Tephra compositional data: are we doing it right?

Tephrochronology is often used for dating of natural archives and for correlation between study sites. Volcanic ashes (tephra) extracted from cores used for climate reconstructions function as common time-marker horizons and become anchor points in comparisons of age models from different studies. Given these uses, tephrochronology is well placed to help overcome the chronological challenges that hinder sufficiently precise dating of palaeoclimate records.

Tephras are identified based on their geographic and stratigraphic contexts, glass shard morphology, and geochemical composition. The geochemistry is most commonly analysed by electron probe microanalyser and presented as weight percentages of oxides of the nine or ten most abundant elements, often normalised to a 100 % total for ease of comparison. A simple exploration of such results and comparison to published data of previous tephra findings is usually enough for confident identification. However, compositional data of tephra findings from new studies continuously add to the complexity of tephrochronological investigations by increasing the amount of data available for comparison, including the addition of new potential candidates for identification. The increased likelihood of multiple candidates—sometimes with overlapping geochemistries—means that statistical data analyses are increasingly necessary.

Tephrochronologists have used principal component analysis and discriminant function analysis in situations needing statistical approaches, but these methods’ validity often requires certain assumptions not to be violated. A rarely considered example of such an issue is that compositional data suffers from the constant-sum constraint and must be converted by log-ratio transformations for some statistical analyses to function properly. As there is presently no consensus on a tephra compositional data curation procedure including log-ratio transformations, we have explored several variations and compared the results to see if a formal recommendation for such a procedure is relevant for the tephra community.