Seismic transitions of the subsurface are typically considered as zero-order singularities (step functions). According to this model, the conventional deconvolution problem aims at recovering the seismic reflectivity as a sparse spike train. However, recent multiscale analysis on sedimentary records revealed the existence of accumulations of varying order singularities in the subsurface, which give rise to fractional-order discontinuities. This observation not only calls for a richer class of seismic reflection waveforms, but it also requires a different methodology to detect and characterize these reflection events. For instance, the assumptions underlying conventional deconvolution no longer hold. Because of the bandwidth limitation of seismic data, multiscale analysis methods based on the decay rate of wavelet coefficients may yield ambiguous results. We avoid this problem by formulating the estimation of the singularity orders by a parametric nonlinear inversion method.

Magnetic Resonance Elastography (MRE) is an emerging medical imaging modality that allows quantification of the mechanical properties of biological tissues in vivo. MRE typically involves time-harmonic tissue excitation followed by the displacement measurements within the tissue obtained by phase-contrast Magnetic Resonance Imaging (MRI) techniques. MRE is believed to have great potential in the detection of wide variety of pathologies, diseases and cancer formations, especially tumors. This thesis concentrates on a thorough assessment and full rheological evaluation of the Rayleigh damping (RD) material model applied to MRE. The feasibility of the RD model to accurately reconstruct viscoelastic and damping properties was assessed. The goal is to obtain accurate quantitative estimates of the mechanical properties for the in vivo healthy brain via the subzone optimization based nonlinear image reconstruction algorithm. The RD model allows reconstruction of not only stiffness distribution of the tissue, but also energy attenuation mechanisms proportionally related to both elastic and inertial effects. The latter allows calculation of the concomitant damping properties of the material. The initial hypothesis behind this research is that accurate reconstruction of the Rayleigh damping parameters may bring additional diagnostic potential with regards to differentiation of various tissue types and more accurate characterisation of certain pathological diseases based on different energy absorbing mechanisms. Therefore, the RD model offers reconstruction of three additional material properties that might be of clinical diagnostic merit and can enhance characterisation of cancer tumors within the brain. A pneumatic-based actuator was specifically developed for in vivo human brain MRE experiments. Performance of the actuator was investigated and the results showed that the actuator produces average displacement in the range of 300 µmicrons and is well suited for generation of shear waves if applied to the human head. Unique features of the the actuator are patient comfort and safety, MRI compatibility, flexible design and good displacement characteristics. In this research, a 3D finite element (FE) subzone-based non-linear reconstruction algorithm using the RD material model has been applied and rigorously assessed to investigate the performance of elastographic based reconstruction to accurately recover mechanical properties and a concomitant damping behaviour of the material. A number of experiments were performed on a variety of homogenous and heterogeneous tissue-simulating damping phantoms comprising a set of materials that mimic range of mechanical properties expected in the brain. The result showed consistent effect of a poor reconstruction accuracy of the RD parameters which suggested the nonidentifiable nature of the RD model. A structural model identifiability analysis further supported the nonidentifiabilty of the RD parameters at a single frequency. Therefore, two approaches were developed to overcome the fundamental identifiability issue. The first one involved application of multiple frequencies over a broad range. The second one was based on parametrisation techniques, where one of the damping parameters was globally defined throughout the reconstruction domain allowing reconstruction of the two remaining parameters. Based on the findings of this research, multi-frequency (MF) elastography was performed on the tissue-simulating phantoms to investigate improvement of the elastographic reconstruction accuracy. Dispersion characteristics of the materials as well as RD changes across different frequencies in various materials were also studied. Simultaneous multi-frequency inversion was undertaken where two models were evaluated: a zero-order model and a power-law model. Furthermore, parametric-based RD reconstruction was carried out to evaluate enhancement of accurate identification of the reconstructed parameters. The results showed that parametric-based RD reconstruction, compared to MF-based RD results, allowed better material characterisation on the reconstructed shear modulus image. Also, significant improvement in material differentiation on the remaining damping parameter image was also observed if the fixed damping parameter was adjusted appropriately. In application to in vivo brain imaging, six repetitive MRE examinations of the in vivo healthy brain demonstrated promising ability of the RD MRE to resolve local variations in mechanical properties of different brain tissue types. Preliminary results to date show that reconstructed real shear modulus and overall damping levels correlate well with the brain anatomical features. Quantified shear stiffness estimates for white and gray matter were found to be 3 kPa and 2.1 kPa, respectively. Due to the non-identifiability of the model at a single frequency, reconstructed RD based parameters limit any physical meaning. Therefore, MF-based and parametric-based cerebral RD elastography was also performed.

The objective of this thesis work is to detect and to characterize three-dimensional targets in a disordered medium, using electromagnetic excitations. This research domain is of great interest in many applications, such as subsoil probing, medical imaging, non-destructive testing and geophysical exploration, etc. In order to extract the target information from the heterogeneities of the medium, we propose to use one of the time reversal technique, namely the DORT method (French acronym for Décomposition de l'Opérateur de Retournement Temporel). This method permits us to generate different waves that focus selectively on each target in high noisy environment. Moreover, this method is also combined with a non-linear inversion algorithm, which permits not only to localize but also to characterize the targets. The reconstruction resolution appears to be better than the ones obtained with the DORT or the inversion procedure alone, especially in the illumination direction. It is also shown that using full-polarized data is indispensable for achieving better performances rather than in scalar configuration. Moreover, in the half-space configuration, it is mandatory to use the frequency-diversity data to get an accurate reconstruction. These theoretical developments are also confronted to experimental data measured in the optical domain. A full-polarization Tomographic Diffractive Microscopy (TDM) is implemented and a resolution about one-fourth of the wavelength is thus obtained. Furthermore, the DORT method is applied in TDM to realize selective focalization and characterization. In the presence of multiple targets, selective characterization of each scatterer is achieved.This thesis work also deals with the characterization problem using transient data. Different inversion algorithms are validated using synthetic and experimental hyper-frequency data.

L'objectif de ce travail de thèse est de détecter et de caractériser des cibles tridimensionnelles dans un milieu désordonné. Ce domaine de recherche est d'intérêt pour de nombreuses applications, telles que le sondage du sous-sol, l'imagerie médicale, la détection non-destructive et l'exploration géophysique, etc. Afin de distinguer les cibles des hétérogénéités du milieu, nous proposons d'utiliser l'une des techniques de retournement temporel, à savoir la méthode DORT (Décomposition de l'Opérateur de Retournement Temporel). La méthode DORT permet de générer des ondes focalisant sélectivement sur chaque cible présente dans un environnement fortement hétérogène. Par ailleurs, la richesse de ces ondes focalisantes est combinée avec un algorithme d'inversion non-linéaire. Ceci nous permet non seulement de localiser, mais aussi de caractériser les cibles (forme et permittivité). La résolution obtenue à l'aide de cette approche est bien meilleure que celles obtenues avec la méthode DORT ou la méthode d'inversion seules, en particulier dans la direction d'illumination. Cette résolution est d'autant meilleure que les données utilisées sont vectorielles. Dans le cas spécifique d'une configuration d'objets enfouis impliquant deux semi-espaces infinis, la caractérisation s'avère problématique. Une solution est apportée en appliquant l'approche de marche récurrente en fréquences. Ces développements théoriques sont également confrontés aux données expérimentales mesurées dans le domaine optique. Une nouvelle Microscopie Tomographique par Diffraction (MTD) est mise en œuvre dans le cadre de cette thèse en tenant compte du caractère vectoriel de la lumière. Ce faisant, une résolution d'environ un quart de la longueur d'onde a été obtenue sur des échantillons en résine déposés sur un substrat de silicium. De plus, nous avons aussi appliqué avec succès la méthode DORT à la MTD afin de focaliser et caractériser de manière sélective plusieurs diffuseurs de tailles différentes.Lors de ce travail de thèse nous avons également développé des méthodes de caractérisation en régime transitoire. Les différentes méthodes d'inversion élaborées dans ce cadre ont été validées sur des données synthétiques et expérimentales dans le domaine des radio-fréquences. / The objective of this thesis work is to detect and to characterize three-dimensional targets in a disordered medium, using electromagnetic excitations. This research domain is of great interest in many applications, such as subsoil probing, medical imaging, non-destructive testing and geophysical exploration, etc. In order to extract the target information from the heterogeneities of the medium, we propose to use one of the time reversal technique, namely the DORT method (French acronym for Décomposition de l'Opérateur de Retournement Temporel). This method permits us to generate different waves that focus selectively on each target in high noisy environment. Moreover, this method is also combined with a non-linear inversion algorithm, which permits not only to localize but also to characterize the targets. The reconstruction resolution appears to be better than the ones obtained with the DORT or the inversion procedure alone, especially in the illumination direction. It is also shown that using full-polarized data is indispensable for achieving better performances rather than in scalar configuration. Moreover, in the half-space configuration, it is mandatory to use the frequency-diversity data to get an accurate reconstruction. These theoretical developments are also confronted to experimental data measured in the optical domain. A full-polarization Tomographic Diffractive Microscopy (TDM) is implemented and a resolution about one-fourth of the wavelength is thus obtained. Furthermore, the DORT method is applied in TDM to realize selective focalization and characterization. In the presence of multiple targets, selective characterization of each scatterer is achieved.This thesis work also deals with the characterization problem using transient data. Different inversion algorithms are validated using synthetic and experimental hyper-frequency data.

Neste trabalho avaliou-se a potencialidade do uso da sísmica rasa de reflexão multicomponente para investigação geológica-geotécnica. Foram abordados vários aspectos relacionados à aquisição dos dados sísmicos de reflexão multicomponente, com o objetivo de entender as vantagens e limitações do método para aplicação em investigações de subsuperfície rasa. Os ensaios de campo foram realizados em duas áreas, ambas em terrenos da Bacia Sedimentar de São Paulo, em área urbana da cidade de São Paulo. Para a interpretação dos dados sísmicos multicomponente foram investigados procedimentos para a inversão não-linear dos tempos de trânsito e das amplitudes. O testes realizados orientaram a escolha da aproximação não-hiperbólica mais apropriada para calculo dos tempos de trânsito visando à análise de velocidades do pacote acima do refletor. O estudo numérico desenvolvido para a inversão das amplitudes mostrou a viabilidade da estimativa das velocidades e densidades, acima e abaixo do refletor, empregando-se as equações de Zoeppritz para as ondas refletidas PP, PSv, SvP e SvSv, antes e depois do ângulo crítico. Dada a complexidade da inversão nao-linear das amplitudes, se fez necessário elaborar uma estratégia estocástica de otimização e desenvolver uma nova abordagem para análise da função objetivo multi-dimensional, garantindo confiabilidade ao resultado da inversão não-linear. Os resultados deste trabalho mostraram o potencial da sísmica de reflexão rasa multicomponente para caracterização geológica-geotécnica, possibilitando um melhor entendimento das camadas superficiais. / This thesis aims to evaluate the useful of the multicomponent seismic methods for shallow investigations, mainly its potential for the geotechnical and geological characterization of the nearsurface. Several aspects regarding the acquisition and processing data of multicomponent seismic data are discussed. They were based on data set acquired in the urban area of Sao Paulo city, Brazil. Two different areas were investigated. Both located in sedimentary terrains belonging to the Sao Paulo Sedimentary Basin. We present a non-linear travel time and seismic amplitude inversion scheme to quantitative interpretation of multicomponent seismic data. Several tests were performed to guide the choice of non-hyperbolic equation more suitable for travel time inversion aiming the velocity analysis above the reflector. A numerical experiment developed to solve the nonlinear inversion of seismic amplitudes showed the feasibility to estimate seismic interval velocities and layer densities above and below the reflector using the exact Zoeppritz equations for PP, PSv, SvP e SvSv reflected waves, before and after critical angle. Due to the apparent complexity of the nonlinear seismic amplitude inversion, it was necessary elaborate the strategy for stochastic optimization and develop a new approach to analyze the multi-dimensional objective function, with different implications for the accuracy and efficiency of the non-linear inversion. The study show the benefits of using the multicomponent seismic method for shallow geological-geotechnical characterization, improving the nearsurface understanding, once allows an integrated analyzes of a more complete record of the wave field.

Neste trabalho avaliou-se a potencialidade do uso da sísmica rasa de reflexão multicomponente para investigação geológica-geotécnica. Foram abordados vários aspectos relacionados à aquisição dos dados sísmicos de reflexão multicomponente, com o objetivo de entender as vantagens e limitações do método para aplicação em investigações de subsuperfície rasa. Os ensaios de campo foram realizados em duas áreas, ambas em terrenos da Bacia Sedimentar de São Paulo, em área urbana da cidade de São Paulo. Para a interpretação dos dados sísmicos multicomponente foram investigados procedimentos para a inversão não-linear dos tempos de trânsito e das amplitudes. O testes realizados orientaram a escolha da aproximação não-hiperbólica mais apropriada para calculo dos tempos de trânsito visando à análise de velocidades do pacote acima do refletor. O estudo numérico desenvolvido para a inversão das amplitudes mostrou a viabilidade da estimativa das velocidades e densidades, acima e abaixo do refletor, empregando-se as equações de Zoeppritz para as ondas refletidas PP, PSv, SvP e SvSv, antes e depois do ângulo crítico. Dada a complexidade da inversão nao-linear das amplitudes, se fez necessário elaborar uma estratégia estocástica de otimização e desenvolver uma nova abordagem para análise da função objetivo multi-dimensional, garantindo confiabilidade ao resultado da inversão não-linear. Os resultados deste trabalho mostraram o potencial da sísmica de reflexão rasa multicomponente para caracterização geológica-geotécnica, possibilitando um melhor entendimento das camadas superficiais. / This thesis aims to evaluate the useful of the multicomponent seismic methods for shallow investigations, mainly its potential for the geotechnical and geological characterization of the nearsurface. Several aspects regarding the acquisition and processing data of multicomponent seismic data are discussed. They were based on data set acquired in the urban area of Sao Paulo city, Brazil. Two different areas were investigated. Both located in sedimentary terrains belonging to the Sao Paulo Sedimentary Basin. We present a non-linear travel time and seismic amplitude inversion scheme to quantitative interpretation of multicomponent seismic data. Several tests were performed to guide the choice of non-hyperbolic equation more suitable for travel time inversion aiming the velocity analysis above the reflector. A numerical experiment developed to solve the nonlinear inversion of seismic amplitudes showed the feasibility to estimate seismic interval velocities and layer densities above and below the reflector using the exact Zoeppritz equations for PP, PSv, SvP e SvSv reflected waves, before and after critical angle. Due to the apparent complexity of the nonlinear seismic amplitude inversion, it was necessary elaborate the strategy for stochastic optimization and develop a new approach to analyze the multi-dimensional objective function, with different implications for the accuracy and efficiency of the non-linear inversion. The study show the benefits of using the multicomponent seismic method for shallow geological-geotechnical characterization, improving the nearsurface understanding, once allows an integrated analyzes of a more complete record of the wave field.

Quantifying the influence of pressure on the effective elastic rock properties is important for applications in rock physics and reservoir characterization. Here I investigate the relationship between effective pressure and seismic velocities by performing inversion on the laboratory-measured data from a suite of clastic, carbonate and igneous rocks, using different analytic and discrete inversion schemes. I explore the utility of a physical model that models a natural fracture as supported by asperities of varying heights, when an effective pressure deforms the tallest asperities, bringing the shorter ones into contact while increasing the overall fracture stiffness. Thus, the model is known as the ?asperity-deformation? (ADM) or ?bed-of-nails? (BNM) model. Existing analytic solutions include one that assumes the host rock is infinitely more rigid than the fractures, and one that takes the host-rock compliance into account. Inversion results indicate that although both solutions can fit the data to within first-order approximation, some systematic misfits exist as a result of using the rigid-host solution, whereas compliant-host inversion returns smaller and random misfits, yet out-of-range parameter estimates. These problems indicate the effects of nonlinear elastic deformation whose degree varies from rock to rock. Consequently, I extend the model to allow for the pressure dependence of the host rock, thereby physically interpreting the nonlinear behaviors of deformation. Furthermore, I apply a discrete grid-search inversion scheme that generalizes the distribution of asperity heights, thus accurately reproduces velocity profiles, significantly improves the fit and helps to visualize the distribution of asperities. I compare the analytic and numerical asperity-deformation models with the existing physical model of elliptical ?pennyshape? cracks with a pore-aspect-ratio (PAR) spectrum in terms of physical meaning and data-fitting ability. The comparison results provide a link and demonstrate the consistency between the use of the two physical models, making a better understanding of the microstructure as well as the contact mechanism and physical behaviors of rocks under pressure. ADM-based solutions, therefore, have the potential to facilitate modeling and interpretation of applications such as time-lapse seismic investigations of fractured reservoirs.