Arithmetic methods for exploring archaeological source provenance using geochemistry – A reply to Pearce et al.

In this reply, we respond to the comment by Pearce et al. regarding our recently proposed arithmetic method for assessing geochemical similarity between lithic artefacts and potential source outcrops. We thank the authors for their critique, which highlights three opportunities for methodological refinement. We agree that issues relating to analytical precision and numerical rounding, certified reference material selection, and the weighting of geochemical variables warrant further consideration. We note, however, that many aspects of our work have been mischaracterised. Both the title and wider narrative running through the comment imply that our study advocates the use of geochemical similarity calculations in isolation from petrographic and other geological evidence. As we demonstrate, this is incorrect. In fact, we explicitly rejected such an approach and instead presented the method as an exploratory tool to be used alongside other data. We also show how some of the criticisms made by the authors are inconsistent with practices adopted in their own studies, including source provenance interpretations based primarily on geochemical datasets. We defend the use of trace element/Zr ratios for silcrete provenancing, discuss the rationale behind element selection in our worked examples, and clarify our treatment of compatible and incompatible elements in igneous rocks. Using case studies, including investigations into the provenance of Mediterranean volcanic artefacts and the Altar Stone at Stonehenge, we illustrate problems arising from the use of bivariate plots for source determination – as recommended by Pearce et al. – and highlight the value of multivariate approaches. We also point out inconsistencies in the authors’ use of a “total petrography” approach. We conclude that our arithmetic method remains a useful and adaptable framework for provenance assessment when applied critically alongside complementary geological and archaeological evidence.