Subsurface geological characterization requires solving a classification problem to obtain a model of facies that is later populated with continuous properties. The classification problem, which consists of assigning a single category to any unsampled location based on observed data, is analyzed and solved in this thesis using geostatistical and machine learning tools. This research proposes an easy-to-implement heuristic technique that uses geostatistical criteria, such as correct classification of the observed data and good reproduction of the global proportions of categories, to obtain from the SVC algorithm a boundary classifier. This boundary is used to generate the facies model. The case studies show that the implementation of the proposed technique is highly automatic. The responses are comparable in terms of prediction accuracy to those obtained by the conventional geostatistical approach. / Mining Engineering

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After the scientific problem of interest is defined, collecting data is the first stage of any statistical analyses. The question of how large the sample should be is thus of great interest. In this thesis we demonstrate that in a geostatistical experiment determining the minimum sample size to achieve a certain precision of an estimator is often not possible due to inconsistencies of the estimators. This thesis is an empirical work extended from a manuscript (Gombay, 2010), which shows that the laws of large numbers may not hold under the spatial setting. It is demonstrated by a simulation study that the variance of the kriged mean converges to a non-zero constant as the sample size keeps increasing. It then followed by further investigations on the simple and ordinary kriging estimators. The conclusions arrived in this thesis lead for further research on the topic. / Statistics

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Medium and short term mine planning require models of mineral deposits that account for internal geological structures that permit scheduling of mine production at a weekly and monthly production periods. Modified kriging estimation techniques are used for accounting for such geologic structures. However, in the case of simulation, it is strongly linked to the use of sequential Gaussian simulation which has difficulties in reproducing internal geologic patterns. This thesis presents: (1) a set of tools to verify the impact of mean and variance trends in a domain; (2) a methodology for identifying highly variable sub-regions within domains; and (3) a simulation methodology that accounts for the internal structures in the domain required by medium and short term planning. Specifically, the simulation approach consists of: (1) moving the domain to a high dimensional space where the features of the internal structures in the domain are more stationary, (2) simulating the realizations via sequential Gaussian simulation, and (3) projecting the results to the initial dimensional space. / Mining Engineering

Rock physical properties are usually associated with important geologic features within mineral deposits and can be used to define the location, depth and size of the deposit, type of ore, or physical property contrast between the host and country rock. Geophysical surveys are sensitive to physical properties and therefore are widely used in mining exploration, especially in concealed terrains. The surveys can be performed at multiple scales, resulting in corresponding physical property datasets at different scales. Survey scale can vary from core or hand sample, involving few cubic centimeters, to regional-scale surveys providing information about physical property contrasts between distinct regional geological features. The understanding of the relationship between the physical property distributions with the sample volume (e.g. district, deposit, and drill-hole scale) is required where point scale physical property measurements are going to be consistent with measurements at larger volumetric scales during the integration of data for geophysical modeling The approach used to address the problem of understanding the scaling relations of physical properties, was achieved by considering them as second order stationary regionalized variables and then applying the random function formalism, provided by geostatistics theory. Geostatistics provide the required framework to characterize, quantify, model and link the spatial variability of the random variable at the different volumetric scales. The aim of this study is to apply geostatistics to effectively integrate data collected at several scales and bring knowledge to the understanding of the scaling relations of magnetic susceptibility. For this purpose, measurements of magnetic susceptibility available from Flin Flon copper-zinc district in Canada will be used. The data available at point scale were collected with hand portable magnetic susceptibility meter. The larger volumetric scale dataset were acquired using frequency domain electromagnetic instruments capable of measuring larger sample volumes, and then used to obtain magnetic susceptibility models using geophysical inversion algorithms. Once different scale models of magnetic susceptibility were available, quantification of the scaling relation using geostatistics, specifically variogram models and dispersion variance were determined. The understanding provided by the scaling analysis of the Flin-Flon magnetic data is applied to data from the Rio Blanco copper district in central Chile. Magnetic susceptibility measurements collected with a hand magnetic susceptibility meter on drill-core is integrated in larger scale volumes used for geophysical inversion modeling of regional scale airborne magnetic field measurements to recover magnetic susceptibility models. The methodology resulting from this application of geostatistics is used to address the problem of integrating multiple scales of physical property data in an effective way. The resulting physical property models capture the small-scale magnetic susceptibility variability observed and can guide larger-scale variability within geophysical inversion models. Establishing reliable statistical correlations between physical properties and rock units controlling ore within deposits are crucial steps leading predictive mine exploration tools. Any numerical modeling approach to establish these correlations should consider in some way the scaling nature of both physical property and ore content.

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