Voici les éléments 1 - 10 sur 187
  • Publication
    Accès libre
    Exploring substitution random functions composed of stationary multi-Gaussian processes
    Simulation of random felds is widely used in Earth sciences for modeling and uncertainty quantifcation. The spatial features of these felds may have a strong impact on the forecasts made using these felds. For instance, in fow and transport problems the connectivity of the permeability felds is a crucial aspect. Multi-Gaussian random felds are the most common tools to analyze and model continuous felds. Their spatial correlation structure is described by a covariance or variogram model. However, these types of spatial models are unable to represent highly or poorly connected structures even if a broad range of covariance models can be employed. With this type of model, the regions with values close to the mean are always well connected whereas the regions of low or high values are isolated. Substitution random functions (SRFs) belong to another broad class of random functions that are more fexible. SRFs are constructed by composing (Z = Y◦T) two stochastic processes: the directing function T (latent feld) and the coding process Y (modifying the latent feld in a stochastic manner). In this paper, we study the properties of SRFs obtained by combining stationary multi-Gaussian random felds for both T and Y with bounded variograms. The resulting SRFs Z are stationary, but as T has a fnite variance Z is not ergodic for the mean and the covariance. This means that single realizations behave diferently from each other. We propose a simple technique to control which values (low, intermediate, or high) are connected. It consists of adding a control point on the process Y to guide every single realization. The conditioning to local values is obtained using a Gibbs sampler.
  • Publication
    Accès libre
    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 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.
  • Publication
    Accès libre
  • Publication
    Métadonnées seulement
    Multiresolution Approach to Condition Categorical Multiple-Point Realizations to Dynamic Data With Iterative Ensemble Smoothing
    A new methodology is presented for the conditioning of categorical multiple-point statistics (MPS) simulations to dynamic data with an iterative ensemble smoother (ES-MDA). The methodology relies on a novel multiresolution parameterization of the categorical MPS simulation. The ensemble of latent parameters is initially defined on the basis of the coarsest-resolution simulations of an ensemble of multiresolution MPS simulations. Because this ensemble is non-multi-Gaussian, additional steps prior to the computation of the first update are proposed. In particular, the parameters are updated at predefined locations at the coarsest scale and integrated as hard data to generate a new multiresolution MPS simulation. The performance of the methodology was assessed on a synthetic groundwater flow problem inspired from a real situation. The results illustrate that the method converges towards a set of final categorical realizations that are consistent with the initial categorical ensemble. The convergence is reliable in the sense that it is fully controlled by the integration of the ES-MDA update into the new conditional multiresolution MPS simulations. Thanks to a massively reduced number of parameters compared to the size of the categorical simulation, the identification of the geological structures during the data assimilation is particularly efficient for this example. The comparison between the estimated uncertainty and a reference estimate obtained with a Monte Carlo method shows that the uncertainty is not severely reduced during the assimilation as is often the case. The connectivity is successfully reproduced during the iterative procedure despite the rather large distance between the observation points.
  • Publication
    Accès libre
    A new perspective to model subsurface stratigraphy in alluvial hydrogeological basins, introducing geological hierarchy and relative chronology
    (2023-1-17)
    Zuffetti, Chiara
    ;
    Communian, Alessandro
    ;
    Bersezio, Riccardo
    ;
    This paper presents a novel perspective for modelling alluvial stratigraphy. It integrates the spatial geological information, geological maps and well log descriptions, with the rules describing the hierarchy and relative chronology of the geological entities. As geological modelling tools are moving fast forward, the urgent need for expert geological input, codified as modelling rules, persists. Concerning subsurface alluvial architectures, the concepts of “stratigraphic hierarchy” and “relative chronology” provide the most relevant rules which permit to link the modelling procedure to the geo-history of a region. The paper shows how to formalize this knowledge into modelling rules. This is illustrated and implemented in a Python™ module named HIEGEO which is applied on a 2-D cross-section from the Po Basin (N-Italy). The stratigraphic correlation yields 2-D pictures of the hierarchic stratigraphy and relative chronology of the units. The input are: an attribute table of stratigraphic boundaries expressing their hierarchy and chronology; contact points where these boundaries cross the control logs. Since the aim of HIEGEO is to illustrate the principle of the method but not to replace existing 3-D geological modelling tools, it implements a linear interpolation algorithm which creates joins between contact points. It plots linear joins framing polygons based on their hierarchy, at any user’s desired detail. HIEGEO highlights potential inconsistencies of the input dataset, helping to re-evaluate the geological interpretation. The proposed workflow allows to: i) translate geological knowledge into modelling rules; ii) compute stratigraphic models constrained by the hierarchy of stratigraphic entities and the relative chronology of geological events; iii) represent internal geometries of the stratigraphic units, accounting for their composite nature; iv) reduce uncertainty in modelling alluvial architectures. It represents a starting point for multi-scale applications and could be easily integrated into 3-D modelling packages, to couple the hierarchical concept proposed here with existing advanced interpolation methods.
  • Publication
    Accès libre
    Stochastic multiple data integration for the characterization of quaternary aquifers
    La gestion des ressources en eaux souterraines nécessite souvent le développement de modèles géologiques et hydrogéologiques. Cependant, la construction de modèles précis peut s’avérer une tâche difficile et longue, en particulier dans les vastes zones présentant des dépôts quaternaires complexes. Or, ces zones sont souvent celles qui sont le plus fréquemment soumises à l’exploitation des ressources et à la pollution. Pour résoudre ce problème, plusieurs études ont proposé des méthodologies innovantes pour intégrer différents types de données, notamment des données sur les puits, des données géophysiques et des données hydrogéologiques. L’objectif est de faciliter la construction de ces modèles dans des cadres cohérents et reproductibles avec une estimation robuste des erreurs. Nous présentons ici quatre études qui proposent de nouvelles méthodologies pour relever ce défi. La première étude présente un vaste et dense ensemble de données électromagnétiques dans le domaine temporel (TDEM) acquises dans la haute vallée de l’Aar, en Suisse, afin d’améliorer la connaissance des variations spatiales des dépôts quaternaires. Les modèles de résistivité inversée dérivés de cette acquisition ont été publiés et pourraient être utilisés pour diverses études futures. Cette étude met également en évidence le potentiel de l’ensemble de données pour le développement d’algorithmes d’intégration de données en raison de l’abondance de diverses données librement disponibles sur la même zone. La deuxième étude propose une nouvelle méthodologie pour combiner les forages et les données géophysiques avec une propagation de l’incertitude pour prédire la probabilité d’argile à l’échelle d’une vallée. Une fonction de translation variant dans l’espace a été utilisée pour estimer la fraction d’argile à partir de la résistivité. Les paramètres de cette fonction sont inversés en utilisant la description des forages comme points de contrôle. Ils combinent cette estimation de la fraction d’argile avec un cadre d’interpolation stochastique 3D non déterministe basé sur un algorithme de statistiques à points multiples et une fonction aléatoire gaussienne afin d’obtenir un modèle 3D réaliste à haute résolution spatiale de la fraction d’argile pour la haute vallée de l’Aar. L’étude démontre la qualité des valeurs prédites et leurs incertitudes correspondantes en utilisant la validation croisée. La troisième étude porte sur la possibilité d’intégrer des données de forage, géophysiques et hydrogéologiques, tout en conservant la cohérence du concept géologique des modèles. Nous avons utilisé un générateur stochastique de modèles géologiques pour construire un ensemble de modèles préalables basés sur les forages. Nous proposons ensuite une approche d’inversion multi-échelle qui combine des modèles peu fidèles et moins précis avec des modèles plus fidèles et plus précis afin de réduire le temps nécessaire à la convergence de l’inversion. Les données géophysiques et hydrogéologiques sont intégrées à l’aide d’un algorithme ES-MDA (Ensemble Smoother with Multiple Data Assimilation Algorithm). Le flux de travail garantit que les modèles sont géologiquement cohérents et estime de manière robuste l’incertitude associée au modèle final. L’étude démontre l’efficacité de cette approche pour un cas synthétique contrôlé. Elle montre que ArchPY et ES-MDA sont capables de générer des réalisations plausibles de la subsurface pour les modèles sédimentologiques du Quaternaire. Enfin, la quatrième étude présente une méthodologie innovante qui combine l’algorithme ES-MDA avec un code de modélisation géologique hiérarchique open-source pour intégrer des sources de données multiples et construire des modèles géologiquement cohérents avec une estimation d’erreur robuste. La méthodologie est appliquée à un cas de terrain dans la haute vallée de l’Aar, en Suisse. Un cadre de validation croisée est mis en oeuvre afin d’évaluer la méthodologie. L’approche aboutit à des modèles finaux qui équilibrent efficacement la précision et l’incertitude et qui peuvent prendre en compte diverses sources de données, y compris des données géophysiques, des connaissances conceptuelles régionales, des forages et des mesures hydrogéologiques à l’échelle d’une vallée. En résumé, cette thèse présente plusieurs méthodes innovantes qui pourraient être appliquées à la réalisation de modèles hydrogéologiques à petite ou grande échelle. ABSTRACT Groundwater resource management often requires the development of geological and hydrogeological models. However, constructing accurate models can be a challenging and time-consuming task, especially in large areas with complex Quaternary deposits. However, these areas are often the most frequently subject to resource exploitation and pollution. To address this issue, several studies have proposed innovative methodologies to integrate various types of data, including wells, geophysical, and hydrogeological data. The objective is to facilitate the construction of these models within coherent and reproducible frameworks with robust error estimation. In these, we present four studies that present novel methodologies to address this challenge. The first study presents a large and dense Time Domain ElectroMagnetic (TDEM) dataset acquired in the upper Aare Valley, Switzerland, to improve knowledge of the spatial variations of Quaternary deposits. The inverted resistivity models derived from this acquisition were published and could be used for various future studies. It also highlights the data set’s potential for data integration algorithm development because of the abundance of various freely available data on the same zone. The second study proposes a new methodology to combine boreholes and geophysical data with a propagation of the uncertainty to predict the probability of clay at the scale of a valley. A spatially varying translator function was used to estimate the clay fraction from resistivity. The parameters of this function are inverted using the description of the boreholes as control points. They combine this clay fraction estimation with a nondeterministic 3D stochastic interpolation framework based on a Multiple Points Statistics algorithm and Gaussian Random Function to obtain a 3D realistic high spatial resolution model of clay fraction for the upper Aare valley. The study demonstrates the quality of the predicted values and their corresponding uncertainties using cross-validation. The third study addresses the possibility of integrating boreholes, geophysical, and hydrogeological data, while keeping the geological concept of the models coherent. We used a stochastic geological model generator to construct a set of prior models based on the boreholes. We then propose a multiscale inversion approach that combines low-fidelity and less accurate models with high-fidelity and more accurate models to reduce the time needed for the inversion to converge. Both geophysical and hydrogeological data are integrated, using an Ensemble Smoother with Multiple Data Assimilation Algorithm (ES-MDA) algorithm. The workflow ensures that the models are geologically consistent and robustly estimate the associated uncertainty with the final model. The study demonstrates the effectiveness of this approach for a controlled synthetic case. It shows that ArchPY and ES-MDA are capable of generating plausible subsurface realizations for Quaternary Sedimentological Models. Finally, the fourth study presents an innovative methodology that combines the ES-MDA algorithm with an open-source hierarchical geological modeling code to integrate multiple data sources and construct geologically consistent models with robust error estimation. The methodology is applied to a field case in the upper Aare Valley, Switzerland. In order to benchmark the methodology, a cross-validation framework is implemented. The approach results in final models that effectively balance accuracy and uncertainty and can take into account various data sources, including geophysical data, regional conceptual knowledge, boreholes, and hydrogeological measurements at a valley scale. In summary, this thesis presents several innovative methods that could be applied on small to large scale hydrogeological model realization.
  • Publication
    Accès libre
    Towards Improved Remedial Outcomes in Categorical Aquifers with an Iterative Ensemble Smoother
    (2023) ; ;
    John Doherty
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    Jeremy White
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    Marc Killingstad
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    Michael Kladias
    AbstractCategorical parameter distributions consisting of geologic facies with distinct properties, for example, high‐permeability channels embedded in a low‐permeability matrix, are common at contaminated sites. At these sites, low‐permeability facies store solute mass, acting as secondary sources to higher‐permeability facies, sustaining concentrations for decades while increasing risk and cleanup costs. Parameter estimation is difficult in such systems because the discontinuities in the parameter space hinder the inverse problem. This paper presents a novel approach based on Traveling Pilot Points (TRIPS) and an iterative ensemble smoother (IES) to solve the categorical inverse problem. Groundwater flow and solute transport in a hypothetical aquifer with a categorical parameter distribution are simulated using MODFLOW 6. Heads and concentrations are recorded at multiple monitoring locations. IES is used to generate posterior ensembles assuming a TRIPS prior and an approximate multi‐Gaussian prior. The ensembles are used to predict solute concentrations and mass into the future. The evaluation also includes an assessment of how the number of measurements and the choice of the geological prior determine the characteristics of the posterior ensemble and the resulting predictions. The results indicate that IES was able to efficiently sample the posterior distribution and showed that even with an approximate geological prior, a high degree of parameterization and history matching could lead to parameter ensembles that can be useful for making certain types of predictions (heads, concentrations). However, the approximate geological prior was insufficient for predicting mass. The analysis demonstrates how decision‐makers can quantify uncertainty and make informed decisions with an ensemble‐based approach.
  • Publication
    Accès libre
    A Novel Methodology for the Stochastic Integration of Geophysical and Hydrogeological Data in Geologically Consistent Models
    AbstractTo address groundwater issues, it is often necessary to develop geological and hydrogeological models. Combining geological, geophysical and hydrogeological data available on a site to build such models is often a challenge. This paper presents a methodology to integrate such data within a geologically consistent model with robust error estimation. The methodology combines the Ensemble Smoother with Multiple Data Assimilation (ESMDA) algorithm with a hierarchical geological modeling approach (ArchPy). Geophysical and hydrogeological field data are jointly assimilated in a stochastic ESMDA framework. To speed up the inversion process, forward responses are computed in lower‐dimensional spaces relevant to each physical problem. By doing so, the final models take into account multiple data sources and regional conceptual geological knowledge. This study illustrates the applicability of this novel approach using actual data from the upper Aare Valley, Switzerland. The results of cross‐validation show that the combination of different data types, each sensitive to different spatial dimensions, enhances the quality of the model within a reasonable computing time. The proposed methodology allows the automatic generation of groundwater models with robust uncertainty estimation and could be applied to a wide variety of hydrogeological issues.
  • Publication
    Accès libre
    Improving understanding of groundwater flow in an alpine karst system by reconstructing its geologic history using conduit network model ensembles
    (2023)
    Chloé Fandel
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    Ty Ferré
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    ; ;
    Nico Goldscheider
    Abstract. Reconstructing the geologic history of a karst area can advance understanding of the system's present-day hydrogeologic functioning and help predict the location of unexplored conduits. This study tests competing hypotheses describing past conditions controlling cave formation in an alpine karst catchment, by comparing an ensemble of modeled networks to the observed network map. The catchment, the Gottesacker karst system (Germany and Austria), is drained by three major springs and a paleo-spring and includes the partially explored Hölloch cave, which consists of an active section whose formation is well-understood and an inactive section whose formation is the subject of debate. Two hypotheses for the formation of the inactive section are the following: (1) glaciation obscured the three present-day springs, leaving only the paleo-spring, or (2) the lowest of the three major springs (Sägebach) is comparatively young, so its subcatchment previously drained to the paleo-spring. These hypotheses were tested using the pyKasso Python library (built on anisotropic fast-marching methods) to generate two ensembles of networks, one representing each scenario. Each ensemble was then compared to the known cave map. The simulated networks generated under hypothesis 2 match the observed cave map more closely than those generated under hypothesis 1. This supports the conclusion that the Sägebach spring is young, and it suggests that the cave likely continues southwards. Finally, this study extends the applicability of model ensemble methods from situations where the geologic setting is known but the network is unknown to situations where the network is known but the geologic evolution is not.