologique qui est à l'origine de ces mesures ? Cette recherche veut déterminer dans quelle mesure une nouvelle branche des statistiques, l'approximate Bayesian computation (ABC), peut nous aider. Notre hypothèse de travail est que l'ABC permet d'améliorer l'estimation des paramètres et le choix du modèle (quel type de modèle du sous-sol est le plus approprié). On s'attend à ce que les résultats soient moins sensibles aux erreurs faites lors de la description de ce qui était déjà connu de la sub-surface), aux erreurs dans notre capacité à simuler les processus physiques et la description des erreurs expérimentales.
Lay summary

Il est relativement facile de déterminer des modèles du sous-sol permettant d'expliquer des milliers de mesures indirects de ses propriétés (p. ex. des données géophysiques). Il est beaucoup plus difficile de répondre à des questions telles que: quelle est l'incertitude d'un paramètre du modèle en particulier ou quel est l'environnement géologique qui est à l'origine de ces mesures ? Ceci est la conséquence d'hypothèses faites lors de l'établissement de modèles de sous-sol à partir de données observées (le problème inverse). En d'autres termes, des choix subjectifs rendent difficile l'utilisation de modèles inverses pour la prédiction. Cette recherche veut déterminer dans quelle mesure une nouvelle branche des statistiques, l'approximate Bayesian computation (ABC), peut nous aider. Notre hypothèse de travail est que l'ABC permet d'améliorer l'estimation des paramètres et le choix du modèle (quel type de modèle du sous-sol est le plus approprié). On s'attend à ce que les résultats soient moins sensibles aux erreurs faites lors de la description de ce qui était déjà connu de la sub-surface (connaissance a priori), aux erreurs dans notre capacité à simuler les processus physiques (le problème direct) et la description des erreurs expérimentales (erreurs d'observations). Un de nos défis est de définir les mesures statistiques appropriées pour comparer des données observées et simulées ainsi que les propriétés attendues des modèles. Nos exemples tests se focaliseront tout d'abord sur des applications environnementales que nous étudierons avec des méthodes géophysiques et hydrologiques. Si cela fonctionne, nous nous attendons que cette recherche contribue à établir des bonnes pratiques pour répondre aux défis scientifiques et sociétaux dans lesquels les sciences de la terre jouent un rôle.

Direct link to Lay Summary Last update: 08.12.2014

Responsible applicant and co-applicants

Employees

Publications

Publication
Probabilistic inference of subsurface heterogeneity and interface geometry using geophysical data
de Pasquale G, Linde N, Doetsch J, Holbrook W S (2019), Probabilistic inference of subsurface heterogeneity and interface geometry using geophysical data, in Geophysical Journal International, 217(2), 816-831.
Impact of petrophysical uncertainty on Bayesian hydrogeophysical inversion and model selection
Brunetti Carlotta, Linde Niklas (2018), Impact of petrophysical uncertainty on Bayesian hydrogeophysical inversion and model selection, in Advances in Water Resources, 111, 346-359.
Changing the prior model description in Bayesian inversion of hydrogeophysics dataset
de Pasquale Giulia (2017), Changing the prior model description in Bayesian inversion of hydrogeophysics dataset, in Groundwater, 55(5), 651-655.
Bayesian model selection in hydrogeophysics: Application to conceptual subsurface models of the South Oyster Bacterial Transport Site, Virginia, USA
Brunetti Carlotta, Linde Niklas, Vrugt Jasper A. (2017), Bayesian model selection in hydrogeophysics: Application to conceptual subsurface models of the South Oyster Bacterial Transport Site, Virginia, USA, in Advances in Water Resources, 102, 127-141.
On structure-based priors in Bayesian geophysical inversion
de Pasquale Giulia, Linde Niklas (2017), On structure-based priors in Bayesian geophysical inversion, in Geophysical Journal International, 208, 1342-1358.
On uncertainty quantification in hydrogeology and hydrogeophysics
Linde Niklas, Ginsbourger David, Irving James, Nobile Fabio, Doucet Arnaud (2017), On uncertainty quantification in hydrogeology and hydrogeophysics, in Advances in Water Resources, 110, 166-181.

Collaboration

Group / person Country
Types of collaboration
Jasper A. Vrugt, University of California Irvine United States of America (North America)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
W. Steven Holbrook, Virginia Tech United States of America (North America)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
Marco Bianchi, British Geological Survey United States of America (North America)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
Joseph Doetsch, ETHZ Switzerland (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication

Scientific events

Active participation

Title Type of contribution Title of article or contribution Date Place Persons involved
Workshop on Frontiers of Uncertainty Quantification in Subsurface Environments Poster Hydrogeological model selection with complex spatial priors 05.09.2018 Pavia, Italy Linde Niklas; de Pasquale Giulia;
European Geoscience Union (EGU) General Assembly Poster Hydrogeological model selection with complex spatial priors 08.04.2018 Vienna, Austria Brunetti Carlotta; Linde Niklas;
European Geoscience Union (EGU) General Assembly Talk given at a conference Probabilistic inversion of geophysical datasets for subsurface interface detection 08.04.2018 Vienna, Austria Linde Niklas; de Pasquale Giulia;
23rd European Meeting of Environmental and Engineering Geophysics Talk given at a conference Bayesian Inversion of Surface-Based ERT Data Using a Structure-based Prior 03.09.2017 Malmö, Sweden de Pasquale Giulia; Linde Niklas;
European Geosciences Union (EGU) General Assembly Poster Effects of petrophysical uncertainty in Bayesian hydrogeophysical inversion and model selection 23.04.2017 Vienna, Austria Brunetti Carlotta; Linde Niklas;
10th International Geostatistical Congress Individual talk On uniform structure constrains in Bayesian inversion 05.09.2016 Valencia, Spain de Pasquale Giulia; Linde Niklas;
10th International Geostatistical Congress Poster Geophysics-based model selection of conceptual subsurface models: Application to the South Oyster Bacterial Transport Site, Virginia, USA 05.09.2016 Valencia, Spain Brunetti Carlotta; Linde Niklas;
Integrated Imaging of the Earth Individual talk On the value of multiple data types and conceptual geological knowledge in hydrogeophysical inversion 11.02.2016 London, Great Britain and Northern Ireland Linde Niklas;
American Geophysical Union Fall Meeting Individual talk The role of multiple-point statistics and model selection in hydrogeophysical studies of the critical zone 12.12.2015 San Francisco, United States of America Linde Niklas;
Summer School on Flow and Transport in Porous and Fractured media: Development, Protection, Management and Sequestration of Subsurface Fluids Poster Use of geophysical data for model selection of competing conceptual hydrological models 20.07.2015 Cargèse, Switzerland Linde Niklas; Brunetti Carlotta; de Pasquale Giulia;


Associated projects

Number Title Start Funding scheme
184574 GEOFACES: GEOphysics-based FAlsification and Corroboration in the Earth Sciences 01.11.2019 Project funding (Div. I-III)
149117 Time-Lapse Analysis and Inversion of Radio Magnetotelluric and Audio Magnetotelluric Data 01.01.2014 Project funding (Div. I-III)
132249 Integrated methods for stochastic ensemble aquifer modelling (ENSEMBLE) 01.03.2011 Sinergia

Abstract

Geophysical data are often affected by heterogeneities at scales smaller than those resolved by traditional geophysical inversion. These sub-resolution effects may provide insights about pore or fine-scale properties, but can also severely degrade Markov chain Monte Carlo (MCMC) inversion results. Similar effects occur when disregarding modeling errors. Statistical inference from sampled realizations can thus be misleading when unaccounted sub-resolution effects and modeling errors are present and when the prior probability density function (pdf) is imperfect. Even in the absence of such limitations, it might happen that model realizations similar to the model used to generate noise-contaminated data are not part of the sampled MCMC realizations. This happens when other parameter combinations (possibly with low geological realism, but still in agreement with the prior pdf) exist with significantly lower data misfits. These problems are increasing when working with large data sets having small errors and model parameterizations involving many degrees of freedom. There is a need for new approaches to account for these effects.Economic and logistic constraints often lead to situations where high-resolution near-surface geophysical data only cover a small fraction of study areas of interest (e.g., a catchment, the hyporheic zone along a river, or an aquifer). Geophysical data are typically used to derive local subsurface information by inverting site-specific data, but the resulting images may provide few insights about expected subsurface characteristics at other locations. An alternative approach is based on formal model selection, in which multiple conceptual subsurface models are compared against the data and the prior pdf. The focus is then placed on inferring general system properties (e.g., a statistical model based on two-point statistics or representative lithological units) that may be used in subsequent probabilistic simulations across the study area. General algorithms for model selection are very time-consuming. An alternative based on summary statistics used in approximate Bayesian computation (ABC) will be investigated. Instead of relying on likelihood functions based on pair-wise comparisons of the observed and simulated data, ABC uses lower-order likelihood-free representations. These so-called summary statistics may, for example, include the spread of the data. In ABC, realizations from the prior pdf are kept as realizations from the posterior pdf if the corresponding summary statistics are within pre-defined distances from those of the observed data. We postulate that working with summary statistics and corresponding thresholds can help to decrease the effects of sub-resolution heterogeneity and modeling errors compared with classical MCMC. We also expect that summary statistics are better suited to target data characteristics that are representative of a given conceptual model. We will work with and adapt state-of-the-art MCMC models to ABC and explore the use of sequential Monte Carlo for model selection with summary statistics. These developments will improve the efficiency of probabilistic inversions and model selection procedures, and provide less biased estimates. We will test and develop algorithms against numerical and field-based test cases with competing conceptual subsurface models and important sub-resolution effects. To focus on common methods with contrasting physics, we will primarily consider the use of crosshole ground penetrating radar (GPR) and surface-based electrical resistivity tomography (ERT) in different hydrological applications.
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