Neste trabalho avaliou-se a potencialidade do uso da sísmica rasa de reflexão multicomponente para investigação geológica-geotécnica. Foram abordados vários aspectos relacionados à aquisição dos dados sísmicos de reflexão multicomponente, com o objetivo de entender as vantagens e limitações do método para aplicação em investigações de subsuperfície rasa. Os ensaios de campo foram realizados em duas áreas, ambas em terrenos da Bacia Sedimentar de São Paulo, em área urbana da cidade de São Paulo. Para a interpretação dos dados sísmicos multicomponente foram investigados procedimentos para a inversão não-linear dos tempos de trânsito e das amplitudes. O testes realizados orientaram a escolha da aproximação não-hiperbólica mais apropriada para calculo dos tempos de trânsito visando à análise de velocidades do pacote acima do refletor. O estudo numérico desenvolvido para a inversão das amplitudes mostrou a viabilidade da estimativa das velocidades e densidades, acima e abaixo do refletor, empregando-se as equações de Zoeppritz para as ondas refletidas PP, PSv, SvP e SvSv, antes e depois do ângulo crítico. Dada a complexidade da inversão nao-linear das amplitudes, se fez necessário elaborar uma estratégia estocástica de otimização e desenvolver uma nova abordagem para análise da função objetivo multi-dimensional, garantindo confiabilidade ao resultado da inversão não-linear. Os resultados deste trabalho mostraram o potencial da sísmica de reflexão rasa multicomponente para caracterização geológica-geotécnica, possibilitando um melhor entendimento das camadas superficiais. / This thesis aims to evaluate the useful of the multicomponent seismic methods for shallow investigations, mainly its potential for the geotechnical and geological characterization of the nearsurface. Several aspects regarding the acquisition and processing data of multicomponent seismic data are discussed. They were based on data set acquired in the urban area of Sao Paulo city, Brazil. Two different areas were investigated. Both located in sedimentary terrains belonging to the Sao Paulo Sedimentary Basin. We present a non-linear travel time and seismic amplitude inversion scheme to quantitative interpretation of multicomponent seismic data. Several tests were performed to guide the choice of non-hyperbolic equation more suitable for travel time inversion aiming the velocity analysis above the reflector. A numerical experiment developed to solve the nonlinear inversion of seismic amplitudes showed the feasibility to estimate seismic interval velocities and layer densities above and below the reflector using the exact Zoeppritz equations for PP, PSv, SvP e SvSv reflected waves, before and after critical angle. Due to the apparent complexity of the nonlinear seismic amplitude inversion, it was necessary elaborate the strategy for stochastic optimization and develop a new approach to analyze the multi-dimensional objective function, with different implications for the accuracy and efficiency of the non-linear inversion. The study show the benefits of using the multicomponent seismic method for shallow geological-geotechnical characterization, improving the nearsurface understanding, once allows an integrated analyzes of a more complete record of the wave field.

Neste trabalho avaliou-se a potencialidade do uso da sísmica rasa de reflexão multicomponente para investigação geológica-geotécnica. Foram abordados vários aspectos relacionados à aquisição dos dados sísmicos de reflexão multicomponente, com o objetivo de entender as vantagens e limitações do método para aplicação em investigações de subsuperfície rasa. Os ensaios de campo foram realizados em duas áreas, ambas em terrenos da Bacia Sedimentar de São Paulo, em área urbana da cidade de São Paulo. Para a interpretação dos dados sísmicos multicomponente foram investigados procedimentos para a inversão não-linear dos tempos de trânsito e das amplitudes. O testes realizados orientaram a escolha da aproximação não-hiperbólica mais apropriada para calculo dos tempos de trânsito visando à análise de velocidades do pacote acima do refletor. O estudo numérico desenvolvido para a inversão das amplitudes mostrou a viabilidade da estimativa das velocidades e densidades, acima e abaixo do refletor, empregando-se as equações de Zoeppritz para as ondas refletidas PP, PSv, SvP e SvSv, antes e depois do ângulo crítico. Dada a complexidade da inversão nao-linear das amplitudes, se fez necessário elaborar uma estratégia estocástica de otimização e desenvolver uma nova abordagem para análise da função objetivo multi-dimensional, garantindo confiabilidade ao resultado da inversão não-linear. Os resultados deste trabalho mostraram o potencial da sísmica de reflexão rasa multicomponente para caracterização geológica-geotécnica, possibilitando um melhor entendimento das camadas superficiais. / This thesis aims to evaluate the useful of the multicomponent seismic methods for shallow investigations, mainly its potential for the geotechnical and geological characterization of the nearsurface. Several aspects regarding the acquisition and processing data of multicomponent seismic data are discussed. They were based on data set acquired in the urban area of Sao Paulo city, Brazil. Two different areas were investigated. Both located in sedimentary terrains belonging to the Sao Paulo Sedimentary Basin. We present a non-linear travel time and seismic amplitude inversion scheme to quantitative interpretation of multicomponent seismic data. Several tests were performed to guide the choice of non-hyperbolic equation more suitable for travel time inversion aiming the velocity analysis above the reflector. A numerical experiment developed to solve the nonlinear inversion of seismic amplitudes showed the feasibility to estimate seismic interval velocities and layer densities above and below the reflector using the exact Zoeppritz equations for PP, PSv, SvP e SvSv reflected waves, before and after critical angle. Due to the apparent complexity of the nonlinear seismic amplitude inversion, it was necessary elaborate the strategy for stochastic optimization and develop a new approach to analyze the multi-dimensional objective function, with different implications for the accuracy and efficiency of the non-linear inversion. The study show the benefits of using the multicomponent seismic method for shallow geological-geotechnical characterization, improving the nearsurface understanding, once allows an integrated analyzes of a more complete record of the wave field.

Originally developed in the 1970s for the optimal control of systems governed by partial differential equations, the adjoint method has found several successful applications, e.g. in meteorology with large-scale 3D or 4D atmospheric data assimilation schemes, for carbon cycle data assimilation in biogeochemistry and climate research, or in oceanographic modelling with efficient adjoint codes of ocean general circulation models.<p><p>Despite the variety of applications in these research fields, adjoint methods have only very recently drawn attention from the ocean acoustics community. In ocean acoustic tomography and geoacoustic inversion, where the inverse problem is to recover unknown acoustic properties of the water column and the seabed from acoustic transmission data, the solution approaches are typically based on travel time inversion or standard matched-field processing in combination with metaheuristics for global optimization. <p><p>In order to complement the adjoint schemes already in use in meteorology and oceanography with an ocean acoustic component, this thesis is concerned with the development of the adjoint of a full-field acoustic propagation model for shallow water environments. <p><p>In view of the increasing importance of global ocean observing systems such as the European Seas Observatory Network, the Arctic Ocean Observing System and Maritime Rapid Environmental Assessment (MREA) systems for defence and security applications, the adjoint of an ocean acoustic propagation model can become an integral part of a coupled oceanographic and acoustic data assimilation scheme in the future. <p><p>Given the acoustic pressure field measured on a vertical hydrophone array and a modelled replica field that is calculated for a specific parametrization of the environment, the developed adjoint model backpropagates the mismatch (residual) between the measured and predicted field from the receiver array towards the source.<p><p>The backpropagated error field is then converted into an estimate of the exact gradient of the objective function with respect to any of the relevant physical parameters of the environment including the sound speed structure in the water column and densities, compressional/shear sound speeds, and attenuations of the sediment layers and the sub-bottom halfspace. The resulting environmental gradients can be used in combination with gradient descent methods such as conjugate gradient, or Newton-type optimization methods tolocate the error surface minimum via a series of iterations. This is particularly attractive for monitoring slowly varying environments, where the gradient information can be used to track the environmental parameters continuously over time and space.<p><p>In shallow water environments, where an accurate treatment of the acoustic interaction with the bottom is of outmost importance for a correct prediction of the sound field, and field data are often recorded on non-fully populated arrays, there is an inherent need for observation over a broad range of frequencies. For this purpose, the adjoint-based approach is generalized for a joint optimization across multiple frequencies and special attention is devoted to regularization methods that incorporate additional information about the desired solution in order to stabilize the optimization process.<p><p>Starting with an analytical formulation of the multiple-frequency adjoint approach for parabolic-type approximations, the adjoint method is progressively tailored in the course of the thesis towards a realistic wide-angle parabolic equation propagation model and the treatment of fully nonlocal impedance boundary conditions. A semi-automatic adjoint generation via modular graph approach enables the direct inversion of both the geoacoustic parameters embedded in the discrete nonlocal boundary condition and the acoustic properties of the water column. Several case studies based on environmental data obtained in Mediterranean shallow waters are used in the thesis to assess the capabilities of adjoint-based acoustic inversion for different experimental configurations, particularly taking into account sparse array geometries and partial depth coverage of the water column. The numerical implementation of the approach is found to be robust, provided that the initial guesses are not too far from the desired solution, and accurate, and converges in a small number of iterations. During the multi-frequency optimization process, the evolution of the control parameters displays a parameter hierarchy which clearly relates to the relative sensitivity of the acoustic pressure field to the physical parameters. <p><p>The actual validation of the adjoint-generated environmental gradients for acoustic monitoring of a shallow water environment is based on acoustic and oceanographic data from the Yellow Shark '94 and the MREA '07 sea trials, conducted in the Tyrrhenian Sea, south of the island of Elba.<p> <p>Starting from an initial guess of the environmental control parameters, either obtained through acoustic inversion with global search or supported by archival in-situ data, the adjoint method provides an efficient means to adjust local changes with a couple of iterations and monitor the environmental properties over a series of inversions. <p><p>In this thesis the adjoint-based approach is used, e.g. to fine-tune up to eight bottom geoacoustic parameters of a shallow-water environment and to track the time-varying sound speed profile in the water column. <p><p>In the same way the approach can be extended to track the spatial water column and bottom structure using a mobile network of sparse arrays.<p><p>Work is currently being focused on the inclusion of the adjoint approach into hybrid optimization schemes or ensemble predictions, as an essential building block in a combined ocean acoustic data assimilation framework and the subsequent validation of the acoustic monitoring capabilities with long-term experimental data in shallow water environments. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

A three-dimensional inversion was implemented for magnetotellurics, which is a passive electromagnetic method in geophysics. It exploits natural electromagnetic fields of the Earth, which function as sources. Their interaction with the conductive parts of the subsurface are registered when components of the electric and the magnetic field are measured and evaluated. The all-at-once approach is an inversion scheme that is relatively new to geophysics. In this approach, the objective function – the basis of each inversion – is called the Lagrangian. It consists of three parts: (i) the data residual norm, (ii) the regularisation part, and (iii) the forward problem. The latter is the significant difference to conventional inversion approaches that are built up of a forward calculation part and an inversion part. In the case of all-at-once, the forward problem is incorporated in the objective function and is therefore already taken into account in each inversion iteration. Thus, an explicit forward calculation is obsolete. As an objective function, the Lagrangian shall reach a minimum and therefore its first and second derivatives are evaluated. Hence, the gradient of the Lagrangian and its Hessian are constituent parts of the KKT system – the Newton-type system that is set up in the all-at-once inversion. Conventional inversion approaches avoid the Hessian because it is a large, dense, not positive definite matrix that is challenging to handle. However, it provides additional information to the inversion, which raises hope for a high quality inversion result. As a first step, the inversion was programmed for the more straightforward one-dimensional magnetotelluric case. This was particularly suitable to become familiar with sQMR – a Krylov subspace method which is essential for the three-dimensional case to be able to work with the Hessian and the resulting KKT system. After the implementation and validation of the one-dimensional forward operator, the Lagrangian and its derivatives were set up to complete the inversion, which successfully solved the KKT system. Accordingly, the three-dimensional forward operator also needed to be implemented and validated, which was done using published data from the 3D-2 COMMEMI model. To realise the inversion, the Lagrangian was assembled and its first and second derivatives were validated with a test that exploits the Taylor expansion. Then, the inversion was initially programmed for the Gauss-Newton approximation where second order information is neglected. Since the system matrix of the Gauss-Newton approximation is positive definite, the solution of this system of equations could be carried out by the conventional solver pcg. Based on that, the complete KKT system (Newton\\\'s method) was set up and preconditioned sQMR solved this system of equations.

Les méthodes géophysiques aéroportées sont très utilisées pour la prospection du sous-sol à l'échelle régionale, permettant ainsi de couvrir de grandes surfaces en particulier les zones difficiles d'accès. Le sujet de thèse concerne le développement de techniques d'interprétation des données géophysiques pour le problème des ressources naturelles et de l'environnement. La première partie de cette thèse concerne le développement d'une méthode de calcul direct des composantes des champs gravimétrique et magnétique à partir d'une structure (corps) géologique modélisé(e) par une grille à base de tétraèdres, ce qui permet de représenter des modèles géologiques très complexes particulièrement en présence de zones faillées et hétérogènes avec un nombre d'éléments optimal. Plusieurs techniques d'inversions utilisent des contraintes mathématiques pour la résolution du problème inverse en modélisation. Ces contraintes permettent de réduire le nombre de modèles possibles. Cependant les solutions proposées appelées aussi « le modèle le plus probable » présentent des solutions lisses, ce qui est loin de représenter la réalité géologique. Pour éluder ce problème, les deuxièmes et troisièmes parties de la thèse proposent des améliorations majeures du processus d'inversion par l'utilisation des méthodes géostatistiques telles que la Simulation Gaussienne Séquentielle ou la Co-Simulation dans le cas d'une inversion conjointe afin d'estimer les probabilités a posteriori des modèles simulés. La quatrième partie de ce mémoire présente une alternative à la simulation de plusieurs variables. L'apprentissage du réseau de neurones supervisé par un certain nombre de points permet d'établir une relation entre les différentes variables / In recent years with the technology developments, airborne geophysical methods (gravity, magnetic, and electromagnetic) are widely used in the natural resource exploration at the regional scale. It covers large areas particularly in the areas with difficult access. The first part of this thesis consist on the development of new forward modeling algorithm for the calculation of the components of the gravity and magnetic fields based on a tetrahedron grid. The tetrahedral mesh allows the representation of very complex geological models holding many heterogeneous and faulted zones with an optimal number of elements, this reduces significantly the time calculation. Several inversion techniques use mathematical constraints for the resolution of the inverse problem in order to reduce the number of possible models. However the proposed solutions called also "the most probable model" provide a smooth solutions that cannot represent the geological reality. To circumvent this problem in the second and the third parts of this thesis, we made two major improvements. The first, we integrate Sequential Gaussian Simulation into the inversion procedure to determine a possible distributions of a single property. The second is that we used the Co-Simulation in the case of joint inversion to estimate a posteriori probabilities of the simulated models. The last part of this thesis presents an alternative to the several variables simulation, supervised learning of neural networks allows to establish a relationship between the different variables

La compréhension de la relation structure-propriétés des parois des cellules végétales s'appuie de plus en plus sur l'utilisation d'approches de modélisation moléculaire en général et de dynamique moléculaire en particulier. A ce jour, le poids numérique que représente une telle démarche à l'échelle de l'atome est la plupart du temps incompatible avec les puissances de calcul disponibles. C'est pourquoi des méthodes d'approximation sont indispensables pour pouvoir mettre en œuvre des simulations numériques à l'échelle de systèmes supramoléculaires réalistes. Dans le cadre de cette thèse, un modèle de dynamique moléculaire, dit « gros grain » a été mis au point à l'échelle du monomère de macromolécules pariétales. Les paramètres de ce modèle ont été calibrés à l'aide de simulations de dynamique moléculaire à l'échelle de l'atome. Ce modèle a fait l'objet de quatre applications : adsorption d'une chaine de xylane sur une surface de cellulose cristalline, arrachement d'une chaine de xylane adsorbée sur une surface de cellulose cristalline par une pointe AFM, adsorption d'une phase amorphe de xylane sur une surface de cellulose cristalline et adsorption d'une phase amorphe de xylane sur un monocristal de cellulose exposant trois surfaces différentes. Des effets de structuration au voisinage de la cellulose sont observés. / Nowadays, the understanding of plant cell walls' structure-properties relationship leans more and more on the use of molecular modeling approaches and of molecular dynamics in particular. To date, numerical weight of such an approach is usually out of the reach of available computing power if the atomic scale is used. As a consequence, building approximate methods is of crucial importance to perform numerical simulation of realistic supramolecular systems. Within the framework of this PhD, a “coarse grain” molecular dynamics model was built at plant cell wall macromolecule monomer's scale, it's parameters being fixed with the help of atom-scale molecular dynamics simulations. Then, several numerical studies were carried out: a single xylan chain was adsorbed on a crystalline cellulose surface, a single xylan chain was pulled from a crystalline cellulose surface with the help of the tip of an AFM cantilever, an amorphous xylan phase was adsorbed on a cellulose surface and an amorphous xylan phase was adsorbed on a cellulose crystal, which three surfaces were exposed. Local structuring effects were observed.

La propagation des ondes sismiques dans les milieux poreux multiphasiques présente des enjeux nombreux, tant sur le plan environnemental (risques naturels, géotechnique, pollutions de nappes...) que pour les réservoirs (aquifères, hydrocarbures, stockages de CO2...). L'utilisation des ondes sismiques pour étudier ces milieux se justifie par le fait qu'en se propageant, les ondes sont déformées par le milieu qu'elles traversent et contiennent ainsi des informations aux capteurs sur les phases fluides et solides et sur le squelette poreux. Ce travail de thèse s'intéresse aux caractéristiques des ondes sismiques dans les milieux multiphasiques (plusieurs phases fluides et solides), depuis la description physique jusqu'à la caractérisation des paramètres constitutifs par inversion, en passant par la modélisation numérique 2D de la propagation. La première partie du travail a consisté à décrire la physique des milieux multiphasiques (phase par phase et leurs intéractions dynamiques) en utilisant des méthodes d'homogénéisation pour se ramener à un milieu équivalent défini par sept paramètres. Ainsi, dans des milieux simple porosité saturés et dans des milieux plus complexes (double porosité, partiellement saturés ou visco-poroélastiques), je peux calculer la propagation des ondes sismiques sans approximation. En effet, j'utilise une méthode numérique dans le domaine fréquence-espace qui permet de prendre en compte tous les termes qui dépendent de la fréquence sans approximation. La discrétisation spatiale utilise une méthode d'éléments finis discontinus (Galerkin discontinu) qui permet de considérer des milieux hétérogènes.Je montre notamment que les attributs sismiques (vitesses et atténuations) des milieux poreux complexes sont fortement dispersifs et les formes d'ondes complètes, calculées sans approximation, sont fortement dépendantes de la description physique du milieu. La caractérisation des paramètres poroélastiques s'effectue par inversion. Une méthode en deux étapes a été proposée : la première consiste en une inversion ``classique`` (tomographie, inversion des formes d'ondes complètes) des données (sismogrammes) pour obtenir des paramètres macro-échelles (attributs sismiques). La seconde étape permet de reconstruire, à partir des paramètres macro-échelles, les paramètres poroélastiques micro-échelles. Cette étape d'inversion utilise une méthode d'optimisation semi-globale (algorithme de voisinage). Une analyse de sensibilité montre qu'en connaissant a-priori certains paramètres, on peut inverser avec précision les paramètres du squelette poroélastique ou retrouver la nature du fluide saturant, à partir des vitesses de propagation. En revanche, pour retrouver la saturation en fluide, il est préférable de connaître les atténuations. Deux applications réalistes (monitoring de réservoir et hydrogéophysique) mettent en oeuvre ce type d'inversion en deux étapes et démontrent qu'à partir de données estimées par des méthodes classiques d'imagerie, on peut remonter à certains paramètres poroélastiques constitutifs. / Seismic wave propagation in multiphasic porous media have various environmental (natural risks, geotechnics, groundwater pollutions...) and ressources (aquifers, oil and gas, CO2 storage...) issues. When seismic waves are crossing a given material, they are distorted and thus contain information on fluid and solid phases. This work focuses on the characteristics of seismic waves propagating in multiphasic media, from the physical complex description to the parameter characterisation by inversion, including 2D numerical modelling of the wave propagation. The first part consists in the description of the physics of multiphasic media (each phase and their interactions), using several upscaling methods, in order to obtain an equivalent mesoscale medium defined by seven parameters. Thus, in simple porosity saturated media and in complex media (double porosity, patchy saturation, visco-poroelasticity), I can compute seismic wave propagation without any approximation. Indeed, I use a frequency-space domain for the numerical method, which allows to consider all the frequency dependent terms. The spatial discretisation employs a discontinuous finite elements method (discontinuous Galerkin), which allows to take into account complex interfaces.The computation of the seismic attributes (velocities and attenuations) of complex porous media shows strong variations in respect with the frequency. Waveforms, computed without approximation, are strongly different if we take into account the full description of the medium or an homogenisation by averages. The last part of this work deals with the poroelastic parameters characterisation by inversion. For this, I develop a two-steps method: the first one consists in a classical inversion (tomography, full waveform inversion) of seismograms data to obtain macro-scale parameters (seismic attributes). The second step allows to recover, from the macroscale parameters, the poroelastic micro-scale properties. This downscaling step uses a semi-global optimisation method (neighbourhood algorithm), which allows the sampling of the full model space (thanks to the low numerical cost of the analytic direct model). With the a-priori knowledge of some parameters, a sensibility analysis shows that I can invert precisely skeleton parameters or the saturating fluid type, from the velocities only. Nevertheless, to recover the fluid saturation, it is preferable to use the attenuations. This two-steps procedure is tested on two realistic applications (reservoir monitoring and subsurface hydrogeophysics) and show that we can recover some constituve poroelastic parameters.

L'inversion acoustique-articulatoire de la parole consiste à récupérer la forme du conduit vocal à partir d'un signal de parole. Ce problème est abordé à l'aide d'une méthode d'analyse par synthèse reposant sur un modèle physique de production de la parole contrôlé par un petit nombre de paramètres décrivant la forme du conduit vocal : l'ouverture de la mâchoire, la forme et la position de la langue et la position des lèvres et du larynx. Afin de s'approcher de la géométrie de notre locuteur, le modèle articulatoire est construit à l'aide de contours articulatoires issus d'images cinéradiographiques présentant une vue sagittale du conduit vocal. Ce synthétiseur articulatoire nous permet de créer une table formée de couples associant un vecteur articulatoire au vecteur acoustique correspondant. Nous n'utiliserons pas les formants (fréquences de résonance du conduit vocal) comme vecteur acoustique car leur extraction n'est pas toujours fiable provoquant des erreurs lors de l'inversion. Les coefficients cepstraux sont utilisés comme vecteur acoustique. De plus, l'effet de la source et les disparités entre le conduit vocal du locuteur et le modèle articulatoire sont pris en compte explicitement en comparant les spectres naturels à ceux produits par le synthétiseur car nous disposons des deux signaux / The acoustic-to-articulatory inversion of speech consist in the recovery of the vocal tract shape from the speech signal. This problem is tackled with an analysis-by-synthesis method depending on a physical model of speech production controlled by a small number of parameters describing the vocal tract shape: the jaw opening, the shape and the position of the tongue and the position of lips and larynx. In order to approach the geometry of the speaker, the articulatory model is built with articulatory contours from cineradiographic images of the sagittal view of the vocal tract. This articulatory synthesizer allows us to create a table made up with couples associating a articulatory vector with the corresponding acoustic vector. The formants (resonance frequency of the vocal tract shape) are not used as acoustic vector because their extraction is not always reliable causing errors during inversion. The cepstral coefficients are used as acoustic vector. Moreover, the source effect and the mismatch between the speaker vocal tract and the articulatory model are considered explicitly comparing the natural spectrum with those produced by the synthesizer because we have the both signals

Dans ce manuscrit, nous étudions le retard distribué et ses applications. Nous présentons la définition du retard distribué et l'étude de ses propriétés. Nous expliquons aussi le problème de la mise en œuvre du retard distribué et donnons une méthode générale pour son approximation. Ensuite nous présentons trois applications à l'aide de retard distribué, qui sont différentes avec les applications apparaissent dans la littérature. Le premier est l'inversion stable et le modèle appariement. Nous introduisons une nouvelle classe d'inversion stable et modèle d'appariement pour les systèmes linéaires de dimension finie invariables dans le temps. L'inversion stable (resp. modèle d'appariement) est une sorte d'inversion (resp. modèle d'appariement) de rapprochement. En fait, nous obtenons l'inversion exacte (resp. exacte modèle d'appariement) après un temps t = h, où le temps t = h peut être choisi arbitrairement. La deuxième application est le contrôle de la stabilité et du pôle placement finie pour une classe de système de dimension infinie. La dernière application du retard distribué est la synthèse de l'observateur pour l'estimation ou la commande de sortie. Nous craignons seulement avec les systèmes linéaires de dimension finie. Nous introduisons une boucle fermée observateurs sans mémoire par injection d'entrée. Convergence asymptotique ainsi que la convergence en temps fini de l'estimation sont analysés par injection de sortie et des informations d'entrée via retard distribué. Enfin, nous introduisons une nouvelle classe de l’approximation des systèmes à paramètres distribués. Nous travaillons sur la topologie du graphe, et montrons que sous certaines hypothèses faibles, une telle approximation peut être réalisé en utilisant retard distribué. / A distributed delay is a linear input-output operators and appears in many control problems. We investigate distributed delay and its applications. After introducing the definition and the main properties of the distributed delay, the numerical implementation problem of distributed delays is analyzed and a general method for its approximation is given. Then three applications are focused on where distributed delay appears. The first application is the stable inversion and model matching. A new class of stable inversion and model matching problem for finite dimensional linear time-invariant systems is defined. The stable inversion (resp. model matching) is an approximation of the inverse of a given model (resp. model matching), where exact inversion (resp. exact matching) is reached after a time $t=h$, which is a parameter of our procedure. The second application is concerned with stabilization and finite spectrum assignment for a class of infinite dimensional systems. The last application concerns observer synthesis for estimation or output control. For linear finite dimensional systems. A closed-loop memoryless observer by input injection is introduced. Asymptotic convergence as well as finite time convergence of the estimation are analyzed by output injection and input information via distributed delay. At last, we introduce a new class for approximation of distributed parameter systems. We work on the graph topology, and show that under some weak assumptions, such an approximation can be realized using distributed delay.

Cette thèse concerne l’étude de la structure géologique de la Crimée orientale et de son prolongement en mer, le fossé Sorokin, dans le but de reconstruire l'évolution tectonique de la marge, inversée, au nord de la Mer Noire Orientale. Ces recherches ont été initiées car l’âge Trias supérieur-Jurassique inférieur des roches les plus anciennes, de type flysch, seraient en fait Albien (Crétacé inférieur) soit 60 à 110 millions d'années plus jeune. Force d'observations sur le terrain, de datations micropaléontologiques, d’une analyse structurale, avec une recherche des paléo-champs de contraintes, d'une analyse de profils de sismiques réflexion de la marge, notre étude permets de réactualiser et de clarifier la géologie de la Crimée orientale. Les principaux résultats de cette thèse sont les suivants : 1) grâce à nos nouvelles datations, les sédiments turbiditiques du Crétacé inférieur ont une plus grande répartition géographique; 2) deux formations de flysch ont été identifiées, l’une du Crétacé inférieur et l’autre du Trias supérieur-Jurassique Moyen (Groupe Tauric); 3) une carte structurale de la Crimée orientale a été réalisée qui permet de mettre en évidence une phase d'extension durant le Crétacé et deux phases compressives durant le Cénozoïque ; 4) ces deux phases compressives (Paléocène-Eocène inférieur et Oligocène-Pliocène moyen) sont confirmées par l’interprétations de 8 profils sismiques en mer qui ont été corrélés avec un forage (Subbotina 403) ; 5) la réalisation de deux transects Terre-Mer permettent de comprendre les structures liées à l'inversion de la marge ; 6) l'analyse des paléo-champs de contraintes révèle plusieurs régimes tectoniques liées aux développement des structures tectoniques; 8) finalement cette thèse propose un vision nouvelle de l'évolution tectonique de la marge nord de la mer Noire orientale, qui subit une inversion depuis le Paléocène, en présentant des cartes de reconstitutions de son évolution depuis le Trias supérieur. / This study is focused on the main structural features of the Eastern Crimean Mountains (CM) and of their closest offshore, with a purpose to derive and reconstruct the tectonic evolution of the northern inverted margin of the Eastern Black Sea. This study was inspired because the Late Triassic-Early Jurassic age of the oldest exposed flysch-like rocks (so-called Tauric Group) “was” defined as 60 to 110 my younger, namely as the Albian (Middle Cretaceous).The aim of this thesis was to obtain by field observations, new dating of rocks, structural analysis, stress-field analysis and seismic interpretation allowing reconsidering the geology of the CM. The main findings of the thesis are: (1) the Lower Cretaceous sediments have a much wider spatial distribution in the Eastern CM; (2) the presence of two flysch units of different age: the youngest flysch unit of the Early Cretaceous age and the oldest, the Tauric Gp and Middle-Jurassic flysch; (3) the structural analysis in the Eastern CM resulted in new structural geological map of the Eastern CM and showed the evidence of extensional tectonics during the Cretaceous and of compressional structures during the Cenozoic; (4) two-stage compression: 1) during the Paleocene-Early Eocene and 2) during the Oligocene-Middle Pliocene were confirmed by interpretation of seismic lines offshore, correlated with the “Subbotina-403” well; (5) both geological and geophysical data in the on-and- off shore transects evidence connection of structures in the northern inverted Black Sea margin; (6) the paleostress analysis of the brittle fault-slip data allow distinguishing of several tectonic regimes responsible for the developments of main tectonic structures of the study area; (8) finally, this thesis presents a new vision of the tectonic evolution of the northern inverted part of the Eastern Black Sea illustrated with paleotectonic maps providing the reconstruction for each main stage of its geological history since the Late Triassic.