Wave propagation in unbounded media is a topic widely studied in different science and engineering fields. Global and local absorbing boundary conditions combined with the finite element method or the finite difference method are the usual numerical treatments. In this dissertation, an alternative is investigated based on the dynamic stiffness and the exponential window method in the space-wave number domain. Applying the exponential window in the space-wave number domain is equivalent to introducing fictitious damping into the system. The Discrete Fourier Transform employed in the dynamic stiffness can be properly performed in a damped system. An open boundary in space is thus created. Since the equation is solved by the finite difference formula in the time domain, this approach is in the time-wave number domain, which provides a complement for the original dynamic stiffness method, which is in the frequency-wave number domain. The approach is tested through different elasto-dynamic models that cover one-, two- and three-dimensional problems. The results from the proposed approach are compared with those from either analytical solutions or the finite element method. The comparison demonstrates the effectiveness of the approach. The incident waves can be efficiently absorbed regardless of incident angles and frequency contents. The approach proposed in this dissertation can be widely applied to the dynamics of railways, dams, tunnels, building and machine foundations, layered soil and composite materials.

Turbidite reservoirs in deep-water depositional systems, such as the oil fields in the offshore Gulf of Mexico and North Sea, are becoming an important exploration target in the petroleum industry. Accurate seismic reservoir characterization, however, is complicated by the heterogeneous of the sand and shale distribution and also by the lack of resolution when imaging thin channel deposits. Amplitude variation with offset (AVO) is a very important technique that is widely applied to locate hydrocarbons. Inaccurate estimates of seismic reflection amplitudes may result in misleading interpretations because of these problems in application to turbidite reservoirs. Therefore, an efficient, accurate, and robust method of modeling seismic responses for such complex reservoirs is crucial and necessary to reduce exploration risk. A fast and accurate approach generating synthetic seismograms for such reservoir models combines wavefront construction ray tracing with composite reflection coefficients in a hybrid modeling algorithm. The wavefront construction approach is a modern, fast implementation of ray tracing that I have extended to model quasishear wave propagation in anisotropic media. Composite reflection coefficients, which are computed using propagator matrix methods, provide the exact seismic reflection amplitude for a stratified reservoir model. This is a distinct improvement over conventional AVO analysis based on a model with only two homogeneous half spaces. I combine the two methods to compute synthetic seismograms for test models of turbidite reservoirs in the Ursa field, Gulf of Mexico, validating the new results against exact calculations using the discrete wavenumber method. The new method, however, can also be used to generate synthetic seismograms for the laterally heterogeneous, complex stratified reservoir models. The results show important frequency dependence that may be useful for exploration. Because turbidite channel systems often display complex vertical and lateral heterogeneity that is difficult to measure directly, stochastic modeling is often used to predict the range of possible seismic responses. Though binary models containing mixtures of sands and shales have been proposed in previous work, log measurements show that these are not good representations of real seismic properties. Therefore, I develop a new approach for generating stochastic turbidite models (STM) from a combination of geological interpretation and well log measurements that are more realistic. Calculations of the composite reflection coefficient and synthetic seismograms predict direct hydrocarbon indicators associated with such turbidite sequences. The STMs provide important insights to predict the seismic responses for the complexity of turbidite reservoirs. Results of AVO responses predict the presence of gas saturation in the sand beds. For example, as the source frequency increases, the uncertainty in AVO responses for brine and gas sands predict the possibility of false interpretation in AVO analysis.

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Thesis (M. Sc.)--University of Hong Kong, 1972. / Mimeographed.

Thesis (M.S.)--Brigham Young University. Dept. of Electrical and Computer Engineering, 2003. / Includes bibliographical references (p. 65-66).

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This thesis gives an outline of the ionosphere and studies that were conducted to investigate / Thesis (M.Sc.) - University of KwaZulu-Natal, 2009.

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