RecMin Variograms: Visualisation and Three-Dimensional Calculation of Variograms in Block Modelling Applications in Geology and Mining

Abstract

Variogram calculation is a fundamental tool for studying ore grade data in mineral deposits. It allows the discovery of hidden structures within the data and preferential directions of mineralization where the geological continuity is longer. The variogram allows us to classify samples and to define both the search radii for interpolation and the use of kriging as an interpolation and resource classification method. It is not difficult to use it in one dimension; complexity increases in two dimensions as the necessity to search for possible grade anisotropies in all directions arises. Three-dimensionally it is even more difficult to try to define the parameters of lag, bandwidth, and tolerances that define the data of the variogram calculation algorithm. There are rules of thumb to help in the development, but a trial-and-error approach is used in order to find enough sample pairs to allow the generation of variograms truly representative of the data. In this paper, two strategies are shown to help in variogram construction, the use of variogram maps and the graphical representation of the pair search areas (cones or pencils). The freeware tool RecMin Variograms has been developed and is freely available for download at its website; it is easy to learn and use. R code based on RGeostats libraries is used to check the operation and results of RecMin Variograms. Applying geostatistics to mineral deposits is essential to know the areas with the highest grades, thus allowing exact planning of future mining exploitation and minimizing mine footprint and environmental impact.