We discuss a systematic methodology that leads to the reconstruction of the material profile of either single, or assemblies of one-dimensional flexural components endowed with Timoshenko-theory assumptions. The probed structures are subjected to user-specified transient excitations: we use the complete waveforms, recorded directly in the time-domain at only a few measurement stations, to drive the profile reconstruction using a partial-differential-equation-constrained optimization approach. We discuss the solution of the ensuing state, adjoint, and control problems, and the alleviation of profile multiplicity by means of either Tikhonov or Total Variation regularization. We report on numerical experiments using synthetic data that show satisfactory reconstruction of a variety of profiles, including smoothly and sharply varying profiles, as well as profiles exhibiting localized discontinuities. The method is well suited for imaging structures for condition assessment purposes, and can handle either diffusive or localized damage without need for a reference undamaged state. / text

L’évaluation des formations géologiques consiste en l’analyse et la synthèse de données de différentes sources, de différentes échelles (microscopique à kilométrique) et acquises à des dates très variables. Le processus conventionnel de caractérisation des formations relève alors de l’interprétation physique spécialisée de chacune de ces sources de données et leur mise en cohérence par des processus de synthèse essentiellement d’ordre statistique (corrélation, apprentissage, up-scaling…). Il s’avère cependant qu’une source de données présente un caractère central : les diagraphies. Ces mesures physiques de différentes natures (nucléaires, acoustiques, électromagnétiques…) sont réalisées le long de la paroi d’un puits à l’aide de différentes sondes. Elles sont sensibles aux propriétés in situ des roches, et ce, sur une gamme d’échelle centimétrique à métrique intermédiaire aux carottes et données de test de production. De par leur profondeur d’investigation, les données diagraphiques sont particulièrement sensibles au phénomène d’invasion de boue se produisant lors du forage dans l’abord puits. Traditionnellement, l’invasion est modélisée de façon frustre au moment de l’interprétation diagraphiques par un simple effet piston. Ce modèle simple permet d’honorer le bilan de volume mais ne prend aucunement en compte la physique réelle d’invasion et prive, de fait, les diagraphies de toute portée dynamique. Des essais de modélisation de l’historique d’invasion couplés aux données diagraphiques ont déjà été élaborés par différents laboratoires et une abondante littérature sur le sujet est disponible. Les limitations majeures de ces approches résident dans le caractère sous déterminé des problèmes inverses issus de ces modèles physiques et dans le fait que la donnée diagraphique est réalisée en général sur un intervalle de temps inadaptée au regard du développement de l’invasion. Nous proposons une approche différente qui s’attèle non pas à décrire la physique de l’écoulement mais celle de l’équilibre radial des fluides dans le domaine envahi lorsque les diagraphies sont acquises. Nous montrons qu’en introduisant quelques contraintes pétrophysiques supplémentaires, il est possible d’inverser efficacement la distribution des propriétés dynamiques pour chaque faciès géologique. L’inversion prend en compte le phénomène d’invasion radial dans la zone à eau ainsi que l’équilibre capillaire vertical caractérisant le profil de saturation dans le réservoir pour chaque facies. A chaque profondeur du puits, sont ainsi obtenues perméabilités, pressions capillaires et facteurs de cimentation avec leurs incertitudes ainsi que les lois pétrophysiques propres à chaque faciès. Cette méthode a été appliquée à deux puits réels. En guise de validation, les résultats d’inversion ont été comparés aux mesures laboratoire faites sur carotte. De plus, les perméabilités inversées ont été comparées aux transitoires de pression de mini-tests. La cohérence des résultats montre que, d’une part, les hypothèses de base du modèle sont validées et que, d’autre part, l’approche fournit une estimation fiable de grandeurs dynamiques à toute échelle pour chaque faciès réservoir, et ce, dès l’acquisition des données diagraphiques. L’approche d’inversion proposée a permis de lever une limitation majeure des précédentes tentatives de prédiction des propriétés dynamiques par les diagraphies en reconsidérant la problématique non pas sous l’angle d’une modélisation phénoménologique exacte mais en l’abordant de manière globale à l’échelle d’une chaîne d’étude complète. Cette approche permet de fait une mise en cohérence très précoce des données, d’identifier les faciès d’intérêt et de qualifier les besoins véritables en données. Cet outil s’avère très puissant pour qualifier et caractériser les hétérogénéités pétrophysiques des formations et aider ainsi à résoudre le problème de mise à l’échelle des grandeurs dynamiques / The current geological formation evaluation process is built on a workflow using data from differentsources, different scales (microscopic to kilometric) and acquired at different times. Theconventional process of formation evaluation belongs to the dedicated study of each of thesesource of data and their reconciliation through a synthesis step, often based on statisticalconsideration (correlation, learning, up-scaling …). It turns out that there exists a source of datawhich is of considerable importance: logs. These physical measurements of different nature(nuclear, acoustic, electro-magnetic…) are acquired all across the well thanks to multiple probes.They are sensitive to the in situ properties of the rock on an intermediate scale between core dataand well tests (from centimeters to several meters). Because of their depth of investigation, logsare particularly sensitive to the mud filtrate invasion, a phenomenon which occurs during thedrilling in the near well-bore environment. The invasion is conventionally modeled in a rough waywith a piston effect hypothesis. This simple model allows to ensure the volume balance but doesnot take into account the physical processes of the invasion and thus prevent any estimation ofdynamic properties from log interpretation. Several attempts of simulating the complete history ofinvasion have been made by different laboratories in the past, and a rich literature is available onthis topic. The major pitfalls of these approaches come from the under-determination of theinverse problems derived from such models. Furthermore, logs are generally made in a time lapsewhich does not allow to fully characterize the process of invasion. We propose a differentapproach which does not fully describe the physics of the invasion but considers that a radialequilibrium has been reached between the fluids in the invaded zone when logs are acquired. Weshow that it is possible to efficiently invert the distribution of dynamical properties for eachgeological facies by adding some petrophysical constraints. The inversion takes into account thephenomenon of radial invasion in the water zone and the vertical capillary equilibrium describingthe water saturation profile in the reservoir for each facies. At each depth, permeabilities, capillarypressures and cementation factors are thus obtained, along with their uncertainties and thepetrophysical laws specific to each facies. This method has been applied to two wells. Weobtained good results when comparing inverted parameters to the measurements made on coresamples in laboratory. Furthermore, inverted permeabilities have also been compared topermeabilities derived from mini-tests. The consistency of the results shows that, on the one hand,the hypothesis behind our model are valid and, on the other hand, this approach can provide areliable estimation of dynamical parameters at different scales for each reservoir facies as soon asthe logs are acquired. The proposed approach allows to overcome a major limitation of theprevious attempts of the dynamical properties estimation from log interpretation. It allows areconciliation of different data and a facies recognition at an early stage of interpretation, and canindicate the real contribution of each source of data. The technique can even help in identifying theformation heterogeneities and for the petrophysical upscaling.

A Tomografia de Impedância Elétrica é uma técnica de obtenção de imagens não invasiva que pode ser usada em aplicações clínicas para estimar a impeditividade dos tecidos a partir de medidas elétricas na superfície do corpo. Matematicamente este é um problema inverso, não linear e mal posto. Geralmente é usado um filtro espacial Gaussiano passa alta como método de regularização para resolver o problema inverso. O objetivo principal deste trabalho é propor o uso de informação estatística fisiológica e anatômica da distribuição de resistividades dos tecidos do tórax, também chamada de atlas anatômico, em conjunto com o filtro Gaussiano como métodos de regularização. A metodologia proposta usa o método dos elementos finitos e o algoritmo de Gauss-Newton para reconstruir imagens de resistividade tridimensionais. A Teoria do Erro de Aproximação é utilizada para reduzir os erros relacionados à discretização e dimensões da malha de elementos finitos. Dados de tomografia de impedância elétrica e imagens de tomografia computadorizada coletados in vivo em um suíno com diferentes alterações fisiológicas pulmonares foram utilizados para validar o algoritmo proposto. As imagens obtidas foram consistentes com os fenômenos de atelectasia, derrame pleural, pneumotórax e variações associadas a diferentes níveis de pressão durante a ventilação mecânica. Os resultados mostram que a reconstrução de imagens de suínos com informação clínica significativa é possível quando tanto o filtro Gaussiano quanto o atlas anatômico são usados como métodos de regularização. / Electrical Impedance Tomography is a non invasive imaging technique that can be used in clinical applications to infer living tissue impeditivity from boundary electrical measurements. Mathematically this is an non-linear ill-posed inverse problem. Usually a spatial high-pass Gaussian filter is used as a regularization method for solving the inverse problem. The main objective of this work is to propose the use of physiological and anatomical priors of tissue resistivity distribution within the thorax, also known as anatomical atlas, in conjunction with the Gaussian filter as regularization methods. The proposed methodology employs the finite element method and the Gauss-Newton algorithm in order to reconstruct three-dimensional resistivity images. The Approximation Error Theory is used to reduce discretization effects and mesh size errors. Electrical impedance tomography data and computed tomography images of physiological pulmonary changes collected in vivo in a swine were used to validate the proposed method. The images obtained are compatible with atelectasis, pneumothorax, pleural effusion and different ventilation pressures during mechanical ventilation. The results show that image reconstruction from swines with clinically significant information is feasible when both the Gaussian filter and the anatomical atlas are used as regularization methods.

<div>Near-Field Acoustical Holography (NAH) is an inverse process in which sound pressure measurements made in the near-field of an unknown sound source can be used to reconstruct the sound field so that source locations can be identified. Usually a large number of measurements is required for the usual NAH methods since a large number of parameters in the source or field model need to be determined. However, a large-scale microphone measurement is costly and hard to perform, so the use of NAH is limited by practical experimental conditions. In the present work, with the motivation of decreasing the number of microphone measurements required, and thus facilitating the measurement process, two sparse Equivalent Source Method (ESM) algorithms were studied: i.e., Wideband Acoustical Holography (WBH) and l_1-norm minimization. Based on these two algorithms, a new hybrid NAH procedure was proposed and demonstrated.To study and verify the above mentioned algorithms, simulations of different sources were conducted and then experiments were conducted on different sources: i.e., a loudspeaker cabinet and a diesel engine.</div>

Esta dissertação apresenta um estudo sobre a utilização de tomografia acústica para reconstruir a distribuição interna de temperaturas de um corpo ou escoamento. Para tanto, o problema inverso foi modelado matematicamente a partir da equação de propagação acústica e de um funcional de erro quantificando a sensibilidade dos perfis de pressão acústica externa relativamente a variações na distribuição interna de impedância acústica. Simulações numéricas foram realizadas em um modelo de um problema real, tendo sido testadas duas técnicas de excitação, a clássica tipo Dirac e uma estratégia otimizada segundo um perfil triangular. / This work presents a study about the utilization of acoustic tomography to reconstruct the internal temperature distribution of a body or a flow. To do this, the inverse problem was mathematically modeled from the acoustic propagation equation and a error functional quantifying the sensitivity of external acoustic pressure profile according to changes in the internal acoustic impedance distribution. Numerical simulations were done in a real problem model, two excitation techniques were tested, the classical Dirac type and a optimized strategy with a triangular profile.

The primary objective of this research was to investigate the feasibility of calibrating ultrasound scanners to measure surface impedance from reflection data. The method proposed uses calibration curves from known impedance interfaces. This plot, or calibration curve, may then be used, with interpolation, to relate measured grey level to impedance for the characterization of tissue specimens with unknown properties. This approach can be used independent of different medical ultrasound scanner systems to solve for reproducible tissue impedance values without offline data processing and complicated custom electronics. <p>Two medical ultrasound machines from different manufacturers were used in the experiment; a 30 MHz and a 7.5 MHz machine. The calibration curves for each machine were produced by imaging the interfaces of a vegetable oil floating over varying salt solutions. <p>To test the method, porcine liver, kidney, and spleen acoustical impedances were determined by relating measured grey levels to reflection coefficients using calibration curves and then inverting the reflection coefficients to obtain impedance values. The 30 MHz ultrasound machines calculated tissue impedances for liver, kidney, and spleen were 1.476 ± 0.020, 1.486 ± 0.020, 1.471 ± 0.020 MRayles respectively. The 7.5 MHz machines tissue impedances were 1.467 ± 0.088, 1.507 ± 0.088, and 1.457 ± 0.088 MRayles respectively for liver, kidney and spleen. The differences between the two machines are 0.61%, 1.41%, and 0.95% for the impedance of liver, kidney, and spleen tissue, respectively. If the grey level is solely used to characterize the tissue, then the differences are 45.9%, 40.3%, and 39.1% for liver, kidney, and spleen between the two machines. The results support the hypothesis that tissue impedance can be determined using calibration curves and be consistent between multiple machines.

This thesis proposes a new proof of the acoustic transparency theorem for material with a bounded variation. The theorem states that if the material properties (density, bulk modulus) is of bounded variation, the net power transmitted through the point z = 0 over a time interval [−T,T] is greater than some constant times the energy at the time zero over a spatial interval [0,Z], provided that T equals the time of travel of a wave from 0 to Z. This means the reflected energy of an input into the earth will be received. Otherwise, the reflections may not arrive at the surface. A proof gives a lower bound for material properties (density, bulk modulus) with bounded variation using sideways energy estimate. A different lower bound that works only for piecewise constant coefficients is also given. It gives a lower bound by analyzing reflections and transmissions of the waves at the jumps of the material properties. This thesis also gives an example to illustrate that the bounded variation assumption may not be necessary for the medium to be transparent. This thesis also discusses relations between the transparency property and the data of an inverse problem.

This thesis provides an introduction to and analysis of the problem of determining nuclear magnetic resonance (NMR) relaxation times of porous media by using the so-called Carr-Purcell-Meiboom-Gill (CPMG) technique. We introduce the principles of NMR, the CPMG technique and the signals produced, porous effects on the NMR relaxation times and discuss various numerical methods for the inverse problem of extracting the relaxation times from CPMG signals. The numerical methods for solving Fredholm integral equations of the first kind are sketched from a series expansion perspective. A method of using arbitrary constituent functions for improving the performance of non-negative least squares (NNLS) is developed and applied to several synthesized data sets and real experimental data sets of saturated porous glass gels. The data sets were obtained by the author of this thesis and the experimental procedure will be presented. We discuss the imperfections in the assumptions on the physical and numerical models, the numerical schemes, and the experimental results, which may lead to new research possibilities.

This thesis provides an introduction to and analysis of the problem of determining nuclear magnetic resonance (NMR) relaxation times of porous media by using the so-called Carr-Purcell-Meiboom-Gill (CPMG) technique. We introduce the principles of NMR, the CPMG technique and the signals produced, porous effects on the NMR relaxation times and discuss various numerical methods for the inverse problem of extracting the relaxation times from CPMG signals. The numerical methods for solving Fredholm integral equations of the first kind are sketched from a series expansion perspective. A method of using arbitrary constituent functions for improving the performance of non-negative least squares (NNLS) is developed and applied to several synthesized data sets and real experimental data sets of saturated porous glass gels. The data sets were obtained by the author of this thesis and the experimental procedure will be presented. We discuss the imperfections in the assumptions on the physical and numerical models, the numerical schemes, and the experimental results, which may lead to new research possibilities.

The primary objective of this research was to investigate the feasibility of calibrating ultrasound scanners to measure surface impedance from reflection data. The method proposed uses calibration curves from known impedance interfaces. This plot, or calibration curve, may then be used, with interpolation, to relate measured grey level to impedance for the characterization of tissue specimens with unknown properties. This approach can be used independent of different medical ultrasound scanner systems to solve for reproducible tissue impedance values without offline data processing and complicated custom electronics. <p>Two medical ultrasound machines from different manufacturers were used in the experiment; a 30 MHz and a 7.5 MHz machine. The calibration curves for each machine were produced by imaging the interfaces of a vegetable oil floating over varying salt solutions. <p>To test the method, porcine liver, kidney, and spleen acoustical impedances were determined by relating measured grey levels to reflection coefficients using calibration curves and then inverting the reflection coefficients to obtain impedance values. The 30 MHz ultrasound machines calculated tissue impedances for liver, kidney, and spleen were 1.476 ± 0.020, 1.486 ± 0.020, 1.471 ± 0.020 MRayles respectively. The 7.5 MHz machines tissue impedances were 1.467 ± 0.088, 1.507 ± 0.088, and 1.457 ± 0.088 MRayles respectively for liver, kidney and spleen. The differences between the two machines are 0.61%, 1.41%, and 0.95% for the impedance of liver, kidney, and spleen tissue, respectively. If the grey level is solely used to characterize the tissue, then the differences are 45.9%, 40.3%, and 39.1% for liver, kidney, and spleen between the two machines. The results support the hypothesis that tissue impedance can be determined using calibration curves and be consistent between multiple machines.