A practical method for assigning uncertainty and improving the accuracy of alpha-ejection corrections and eU concentrations in apatite (U–Th) ∕ He chronology
<p>Apatite (U–Th) <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M2" display="inline" overflow="scroll" dspmath="mathml"><mo>/</mo></math><span><svg:svg xmlns:s...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2023-05-01
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| Series: | Geochronology |
| Online Access: | https://gchron.copernicus.org/articles/5/197/2023/gchron-5-197-2023.pdf |
| _version_ | 1797256759666016256 |
|---|---|
| author | S. D. Zeigler J. R. Metcalf R. M. Flowers |
| author_facet | S. D. Zeigler J. R. Metcalf R. M. Flowers |
| author_sort | S. D. Zeigler |
| collection | DOAJ |
| description | <p>Apatite (U–Th) <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M2" 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="527256ea34e0af356380afd605ccefc0"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gchron-5-197-2023-ie00003.svg" width="8pt" height="14pt" src="gchron-5-197-2023-ie00003.png"/></svg:svg></span></span> 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 (<span class="inline-formula"><i>V</i></span>),
alpha-ejection corrections (<span class="inline-formula"><i>F</i><sub>T</sub></span>), equivalent spherical radius
(<span class="inline-formula"><i>R</i><sub>FT</sub></span>), effective uranium concentration (eU), and corrected (U–Th) <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M6" 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="073414a2b77546d8d5847ae97897d626"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gchron-5-197-2023-ie00004.svg" width="8pt" height="14pt" src="gchron-5-197-2023-ie00004.png"/></svg:svg></span></span> He
date. It is well-known that this assumption is not true. In this work, we
present a set of corrections and uncertainties for <span class="inline-formula"><i>V</i></span>, <span class="inline-formula"><i>F</i><sub>T</sub></span>, and <span class="inline-formula"><i>R</i><sub>FT</sub></span>
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 <span class="inline-formula"><i>V</i></span>, <span class="inline-formula"><i>F</i><sub>T</sub></span>, and
<span class="inline-formula"><i>R</i><sub>FT</sub></span> 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
<span class="inline-formula"><i>V</i></span>, <span class="inline-formula"><i>F</i><sub>T</sub></span>, and <span class="inline-formula"><i>R</i><sub>FT</sub></span>. With this approach, apatite <span class="inline-formula"><i>V</i></span>, <span class="inline-formula"><i>F</i><sub>T</sub></span>, and
<span class="inline-formula"><i>R</i><sub>FT</sub></span> 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 <span class="inline-formula">1<i>σ</i></span>
uncertainties in <span class="inline-formula"><i>V</i></span>, <span class="inline-formula"><i>F</i><sub>T</sub></span>, and <span class="inline-formula"><i>R</i><sub>FT</sub></span> 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 <span class="inline-formula"><i>F</i><sub>T</sub></span> uncertainty. Application of these corrections
and uncertainties to a real dataset (<span class="inline-formula"><i>N</i>=24</span> AHe analyses) yields <span class="inline-formula">1<i>σ</i></span>
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 <span class="inline-formula"><i>F</i><sub>T</sub></span>
and eU values and for incorporating this oft neglected geometric
uncertainty into AHe dates.</p> |
| first_indexed | 2024-04-24T22:26:51Z |
| format | Article |
| id | doaj.art-218fa82ae20241d09e5e411edc9c4d9e |
| institution | Directory Open Access Journal |
| issn | 2628-3697 2628-3719 |
| language | English |
| last_indexed | 2024-04-24T22:26:51Z |
| publishDate | 2023-05-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Geochronology |
| spelling | doaj.art-218fa82ae20241d09e5e411edc9c4d9e2024-03-19T22:35:39ZengCopernicus PublicationsGeochronology2628-36972628-37192023-05-01519722810.5194/gchron-5-197-2023A practical method for assigning uncertainty and improving the accuracy of alpha-ejection corrections and eU concentrations in apatite (U–Th) ∕ He chronologyS. D. ZeiglerJ. R. MetcalfR. M. Flowers<p>Apatite (U–Th) <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M2" 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="527256ea34e0af356380afd605ccefc0"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gchron-5-197-2023-ie00003.svg" width="8pt" height="14pt" src="gchron-5-197-2023-ie00003.png"/></svg:svg></span></span> 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 (<span class="inline-formula"><i>V</i></span>), alpha-ejection corrections (<span class="inline-formula"><i>F</i><sub>T</sub></span>), equivalent spherical radius (<span class="inline-formula"><i>R</i><sub>FT</sub></span>), effective uranium concentration (eU), and corrected (U–Th) <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M6" 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="073414a2b77546d8d5847ae97897d626"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gchron-5-197-2023-ie00004.svg" width="8pt" height="14pt" src="gchron-5-197-2023-ie00004.png"/></svg:svg></span></span> He date. It is well-known that this assumption is not true. In this work, we present a set of corrections and uncertainties for <span class="inline-formula"><i>V</i></span>, <span class="inline-formula"><i>F</i><sub>T</sub></span>, and <span class="inline-formula"><i>R</i><sub>FT</sub></span> 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 <span class="inline-formula"><i>V</i></span>, <span class="inline-formula"><i>F</i><sub>T</sub></span>, and <span class="inline-formula"><i>R</i><sub>FT</sub></span> 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 <span class="inline-formula"><i>V</i></span>, <span class="inline-formula"><i>F</i><sub>T</sub></span>, and <span class="inline-formula"><i>R</i><sub>FT</sub></span>. With this approach, apatite <span class="inline-formula"><i>V</i></span>, <span class="inline-formula"><i>F</i><sub>T</sub></span>, and <span class="inline-formula"><i>R</i><sub>FT</sub></span> 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 <span class="inline-formula">1<i>σ</i></span> uncertainties in <span class="inline-formula"><i>V</i></span>, <span class="inline-formula"><i>F</i><sub>T</sub></span>, and <span class="inline-formula"><i>R</i><sub>FT</sub></span> 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 <span class="inline-formula"><i>F</i><sub>T</sub></span> uncertainty. Application of these corrections and uncertainties to a real dataset (<span class="inline-formula"><i>N</i>=24</span> AHe analyses) yields <span class="inline-formula">1<i>σ</i></span> 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 <span class="inline-formula"><i>F</i><sub>T</sub></span> and eU values and for incorporating this oft neglected geometric uncertainty into AHe dates.</p>https://gchron.copernicus.org/articles/5/197/2023/gchron-5-197-2023.pdf |
| spellingShingle | S. D. Zeigler J. R. Metcalf R. M. Flowers A practical method for assigning uncertainty and improving the accuracy of alpha-ejection corrections and eU concentrations in apatite (U–Th) ∕ He chronology Geochronology |
| title | A practical method for assigning uncertainty and improving the accuracy of alpha-ejection corrections and eU concentrations in apatite (U–Th) ∕ He chronology |
| title_full | A practical method for assigning uncertainty and improving the accuracy of alpha-ejection corrections and eU concentrations in apatite (U–Th) ∕ He chronology |
| title_fullStr | A practical method for assigning uncertainty and improving the accuracy of alpha-ejection corrections and eU concentrations in apatite (U–Th) ∕ He chronology |
| title_full_unstemmed | A practical method for assigning uncertainty and improving the accuracy of alpha-ejection corrections and eU concentrations in apatite (U–Th) ∕ He chronology |
| title_short | A practical method for assigning uncertainty and improving the accuracy of alpha-ejection corrections and eU concentrations in apatite (U–Th) ∕ He chronology |
| title_sort | practical method for assigning uncertainty and improving the accuracy of alpha ejection corrections and eu concentrations in apatite u th thinsp thinsp he chronology |
| url | https://gchron.copernicus.org/articles/5/197/2023/gchron-5-197-2023.pdf |
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