Short communication: Inverse isochron regression for Re–Os, K–Ca and other chronometers

Li, Yang; Vermeesch, Pieter

Conventional Re–Os isochrons are based on mass spectrometric estimates of inline-formula M1inlinescrollmathml chem normal 187 normal Re / normal 188 normal Os 64pt15ptsvg-formulamathimgddb9b773837d7735adead78fc4c3577a gchron-3-415-2021-ie00001.svg64pt15ptgchron-3-415-2021-ie00001.png and inline-formula M2inlinescrollmathml chem normal 187 normal Os / normal 188 normal Os 64pt15ptsvg-formulamathimg421e33d94156b20892e5c16c5a214d7a gchron-3-415-2021-ie00002.svg64pt15ptgchron-3-415-2021-ie00002.png , which often exhibit strong error correlations that may obscure potentially important geological complexity. Using an approach that is widely accepted in inline-formula M3inlinescrollmathml chem normal 40 normal Ar / normal 39 normal Ar 49pt15ptsvg-formulamathimg581fb8b0d6f0045e486f57fce7236dcc gchron-3-415-2021-ie00003.svg49pt15ptgchron-3-415-2021-ie00003.png and U–Pb geochronology, we here show that these error correlations are greatly reduced by applying a simple change of variables, using inline-formula187Os as a common denominator. Plotting inline-formula M5inlinescrollmathml chem normal 188 normal Os / normal 187 normal Os 64pt15ptsvg-formulamathimg163d443ff8a7649d67a806a720d985f7 gchron-3-415-2021-ie00004.svg64pt15ptgchron-3-415-2021-ie00004.png vs. inline-formula M6inlinescrollmathml chem normal 187 normal Re / normal 187 normal Os 64pt15ptsvg-formulamathimg6f78bb2a8c9e27671a471dc333df1b82 gchron-3-415-2021-ie00005.svg64pt15ptgchron-3-415-2021-ie00005.png produces an “inverse isochron”, defining a binary mixing line between an inherited Os component whose inline-formula M7inlinescrollmathml chem normal 188 normal Os / normal 187 normal Os 64pt15ptsvg-formulamathimg5e04ab507fa52b57ee2d6400292c9012 gchron-3-415-2021-ie00006.svg64pt15ptgchron-3-415-2021-ie00006.png ratio is given by the vertical intercept, and the radiogenic inline-formula M8inlinescrollmathml chem normal 187 normal Re / normal 187 normal Os 64pt15ptsvg-formulamathimgd34f0c49855ba4bf898d1ddc6614ca52 gchron-3-415-2021-ie00007.svg64pt15ptgchron-3-415-2021-ie00007.png 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 IsoplotR toolbox for geochronology, which automatically converts conventional isochron ratios into inverse ratios, and vice versa.

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Li, Yang / Vermeesch, Pieter: Short communication: Inverse isochron regression for Re–Os, K–Ca and other chronometers. 2021. Copernicus Publications.

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