Discussion - Ultimate Pit Limit Design Methodologics Using Computer Models - The State of the Art – Kim, Young C. – Technical Papers, MINING ENGINEERING, Vol. 30, No. 10, October 1978, pp. 1454-1459

Professor Kim's excellent review article1 on ultimate pit planning contains a statement of the apparently widely held but incorrect belief that "kriging provides information on the confidence limits around the estimate which no other extension technique is capable of supplying." If a geostatistical approach is valid, there are several good reasons for using kriging but uniquely provided confidence limits is not among them. If kriging is possible, then confidence limits can be calculated for any other linear estimate. Kriging is the procedure which finds the weighing coefficients which minimize the estimation variance [ ] is the variance of blocks like the one being estimated. wi is the covariance of the estimated block and the i-th sample. oij is the covariance of the i-th sample and the j-th sample. Ai is the weighing coefficient for the i-th sample. N is the number of samples. The formula for estimation variance can also be used to calculate confidence limits on blocks estimated by any linear combination of sample grades including: 1) Polygons a. Hole nearest block centroid is assigned weight 1. All other holes are assigned weight 0. b. Polygonal area weighing. The samples are assigned weights directly proportional to their polygonal areas of influence within the block. The weights sum to 1. 2) Inverse distance weighing. The samples are assigned weights directly proportional to the reciprocal of their distance to some power from the block centriod. The weights sum to 1. Often only holes nearer than a certain distance and/or the nearest hole in each octant is considered. If there is an antisotropy to the ore body, an elliptical transformation often gives more accurate results. The most popular inverse distance weighing function is inverse squared distances (IDS). 3) Simple average. All samples within a certain distance are assigned the same weights which sum to 1. As an example of the applicability of the above formula to any linear estimate an internal verification on copper grade of 665 blast holes on the 1040 bench at Utah's Island Copper mine is presented. Internal verification is simple and applicable to non-linear estimates as well. Any sample (drill hole, bulk, trench, or chip) is dropped out, the value of the dropped sample estimated and compared with the actual value. If this is done for all samples, a measure of confidence limits is obtained. Internal verification is used in Cominco's MEPS system4 and in the BLUEPACK system.5 Comparison of block values against estimates697 is not dissimilar to internal verification. Results of the internal verification are presented below: