Dissertations / Theses on the topic 'Inversion full wave'

Orientador: Dietrich Wilhelm Schleicher
Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica, Instituto de Geociências
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Resumo: A inversão de onda completa (FWI, do inglês ''full waveform inversion'') nãolinear baseada em gradientes (métodos de descida) é, a princípio, capaz de levar em conta todos os aspectos da propagação de onda contida nos dados síismicos. Porém, FWI baseada em gradientes é limitada pela sua bem conhecida sensibilidade no que diz respeito à escolha do modelo inicial. Com o intuito de melhor entender algumas questões relacionadas à convergência do modelo na FWI, nós estudamos uma decomposição baseada na teoria de espalhamento que permite dividir os núcleos de sensibilidade dos campos de onda acústica em função dos parâmetros do modelo em duas partes: uma relativa ao componente de fundo, outra relativa à componente singular do modelo. Estimativas para a perturbação de fundo, bem como para a perturbação da parte singular do modelo obtidas com os adjuntos destes subnúcleos são componentes da estimativa obtida com o adjunto do núcleo total de sensibilidade. Os experimentos numéricos suportam a tese de que a decomposiçao em subnúcleos permite que se retroprojete somente os resíduos do campo de onda espalhado de modo a obter estimativas razoáveis da perturbação de fundo do modelo. Em um experimento com geometria de aquisição restrita (dados de reflexão com afastamento curto), os subnúcleos baseados em espalhamento múltiplo se aproveitam da autoiluminacão do meio devido às ondas multiplamente espalhadas. A autoiluminação fornece estimativas melhores com conteúdo espectral mais rico nas baixas frequências
Abstract: While in principle nonlinear gradient-based full-waveform inversion (FWI) is capable of handling all aspects of wave propagation contained in the data, including full nonlinearity, in practice, it is limited due to its notorious sensitivity to the choice of the starting model. To help addressing model-convergence issues in FWI, we study a decomposition based on the scattering theory that allows to break the acoustic-wavefield sensitivity kernels with respect to model parameters into background and singular parts. The estimates for both background perturbation and/or singular-part perturbation obtained with the subkernels' adjoints are components of the estimate obtained with the total kernel's adjoint. Our numerical experiments shows the feasibility of our main claim: the decomposition into subkernels allows to backproject the scattered-wavefield residuals only so as to obtain reasonable background-model perturbation estimates. In an experiment with restricted acquisition geometry (reflection data, narrow offset), the multiple-scattering subkernels take advantage of medium self-illumination provided by the scattered wavefields. This self-illumination provides better estimates, with longer wavelengh content
Doutorado
Reservatórios e Gestão
Doutor em Ciências e Engenharia de Petróleo

Humanitarian clearance of minefields is most often carried out by hand, conventionally using a a metal detector and a probe. Detection is a very slow process, as every piece of detected metal must treated as if it were a landmine and carefully probed and excavated, while many of them are not. The process can be safely sped up by use of Ground-Penetrating Radar (GPR) to image the subsurface, to verify metal detection results and safely ignore any objects which could not possibly be a landmine. In this thesis, we explore the possibility of using Full Wave Inversion (FWI) to improve GPR imaging for landmine detection. Posing the imaging task as FWI means solving the large-scale, non-linear and ill-posed optimisation problem of determining the physical parameters of the subsurface (such as electrical permittivity) which would best reproduce the data. This thesis begins by giving an overview of all the mathematical and implementational aspects of FWI, so as to provide an informative text for both mathematicians (perhaps already familiar with other inverse problems) wanting to contribute to the mine detection problem, as well as a wider engineering audience (perhaps already working on GPR or mine detection) interested in the mathematical study of inverse problems and FWI.We present the first numerical 3D FWI results for GPR, and consider only surface measurements from small-scale arrays as these are suitable for our application. The FWI problem requires an accurate forward model to simulate GPR data, for which we use a hybrid finite-element boundary-integral solver utilising first order curl-conforming N\'d\'{e}lec (edge) elements. We present a novel `line search' type algorithm which prioritises inversion of some target parameters in a region of interest (ROI), with the update outside of the area defined implicitly as a function of the target parameters. This is particularly applicable to the mine detection problem, in which we wish to know more about some detected metallic objects, but are not interested in the surrounding medium. We may need to resolve the surrounding area though, in order to account for the target being obscured and multiple scattering in a highly cluttered subsurface. We focus particularly on spatial sensitivity of the inverse problem, using both a singular value decomposition to analyse the Jacobian matrix, as well as an asymptotic expansion involving polarization tensors describing the perturbation of electric field due to small objects. The latter allows us to extend the current theory of sensitivity in for acoustic FWI, based on the Born approximation, to better understand how polarization plays a role in the 3D electromagnetic inverse problem. Based on this asymptotic approximation, we derive a novel approximation to the diagonals of the Hessian matrix which can be used to pre-condition the GPR FWI problem.

In most cases of seismic processing and interpretation, elastic isotropy is assumed. However, velocity anisotropy is found to exist in most subsurface media. Hence, there exists a fundamental inconsistency between theory on the one hand, and practice on the other. If not recognised, this can invalidate interpretation of seismic data. In this thesis, inversion methods for elastic parameters are developed to quantify the degree of velocity anisotropy of multi-layered transversely isotropic media. This primarily involves examining the velocity fields of layered media using anisotropic elastic wave propagation theory, and developing inversion programs to recover elastic parameters from those velocity fields. The resolved elastic parameter information is used in carrying out further studies on the effects of seismic anisotropy on normal moveout (NMO). Mathematical analyses, numerical simulations, and physical modelling experiments are used in this research for verification purposes before application to field survey data. Numerical studies show the transmission velocity field through layered media appears to be equivalent to that through a single-layered medium, within the practical offset limits in field surveys. The elastic parameters, which describe the property of such equivalent single-layered media, can be used as apparent elastic parameters to describe the collective mechanical property of the layered media. During this research, Snell's law was used in ray tracing to determine ray paths through the interface between any two component layers. By analyzing the signals recorded by any receiver in a walkaway VSP survey, the apparent transmission velocity field for the layered media above this receiver depth was inverted.
Software was developed to recover the apparent elastic parameters for the layered media above this receiver depth using the transmission velocity field as input. Based on a two-layered model, another method was developed to recover the interval elastic parameters for an individual layer of interest, using the signals recorded by receivers on the upper and lower surfaces of this layer. The recovered elastic parameters may be considerably different from the real values if a transversely isotropic medium with a tilted symmetry axis (TTI) is treated as a transversely isotropic medium with a vertical symmetry axis (VTI). A large angle of tilt of the symmetry axis significantly influences the recorded velocity field through the medium. An inversion program was written to recover the value of the tilt angle of a TTI medium, and the elastic parameters of the medium. Programs were also developed to combine information from P, SV, and SH-waves in an inversion procedure. This capability in inversion programs enables us to use the additional information provided by a multi-component VSP survey to obtain accurate estimates of the elastic parameters of geological formations. Software testing and development was carried out on numerically generated input data. Up to 10 milliseconds of random noise in travel time was added to the input to confirm the stability of the inversion software. Further testing was carried out on physical model data where the parameters of the model were known from direct measurements. Finally the inversion software was applied to actual field data and found to give plausible results.
In software testing in the physical modelling laboratory, other practical problems were encountered. System errors caused by the disproportionately large size of the transducers used affected the accuracy of the inversion results obtained. Transducer performance was studied, and it was found that reducing the size of transducers or making offset corrections would decrease the errors caused by the disproportionately large transducer dimensions. In using the elastic parameters recovered, it was found that the elastic parameter δ significantly influences the seismic records from a horizontal reflector. The normal moveout velocity was found to show variations from the zero-offset normal moveout velocity depending on the value and sign of elastic parameter δ. New approximate expressions for anisotropic normal moveout, phase and ray velocity functions at short offsets were developed. The value of anisotropic parameter δ was found to be the major factor controlling these relations. If the recovered parameter δ has a large negative value, analytical and numerical studies demonstrated that the new expression for moveout velocity developed herein should be used instead of Thomsen's normal moveout equation.

Les techniques d'imagerie sismique jouent un rôle crucial dans l'exploration et la compréhension des structures sous la surface de la terre. Dans le domaine de l'exploration pétrolière les zones sous les corps de sel (dites subsalt) représentent un défi pour les techniques d'imagerie conventionnelles. L'application de la full-wave inversion (FWI) aux données sismiques de puits devrait permettre de résoudre au moins partiellement ces difficultés. Dans ce contexte subsalt, l'objectif principal est d'imager et aussi de caractériser les réservoirs d'hydrocarbures pouvant se trouver aux flancs et sous les corps de sel. Néanmoins, le contexte particulier de la sismique de puits, combiné aux défis liés à l'imagerie sous et autour des corps de sel nécessitent l'introduction de contraintes fortes dans le problème inverse géophysique en raison d'une sous-détermination du problème. La présente thèse propose une approche en trois étapes pour aborder ces défis. Tout d'abord, elle suggère d'incorporer de l'information géologique extit{a priori} dans le processus d'inversion en définissant des objets géologiques délimités par des discontinuités permettant aussi une introduction plus fine de l'information ext{a priori} sur les paramètres physiques par objet. Ensuite, elle vise à formaliser et à calculer le gradient par rapport aux paramètres géométriques du modèle qui définissent ces discontinuités. Enfin, elle propose de mettre en place un algorithme d'inversion full-wave hybride qui combine les approches de type champ et de type objet. Cette FWI hybride utilise à la fois le gradient des champs physiques et le gradient relatif aux paramètres géométriques. Le contenu de la thèse est réparti en quatre chapitres. Le premier chapitre présente les concepts fondamentaux utilisés dans l'algorithme FWI hybride. Il met l'accent sur des approches de représentation duale des interfaces (explicite/implicite) par l'utilisation de maillages non-structurés déformables pour la discrétisation des discontinuités et de la méthode level set pour la représentation implicite des objets géologiques dans le problème inverse. Le chapitre 2 décrit les étapes du développement d'une plateforme logicielle permettant l'implémentation numérique de ces approches et la réalisation de tests FWI hybride. Cette plateforme logicielle comprend un code de modélisation de la propagation des ondes par la méthode des éléments spectraux et un code d'inversion basé sur le calcul des gradients simples ou conjugués, avec une approche probabiliste du problème inverse. Le troisième chapitre détaille les différentes étapes de l'algorithme FWI géométrique et sa mise en application à des données de sismique de puits pour estimer la position des interfaces sel/sédiment pour un milieu 2D. Enfin, le quatrième chapitre présente l'algorithme d'inversion hybride et sa mise en oeuvre avec des données de sismique de puits dans le but d'estimer les vitesses des ondes de compression et de cisaillement, ainsi que la position de la frontière des corps de sel pour un milieu 2D. Les résultats des tests numériques présentés sont prometteurs, ce qui permet de valider notre approche d'inversion hybride
Seismic imaging techniques play a crucial role in the exploration and understanding of subsurface structures. In the field of petroleum exploration, subsalt zones present a challenge for conventional imaging techniques and full-wave inversion (FWI). The application of FWI to seismic well data is expected to overcome these challenges. The primary goal is to characterize hydrocarbon reservoirs that may be located beneath and alongside salt bodies. However, the context of well seismic imaging, combined with the challenges of imaging beneath and around salt bodies, requires the introduction of strong constraints into the geophysical inverse problem due to its underdetermined nature.This thesis presents a three-step approach to tackle these challenges. Firstly, it suggests incorporating extit{a priori} geological information into the inversion process by defining geological objects bounded by discontinuities. Secondly, it aims to formalize and compute the gradient with respect to the geometric parameters that define these discontinuities. Thirdly, it proposes the implementation of a hybrid full-wave inversion algorithm that combines field and object-based approaches. This hybrid FWI utilizes both the gradient of physical fields and the gradient relative to geometric parameters.The thesis content is divided into four distinct chapters. The first chapter introduces the fundamental concepts used in the hybrid FWI algorithm. It highlights the approach based on a dual representation of interfaces (explicit/implicit) using deformable unstructured meshes for the explicit discretization of discontinuities and the level-set method for the implicit representation of the geological objects in the inverse problem. Chapter 2 describes the development steps of a software platform for the numerical implementation of these approaches and the execution of hybrid FWI tests. This software platform includes a wave propagation modeling code based on the spectral elements method and an inversion code based on the gradient computation using the Green's function method, with a probabilistic approach to the inverse problem. The third chapter outlines the various stages of the geometric FWI algorithm and its application to well seismic data to estimate the position of salt/sediment interfaces in 2D environments. Finally, the fourth chapter presents the hybrid inversion algorithm and its implementation with well seismic data to estimate the velocities of compression and shear waves, as well as the position of salt body boundaries in 2D environments. The results of the presented numerical tests are promising, validating our hybrid inversion approach

Full Waveform Inversion has become an important research field in the context of seismic exploration, due to the possibility to estimate a high-resolution model of the subsurface in terms of acoustic and elastic parameters. To this aim, issues such as an efficient implementation of wave equation solution for the forward problem, and optimization algorithms, both local and global, for this high non-linear inverse problem must be tackled. In this thesis, in the framework of 2D acoustic approximation, I implemented an efficient numerical solution of the wave equation based on a local order of approximation of the spatial derivatives to reduce the computational time and the approximation error. Moreover, for what concerns the inversion, I studied two different global optimization algorithms (Simulated Annealing and Genetic Algorithms) on analytic functions that represent different possible scenarios of the misfit function to estimate an initial model for local optimization algorithm in the basin of attraction of the global minimum. Due to the high number of unknowns in seismic exploration context, of the order of some thousands or more, different strategies based on the adjoint method must be used to compute the gradient of the misfit function. By this procedure, only three wave equation solutions are required to compute the gradient instead of a number of solutions proportional to the unknown parameters. The FWI approach developed in this thesis has been applied first on a synthetic inverse problem on the Marmousi model to validate the whole procedure, then on two real seismic datasets. The first is a land profile with two expanding spread experiments and is characterized by a low S/N ratio. In this case, the main variations of the estimated P-wave velocity model well correspond to the shallow events observed on the post-stack depth migrated section. The second is a marine profile extracted from a 3D volume where the local optimization, based on the adjoint method, allows to estimate a high-resolution velocity model whose reliability has been checked by the alignment of the CIGs computed by pre-stack depth migration.

This thesis presents an empirical study comparing the ability of multi-static and bi-static, handheld, ground penetrating radar (GPR) systems, using full wave inversion (FWI), to determine the properties of buried anti-personnel (AP) landmines. A major problem associated with humanitarian demining is the occurrence of many false positives during clearance operations. Therefore, a reduction of the false alarm rate (FAR) and/or increasing the probability of detection (POD) is a key research and technical objective. Sensor fusion has emerged as a technique that promises to significantly enhance landmine detection. This study considers a handheld, combined metal detector (MD) and GPR device, and quantifies the advantages of the use of antenna arrays. During demining operations with such systems, possible targets are detected using the MD and further categorised using the GPR, possibly excluding false positives. A system using FWI imaging techniques to estimate the subsurface parameters is considered in this work. A previous study of multi-static GPR FWI used simplistic, 2D far-field propagation models, despite the targets being 3D and within the near field. This novel study uses full 3D electromagnetic (EM) wave simulation of the antenna arrays and propagation through the air and ground. Full EM simulation allows the sensitivity of radio measurements to landmine characteristics to be determined. The number and configuration of antenna elements are very important and must be optimised, contrary to the 2D sensitivity studies in (Watson, Lionheart 2014, Watson 2016) which conclude that the degree (number of elements) of the multi-static system is not critical. A novel sensitivity analysis for tilted handheld GPR antennas is used to demonstrate the positive impact of tilted antenna orientation on detection performance. A time domain GPR and A-scan data, consistent with a commercial handheld system, the MINEHOUND, is used throughout the simulated experiments which are based on synthetic GPR measurements. Finally, this thesis introduces a novel method of optimising the FWI solution through feature extraction or estimation of the internal air void typically present in pressure activated mines, to distinguish mines from non-mine targets and reduce the incidence of false positives.

Dans ce projet, nous étudions la reconstruction de milieux terrestres souterrains.L’imagerie sismique est traitée avec un problème de minimisation itérative àgrande échelle, et nous utilisons la méthode de l’inversion des formes d’ondes(Full Waveform Inversion, FWI method). La reconstruction est basée sur desmesures d’ondes sismiques, car ces ondes sont caractérisées par le milieu danslequel elles se propagent. Tout d’abord, nous présentons les méthodesnumériques qui sont nécessaires pour prendre en compte l’hétérogénéité etl’anisotropie de la Terre. Ici, nous travaillons avec les solutions harmoniques deséquations des ondes, donc dans le domaine fréquentiel. Nous détaillons leséquations et l’approche numérique mises en place pour résoudre le problèmed’onde.Le problème inverse est établi afin de reconstruire les propriétés du milieu. Ils’agit d’un problème non-linéaire et mal posé, pour lequel nous disposons de peude données. Cependant, nous pouvons montrer une stabilité de type Lipschitzpour le problème inverse associé avec l’équation de Helmholtz, en considérantdes modèles représentés par des constantes par morceaux. Nous explicitons laborne inférieure et supérieure pour la constante de stabilité, qui nous permetd’obtenir une caractérisation de la stabilité en fonction de la fréquence et del’échelle. Nous revoyons ensuite le problème de minimisation associé à lareconstruction en sismique. La méthode de Newton apparaît comme naturelle,mais peut être difficilement accessible, dû au coup de calcul de la Hessienne.Nous présentons une comparaison des méthodes pour proposer un compromisentre temps de calcul et précision. Nous étudions la convergence de l’algorithme,en fonction de la géométrie du sous-sol, la fréquence et la paramétrisation. Celanous permet en particulier de quantifier la progression en fréquence, en estimantla taille du rayon de convergence de l’espace des solutions admissibles.A partir de l’étude de la stabilité et de la convergence, l’algorithme deminimisation itérative est conduit en faisant progresser la fréquence et l’échellesimultanément. Nous présentons des exemples en deux et trois dimensions, etillustrons l’incorporation d’atténuation et la considération de milieux anisotropes.Finalement, nous étudions le cas de reconstruction avec accès aux données deCauchy, motivé par les dual sensors développés en sismique. Cela nous permetde définir une nouvelle fonction coût, qui permet de prometteuses perspectivesavec un besoin minimal quant aux informations sur l’acquisition
In this project, we investigate the recovery of subsurface Earth parameters. Weconsider the seismic imaging as a large scale iterative minimization problem, anddeploy the Full Waveform Inversion (FWI) method, for which several aspects mustbe treated. The reconstruction is based on the wave equations because thecharacteristics of the measurements indicate the nature of the medium in whichthe waves propagate. First, the natural heterogeneity and anisotropy of the Earthrequire numerical methods that are adapted and efficient to solve the wavepropagation problem. In this study, we have decided to work with the harmonicformulation, i.e., in the frequency domain. Therefore, we detail the mathematicalequations involved and the numerical discretization used to solve the waveequations in large scale situations.The inverse problem is then established in order to frame the seismic imaging. Itis a nonlinear and ill-posed inverse problem by nature, due to the limitedavailable data, and the complexity of the subsurface characterization. However,we obtain a conditional Lipschitz-type stability in the case of piecewise constantmodel representation. We derive the lower and upper bound for the underlyingstability constant, which allows us to quantify the stability with frequency andscale. It is of great use for the underlying optimization algorithm involved to solvethe seismic problem. We review the foundations of iterative optimizationtechniques and provide the different methods that we have used in this project.The Newton method, due to the numerical cost of inverting the Hessian, may notalways be accessible. We propose some comparisons to identify the benefits ofusing the Hessian, in order to study what would be an appropriate procedureregarding the accuracy and time. We study the convergence of the iterativeminimization method, depending on different aspects such as the geometry ofthe subsurface, the frequency, and the parametrization. In particular, we quantifythe frequency progression, from the point of view of optimization, by showinghow the size of the basin of attraction evolves with frequency. Following the convergence and stability analysis of the problem, the iterativeminimization algorithm is conducted via a multi-level scheme where frequencyand scale progress simultaneously. We perform a collection of experiments,including acoustic and elastic media, in two and three dimensions. Theperspectives of attenuation and anisotropic reconstructions are also introduced.Finally, we study the case of Cauchy data, motivated by the dual sensors devicesthat are developed in the geophysical industry. We derive a novel cost function,which arises from the stability analysis of the problem. It allows elegantperspectives where no prior information on the acquisition set is required

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
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

L'inversion des formes d'onde (full waveform inversion, FWI) a suscité un intérêt dans le monde entier pour sa capacité à estimer de manière précise et détaillée les propriétés physiques du sous-sol. La FWI est généralement formulée sous la forme d'un problème d'ajustement des données par moindres carrés et résolus par une approche linéarisée utilisant des méthodes d'optimisation locales. Cependant, la FWI est bien connue de souffrir du problème de saut de phase rendant les résultats fortement dépendant de la qualité des modèles initiaux. L'inversion des formes d'ondes des arrivées réfléchies (reflection waveform inversion, RWI) a récemment été proposée pour atténuer ce problème en supposant une séparation d'échelle entre le modèle de vitesse lisse et le modèle de réflectivité à haut nombre d'onde. La formulation de RWI considère explicitement les ondes réfléchies afin d'extraire de ces ondes une information sur les variations lisses de vitesse des zones profondes. Cependant, la méthode néglige les ondes transmises qui contraignant les informations lisses de vitesse en proche surface.Dans cette thèse, une étude de la sensibilité en nombre d'ondes des méthodes de FWI et RWI a d'abord été revisitée dans le cadre de la tomographie en diffraction et des décompositions orthogonales. A partir de cette analyse, je propose une nouvelle méthode, à savoir l'inversion jointe des formes d'ondes transmises et réfléchies (joint full waveform inversion, JFWI). La méthode propose une formulation unifiée pour combiner la FWI des transmissions et la RWI pour les réflexions, donnant naturellement une sensibilité commune aux petits nombres d'onde venant des arrivées grand-angle et réfléchies. Les composantes à hauts nombres d'onde sont naturellement atténuées par la formulation. Pour satisfaire l'hypothèse de séparation d'échelle, j'utilise une paramétrisation du sous-sol basée sur la vitesse des ondes de compression et l'impédance acoustique. La complexité temporelle de cette approche est le double de la méthode de FWI classique et la requête mémoire reste la même.Une procédure d'inversion est ensuite proposée, permettant d'estimer alternativement le modèle de la vitesse du sous-sol par JFWI et l'impédance inversion de formes d'ondes réfléchies. Un exemple synthétique réaliste du modèle de Valhall est d'abord utilisé avec des données de streamer et à partir d'un modèle initial très lisse. Dans ce cadre, alors que la FWI converge vers un minimum local, la JFWI réussit à reconstruire un modèle de vitesse lisse de bonne qualité. La prise en compte des ondes tournante par la JFWI montre un fort intérêt pour la qualité de reconstruction superficielle, comparée à la méthode RWI seule. Cela se traduit ensuite par une reconstruction améliorée en profondeur. Le modèle de vitesse lisse construit par JFWI peut ensuite être considéré comme modèle initial pour la FWI classique, afin d'injecter le contenu en haut nombres d'onde tout en évitant le problème de saut de phase.Les avantages et limites de l'approche de JFWI sont ensuite étudiés dans une application sur données réelles, venant d'un profil 2D de données de fond de mer (OBC) recoupant un nuage de gaz au dessus d'un réservoir. Plusieurs modèles initiaux et stratégies d'inversion sont testés afin de minimiser le problème de saut de phase, tout en construisant des modèles de sous-sol avec une résolution suffisante. Sous réserve de mettre en œuvre des stratégies limitant le problème de saut de phase, la JFWI montre qu'elle peut produire un modèle de vitesse acceptable, injectant les bas nombres d'onde dans le modèle de vitesse. L'amélioration de l'éclairage en angles de diffraction fournie par des acquisitions 3D devrait permettre de pouvoir commencer l'inversion par JFWI à partir de modèle encore moins bien définis
Full waveform inversion (FWI) has attracted worldwide interest for its capacity to estimate the physical properties of the subsurface in details. It is often formulated as a least-squares data-fitting procedure and routinely solved by linearized optimization methods. However, FWI is well known to suffer from cycle skipping problem making the final estimations strongly depend on the user-defined initial models. Reflection waveform inversion (RWI) is recently proposed to mitigate such cycle skipping problem by assuming a scale separation between the background velocity and high-wavenumber reflectivity. It explicitly considers reflected waves such that large-wavelength variations of deep zones can be extracted at the early stage of inversion. Yet, the large-wavelength information of the near surface carried by transmitted waves is neglected.In this thesis, the sensitivity of FWI and RWI to subsurface wavenumbers is revisited in the frame of diffraction tomography and orthogonal decompositions. Based on this analysis, I propose a new method, namely joint full waveform inversion (JFWI), which combines the transmission-oriented FWI and RWI in a unified formulation for a joint sensitivity to low wavenumbers from wide-angle arrivals and short-spread reflections. High-wavenumber components are naturally attenuated during the computation of model updates. To meet the scale separation assumption, I also use a subsurface parameterization based on compressional velocity and acoustic impedance. The temporal complexity of this approach is twice of FWI and the memory requirement is the same.An integrated workflow is then proposed to build the subsurface velocity and impedance models in an alternate way by JFWI and waveform inversion of the reflection data, respectively. In the synthetic example, JFWI is applied to a streamer seismic data set computed in the synthetic Valhall model, the large-wavelength characteristics of which are missing in the initial 1D model. While FWI converges to a local minimum, JFWI succeeds in building a reliable velocity macromodel. Compared with RWI, the involvement of diving waves in JFWI improves the reconstruction of shallow velocities, which translates into an improved imaging at greater depths. The smooth velocity model built by JFWI can be subsequently taken as the initial model for conventional FWI to inject high-wavenumber content without obvious cycle skipping problems.The main promises and limitations of the approach are also reviewed in the real-data application on the 2D OBC profile cross-cutting gas cloud.Several initial models and offset-driven strategies are tested with the aim to manage cycle skipping while building subsurface models with sufficient resolution. JFWI can produce an acceptable velocity model provided that the cycle skipping problem is mitigated and sufficient low-wavenumber content is recovered at the early stage of inversion. Improved scattering-angle illumination provided by 3D acquisitions would allow me to start from cruder initial models

La caractérisation de la proche surface est un enjeu majeur pour l'industrie pétrolière. Lors des acquisitions terrestres et Ocean Bottom Cable (OBC), les couches superficielles généralement altérées ou peu consolidées, présentent des structures géologiques complexes et ont éventuellement des variations topographiques importantes. Les ondes de surface, énergétiques, se propagent dans ce milieu complexe et dominent les sismogrammes, ce qui masque le signal utile pour le traitement sismique classique et rend difficile l'imagerie à la profondeur du réservoir.Il est donc important de pouvoir atténuer ces ondes, éventuellement d'appliquer des corrections statiques et/ou d'amplitude. Ceci qui nécessite une connaissance précise du modèle de vitesse de la proche surface. L'étude de la dispersion des ondes de surface est couramment utilisée en sismologie globale et à l'échelle géotechnique pour évaluer les propriétés des milieux terrestres. Il existe néanmoins des limitations: la mesure de cette dispersion est souvent difficile et les profils de vitesses obtenus sont 1D. A l'échelle pétrolière, l'hypothèse 1D n'est pas toujours adaptée, ce qui motive l'utilisation d'une méthode alternative d'imagerie plus haute résolution, la méthode d'inversion de la forme d'onde (FWI). Cependant, le modèle de vitesse initial doit être assez précis pour éviter le "cycle-skipping" et permettre la convergence vers la solution optimale.Cette étude explore différentes alternatives de fonctions coûts pour résoudre le "cycle-skipping" et diminuer la dépendance de l'inversion à la qualité du modèle initial. En exprimant les fonctions coûts dans le domaine f-k (fréquence-nombre d'onde) et le domaine f-p (fréquence-lenteur), la FWI est plus robuste. A l'aide d'exemples synthétiques, nous démontrons l'efficacité de ces nouvelles approches qui permettent bien de retrouver les variations latérales de vitesses d'onde S.Dans une seconde partie, nous développons une inversion FWI en "layer stripping", adaptée spécifiquement à la physique des ondes de surface. Comme la profondeur de pénétration de ces ondes dépend de leur longueur d'onde, et donc, de leur contenu fréquentiel, nous proposons d'inverser séquentiellement des plus hautes aux plus basses fréquences de ces ondes pour contraindre successivement les couches superficielles jusqu'aux plus profondes. Un fenêtrage selon la distance source-station est également appliqué. Dans un premier temps seules les courtes distances sont inversées, au fur à mesure les données associées à des plus grandes distances sont rajoutées, plus fortement impactées par le "cycle-skipping". Nous démontrons à l'aide d'exemples synthétiques l'avantage de cette méthode par rapport aux méthodes multi-échelles conventionnelles inversant des basses vers les hautes fréquences.Enfin, l'inversion des ondes de surface pour la caractérisation de la proche surface est confrontée à un cas réel. Nous discutons la construction et la pertinence du modèle initial et les difficultés rencontrées lors de l'inversion
The characterization of the near surface is an important topic for the oil and gas industry. For land and Ocean Bottom Cable (OBC) acquisitions, weathered or unconsolidated top layers, prominent topography and complex shallow structures may make imaging at target depth very difficult. Energetic and complex surface waves often dominate such recordings, masking the signal and challenging conventional seismic processing. Static corrections and the painstaking removal of surface waves are required to obtain viable exploration information.Yet surface waves, which sample the near surface region, are considered as signal on both the engineering and geotechnical scale as well as the global seismology scale. Their dispersive property is conventionally used in surface wave analysis techniques to obtain local shear velocity depth profiles. But limitations such as the picking of dispersion curves and poor lateral resolution have lead to the proposal of Full Waveform Inversion (FWI) as an alternative high resolution technique. FWI can theoretically be used to explain the complete waveforms recoded in seismograms, but FWI with surface waves has its own set of challenges. A sufficiently accurate initial velocity model is required or otherwise cycle-skipping problems will prevent the inversion to converge.This study investigates alternative misfit functions that can overcome cycle-skipping and decrease the dependence on the initial model required. Computing the data-fitting in different domains such as the frequency-wavenumber (f-k) and frequency-slowness (f-p) domains is proposed for robust FWI, and successful results are achieved with a synthetic dataset, in retrieving lateral shear velocity variations.In the second part of this study a FWI layer stripping strategy, specifically adapted to the physics of surface waves is proposed. The penetration of surface waves is dependent on their wavelength, and therefore on their frequency. High-to-low frequency data is therefore sequentially inverted to update top-to-bottom layer depths of the shear velocity model. In addition, near-to-far offsets are considered to avoid cycle-skipping issues. Results with a synthetic dataset show that this strategy is more successful than conventional multiscale FWI in using surface waves to update the shear velocity model.Finally inversion of surface waves for near surface characterization is attempted on a real dataset at the oil and gas exploration scale. The construction of initial models and the difficulties encountered during FWI with real data are discussed

Les dorsales ultra-lentes quasi-amagmatiques constituent une nouvelle catégorie de dorsales océaniques caractérisées par une accrétion crustale, exposant sur le fond marin des quantités considérables de péridotites provenant du manteau. L’étude de la contribution des processus tectoniques, magmatiques et d’autres processus impliqués est nécessaire pour obtenir un modèle conceptuel complet des dorsales océaniques à accrétion ultra-lente. L’imagerie des structures de la croûte et du manteau supérieur peut nous aider à comprendre les activités géologiques passées et actuelles sur les dorsales à accrétion océanique ultra-lente. L’objectif du projet est de comprendre la croûte océanique formée dans une dorsale à accrétion ultra-lente appelée ride sud-ouest indienne, à faible apport de magma. Notre projet de recherche est basé sur le traitement et la modélisation de données sismiques actives et passives dans la partie la plus orientale de la dorsale Sud-Ouest Indienne. L’acquisition des données géophysiques a eu lieu en 2014 lors de la campagne SISMOSMOOTH, à bord du N/O Marion-Dufresne. Nous avons analysé les enregistrements des composantes verticales de 43 sismomètres fond de mer (OBS) dans notre approche sismique passive et les composantes hydrophones de 16 sismomètres fond de mer pour l’approche sismique active. L’interférométrie de bruit ambiant et l’inversion de forme d’onde complète (FWI) des données de réfraction ont été utilisées pour imager les structures internes de la croûte et de la lithosphère. Grâce à la modélisation de l’interférométrie de bruit ambiant, on trouve une épaisseur moyenne de croûte de 7 km avec une couche peu profonde de faibles vitesses de cisaillement. De plus, nous en déduisons que les 2 km supérieurs sont très poreux et peuvent être fortement serpentinisés. La vitesse moyenne des ondes de cisaillement entre la base de la croûte et la profondeur maximale de notre modèle (15 km) est inférieure à la valeur de référence globale de 4.5 km/s et peut s’expliquer par le jeune âge des fonds marins de notre zone. Notre modèle bi-dimensionnel de vitesse des ondes P obtenu à partir de notre analyse FWI suggère des variations considérables de composition dans la partie supérieure le long du profil parallèle à l’axe. Notre étude propose un domaine de transition entre un domaine à prédominance volcanique et un non magmatique, entre ∼65 à 95 km de distance sur le profil. Des injections magmatiques dans des dikes sont proposées dans le domaine oriental non volcanique. Une augmentation vers l’ouest de l’apport de matériel magmatique est confirmée pour le mode d’accrétion océanique. Le modèle de vitesse des ondes P associé aux variations de serpentinisation suggère que le Moho est une transition graduelle d’une péridotite hydratéevers une péridotite non altérée
Ultra-slow spreading ridges are a new category of spreading ridges characterized by quasi-amagmatic crustal accretion, exposing considerable amounts of mantle derived peridotites on the seafloor. Investigating the contributions of tectonic, magmatic, and other involved processes is necessary to gain a comprehensive conceptual model of ultra-slow spreading ridges. Imaging the crustal and upper mantle structures can help us to understand the past and current geological activities in the ultra-slow spreading ridges. The aim of the project is to understand the oceanic crust formed in an ultra-slow spreading ridge called the Southwest Indian Ridge with a low melt supply. Our research project is based on the processing and modeling of the active and passive seismic data in the easternmost part of Southwest Indian Ridge. The data acquisition took place in 2014 during the SISMOSMOOTH cruise. We analyzed vertical component recordings from 43 ocean-bottom seismometers in our passive seismic approach and the hydrophone components of 16 ocean-bottom seismometers in the active seismic approach. Ambient-noise interferometry and full-waveform inversion (FWI) of refraction data were used to image the internal structures of the lithosphere. In the modeling of ambient-noise interferometry, we find an average crustal thickness of 7 km with a shallow layer of low shear velocities. Moreover, we infer that the uppermost 2 km are highly porous and may be strongly serpentinized. The average shear wave velocity between the base of the crust and the maximum depth of our model (15 km) was less than the global reference value of 4.5 km/s and was explained by the younger age of the seafloor in our area. Our two-dimensional P-wave velocity model obtained from FWI suggests considerable variations in the upper lithospheric compositions along the axis-parallel profile. A transition is expected at a distance of ∼65-95 km along the profile from the predominantly volcanic domain in the western zone to variable serpentinized peridotite in the eastern zone. Dike injections are predicted in this area. A westward increase in melt supply is proposed in the seafloor accretion mode. The serpentinization and P-wave velocity model suggests that the Moho is a gradual transition from hydrated to unaltered peridotite

Le radar géologique est une méthode d'investigation géophysique basée sur la propagation d'ondes électromagnétiques dans le sous-sol. Avec des fréquences allant de 5 MHz à quelques GHz et une forte sensibilité aux propriétés électriques, le géoradar fournit des images de réflectivité dans des contextes et à des échelles très variés : génie civil, géologie, hydrogéologie, glaciologie, archéologie. Cependant, dans certains cas, la compréhension fine des processus étudiés dans la subsurface nécessite une quantification des paramètres physiques du sous-sol. Dans ce but, l'inversion des formes d'ondes complètes, méthode initialement développée pour l'exploration sismique qui exploite l'ensemble des signaux enregistrés, pourrait s'avérer efficace. Dans cette thèse, je propose ainsi des développements méthodologiques par une approche d'inversion multiparamètres (permittivité diélectrique et conductivité), pour des configurations en transmission, en deux dimensions.Ces développements sont ensuite appliqués à un jeu de données réelles acquises entre forages.Dans une première partie, je présente tout d'abord la méthode numérique utilisée pour modéliser la propagation des ondes électromagnétiques dans un milieu 2D hétérogène, élément indispensable pour mener à bien le processus d'imagerie. Ensuite, j’introduis puis étudie le potentiel des méthodes d’optimisation locale standards (gradient conjugué non linéaire, l-BFGS, Newton tronqué dans ses versions Gauss-Newton et Exact-Newton) pour découpler la permittivité diélectrique et la conductivité électrique. Je montre notamment qu’un découplage effectif n’est possible qu’avec un modèle initial suffisamment précis et la méthode la plus sophistiquée (Newton tronqué). Comme dans le cas général, ce modèle initial n’est pas disponible, il s’avère nécessaire d'introduire un facteur d'échelle qui répartit le poids relatif de chaque classe de paramètres dans l'inversion. Dans un milieu réaliste avec une acquisition entre puits, je montre que les différentes méthodes d'optimisation donnent des résultats similaires en matière de découplage de paramètres. C'est finalement la méthode l-BFGS qui est retenue pour l'application aux données réelles, en raison de coûts de calcul plus faibles.Dans une deuxième partie, j'applique cette méthodologie à des données réelles acquises entre deux forages localisés dans des formations carbonatées, à Rustrel (France, 84). Cette inversion est réalisée en parallèle d'une approche synthétique à l'aide d'un modèle représentatif du site étudié et des configurations d'acquisition similaires. Ceci permet de pouvoir comprendre, contrôler et valider les observations et conclusions obtenues sur les données réelles. Cette démarche montre que la reconstruction de la permittivité est très robuste. A contrario, l'estimation de la conductivité souffre de deux couplages majeurs, avec la permittivité diélectrique, d'une part, et avec l'amplitude de la source estimée, d'autre part. Les résultats obtenus sont confrontés avec succès à des données indépendantes (géophysique depuis la surface, analyse sur échantillons de roche), et permet de bénéficier d'une image haute-résolution des formations géologiques. Enfin, une analyse 3D confirme que les structures 3D à fort contraste de propriétés, telles que la galerie enfouie sur notre site, nécessiteraient une approche de modélisation 3D, notamment pour mieux expliquer les amplitudes observées
Ground Penetrating Radar (GPR) is a geophysical investigation method based on electromagnetic waves propagation in the underground. With frequencies ranging from 5 MHz to a few GHz and a high sensitivity to electrical properties, GPR provides reflectivity images in a wide variety of contexts and scales: civil engineering, geology, hydrogeology, glaciology, archeology. However, in some cases, a better understanding of some subsurface processes requires a quantification of the physical parameters of the subsoil. For this purpose, inversion of full waveforms, a method initially developed for seismic exploration that exploits all the recorded signals, could prove effective. In this thesis, I propose methodological developments using a multiparameter inversion approach (dielectric permittivity and conductivity), for two-dimensional transmission configurations. These developments are then applied to a real data set acquired between boreholes.In a first part, I present the numerical method used to model the propagation of electromagnetic waves in a heterogeneous 2D environment, a much-needed element to carry out the process of imaging. Then, I introduce and study the potential of standard local optimization methods (nonlinear conjugate gradient, l-BFGS, Newton truncated in its Gauss-Newton and Exact-Newton versions) to fight the trade-off effects related to the dielectric permittivity and to the electrical conductivity. In particular, I show that effective decoupling is possible only with a sufficiently accurate initial model and the most sophisticated method (truncated Newton). As in the general case, this initial model is not available, it is necessary to introduce a scaling factor which distributes the relative weight of each parameter class in the inversion. In a realistic medium and for a cross-hole acquisition configuration, I show that the different optimization methods give similar results in terms of parameters decoupling. It is eventually the l-BFGS method that is used for the application to the real data, because of lower computation costs.In a second part, I applied the developed Full waveform inversion methodology to a set of real data acquired between two boreholes located in carbonate formations, in Rustrel (France, 84). This inversion is carried out together with a synthetic approach using a model representative of the studied site and with a similar acquisition configuration. This approach enables us to monitor and validate the observations and conclusions derived from data inversion. It shows that reconstruction of dielectrical permittivity is very robust. Conversely, conductivity estimation suffers from two major couplings: the permittivity and the amplitude of the estimated source. The derived results are successfully compared with independent data (surface geophysics and rock analysis on plugs) and provides a high resolution image of the geological formation. On the other hand, a 3D analysis confirms that 3D structures presenting high properties contrasts, such as the buried gallery present in our site, would require a 3D approach, notably to better explain the observed amplitudes

Massive shales and fractures are the main cause of seismic anisotropy in the upper-most part of the crust, caused either by sedimentary or tectonic processes. Neglecting the effect of seismic anisotropy in seismic processing algorithms may incorrectly image the seismic reflectors. This will also influence the quantitative amplitude analysis such as the acoustic or elastic impedance inversion and amplitude versus offsets analysis. Therefore it is important to obtain anisotropy parameters from seismic data. Conventional layer stripping inversion schemes and reflector based reflectivity inversion methods are solely dependent upon a specific reflector, without considering the effect of the other layers. This, on one hand, does not take the effect of transmission in reflectivity inversion into the account, and on the other hand, ignores the information from the waves travelling toward the lower layers. I provide a framework to integrate the information for each specific layer from all the rays which have travelled across this layer. To estimate anisotropy parameters I have implemented unconstrained minimization algorithms such as nonlinear conjugate gradients and variable metric methods, I also provide a nonlinear least square method, based on the Levenberg-Marquardt algorithm. In a stack of horizontal transversely isotropic layers with vertical axis of symmetry, where the layer properties are laterally invariant, we provide two different inversion schemes; traveltime and waveform inversion.
Both inversion schemes utilize compressional and joint compressional and converted shear waves. A new exact traveltime equation has been formulated for a dipping transversely isotropic system of layers. These traveltimes are also parametrized by the ray parameters for each ray element. I use the Newton method of minimization to estimate the ray parameter using a random prior model from a uniform distribution. Numerical results show that with the assumption of weak anisotropy, Thomsen’s anisotropy parameters can be estimated with a high accuracy. The inversion algorithms have been implemented as a software package in a C++ object oriented environment.

La détection, la localisation et le suivi de l’évolution de défauts dans les milieux périodiques et les guides d’ondes est un enjeu majeur dans le domaine du Contrôle Non Destructif (CND). La propagation d’ondes dans ce genre de milieux est complexe, par exemple lorsque la vitesse dépend de la fréquence (dispersion) ou de la direction de propagation (anisotropie). La signature du défaut peut également être « noyée » dans le champ acoustique renvoyé par la structure (réverbération ou diffusion multiple). C’est pour répondre à ces enjeux de taille que l’Optimisation Topologique (OT) a été adaptée aux problèmes de diffraction des ondes acoustiques par des défauts infinitésimaux afin d’obtenir des images de réflectivité des milieux inspectés. La méthode peut être appliquée à toutes sortes de milieux, quelle que soit leur complexité, à condition d’être capable de simuler correctement (sur un milieu de référence) la propagation des ondes de l’expérience physique. En s’inspirant de l’OT, les travaux de cette thèse proposent de mettre en oeuvre des méthodes d’imagerie qualitatives adaptées aux spécificités des Cristaux Phononiques (CP) et des guides d’ondes. Dans un premier temps, nous nous attachons à la description du formalisme mathématique de l’Optimisation Topologique et de la Full Waveform Inversion (FWI). Bien que ces méthodes ne cherchent pas à résoudre les mêmes problèmes inverses, nous mettons en évidence leurs points communs. Dans un deuxième temps, nous appliquons l’Imagerie Topologique (IT) à l’inspection en réflexion des milieux faiblement hétérogènes. Dans un troisième temps, nous nous inspirons de l’IT pour définir une nouvelle variante de celle-ci nommée Imagerie Topologique Hybride (ITH). Nous appliquons ces méthodes pour l’inspection en réflexion des CP crées par des tiges d’acier immergées dans l’eau. Nous comparons les performances de ces méthodes en fonction du type de défaut dans le CP. Les simulations numériques correspondantes à certains cas d’étude sont appuyées par des essais expérimentaux concluants. Dans un quatrième temps, nous adaptons l’IT à une configuration d’inspection en transmission afin de mette en oeuvre une méthode de Structural Health Monitoring (SHM) des guides d’ondes. A ce propos, nous avons mis au point une nouvelle méthode d’imagerie mieux adaptée que l’IT aux configurations d’inspection en transmission
The detection, localization and monitoring of the evolution of defects in periodic media and waveguides is a major issue in the field of Non-Destructive Testing (NDT). Wave propagation in such media is complex, for example when the velocity depends on the frequency (dispersion) or direction of propagation (anisotropy). The signature of the defect can also be "embedded" in the acoustic field reflected by the structure (reverberation or multiple diffusion). It is to answer these stakes of the size that the Topological Optimization (TO) has been adapted to the problems of diffraction of the acoustic waves by infinitesimal defects in order to obtain reflectivity images of the inspected media. The method can be applied to all kinds of media, regardless of their complexity, provided an exact simulation of the wave propagation in a reference medium (without defects) is performed. Inspired by the TO, the work of this thesis proposes to implement qualitative imaging methods adapted to the specificities of Phononic Crystals (PC) and waveguides. First, we focus on the description of the mathematical formalism of Topological Optimization and Full-Waveform Inversion (FWI). Although these methods do not try to solve the same inverse problems, we highlight their similarities. In a second step, we apply Topological Imaging (TI) to the inspection in pulse-echo configuration of weakly heterogeneous media. Thirdly, we draw inspiration from TI to define a new variant of this method called Hybrid Topological Imaging (HTI).We apply these methods for the pulse-echo configuration inspection of PCs created by steel rods immersed in water.We compare the performance of these methods according to the kind of defects in the PC. Numerical simulations for some case studies are supported by conclusive experimental trials. In a fourth step, we adapt the TI to a pitch-catch configuration in order to implement a new method of Structural Health Monitoring (SHM) of waveguides. In this regard, we have developed a new imaging method that is better suited than TI to pitch-catch configurations

Ce travail de recherche a été principalement motivé par les avantages importants apportés par la technologie UTBB FDSOI aux applications analogiques et RF de faible puissance. L'objectif principal est d'étudier le comportement dynamique du transistor MOSFET du type UTBB FDSOI et de proposer des modèles prédictifs et des recommandations pour la conception de circuits intégrés RF, en mettant un accent particulier sur le régime d'inversion modérée. Après une brève analyse des progrès réalisés au niveau des architectures du transistor MOSFET, un état de l’art de la modélisation du transistor MOSFET UTBB FDSOI est établi. Les principaux effets physiques impliqués dans le transistor à double grille avec une épaisseur du film de 7 nm sont passés en revue, en particulier l’impact de la grille arrière, à l’aide de mesures et de simulations TCAD. La caractéristique gm/ID en basse fréquence et la caractéristique ym/ID proposée pour la haute fréquence sont étudiées et utilisées dans une conception analogique efficace. Enfin, le modèle NQS haute fréquence proposé reproduit les mesures dans toutes les conditions de polarisation y compris l’inversion modérée jusqu’à 110 GHz
This research work has been motivated primarily by the significant advantages brought about by the UTBB FDSOI technology to the Low power Analog and RF applications. The main goal is to study the dynamic behavior of the UTBB FDSOI MOSFET in light of the recent technology advances and to propose predictive models and useful recommendations for RF IC design with particular emphasis on Moderate Inversion regime. After a brief review of progress in MOSFET architectures introduced in the semiconductor industry, a state-of-the-art UTBB FDSOI MOSFET modeling status is compiled. The main physical effects involved in the double gate transistor with a 7 nm thick film are reviewed, particularly the back gate impact, using measurements and TCAD. For better insight into the Weak Inversion and Moderate Inversion operations, both the low frequency gm/ID FoM and the proposed high frequency ym/ID FoM are studied and also used in an efficient first-cut analog design. Finally, a high frequency NQS model is developed and compared to DC and S-parameters measurements. The results show excellent agreement across all modes of operation including very low bias conditions and up to 110 GHz

I present a general methodology for inverting seismic data in either the data or image domains. It partially overcomes one of the most serious problems with current waveform inversion methods, which is the tendency to converge to models far from the actual one. The key idea is to develop a multiscale misfit function that is composed of both a simplified version of the data and one associated with the complex part of the data. Misfit functions based on simple data are characterized by many fewer local minima so that a gradient optimization method can make quick progress in getting to the general vicinity of the actual model. Once we are near the actual model, we then use the gradient based on the more complex data. Below, we describe two implementations of this multiscale strategy: wave equation traveltime inversion in the data domain and generalized differential semblance optimization in the image domain. • Wave Equation Traveltime Inversion in the Data Domain (WT): The main difficulty with iterative waveform inversion is that it tends to get stuck in local minima associated with the waveform misfit function. To mitigate this problem and avoid the need to fit amplitudes in the data, we present a waveequation method that inverts the traveltimes of reflection events, and so is less prone to the local minima problem. Instead of a waveform misfit function, the penalty function is a crosscorrelation of the downgoing direct wave and the upgoing reflection wave at the trial image point. The time lag which maximizes the crosscorrelation amplitude represents the reflection-traveltime residual that is back-projected along the reflection wavepath to update the velocity. Shot- and angle-domain crosscorrelation functions are introduced to estimate the reflection-traveltime residual by semblance analysis and scanning. In theory, only the traveltime information is inverted and there is no need to precisely fit the amplitudes or assume a high-frequency approximation. Results with both synthetic data and field records reveal both the benefits and limitations of WT. • Generalized Differental Semblance Optimization in the Image Domain (GDSO): We now extend the multiscale physics approach to differential semblance optimization (DSO) in the image domain. That is, we identify the space-lag offset H(x, z, h) in the subsurface-offset domain as an implicit function of velocity. It describes the smoothly varying moveout H(x, z, h) of the migration image m(x, z, h) in the subsurface-offset domain, which is analogous to the smoothly varying traveltime residual ∆τ(x) of a reflection event in a shot gather. The velocity model is found that minimizes the objective function ∑x,z,h H(x, z, h)2m(x, z, h)2, where coherent noise is eliminated everywhere except along the picked curve H(x, z, h). This method is denoted as generalized DSO (GDSO) and mitigates the coherent noise problem with DSO. Numerical examples are presented that empirically demonstrate its effectiveness in providing more accurate velocity models compared to conventional DSO.

This thesis concerns the study of time reversal and plane-wave decomposition in various geophysical applications. Time reversal is a key step in seismic interferometry, reverse time migration and full waveform inversion. The plane-wave transform, also known as the tau-p transform or slant-stack, can separate waves based on their ray parameters or their emergence angles at the surface. I propose a new approach to retrieve virtual full-wave seismic responses from crosscorrelating recorded seismic data in the plane-wave domain. Unlike a traditional approach where the correlogram is obtained from crosscorrelating recorded data, which contains the full range of ray parameters, this method directly chooses common ray parameters to cancel overlapping ray paths. Thus, it can sometime avoid spurious arrivals when the acquisition requirement of seismic interferometry is not strictly met. I demonstrate the method with synthetic examples and an ocean bottom seismometer data example. I show a multi-scale application of plane-wave based full waveform inversion (FWI) with the aid of frequency domain forward modeling. FWI uses the two-way wave-equation to produce high-resolution velocity models for seismic imaging. This technique is implemented by an adjoint-state approach, which viii involves a time-reversal propagation of the residual wavefield at receivers, similar to seismic interferometry. With a plane-wave transformed gather, we can decompose the data by ray parameters and iteratively update the velocity model with selected ray parameters. This encoding approach can significantly reduce the number of shots and receivers required in gradient and Hessian calculations. Borrowing the idea of minimizing different data residual norms in FWI, I study the effect of different scaling methods to the receiver wavefield in the reverse time migration. I show that this type of scaling is able to significantly suppress outliers compared to conventional algorithms. I also show that scaling by its absolute norm generally produces better results than other approaches. I propose a robust stochastic time-lapse seismic inversion strategy with an application of monitoring Cranfield CO2 injection site. This workflow involves two steps. The first step is the baseline inversion using a hybrid starting model that combines a fractal prior and the low-frequency prior from well log data. The second step is to use a double-difference inversion scheme to focus on the local areas where time-lapse changes have occurred. Synthetic data and field data show the effectiveness of this method.
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We are concerned with the high-fidelity subsurface imaging of the soil, which commonly arises in geotechnical site characterization and geophysical explorations. Specifically, we attempt to image the spatial distribution of the Lame parameters in semi-infinite, three-dimensional, arbitrarily heterogeneous formations, using surficial measurements of the soil's response to probing elastic waves. We use the complete waveforms of the medium's response to drive the inverse problem. Specifically, we use a partial-differential-equation (PDE)-constrained optimization approach, directly in the time-domain, to minimize the misfit between the observed response of the medium at select measurement locations, and a computed response corresponding to a trial distribution of the Lame parameters. We discuss strategies that lend algorithmic robustness to the proposed inversion schemes. To limit the computational domain to the size of interest, we employ perfectly-matched-layers (PMLs). The PML is a buffer zone that surrounds the domain of interest, and enforces the decay of outgoing waves. In order to resolve the forward problem, we present a hybrid finite element approach, where a displacement-stress formulation for the PML is coupled to a standard displacement-only formulation for the interior domain, thus leading to a computationally cost-efficient scheme. We discuss several time-integration schemes, including an explicit Runge-Kutta scheme, which is well-suited for large-scale problems on parallel computers. We report numerical results demonstrating stability and efficacy of the forward wave solver, and also provide examples attesting to the successful reconstruction of the two Lame parameters for both smooth and sharp profiles, using synthetic records. We also report the details of two field experiments, whose records we subsequently used to drive the developed inversion algorithms in order to characterize the sites where the field experiments took place. We contrast the full-waveform-based inverted site profile against a profile obtained using the Spectral-Analysis-of-Surface-Waves (SASW) method, in an attempt to compare our methodology against a widely used concurrent inversion approach. We also compare the inverted profiles, at select locations, with the results of independently performed, invasive, Cone Penetrometer Tests (CPTs). Overall, whether exercised by synthetic or by physical data, the full-waveform inversion method we discuss herein appears quite promising for the robust subsurface imaging of near-surface deposits in support of geotechnical site characterization investigations.

We discuss a full-waveform based material profile reconstruction in two-dimensional heterogeneous semi-infinite domains. In particular, we try to image the spatial variation of shear moduli/wave velocities, directly in the time-domain, from scant surficial measurements of the domain's response to prescribed dynamic excitation. In addition, in one-dimensional media, we try to image the spatial variability of elastic and attenuation properties simultaneously. To deal with the semi-infinite extent of the physical domains, we introduce truncation boundaries, and adopt perfectly-matched-layers (PMLs) as the boundary wave absorbers. Within this framework we develop a new mixed displacement-stress (or stress memory) finite element formulation based on unsplit-field PMLs for transient scalar wave simulations in heterogeneous semi-infinite domains. We use, as is typically done, complex-coordinate stretching transformations in the frequency-domain, and recover the governing PDEs in the time-domain through the inverse Fourier transform. Upon spatial discretization, the resulting equations lead to a mixed semi-discrete form, where both displacements and stresses (or stress histories/memories) are treated as independent unknowns. We propose approximant pairs, which numerically, are shown to be stable. The resulting mixed finite element scheme is relatively simple and straightforward to implement, when compared against split-field PML techniques. It also bypasses the need for complicated time integration schemes that arise when recent displacement-based formulations are used. We report numerical results for 1D and 2D scalar wave propagation in semi-infinite domains truncated by PMLs. We also conduct parametric studies and report on the effect the various PML parameter choices have on the simulation error. To tackle the inversion, we adopt a PDE-constrained optimization approach, that formally leads to a classic KKT (Karush-Kuhn-Tucker) system comprising an initial-value state, a final-value adjoint, and a time-invariant control problem. We iteratively update the velocity profile by solving the KKT system via a reduced space approach. To narrow the feasibility space and alleviate the inherent solution multiplicity of the inverse problem, Tikhonov and Total Variation (TV) regularization schemes are used, endowed with a regularization factor continuation algorithm. We use a source frequency continuation scheme to make successive iterates remain within the basin of attraction of the global minimum. We also limit the total observation time to optimally account for the domain's heterogeneity during inversion iterations. We report on both one- and two-dimensional examples, including the Marmousi benchmark problem, that lead efficiently to the reconstruction of heterogeneous profiles involving both horizontal and inclined layers, as well as of inclusions within layered systems.
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We introduce a mathematical framework for the inverse medium problem arising commonly in geotechnical site characterization and geophysical probing applications, when stress waves are used to probe the material composition of the interrogated medium. Specifically, we attempt to recover the spatial distribution of Lame's parameters ( and μ) of an elastic semi-infinite arbitrarily heterogeneous medium, using surface measurements of the medium's response to prescribed dynamic excitations. The focus is on characterizing near-surface deposits, and to this end, we develop a method that is implemented directly in the time-domain, is driven by the full waveform response collected at receivers on the surface, while the domain of interest is truncated using Perfectly-Matched-Layers (PMLs) to limit the originally semi-infinite extent of the physical domain. There are two key issues associated with the problem at hand: (a) the forward problem, namely the numerical simulation of the wave motion in the domain of interest; and (b) the framework and strategies for tackling the inverse problem. To address the forward problem, it is necessary that the domain of interest be truncated, and the resulting finite domain be forced to mimic the physics of the original problem: to this end, we introduce unsplit-field PMLs, and develop and implement two new formulations, one fully-mixed and one hybrid (mixed coupled with a non-mixed approach) that model wave motion within the, now PML-truncated, domain. To address the inverse problem, we adopt a partial-differential-equation-constrained optimization framework that results in the usual triplet of an initial-and-boundary-value forward problem, a final-and-boundary-value adjoint problem, and a time-independent boundary-value control problem. This triplet of boundary-value-problems is used to guide the optimizer to the target profile of the spatially distributed Lame parameters. Given the multiplicity of solutions, we assist the optimizer, by deploying regularization schemes, continuation schemes (regularization factor and source-frequency content), as well as a physics-driven simple procedure to bias the search directions. We report numerical examples attesting to the quality, stability, and efficiency of the forward wave modeling. We also report moderate success with numerical experiments targeting inversion of both smooth and sharp profiles in two dimensions.
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The primary focus of this thesis is to examine the detailed seismic structure of the northern Cascadia margin, including the Cascadia basin, the deformation front and the continental shelf. The results of this study are contributing towards understanding sediment deformation and tectonics on this margin. They also have important implications for exploration of hydrocarbons (oil and gas) and natural hazards (submarine landslides, earthquakes, tsunamis, and climate change). The first part of this thesis focuses on the role of gas hydrate in slope failure observed from multibeam bathymetry data on a frontal ridge near the deformation front off Vancouver Island margin using active-source ocean bottom seismometer (OBS) data collected in 2010. Volume estimates (∼ 0.33 km^3) of the slides observed on this margin indicate that these are capable of generating large (∼ 1 − 2 m) tsunamis. Velocity models from travel time inversion of wide angle reflections and refractions recorded on OBSs and vertical incidence single channel seismic (SCS) data were used to estimate gas hydrate concentrations using effective medium modeling. Results indicate a shallow high velocity hydrate layer with a velocity of 2.0 − 2.1 km/s that corresponds to a hydrate concentration of 40% at a depth of 100 m, and a bottom simulating reflector (BSR) at a depth of 265 − 275 m beneath the seafloor (mbsf). These are comparable to drilling results on an adjacent frontal ridge. Margin perpendicular normal faults that extend down to BSR depth were also observed on SCS and bathymetric data, two of which coincide with the sidewalls of the slump indicating that the lateral extent of the slump is controlled by these faults. Analysis of bathymetric data indicates, for the first time, that the glide plane occurs at the same depth as the shallow high velocity layer (100±10 mbsf). In contrast, the glide plane coincides with the depth of the BSR on an adjacent frontal ridge. In either case, our results suggest that the contrast in sediments strengthened by hydrates and overlying or underlying sediments where there is no hydrate is what causing the slope failure on this margin. The second part of this dissertation focuses on obtaining the detailed structure of the Cascadia basin and frontal ridge region using mirror imaging of few widely spaced OBS data. Using only a small airgun source (120 cu. in.), our results indicate structures that were previously not observed on the northern Cascadia margin. Specifically, OBS migration results show dual-vergence structure, which could be related to horizontal compression associated with subduction and low basal shear stress resulting from over-pressure. Understanding the physical and mechanical properties of the basal layer has important implications for understanding earthquakes on this margin. The OBS migrated image also clearly shows the continuity of reflectors which enabled the identification of thrust faults, and also shows the top of the igneous oceanic crust at 5−6 km beneath the seafloor, which were not possible to identify in single-channel and low-fold multi-channel seismic (MCS) data. The last part of this thesis focuses on obtaining detailed seismic structure of the Vancouver Island continental shelf from MCS data using frequency domain viscoacoustic full waveform inversion, which is first of its kind on this margin. Anelastic velocity and attenuation models, derived in this study to subseafloor depths of ∼ 2 km, are useful in understanding the deformation within the Tofino basin sediments, the nature of basement structures and their relationship with underlying accreted terranes such as the Crescent and the Pacific Rim terranes. Specifically, our results indicate a low-velocity zone (LVZ) with a contrast of 200 m/s within the Tofino basin sediment section at a depth 600 − 1000 mbsf over a lateral distance of 10 km. This LVZ is associated with high attenuation values (0.015 − 0.02) and could be a result of over pressured sediments or lithology changes associated with a high porosity layer in this potential hydrocarbon environment. Shallow high velocities of 4 − 5 km/s are observed in the mid-shelf region at depths > 1.5 km, which is interpreted as the shallowest occurrence of the Eocene volcanic Crescent terrane. The sediment velocities sharply increase about 10 km west of Vancouver Island, which probably corresponds to the underlying transition to the Mesozoic marine sedimentary Pacific Rim terrane. High attenuation values of 0.03 − 0.06 are observed at depths > 1 km, which probably corresponds to increased clay content and the presence of mineralized fluids.
Graduate
0373
0372
0605
subbarao@uvic.ca