Geostatistics and Machine Learning Applied to Recoverable Resources Assessment and Uncertainty Quantification

The thesis focuses on the assessment of recoverable resources and their uncertainty in mineral deposits. A proper mineral resources characterization and their associated uncertainty are fundamental in mining projects, especially at preliminary stages, where limited sample data is available, to decide whether to continue or abandon a project. Three approaches are proposed to address the main challenges identified in current practices for mineral resource assessment, namely the generation of non-smoothed predictions and the uncertainty quantification on recoverable resources for univariate and multi-element deposits. A series of comparisons against traditional geostatistical techniques are carried out to evaluate the suitability of the proposed approaches to be incorporated as part of current practices within the mining field. The first proposal is constrained kriging (CK), an approach that generates non-smoothed predictions of recoverable resources. The prediction performance is validated by using a synthetic dataset and two real case studies, including a gold deposit. CK outperforms ordinary kriging, which is the standard used in technical and statutory resource assessment reports, as it renders a better prediction of the tonnage, ore grade, and conventional benefit. Although CK yields results comparable to those of uniform conditioning, the latter does not directly localize the resources and relies on a strong assumption on the grade distribution. CK exhibits robustness under different sampling densities, and the predicted recoverable resources are not highly affected by the selected variogram parameters. However, even though CK may become an alternative to the traditional geostatistical approaches, it cannot provide an uncertainty assessment of the predicted recoverable resources. The use of supervised machine learning (ML) techniques is suggested to address the drawback of the previous method, i.e., the lack of uncertainty quantification while dealing with erratic experimental variograms. The basic idea is to provide an uncertainty quantification avoiding the definition of a unique variogram model as usually done with kriging or geostatistical simulation. To this end, numerous non-conditional grade simulations are generated with variogram model parameters defined in intervals of possible values. From each simulation, a reference deposit is used to determine the input variables, and the realizations establish the output variables (i.e., tonnage and confidence interval curves). The supervised learning is carried out employing the input-output variables to render predictive models, which can be subsequently applied to obtain the recoverable resources and their uncertainty using features extracted from the available data. Among the ML techniques, multiple linear regression (MLR) is deemed the most suitable approach since it provides similar results faster and easier compared to other ML techniques, such as artificial neural networks, in a synthetic study. MLR characterizes recoverable resources better than traditional geostatistical approaches, and as well as the discrete Gaussian model. Nevertheless, the latter model shows a relatively strong sensitivity to variations on the chosen variogram model and cannot provide an uncertainty assessment. The appropriate MLR capability to quantify uncertainty is obtained by using a correction function that allows the coverage probabilities to achieve the nominal probabilities for a set of defined cut-off grades. A multivariate extension of the ML approach is included as the third proposal, which allows assessing multi-element ore deposits characterized by several spatially correlated variables and deposits where contaminants can affect the recoverability and quality of the primary variable. This approach avoids the complex definition of a linear coregionalization model by utilizing intervals of possible values to generate admissible models. The proposed multivariate ML approach is validated using a lateritic nickel deposit, where the metallurgical processing of the primary variable (nickel grade) is restricted by a maximum threshold for the silica/magnesia ratio. A bivariate MLR training of nickel grade and silica/magnesia ratio is carried out employing tonnage surfaces. As a result, the multivariate ML approach provides accurate predictions and an uncertainty assessment of the recoverable resources of nickel and of the nickel constrained by the silica/magnesia ratio. Furthermore, complementary analyses validate the robustness and applicability of the ML approach. First, the resources of physical models that, a priori, do not exhibit a multivariate Gaussian distribution are properly assessed. This approach is able not only to incorporate the effect of the amount of data on the estimated confidence intervals, but also to adequately predict tonnage for resource categories (i.e., measured and indicated). Finally, the results indicate a precise quantification of the conventional benefit and provide credible confidence intervals on the benefit assessment. In addition, these confidence intervals are wider compared to those obtained for the tonnage function. Ultimately, the research contributes to proving the applicability of CK in the mining field, emphasizing its suitability when a localization of the resources is required while avoiding the smoothing effect of ordinary kriging. Moreover, the study provides novel and robust ML approaches to overcome subjective decisions behind the parameter definition to characterize the spatial structure in geostatistical approaches. The ML approaches are appropriate to evaluate univariate and multivariate ore deposits. Furthermore, the ML approaches can assess predicted resources uncertainty and reproduce the nominal confidence intervals. Overall, the three proposed approaches are recommended at initial stages of recoverable mineral resources evaluation because the limited amount of available data may be insufficient for the use of traditional geostatistical methods. It is expected that these approaches can improve the recoverable resources prediction and their uncertainty quantification to help make betterinformed decisions throughout mining projects evaluation.