Comments on "The Estimation of Mineralized Veins: A Comparative Study of Direct and Indirect Approaches," by D. Marcotte and A. Boucher

Abstract

In their paper, Marcotte and Boucher (2001) cast some new light on the old problem of 2D estimation of vein-type deposits with thickness and grade of intercepts. Using a theoretical approach, some extensive simulation experiments and the Walker Lake data, they show that the direct approach (interpolation of grade at points on a regular grid) gives better estimates of the true grade at those points than the indirect approach (interpolation of grade x thickness or accumulation and interpolation of thickness) when there is some positive correlation between grade and thickness and that this better performance increases with the correlation of grade and thickness as well as the variability of both variables. We would like to bring some reservations to that conclusion by showing that even if direct point grade estimates are better than indirect ones, it is not necessarily true for block estimates and in particular for the estimated grade of the whole orebody itself. We have processed the well known Walker Lake data in a manner similar to Marcotte and Boucher (2001). Our limited sampling of the data set is slightly different: instead of the 318 data points mentioned by the authors, we use the set of 140 clusterized data points that is described in Deutsch and Journel (1992). Using the same variogram models as Marcotte and Boucher (2001), we ran an ordinary kriging of grade, thickness, and accumulation at the 2500 nodes of the grid 50 by 50. From true values at those points, we have the 2500 estimation errors of direct kriging of grade and those of indirect kriging of grade (kriged accumulation divided by kriged thickness). Median of absolute errors is 1.13 in the first case and 2.03 in the second case which confirms the superiority of the direct estimate [Marcotte and …