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at 1atm and 1200°C. Kress & Carmichael, 1991 0.59 Studies using the standard glasses of Cottrell et al., 2009, are recalculated using the Fe3+/Fe2+ ratios reported by Zhang et al., 2018 Brounce et al., 2017; Moussallam et al., 2014; Helz et al., 2017; Moussallam et al., 2016; Shorttle et al., 2015; Hartley et al., 2017; Moussallam et al., 2019 plume –0.25 (0.55) lavas 47 mag‐ilm pairs fO₂ at T recorded and 1 atm. Ghiorso & Evans, 2008 0.25** passes Bacon & Hirschmann, 1988, test for equilibrium Carmichael, 1967a,b; Anderson & Wright, 1972; Wolfe et al., 1997; Hasse et al., 1997; Gunnarsson et al., 1998; Beier et al., 2006; Genske et al., 2012; Portnyagin et al., 2012 plume 0.82 (1.40) at 0.6 GPa and 0.10 (1.42) at 2.5 GPa peridotite and pyroxenite xenoliths 143 sp‐oxybarometry fO₂ at T and 0.6GPa. Mattioli & Wood, 1988; and Wood & Virgo, 1989; with aFe₃O₄ from Sack & Ghiorso, 1991a, 1991b; http://melts.ofm‐research.org/CalcForms/index.html; Temperature from spinel‐olivine Fe‐Mg exchange thermometer of Li et al., 1995 Between about +1.2/–2.0 and ±0.4 depending on spinel Fe³⁺/∑Fe ratio of spinel (see Methods Appendix and Davis et al., 2017)*** see Davis et al., 2017; and Birner et al. 2017; for discussions of a‐X model choices Abu El‐Rus et al., 2006; Bonadiman et al., 2005; Davis et al., 2017; Grégoire et al., 2000; Hauri & Hart, 1994; Kyser et al., 1981; Neumann, 1991; Neumann et al., 1995; Neumann et al., 2002; Ryabchikov et al. 1995; Sen, 1987; Sen, 1988; Sen & Leeman, 1991; Sen & Presnall, 1986; Tracy, 1980; Wasilewski et al., 2017; Wulff‐Pedersen et al. 1996 Note: *Authors of these studies infer higher fO₂ for primitive, near primary, melts based on these data: Mauna Kea >QFM 0.6 (Brounce et al., 2017); Kilauea QFM +0.4 to 0.7 (Helz et al., 2017, Moussallam et al., 2016); Iceland ~QFM + 0.4 (Shorttle et al., 2015; Hartley et al., 2017); Erebus ~QFM + 1.4 (Moussallam et al., 2014); Canary Islands ~QFM + 1.0 (Moussallam et al., 2019) Note: **Magnetite‐Ilmenite oxygen barometery errors reflect the average residual of model calcluations and the calibration dataset: (Ghiroso & Evans [2008] oxygen barometer‐derived fO₂ – known fO₂ from calibration dataset), presented in supplemental material of Waters & Lange (2016) Note: ***Uncertainty in fO₂ calculated from spinel oxybarometry is asymmetrical and decreases in magnitude as Fe³⁺/∑Fe ratio of spinel increases. Spinels that have Fe³⁺/∑Fe = 0.05 have an uncertainty in log fO₂ at the high end listed and those with Fe³⁺/∑Fe ≥ 0.4 at the low end. Hotspot residues, except four from Davis et al. (2017), are samples with spinel Fe³⁺/∑Fe ratios determined without Mössbauer correction standards, which roughly doubles uncertainty compared to corrected analyses (Davis et al., 2017).

Early estimates based on wet chemistry and magnetite–ilmenite pairs indicated that mid‐ocean ridge basalts (MORBs) record fO₂s similar to QFM (Carmichael & Ghiorso, 1986; Haggerty, 1976). However, upon reexamining data from the literature compiled by Haggerty (1976), we found only one sample with multiple pairs of magnetite and ilmenite in equilibrium at magmatic temperatures according to Bacon and Hirschmann (1988), and that sample (15.6m cooling unit from DSDP Leg34: site 319A) records QFM+0.16 (±0.1) at 1232 (±37)°C (Mazzullo & Bence, 1976). Subsequent wet chemical work found that MORBs record fO₂s low enough to suggest graphite is a stable phase in the MORB source (i.e., ~QFM‐1, Christie et al., 1986), but more recent wet‐chemical work and Fe K‐edge XANES analyses have revised average MORB fO₂ estimates back upwards to QFM (Bezos & Humler, 2005; Cottrell & Kelley, 2011; O’Neill et al., 2018; Zhang et al., 2018). Five recent studies determine Fe³⁺/∑Fe ratios spectroscopically by XANES to determine the fO₂ of average MORB (Fig. 3.1, Fig. 3.2a) (Birner et al., 2018; Cottrell & Kelley, 2011; Le Voyer et al., 2015; O’Neill et al., 2018; Zhang et al., 2018). Determinations for 166 MORB glasses that use the calibration of Zhang et al. (2018) find a narrow distribution around QFM –0.17±0.15 (all uncertainty is 1 standard deviation [σ] unless otherwise noted). Determinations for 42 MORB using the calibration of Berry et al. (2018) by O’Neill et al. (2018) return a mean of QFM +0.19 ±0.36. It is notable that O’Neill et al. (2018)’s corresponding Fe³⁺/∑Fe ratios for average MORB are lower by ~0.04 than those from the global survey of Zhang et al. (2018), despite their equation to higher fO₂. The difference stems from O’Neill et al. (2018)’s application of a new compositional parameterization of fO₂, which we choose not to apply in this study (see Methods Appendix for a description and assessment of parameterizations). The important point for our purpose here is that, regardless of the value of the Fe³⁺/∑Fe ratio of natural MORB, the Fe‐XANES spectra of natural MORB glasses resemble the spectra of experimental MORB‐composition glasses equilibrated at fO₂ similar to the QFM buffer (see Methods Appendix, Fig. S1), and there is general agreement among all recent spectroscopic studies that MORB glasses record QFM. The fO₂s recorded by average MORBs (7.58 wt.% MgO, Gale et al., 2013b) will be maxima with respect to the fO₂ of the mantle from which they derive, because Fe³⁺ is moderately incompatible during low‐pressure fractional crystallization and average MORBs are not primary melts of the mantle (Fe³⁺/∑Fe ratios increase by 0.03 as MgO falls from 10 to 5 wt.%; Cottrell & Kelley, 2011).

Figure 3.1 Locations of samples compiled in this study as a function of tectonic setting, lithology, and methodology. Symbol size scales linearly with the number of samples at a given locality.

Figure 3.2 Distribution of fO₂ recorded by volcanics globally in different tectonic settings and by multiple methods of oxybarometry. We have recalculated the fO₂ recorded by each sample based on the reported chemical analyses except for the separate light gray dataset in panel (a), which are the observations as reported by O’Neill et al. (2018). The O’Neill et al. (2018) dataset was collected using a different set of primary standards, as described in our methods appendix. Vertical, dashed lines reflect calculated average values of fO₂. Note that volcanics in (e) include plume‐affected ridge segments, which cause them to record bimodal fO₂; the fO₂s inferred for primitive plume magmas are higher than the average and we represent each plume’s primitive magma fO₂ as a filled orange circle (as reported by those authors). See Table 3.1 and

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