Coregionalizations

The concepts of variogram and various variances, which so far have been defined for the regionalization of one variable, can be generalized to spatial coregionalizations of several variables. In a lead-zinc deposit, for example, the regionalizations of the grades in lead, $Z_1(/boma{x})$, and in zinc $Z_2(/boma{x})$, are characterized by their respective variograms $2/gamma_1(/boma{h})$ and $2/gamma_2(/boma{h})$. However, these two variabilities are not independent of each other and we can define a cross-variogram for lead and zinc:

Once the cross-variogram is calculated, we can form the matrix

called the coregionalization matrix. This coregionalization matrix can then be used to estimate the unknown lead grade $Z_l(/boma{x})$ from neighboring lead and zinc data.

Sometimes, two different types of data relating to the same metal can be used in block estimation. One set may be the precise data taken from core samples, while the other may be imprecise data taken from cuttings and blast-holes. A study of coregionalization of these two types of data will determine the proper weights to be assigned to them during evaluation.