Quantitative Kriging Neighbourhood Analysis for the Mining Geologist ù A Description of the Method With Worked Case Examples

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 ækriging neighbourhoodÆ 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. In particular, a neighbourhood that is too restrictive can result in serious conditional biases. The methodology for quantitatively assessing the suitability of a kriging neighbourhood involves some simple tests (which we call æQuantified Kriging Neighbourhood AnalysisÆ or QKNA) that are well established in the geostatistical literature. The authors argue that QKNA is a mandatory step in setting up any kriging estimate, including one used for conditioning a simulation. Kriging is commonly described as a æminimum variance estimatorÆ but this is only true when the neighbourhood is properly defined. Arbitrary decisions about searches are highly risky, because the kriging weights are directly related to the variogram model, data geometry and block/sample support involved in the kriging. The criteria to look at when evaluating a particular kriging neighbourhood are the following: the slope of the regression of the ætrueÆ block grade on the æestimatedÆ block grade; the weight of the mean for a simple kriging; the distribution of kriging weights themselves (including the proportion of negative weights); and the kriging variance. Outside of the technical geostatistical literature, there is little in the published domain to describe the nature of QKNA and no practical presentation of case examples. In this paper we attempt to redress this by setting out the calculations required for QKNA and defining some approaches to interpreting the results. Several practical worked mining case examples are also given. Finally some comments are made on using the results of QKNA to assist with block size selection, choice of discretisation and mineral resource classification decisions.