Mixture modeling of multi-component data sets with application to ion-probe zircon ages

A method is presented for detecting multiple components in a population of analytical observations for zircon and other ages. The procedure uses an approach known as mixture modeling, in order to estimate the most likely ages, proportions and number of distinct components in a given data set. Particular attention is paid to estimating errors in the estimated ages and proportions. At each stage of the procedure several alternative numerical approaches are suggested, each having their own advantages in terms of efficiency and accuracy. The methodology is tested on synthetic data sets simulating two or more mixed populations of zircon ages. In this case true ages and proportions of each population are known and compare well with the results of the new procedure. Two examples are presented of its use with sets of SHRIMP ²³⁸U²⁰⁶Pb zircon ages from Palaeozoic rocks. A published data set for altered zircons from bentonite at Meishucun, South China, previously treated as a single-component population after screening for gross alteration effects, can be resolved into two components by the new procedure and their ages, proportions and standard errors estimated. The older component, at 530 ± 5 Ma (2σ), is our best current estimate for the age of the bentonite. Mixture modeling of a data set for unaltered zircons from a tonalite elsewhere defines the magmatic ²³⁸U²⁰⁶Pb age at high precision (2σ ± 1.5 Ma), but one-quarter of the 41 analyses detect hidden and significantly older cores.