Caroline Hasler Anthony Fuentes Andrew Tholt Leah E. Morgan Paul R. Renne Jack N. Carter 2025 <p><span>The K/Ar and&nbsp;</span>⁴⁰<span>Ar/</span>³⁹<span>Ar geochronometers are based on the naturally occurring radionuclide&nbsp;</span>⁴⁰<span>K. Their precision and accuracy are limited by uncertainties on the&nbsp;</span>⁴⁰<span>K decay constants and, in the case of the&nbsp;</span>⁴⁰<span>Ar/</span>³⁹<span>Ar geochronometer, the isotopic composition of neutron fluence monitors. To address these limitations, we introduce a Bayesian calibration of the&nbsp;</span>⁴⁰<span>K decay scheme. We formulate robust priors for all model parameters including partial&nbsp;</span>⁴⁰<span>K decay constants,&nbsp;</span>²³⁸<span>U and&nbsp;</span>²³⁵<span>U decay constants, and age offset parameters to account for phenomena that can perturb apparent U-Pb and&nbsp;</span>⁴⁰<span>Ar/</span>³⁹<span>Ar ages. We then harness a set of complementary&nbsp;</span>⁴⁰<span>Ar/</span>³⁹<span>Ar,&nbsp;</span>²³⁸<span>U/</span>²⁰⁶<span>Pb, and&nbsp;</span>²³⁵<span>U/</span>²⁰⁷<span>Pb data from well- characterized geological samples with ages from 1.919 ka to 2000 Ma to derive Bayesian estimates of the&nbsp;</span>⁴⁰<span>K decay constants. Posterior values for the partial&nbsp;</span>⁴⁰<span>K decay constants are&nbsp;</span><span class="math"><span id="MathJax-Element-1-Frame" class="MathJax_SVG" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><msub is=&quot;true&quot;><mi is=&quot;true&quot;>&amp;#x3BB;</mi><msup is=&quot;true&quot;><mrow is=&quot;true&quot;><mi is=&quot;true&quot;>&amp;#x3B2;</mi></mrow><mo is=&quot;true&quot;>-</mo></msup></msub></math>"><span class="MJX_Assistive_MathML">λ_β-</span></span></span><span>= (4.9252&nbsp;</span><span class="math"><span id="MathJax-Element-2-Frame" class="MathJax_SVG" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mo is=&quot;true&quot;>&amp;#xB1;</mo></math>"><span class="MJX_Assistive_MathML">±</span></span></span><span>&nbsp;0.0054)&nbsp;</span><span class="math"><span id="MathJax-Element-3-Frame" class="MathJax_SVG" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mo is=&quot;true&quot;>&amp;#xD7;</mo></math>"><span class="MJX_Assistive_MathML">×</span></span></span><span>&nbsp;10</span>⁻¹⁰<span>&nbsp;yr</span>⁻¹<span>,&nbsp;</span><span class="math"><span id="MathJax-Element-4-Frame" class="MathJax_SVG" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><msub is=&quot;true&quot;><mi is=&quot;true&quot;>&amp;#x3BB;</mi><msup is=&quot;true&quot;><mrow is=&quot;true&quot;><mi is=&quot;true&quot;>&amp;#x3B2;</mi></mrow><mo is=&quot;true&quot;>+</mo></msup></msub></math>"><span class="MJX_Assistive_MathML">λ_β+</span></span></span><span>&nbsp;= (5.6658&nbsp;</span><span class="math"><span id="MathJax-Element-5-Frame" class="MathJax_SVG" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mo is=&quot;true&quot;>&amp;#xB1;</mo></math>"><span class="MJX_Assistive_MathML">±</span></span></span><span>&nbsp;0.1543)&nbsp;</span><span class="math"><span id="MathJax-Element-6-Frame" class="MathJax_SVG" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mo is=&quot;true&quot;>&amp;#xD7;</mo></math>"><span class="MJX_Assistive_MathML">×</span></span></span><span>&nbsp;10</span>⁻¹⁵<span>&nbsp;yr</span>⁻¹<span>,&nbsp;</span><span class="math"><span id="MathJax-Element-7-Frame" class="MathJax_SVG" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><msub is=&quot;true&quot;><mi is=&quot;true&quot;>&amp;#x3BB;</mi><msup is=&quot;true&quot;><mrow is=&quot;true&quot;><mi mathvariant=&quot;italic&quot; is=&quot;true&quot;>EC</mi></mrow><mrow is=&quot;true&quot;><mo is=&quot;true&quot;>&amp;#x2217;</mo></mrow></msup></msub></math>"><span class="MJX_Assistive_MathML">λ_EC0</span></span></span><span>&nbsp;= (5.7404&nbsp;</span><span class="math"><span id="MathJax-Element-8-Frame" class="MathJax_SVG" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mo is=&quot;true&quot;>&amp;#xB1;</mo></math>"><span class="MJX_Assistive_MathML">±</span></span></span><span>&nbsp;0.0053)&nbsp;</span><span class="math"><span id="MathJax-Element-9-Frame" class="MathJax_SVG" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mo is=&quot;true&quot;>&amp;#xD7;</mo></math>"><span class="MJX_Assistive_MathML">×</span></span></span><span>&nbsp;10</span>⁻¹¹<span>&nbsp;yr</span>⁻¹<span>, and&nbsp;</span><span class="math"><span id="MathJax-Element-10-Frame" class="MathJax_SVG" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><msub is=&quot;true&quot;><mi is=&quot;true&quot;>&amp;#x3BB;</mi><msub is=&quot;true&quot;><mrow is=&quot;true&quot;><mi mathvariant=&quot;italic&quot; is=&quot;true&quot;>EC</mi></mrow><mn is=&quot;true&quot;>0</mn></msub></msub></math>"><span class="MJX_Assistive_MathML">λ_EC0</span></span></span><span>= (4.9060&nbsp;</span><span class="math"><span id="MathJax-Element-11-Frame" class="MathJax_SVG" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mo is=&quot;true&quot;>&amp;#xB1;</mo></math>"><span class="MJX_Assistive_MathML">±</span></span></span><span>&nbsp;0.2942)</span><span class="math"><span id="MathJax-Element-12-Frame" class="MathJax_SVG" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mo is=&quot;true&quot;>&amp;#xD7;</mo></math>"><span class="MJX_Assistive_MathML">×</span></span></span><span>&nbsp;10</span>⁻¹³<span>&nbsp;yr</span>⁻¹<span>&nbsp;(uncertainties reported at the 68 % (1&nbsp;</span><span class="math"><span id="MathJax-Element-13-Frame" class="MathJax_SVG" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mi is=&quot;true&quot;>&amp;#x3C3;</mi></math>"><span class="MJX_Assistive_MathML">σ</span></span></span><span>) credible interval). These combine to a total&nbsp;</span>⁴⁰<span>K decay constant&nbsp;</span><span class="math"><span id="MathJax-Element-14-Frame" class="MathJax_SVG" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><msub is=&quot;true&quot;><mi is=&quot;true&quot;>&amp;#x3BB;</mi><mrow is=&quot;true&quot;><mi mathvariant=&quot;italic&quot; is=&quot;true&quot;>tot</mi></mrow></msub></math>"><span class="MJX_Assistive_MathML">λ_tot</span></span></span><span>= (5.5042&nbsp;</span><span class="math"><span id="MathJax-Element-15-Frame" class="MathJax_SVG" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mo is=&quot;true&quot;>&amp;#xB1;</mo></math>"><span class="MJX_Assistive_MathML">±</span></span></span><span>&nbsp;0.0054)</span><span class="math"><span id="MathJax-Element-16-Frame" class="MathJax_SVG" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mo is=&quot;true&quot;>&amp;#xD7;</mo></math>"><span class="MJX_Assistive_MathML">×</span></span></span><span>&nbsp;10</span>⁻¹⁰<span>&nbsp;yr</span>⁻¹<span>. Model estimates of the&nbsp;</span>²³⁸<span>U and&nbsp;</span>²³⁵<span>U decay constants are statistically indistinguishable from those reported by&nbsp;</span><span class="anchor-text-container"><span class="anchor-text">Jaffey</span></span><span class="anchor-text-container"><span class="anchor-text"> et al. (1971)</span></span><span>. Posterior values of the&nbsp;</span>⁴⁰<span>K decay constants and the&nbsp;</span>⁴⁰<span>Ar*/</span>⁴⁰<span>K isotopic composition of Fish Canyon sanidine (FCs) define a K/Ar FCs age of 28.183&nbsp;</span><span class="math"><span id="MathJax-Element-17-Frame" class="MathJax_SVG" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mo is=&quot;true&quot;>&amp;#xB1;</mo></math>"><span class="MJX_Assistive_MathML">±</span></span></span><span>&nbsp;0.017 Ma (1&nbsp;</span><span class="math"><span id="MathJax-Element-18-Frame" class="MathJax_SVG" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mi is=&quot;true&quot;>&amp;#x3C3;</mi></math>"><span class="MJX_Assistive_MathML">σ</span></span></span><span>). Significantly, Bayesian calibrated&nbsp;</span>⁴⁰<span>Ar/</span>³⁹<span>Ar ages align with astronomically tuned ages throughout the Cenozoic and with&nbsp;</span>²³⁸<span>U/</span>²⁰⁶<span>Pb and&nbsp;</span>²³⁵<span>U/</span>²⁰⁷<span>Pb ages in the Mesozoic, Paleozoic, and Proterozoic, as well as having comparable precision to the&nbsp;</span>²³⁸<span>U/</span>²⁰⁶<span>Pb method. Thus, Bayesian calibration of the 40 K decay scheme and the K/Ar age of FCs reconciles the&nbsp;</span>⁴⁰<span>Ar/</span>³⁹<span>Ar, U-Pb, and astronomical chronometers.</span></p> application/pdf 10.1016/j.gca.2025.03.024 en Elsevier Bayesian calibration of the 40K decay scheme with implications for 40K-based geochronology article