Geochemistry

Quantum mechanics

Zircon

Compositional data

Statistics

Mineralogy

Geochronology

Fraction (chemistry)

Geology

Physics

Organic chemistry

Mathematics

Concordance

Provenance

Internal medicine

Medicine

Chemistry

Cutoff

Abstract. Zircon U–Pb geochronology is a staple of crustal evolution studies and sedimentary provenance analysis. Constructing (detrital) U–Pb age spectra is straightforward for concordant 206Pb/238U and 207Pb/206Pb compositions. But unfortunately, many U–Pb datasets contain a significant proportion of discordant analyses. This paper investigates two decisions that must be made when analysing such discordant U–Pb data. First, the analyst must choose whether to use the 206Pb/238U or the 207Pb/206Pb date. The 206Pb/238U method is more precise for young samples, whereas the 207Pb/206Pb method is better suited for old samples. However there is no agreement which “cutoff” should be used to switch between the two. This subjective decision can be avoided by using single-grain concordia ages. These represent a kind of weighted mean between the 206Pb/238U and 207Pb/206Pb methods, which offers better precision than either of the latter two methods. A second subjective decision is how to define the discordance cutoff between “good” and “bad” data. Discordance is usually defined as (1) the relative age difference between the 206Pb/238U and 207Pb/206Pb dates. However, this paper shows that several other definitions are possible as well, including (2) the absolute age difference; (3) the common-Pb fraction according to the Stacey–Kramers mantle evolution model; (4) the p value of concordance; (5) the perpendicular log ratio (or “Aitchison”) distance to the concordia line; and (6) the log ratio distance to the maximum likelihood composition on the concordia line. Applying these six discordance filters to a 70 869-grain dataset of zircon U–Pb compositions reveals that (i) the relative age discordance filter tends to suppress the young age components in U–Pb age spectra, whilst inflating the older age components; (ii) the Stacey–Kramers discordance filter is more likely to reject old grains and less likely to reject young ones; (iii) the p-value-based discordance filter has the undesirable effect of biasing the results towards the least precise measurements; (iv) the log-ratio-based discordance filters are strictest for Proterozoic grains and more lenient for Phanerozoic and Archaean age components; (v) of all the methods, the log ratio distance to the concordia composition produces the best results, in the sense that it produces age spectra that most closely match those of the unfiltered data: it sharpens age spectra but does not change their shape. The popular relative age definition fares the worst according to this criterion. All the methods presented in this paper have been implemented in the IsoplotR toolbox for geochronology.

On the treatment of discordant detrital zircon U–Pb data