14 Feb 2024
 | 14 Feb 2024
Status: a revised version of this preprint is currently under review for the journal GChron.

(anchored) isochrons in IsoplotR

Pieter Vermeesch

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 'errochrons', 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, Chemical Geology 26.3-4: 183-195). The new algorithm offers the ability to attribute any excess dispersion to either the inherited component ('model 3a') or to diachronous closure of the isotopic system ('model 3b'). It provides an opportunity to anchor isochrons either to a fixed age, or to a fixed nonradiogenic composition. 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.

Pieter Vermeesch

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on gchron-2024-5', Donald Davis, 07 Mar 2024
    • AC1: 'Reply on RC1', Pieter Vermeesch, 09 Apr 2024
  • RC2: 'Comment on gchron-2024-5', John Rudge, 28 Mar 2024
    • AC2: 'Reply on RC2', Pieter Vermeesch, 09 Apr 2024
Pieter Vermeesch
Pieter Vermeesch


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Short summary
The age of some geological materials can be estimated from the ratio of certain radiogenic 'daughter' isotopes to their radioactive 'parent'. However, in many cases, the age estimation process is complicated by the presence of an inherited component of nonradiogenic daughter isotopes. This paper presents an improved algorithm to estimate the radiogenic and non-radiogenic components, either separately or jointly.