Thesis (PhD)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: Please refer to full text for abstract. / AFRIKAANSE OPSOMMING: Sien asb volteks vir opsomming.

Shear-wave splitting and azimuthal variations of seismic attributes are two major anisotropic effects induced by vertically-aligned fractures. They both have influences on seismic data processing and interpretation, and provide information on fracture properties. Azimuthal variations in P-wave data have been intensively studied to improve imaging and obtain fracture parameters. However, azimuthal variations in PS-converted wave seismic data, particularly the velocity variation in PS-converted wave data, have not been well studied. Shear-wave splitting has been frequently used to estimate fracture directions and densities. However, its influence on the azimuthal variations of PS-converted wave data has also lacked a proper analysis. In this thesis, I analyse the anisotropic behaviour of PS-converted wave seismic data in the presence of azimuthal anisotropy, which includes the azimuthal variation of the PSconverted wave and PS-converted wave splitting. First, I demonstrate the robustness of PS-converted wave splitting for fracture characterisation. PS-converted wave seismic data is also influenced by the splitting effect due to its upgoing shear-wave leg. This important feature enables the application of shear-wave splitting analysis to PS-converted wave seismic data. I use synthetic data to show the necessity for separation of the split PS-converted waves. Then I apply the PS-converted wave splitting analysis to Sanhu 3D3C land seismic data. By separation of the fast and slow PS-converted waves and compensation for the time delays, the imaging quality has been improved. Dominant fracture properties obtained from the splitting analysis show a good correlation with the stress-field data. However, this work is accomplished by assuming only one set of vertical fractures in processing a given time window. In future work a specific layer-stripping algorithm could be constructed and applied. . Second, I study azimuthal variations of velocities in PS-converted wave seismic data. It involves two major parts: analysing azimuthal variations of NMO velocities to improve imaging, and examining the sensitivity of azimuthal variations to different fluid saturations. For a layer with HTI anisotropy induced by a set of vertical fractures, seismologists usually analyse the azimuthal behaviour exhibited on the radial and transverse components, on which PS-converted wave data are recorded. However, PS-converted waves also undergo shear-wave splitting, which complicates the azimuthal variations of PS-converted wave data. I demonstrate that it is essential to separate the fast P-SV1 wave from the slow P-SV2 wave, before applying any azimuthal analysis. I derive an equation describing the azimuthal variation in PSconverted wave NMO velocities, which shows the variation can be approximated into an ellipse. Based on this theory, I build a workflow to analyse the azimuthal variations of velocities in PS-converted wave data and apply this workflow to synthetic data. The imaging quality can be improved by using this workflow. Different fluid saturations in fractures have different influences on the azimuthal variations of both P-wave and PS-converted wave data. I perform a numerical study to understand how dry or water-saturated fractures control the azimuthal variations. Through theoretical and synthetic studies, I find that the azimuthal variation of velocities in PS-converted wave data is sensitive to different fluid saturations. By analysing the azimuthal variation, the fracture properties can also be estimated, but results are not as robust as those from PS-converted wave splitting analysis. I find that azimuthal variations of fast P-SV1 and slow P-SV2 waves show in-phase characteristics in dry fractures, but exhibit out-of-phase characteristics in water-saturated fractures. This important feature could open a new application for using PS-converted wave seismic data to distinguish oil-filled fractures from gas-filled fractures. In cases where multiple HTI layers are involved, I have developed a specific layer-stripping method to analyse both azimuthal variations and splitting effects of PS-converted waves. By applying this method to synthetic data, the fracture properties of each HTI layer can be estimated. The analysis of azimuthal variations in PS-converted wave velocities is applied to Daqing 3D3C land data. By using azimuthal velocity models in the PS-converted wave seismic data processing, the imaging quality is improved, especially in the anticline area where intensive fractures are likely to be developed. Furthermore, all fracture information obtained from analysis of azimuthal variations and splitting effects is compared with the stress-field data. The results from splitting analysis show a better correlation with the stress-field study. Finally, it is important to conclude that the analysis of PS-converted wave splitting is a robust method to estimate fracture directions and densities. However, it is not sensitive to different fluid saturations, which limits its application to fractured reservoir characterisation. Azimuthal variations of PS-converted wave seismic data can be analysed to improve imaging quality. Moreover their sensitivity to fluid saturations may provide a new way to discriminate between oil-filled and gas-filled fractures. However, the analysis of azimuthal variations is not as robust as the analysis of splitting effects, and it may require appropriate calibration with other fracture characterisation methods.

In this work, two distinct types of Diffractive Optical Elements (DOEs) are designed to laterally distribute the solar spectrum across multiple photovoltaic (PV) cells. Each PV cell receives a spectral band near its bandgap energy to maximize overall solar-to-electric conversion efficiency of the system. The first DOE is an off-axis volume holographic lens. Design parameters include lateral grating period and slant angle, index modulation, film thickness, and control of swelling and index modulation attenuation in the film development process. Diffraction efficiency across the holographic lens is simulated using Rigorous Coupled Wave Analysis (RCWA). A full system model is created, and non-sequential raytracing is performed. Performance is evaluated under AM 1.5 conditions and annual insolation in Tucson, AZ, and Seattle, WA. A proof-of-concept off-axis holographic lens is fabricated and its performance is measured to confirm the optical properties of this system. The second DOE is an algorithmically-designed freeform surface relief structure. The Gerchberg-Saxton design algorithm is expanded to consider multiple wavelengths, resulting in a Broadband Gerchberg-Saxton (BGS) algorithm. All design variables are evaluated in a parametric study of the algorithm. Several DOE designs are proposed for spectrum splitting, and two of these designs are fabricated and measured. Additional considerations, such as finite sampling of the discrete Fourier transform, fabrication error, and solar divergence are addressed. The dissertation will conclude with a summary of spectrum splitting performance of all proposed DOEs, as well as a comparison to ideal spectrum splitting performance and discussion of areas for improvement and future work.

No description available.

Azimuthal anisotropy, assumed to be associated with vertical, aligned cracks, fractures, and subsurface stress regimes, causes vertically propagating shear waves to split into a fast component, with particle motion polarized parallel to fracture strike, and a slow component, with particle motion polarized perpendicular to fracture strike. Determining the polarization of each split shear wave and the time lag between them provides valuable insight regarding fracture azimuth and intensity. However, analysis of shear wave polarizations in seismic data is hampered by reflection-induced polarization distortion. Traditional polarization analysis methods are limited to zero offset and are not valid if implemented over the full range of offsets available in typical 3D seismic data sets. Recent proposals for normalizing amplitudes recorded at non-normal incidence to values recorded at normal incidence may provide an extension to correcting offset-dependent shear wave polarization distortion. Removing polarization distortion from shear wave reflections allows a larger range of offsets to be used when determining shear wave polarizations. Additional complexities arise, however, if fracture orientation changes with depth. Reflections from layers with different fracture orientations retain significant energy on off-diagonal components after initial rotations are applied. To properly analyze depth-variant azimuthal anisotropy, time lags associated with each interval of constant anisotropy are removed and additional iterative rotations applied to subsequent offset-normalized reflections. Synthetic data is used to evaluate the success of these methods, which depends largely on the accuracy of AVA approximations used in the correction. The polarization correction effectively removes SV polarity reversals but may be limited in corrections to SH polarizations at very far offsets. After the polarization correction is applied, energy calculations including incidence angles up to 20° more effectively compensates individual SV and SH reflection components, allowing for more faithful polarization information identification of the isotropy plane and the symmetry axis. The polarization correction also localizes diagonal component energy maxima and off-diagonal component energy minima closer to the true orientation of the principal axes when a range of incidence angles up to 20° is used. / text

Cette thèse avait comme but le développement, l'analyse et l'application de schémas numériques pour la simulation de modèles cinétiques basés sur l'équation de Vlasov, notamment de schémas basés sur le splitting de Strang et une méthode d'interpolation essentiellement non oscillatoire (WENO). Les schémas sont testés sur des cas test de plus en plus compliqués, et finalement sur un modèle Boltzmann-Schrödinger-Poisson qui décrit les états transitoires d'un transistor à l'echelle nanométrique.

Exurbanization is occurring where large tracts of land are being sold to developers. Typically these are ranches that are then divided into 40-acre parcels and sold by developers, avoiding subdivision regulations requiring paved streets, utilities and other amenities. The result is an unplanned subdivision with no infrastructure, and tax revenues that cannot offset the cost of providing it. Interviews with professional planners suggested there may be independent variables capable of predicting the amount of human disturbance in an exurban area: parcel size, full cash value, tenure, distance to paved roads, site-built housing, mobile homes, and presence of biological or riparian areas. A total of 7,465 acres (3,022 ha) of parcel disturbance were digitized in exurban Arivaca, acreage values were converted to a binary dependent variable and used in logistic regression analysis to test independent variables' predictive value. Four were statistically significant: parcel size, full cash value, mobile homes and site-built housing. Landscape fragmentation was also tested using the presence of the variable scoring highest in probability - site-built housing. Zones of influence with a negative ecological influence surrounded the homes - up to 5,055 acres (2,046 ha) were impacted. Interviews with an exemplary sample of residents regarding their land use ethic found all had very strong opinions on how their properties should be treated as well as undesirable land uses such as overgrazing, over-use of groundwater for short-term economic gain and use of off-road vehicles. An explanation of the small sample size of both planners and residents is warranted. Planners were limited to those working in Pima County government who had professional experience with the study area of Arivaca and were familiar with its particular situation. The number of Arivaca residents interviewed was intended to discern an exemplary group's opinions based on how large a parcel they owned, the various sizes being a typical cross-section of acreage in the study area. What these findings illustrate is (1) the difficulty of predicting human-induced disturbance, (2) land fragmentation is more than the actual areas of physical disturbance and (3) some residents are aware of impacts related to their activities, mitigating damage wherever possible.

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This thesis presents two dimensional discrete dynamical system, the extended standard family of maps, which approximates homoclinic bifurcations of continuous dissipative systems. The main subject of study is the problem of separatrix splitting which was first discovered by Poincaré in the context of the n-body problem. Separatrix splitting leads to chaotic behaviour of the system on exponentially small region in parameter space. To estimate the size of the region the dissipative map is extended to complex variables and approximated by differential equation on a specific domain. This approach was proposed by Lazutkin to study separatrix splitting for Chirikov’s standard map. Furthermore the complex nearly periodic function is used to estimate the width of the exponentially small region where chaos prevails and the map is related to the semistandard map. Numerical computations require solving complex differential equation and provide the constants involved in the asymptotic formula for the size of the region. Another problem studied in this thesis is the prevalence of resonance for the dissipative standard map on a specific invariant set, which for one dimensional map corresponds to a circle. The regions in parameter space where periodic behaviour occurs on the invariant set is known as Arnold tongues. The width of Arnold tongue is studied and numerical results obtained by iterating the map and solving differential equation are related to the semistandard map.

In Chinese orthography, phonetic compounds comprise about 80% of the most frequent characters. They contain separate phonological and semantic elements, referred to as phonetic and semantic radicals respectively. A dominant type exists in which the se-mantic radical appears on the left and the phonetic radical on the right (SP characters); an opposite, minority structure also exists in which the semantic radical appears on the right and the phonetic radical on the left (PS characters). Through statistical analyses, connectionist modelling, behavioural experiments, and neuroimaging studies, this dis-sertation demonstrates that the distinct structures of these two types of characters allow us crucial insights into the relationship between brain structure and reading processes. The statistical analyses of a Chinese lexical database show that, because of the different information profiles of SP and PS characters and the imbalanced distribution between them in the lexicon, the overall information is skewed to the right. This information skew provides important opportunities to examine the interaction between foveal split-ting and the information structure of the characters. The foveal splitting hypothesis as-sumes a vertical meridian split in the foveal representation and the consequent contra-lateral projection to the two cerebral hemispheres; it has been shown to have important implications for visual word recognition. The square shape and the condensed structure of Chinese characters make them a severe test case for the split fovea claim. Through a lateralized cueing examination and a TMS study of the semantic radical combinability effect with foveally presented characters in character semantic judgements, a flexible division of labour between the hemispheres in character recognition is demonstrated, with each hemisphere responding optimally to the information in the contralateral visual hemifield. The interaction between stimulation site and radical combinability in the TMS study also provides further support for the split fovea claim, suggesting functional foveal splitting as a universal processing constraint in reading. Even if foveal splitting is true, it is still unclear about how far the effects of foveal split-ting can extend from the retina into the process of character recognition. We show that, in naming isolated, foveally presented SP and PS characters, adult male and female readers process them differently, with opposite patterns of ease and difficulty: males responded significantly faster to SP than PS characters; females showed a non-significant tendency in the opposite direction. This result is also supported by a corre-sponding ERP study showing larger N350 amplitude elicited by PS character than SP characters in the male brain, and an opposite pattern in the female brain. The split fovea claim suggests that the two halves of a centrally fixated character are initially processed in different hemispheres. The male brain typically relies more on the left hemisphere for phonological processing compared with the female brain, causing this gender difference to emerge. This interaction is also predicted by an implemented computational model, contrasting a split cognitive architecture, in which the mapping between orthography to phonology is mediated by two partially encapsulated, interconnected processing do-mains, and a non-split cognitive architecture, in which the mapping is mediated by a single, undifferentiated processing domain. Thus, the effects of foveal splitting in read-ing extend far enough to interact with the gender of the reader in a naturalistic reading task. In short, this dissertation demonstrates that foveal splitting is a universal language proc-essing phenomenon, precise enough to project the two radicals of a centrally-fixated Chinese character to different hemispheres to allow a flexible division of labour be-tween the two hemispheres to emerge, and its effects in reading extend far enough into word recognition to interact with the gender of the reader in a naturalistic reading task. The results can also be extrapolated to Chinese word and sentence processing as well as to other languages. This dissertation thus has contributed to a better understanding of the relationship between brain structure and language processes.