Este trabalho trata da simulação da propagação de ondas eletromagnéticas (1-D) em meios geológicos de propriedades físicas conhecidas (espessura, condutividade e permissividade elétrica), do registro das ondas EM refletidas (dados sintéticos) para uma antena receptora, e do uso desse registro em algoritmos de inversão e otimização que procuram estimar as propriedades físicas dos meios geológicos. Adotou-se modelos geológicos estratificados de pequena espessura (< 1,2 m) e altas frequências para a onda eletromagnética (800, 1000 e 1200 MHz). A propagação da onda eletromagnética é modelada por meio da resolução das equações de Maxwell no método FDTD. Os métodos de inversão Quasi-Newton e Otimização Ant Colony modificado são aplicados sobre os dados sintéticos para estimar os parâmetros elétricos para cada camada geológica. Ambos os métodos foram aplicados alternadamente para aumentar a precisão e a convergência ao longo da profundidade. Os métodos de inversão foram capazes de estimar simultaneamente duas propriedades eletromagnéticas do modelo geológico: a permissividade elétrica e a condutividade elétrica. Os métodos de inversão alcançaram bons resultados quando executados simultaneamente sobre os dados sintéticos em 3 diferentes frequências. Exemplos de estimativas dos perfis de condutividade e permissividade elétricas unidimensionais são apresentados, com e sem inserção de ruídos nos dados. Os resultados indicam que a combinação dos métodos de inversão (ACO modificado e Quasi-Newton) pode fornecer bons resultados para as estimativas dos parâmetros físicos de meios geológicos e geotécnicos em meios rasos. Além disso, essa combinação de métodos de inversão abre novas perspectivas para o processamento de dados georradar multi-canais. As investigações também mostram que a simulação dos perfis sintéticos por meio do método FDTD pode propagar erros em espessuras maiores de subsolo, devido ao fato de ser um método explícito. / This work deals with simulation of a 1-D electromagnetic wave propagating into a geological structure of known physical properties (thickness, electric conductivity and permittivity), the record of the reflected EM wave (synthetic data), and the use of these records in inversion and optimization algorithms to estimate back the physical properties of the geological structure. A stratified and thin (< 1.2 m) geological structure was initially constructed in order to be scanned by high frequency EM waves (800, 1000, and 1200 MHz). The EM wave propagation is simulated by Maxwell equations through FDTD method. The Quasi-Newton inversion and Ant Colony Optimization methods were applied into synthetic data to estimate original physical parameters of each geological layer. Both methods were applied in order to increase precision and convergence along depth. These methods were able to simultaneously estimate two physical properties of the geological structure: electrical permittivity and conductivity. The methods showed good results when applied simultaneously upon synthetic data of all three frequencies. Electric permittivity and conductivity profiles are shown with and without noise in the data. The results indicate that combined inversion methods can show good results to estimate physical properties of thin geological and geothecnical structures. The combined inversion methods open new perspectives to multichannel GPR data processing. The investigations also show that simulation of synthetic data through FDTD can propagate errors when dealing with thick geological structures, due to the fact that FDTD is an explicit method.

Si les avancées majeures en imagerie ultrasonore ont longtemps été liées à la qualité de l'instrumentation, l'avènement de l'informatique a incontestablement changé la donne en introduisant des possibilités croissantes de traitement des données pour obtenir une meilleure image. Par ailleurs, les GPUs, composants principaux des cartes graphiques, offrent de par leur architecture des vitesses de calcul bien supérieures aux processeurs, y compris à des fins de calcul scientifique. Le but de cette thèse a été de tirer parti de ce nouvel outil de calcul, en ciblant deux applications complémentaires. La première est d'autoriser une imagerie en temps réel de meilleure qualité que les autres techniques d'imagerie échographique, en parallélisant le procédé d'imagerie FTIM (Fast Topological IMaging). La seconde est d'introduire l'imagerie quantitative et en particulier la reconstruction de la carte de vitesse du milieu inconnu, en utilisant l'inversion de la forme d'onde complète. / If the most important progresses in ultrasound imaging have been closely linked to the instrumentation's quality, the advent of computing science revolutionized this discipline by introducing growing possibilities in data processing to obtain a better picture. In addition, GPUs, which are the main components of the graphics cards deliver thanks to their architecture a significantly higher processing speed compared with processors, and also for scientific calculation purpose. The goal of this work is to take the best benefit of this new computing tool, by aiming two complementary applications. The first one is to enable real-time imaging with a better quality than other sonographic imaging techniques, thanks to the parallelization of the FTIM (Fast Tpological IMaging) imaging process. The second one is to introduce quantitative imaging and more particularly reconstructing the wavespeed map of an unknown medium, using Full Waveform Inversion.

Este trabalho trata da simulação da propagação de ondas eletromagnéticas (1-D) em meios geológicos de propriedades físicas conhecidas (espessura, condutividade e permissividade elétrica), do registro das ondas EM refletidas (dados sintéticos) para uma antena receptora, e do uso desse registro em algoritmos de inversão e otimização que procuram estimar as propriedades físicas dos meios geológicos. Adotou-se modelos geológicos estratificados de pequena espessura (< 1,2 m) e altas frequências para a onda eletromagnética (800, 1000 e 1200 MHz). A propagação da onda eletromagnética é modelada por meio da resolução das equações de Maxwell no método FDTD. Os métodos de inversão Quasi-Newton e Otimização Ant Colony modificado são aplicados sobre os dados sintéticos para estimar os parâmetros elétricos para cada camada geológica. Ambos os métodos foram aplicados alternadamente para aumentar a precisão e a convergência ao longo da profundidade. Os métodos de inversão foram capazes de estimar simultaneamente duas propriedades eletromagnéticas do modelo geológico: a permissividade elétrica e a condutividade elétrica. Os métodos de inversão alcançaram bons resultados quando executados simultaneamente sobre os dados sintéticos em 3 diferentes frequências. Exemplos de estimativas dos perfis de condutividade e permissividade elétricas unidimensionais são apresentados, com e sem inserção de ruídos nos dados. Os resultados indicam que a combinação dos métodos de inversão (ACO modificado e Quasi-Newton) pode fornecer bons resultados para as estimativas dos parâmetros físicos de meios geológicos e geotécnicos em meios rasos. Além disso, essa combinação de métodos de inversão abre novas perspectivas para o processamento de dados georradar multi-canais. As investigações também mostram que a simulação dos perfis sintéticos por meio do método FDTD pode propagar erros em espessuras maiores de subsolo, devido ao fato de ser um método explícito. / This work deals with simulation of a 1-D electromagnetic wave propagating into a geological structure of known physical properties (thickness, electric conductivity and permittivity), the record of the reflected EM wave (synthetic data), and the use of these records in inversion and optimization algorithms to estimate back the physical properties of the geological structure. A stratified and thin (< 1.2 m) geological structure was initially constructed in order to be scanned by high frequency EM waves (800, 1000, and 1200 MHz). The EM wave propagation is simulated by Maxwell equations through FDTD method. The Quasi-Newton inversion and Ant Colony Optimization methods were applied into synthetic data to estimate original physical parameters of each geological layer. Both methods were applied in order to increase precision and convergence along depth. These methods were able to simultaneously estimate two physical properties of the geological structure: electrical permittivity and conductivity. The methods showed good results when applied simultaneously upon synthetic data of all three frequencies. Electric permittivity and conductivity profiles are shown with and without noise in the data. The results indicate that combined inversion methods can show good results to estimate physical properties of thin geological and geothecnical structures. The combined inversion methods open new perspectives to multichannel GPR data processing. The investigations also show that simulation of synthetic data through FDTD can propagate errors when dealing with thick geological structures, due to the fact that FDTD is an explicit method.

Cette thèse de doctorat vise l’examen critique de certaines théories de champ moyen nucléaire phénoménologiques, en se focalisant sur la description fiable des niveaux de particules individuelles. L’approche suivie ici est nouvelle en ce sens que elle permet non seulement la prédiction des valeurs numériques obtenues avec ce formalisme, mais également une estimation des distributions de probabilités correspondant aux résultats expérimentaux. Nous introduisons le concept des ≪erreurs théoriques≫, visant estimer, dans un cadre mathématique bien établi, les incertitudes relatives aux modélisations théoriques. Il est également introduit une notion subjective de pouvoir prédictif des Hamiltoniens nucléaires, qui est analysé dans le contexte des spectres énergétiques de particules individuelles. Le concept mathématique du ≪Problème Inverse≫ est appliqué aux Hamiltoniens de champ moyen réalistes. Cette technique permet la prédiction de propriétés du système partir d’un nombre limité de données. Afin d'approfondir notre connaissance des Problèmes Inverses, nous focalisons notre attention sur un problème mathématique simple. Une fonction dépendant de quatre paramètres libres est introduite afin de reproduire des données ≪expérimentales≫. Nous étudions le comportement des paramètres ≪fittés≫, leur corrélation, ainsi que les erreurs associées. Cette étude nous aide comprendre la signification de la formulation correcte du problème en question. Il nous montre également l'importance d'inclure les erreurs expérimentales et théoriques dans la solution. / This thesis is a critical examination of phenomenological nuclear mean field theories, focusing on reliable description of levels of individual particles. The approach presented here is new in the sense that it not only allows to predict the numerical values obtained with this formalism, but also yields an estimate of the probability distributions corresponding to the experimental results. We introduce the concept of ‘theoretical errors’ to estimate uncertainties in theoreticalmodels. We also introduce a subjective notion of ‘Predictive Power’ of nuclear Hamiltonians, which is analyzed in the context of the energy spectra of individual particles. The mathematical concept of ‘Inverse Problem’ is applied to a realistic mean-field Hamiltonian. This technique allows to predict the properties of a system from a limited number of data. To deepen our understanding of Inverse Problems, we focus on a simple mathematical problem. A function dependent on four free parameters is introduced in order to reproduce ‘experimental’ data. We study the behavior of the ‘fitted’ parameters, their correlation and the associated errors. This study helps us understand the importance of the correct formulation of the problem. It also shows the importance of including theoretical and experimental errors in the solution.

Cette thèse porte sur la synthèse des sources électromagnétiques (EM) rayonnantes, par la méthode TLM (Transmission Line Matrix) inverse. Les applications large-bande sont particulièrement visées. L'objectif est d'utiliser la théorie du retournement temporel des ondes EM, afin d'implémenter et développer une nouvelle méthode de synthèse des sources rayonnantes, à partir d'un diagramme de rayonnement connu. La retro-propagation des ondes est réalisée numériquement, par la méthode TLM inverse, en trois dimensions (3D), à nœuds symétriques condensés (SCN). L'algorithme proposé est utilisé pour retrouver des sources EM primaires, ponctuelles et réparties, émettant des signaux à large-bande [26GHz - 34GHz] et placées dans l'espace libre (sans pertes, homogène et non-dispersif). Les bases, le potentiel et les limites de cette approche inverse sont étudiés. Une étape supplémentaire est ajoutée afin d'améliorer la résolution spatiale de la reconstruction des sources ponctuelles et réparties. Une résolution inferieure à la demi-longueur d'onde de l'excitation est ainsi obtenue. La reconstruction des sources secondaires 1D et 2D, induites sur les surface métalliques des antennes est ensuite étudiée. Ces études ont abouti au développement d'un nouvel outil de simulation, basé sur une méthode hybride TLM-analytique. La synthèse des sources induites sur la surface d'une antenne-monopôle est ainsi réalisée, à partir du CL mesuré. L'orientation et la position des sources sont trouvées. Les avantages et les limitations de la technique sont enfin discutés. / This thesis deals with wide-band electromagnetic (EM) source synthesis, by Reversed-TLM (Transmission Line Matrix) method. The work is particularly focused on wide-band applications. The main objective is to use the time reversal wave theory in order to develop a new simulation tool, which can synthesize an unknown source distribution from a far-field radiation pattern. Wave time-reversal is numerically simulated by 3D Reversed-TLM method, in based on symmetrical condensed nodes (SCN). Our method is first applied to lumped sources, transmitting wide band signals in the frequency range [26GHz - 34 GHz], placed in a lossless, homogeneous and non-dispersive 3D free-space. Source reconstruction results show that by using this method, the “classical” half-wavelength resolution limit is overcome. The synthesis of 1D and 2D secondary sources, induced on metallic antenna surfaces are also studied. These studies resulted in the development of a new simulation tool, based on a hybrid TLM-analytical method. Reversed - TLM method is then applied for synthesizing a monopole antenna from its measured far-field radiation pattern. Initial source orientation and localization are found. Advantages and limitations of this technique are discussed.

On se propose dans un premier temps d'étudier des jeux de données topographiques sur la lune glacée de Jupiter Ganymède et d'estimer l'impact de la topographie sur les performances du futur radar sondeur. Les principaux résultats sont présentés dans [1]. Une seconde partie est dédiée à l'expression mathématique du problème direct du sondage radar planétaire (physique et instrumentation). On rappelle ainsi comment dériver à partir des formulations de Stratton-Chu les formulations volumiques classiques et surfaciques (i.e. Huygens-Fresnel). On s'attache ensuite à détailler un algorithme performant basé sur la formulation surfacique pour simuler des échos radar à partir d'une surface planétaire maillée. Cette approche est largement inspirée par le travail de J.-F. Nouvel [2]. Une troisième partie s'intéresse à l'inversion des paramètres géophysiques de surface à partir des mesures radar. On écrit ainsi le problème dans un cadre probabiliste (c.f. [3]) et on présente trois grandes familles d'algorithmes : (i) une approche avec une linéarisation du problème, (ii) une approche itérative basée sur une méthode de gradient et (iii) une approche statistique pour estimer les densités de probabilités a posteriori. Ces algorithmes sont appliqués à des jeux de données synthétiques pour illustrer leurs performances. [1] Y. Berquin, W. Kofman, A. Herique, G. Alberti, and P. Beck. A study on ganymede's surface topography: Perspectives for radar sounding. Planetary and Space Science, (0), 2012. [2] J.-F. Nouvel, A. Herique, W. Kofman, and A. Safaeinili. Radar signal simulation: Surface modeling with the Facet Method. Radio Science, 39:RS1013, February 2004. [3] A. Tarantola. Inverse problem theory and methods for model parameter estimation. SIAM, 2005. / The manuscript details the work performed in the course of my PhD on planetary sounding radar. The main goal of the study is to help designing and assessing the sounding radar performances. This instrument will be embarked on the ac{ESA}'s large class mission ac{JUICE} to probe Jupiter's environment and Jupiter's icy moons Callisto, Ganymede and Europa. As an introduction to the problem, a study on Ganymede's surface ac{DEM} and its implications with regard to the radar performances was performed. The results of this work put forward issues due to a hostile environment with important surface clutter which eventually lead to a decrease in the radar signal bandwidth to 8--10 MHz. A first section is then dedicated to the formulation of the direct problem of sounding radar with a focus on surface formulations. This section eventually leads to a novel algorithm for radar surface echo computation from meshed surfaces which proves to be both efficient and accurate. A second section studies the possibility to use surface formulation to recover geophysical surface parameters from sounding radar data. For that purpose, three main approaches are discussed namely (i) a linear approach, (ii) a gradient-based approach and (iii) a statistical approach. These techniques rely on a probabilistic view of the inverse problem at hand and yield good result with different setups. Although we mainly focus on surface reflectivity, we also discuss surface topography inversion. Finally, a last section discusses the work presented in the manuscript and provides perspectives for future work.

La caractérisation non-destructive de la variabilité spatiale et temporelle de la teneur en eau pour des milieux hétérogènes superficiels est un enjeu de taille pour la compréhension du fonctionnement hydrogéologique de certaines zones critiques.Pour répondre à ces besoins, une candidate potentielle est la méthode de Résonance Magnétique des Protons (RMP), technique géophysique récente qui permet d'imager la teneur en eau de la subsurface de façon directe. Ses déclinaisons opérationnelles en 2-D et en 3-D sont émergentes et nécessitent une étude exhaustive afin d'en comprendre les possibilités et les limitations.Le caractère intégrateur de la mesure RMP, en conjonction avec l'erreur expérimentale qui la contamine, limite la résolution de la méthode. Conséquence : la traduction d'un jeu de mesures sous la forme d'une distribution spatiale de teneur en eau n'est pas unique. Certaines sont plus désirables que d'autres, aussi des aprioris géométriques sont-ils utilisés pour limiter l'espace des solutions possibles. De ce fait, l'estimation qui est faite de la teneur en eau est biaisée (aprioris) et entachée d'incertitudes (bruit), jamais quantifiées à ce jour à plus d'une dimension.Afin de mettre à jour les processus qui vont influencer la résolution spatiale et l'estimation du volume d'eau, les propriétés du problème direct de l'imagerie RMP sont analysées au moyen d'outils non-biaisés telles que les corrélations.Le problème d'imagerie RMP inverse étant non-linéaire, ce travail de thèse propose une méthodologie de reconstruction d'images de la teneur en eau qui offre l'accès aux analyses des incertitudes, axée sur un algorithme d'échantillonnage inverse de Monte-Carlo (Metropolis-Hastings). Une étude intensive des biais introduits par l'apriori sur la reconstruction de différents volumes 3D est effectuée.Enfin, les possibilités d'imageries RMP sont illustrées sur deux cas d'applications réels en milieux hétérogènes karstiques ou thermo-karstiques, validés par comparaison avec d'autres sources d'informations. Le premier cas est une imagerie 2-D du conduit karstique de Poumeyssens, dont la cartographie est connue.Le deuxième cas est l'imagerie 3-D d'une poche d'eau sous-glaciaire dans le glacier de Têre-Rousse laquelle est explorée par de nombreux forages et d'autres méthodes géophysiques. / The non-destructive observation of the ground water content's variaiblity in time and space is a major issue to understand the hydrodynamical functioning of heterogeneous media.Although many geophysical methods derive the water content of the subsurface from intermediate physical parameters, the method of surface nuclear magnetic resonance (SNMR) provide a direct estimate of ground water content. For this method, 2-D or 3-D SNMR tomography applications are only emerging and an in-depth analysis is required to assess their possibilities and limitations.The general resolution of the method is limited because the measurement characterize an important volume and is contaminated by electromagnetic noise. Consequently, the translation of measurement into an image of water content admit many solutions. Among them, several are more desirable than others from a structural/geometrical stand point. Geometrical prior knowledge are used to limit the infinite solution space. The resulting water content estimate is necessarily biased (prior knowledge) and affected by uncertainties (noise). To date, those aspects have never been quantified for 2-D and 3-D SNMR data sets.The processes that are controlling the geometrical rendering and the estimated water volume, properties of the SNMR imaging problem are analyzed using correlations and linear regressions as they are unbiased tools for the data space analysis.As the MRS inverse problem is non-linear, this thesis proposes a monte carlo based methodology (Metropolis- Hastings) to provide water content and uncertainty estimates. As the geometrical prior expectations control the estimates, the resulting bias is explored and discussed for different water content configuration.Finally, the possibilities of MRS imaging are illustrated by means of two highly heterogeneous environments: thermo-karstic and karstic. The results of the MRS imagery are compared and validated with other types of knowledge. The first case is a 2-D imaging of the conduit Poumeyssens karst. The latter geometry is precisely known. The second case is the 3-D imaging of a internal cavity inside the french alp glacier Tete-Rousse, explored by multiple other destructive and non-destructive methods.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Techniques for estimating unknown terms - such as eddy diffusivity and counter-gradient - in atmospheric flow are presented in this study. The methos is also used to identify the source term in atmospheric pollution. The scheme adopted is based on inverse problem methodology. The inverse problem is formulated as a non-linear optimization problem, where the objective function is defined as the square difference between observational data and data from a transport mathematical model. For estimating the properties of the atmospheric flux, an implicit strategy was used, and an Eulerian model was used as forward model. The estimation of the pollutant source term was tested employing a source-repector technique. In the pollutant dispersion simulation, a Lagrangian model was applied. For some inversions, regularized solutions should be searched. The Tikhonov and entropy regularizations were considered. Three different optimization methods were used: Levenberg-Marquardt, quasi-Newton (deterministic) e simulated annealing (stochastic). The results show a good performance of the proposed methodology in many tested situations. / Neste estudo apresentam-se técnicas para estimar termos desconhecidos em fluxos atmosféricos, tais como coeficiente de difusão turbulento e termo de contra-gradiente. O método é também usado para a estimação de termos de fonte em poluição atmosférica. O esquema adotado é baseado na metodologia de problema inverso. O problema inverso é formulado como um problema de otimização não linear, onde a função objetivo é definida como a diferença quadrática entre dados experimentais e dados obtidos através de um modelo matemático de transporte. Para a estimação de propriedades de fluxo atmosféricos, uma estratégia de inversão implícita foi utilizada, onde um modelo eureliano foi empregado como modelo matemático. Para a estimação do termo de fonte de poluição, um procedimento de inversão empregando a técnica fonte-receptor foi testado em diversos cenários físicos. Para simulação da dispersão de poluentes na atmosfera foi empregado um modelo lagrangeano. Em alguns casos tornou-se necessário aplicar técnicas de regularização na obtenção da solução inversa. Regularização de Tikhonov e em entrópicas foram empregadas, quando necessário. Três diferentes métodos de otimização são utilizados: Levenberg-Marquardt e quase-Newton (determinísticos) e recozimento simulado (estocástico). Os resultados comprovam a robustez do método de inversão nas diversas situações testadas.

Made available in DSpace on 2015-05-15T11:46:15Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1506315 bytes, checksum: c118c0832159e55c3a04343c6d51f74a (MD5) Previous issue date: 2012-05-10 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / We consider a transmission wave equation in two embedded domains in R2, where the speed is a1 > 0 in the inner domain and a2 > 0 in the outer domain. We prove a global Carleman inequality for this problem under the hypothesis that the inner domain is strongly convex and a1 > a2. As a consequence of this inequality, uniqueness and Lipschitz stability are obtained for the inverse problem of retrieving a stationary potential for the wave equation with Dirichlet data and discontinuous principal coeficient from a single time dependent Neumann boundary measurement. / Considerando uma equação da onda de transmissão em dois domínios imersos em R2, onde a velocidade é a1 > 0 no domínio interior e a2 > 0 no domínio exterior, provamos uma desigualdade de Carleman global para este problema sobre a hipótese de o domínio interior ser fortemente convexo e a1 > a2. Como consequência dessa desigualdade, são obtidas a unicidade e a estabilidade lipschitziana para o problema inverso de retomar um potencial estacionário para a equação da onda com dados de Dirichlet e coeficiente principal descontínuo. Estes dois resultados são obtidos a partir de um único dado (dependente do tempo) de Neumann na fronteira.

Esta tese apresenta o desenvolvimento de uma técnica de processamento numérico capaz de reconstruir o sinal da temperatura do processo original a partir do sinal distorcido, atrasado e ruidoso, medido através de uma sonda intrusiva. Uma técnica de regularização foi adotada para contornar o mau condicionamento do modelo numérico inverso da equação de transdução para obter o sinal do processo, que considera o acúmulo térmico e as transferências de calor convectivo e radiativo entre o meio e o sensor térmico. O método dos mínimos quadrados simplificado foi implementado como técnica de regularização, por ser um método rápido e possuir um código computacional pequeno, permitindo, obter os dados em tempo real e desenvolver um sensor térmico inteligente. Testes numéricos demonstraram as discrepâncias introduzidas pela inércia térmica, convecção e radiação, bem como a extrema sensibilidade da presença de ruídos quando o problema inverso é resolvido. Testes experimentais foram conduzidos para validar o algoritmo de reconstrução sob condições práticas com sinais obtidos por um termopar encapsulado / This thesis presents the development of a numerical processing technique capable of reconstructing the original process temperature signal from distorted, late and noisy measured signal obtained from an intrusive probe. A regularization technique was adopted to palliate the ill conditioning of the inverse numerical model of the transduction equation to obtain the process signal, which considers thermal accumulation and convective and radiative heat transfers between the medium and the thermal sensor. The simplified least square method was implemented as the regularization technique, because it is a fast method and results in a small computational code, which produces on-line information and allow the development an intelligent temperature sensor. Numerical tests demonstrated the discrepancies introduced by thermal inertia, convection and radiation, as well as the extreme sensitivities to the presence of noise when solving the inverse problem. Experimental tests were carried out to validate the reconstruction algorithm under realistic experimental conditions with the signals obtained by the sheathed thermocouple