The definition of the search neighbourhood in kriging can have a significant impact on the resulting estimates. Stationary domains are usually estimated using a unique search strategy for the entire domain. However, the use of a global search neighbourhood ignores the local variations within each domain, i.e. all blocks are interpolated using a unique search strategy. In this paper, localised kriging parameter optimisation (LKPO) is proposed as an alternative methodology that considers the best 'local estimation parameter settings' block by block. The optimisation process is based on absolute error minimisation obtained in crossvalidation. Two datasets are presented, the first is a synthetic mineral deposit (2D) and the second is a gold deposit (3D). A wide variety of validation checks show that the use of local kriging parameters significantly improves the grade estimation, obtaining more precise and accurate results than the methodologies currently available in the geostatistical literature.
Kriging methods require parameters to define search strategy (kriging neighbourhood). These parameters affect the precision and accuracy of its estimates. Frequently, the choice of these parameters is merely subjective. Some practitioners prioritise estimates that lead to models with a reduced smoothing effect or a regression slope as close as possible to one. However, it is prevalent to use the same kriging neighbourhood or search strategy for all blocks estimated within a stationary domain. This study presents a contribution that challenges this concept by using a block-by-block optimisation approach focused on the localised kriging parameter optimisation (LKPO) methodology. A comparative study is carried out, and some of the metrics analysed include the kriging efficiency and the slope of regression (typical in optimising methodologies in the mining industry). The results indicate that the LKPO methodology provides more accurate and precise estimates than those based on a global kriging neighbourhood.
The inclusion of grade uncertainty for multivariate mineral deposits is of great importance for the correct management of subsequent decisions involved in mining planning. Mapping grade uncertainties allows maximization of profit and resource extraction. In this article, the co-simulation turning band algorithm is applied with the aim of predicting multivariate grade uncertainties. Moreover, a probabilistic analysis in long term mining sequencing is proposed in order to select the best given grade scheduling uncertainty derived from the simulations. A case study in a phosphate mine shows that the correlation of co-simulated variables honors the original data and there is an improvement in the project by an increase in Net Present Value (NPV) planning considering grade uncertainties. A comparison is performed with the results derived from the selected schedule and the results using the model based on kriged grades.
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