Description statistique de la surface océanique et mesures conjointes micro-ondes (une analyse cohérente)

De plus en plus de données satellitales ou aéroportées acquises au dessus de la surface de la mer sont disponibles notamment dans la gamme micro-ondes. Pour interpréter correctement ces données, il est nécessaire de disposer d'une part d'un modèle de diffusion qui soit capable de prendre en compte l'aspect multi-échelles de la surface de mer et d'autre part une bonne représentation spectrale de la surface de mer. Ces dernières années, plusieurs modèles de diffusion électromagnétiques unifiés (capables de prendre en compte la diffusion électromagnétique pour les petites et grandes vagues) ont été développés sous statistiques gaussiennes de la surface de mer. Cependant, ces modèles sont insuffisants pour interpréter les observations lorsque différents jeux de données (multi-bande et multi-incidence) sont confrontés. Le plus de cette thèse est de progresser dans une modélisation cohérente de ces données radar.La première étape est d'incorporer les aspects non-gaussiens de la surface de mer, connus pour influer significativement sur la section efficace de rétrodiffusion (SER). Cela est réalisé dans le cadre du modèle électromagnétique "Weighted Curvature Approximation (WCA) en introduisant le kurtosis des pentes et en se limitant à la SER omnidirectionnelle et à la polarisation verticale.Ces corrections permettent une meilleure modélisation de la section efficace radar mais ne sont pas suffisantes pour obtenir un accord avec les données dans toutes les configurations (bande, incidence, vent). Cela suggère une amélioration nécessaire du spectre des vagues courtes, qui fait l'objet de la deuxième partie de ces travaux de recherche.Un nouveau spectre omnidirectionnel est calculé afin d'obtenir une meilleure modélisation de la SER omnidirectionnelle en polarisation verticale tout en respectant des contraintes a priori sur les pentes mesurées par des techniques optiques. Ce spectre s'avère assez semblable au spectre unifié d'Elfouhaily, avec quelques différences notables cependant dans la gamme des échelles décimétriques.More and more micro-wave data are available from spatial and airborne measurements over sea surface. An accurate backscattering model which is capable of taking the multi-scale aspect of the sea surface into account, is required to model correctly the data as well as a precise sea spectrum. Several unified backscattering models have been developed in recent years under Gaussian statistics. However, these models are not able to give a correct modelization of the backscattered signal when different data sets are studied together. One of the objectives of this study is to improve the modelization of the backscattered signal to get better agreement with the data.The first step of this study is to include non Gaussian statistics into backscattering model as it is well known they have a significant impact on the normalized radar cross section (NRCS). Then, a non Gaussian version of the Weighted Curvature Approximation was developed taking the kurtosis of slopes into account. This work was based only upon vertical polarization.It is then shown that the corrections allow a better agreement with the data but they are not sufficient to get a good estimation of the NRCS for all incidences and electromagnetic frequencies. This induces the hypothesis of a modification of the short wave sea spectrum.Then, a new parametrisation of the omnidirectional sea spectrum is suggested to get a better agreement with the multiband data sets and is based on the spectrum developed by Elfouhaily et al. The new omnidirectional short wave sea spectrum is quite alike the Elfouhaily s spectrum with some noticeable differences for the decimetric scales.TOULON-Bibliotheque electronique (830629901) / SudocSudocFranceF

One-Dimensional Quantum Scattering for Potentials Defined as Measures

We generalize the basic one-dimensional scattering formalism to potentials defined as measures and retrieve the classical results that hold for smooth potentials. We introduce a set of generalized eigenfunctions for the corresponding Schrödinger operator and study their analytical properties. This allows a characterization of the spectrum and an eigenfunction expansion. We also prove the existence and completeness of the wave operators and give explicit formulae for these latter

Wavelet Analysis and Covariance Structure of Some Classes of Non-Stationary Processes

: We study four classes of non-stationary processes: processes with stationary n- increments, processes with stationary fractional increments, locally stationary processes and processes with locally stationary n-increments. We establish a simple characterisation of each class of processes by means of the continuous wavelet transform. Then we give two applications of these results. First, we derive the explicit covariance structure of processes with stationary n-increments. Second, we prove that the fractional Brownian motion with Hurst parameter H has stationary fractional ff-increments for ff ? H. key-words: wavelet analysis, stationary nth increments, stationary fractional increments, locally stationary processes, locally stationary nth increments, fractional Brownian motion. 1 Introduction The aim of this paper is to present a unified approach in the light of wavelet analysis of four classes of non-stationary stochastic processes: processes with stationary n-increments, proces..

Diffusion électromagnétique par des matériaux hétérogènes rugueux : homogénéisation et couplage surface/volume

L étude de la diffusion par des surfaces rugueuses hétérogènes est un sujet de recherche qui trouve de plus en plus d applications (furtivité, imagerie, télédétection ). Elle soulève deux problèmes, individuellement très compliqués : diffusion par des ensembles aléatoires de particules et diffusion par une surface rugueuse aléatoire. A cela s ajoute le couplage entre la surface et les hétérogénéités qu elle recouvre. Cette thèse est une contribution visant à modéliser ces phénomènes. Nous débutons en étudiant la possibilité d homogénéiser les milieux diffusants (3D), composés de petites particules réparties aléatoirement dans un volume test. Nous montrons qu il est possible de déterminer une constante diélectrique effective tenant compte de la taille du volume et des effets de diffusion multiple. Nous proposons ensuite une description du couplage des diffusions de surface et de volume pour de petits diffuseurs répartis sous une surface rugueuse. L approche permet une résolution numérique du problème ainsi que l identification des différentes contributions présentes dans le phénomène de diffusion (couplage diffuseurs/diffuseurs et couplage surface/diffuseurs).AIX-MARSEILLE3-BU Sc.St Jérô (130552102) / SudocSudocFranceF

Scattering on Fractal Measures

We study the one-dimensional potential-scattering problem when the potential is a Radon measure with compact support. We show that the usual reflection and transmission amplitude r(p) and t(p) of an incoming wave e ipx are well defined. We also show that the scattering problem on fractal potentials can be obtainded as a limit case of scattering on smooth potentials. We then explain how to retrieve the fractal 2-wavelet dimension and/or the correlation dimension of the potential by mean of the reflexion amplitude r(p). We study the particular case of self-similar measures and show that, under some general conditions, r(p) has a large scale renormalisation. A numerical application is presented. Key-Words : potential scattering, wavelet-dimension, correlation dimension, large scale renormalisation. 1991 MSC:28,42A,45 Number of figures: 10 March 1996 CPT-96/P.3328 anonymous ftp or gopher: cpt.univ-mrs.fr Unit'e Propre de Recherche 7061 1 e-mail: [email protected] 2 e-mail: ho..

Second-order Lagrangian description of tri-dimensional gravity wave interactions

We revisit and supplement the description of gravity waves based on perturbation expansions in Lagrangian coordinates. A general analytical framework is developed to derive a second-order Lagrangian solution to the motion of arbitrary surface gravity wave fields in a compact and vectorial form. The result is shown to be consistent with the classical second-order Eulerian expansion by Longuet-Higgins (J. Fluid Mech., vol. 17, 1963, pp. 459-480) and is used to improve the original derivation by Pierson (1961 Models of random seas based on the Lagrangian equations of motion. Tech. Rep. New York University) for long-crested waves. As demonstrated, the Lagrangian perturbation expansion captures nonlinearities to a higher degree than does the corresponding Eulerian expansion of the same order. At the second order, it can account for complex nonlinear phenomena such as wave-front deformation that we can relate to the initial stage of horseshoe-pattern formation and the Benjamin-Feir modulational instability to shed new light on the origins of these mechanisms

Scattering From Nonlinear Gravity Waves: The "Choppy Wave" Model

To progress in the understanding of the impact of nonlinear wave profiles in scattering from sea surfaces, a nonlinear model for infinite-depth gravity waves is considered. This model, termed as the "Choppy Wave" Model (CWM), is based on horizontal deformation of a linear reference random surface. It is numerically efficient and enjoys explicit second-order statistics for height and slope, which makes it well adapted to a large family of scattering models. We incorporate the CWM into a Kirchhoff or small-slope approximation and derive statistical expressions for the corresponding incoherent cross section. We insist on the importance of "undressing" the wavenumber spectrum to generate a nonlinear surface with a prescribed spectrum. Interestingly, the inclusion of nonlinearities is found to be practically compensated by the spectral undressing process; an effect which might be specific to the CWM and needs to be investigated in the framework of fully nonlinear models. Accordingly, the difference between the respective normalized radar cross section is rather small. The most noticeable changes are faster azimuthal variations and a slight increase of the radar returns at nadir. A statistical analysis of sea clutter in the framework of a two-scale model is also performed at large but nongrazing incidence. It shows a pronounced polarization dependence of the distribution of large backscattered amplitudes, the tail being much larger in horizontal polarization and for small resolution cell. Surface nonlinearities are shown to increase the tail of the amplitude distribution, as expected. Less obviously, their relative impact is found lesser in horizontal polarization. This raises the question of the actual contribution of nonlinearities in radar sea spikes at nongrazing angles

Revisiting the Short-Wave Spectrum of the Sea Surface in the Light of the Weighted Curvature Approximation

Existing models for the short-wave spectrum of the sea surface are not consistent with microwave satellite data when multi-bands and multi-incidence data sets are considered. We devise a simple parametric model for the short-wave omnidirectional spectrum of the sea surface on the basis of a three-band (C, Ku, and Ka) and multi-incidence (low, moderate, and large) data set and an improved analytical scattering model, namely the non-Gaussian Weighted Curvature Approximation. This spectrum is also constrained by several optical measurements which provide a priori conditions on the total and filtered mean-square slopes. It is compared with classical models such as Elfouhaily and Kudryavtsev unified curvature spectra. Significant differences are observed at wave numbers corresponding to the range of decimeter scales. The new spectrum is by construction fully consistent with the omnidirectional normalized radar cross section of the multi-band data set