Using the proportion of barren samples as a proxy for minimum grade in a diamondiferous linear beach deposit - an application of the Nachman model

Abstract

�7.,!*-* Over the past 80 years, the Namibian diamondiferous marine placer has been studied extensively to develop solutions for mining and sampling challenges. The types of studies include the statistical modelling of the distributions of the stone counts per sample; investigating the relationship between geology and the grade distribution; assessing the quality potential of the entrapment of the available diamond pulse; using predetermined acceptability of barren samples (zero proportion (Z p) samples) to model distributions; optimal sample sizes; and more. During early-stage project evaluation it is more important to find out if a particular area is likely to be above a specific cut-off grade than to focus on sampling for the purpose of accurate resource estimation. Previous work using mixed Poisson and Sichel distributions to model the abundant onshore diamond data has been very successful in modelling the long- tailed nature of these linear beach deposits. The means of these distrib- utions are, however, sensitive to extreme values. Technical and cost constraints prevent a similar scale of sample collection in an adjacent, geologically equivalent, submerged beach environment. A method not sensitive to extreme values is thus required to make early-stage assessments of the likelihood that the grade of a particular target is above a minimum cut-off grade. The Nachman model describes the functional relationship between the mean population density and proportion of barren patches (Z