Evaluating The Formation Pressure Of Diamond-Hosted Majoritic Garnets: A Machine Learning Majorite Barometer

Diamond-hosted majoritic garnet inclusions provide unique insights into the Earth's deep, and otherwise inaccessible, mantle. Compared with other types of mineral inclusions found in sub-lithospheric diamonds, majoritic garnets can provide the most accurate estimates of diamond formation pressures because laboratory experiments have shown that garnet chemistry varies strongly as a function of pressure. However, evaluation using a compilation of experimental data demonstrates that none of the available empirical barometers are reliable for predicting the formation pressure of many experimental majoritic garnets and cannot be applied with confidence to diamond-hosted garnet inclusions. On the basis of the full experimental data set, we develop a novel type of majorite barometer using machine learning algorithms. Cross validation demonstrates that Random Forest Regression allows accurate prediction of the formation pressure across the full range of experimental majoritic garnet compositions found in the literature. Applying this new barometer to the global database of diamond-hosted inclusions reveals that their formation occurs in specific pressure modes. However, exsolved clinopyroxene components that are often observed within garnet inclusions are not included in this analysis. Reconstruction of inclusions, in the 8 cases where this is currently possible, reveals that ignoring small exsolved components can lead to underestimating inclusion pressures by up to 7 GPa (similar to 210 km). The predicted formation pressures of majoritic garnet inclusions are consistent with crystallization of carbon-rich slab-derived melts in Earth's deep upper mantle and transition zone.