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1
Kamm, Jochen. « Inversion and Joint Inversion of Electromagnetic and Potential Field Data ». Doctoral thesis, Uppsala universitet, Geofysik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-215673.
Texte intégralRésumé :
In this thesis, four inversion problems of different scale and difficulty are solved. Two of them are electromagnetic inverse problems. Two more are joint inversion problems of potential field data and other types of data. First, a linear approximation, which is a generalization of the low-induction-number approximation standard in slingram dual-loop interpretation is developed and used for rapid two and three dimensional inversion. The approximation takes induction within a background half-space into account and can thus be applied in conductive scenarios, where otherwise a rigorous electromagnetic modeling would be required. Second, a three-dimensional inversion of airborne tensor very-low-frequency data with a rigorous forward modeling at its core is developed. For dealing with the large scale of the forward problem, a nested fast-Fourier-transform-based integral equation method is introduced, wherein electromagnetic interactions are arranged according to their range and larger ranges are treated with less accuracy and effort. The inversion improves the traditional interpretation through data derived maps by providing a conductivity model, thus constraining the upper few hundred meters of the crust down to the shallowest conductor and allowing the study of its top in three dimensions. The third inversion problem is the the joint inversion of refraction and geoelectric data. By requiring the velocity and resistivity models to share a common, laterally variable layered geometry, easily interpretable models, which are reasonable in many geological near surface situations (e.g., groundwater exploration in Quaternary sediments), are produced directly from the joint inversion. Finally, a joint inversion of large scale potential field data from a gabbro intrusion is presented. Gravity and magnetic data are required to abide to a petrophysical constraint, which is derived from extensive field sampling. The impact of the constraint is maximized under the provision that both data sets are explained equally well as they would be through individual inversions. This leads to a simple and clearly defined intrusion geometry, consistent for both the density and magnetic susceptibility distribution. In all presented inversion problems, field data sets are successfully inverted, the results are appraised through synthetic tests and, if available, through comparison with independent data.Diese Arbeit hat die Lösung von vier geophysikalischen Umkehraufgaben, sogenannten Inversionsproblemen, zum Gegenstand. Zwei dieser Aufgaben befassen sich mit der Inversion elektromagnetischer Daten, zwei weitere sind Probleme der kombinierten Inversion von Datensätzen aus unterschiedlichen geophysikalischen Messverfahren. Im ersten Problem wird die für die Auswertung elektromagnetischer Zweispulensystemdaten typische lineare Näherung der kleinen Induktionszahlen als Bornsche Näherung verallgemeinert, ihre Anwendbarkeit durch exakte Berücksichtigung der Induktionsvorgänge in einem beliebigen homogenen Halbraum von schlechtleitenden auf gutleitende Untergründe ausgedehnt und schließlich zur zwei- und dreidimensionalen Inversion eingesetzt. Dadurch kann auch im leitfähigen Untergrund eine aufwändige exakte Modellierung vermieden werden. Im zweiten Problem wird eine dreidimensionale Inversion von flugzeuggestützten Längstwellenmessungen entwickelt und als ihre Grundlage eine exakte elektromagnetische Rechnung erdacht. Damit wird traditionelle kartengestützte Dateninterpretation durch ein dreidimensionales Leitfähigkeitsmodell ergänzt, welches die oberen hundert bis dreihundert Meter der Erdkruste bis hin zur Tiefe des obersten Leiters abbildet, so dass dessen Oberflächenform erkundet werden kann. Die enorme Problemgröße wird durch eine Fouriertransformationsmethode bewältigt, welche die elektromagnetischen Wechselwirkungen nach ihrer Reichweite einteilt, die Fernwirkungen mit entsprechend verringerter Genauigkeit behandelt und dadurch eine erhebliche Anzahl an Rechnungen einspart. Im dritten Problem werden refraktionsseismische und geoelektrische Messungen kombiniert, indem sowohl das Geschwindigkeits- als auch das Widerstandsmodell mit einer gemeinsamen, lateral veränderlichen und durch beide Datensätze bestimmten Schichtstruktur versehen werden. Ein solches, durch Schichten definiertes Inversionsergebnis, stellt in vielen oberflächennahen Anwendungen, beispielsweise im Grundwasserbereich, ein sinnvolles Abbild der Erde dar. Im vierten Problem werden Schweremessungen und Magnetfeldmessungen, die über einer Gabbrointrusion aufgenommen wurden, mittels einer empirischen petrophysikalischen Beziehung vereinigt, welche aus Labormessungen an einer großen Anzahl von Gesteinsproben abgeleitet wurde. Hierbei wird der Einfluss dieser Modellkopplung solange maximiert, wie beide Datensätze mit derjenigen Genauigkeit angepasst werden können, welche vorher in Einzelinversionen erreicht wurde. Das Ergebnis ist ein einfaches, geometrisch konsistentes Modell der Verteilungen von Dichte und magnetischer Suszeptibilität. In allen vier Aufgaben wurden erfolgreich reale Felddaten invertiert. Die Güte der Ergebnisse wurde mittels synthetischer Experimente untersucht und, so vorhanden, mit unabhängigen Informationen verglichen.
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Saunders, Jonathan Howard. « Electrical inversion and characterisation methods in geophysics ». Thesis, Imperial College London, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.413721.
Texte intégral
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MACIEL, Jonathas da Silva. « Structural constraints for image-based inversion methods ». Universidade Federal do Pará, 2016. http://repositorio.ufpa.br/jspui/handle/2011/9021.
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Esta tese apresenta duas metodologias de regularização estrutural para os métodos de análise de velocidade com migração e inversão conjunta com migração: regularização gradiente cruzado e filtragem com operadores morfológicos. Na análise de velocidade com migração, a regularização de gradiente cruzado tem como objetivo vincular os contrates de velocidade com o mapa de refletividade, através da paralelização dos vetores gradiente de velocidade com os vetores gradiente da imagem. Propõe-se uma versão com gradiente cruzado das funções objeto de minimização: Differential Semblance, Stack Power e Partial Stack Power. Combina-se a função Partial Stack Power com sua versão de gradiente cruzados, com o objetivo de aumentar gradativamente a resolução do modelo de velocidade, sem comprometer o ajuste das componentes de longo comprimento de onda do modelo de velocidade. Na inversão conjunta com migração propõe-se aplicar os operadores morfológicos de erosão e dilatação, no pré-condicionamento do modelo de velocidade em cada iteração. Os operadores usam o mapa de refletividade para delimitar as regiões com mesmo valor de propriedade física. Eles homogenizam a camada geológica e acentuam o contraste de velocidade nas bordas. Os vínculos estruturais não apenas irão reduzir a ambiguidade na estimativa do modelo de velocidade, mas tornará os métodos de inversão com migração mais estáveis, reduzindo artefatos, delineando soluções geologicamente plausíveis e acelerando a convergência da função objeto de minimização.
This thesis presents two methodologies of structural regularization for Wave-Equation Migration Velocity Analysis and Joint Migration Inversion: cross-gradient regularization and filtering with morphological operators. In Wave-Equation Migration Velocity Analysis, the cross-gradient regularization aims to constrain the velocity contrasts with the reflectivity map by parallelization of the velocity gradient vector and the image gradient vector. We propose a version with cross-gradient of the objective functions: Differential Semblance, Stack Power and Partial Stack Power. We combine the Partial Stack Power with its version of cross-gradient, in order to gradually increase the resolution of the velocity model without compromising the adjustment of the long wavelengths of the velocity model. In Joint Migration Inversion, we propose to apply morphological operators of erosion and dilation in the preconditioning of the velocity model in each iteration. Operators use the reflectivity map to mark the regions with the same value of physical property. They homogenize the geological layer and accentuate the velocity contrast at the edges. Structural constraints do not only reduce the ambiguity in estimating a velocity model, but also make the migration/inversion methods more stable, reducing artifacts, delineating geologically plausible solutions, and accelerating the convergence of the objective function.
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Walker, Matthew James. « Methods for Bayesian inversion of seismic data ». Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/10504.
Texte intégralRésumé :
The purpose of Bayesian seismic inversion is to combine information derived from seismic data and prior geological knowledge to determine a posterior probability distribution over parameters describing the elastic and geological properties of the subsurface. Typically the subsurface is modelled by a cellular grid model containing thousands or millions of cells within which these parameters are to be determined. Thus such inversions are computationally expensive due to the size of the parameter space (being proportional to the number of grid cells) over which the posterior is to be determined. Therefore, in practice approximations to Bayesian seismic inversion must be considered. A particular, existing approximate workflow is described in this thesis: the so-called two-stage inversion method explicitly splits the inversion problem into elastic and geological inversion stages. These two stages sequentially estimate the elastic parameters given the seismic data, and then the geological parameters given the elastic parameter estimates, respectively. In this thesis a number of methodologies are developed which enhance the accuracy of this approximate workflow. To reduce computational cost, existing elastic inversion methods often incorporate only simplified prior information about the elastic parameters. Thus a method is introduced which transforms such results, obtained using prior information specified using only two-point geostatistics, into new estimates containing sophisticated multi-point geostatistical prior information. The method uses a so-called deep neural network, trained using only synthetic instances (or `examples') of these two estimates, to apply this transformation. The method is shown to improve the resolution and accuracy (by comparison to well measurements) of elastic parameter estimates determined for a real hydrocarbon reservoir. It has been shown previously that so-called mixture density network (MDN) inversion can be used to solve geological inversion analytically (and thus very rapidly and efficiently) but only under certain assumptions about the geological prior distribution. A so-called prior replacement operation is developed here, which can be used to relax these requirements. It permits the efficient MDN method to be incorporated into general stochastic geological inversion methods which are free from the restrictive assumptions. Such methods rely on the use of Markov-chain Monte-Carlo (MCMC) sampling, which estimate the posterior (over the geological parameters) by producing a correlated chain of samples from it. It is shown that this approach can yield biased estimates of the posterior. Thus an alternative method which obtains a set of non-correlated samples from the posterior is developed, avoiding the possibility of bias in the estimate. The new method was tested on a synthetic geological inversion problem; its results compared favourably to those of Gibbs sampling (a MCMC method) on the same problem, which exhibited very significant bias. The geological prior information used in seismic inversion can be derived from real images which bear similarity to the geology anticipated within the target region of the subsurface. Such so-called training images are not always available from which this information (in the form of geostatistics) may be extracted. In this case appropriate training images may be generated by geological experts. However, this process can be costly and difficult. Thus an elicitation method (based on a genetic algorithm) is developed here which obtains the appropriate geostatistics reliably and directly from a geological expert, without the need for training images. 12 experts were asked to use the algorithm (individually) to determine the appropriate geostatistics for a physical (target) geological image. The majority of the experts were able to obtain a set of geostatistics which were consistent with the true (measured) statistics of the target image.
5
Li, Song. « Numerical methods for stable inversion of nonlinear systems ». Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/15028.
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Wilson, Adam. « Theory and methods of frequency-dependent AVO Inversion ». Thesis, University of Edinburgh, 2010. http://hdl.handle.net/1842/4740.
Texte intégralRésumé :
Amplitude-versus-offset, AVO, approximations allow the estimation of various properties from pre-stack seismic gathers. Recently it has been suggested that fluid mobility is a controlling factor in pore pressure equalisation and can result in anomalous velocity dispersion in the seismic bandwidth. However, current approximations all assume an elastic subsurface and are unable to account for velocity dispersion. I have applied existing methodologies to a real dataset to qualitatively detect and interpret spectral amplitude anomalies. Three areas had AVO and spectral signature consistent with frequency-dependent AVO theory. The results suggest that it is feasible to measure such effects on real data in the presence of random noise. It would imply that the relaxation parameter, tau, is larger in the field than has been measured in water-saturated real and synthetic sandstones in the laboratory. I extended a two-term AVO approximation by accounting for velocity dispersion and showed how the resultant reflection coefficient becomes frequency-dependent. I then used this to measure P- and S-wave reflectivity dispersion using spectrally-balanced amplitudes. The inversion was able to quantify the affect of the P-wave velocity dispersion as an instantaneous effect on the reflection. NMO stretch was an issue at the far offsets and I limited myself to the near offsets and effectively measured only the P-wave reflectivity dispersion. I showed how the P-wave reflectivity dispersion signs depend on the AVO classification of the reflection whilst the magnitude depends on the crack density of my model. I showed how the effect of noise and thin-bed tuning can enter uncertainties into the interpretation of spectral anomalies. Whilst it is possible to detect frequency-dependent AVO signatures on pre-stack gathers, the interpretation remains non-unique. I have quantitatively measured a new physical property, reflectivity dispersion, from pre-stack seismic data. I have presented a method of detecting and measuring velocity dispersion in pre-stack gathers but there remain ambiguities in the interpretation of such results. The approach incorporates spectrally decomposed data in an extended AVO inversion scheme. Future work should investigate the application of the methodology to a real seismic dataset.
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Sawyer, Nicolas B. E. « Novel optical surface metrology methods ». Thesis, University of Nottingham, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.287239.
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Thurin, Julien. « Uncertainties estimation in Full Waveform Inversion using Ensemble methods ». Thesis, Université Grenoble Alpes, 2020. https://tel.archives-ouvertes.fr/tel-02570602.
Texte intégralRésumé :
L'inversion de forme d'onde complète (FWI) est une méthode d'inversion non-linéaire qui a pour but l'obtention de modèles précis des propriétés physiques du sous-sol terrestre. Ces modèles, véritables cartes de propriétés physiques, sont indispensables pour l'exploration et l'étude des structures internes de la Terre.Généralement formulée sous la forme d'un schéma d'optimisation par la méthode des moindres carrés, la FWI compare des enregistrements sismiques observés en surface, avec des données synthétiques calculées à partir d'un modèle numérique de sous-sol. Alors qu'une infinité de modèles peut potentiellement expliquer les observations, la FWI, du fait de sa formulation, ne permet d'obtenir qu'un seul modèle du sous-sol fortement conditionné par le choix de modèle de départ. À cette ambiguïté s'ajoute la difficulté d'estimer l'incertitude de la solution, à cause du coût de calcul prohibitif de la FWI. La non-unicité de la solution et le manque de moyens d'estimation d'incertitude rend l'exploitation des modèles de FWI compliquée.Dans cette thèse, nous proposons une méthode non conventionnelle et abordable, intégrant l’estimation d’incertitude au coeur de la solution de FWI. Notre méthode combine la FWI conventionnelle et l’assimilation de données par méthodes d’ensemble. De ce fait, elle tire avantage de la vitesse de convergence de la FWI conventionnelle, ainsi que des capacités d'estimation d'incertitude du Filtre de Kálmán d'Ensemble dit "Transform" (ETKF). Cette combinaison est permise par les fondements théoriques communs aux problèmes d'optimisation en FWI conventionnelle et au filtrage bayésien de l'ETKF. Nous utilisons ce schéma, l’ETKF-FWI, afin de transposer le problème de FWI dans le cadre de l'inférence Bayésienne locale. Au lieu d’une unique solution, l’ETKF-FWI retourne un ensemble de modèles qui permet à la fois de calculer la meilleure solution au sens des moindres carrés, mais aussi l'information d’incertitude et de résolution associée à chaque paramètre. Cette estimation d’incertitude est rendue possible par l’approximation de bas-rang de la matrice de covariance a posteriori, calculée à partir de l’ensemble. Les valeurs de variance permettent d’évaluer le degré de variabilité de la solution au sein de l’ensemble. La résolution est quant à elle, donnée par les termes hors diagonaux de la matrice de corrélation, qui est préférée à la matrice de covariance pour sa nature adimensionnelle.L'application de l'ETKF-FWI à deux cas d'études (un test synthétique et une application sur données de terrain) nous permet d'évaluer la faisabilité, ainsi que les limites de notre technique. Malgré le coût de calcul important lié à la représentation d’ensemble, cette stratégie permet une implémentation complètement parallèle, la rendant avantageuse au regard des solutions existant dans la littérature.Ces tests nous permettent d’évaluer l’influence de la taille de l’ensemble sur l’estimation de la variance, en caractérisant le biais de sous-échantillonnage associé aux petits ensembles. Bien que ce biais soit classiquement corrigé grâce aux méthodes d’inflation d’ensemble, celles-ci ne semblent pas adaptées à l’ETKF-FWI, limitant l’estimation d’incertitude à des évaluations qualitatives. De plus, la complexité de l’application sur données de terrain impacte la création de l’ensemble initial, ce qui influence directement les capacités de l’ETKF-FWI à produire une estimation quantitative de l’incertitude.Nous terminons par l’application de l'ETKF-FWI à une inversion de plusieurs paramètres physique (vitesse des ondes P et densité), considéré comme un défi majeur en FWI conventionnelle. Ce test nous permet d’évaluer qualitativement les liens de corrélation et d'ambiguïté entre vitesse et densité, ainsi que leurs incertitude et résolution respectives. De plus, le modèle moyen issu de l’ETKF-FWI semble être de qualité supérieure, ce qui laisse supposer d’un possible effet de préconditionnement fourni par la covarianceFull Waveform Inversion (FWI) is an ill-posed non-linear inverse problem, aiming at recovering detailed pictures of subsurface physical properties, which are crucial to explore and understand Earth structures.Classically formulated as a least-squares optimization scheme, FWI yields a single subsurface model amongst an infinite possibility of solutions. With the general lack of systematic and scalable uncertainty estimation, this formulation makes interpretation of FWI's outcomes complex.In this thesis, we propose an unconventional, scalable way of tackling the lack of uncertainty estimation in FWI, thanks to data assimilation ensemble methods. We develop a scheme combining both classical FWI and the Ensemble Transform Kalman Filter, that we call ETKF-FWI, and which is successfully applied on two 2-D test cases. This scheme takes advantage of the theoretical common-ground between least-squares optimization problems and Bayesian filtering. We use it to recast FWI in a local Bayesian inference framework, thanks to the ensemble representation. The ETKF-FWI provides high-resolution subsurface tomographic models and yields a low-rank approximation of the posterior covariance, holding the uncertainty and resolution information of the proposed solution. We show how the ETKF-FWI can be applied to qualitatively evaluate uncertainty and resolution of the solution. Instead of providing a single solution, the filter yields an ensemble of models, from which statistical information can be inferred.Uncertainty is evaluated from the ensemble's variance, which relates to the diversity of solution amongst the ensemble members for each parameter. We show that lines of the correlation matrix are ideal to evaluate qualitatively parameters resolution, thanks to their adimentionality. While the methodology is computationally intensive, it has the benefit of being fully scalable. Its applicability is demonstrated on a synthetic benchmark. This preliminary test allows us to assess the sensitivity of the ensemble representation to the common undersampling bias encountered in ensemble data assimilation. While undersampling does not affect the image reconstruction in any way, it results in variance underestimation, which makes the whole exercise of quantitative uncertainty assessment complicated. Ensemble inflation has been used to mitigate this bias, but does not seems to be a practical solution.A field data experiment is also discussed in this thesis. It makes it possible to test the sensitivity of the ETKF-FWI to complex noise structure and realistic physics. As it stands, the complexity of the problem reduces flexibility in the ensemble generation, and hence on the uncertainty estimate. Despite these limitations, results are consistent with the synthetic benchmark, and we are able to provide a qualitative uncertainty assessment. The field data case also allows us to evaluate the possibilities to use the ETKF-FWI on multiparameter inversion, which is still regarded as a challenging topic in FWI. The ETKF-FWI multiparameter inversion yields improved models compared with conventional ones. More importantly, it makes it possible to assess the uncertainty associated with parameters cross-talks
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Kim, Junkyoung. « Complex seismic sources and time-dependent moment tensor inversion ». Diss., The University of Arizona, 1989. http://hdl.handle.net/10150/184841.
Texte intégralRésumé :
There are many examples of earthquakes whose surface expressions are much more complicated than the seismologically derived faulting models. Seismologists also have found seismic source complexity and improved seismicity data have shown that rupture may occur on irregular or multiple shear surfaces. To simultaneously map both geometrical and temporal variation of the seismic sources for a complex rupture history from observed seismograms, it is possible to use a time dependent moment tensor (TDMT) inversion. The TDMT inversion algorithm has been tested with three synthetic data examples with varying degrees of complexity. The first example demonstrates that a multiple source with no focal depth change can be recovered, and the source parameters of each of the subevents can be accurately determined. In the second case we allowed the depth to vary for subevents (9-km and 13-km source depth, respectively). The two subevents can be identified on the basis of simultaneous shape-change of the moment tensor elements along with non-causality and the size of the CLVD component. The third example introduced source complexity by having two subevents which overlapped in time. The overlapped period could be seen in the moment tensor elements as unusually abrupt changes in the time function shape. The TDMT inversion was also performed on long-period body waves for three earthquakes: the 1982 Yemen earthquake, the 1971 San Fernando earthquake, and the 1952 Kern County earthquake. The Yemen earthquake was mapped as two simple, normal-slip subevents (with onset timing of the second subevent 5 seconds after the first) without a significant component of left- or right-lateral displacement or source depth change. The San Fernando earthquake is interpreted as two shear dislocation sources with changing source depths, possibly indicating upward rupture propagation (from 13-km to 7-km). The interpretation of the TDMT inversion for the Kern County earthquake was also a double point source which propagates upward from 20-km to 5-km. The resultant moment tensor functions from inversion of the synthetic waveforms, a combination of isotropic and tectonic release, demonstrated that the tectonic release associated with underground nuclear explosion can be separated and identified if the source depth between the explosions and tectonic release are different.
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Michelen, Strofer Carlos Alejandro. « Machine Learning and Field Inversion approaches to Data-Driven Turbulence Modeling ». Diss., Virginia Tech, 2021. http://hdl.handle.net/10919/103155.
Texte intégralRésumé :
There still is a practical need for improved closure models for the Reynolds-averaged Navier-Stokes (RANS) equations. This dissertation explores two different approaches for using experimental data to provide improved closure for the Reynolds stress tensor field. The first approach uses machine learning to learn a general closure model from data. A novel framework is developed to train deep neural networks using experimental velocity and pressure measurements. The sensitivity of the RANS equations to the Reynolds stress, required for gradient-based training, is obtained by means of both variational and ensemble methods. The second approach is to infer the Reynolds stress field for a flow of interest from limited velocity or pressure measurements of the same flow. Here, this field inversion is done using a Monte Carlo Bayesian procedure and the focus is on improving the inference by enforcing known physical constraints on the inferred Reynolds stress field. To this end, a method for enforcing boundary conditions on the inferred field is presented. The two data-driven approaches explored and improved upon here demonstrate the potential for improved practical RANS predictions.Doctor of Philosophy
The Reynolds-averaged Navier-Stokes (RANS) equations are widely used to simulate fluid flows in engineering applications despite their known inaccuracy in many flows of practical interest. The uncertainty in the RANS equations is known to stem from the Reynolds stress tensor for which no universally applicable turbulence model exists. The computational cost of more accurate methods for fluid flow simulation, however, means RANS simulations will likely continue to be a major tool in engineering applications and there is still a need for improved RANS turbulence modeling. This dissertation explores two different approaches to use available experimental data to improve RANS predictions by improving the uncertain Reynolds stress tensor field. The first approach is using machine learning to learn a data-driven turbulence model from a set of training data. This model can then be applied to predict new flows in place of traditional turbulence models. To this end, this dissertation presents a novel framework for training deep neural networks using experimental measurements of velocity and pressure. When using velocity and pressure data, gradient-based training of the neural network requires the sensitivity of the RANS equations to the learned Reynolds stress. Two different methods, the continuous adjoint and ensemble approximation, are used to obtain the required sensitivity. The second approach explored in this dissertation is field inversion, whereby available data for a flow of interest is used to infer a Reynolds stress field that leads to improved RANS solutions for that same flow. Here, the field inversion is done via the ensemble Kalman inversion (EKI), a Monte Carlo Bayesian procedure, and the focus is on improving the inference by enforcing known physical constraints on the inferred Reynolds stress field. To this end, a method for enforcing boundary conditions on the inferred field is presented. While further development is needed, the two data-driven approaches explored and improved upon here demonstrate the potential for improved practical RANS predictions.
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Pugh, David James. « Bayesian source inversion of microseismic events ». Thesis, University of Cambridge, 2016. https://www.repository.cam.ac.uk/handle/1810/253751.
Texte intégralRésumé :
Rapid stress release at the source of an earthquake produces seismic waves. Observations of the particle motions from such waves are used in source inversion to characterise the dynamic behaviour of the source and to help in understanding the driving processes. Earthquakes either occur naturally, such as in volcanic eruptions and natural geothermal fields, or are linked to anthropogenic activities including hydrofracture of gas and oil reservoirs, mining events and extraction of geothermal fluids. Source inversion is very sensitive to uncertainties in both the model and the data, especially for low magnitude, namely microseismic, events. Many of the uncertainties can be poorly quantified, and are often not included in source inversion. This thesis proposes a Bayesian framework enabling a complete inclusion of uncertainties in the resultant probability distribution using Bayesian marginalisation. This approach is developed for polarity and amplitude ratio data, although it is possible to use any data type, provided the noise model can be estimated. The resultant posterior probability distributions are easily visualised on different plots for orientation and source-type. Several different algorithms can be used to search the source space, including Monte Carlo random sampling and Markov chain Monte Carlo sampling. Relative information between co-located events may be used as an extension to the framework, improving the constraint on the source. The double-couple source is the commonly assumed source model for many earthquakes, corresponding to slip on a fault plane. Two methods for estimating the posterior model probability of the double-couple source type are explored, one using the Bayesian evidence, the other using trans-dimensional Markov chain Monte Carlo sampling. Results from both methods are consistent with each other, producing good estimates of the probability given sufficient samples. These provide estimates of the probability of the source being a double-couple source or not, which is very useful when trying to understand the processes causing the earthquake. Uncertainty on the polarity estimation is often hard to characterise, so an alternative approach for determining the polarity and its associated uncertainty is proposed. This uses a Bayesian estimate of the polarity probability and includes both the background noise and the arrival time pick uncertainty, resulting in a more quantitative estimate of the polarity uncertainty. Moreover, this automated approach can easily be included in automatic event detection and location workflows. The inversion approach is discussed in detail and then applied to both synthetic events generated using a finite-difference code, and to real events acquired from a temporary seismometer network deployed around the Askja and Krafla Volcanoes, Iceland.
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Hicks, Graham John. « Seismic velocities from reflection waveforms : the application of Newton inversion methods ». Thesis, Imperial College London, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.325127.
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Yang, Di Ph D. Massachusetts Institute of Technology. « Full wavefield inversion methods for monitoring time-lapse subsurface velocity changes ». Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/95558.
Texte intégralRésumé :
Thesis: Ph. D. in Geophysics, Massachusetts Institute of Technology, Department of Earth, Atmospheric, and Planetary Sciences, 2014.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 243-252).
Quantitative measurements of seismic velocity changes from time-lapse seismic experiments provide dynamic information about the subsurface that improves the understanding of the geology and reservoir properties. In this thesis, we propose to achieve the quantitative analysis using full wavefield inversion methods which are robust in complex geology. We developed several methodologies in both the data domain and image domain to handle different time-lapse seismic acquisitions. In the data domain, we implemented double-difference waveform inversion (DDWI), and investigated its robustness and feasibility with realistic acquisition non-repeatabilities. Well-repeated time-lapse surveys from Valhall in the North Sea are used to compare DDWI and conventional time-lapse full waveform inversion (FWI) schemes. An FWI approach that uses the baseline and monitor datasets in an alternating manner is proposed to handle time-lapse surveys without restrictions on geometry repeatability, and to provide an uncertainty analysis on the time-lapse changes. In the image domain, we propose time-lapse image domain wavefield tomography (IDWT) that inverts for P- and S-wave velocity changes by matching baseline and monitor images produced with small offset reflection surveys. This method is robust to survey geometry non-repeatabilities and baseline velocity errors. A low velocity zone caused by local CO2 injections in SACROC, West Texas is found by IDWT with time-lapse walkaway vertical seismic profile surveys. The methods in this thesis combined, allow for an integrated velocity inversion to achieve high-resolution subsurface monitoring with various types of acquisitions in complex geology.
by Di Yang.
Ph. D. in Geophysics
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Virtanen, I. (Ilkka). « Multi-purpose methods for ionospheric radar measurements ». Doctoral thesis, Oulun yliopisto, 2009. http://urn.fi/urn:isbn:9789514292842.
Texte intégralRésumé :
Abstract
From the very beginning of modern ionospheric science, different radar applications have been utilised in ionospheric measurements. The most sophisticated ionospheric radars are the incoherent scatter radars, which detect the extremely weak scattering of radio waves from thermal fluctuations in the ionospheric plasma. Besides the low signal level, the stochastic nature of the scattering process causes further complications to the measurements. The scattering produces a zero-mean random signal, whose autocorrelation function contains the information of the ionospheric plasma parameters. Incoherent scatter radars have been used for about half a century, but the demanding task of developing transmission modulation and data analysis is still in progress.
In this thesis, a statistical inversion based method for removing range ambiguities from the autocorrelation functions, lag profile inversion, is applied to incoherent scatter radar data. The data have been recorded with the EISCAT incoherent scatter radars, located in Northern Fennoscandia. The method is first applied to standard EISCAT experiments, the results giving strong evidence that the method is applicable for the purpose, and it provides results of at least equal quality with the present standard methods. In subsequent studies, new radar modulation methods are developed, which may provide significant improvements to the present incoherent scatter radar experiments. All the methods have been tested with a real radar, and lag profile inversion has been successfully applied to the recorded data. The methods are also put to use in order to measure the predicted effects of artificial heating of the free electrons in the D-region of the ionosphere.
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POONDRU, SHIRDISH. « A NEW DIRECT MATRIX INVERSION METHOD FOR ECONOMICAL AND MEMORY EFFICIENT NUMERICAL SOLUTIONS ». University of Cincinnati / OhioLINK, 2003. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1060976742.
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Seyfried, Ruben [Verfasser]. « Summability Methods for the Inversion of the Spherical Mean Operator / Ruben Seyfried ». Aachen : Shaker, 2014. http://d-nb.info/1059344386/34.
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Jokinen, J. (Jarkko). « Uncertainty analysis and inversion of geothermal conductive models using random simulation methods ». Doctoral thesis, University of Oulu, 2000. http://urn.fi/urn:isbn:9514255909.
Texte intégralRésumé :
Abstract
Knowledge of the thermal conditions in the lithosphere is
based on theoretical models of heat transfer constrained by geological
and geophysical data. The present dissertation focuses on the uncertainties of
calculated temperature and heat flow density results and on how
they depend on the uncertainties of thermal properties of rocks,
as well as on the relevant boundary conditions. Due to the high
number of involved variables of typical models, the random simulation
technique was chosen as the applied tool in the analysis. Further,
the random simulation technique was applied in inverse Monte Carlo solutions
of geothermal models. In addition to modelling technique development,
new measurements on thermal conductivity and diffusivity of middle
and lower crustal rocks in elevated pressure and temperature were
carried out.
In the uncertainty analysis it was found that a temperature
uncertainty of 50 K at the Moho level, which is at a 50 km's
depth in the layered model, is produced by an uncertainty of only
0.5 W m-1 K-1 in
thermal conductivity values or 0.2 orders of magnitude uncertainty
in heat production rate (mW m-3). Similar
uncertainties are obtained in Moho temperature, given that the lower
boundary condition varies by ± 115 K in temperature (nominal
value 1373 K) or ± 1.7 mW m-2 in
mantle heat-flow density (nominal value 13.2 mW m-2).
Temperature and pressure dependencies of thermal conductivity are
minor in comparison to the previous effects.
The inversion results indicated that the Monte Carlo technique
is a powerful tool in geothermal modelling. When only surface heat-flow
density data are used as a fitting object, temperatures at the depth
of 200 km can be inverted with an uncertainty of 120 - 170 K. When
petrological temperature-depth (pressure) data on kimberlite-hosted
mantle xenoliths were used also as a fitting object, the uncertainty
was reduced to 60 - 130 K. The inversion does not remove the ambiguity
of the models completely, but it reduces significantly the uncertainty
of the temperature results.
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Sievert, Thomas. « GNSS Radio Occultation Inversion Methods and Reflection Observations in the Lower Troposphere ». Licentiate thesis, Blekinge Tekniska Högskola, Institutionen för matematik och naturvetenskap, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-17484.
Texte intégralRésumé :
GNSS Radio Occultation (GNSS-RO) is an opportunistic Earth sensing technique where GNSS signals passing through the atmosphere are received in low Earth orbit and processed to extract meteorological parameters. As signals are received along an orbit, the measured Doppler shift is transformed to a bending angle profile (commonly referred to as bending angle retrieval), which, in turn, is inverted to a refractivity profile. Thanks to its high vertical resolution and SI traceability, GNSS-RO is an important complement to other Earth sensing endeavors. In the lower troposphere, GNSS-RO measurements often get degraded and biased due to sharp refractive gradients and other complex structures. The main objective of this thesis is to explore contemporary retrieval methods such as phase matching and full spectrum inversion to improve their performance in these conditions. To avoid the bias caused by the standard inversion, we attempt to derive additional information from the amplitude output of the examined retrieval operators. While simulations indicate that such information could be found, it is not immediately straightforward how to achieve this with real measurements. The approach chosen is to examine reflected signal components and their effect on the amplitude output.
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Berkel, Paula. « Multiscale methods for the combined inversion of normal mode and gravity variations ». Aachen Shaker, 2009. http://d-nb.info/997085304/04.
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Gower, Robert Mansel. « Sketch and project : randomized iterative methods for linear systems and inverting matrices ». Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/20989.
Texte intégralRésumé :
Probabilistic ideas and tools have recently begun to permeate into several fields where they had traditionally not played a major role, including fields such as numerical linear algebra and optimization. One of the key ways in which these ideas influence these fields is via the development and analysis of randomized algorithms for solving standard and new problems of these fields. Such methods are typically easier to analyze, and often lead to faster and/or more scalable and versatile methods in practice. This thesis explores the design and analysis of new randomized iterative methods for solving linear systems and inverting matrices. The methods are based on a novel sketch-and-project framework. By sketching we mean, to start with a difficult problem and then randomly generate a simple problem that contains all the solutions of the original problem. After sketching the problem, we calculate the next iterate by projecting our current iterate onto the solution space of the sketched problem. The starting point for this thesis is the development of an archetype randomized method for solving linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random intersect, random linear solve, random update and random fixed point. By varying its two parameters – a positive definite matrix (defining geometry), and a random matrix (sampled in an i.i.d. fashion in each iteration) – we recover a comprehensive array of well known algorithms as special cases, including the randomized Kaczmarz method, randomized Newton method, randomized coordinate descent method and random Gaussian pursuit. We also naturally obtain variants of all these methods using blocks and importance sampling. However, our method allows for a much wider selection of these two parameters, which leads to a number of new specific methods. We prove exponential convergence of the expected norm of the error in a single theorem, from which existing complexity results for known variants can be obtained. However, we also give an exact formula for the evolution of the expected iterates, which allows us to give lower bounds on the convergence rate. We then extend our problem to that of finding the projection of given vector onto the solution space of a linear system. For this we develop a new randomized iterative algorithm: stochastic dual ascent (SDA). The method is dual in nature, and iteratively solves the dual of the projection problem. The dual problem is a non-strongly concave quadratic maximization problem without constraints. In each iteration of SDA, a dual variable is updated by a carefully chosen point in a subspace spanned by the columns of a random matrix drawn independently from a fixed distribution. The distribution plays the role of a parameter of the method. Our complexity results hold for a wide family of distributions of random matrices, which opens the possibility to fine-tune the stochasticity of the method to particular applications. We prove that primal iterates associated with the dual process converge to the projection exponentially fast in expectation, and give a formula and an insightful lower bound for the convergence rate. We also prove that the same rate applies to dual function values, primal function values and the duality gap. Unlike traditional iterative methods, SDA converges under virtually no additional assumptions on the system (e.g., rank, diagonal dominance) beyond consistency. In fact, our lower bound improves as the rank of the system matrix drops. By mapping our dual algorithm to a primal process, we uncover that the SDA method is the dual method with respect to the sketch-and-project method from the previous chapter. Thus our new more general convergence results for SDA carry over to the sketch-and-project method and all its specializations (randomized Kaczmarz, randomized coordinate descent ... etc.). When our method specializes to a known algorithm, we either recover the best known rates, or improve upon them. Finally, we show that the framework can be applied to the distributed average consensus problem to obtain an array of new algorithms. The randomized gossip algorithm arises as a special case. In the final chapter, we extend our method for solving linear system to inverting matrices, and develop a family of methods with specialized variants that maintain symmetry or positive definiteness of the iterates. All the methods in the family converge globally and exponentially, with explicit rates. In special cases, we obtain stochastic block variants of several quasi-Newton updates, including bad Broyden (BB), good Broyden (GB), Powell-symmetric-Broyden (PSB), Davidon-Fletcher-Powell (DFP) and Broyden-Fletcher-Goldfarb-Shanno (BFGS). Ours are the first stochastic versions of these updates shown to converge to an inverse of a fixed matrix. Through a dual viewpoint we uncover a fundamental link between quasi-Newton updates and approximate inverse preconditioning. Further, we develop an adaptive variant of the randomized block BFGS (AdaRBFGS), where we modify the distribution underlying the stochasticity of the method throughout the iterative process to achieve faster convergence. By inverting several matrices from varied applications, we demonstrate that AdaRBFGS is highly competitive when compared to the well established Newton-Schulz and approximate preconditioning methods. In particular, on large-scale problems our method outperforms the standard methods by orders of magnitude. The development of efficient methods for estimating the inverse of very large matrices is a much needed tool for preconditioning and variable metric methods in the big data era.
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Downs, M. L. N. « Mobius inversion of some classical groups and their application to the enumeration of regular hypermaps ». Thesis, University of Southampton, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.381232.
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Berkel, Paula [Verfasser]. « Multiscale Methods for the Combined Inversion of Normal Mode and Gravity Variations / Paula Berkel ». Aachen : Shaker, 2009. http://d-nb.info/1159835357/34.
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Prieto, Moreno Kernel Enrique. « Novel mathematical techniques for structural inversion and image reconstruction in medical imaging governed by a transport equation ». Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/novel-mathematical-techniques-for-structural-inversion-and-image-reconstruction-in-medical-imaging-governed-by-a-transport-equation(b45f5566-daa7-4d47-a982-cf479e360c6f).html.
Texte intégralRésumé :
Since the inverse problem in Diffusive Optical Tomography (DOT) is nonlinear and severely ill-posed, only low resolution reconstructions are feasible when noise is added to the data nowadays. The purpose of this thesis is to improve image reconstruction in DOT of the main optical properties of tissues with some novel mathematical methods. We have used the Landweber (L) method, the Landweber-Kaczmarz (LK) method and its improved Loping-Landweber-Kaczmarz (L-LK) method combined with sparsity or with total variation regularizations for single and simultaneous image reconstructions of the absorption and scattering coefficients. The sparsity method assumes the existence of a sparse solution which has a simple description and is superposed onto a known background. The sparsity method is solved using a smooth gradient and a soft thresholding operator. Moreover, we have proposed an improved sparsity method. For the total variation reconstruction imaging, we have used the split Bregman method and the lagged diffusivity method. For the total variation method, we also have implemented a memory-efficient method to minimise the storage of large Hessian matrices. In addition, an individual and simultaneous contrast value reconstructions are presented using the level set (LS) method. Besides, the shape derivative of DOT based on the RTE is derived using shape sensitivity analysis, and some reconstructions for the absorption coefficient are presented using this shape derivative via the LS method.\\Whereas most of the approaches for solving the nonlinear problem of DOT make use of the diffusion approximation (DA) to the radiative transfer equation (RTE) to model the propagation of the light in tissue, the accuracy of the DA is not satisfactory in situations where the medium is not scattering dominant, in particular close to the light sources and to the boundary, as well as inside low-scattering or non-scattering regions. Therefore, we have solved the inverse problem in DOT by the more accurate time-dependant RTE in two dimensions.
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Jiang, Zixian. « Some inversion methods applied to non-destructive testings of steam generator via eddy current probe ». Palaiseau, Ecole polytechnique, 2014. http://pastel.archives-ouvertes.fr/docs/00/94/36/13/PDF/Thesis.pdf.
Texte intégralRésumé :
L'objectif principal de cette thèse est de proposer et de tester quelques méthodes de l'optimisation de forme afin d'identifier et de reconstruire des dépôts qui couvrent la paroi extérieure d'un tube conducteur dans un générateur de vapeurs en utilisant des signaux courant de Foucault. Ce problème est motivé par des applications industrielles en contrôle non-destructive dans le secteur de l'énergie nucléaire. En fait, des dépôts peuvent obstruer le passage de circuit de refroidissement entre les tubes et les plaques entretoises qui les soutiennent, ce qui entraînerait une baisse de productivité et mettrait la structure en danger. On considère dans un premier temps un cas axisymétrique dans le cadre duquel on construit un modèle 2-D par des équations aux dérivées partielles pour le courant de Foucault, ce qui nous permet ensuite de reproduire des mesures d'impédances qui correspondent en réalité les signaux courants de Foucault. Pour réduire le coût de calculs de la simulation numérique, on tronque le domaine du problème en posant des conditions aux bords artificielles basées sur des études sur le comportement de la solution, notamment sur un calcul semi-analytique de l'opérateur Dirichlet-to-Neumann dans la direction axiale. Pour la partie identification et reconstruction, on distingue deux sortes de dépôts et établit pour chacun une méthode d'inversion spécifique. Le premier cas concernent des dépôts dont la conductivité est relativement faible (d'environs 1. E4 S/m). On utilise la méthode d'optimisation de forme qui consiste à exprimer explicitement la dérivée des mesures d'impédance par rapport au domaine du dépôt en fonction d'une déformation et à représenter le gradient d'un fonctionnel de coût à minimiser par l'intermédiaire d'un état adjoint proprement défini. Motivée par la présence des dépôts et des plaques de maintient non-axisymétriques, on fait aussi une extension en 3-D des méthodes précédentes. Pour le deuxième cas, des dépôts sont fortement conducteurs et sous forme de couche mince d'une épaisseur de l'ordre de micron. La méthode adaptée à la première sorte de dépôts devient ici trop coûteuse à cause du degré de liberté très élevé des éléments finis sur un maillage extrêmement raffiné à l'échelle de la couche mince. Pour relever cette difficulté, les études sont portées sur plusieurs modèles asymptotiques qui remplace la couche mince par des conditions d'interface sur la surface du tube portante du dépôt. Le nom de modèle asymptotique vient du fait que les conditions d'interface effectives sont obtenues par le développement asymptotique de la solution en fonction d'un paramètre caractérisant la conductivité et l'épaisseur de la couche mince. La validation numérique a permis de retenir un modèle asymptotique qui est à la fois suffisamment précis et simple à inverser. L'inversion (recherche de l'épaisseur du dépôt) consiste alors à rechercher des paramètres dans les conditions d'interface (non standard). Pour les deux cas, la validation et des exemples numériques sont proposés pour le modèle direct et l'inversionThe main objective of this thesis is to propose and test some shape optimization techniques to identify and reconstruct deposits at the shell side of conductive tubes in steam generators using signals from eddy current coils. This problem is motivated by non-destructive testing applications in the nuclear power industry where the deposit clogging the cooling circuit may affect power productivity and structural safety. We consider in a first part an axisymmetric case for which we set the model by establishing a 2-D differential equation describing the eddy current phenomenon, which enable us to simulate the impedance measurements as the observed signals to be used in the inversion. To speed up numerical simulations, we discuss the behavior of the solution of the eddy current problem and build artificial boundary conditions, in particular by explicitly constructing DtN operators, to truncate the domain of the problem. In the deposit reconstruction, we adapt two different methods according to two distinct kinds of deposits. The first kind of deposit has relatively low conductivity (about 1e4 S/m). We apply the shape optimization method which consists in expliciting the signal derivative due to a shape perturbation of the deposit domain and to build the gradient by using the adjoint state with respect to the derivative and the cost functional. While for the second kind of deposit with high conductivity (5. 8e7 S/m) but in the form of thin layer (in micrometers), the previous method encounter a high numerical cost due to the tiny size of the mesh used to model the layer. To overcome this difficulty, we build an adapted asymptotic model by appropriately selecting the the family of effective transmissions conditions on the interface between the deposit and the tube. The name of the asymptotic model is due to the fact that the effective transmissions conditions are derived from the asymptotic expansion of the solution with respect to a small parameter "delta" characterizing the thickness of the thin layer and the conductivity behavior. Then the inverse problem consists in reconstructing the parameters representing the layer thickness of the deposit. For both of the two approaches, we validate numerically the direct and inverse problems. In a second part we complement this work by extending the above methods to the 3-D case for a non-axisymmetric configuration. This is motivated by either non axisymmetric deposits or the existence of non axisymmetric components like support plates of steam generator tubes
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Günther, Thomas. « Inversion methods and resolution analysis for the 2D/3D reconstruction of resistivity structures from DC measurements ». Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2009. http://nbn-resolving.de/urn:nbn:de:swb:105-4152277.
Texte intégralRésumé :
The presented thesis deals with the multi-dimensional reconstruction of the earth's conductivity distribution based on DC resistivity data. This task represents a nonlinear and ill-posed minimization problem with many degrees of freedom. In this work, techniques for regularization and controlling of this problem are depicted and classified. Particularly, it is concentrated on explicit regularization types, which impose constraints onto the model. The system of equations as resulting from the application of the Gauss-Newton minimization can be solved efficiently. Furthermore, it is shown how the regularization strength can be controlled. The method of non-linear resolution analysis plays a central role in the thesis. It represents a powerful tool to estimate the quality of inversion results. Furthermore, the derived resolution measures provide the basis for the optimization of experimental design concerning information content and efficiency. Methods of error estimation, forward modeling and the calculation of the Jacobian matrix for DC resistivity data are developed. Procedures for appropriate parameterization and inversion control are pointed out by studies of synthetic models. Different inversion and regularization methods are examined in detail. A linearized study is used to compare different data sets considering their efficiency. Moreover, a triplegrid-technique for the incorporation of topography into three-dimensional inversion is presented. Finally the inversion methods are applied to field data. The depicted optimization strategies are realized in practice, which increases the economic relevance of threedimensional data acquisition. The structure of the subsurface is imaged in detail for several applications in the fields of cavity detection, archaeology and the investigation of ground falls. The resolution analysis is successfully established to appraise the obtained results.
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Blick, Christian [Verfasser]. « Multiscale Potential Methods in Geothermal Research : Decorrelation Reflected Post-Processing and Locally Based Inversion / Christian Blick ». München : Verlag Dr. Hut, 2015. http://d-nb.info/1080754636/34.
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Sheffer, Megan Rae. « Forward modelling and inversion of streaming potential for the interpretation of hydraulic conditions from self-potential data ». Thesis, University of British Columbia, 2007. http://hdl.handle.net/2429/235.
Texte intégralRésumé :
The self-potential method responds to the electrokinetic phenomenon of streaming potential and has been applied in hydrogeologic and engineering investigations to aid in the evaluation of subsurface hydraulic conditions. Of specific interest is the application of the method to embankment dam seepage monitoring and detection. This demands a quantitative
interpretation of seepage conditions from the geophysical data.
To enable the study of variably saturated flow problems of complicated geometry, a three-dimensional finite volume algorithm
is developed to evaluate the self-potential distribution resulting from subsurface fluid flow. The algorithm explicitly calculates
the distribution of streaming current sources and solves for the self-potential given a model of hydraulic head and prescribed distributions of the streaming current cross-coupling conductivity and electrical resistivity. A new laboratory apparatus is developed to measure the streaming potential coupling coefficient
and resistivity in unconsolidated soil samples. Measuring both of these parameters on the same sample under the same conditions
enables us to properly characterize the streaming current cross-coupling conductivity coefficient. I present the results of a laboratory investigation to study the influence of soil and fluid parameters on the cross-coupling coefficient, and characterize this property for representative well-graded embankment soils. The streaming potential signals associated with preferential seepage through the core of a synthetic embankment dam model are studied using the forward modelling algorithm and measured electrical properties to assess the sensitivity of the self-potential method in detecting internal erosion. Maximum self-potential anomalies are shown to be linked to large localized
hydraulic gradients that develop in response to piping, prior to any detectable increase in seepage flow through the dam. A linear
inversion algorithm is developed to evaluate the three-dimensional distribution of hydraulic head from self-potential data, given a known distribution of the cross-coupling coefficient and electrical resistivity. The inverse problem is solved by
minimizing an objective function, which consists of a data misfit that accounts for measurement error and a model objective function that incorporates a priori information. The algorithm is suitable
for saturated flow problems or where the position of the phreatic surface is known.
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Rojas, Jose G. « Geoacoustic inversion using direct methods of ambient noise and explosive acoustic data in a shallow water waveguide ». Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1998. http://handle.dtic.mil/100.2/ADA343684.
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Ernesti, Johannes [Verfasser], et C. [Akademischer Betreuer] Wieners. « Space-Time Methods for Acoustic Waves with Applications to Full Waveform Inversion / Johannes Ernesti ; Betreuer : C. Wieners ». Karlsruhe : KIT-Bibliothek, 2018. http://d-nb.info/1160303525/34.
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Guan, Borui. « Characterization of building materials by electromagnetic non-destructive methods : application to limestone ». Thesis, Nantes, 2018. http://www.theses.fr/2018NANT4003/document.
Texte intégralRésumé :
Le tuffeau est un matériau de construction calcaire largement utilisé dans la vallée de la Loire pour les bâtiments historiques. Le temps passant, il est confronté à des problèmes de pathologies, principalement liées à sa teneur en eau. Pour évaluer cet indicateur, le radar à sauts de fréquence (SFR) a été retenu parmi les techniques d’évaluation non destructives. Cette dernière peut être associée à une technique d’inversion « forme d’onde » dans le domaine fréquentiel (FWFI), technique performante pour obtenir la permittivité, directement en lien avec la teneur en eau. L’inversion FWFI d’un signal SFR utilise, pour le calcul direct, un modèle analytique de propagation des ondes, basé sur les fonctions de Green d’un dipôle, et sur le modèle de dispersion de Jonscher pour la caractérisation EM du milieu. Ce modèle direct est validé par une approche numérique utilisant le logiciel HFSS et par une approche expérimentale sur des blocs tests. Le problème inverse, comprenant une fonction Objectif et un algorithme de minimisation de type génétique, est ensuite étudié pour obtenir la permittivité du milieu ausculté. En parallèle, une base de données entre teneur en eau et permittivité du tuffeau est construite à l’aide de mesures EM en cellule sur des échantillons homogènes. Elle est associée à une analyse de régression de type vecteur-support pour prédire la teneur en eau du milieu à partir de la mesure de permittivité. Enfin, cette méthode est validée sur plusieurs applications pratiques, comprenant l’acquisition d’informations géométriques (estimation d’un front d’eau) et la caractérisation du matériau (estimation du gradient d’eau et cartographie hydrique)Limestone is a historical building material widely used in Loire Valley of France. Time passed, it is facing to health problems, mainly due to water content. To evaluate this indicator, stepped-frequency radar is an efficient technique among all non-destructive testing techniques. It can be combined with a frequency-domain full-waveform inversion technique, which is an efficient signal processing method to achieve permittivity that is the observable of water content, after a calibration process. To do signal inversion, an analytical model of ultrawide band radar wave propagation through limestone is built in the forward study. This model is based on one-dipole Green’s function, for the EM propagation, and 4-parameters’ Jonscher dispersion model, for the EM characterization of the medium. This direct model is validated by a numerical approach using HFSS and an experimental approach using an experimental platform of Cerema. The inverse problem, including objective function and minimization algorithm, to achieve the permittivity, is then studied. An inversion method based on genetic algorithm is proposed and validated using numerical and experimental approaches. Afterwards, a large database between water content and permittvity of limestone is constructed using the electromagnetic cell test on cylindrical samples, based on which a support vector regression analysis is performed to predict water content using permittivity. Finally, this method is validated on several practical applications including geophysical information acquisition (water front estimation) and material characterization (water gradient estimation and hydric mapping)
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Cazenave, Quitterie. « Development and evaluation of multisensor methods for EarthCare mission based on A-Train and airborne measurements ». Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLV020/document.
Texte intégralRésumé :
L'impact des nuages de glace sur le cycle de l'eau et le bilan radiatif est encore incertain en raison de la complexité des processus nuageux qui rend difficile l'acquisition d'observations adéquates sur les propriétés des nuages de glace et leur représentation dans les modèles de circulation générale. Les instruments de télédétection actifs et passifs, tels que les radiomètres, les radars et les lidars, sont couramment utilisés pour les étudier. La restitution des propriétés microphysiques des nuages (extinction, contenu en glace, rayon effectif, ...) peut être effectuée à partir d'un seul instrument ou de la combinaison de plusieurs instruments. L’intérêt de l’utilisation de synergies instrumentales pour restituer les propriétés nuageuses réside dans le fait que cela permet de réduire les incertitudes dues aux lacunes des différents instruments pris séparément. La constellation de satellites A-Train a considérablement amélioré notre connaissance des nuages. Depuis 2006, le lidar à rétrodiffusion visible CALIOP embarqué à bord du satellite CALIPSO et le radar nuage à 94GHz CPR embarqué à bord du satellite CloudSat ont permis l’acquisition de profils nuageux sur l’ensemble du globe et de nombreuses méthodes synergiques de restitution ont été adaptées à ces instruments. En 2021 sera lancé un nouveau satellite, EarthCARE, embarquant des instruments de télédétection de pointe, notamment ATLID, un lidar à haute résolution spectrale (HSRL) à 355 nm et un radar nuage Doppler à 94 GHz. La mission principale de ce satellite est de quantifier les interactions entre les nuages, les aérosols et le bilan radiatif de la Terre afin d'améliorer les prévisions météorologiques et des modèles climatiques. Grâce à son instrumentation avancée installée sur une plate-forme unique, cette nouvelle mission devrait fournir des observations sans précédent des nuages depuis l'espace. Cependant, pour ce faire, les algorithmes synergiques développés pour les mesures de l'A-Train doivent être adaptés à cette nouvelle configuration instrumentale. Au cours de ma thèse, je me suis concentrée sur l'algorithme Varcloud développé en 2007 par Delanoë et Hogan et basé sur une technique variationnelle. La première partie du travail a consisté à adapter certains paramètres du modèle microphysique de l’algorithme aux études récentes d’une large base de données in situ. En particulier, les questions de la paramétrisation du rapport lidar et du choix de la relation masse-diamètre pour les cristaux de glace ont été abordées. La deuxième partie de mon travail a consisté à adapter l'algorithme de restitution Varcloud aux plates-formes aéroportées. Les plates-formes aéroportées sont idéales pour préparer et valider les missions spatiales, permettant de réaliser des mesures sous-trace, colocalisées avec les instruments spatiaux. En particulier, le HALO allemand et le Falcon 20 français ont des charges utiles très complémentaires et sont parfaitement conçus pour la préparation et la validation de la mission EarthCare. Les deux avions embarquent notamment un lidar à haute résolution spectrale (355 nm sur le Falcon et 532 nm sur le HALO) et un radar Doppler à 36 GHz (HALO) et 95 GHz (Falcon). À l'automne 2016, une campagne aéroportée dans laquelle les deux avions étaient impliqués s'est déroulée en Islande, à Keflavik, dans le cadre du projet NAWDEX. Les mesures recueillies au cours de cette campagne fournissent un ensemble de données intéressant pour caractériser la microphysique et la dynamique des nuages dans l'Atlantique Nord, région qui présent un grand intérêt pour les missions Cloudsat-CALIPSO et EarthCARE. En outre, une série de vols communs avec observation de la même scène nuageuse par les deux plates-formes ont été réalisées, fournissant des données permettant d'étudier l'influence de la configuration instrumentale sur les propriétés des nuages de glace restituéesThe impact of ice clouds on the water cycle and radiative budget is still uncertain due to the complexity of cloud processes that makes it difficult to acquire adequate observations of ice cloud properties and parameterize them into General Circulation Models. Passive and active remote sensing instruments, radiometers, radars and lidars, are commonly used to study ice clouds. Inferring cloud microphysical properties (extinction, ice water content, effective radius, ...) can be done from one instrument only, or from the synergy of several. The interest of using instrumental synergies to retrieve cloud properties is that it can reduce the uncertainties due to the shortcomings of the different instruments taken separately. The A-Train constellation of satellites has considerably improved our knowledge of clouds. Since 2006, the 532nm backscattering lidar CALIOP on board the satellite CALIPSO and the 94GHz cloud radar CPR on board the satellite CloudSat have acquired cloud vertical profiles globally and many lidar-radar synergetic methods have been adapted to CloudSat and CALIPSO data. In 2021 will be launched a new satellite, EarthCARE, boarding state of the art remote sensing instrumentation, in particular ATLID, a High Spectral Resolution Lidar (HSRL) at 355nm and a Doppler cloud radar at 94 GHz. The main mission of this satellite is to quantify interactions between clouds, aerosols and the Earth's radiation budget in order to improve weather prediction and climate models. Thanks to its advanced instrumentation mounted on a single platform, this new mission is expected to provide unprecedented observations of clouds from space. However, to do so, the synergistic algorithms that were developed for A-Train measurements have to be adapted to this new instrumental configuration. During my PhD, I focused on the Varcloud algorithm that was developed in 2007 by Delanoë and Hogan, based on a variational technique. The first part of the work consisted in adapting some parameters of the microphysical model of the algorithm to recent studies of a large dataset of in-situ measurements. In particular, the questions of a parameterization of the lidar extinction-to-backscatter ratio and the choice of the mass-size relationship for ice crystals were addressed. The second part of my work consisted in adapting the Varcloud retrieval algorithm to airborne platforms. Airborne platforms are ideal to prepare and validate space missions, allowing for direct underpasses of spaceborne instruments. Moreover, German and French aircraft, respectively HALO and French Falcon 20 have very complementary payloads and are perfectly designed for the preparation, the calibration and the validation of EarthCare. Both aircraft board a high spectral resolution lidar (355 nm on the French Falcon and 532 nm on the HALO) and a Doppler radar at 36 GHz (HALO) and 95 GHz (Falcon). In fall 2016 a field campaign related to the NAWDEX project took place in Iceland, Keflavik with both aircraft involved. The measurements collected during this campaign provide an interesting dataset to characterize cloud microphysics and dynamics in the North Atlantic, which are of high interest regarding the Cloudsat-CALIPSO and EarthCARE missions. In addition, a series of common legs with the same cloud scene observed by both platforms were performed, providing data to study the influence of the instrumental configuration on the retrieved ice cloud properties
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Christodoulou, Apostolos A. « Etude sismotectonique et inversion tridimensionnelle en Grèce du Nord ». Grenoble 1, 1986. http://www.theses.fr/1986GRE10086.
Texte intégralRésumé :
Première Partie: Etude sismotectonique d'un graben complexe, exemple: le graben Mygdonien (Grèce du Nord). Durant les printemps de 1984 et 1985 nous avons installé un réseau sismologique de 29 stations portables dans la région du graben Mydgonien près de Thessaloniki. La sismicité et les mécanismes au foyer ont montré une structure complexe. Des phénomènes compressifs ont été observés au centre du graben. Nous proposons un modèle pour la formation et l'évolution du graben. Au départ la déformation a lieu le long des failles pré-existantes de direction NW-SE ou NNE-SSW avec des mouvements normaux ou décrochants. Dans une deuxième étape il y a formation d'une nouvelle famille de failles normales, dirigées E-W. Cette famille a une direction perpendiculaire à l'axe T moyen, trouvé par les mécanismes au foyer et vient se superposer aux failles initiales. Elle devient rapidement la famille principale et les failles initiales jouent un rôle d'ajusteur de déformation dans cet ensemble. En outre les anciennes failles fonctionnent comme des barrières à l'évo lution des failles dirigées E-W. Deuxième partie: Etudes tridimensionnelle de la croûte et du manteau supérieur à partir de l'inversion des ondes P des téléséismes. A partir des résidus relatifs de temps de parcours des ondes P des téléséismes, enregistrés par le réseau permanent du laboratoire de Géophysique de Thessaloniki, nous avons tenté une inversion tridimensionnelle selon la méthode de Aki, Christofferson et Husebye. Nous avons obtenu des modèles de vitesse en 3D pour les ondes P sous la Grèce du nord, jusqu'à une profondeur de 250 km. Nous avons essayé d'expliquer les variations latérales des vitesses observées, à l'aide de l'isostasie, du flux de chaleur et de la sismicité
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Chanet, Alain. « Determination de vitesses sismiques entre puits, inversion des temps de parcours par modelisation iterative ». Paris 6, 1988. http://www.theses.fr/1988PA066134.
Texte intégralRésumé :
La tomographie appliquee a la geologie presentee dans ce travail repose sur l'estimation d'une grille de repartition des vitesses sismiques entre puits. Cette estimation est faite a partir des temps de parcours d'ondes sismiques traversant la zone a explorer, elle est effectuee suivant un processus iteratif. Ce processus se presente sous deux aspects : - resolution du probleme direct correspondant aux calculs de temps de parcours theoriques en fonction d'une repartition donnee de vitesses de propagation. - resolution du probleme inverse qui consite a fixer un schema de repartition des vitesses repondant au mieux aux temps de parcours mesures sur le terrain. On teste les solutions des deux tomographies ainsi developpees a partir d'exemples synthetiques simples. L'experience acquise permet d'appliquer ces processus a des donnees reelles dans le domaine du genie civil et pour une etude grande profondeur.
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Tan, Xihe [Verfasser], Julia [Akademischer Betreuer] Kowalski et Andreas [Akademischer Betreuer] Kemna. « Development of electromagnetic induction measurement and inversion methods for soil electrical conductivity investigations / Xihe Tan ; Julia Kowalski, Andreas Kemna ». Aachen : Universitätsbibliothek der RWTH Aachen, 2020. http://d-nb.info/1238602371/34.
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Indratno, Sapto Wahyu. « Numerical methods for solving linear ill-posed problems ». Diss., Kansas State University, 2011. http://hdl.handle.net/2097/8109.
Texte intégralRésumé :
Doctor of PhilosophyDepartment of Mathematics
Alexander G. Ramm
A new method, the Dynamical Systems Method (DSM), justified recently, is applied to solving ill-conditioned linear algebraic system (ICLAS). The DSM gives a new approach to solving a wide class of ill-posed problems. In Chapter 1 a new iterative scheme for solving ICLAS is proposed. This iterative scheme is based on the DSM solution. An a posteriori stopping rules for the proposed method is justified. We also gives an a posteriori stopping rule for a modified iterative scheme developed in A.G.Ramm, JMAA,330 (2007),1338-1346, and proves convergence of the solution obtained by the iterative scheme. In Chapter 2 we give a convergence analysis of the following iterative scheme: u[subscript]n[superscript]delta=q u[subscript](n-1)[superscript]delta+(1-q)T[subscript](a[subscript]n)[superscript](-1) K[superscript]*f[subscript]delta, u[subscript]0[superscript]delta=0, where T:=K[superscript]* K, T[subscript]a :=T+aI, q in the interval (0,1),\quad a[subscript]n := alpha[subscript]0 q[superscript]n, alpha_0>0, with finite-dimensional approximations of T and K[superscript]* for solving stably Fredholm integral equations of the first kind with noisy data. In Chapter 3 a new method for inverting the Laplace transform from the real axis is formulated. This method is based on a quadrature formula. We assume that the unknown function f(t) is continuous with (known) compact support. An adaptive iterative method and an adaptive stopping rule, which yield the convergence of the approximate solution to f(t), are proposed in this chapter.
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Srivastava, Deepansh. « NMR methods and analysis for determining correlated structural distributions in amorphous solids ». The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1531928644070636.
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Chibawara, Trust. « Pricing and hedging asian options using Monte Carlo and integral transform techniques ». Thesis, Stellenbosch : University of Stellenbosch, 2010. http://hdl.handle.net/10019.1/4292.
Texte intégralRésumé :
Thesis (MSc (Mathematics))--University of Stellenbosch, 2010.ENGLISH ABSTRACT: In this thesis, we discuss and apply the Monte Carlo and integral transform methods in pricing options. These methods have proved to be very e ective in the valuation of options especially when acceleration techniques are introduced. By rst pricing European call options we have motivated the use of these methods in pricing arithmetic Asian options which have proved to be di cult to price and hedge under the BlackScholes framework. The arithmetic average of the prices in this framework, is a sum of correlated lognormal distributions whose distribution does not admit a simple analytic expression. However, many approaches have been reported in the academic literature for pricing these options. We provide a hedging strategy by manipulating the results by Geman and Yor [42] for continuous xed strike arithmetic Asian call options. We then derive a double Laplace transform formula for pricing continuous Asian call options following the approach by Fu et al. [39]. By applying the multi-Laguerre and iterated Talbot inversion techniques for Laplace transforms to the resulting pricing formula we obtain the option prices. Finally, we discuss the shortcomings of using the Laplace transform in pricing options.
AFRIKAANSE OPSOMMING: In hierdie tesis bespreek ons Monte Carlo- en integraaltransform metodes om die pryse van nansi ele opsies te bepaal. Hierdie metodes is baie e ektief, veral wanneer versnellingsmetodes ingevoer word. Ons bepaal eers die pryse van Europese opsies as motivering, voordat ons die bostaande metodes gebruik vir prysbepaling van Asiatiese opsies met rekenkundige gemiddeldes, wat baie moeiliker is om te hanteer in die BlackScholes raamwerk. Die rekenkundige gemiddelde van batepryse in hierdie raamwerk is 'n som van gekorreleerde lognormale distribusies wie se distribusie nie oor 'n eenvoudige analitiese vorm beskik nie. Daar is egter talle benaderings vir die prysbepaling van hierdie opsies in die akademiese literatuur. Ons bied 'n verskansingsstrategie vir Asiatiese opsies in kontinue tyd met 'n vaste trefprys aan deur die resultate van Geman en Yor [42] te manipuleer. Daarna volg ons Fu et al. [39] om 'n dubbele Laplace transform formule vir die pryse af te lei. Deur toepassing van multi-Laguerre en herhaalde Talbotinversie tegnieke vir Laplace transforms op hierdie formule, bepaal ons dan die opsiepryse. Ons sluit af met 'n bespreking van die tekortkominge van die gebruik van die Laplace transform vir prysbepaling.
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Wittke, Jan [Verfasser], Bülent [Gutachter] Tezkan, Klaus [Gutachter] Spitzer et Becken [Gutachter] Michael. « Meshless methods for Maxwell’s equations with applications to magnetotelluric modelling and inversion / Jan Wittke ; Gutachter : Bülent Tezkan, Klaus Spitzer, Becken Michael ». Köln : Universitäts- und Stadtbibliothek Köln, 2017. http://d-nb.info/1148623698/34.
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Han, Chao. « Advanced signal and imaging methods in ultrasound cortical bone assessment ». Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS144.
Texte intégralRésumé :
La technologie à ultrasons constitue un moyen abordable de mettre en œuvre des solutions non invasives pour évaluer de manière diagnostique les caractéristiques mécaniques de l'os. Dans cette thèse nous introduisons la poursuite orthogonale (OMP) pour obtenir une reconstruction robuste de la forme d'onde de chaque écho après rebond sur les faces externe et interne de l'os cortical. Le temps de vol et les fréquences centrales des échos sont utilisés pour calculer l'atténuation normalisée à large bande (nBUA). Des mesure in vivo ont été effectuées avec succès en mode écho et des données de référence ont été obtenues à partir de mesures HR-pQCT (épaisseur corticale, vBMD). Il est ainsi apparu que Ct.Th et nBUA étaient fortement corrélés aux valeurs d'épaisseur de référence (r2=0,90), respectivement. La deuxième contribution principale de ces travaux consiste en l'utilisation de la méthode TDTE (Time Domain Topological Energy) et de la migration dans l'imagerie de l'os cortical. L'approche TDTE montre de bonnes performances dans l'imagerie de la structure de l'os cortical (faces interne et externe de l'os, ainsi que la structure poreuse à l'intérieur de l'os). La migration quant à elle peut fournir une distribution quantitative approximative de la densité, de la vitesse de compression et de la vitesse de cisaillementUltrasound technology provides an affordable means to implement non-invasive solutions to diagnostically assess the mechanical characteristics of the bone. In this thesis we introduce Orthogonal Matching Pursuit (OMP) to obtain a robust reconstruction of the waveform of each echo bouncing off the cortical bone surfaces. Echoes' time-of-flight and central frequencies are used to calculate Ct.Th and normalized broadband attenuation (nBUA). In vivo measurements have been successfully performed with pulse-echo ultrasound and reference data wase obtained with HR-pQCT (cortical thickness, vBMD). Ct.Th and nBUA were highly correlated to reference thickness values (r2=0.90) and vBMD (r2=0,90), respectively. The second main contribution is that we introduce Time Domain Topological Energy (TDTE) method and migration into cortical bone imaging. TDTE shows well performance in extracting the structure of cortical bone, including the external, internal boundary of cortical bone and porous structure inside the cortical bone. Migration can provide a rough quantitative distribution of density, compression wave speed, and shear wave speed
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Galiana, Blanch Savitri. « Two-dimensional modeling and inversion of the controlled-source electromagnetic and magnetotelluric methods using finite elements and full-space PDE-constrained optimization strategies ». Doctoral thesis, Universitat de Barcelona, 2016. http://hdl.handle.net/10803/400616.
Texte intégralRésumé :
The controlled-source electromagnetics (CSEM) and magnetotellurics (MT) methods are common geophysical tools for imaging the Earth's electrical interior. To appreciate measured data, both methods require forward and inverse modeling of the subsurface with the ultimate goal of finding a feasible model for which the simulated data reasonably fits the observations. The goodness of this fit depends on the error in the measured data, on the numerical error and on the degree of approximation inferred by numerical modeling. Therefore, active research focuses on new methods for modeling and inversion to improve accuracy and reliability for increasingly complex scenarios. In a first step, physical factors such as anisotropy, topography and realistic sources must be taking into account. Second, numerical methods need to be assessed in terms of solution accuracy, time efficiency and memory demand. The finite elements (FE) methods offer much flexibility in model geometry and contain quality control mechanisms for the solution, as shape function order and adaptive mesh refinement. Most emerging modeling programs are based on FE, however, inversion programs are generally based on finite differences (FD) or integral equation (IE) methods. On the other hand, inverse modeling is usually based on gradient methods and formulated in the reduced-space, where the electrical conductivity is the only optimization variable. Originally, the inverse problem is stated for the EM fields and the conductivity parameter (in the full-space), and constrained by governing partial differential equations (PDEs). The reduced-space strategy eliminates the field variables by applying equality constraints and solves then, the unconstrained problem. A common drawback of this is the repeated costly computation of the forward solution. Solving the PDE-constrained optimization problem directly, in the full-space, has the advantage that it is only necessary to exactly solve the PDEs at the end of the optimization, but it comes at the cost of a larger number of variables.
This thesis develops a robust and versatile adaptive unstructured mesh FE program to model the total field for two-dimensional (2-D) anisotropic CSEM and MT data, allowing for arbitrarily oriented, three-dimensional (3-D) sources, for which a two-and-a-half-dimensional (2.5-D) approximation is employed. The formulations of the problems in a FE framework are derived for isotropic and anisotropic subsurface conductivity structures. The accuracy of the solution is controlled and improved by a goal-oriented adaptive mesh refinement algorithm. Exhaustive numerical experiments validate the adaptive FE program for both CSEM and MT methods and on land and marine environments. The influence of the model dimensions, mesh design and order of shape functions on the solution accuracy is studied and notably, an outperformance of quadratic shape functions is found (compared to linear and cubic). Several examples demonstrate the effect of complex scenarios on EM data. In particular, we study the distortion caused by: the bathymetry, the orientation and geometry of the sources and the anisotropy, considering vertical and dipping cases. All examples showcase the importance of adequate consideration of these very common physical features of real world data. Further, a formulation for the 2.5-D CSEM inversion as a PDE-constrained optimization in full-space is derived within a FE framework following two strategies: discretize-optimize and optimize-discretize. The discretize-optimize formulation is implemented using a general purpose optimization algorithm. Two examples, a canonical reservoir model and a more realistic marine model with topography, demonstrate the performance of this inversion scheme, recovering in both cases the model’s main structures within an acceptable data misfit. Finally, the optimize-discretize formulation is derived in a FE framework, as a first step towards a development of an inversion scheme using adaptive FE meshes.[cat] El mètode de font electromagnètica controlada (CSEM) i el mètode magnetotel.lúric (MT) són tècniques geofísiques usades habitualment per obtenir una imatge de les propietats elèctriques del subsòl terrestre i s'utilitzen independentment, conjuntament i en combinació amb altres tècniques geofísiques. Per poder interpretar les dades, ambdós mètodes necessiten la modelització directa i inversa de la conductivitat elèctrica del subsòl amb l'objectiu final d'obtenir un model coherent per al qual les dades simulades s'ajustin de forma raonable a les observacions. Naturalment, la qualitat d'aquest ajust no només depèn de l'error en les dades mesurades i de l'error numèric, sinó també del grau en l'aproximació física inferit per la modelització numèrica. D'aquesta manera, les recerques actuals se centren a investigar noves metodologies per a la modelització i inversió, per tal d'obtenir models acurats i fiables de les estructures de la Terra en escenaris cada cop més complexos. Un primer pas és millorar les aproximacions en la modelització tenint en compte factors físics com ara l'anisotropia, la topografia o fonts més realistes. En segon lloc, per tal d'acomodar aquests factors en un programa de modelització i inversió i per poder tractar els conjunts de dades típicament llargs, els mètodes numèrics han de ser avaluats en termes de la precisió de la solució, l'eficiència en temps i la demanda en memòria. Els mètodes de modelització en elements finits (FE) són coneguts per oferir una major flexibilitat en la modelització de la geometria i contenen mecanismes de control de la solució, com ara l'ordre de les funcions forma i la tècnica de refinament adaptatiu de la malla. La majoria de programes de modelització emergents estan basats en els FE, i mostren avantatges significatius, però gairebé tots els programes de modelització inversa, encara avui dia, estan basats en el mètode de les diferències finites (FD) o en el mètode de l'equació integral (IE). A més a més, la modelització inversa desenvolupada per a dades electromagnètiques (EM) es basa generalment en mètodes del gradient i es formula en un espai reduït, on les úniques variables d'optimització són els paràmetres del model, és a dir, la conductivitat elèctrica del subsòl. Originalment, el problema invers es formula per als camps EM i per al paràmetre conductivitat, i està constret per les equacions diferencials en derivades parcials (PDEs) que governen les variables camps EM. L'estratègia d'espai reduït elimina les variables camps aplicant lligams d'igualtat i soluciona, doncs, el problema no constret en l'espai reduït dels paràmetres del model. Un desavantatge general d'aquests mètodes és la costosa repetició del càlcul de la solució del problema directe i de la matriu jacobiana de sensibilitats (per mètodes basats en Newton). D'altra banda, també és possible de solucionar el problema invers en l'espai complet de les variables camps EM i del paràmetre conductivitat. Solucionar-hi el problema d'optimització constret per les PDEs té l'avantatge que només és necessari de solucionar exactament el problema directe al final del procés d'optimització, però això comporta el cost addicional de tenir moltes més variables d'optimització i de la presència de lligams d'igualtat. També, en particular, en el marc dels FE, el problema d'optimització constret per les PDEs té l'avantatge afegit d'incloure tècniques sofisticades pròpies dels FE en el procés d'inversió, com ara el refinament adaptatiu de la malla. Aquesta tesi desenvolupa un programa robust i versàtil amb FE i malles irregulars adaptatives per modelar numèricament el camp total de dades CSEM i MT bidimensionals (2D) i anisòtropes, que permet l'ús de fonts tridimensionals (3D) orientades arbitràriament. Per tal de representar fonts CSEM 3D en un model físic 2D, s'utilitza una aproximació dos i mig dimensional (2.5D). Les formulacions FE es deriven per a ambdós mètodes, per a estructures de conductivitat del subsòl isòtropes i anisòtropes. Encara que el cas anisòtrop no és general, inclou anisotropia vertical i de cabussament. La precisió en la solució es controla i millora amb un algoritme de refinament adaptatiu de la malla utilitzant mètodes d'estimació de l'error a posteriori. Una sèrie exhaustiva d'experiments numèrics valida el programa de FE adaptatius per ambdós mètodes, CSEM i MT, i en escenaris terrestres i marins. S'estudia la influència de les dimensions del model, del disseny de la malla i de l'ordre de les funcions forma en l'exactitud de la solució i es troba un comportament notablement superior de les funcions forma quadràtiques comparades amb les lineals o cúbiques. Diferents exemples mostren l'efecte d'escenaris complexos sobre les dades EM, en particular, un model amb batimetria, un model terrestre i un de marí amb fonts orientades i de dimensió finita, un medi amb anisotropia vertical amb un reservori encastat i un altre amb un reservori encastat en una estructura anticlinal. Aquests exemples demostren la importància de considerar adequadament (en termes de modelització directa) característiques físiques com la topografia, l'orientació i geometria de la font i l'anisotropia del medi, que sovint es troben en mesures reals. Juntament amb això, es deriva una formulació per al problema invers 2.5D CSEM com una optimització constreta per les PDEs en l'espai complet i en un marc de FE, seguint dues estratègies diferents: discretització-optimització i optimització-discretització. L'estratègia de discretització-optimització considera que el problema invers es troba en forma discretitzada i deriva les condicions d'optimitat de la Lagrangiana i el pas de Newton. Contràriament, l'aproximació optimització-discretització deriva primer les condicions d'optimitat i el pas de Newton o una aproximació d'aquest, i després discretitza les equacions resultants. La implementació de la formulació discretització-optimització es mostra en dos exemples, un model canònic de reservori i un model marí més realista amb topografia, utilitzant un programa d'optimització de propòsit general, que és una implementació d'un algoritme de programació quadràtica seqüencial (SQP). Encara que no s'utilitza una regularització explícita, l'ús de diferents malles per al paràmetre del model i per a les variables camps, permet recuperar les principals estructures del model i obtenir un ajust de les dades acceptable. Cal dir, però, que l'eficiència en temps i memòria del programa hauria de millorar-se. Finalment, el problema invers 2.5D CSEM es formula com un problema d'optimització constret per les PDEs en l'espai complet i en un marc de FE utilitzant una estratègia d'optimització-discretització i com un primer pas per al desenvolupament d'un esquema d'inversió que utilitzi malles adaptatives de FE.
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Line, Michael R., Kevin B. Stevenson, Jacob Bean, Jean-Michel Desert, Jonathan J. Fortney, Laura Kreidberg, Nikku Madhusudhan, Adam P. Showman et Hannah Diamond-Lowe. « NO THERMAL INVERSION AND A SOLAR WATER ABUNDANCE FOR THE HOT JUPITER HD 209458B FROM HST /WFC3 SPECTROSCOPY ». IOP PUBLISHING LTD, 2016. http://hdl.handle.net/10150/622434.
Texte intégralRésumé :
The nature of the thermal structure of hot Jupiter atmospheres is one of the key questions raised by the characterization of transiting exoplanets over the past decade. There have been claims that many hot Jupiters exhibit atmospheric thermal inversions. However, these claims have been based on broadband photometry rather than the unambiguous identification of emission features with spectroscopy, and the chemical species that could cause the thermal inversions by absorbing stellar irradiation at high altitudes have not been identified despite extensive theoretical and observational effort. Here we present high-precision Hubble Space Telescope WFC3 observations of the dayside thermal emission spectrum of the hot Jupiter HD 209458b, which was the first exoplanet suggested to have a thermal inversion. In contrast to previous results for this planet, our observations detect water in absorption at 6.2 sigma confidence. When combined with Spitzer photometry, the data are indicative of a monotonically decreasing temperature with pressure over the range of 1-0.001 bars at 7.7 sigma confidence. We test the robustness of our results by exploring a variety of model assumptions, including the temperature profile parameterization, presence of a cloud, and choice of Spitzer data reduction. We also introduce a new analysis method to determine the elemental abundances from the spectrally retrieved mixing ratios with thermochemical self-consistency and find plausible abundances consistent with solar metallicity (0.06-10 x solar) and carbon-to oxygen ratios less than unity. This work suggests that high-precision spectrophotometric results are required to robustly infer thermal structures and compositions of extrasolar planet atmospheres and to perform comparative exoplanetology.
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Pinard, Hugo. « Imagerie électromagnétique 2D par inversion des formes d'ondes complètes : Approche multiparamètres sur cas synthétiques et données réelles ». Thesis, Université Grenoble Alpes (ComUE), 2017. http://www.theses.fr/2017GREAU041/document.
Texte intégralRésumé :
Le radar géologique est une méthode d'investigation géophysique basée sur la propagation d'ondes électromagnétiques dans le sous-sol. Avec des fréquences allant de 5 MHz à quelques GHz et une forte sensibilité aux propriétés électriques, le géoradar fournit des images de réflectivité dans des contextes et à des échelles très variés : génie civil, géologie, hydrogéologie, glaciologie, archéologie. Cependant, dans certains cas, la compréhension fine des processus étudiés dans la subsurface nécessite une quantification des paramètres physiques du sous-sol. Dans ce but, l'inversion des formes d'ondes complètes, méthode initialement développée pour l'exploration sismique qui exploite l'ensemble des signaux enregistrés, pourrait s'avérer efficace. Dans cette thèse, je propose ainsi des développements méthodologiques par une approche d'inversion multiparamètres (permittivité diélectrique et conductivité), pour des configurations en transmission, en deux dimensions.Ces développements sont ensuite appliqués à un jeu de données réelles acquises entre forages.Dans une première partie, je présente tout d'abord la méthode numérique utilisée pour modéliser la propagation des ondes électromagnétiques dans un milieu 2D hétérogène, élément indispensable pour mener à bien le processus d'imagerie. Ensuite, j’introduis puis étudie le potentiel des méthodes d’optimisation locale standards (gradient conjugué non linéaire, l-BFGS, Newton tronqué dans ses versions Gauss-Newton et Exact-Newton) pour découpler la permittivité diélectrique et la conductivité électrique. Je montre notamment qu’un découplage effectif n’est possible qu’avec un modèle initial suffisamment précis et la méthode la plus sophistiquée (Newton tronqué). Comme dans le cas général, ce modèle initial n’est pas disponible, il s’avère nécessaire d'introduire un facteur d'échelle qui répartit le poids relatif de chaque classe de paramètres dans l'inversion. Dans un milieu réaliste avec une acquisition entre puits, je montre que les différentes méthodes d'optimisation donnent des résultats similaires en matière de découplage de paramètres. C'est finalement la méthode l-BFGS qui est retenue pour l'application aux données réelles, en raison de coûts de calcul plus faibles.Dans une deuxième partie, j'applique cette méthodologie à des données réelles acquises entre deux forages localisés dans des formations carbonatées, à Rustrel (France, 84). Cette inversion est réalisée en parallèle d'une approche synthétique à l'aide d'un modèle représentatif du site étudié et des configurations d'acquisition similaires. Ceci permet de pouvoir comprendre, contrôler et valider les observations et conclusions obtenues sur les données réelles. Cette démarche montre que la reconstruction de la permittivité est très robuste. A contrario, l'estimation de la conductivité souffre de deux couplages majeurs, avec la permittivité diélectrique, d'une part, et avec l'amplitude de la source estimée, d'autre part. Les résultats obtenus sont confrontés avec succès à des données indépendantes (géophysique depuis la surface, analyse sur échantillons de roche), et permet de bénéficier d'une image haute-résolution des formations géologiques. Enfin, une analyse 3D confirme que les structures 3D à fort contraste de propriétés, telles que la galerie enfouie sur notre site, nécessiteraient une approche de modélisation 3D, notamment pour mieux expliquer les amplitudes observéesGround Penetrating Radar (GPR) is a geophysical investigation method based on electromagnetic waves propagation in the underground. With frequencies ranging from 5 MHz to a few GHz and a high sensitivity to electrical properties, GPR provides reflectivity images in a wide variety of contexts and scales: civil engineering, geology, hydrogeology, glaciology, archeology. However, in some cases, a better understanding of some subsurface processes requires a quantification of the physical parameters of the subsoil. For this purpose, inversion of full waveforms, a method initially developed for seismic exploration that exploits all the recorded signals, could prove effective. In this thesis, I propose methodological developments using a multiparameter inversion approach (dielectric permittivity and conductivity), for two-dimensional transmission configurations. These developments are then applied to a real data set acquired between boreholes.In a first part, I present the numerical method used to model the propagation of electromagnetic waves in a heterogeneous 2D environment, a much-needed element to carry out the process of imaging. Then, I introduce and study the potential of standard local optimization methods (nonlinear conjugate gradient, l-BFGS, Newton truncated in its Gauss-Newton and Exact-Newton versions) to fight the trade-off effects related to the dielectric permittivity and to the electrical conductivity. In particular, I show that effective decoupling is possible only with a sufficiently accurate initial model and the most sophisticated method (truncated Newton). As in the general case, this initial model is not available, it is necessary to introduce a scaling factor which distributes the relative weight of each parameter class in the inversion. In a realistic medium and for a cross-hole acquisition configuration, I show that the different optimization methods give similar results in terms of parameters decoupling. It is eventually the l-BFGS method that is used for the application to the real data, because of lower computation costs.In a second part, I applied the developed Full waveform inversion methodology to a set of real data acquired between two boreholes located in carbonate formations, in Rustrel (France, 84). This inversion is carried out together with a synthetic approach using a model representative of the studied site and with a similar acquisition configuration. This approach enables us to monitor and validate the observations and conclusions derived from data inversion. It shows that reconstruction of dielectrical permittivity is very robust. Conversely, conductivity estimation suffers from two major couplings: the permittivity and the amplitude of the estimated source. The derived results are successfully compared with independent data (surface geophysics and rock analysis on plugs) and provides a high resolution image of the geological formation. On the other hand, a 3D analysis confirms that 3D structures presenting high properties contrasts, such as the buried gallery present in our site, would require a 3D approach, notably to better explain the observed amplitudes
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Ben, Youssef Atef. « Contrôle de têtes parlantes par inversion acoustico-articulatoire pour l’apprentissage et la réhabilitation du langage ». Thesis, Grenoble, 2011. http://www.theses.fr/2011GRENT088/document.
Texte intégralRésumé :
Les sons de parole peuvent être complétés par l'affichage des articulateurs sur un écran d'ordinateur pour produire de la parole augmentée, un signal potentiellement utile dans tous les cas où le son lui-même peut être difficile à comprendre, pour des raisons physiques ou perceptuelles. Dans cette thèse, nous présentons un système appelé retour articulatoire visuel, dans lequel les articulateurs visibles et non visibles d'une tête parlante sont contrôlés à partir de la voix du locuteur. La motivation de cette thèse était de développer un tel système qui pourrait être appliqué à l'aide à l'apprentissage de la prononciation pour les langues étrangères, ou dans le domaine de l'orthophonie. Nous avons basé notre approche de ce problème d'inversion sur des modèles statistiques construits à partir de données acoustiques et articulatoires enregistrées sur un locuteur français à l'aide d'un articulographe électromagnétique (EMA). Notre approche avec les modèles de Markov cachés (HMMs) combine des techniques de reconnaissance automatique de la parole et de synthèse articulatoire pour estimer les trajectoires articulatoires à partir du signal acoustique. D'un autre côté, les modèles de mélanges gaussiens (GMMs) estiment directement les trajectoires articulatoires à partir du signal acoustique sans faire intervenir d'information phonétique. Nous avons basé notre évaluation des améliorations apportées à ces modèles sur différents critères : l'erreur quadratique moyenne (RMSE) entre les coordonnées EMA originales et reconstruites, le coefficient de corrélation de Pearson, l'affichage des espaces et des trajectoires articulatoires, aussi bien que les taux de reconnaissance acoustique et articulatoire. Les expériences montrent que l'utilisation d'états liés et de multi-gaussiennes pour les états des HMMs acoustiques améliore l'étage de reconnaissance acoustique des phones, et que la minimisation de l'erreur générée (MGE) dans la phase d'apprentissage des HMMs articulatoires donne des résultats plus précis par rapport à l'utilisation du critère plus conventionnel de maximisation de vraisemblance (MLE). En outre, l'utilisation du critère MLE au niveau de mapping direct de l'acoustique vers l'articulatoire par GMMs est plus efficace que le critère de minimisation de l'erreur quadratique moyenne (MMSE). Nous constatons également trouvé que le système d'inversion par HMMs est plus précis celui basé sur les GMMs. Par ailleurs, des expériences utilisant les mêmes méthodes statistiques et les mêmes données ont montré que le problème de reconstruction des mouvements de la langue à partir des mouvements du visage et des lèvres ne peut pas être résolu dans le cas général, et est impossible pour certaines classes phonétiques. Afin de généraliser notre système basé sur un locuteur unique à un système d'inversion de parole multi-locuteur, nous avons implémenté une méthode d'adaptation du locuteur basée sur la maximisation de la vraisemblance par régression linéaire (MLLR). Dans cette méthode MLLR, la transformation basée sur la régression linéaire qui adapte les HMMs acoustiques originaux à ceux du nouveau locuteur est calculée de manière à maximiser la vraisemblance des données d'adaptation. Finalement, cet étage d'adaptation du locuteur a été évalué en utilisant un système de reconnaissance automatique des classes phonétique de l'articulation, dans la mesure où les données articulatoires originales du nouveau locuteur n'existent pas. Finalement, en utilisant cette procédure d'adaptation, nous avons développé un démonstrateur complet de retour articulatoire visuel, qui peut être utilisé par un locuteur quelconque. Ce système devra être évalué de manière perceptive dans des conditions réalistesSpeech sounds may be complemented by displaying speech articulators shapes on a computer screen, hence producing augmented speech, a signal that is potentially useful in all instances where the sound itself might be difficult to understand, for physical or perceptual reasons. In this thesis, we introduce a system called visual articulatory feedback, in which the visible and hidden articulators of a talking head are controlled from the speaker's speech sound. The motivation of this research was to develop such a system that could be applied to Computer Aided Pronunciation Training (CAPT) for learning of foreign languages, or in the domain of speech therapy. We have based our approach to this mapping problem on statistical models build from acoustic and articulatory data. In this thesis we have developed and evaluated two statistical learning methods trained on parallel synchronous acoustic and articulatory data recorded on a French speaker by means of an electromagnetic articulograph. Our Hidden Markov models (HMMs) approach combines HMM-based acoustic recognition and HMM-based articulatory synthesis techniques to estimate the articulatory trajectories from the acoustic signal. Gaussian mixture models (GMMs) estimate articulatory features directly from the acoustic ones. We have based our evaluation of the improvement results brought to these models on several criteria: the Root Mean Square Error between the original and recovered EMA coordinates, the Pearson Product-Moment Correlation Coefficient, displays of the articulatory spaces and articulatory trajectories, as well as some acoustic or articulatory recognition rates. Experiments indicate that the use of states tying and multi-Gaussian per state in the acoustic HMM improves the recognition stage, and that the minimum generation error (MGE) articulatory HMMs parameter updating results in a more accurate inversion than the conventional maximum likelihood estimation (MLE) training. In addition, the GMM mapping using MLE criteria is more efficient than using minimum mean square error (MMSE) criteria. In conclusion, we have found that the HMM inversion system has a greater accuracy compared with the GMM one. Beside, experiments using the same statistical methods and data have shown that the face-to-tongue inversion problem, i.e. predicting tongue shapes from face and lip shapes cannot be solved in a general way, and that it is impossible for some phonetic classes. In order to extend our system based on a single speaker to a multi-speaker speech inversion system, we have implemented a speaker adaptation method based on the maximum likelihood linear regression (MLLR). In MLLR, a linear regression-based transform that adapts the original acoustic HMMs to those of the new speaker was calculated to maximise the likelihood of adaptation data. Finally, this speaker adaptation stage has been evaluated using an articulatory phonetic recognition system, as there are not original articulatory data available for the new speakers. Finally, using this adaptation procedure, we have developed a complete articulatory feedback demonstrator, which can work for any speaker. This system should be assessed by perceptual tests in realistic conditions
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Böhm, Christian [Verfasser], Michael [Akademischer Betreuer] Ulbrich, Anton [Akademischer Betreuer] Schiela et Georg [Akademischer Betreuer] Stadler. « Efficient Inversion Methods for Constrained Parameter Identification in Full-Waveform Seismic Tomography / Christian Böhm. Gutachter : Anton Schiela ; Georg Stadler ; Michael Ulbrich. Betreuer : Michael Ulbrich ». München : Universitätsbibliothek der TU München, 2015. http://d-nb.info/1071948024/34.
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Böhm, Christian Verfasser], Michael [Akademischer Betreuer] [Ulbrich, Anton [Akademischer Betreuer] Schiela et Georg [Akademischer Betreuer] Stadler. « Efficient Inversion Methods for Constrained Parameter Identification in Full-Waveform Seismic Tomography / Christian Böhm. Gutachter : Anton Schiela ; Georg Stadler ; Michael Ulbrich. Betreuer : Michael Ulbrich ». München : Universitätsbibliothek der TU München, 2015. http://nbn-resolving.de/urn:nbn:de:bvb:91-diss-20150227-1232040-1-7.
Texte intégral
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Popov, Mikhail. « Analytic and Numerical Methods for the Solution of Electromagnetic Inverse Source Problems ». Doctoral thesis, KTH, Electromagnetic Theory, 2001. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3134.
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Nguyen, Thi Minh Phuong. « Lead acid batteries in extreme conditions : accelerated charge, maintaining the charge with imposed low current, polarity inversions : Introducing non-conventional charge methods ». Montpellier 2, 2009. http://www.theses.fr/2009MON20063.
Texte intégralRésumé :
Les trois grands domaines d'application de batteries au plomb sont les batteries de démarrage, les batteries de traction et les batteries stationnaires. Les évolutions des marchés, notamment celui de l'énergie, ouvrent de nouvelles applications de stockage par accumulateur au plomb: transports électriques, énergies renouvelables dont éolien et photovoltaïque, stockage réseau, qualité, secours. Dans la plupart des cas, les contraintes de l'application mènent à revoir profondément les algorithmes de charge. Nous avons mené différentes études sur les batteries au plomb dans des conditions extrêmes: charge rapide pour batteries ouvertes, maintien en charge pour batteries stationnaires, décharge profonde avec inversion de polarité. À partir de ces travaux, un nouvel algorithme de charge rapide avec une phase de déstratification précoce a été mis au point. De plus, une nouvelle méthode de maintien en charge par faible courant imposé a été testée sur différentes technologies de batteries au plomb. Elle montre plusieurs avantages en termes de réduction importante de la corrosion, de diminution de la perte d'eau due à la corrosion et de besoin de charges périodiquesThree main applications of lead acid batteries are: starting, lighting and ignition batteries (SLI batteries), motive batteries and stationary batteries. Increasing attention to the global climate change and the sustainable development open new applications for the energy storage using lead acid batteries: electric transport, renewable energies such as photovoltaic and wind, grid storage, quality and emergency supplies. In some cases, new applications need new charge algorithms. Various studies were conducted with lead acid batteries in extreme conditions: accelerated charge for vented batteries, maintaining the charge with imposed low current for stationary batteries and deep discharge with polarity inversion. A new charge method for accelerated and fast charges of flooded lead acid batteries is developed. A new method of maintaining the charge with imposed low currents and periodical charges is tested on different technologies of lead acid batteries. It has the advantages of reducing drastically corrosion, of limiting water loss due to corrosion and the need of periodical charges
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Klein, Ole [Verfasser], et Peter [Akademischer Betreuer] Bastian. « Preconditioned and Randomized Methods for Efficient Bayesian Inversion of Large Data Sets and their Application to Flow and Transport in Porous Media / Ole Klein ; Betreuer : Peter Bastian ». Heidelberg : Universitätsbibliothek Heidelberg, 2016. http://d-nb.info/1180617002/34.
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Bellis, Cédric. « Qualitative Methods for Inverse Scattering in Solid Mechanics ». Phd thesis, Ecole Polytechnique X, 2010. http://pastel.archives-ouvertes.fr/pastel-00557545.
Texte intégralRésumé :
Contexte. Les problèmes inverses, qui font l'objet de nombreuses études aujourd'hui, apparaissent dans une large gamme d'applications : imagerie et tomographie, identification de propriétés matérielles, contrôle non destructif,... L'étude présentée s'inscrit dans le cadre de ce dernier exemple. Elle a pour objet la recherche de nouvelles méthodes, numériquement rapides, permettant une identification qualitative d'objets (inclusions, cavités, fissures,...) enfouis dans des milieux élastiques linéaires, en connaissant (au moins partiellement) la réponse en surface à une sollicitation dynamique. La plupart des méthodes classiquement utilisées pour traiter ce type de problèmes sont fondées sur des algorithmes itératifs de minimisation qui requièrent un grand nombre de simulations directes. Dans le contexte considéré pour cette étude (propagation d'ondes dans des solides élastiques tridimensionnels), ces simulations sont très coûteuses numériquement. L'émergence récente de techniques permettant de sonder, numériquement, de façon non-itérative un milieu donné, a permis d'aborder ces problèmes sous un nouveau jour. Un ensemble d'études a en particulier montré, dans le cadre des hypothèses adoptées pour cette thèse, l'intérêt de méthodes telles que la Sensibilité Topologique ou le Linear Sampling, pour une détection approchée mais rapide. Objectifs de la thèse. L'étude qui est présentée ici, s'inscrit dans la perspectives du développement des deux méthodes mentionnées, dans le contexte de la mécanique des solides déformables, c'est-à-dire pour des problèmes de diffraction inverse en acoustique et en élasticité. Les différents point abordés dans ce travail sont les suivants : • Appréciation des capacités et des performances respectives des deux méthodes, en particulier lorsqu'elles sont mises en œuvre dans des codes numériques usuels, fondés par exemple sur la méthode des éléments finis. • Utilisation de ces développements pour une identification qualitative combinant géométrie et propriétés matérielles des défauts diffractants inconnus. • Extension de ces méthodes, ainsi que démonstration de leurs pertinences, pour des problèmes de diffraction inverse dans le domaine temporel ou utilisation des mesures multi-fréquentielles des champs diffractés. • Etude de quelques problèmes théoriques fondamentaux pour la justification et la mise en œuvre rigoureuse de ces méthodes. • Compréhension des liens théoriques pouvant exister entre la méthode de sensibilité topologique et la méthode de ”linear sampling”.
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Rambourg, Dimitri. « Transposition de paramètres estimés par inversion d'un modèle hydrodynamique bidimensionnel à un modèle de transport de soluté tridimensionnel : méthodologie et application à un aquifère alluvial ». Thesis, Strasbourg, 2020. http://www.theses.fr/2020STRAH014.
Texte intégralRésumé :
La thèse propose un outil de modélisation des écoulements et du transport des polluants dissous dans les aquifères, avec un exemple d’application au site du CEA de Marcoule (Gard). Les développements méthodologiques et l’application au site d’étude s’échelonnent en trois phases. Une inversion des paramètres hydrodynamiques de l’aquifère en 2D, avec une formulation adaptée au contexte du site d’étude (contrainte de la topographie complexe du substratum de l’aquifère, intégration de données géologiques à grande échelle), permet de reproduire avec fidélité et robustesse le comportement de la nappe alluviale au droit de Marcoule. Des modèles hydrogéologiques 3D sont ensuite construits en procédant à l’interpolation de données de sondage via deux méthodes (une approche stochastique et une approche déterministe). La paramétrisation des hétérogénéités produites par l’interpolation exploite les valeurs de transmissivité issues de l’inversion 2D. Pour finir, le modèle hydrogéologique paramétré est exploité pour simuler d’écoulement et de transport de contaminants dissous en trois dimensions, en zone saturée et en zone insaturéeThe thesis proposes a tool for modelling flows and the transport of dissolved pollutants in aquifers, with an example of application to the CEA site at Marcoule (Gard). The methodological developments and the application to the study site are divided into three phases. An inversion of the hydrodynamic parameters of the aquifer in 2D, with a formulation adapted to the context of the study site (constraint of the complex topography of the aquifer bedrock, integration of large-scale geological data), allows the behaviour of the alluvial water table at Marcoule to be reproduced with fidelity and robustness. 3D hydrogeological models are then constructed by interpolating borehole data using two methods (a stochastic approach and a deterministic approach). The parameterisation of the heterogeneities produced by the interpolation exploits the 2D inversion’s transmissivity values. Finally, the parameterised hydrogeological model is used to simulate the flow and transport of dissolved contaminants in three dimensions, in the saturated zone and the vadose zone