<p>In the realm of tunable optical devices, 3D nanostructures with metals and dielectrics have been utilized in a wide variety of practical applications ranging from optical switching to beam-steering devices. 2D materials, on the other hand, have enabled the exploration of truly new physics unattainable with 3D systems due to quantum confinement leading to unique optical properties and enhanced light-matter interactions. Transdimensional materials (TDMs) – atomically thin films of metals – can couple the robustness of 3D nanostructures with the new physics enabled by 2D features. However, the evolution of the optical properties in the transdimensional regime between 3D and 2D is still underexplored. The optical properties of metallic TDMs are expected to show unprecedented tailorability, including strong dependences on the film thickness, composition, strain, and surface termination. They also have an increased sensitivity to external optical and electrical perturbations, owing to their extraordinary light-confinement. Additionally, the small atomic thicknesses may lead to strongly confined surface plasmons and quantum and nonlocal phenomena. The strong tunability and light-confinement offered by TDMs have resulted in a search for atomically thin plasmonic material platforms that facilitate active metasurfaces with novel functionalities in the visible and near infrared (NIR) range. In this research, we explore the plasmonic properties and tailorability of atomically thin titanium nitride (TiN). We experimentally and theoretically study the thickness-dependent optical properties of epitaxial TiN films with thicknesses down to 1 nm to demonstrate confinement induced optical properties. Overall, this research demonstrates the potential of TDMs for unlocking novel optical phenomena at visible and NIR wavelengths and realizing a new generation of atomically thin tunable nanophotonic devices. </p>

Seismic records contain information that allows geoscientists to make inferences about the structure and properties of the Earth’s interior. Traditionally, seismic imaging and tomography methods require wavefields to be generated and recorded by identifiable sources and receivers, and use these directly-recorded signals to create models of the Earth’s subsurface. However, in recent years the method of seismic interferometry has revolutionised earthquake seismology by allowing unrecorded signals between pairs of receivers, pairs of sources, and source-receiver pairs to be constructed as Green’s functions using either cross-correlation, convolution or deconvolution of wavefields. In all of these formulations, seismic energy is recorded and emitted by surrounding boundaries of receivers and sources, which need not be active and impulsive but may even constitute continuous, naturally-occurring seismic ambient noise. In the first part of this thesis, I provide a comprehensive overview of seismic interferometry, its background theory, and examples of its application. I then test the theory and evaluate the effects of approximations that are commonly made when the interferometric formulae are applied to real datasets. Since errors resulting from some approximations can be subtle, these tests must be performed using almost error-free synthetic data produced with an exact waveform modelling method. To make such tests challenging the method and associated code must be applicable to multiply-scattering media. I developed such a modelling code specifically for interferometric tests and applications. Since virtually no errors are introduced into the results from modelling, any difference between the true and interferometric waveforms can safely be attributed to specific origins in interferometric theory. I show that this is not possible when using other, previously available methods: for example, the errors introduced into waveforms synthesised by finite-difference methods due to the modelling method itself, are larger than the errors incurred due to some (still significant) interferometric approximations; hence that modelling method can not be used to test these commonly-applied approximations. I then discuss the ability of interferometry to redatum seismic energy in both space and time, allowing virtual seismograms to be constructed at new locations where receivers may not have been present at the time of occurrence of the associated seismic source. I present the first successful application of this method to real datasets at multiple length scales. Although the results are restricted to limited bandwidths, this study demonstrates that the technique is a powerful tool in seismologists’ arsenal, paving the way for a new type of ‘retrospective’ seismology where sensors may be installed at any desired location at any time, and recordings of seismic events occurring at any other time can be constructed retrospectively – even long after their energy has dissipated. Within crustal seismology, a very common application of seismic interferometry is ambient-noise tomography (ANT). ANT is an Earth imaging method which makes use of inter-station Green’s functions constructed from cross-correlation of seismic ambient noise records. It is particularly useful in seismically quiescent areas where traditional tomography methods that rely on local earthquake sources would fail to produce interpretable results due to the lack of available data. Once constructed, interferometric Green’s functions can be analysed using standard waveform analysis techniques, and inverted for subsurface structure using more or less traditional imaging methods. In the second part of this thesis, I discuss the development and implementation of a fully non-linear inversion method which I use to perform Love-wave ANT across the British Isles. Full non-linearity is achieved by allowing both raypaths and model parametrisation to vary freely during inversion in Bayesian, Markov chain Monte Carlo tomography, the first time that this has been attempted. Since the inversion produces not only one, but a large ensemble of models, all of which fit the data to within the noise level, statistical moments of different order such as the mean or average model, or the standard deviation of seismic velocity structures across the ensemble, may be calculated: while the ensemble average map provides a smooth representation of the velocity field, a measure of model uncertainty can be obtained from the standard deviation map. In a number of real-data and synthetic examples, I show that the combination of variable raypaths and model parametrisation is key to the emergence of previously-unobserved, loop-like uncertainty topologies in the standard deviation maps. These uncertainty loops surround low- or high-velocity anomalies. They indicate that, while the velocity of each anomaly may be fairly well reconstructed, its exact location and size tend to remain uncertain; loops parametrise this location uncertainty, and hence constitute a fully non-linearised, Bayesian measure of spatial resolution. The uncertainty in anomaly location is shown to be due mainly to the location of the raypaths that were used to constrain the anomaly also only being known approximately. The emergence of loops is therefore related to the variation in raypaths with velocity structure, and hence to 2nd and higher order wave-physics. Thus, loops can only be observed using non-linear inversion methods such as the one described herein, explaining why these topologies have never been observed previously. I then present the results of fully non-linearised Love-wave group-velocity tomography of the British Isles in different frequency bands. At all of the analysed periods, the group-velocity maps show a good correlation with known geology of the region, and also robustly detect novel features. The shear-velocity structure with depth across the Irish Sea sedimentary basin is then investigated by inverting the Love-wave group-velocity maps, again fully non-linearly using Markov chain Monte Carlo inversion, showing an approximate depth to basement of 5 km. Finally, I discuss the advantages and current limitations of the fully non-linear tomography method implemented in this project, and provide guidelines and suggestions for its improvement.

La tomographie des temps de première arrivée vise à retrouver un modèle de vitesse de propagation des ondes sismiques à partir des temps de première arrivée mesurés. Cette technique nécessite la résolution d’un problème inverse afin d’obtenir un modèle sismique cohérent avec les données observées. Il s'agit d'un problème mal posé pour lequel il n'y a aucune garantie quant à l'unicité de la solution. L’approche bayésienne permet d’estimer la distribution spatiale de la vitesse de propagation des ondes sismiques. Il en résulte une meilleure quantification des incertitudes associées. Cependant l’approche reste relativement coûteuse en temps de calcul, les algorithmes de Monte Carlo par chaînes de Markov (MCMC) classiquement utilisés pour échantillonner la loi a posteriori des paramètres n'étant efficaces que pour un nombre raisonnable de paramètres. Elle demande, de ce fait, une réflexion à la fois sur la paramétrisation du modèle de vitesse afin de réduire la dimension du problème et sur la définition de la loi a priori des paramètres. Le sujet de cette thèse porte essentiellement sur cette problématique.Le premier modèle que nous considérons est basé sur un modèle de mosaïque aléatoire, le modèle de Jonhson-Mehl, dérivé des mosaïques de Voronoï déjà proposées en tomographie bayésienne. Contrairement à la mosaïque de Voronoï, les cellules de Johsnon-mehl ne sont pas forcément convexes et sont bornées par des portions d’hyperboloïdes, offrant ainsi des frontières lisses entre les cellules. Le deuxième modèle est, quant à lui, décrit par une combinaison linéaire de fonctions gaussiennes, centrées sur la réalisation d'un processus ponctuel de Poisson. Pour chaque modèle, nous présentons un exemple de validation sur des champs de vitesse simulés. Nous appliquons ensuite notre méthodologie à un modèle synthétique plus complexe qui sert de benchmark dans l'industrie pétrolière. Nous proposons enfin, un modèle de vitesse basé sur la théorie du compressive sensing pour reconstruire le champ de vitesse. Ce modèle, encore imparfait, ouvre plusieurs pistes de recherches futures.Dans ce travail, nous nous intéressons également à un jeu de données réelles acquises dans le contexte de la fracturation hydraulique. Nous développons dans ce contexte une méthode d'inférence bayésienne trans-dimensionnelle et hiérarchique afin de traiter efficacement la complexité du modèle à couches. / First arrival time tomography aims at inferring the seismic wave propagation velocity using experimental first arrival times. In our study, we rely on a Bayesian approach to estimate the wave velocity and the associated uncertainties. This approach incorporates the information provided by the data and the prior knowledge of the velocity model. Bayesian tomography allows for a better estimation of wave velocity as well asassociated uncertainties. However, this approach remains fairly expensive, and MCMC algorithms that are used to sample the posterior distribution are efficient only as long as the number of parameters remains within reason. Hence, their use requires a careful reflection both on the parameterization of the velocity model, in order to reduce the problem's dimension, and on the definition of the prior distribution of the parameters. In this thesis, we introduce new parsimonious parameterizations enabling to accurately reproduce the wave velocity field with the associated uncertainties.The first parametric model that we propose uses a random Johnson-Mehl tessellation, a variation of the Voronoï tessellation. The second one uses Gaussian kernels as basis functions. It is especially adapted to the detection of seismic wave velocity anomalies. Each anomaly isconsidered to be a linear combination of these basis functions localized at the realization of a Poisson point process. We first illustrate the tomography results with a synthetic velocity model, which contains two small anomalies. We then apply our methodology to a more advanced and more realistic synthetic model that serves as a benchmark in the oil industry. The tomography results reveal the ability of our algorithm to map the velocity heterogeneitieswith precision using few parameters. Finally, we propose a new parametric model based on the compressed sensing techniques. The first results are encouraging. However, the model still has some weakness related to the uncertainties estimation.In addition, we analyse real data in the context of induced microseismicity. In this context, we develop a trans-dimensional and hierarchical approach in order to deal with the full complexity of the layered model.

Rough surface scattering is a problem of interest in underwater acoustic remote sensing applications. To model this problem, a fully three-dimensional (3D) finite element model has been developed, but it requires an abundance of time and computational resources. Two-dimensional (2D) models that are much easier to compute are often employed though they don’t natively represent the physical environment. Three quantities have been developed that, when applied, allow 2D rough surface scattering models to be used to predict 3D scattering. The first factor, referred to as the spreading factor, adopted from the work of Sumedh Joshi [1], accounts for geometrical differences between equivalent 2D and 3D model environments. A second factor, referred to as the perturbative factor, is developed through the use of small perturbation theory. This factor is well-suited to account for differences in the scattered field between a 2D model and scattering from an isotropically rough 2D surface in 3D. Lastly, a third composite factor, referred to as the combined factor, of the previous two is developed by taking their minimum. This work deals only with scattering within the plane of the incident wave perpendicular to the scatterer. The applicability of these factors are tested by comparing a 2D scattering model with a fully three-dimensional Monte Carlo finite element method model for a variety of von Karman and Gaussian power spectra. The combined factor shows promise towards a robust method to adequately characterize isotropic 3D rough surfaces using 2D numerical simulations. / text

Over a decade ago, it was discovered that the earth’s natural seismic wavefields, propagating as seismic noise, can be processed using correlation methods to produce surface waves, similar to those generated by earthquakes. This discovery represents a paradigm shift in seismology and has led to several tomographic studies of earth structures, at different scales and resolutions, in previously difficult-to-study areas around the world. This PhD dissertation presents research results on multi-scale and multi-purpose applications of ambient seismic noise wavefields under three topics: (1) Imaging of sedimentary basins and sub-basin structures in eastern and western Canada using ambient seismic noise, (2) Combining measurements from ambient seismic noise with earthquake datasets for imaging crustal and mantle structures, and (3) Temporal variation in cultural seismic noise and noise correlation functions (NCFs) during the COVID-19 lockdown in Canada. The first topic involved imaging the sedimentary basins in eastern and western Canada using shear wave velocities derived from ambient noise group velocities. The results show that the basins are characterized by varying depths, with maximums along the studied cross-sections in excess of 10 km, in eastern and western Canada. Characteristics of accreted terranes in eastern and western Canada are also revealed in the results. A seismically distinct basement is imaged in eastern Canada and is interpreted to be a vestige of the western African crust trapped beneath eastern Canada at the opening of the Atlantic Ocean. In western Canada, the 3D variation of the Moho and sedimentary basin depths is imaged. The thickest sediments in eastern Canada are found beneath the Queen Charlotte, Williston and the Alberta Deep basins, while the Moho is the deepest beneath the Williston basin and parts of Alberta basin and northern British Columbia. For the second topic, I worked on improving the seismological methodology to construct broadband (period from 2 to 220 s) dispersion curves by combining the dispersion measurements derived from ambient seismic noise with those from earthquakes. The broadband dispersion curves allow for imaging earth structures spanning the shallow crust to the upper mantle. For the third topic, I used ambient seismic data from the earlier stages of the COVID-19 pandemic to study the temporal variation of seismic power spectra and the potential impacts of COVID-19 lockdown on ambient NCFs in four cities in eastern and western Canada. The results show mean seismic power drops of 24% and 17% during the lockdown in eastern Canada, near Montreal and Ottawa respectively and reductions of 27% and 17% near Victoria and Sidney respectively. NCF signal quality within the secondary microseism band reached maximum before the lockdown, minimum during lockdown and at intermediate levels during the gradual reopening phase for the western Canada station pair. / Graduate

The primary objective of this dissertation is to utilise, adapt and extend current stochastic models and statistical inference techniques to describe the transmission of nosocomial pathogens, i.e. hospital-acquired pathogens, and multiply-resistant organisms within the hospital setting. The emergence of higher levels of antibiotic resistance is threatening the long term viability of current treatment options and placing greater emphasis on the use of infection control procedures. The relative importance and value of various infection control practices is often debated and there is a lack of quantitative evidence concerning their effectiveness. The methods developed in this dissertation are applied to data of methicillin-resistant Staphylococcus aureus occurrence in intensive care units to quantify the effectiveness of infection control procedures. Analysis of infectious disease or carriage data is complicated by dependencies within the data and partial observation of the transmission process. Dependencies within the data are inherent because the risk of colonisation depends on the number of other colonised individuals. The colonisation times, chain and duration are often not visible to the human eye making only partial observation of the transmission process possible. Within a hospital setting, routine surveillance monitoring permits knowledge of interval-censored colonisation times. However, consideration needs to be given to the possibility of false negative outcomes when relying on observations from routine surveillance monitoring. SI (Susceptible, Infected) models are commonly used to describe community epidemic processes and allow for any inherent dependencies. Statistical inference techniques, such as the expectation-maximisation (EM) algorithm and Markov chain Monte Carlo (MCMC) can be used to estimate the model parameters when only partial observation of the epidemic process is possible. These methods appear well suited for the analysis of hospital infectious disease data but need to be adapted for short patient stays through migration. This thesis focuses on the use of Bayesian statistics to explore the posterior distributions of the unknown parameters. MCMC techniques are introduced to overcome analytical intractability caused by partial observation of the epidemic process. Statistical issues such as model adequacy and MCMC convergence assessment are discussed throughout the thesis. The new methodology allows the quantification of the relative importance of different transmission routes and the benefits of hospital practices, in terms of changed transmission rates. Evidence-based decisions can therefore be made on the impact of infection control procedures which is otherwise difficult on the basis of clinical studies alone. The methods are applied to data describing the occurrence of methicillin-resistant Staphylococcus aureus within intensive care units in hospitals in Brisbane and London