Errorchrons and anchored isochrons in IsoplotR

Abstract

Isochrons are usually fitted by “York regression”, which uses a weighted least-squares approach that accounts for correlated uncertainties in both variables. Despite its tremendous popularity in modern geochronology, the York algorithm has two important limitations that reduce its utility in several applications. First, it does not provide a satisfactory mechanism to deal with so-called “errorchrons”, i.e. datasets that are overdispersed with respect to the analytical uncertainties. Second, York regression is not readily amenable to anchoring, in which either the slope or the intercept of the isochron is fixed based on some external information. Anchored isochrons can be very useful in cases where the data are insufficiently spread out to constrain both the radiogenic and non-radiogenic isotopic composition. This paper addresses both of these issues by extending a maximum likelihood algorithm that was first proposed by Titterington and Halliday (1979). The new algorithm offers the ability to attribute any excess dispersion to either the inherited component (“model 3a”) or diachronous closure of the isotopic system (“model 3b”). It provides an opportunity to anchor isochrons to either a fixed non-radiogenic composition or a fixed age. Last but not least, it allows the user to attach meaningful analytical uncertainty to the anchor. The new method has been implemented in IsoplotR for immediate use in Ar/Ar, Pb/Pb, U/Pb, Th/Pb, Rb/Sr, Sm/Nd, Lu/Hf, Re/Os, K/Ca, and U–Th–He geochronology.