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by ocean island xenoliths; however, we cannot draw a genetic relationship between all lithospheric mantle xenoliths and the mantle melts that exhume them at plumes (compare Fig. 3.2e to 3.3d). Presumably, many of these xenoliths represent lithospheric mantle that has experienced limited chemical interaction with plume‐derived melts. Others are likely products of melt‐rock reaction between lithospheric peridotite and plume‐generated melts. The pyroxenite xenoliths were especially likely to have been derived in this way (e.g., Sen & Leeman, 1991), but it is unclear how many of the peridotites were also influenced by plume‐sourced melts. There is another caveat; we do not know the equilibration pressure at the closure temperature of these plume xenoliths. At ridges, we can reasonably infer pressure from peridotite thermometry because geothermal gradients are reasonably well‐characterized. That is not the case in plume settings, where thermal gradients are radial as well as vertical (e.g., Farnetani & Hofmann, 2010). In Figure 3.3e we demonstrate how equilibration at 2.5 GPa, instead of 0.6 GPa, would shift fO₂ down by two thirds of a log unit. This illustrates our community’s need for better peridotite mineral barometry.

      We venture that a more appropriate comparison might be drawn between peridotitic ocean island xenoliths and ridge peridotites. Both may initiate as residues of melting at ridges, with the former transiting and cooling prior to interacting with a mantle plume. The range of fO₂s recorded by ocean island xenoliths encompasses the range of ridge peridotites but skews to higher fO₂s by 0.37 log units if we hold pressure constant at 0.6 GPa (t_stat = 2.6, t_crit = 2.0, df = 211, p‐value = 0.01). Notably, spinel‐olivine Fe‐Mg exchange (Li et al., 1995) records higher temperatures in the ocean island xenoliths than in the ridge peridotites. This difference in temperature could be the result of heating of the oceanic lithosphere beneath oceanic islands by the plume (Ballhaus, 1993), or it could result from exhumation of these xenoliths from greater depths than the depth of last equilibration experienced by ridge peridotites. In the former case, temperature‐dependent exchange reactions suggest that a mantle parcel preserving a record of hotter conditions should record lower fO₂ than a parcel at the same pressure that records cooler conditions (Birner et al., 2018). Consideration of these subsolidus reactions would thus predict ocean island xenoliths to be more reduced than ridge peridotites, in contrast to what we observe. If this interpretation is correct, then the difference in fO₂ between ridge peridotites and OIB xenolith source mantle prior to plume heating is even greater than the 0.6 GPa plots in Figure 3.3 suggest, perhaps driven by the interaction of some of these xenoliths with oxidized plume melts. In the latter case, changes in fO₂ due to changes in pressure would additionally have to be accounted for to make a direct comparison between ridge peridotites and OIB xenoliths. If no changes in mineral composition or mode are considered, the lower average fO₂ calculated assuming a higher pressure of equilibration (Fig. 3.3) suggests that if OIB xenoliths do generally sample deeper portions of the lithosphere than ridge peridotite, then average fO₂ of the two are comparable. While exchange reactions and modal changes during ascension and cooling may complicate this relationship, at this time, the data do not suggest that xenoliths recovered from plumes significantly differ in their fO₂ compared to peridotites recovered in the ridge setting. Constraints on pressure and effects of temperature on the fO₂ recorded by peridotites below their solidus remain poorly understood, and further work is needed to clarify the fO₂ signature of xenoliths entrained within plume lavas.

      3.3.2. V/Yb Concentrations

V/Yb ratios range from 17–195 in MORB, 60–238 for BABB, and 65–422 in arcs (excluding one arc basalt with a ratio of > 800). We find average V/Yb concentrations in each tectonic setting that are all statistically distinct (p‐values <<< 0.001) with V/Yb of MORB (93 ±17) < BABB (107 ±25) < arcs (158 ±60). We illustrate this in Figure 3.4 with a plot of V/Yb ratios against MgO concentrations in ridge, back‐arc, and arc settings. Translating trace element ratios measured in glass (magmatic liquid) to the oxygen fugacity of the source rock (residue) depends on having accurate, composition‐dependent, mineral‐melt partition coefficients, an accurate knowledge of the source composition, and an accurate melting model (e.g., Canil, 1997; Lee et al., 2003; Lee et al., 2005; Mallmann & O’Neill, 2009; Mallmann et al., 2019). Mallmann and O’Neill (2013), Nicklas et al. (2019), Mallmann et al. (2019), Bucholz and Kelemen (2019), and others have discussed the difficulty in translating V/Sc ratios or olivine‐melt partition coefficients into source fO₂s. For example, the fO₂ of modern MORB, or Archean mantle, based on V partitioning is up to a log unit higher than that implied by modern MORB Fe³⁺/∑Fe ratios (Mallmann and O’Neill, 2013; Nicklas et al., 2019). For these reasons, we do not calculate fO₂ for each tectonic setting based on the V/Yb ratio, but simply infer the relative oxygen fugacity of each tectonic setting based on the premise that basalt V/Yb will rise with the fO₂ of the mantle source that generated the basalt. Under these assumptions, it is clear that fO₂ ridges < fO₂ back arcs < fO₂ arcs.

Figure 3.4 V/Yb ratios of ridge (gray “+” symbols, Gale et al., 2013), back‐arc (blue triangles, Gale et al., 2013), and arc lavas (teal circles, Turner & Langmuir, 2015) as a function of weight percent MgO. We filtered each published data compilation for 6 wt.% < MgO < 12 wt.% and for Dy/Yb < 2 (Laubier et al., 2014). See text for details.

3.4. DISCUSSION

      Our compilation and reprocessing of analytical data from the literature yields a synoptic picture of the fO₂s recorded by volcanic and mantle rocks across tectonic settings. Some three decades have passed since the seminal compilations from last century (e.g., Ballhaus et al., 1991; Carmichael, 1991; Christie et al., 1986; Frost & Lindsley, 1992; Wood et al., 1990). The volume of data and geographic coverage have increased tremendously and the analytical techniques and activity models have evolved; however, a key finding from those studies remains robust today. Volcanic and mantle rocks from arc settings record significantly higher fO₂ than those from ridges. Recycling of oceanic crust and lithosphere back into the Earth at subduction zones generates arc volcanics and related mantle lithologies that record higher fO₂ relative to those recovered from ridges. Additional work, particularly in forearc and back‐arc settings, support this observation by showing that fO₂ becomes elevated in proportion to the rock’s subduction affinity (Benard et al., 2018; Birner et al., 2017; Brounce et al., 2014; Brounce et al., 2021; Brounce et al., 2015; Kelley & Cottrell, 2009; 2012; Parkinson & Arculus, 1999). This remains true for the back‐arc basin basalts erupted at pressures > 200 bar and through a comparable crustal column to normal MORB. Moreover, in both the ridge and arc settings, melts (lavas and tephras) and mantle (peridotites and pyroxenites) both record an offset in oxygen fugacity of similar magnitude between the two settings. While these observations are robust, the mechanism by which subduction generates more oxidized lavas and associated mantle lithologies remains a matter of debate and is beyond the scope of this contribution to review (e.g., Andreani et al., 2013; Benard et al., 2018; Canil & Fellows, 2017; Carmichael, 1991; Chin et al., 2018; Debret et al., 2014; Evans, this volume; Farner & Lee, 2017; Foden et al., 2018; Gaillard et al., 2015; Kelley & Cottrell, 2009; Lecuyer & Ricard, 1999; Lee et al., 2005; Mungall, 2002; Nebel et al., 2015; Parkinson & Arculus, 1999; Tang et al., 2018; Tollan & Hermann, 2019; Williams et al., 2004; Wood et

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