The Geometric Correction Method for zircon (U–Th) ∕ He chronology: correcting systematic error and assigning uncertainties to alpha-ejection corrections and eU concentrations

The conventional zircon (U–Th) $/$ He (ZHe) method typically uses microscopy measurements of the dated grain together with the assumption that the zircon can be appropriately modeled as a geometrically perfect tetragonal or ellipsoidal prism in the calculation of volume (V), alpha-ejection correction (F_T), equivalent spherical radius (R_FT), effective uranium concentration (eU), and corrected (U–Th) $/$ He date. Here, we develop a set of corrections for systematic error and determine uncertainties to be used in the calculation of the above parameters for zircon, using the same methodology as Zeigler et al. (2023) for apatite. Our approach involved acquiring both “2D” microscopy measurements and high-resolution “3D” nano-computed tomography (CT) data for a suite of 223 zircon grains from nine samples showcasing a wide range of morphology, size, age, and lithological source, calculating the V, F_T, and R_FT values for the 2D and 3D measurements and comparing the 2D vs. 3D results. We find that the values derived from the 2D microscopy data overestimate the true 3D V, F_T, and R_FT values for zircon, with one exception (V of ellipsoidal grains). Correction factors for this misestimation determined by regressing the 3D vs. 2D data range from 0.81–1.04 for V, 0.97–1.0 for F_T, and 0.92–0.98 for R_FT, depending on zircon geometry. Uncertainties (1σ) derived from the scatter of data around the regression line are 13 %–21 % for V, 5 %–1 % for F_T, and 8 % for R_FT, again depending on zircon morphologies. Like for apatite, the main control on the magnitude of the corrections and uncertainties is grain geometry, with grain size being a secondary control on F_T uncertainty. Propagating these uncertainties into a real dataset (N=28 ZHe analyses) generates 1σ uncertainties of 12 %–21 % in eU and 3 %–7 % in the corrected ZHe date when both analytical and geometric uncertainties are included. Accounting for the geometric corrections and uncertainties is important for appropriately reporting, plotting, and interpreting ZHe data. For both zircon and apatite, the Geometric Correction Method is a practical and straightforward approach for calculating more accurate (U–Th) $/$ He data and for including geometric uncertainty in eU and date uncertainties.