Statistical Methods for Mineral Models of Drill Cores

University essay from KTH/Matematisk statistik

Abstract: In modern mining industry, new resource efficient and climate resilient methods have been gaining traction. Commissioned efforts to improve the efficiency of European mining is further helping us to such goals. Orexplore AB's X-ray technology for analyzing drill cores is currently involved in two such project. Orexplore AB wishes to incorporate geostatistics (spatial statistics) into their analyzing process in order to further extend the information gained from the mineral data. The geostatistical method implemented here is ordinary kriging which is an interpolation method that, given measured data, predicts intermediate values governed by prior covariance models. Ordinary kriging facilitates prediction of mineral concentrations on a continuous grid in 1-D up to 3-D. Intermediate values are predicted on a Gaussian process regression line, governed by prior covariances. The covariance is modeled by fitting a model to a calculated experimental variogram. Mineral concentrations are available along the lateral surface of the drill core. Ordinary kriging is implemented to sequentially predict mineral concentrations on shorter sections of the drill core, one mineral at a time. Interpolation of mineral concentrations is performed on the data considered in 1-D and 3-D. The validation is performed by calculating the corresponding density at each section that concentrations are predicted on and compare each such value to measured densities. The performance of the model is evaluated by subjective visual evaluation of the fit of the interpolation line, its smoothness, together with the variance. Moreover, the fit is tested through cross-validation using different metrics that evaluates the variance and prediction errors of different models. The results concluded that this method accurately reproduces the measured concentrations while performing well according to the above mentioned metrics, but does not outperform the measured concentrations when evaluated against the measured densities. However, the method was successful in providing information of the minerals in the drill core by producing mineral concentrations on a continuous grid. The method also produced mineral concentrations in 3-D that reproduced the measured densities well. It can be concluded that ordinary kriging implemented according to the methodology described in this report efficiently produces mineral concentrations that can be used to obtain information of the distribution of concentrations in the interior of the drill core. 

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