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Journal of the Southern African Institute of Mining and Metallurgy

On-line version ISSN 2411-9717

Abstract

MALEKI, M.; MADANI, N.  and  EMERY, X.. Capping and kriging grades with long-tailed distributions. J. S. Afr. Inst. Min. Metall. [online]. 2014, vol.114, n.3, pp. 255-263. ISSN 2411-9717.

Variogram analysis and kriging lack robustness in the presence of outliers and data with long-tailed distributions, which often arises when estimating grades in precious metal deposits. The capping technique, consisting of truncating the data to some top-cut grade, is widely used in order to mitigate the influence of the values in the upper tail of the distribution. However, this procedure omits part of the grade variability and is likely to provoke a bias in the estimates. To avoid these issues, a recently proposed approach is to decompose the grade of interest into three components (the truncated grade, a weighted indicator above the top-cut grade, and a zero-mean residual) and jointly estimate the truncated grade and the indicator by cokriging. This approach is attractive as it provides unbiased grade estimates, allows choosing the 'optimal' top-cut value, and essentially works with truncated and indicator data, thus avoiding the use of outlying values for calculating sample variograms and performing spatial interpolation. This work presents an application of this approach to a disseminated gold deposit that has been identified through exploration drilling. The effect of using an indicator covariate is assessed through leave-one-out cross-validation, by comparing the grade estimates with the true grades and with the grade estimates obtained with the conventional capping approach, which considers only the truncated grade as the variable of interest. As a result, cokriging the truncated grade and the indicator above top-cut grade outperforms the conventional capping approach, yielding significantly more accurate estimates. A few complementary guidelines are provided for validating the model hypotheses and for the implementation of cokriging

Keywords : Top-cut model; high values; outliers; cokriging; indicator.

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