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Funding Information: Received by the editors February 3, 2021; accepted for publication (in revised form) October 19, 2021; published electronically March 15, 2022. https://doi.org/10.1137/21M1396125 Funding: The work of the first author was supported by the Institut Fran\cc ais de Finlande, the Embassy of France in Finland, the French Ministry of Higher Education, Research, and Innovation, the Finnish Society of Sciences and Letters, and the Finnish Academy of Science and Letters (2019 Maupertuis program). The work of the second and third authors was supported by the Academy of Finland grant 312124. The work of the fourth author was supported by the Academy of Finland grants 314701 and 320022. Publisher Copyright: © 2022 Society for Industrial and Applied Mathematics Electrical impedance tomography is an imaging modality for extracting information on the interior structure of a physical body from boundary measurements of current and voltage. This work studies a new robust way of modeling the contact electrodes used for driving current patterns into the examined object and measuring the resulting voltages. The idea is to not define the electrodes as strict geometric objects on the measurement boundary but only to assume approximate knowledge about their whereabouts and let a boundary admittivity function determine the actual locations of the current inputs. Such an approach enables reconstructing the boundary admittivity, i.e., the locations and strengths of the contacts, at the same time and with analogous methods as the interior admittivity. The functionality of the new model is verified by two-dimensional numerical experiments based on water tank data.

The objective of the thesis is to develop a statistical learning technique suitable for the inversion of complex physical models. The two main difficulties addressed are on the one hand the massive amount of observations to be reversed and on the other hand the need to quantify the uncertainty on the inversion, which can come from the physical model or from the measurements. In a Bayesian inversion framework, we therefore propose a two-step approach: a learning step of a parametric statistical model (GLLiM), common to all the observations, then a prediction step, repeated for each measurement, but fast enough to support a large dataset. In addition, we explore sampling techniques to refine the trade-off between computation time and inversion precision.Although general, the proposed approach is applied mainly to a complex inverse problem in planetary remote sensing. This involves using a semi-empirical spectrophotometric model (Hapke's model) to analyze reflectance measurements and indirectly find the textural characterization of the material examined. Several datasets are studied, both from laboratory measurements and massive satellite images.Finally, we exploit the versatility of the GLLiM model to explore several issues related to Bayesian inversion. In particular, we propose an indicator to assess the influence of the choice of the direct model on the quality of the inversion. We also extend the GLLiM model to take into account a priori information, making it suitable for solving data assimilation problems.; L'objectif de la thèse est de mettre au point une technique d'apprentissage statistique adaptée à l’inversion de modèles physiques complexes. Les deux principales difficultés adressées sont d’une part la quantité massive d’observations à inverser et d’autre part la nécessité de quantifier l’incertitude sur l’inversion, qui peut provenir du modèle physique ou des mesures. Dans un cadre d’inversion Bayésienne, nous proposons donc une approche en deux temps : une phase d’apprentissage d’un modèle statistique paramétrique (GLLiM), commune à toutes les observations, puis une phase de prédiction, répétée pour chaque mesure, mais suffisamment rapide pour prendre en charge un large jeu de données. De plus, nous explorons des techniques d’échantillonnages pour affiner le compromis entre temps de calcul et précision de l’inversion. Bien que générale, l’approche proposée est appliquée principalement sur un problème inverse complexe en télédétection planétaire. Il s’agit d’utiliser un modèle spectro-photométrique semi-empirique (le modèle de Hapke) pour analyser des mesures de réflectance et retrouver indirectement la caractérisation texturale du matériau examiné. Plusieurs jeux de données sont étudiés, aussi bien provenant de mesures de laboratoire que d’images satellitaires massives.Enfin, nous exploitons la polyvalence du modèle GLLiM pour explorer plusieurs problématiques liées à l’inversion Bayésienne. En particulier, nous proposons un indicateur pour évaluer l’influence du choix du modèle direct sur la qualité de l’inversion. Nous étendons aussi le modèle GLLiM pour prendre un compte une information a-priori, le rendant adapté à la résolution de problèmes d’assimilation de données.

International audience; Urban areas, where more than 55% of the global population gathers, contribute more than 70% of anthropogenic fossil fuel carbon dioxide (CO2ff) emissions. Accurate quantification of CO2ff emissions from urban areas is of great importance for formulating global warming mitigation policies to achieve carbon neutrality by 2050. Satellite-based inversion techniques are unique among “top-down” approaches, potentially allowing us to track CO2ff emission changes over cities globally. However, their accuracy is still limited by incomplete background information, cloud blockages, aerosol contamination, and uncertainties in models and priori emission inventories. To evaluate the current potential of space-based quantification techniques, we present the first attempt to monitor long-term changes in CO2ff emissions based on the OCO-2 satellite measurements of column-averaged dry-air mole fractions of CO2 (XCO2) over a fast-growing Asian metropolitan area: Lahore, Pakistan. We first examined the OCO-2 data availability at global scale. About 17% of OCO-2 soundings over the global 70 most populated cities from 2014 to 2019 are marked as high-quality. Cloud blockage and aerosol contamination are the two main causes of data loss. As an attempt to recover additional soundings, we evaluated the effectiveness of OCO-2 quality flags at the city level by comparing three flux quantification methods (WRF-Chem, X-STILT, and the flux cross-sectional integration method). The satellite/bottom-up emissions (OCO-2/ODIAC) ratios of the high-quality tracks with reduced uncertainties in emissions are better agreed across the three methods compared to the all-data tracks. This demonstrates that OCO-2 quality flags are useful filters of low-quality OCO-2 retrievals at local scales. All three methods consistently suggested that the ratio medians are greater than 1, implying that the ODIAC slightly underestimated CO2ff emissions over Lahore. Additionally, our estimation of the a posteriori CO2ff emission trend was about 734 kt C/year (i.e., an annual 6.7% increase). 10,000 Monte Carlo simulations of the Mann-Kendall upward trend test showed that less than 10% prior uncertainty for 8 tracks (or less than 20% prior uncertainty for 25 tracks) is required to achieve a greater-than-50% trend significant possibility at a 95% confidence level. It implies that the trend is driven by the prior and not due to the assimilation of OCO-2 retrievals. The key to improving the role of satellite data in CO2 emission trend detection lies in collecting more frequent high-quality tracks near metropolitan areas to achieve significant constraints from XCO2 retrievals.

During the seismic cycle, the deformation accumulated by the earth's lithosphere can be released anelastically during earthquakes causing numerous human and material losses. The analysis of the seismic risk requires the study of this deformation during the different stages of the seismic cycle. In particular, the geodetic study of the earth surface displacement allows to understand and to localize the accumulation of the elastic deformation during the interseismic phases. With the expansion of GNSS networks, it has become possible to obtain the strain rate tensor from surface displacement velocities in order to study and constrain crustal deformation. However, computing a continuous deformation gradient surface from discrete GNSS data is an inverse problem with a higly non-unique solution. As a result, many methods with different characteristics have emerged in the last decades, each with its own advantages and disadvantages. However, some limitations of the direct inversion schemes used until now persist and compromise the reliability of the results. In particular, the need to use ad hoc parameters defined by the operator such as a smoothing parameter, the sensitivity to the geometry of the GNSS network and the difficulty to determine in a robust way the uncertainties associated with the results, which are necessary for the integration of deformation maps in seismic risk analysis methods. In order to overcome these shortcomings in existing models, we develop a new transdimensional Bayesian method to invert discrete GNSS data in order to obtain the 2D continuous velocity field, its gradient and the associated deformation tensor. The velocity field is described by a parameterization based on Delaunay triangulation, and the a posteriori distribution is sampled using a reversible jump Metropolis-Hasting algorithm, which belongs to the McMC class. This algorithm has an adaptive mesh that takes into account the spatial, velocity and noise level heterogeneities present in the data. Unlike classical inversion methods that propose a single model, the solution is a complete probability distribution function for each component of the deformation velocity field. Synthetic tests compare the proposed approach to a standard bicubic spline interpolation scheme. This method is shown to be more robust to the presence of outliers in the data as well as to a spatially heterogeneous distribution of the data, while providing uncertainties associated with the recovered velocities and strain rates. It is then applied to the southwestern United States, a heavily studied and monitored region, providing probabilistic strain rates along major fault systems, including the San Andreas Fault, from the GNSS interseismic velocity inversion. The characteristics of several key points in this region are represented by exploiting the a posteriori probability distribution functions of the different inverted parameters. The current limitations as well as the different perspectives of improvement of this method are discussed in the conclusion of this thesis., Au cours du cycle sismique, la déformation accumulée par la lithosphère terrestre peut être relâchée de manière anélastique lors de séismes provoquant de nombreuses pertes humaines et matérielles. L’analyse du risque sismique passe par l’étude de cette déformation lors des différentes étapes du cycle sismique. En particulier, l’étude géodésique du déplacement de la surface terrestre permet de comprendre et de localiser l’accumulation de la déformation élastique lors des phases intersismiques. Avec l’expansion des réseaux GNSS, il est devenu possible d’obtenir le tenseur du taux de déformation à partir des vitesses de déplacement surfacique dans le but d’étudier et de contraindre la déformation crustale. Or, calculer une surface continue de gradient de déformation à partir de données GNSS discrètes consiste en un problème inverse dont la solution est fortement non-unique. De ce fait, de nombreuses méthodes aux caractéristiques diverses ont vu le jour au cours des dernières décennies, chacune comportant ses avantages et ses inconvénients propres. Cependant, certaines limitations des schémas d’inversion direct employés jusqu’alors persistent et compromettent la fiabilité des résultats. En particulier, la nécessité d’employer des paramètres ad hoc définis par l’opérateur tel qu’un paramètre de lissage, la sensibilité à la géométrie du réseau GNSS et la difficulté à déterminer de manière robuste les incertitudes associées aux résultats, pourtant nécessaires à l’intégration des cartes de déformation dans les méthodes d’analyse du risque sismique. Afin de pallier ces lacunes dans les modèles existants, nous développons une nouvelle méthode bayésienne transdimensionnelle permettant d’inverser des données GNSS discrètes afin d’obtenir le champ 2D continu de vitesse, son gradient et le tenseur de déformation associés. Le champ de vitesse est décrit par une paramétrisation reposant sur la triangulation de Delaunay, et la distribution a posteriori est échantillonnée grâce à un algorithme de Metropolis-Hasting à saut réversible, qui appartient à la classe des McMC. Cet algorithme dispose d’un maillage adaptatif qui prend en compte les hétérogénéités spatiale, de vitesse et de niveau de bruit présentes dans les données. Contrairement aux méthodes d’inversion classiques qui proposent un modèle unique, la solution est une fonction de distribution de probabilité complète pour chaque composante du champ de vitesse de déformation. Des tests synthétiques permettent de comparer l’approche proposée à un schéma d'interpolation en spline bicubique standard. Cette méthode s’avère plus résistante à la présence d’outliers dans les données ainsi qu’à une répartition spatialement hétérogène de celles-ci, tout en fournissant des incertitudes associées aux vitesses et aux taux de déformation récupérés. Elle est ensuite appliquée au sud-ouest des États-Unis, une région fortement étudiée et surveillée, ce qui permet d’obtenir les taux de déformation probabilistes le long des principaux systèmes de failles, y compris celui de San Andreas, à partir de l'inversion des vitesses intersismiques GNSS. Les caractéristiques de plusieurs points clefs de cette région sont représentées grâce à l’exploitation des fonctions de distribution de probabilité a posteriori des différents paramètres inversés. Les limitations actuelles ainsi que les différentes perspectives d’amélioration de cette méthode sont discutées en conclusion de cette thèse.

Seismic anisotropy is often used as a proxy for rock deformation. It arises from the preferred orientation of anisotropic minerals. For instance, olivine in mantellic peridotites align according to mantle flow. However, anisotropy in tomographic models can be the result of small scale heterogeneities unresolved by long period seismic waves. It is thus considered as artificial. Theories and methodological developments do not allow to distinguish the relative contributions of real and artificial anisotropy in seismic signals. In this thesis, we used simple models of the Earth’s mantle to analytically and numerically study the link between unresolved heterogeneities and the level of artificial radial anisotropy. We concluded that anisotropy is proportional to the square of heterogeneities and that 10% of velocity contrast can be responsible for 3% of anisotropy, which is non negligible compared to the observed anisotropy in tomography. A 3-D anisotropic model of Europe, focusing on the Alps and Apennines, was constructed from surface waves data. The dispersion measurements were made from noise correlation and allow to image the crust and uppermost mantle. The isotropic structure of the model shows particularly well the Adriatic plate subducting under the Apennines, as well as a slab break-off in the Southern part of the chain. The method used for the depth inversion takes into account the trade-off between layering and anisotropy. Our model is therefore the first 3-D model of radial anisotropy built at shallow depths in Europe. Our results suggest that the lower crust has a horizontal organization in the Apennines, probably related to the extensive regime observed in the area., L’anisotropie est souvent utilisée en sismologie comme proxy de la déformation des roches. Elle se développe lorsque des minéraux acquièrent une orientation préférentielle. C’est le cas de l’olivine des péridotites du manteau qui s’aligne selon la direction des flux de matière. Néanmoins, l’anisotropie observée en tomographie peut aussi provenir d’hétérogénéités chimiques non résolues par les ondes sismiques longues périodes : elle s’apparente alors à̀ de l’anisotropie artificielle. Les théories et développements méthodologiques actuels ne permettent pas de distinguer l’anisotropie réelle de l’anisotropie artificielle dans les signaux sismiques. Dans cette thèse nous avons utilisé des modèles simples de manteau terrestre pour étudier théoriquement et numériquement le lien entre le niveau d’hétérogénéités non résolues et l’anisotropie radiale artificielle. Nous en avons conclu que l’anisotropie est proportionnelle au carré des hétérogénéités et que 10% de contraste de vitesse sismique peut engendrer plus de 3% d’anisotropie, un niveau non négligeable au regard des observations tomographiques. Une tomographie 3-D anisotrope de l’Europe, centrée sur les Alpes et les Apennins, a également enté réalisée. Les données d’ondes de surface utilisées sont issues de corrélations de bruit sismique et permettent d’imager la croûte et le manteau supérieur. La structure isotrope de notre modelé illumine particulièrement bien la plaque adriatique en subduction sous les Apennins ainsi qu’une rupture de ce panneau située au sud de la chaîne. Par ailleurs, la méthode d’inversion en profondeur utilisée prend en compte le biais entre anisotropie et hétérogénéités. Nous présentons ainsi le premier modelé 3-D d’anisotropie radiale en Europe réalisé pour des profondeurs aussi faibles. Nos résultats suggèrent que la croûte inférieure est marquée par une structuration horizontale dans les Apennins, probablement en lien avec la déformation extensive actuelle observée dans la région.

SUMMARY Using a fully nonlinear Bayesian approach based on forward modelling of granular flow, we invert for landslide parameters (volume, release geometry and rheology) from different kinds of observations. Synthetic tests show that the runout distance and the deposit area by themselves do not constrain landslide parameters. Better constraints on landslide parameters are obtained from the thickness distribution of the landslide deposits, as well as from the force history applied by the landslide to the ground, which contains information on the landslide dynamics. Therefore, inverting force histories calculated from seismic broad-band records is an important alternative to inverting thickness distributions of landslide deposits, which are usually difficult to obtain. We test the method on the 1997 Boxing Day debris avalanche on Montserrat Island, which involved 40 − 50 Mm3. The Bayesian inversion and granular flow model provide good estimates for volume, release geometry and effective friction coefficient. This study thus underlines the value of broad-band seismic records as observations to monitor landslides and validation for their numerical flow models.

Jupiter's icy moons are of great interest in the search for habitability in our Solar System. They probably all harbor liquid water ocean underneath their icy crust. Their surfaces present different stages of evolution – Callisto is heavily cratered and the oldest, Ganymede shows a combination of dark cratered terrain and younger bright plains and Europa’s surface is the youngest with signs of recent and maybe current activity. This work focuses on photometry, i.e. the study of the light scattered by a surface in relation to the illumination and observation geometry. Photometric studies give us insight on the physical state and microtexture of the surface (compaction, internal structure, shape, roughness, transparency…). A good photometric knowledge is also of crucial importance in the correction of datasets for any mapping or spectroscopic study as well as for the future missions of this decade – NASA’s Europa Clipper and ESA’s JUpiter ICy moons Explorer.Two pieces of information are necessary to conduct a photometric study – reflectance data and geometric information (illumination, viewing conditions). For the former, we have used and calibrated images from past space missions – Voyager, New Horizons and Galileo. For the latter, we have developed tools to correct these images metadata (e.g. spacecraft position and orientation) to derive precise geometric information. Moreover, we have developed a Bayesian inversion tool to estimate Hapke’s photometric parameters on regions of Europa, Ganymede and Callisto. We estimate all parameters on our entire dataset at once. Finally, we discuss the possible links between the photometric parameters, the surface microtexture and endogenic/exogenic processes.; Les satellites glacés de Jupiter sont d'un grand intérêt scientifique dans la recherche d'habitabilité au sein de notre système solaire. Elles abritent probablement toutes trois des océans d'eau liquide sous leur croûte glacée. Leurs surfaces présentent différents stades d’évolution – celle de Callisto est très ancienne et entièrement recouverte de cratères, celle de Ganymede est un mélange de terrains sombres et cratérisés et de plaines claires et plus jeunes et la surface d’Europa est la plus jeune et présente des signes d’activité récente. Cette thèse porte sur la photométrie, c’est à dire l’étude de l’énergie lumineuse réfléchie par une surface, en fonction des géométries d’éclairement et d’observation. Les études photométriques permettent de déterminer l’état physique et la microtexture des surfaces (porosité, structure interne, forme des grains, rugosité, transparence…). Une bonne connaissance photométrique est également d'une importance cruciale dans la correction des jeux de données pour toute étude cartographique ou spectroscopique ainsi que pour les futures missions de cette décennie : Europa Clipper de la NASA et JUpiter ICy Moons Explorer de l’ESA.Deux types d’information sont nécessaires pour réaliser une étude photométrique : des données de réflectance et des données géométriques (conditions d’illumination et d'observation). Pour obtenir les premières, nous avons utilisé et calibré des images de missions spatiales passées - Voyager, New Horizons et Galileo. Pour obtenir les secondes, nous avons développé des outils permettant de corriger les métadonnées de ces images (ex : la position et l'orientation des sondes) afin d’obtenir des informations géométriques précises. Nous avons, d’autre part, développé un outil d’inversion pour estimer les paramètres photométriques de Hapke sur des régions d’Europa, Ganymede et Callisto sur l’ensemble du jeu de données en un seul calcul. Enfin, nous discutons des liens possibles entre les paramètres photométriques estimés, la microtexture de la surface et les processus endogènes/exogènes mis en jeu.

The surface of Europa is geologically young and shows signs of current activity. Studying it from a photometric point of view gives us insight on its physical state. We used a collection of 57 images from Voyager's Imaging Science System and New Horizons' LOng Range Reconnaissance Imager for which we corrected the geometric metadata and projected every pixel to compute photometric information (reflectance and geometry of observation). We studied 20 areas scattered across the surface of Europa and estimated their photometric behavior using the Hapke radiative transfer model and a Bayesian framework in order to estimate their microphysical state. We have found that most of them were consistent with the bright backscattering behavior of Europa, already observed at a global scale, indicating the presence of grains maturated by space weathering. However, we have identified very bright areas showing a narrow forward scattering possibly indicating the presence of fresh deposits that could be attributed to recent cryovolcanism or jets. Overall, we showed that the photometry of Europa's surface is more diverse than previously thought and so is its microphysical state., Comment: 46 pages, 17 figures, 3 tables

International audience; We propose a probabilistic methodology for data-driven updating of non-Gaussian high-dimensional symmetric positive-definite matrices involved in computational models. We cast the data-driven updating as a Bayesian identification of the symmetric positive-definite matrices. The posterior thus obtained exhibits several hyperparameters that control the dispersion of the prior and the weight of the weighted distance that represents the model-data misfit in the likelihood function. Using an identification criterion that quantifies the agreement between the predictions and the data, we identify these hyperparameters so as to obtain not only improved predictions but also a probabilistic representation of model uncertainties. The numerical implementation of the Bayesian inversion by using a Markov chain Monte Carlo (MCMC) method is computationally challenging because the support of the posterior is restricted to a set of symmetric positive-definite matrices and the dimensionality of the problem grows with the square of the matrix dimension and hence can be high. We thus use a transformation of measure to set up the Markov chain in terms of real-valued state variables whose distribution is Gaussian under the prior but non-Gaussian under the posterior. This transformation of measure allows us to sample the posterior using an Itô-SDE-based MCMC method that inherits computational efficiency in high dimension from leveraging the gradient of the posterior. We apply this methodology to a problem of a data-driven updating of a reduced-order model in computational structural dynamics.

This paper introduces a categorical framework to study the exact and approximate semantics of probabilistic programs. We construct a dagger symmetric monoidal category of Borel kernels where the dagger-structure is given by Bayesian inversion. We show functorial bridges between this category and categories of Banach lattices which formalize the move from kernel-based semantics to predicate transformer (backward) or state transformer (forward) semantics. These bridges are related by natural transformations, and we show in particular that the Radon-Nikodym and Riesz representation theorems - two pillars of probability theory - define natural transformations. With the mathematical infrastructure in place, we present a generic and endogenous approach to approximating kernels on standard Borel spaces which exploits the involutive structure of our category of kernels. The approximation can be formulated in several equivalent ways by using the functorial bridges and natural transformations described above. Finally, we show that for sensible discretization schemes, every Borel kernel can be approximated by kernels on finite spaces, and that these approximations converge for a natural choice of topology. We illustrate the theory by showing two examples of how approximation can effectively be used in practice: Bayesian inference and the Kleene star operation of ProbNetKAT., Comment: 17 pages, 4 figures

Dam breach models are commonly used to predict outflow hydrographs of potentially failing dams and are key ingredients for evaluating flood risk. In this paper a new dam breach modeling framework is introduced that shall improve the reliability of hydrograph predictions of homogeneous earthen embankment dams. Striving for a small number of parameters, the simplified physics‐based model describes the processes of failing embankment dams by breach enlargement, driven by progressive surface erosion. Therein the erosion rate of dam material is modeled by empirical sediment transport formulations. Embedding the model into a Bayesian multilevel framework allows for quantitative analysis of different categories of uncertainties. To this end, data available in literature of observed peak discharge and final breach width of historical dam failures were used to perform model inversion by applying Markov chain Monte Carlo simulation. Prior knowledge is mainly based on noninformative distribution functions. The resulting posterior distribution shows that the main source of uncertainty is a correlated subset of parameters, consisting of the residual error term and the epistemic term quantifying the breach erosion rate. The prediction intervals of peak discharge and final breach width are congruent with values known from literature. To finally predict the outflow hydrograph for real case applications, an alternative residual model was formulated that assumes perfect data and a perfect model. The fully probabilistic fashion of hydrograph prediction has the potential to improve the adequate risk management of downstream flooding. ISSN:0043-1397 ISSN:1944-7973

International audience; Inversion of controlled-source electromagnetic data is dealt with for a geophysical application. The goal is to retrieve a map of conductivity of an unknown body embedded in a layered underground from measurements of the scattered electric field that results from its interaction with a known interrogating wave. This constitutes an inverse scattering problem whose associated forward problem is described by means of electric field domain integral equations. The inverse problem is solved in a Bayesian framework in which prior information is introduced via a Gauss-Markov-Potts model. This model describes the body as being composed of a finite number of different materials distributed into compact homogeneous regions. The posterior distribution of the unknowns is approached by means of the variational Bayesian approximation as a separable distribution that minimizes the Kullback-Leibler divergence with respect to the posterior law. Thus, we get a parametric model for the distributions of the induced currents, the conductivity contrast, and the various parameters of the prior model that are obtained following a semisupervised iterative approach. This method is applied to multifrequency synthetic data corresponding to a 3D crosswell configuration in which the sought body is made of two separated anomalies, a conductive heterogeneity and a resistive one, and its results are compared with that given by the classic contrast source inversion (CSI). The method succeeds in retrieving compact homogeneous regions that correspond to the two anomalies whose shape and conductivities are obtained with a good precision compared with that obtained with CSI.Read More: https://library.seg.org/doi/10.1190/geo2016-0682.1

International audience; A new analytical solution is developed for interference hydraulic pumping tests in fractal fractured porous media using the dual-porosity concept. Heterogeneous fractured reservoirs are considered with hydrodynamic parameters assumed to follow power-law functions in radial distance. The developed analytical solution is verified by comparison against a finite volume numerical solution. The comparison shows that the numerical solution converges toward the analytical one when the size of the time step decreases. The applicability of the fractal dual-porosity model is then assessed by investigating the identifiability of the parameters from a synthetic interference pumping test with a set of noisy data using Bayesian parameter inference. The results show that if the storage coefficient in the matrix is fixed, the rest of the parameters can be appropriately inferred; otherwise, the identification of the parameters is faced with convergence problems because of equifinality issues.

International audience; The resonance associated with the Free Core Nutation (FCN) has been widely studied in Very Long Base Interferometry (VLBI) network measurements and in superconducting gravity records, but few experiments have been done with tiltmeters. In this study we use records collected with a pair of about 100 m long hydrostatic silica tiltmeters, orthogonally installed in an abandoned silver mine at Sainte Croix aux Mines (Alsace, in North-Eastern France). Main difficulties in retrieving FCN parameters from tidal analysis arise from the weak amplitude of PSI1 tidal wave (the closest in frequency to the FCN), as well as from the inaccuracy of the available ocean loading correction. Moreover because of the closeness in frequency of the single constituents of the diurnal tidal band, long (>1 year) records are needed for resolving K1, PSI1 and PHI1 waves. Hence we analyze a 10-year dataset of tilt records, hich has preliminarily required a critical review and a relevant editing for making records suitable for tidal analysis and subsequent inversion of the tidal parameters. A Bayesian inversion is used for a preliminary retrieval of the FCN parameters.

We estimate crustal and uppermost mantle shear velocity structure beneath 30 stations in North America by jointly inverting the high frequency scattered wavefield observed in the P wave coda, together with long period surface wave phase and group dispersion data. Several features distinguish our approach from previous such joint inversions. 1) We apply a cross-convolution method, rather than more standard deconvolution approaches used in receiver function studies, and consider both Love and Rayleigh wave dispersion, allowing us to infer profiles of radial anisotropy. 2) We generate probabilistic 1D radially anisotropic depth profiles across the whole uppermost mantle, down to similar to 350 km depth. 3) The inverse problem is cast in a trans-dimensional Bayesian formalism, where the number of isotropic and anisotropic layers is treated as unknown, allowing us to obtain models described with the least number of parameters. Results show that the tectonically active region west of the Rocky Mountain Front is marked by a Lithospheric Asthenosphere Boundary and a Lehmann Discontinuity occurring at relatively shallow depths (60-150 km and 100-200 km, respectively), whereas further east, in the stable craton, these discontinuities are deeper (170-200 km and 200-250 km, respectively). In addition, in the stable part of the continent, at least two Mid-Lithospheric Discontinuities are present at intermediate depths, suggesting the existence of strong lithospheric layering, and a mechanism for lithospheric thickening by underplating of additional layers as cratonic age increases. The Moho across the continent as well as mid-crustal discontinuities in the craton are also imaged, in agreement with independent studies. (C) 2016 Elsevier B.V. All rights reserved.

International audience; The geological record of SE Canada spans more than 2.5Ga, making it a natural laboratory for the study of crustal formation and evolution over time. We estimate the crustal thickness, Poisson's ratio, a proxy for bulk crustal composition, and shear velocity (V-s) structure from receiver functions at a network of seismograph stations recently deployed across the Archean Superior Craton, the Proterozoic Grenville, and the Phanerozoic Appalachian provinces. The bulk seismic crustal properties and shear velocity structure reveal a correlation with tectonic provinces of different ages: the post-Archean crust becomes thicker, faster, more heterogeneous, and more compositionally evolved. This secular variation pattern is consistent with a growing consensus that crustal growth efficiency increased at the end of the Archean. A lack of correlation among elevation, Moho topography, and gravity anomalies within the Proterozoic belt is better explained by buoyant mantle support rather than by compositional variations driven by lower crustal metamorphic reactions. A ubiquitous approximate to 20km thick high-V-s lower crustal layer is imaged beneath the Proterozoic belt. The strong discontinuity at 20km may represent the signature of extensional collapse of an orogenic plateau, accommodated by lateral crustal flow. Wide anorthosite massifs inferred to fractionate from a mafic mantle source are abundant in Proterozoic geology and are underlain by high-V-s lower crust and a gradational Moho. Mafic underplating may have provided a source for these intrusions and could have been an important post-Archean process stimulating mafic crustal growth in a vertical sense.

An acoustic wave propagating in the underwater environment carries information about the source (range, depth,...) and about the physical properties of the oceanic environment (water depth, sound speed in the water column and the bottom,...). Such information can be obtained by solving an inverse problem. This inverse problem is conventionally addressed through the minimization of an error function between the measured pressure field and the pressure field obtained from a propagation model (matched-field processing methods). The result of the inversion is inherently uncertain: on the one hand the measurements are affected by noise and on the other hand the propagation model is imperfectly known because of the complexity of the marine environment. The first part of the present study deals with performance analysis of these estimation methods. The estimation of the parameters of interest is a nonlinear problem which suffers from significant ambiguities beyond a certain noise level and errors in the assumed propagation medium are a considerable difficulty of these methods that should not be neglected in performance analysis. Statistical tools for predicting the performance of these inverse problems are developed. The Ziv-Zakai bound and the method of interval error are considered. These tools are then used to analyze the performance of a particular source localization problem. The second part of our work aims to increase source localization's robustness against modeling errors of the oceanic environment. A Bayesian source localization method that handles uncertainty in the oceanic environment is developed. The Green's function is considered as a random vector that accounts for environmental uncertainty through its probability density. A physical a priori on modal propagation enhances performance when the environment is poorly known. In addition, the Bayesian formalism provides a quantitative measure of the confidence that can be given to each estimate of the source position, which is a very valuable information in an operational context.; Une onde acoustique se propageant au sein du milieu sous-marin est porteuse d'informations sur la source (distance, profondeur,...) et sur les propriétés physiques de l'environnement océanique (profondeur d'eau, célérités dans l'eau et dans le fond,...). Ces informations peuvent être obtenues par la résolution d'un problème inverse. Ce problème est classiquement abordé comme un problème d'optimisation visant à minimiser une fonction d'erreur entre le champ de pression observé et celui issu d'un modèle de propagation (méthodes dites de matched-field processing). Le résultat de l'inversion est fondamentalement incertain car d'une part les mesures sont affectées de bruit et d'autre part le modèle de propagation est imparfaitement connu du fait de la complexité du milieu marin. Le premier axe de notre étude concerne l'analyse des performances de ces méthodes d'estimation. L'estimation des paramètres d'intérêt est un problème non-linéaire qui souffre d'ambiguïtés importantes au-delà d'un certain niveau de bruit et la méconnaissance du milieu de propagation est une difficulté considérable de ces méthodes qui ne doit pas être négligée dans l'analyse des performances. Des outils statistiques adaptés à la prédiction des performances de ces problèmes inverses sont mis au point. La borne minimale d'estimation de Ziv-Zakai et la méthode des erreurs d'intervalle sont considérées. Ces outils sont ensuite utilisés pour analyser les performances d'un problème particulier de localisation de source. Le second axe abordé au cours de la thèse vise à perfectionner les méthodes de localisation de source pour accroitre leur robustesse vis-à-vis des erreurs de modélisation de l'environnement océanique. Une méthode bayésienne de localisation de source adaptée aux milieux de propagation sous-marins incertains est développée. La fonction de Green est modélisée comme vecteur aléatoire dont la densité de probabilité représente l'incertitude sur l'environnement. L'introduction d'un a priori physique sur la propagation modale améliore les performances quand l'environnement de propagation est mal connu. En outre, le formalisme bayésien fournit une mesure quantitative de la confiance pouvant être accordée à chaque estimation de la position de la source, information très précieuse en contexte opérationnel.

An acoustic wave propagating in the underwater environment carries information about the source (range, depth,...) and about the physical properties of the oceanic environment (water depth, sound speed in the water column and the bottom,...). Such information can be obtained by solving an inverse problem. This inverse problem is conventionally addressed through the minimization of an error function between the measured pressure field and the pressure field obtained from a propagation model (matched-field processing methods). The result of the inversion is inherently uncertain: on the one hand the measurements are affected by noise and on the other hand the propagation model is imperfectly known because of the complexity of the marine environment. The first part of the present study deals with performance analysis of these estimation methods. The estimation of the parameters of interest is a nonlinear problem which suffers from significant ambiguities beyond a certain noise level and errors in the assumed propagation medium are a considerable difficulty of these methods that should not be neglected in performance analysis. Statistical tools for predicting the performance of these inverse problems are developed. The Ziv-Zakai bound and the method of interval error are considered. These tools are then used to analyze the performance of a particular source localization problem. The second part of our work aims to increase source localization's robustness against modeling errors of the oceanic environment. A Bayesian source localization method that handles uncertainty in the oceanic environment is developed. The Green's function is considered as a random vector that accounts for environmental uncertainty through its probability density. A physical a priori on modal propagation enhances performance when the environment is poorly known. In addition, the Bayesian formalism provides a quantitative measure of the confidence that can be given to each estimate of the source position, which is a very valuable information in an operational context., Une onde acoustique se propageant au sein du milieu sous-marin est porteuse d'informations sur la source (distance, profondeur,...) et sur les propriétés physiques de l'environnement océanique (profondeur d'eau, célérités dans l'eau et dans le fond,...). Ces informations peuvent être obtenues par la résolution d'un problème inverse. Ce problème est classiquement abordé comme un problème d'optimisation visant à minimiser une fonction d'erreur entre le champ de pression observé et celui issu d'un modèle de propagation (méthodes dites de matched-field processing). Le résultat de l'inversion est fondamentalement incertain car d'une part les mesures sont affectées de bruit et d'autre part le modèle de propagation est imparfaitement connu du fait de la complexité du milieu marin. Le premier axe de notre étude concerne l'analyse des performances de ces méthodes d'estimation. L'estimation des paramètres d'intérêt est un problème non-linéaire qui souffre d'ambiguïtés importantes au-delà d'un certain niveau de bruit et la méconnaissance du milieu de propagation est une difficulté considérable de ces méthodes qui ne doit pas être négligée dans l'analyse des performances. Des outils statistiques adaptés à la prédiction des performances de ces problèmes inverses sont mis au point. La borne minimale d'estimation de Ziv-Zakai et la méthode des erreurs d'intervalle sont considérées. Ces outils sont ensuite utilisés pour analyser les performances d'un problème particulier de localisation de source. Le second axe abordé au cours de la thèse vise à perfectionner les méthodes de localisation de source pour accroitre leur robustesse vis-à-vis des erreurs de modélisation de l'environnement océanique. Une méthode bayésienne de localisation de source adaptée aux milieux de propagation sous-marins incertains est développée. La fonction de Green est modélisée comme vecteur aléatoire dont la densité de probabilité représente l'incertitude sur l'environnement. L'introduction d'un a priori physique sur la propagation modale améliore les performances quand l'environnement de propagation est mal connu. En outre, le formalisme bayésien fournit une mesure quantitative de la confiance pouvant être accordée à chaque estimation de la position de la source, information très précieuse en contexte opérationnel.

International audience; The subduction zone in northern Chile is a well-identified seismic gap that last ruptured in 1877. On April 1, 2014, this region was struck by a large earthquake following a two-week-long series of foreshocks. This study combines a wide range of observations, including geodetic, tsunami and seismic data, to produce a reliable kinematic slip model of the Mw = 8.1 mainshock and a static slip model of the Mw= 7.7 aftershock. We use a novel Bayesian modeling approach that accounts for uncertainty in the Green's functions, both static and dynamic, while avoiding non-physical regularization. The results reveal a sharp slip zone, more compact than previously thought, located downdip of the foreshock sequence and up-dip of high-frequency sources inferred by back-projection analysis. Both the mainshock and the Mw = 7.7 aftershock did not rupture to the trench and left most of the seismic gap unbroken, leaving the possibility of a future large earthquake in the region.

In this manuscript-based thesis we propose statistical methods to analyse geophysical time-series. We particularly focus on ocean colour and sea surface temperature observed from space. The specific characteristics of the geophysical signal, i.e. noise autocorrelation, discontinuities in the observations, and the mixing of physical and biological processes showing distinct modes of variability, is integrated in the proposed methodologies. The first chapter includes details on the physical measurement principles of the variables of interest. Then we describe a methodology to estimate linear trends and associated uncertainties, using several time series, to optimise in-situ and satellite-based observation networks for the long term monitoring. We characterise after the significant time-scales of "El Niño Southern Oscillation" in the sea surface temperature using a normalised Gaussian mixture model to take into account the natural distribution of the scales of the events observed in the nature. The fourth chapter details the forecasting of a non-stationary process subject to seasonal forcing conditions, the sea surface turbidity, using four hidden Markov models. The hidden variables are used to estimate different relationships between the variable to estimate and its predictors. The last chapters details a Bayesian model, with dynamical updates of the a priori models, to inverse the sea surface reflectance in complex coastal areas for the OLCI sensor embedded onto the Sentinel 3 satellite. The perspectives are enhancements of satellite products provided by spatial agencies, operational forecasting using statistical models based on observations and learning, and the optimisation of observation networks.; Dans cette thèse sur articles nous proposons des méthodes statistiques pour l¿analyse de séries temporelles géophysiques. Nous nous intéressons à la couleur de l¿eau et la température de surface de la mer observées depuis l¿espace. La nature du signal géophysique, i.e. l¿autocorrélation du bruit, la discontinuité des observations, et le mélange des processus physiques et biologiques pouvant comporter des modes distincts de variabilité, est partie intégrante des méthodes d¿analyses proposées. Le premier chapitre contient des informations sur la mesure physique des variables d¿intérêt. Nous décrivons ensuite une méthode d¿estimation de tendances linéaires et des incertitudes associées, à partir de plusieurs séries temporelles, dans le but d¿optimiser les réseaux d¿observations satellitaires et in-situ pour la surveillance à long terme de l¿environnement. Puis nous caractérisons les échelles temporelles du signal climatique "El Niño Southern Oscillation" dans la température de surface à partir d¿un mélange de Gaussiennes prenant en compte un facteur de normalisation pour corriger de la distribution naturelle des évènements. Le quatrième chapitre décrit la prévision temporelle d¿un processus non-stationnaire soumis à des forçages saisonniers, la turbidité de surface, en utilisant quatre différents modèles de Markov cachés. Les variables cachées sont utilisées pour identifier des relations distinctes entre la variable à estimer et ses prédicteurs. Le dernier chapitre décrit un modèle Bayésien avec mise à jour dynamique des modèles a priori pour l¿inversion de la réflectance marine en milieux côtiers complexes pour le capteur OLCI embarqué sur le satellite Sentinel 3. Les perspectives sont l¿amélioration des produits satellitaires fournis par les agences spatiales, la prévision opérationnelle avec des modèles statistiques basés sur des observations et de l¿apprentissage, et l¿optimisation des réseaux de surveillance.

Imaging spectrometer, Imaging spectro-photometer and high resolution spectrometer constitute the last generation of space instruments that strongly modified the study of planetary bodies. Such instruments allow us to follow the soil and atmospheric optical properties through space and time. The first objective of this Habilitation thesis is to propose some tools to analyze a huge amount of data in planetological perspectives. Three types of methods are introduced to examine the hyperspectral data acquired by OMEGA (Mars Express/ESA) and CRISM (Mars Reconnaissance Orbiter/NASA) instruments : (i) WAVANGLET, a fast detection algorithm based on wavelets to identify the presence of chemical species at the ground, (ii) BPSS, a blind source separation method that is able to detect chemical species without a priori, (iii) supervised unmixing algorithm using LinMin strategy. Also atmospheric correction methods, coupled to Bayesian inversion of photometric model, allow us to deal with the full CRISM photometric dataset. Finally, a method of micro-vibrations correction has been proposed in order to improve the quality of the PFS instrument (Mars Express/ESA) using semi-blind deconvolution.The Martian annual cycle of CO2 consists of an exchange between surface and atmosphere, which is particularly relevant in polar regions. During the polar night, atmospherical CO2 condensates at the ground, whereas it starts to sublimate again during the spring, when the solar light bring energy to the surface. This major climatic cycle has been identified in the 1960th but even today, the microphysic of interaction between surface and atmosphere is still unknown. Recent images at high spatial resolution (50 cm) from HiRISE (Mars Reconnaissance Orbiter/NASA) instrument show many active processes associated to sublimation. The second objective of this thesis is to build a model of the seasonal deposits sublimation, by simulating the mass balance but also by geomorphological and spectroscopic studies. Results show that the seasonal south polar cap sublimation is mainly controlled by its albedo. Further studies must determine the exact mechanisms in the origin of this albedo variability.The third objective of this thesis is to discuss the possibility of clathrate hydrate in the climatic history of Mars. A scenario, implying formation of clathrate hydrate of S and CO2 is examined in comparison with geomorphological clues of the Martian surface., L’étude de Mars a été profondément modifiée par les dernières générations d’instruments spatiaux : les spectro-imageurs, les spectro-imageurs-photomètres et les spectroscopes à haute résolution spectrale. Ils permettent un suivi spatial et temporel des propriétés optiques des sols et de l’atmosphère. Le premier objectif de cette thèse d’Habilitation à Diriger des Recherches est méthodologique et consiste à proposer des outils permettant de traiter la grande quantité de données afin d’aborder des probléma- tiques planétologiques. Plusieurs types d’outils d’analyse des images hyperspectrales, notamment celles produites par les instruments OMEGA (Mars Express/ESA) et CRISM (Mars Reconnaissance Orbiter/NASA), ont été proposés : (i) WAVANGLET, une méthode rapide de détection des corps chimiques au sol basée sur la transformée en ondelette, (ii) BPSS, une méthode de séparation de source en aveugle qui détecte des corps chimiques sans a priori, (iii) des méthodes de dé-mélanges linéaires supervisées rapides utilisant la stratégie LinMin. Aussi des outils de correction atmosphérique couplés à des mé- thodes d’inversion bayésienne de modèle photométrique de surface ont été développés pour l’instrument CRISM. Enfin, une méthode de correction des effets de vibrations par déconvolution semi-aveugle a été développée pour PFS (Mars Express/ESA).Les régions polaires de Mars sont le siège d’un cycle climatique annuel d’échange de CO2 entre atmosphère et surface. Pendant la nuit polaire, le CO2 atmosphérique se condense au sol, tandis qu’il se sublime à nouveau, dès les premiers rayons du soleil. Ce cycle a été mis à jour depuis les années 1960 mais aujourd’hui encore, la microphysique d’interaction surface/atmosphère demeure inconnue. Des observations d’imagerie à haute résolution spatiale (50 cm) par HiRISE (Mars Reconnaissance Orbiter/NASA) ont montré une multitude de phénomènes actifs associés à la sublimation. Le second objectif de cette thèse est d’établir un modèle de sublimation des dépôts saisonniers, à la fois par simulation du bilan de masse mais aussi par étude géomorphologique et spectroscopique. Les résultats montrent que la sublimation de la calotte saisonnière sud de Mars est contrôlée majoritairement par son albédo mais des travaux plus détaillés seront nécessaires pour déterminer les mécanismes à l’origine des variations d’albedo.Le troisième objectif de cette thèse est de discuter les implications de la présence de clathrate hydrate en surface dans l’histoire climatique de Mars. Un scénario impliquant la formation de clathrate hydrate mixte de soufre et CO2 est proposé au regard des traces géomorphologiques du paysage martien.

Imaging spectrometer, Imaging spectro-photometer and high resolution spectrometer constitute the last generation of space instruments that strongly modified the study of planetary bodies. Such instruments allow us to follow the soil and atmospheric optical properties through space and time. The first objective of this Habilitation thesis is to propose some tools to analyze a huge amount of data in planetological perspectives. Three types of methods are introduced to examine the hyperspectral data acquired by OMEGA (Mars Express/ESA) and CRISM (Mars Reconnaissance Orbiter/NASA) instruments : (i) WAVANGLET, a fast detection algorithm based on wavelets to identify the presence of chemical species at the ground, (ii) BPSS, a blind source separation method that is able to detect chemical species without a priori, (iii) supervised unmixing algorithm using LinMin strategy. Also atmospheric correction methods, coupled to Bayesian inversion of photometric model, allow us to deal with the full CRISM photometric dataset. Finally, a method of micro-vibrations correction has been proposed in order to improve the quality of the PFS instrument (Mars Express/ESA) using semi-blind deconvolution.The Martian annual cycle of CO2 consists of an exchange between surface and atmosphere, which is particularly relevant in polar regions. During the polar night, atmospherical CO2 condensates at the ground, whereas it starts to sublimate again during the spring, when the solar light bring energy to the surface. This major climatic cycle has been identified in the 1960th but even today, the microphysic of interaction between surface and atmosphere is still unknown. Recent images at high spatial resolution (50 cm) from HiRISE (Mars Reconnaissance Orbiter/NASA) instrument show many active processes associated to sublimation. The second objective of this thesis is to build a model of the seasonal deposits sublimation, by simulating the mass balance but also by geomorphological and spectroscopic studies. Results show that the seasonal south polar cap sublimation is mainly controlled by its albedo. Further studies must determine the exact mechanisms in the origin of this albedo variability.The third objective of this thesis is to discuss the possibility of clathrate hydrate in the climatic history of Mars. A scenario, implying formation of clathrate hydrate of S and CO2 is examined in comparison with geomorphological clues of the Martian surface.; L’étude de Mars a été profondément modifiée par les dernières générations d’instruments spatiaux : les spectro-imageurs, les spectro-imageurs-photomètres et les spectroscopes à haute résolution spectrale. Ils permettent un suivi spatial et temporel des propriétés optiques des sols et de l’atmosphère. Le premier objectif de cette thèse d’Habilitation à Diriger des Recherches est méthodologique et consiste à proposer des outils permettant de traiter la grande quantité de données afin d’aborder des probléma- tiques planétologiques. Plusieurs types d’outils d’analyse des images hyperspectrales, notamment celles produites par les instruments OMEGA (Mars Express/ESA) et CRISM (Mars Reconnaissance Orbiter/NASA), ont été proposés : (i) WAVANGLET, une méthode rapide de détection des corps chimiques au sol basée sur la transformée en ondelette, (ii) BPSS, une méthode de séparation de source en aveugle qui détecte des corps chimiques sans a priori, (iii) des méthodes de dé-mélanges linéaires supervisées rapides utilisant la stratégie LinMin. Aussi des outils de correction atmosphérique couplés à des mé- thodes d’inversion bayésienne de modèle photométrique de surface ont été développés pour l’instrument CRISM. Enfin, une méthode de correction des effets de vibrations par déconvolution semi-aveugle a été développée pour PFS (Mars Express/ESA).Les régions polaires de Mars sont le siège d’un cycle climatique annuel d’échange de CO2 entre atmosphère et surface. Pendant la nuit polaire, le CO2 atmosphérique se condense au sol, tandis qu’il se sublime à nouveau, dès les premiers rayons du soleil. Ce cycle a été mis à jour depuis les années 1960 mais aujourd’hui encore, la microphysique d’interaction surface/atmosphère demeure inconnue. Des observations d’imagerie à haute résolution spatiale (50 cm) par HiRISE (Mars Reconnaissance Orbiter/NASA) ont montré une multitude de phénomènes actifs associés à la sublimation. Le second objectif de cette thèse est d’établir un modèle de sublimation des dépôts saisonniers, à la fois par simulation du bilan de masse mais aussi par étude géomorphologique et spectroscopique. Les résultats montrent que la sublimation de la calotte saisonnière sud de Mars est contrôlée majoritairement par son albédo mais des travaux plus détaillés seront nécessaires pour déterminer les mécanismes à l’origine des variations d’albedo.Le troisième objectif de cette thèse est de discuter les implications de la présence de clathrate hydrate en surface dans l’histoire climatique de Mars. Un scénario impliquant la formation de clathrate hydrate mixte de soufre et CO2 est proposé au regard des traces géomorphologiques du paysage martien.

In this manuscript-based thesis we propose statistical methods to analyse geophysical time-series. We particularly focus on ocean colour and sea surface temperature observed from space. The specific characteristics of the geophysical signal, i.e. noise autocorrelation, discontinuities in the observations, and the mixing of physical and biological processes showing distinct modes of variability, is integrated in the proposed methodologies. The first chapter includes details on the physical measurement principles of the variables of interest. Then we describe a methodology to estimate linear trends and associated uncertainties, using several time series, to optimise in-situ and satellite-based observation networks for the long term monitoring. We characterise after the significant time-scales of "El Niño Southern Oscillation" in the sea surface temperature using a normalised Gaussian mixture model to take into account the natural distribution of the scales of the events observed in the nature. The fourth chapter details the forecasting of a non-stationary process subject to seasonal forcing conditions, the sea surface turbidity, using four hidden Markov models. The hidden variables are used to estimate different relationships between the variable to estimate and its predictors. The last chapters details a Bayesian model, with dynamical updates of the a priori models, to inverse the sea surface reflectance in complex coastal areas for the OLCI sensor embedded onto the Sentinel 3 satellite. The perspectives are enhancements of satellite products provided by spatial agencies, operational forecasting using statistical models based on observations and learning, and the optimisation of observation networks., Dans cette thèse sur articles nous proposons des méthodes statistiques pour l¿analyse de séries temporelles géophysiques. Nous nous intéressons à la couleur de l¿eau et la température de surface de la mer observées depuis l¿espace. La nature du signal géophysique, i.e. l¿autocorrélation du bruit, la discontinuité des observations, et le mélange des processus physiques et biologiques pouvant comporter des modes distincts de variabilité, est partie intégrante des méthodes d¿analyses proposées. Le premier chapitre contient des informations sur la mesure physique des variables d¿intérêt. Nous décrivons ensuite une méthode d¿estimation de tendances linéaires et des incertitudes associées, à partir de plusieurs séries temporelles, dans le but d¿optimiser les réseaux d¿observations satellitaires et in-situ pour la surveillance à long terme de l¿environnement. Puis nous caractérisons les échelles temporelles du signal climatique "El Niño Southern Oscillation" dans la température de surface à partir d¿un mélange de Gaussiennes prenant en compte un facteur de normalisation pour corriger de la distribution naturelle des évènements. Le quatrième chapitre décrit la prévision temporelle d¿un processus non-stationnaire soumis à des forçages saisonniers, la turbidité de surface, en utilisant quatre différents modèles de Markov cachés. Les variables cachées sont utilisées pour identifier des relations distinctes entre la variable à estimer et ses prédicteurs. Le dernier chapitre décrit un modèle Bayésien avec mise à jour dynamique des modèles a priori pour l¿inversion de la réflectance marine en milieux côtiers complexes pour le capteur OLCI embarqué sur le satellite Sentinel 3. Les perspectives sont l¿amélioration des produits satellitaires fournis par les agences spatiales, la prévision opérationnelle avec des modèles statistiques basés sur des observations et de l¿apprentissage, et l¿optimisation des réseaux de surveillance.

Whether in natural sciences, in economics, or in the industry, a number of modelling problems involve functions that are expensive to evaluate. This includes, for instance, flow simulations used in hydrogeology, where time-consuming solvers are used to compute a misfit between observed and theoretical tracer concentrations. In such a case, the solver can be seen as a ``black box'' deterministic function returning the misfit as a function of parameter fields describing the subsurface physics and geology. Given observations, a typical hydrogeological problem would be to ``invert'' that function, i.e. to uncover parameter fields that lead to an outcome close to the observations. This includes also Monte Carlo simulations, used in a broad class of applications ranging from finance to neutronics through climate, where expectations are approximated by averages over a large number of particles. Such simulations may be used, e.g., to determine the best design in engineering, the most profitable product under legal constraints in insurance, or the worst case scenario on a power plant subject to climatic hazards. All three examples boil down to solving an optimization problem, be it a constrained or unconstrained, deterministic or noisy, minimization or maximization problem. What is drastically varying is the nature of the objective function. The contributions presented here essentially focus on stochastic methods for approximating, optimizing, and more generally for studying multivariate functions under very limited evaluation budget. In mathematical terms, we typically consider a function $f: D\subset \mathbb{R}^{d}\rightarrow \mathbb{R}$ and try to approximate it over $D$, locate its points of optima and/or determine regions where $f$ takes a prescribed range of values, relying on a finite number of evaluation results $\{(\x_{i}, f(\x_i)), 1\leq i \leq n\}$. Obviously, further hypotheses on $f$ are needed in order to say something meaningful on its values outside of $\{\x_{1}, \dots, \x_{n}\}$. Now, approximating functions based on a finite number of point-wise evaluations is a problem that has been intensively studied throughout mathematics, and a plethora of interpolation and approximation techniques exists to reconstruct $f$ from available information.A particularity of the approaches considered here is that, even though there is nothing intrinsically random about the objective function, probabilistic and statistical concepts are used to model it. More precisely, $f$ is typically seen as one realization of a Gaussian random field (GRF), a mathematical object coming from spatial statistics. While appealing to such approach may seem unnatural at first, it has recently become commonplace in several application domains such as those cited above. In fact, approximation methods and sequential strategies based on Gaussian random field models proved efficient for a variety of problems and goals, including global optimization and probability of failure estimation. The work presented in this habilitation thesis deals with three questions related to GRF models and their use in sequential strategies for optimizing and inverting deterministic functions under limited evaluation budget. The first question, discussed in Chapter $1$, concerns the incorporation of prior information on $f$ through the type of Gaussian random field model considered. Centred Gaussian random fields being characterized by their covariance, several kinds of so-called ``structural'' priors that can be imposed through the kernel are studied. It is shown that various properties including (but not restricted to) symmetries and additivity may be embedded within GRF modelling and that, when applicable, such prescribed features may partly compensate for the scarcity of observations. Chapter $2$ focuses on sequential evaluation strategies dedicated to global optimization, and to further goals such as probability of excursion and excursion set estimation. A state-of-the-art criterion, the \textit{Expected Improvement}, is studied in finite time settings, and adapted to a noisy optimization problem with tunable noise variance. The latter enables in particular reducing computation time when optimizing a function $f$ whose evaluations are done through Monte Carlo simulations. Finally, strategies for learning regions of the parameter space where $f$ exceeds a given threshold are studied and a criterion for quantifying the uncertainty about such regions is introduced. Lastly, Chapter $3$ contains a discussion on various aspects of interdisciplinary research projects, and on applications and implementations of the methods presented in the two previous chapters. In particular, some results obtained on a stochastic hydrogeology test case are commented, and open source software implementations (R packages) including part of the methods presented so far are presented. Each chapter is complemented by several publications (four for Chapter $1$, four for Chapter $2$, and two for Chapter $3$), and the Appendix contains a few additional proofs as well as a CV, a publication list, and a teaching statement of the author.

International audience; The detection of rainfall remains a challenge for the monitoring of precipitation from space. A methodology is presented to identify rain events from spaceborne passive microwave data using neural networks. We focus on BRAIN, the algorithm that provides instantaneous quantitative precipitation estimates at the surface, based on the MADRAS radiometer onboard the Megha-Tropiques satellite. A version of BRAIN using data from the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) has been used to compare several multilayer perceptrons (MLP) trained on different combinations of TMI brightness temperatures with the conventional GSCAT-2 algorithm approach used for rainfall detection. These classifiers were compared at a global scale to reference values from the TRMM Precipitation Radar (PR). They were also compared to ground measurements using two 1° × 1° dense rain-gauge networks from different climatic zones in West Africa to assess the influence of rainfall types. At the global scale the MLPs provide better Probability of Detection than the GSCAT-2 decision tree but tend to have a higher False Alarm Rate. While no unique solution exists given the strong regional dependence of the classifiers' performances, the screen based on the 19, 21 and 85 GHz channels provides the best detection results at the instantaneous scales. As to accumulated rainfall, the screen that exhibits the lower bias relative to the PR makes use of the 37 and 85 GHz channels. The evaluation over West Africa using 10 years of TRMM overpasses shows that MLPs are in better agreement with both the PR and the gauges than GSCAT-2. The MLP trained on the 37 and 85 GHz channels increases the Probability of Detection by nearly 35% compared to the former screening over the two studied regions. Better results are obtained in the case of organized systems.

International audience; We use the Bayesian method to invert a simple two-layer pedological horizon (1-D with a topsoil and a subsoil) of a surveyed site to be assessed. We show how the Bayesian method is well suited to the determination of topsoil/subsoil features, and can be used in particular as a tool for the analysis of parameters to be retrieved in terms of information content. Our approach is devoted mainly to the assessment of topsoil thickness, and of topsoil and subsoil conductivities, which are provided in terms of probability density functions. We first summarize the methodology implemented with the Geonics EM38-MK2 conductivity meter, and discuss the adaptation of field procedures and post-processing methods to mitigate the effects of drift and bias. We briefly review some non-Bayesian approaches, and then develop the Bayesian approach for the context of our geophysical survey, highlighting its merits. Positivity constraints (on thickness and conductivity) are included in the form of log parameters. A priori knowledge, based on an objective choice made by the geophysicist, is naturally included in the Bayesian scheme. We discuss the equivalence problem associated with the application of the Slingram method to soil structure analysis. The survey of a luvisol at the Kwazulu-Natal (South Africa) site of Potshini is used to illustrate an ecological application of the Slingram and Bayesian methods, used to define the geo-electrical structure of the near-surface soil. These algorithms have demonstrated their usefulness in mapping the clay content of the Bt horizon associated with the control of encroaching trees. (C) 2013 Elsevier B.V. All rights reserved.

International audience; —Structured illumination microscopy is a recent imaging technique that aims at going beyond the classical optical resolution by reconstructing high-resolution (HR) images from low-resolution (LR) images acquired through modulation of the transfer function of the microscope. The classical implementation has a number of drawbacks, such as requiring a large number of images to be acquired and parameters to be manually set in an ad-hoc manner that have, until now, hampered its wide dissemination. Here, we present a new framework based on a Bayesian inverse problem formulation approach that enables the computation of one HR image from a reduced number of LR images and has no specific constraints on the modulation. Moreover, it permits to automatically estimate the optimal reconstruction hyperparameters and to compute an uncertainty bound on the estimated values. We demonstrate through numerical evaluations on simulated data and examples on real microscopy data that our approach represents a decisive advance for a wider use of HR microscopy through structured illumination.

Co-encadrement de la thèse : Laurent Praly; In a context of permanent concern of energy saving, the importance of developing strategies to minimize the energy consumption of a building is not to be any more demonstrated. Whether these strategies consist in recommending building insulation, suggesting the modification of the management of heating/air conditioning systems or advising the change of certain occupants' habits, a preliminary step of characterizing the thermal behavior of the building turns out inevitable.Contrary to the previous studies, the approach developed here does not require instrumentation of the building. Also, we consider buildings in normal occupation, that is in the presence of heating regulator, which is an additional unknown of the problem. So, we identify a global system of the building together with its heating system from: meteorological data of the closest Meteo France station; reference indoor temperature reconstructed by sector-based knowledge; heating consumption collected either from Building Management Systems or from smart meters; other heat supply (like lighting or presence of persons) estimated by sector-based and thermal knowledge. The identification is made at first by estimation of the parameters (7) defining the global model, by minimizing one step prediction error. Then we adopted an approach of bayesian inversion which provides a simulation of the posterior distributions of parameters and building indoor temperature.The analysis of the stochastic simulations aims at studying the contribution of additional knowledge of the problem (typical values of the parameters) and at showing the limits of the modeling hypotheses in the case of certain real data sets.; Dans un contexte de préoccupation accrue d'économie d'énergie, l'intérêt que présente le développement de stratégies visant à minimiser la consommation d'un bâtiment n'est plus à démontrer. Que ces stratégies consistent à recommander l'isolation des parois, à améliorer la gestion du chauffage ou à préconiser certains comportements de l'usager, une démarche préalable d'identification du comportement thermique de bâtiment s'avère inévitable.Contrairement aux études existantes, la démarche menée ici ne nécessite pas d'instrumentation du bâtiment. De même, nous considérons des bâtiments en occupation normale, en présence de régulateur de chauffage : inconnue supplémentaire du problème. Ainsi, nous identifions un système global du bâtiment muni de son régulateur à partir de :données de la station Météo France la plus proche ; la température de consigne reconstruite par connaissance sectorielle ; la consommation de chauffage obtenue par système de Gestion Technique du Bâtiment ou par compteur intelligent ; autres apports calorifiques (éclairage, présence de personnes...) estimés par connaissance sectorielle et thermique. L'identification est d'abord faite par estimation des paramètres (7) définissant le modèle global, en minimisant l'erreur de prédiction à un pas. Ensuite nous avons adopté une démarche d'inversion bayésienne, dont le résultat est une simulation des distributions a posteriori des paramètres et de la température intérieure du bâtiment.L'analyse des simulations stochastiques obtenues vise à étudier l'apport de connaissances supplémentaires du problème (valeurs typiques des paramètres) et à démontrer les limites des hypothèses de modélisation dans certains cas.

Co-encadrement de la thèse : Laurent Praly; In a context of permanent concern of energy saving, the importance of developing strategies to minimize the energy consumption of a building is not to be any more demonstrated. Whether these strategies consist in recommending building insulation, suggesting the modification of the management of heating/air conditioning systems or advising the change of certain occupants' habits, a preliminary step of characterizing the thermal behavior of the building turns out inevitable.Contrary to the previous studies, the approach developed here does not require instrumentation of the building. Also, we consider buildings in normal occupation, that is in the presence of heating regulator, which is an additional unknown of the problem. So, we identify a global system of the building together with its heating system from: meteorological data of the closest Meteo France station; reference indoor temperature reconstructed by sector-based knowledge; heating consumption collected either from Building Management Systems or from smart meters; other heat supply (like lighting or presence of persons) estimated by sector-based and thermal knowledge. The identification is made at first by estimation of the parameters (7) defining the global model, by minimizing one step prediction error. Then we adopted an approach of bayesian inversion which provides a simulation of the posterior distributions of parameters and building indoor temperature.The analysis of the stochastic simulations aims at studying the contribution of additional knowledge of the problem (typical values of the parameters) and at showing the limits of the modeling hypotheses in the case of certain real data sets.; Dans un contexte de préoccupation accrue d'économie d'énergie, l'intérêt que présente le développement de stratégies visant à minimiser la consommation d'un bâtiment n'est plus à démontrer. Que ces stratégies consistent à recommander l'isolation des parois, à améliorer la gestion du chauffage ou à préconiser certains comportements de l'usager, une démarche préalable d'identification du comportement thermique de bâtiment s'avère inévitable.Contrairement aux études existantes, la démarche menée ici ne nécessite pas d'instrumentation du bâtiment. De même, nous considérons des bâtiments en occupation normale, en présence de régulateur de chauffage : inconnue supplémentaire du problème. Ainsi, nous identifions un système global du bâtiment muni de son régulateur à partir de :données de la station Météo France la plus proche ; la température de consigne reconstruite par connaissance sectorielle ; la consommation de chauffage obtenue par système de Gestion Technique du Bâtiment ou par compteur intelligent ; autres apports calorifiques (éclairage, présence de personnes...) estimés par connaissance sectorielle et thermique. L'identification est d'abord faite par estimation des paramètres (7) définissant le modèle global, en minimisant l'erreur de prédiction à un pas. Ensuite nous avons adopté une démarche d'inversion bayésienne, dont le résultat est une simulation des distributions a posteriori des paramètres et de la température intérieure du bâtiment.L'analyse des simulations stochastiques obtenues vise à étudier l'apport de connaissances supplémentaires du problème (valeurs typiques des paramètres) et à démontrer les limites des hypothèses de modélisation dans certains cas.

nb de pages: 4; International audience; In this paper, we combine inverse problem and classification for LC-MS data in a joint Bayesian context, given a set of biomarkers and the statistical characteristics of the biological classes. The data acquisition is modelled in a hierarchical way, including random decomposition of proteins into peptides and peptides into ions associated to peaks on the LC-MS measurement. A Bayesian global inversion, based on the hierarchical model for the direct problem, enables to take into account the biological and technological variabilities from those random processes and to estimate the parameters efficiently. We describe the statistical theoretical framework including the hierarchical direct model, the prior and posterior distributions and the estimators for the involved parameters. We resort to the MCMC algorithm and give preliminary results on a simulated data set.

International audience; Markov chains Monte-Carlo (MCMC) methods are known to produce samples of virtually any distribution. They have already been widely used in the resolution of non-linear inverse problems where no analytical expression for the forward relation between data and model parameters is available, and where linearization is unsuccessful. However, in Bayesian inversion, the total number of simulations we can afford is highly related to the computational cost of the forward model. Hence, the complete browsing of the support of the posterior distribution is hardly performed at final time, especially when the posterior is high dimensional and/or multimodal. In the latter case, the chain may stay stuck in one of the modes. Recently, the idea of making interact several Markov chains at different temperatures has been explored. These methods improve the mixing properties of classical single MCMC. Furthermore, these methods can make efficient use of large CPU clusters, without increasing the global computational cost with respect to classical MCMC.

The work involves data processing for super-resolution imaging with an application in astronomy. We are particularly interested in data from the SPIRE instrument of the spatial observatory Herschel of ESA, dedicated to far-infrared. The problems are mainly: the convolution of the spatial optical response, the sub-sampling and the presence of a thermal drift. The proposed approach is the inversion of data, ie taking into account the acquisition process as well as prior information to estimate the sky of interest. The first part of the work concerns the modelisation of the data acquisition process. The model consists of the mirror and feed-horns, the wavelength filter, the temperature sensitive sensor based on bolometers and scanning protocol. The obtained model, linear but not invariant due to sampling, is studied. Interesting properties, including perspective on data processing, are obtained especially in connection with the super-resolution capacity. The analysis also show useful properties for efficient algorithm. The second part of the work relies on a inference framework based on the usual Bayesian formalism. Since information is degraded, the inverse problem is ill-conditioned. The used method offers parameter estimation laws governing the balance between different information sources (hyper-parameters), in addition to the formalization of spatial regularity. Moreover, the proposed approach allows instrument parameters estimation and estimation of a slow thermal drift affecting all the sensor in conjunction with all the other parameters. All the information used to solve the problem is formalized through a posterior law. The estimator is chosen as the posterior mean calculated by means of an MCMC algorithm. An experimental study demonstrates the capacity of the approach to restore high spatial frequencies. The study also shows the potential of the approach for estimating hyper-parameters and instrument parameters.; Les travaux concernent le traitement de données pour l'imagerie sur-résolue avec une application en astronomie. On s'intéresse en particulier aux données issues de l'instrument SPIRE de l'observatoire spatial Herschel de l'ESA, dédié aux infrarouges lointains. Les problèmes soulevés sont principalement : la réponse de l'optique qui atténue les fréquences spatiales, le sous-échantillonnage ainsi que la présence d'une dérive thermique. L'approche proposée est l'inversion de données, c'est à dire la prise en compte du processus d'acquisition en plus d'information a priori, pour estimer le ciel d'intérêt. La première partie des travaux concerne la modélisation du processus d'acquisition des données. Le modèle est composé d'une optique, de filtres en longueur d'onde, du capteur sensible à la température à base de bolomètres ainsi que du protocole de pointage. Le modèle obtenu, linéaire mais non invariant à cause de l'échantillonnage, est étudié. Des propriétés intéressantes, notamment dans une perspective de traitement de données, sont dégagées en particulier en lien avec la sur-résolution. L'analyse du modèle permet également de faire ressortir des propriétés utiles pour un algorithmique de calcul. La deuxième partie des travaux repose sur une démarche d'inférence inscrite dans le formalisme bayésien usuel. Toute l'information ne passant pas à travers l'instrument ou étant dégradée, le problème inverse est mal-conditionné. La méthode employée, en plus de formaliser une information de régularité spatiale sur le ciel permettant de lever le problème de conditionnement, propose l'estimation des paramètres des lois réglant le compromis entre les différentes sources d'information (hyper-paramètres). De plus, l'approche proposée permet l'estimation de paramètres instruments ainsi que l'estimation d'une dérive thermique lente affectant l'ensemble du capteur conjointement aux autres paramètres. L'ensemble de l'information utilisée pour résoudre le problème est formalisé au travers d'une loi a posteriori jointe pour l'ensemble des inconnues. L'estimateur choisi est la moyenne a posteriori calculée par un algorithme MCMC. Une étude expérimentale démontre la capacité de la méthode à restaurer de hautes fréquences spatiales. L'étude montre également le potentiel de l'approche pour l'estimation des hyper-paramètres et des paramètres instruments.

The work involves data processing for super-resolution imaging with an application in astronomy. We are particularly interested in data from the SPIRE instrument of the spatial observatory Herschel of ESA, dedicated to far-infrared. The problems are mainly: the convolution of the spatial optical response, the sub-sampling and the presence of a thermal drift. The proposed approach is the inversion of data, ie taking into account the acquisition process as well as prior information to estimate the sky of interest. The first part of the work concerns the modelisation of the data acquisition process. The model consists of the mirror and feed-horns, the wavelength filter, the temperature sensitive sensor based on bolometers and scanning protocol. The obtained model, linear but not invariant due to sampling, is studied. Interesting properties, including perspective on data processing, are obtained especially in connection with the super-resolution capacity. The analysis also show useful properties for efficient algorithm. The second part of the work relies on a inference framework based on the usual Bayesian formalism. Since information is degraded, the inverse problem is ill-conditioned. The used method offers parameter estimation laws governing the balance between different information sources (hyper-parameters), in addition to the formalization of spatial regularity. Moreover, the proposed approach allows instrument parameters estimation and estimation of a slow thermal drift affecting all the sensor in conjunction with all the other parameters. All the information used to solve the problem is formalized through a posterior law. The estimator is chosen as the posterior mean calculated by means of an MCMC algorithm. An experimental study demonstrates the capacity of the approach to restore high spatial frequencies. The study also shows the potential of the approach for estimating hyper-parameters and instrument parameters., Les travaux concernent le traitement de données pour l'imagerie sur-résolue avec une application en astronomie. On s'intéresse en particulier aux données issues de l'instrument SPIRE de l'observatoire spatial Herschel de l'ESA, dédié aux infrarouges lointains. Les problèmes soulevés sont principalement : la réponse de l'optique qui atténue les fréquences spatiales, le sous-échantillonnage ainsi que la présence d'une dérive thermique. L'approche proposée est l'inversion de données, c'est à dire la prise en compte du processus d'acquisition en plus d'information a priori, pour estimer le ciel d'intérêt. La première partie des travaux concerne la modélisation du processus d'acquisition des données. Le modèle est composé d'une optique, de filtres en longueur d'onde, du capteur sensible à la température à base de bolomètres ainsi que du protocole de pointage. Le modèle obtenu, linéaire mais non invariant à cause de l'échantillonnage, est étudié. Des propriétés intéressantes, notamment dans une perspective de traitement de données, sont dégagées en particulier en lien avec la sur-résolution. L'analyse du modèle permet également de faire ressortir des propriétés utiles pour un algorithmique de calcul. La deuxième partie des travaux repose sur une démarche d'inférence inscrite dans le formalisme bayésien usuel. Toute l'information ne passant pas à travers l'instrument ou étant dégradée, le problème inverse est mal-conditionné. La méthode employée, en plus de formaliser une information de régularité spatiale sur le ciel permettant de lever le problème de conditionnement, propose l'estimation des paramètres des lois réglant le compromis entre les différentes sources d'information (hyper-paramètres). De plus, l'approche proposée permet l'estimation de paramètres instruments ainsi que l'estimation d'une dérive thermique lente affectant l'ensemble du capteur conjointement aux autres paramètres. L'ensemble de l'information utilisée pour résoudre le problème est formalisé au travers d'une loi a posteriori jointe pour l'ensemble des inconnues. L'estimateur choisi est la moyenne a posteriori calculée par un algorithme MCMC. Une étude expérimentale démontre la capacité de la méthode à restaurer de hautes fréquences spatiales. L'étude montre également le potentiel de l'approche pour l'estimation des hyper-paramètres et des paramètres instruments.

We propose an inverse method to recover the roughness parameters (altitude range Delta h(0), and Hurst exponent H) of self-affine surfaces from the energy spectrum of backscattered waves. A stochastic forward modelling of the spectrum of the backscattered wavefield averaged along a profile of finite length is proposed in the near-nadir and far-field configuration. A Bayesian formulation of the inverse problem is used to account for the random nature of both the data and the forward problem. An acoustic backscattering experiment is performed with a natural rough self-affine surface for which Delta h(0) and H are determined through direct measurements of the topography. The inversion of the experimental spectrum of the backscattered acoustic waves shows that a good determination of H is possible, while Delta h(0) is an unresolved parameter. Modifier Supprimer Envoyer par email Ajouter au panier Imprimer Données de gestion