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Single frame ultrasound B-mode image quality is largely governed by the ability to focus the ultrasound beam over a range in depths both in transmission and reception. By developing a comprehensive understanding of acoustic wave propagation two signal processing methods were identified for solving the transmission problem. We made use of both the impulse response using the classical point spread function (PSF) and the spatial sensitivity function (SSF) which describes the spatial distribution at a particular time. Using the angular spectrum method, an accurate analytical model was developed for the field distribution arising from a finite geometry, apodized and focused, plane piston transducer. While there is a thorough understanding of the radiated field arising from uniformly excited plane piston transducers, the focused equivalent (i.e., one that allows a continuous change in phase over the plane piston surface) is incomplete and assumes the Fresnel approximation. Our model addresses the effects of diffraction and evanescent waves without the use of the Fresnel approximation and is applicable at all near- and far-field locations in a lossless medium. The model was analyzed to identify new insights into wave propagation and compared with the Fresnel approximation and the spherically-focused, concave transducer. The piston transducer model was then extended to an attenuating and dispersive medium. After analysing existing models of power-law frequency dependent attenuation, a causal, spherical wave Green’s function was derived from the Navier-Stokes equation for a classical viscous medium. Modifications to the angular spectrum method were presented and used to analyze the radiated field of a focused, planar piston transducer. Finally, after presenting our signal processing strategy for improving imaging spatial resolution through minimization of the SSF, two signal processing methods were derived and analysed in simulation: a deconvolution technique to remove the effects of the ultrasound excitation wave and suppress additive noise from the received ultrasound signal, and a retrospective transmit focusing method that changed the response from a predefined transmit focus to an arbitrary transmit focal depth. Proof-of-concept simulations were presented using a variable number of scatterers and compared with the traditional matched filtering and envelope detection technique.

The main crux of this thesis was to produce a model that was capable of simulating the theoretical performance of different configurations for a spatial measurement system using radio frequency technology. It has been important to study new modalities of spatial measurement since spatial measurement systems are an enabling technology that have allowed for the creation of better medical procedures and techniques, provided valuable data for motion capture in animation and biomechanics, and have improved the quality of manufacturing processes in many industries. However, there has been room for improvement in the functional design and accuracy of spatial measurement systems that will enhance current applications and further develop new applications in medicine, research and industry. <br /><br /> In this thesis, a modelling framework for the investigation of spatial measurement based on radio frequency signals was developed. The simulation framework was designed for the purpose of investigating different position determination algorithms and sensor geomatries. A finite element model using the FEMLAB partial differential equation modelling tool was created for a time-domain model of electromagnetic wave propagation in order to simulate the radio frequency signals travelling from a transmitting source antenna to a set of receiving antenna sensors. Electronic line signals were obtained using a simple receiving infinitesimal dipole model and input into a time difference of arrival localization algorithm. The finite element model results were validated against a set of analytical solutions for the free space case. The accuracy of the localization algorithm was measured against a set of possible applications for a potential radio frequency spatial measurement system design. <br /><br /> It was concluded that the simulation framework was successful should one significant deficiency be corrected in future research endeavours. A phase error was observed in the signals extracted at the receiving antenna locations. This phase error, which can be up to 40??, was attributed to the zeroth order finite elements implemented in the finite element model. This phase error can be corrected in the future if higher order vector elements are introduced into future versions of FEMLAB or via the development of custom finite element analysis software but were not implemented in this thesis due to time constraints. Other improvements were also suggested for future work.

In Chapter 2, we consider the hydrostatic equilibrium figure of a rotating earth model with arbitrary radial density profile. We derive an exact non-linear partial differential equation describing the equilibrium figure. Perturbation theory is used to obtain approximate forms of this equation, and we show that the first-order theory is equivalent to Clairaut's equation. In Chapter 3, a method for parametrizing the possible equilibrium stress fields of a laterally heterogeneous earth model is described. In this method a solution of the equilibrium equations is first found that satisfies some desirable physical property. All other solutions can be written as the sum of this equilibrium stress field and a divergence-free stress tensor field whose boundary tractions vanish. In Chapter 4, we consider the minor vector method for the stable numerical solution of systems of linear ordinary differential equations. Results are presented for the application of the method to the calculation of seismic displacement fields in spherically symmetric, self-gravitating earth models. In Chapter 5, we present a new implementation of the direct solution method for calculating normal mode spectra in laterally heterogeneous earth models. Numerical tests are presented to demonstrate the validity and effectiveness of this method for performing large mode coupling calculations. In Chapter 6, we consider the theoretical basis for the viscoelastic normal mode method which is used in studies of seismic wave propagation, post-glacial rebound, and post-seismic deformation. We show how the time-domain solution to the viscoelastodynamic equation can be written as a normal mode sum in a rigorous manner.

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Ambient seismic noise from generation to its application for determination of sub-surface velocity structures is analyzed using continuous data recordings from the Swedish National Seismic Network (SNSN). The fundamental aim of the thesis is to investigate the applicability of precise velocity measurements from ambient noise data. In the ambient noise method, a form of interferometry, the seismic signal is constructed from long-term cross correlation of a random noise field. Anisotropy of the source distribution causes apparent time shifts (velocity bias) in the interferometric signals. The velocity bias can be important for the study area (Sweden) which has relatively small velocity variations. This work explores the entire data path, from investigating the noise-source distribution to a tomographic study of southern Sweden. A new method to invert for the azimuthal source distribution from cross-correlation envelopes is introduced. The method provides quantitative estimates of the azimuthal source distribution which can be used for detailed studies of source generation processes. An advantage of the method is that it uses few stations to constrain azimuthal source distributions. The results show that the source distribution is inhomogeneous, with sources concentrated along the western coast of Norway. This leads to an anisotropic noise field, especially for the secondary microseisms. The primary microseismic energy comes mainly from the northeast. The deduced azimuthal source distributions are used to study the level of expected bias invelocity estimates within the SNSN. The results indicate that the phase-velocity bias is less than 1% for most station pairs but can be larger for small values of the ratio of inter-station distance over wavelength. In addition, the nature of velocity bias due to a heterogeneous source field is investigated in terms of high and finite-frequency regimes. Graphical software for phase-velocity dispersion measurements based on new algorithms is presented and validated with synthetic data and by comparisons to other methods. The software is used for phase-velocity measurements, and deduced azimuthal source distributions are used for velocity-bias correction. Derived phase-velocity dispersion curves are used to construct two-dimensional velocity maps of southern Sweden at different periods based on travel-time tomography. The effect of the bias correction is investigated, and velocity maps are interpreted in comparison to previous geological and geophysical information.

Approved for public release; distribution is unlimited / Variability of the MABL and its effect on the electromagnetic (EM) refractive structure around the Greenland Sea marginal ice zone were examined. Rawinsonde profiles and surface observations collected from 3 ships during MIZEX-87(20 March-11 April) served as the data set. A program, developed to calculate the refractivity at each vertical level of the rawinsonde profiles, also identified the levels at which trapping, superrefraction and subrefraction occurred. Temporal studies showed that a higher incidence of anomalous refractive layers occurred during periods when the region was under the influence of high pressure. More than 50% of the time, trapping and super-refractive layers were attributed to development of a capping inversion just above the MABL during these periods. Spatial studies showed that the refractive structure varied relative to distance from the ice edge as did the depth of the MABL. An upward slope in refractive layer heights was observed from the ice toward the open water. Significant spatial inhomogeneity was observed over horizontal ranges of less than 100 km. This was attributed to both the large-scale synoptic forcing affecting the region and to variations in the surface fluxes of heat and moisture over the ice and over the water. A range-dependent ray trace model developed at the Naval Ocean Systems Center was used to show how the ray paths of EM waves vary with a changing refractive structures. Keywords: Air water interactions, Greenland Sea, Atmospheric refraction, Electromagnetic wave propagation, Heat flux, Sea ice. Theses. (EDC) / http://archive.org/details/temporalspatialv00grot / Lieutenant, United States Navy

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Crystallographic texture in polycrystalline HCP and cubic materials, often developed during thermomechanical deformations, has profound effects on properties at the macroscopic or component level. Given the respective natures of current detection techniques, a non-destructive, three-dimensional bulk texture detection method for these materials has not yet been developed. This thesis aims to achieve this goal through systematic studies on the relationship between ultrasonic wave velocity and texture. The feasibility of such development is firstly reviewed via the combination of computational and experimental studies on exemplary HCP materials. Numerical results obtained via a representative volume element (RVE) methodology reveal that the wave speed varies progressively and significantly with changing texture, and experimental ultrasound studies combined with EBSD characterisation demonstrate distinguished velocity profiles for samples with different textures. Thus the possibility of the development is demonstrated from these combined results. A novel convolution theorem is then presented, which couples the single crystal wave speed (the kernel function) with polycrystal orientation distribution function to give the resultant polycrystal wave speed function. Firstly developed on HCP and then successfully extended to general anisotropic materials, the theorem expresses the three functions as harmonic expansions thus enabling the calculation of any one of them when the other two are known. Hence, the forward problem of determination of polycrystal wave speed is solved for all crystal systems with verifications on varying textures showing near-perfect representation of the sensitivity of wave speed to texture as well as quantitative predictions of polycrystal wave speed. More importantly, the theorem also presents a solution to the long-standing inverse problem for HCP and cubic materials, with proof of principle established where groups of HCP and cubic textures are recovered solely from polycrystal wave velocities through the theorem and the results show good agreements with the original textures. Therefore the theorem opens up the possibility of developing a powerful technique for bulk texture measurement and wave propagation studies in HCP, cubic materials and beyond.

This thesis examines the properties of transmission and transport of light and charged particles in periodic or quasiperiodic systems of solid state and optics, especially the nonlinear and external field effects and the dynamic properties of these systems.