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.

Bien que les modèles hydrologiques soient aujourd'hui utilisés pour la prévision des crues, leur mise en place sur un territoire particulier peut encore poser question. Classiquement, elle nécessite des chronologies observées de pluies et de débits. Cependant, ces données peuvent s'avérer incertaines, insuffisantes voire indisponibles. Cela impact alors l'identification des modèles ainsi que leurs prévisions en les rendant elles-mêmes incertaines et potentiellement inopérantes.Dans cette thèse, nous avons cherché à revisiter ces problématiques liées à la mise en place des modèles, en proposant des approches innovantes étalonnant les modèles sans certaines données pouvant s'avérer trop incertaines ou indisponibles. Ces dernières, habituellement exigées pour l'identification des modèles, sont de plus estimées au cours de l'étalonnage. Deux méthodes applicables quelque-soit la nature du modèle considéré sont proposées. La première est une méthode d'inversion des pluies et des paramètres. Elle permet d'étalonner un modèle hydrologique à partir de chronologies observées de débits et de cumuls de pluies seulement. Cette méthode identifie de plus simultanément les chronologies des pluies au pas de temps horaire. Une application particulière de cette méthode à des modèles déjà établis généralise par ailleurs à des modèles non-analytiques l'approche d'inversion des pluies proposée par Kirchner (2009). La seconde est une méthode de calibration pluie-hauteur d'eau. À partir de chronologies observées de pluies et de hauteurs d'eau seulement, elle permet de mettre en place un modèle hydrologique et d'identifier une courbe de tarage. Outre les analyses originales pouvant être menées sur les chronologies de pluies ou les courbes de tarage estimées par ces méthodes, ces dernières étendent à des contextes plus restreints en données, la possibilité d'identification de modèles pluie-débits et offrent des applications en opérationnel.En parallèle du développement de ces méthodes, cette thèse nous a aussi amené à construire une représentation conceptuelle appelée espace des connaissances. Celle-ci permet d'appréhender de manière commune les questions nouvelles ayant été étudiées ainsi que des approches plus classiques comme la calibration ou la simulation. / Rainfall-runoff models are used for flood forecasting by warning authorities. However their implementation on a particular territory is still a challenge. Indeed, they generally need to be calibrated by using observed rainfall and discharge time series. These data may be subject to errors and uncertainties. They are not always available. Then, the model calibration relevancy may be affected and the forecasts may also be subject to significant uncertainties. This research would like to address such issues related to the rainfall-runoff models calibration, by proposing original methods which may set up a model by using less data than the ``classical'' calibration. The unused data might be either subject to uncertainties or not available. Moreover, these unused data may be estimated by the methods. Two model independant approach were suggested. Both are an heuristic inversion algorithm of rainfall-runoff models. The first method estimates simultaneously hourly rainfall time series and models parameters, by using only observed hourly discharge time series and total areal rainfall of flood events. A specific application of this method to set up models (with fixed parameters), generalises to models which are not invertible analyticaly, the ``hydrology backward'' approach proposed by Kirchner (2009).The second method estimates simultaneously models parameters and a rating-curve, by using only observed hourly rainfall and stage time series. Original analysis may be performed on the rainfall time series and the rating-curve estimated by the methods. Also, they extend the applicability rainfall-runoff models to hydrological context with restricted available data and offer promising operational applications. Yet, this research lead us to build a conceptual framework, denoted knowledge space. This framework unifies not only the original approaches which were proposed, but also some more ``classical'' approaches to hydrology as the calibration and the simulation.

Title: The source process of Greek earthquakes Author: Dana K ížová Department: Department of Geophysics Supervisor of the doctoral thesis: Prof. RNDr. Ji í Zahradník DrSc., Department of Geophysics Abstract: Investigations of moment tensor (MT) and its uncertainty are topical. This thesis is focused on isotropic component of three shallow earthquakes: Event A in Cretan Sea (Mw 5.3) and two events near Santorini island, B (Mw 4.9) and C (Mw 4.7). MT is inverted from full waveforms in an assumed 1D velocity model. The inverse problem is non-linear in centroid depth and time, and linear in six MT parameters, one is the MT-trace. Uncertainty of isotropic component is studied by a new approach (K ížová et al., 2013). The trace is systematically varied, and remaining parameters are optimized. The method reveals tradeoffs between the isotropic component, depth, time, and focal mechanism. From two existing velocity models, we prefer the one with lower condition number, in which a (positive) isotropic component is indicated for event B. To rapidly assess a likely existence of isotropic component, an empirical method is proposed (K ížová et al., 2016). It is based on comparison between depth- dependences of waveform correlation in full and deviatoric modes. Based on extensive synthetic tests, the method confirms a...

Audiomagnetotelluric measurements with (CSAMT) and without (AMT) a controlled source were performed near Gällivare and Kiruna in Swedish Lapland in order to retrieve representative conductivity models of the subsurfaces. Magnetotelluric transfer functions were gained from processed time series’ and subsequently inverted to generate the sought models successfully. Additionally, a strike angle analysis was performed to determine the dimension of the ground structures. That information was used to justify the approaches of 1D and 2D inversions of the data sets and to judge their applicability. In Kiruna, two profiles were installed. One profile is considered to be in line with the strike direction, the other profile was oriented rather orthogonal to the strike direction. In Gällivare, only one profile was installed orthogonally with respect to the strike direction. The strike analysis showed a preferentially 2-dimensional structure for Kiruna’s parallel profile. For the orthogonal oriented profiles from Kiruna and Gällivare, the analysis revealed a 2D (with distortions) to 3D dimension of the ground structures. For the AMT method, it was possible to generate 1-dimensional and 2-dimensional models. Regarding the CSAMT data, it was only possible to generate a 1D conductivitymodel for the subsurface. Due to a significant transmitter overprint, no undistorted start model for the 2-dimensional CSAMT data inversion could be produced. The models from Kiruna had a sufficient data quality and thus resulted in reliable 2D AMT resistivity models with, locally, 2 to 3 layers. However, in combination with the 1D models for AMT and CSAMT, a 3-layer structure was predicted, where a resistive layer is covered by a thin conductive layer and underlaid by a rather conductive basement. For Gällivare’s profile, the data quality was good such that for all inversion methods good results were achieved. The predicted 2-layer models were resolved for for depths between 10m and 10,000m and coincide with the at hand geological maps and cross sections.

This thesis presents Bayesian geoacoustic inversion of seabed reflection-coefficient data as part of the U.S. Office of Naval Research Seabed Characterization Experiment 2017 at the New England Mud Patch. First, a linearized, ray-based Bayesian inversion of acoustic arrival times is carried out for high-precision estimation of experiment geometry and uncertainties, representing an important first step to inferring seabed properties using geoacoustic inversion methods such as reflection inversion. The high-precision estimates for source-receiver ranges, source depths, receiver depths, and water depths at reflection points along the survey track are used to calculate grazing angles, with angle uncertainties computed using Monte Carlo methods. The experiment geometry uncertainties are obtained using analytic linearized estimates, and verified with nonlinear analysis. Second, a trans-dimensional (trans-D) Bayesian inversion of reflection-coefficient data is carried out for geoacoustic parameters and uncertainties of fine-grained/cohesive sediments. The trans-D inversion samples probabilistically over an unknown number of seabed interfaces and the parameters of a zeroth- or first-order autoregressive error model. The numerical method of parallel tempering reversible jump Markov-chain Monte Carlo sampling is employed. Spherical-wave reflection coefficient modelling is applied using plane-wave decomposition in the Sommerfeld integral. The inversion provides marginal posterior probability profiles for Buckingham's viscous grain-shearing parameters: porosity, grain-to-grain compressional modulus, material exponent, and compressional viscoelastic time constant as a function of depth in the sediment. These parameters are used to compute dispersion relationships for each layer in the model, providing marginal posterior probability profiles for compressional-wave velocity and attenuation at different frequencies, as well as density. The geoacoustic inversion results are compared to independent measurements of sediment properties. / Graduate

This thesis applies three-dimensional (3-D) non-linear seismic tomography to image crustal/upper mantle structure of S.W. British Columbia and N.W. Washington. Two tomographic inversions are carried out including high-resolution imaging of upper crustal structure using controlled source data, and deeper imaging by simultaneous inversion of controlled source and earthquake data. Non-linear first arrival travel-time tomography is applied to controlled source data from the Seismic Hazards Investigation of Puget Sound (SHIPS) experiment conducted in 1998. Nearly 175,000 first arrival travel-times are inverted to obtain a minimum structure upper crustal velocity model to a depth of 12 km with a cubical cell size of 1 km. Results from checker-board tests for this velocity model indicate a lateral resolution of 20 km and above. The main geological and structural features in the study area are well defined by this velocity model. The structural outline of the sedimentary basins in the Straits of Georgia and Juan de Fuca are distinctly mapped. The Crescent Terrane is mapped beneath southern Vancouver Island with velocities up to 7 km/s that correlate well with the presence of gabbro in the subsurface. The northwest-southeast structural trend observed in the Strait of Georgia correlates with the observed seismicity. Shallow seismicity observed at the southern tip of Vancouver Island correlates with the location of the Leech River Fault. An earthquake tomography algorithm was developed for joint estimation of hypocentral and velocity parameters, and tested on a synthetic data set. Using this algorithm, tomographic inversion was performed simultaneously on earthquake and controlled source data from southwestern British Columbia and northwestern Washington. Approximately 15,000 first arrivals from 1,400 earthquakes and 40,000 first arrivals from the SHIPS experiment were simultaneously inverted for hypocentral parameters and velocity structure. Model resolution studies indicate a lateral resolution of 30 km and above. Upper-crustal earthquakes close to southern Vancouver Island correlate with the velocity contrasts associated with the Leech River, Southern Whidbey Island, and Darrington-Devils Mountain faults. Three mafic to ultramafic high velocity units are identified at approximately 25 km depth beneath the Crescent Terrane and above the subducting Juan de Fuca crust. The continental crust and subducting Juan de Fuca crust and mantle are well mapped. The transition zone to continental mantle occurs at 35 km depth beneath the eastern Strait of Georgia. The slab seismicity beneath the Strait of Georgia at depths >65 km lies below a low velocity zone mapped in the mantle wedge at depths of about 45–55 km. This low velocity zone may be indicative of the presence of fluids released during the phase change from basalt/gabbro to eclogite in the subducting slab. / Graduate

Made available in DSpace on 2014-06-11T19:25:29Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-12-12Bitstream added on 2014-06-13T20:33:08Z : No. of bitstreams: 1 furtadoneto_a_me_guara.pdf: 575510 bytes, checksum: 6a1a49e71ce6fbc8113435f66d99a240 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O foco deste trabalho é o espectro de inversão da molécula de amônia, resultado do fenômeno do tunelamento quântico. Para isso, usamos um modelo simpli cado, uni- dimensional, suscetível a uma análise teórica rigorosa usando a mecânica quântica não- relativística. Dentre as diversas funções hamiltonianas já estudadas para este modelo, zemos uma rápida apreciação dos trabalhos de Cohen, Dennison-Uhlenbeck, Manning, Merzbacher e Rosen-Morse. Para um estudo mais profundo, usamos o potencial do poço duplo nito que, posteriormente, descobrimos já fora analisado por Peacock-López. Re- zemos a análise deste potencial usando um caminho diferente do realizado por aquele autor. Analisamos os casos limites para este potencial e notamos que realmente, nesses regimes, ele tende para um poço nito único ou dois poços nitos separados. Então, de- senvolvemos um software grá co centrado no pacote MINUIT, desenvolvido pelo CERN, para analisar e ajustar os parâmetros aos dados experimentais da amônia e, ao nal, comparamos os resultados obtidos com aqueles encontrados na literatura. No ajuste dos parâmetros à amônia, houve uma melhoria acentuada quando passamos de uma fórmula mais simples da massa reduzida para outra mais so sticada. No caso especí co do po- tencial de Peacock-López, a comparação revela que os nossos resultados, de uma maneira geral, são mais precisos. Nossa análise se soma àquelas que contêm uma discussão quan- titativa do potencial de poço duplo. Como parte integrante deste trabalho, uma versão unidimensional simétrica do potencial de Morse foi exatamente resolvida em termos de funções de Kummer e um par de equações transcendentes para as autoenergias. A tentativa de ajustar este resultado à molécula de amônia, porém, mostrou que os padrões de poço duplo deste potencial... / The focus of this work is the inversion spectrum of the ammonia molecule, a result of the phenomenon of quantum tunneling. For this, we use a simpli ed, one-dimensional model, amenable to a rigorous theoretical analysis using the non-relativistic quantum me- chanics. Among the various Hamiltonian functions previously studied for this model, we made a quick appraisal of the work of Cohen, Dennison-Uhlenbeck, Manning, Merzbacher and Rosen-Morse. For a deeper study, we used the nite double-well potential which, as we later discovered, had been considered by Peacock-López. We redid the analysis of this potential using a di¤erent path made by that author. We analyze the limiting cases for this potential and actually noticed that in these schemes, it tends to one nite well or two separate nite wells. So, we developed a graphical software centered on the MINUIT pack- age, developed by CERN, to analyze and adjust the parameters to the experimental data of ammonia and at the end, we compared the results with those found in the literature. In setting the parameters of ammonia, there was a marked improvement when we move from a simpler formula for the reduced mass to a more sophisticated one. In the speci c case of the potential of Peacock-López, the comparison shows that our results, in general, are more accurate and precise. Our analysis adds to those that contain a quantitative discussion of the double-well potential. As part of this work, a symmetric one-dimensional version of the Morse potential is exactly solved in terms of the Kummer functions and a pair of transcendental equations for the eigenenergies. Attempting to adjust this result to the ammonia molecule, however, showed that the double-well patterns of this potential well are irreconcilable with the energy spectrum of ammonia: Close pairs separated by long intervals

Orientador: Antonio Soares de Castro / Banca: Denis Dalmazi / Banca: Manuel Bastos Malheiro de Oliveira / Resumo: O foco deste trabalho é o espectro de inversão da molécula de amônia, resultado do fenômeno do tunelamento quântico. Para isso, usamos um modelo simpli…cado, uni- dimensional, suscetível a uma análise teórica rigorosa usando a mecânica quântica não- relativística. Dentre as diversas funções hamiltonianas já estudadas para este modelo, …zemos uma rápida apreciação dos trabalhos de Cohen, Dennison-Uhlenbeck, Manning, Merzbacher e Rosen-Morse. Para um estudo mais profundo, usamos o potencial do poço duplo …nito que, posteriormente, descobrimos já fora analisado por Peacock-López. Re- …zemos a análise deste potencial usando um caminho diferente do realizado por aquele autor. Analisamos os casos limites para este potencial e notamos que realmente, nesses regimes, ele tende para um poço …nito único ou dois poços …nitos separados. Então, de- senvolvemos um software grá…co centrado no pacote MINUIT, desenvolvido pelo CERN, para analisar e ajustar os parâmetros aos dados experimentais da amônia e, ao …nal, comparamos os resultados obtidos com aqueles encontrados na literatura. No ajuste dos parâmetros à amônia, houve uma melhoria acentuada quando passamos de uma fórmula mais simples da massa reduzida para outra mais so…sticada. No caso especí…co do po- tencial de Peacock-López, a comparação revela que os nossos resultados, de uma maneira geral, são mais precisos. Nossa análise se soma àquelas que contêm uma discussão quan- titativa do potencial de poço duplo. Como parte integrante deste trabalho, uma versão unidimensional simétrica do potencial de Morse foi exatamente resolvida em termos de funções de Kummer e um par de equações transcendentes para as autoenergias. A tentativa de ajustar este resultado à molécula de amônia, porém, mostrou que os padrões de poço duplo deste potencial... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract:The focus of this work is the inversion spectrum of the ammonia molecule, a result of the phenomenon of quantum tunneling. For this, we use a simpli…ed, one-dimensional model, amenable to a rigorous theoretical analysis using the non-relativistic quantum me- chanics. Among the various Hamiltonian functions previously studied for this model, we made a quick appraisal of the work of Cohen, Dennison-Uhlenbeck, Manning, Merzbacher and Rosen-Morse. For a deeper study, we used the …nite double-well potential which, as we later discovered, had been considered by Peacock-López. We redid the analysis of this potential using a di¤erent path made by that author. We analyze the limiting cases for this potential and actually noticed that in these schemes, it tends to one …nite well or two separate …nite wells. So, we developed a graphical software centered on the MINUIT pack- age, developed by CERN, to analyze and adjust the parameters to the experimental data of ammonia and at the end, we compared the results with those found in the literature. In setting the parameters of ammonia, there was a marked improvement when we move from a simpler formula for the reduced mass to a more sophisticated one. In the speci…c case of the potential of Peacock-López, the comparison shows that our results, in general, are more accurate and precise. Our analysis adds to those that contain a quantitative discussion of the double-well potential. As part of this work, a symmetric one-dimensional version of the Morse potential is exactly solved in terms of the Kummer functions and a pair of transcendental equations for the eigenenergies. Attempting to adjust this result to the ammonia molecule, however, showed that the double-well patterns of this potential well are irreconcilable with the energy spectrum of ammonia: Close pairs separated by long intervals / Mestre

Since they were first envisioned, quantum computers have oft been portrayed as devices of limitless power, able to perform calculations in a mere instant that would take current computers years to determine. This is, of course, not the case. A huge amount of effort has been invested in trying to understand the limits of quantum computers---under which circumstances they outperform classical computers, how large a speed-up can be gained, and what draws the distinction between quantum and classical computing. In this Ph.D. thesis, I investigate a few intriguing properties of quantum computers involving quantum oracles and classically-simulatable quantum circuits. In Part I I study the notion of black-box unitary operations, and procedures for effecting the inverse operation. Part II looks at how quantum oracles can be used to test properties of probability distributions, and Part III considers classes of quantum circuits that can be simulated efficiently on a classical computer. In more detail, Part I studies procedures for inverting black-box unitary operations. Known techniques are generally limited in some way, often requiring ancilla systems, working only for restricted sets of operators, or simply being too inefficient. We develop a novel procedure without these limitations, and show how it can be applied to lift a requirement of the Solovay-Kitaev theorem, a landmark theorem of quantum compiling. Part II looks at property testing for probability distributions, and in particular considers a special type of access known as the \textit{conditional oracle}. The classical conditional oracle was developed by Canonne et al. in 2015 and subsequently greatly explored. We develop a quantum version of this oracle, and show that it has advantages over the classical process. We use this oracle to develop an algorithm that decides whether or not a mixed state is fully mixed. In Part III we study classically-simulatable quantum circuits in more depth. Two well-known classes are Clifford circuits and matchgate circuits, which we briefly review. Using these as inspiration, we use the Jordan-Wigner transform to develop new classes of non-trivial quantum circuits that are also classically simulatable.

Neste trabalho analisamos o movimento de carga espacial monopolar livre em dielétricos, procurando fornecer subsídios para a interpretação de resultados experimentais. São mostradas as soluções para diversos tipos de distribuições iniciais de carga. A partir daí são encontradas relações que nos levam a algumas conclusões a respeito da relação entre distribuição e corrente externa produzida. São propostos métodos para a determinação da mobilidade dos portadores de carga no dielétrico e da concavidade de uma distribuição desconhecida. Analisamos também as condições para o aparecimento de inversão de corrente / On this work, we study the monopolar space charge motion in dielectrics in the aim of providing general information about it to the experimentalist. The electric current is obtained for many initial charge distributions and some relations are derived linking the behavior of the current to the initial charge distribution. We propose methods for obtaining the mobility of the carriers from experimental results. Finally the conditions for observation of current reversals are analyzed