A Top-Cut Model for Deposits with Heavy-Tailed Grade Distribution

Abstract

In some ore deposits, the grade distribution is heavy-tailed and high values make the inference of first- and second-order statistics nonrobust. In the case of gold data, high values are usually cut and the block estimation is performed using truncated grades. With this method, a part of the deposit is omitted, resulting in a potential bias on resources figures. Ad-hoc corrections can be applied on the final figures to take into account the tail of the grade distribution, but no theoretical guidelines are available. A geostatistical model has been developed to handle high values based on the assumption that for high grade zones, the only tangible information is the geometry. The grade variable z can be split into three parts: the truncated grade ($\operatorname{Min} (z, z_{\mathrm{e}})$ where z _e is the top-cut grade), a weighted indicator above top-cut grade (1{z≥z _e}), and a residual. Within this framework, the residual is poorly structured, and in most cases is a pure nugget-effect. Moreover, it has no spatial correlation with the truncated grade and the indicator above top-cut grade. This decomposition makes the variographic study more robust because variables (indicator and truncated grade) do not keep high grade values. The underlying hypotheses can be tested on experimental indicator variograms and the top-cut grade can be justified. Finally, the estimation is based on a truncated grade and indicator cokriging. The model is applied to blast holes from a gold deposit and on a simulated example. Both cases illustrate the benefits of keeping the high values in the estimation process via an appropriate mathematical model.