Truncated fractal frequency distribution of element abundance data: A dynamic model for the metasomatic enrichment of base and precious metals

The frequency distributions of elements in rocks and ore deposits do not conform to a universal scaling law, but vary in dependence of the mechanism of element enrichment. In the present contribution a dynamic model is proposed that describes element enrichments taking place by metasomatic processes causing the formation of hydrothermal ore deposits. It is shown that metasomatic element enrichment can result in a fractal distribution of element abundance data in the low concentration region with a smooth truncation at higher concentration values due to the existence of physical upper concentration limits imposed by the mineralogical nature of the ore. The developed model is tested on the basis of base and precious metal concentration data determined on diamond drill core samples collected from the Waterloo massive sulfide deposit, Australia. It is shown that the frequency distributions of Zn, Pb, Cu, and Ag conform relatively well to truncated power–law relationships as predicted by the model. In contrast, the frequency distribution of the Au data was found to be better described by the log-normal law, presumably due to syn-genetic processes of element redistribution that have not been modeled by the proposed dynamic model.