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Digital analysis of thematic mapper images and digital elevation model (DEM) of the Puerto Libertad area, emphasized a NE-E structural pattern and a less evident N-S structural trend. These structures may correspond to the distensive mechanisms of the opening of the Gulf of California. Also, semicircular structures in the area were recognized. These are associated to plutonic bodies or local volcanic centers. Exploration targets are most likely to occur in the last type of structures. Analysis included multispectral ratios of bands 5/7 and 5/1 to enhance lithologic discrimination and alteration zones especially hydroxyl-bearing and ferric iron alterations. Principal component analysis to enhance spectral data was also performed. Images revealed new lithologic subdivisions in units previously mapped. Analysis of DEM data and gradient operators from the first principal component image were analyzed to extract textural information.

This thesis discusses the suitability of the box-counting method as a tool describing complex geometrical phenomena in nature by estimating their fractal dimensions, D. The study evaluated the influence of the parameters of the box counting method on the estimated fractal dimension using Koch curves of known fractal properties. It became clear that the employed size range of the applied box networks has the strongest influence on the obtained fractal dimension. A successful application of the box-counting method to generated 2-D joint patterns proved the ability of the fractal dimension to capture the influence of joint size and density on the statistical homogeneity of rock masses. Joint data from a tunnel of the Three Gorges Dam site in China was examined for potential statistical homogeneity. It was possible to find five different statistically homogeneous regions by combining the estimated fractal dimension and a visual geological evaluation of the joint maps.

Groups and individuals concerned with the search for mineral deposits use a great deal of information with high spatial content to generate prospecting targets. The information is commonly in the form of maps and may be subjected to a variety of qualitative and quantitative techniques of map analysis, the objective of which is to avoid mindless wandering in the field by reducing the exploration area while retaining a high potential for success. Geographic information systems are of great interest as a means of managing map-based information. The systems are used in government but costs and complexity are slowing their acceptance in the for-profit sector. This research demonstrates low-cost software on a widely available computer system to explore five alternative methods of applying a geographic information system to the problem of generating prospecting targets. The methodology could be applied equally well to defining targets of other kinds, from sites for toxic waste disposal to candidates for mass marketing. Success of the applications is measured by their ability to reduce the exploration area while retaining a high proportion of the known mineral deposits that provide an estimate of the undiscovered deposits. Area reductions range from zero percent, a worst case, to 98%; retentions of known deposits range from 100% to 29%. Efficiency, a ratio of the area containing known deposits within the favorable area to the entire favorable area, is introduced as a comparative measure of success. The most efficient approach is more than 40 times as efficient as the least efficient. Two of the approaches demonstrated are new, and provide a formal approach to map analysis. The research demonstrates the utility and flexibility of a low-cost, raster-format geographic information system in a pioneer application to the east half of the Tucson quadrangle, an area of over 10,000 square kilometers.

Rock contains discontinuities at all scales. These discontinuities make rock behave in a complex way. This dissertation discusses a new approach to underground design based on the theory of rock fracture mechanics. Due to the important role of coal for energy in the US, coal which is classified as a weak rock was selected as a test material. The mechanism of deformation and failure of coal obtained from the McKinley Mine and the Twenty Mile Coal Mine were studied by observing the distributions of length, orientation, and spacing of the pre-existing as well as stress-induced cracks. Different types of laboratory tests were employed to observe the different scales of cracks and to obtain different types of crack information. The crack information is dependent on the scale used. The cracks propagate along the intersections of the pre-existing cracks, and both extensile and shear crack growth occurs depending on the direction of the load relative to the bedding planes. An analytical model that takes into account both shear and extensile crack growth was developed to predict the nonlinear stress-strain behavior of coal including strain-hardening and strain-softening. In order to solve problems with complex boundary conditions, this model was implemented into two and three dimensional finite element programs. The implementation involved a series of modifications that took into account stress transformation, transverse isotropy, and the calculation of the effective elastic moduli due to cracks. Simple examples were taken to verify the results of the numerical analyses.