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. There exist at least 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, whereas the isochron age can be used to detect "parentless helium". The central age is the most accurate 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% (1se). The (U-Th)/He age equation can be visualized on a ternary diagram to illustrate that the alpha-ejection correction should be applied before, and not after age calculation, in order to avoid a partial linearization of the age equation. To facilitate the calculation of the central age, a web-based calculator is provided at \ttt{http://pvermees.andropov.org/central}