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Mathematical Physics
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PhD students:

Clément Roussel (2019):

Stochastic differential equations for the electromagnetic field scattered by the sea surface : applications to remote sensing

Radar remote sensing in a maritime context is often hindered by radar waves reflected by the sea, termed sea clutter due to its noise-like character. A thorough understanding of it is required for detection and imaging applications. Statistical models have long been used for the sea clutter (K distribution, Weibull distribution etc) but they are static in nature. We propose to use a dynamic model developed by T. R. Field, which represents the sea clutter as a stochastic process solving stochastic differential equations. We introduce Field's model for the sea surface radar cross section (RCS) and speckle. The complex reflectivity of the sea surface then depends on three parameters: A, B and α. We compute the transition probabilities of the RCS and speckle by analytical resolution of Fokker-Planck equations, and propose to use them as a tool for synchronizing observations taken at differents positions and times, as in Synthetic Aperture Radar. We derive maximum likelihood (ML) estimators for A and B, and show numerically that the exact transition probabilities from the Fokker-Planck equations can be approximated in a satisfactory manner by Gaussians using Euler-Maruyama's scheme. α, for its part, is estimated by ergodicity (moment). We adapt Field's model to account for the presence of a simple target and show that it is possible to estimate the target constant by ML using Gaussian approximations for the transition probabilities. In the last part, we address the non-observability of the RCS by estimating it from the complex reflectivity (observable). We obtain a sequence of estimators applicable to real data. Finally, bayesian estimation of the clutter parameters, and target detection, are introduced and discussed as potential future directions for research.

Refzul Khairi (2013):

Modélisation de la diffusion électromagnétique par les vagues côtières déferlantes

The objective of this thesis work is to study the interaction of electromagnetic waves in L band with breaking coastal sea waves, in particular for an observer situated close to the surface. The work attempts to realize a precise electromagnetic modeling in narrow link with hydrodynamic model. To model and calculate electromagnetic fields scattered by breaking sea waves, we use a numerical approach by boundary integral, in particular Method of Moments (MoM). In this frame, we focus on the reliability and the convergence problem of numerical computation for strong curvature geometries as the surfaces of breaking sea waves are. After a thorough analysis of the problem, we show that a solution based on Higher-Order Method of Moments (HO-MoM) combined with Non Uniform Rational Basis Splines (NURBS) meshing technique allows the improvement of the performances of Classical- MoM. In parallel of the work on electromagnetic modeling, we attempt to introduce a hydrodynamic model able to precisely simulate the movement and the deformation of waves near the coast. We choose a hydrodynamic modeling based on Desingularized Method. This methodological approach allows studying the evolution of the waves according to the slope of the bottom, the relative height and the curve of waves. The combination of the results obtained from the numerical electromagnetic modeling and from the hydrodynamic description allows us to estimate the evolution of the electromagnetic fields scattered by breaking coastal sea waves according to time for three types of standard breaking : spilling, plunging and surging.

Sarab Tay (2012):

Analyse et modélisation de l’utilisation de signaux GNSS en environnement marin

For many years now, passive observation of the ocean surface, using in particular, sources of opportunities from positioning satellites (GNSS), has been a very dynamic research and development topic. Several research teams have already demonstrated the relevance of such approaches for airborne observations. The aim of this thesis is to address the feasibility of passive measurements from GPS system signals near the sea surface (a few meters) for recovering oceanographic information in coastal zones. The sea surface cannot anymore, in this case, be considered as a stationary rough surface. GPS reflected signals must consider the kinematic evolution of the sea surface and the wave motion. The processing of these signals can reveal the temporal variation of the surface, and identify the displacement of the main scatterers (wave crest, buoy on sea surface). The motions described here are very slow (some Hz), with respect to the incident wave frequencies (some GHz). The movement amplitude is limited, which induces very short time delay differences.

Naheed Sajjad (2011):

Bistatic scattering of electromagnetic waves from rough surface by using second order twoscale model : Application to sea and bare soil surface

The estimation of radar cross section (RCS) of randomly rough surfaces is essential for designing terrain and sea surface remote sensing systems. The particular problem of wave scattering at low grazing angles is of great interest because of its importance for the low-altitude/long-range radar surveillance, target tracking, communication and navigation systems operating at low grazing conditions above the rough surface. The radar cross section from a rough surface becomes very small at grazing incidence, since most part of the incident power is scattered around the specular direction (depending on the degree of surface roughness). Moreover, the dominant scattering mechanisms at low and high grazing angles are different e.g., the effects of multiple scattering (or higher order scattering), shadowing, fading and mechanisms attributable to wave breaking are particularly marked in the low grazing angle regime. Therefore, in this context the research has been conducted in this thesis. A second order two-scale model (TSM2) has been developed to study the bistatic scattering enhancement at grazing angles and the accurate depolarization estimation in a radar return. The applications of TSM2 are presented for sea and bare soil surfaces. The results obtained from newly developed model are compared with the available experimental data and other models to demonstrate the validity and efficiency of TSM2.
  • pdf (in english)
  • Ahmad Awada (2007):

    Diffusion bistatique des ondes électromagnétiques par une surface rugueuse en utilisant l’approximation SSA : Application à la surface maritime

    The purpose of this thesis is to establish an algorithm allowing the analysis of electromagnetic waves scattering from rough surfaces. Our study focuses on the bistatic configuration especially in the sea surface case. To solve this problem, we have studieff and applied the SSA (Small Slope Approximation) model to evaluate bistatic scattering coefficients, according to different physical and geometrical parameters. We have privileged the L and Ku frequency bands in the analysis. Then, we have compared the results obtained with those published in literature and mainly to those predicted by the two scale model in bistatic configuration. Finally, we have introduced the modification suggested by McDaniel, concerning a change in the sea spectrum of Elfouhaily. This change leads to an improvement on the results in particular for transverse wind directions and for relatively low wind speeds. The results obtained make it possible to provide a mapping of polarimetric behaviour of the sea surface in bistatic configuration, and to present new prospects offered by this subject in oceanic remote sensing.

    Yassine Ayari (2006):

    Détection électromagnétique d’éléments polluants au dessus de la surface maritime

    The project of the thesis has the objective to supply methodological means on making it possible to detect the pollutants on the surface of the sea (oil, residues petrochemical...) by electromagnetic methods (radar). One of the additional difficulties to the problem arising relates to the adopted configuration, it acts of the bistatic configuration where the transmitter and the receiver are separate (contrary to the case often used : backscattering configurtion). Until now, few studies were interested in electromagnetic detection of pollutants on sea surface and less in the scattering problems by rough surfaces in bistatic configuration. The majority of the current detection methods are based either on the technique of satellite photos or on radar imagery (SAR...). The latter are not easily exploitable and do not give a precise idea as for the nature of pollutant. Indeed, SAR images give similar effects for a covered surface with pollutants and another sheltered wind surface. During this work we have studied the effect of the pollutant on physical and geometrical sea surface characteristics and correlated this study with the electromagnetic scattering models in order to have a precise idea on the effect of the pollutant on the electromagnetic surface scattering for different configurations and various transmitter and the receiver polarizations.

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