A machine learning-based thermometer, barometer and hygrometer for magmatic liquids

Experimentally calibrated models to recover pressures, temperatures and water contents of magmas, are widely used in igneous petrology. However, large errors, especially in barometry, limit the capacity of these models to resolve the architecture of crustal igneous systems. Here we apply machine learning to a large experimental database to calibrate new regression models that recover P-T-H2O of magmas based on either melt composition or melt composition plus associated phase assemblage. The method is applicable to compositions from basalt to rhyolite, pressures from 0.2 to 14.5 kbar, temperatures of 675-1425°C, and H2O contents up to 15 wt.%. Testing and optimisation of the model show that pressures can be recovered with root-mean-square-error (RMSE) of 1.2 and 1.0 kbar for the melt-only and melt-phase assemblage models respectively. Errors on temperature estimates are 22-25°C and 1.0-1.3 wt.% for H2O. Our findings demonstrate that melt chemistry is a reliable recorder of magmatic variables. This is a consequence of the relatively low thermodynamic variance of natural magma compositions despite their relatively large number of constituent oxide components. We apply our model to three contrasting cases with well-constrained geophysical information: Mount St. Helens volcano in the Cascades arc (USA), the Altiplano-Puna Volcanic Complex (APVC) in Chile, and the Askja caldera in Iceland. Dacite whole-rocks from Mount St Helens erupted 1980-1986 yield magma source pressures of 3.3-4.3 kbar in excellent agreement with experimental petrology, seismic tomography, magnetotelluric images and earthquake hypocentres. Melt inclusions and matrix glasses record lower pressures, consistent with magma crystallisation during ascent. Glasses and phase assemblages for three large magnitude APVC eruptions (Atana, Toconao, Purico ignimbrites) yield magma storage pressures and temperatures of 1.7-2.4 kbar and 726-789°C, in excellent agreement with previous thermobarometry. While these pressures are shallower than the underlying Altiplano-Puna Magma Body (APMB), rhyolite whole-rock compositions indicate pressures equivalent to the top of the APMB. We suggest that extraction of rhyolitic liquids from the APMB mush, followed by crystallisation at shallower depth preceded each eruption. Magma reservoir depth estimates for historical eruptions from Askja match the location of seismic wave speed anomalies. We show that Vp/Vs anomalies at 5-10 km depth correspond to hot (~1000°C) rhyolite source regions, while basaltic magmas (~1150°C) were stored at 15 km depth under the caldera. These examples illustrate how our model can link petrology and geophysics to better constrain the architecture of volcanic feeding systems. Our model (MagMaTaB) is accessible through a user-friendly web application (https://igdrasil.shinyapps.io/MagMaTaBv23/).