40Ar/39Ar Eruption Age Estimation Via Bayesian Mixture Modeling

40Ar/39Ar geochronology is one of the most widely used methods for measuring geologic time, providing ages and duration estimates of geologic processes from historically recorded eruptions to some of the earliest events in the Solar System. As analytical precision has improved, single-crystal datasets, primarily from tephras, increasingly resolve geological complexity within individual samples. Here we focus on volcanic ejecta (i.e. tephra deposits and lavas), which record well-defined, discrete eruption events for which ages are sought. In many cases, not every crystal records the eruption age: some grains may record older or younger ages which have been biased by geological, analytical, and/or other processes. This complexity motivates treating single-crystal datasets as mixtures of distinct populations rather than as a single population to be averaged after filtering. Here, we present a Bayesian mixture model for estimating eruption ages from 40Ar/39Ar single-crystal datasets, which uses age, K/Ca, and percent radiogenic 40Ar as input data. The model represents each dataset as a mixture of eruption age, older, and younger components. For each analysis, its measured age and uncertainty are evaluated jointly with its K/Ca and percent radiogenic 40Ar to determine the probability that it belongs to each component. Eruption age, mixture proportions, and grain-level assignments are inferred simultaneously, eliminating the need to explicitly accept or reject analyses before calculating an age. The resulting eruption-age estimate therefore incorporates both analytical uncertainty and the uncertainty in identifying which grains record the eruption.