Este trabalho apresenta um procedimento de inversão magnética de três etapas no qual quantidades invariantes em relação à fonte magnética são sequencialmente invertidas para recuperar i) a geometria da fonte no substrato, ii) sua intensidade de magnetização e iii) a inclinação da magnetização da fonte. A primeira quantidade invertida (chamada função geométrica) é obtida pela razão entre a intensidade do gradiente da anomalia magnética e a intensidade do campo magnético anômalo. Para fontes homogêneas, a função geométrica depende apenas da geometria da fonte, o que permite a reconstrução da forma do corpo usando valores arbitrários para a magnetização. Na segunda etapa, a forma da fonte é fixa e a intensidade de magnetização é estimada ajustando o módulo do gradiente da anomalia magnética, uma quantidade invariante com a direção da magnetização e equivalente à amplitude do sinal analítico. Na última etapa, a forma da fonte e a intensidade da magnetização são fixas e a inclinação da magnetização é determinada ajustando a anomalia magnética. Além de recuperar a forma e a magnetização de fontes homogêneas, esta técnica permite, em alguns casos, verificar se as fontes magnéticas são homogêneas. Isto é possível pois a função geométrica de fontes heterogêneas pode ser ajustada por um modelo homogêneo, mas o modelo assim obtido não permite o ajuste da amplitude do sinal analítico nem da anomalia magnética. Esse é um critério que parece efetivo no reconhecimento de fontes fortemente heterogêneas. O método de inversão por etapas é testado em experimentos numéricos de computador e utilizado para interpretar uma anomalia magnética gerada por rochas básicas intrusivas da Bacia do Paraná. / This work presents a three step magnetic inversion procedure in which invariant quantities related to source parameters are sequentially inverted to provide i) cross-section of two-dimensional sources; ii)intensity of source magnetization, and iii) inclination of source magnetization. The first inverted quantity (called geometrical function) is obtained by rationing intensity gradient of total field anomaly and intensity of vector anomalous field. For homogenous sources, geometrical function depends only on source geometry thus allowing shape reconstruction by using arbitrary values for source magnetization. In the second step, source shape is fixed and magnetization intensity is estimated by fitting intensity gradient of total field anomaly, an invariant quantity with magnetization direction and equivalent to amplitude of the analytical signal. In the last step, source shape and magnetization intensity are fixed and magnetization inclination is determined by fitting magnetic anomaly. Besides furnishing shape and magnetization of homogeneous two-dimensional sources, this technique allows to check in some cases if causative sources are homogeneous. It is possible because geometrical function from inhomogeneous sources can be fitted by a homogeneous model but a model thus obtained does not fit the amplitude of analytical signal nor magnetic anomaly itself. This is a criterion that seems efective in recognizing strongly inhomogeneous sources. The proposed technique is tested with numerical experiments, and used to model a magnetic anomaly from intrusive basic rocks of Paraná Basin, Brazil.

Seismic reflection surveying is used to generate acoustic images of the water column. This technique employs conventional multi-channel equipment which is used to image the solid Earth. In the water column, acoustic impedance contrasts are produced by variations in temperature and, to some extent, salinity. Acoustic impulses generated by an array of airguns suspended behind a vessel are reflected from these contrasts and recorded on long cables of hydrophones that are towed below the sea-surface. In this way, two- and three-dimensional images of thermohaline circulation can be generated. Critically, these images have equal vertical and horizontal resolutions of \textit{O}(10)~m. Here, I describe, process, and analyse a calibrated two-dimensional seismic survey from the Bellingshausen Sea of the Southern Ocean and a three-dimensional seismic survey from the Brazil-Falkland Confluence located offshore Uruguay. First, the Bellingshausen survey was designed to image the thermohaline structure across the west Antarctic shelf where warm-core eddies are reported. Processed and calibrated seismic images reveal the detailed thermohaline structure of Circumpolar Deep Water. Many warm-core eddies are observed, which have diameters of 1--12~km and thicknesses of 100--200~m. Pre-stack analysis demonstrates that this eddy field is being advected onto the shelf at speeds of \textit{O}(0.1)~m~s$^{-1}$. An iterative inverse modelling procedure is used to convert reflectivity into temperature and salinity, which confirms that the eddies have anomalously warm centres (i.e. $\sim$1$^{\circ}$C). These results have significant implications for ice shelf melting. Secondly, the Uruguay survey is used to investigate a large-scale frontal system. Although this system has been studied using hydrographic methods, these studies either have limited spatial resolution or have restricted depth penetration. The three-dimensional seismic survey, which was acquired in a `racetrack' pattern, permits the volume to be interrogated. Since the frontal system migrates southwestwards at a speed of \textit{O}(10)~km~day$^{-1}$, this survey is time-lapse in nature. Processed images reveal a band of dipping reflections that extend to depths of $\sim$2000~m. These reflections represent the frontal interface between the Brazil and Falkland currents. Physical oceanographic properties are calculated for images that cross this front. On the warm side of the front, the water mass is characterised by flat and continuous reflectivity. On the cold side of the front, the water mass is characterised by deformed reflectivity on all scales. Pre-stack analysis suggests that near-surface flow at the frontal interface is convergent. Between 0.5 and 1~km depth, a substantial eddy that is 30~km long and 250~m thick is visible on the cold side of the front. Detailed mapping suggests that this eddy grew and decayed over a period of 6~days. Its observed scale and duration are inconsistent with analytical and numerical studies of intra-thermocline eddies. Nevertheless, its duration is consistent with scaling arguments of frictional spin-down. Spatial and temporal distributions of mixing rates (i.e. diapycnal diffusivities) are estimated by spectrally analysing vertical displacements of automatically tracked reflections. Both internal wave and turbulent regimes are identifiable. Recovered diapycnal diffusivities are of \textit{O}($10^{-6}$--$10^{-2.2}$)~m$^{2}$~s$^{-1}$, consistent with hydrographically determined estimates. Mixing is suppressed and enhanced on the warm and cold sides of the front, respectively. Seismic Oceanography has considerable potential to quantify aspects of thermohaline circulation on multiple scales.

La positivité gamma d’une suite combinatoire unifie à la fois l’unimodalité et la symétrie de cette suite. Trouver des nouvelles familles d’objets dont les polynômes énumératives ont une positivité gamma est un défi et un sujet important en combinatoire et géométrie. Il a attiré beaucoup d’attention ces derniers temps en raison de la conjecture de Gal, qui affirme que le gamma-vecteur a des coefficients positifs pour n’importe quel polytope simple. Souvent, le h-polynôme pour les polytopes simpliciaux de signification combinatoire peut être donné en tant que fonction génératrice sur un ensemble d’objets combinatoires apparentés par rapport à une statistique telle que le nombre des descentes, dont les polynômes énumératifs sur les permutations sont des polynômes Eulériens. Ce travail traite des propriétés gamma de plusieurs polynômes énumératifs de permutations tels que les polynômes Eulériens et les polynômes de Narayana. Cette thèse contient cinq chapitres / The gamma positivity of a combinatorial sequence unifies both unimodality and symmetry. Finding new family of objets whose enumerative sequences have gamma positivity is a challenge and important topic in recent years. it has received considerable attention in recent times because of Gal’s conjecture, which asserts that the gamma-vector has nonnegative entries for any flag simple polytope. Often times, the h-polynomial for simplicial polytopes of combinatorial signification can be given as a generating function over a related set of combinatorial objects with respect to some statistic like the descent numbers, whose enumerative polynomials on permutations are Eulerian polynomials.This work deals with the gamma properties of several enumerative polynomials of permutation such as Eulerian polynomials and Narayana polynomials. This thesis contains five chapters

Graduation date: 1994

The Method of Manufactured Universes is presented as a validation framework for uncertainty quantification (UQ) methodologies and as a tool for exploring the effects of statistical and modeling assumptions embedded in these methods. The framework calls for a manufactured reality from which "experimental" data are created (possibly with experimental error), an imperfect model (with uncertain inputs) from which simulation results are created (possibly with numerical error), the application of a system for quantifying uncertainties in model predictions, and an assessment of how accurately those uncertainties are quantified. The application presented for this research manufactures a particle-transport "universe," models it using diffusion theory with uncertain material parameters, and applies both Gaussian process and Bayesian MARS algorithms to make quantitative predictions about new "experiments" within the manufactured reality. To test further the responses of these UQ methods, we conduct exercises with "experimental" replicates, "measurement" error, and choices of physical inputs that reduce the accuracy of the diffusion model's approximation of our manufactured laws. Our first application of MMU was rich in areas for exploration and highly informative. In the case of the Gaussian process code, we found that the fundamental statistical formulation was not appropriate for our functional data, but that the code allows a knowledgable user to vary parameters within this formulation to tailor its behavior for a specific problem. The Bayesian MARS formulation was a more natural emulator given our manufactured laws, and we used the MMU framework to develop further a calibration method and to characterize the diffusion model discrepancy. Overall, we conclude that an MMU exercise with a properly designed universe (that is, one that is an adequate representation of some real-world problem) will provide the modeler with an added understanding of the interaction between a given UQ method and his/her more complex problem of interest. The modeler can then apply this added understanding and make more informed predictive statements.

A field study of positive inversion is conducted to describe associated structural fabrics and to infer kinematic development of the Palisades Monocline, Grand Canyon, Arizona. These features are then compared to sand, clay and solid rock models of positive inversion to test model results and improve understanding of inversion processes. The N40W 90 oriented Palisades fault underlying the monocline has experienced northeast-southwest Precambrian extension and subsequent northeastsouthwest Laramide contraction. The magnitude of inversion is estimated to be 25% based on vertical offset across the fault, although this does not account for flexure or horizontal shortening. The preferred N50W 90 joint and vein orientation and N50W 68 NE and SW conjugate normal faults are consistent with the Palisades fault and northeastsouthwest extension. The N45E 90 joint orientation and approximately N40W 28 NE and SW conjugate thrust faults are consistent with northeast-southwest contraction. The deformation is characterized by three domains across the fault zone: 1) the hanging wall, 2) the footwall, and 3) an interior, fault-bounded zone between the hanging wall and footwall. Extensional features are preserved and dominate the hanging wall, contractional features define footwall deformation, and the interior, fault-bounded zone is marked by the co-existence of extensional and contractional features. Extension caused a master normal fault and hanging wall roll-over with distributed joints, veinsand normal faults. During inversion, contraction induced reverse reactivation of existing hanging wall faults, footwall folding and footwall thrust-faulting. Precambrian normal slip along the master normal fault and subsequent Laramide reverse slip along the new footwall bounding fault created an uplifted domain of relatively oldest strata between the hanging wall and footwall. Physical models of co-axial inversion suggest consistent development of the three domains of deformation described at the Palisades fault, however the models often require magnitudes of inversion greater than 50%. Although vertical block motion during horizontal compression is not predicted directly by the Mohr-Coulomb criterion, physical models and analytical solutions (incorporating Mohr- Coulomb criterion) suggest maximum stress trajectories and near vertical failure above high angle basement faults that compare favorably with the Palisades fault zone.

Texte remanié de: Proefschrift--Amsterdam--Vrije universiteit, 2004. / Bibliogr. p. 261-267. Résumé en anglais.

Thèse de doctorat : Informatique : Nice : 2004. / Bibliogr. p. 191-202. Résumés en français et en anglais.

Thesis (M. Sc.)--University of Alberta, 2009. / Title from PDF file main screen (viewed on Feb. 19, 2010). A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of Master of Science in Geophysics, Department of Physics, University of Alberta. Includes bibliographical references.

This work focuses on developing an inversion scheme to estimate water-column sound-speed fields in three dimensions. The inversion scheme is based on a linearized perturbative technique which utilizes estimates of modal travel times. The technique is appropriate in the littoral ocean where measurements are made across range and cross-range distances greater than 10 km to ensure sufficient modal dispersion. Previous applications of then inversion technique has been limited to one or two dimensions and/or focused primarily on the seabed. Compared to past applications, the accuracy and uncertainty of the solution is improved by employing approximate equality constraints within the context of \textit{a priori} estimates of model and data covariances. The effectiveness of the constrained technique is explored through a one-dimensional example. The robustness of the technique is illustrated by introducing different types of errors into the inversion and considering the accuracy. A further examination of the technique is given by exploring a three-dimensional example. Several case studies are presented to investigate the effects of different levels of environmental variability and spatial sampling. / text