Comparisons of Geostatistical Approaches for Drillhole Site Selection

During the exploration phase of mine development, drilling location is in the hands of the geologist, and drilling is spread over the entire domain of the property or deposit boundary. During the mine planning and production phases, however, the mining engineer also needs to use the information obtained from the drilling program. Thus it is important that he/she have some input into the selection of the drillhole locations. Usually, when exploitation will center on one portion of the property for the immediate future, the mine engineer will want to have more of the drilling performed in this area. In the early stages, the purpose of the drilling was to make a decision concerning whether or not to develop a mine. Once the decision is made to proceed with this development, the mine engineer needs to know, with as much confidence as possible, the estimate of the ore grade at each location where mining will occur. This paper addresses the problem of drillhole location for the needs of the mining engineer. The goal is to compare a variety of approaches to drillhole location with a new approach developed by the author. This approach is based on the theory of geostatistics, with the estimation variance used as the quantitative measure of the confidence attained. The goal of the algorithm is to select those locations that minimize the estimation variance subject to constraints on the number of drillholes and the total cost of the drilling program. The kriging equations are used as another set of constraints. The resulting nonlinear optimization model is expressed in terms of binary (0 - 1) decision variables leading to a solution by the branch-and-bound procedure. The algorithm has been applied at a number of operating properties, and practical results and suggestions for implementation are provided.