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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.