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Mid‐ocean ridges sample Earth’s convecting mantle and represent the majority of volcanism on the planet. Both melts and mantle lithologies offer opportunities for oxybarometry. We begin with the volcanics.

Table 3.1 Results and Method Summary.

Tectonic setting	δQFM (s)	Lithology	n	Method	Activity‐composition models and other method notes	Method error in fO2 in log units	Notes	Data included
mid‐ocean ridge	–0.17 (0.15)	basalt pillow glass	160	XANES	At 1atm. Kress & Carmichael, 1991; parameterization of fO2 as a function of composition	0.27	Fe oxidation state determined using the Mössbauer calibration of Zhang et al., 2018	Cottrell & Kelley, 2011; Le Voyer et al., 2015 (except the 6 analyses of hydrothermally altered dredge 16D); Birner et al., 2018
mid‐ocean ridge	0.19 (0.36)	basalt pillow glass	42	XANES	At 1atm. O’Neill et al., 2018; parameterization of fO2 as a function of composition	0.52	Fe oxidation state determined using the Mössbauer calibration of Berry et al., 2018	O’Neill et al., 2018
mid‐ocean ridge	0.16 (–)	lava	1	mag‐ilm pairs	fO2 at T recorded and 1 atm. Ghiorso & Evans 2008	0.25**	passes Bacon & Hirschmann, 1988, test for equilibrium	Mazzullo & Bence, 1976
mid‐ocean ridge	0.31 (0.73)	peridotite	72	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 +0.6/–1.0 and ±0.2 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	Bryndzia & Wood, 1990; Birner et al., 2018
back arc basin spreading center	0.22 (0.30)	submarine lava	37	XANES	at 1atm and 1200°C. Kress & Carmichael, 1991	0.27		Kelley & Cottrell, 2009; Brounce et al., 2014
arc front	0.96 (0.39)	basalt glass in olivine‐hosted inclusions, basalt pillow glass	119	XANES	at 1atm and 1200°C. Kress & Carmichael, 1991	0.27		Bonnin‐Mosbah, 2001; Kelley & Cottrell, 2009; Kelley & Cottrell, 2012; Brounce et al., 2014; Brounce et al., 2016 (data from Gaetani et al., 2012, excluded from average due to oxidative beam damage)
arc front	1.28 (0.64)	volcanics (lavas and tephra)	114	mag‐ilm pairs	fO2 at T recorded and 1 atm. Ghiroso & Evans, 2008	0.25**	passes Bacon & Hirschmann, 1988, test for equilibrium	Carmichael, 1967; Luhr & Carmichael, 1980; Wallace & Carmichael, 1994; Rutherford & Devine, 1996; Mandeville et al., 1996; Luhr, 2000; Coombs & Gardner, 2001; Devine et al., 2003; Costa et al., 2004; Grove et al., 2005; Larsen, 2006; Toothill et al., 2007; Izbekov et al., 2002; Browne et al., 2010; Baggerman & Debari, 2011; Crabtree & Lange, 2011; Stelten & Cooper, 2012; Arce et al., 2013; Waters & Lange, 2013; Howe et al., 2014; Frey & Lange, 2011; Muir et al., 2014; Waters et al., 2015; Grocke et al., 2016; Crabtree & Waters, 2017; Waters & Frey, 2018
arc front	0.96 (0.81)	peridotite xenoliths	47	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 +0.6/–1.0 and ±0.2 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	Wood & Virgo, 1989; Canil, 1990; Brandon & Draper, 1996; Parkinson et al., 2003; Bénard et al., 2018
forearc	0.22 (0.75)	trench wall peridotite and peridotite xenoliths	64	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 +0.6/–1.0 and ±0.2 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	Parkinson & Pearce, 1998; Pearce et al., 2000; Birner et al., 2017
plume	0.10* (0.71)	basalt pillow glass	334	XANES	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 text for details.

Oxybarometry of mid‐ocean ridge peridotites has only been investigated in two studies (Birner et al., 2018 and Bryndzia & Wood, 1990) and in a handful of localities (Fig. 3.1). Global ridge peridotites record fO₂ = QFM +0.31 (±0.73), but we note that more than half of these data derive from a single ridge segment (Fig. 3.1, Fig. 3.3a). Birner et al. (2018) found that n=41 peridotites dredged from the Southwest Indian Ridge (SWIR) record QFM +0.61 (±0.63) at 0.6 GPa and the closure temperature of olivine‐spinel exchange. This is significantly higher than the fO₂ recorded by basalts on the same segment (p‐value < 0.01); however, the discrepancy disappears once the peridotites’ conditions of last equilibration with basalt are considered (Birner et al., 2018). The method of projecting peridotite fO₂ to the PTX conditions of last equilibration with basalt considers three sub‐solidus reactions that may alter the fO₂ recorded by the rock: Mg–Fe exchange between olivine and spinel, Al–Cr exchange between spinel and orthopyroxene, and a Tschermak reaction that produces spinel at the expense of olivine and Al‐rich orthopyroxene during cooling. Although a dearth of knowledge as to ferric iron partitioning behavior between spinel and pyroxenes during cooling leads to significant uncertainty in the magnitude of projection (±0.5 log units, Birner et al., 2018), the direction of the model is to decrease recorded peridotite fO₂ values when projecting back to high temperature‐pressure source conditions. This projection thus brings peridotite fO₂ values into closer agreement with basalt fO₂ values, suggesting that fO₂ values recorded by peridotites, without these corrections, may systematically overestimate the redox conditions of MORB‐source mantle (Birner et al., 2018).

Figure 3.3 Distribution of fO₂ recorded by mantle lithologies (peridotites and olivine‐orthopyroxene‐spinel‐bearing pyroxenites) globally in different tectonic settings. We have recalculated the fO₂ recorded by each sample at 0.6 GPa (2.5 GPa in [e]) and temperature recorded by spinel‐olivine thermometry using the methodology of Birner et al. (2018) and Davis et al. (2017) based on the reported chemical analyses. All samples are peridotites except for (d) where the overlain histogram in red are pyroxenites. We caution against overinterpreting the wide range of xenolith fO₂s recovered at plumes due to (i) the near absence of samples from this setting characterized using Mössbauer‐characterized spinel standards or Mössbauer spectroscopy; (ii) uncertainty in the barometry and metamorphic history of these samples (which will alter the fO₂ they record); and (iii) limited data by which we may judge the extent to which these lithospheric xenoliths record ridge versus plume fO₂.

We highlight that peridotites along SWIR record five times greater range in fO₂ when compared to basalts dredged from the same segment. On the global scale, Bryndzia and Wood (1990) investigated the fO₂ of 35 ridge peridotites from 12 localities. When filtered to exclude four samples from two anomalous locations (the sub‐aerial St. Paul’s Rocks and the tectonically complex Mid‐Cayman Rise), and recalculated according to the methods presented here, this sample set records fO₂ of QFM ‐0.08 ±0.68 and spans a range of nearly 2.5 orders of magnitude in fO₂ (Birner et al., 2018). When comparing Fig. 3.2a and 3.3a, we observe that global mid‐ocean ridge volcanics display low variance relative to ridge peridotites. These limited data suggest that basalts may homogenize kilometer‐scale redox heterogeneity in the upper mantle (Birner et al., 2018). Globally, ridge peridotites calculated at 0.6 GPa and the temperature of olivine‐spinel closure record average fO₂s about half a log unit higher than basalts calculated at 1 bar and 1200 °C. Because we have not attempted here to account for subsolidus processes in the peridotites globally, comparisons between the two distributions should not be overinterpreted. A more comprehensive global peridotite dataset is required to evaluate the response of mantle residues to melt extraction and subsolidus re‐equilibration.