Application of Cokriging in iron ore evaluation: Iron ore quadrangle - Brazil

The size distribution is a very important item in iron ore evaluation, The first geostatistical works carried out for Brazilian iron ore mining companies were based on methods applied to independent variables. Cokriging is a multivariate geostatistical method which minimizes the estimation variance by using a multivariate variogram or covariance model and a multivariate data set. The aim of this work is to compare two Cokriging methods with different sets of non-bias conditions by making use of a cross-validation exercise. The first Cokriging (ck1) was done using the traditional conditions: sum of primary weights must equal to one and sum of the secondary weights must equal to zero. For the second Cokriging (ck2) only one non-bias condition is used: sum of all weights equals to one. The data base is represented by the percentage in weight of three granulometric class size: class 1 (size fraction between 50 mm and 6.3 mm), class 2 ( size fraction between 6.3 mm and 0.15 mm) and class 3 (size fraction lesser than 0.15 mm). The percentages in weight (w(i); i = 1 to 3) are considered as dependent variables and realizations of stationary random functions in space (w(i)(x)). Thus, one needs to assert the coherence in the sample data base (sum of w(i)(x) is equal to 100%) to estimate w(i)*(v) The Linear Model of Coregionalization denotes a good fit for this case and it is appropriate for the data at hand. The coherence between size-class weight percentage was preserved by both Cokriging estimations, i,e. the sum of w(i)*(v)(ck) is equal to 100. A good improvement of conditional non-bias was obtained by using the second Cokriging method (ck2), particularly when the estimator is associated to high Cokriging variance values.