Cokriging of additive log-ratios (alr) for grade estimation in iron ore deposits

Iron ore products are defined by their iron and contaminant grades and also by the granulometric partitions. Data from iron ore deposits constitute compositional data, involving a vector of variables adding up to a constant sum given by the mass balance among granulometric partitions or among chemical species in each granulometric fraction. The closed sums lead to spurious correlations and to a negative bias condition. This condition leads to estimates that do not satisfy the balances and estimates that take negative values or do not belong to the interval of values of the original data. Classic geostatistical methodologies do not take these facts into account and the common practices force the sum through determining one variable by difference, distributing the sum error or using an intrinsic corregionalization model and substituting of the negative values by valid ones. In this paper, cokriging of additive log-ratios (alr), a transformation developed for compositional data, is presented as an alternative methodology to estimate grades in iron ores, in presence of multiple correlated variables with a closed sum. Results obtained through this methodology are better than the ones obtained by direct cokriging of the original data, leading to positive estimates, all in the original data interval and satisfying the considered constant sums, without post-processing.

Compositional data; cokriging; iron ore; corregionalization