Kriging parameter optimisation: global versus local search strategies

Abstract

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.

Localized kriging parameters optimization using local uncertainty

“…In addition, estimates with high SR values tend to produce excessive smoothing in the block model, and these values do not necessarily result in more precise estimates. As commented by Fonseca et al (2021), the SR is directly related to conditional bias produced in kriging. Nowak and Leuangthong (2016) is preferable to have conditionally biased estimates (higher variance) than conditionally unbiased estimates (SR closest to one).…”

“…On the other hand, Deutsch et al (2014) relate the bias-variance trade-off to the objective of the estimate. In the case of evaluating the tonnage of a mineral deposit above the cut-off grade, the authors recommend that conditionally biased estimates are preferable (apud Fonseca et al 2021).…”

“…all blocks within a stationary domain are interpolated using a unique search strategy. The second line of research is related to the Localized Kriging Neighbourhood Analysis – LKNA, Localized Kriging Parameter Optimization – LKPO and Localized Kriging Neighbourhood Optimization – LKNO (Coombes and Boamah 2015; Hundelshaussen et al 2018; Coombes et al 2020; Fonseca et al 2021) which seek to optimize the search strategy locally (each block of the entire block model is interpolated using the best search strategy). Although these methods use the same concept (optimization block by block), they all differ in the metric used in the optimization process.…”