Declustering Weights as a Measure of Average Sample Spacing, Applications in Mineral Resource Classification

Mineral resource classification is described in both the SME and CIM Standards for Mineral Resource Reporting. The CIM Standard states “… sampling … is sufficient to assume geological and grade or quality continuity between points of observation”, thus is a function of continuity and sample spacing. Continuity can be measured by use of a variogram model, but average sample spacing in three dimensions is more difficult to measure. The declustering algorithms provided with Geostatistics software, are commonly used to weight data for statistical analysis due to the sometimes-irregular spacing between drill holes during exploration. The weights are lower when data is closer, reflecting shared influence between samples, and higher for isolated samples reflecting independence. This paper will discuss the potential to use estimates of the declustering weight as an inverse relative measure for average sample spacing to gauge the confidence of the estimate independent of the single nearest sample. PROBLEM The classification of mineral resources and reserves has long been a combination of science, past experience of the estimator, judgment, and feeling. All of the definitions as presented in the standards of the various countries that participate in CRIRSCO are similar and deal with “sample points sufficiently closely spaced to support confidence in the continuity of …” This has been interpreted as the distance between the block estimated and the nearest sample (or samples). Geostatistics gave us the calculation of the estimation variance of the block, an implicit part of the calculation of weights in Kriging, to account for the confidence in the estimate. More recently, “Kriging Efficiency” has been used, however it is still dependent on the estimation error and responds in a similar fashion to the distance to the closest sample. It is also sensitive to the variogram nugget. Many of these methods result in very low distance/high confidence measures for blocks adjacent to a sample point with confidence decreasing (sometimes rapidly) as the distance to one nearest sample increases. This results in the “spotted dog” phenomenon where individual samples are surrounded by a higher classification near each sample decaying into pattern of decreasing confidence halos. In addition to the visual image of the spots, this raises the more practical problem of mine design when the classification changes between measured, indicated and inferred. This has led to ad hoc methods to classify material within the mining block so all of the stope receives that classification. These manual methods re both labor intensive and subjective. A popular technique is a multiple search method, where the estimator defines a minimum of number of samples from a minimum number of holes within a nested set of search distance that are used to classify estimates. These specified set of increasing distances are usually proportional to the variogram range. While this is generally a good technique and overcomes the spottiness of the closest sample or kriging error, it has certain issues including: