Academic literature on the topic 'Full-wave 3d electromagnetic modelling'

Les premiers mètres à centaines de mètres de la proche surface terrestre sont le siège de processus naturels dont la compréhension requiert une caractérisation fine de la subsurface, via une estimation quantifiée de ses paramètres. Le géoradar est un outil de prospection indirecte à même d'ausculter les milieux naturels et d'en estimer les propriétés électriques (permittivité et conductivité). Basé sur la propagation d'ondes électromagnétiques à des fréquences allant du MHz à quelques GHz, le géoradar est utilisé à des échelles et pour des applications variées concernant la géologie, l'hydrologie ou le génie civil. Dans ce travail de thèse, je propose une méthode d'imagerie quantitative des propriétés électriques sur des sections 2D de la subsurface, à partir de données radar acquises à la surface du sol. La technique mise en oeuvre est l'inversion des formes d'ondes, qui utilise l'intégralité du champ d'ondes enregistré.Dans une première partie, je présente les principes physiques et l'outil de modélisation numérique utilisés pour simuler la propagation des ondes électromagnétiques dans les milieux hétérogènes à deux dimensions. Pour cela, un algorithme de différences finies en domaine fréquentiel développé dans le cadre des ondes visco-acoustiques est adapté au problème électromagnétique 2D grâce à une analogie mathématique.Dans une deuxième partie, le problème d'imagerie est formulé sous la forme d'une optimisation multi-paramètre puis résolu avec l'algorithme de quasi-Newton L-BFGS. Cet algorithme permet d'estimer l'effet de la matrice Hessienne, dont le rôle est crucial pour la reconstruction de paramètres de différents types comme la permittivité et la conductivité. Des tests numériques montrent toutefois que l'algorithme reste sensible aux échelles utilisées pour définir ces paramètres. Dans un exemple synthétique représentatif de la proche surface, il est cependant possible d'obtenir des cartes 2D de permittivité et de conductivité à partir de données de surface, en faisant intervenir des facteurs d'échelle et de régularisation visant à contraindre les paramètres auxquelles l'inversion est la moins sensible. Ces facteurs peuvent être déterminés en analysant la qualité de l'ajustement aux données, sans hypothèse a priori autre que la contrainte de lissage introduite par la régularisation.Dans une dernière partie, la méthode d'imagerie est confrontée à deux jeux de données réelles. Dans un premier temps, l'examen de données expérimentales permet de tester la précision des simulations numériques vis-à-vis de mesures effectuées en environnement contrôlé. La connaissance des cibles à imager permet en outre de valider la méthodologie proposée pour l'imagerie multiparamètre dans des conditions très favorables puisqu'il est possible de calibrer le signal source et de considérer l'espace libre environnant les cibles comme modèle initial pour l'inversion.Dans un deuxième temps, j'envisage le traitement d'un jeu de données radar multi-offsets acquises au sein d'un massif calcaire. L'interprétation de ces données est rendue beaucoup plus difficile par la complexité du milieu géologique environnant, ainsi que par la méconnaissance des caractéristiques précises des antennes utilisées. L'application de la méthode d'inversion des formes d'ondes à ces données requiert donc une étape préliminaire impliquant une analyse de vitesse plus classique, basée sur les arrivées directes et réfléchies, et des simulations numériques dans des modèles hypothétiques à même d'expliquer une partie des données. L'estimation du signal source est effectuée à partir d'arrivées sélectionnées, simultanément avec des valeurs moyennes de conductivité et de hauteur d'antennes de façon à reproduire au mieux les amplitudes observées. Un premier essai d'inversion montre que l'algorithme est capable d'expliquer les données dans la gamme de fréquences considérée et de reconstruire une ébauche des principaux réflecteurs<br>The quantitative characterization of the shallow subsurface of the Earth is a critical issue for many environmental and societal challenges. Ground penetrating radar (GPR) is a geophysical method based on the propagation of electromagnetic waves for the prospection of the near subsurface. With central frequencies between 10~MHz and a few GHz, GPR covers a wide range of applications in geology, hydrology and civil engineering. GPR data are sensitive to variations in the electrical properties of the medium which can be related, for instance, to its water content and bring valuable information on hydrological processes. In this work, I develop a quantitative imaging method for the reconstruction of 2D distributions of permittivity and conductivity from GPR data acquired from the ground surface. The method makes use of the full waveform inversion technique (FWI), originating from seismic exploration, which exploits the entire recorded radargrams and has been proved successful in crosshole GPR applications.In a first time, I present the numerical forward modelling used to simulate the propagation of electromagnetic waves in 2D heterogeneous media and generate the synthetic GPR data that are compared to the recorded radargrams in the inversion process. A frequency-domain finite-difference algorithm originally developed in the visco-acoustic approximation is adapted to the electromagnetic problem in 2D via an acoustic-electromagnetic mathematical analogy.In a second time, the inversion scheme is formulated as a fully multiparameter optimization problem which is solved with the quasi-Newton L-BFGS algorithm. In this formulation, the effect of an approximate inverse Hessian is expected to mitigate the trade-off between the impact of permittivity and conductivity on the data. However, numerical tests on a synthetic benchmark of the literature display a large sensitivity of the method with respect to parameter scaling, showing the limits of the L-BFGS approximation. On a realistic subsurface benchmark with surface-to-surface configuration, it has been shown possible to ally parameter scaling and regularization to reconstruct 2D images of permittivity and conductivity without a priori assumptions.Finally, the imaging method is confronted to two real data sets. The consideration of laboratory-controlled data validates the proposed workflow for multiparameter imaging, as well as the accuracy of the numerical forward solutions. The application to on-ground GPR data acquired in a limestone massif is more challenging and necessitates a thorough investigation involving classical processing techniques and forward simulations. Starting permittivity models are derived from the velocity analysis of the direct arrivals and of the reflected events. The estimation of the source signature is performed together with an evaluation of an average conductivity value and of the unknown antenna height. In spite of this procedure, synthetic data do not reproduce the observed amplitudes, suggesting an effect of the radiation pattern of the shielded antennae. In preliminary tests, the inversion succeeds in fitting the data in the considered frequency range and can reconstruct reflectors from a smooth starting model

An inverse problem in Electromagnetics (EM) refers to the process of reconstructing the physical system by processing the measured data of its electromagnetic properties. Inverse problems are typically ill-posed, and this makes them far more challenging than the typically well-posed forward problem. The solution of such inverse problems finds applications in nondestructive testing and evaluation, biomedical imaging, geophysical exploration etc. This thesis addresses some inverse problems specific to the area of electromagnetics, arising in three different scenarios. The first problem is 3-D quantitative imaging primarily targeted towards bio-medical applications. The task is to retrieve the dielectric properties, location and the shape of an unknown object from the measured scattered field. The unknown object is modeled by discretization into several voxels, with each voxel having its own dielectric property. As the inverse problem is non-linear, typically an iterative optimization process is adopted, and a forward problem needs to be solved at every iteration. The total time for reconstruction depends on the forward solver time and the number of iterations. In many cases, the number of unknowns to be reconstructed is prohibitively large. Further, the non-convergence or false-convergence of the optimization process presents its own challenge. This thesis proposes two methodologies to solve these challenges. In the first approach a multilevel methodology is proposed where voxels are hierarchically decomposed into smaller voxels based on an appropriate indicator, leading to a non-uniform multilevel voxel structure aimed at reducing the eventual number of unknowns to be solved for, also enabling faster convergence. In the second approach, a two-stage framework is proposed comprising of Machine Learning classification followed by optimization (ML-OPT). The first stage generates an appropriate adaptive grid for the optimization process and provides a suitable initial guess aiding convergence to the global minima. This approach is aimed at detecting breast tumors where the optimization algorithm can aim for higher resolution in the suspected tumor region, while using lower resolution elsewhere. The second problem is in the domain of high-speed circuits and is focused on synthesis of transmission line physical parameters given the desired electrical parameters like characteristic impedance and propagation constant. A forward solver is used to train Neural network for several different configurations for analysis and an optimization algorithm is used for synthesis. The third problem is focused on finding the source of radiation in an electronic system e.g. an automotive ECU, given the measured field at the antenna in the radiated emissions setup. The source of radiation can be from common mode current on the cable harness or from the Design Under Test (DUT). A method based on Huygens box is proposed to quantify the radiation from cable and DUT at each frequency. On each cell of the Huygens box the value of electric field computed at the observation point taking the Electric Current (J) and Magnetic Current (M) on that cell as sources and this information on the Huygens box is used to quantify the radiation. Some part of the presented work is used via technology-transfer at Simyog Technology Pvt. Ltd., an IISc incubated startup, to develop a simulation software called Compliance-scope which allows the hardware designer to predict the EMI/EMC performance of electronics modules from an early design stage.

This dissertation deals with electromagnetic modelling and data analysis, related to radar remote sensing and applied to forward scatter and meteorological polarimetric systems. After an overview of radar fundamentals to introduce the general terminology and concepts, results are presented at the end of each chapter. In this respect, a generalized electromagnetic model is first presented in order to predict the response of forward scatter radars (FSRs) for airtarget surveillance applications in both near-field and far-field regions. The model is discussed for increasing levels of complexity: a simplified near-field model, a near-field receiver model and a near-field receiver and transmitter model. FSR results have been evaluated in terms of the effects of different target electrical sizes and detection distances on the received signal, as well as the impact of the trajectory of the moving objects and compared with a customized implementation of a full-wave numerical tool. Secondly, a new data processing methodology, based on the statistical analysis of ground-clutter echoes and aimed at investigating the monitoring of the weather radar relative calibration, is presented. A preliminary study for an improvement of the ground-clutter calibration technique is formulated using as a permanent scatter analysis (PSA) and applied to real radar scenarios. The weather radar relative calibration has been applied to a dataset collected by a C-band weather radar in southern Italy and an evaluation with statistical score indexes has drawn through the comparison with a deterministic clutter map. The PSA technique has been proposed using a big metallic roof with a periodic mesh grid structure and having a hemispherical shape in the near-field of a polarimetric C-band radar and evaluated also with an ad-hoc numerical implementation of a full-wave solution. Finally, a radar-based snowfall intensity retrieval is investigated at centimeter and millimeter wavelengths (i.e., at X, Ka and W band) using a high-quality database of collocated ground-based precipitation measurements and radar multi-frequency observations. Coefficients for the multifrequency radar snowfall intensity retrieval are empirically derived using multivariate regression techniques and their interpretation is carried out by particle scattering simulations with soft-ice spheroids. For each topic, conclusions are proposed to highlight the goals of the whole work and pave the way for future studies.