A new and different approach to the solution of the normal equations of minimum entropy deconvolution (MED) is developed. This approach which uses singular value decomposition in the iterative solution of the MED equations increases the signal-to-noise ratio of the deconvolved output and enhances the resolution of MEC. The problem of deconvolution, and in particular wavelet estimation, is formulated as a linear inverse problem. Both generalized linear inverse methods and Backus-Gilbert inversion are considered. The proposed wavelet estimation algorithm uses the MED output as a first approximation to the earth response. The approximated response and the observed seismograms serve as an input to the inversion schemes and the outputs are the estimated wavelets. The remarkable performance of the linear inverse schemes for cases of highly noisy data is demonstrated. A debubbling example is used to show the completeness of the linear inverse schemes. First the wavelet estimation part was carried out and then the debubbling problem was formulated as a generalized linear inverse problem which was solved using the estimated wavelet. This work demonstrates the power of the linear inverse schemes when dealing with highly noisy data. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

The Rayleigh-Taylor instability of a water-air interface was investigated using electrical and photographic methods. An apparatus is described which accelerates a rectangular tank of water downwards and produces reproducible instabilities from a pure sinusoidal standing surface water wave of known phase and amplitude. The electrical measurements revealed that in addition to the bulk motion, films of water are produced on the walls of the water tank. The existence of these and other features of the instability are substantiated by photographs of the various instabilities that were produced. The electrical measurements led to a new scaling law for the phenomenon of climbing fluid films at accelerations greater than gravity. Several linear devices were also developed for measuring the amplitudes of surface water waves. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Approximate gravitational field equations in an alternative theory of gravity are solved for a class of boundary conditions. The generation of gravitational radiation from spatially bounded sources is analyzed, and it is found that the theory predicts the emission of dipole gravitational radiation. However, the dipole radiation vanishes for slow-motion post-Newtonian sources. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Part I of this thesis develops a theory of nonlinear resonant interactions between continental shelf waves. From the inviscid, unforced long-wave equations for a rotating, homogeneous fluid, it is shown that resonant interactions between three continental shelf waves can occur. Evolution equations governing the amplitude and the energy of individual waves in a resonant triad are derived. The nonlinearity in the governing equations allows energy to be transferred between the waves, but with the total energy conserved. In particular, interactions on an exponential shelf are studied. Part II of this thesis compares the theory from Part I with observations and data from the Oregon shelf. Rotary spectral analysis and cross-shelf modal fitting are the two techniques used for shelf wave detection. Many features characteristic of shelf waves and of the resonant triad interaction theory are found in the current and sea level data. Also, for the first time, shelf waves have been unambiguously identified in both the alongshore and cross-shelf dimensions. The data indicate that the wind generates long continental shelf waves at low frequencies. Nonlinear resonant interactions then transfer energy from the low-frequency long waves to higher frequency shelf waves with much shorter wavelengths. The good agreement between theory and observation suggests that nonlinear energy transfer may play a significant role in shelf wave dynamics. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

The first part of this thesis is concerned with theoretical and experimental investigations of step discontinuities on a planar surface waveguide. An approximate theoretical solution to the unbounded discontinuity problem is obtained by bounding the open structure with perfect conductors, since there is a direct relationship between the mode spectra of the two configurations. Mode-matching is used to solve the bounded case. The method is "tested" on four discontinuity configurations considered by other workers. Good agreement with the previous results is obtained in all cases except one for which the original results are shown to be inaccurate. The experimental investigation is carried out on a dielectric coated conductor surface waveguide, supporting the first TM mode, at a frequency of 30 GHz. Standing wave measurements are obtained using a X/2 dipole oriented along the longitudinal component of electric field. The parameters of interest are the magnitude and the phase of the reflection coefficient. The experimental results confirm those obtained theoretically. The theoretical and experimental techniques are later applied in an investigation of a cascaded step discontinuity configuration. The theoretical approach involves the use of wave transmission matrices. Experimental results for the magnitude of the reflection coefficient are found to be in reasonable agreement with theory. The second part of this work describes a theoretical and experimental study of dielectric waveguides, of circular cross-sections, perturbed by axial slots. In particular, the normalized propagation coefficient of the dominant modes with each polarization is determined analytically using a standard perturbation technique and experimentally using an open resonant cavity. The perturbation results give quite a good indication of the trends observed experimentally. It is found that there is an optimum size of the perturbation which gives the maximum separation between the normalized propagation coefficients of the two polarizations. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

The effect of optical mixing of two tunable dye lasers at frequencies near the plasma frequency has been experimentally investigated in a helium plasma jet. It has been shown that the wave mixing produces longitudinal plasma oscillations at the frequency and wave vector of the mixing force. The driven waves were detected by scattering a third diagnostic light wave from their density fluctuation. The scattering signals increased to as much as seven times the signal observed when scattering from the thermal fluctuations alone. The spectrum of the spectral density function of the induced fluctuations has been measured, as well as the dependence of its amplitude on the power of the mixing light beams. These results agree well with theoretical calculations based on a simple model of the mixing effect of a single electron in the field of two electromagnetic waves. The response of the plasma to optical mixing at different frequencies has also been measured. This spectrum agrees in part with theoretical predictions, but has features not explained by the simple model. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The stability of converging waves was analysed with theory and by experiment. A computer code was written in FORTRAN language for the calculation of wavefront positions of plane shock waves and cylindrical converging shock waves in ideal gas. The criteria for stability were defined and the limit of stability of imploding shock waves was obtained using the code. In order to test the model, an experiment was set up to generate shock waves in an electrothermal shock tube. These shock waves were made to propagate into a wedged channel, and the variations of the shapes of the waves front were measured from high speed framing camera pictures. Good agreement was found between the experimentally observed velocity and the model calculation, indicating that the computer procedure is a valid method to analyse the stability of converging waves. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

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