Reply on RC2

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 at 1) “undoing” the systematic deviation from the idealized geometry and 2) quantifying the contribution of geometric uncertainty to the total uncertainty budget on 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 deviate from geometric models, we selected 267 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. We then compared the V, FT, and RFT calculated from 2D-microscopy measurements with those calculated from the ‘real’ 3D measurements. We find that 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 1s uncertainties on 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 yields 1s analytical and geometric uncertainties of 15–16 % on eU and 3–7 % on the corrected date. These geometric corrections and uncertainties are substantial and should not be ignored when reporting, plotting, and interpreting (U-Th)/He datasets. The Geometric Correction Method 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.