Three new ways to calculate average (U–Th)/He ages

Traditionally the “average” age of multiple (U–Th)/He analyses has been calculated as the arithmetic mean age. This paper presents three alternative methods: (a) in analogy with the fission track method, the pooled age is calculated by adding the respective U, Th and He abundances of several grains together, thereby generating one “synthetic” multi-grain measurement; (b) the isochron age is the slope of helium concentration versus present-day helium production; (c) the central age is computed from the geometric mean U–Th–He composition. Each of these methods is more appropriate than the arithmetic mean age in certain applications. The pooled age is useful for comparing single-grain with multi-grain analyses, while the isochron age can be used to detect “parentless helium”. The central age is the most accurate and statistically robust way to calculate a sample average of several single-grain analyses because U, Th and He form a ternary system and only the central age adequately captures the statistics of this compositional data space. Fortunately, the expected difference between the arithmetic mean age and the central age is relatively small, less than 1% if the external age reproducibility is better than 15% (1σ). Finally, the (U–Th)/He age equation is visualized on a ternary diagram to illustrate that the α-ejection correction should be applied before, and not after age calculation, in order to avoid a partial linearization of the age equation. Including Sm as a fourth parent element precludes a straightforward visualization of the age equation on a two-dimensional plot. Nevertheless, the pooled, isochron and central age methods can be easily generalized to the case of (U–Th–Sm)/He dating. To facilitate the calculation of the central age, a web-based calculator is provided at http://pvermees.andropov.org/central.