Provenancing ancient materials with lead isotopes: overlap uncovered

Lead isotope analysis has been used to provenance metals such as lead, silver and bronze for many decades. Different approaches to interpret lead isotope ratios were proposed, and various limitations of the method have been discussed and addressed. Overlap in composition between different possible ore sources is always mentioned as a major limitation in lead isotope studies. However, it has never been comprehensively studied using a multivariate statistical approach. In this paper, the kernel density estimation (KDE) approach previously proposed by the authors is applied to calculate overlap between possible ore source regions. Firstly, the copper and lead ores of the same regions are compared, to assess if they are consistent and thus can be combined to increase sample size for provenance studies. Secondly, the pair-wise overlap between all the mining regions is calculated to determine if the distinction can actually be made between those ore fields. The use of one-dimensional KDE's is very effective for calculation and assessment of the overlap between ore sources. This study argues that merging the lead and copper ore data might increase the reliability of a region's KDE's in most cases, but the overlap should be assessed beforehand. Furthermore, the study provides useful tools to verify for every pair of possible ore sources if it is theoretically possible to discriminate between them, and to what extent.