A Machine Learning-Based Thermobarometer for Magmatic Liquids

Abstract Experimentally calibrated models to recover pressures and temperatures 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 of magmas based on melt composition plus associated phase assemblage. The method is applicable to compositions from basalt to rhyolite, pressures from 0.2 to 15 kbar, and temperatures of 675°C to 1400°C. Testing and optimisation of the model with a filter that removes estimates with standard deviation above the 50th percentile show that pressures can be recovered with root-mean-square-error (RMSE) of 1.1 to 1.3 kbar and errors on temperature estimates of 21°C. Our findings demonstrate that, given constraints on the coexisting mineral assemblage, 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 two contrasting cases with well-constrained geophysical information: Mount St. Helens volcano (USA), and Askja caldera in Iceland. Dacite whole-rocks from Mount St Helens erupted 1980 to 1986, inferred to represent liquids extracted from cpx–hbl–opx–plag–mt–ilm mush, yield melt extraction source pressures of 5.1 to 6.7 kbar in excellent agreement with geophysical constraints. Melt inclusions and matrix glasses record lower pressures (0.7–3.8 kbar), consistent with magma crystallisation within the upper reaches of the imaged geophysical anomaly and during ascent. Magma reservoir depth estimates for historical eruptions from Askja match the location of seismic wave speed anomalies. Vp/Vs anomalies at 5 to 10 km depth correspond to hot (~990°C) rhyolite source regions, while basaltic magmas (~1120°C) were stored at 7 to 17 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/MagmaTaBv4/).