Extended Data Fig. 10: Liquid f_O2.

Instantaneous/aggregated liquid f_O2 calculated for model runs. Differences between dotted lines (instantaneous liquids) and solid lines (aggregated liquids) demonstrate the homogenizing effect of melt aggregation. Although the residue, and thus instantaneous liquids, may reach very low f_O2 at high degrees of melting and high potential temperature, the aggregated liquids are less reduced owing to the influence of early, more oxidized liquids. Row 1 shows the raw pMELTS output, which calculates liquid f_O2 from the algorithm in ref. ⁷⁹. Depending on P–T conditions, instantaneous liquids (dotted lines) may have higher or lower f_O2 than the f_O2 returned by the solid-phase assemblage using the ‘alternative-fO2’ tag in pMELTS (residue**) (see Methods). We also calculate f_O2 values from pMELTS solid-phase output using spinel oxybarometry (residue*), as applied in the main-text figures. Because ref. ⁷⁹ is not well calibrated on our model compositions, we used two other methods for calculating liquid f_O2: (1) the compositional framework of ref. ⁸⁴ combined with the ref. ⁷⁹ pressure term (rows 2 and 4) and (2) the model of ref. ⁸⁷, which revises ref. ⁸⁴ and applies the pressure term of ref. ⁸⁸ (rows 3 and 5). These frameworks offer an improvement, although large uncertainties remain (see Methods). As well as uncertainty related to translation between melt composition and melt f_O2, we emphasize that neither model forces instantaneous liquids to be in f_O2 equilibrium with their residues (see Methods and ref. ²⁴ for discussion), despite that requirement in nature. Furthermore, calculated liquid f_O2 values from pMELTS and our empirical model are particularly uncertain at high T_p, at which Fe³⁺-partitioning and f_O2-compositional relationships are less well constrained. Finally, liquids in our empirical model do not extend beyond cpx-out and so contributions from shallow pressures are absent. Despite these caveats and uncertainties, we expect that high-temperature, garnet-field melting could lead to aggregated liquids that are slightly more reduced than aggregated liquids from spinel-field melting, although not as reduced as the peridotite residues observed in this study owing to melt aggregation and homogenization.