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

<p>The conventional zircon (U–Th) <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M3" display="inline" overflow="scroll" dspmath="mathml"><mo>/</mo></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="8pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="e653eaf840568ee76bb20ba3bf368ae0"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gchron-6-199-2024-ie00004.svg" width="8pt" height="14pt" src="gchron-6-199-2024-ie00004.png"/></svg:svg></span></span> 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 (<span class="inline-formula"><i>V</i></span>), alpha-ejection correction (<span class="inline-formula"><i>F</i>_T</span>), equivalent spherical radius (<span class="inline-formula"><i>R</i>_FT</span>), effective uranium concentration (eU), and corrected (U–Th) <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M7" display="inline" overflow="scroll" dspmath="mathml"><mo>/</mo></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="8pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="36bd7baae116a5efc17e692d563c2b51"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gchron-6-199-2024-ie00005.svg" width="8pt" height="14pt" src="gchron-6-199-2024-ie00005.png"/></svg:svg></span></span> 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 <span class="inline-formula"><i>V</i></span>, <span class="inline-formula"><i>F</i>_T</span>, and <span class="inline-formula"><i>R</i>_FT</span> 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 <span class="inline-formula"><i>V</i></span>, <span class="inline-formula"><i>F</i>_T</span>, and <span class="inline-formula"><i>R</i>_FT</span> values for zircon, with one exception (<span class="inline-formula"><i>V</i></span> of ellipsoidal grains). Correction factors for this misestimation determined by regressing the 3D vs. 2D data range from 0.81–1.04 for <span class="inline-formula"><i>V</i></span>, 0.97–1.0 for <span class="inline-formula"><i>F</i>_T</span>, and 0.92–0.98 for <span class="inline-formula"><i>R</i>_FT</span>, depending on zircon geometry. Uncertainties (1<span class="inline-formula"><i>σ</i></span>) derived from the scatter of data around the regression line are 13 %–21 % for <span class="inline-formula"><i>V</i></span>, 5 %–1 % for <span class="inline-formula"><i>F</i>_T</span>, and 8 % for <span class="inline-formula"><i>R</i>_FT</span>, 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 <span class="inline-formula"><i>F</i>_T</span> uncertainty. Propagating these uncertainties into a real dataset (<span class="inline-formula"><i>N</i>=28</span> ZHe analyses) generates 1<span class="inline-formula"><i>σ</i></span> 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) <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M25" display="inline" overflow="scroll" dspmath="mathml"><mo>/</mo></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="8pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="64e3733ac81609367f37ca130d7132b9"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gchron-6-199-2024-ie00006.svg" width="8pt" height="14pt" src="gchron-6-199-2024-ie00006.png"/></svg:svg></span></span> He data and for including geometric uncertainty in eU and date uncertainties.</p>