An investigation on the impact of low-grade material in the selection of a Global Mean for Simple Kriging on an economic reef horizon at South Deep Gold Mine

Abstract

In this research study, the impact of using low-grade samples, here also referred to as lowgrade material, in the estimation of the global mean for an economic reef horizon at South Deep Gold Mine is investigated, where, due to sparse data density, Ordinary Kriging would not be optimal. Simple Kriging, which is reliant on a global mean, is thus the estimation method of choice. The global mean, therefore, plays an important role and due to the positively skewed nature of the probability distribution of the gold grades, the estimation of a global mean poses a problem. Three grade zones have been identified on the Modderfontein B bottom band auriferous reef, namely a high-, a medium-, and a low-grade zone. From each of these zones one grade domain is selected for the investigation. For each of these domains three bottom cut values were then defined relative to the average grade of each domain. The bottom cut defined the threshold at which low-grade material was removed before declustering at an optimal block size. The research study showed that low-grade material does impact the estimate of the global mean of a domain, inclusion of low-grades results in low mean grade estimates. As expected, the global mean estimate increased as the bottom cutoff grades increased for all the domains. The research study also showed specifically for the low-grade domain investigated, that the low-grade samples should be removed before declustering, additional research into other low-grade domains would be required to verify if this holds true. It was found that the low-grades have a greater impact on the local mean estimate for individual declustered blocks than on the declustered average grade estimate of the domain. Where the number of samples within the individual declustered blocks is small, it is recommended that a Sichel-t estimator for the mean grade be considered. The grade estimates produced in this research study were dissimilar to estimates used by South Deep, and although the grade differences were not excessive it produced significantly higher gold content estimates as the bottom cut-off grade increased. It follows that, if the low-grade material are indeed low-grade outliers, then the Mineral Resources could be underestimated. Two-parameter lognormal estimates of the global mean produced, for the three domains investigated, were found to be high compared to the global mean estimates obtained using the bottom cut-off grades. Mineral Resource estimation was therefore not conducted using the lognormal estimates. It is further recommended that an investigation into other domains be conducted to potentially develop a structured methodology for determining a global mean estimate at South Deep Gold Mine. Different methodologies may be required for different domains.