| Summary: | <p>Conventional Re–Os isochrons are based on mass spectrometric estimates of <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1" display="inline" overflow="scroll" dspmath="mathml"><mrow class="chem"><msup><mi/><mn mathvariant="normal">187</mn></msup><mi mathvariant="normal">Re</mi><msup><mo>/</mo><mn mathvariant="normal">188</mn></msup><mi mathvariant="normal">Os</mi></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="64pt" height="15pt" class="svg-formula" dspmath="mathimg" md5hash="ddb9b773837d7735adead78fc4c3577a"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gchron-3-415-2021-ie00001.svg" width="64pt" height="15pt" src="gchron-3-415-2021-ie00001.png"/></svg:svg></span></span> and <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M2" display="inline" overflow="scroll" dspmath="mathml"><mrow class="chem"><msup><mi/><mn mathvariant="normal">187</mn></msup><mi mathvariant="normal">Os</mi><msup><mo>/</mo><mn mathvariant="normal">188</mn></msup><mi mathvariant="normal">Os</mi></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="64pt" height="15pt" class="svg-formula" dspmath="mathimg" md5hash="421e33d94156b20892e5c16c5a214d7a"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gchron-3-415-2021-ie00002.svg" width="64pt" height="15pt" src="gchron-3-415-2021-ie00002.png"/></svg:svg></span></span>, which often exhibit
strong error correlations that may obscure potentially important geological complexity. Using an approach that is widely accepted in <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M3" display="inline" overflow="scroll" dspmath="mathml"><mrow class="chem"><msup><mi/><mn mathvariant="normal">40</mn></msup><mi mathvariant="normal">Ar</mi><msup><mo>/</mo><mn mathvariant="normal">39</mn></msup><mi mathvariant="normal">Ar</mi></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="49pt" height="15pt" class="svg-formula" dspmath="mathimg" md5hash="581fb8b0d6f0045e486f57fce7236dcc"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gchron-3-415-2021-ie00003.svg" width="49pt" height="15pt" src="gchron-3-415-2021-ie00003.png"/></svg:svg></span></span> and U–Pb geochronology, we here show that these error correlations are greatly reduced by applying a simple change of variables, using <span class="inline-formula"><sup>187</sup>Os</span> as a common denominator. Plotting
<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M5" display="inline" overflow="scroll" dspmath="mathml"><mrow class="chem"><msup><mi/><mn mathvariant="normal">188</mn></msup><mi mathvariant="normal">Os</mi><msup><mo>/</mo><mn mathvariant="normal">187</mn></msup><mi mathvariant="normal">Os</mi></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="64pt" height="15pt" class="svg-formula" dspmath="mathimg" md5hash="163d443ff8a7649d67a806a720d985f7"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gchron-3-415-2021-ie00004.svg" width="64pt" height="15pt" src="gchron-3-415-2021-ie00004.png"/></svg:svg></span></span> vs. <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M6" display="inline" overflow="scroll" dspmath="mathml"><mrow class="chem"><msup><mi/><mn mathvariant="normal">187</mn></msup><mi mathvariant="normal">Re</mi><msup><mo>/</mo><mn mathvariant="normal">187</mn></msup><mi mathvariant="normal">Os</mi></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="64pt" height="15pt" class="svg-formula" dspmath="mathimg" md5hash="6f78bb2a8c9e27671a471dc333df1b82"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gchron-3-415-2021-ie00005.svg" width="64pt" height="15pt" src="gchron-3-415-2021-ie00005.png"/></svg:svg></span></span> produces an
“inverse isochron”, defining a binary mixing line between an inherited
Os component whose <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M7" display="inline" overflow="scroll" dspmath="mathml"><mrow class="chem"><msup><mi/><mn mathvariant="normal">188</mn></msup><mi mathvariant="normal">Os</mi><msup><mo>/</mo><mn mathvariant="normal">187</mn></msup><mi mathvariant="normal">Os</mi></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="64pt" height="15pt" class="svg-formula" dspmath="mathimg" md5hash="5e04ab507fa52b57ee2d6400292c9012"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gchron-3-415-2021-ie00006.svg" width="64pt" height="15pt" src="gchron-3-415-2021-ie00006.png"/></svg:svg></span></span> ratio is given by the
vertical intercept, and the radiogenic <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M8" display="inline" overflow="scroll" dspmath="mathml"><mrow class="chem"><msup><mi/><mn mathvariant="normal">187</mn></msup><mi mathvariant="normal">Re</mi><msup><mo>/</mo><mn mathvariant="normal">187</mn></msup><mi mathvariant="normal">Os</mi></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="64pt" height="15pt" class="svg-formula" dspmath="mathimg" md5hash="d34f0c49855ba4bf898d1ddc6614ca52"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gchron-3-415-2021-ie00007.svg" width="64pt" height="15pt" src="gchron-3-415-2021-ie00007.png"/></svg:svg></span></span> ratio, which corresponds to the horizontal intercept. Inverse isochrons facilitate
the identification of outliers and other sources of data dispersion.
They can also be applied to other geochronometers such as the K–Ca
method and (with less dramatic results) the Rb–Sr, Sm–Nd and Lu–Hf
methods. Conventional and inverse isochron ages are similar for
precise datasets but may significantly diverge for imprecise ones. A
semi-synthetic data simulation indicates that, in the latter case, the
inverse isochron age is more accurate. The generalised inverse
isochron method has been added to the <code>IsoplotR</code> toolbox for
geochronology, which automatically converts conventional isochron
ratios into inverse ratios, and vice versa.</p>
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