On the use of the Semivariogram to Detect Sources of Non-Stationarity in Mineral Grades

Trends in the mean and/or variance are a longstanding challenge in mineral resource modeling. Geologic modeling and/or grade domaining are often employed to account for heterogeneities in mineral grades; however, this is only practical up to a certain point since the number of data available for reliable model construction can be severely reduced. In such cases, trends remain present in certain geologic/grade domains and directly impact the modeling methodology; the trend must either be handled explicitly or a suitable approach is adopted to implicitly account for it. This is highly dependent on understanding the source of the trend. We propose an approach that detects the source of non-stationarity, which is based on quantifying the impact of non-stationarity in the mean and the variance via the semivariogram. By expanding the methodof- moments approximation of the semivariogram, we decompose the experimental semivariogram is into three terms: 1) trend in mean component, 2) trend in variance component and 3) stationary component. We can then assess the source of trend by calculating the contribution of each component at every lag. Two cases are presented to illustrate this tool. Firstly, a synthetic reference model is simulated and different trend patterns are added; the influence of these patterns in the experimental semivariogram calculation are analyzed and discussed. Secondly, a real dataset is considered where the impact due to the presence of trends in the mean and variance are assessed. The results of this paper reveal the semivariogram to be a tremendously powerful tool in determining the source of the trend. This insight may be useful in the selection of a suitable modeling approach for resource estimation.