Capping and kriging grades with longtailed distributions
M Maleki, N Madani, X Emery
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.