A practical method for assigning uncertainty and improving the accuracy of alpha-ejection corrections and eU concentrations in apatite (U–Th) ∕ He chronology

Abstract. Apatite (U–Th) / He (AHe) dating generally assumes that grains can be accurately and precisely modeled as geometrically perfect hexagonal prisms or ellipsoids in order to compute the apatite volume (V), alpha-ejection corrections (FT), equivalent spherical radius (RFT), effective uranium concentration (eU), and corrected (U–Th) / He date. It is well-known that this assumption is not true. In this work, we present a set of corrections and uncertainties for V, FT, and RFT aimed (1) at “undoing” the systematic deviation from the idealized geometry and (2) at quantifying the contribution of geometric uncertainty to the total uncertainty budget for eU and AHe dates. These corrections and uncertainties can be easily integrated into existing laboratory workflows at no added cost, can be routinely applied to all dated apatite, and can even be retroactively applied to published data. To quantify the degree to which real apatite deviates from geometric models, we selected 264 grains that span the full spectrum of commonly analyzed morphologies, measured their dimensions using standard 2D microscopy methods, and then acquired 3D scans of the same grains using high-resolution computed tomography (CT). We then compared our apatite 2D length, maximum width, and minimum width measurements with those determined by CT, as well as the V, FT, and RFT values calculated from 2D microscopy measurements with those from the “real” 3D measurements. While our 2D length and maximum width measurements match the 3D values well, the 2D minimum width values systematically underestimate the 3D values and have high scatter. We therefore use only the 2D length and maximum width measurements to compute V, FT, and RFT. With this approach, apatite V, FT, and RFT values are all consistently overestimated by the 2D microscopy method, requiring correction factors of 0.74–0.83 (or 17 %–26 %), 0.91–0.99 (or 1 %–9 %), and 0.85–0.93 (or 7 %–15 %), respectively. The 1σ uncertainties in V, FT, and RFT are 20 %–23 %, 1 %–6 %, and 6 %–10 %, respectively. The primary control on the magnitude of the corrections and uncertainties is grain geometry, with grain size exerting additional control on FT uncertainty. Application of these corrections and uncertainties to a real dataset (N=24 AHe analyses) yields 1σ analytical and geometric uncertainties of 15 %–16 % in eU and 3 %–7 % in the corrected date. These geometric corrections and uncertainties are substantial and should not be ignored when reporting, plotting, and interpreting AHe datasets. The Geometric Correction Method (GCM) presented here provides a simple and practical tool for deriving more accurate FT and eU values and for incorporating this oft neglected geometric uncertainty into AHe dates.