1993; Wood et al., 1990), magnetite‐ilmenite equilibria (e.g., Frost & Lindsley, 1992), or bulk rock and/or sediment Fe3+/∑Fe ratios (e.g., Carmichael, 1991; Lecuyer & Ricard, 1999). In this chapter, we do not compile fO2 calculated for bulk “glass” Fe3+/∑Fe ratios because in most cases the metadata provided in publications are absent or insufficient to ensure that the samples have not suffered post‐eruptive oxidation or are free of phenocrysts, both of which have been shown to compromise the fidelity of fO2 proxies (Bezos & Humler, 2005; Brounce et al., 2017; Cottrell & Kelley, 2011; Grocke et al., 2016; Stolper & Bucholz, 2019; Bezos et al., 2021). Further, while very convenient for generating large datasets and informing box models (e.g., Brounce et al., 2019; Canil & Fellows, 2017; Evans, this volume; Evans & Tomkins, 2011; Evans et al., 2012; Lecuyer & Ricard, 1999; Stolper & Bucholz, 2019), applications of bulk “glass” or whole rock Fe3+/∑Fe ratios are limited because the Fe3+/∑Fe ratios of crystalline rocks and mixtures (like cumulates and sediments) cannot be directly equated to fO2 – as detailed above.
3.1.3. Trace‐Element Oxybarometry
In addition to iron, the periodic table offers us a wealth of elements that undergo valence state changes in response to changes in fO2. The theory that underpins trace element oxybarometry is that fO2‐driven valence state changes will result in changes to mineral‐melt partition coefficients. Thus, the concentration of a multivalent trace element in melt should reflect the residual mineralogy, the melt composition, and the pressure, temperature, and oxygen fugacity of the system during melting. In this way, the power of redox‐sensitive minor and trace element partitioning can be harnessed to monitor the fO2 of geologically relevant lithologies, and can offer advantages over Fe. Trace element concentrations offer advantages because they are (i) relatively straightforward to measure and (ii) should be less susceptible than formal valence state to modification after the melt separates from the residue. A wide range of redox‐sensitive elements (e.g., Ti, V, Cr, Ce, Eu, U, Mo, W, Re) are discussed separately by Mallmann et al. (2021) within this volume, and we refer the interested reader to that chapter. Several trace elements, however, have been employed to infer the fO2 of basalt source rocks (the mantle) as a function of tectonic setting (e.g., Bali et al., 2012; Bucholz & Kelemen, 2019; Canil, 1997; Laubier et al., 2014; Lee et al., 2005; Lee et al., 2010; Lee et al., 2012; Mallmann & O’Neill, 2009; Mallmann & O'Neill, 2013; Shervais, 1982). A review of all of these studies and proxies is beyond the scope of this chapter; however, we will discuss vanadium (V) – the most widely applied of these proxies. Vanadium valence can be V2+, V3+, V4+, or V5+ in geologically relevant systems. The incompatibility of V3+ in mantle minerals is similar to many other trivalent elements, such as the rare earth elements, Sc, Y, and Ga, while V4+ and V5+ are more highly incompatible. Therefore, with all other parameters equal, melting peridotite at higher fO2 should result in systematically higher melt V concentrations relative to other trivalent trace elements (Canil, 1997; Lee et al., 2003, 2005).
3.1.4. Other Oxybarometers
We emphasize that there are many additional, and very valuable, proxies for fO2 that are not yet widely applied to volcanics from arc, ocean island, and mid‐ocean ridge settings, but may be in the future, such as stable isotope proxies (Dauphas et al., 2009; Nebel et al., 2015; Williams et al., 2005). Similarly, microprobe peak energies (e.g., Carroll & Rutherford, 1988) and S X‐ray Absorption Near Edge Structure spectra (e.g., Fleet et al., 2005) can determine sulfur oxidation state, but analyses from both techniques can be compromised by beam damage during analysis (e.g., Klimm et al., 2012; Rowe et al., 2007; Wilke et al., 2008), leaving only a handful of vetted analyses. For these, we point the interested reader to other chapters in this volume that describe some of these approaches in detail.
3.2. SAMPLE SELECTION, METHODOLOGY, AND DESIGN OF THIS STUDY
We can envision many valid approaches for compiling fO2 determinations from the literature. In this contribution, we focus on the oxybarometric approach and apply oxybarometers that have all been cross‐calibrated at 1 atmosphere under controlled atmosphere conditions at known fO2. We compile published compositions from Earth’s ridges, back arcs, forearcs, arcs, and plumes and recalculate the fO2 values recorded by these volcanics (lavas and tephras) and mantle lithologies (mostly peridotites). We have opted to include samples wherein the original publications provide sufficient information to recalculate fO2 (e.g., microprobe analyses) such that we may apply a single set of activity models and methodologies to all of the compositional data collected in disparate studies. This is essential, because the fO2 calculated from a given composition may vary by up to a log unit depending on the activity model employed (e.g., Birner et al., 2017; Herd, 2008; Wood, 1990). Further, many publications do not report the formulation of the reference buffer (for example, QFM from O’Neill [1987] vs Frost [1991] vs Myers & Eugster [1983]), such that reported fO2s may not be comparable.
We describe our methods, including chosen activity models, in detail in our methods appendix. In brief, we include widely applied oxybarometric techniques that have documented intra‐technique consistency, and which require minimal metadata: magnetite‐ilmenite pairs, spinel‐oxybarometry, and glass spectroscopy. For example, Davis and Cottrell (2018) show that both the spinel oxybarometric method of Wood and Virgo (1989) and the Fe3+/Fe2+ activity model of Kress and Carmichael (1991) return the experimentally imposed fO2 of gas‐mixing experiments containing spinel, olivine, and orthopyroxene in basaltic andesite liquid. Likewise, Fe3+/∑Fe ratios of glasses converted to fO2 via the Kress and Carmichael (1991) algorithm are consistent with magnetite‐ilmenite oxybarometry using the activity model of Ghiorso and Evans (2008) (Crabtree & Lange, 2011; Waters & Lange, 2016). Table 3.1 summarizes the oxybarometric methods we apply and the studies we include. A more detailed discussion of alternative parameterizations for fO2 can be found in the methods appendix. The compiled dataset can be downloaded as a data library (Cottrell et al., 2021). The dataset is unique in that we aggregate fO2 data from different studies, different authors, and with different proxies, but we reprocess and quality check the data to facilitate global comparisons. This exercise also identifies which regions and tectonic settings lack direct fO2 constraints (Figure 3.1).
We first present the Fe‐proxy‐based fO2s recorded by rocks from each tectonic setting (ridge, back arc, arc, and plume). We discuss the processes that may perturb these proxies and the extent to which the fO2 recorded by rock samples is representative of the mantle source. We then compare Fe‐based proxies to the inferences that can be drawn from magmatic V concentrations across tectonic settings. Like all elements, the V concentrations of basaltic liquids change as fractional crystallization proceeds, necessitating the normalization of V concentration to another trace element. Although many studies normalize V concentrations to Scandium (Sc), Mallmann and O’Neill (2009) and Laubier et al. (2014) critically evaluate candidate trivalent cations and conclude that the V/Sc ratio does not remain constant as fractionation proceeds. V/Sc begins to rise as MgO falls below 8 wt.%, making this ratio unsuitable to evaluate primitive arc basalts (Laubier et al., 2014). Following Laubier et al. (2014) we choose Yb for normalization because it remains constant during crystallization of typical basalts down to < 6 wt.% MgO. We use the compilation of Gale et al. (2013a) for MORB and BABB chemistry, which ensures that samples derive from on‐axis locations and that trace element analyses are of high quality. We use the compilation of Turner and Langmuir (2015) for arc basalt chemistry, which ensures that samples derive from arc‐front
