AI-GEOSTATS: Negative Kriging Weights & Estimates

[Colin Badenhorst]

I have recently carried out ordinary kriging for a ore reserve estimation exercise (using GSLIB), and noted that a very few of the grade estimates are negative (always a very small number e.g. 0.002 ppm). I have been able to trace this back to negative kriging weights, and would like some confirmation of my understanding of how this occurs.   My understanding is that samples lying close to the block centroids being estimated recieve a high weighting, and samples further away recieve a lower weighting. However, if the sample search neighbourhood is very large, and since the sum of the weights must equal 1, the samples lying furtherest away the centroid/s are assigned a very small negative weight, in order for the closer samples to maintain their higher weighting, and for the sum of the weights to equal 1.   Is my understanding of this "compensation" correct? Why wouldn't the weights for the furtherest samples be calculated by subtracting the weighting of the closer samples from 1, instead of compensating using negative weights afterwards?   Colin