A Comparison of Indirect Lognormal and Discrete Gaussian Change Of Support Methods for Various Variogram Estimators

"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. IntroductionWhen reporting resource estimates,practitioners are required to follow generalstandards described in the NI43-101 (CIMguidelines), JORC, or SAMREC codes. One cangenerally recognize three main parts directlyrelated to the block model:•,Pre-processing: exploratory data analysis (EDA), domaining, capping, compositing, declustering, variography•,Processing: block size, neighbourhood, interpolation types (linear or nonlinear)•,Post-processing: classification, reporting.Pre-processing aims to simplify and strengthen the processing step. Ideally, domaining, capping. and compositing is aimed at defining a single homogenous population. During the processing phase, a common practice is to use a block size corresponding to the planned selective mining unit (SMU). In most precious metal deposits (gold, notably), the SMU size is frequently smaller than the recommended half data spacing (Journel and Huijbregts 1978), resulting in high estimation variance and either a high degree of smoothing if the regression slope is managed or a high degree of conditional bias if it is not. Most actual resource estimates are made using block sizes between one-quarter to one-sixth of the average data spacing, sometimes even smaller. In addition to the block size, the interpolation choices for the neighbourhood selection and interpolator (e.g. inverse distance (ID) or ordinary kriging) are often based on the Qualified Person’s (the QP) experience and some basic validation plots that often do not consider the conditional bias (e.g. trends or SWATHs plots, which are designed to compare two sets of population using a one-dimensional graph)."