Minimum/maximum autocorrelation factors applied to grade estimation

There are many situations in the mining industry where grade estimation of multiple correlated variables is required. The resulting model is expected to reproduce the data correlation, but there is no guarantee that the correlation observed among data will be reproduced by the model if the variables are independently estimated by kriging, and the correlation is not explicitly taken into account. The best geostatistical approach to address this estimation problem is to use co-kriging, which requires both cross and direct covariance modeling of all variables. However, the co-kriging method is labor-intensive when the problem involves more than three attributes. An alternative is to decorrelate the variables and estimate each one independently, using, for instance, the minimum/maximum autocorrelation factors (MAF) approach. This method involves the application of a linear transformation to the correlated variables, transforming the original data into a space where they are uncorrelated. The resulting transformed data can be individually estimated using kriging, avoiding the use of the linear model of coregionalization. Once the kriging has been performed, the MAF estimates are back-transformed to the original data space, re-establishing their correlation.The methodology is illustrated in a case study where there are two variables with correlation coefficient, rho = -0.98. The MAF transformation was applied in combination with ordinary kriging (herein denoted as KMAF). Co-kriging was performed to provide a benchmark for comparing the results obtained through KMAF. The results obtained by co-kriging and KMAF showed less than 1 % average deviation between the two block models.