Comparison of three recent discrete stochastic inversion methods and influence of the prior choice
Groundwater flow depends on subsurface heterogeneity, which often calls for categorical fields to represent different geological facies. The knowledge about subsurface is however limited and often provided indirectly by state variables, such as hydraulic heads of contaminant concentrations. In such...
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Académie des sciences
2022-10-01
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| Series: | Comptes Rendus. Géoscience |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/geoscience/articles/10.5802/crgeos.160/ |
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| author | Juda, Przemysław Straubhaar, Julien Renard, Philippe |
| author_facet | Juda, Przemysław Straubhaar, Julien Renard, Philippe |
| author_sort | Juda, Przemysław |
| collection | DOAJ |
| description | Groundwater flow depends on subsurface heterogeneity, which often calls for categorical fields to represent different geological facies. The knowledge about subsurface is however limited and often provided indirectly by state variables, such as hydraulic heads of contaminant concentrations. In such cases, solving a categorical inverse problem is an important step in subsurface modeling. In this work, we present and compare three recent inverse frameworks: Posterior Population Expansion (PoPEx), Ensemble Smoother with Multiple Data Assimilation (ESMDA), and DREAM-ZS (a Markov chain Monte Carlo sampler). PoPEx and ESDMA are used with Multiple-point statistics (MPS) as geostatistical engines, and DREAM-ZS is used with a Wasserstein generative adversarial network (WGAN). The three inversion methods are tested on a synthetic example of a pumping test in a fluvial channelized aquifer. Moreover, the inverse problem is solved three times with each method, each time using a different training image to check the performance of the methods with different geological priors. To assess the quality of the results, we propose a framework based on continuous ranked probability score (CRPS), which compares single true values with predictive distributions. All methods performed well when using the training image used to create the reference, but their performances were degraded with the alternative training images. PoPEx produced the least geological artifacts but presented a rather slow convergence. ESMDA showed initially a very fast convergence which reaches a plateau, contrary to the remaining methods. DREAM-ZS was overly confident in placing some incorrect geological features but outperformed the other methods in terms of convergence. |
| format | Article |
| id | doaj-art-42977eb8771c49eea2ca884271710a53 |
| institution | Kabale University |
| issn | 1778-7025 |
| language | English |
| publishDate | 2022-10-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Géoscience |
| spelling | doaj-art-42977eb8771c49eea2ca884271710a532025-02-07T10:40:14ZengAcadémie des sciencesComptes Rendus. Géoscience1778-70252022-10-01355S1194410.5802/crgeos.16010.5802/crgeos.160Comparison of three recent discrete stochastic inversion methods and influence of the prior choiceJuda, Przemysław0https://orcid.org/0000-0002-5037-5893Straubhaar, Julien1https://orcid.org/0000-0003-2718-4332Renard, Philippe2https://orcid.org/0000-0003-4504-435XStochastic Hydrogeology and Geostatistics Group, Centre for Hydrogeology and Geothermics, University of Neuchâtel, Rue Emile-Argand 11, 2000 Neuchâtel, SwitzerlandStochastic Hydrogeology and Geostatistics Group, Centre for Hydrogeology and Geothermics, University of Neuchâtel, Rue Emile-Argand 11, 2000 Neuchâtel, SwitzerlandDepartment of Geosciences, University of Oslo, Oslo, Norway; Stochastic Hydrogeology Group, University of Neuchâtel, Rue Emile-Argand 11, 2000 Neuchâtel, SwitzerlandGroundwater flow depends on subsurface heterogeneity, which often calls for categorical fields to represent different geological facies. The knowledge about subsurface is however limited and often provided indirectly by state variables, such as hydraulic heads of contaminant concentrations. In such cases, solving a categorical inverse problem is an important step in subsurface modeling. In this work, we present and compare three recent inverse frameworks: Posterior Population Expansion (PoPEx), Ensemble Smoother with Multiple Data Assimilation (ESMDA), and DREAM-ZS (a Markov chain Monte Carlo sampler). PoPEx and ESDMA are used with Multiple-point statistics (MPS) as geostatistical engines, and DREAM-ZS is used with a Wasserstein generative adversarial network (WGAN). The three inversion methods are tested on a synthetic example of a pumping test in a fluvial channelized aquifer. Moreover, the inverse problem is solved three times with each method, each time using a different training image to check the performance of the methods with different geological priors. To assess the quality of the results, we propose a framework based on continuous ranked probability score (CRPS), which compares single true values with predictive distributions. All methods performed well when using the training image used to create the reference, but their performances were degraded with the alternative training images. PoPEx produced the least geological artifacts but presented a rather slow convergence. ESMDA showed initially a very fast convergence which reaches a plateau, contrary to the remaining methods. DREAM-ZS was overly confident in placing some incorrect geological features but outperformed the other methods in terms of convergence.https://comptes-rendus.academie-sciences.fr/geoscience/articles/10.5802/crgeos.160/Stochastic inversionMultiple-point statisticsMonte Carlo samplingPosterior Population ExpansionEnsemble smootherGroundwater flowScoring rules |
| spellingShingle | Juda, Przemysław Straubhaar, Julien Renard, Philippe Comparison of three recent discrete stochastic inversion methods and influence of the prior choice Comptes Rendus. Géoscience Stochastic inversion Multiple-point statistics Monte Carlo sampling Posterior Population Expansion Ensemble smoother Groundwater flow Scoring rules |
| title | Comparison of three recent discrete stochastic inversion methods and influence of the prior choice |
| title_full | Comparison of three recent discrete stochastic inversion methods and influence of the prior choice |
| title_fullStr | Comparison of three recent discrete stochastic inversion methods and influence of the prior choice |
| title_full_unstemmed | Comparison of three recent discrete stochastic inversion methods and influence of the prior choice |
| title_short | Comparison of three recent discrete stochastic inversion methods and influence of the prior choice |
| title_sort | comparison of three recent discrete stochastic inversion methods and influence of the prior choice |
| topic | Stochastic inversion Multiple-point statistics Monte Carlo sampling Posterior Population Expansion Ensemble smoother Groundwater flow Scoring rules |
| url | https://comptes-rendus.academie-sciences.fr/geoscience/articles/10.5802/crgeos.160/ |
| work_keys_str_mv | AT judaprzemysław comparisonofthreerecentdiscretestochasticinversionmethodsandinfluenceofthepriorchoice AT straubhaarjulien comparisonofthreerecentdiscretestochasticinversionmethodsandinfluenceofthepriorchoice AT renardphilippe comparisonofthreerecentdiscretestochasticinversionmethodsandinfluenceofthepriorchoice |