A comparison of indirect lognormal and discrete Gaussian change of support methods for various variogram estimators

Abstract

In mineral resource evaluations, geostatistical methods known as global change of support allow prediction of the theoretical histogram and gradetonnage curves prior to interpolations or simulations of grades. Two methods commonly used by professionals to guide the choice of interpolation parameters and assess results are the discrete Gaussian model (DGM) and the indirect lognormal correction (IndLog). These models rely upon an estimate of the dispersion variance of the blocks, which is derived by numerical integration of the variogram model over a discretized block. Due to difficulties in obtaining well-formed traditional experimental variograms (especially in the presence of outliers and limited clustered data), many professionals prefer to use 'normalized' variograms such as correlogram (non-ergodic variogram), pairwise-relative, or variogram of the normal score transform. A series of simulations with different grade distributions and variogram models are used to assess the performances and robustness of the various variogram estimators with respect to the DGM and IndLog global change of support. Our results show that the traditional variogram, the correlogram, and normal score variogram have better performances, compared to pairwise, for both DGM and IndLog. Moreover, DGM provided better results than IndLog for the grade distributions that are not strictly lognormal. These findings provide valuable guides for geostatistics practitioners.