Witwatersrand gold reef evaluation: The 'variancegram' tool
Journal of the Southern African Institute of Mining and Metallurgy
Geological and Geostatistical Services, Johannesburg, South Africa; Asfaltowa, Warsaw, Poland
The resolution with which the different categories of resources are forecast for Witwatersrand gold reefs should ideally tie in with block sizes that are optimal in terms of the variability structures of the reefs. A tool, called the 'variancegram', is proposed as a basis for block size choice. A variancegram is intrinsic to the particular reef and mine concerned. A further requirement is the ability to attach global confidence limits to weighted average estimates built up from combinations of local kriged estimates. Approximations to derive global kriging variances based on variables derived from local kriging deliver hugely inflated results if ordinary kriging is used, and markedly better, but not accurate, values if simple kriging is used. These approximations improve as the number of samples used in kriging each block is increased. It is shown that the behaviour of the different components of the global kriging variance with increasing number of samples, all differs, but they all link to the variancegram for the particular reef. The variancegram can thus be used to correct the different components to the values they would have had if all samples were used in kriging each block, and so deliver the 'correct' global kriging variance, even though only a limited number of samples were used in kriging each block. The desirability of having very stable solutions implemented in production systems is taken into account in the proposals. It is anticipated that the same variancegram findings will also hold for other densely sampled deposits, but this remains to be investigated. © The Southern African Institute of Mining and Metallurgy, 2014.
Classification (of information); Gold; Reefs; Confidence limit; Kriging; Number of samples; Ordinary kriging; Production system; Resources; Stable solutions; Weighted averages; Interpolation