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[pt] No estado do Rio de Janeiro, os movimentos de massa em encostas passaram a representar um dos problemas mais importantes em geotecnia devido ao seu relevo acidentado, forma de ocupação e condições climáticas rigorosas. Visando identificar uma alternativa para avaliar encostas usando métodos não invasivos que possibilitem o trabalho em locais de difícil acesso, com rapidez e aquisição contínua de dados, neste trabalho é exposto uma análise teórica e prática deste processo de avaliação utilizando métodos geofísicos e o monitoramento contínuo da água no solo por meio de sensores. Os levantamentos geofísicos com uso do georadar e da análise multicanal de ondas superficiais para investigação da estratigrafia da encosta estudada, possibilitaram a identificação de três camadas: solo maduro, solo residual jovem e rocha. Para o monitoramento contínuo, são usados sensores de umidade volumétrica, sucção e um pluviômetro durante um período de 6 meses com a coleta de dados a cada 10 minutos. Com a interpretação dos dados coletados, verificou-se uma boa funcionalidade do monitoramento para avaliar as respostas de sucção e umidade volumétrica ao longo de períodos com intervalos irregulares de chuva. Os dados de precipitação e estratigrafia identificados são usados nas análises de infiltração e estabilidade saturada e não saturada, que possibilitaram a identificação de seções críticas com fator de segurança abaixo de 1,5, onde são necessárias intervenções para garantir a segurança da vizinhança. / [en] In the state of Rio de Janeiro, mass movements on slopes have become one of the most important geotechnical problems due to their rugged terrain, occupation and harsh weather conditions. In order to identify an alternative to evaluate slopes using non-invasive methods that enable work in hard to reach places, with rapid and continuous data acquisition, this paper presents a theoretical and practical analysis of this evaluation process using geophysical methods and continuous monitoring ground water through sensors. Geophysical surveys using georadar and multichannel analysis of surface wave to investigate the stratigraphy of the studied slope, allowed the identification of three layers: mature soil, young residual soil and rock. For the continuous monitoring, volumetric humidity and suction sensors and a rain gauge are used for a period of 6 months with data collection every 10 minutes. With the interpretation of the collected data, a good monitoring functionality was verified to evaluate the suction and volumetric humidity responses during periods with irregular rain intervals. The identified precipitation and stratigraphy data are used in the infiltration and saturated stability analyzes, which allowed the identification of critical sections with safety factor below 1.5, where interventions are necessary to ensure the safety of the neighborhood.

The omnicopter is a small unmanned aerial vehicle capable of executing decoupled translational and rotational motion (six degree of freedom, 6DOF, motion). The development of controllers for various 6DOF controllable multirotors has been much more limited than development for quadrotors, which makes selecting a controller for a 6DOF multirotor difficult. The omnicopter is subject to various uncertainties and disturbances from hardware changes, structural dynamics, and airflow, making adaptive controllers particularly interesting to investigate. The goal of this research is to design and evaluate the performance of various position and attitude controller combinations for the omnicopter, specifically focusing on adaptive controllers. Simulations are first used to compare combinations of three position controllers, PID, model reference adaptive control, augmented model reference adaptive control (aMRAC), and four attitude controllers, PI/feedback linearization (PIFL), augmented model reference adaptive control, backstepping, and adaptive backstepping (aBack). For the simulations, the omnicopter is commanded to point at and track a stationary aim point as it travels along a $C^0$ continuous trajectory and a trajectory that is $C^1$ continuous. The controllers are stressed by random disturbances and the addition of an unaccounted for suspended mass. The augmented model reference adaptive controller for position control paired with the adaptive backstepping controller for attitude control is shown to be the best controller combination for tracking various trajectories while subject to disturbances. Based on the simulation results, the PID/PIFL and aMRAC/aBack controllers are selected to be compared during three different flight tests. The first flight test is on a $C^1$ continuous trajectory while the omnicopter is commanded to point at and track a stationary aim point. The second flight test is a hover with an unmodeled added weight, and the third is a circular trajectory with a broken blade. As with the simulation results, the adaptive controller is shown to yield better performance than the nonadaptive controller for all scenarios, particularly for position tracking. With an added weight or a broken propeller, the adaptive attitude controller struggles to return to level flight, but is capable of maintaining steady flight when the nonadaptive controller tends to fail. Finally, while model reference adaptive controllers are shown to be effective, their nonlinearity can make them difficult to tune and certify via standard certification methods, such as gain and phase margin. A method for using time delay margin estimates, a potential certification metric, to tune the adaptive parameter tuning gain matrix is shown to be useful when applied to an augmented MRAC controller for a quadrotor. / Doctor of Philosophy / The omnicopter is a small unmanned aerial vehicle capable of executing decoupled translational and rotational motion. The development of controllers for these types of vehicles has been limited, making controller selection difficult. The omnicopter is subject to variations in hardware and airflow, making adaptive controllers particularly interesting to investigate. The goal of this research is to design and compare the performance of various position and attitude controller combinations for the omnicopter, specifically focusing on adaptive controllers. Simulations are first used to compare combinations of several position and attitude controllers on various trajectories and disturbances. Simulation results showed that a fully adaptive controller combination produced the best trajectory tracking while subject to disturbances. As with the simulation results, flight tests showed the adaptive controller yields better performance than the nonadaptive controller for all scenarios, particularly for position tracking. Finally, while the adaptive position controller was shown to be effective, it is difficult to tune and certify for widespread use. A method for using time delay margin estimates, a potential certification metric, to tune the adaptive controller is shown to be useful when applied to an adaptive controller for a quadrotor.

Les cellules sanguines jouent un rôle fondamental dans le bon fonctionnement du corps et sont régulées de manière à répondre à ses besoins immédiats. Malgré leurs fonctions distinctes, plusieurs études suggèrent que les processus de régulations des globules rouges et des plaquettes sanguines interagissent entre eux, notamment par l'intervention d'hormones. On s'intéresse ici aux interactions conceptuelles entre ces deux familles de cellules sanguines à l'aide d'un modèle de deux équations différentielles à délais couplées. L'analyse de la distribution des valeurs propres de l'équation caractéristique du modèle linéarisé permet de dresser un portrait de stabilité de l'équilibre du système dans un plan de paramètre approprié. On s'intéresse notamment aux possibilités de déstabilisation et de restabilisation par le couplage des deux équations. L'analyse des diagrammes de stabilité pour ces différents cas de figure permet de mettre en évidence des dynamiques intéressantes comme des alternances de stabilité par l'action des délais et différents types de bifurcations déstabilisatrices de l'équilibre. / Blood cells play a fundamental role in the proper functioning of the body and are regulated to respond to its immediate needs. Despite their distinct functions, several studies suggest that the regulatory processes of red blood cells and blood platelets interact with each other, notably through the intervention of hormones. We aim to study the conceptual interactions between these two families of blood cells using a coupled two-delay differential equation model. The analysis of the distribution of eigenvalues of the characteristic equation of the linearized model allows us to outline a stability portrait of the system in a suitable parameter plane. We are particularly interested in exploring the possibilities of destabilization and restabilization through the coupling of the two equations. The analysis of stability diagrams for these different scenarios highlights interesting dynamics such as stability switches due to the influence of delays and various types of destabilizing bifurcations of the equilibrium.

[pt] Os últimos leilões do pré-sal para exploração e produção de petróleo e gás no Brasil indicam que as operações de perfuração se tornarão mais intensas nos próximos anos. O processo de perfuração rotativo é amplamente utilizado para alcançar os reservatórios de petróleo e devido à relação diâmetro/comprimento do sistema de perfuração, o modo de vibração torcional está presente em quase todos os processos de perfuração, podendo chegar a um estado crítico indesejável: o fenômeno de stick-slip. Com o intuito de abordar este problema, o modo torcional é isolado e o stick-slip é observado em uma coluna de perfuração em escala reduzida completamente instrumentada. Durante o stick-slip, outro torque pode ser aplicado em uma posição intermediária da bancada de teste. O modelo matemático de parâmetros concentrados é obtido e o modelo é comparado com dados experimentais com o propósito de verificar se o modelo matemático representa o aparato experimental. Uma análise de estabilidade é feita usando o modelo validado com o objetivo de identificar soluções estáveis do sistema. Com isso, observou-se que existe uma faixa do parâmetro de bifurcação na qual soluções de equilíbrio e periódicas estáveis coexistem. Para uma dada situação de stick-slip na faixa de biestabilidade, duas estratégias de mitigação de vibração torcional foram consideradas e consistiram em impor perturbações no sistema por meio do torque na posição intermediária da bancada de teste: (i) torques aplicados apenas contra a direção de movimento do sistema, e (ii) torques aplicados em ambas as direções. As estratégias foram testadas numericamente e apresentaram eficiência de tal modo que o stick-slip foi completamente mitigado: as energias do sistema e o trabalho gerado pelo torque intermediário aplicado foram comparados com o propósito de avaliar a factibilidade e razoabilidade da estratégia. Experimentalmente, o sistema continuou a oscilar, porém apresentou uma significante redução na fase de stick mesmo com limitações de aplicações de torque. / [en] The latter round bids of the pre-salt for exploration and production of oil and natural gas in Brazil indicate the drilling operations will become more intense in coming years. The rotational drilling process is largely used to reach the oil reservoirs and because of diameter-to-length ratio of the drilling system, torsional vibration mode is present in most all drilling processes and may reach an undesired severe stage: the stick-slip phenomenon. In order to address this problem, the torsional vibration mode is isolated and the stick-slip is observed in a fully instrumented drill-string experimental set-up in this work. During this phenomenon, another torque may be applied on an intermediate position of the test bench. The lumped parameter mathematical model is obtained and it is compared to experimental data to validate whether the mathematical model represents the experimental apparatus. A stability analysis is performed using the validated mathematical model in order to identify stable solutions of the system. Therewith, one observed that there is a range of the bifurcation parameter in which stable equilibrium and periodic solutions may coexist. For a given stick-slip situation in bi-stability range, two mitigation strategies of torsional vibration were considered which consisted of imposing perturbations in the system via torques on the intermediate position of the test bench: (i) torques applied only against the direction of motion of the system, and (ii) torques applied in both directions. The strategies were tested numerically and presented eficiency so that the stickslip was completely mitigated: the energies of the system and the work created by the intermediate torque were compared in order evaluate the feasibility and reasonableness of the strategy. Experimentally, the system continued to oscillate, however it presented a significant reduction of stick phase even with limitations of torque applications.

Dans la production d'électricité, un des leviers centraux pour réduire les détériorations et les pertes causées par l'humidité dans les turbines à vapeur est l'étude des films liquides. Ces films minces, sont créés par la déposition de gouttes et sont fortement cisaillés. Des gouttes peuvent ensuite être arrachées du film. A l'heure actuelle, aucun modèle complet et valide n'existe pour décrire ce phénomène. Un modèle 2D à formulation intégrale associé à des lois de fermetures a été dérivé pour représenter ce film. Comparé aux équations classiques de Saint-Venant, le modèle prend en compte davantage d'effets : le transfert de masse, l'impact des gouttes, le cisaillement à la surface libre, la tension de surface, le gradient de pression et la rotation. Une analyse des propriétés du modèle (hyperbolicité, entropie, conservativité, analyse de stabilité linéaire, invariance par translation et par rotation) est réalisée pour juger de la pertinence du modèle. Un nouveau code 2D est implémenté dans un module de développement libre du code EDF Code Saturne et une méthode de volumes finis pour un maillage non-structure a été développée. La vérification du code est ensuite effectuée avec des solutions analytiques dont un problème de Riemann. Le modèle, qui dégénère en modèle classique de Saint-Venant pour le cas d'un film tombant sur un plan inclinée, est validé par l'expérience de Liu and Gollub, 1994, PoF et comparé à des modèles de références (Ruyer-Quil and Manneville, 2000, EPJ-B et Lavalle, 2014, PhD thesis). Un autre cas d'étude met en scène un film cisaillé en condition basse-pression de turbine à vapeur et, est validé par l'expérience de Hammitt et al., 1981, I. Enfin, le code film est couplé aux données 3D du champ de vapeur autour d'un stator d'une turbine basse-pression du parc EDF, issues de Blondel, 2014, PhD thesis. Cette application industrielle montre la faisabilité d'une simulation d'un film en condition réelle du turbine à vapeur. / In the electricity production, one central key to reduce damages and losses due to wetness in steam turbines is the study of liquid films. These thin films are created by the deposition of droplets and are highly sheared. This film may then be atomized into coarse water. At the moment, no comprehensive and validated model exists to describe this phenomenon. A 2D model based on a integral formulation associated with closure laws is developed to represent this film. Compared to classical Shallow-Water equation, the model takes into account additional effect : mass transfer, droplet impact, shearing at the free surface, surface tension, pressure gradient and the rotation. The model properties (hyperbolicity, entropy, conservativity, linear stability, Galilean invariance and rotational invariance) has been analyzed to judge the pertinence of the model. A new 2D code is implemented in a free module of the code EDF Code Saturne and a finite volume method for unstructured mesh has been developed. The verification of the code is then carried out with analytical solutions including a Riemann problem. The model, which degenerates into classical Shallow-Water equations for the case of a falling liquid film on a inclined plane, is validated by the experiment of Liu and Gollub, 1994, PoF and compared to reference models (Ruyer-Quil and Manneville, 2000, EPJ-B et Lavalle, 2014, PhD thesis). Another study depicts a sheared film under low-pressure steam turbine conditions and is validated by the experiment of Hammitt et al., 1981, FiI. Lastly, the code film is coupled to 3D steam data around a fixed blade of a BP100 turbine, from Blondel, 2014, PhD thesis. This industrial application shows the feasibility of liquid film's simulation in real steam turbine condition.

Este trabalho tem a finalidade de estudar a influência da parede de concreto na análise de estabilidade de contenções atirantadas bem como discutir sobre segurança nestas análises. Para isto foram elaborados modelos em estado plano de deformação por meio do método dos elementos finitos, MEF, para análise. A parede de concreto foi modelada com variações de rigidez e modelos reológico, com o fim de se entender sua influência no fator de segurança. Por fim foi realizado um breve estudo sobre a utilização dos métodos estatísticos na análise de estabilidade de contenções. / This work has the purpose of study the influence of the concrete wall in the stability analysis of tieback retaining walls and to discuss these safety analysis. Models were developed using plane strain state via the finite element method, FEM, for analysis. The concrete wall was modeled with variations of stiffness and rheological models, in order to bore its influence on the safety factor. Finally a brief study was conducted on the use of statistical methods in stability analysis of retaining walls.

El objetivo de este trabajo es el desarrollo de técnicas para la simulación y optimización del diseño de circuitos osciladores y lazos de enganche en fase de microondas. La intención de estas técnicas es que puedan ser utilizadas por el diseñador para optimizar las prestaciones de este tipo de circuitos durante la etapa de diseño. Por este motivo, se ha intentado que en todo momento las técnicas puedan ser utilizadas en combinación con un programa comercial de simulación de circuitos de microondas.En el caso de los circuitos osciladores, inicialmente se han optimizado sus prestaciones cuando se utilizan como osciladores controlados por tensión. De esta forma, se han desarrollado una serie de técnicas que, en combinación con simulaciones en un programa comercial, permiten la linealización y extensión de la característica tensión-frecuencia. Mediante una técnica de control de estabilidad, se ha optimizado la respuesta dinámica del oscilador ante entradas variantes en el tiempo. En concreto, se ha aumentado la rapidez de respuesta eliminando transitorios lentos oscilantes que distorsionan la señal de salida deseada. Esta técnica se ha aplicado al caso particular de osciladores controlados por tensión utilizados para generar señales chirp, como puede ser en radares Frequency Modulated Continuos Wave (FMCW). Se ha analizado también el fenómeno del "injection-pulling", en el que una señal interferente desplaza la frecuencia de oscilación. Para ello, se ha desarrollado una formulación tipo transitorio de envolvente cuyos coeficientes pueden ser identificados mediante simulaciones de balance armónico en un simulador comercial. La técnica permite incrementar la robustez del circuito oscilador ante estas señales interferentes. Dados los problemas observados en el simulador comercial para simular la característica de ruido de fase en osciladores con estructuras acopladas, se ha desarrollado una técnica de simulación de ruido de fase que solventa estos problemas. La técnica obtiene la característica de ruido de fase a través de simulaciones de transitorio de envolvente en combinación con el uso de generadores auxiliares. Estas simulaciones pueden realizarse sin problemas usando un simulador comercial. Los resultados de todas las técnicas han sido corroborados mediante medidas en varios tipos de osciladores de microondas. Finalmente, se ha realizado un estudio preliminar para combinar el uso de series de Volterra con la técnica de transitorio de envolvente para la simulación de la respuesta transitoria de los osciladores.En el caso de los lazos de enganche en fase, se ha desarrollado un programa propio que realiza un análisis no lineal de lazos acoplados o "Coupled Phase-Locked Loops" (CPLL). Estos sistemas son utilizados en aplicaciones tales como en control de apuntamiento de antenas "phased-array". El programa, basado en una formulación tempo-frecuencial del sistema, permite la obtención de los rangos de operación del CPLL mediante una caracterización no lineal de los elementos que componen el lazo. Se delimitan los rangos de histéresis, y se analiza la variación de estos rangos en función de los parámetros del sistema. Se analiza la estabilidad de las soluciones estacionarias, teniendo en cuenta parámetros tales como el retardo del lazo. Mediante el control de la estabilidad y un análisis de tipo transitorio de envolvente, se optimiza la rapidez del sistema en el seguimiento de entradas moduladas. Finalmente, se analiza el ruido de fase, separando la perturbación en fase en distintas componentes. Esta separación permite clarificar el efecto del ruido en el control de apuntamiento de un array de antenas. Las predicciones de las técnicas han sido validadas mediante medidas en un sistema CPLL a 2 GHz. / The objective of this work is the development of techniques for the simulation and optimization of the design of microwave oscillator circuits and phase-locked loops. The intention of these techniques is that they can be used by the designer to optimize the features of these kinds of circuits during the design stage. For this reason, a lot of effort has been put along this thesis to ensure that the techniques can be used in combination with commercial microwave circuit simulators.In the case of the oscillator circuits, initially, their features have been optimized when used as voltage controlled oscillators (VCO). In this way, different techniques are proposed for the computer aided design of these circuits. The first technique allows setting the operation frequency band for specific values of the tuning voltage. The second technique imposes a linear frequency-voltage characteristic with the aid of an auxiliary generator. To follow this characteristic, the circuit is solved in terms of an ideal capacitance, synthesized, at a later stage, with the tuning varactor embedded in a linear network. In the third technique, the oscillator response to a sawtooth input, used to generate a chirp signal, is improved, eliminating spurious frequencies, not observable in steady state. To illustrate the techniques, a VCO operating in the C-band has been optimized and used to generate a chirp signal with low nonlinear frequency distortion. The injection-pulling phenomenon in oscillator circuits has been also analyzed. Injection pulling by interference signals is an undesired phenomenon in front-end oscillators, which causes a shift of the oscillation frequency and degrades the output spectrum. A semi-analytical formulation for the insightful analysis of injection-pulling phenomena in the presence of a modulated carrier or chirp signal is presented. The formulation enables an efficient analysis of interference problems difficult to simulate with harmonic balance or standard envelope transient. It allows the modification of the original design in order to reduce the injection pulling to the desired levels. The techniques have been applied to an oscillator at 6 GHz. Considering the problems found in commercial software to simulate the phase noise characteristic of coupled oscillator topologies, a numerical technique for the determination of the phase-noise spectrum of free-running oscillators is presented. The technique is based on envelope transient and can be applied to any commercial simulator on which this analysis method is available. The main advantage of the technique is that it allows simulating the near carrier phase noise spectrum, including possible resonances. The elements providing the oscillator phase-noise spectrum are obtained from envelope-transient simulations of low-computational cost. Comparisons are performed between the presented technique and other existing techniques, such as the carrier modulation approach. The technique has been successfully tested on the simulation of the near carrier phase noise spectrum of an oscillator circuit at 6.3 GHz. Finally, a preliminary study has been carried out to combine the use of Volterra series with the envelope transient technique for the simulation of oscillator transients.Regarding the phase-locked loops, in this thesis, harmonic-balance (HB) and envelope-transient formulations of coupled phase-locked loops (CPLLs) are presented. The CPLL has the added difficulty of its autonomous behavior since no reference oscillator is present. The new formulation takes into account the autonomy of the system, introducing a special set of state variables, which depend on the autonomous frequencies. The hysteresis phenomenon in CPLLs is analyzed in detail, efficiently obtaining the pull-in and hold-in ranges through HB. The pole analysis of the perturbed HB system enables an accurate prediction of instabilities and resonances. Due to the CPLL autonomy, there exists an inherent noise accumulation effect. This effect is taken into account, analyzing the perturbation in terms of accumulation and deviation components. The envelope formulation allows simulating the CPLL behavior in presence of modulation signals. The influence of the stability of the steady-state solution on the modulated signals is investigated. The simulation results have been successfully compared with the measurements in a manufactured CPLL system at 2 GHz.

Diese Arbeit stützt sich auf die theoretische und experimentelle Untersuchung der Thermodiffusion im Magnetfeld. Bei magnetischen Flüssigkeiten als kolloidalen Suspensionen versteht man unter der Thermodiffusion einen durch einen Temperaturgradienten angestoßenen unidirektionalen Partikeltransport, der zur Separation des Fluids führt. Beschrieben wird die Thermodiffusion theoretisch über das Konzentrationsprofil der Partikel in Abhängigkeit von Zeit und Ort in einer Fluidschicht. Die Experimente detektieren die Separation des Fluids über die Konzentrationsdifferenz zwischen zwei Fluidkammern. Die Bestimmung des Soret-Koeffizienten erfolgt über einen Datenfit zwischen experimentellen und theoretischen Daten. Für das kerosinbasierte Ferrofluid EMG905 wurden zwei Effekte festgestellt. Bei kleinen Magnetfeldstärken wandern die Partikel zum kalten Rand der Schicht (ST>0), bei steigenden Feldstärken kehrt sich diese Richtung um (ST<0). Die Ergebnisse der Untersuchungen zur Thermodiffusion gehen dann in eine lineare Stabilitätsanalyse einer Ferrofluidschicht bei anliegendem Temperaturgradienten und Magnetfeld ein. Dabei wird festgestellt, dass die kritische Rayleigh-Zahl als charakteristische Größe zum Einsetzen von Konvektion von dem Soret-Koeffizienten abhängt. Ist letzterer positiv, wird das Einsetzen von Konvektion begünstigt, ist er wiederum negativ, so kann Konvektion vollständig unterdrückt werden.

Dans ce projet, nous étudions la reconstruction de milieux terrestres souterrains.L’imagerie sismique est traitée avec un problème de minimisation itérative àgrande échelle, et nous utilisons la méthode de l’inversion des formes d’ondes(Full Waveform Inversion, FWI method). La reconstruction est basée sur desmesures d’ondes sismiques, car ces ondes sont caractérisées par le milieu danslequel elles se propagent. Tout d’abord, nous présentons les méthodesnumériques qui sont nécessaires pour prendre en compte l’hétérogénéité etl’anisotropie de la Terre. Ici, nous travaillons avec les solutions harmoniques deséquations des ondes, donc dans le domaine fréquentiel. Nous détaillons leséquations et l’approche numérique mises en place pour résoudre le problèmed’onde.Le problème inverse est établi afin de reconstruire les propriétés du milieu. Ils’agit d’un problème non-linéaire et mal posé, pour lequel nous disposons de peude données. Cependant, nous pouvons montrer une stabilité de type Lipschitzpour le problème inverse associé avec l’équation de Helmholtz, en considérantdes modèles représentés par des constantes par morceaux. Nous explicitons laborne inférieure et supérieure pour la constante de stabilité, qui nous permetd’obtenir une caractérisation de la stabilité en fonction de la fréquence et del’échelle. Nous revoyons ensuite le problème de minimisation associé à lareconstruction en sismique. La méthode de Newton apparaît comme naturelle,mais peut être difficilement accessible, dû au coup de calcul de la Hessienne.Nous présentons une comparaison des méthodes pour proposer un compromisentre temps de calcul et précision. Nous étudions la convergence de l’algorithme,en fonction de la géométrie du sous-sol, la fréquence et la paramétrisation. Celanous permet en particulier de quantifier la progression en fréquence, en estimantla taille du rayon de convergence de l’espace des solutions admissibles.A partir de l’étude de la stabilité et de la convergence, l’algorithme deminimisation itérative est conduit en faisant progresser la fréquence et l’échellesimultanément. Nous présentons des exemples en deux et trois dimensions, etillustrons l’incorporation d’atténuation et la considération de milieux anisotropes.Finalement, nous étudions le cas de reconstruction avec accès aux données deCauchy, motivé par les dual sensors développés en sismique. Cela nous permetde définir une nouvelle fonction coût, qui permet de prometteuses perspectivesavec un besoin minimal quant aux informations sur l’acquisition. / In this project, we investigate the recovery of subsurface Earth parameters. Weconsider the seismic imaging as a large scale iterative minimization problem, anddeploy the Full Waveform Inversion (FWI) method, for which several aspects mustbe treated. The reconstruction is based on the wave equations because thecharacteristics of the measurements indicate the nature of the medium in whichthe waves propagate. First, the natural heterogeneity and anisotropy of the Earthrequire numerical methods that are adapted and efficient to solve the wavepropagation problem. In this study, we have decided to work with the harmonicformulation, i.e., in the frequency domain. Therefore, we detail the mathematicalequations involved and the numerical discretization used to solve the waveequations in large scale situations.The inverse problem is then established in order to frame the seismic imaging. Itis a nonlinear and ill-posed inverse problem by nature, due to the limitedavailable data, and the complexity of the subsurface characterization. However,we obtain a conditional Lipschitz-type stability in the case of piecewise constantmodel representation. We derive the lower and upper bound for the underlyingstability constant, which allows us to quantify the stability with frequency andscale. It is of great use for the underlying optimization algorithm involved to solvethe seismic problem. We review the foundations of iterative optimizationtechniques and provide the different methods that we have used in this project.The Newton method, due to the numerical cost of inverting the Hessian, may notalways be accessible. We propose some comparisons to identify the benefits ofusing the Hessian, in order to study what would be an appropriate procedureregarding the accuracy and time. We study the convergence of the iterativeminimization method, depending on different aspects such as the geometry ofthe subsurface, the frequency, and the parametrization. In particular, we quantifythe frequency progression, from the point of view of optimization, by showinghow the size of the basin of attraction evolves with frequency. Following the convergence and stability analysis of the problem, the iterativeminimization algorithm is conducted via a multi-level scheme where frequencyand scale progress simultaneously. We perform a collection of experiments,including acoustic and elastic media, in two and three dimensions. Theperspectives of attenuation and anisotropic reconstructions are also introduced.Finally, we study the case of Cauchy data, motivated by the dual sensors devicesthat are developed in the geophysical industry. We derive a novel cost function,which arises from the stability analysis of the problem. It allows elegantperspectives where no prior information on the acquisition set is required.