Machine Learning Thermobarometry for Biotite‐Bearing Magmas

Abstract

Abstract Biotite ( sensu lato ) is a widespread rock‐forming mineral in magmatic rocks that can be stable in a broad range of pressure and temperature, but appropriate biotite thermometers or barometers are lacking. Based on a collected experimental dataset ( n = 839, T = 625–1,325°C, P = 1–48 kbar) containing biotites that span a wide compositional range [e.g., Mg/(Mg + Fe) = 0–1, TiO 2 = 0–9 wt%], we have trained several machine learning algorithms for calibrating a biotite thermobarometer. Our evaluation on model performance reveals that the thermobarometry derived from extremely randomized trees is the best option, which returns coefficients of determination ( R 2 ) ≥0.97 for estimating both temperature and pressure using either biotite‐only or biotite + melt model. The model reliability were evaluated using three different approaches for the biotite‐only and biotite + melt thermobarometers respectively, including Monte Carlo cross‐validation (RMSEs are 65°C and 4.7 kbar, 38°C and 3.2 kbar, respectively), testing with independent test set (RMSEs are 54°C and 4.4 kbar, 35°C and 2.4 kbar, respectively), and error propagation from assumed analytical uncertainty (2*MAD are 54°C and 1.27 kbar, 10°C and 1.26 kbar, respectively). Quantified relative importance of involved components in the thermobarometers supports an intrinsic control of thermodynamics in the stability of biotite as a function of pressure and temperature. We applied the new biotite thermobarometer for biotite‐bearing andesitic, phonolitic and rhyolitic volcanic systems provide reliable constraints of temperature and pressure for magma storage, ascent, and evolution. We also offer a user‐friendly webpage for online performance of the thermobarometers ( https://lixiaoyan.shinyapps.io/Biotite_thermobarometer/ ).

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