RECOVERING ‘PHANTOM MELTS’ WITH CUMULATE INVERSION USING MELTS THERMODYNAMIC MODELLING AND MACHINE LEARNING

Cumulates are the crystalline residue left behind after the fractional removal of liquid magma from a crystalline mush. This evacuated liquid might be emplaced plutonically elsewhere in the magmatic system or erupted on the surface as a volcanic rock, but it is no longer present in close association with the cumulate and generally cannot be sampled. Igneous petrologists have often tried to determine the composition of this ‘phantom melt’ from observations of the cumulate left behind, to better understand the architecture of the transcrustal magmatic systems where magmatic differentiation takes place.

We built a cumulate inverter, a machine learning-assisted thermodynamic model that infers the composition of a cumulate’s conjugate melt. It relies on the principle that the liquid saturated at the solidus of the cumulate is identical to the liquid present at the cumulate-melt separation event at equal pressure, temperature, and fO₂, assuming the liquid and all the mineral phases were in equilibrium at the moment of separation. The inverter utilizes an artificial neural network (ANN) barometer to infer the pressure of the cumulate-melt separation event. At this inferred pressure, we use rhyolite-MELTS 1.2.0 to find the solidus temperature, at which the infinitely small fraction of liquid produced is taken to be the conjugate ‘phantom melt’ from which the cumulate was derived.

Our model is self-consistent: it reproduces evacuated ‘phantom’ melts from cumulates generated from MELTS simulations at unknown pressure and temperature with small errors. We report some Standard Errors of Estimate (SEE) of the model: 257 bars in Pressure; 25.2˚C in Temperature; 4.5 wt% in SiO₂; 1.13 wt% in CaO; 1.30 wt% in Al₂O₃; and 0.29 wt% in MgO. Our current and future work focuses on extending the idealized model to more realistic cases where fewer phases are present, where the compositions of cumulate phases have analytical errors, and where the minerals may not satisfy the assumption of perfect equilibrium with a single liquid at a single condition.

Acknowledgments to Peter Kelemen for asking a question, years ago, that eventually led to this work.