Fundamental Sampling Error and Sampling Precision in Resource Estimation – A Discussion

摘要

For the sampling of particulate materials in mineral exploration and mining, the fundamentalrnsampling error (FSE) introduced by Gy is a measure of the constitutional heterogeneity of thernsample lot and is expressed as the relative standard deviation of subsample grades of a particularrnmass. The FSE is presently regarded as an important indicator of quality for samples used inrnresource estimation. Constitutional heterogeneity describes an ideal state of heterogeneity withrnrespect to all constituents of the lot such that the fundamental error among subsamples of arnparticular mass is minimised.rnIn this paper, the term ‘sampling precision’ used in relation to mineral resource sampling usuallyrnrefers to a statistic based on the assay results drawn from pairs of separate subsample splits ofrnmultiple sample lots. The pairs of splits are extracted after the lots have been prepared by crushingrnand pulverising to meet specifi ed criteria of grain size and subsample mass. There is presently norngenerally accepted method of calculating the ‘sampling precision’ from such paired data but somernform of the relative standard deviation that is consistent with defi nition of the FSE is preferredrnhere. The work of Thompson and Howarth in the 1970s on geochemical analytical precision, whichrnhas been subjected to extensive examination and criticism by Stanley and Lawie (2007), and thatrnof Francois-Bongar?on since the 1990s forms the background to the discussion in the paper.rnA signifi cant aspect of the application of Gy’s sampling theory to sampling in gold deposits isrnthe requirement that the fundamental error be maintained at less than ±20 per cent. The mostrnimportant reason for this is to ensure that the effects of other sampling errors such as the groupingrnand segregation, and increment delimitation which can cause local and global biases in samplingrnare kept as small as possible.rnThis paper is focused mainly on the quality of sampling in gold deposits and looks at anrnalternative to the use of a constant sampling precision applied to a collection of lots with varyingrnaverage grade. A theoretical model for the FSE based on duplicate sampling is presented and thernsimulated results of the model are compared to practical outcomes of real duplicate pairs drawnrnfrom multiple sample lots. The goal of the work is to present a more informative analysis ofrnduplicate sample data from multiple lots which may allow a more informed view of the potentialrnfor bias generating errors during sample preparation and processing.