The history of diffraction theory, exact frequency domain solutions and selected past time domain solutions are briefly reviewed. Exact time domain solutions for scattering of plane, cylindrical and spherical acoustic waves by a half plane are derived by inverse Fourier transforming the frequency domain integral solutions. The solutions consist of two diffraction terms, a reflected term and a direct term. The diffracting edge induces step function discontinuities in the direct and reflected terms at two shadow boundaries. At each boundary, the associated diffraction term reaches a maximum amplitude of half the geometrical optics term and has a signum function discontinuity, so that the total field remains continuous. A physical interpretation is developed in terms of Huygen's principle near the diffracting edge. Solutions for practical point source configurations are evaluated by numerically convolving the impulse diffraction responses with a wavelet. The numerical problems presented by convolution with a singular, truncated operator are solved by analytically derived correction techniques, which are favourably compared to those used by earlier authors. The diffraction solution collapses into a compact discretized formulation. The half plane is shown to be a limiting form of wedge solutions, which can thus be computed using similar algorithms. Two zero offset sections are produced and compared to approximate Kirchhoff integral solutions. The exact diffraction hyperbola is noticeably non-symmetric, with higher amplitudes on the reflector side of the edge. Near the apex of the hyperbola the Kirchhoff solution is nearly equivalent to the exact diffraction term symmetric in amplitude about the reflection shadow boundary but fails to describe the other, low amplitude, term equivalent to half the response of a line scatterer. The differences are more noticeable on the flanks of the hyperbola, where the two terms are comparable in amplitude, and at shallow depths, due to an aperture effect. Increasing either the depth of the edge or the angle of the seismic line to the normal to the edge results in a flatter diffraction hyperbola showing little amplitude variation with moveout. As the seismic line becomes parallel to the edge the diffraction curve becomes flat and is indistinguishable from a reflection event. At great depth diffraction events may be mistaken for reflection events as well. Examples of CDP and CSP gathers, when compared to the Common Offset (CO) gathers, demonstrate that CO gathers are optimal for diffraction processing. Also, since the diffraction moveout and reflection moveout curves differ widely except for depth points near the edge, normal moveout stacking will distort the diffractions and diffraction stacking is essential to retain diffraction information. Strips of varying width are modelled by superposition of half planes to demonstrate resolution effects and show that the limit of a strip is a line scatterer. A dipping strip and an offset half plane model are produced and added for later comparison with wedge solutions. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

This thesis is concerned with the problem of estimating broadband acoustic impedance from normal incidence reflection seismograms. This topic is covered by following the linear inverse formalisms described by Parker (1977) and Oldenburg (1980). The measured seismogram is modelled as a convolution of subsurface reflectivity with a source wavelet. Then an appraisal of the seismogram is performed to obtain unique bandlimited reflectivity information. This bandlimited reflecitivity information is then utilized in two different construction algorithms which provide a broadband estimate of reflectivity; from which a broadband impedance function may be computed. The first construction method is a maximum entropy method which uses an autoregressive representation of a small portion of the reflectivity spectrum to predict spectral values outside that small portion. The second and most versatile construction method is the linear programming approach of Levy and Fullagar (1981) which utilizes the unique bandlimited spectral information obtained from an appraisal and provides a broadband reflectivity function which has a minimum 1( norm. Both methods have been tested on synthetic and real seismic data and have shown good success at recovering interpretable broadband impedance models. Errors in the data and the uniqueness of constructed reflectivity models play important roles in estimating the impedance function and in assessing its uniqueness. The Karhunen-Loeve transformation is discussed and applied on real data to stabilize the construction results in the presence of noise. The generally accepted idea that low frequency impedance information must be supplied from well log or velocity analyses because of the bandlimited nature of seismic data has been challenged. When accurate, bandlimited reflectivity information can be recovered from the seismic trace, then an interpretable, broadband impedance model may be recovered using the two construction algorithms presented in this thesis. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

The seismic design of buildings is usually performed using one-way analysis for each of main axes independently. However, seismic events have fairly random behaviour and impose bidirectional solicitations on structures. In this work, the study of the response in structures subjects to earthquake loads with irregularity of l-shaped plan and soft story is carried out. For this, the linear time-story analysis (LTHA) of these has been carried out imposing seismic solicitations in two orthogonal directions. Thus, the structural response with incidence angle variations of 10 is obtained and compared with the response derived from the unidirectional analysis. Variations of up to 50% and 72% are obtained for model structures with l-shaped plan and soft story respectively.

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Time-lapse passive seismic velocity tomography was conducted utilizing data from three underground longwall coal mines to produce a better understanding of the processes that lead to ground failure in mines, especially large, violent failures, such as bumps. Two of the datasets, US Western I and US Western II, were collected at bump-prone underground longwall coal mines in the Western United States using surface mounted receiver arrays, while the third data set was collected at an underground longwall coal mine in Australia utilizing an underground array. The Australian mine was experiencing problems with periodic caving and subsequent wind blasts, rather than bumps. Seismic velocity tomography allows for non-invasive imaging of a rock mass and inference of stress redistribution from the velocity images. These tomograms are unique as they are generated using source data that was collected remotely and the sources are mining-induced. Tomograms were generated using three inversion methods: simultaneous iterative reconstructive technique (SIRT), double difference least squares event relocation, and least squares event relocation. The three methods were compared and contrasted to determine if one is superior and if event relocation improves the image. Also, the tomograms were analyzed to determine if passive seismic velocity tomography is an appropriate technology for the study of stress in mines and assistance in forecasting of bumps. The tomograms were compared with known roof events, face advance, and fall locations at the mines to establish if expected stress features can be imaged with velocity. Finally, synthetic tomograms were generated using a starting velocity model that approximates the predicted "true" model for each mine to determine if the velocity images produced correlate with the theoretical stress state at the mine. Results indicate that high velocity zones correlating with high stress abutment regions can be imaged for the US Western I data set with all three inversion methods, but the SIRT method provided the best agreement when the synthetic tomogram was generated. Additionally, a low velocity zone that correlates with the gob is consistently imaged. These features also redistribute with face advance. The US Western II data set was not as densely sampled as the US Western I data set. A low velocity region was consistently present in the gob area and redistributed with face advance, but abutment stress features were not evident. Additionally an unexplained high velocity feature was evident on several of the tomograms. Synthetic tomography indicated that the double difference least squares event relocation method is most appropriate for this data set. Finally, the Moonee Colliery results, which were also not as densely sampled as US Western I were uncertain. While velocity anomalies were often present in the vicinity of a fall, the anomalies were not reliably high or low. Again, synthetic tomography indicated that the double difference damped least squares event relocation method was most appropriate for this data set. The tomograms presented indicate that source-receiver configuration and density and variable gridding are extremely important in the application of passive seismic velocity tomography to mines. The source-receiver configuration and density determine how well various areas of a model are constrained, and the variable gridding allows areas that are not well sampled to still be adequately constrained. As a result of this work several things can be drawn about requirements that must be met in order to utilize seismic velocity tomography for inference of stress in underground mines. First, typical longwall stress abutment patterns can be inferred from velocity images of underground coal mines. Second, synthetic tomography and analysis of this tomography, in addition to some knowledge of the general location and frequency of microseismic events, is necessary prior to designing receiver arrays for passive seismic velocity tomography. Suboptimal source-receiver configurations may be used for passive seismic velocity tomography, but there is a minimum threshold for the number of raypaths that must be met that is unique to each site. Finally, a good understanding of the mechanics of stress and failure at the site is necessary to interpret the tomograms. / Ph. D.

Geothermal energy can make an important contribution to the U.S. energy portfolio. Production areas require seismic monitoring tools to develop and monitor production capability. This paper describes modifications made to a prototypical seismic tool to implement improvements that were identified during previous tool applications. These modifications included changing the motor required for mechanical coupling the tool to a bore-hole wall. Additionally, development of a closed-loop process control utilized feedback from the contact force between the coupling arm and bore-hole wall. Employing a feedback circuit automates the tool deployment/anchoring process and reduces reliance on the operator at the surface. The tool components were tested under high temperatures and an integrated system tool test demonstrated successful tool operations. / Master of Science