parameterizations predict the known furnace fO2 of those 435 experiments given their independently‐determined compositions. For the indicated terrestrial range, O’Neill et al. (2018)’s parameterization returns furnace fO2s that are, on average, 0.56 (±0.55) log units higher than measured, Kress and Carmichael (1991)’s returns furnace fO2s that are 0.09 (±0.58) lower than measured, and Borisov et al., (2018)’s returns 0.05 (±0.52) lower than measured. Standard errors on the estimates are reported in Table A2. We could therefore move forward confidently with either Kress and Carmichael (1991) or Borisov et al. (2018) but use the former simply because we had completed our analysis before Borisov et al. (2018) was published. Table A2 reports the standard error of each parameterization for the entire compilation and compositional subsets as defined in Table A1. Our analysis assumes that there is no systematic inaccuracy amongst the wet‐chemical studies compiled by Borisov et al., (2018). O’Neill et al. (2018) raise the possibility that some wet‐chemical determinations could be erroneous, and cite four suspect studies. Of these four, only two are included in the compilation of Borisov et al. (2018), and of these, 80% are from the study of Thornber et al. (1980). We therefore assessed whether inclusion/exclusion of the Thornber et al. (1980) data would significantly impact our analysis. It does not. For example, excluding data from Thornber et al. (1980) from the terrestrial data set (n = 55 without Thornber) causes the standard error of O’Neill et al. (2018) parameterization to degrade to 0.84, while the standard error of Kress and Carmichael (1991) stays constant and that of Borisov et al. (2018) improves to 0.50.
Table A2 Standard error (σest) of three fO2 parameterizations.
| reference | n=435 | n=98 | n=33 |
|---|---|---|---|
| (all expts compiled by [Borisov et al., 2018]) | (“terrestrial” lavas) | (“MORB‐like” lavas) | |
| Kress & Carmichael, 1991 | 0.56 | 0.59 | 0.53 |
| Hugh St C. O’Neill et al., 2018 | 0.58 | 0.79 | 0.8 |
| Borisov et al., 2018 | 0.38 | 0.53 | 0.49 |
c. Vanadium oxybarometry using V/Yb ratios.
All method details provided in the main text.
Mantle Lithologies
We calculated the oxygen fugacity of mantle lithology (peridotites and olivine‐orthopyroxene‐spinel bearing pyroxenites) by spinel oxybarometry, following the procedures of Davis et al. (2017). This method uses phase equilibrium between olivine, orthopyroxene, and spinel to constrain the oxygen fugacity of the system.
Calculated oxygen fugacity values are highly dependent on mineral activity models. We have thus recalculated all literature data to use a single set of activity models. For olivine and orthopyroxene, we use the activity models cited in Wood and Virgo (1989). For spinel, we use the activity model developed by Sack and Ghiorso (1991a,b). This spinel activity model better reproduces the experimental data of Wood (1990) than do other commonly used spinel activity models such as those of Mattioli and Wood (1988) and Nell and Wood (1991) (see Davis et al., 2017, for further discussion). Additionally, the Sack and Ghiorso (1991a,b) model is more applicable to spinels at high Cr#, such as the arc and forearc peridotites reported in this work (see Birner et al., 2017, for further discussion).
The activity of magnetite in spinel is itself highly dependent on accurate determination of the ferric iron content within the spinel phase. The studies included in this compilation determine ferric iron content in spinel using either Mössbauer spectroscopy or electron probe microanalysis (EPMA). In the case of EPMA, ferric iron content cannot be determined directly and is instead calculated using stoichiometric constraints. The preferred method of determining ferric iron content in this manner involves correcting the values based on a set of calibration spinels, with ferric iron contents independently determined by Mössbauer, run at the beginning and end of each EPMA session (e.g., Wood & Virgo, 1989; Davis et al., 2017). For peridotites from ridges, arcs, and forearcs compiled in this study, we have only included data in which the Fe3+/∑Fe ratio of spinel was determined via Mössbauer or corrected EPMA. In the case of xenoliths from OIB localities, we have chosen to additionally include a number of studies in which this correction was not applied, due to the paucity of measurements using spinel standards for correction. Uncertainty in fO2 increases when uncorrected EPMA analyses of spinels are used to calculate fO2, but the degree to which that uncertainty increases is dependent on the Fe3+/∑Fe ratio of the spinel. Uncertainty in fO2 is greater for spinels with lower Fe3+/∑Fe ratios and lesser for spinels with higher Fe3+/∑Fe ratios (Ballhaus et al. 1991; Davis et al. 2017). For example, fO2 calculated from corrected EPMA analyses of spinels with Fe3+/∑Fe = 0.10 has an fO2 uncertainty of about +0.3/‐0.4 log units, whereas the uncertainty roughly doubles for uncorrected spinel analyses. At Fe3+/∑Fe > 0.35, fO2 uncertainty is only about 0.1 log units for corrected EPMA analyses, and doubles to about 0.2 log units when the analyses are uncorrected. Therefore, the potential effects of including uncorrected analyses on the distribution of fO2 recorded by peridotites from an oxidized setting is likely to be small.
The calculation of oxygen fugacity also depends highly on assumptions about the temperature and pressure of equilibration. In order to maintain consistency between datasets, we calculate the fO2 values of all mantle lithologies at 0.6 GPa and the temperature recorded by spinel‐olivine thermometry. Justification for this choice can be found in Birner et al. (2017) for forearc/arc peridotites and Birner et al. (2018) for mid‐ocean ridge peridotites. Although we choose these values to maintain consistency, there is no rigorous method available to estimate pressure recorded by spinel peridotite xenoliths and no thermal model that can be easily applied to plume‐influenced lithosphere that would allow recorded temperature to be related to a depth along a geotherm. OIB xenoliths could potentially have been exhumed from any depth within the spinel stability field. Assuming a maximum pressure of 2.5 GPa, the choice to calculate fO2 at 0.6 GPa may lead to an overestimation of fO2 relative to QFM by as much as 0.6 to 0.8 log units. This difference in fO2 relative to QFM is owing to the differences in ΔV of the QFM reaction and the reaction underlying the spinel oxybarometer (fayalite‐ferrosilite‐magnetite).
Modeling in DCompress. We modeled the change in magmatic fO2 with progressive degassing of a C‐O‐H‐S vapor using the gas‐melt equilibrium model of Burgisser et al. (2015). This thermodynamic model computes C, H, O, and S concentrations and speciation in coexisting gas and silicate melt as functions of pressure, temperature, melt composition, and fO2, based on experimental calibrations of melt solubility and homogeneous equilibrium in the gas phase for H2, H2O, CO, CO2, SO2, H2S, and S2 species. The melt does not change in major element composition during degassing (i.e., there is no crystallization) and it is not permitted to precipitate separate sulfide or carbon phases.
We followed the methodology of Brounce et al. (2017) to compute the degassing trajectories,
