HelioPlot, and the treatment of overdispersed (U–Th–Sm)/He data

More often than not, (U–Th–Sm)/He ages are overdispersed with respect to the formal analytical uncertainty. The Mean Square of the Weighted Deviates (MSWD) is a useful tool for assessing the amount of overdispersion. If the MSWD is significantly greater than one, the ages can be parameterised by a (log)normal distribution with two sources of variance, which can be iteratively solved using the method of maximum likelihood. The overdispersion of replicate (U–Th–Sm)/He ages is caused by the overdispersion of the underlying U–Th–Sm–He compositions, the geometric mean of which gives rise to the so-called ‘central age’. These compositions can be normalised to unity and parameterised by a multivariate logistic normal distribution with two sources of variance, which can be iteratively solved by a multivariate generalisation of the aforementioned age-averaging algorithm. Exact and asymmetric confidence intervals for the central age are obtained using a deterministic Bayesian algorithm. HelioPlot is a Java application developed for the purpose of plotting U–Th–(Sm)–He data on ternary diagrams and logratio plots that implements all these calculations. The program can be downloaded from http://pvermees.andropov.org/helioplot.