Mixing model parameters

In order to account for the three most important parameters indicative of sediment assimilation in NSB TTGs (high δ¹⁸O, high A/CNK, and low δ⁴⁴Ca) we chose to perform three end-member mixing calculations in A/CNK vs. δ¹⁸O and δ⁴⁴Ca vs. δ¹⁸O parameter space, with the results shown in Fig. 3 of the main text. We use (i) average shale^22,55 [δ¹⁸O = +15‰, A/CNK = 1.87, and [Ca] = 1 wt%] with δ⁴⁴Ca = −0.3‰ [the average value from shale standards SGR-1 and SBC-1^39,44,56,57], (ii) average TTG (δ¹⁸O = +6.5‰, A/CNK = 1.02, and [Ca] = 2 wt%) with δ⁴⁴Ca = −0.25‰ (this study), and (iii) average carbonate [δ¹⁸O = +26‰, A/CNK = 0.18, and [Ca] = 40 wt%²²] with δ⁴⁴Ca = −1.25‰ (corresponding to precipitation from BSE-like seawater). The A/CNK of average carbonate comes from a compilation of data for Phanerozoic limestones with available Al₂O₃, CaO, Na₂O, and K₂O concentrations (n = 908) from the Earthchem database (http://www.earthchem.org/portal downloaded June 26, 2020, Supplementary Data ⁵). We note that assimilation of average continental crust cannot lead to high enough A/CNK or δ¹⁸O values [shown in Fig. 3 of the main text^22,58] to explain the composition of our NSB samples.

We assume that (i) all three end-members have equivalent [O] concentrations, (ii) A/CNK mixes linearly, and that (iii) δ⁴⁴Ca is dependent on [Ca] and thus produces curved mixing lines in δ⁴⁴Ca vs. [Ca] parameter space (cf. straight mixing lines in ref. ⁵⁹). For NSB sample INO5003, we find that an assimilated sediment fraction (80% shale with 20% carbonates) of ~0.3 explains the A/CNK, δ¹⁸O, and δ⁴⁴Ca values, while sample INO5012 requires a sediment fraction of ~0.5 (95% shale with 5% carbonates). The mixing calculations yield final [Ca] concentrations for INO5003 and INO5012 of 4.0 and 2.5 wt%, respectively, which is moderately (but not grossly) higher than measured by Q-ICP-MS (Supplementary Data ¹), potentially suggesting that the average [Ca] used in our mixing models (for the TTG and/or shale end-members) may be slightly high. Lower [Ca] estimates for TTG and shale end-members would mainly serve to lower [Ca] in the resulting mixtures but would not lead to significant differences in the estimated sediment fractions (due to the overwhelming influence of carbonate [Ca] on δ⁴⁴Ca). The similar estimates for sediment fractions in both A/CNK vs. δ¹⁸O and δ⁴⁴Ca vs. δ¹⁸O space, however, suggest that our mixing models are relatively robust and that the estimated parameters (e.g., δ⁴⁴Ca of Eoarchean carbonates) are reasonable.