Quantitative kriging neighbourhood analysis for the mining geologist — A description of the method with worked case examples / Количественный анализ методом кригинга (методом ближайшего соседа) для рудничного геолога - описание метода с рабочими примерами

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. 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 ‘Quantified Kriging Neighbourhood Analysis’ 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 ‘minimum variance estimator’ 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:
1. the slope of the regression of the ‘true’ block grade on the ‘estimated’ block grade;
2. the weight of the mean for a simple kriging;
3. the distribution of kriging weights themselves (including the proportion of negative weights); and
4. the kriging variance. <...>