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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).

Schematic illustration of distribution of fO2 recorded by mantle lithologies (peridotites and olivine-orthopyroxene-spinel bearing pyroxenites) globally in different tectonic settings.

      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.

       Arcs and Back Arcs.

      Subduction influences the composition of mantle melts and arc volcanics, generating continental crust in the process (e.g., Elliott et al., 1997; Gill, 1981; Grove et al., 2012; Kelemen et al., 2003; Kelemen et al., 2007; Osborn, 1959; Plank & Langmuir, 1988; Stolper & Newman, 1994; Turner & Langmuir, 2015; Zimmer et al., 2010). Both melts and mantle lithologies offer opportunities for oxybarometry. We begin with the volcanics.

      Seminal contributions by Carmichael (1991) and Frost and Lindsley (1992) surveyed the fO2s recorded by arc rocks using wet‐chemistry and magnetite‐ilmenite pairs, respectively, and found that arc rocks record fO2s up to several orders of magnitude higher than MORBs. Our compilation of 5 XANES spectroscopic studies (n=119 samples, Figure 3.2c) of olivine‐hosted melt inclusions and submarine pillow glasses shows that arc basalts record, on average, QFM +0.96 (±0.39). One set of outliers from Cerro Negro record QFM +4.75 (±0.40) (Gaetani et al., 2012), but spectra from these hydrous samples have suffered from radiation‐induced beam damage (Cottrell et al., 2018, Gaetani, pers. comm.) and are not included in our statistical analysis. Nearly 90% of samples with XANES measurements erupted through the thin crust (~25 km, Takahashi et al., 2007) of the active Mariana arc front (Fig. 3.1a), and thus there is significant location bias in this dataset.

      Globally, magnetite–ilmenite pairs, from 114 arc lavas sampling 11 different arcs, record QFM +1.28 (±0.64) (Figure 3.2d; see methods appendix and the online data library associated with this contribution, Cottrell et al., 2021, for citations). These samples contain Fe–Ti oxides with compositions that record a range of temperatures (700–1085 °C), span a wide range of compositions (basaltic andesite to rhyolite) but are predominantly dacitic, and erupt through crust ranging from 25 to 66km thick.

      The mean fO2 recorded by olivine‐hosted melt inclusions and submarine arc‐front glasses (ΔQFM = 0.96±0.39, n=119) is slightly lower than that recorded by magnetite‐ilmenite pairs (ΔQFM = 1.28±0.64 n=114) at the 95% confidence level (tstatistic = 4.6, tcritical = 2.0, degrees of freedom [DF] = 186, p‐value < 0.001). (When we compare distribution means in this contribution, we will always apply a two‐sample student’s t‐test with α= 0.05 [Krzywinski & Altman, 2013] for samples of unequal variance.) We caution that the datasets are not directly comparable because of the limited geographic distribution of the melt inclusion and submarine glass dataset; because there are no samples in common between the two distributions; and because the melt inclusions may reflect magma compositions that precede magnetite and ilmenite saturation. Thus, to first order, our global result is not inconsistent with the results of Waters and Lange (2016) and Crabtree and Lange (2011) who found congruence when they compared magnetite‐ilmenite oxybarometry to wet‐chemical titration on the same suite of very fresh aphyric lavas.

      A more direct comparison can be made between the olivine‐hosted melt inclusions and submarine glasses erupted along the active Mariana Arc, and back arc basin (BAB) glasses erupted at depth along the associated back arc spreading center: the Mariana Trough. Both datasets apply the same method (XANES) to arrive at fO2 estimates, and both sample suites comprise basaltic to basaltic andesite glasses representing similar stages of differentiation in thin crust (similar MgO). The Mariana arc front samples record fO2s that are on average 0.73 log units higher than

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