No description available.

The determination of the figure of the Earth and its gravity field has long relied on methodologies that approximate the Earth by a sphere, but this level of accuracy is no longer adequate for many applications, due to the advent of new and advanced measurement techniques. New, practical and highly accurate methodologies for gravity field modelling that describe the Earth as an oblate ellipsoid of revolution are therefore required. The foundation for these methodologies is formed by solutions to ellipsoidal geodetic boundary-value problems. In this thesis, new solutions to the ellipsoidal Dirichlet, Neumann and second-order boundary-value problems, as well as the fixed- and free-geodetic boundary-value problems, are derived. These solutions do not rely on any spherical approximation, but are nevertheless completely based on a simple spherical harmonic expansion of the function that is to be determined. They rely on new relations among spherical harmonic base functions. In the new solutions, solid spherical harmonic coefficients of the desired function are expressed as a weighted summation over surface spherical harmonic coefficients of the data on the ellipsoidal boundary, or alternatively as a weighted summation over coefficients that are computed under the approximation that the boundary is a sphere. / Specific applications of the new solutions are the computation of geopotential coefficients from terrestrial gravimetric data and local or regional gravimetric geoid determination. Numerical closed-loop simulations have shown that the accuracy of geopotential coefficients obtained with the new methods is significantly higher than the accuracy of existing methods that use the spherical harmonic framework. The ellipsoidal corrections to a Stokesian geoid determination computed from the new solutions show strong agreement with existing solutions. In addition, the importance of the choice of the reference sphere radius in Stokes's formula and its effect on the magnitude and spectral sensitivity of the ellipsoidal corrections are pointed out.

This paper presents a method to reduce time complexity of the computation of higher–order tensor lines. The method can be applied to higher–order tensors and the spherical harmonics representation, both widely used in medical imaging. It is based on a gradient descend technique and integrates well into fiber tracking algorithms. Furthermore, the method improves the angular resolution in contrast to discrete sampling methods which is especially important to tractography, since there, small errors accumulate fast and make the result unusable. Our implementation does not interpolate derived directions but works directly on the interpolated tensor information. The specific contribution of this paper is a fast algorithm for tracking lines tensor fields of arbitrary order that increases angular resolution compared to previous approaches.

In this thesis work the accuracy of the spherical harmonic synthesis and analysis are investigated, by simulated numerical studies.The main idea is to investigate the loss of accuracy, in the geopotential coeffcients, by the following testing method. We start with a synthesis calculation, using the coefficients(EGM2008), to calculate geoid heights on a regular grid. Those geoid heights are then used in an analysis calculation to obtain a new set of coeffcients, which are in turn used to derive a new set of geoid heights. The difference between those two sets of geoid heights will be analyzed to assess the accuracy of the synthesis and analysis calculations.The tests will be conducted with both point-values and area-means in the blocks in the grid. The area-means are constructed in some different ways and will also be compared to the mean value from 10000 point values as separate tests. Numerical results from this investigation show there are signifi…cant systematic errors in the geoid heights computed by spherical harmonic synthesis and analysis, sometimes reaching as high as several meters. Those big errors are most common at the polar regions and at the mid-latitude regions.

Penser les traitements du son spatialisés en ambisonie permet de mettre en valeur le potentiel musical de la décomposition du champ sonore en harmoniques sphériques, et amène à redéfinir la représentation de l’espace sonore. Cette thèse défend que les représentations abstraites et intermédiaires de l’espace sonore permettent d’élaborer de nouvelles approches originales de la mise en espace du son. Le raisonnement amenant à cette affirmation commence par l’appropriation musicale de l’approche ambisonique. La création de nouveaux traitements de l’espace et du son amène à utiliser de manière originale les signaux associés aux harmoniques sphériques, et à concevoir différemment les relations qui les régissent, ainsi que leur hiérarchisation. La particularité de ces approches expérimentales et les caractéristiques singulières des champs sonores générés, nécessitent de concevoir de nouveaux outils théoriques et pratiques pour leur analyse et leur restitution. Les changements opérés permettent alors de libérer cette approche des enjeux techniques et matériels initiaux en ambisonie. Mais ils permettent surtout de s’émanciper des modèles psychoacoustiques et acoustiques sur lesquels ces techniques reposent originellement. Dans ce contexte, les signaux associés aux harmoniques sphériques ne sont plus nécessairement une représentation rationnelle du champ sonore, mais deviennent une représentation abstraite de l’espace sonore possédant en soi, un potentiel musical. Cette thèse propose alors un nouveau modèle de spatialisation fondé sur une décomposition matricielle de l’espace sonore permettant de valider les hypothèses. / The creation of sound effects in space with Ambisonics highlights the musical potential of sound field decomposition by spherical harmonics, and redefines the representation of the sound space. This thesis defends that the abstract and intermediate representations of the sound space make it possible to develop new original approaches to sound spatialization. The reasoning that leads to this affirmation begins with the musical appropriation of the ambisonic approach. The creation of new space and sound processing patterns in Ambisonics leads to an original way of using signals associated with spherical harmonics, and to a different conception of the relations between them, and their hierarchization. The specificities of these experimental approaches and the singular characteristics of the sound fields generated call for the design of new theoretical and practical tools, for their analysis and restitution. The performed changes make it possible to free this approach from the initial technical and material issues of Ambisonics. But above all, it emancipates this approach from the psychoacoustic and acoustic models on which ambisonic techniques are originally defined. In this context, the signals associated with spherical harmonics are no longer necessarily a rational representation of the sound field but become an abstract representation of the sound space possessing in itself a musical potential. To validate the hypotheses, this thesis then proposes a new spatialization model based on a matrix decomposition of the sound space.

No description available.

Le véhicule électrique rassemble beaucoup d'équipements électrotechniques. Tous sont potentiellement source de champ magnétique dans l'habitacle : zone confinée où se trouvent les passagers. Il est illusoire de réaliser un modèle numérique complet tant le nombre de paramètres est important. Il est également impossible de placer des capteurs de champ partout à l'intérieur de l'habitacle. Après une étude approfondie des caractéristiques du champ magnétique mesuré dans l'habitacle, nous proposons d'allier modèle a priori et mesure de champ dans une approche Bayésienne du problème inverse. Basée sur le développement en harmonique sphérique du champ, l'apport d'information a priori oriente la solution et permet l'identification de nombreux paramètres avec très peu de mesure. / Electric vehicles have a lot of electrical devices onboard. All of them may generate electromagnetic field inside the car: a quite small space containing the passengers. A complete modeling of the vehicle can hardly be done because of the parameters number. The magnetic field measurement everywhere inside the car is also impossible. We first measure the magnetic field inside the car to study its characteristics. Then we propose to merge together a priori modeling with measurements into a Bayesian approach of the inverse problem. Based on spherical harmonic decomposition of the magnetic field, a priori information helps the resolution and gives the identified parameters with a very few measurements.

A maneira mais direta de detectar as anomalias da densidade é pelo estudo do potencial gravitacional e de suas derivadas. A disponibilidade global e a boa resolução dos dados do satélite GOCE, aliadas à disponibilidade de dados de gravimetria terrestre, são ideais para a comparação e classificação das bacias de larga escala, como as bacias sedimentares do Solimões e do Amazonas dentro do Craton amazônico. Foram processados um conjunto de dados, produtos GOCE EGG_TRF_2 Level 2, ao longo das trajetórias do satélite para remover o ruído (shift/drift) nos gradientes da gravidade a partir da técnica crossover (XO). Calculamos a redução das massas topográfica a fim de obter os componentes do gradiente da gravidade e anomalia da gravidade usando modelagem direta com prismas esféricos a partir do modelo de elevação digital, ETOPO1. Desta maneira, a comparação dos dados somente do satélite GOCE com as reduções das massas topográficas referentes aos componentes do gradiente da gravidade permitiram estimar quantidades invariantes que trouxeram uma melhoria na interpretação dos dados do tensor de gravidade. Além disso, comparamos dados terrestres do campo de gravidade com dados do campo de gravidade dos modelos geopotenciais EGM2008 e GOCE, uma vez que os dados terrestres podem ser afetados por erros em longos comprimentos de onda devido a erros de nivelamento, diferentes referenciais de altitudes, e aos problemas em interligar diferentes campanhas de medidas da gravidade. Portanto, estimamos uma melhora e uma nova representação dos mapas das anomalias de gravidade e do tensor gradiente da gravidade nas áreas inacessíveis do Craton Amazônico. As observações forneceram novas entradas para determinar campos regionais a partir dados brutos pre-processados (gradiente de gravidade EGG_TRF_2 L2), bem como a partir de um modelo geopotencial mais recente até grau e ordem 250 dos harmonicos esféricos derivados de dados somente do satélite GOCE para a representação do campo de gravidade como geóide, anomalias da gravidade e os componentes tensor da gravidade, os quais foram quantidades importantes para interpretação, modelagem e estudo dessas estruturas. Finalmente, obtivemos um modelo isostático considerando a estrutura de densidade litosférica estudada através de uma modelagem direta 3D da distribuição de densidade por prismas esféricos usando a geometria do embasamento e descontinuidade do Moho. Além do que, constatamos através da modelagem direta das soleiras de diabásios dentro dos sedimentos mostramos que somente as soleiras dentro da Bacia do Amazonas não são as únicas responsáveis pela anomalia de gravidade positiva que coincide aproximadamente com as espessuras máximas dos sedimentos da Bacia. Talvez, isso possa ser também um resultado de movimentos relativos do Escudo das Guianas situado ao norte da Bacia, e o Escudo Brasileiro situado ao sul. Embora isso seja apenas uma evidência adicional preliminar, não podemos confirmá-las a partir das estimativas do campo da gravidade. Portanto, é necessário outros tipos de dados geofísicos, como por exemplo, evidências mais claras advindas do paleomagnetismo. / The most direct way to detect density anomalies is the study of the gravity potential field and its derivatives. The global availability and good resolution of the GOCE mission coupled with the availability of terrestrial gravity data are ideal for the scope of intercomparison and classification of the two large-scale Amazon and Solimoes sedimentary basins into area of the Amazon Craton. The GOCE data set obtained in satellite tracks were processed from EGG_TRF_2 Level 2 Products generated with the correction needed to remove the noise (shift/drift), and so, to recover the individual components of the gravity gradient tensor using the crossover (XO) points technique. We calculated the topographic masses reductions in order to obtain the gravity gradient components and gravity anomaly (vertical component) using forward modelling from tesseroids from Digital Elevation Model, ETOPO1. Thus, the comparison of the only-satellite GOCE data with the reductions of the topographic masses for the gradient components allowed to estimate invariants quantities for bring an improvement in the interpretation of the gravity tensor data. Furthermore, we compared the terrestrial data gravity field with EGM2008 and GOCE-deduced gravity field because the terrestrial fields may be affected by errors at long wavelengths due to errors in leveling, different height references, and problems in connecting different measurement campaigns. However, we have estimated an improvement and new representations of the gravity anomalies maps and gravity gradient tensor components primary in inaccessible areas of the Amazon Craton. GOCE observations provide new inputs to determine the regional fields from the preprocessed raw data (EGG_TRF_2 L2 gravity gradients), as well from the most recent global geopotential model available up to degree and order 250 developed in spherical harmonics derived only-satellite GOCE data for representing of geoid and others gravity field as gravity anomaly and gravity gradient tensor components, which are important quantities for modelling and studying these structures. Finally, we obtained the isostatic model considering the lithospheric density structure studied through a 3D direct modelling of density distribution using the geometry of basement and Moho discontinuity, assumed to be known as initial constraint. In addition, we found through direct modeling sills and sediment has shown that the diabase sills are not the only ones responsible for positive gravity anomaly map that transects the Amazon Basin, roughly coincident with the maximum thickness of sedimentary rocks or the trough of the basin. Maybe, this could be the result of the relative movements of the Guiana Shield, situated at the north of the Amazon basin, and the Brazilian Shield, situated at the south. Although this is only a preliminary additional evidence, we cannot confirm it only from the data of gravity. It is necessary others types of geophysical data, for example, more clear evidences obtained from paleomagnetism.

A maneira mais direta de detectar as anomalias da densidade é pelo estudo do potencial gravitacional e de suas derivadas. A disponibilidade global e a boa resolução dos dados do satélite GOCE, aliadas à disponibilidade de dados de gravimetria terrestre, são ideais para a comparação e classificação das bacias de larga escala, como as bacias sedimentares do Solimões e do Amazonas dentro do Craton amazônico. Foram processados um conjunto de dados, produtos GOCE EGG_TRF_2 Level 2, ao longo das trajetórias do satélite para remover o ruído (shift/drift) nos gradientes da gravidade a partir da técnica crossover (XO). Calculamos a redução das massas topográfica a fim de obter os componentes do gradiente da gravidade e anomalia da gravidade usando modelagem direta com prismas esféricos a partir do modelo de elevação digital, ETOPO1. Desta maneira, a comparação dos dados somente do satélite GOCE com as reduções das massas topográficas referentes aos componentes do gradiente da gravidade permitiram estimar quantidades invariantes que trouxeram uma melhoria na interpretação dos dados do tensor de gravidade. Além disso, comparamos dados terrestres do campo de gravidade com dados do campo de gravidade dos modelos geopotenciais EGM2008 e GOCE, uma vez que os dados terrestres podem ser afetados por erros em longos comprimentos de onda devido a erros de nivelamento, diferentes referenciais de altitudes, e aos problemas em interligar diferentes campanhas de medidas da gravidade. Portanto, estimamos uma melhora e uma nova representação dos mapas das anomalias de gravidade e do tensor gradiente da gravidade nas áreas inacessíveis do Craton Amazônico. As observações forneceram novas entradas para determinar campos regionais a partir dados brutos pre-processados (gradiente de gravidade EGG_TRF_2 L2), bem como a partir de um modelo geopotencial mais recente até grau e ordem 250 dos harmonicos esféricos derivados de dados somente do satélite GOCE para a representação do campo de gravidade como geóide, anomalias da gravidade e os componentes tensor da gravidade, os quais foram quantidades importantes para interpretação, modelagem e estudo dessas estruturas. Finalmente, obtivemos um modelo isostático considerando a estrutura de densidade litosférica estudada através de uma modelagem direta 3D da distribuição de densidade por prismas esféricos usando a geometria do embasamento e descontinuidade do Moho. Além do que, constatamos através da modelagem direta das soleiras de diabásios dentro dos sedimentos mostramos que somente as soleiras dentro da Bacia do Amazonas não são as únicas responsáveis pela anomalia de gravidade positiva que coincide aproximadamente com as espessuras máximas dos sedimentos da Bacia. Talvez, isso possa ser também um resultado de movimentos relativos do Escudo das Guianas situado ao norte da Bacia, e o Escudo Brasileiro situado ao sul. Embora isso seja apenas uma evidência adicional preliminar, não podemos confirmá-las a partir das estimativas do campo da gravidade. Portanto, é necessário outros tipos de dados geofísicos, como por exemplo, evidências mais claras advindas do paleomagnetismo. / The most direct way to detect density anomalies is the study of the gravity potential field and its derivatives. The global availability and good resolution of the GOCE mission coupled with the availability of terrestrial gravity data are ideal for the scope of intercomparison and classification of the two large-scale Amazon and Solimoes sedimentary basins into area of the Amazon Craton. The GOCE data set obtained in satellite tracks were processed from EGG_TRF_2 Level 2 Products generated with the correction needed to remove the noise (shift/drift), and so, to recover the individual components of the gravity gradient tensor using the crossover (XO) points technique. We calculated the topographic masses reductions in order to obtain the gravity gradient components and gravity anomaly (vertical component) using forward modelling from tesseroids from Digital Elevation Model, ETOPO1. Thus, the comparison of the only-satellite GOCE data with the reductions of the topographic masses for the gradient components allowed to estimate invariants quantities for bring an improvement in the interpretation of the gravity tensor data. Furthermore, we compared the terrestrial data gravity field with EGM2008 and GOCE-deduced gravity field because the terrestrial fields may be affected by errors at long wavelengths due to errors in leveling, different height references, and problems in connecting different measurement campaigns. However, we have estimated an improvement and new representations of the gravity anomalies maps and gravity gradient tensor components primary in inaccessible areas of the Amazon Craton. GOCE observations provide new inputs to determine the regional fields from the preprocessed raw data (EGG_TRF_2 L2 gravity gradients), as well from the most recent global geopotential model available up to degree and order 250 developed in spherical harmonics derived only-satellite GOCE data for representing of geoid and others gravity field as gravity anomaly and gravity gradient tensor components, which are important quantities for modelling and studying these structures. Finally, we obtained the isostatic model considering the lithospheric density structure studied through a 3D direct modelling of density distribution using the geometry of basement and Moho discontinuity, assumed to be known as initial constraint. In addition, we found through direct modeling sills and sediment has shown that the diabase sills are not the only ones responsible for positive gravity anomaly map that transects the Amazon Basin, roughly coincident with the maximum thickness of sedimentary rocks or the trough of the basin. Maybe, this could be the result of the relative movements of the Guiana Shield, situated at the north of the Amazon basin, and the Brazilian Shield, situated at the south. Although this is only a preliminary additional evidence, we cannot confirm it only from the data of gravity. It is necessary others types of geophysical data, for example, more clear evidences obtained from paleomagnetism.