Ordinary kriging and non-linear geostatistical estimators are now well accepted methods in mining grade control and mine resource estimation. Kriging is also a necessary step in the most commonly used methods of conditional simulation used in the mining industry. In both kriging and conditional simulation, the search volume or ‘kriging neighbourhood’ is defined by the user. The definition of this search can have a very significant impact on the outcome of the kriging estimate or the quality of the conditioning of a simulation.

Geostatistics, which can be de¯ned as the tools for studying and predicting the spatial structure of georeferenced variables, have been mainly used in soil science during the past two decades. Since now, hundreds of geostatistical papers have been published on soil science issues (see bibliography ibid., this volume). The use of geostatistical tools in soil science is diverse and extensive. It can be for studying and predicting soil contamination in industrial areas, for building agrochemical maps at the ¯eld level, or even to map physical and chemical soil properties for a global extent. The users of the output maps are going from soil scientists to environmental modelers. One of the speci¯city of geostatistical outputs is the assessment of the spatial accuracy associated to the spatial prediction of the targeted variable. The results which are quantitative are then associated to a level of con¯dence which is spatially variable. The spatial accuracy can then be integrated into environmental models, allowing for a quantitative assessment of soil scenarios. <...>

A requirement in geostatistical modeling is to find an appropriate and stable variogram. The traditional variogram is sensitive to outliers and sparse data. A number of robust alternatives have been proposed. Although the correlogram, indicator variogram and normal scores variograms sometimes work, the pairwise relative variogram is a remarkably robust estimator of the true underlying spatial structure. The variogram is adjusted by the squared mean of each data pair. A challenge in the interpretation of the pairwise relative variogram is that the sill of the pairwise relative variogram has not been well documented. The goal of this paper is to understand the sill of the pairwise relative variogram in order to standardize it for improved interpretation. <...>