Mineral prospectivity analysis is unstable to changes in pixel size

Abstract

In mineral prospectivity mapping, the spatial coordinates of mineral deposits and other geological features are often recorded originally in vector form, and converted to a grid of cells (a raster of pixels) for analysis. Although the results of the analysis clearly depend on the choice of pixel size, it is widely believed that, if pixel size is progressively reduced, results should converge to a stable value. However, we show that this is not true. Using a database of gold deposits in the Murchison region of Western Australia, the Weights of Evidence (WofE) contrast statistic $C$ was calculated for raster conversions with pixel widths varying from 5 km to 100 m, using the vector-to-raster conversion algorithms common in mainstream GIS packages. In response to even the slightest changes in pixel width, the calculated value of $C$ fluctuated by 1.5 units, and the calculated probability of a deposit fluctuated by a factor of 4.5. As pixel size was progressively reduced, the results did not converge. We investigate this instability phenomenon experimentally and theoretically, and establish that it could be widespread. It could arise in any form of prospectivity analysis (including logistic regression, machine learning and deep learning) where the explanatory variables are discontinuous. We have confirmed that it also occurs with logistic regression. Instability is primarily associated with deposit points which lie close to a discontinuity such as a feature boundary, and could be characterised as a failure to respect “ground truth” at the deposit location. Accordingly, instability can persist even with very small pixel sizes (as small as 3 m in the Murchison example). We propose a new algorithm for vector-to-raster conversion which respects ground truth, and produces results which converge rapidly as pixel size decreases. In the Murchison example, this algorithm provides stable results for pixel widths of 500 m or less. Our theoretical results predict the maximum error as a function of pixel width, and allow the geologist to select an appropriate pixel size for the data available. Potential fields of application include species distribution modelling and geospatial risk analysis.