Calculation of uncertainty in the (U–Th) ∕ He system - P. E. Martin; J. R. Metcalf; R. M. Flowers (Geochronology, 2023)
Although rigorous uncertainty reporting on (U–Th) /<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-5-91-2023-ie00004.svg" width="8pt" height="14pt" src="gchron-5-91-2023-ie00004.png"/></svg:svg> He dates is key for interpreting the expected distributions of dates within individual samples and for comparing dates generated by different labs, the methods and formulae for calculating single-grain uncertainty have never been fully described and published. Here we publish two procedures to derive (U–Th) /<svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="8pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="57ee8123d9c9aefcf23d9c7f6463c158"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gchron-5-91-2023-ie00005.svg" width="8pt" height="14pt" src="gchron-5-91-2023-ie00005.png"/></svg:svg> He single-grain date uncertainty (linear and Monte Carlo uncertainty propagation) based on input 4He, radionuclide, and isotope-specific FT (alpha-ejection correction) values and uncertainties. We also describe a newly released software package, HeCalc, that performs date calculation and uncertainty propagation for (U–Th) /<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-5-91-2023-ie00006.svg" width="8pt" height="14pt" src="gchron-5-91-2023-ie00006.png"/></svg:svg> He data. Propagating uncertainties in 4He and radionuclides using a compilation of real (U–Th) /<svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="8pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="880d1b22cfae9b4167ff115d05c6894c"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gchron-5-91-2023-ie00007.svg" width="8pt" height="14pt" src="gchron-5-91-2023-ie00007.png"/></svg:svg> He data (N=1978 apatites and 1753 zircons) reveals that the uncertainty budget in this dataset is dominated by uncertainty stemming from the radionuclides, yielding median relative uncertainty values of 2.9 % for apatite dates and 1.7 % for zircon dates (1 s equivalent). When uncertainties in FT of 2 % or 5 % are assumed and additionally propagated, the median relative uncertainty values increase to 3.5 % and 5.8 % for apatite dates and 2.6 % and 5.2 % for zircon dates. The potentially strong influence of FT on the uncertainty budget underscores the importance of ongoing efforts to better quantify and routinely propagate FT uncertainty into (U–Th) /<svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="8pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="539a58614ea8688159b8effbc6d3da8d"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gchron-5-91-2023-ie00008.svg" width="8pt" height="14pt" src="gchron-5-91-2023-ie00008.png"/></svg:svg> He dates. Skew is generally positive and can be significant, with ∼ 17 % of apatite dates and ∼ 6 % of zircon dates in the data compilation characterized by skewness of 0.25 or greater assuming 2 % uncertainty in FT. This outcome indicates the value of applying Monte Carlo uncertainty propagation to identify samples with substantially asymmetric uncertainties that should be considered during data interpretation. The formulae published here and the associated HeCalc software can aid in more consistent and rigorous (U–Th) /<svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="8pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="62d2c8208bbdf49afb8db19c9f7b6b50"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gchron-5-91-2023-ie00009.svg" width="8pt" height="14pt" src="gchron-5-91-2023-ie00009.png"/></svg:svg> He uncertainty reporting, which is also a key first step in quantifying whether multiple aliquots from a sample are over-dispersed, with dates that differ beyond what is expected from analytical and FT uncertainties.