Detrital zircon age distributions in Bayes-Hilbert spaces

A growing number of researchers in the Earth Science community use the information provided by the UPb ages of detrital zircon in sedimentary environments, be these modern (sediments) or ancient (sedimentary or metasedimentary rocks). This information is key to understanding detritus's past and present flow on Earth and its attendant geological implications. An essential component of the investigation concerning detrital zircon age distributions (DZD) and their bearing on several sedimentological, tectonic, geodynamic, paleogeographic, or climatic issues is to compare DZD from different samples. Much theoretical and empirical research has been devoted to ascertaining how to best compare and measure the dissimilarity/distance between DZDs. This ongoing endeavour has generated a variety of metrics and statistical procedures to perform such tasks. In this contribution, a metric based on the Aitchison distance to measure the dissimilarity of any given set of DZD (samples represented by density functions) is presented. The Aitchison distance is used in the reference framework of the Bayes-Hilbert spaces, whose properties help to avoid some of the limitations of previously used metrics. The mathematical and methodological foundations are presented and illustrated with three geological examples taken from the recent literature, using both sedimentary rocks and recent sediments in different geological and geographical settings. The proposed approach results in a consistent statistical tool to determine whether a set of samples is likely to be derived from a common source or, at least, from indistinguishable sources based on DZD data alone.