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- PublicationAccès libreOptimisation issues in 3D multiple-point statistics simulation(: Julián M. Ortiz and Xavier Emery, Mining Engineering Department, University of Chile., 2008-12)
; ;Walgenwitz, Alexandre ;Froidevaux, Roland ;Multiple-point statistics simulation has gained wide acceptance in recent years and is routinely used for simulating geological heterogeneity in hydrocarbon reservoirs and aquifers. In classical implementations, the multiple-point statistics inferred from the reference training image are stored in a dynamic data structure called search tree. The size of this search tree depends on the search template used to scan the training image and the number of facies to be simulated. In 3D applications this size can become prohibitive. One promissing avenue for drastically reducing the RAM requirements consists of using dynamically allocated lists instead of search trees to store and retrieve the multiple–point statistics. Each element of this list contains the identification of the data event together with occurence counters for each facies. First results show that implementing this list based approach results in reductions of RAM requirement by a factor 10 and more. The paper discusses in detail this novel list based approach, presents RAM and CPU performance comparisons with the (classical) tree based approach.
- PublicationAccès libreMultiple-point statistics using multi-resolution images(2020-2-4)
; ;Chugunova, TatianaMultiple-point statistics (MPS) is a simulation technique allowing to generate images that reproduce the spatial features present in a training image (TI). MPS algorithms consist in sequentially filling a simulation grid such that patterns around the simulated values come from the TI. Following this principle, joint simulations of multiple variables can be handled and complex heterogeneous fields can be generated. However, inconsistent patterns are often found in the results and some spatial features can be difficult to reproduce. In this paper, a new MPS algorithm based on a multi-resolution representation of the TI is proposed to enhance the quality of the realizations. The method consists in first building a pyramid of images from the TI by successive convolution using Gaussian-like kernels. Secondly, a MPS simulation is done at the lowest resolution level. Then, the result is expanded to the next level of resolution (one rank higher) and used as a conditioning variable for a joint MPS simulation at that level. This last step is repeated up to the initial resolution, where the final simulation is retrieved. The method is implemented in the DeeSse code based on the direct sampling algorithm. Most of the features provided by the direct sampling (conditioning to hard data, uni- or multi-variate simulation of categorical and continuous variables, scaling and rotation of the training structures) are compatible with the proposed method and the usability is maintained. Finally, various examples show that in most of the situations, combining Gaussian pyramids with MPS allows to get results of better quality and in less time compared to direct MPS simulations.
- PublicationAccès librePréconditionnement de systèmes linéaires symétriques définis positifs: application à la simulation numérique d’écoulements océaniques tridimensionnelsCette thèse est constituée de deux parties distinctes. La première partie est consacrée au développement de préconditionneurs de systèmes linéaires symétriques définis positifs. Les systèmes considérés sont de grande taille et creux (i.e. les matrices ont une faible proportion de coefficients non nuls). Ils sont résolus avec l’algorithme du gradient conjugué dont la vitesse de convergence est contrôlée par la condition de la matrice. Une nouvelle classe de préconditionneurs dépendant de plusieurs paramètres est présentée. Elle est basée sur un procédé d’orthogonalisation conjuguée de Gram-Schmidt et une méthode de moindres carrés. Des résultats théoriques sont donnés, notamment une majoration de la condition du système préconditionné. Différentes variantes (couplage, traitement par blocs) sont considérées. Cette nouvelle classe de préconditionneurs est comparée à quelques préconditionneurs connus à l’aide de tests numériques. De plus, la parallélisation des méthodes est étudiée et des tests numériques sont effectués afin d’évaluer la performance des algorithmes en termes de speed-up et d’efficience. Le but de la seconde partie est de simuler des écoulements océaniques tridimensionnels induits par les vents en surface. Pour cela, les équations de Navier-Stokes non stationnaires sont formulées pour un fluide incompressible anisotrope à densité constante. La force de Coriolis est prise en compte et les tractions dues aux vents constituent le moteur du système. Un vecteur de viscosité turbulente intègre l’influence du rapport d’aspect du bassin (i.e. ε = h 0 /d, où h 0 est la profondeur maximale et d le diamètre horizontal) de sorte à vérifier asymptotiquement l’approximation hydrostatique. Ceci donne le caractère anisotrope du fluide. Un modèle numérique pour la résolution de ces équations est présenté en détails. La discrétisation temporelle est traitée avec des méthodes de prédicteur-correcteur afin de dissocier le calcul de la vitesse et de la pression. Chaque pas de temps est décomposé en deux sous-pas, le premier consiste en une étape de prédiction et le second en une étape de correction. Des éléments finis de type Q 1 et Q 2 sont utilisés pour la discrétisation spatiale. Les problèmes faibles approchés obtenus sont des systèmes linéaires symétriques définis positifs et creux. Une méthode de pénalisation est considérée pour le calcul de la pression dont la matrice du système est mal conditionnée. Finalement, les méthodes de préconditionnement de la première partie et la mise en œuvre de logiciels parallèles ont permis de traiter le cas de l’océan Atlantique nord. Des cartes de courants sont présentées. Les données (bathymétrie, vents) ont été fournies par le projet de recherche français Mercator Océan (http://www.mercator-ocean.fr/). Les logiciels parallèles nécessaires à ce travail ont été développés sur les machines parallèles CRAY XT3 du CSCS (Swiss National Supercomputing Center, http://www.cscs.ch).
- PublicationAccès libre3D multiple-point statistics simulations of the Roussillon Continental Pliocene aquifer using DeeSse(2020-10)
;Dall'Alba, Valentin ; ; ;Issautier, BenoîtCabellero, YvanThis study introduces a novel workflow to model the heterogeneity of complex aquifers using the multiplepoint statistics algorithm DeeSse. We illustrate the approach by modeling the Continental Pliocene layer of the Roussillon aquifer in the region of Perpignan (southern France). When few direct observations are available, statistical inference from field data is difficult if not impossible and traditional geostatistical approaches cannot be applied directly. By contrast, multiple-point statistics simulations can rely on one or several alternative conceptual geological models provided using training images (TIs). But since the spatial arrangement of geological structures is often non-stationary and complex, there is a need for methods that allow to describe and account for the non-stationarity in a simple but efficient manner. The main aim of this paper is therefore to propose a workflow, based on the direct sampling algorithm DeeSse, for these situations. The conceptual model is provided by the geologist as a 2D non-stationary training image in map view displaying the possible organization of the geological structures and their spatial evolution. To control the non-stationarity, a 3D trend map is obtained by solving numerically the diffusivity equation as a proxy to describe the spatial evolution of the sedimentary patterns, from the sources of the sediments to the outlet of the system. A 3D continuous rotation map is estimated from inferred paleoorientations of the fluvial system. Both trend and orientation maps are derived from geological insights gathered from outcrops and general knowledge of processes occurring in these types of sedimentary environments. Finally, the 3D model is obtained by stacking 2D simulations following the paleotopography of the aquifer. The vertical facies transition between successive 2D simulations is controlled partly by the borehole data used for conditioning and by a sampling strategy. This strategy accounts for vertical probability of transitions, which are derived from the borehole observations, and works by simulating a set of conditional data points from one layer to the next. This process allows us to bypass the creation of a 3D training image, which may be cumbersome, while honoring the observed vertical continuity.
- PublicationAccès libreIntegrating aerial geophysical data in multiple-point statistics simulations to assist groundwater flow models(2015-10)
;Dickson, Neil ;Comte, Jean-Christophe ; ; ;McKinley, JenniferOfterdinger, UlrichThe process of accounting for heterogeneity has made significant advances in statistical research, primarily in the framework of stochastic analysis and the development of multiple-point statistics (MPS). Among MPS techniques, the direct sampling (DS) method is tested to determine its ability to delineate heterogeneity from aerial magnetics data in a regional sandstone aquifer intruded by low-permeability volcanic dykes in Northern Ireland, UK. The use of two two-dimensional bivariate training images aids in creating spatial probability distributions of heterogeneities of hydrogeological interest, despite relatively `noisy' magnetics data (i.e. including hydrogeologically irrelevant urban noise and regional geologic effects). These distributions are incorporated into a hierarchy system where previously published density function and upscaling methods are applied to derive regional distributions of equivalent hydraulic conductivity tensor K. Several K models, as determined by several stochastic realisations of MPS dyke locations, are computed within groundwater flow models and evaluated by comparing modelled heads with field observations. Results show a significant improvement in model calibration when compared to a simplistic homogeneous and isotropic aquifer model that does not account for the dyke occurrence evidenced by airborne magnetic data. The best model is obtained when normal and reverse polarity dykes are computed separately within MPS simulations and when a probability threshold of 0.7 is applied. The presented stochastic approach also provides improvement when compared to a previously published deterministic anisotropic model based on the unprocessed (i.e. noisy) airborne magnetics. This demonstrates the potential of coupling MPS to airborne geophysical data for regional groundwater modelling.
- PublicationAccès libreSimulation of rainfall time series from different climatic regions using the direct sampling techniqueThe direct sampling technique, belonging to the family of multiple-point statistics, is proposed as a nonparametric alternative to the classical autoregressive and Markovchain-based models for daily rainfall time-series simulation. The algorithm makes use of the patterns contained inside the training image (the past rainfall record) to reproduce the complexity of the signal without inferring its prior statistical model: the time series is simulated by sampling the training data set where a sufficiently similar neighborhood exists. The advantage of this approach is the capability of simulating complex statistical relations by respecting the similarity of the patterns at different scales. The technique is applied to daily rainfall records from different climate settings, using a standard setup and without performing any optimization of the parameters. The results show that the overall statistics as well as the dry/wet spells patterns are simulated accurately. Also the extremes at the higher temporal scale are reproduced adequately, reducing the well known problem of overdispersion.
- PublicationAccès libreIce volume and basal topography estimation using geostatistical methods and GPR measurements: Application on the Tsanfleuron and Scex Rouge glacier, Swiss Alps(2021-7)
;Neven, Alexis ;Dall'Alba, Valentin ; ;Ground Penetrating Radar (GPR) is nowadays widely used for determining glacier thickness. However, this method provides thickness data only along the acquisition lines and therefore interpolation has to be made between them. Depending on the interpolation strategy, calculated ice volumes can differ and can lack an accurate error estimation. Furthermore, glacial basal topography is often characterized by complex geomorphological features, which can be hard to reproduce using classical 5 interpolation methods, especially when the conditioning data are sparse or when the morphological features are too complex. This study investigates the applicability of multiple-point statistics (MPS) simulations to interpolate glacier bedrock topography using GPR measurements. In 2018, a dense GPR data set was acquired on the Tsanfleuron Glacier (Switzerland). The results obtained with the direct sampling MPS method are compared against those obtained with kriging and sequential Gaussian simulations (SGS) on both a synthetic data set – with known reference volume and bedrock topography – and the real data 10 underlying the Tsanfleuron glacier. Using the MPS modelled bedrock, the ice volume for the Scex Rouge and Tsanfleuron Glacier is estimated to be 113.9 ± 1.6 Miom3 . The direct sampling approach, unlike the SGS and the kriging, allowed not only an accurate volume estimation but also the generation of a set of realistic bedrock simulations. The complex karstic geomorphological features are reproduced, and can be used to significantly improve for example the precision of under-glacial flow estimation.
- PublicationAccès libreThe Direct Sampling method to perform multiple-point geostatistical simulationsMultiple-point geostatistics is a general statistical framework to model spatial fields displaying a wide range of complex structures. In particular, it allows controlling connectivity patterns that have a critical importance for groundwater flow and transport problems. This approach involves considering data events (spatial arrangements of values) derived from a training image (TI). All data events found in the TI are usually stored in a database, which is used to retrieve conditional probabilities for the simulation. Instead, we propose to sample directly the training image for a given data event, making the database unnecessary. Our method is statistically equivalent to previous implementations, but in addition it allows extending the application of multiple-point geostatistics to continuous variables and to multivariate problems. The method can be used for the simulation of geological heterogeneity, accounting or not for indirect observations such as geophysics. We show its applicability in the presence of complex features, nonlinear relationships between variables, and with various cases of nonstationarity. Computationally, it is fast, easy to parallelize, parsimonious in memory needs, and straightforward to implement.
- PublicationAccès libreSimulation of braided river elevation model time series with multiple-point statisticsA new method is proposed to generate successive topographies in a braided river system. Indeed, braided river morphologymodels are a key factor influencing river–aquifer interactions and have repercussions in ecosystems, flood risk or water management. It is essentially based on multivariate multiple-point statistics simulations and digital elevation models as training data sets. On the one hand, airborne photography and LIDAR acquired at successive time steps have contributed to a better understanding of the geomorphological processes although the available data are sparse over time and river scales. On the other hand, geostatistics provide simulation tools for multiple and continuous variables, which allow the exploration of the uncertainty of many assumption scenarios. Illustration of the approach demonstrates the ability of multiple-point statistics to produce realistic topographies from the information provided by digital elevation models at two time steps.
- PublicationAccès libreSimulation of rainfall time series from different climatic regions using the direct sampling techniqueThe direct sampling technique, belonging to the family of multiple-point statistics, is proposed as a nonparametric alternative to the classical autoregressive and Markov-chain-based models for daily rainfall time-series simulation. The algorithm makes use of the patterns contained inside the training image (the past rainfall record) to reproduce the complexity of the signal without inferring its prior statistical model: the time series is simulated by sampling the training data set where a sufficiently similar neighborhood exists. The advantage of this approach is the capability of simulating complex statistical relations by respecting the similarity of the patterns at different scales. The technique is applied to daily rainfall records from different climate settings, using a standard setup and without performing any optimization of the parameters. The results show that the overall statistics as well as the dry/wet spells patterns are simulated accurately. Also the extremes at the higher temporal scale are reproduced adequately, reducing the well known problem of overdispersion.