Thesis advisor: John E. Ebel / Determination of the source parameters of a local earthquake from full seismic waveforms requires seismograms with clear body-wave signals from the earthquake source. Coherence of the earthquake body-wave seismograms recorded at two different receivers can be used to estimate the signal-to-noise ratio (SNR) of the body-wave energy radiated by the source. In this study, the coherence of earthquake body waves recorded in the Northeastern United States and Southeastern Canada (NEUSSEC) is measured as a function of frequency, interstation distance, and ambient SNR, and then used as an estimate of body-wave SNR. Seismograms from the CN, IU, LD, N4, NE, TA, and US arrays were used to measure coherence between stations with a mean separation of 70 km. Seismograms from the Acton Littleton Seismic Array (ALSA) were used to measure coherence at 5 km mean station separation. Coherence is measured at frequencies between 0.05-10 Hz for Pn and Sn phases from NEUSSEC earthquakes with magnitudes (M) between 0.0 and 4.7 at epicentral distances between 180-1800 km as well as at frequencies between 0.05-10 Hz for the first arrivals of P and S waves from earthquakes M>6 at distances >2500 km. The teleseismic P waves display values of coherence greater than 0.9 out to interstation distances of 1500 km at frequencies <0.8 Hz, but as frequency increases, the interstation distance at which coherence falls below 0.9 decreases. Teleseismic S and regional Pn and Sn waves display coherence values around 0.5, suggesting the amplitudes of the body-waves are smaller than those of the noise, which likely is the result of converted and reflected or refracted P waves and/or smaller signal amplitudes. These coherence values are compared to the coherence values of ambient noise. For any two P, S, Pn or Sn waveforms recorded in the NEUSSEC at 3-5 Hz there is a 50% or greater chance of those two waveforms containing coherent energy that is not ambient noise; these frequencies are where this percent chance is greatest for all seismic phases. At frequencies between 3-5 Hz the effects of scattering are most pronounced on the coherence values of regional seismic phases, suggesting that most scattering in the crust of the NEUSSEC takes place at these frequencies. Teleseismic seismic phases do not include as much scattered energy as the regional seismic phases at 3-5 Hz, and must therefore encounter fewer scattering heterogeneities along their travel path than the regional seismic phases. / Thesis (MS) — Boston College, 2021. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Earth and Environmental Sciences.

Esta tese apresenta uma nova aproximação variacional baseada no Método da Coordenada Geradora e na Teoria do Funcional da Densidade. Nesta nova aproximação, a função de onda de muitos corpos é representada como uma superposição de determinantes de Slater Kohn-Sham não-ortogonais calculados a partir de Hamiltonianos diferentes que carregam uma coordenada geradora atuando como parâmetro de deformação. A discretização integral sobre o conjunto de coordenadas geradoras fornece a energia total variacional do sistema e a contribuição de cada determinante na combinação da respectiva função de onda de muitos corpos. A flexibilidade desta nova metodologia permitiu aplicá-la no estudo das energias totais do estado fundamental e excitado dos átomos da série isoeletrônica do Hélio, utilizando diferentes conjuntos de coordenadas geradoras, diferentes aproximações para o potencial de troca e correlação e diferentes maneiras de implementar a coordenada geradora dentro do Hamiltoniano Kohn-Sham. Em seguida, as bases desta nova metodologia foram estendidas para o caso dependente do tempo, permitindo estudar, por exemplo, processos não-lineares como excitações duplas, conhecidas por sua forte dependência dos efeitos de memória. A nova metodologia foi aplicada no estudo das oscilações paramétricas de um sistema de dois elétron sob um potencial harmônico, o átomo de Hooke. Os resultados demonstram que a escolha adequada das coordenadas geradoras reproduz com precisão os efeitos lineares e não-lineares dos elétrons do sistema que não podem ser descritos pela Teoria do Funcional da Densidade Dependente do Tempo utilizando a aproximação adiabática. Assim, a nova metodologia mostra-se: flexível, pois permite calcular propriedades do estado fundamental e excitado, estáticas e dinâmicas dos sistemas eletrônicos fornecendo ainda uma aproximação variacional para as respectivas funções de onda de muitos corpos em todos os casos; e também viável, pois fornece resultados promissores no caso independente do tempo constituindo uma ferramenta simples e computacionalmente barata de incluir os efeitos de memória em qualquer aproximação adiabática no caso dependente do tempo. / A new variational approach based on the Generator Coordinate Method and Density- Functional Theory is presented. It represents the interacting many-body wave function as a superposition of non-orthogonal Kohn-Sham Slater determinants arising from different Hamiltonians featuring a generator coordinate acting as a deformation parameter. An integral discretization procedure over the set of generator coordinates provides the variational total energy of the system and the weight of each determinant in the approximation of the respective interacting many-body wave functions. The method was used to calculate the ground and excited state total energies of the Helium isoelectronic serie of atoms using different sets of generator coordinates, different approximations to the exchange-correlation potential and different implementations of the generator coordinate whithin the Kohn-Sham Hamiltonian. Next, the time dependent extension of the method is presented allowing its application, for example, on the study of nonlinear processess as double excitations which are known to be strongly dependent of the memory effects. As an illustration, the method is sucessfully applied to driven parametric oscillations of a two interacting electrons in a harmonic potential, the Hooke\'s atom. It is demonstrated that a proper choice of time-dependent generator coordinates in conjunction with the adiabatic local-density approximation reproduces the exact linear and nonlinear twoelectron dynamics quite accurately, including features associated with double excitations that cannot be captured by Time-Dependent Density-Functional Theory in the adiabatic approximation. Therefore, the method is considered, flexible since it allows to calculate ground and excited-states, static and dynamic properties of the electronic systems yeilding a variational approach to the interacting many-body wave functions for all cases, and feasible, since it improves the results for ground and excited-states total energies in the time-independente case, besides to be a conceptually and computationally simple tool to build memory effects into any existing adiabatic exchange-correlation potential in the time-dependent case.

Cette thèse s’intéresse à divers aspects de l’atténuation sismique dans le manteau terrestre et aux implications de celle-ci quant à la structure de ce dernier. L’enjeu est de mieux comprendre les mécanismes d’atténuation ainsi que les mesures que l’on peut effectuer afin d’améliorer les modèles radiaux d’atténuation dont on dispose et in fine l’interprétation des modèles de tomographie. Je me suis concentrée sur deux exemples de mécanismes d’atténuation, appartenant à deux grands types d’atténuation : l’atténuation intrinsèque, liée à l’absorption par le milieu d’une partie de l’énergie sismique dissipée irréversiblement sous forme de chaleur, et l’atténuation extrinsèque, liée à la dispersion de cette énergie par le milieu. Dans le premier cas, j'ai regardé l’effet des transitions de phase sur l’atténuation des ondes sismiques. En appliquant un modèle thermomécanique développé par Ricard et al., 2009, pour prédire l’atténuation des ondes sismiques liée à la transition de phase uniquement et en comparant les valeurs obtenues aux mesures dont on dispose, j'ai pu contraindre la cinétique d’une transition de phase mantellique. Dans le second cas, j'ai testé l’effet de l’anisotropie comme mécanisme d'atténuation apparente, le but étant de trouver une distribution statistique d’orientation d’anisotropie pouvant reproduire la quasi-constance du facteur de qualité Q avec la fréquence, observée en sismologie et lors d’expériences de laboratoire (Knopoff, 1964), et aujourd’hui expliquée par un modèle ad-hoc seulement (Liu, 1976).Enfin, je me intéressée à mesurer cette atténuation sismique sur des enregistrements réels. Après avoir testé la méthode dite de la fréquence instantanée (Ford et al., 2012), je me suis concentrée sur deux régions, l’Amérique centrale et l’Alaska pour l'appliquer. Ces mesures sont ensuite interprétées en termes de modèle radial d’atténuation révélant un manteau inférieur hétérogène atténuant. Je montre aussi qu’une origine compositionnelle est la plus probable pour expliquer ces anomalies d’atténuation. / This thesis is devoted to various aspects of seismic attenuation in the Earth's mantle and the consequences on the mantle structure. The challenge is to better understand the attenuation mechanisms, as well as the measurements that can be done, in order to improve the published radial profiles of attenuation and in fine the interpretation of tomographic models.I focus on two examples of attenuation mechanisms, belonging to two kinds of attenuation: the intrinsic attenuation related to the absorption by the medium of a part of the seismic energy then irreversibly dissipated as heat, and the extrinsic attenuation related to the dispersion of the seismic energy by the medium. In the first case, I investigate the effect of phase transitions upon seismic attenuation. Applying the thermo-mechanical model developped by Ricard et al., 2012, to calculate the attenuation of seismic waves due to the phase transition only and comparing the obtained values to published measurements, I succeed in constraining the kinetics of a mantle phase transition. In the second case, I test the seismic anisotropy as a mechanism of extrinsic attenuation, the aim being to find a statistical distribution of anisotropy orientation and layer thicknesses that can reproduce the observed quasi-frequency independence of Q in seismology and laboratory experiments (Knopoff, 1964), and which is, today, only explained by an ad-hoc model (Liu, 1976).Finally, I was interested in measuring the seismic attenuation on real seismograms. After having tested the method of the instantaneous frequency (Ford et al., 2012), I applied it to seismic records sampling the mantle below Central America and Alaska. These measurements are then inverted for a radial profile of shear attenuation which reveals the existence of an attenuating zone in the lower mantle. I also show that these attenuation anomalies are likely to be of chemical origin.

Esta tese apresenta uma nova aproximação variacional baseada no Método da Coordenada Geradora e na Teoria do Funcional da Densidade. Nesta nova aproximação, a função de onda de muitos corpos é representada como uma superposição de determinantes de Slater Kohn-Sham não-ortogonais calculados a partir de Hamiltonianos diferentes que carregam uma coordenada geradora atuando como parâmetro de deformação. A discretização integral sobre o conjunto de coordenadas geradoras fornece a energia total variacional do sistema e a contribuição de cada determinante na combinação da respectiva função de onda de muitos corpos. A flexibilidade desta nova metodologia permitiu aplicá-la no estudo das energias totais do estado fundamental e excitado dos átomos da série isoeletrônica do Hélio, utilizando diferentes conjuntos de coordenadas geradoras, diferentes aproximações para o potencial de troca e correlação e diferentes maneiras de implementar a coordenada geradora dentro do Hamiltoniano Kohn-Sham. Em seguida, as bases desta nova metodologia foram estendidas para o caso dependente do tempo, permitindo estudar, por exemplo, processos não-lineares como excitações duplas, conhecidas por sua forte dependência dos efeitos de memória. A nova metodologia foi aplicada no estudo das oscilações paramétricas de um sistema de dois elétron sob um potencial harmônico, o átomo de Hooke. Os resultados demonstram que a escolha adequada das coordenadas geradoras reproduz com precisão os efeitos lineares e não-lineares dos elétrons do sistema que não podem ser descritos pela Teoria do Funcional da Densidade Dependente do Tempo utilizando a aproximação adiabática. Assim, a nova metodologia mostra-se: flexível, pois permite calcular propriedades do estado fundamental e excitado, estáticas e dinâmicas dos sistemas eletrônicos fornecendo ainda uma aproximação variacional para as respectivas funções de onda de muitos corpos em todos os casos; e também viável, pois fornece resultados promissores no caso independente do tempo constituindo uma ferramenta simples e computacionalmente barata de incluir os efeitos de memória em qualquer aproximação adiabática no caso dependente do tempo. / A new variational approach based on the Generator Coordinate Method and Density- Functional Theory is presented. It represents the interacting many-body wave function as a superposition of non-orthogonal Kohn-Sham Slater determinants arising from different Hamiltonians featuring a generator coordinate acting as a deformation parameter. An integral discretization procedure over the set of generator coordinates provides the variational total energy of the system and the weight of each determinant in the approximation of the respective interacting many-body wave functions. The method was used to calculate the ground and excited state total energies of the Helium isoelectronic serie of atoms using different sets of generator coordinates, different approximations to the exchange-correlation potential and different implementations of the generator coordinate whithin the Kohn-Sham Hamiltonian. Next, the time dependent extension of the method is presented allowing its application, for example, on the study of nonlinear processess as double excitations which are known to be strongly dependent of the memory effects. As an illustration, the method is sucessfully applied to driven parametric oscillations of a two interacting electrons in a harmonic potential, the Hooke\'s atom. It is demonstrated that a proper choice of time-dependent generator coordinates in conjunction with the adiabatic local-density approximation reproduces the exact linear and nonlinear twoelectron dynamics quite accurately, including features associated with double excitations that cannot be captured by Time-Dependent Density-Functional Theory in the adiabatic approximation. Therefore, the method is considered, flexible since it allows to calculate ground and excited-states, static and dynamic properties of the electronic systems yeilding a variational approach to the interacting many-body wave functions for all cases, and feasible, since it improves the results for ground and excited-states total energies in the time-independente case, besides to be a conceptually and computationally simple tool to build memory effects into any existing adiabatic exchange-correlation potential in the time-dependent case.

Ce travail vise à améliorer la compréhension des signaux sismiques dérivés des fonctions de corrélation inter-récepteur du bruit sismique, ce qui est critique pour une imagerie fiable de la Terre profonde basée sur le bruit. La thèse comprend sept chapitres. Le chapitre 1 introduit les connaissances de base sur le bruit sismique, de la terminologie à ses origines diverses. Le chapitre 2 fournit une vue d'ensemble de la littérature sur l'historique et le développement de la méthode récente de corrélation de bruit, et passe en revue diverses techniques pour le prétraitement des données de bruit sismique et le post-traitement des fonctions de corrélation de bruit. Des méthodes de traitement du bruit basées sur les statistiques et un schéma modifié pour calculer la fonction de corrélation sont développés dans ce chapitre. Le chapitre 3 propose plusieurs techniques basées sur la transformée de Radon pour mesurer les lenteurs des champs d'ondes corrélés et analyser en termes de phases sismiques les signaux dérivés du bruit. Le chapitre 4 montre que les ondes de volume sondant la Terre profonde peuvent être extraites des corrélations de bruit à des distances télésismiques, avec des enregistrements de bruit provenant de deux réseaux sismiques régionaux. Le chapitre 5 applique les techniques proposées au chapitre 3 aux corrélations de bruit entre deux réseaux calculées au chapitre 4, et permet de comprendre l’origine de la phase précoce non-physique observée dans les données. Le chapitre 6 discute des conditions dans lesquelles apparaissent des phases sans correspondance dans la réponse physique de la Terre qui peuvent fausser les analyses des structures profondes basées sur le bruit.. Le dernier chapitre fournit un résumé sur les contributions de cette thèse et une perspective de plusieurs travaux soit en cours soit envisagés pour le futur. / This work aims toward an improved understanding of the seismic signals derived from the inter-receiver correlation functions of seismic noise, which is valuable and critical for a reliable noise-based deep Earth imaging. The thesis consists of seven chapters. Chapter 1 introduces background knowledge on seismic noise, from its classifications to various origins. Chapter 2 provides a literature overview on the history and development of the emerging noise correlation method, and reviews various techniques for the pre-processing of seismic noise data and post-processing of noise correlation functions. Statistics-based noise processing methods and a modified scheme for computing correlation function are developed in this chapter. Chapter 3 proposes several Radon-based techniques to analyze the slownesses of correlated wavefields and to unveil the origin of noise-derived seismic signals. Chapter 4 shows that body waves penetrating into deep Earth can be extracted from noise correlations at teleseismic distances, with noise records from two regional seismic networks. Chapter 5 applies the techniques proposed in chapter 3 to the double-array nose correlations computed in chapter 4, and accordingly reveals the origin of an early spurious phase observed in chapter 4. Chapter 6 discusses several situations that bring ambiguities into the noise-derived seismic signals and can potentially bias the noise-based imaging of subsurface structure. The last chapter provides a summarization over the contributions of this thesis and an outlook of several ongoing and prospected works.