Wavefield extrapolation in orthorhombic anisotropic media incorporates complicated but realistic models, to reproduce wave propagation phenomena in the Earth's subsurface. Compared with the representations used for simpler symmetries, such as transversely isotropic or isotropic, orthorhombic models require an extended and more elaborated formulation that also involves more expensive computational processes. The acoustic assumption yields more efficient description of the orthorhombic wave equation that also provides a simplified representation for the orthorhombic dispersion relation. However, such representation is hampered by the sixth-order nature of the acoustic wave equation, as it also encompasses the contribution of shear waves. To reduce the computational cost of wavefield extrapolation in such media, I generate effective isotropic inhomogeneous models that are capable of reproducing the first-arrival kinematic aspects of the orthorhombic wavefield. First, in order to compute traveltimes in vertical orthorhombic media, I develop a stable, efficient and accurate algorithm based on the fast marching method. The derived orthorhombic acoustic dispersion relation, unlike the isotropic or transversely isotropic one, is represented by a sixth order polynomial equation that includes the fastest solution corresponding to outgoing P-waves in acoustic media. The effective velocity models are then computed by evaluating the traveltime gradients of the orthorhombic traveltime solution, which is done by explicitly solving the isotropic eikonal equation for the corresponding inhomogeneous isotropic velocity field. The inverted effective velocity fields are source dependent and produce equivalent first-arrival kinematic descriptions of wave propagation in orthorhombic media. I extrapolate wavefields in these isotropic effective velocity models using the more efficient isotropic operator, and the results compare well, especially kinematically, with those obtained from the more expensive anisotropic extrapolator.

This thesis addresses the efficiency improvement of seismic wave modeling and migration in anisotropic media. This improvement becomes crucial in practice as the process of imaging complex geological structures of the Earth's subsurface requires modeling and migration as building blocks. The challenge comes from two aspects. First, the underlying governing equations for seismic wave propagation in anisotropic media are far more complicated than that in isotropic media which demand higher computational costs to solve. Second, the usage of whole prestack seismic data still remains a burden considering its storage volume and the existing wave equation solvers. In this thesis, I develop two approaches to tackle the challenges. In the first part, I adopt the concept of prestack exploding reflector model to handle the whole prestack data and bridge the data space directly to image space in a single kernel. I formulate the extrapolation operator in a two-way fashion to remove he restriction on directions that waves propagate. I also develop a generic method for phase velocity evaluation within anisotropic media used in this extrapolation kernel. The proposed method provides a tool for generating prestack images without wavefield cross correlations. In the second part of this thesis, I approximate the anisotropic models using effective isotropic models. The wave phenomena in these effective models match that in anisotropic models both kinematically and dynamically. I obtain the effective models through equating eikonal equations and transport equations of anisotropic and isotropic models, thereby in the high frequency asymptotic approximation sense. The wavefields extrapolation costs are thus reduced using isotropic wave equation solvers while the anisotropic effects are maintained through this approach. I benchmark the two proposed methods using synthetic datasets. Tests on anisotropic Marmousi model and anisotropic BP2007 model demonstrate the applicability of my approaches.

Traveltimes are conventionally evaluated by solving the zero-order approximation of the Wentzel, Kramers and Brillouin (WKB) expansion of the wave equation. This high frequency approximation is good enough for most imaging applications and provides us with a traveltime equation called the eikonal equation. The eikonal equation is a non-linear partial differential equation which can be solved by any of the familiar numerical methods. Among the most popular of these methods is the method of characteristics which yields the ray tracing equations and the finite difference approaches. In the first part of the Master Thesis, we use the ray tracing method to solve the eikonal equation to get P-waves traveltimes for orthorhombic models with arbitrary orientation of symmetry planes. We start with a ray tracing procedure specified in curvilinear coordinate system valid for anisotropy of arbitrary symmetry. The coordinate system is constructed so that the coordinate lines are perpendicular to the symmetry planes of an orthorohombic medium. Advantages of this approach are the conservation of orthorhombic symmetry throughout the model and reduction of the number of parameters specifying the model. We combine this procedure with first-order ray tracing and dynamic ray tracing equations for P waves propagating in smooth, inhomogeneous, weakly anisotropic media. The first-order ray tracing and dynamic ray tracing equations are derived from the exact ones by replacing the exact P-wave eigenvalue of the Christoffel matrix by its first-order approximation. In the second part of the Master Thesis, we compute traveltimes using the fast marching method and we develop an approach to estimate the anisotropy parameters. The idea is to relate them analytically to traveltimes which is challenging in inhomogeneous media. Using perturbation theory, we develop traveltime approximations for transversely isotropic media with horizontal symmetry axis (HTI) as explicit functions of the anellipticity parameter and the symmetry axis azimuth in inhomogeneous background media. Specifically, our expansion assumes an inhomogeneous elliptically anisotropic background medium, which may be obtained from well information and stacking velocity analysis in HTI media. This formulation has advantages on two fronts: on one hand, it alleviates the computational complexity associated with solving the HTI eikonal equation, and on the other hand, it provides a mechanism to scan for the best fitting parameters without the need for repetitive modeling of traveltimes, because the traveltime coefficients of the expansion are independent of the perturbed parameters.

Electrical transport measurement of small, irregular shape sample is difficult task. In order to overcome these limitations, this thesis employed a focused ion beam microfabrication. Process of microfabrication is successfully tested on a room temperature antiferromagnet CuMnAs. Temperature dependence resistivity and magnetoresistance of tetragonal bulk CuMnAs single crystal is found to be strongly anisotropic due to layered structure and magnetic order. Anisotropic magnetoresistance shows two fold symmetry and reached a magnitude of 0.12 %. Employing the∼ phenomenological Stoner-Wohlfarth we conclude that the sample has uniaxial magnetic anisotropy with an easy axis not pointing along any principal crystallographic direction and behaves like a two domain antiferromagnet.

I present new models of the elastic structure of the Pacific upper mantle that address the formation and evolution of oceanic plates. Using a surface-wave dispersion dataset, I perform anisotropic tomography to construct two-dimensional phase-velocity maps and three-dimensional velocity models of the Pacific basin. My three-dimensional elastic models describe both the radial and azimuthal anisotropy of seismic waves. In order to constrain these models, I develop regularization techniques that incorporate a priori information about the nature of the oceanic upper mantle, including both the age dependence of seismic velocities and the expected scaling relationships between azimuthal anisotropy parameters derived from realistic peridotite elastic tensors. I observe a strong cooling signal in the upper-mantle seismic velocities that is consistent with halfspace cooling of the lithospheric plate; deviations from this simple cooling signature are related to the influence of mantle plumes or other thermal alteration of the lithosphere. As plate age increases, the depth to the thermally controlled lithosphere-asthenosphere boundary increases as well. This thermal boundary, as seen in the negative gradient in seismic velocities, is consistent with the depth at which there is a transition in anisotropy fast-axis orientation. This change in anisotropy orientation is due to the transition from frozen-in lithospheric anisotropy to asthenospheric anisotropy that is related to geologically recent shear beneath the base of the plate. The anisotropy orientations and strength that we observe throughout the plate are only consistent with A-type olivine fabric. There are regions where anisotropy orientations do not align with paleospreading directions in the lithosphere or absolute-plate-motion in the asthenosphere, suggesting that small-scale convection, mantle flow, and plumes could all lead to changes in the orientation of seismic anisotropy. There is a dependence on the strength of anisotropy on spreading rate at shallow depths; this implies that corner flow at faster-spreading ridges is more effective at aligning olivine crystals in the direction of shear. I also present a new set of local surface-wave amplification maps spanning the contiguous United States. I perform a synthetic-tomography experiment in order to assess our ability to resolve variations in surface-wave amplification due to variations in local elastic structure. Local amplification derived from synthetic seismograms is very highly correlated with direct predictions of amplification, suggesting that we are able to resolve this signal well and that local amplification observations reflect elastic structure local to the station on which they are measured. Local amplification can be used as a complementary constraint to phase velocity in order to map upper-mantle elastic structure.

Magnetic materials have many applications in technology. The magnetic properties of materials are therefore important to catalogue for future use. In this project, the magnetic properties of thin films of permalloy are investigated. Specifically, the goal is to find the perpendicular magnetic anisotropy energy (PMAE) of thin film geometries of permalloy of varying film thickness. The PMAE is computed with powerful parallel computers using density functional theory (DFT) as implemented in the open-source DFT package OpenMX. The project consists of two parts: Computations on the bulk system and computations on six thin film systems of varying thickness. The thin films are periodic in the basal plane (the permalloy has a tetragonal crystal structure). The easy axis of magnetization was found to be along the c-axis of the tetragonal structure, both for bulk and thin film geometries. For the thin film geometries, this corresponds to an out-of-plane easy axis. The PMAE of the thinnest thin film geometries (4-5 atomic layers) were several times greater than that of the bulk system. Thin films with one more layer of Fe than Ni have especially great PMAE. When comparing the results to another study, the magnetocrystalline anisotropy as computed in this project turned out to be more than two orders of magnitude greater than in the previous study. It is hypothesised that this is because of the differing crystal structure of permalloy used in the study.

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Solid-state NMR serves as a powerful method for investigating atomic-level details of insoluble biomolecules, enabling the determination of protein 3D structures and probing molecular motions across a broad range of timescales. In this thesis, I present structural studies on a novel heterotypic and functional amyloid, dynamics studies, and chemical shift anisotropy studies of a microcrystalline protein, ubiquitin. In Chapter 1, I provide a summary of the main interactions in solid-state NMR and discuss relevant pulse sequences employed in this thesis. Chapter 2 briefly explores the characteristic properties of amyloids, highlighting well-studied examples of disease-related and functional amyloids. Special treatments employed in amyloid structure determination using solid-state NMR are also summarized. Chapter 3 presents structural studies on a heterotypic functional amyloid, mcmvM45-hsRIPK3, where M45 is a protein encoded by murine cytomegalovirus (MCMV) and RIPK3 is from humans. Both M45 and RIPK3 belong to a family of RHIM-containing proteins, which are involved in innate immunity and immune response through necroptosis. SSNMR data on various isotopically labeled samples enable the chemical shift assignment for both M45 and RIPK3, providing intra- and inter-molecular contacts. By combining these constraints, we calculate the structure of the hetero-amyloid M45-RIPK3, reporting two structures distinct from RIPK1-RIPK3. In Chapter 4, I measure backbone 15N-13CO order parameters of microcrystalline ubiquitin using DCP-REDOR. Two isotopically labeled samples, 1-13C-glucose and 1,3-13C-glycerol, D₂O labeled, are studied and compared, identifying mobile residues and assessing the effect of isotropic labeling on the measurements of backbone 15N-13Co order parameters. Experimental order parameters are compared with a 1μs MD simulation for insights. Chapter 5 focuses on the chemical shift anisotropy (CSA) of uniformly labeled microcrystalline ubiquitin using a novel pulse sequence allowing the measurement of large CSAs under practical conditions. We explore CSA parameter trends, correlations between isotropic shifts, and hydrogen bond geometries. Comparison with solution-NMR results demonstrates high consistencies with asymmetry parameters (η), providing insights into the motion modes of microcrystalline proteins alongside order parameter measurements. Chapter 6 provides a comprehensive summary of the conclusions drawn from the preceding chapters, while also outlining future directions for each project.