Supplemental Information for Mantle Thermochemical Variations beneath the Continental United States Through Petrologic Interpretation of Seismic Tomography
William J. Shinevar1*, Eva M. Golos2, Oliver Jagoutz3, Mark D. Behn4, Robert Van der Hilst3
1 MIT/WHOI Joint Program in Oceanography/Applied Ocean Engineering
2 Brown University
3 Massachusetts Institute of Technology
4 Boston College
*now at University of Colorado Boulder
This supplement contains two supplemental tables containing compiled xenolith and primary magma thermobarometry, two supplemental figures, and a data file containing the results plotted in Figures 3‒6.

Supplementary Information:

Comparison with primary magma thermobarometry

Another temperature comparison is with primary magma thermobarometry, which uses compositions of primary magmas and primary melt inclusions to calculate the pressure and temperature at which a melt was last in equilibrium with the mantle (c.f. Till, 2017). Here we use temperatures estimated from different thermometers that incorporate both tholeiitic and alkaline samples (Leeman et al. , 2005; Ruscitto et al. , 2010; Till et al. , 2013; Plank and Forsyth, 2016; Till, 2017). We also include recalculated temperature estimates from high-Mg andesites from Mt. Shasta (Baker et al., 1994; Grove et al., 2002) using the thermometer of Mitchell and Grove (2015) at 1.5 GPa (Mt. Shasta, coldest blue square, Figure S7) (Supplementary Table 2). Due to the importance of measuring H2O and CO2 on the liquidus temperature and pressure, we only use estimates made with measured H2O based on melt inclusions. As volatiles rapidly diffuse from melt inclusions (Bucholz et al., 2013; Gaetani et al., 2012), the temperature estimates for hydrous melting using these water contents are an upper bound (Till, 2017), but generally agree with estimates from regional tholeiitic primary magmas. To compare regions with different numbers of estimates, we bin magmatic temperature estimates into 0.5°x0.5° regions for pressure estimates within 0.3 GPa of the regional pressures at 60 and 80 km. We take the uncertainty in the magmatic temperature estimates to be the maximum of the reported uncertainty or the standard deviation of averaged estimates. This binned temperature estimate is compared with the mean temperature of our results at the relative depths slices within 0.5° arc-distance. Uncertainty in our temperature results is defined as the maximum between the average temperature uncertainty and the standard deviation of averaged temperatures.
Our results underpredict magmatic temperatures estimates (square, Figure S1). On average, we underpredict magmatic temperature estimates beyond estimated uncertainty (RMSE=260°C at 60 km, 110°C at 80 km). There are multiple hypotheses for this disagreement: (1) scale of the temperature estimates, (2) error in the anelastic correction of seismic wave speeds, (3) error in the magmatic thermobarometers, or (4) error in the forward calculation of mantle seismic wave speeds, potentially due to the exclusion of melt or hydrous phases. The following paragraphs discuss these possibilities.
The first potential cause for the systematic difference in our results and magmatic temperature estimates is the scale over which each is measuring. Magmatic temperature estimates sample the temperature at which the melt was in equilibrium with the mantle and may only represent small regions (~1 m) of the mantle, especially if melt is focused (e.g., Kelemen and Dick, 1995) and/or escapes the mantle on short (~10 kyr) timescales (Feineman and DePaolo, 2003). Conversely, seismic tomographic inversions such as MITPS_20 are limited to resolving seismic anomalies greater than ~1.5°x1.5° with vertical resolution on the order of 10 km (Golos et al., 2020). Thus, non-pervasive, small-scale seismic anomalies due to thermal upwellings or melt may be smeared or not sensed. Furthermore, seismic inversions smooth their wave speeds in order to stabilize the inversion, though MITPS_20 corrects for some of this effect (see Methodology). Subduction zones are especially difficult to image due to any smearing of the cold, subducting lithosphere, which increases seismic wave speed, decreasing the temperature estimate. The fact that the 80-km temperatures are in better agreement with magmatic estimates may suggest that at 60 km, vertical smearing may increase the inverted seismic wave speeds as the tomography samples from starkly colder lithosphere along a steep geotherm. Regional, high-resolution seismic studies are necessary to understand these effects.
A second reason for the temperature discrepancy could be error in anelastic corrections of seismic wave speed. Anelasticity experiments on olivine and peridotite are difficult, with various experimental groups giving different results and sensitivities (Faul and Jackson, 2015; Karato and Park, 2018). The Behn et al. (2009) power-law formulation of anelasticity does not fit experimental data well at low quality factors (Q-1>0.1, high temperatures or melt present. Jackson and Faul, 2010). Certain parameters in the both anelasticities are relatively unconstrained, like the activation volume that controls the pressure sensitivity (Faul and Jackson, 2015; Jackson and Faul, 2010). Other comparisons of high-quality seismic experiments and forward calculations of peridotite seismic wave speeds required altering the relaxation peak of the frequencies in order for the observations to be interpreted by the Jackson and Faul (2010) anelasticity (Ma et al., 2020). Furthermore, the effect of water content on anelasticity is currently debated (Aizawa et al., 2008; Cline et al., 2018; Karato and Park, 2018). Increasing the water content decreases Vs at high temperatures, thus shifting all forward calculations above ~900°C to the left in Figure 2. As we assumed relatively dry water contents (COH=50 H/106 Si), assuming an increased water content would decrease the interpreted temperatures. While grain size is an important parameter for anelasticities (Behn et al., 2009; Faul and Jackson, 2005), we have assumed a reasonable grain size near the upper bound observed in xenoliths. Any grain size reduction increases anelastic effects, thus reducing the modeled temperature. Therefore, variable grain size and its effect on anelasticity cannot reconcile the temperature discrepancy discussed here. Oxidation has been found to increase dissipation (Cline et al., 2018), not incorporated in our methods. This would also reduce our temperature results in arc settings as arc mantle is more oxidized (Kelley and Cottrell, 2012). Conversely, as long as melt and fluids are focused, oxidation would not decrease large-scale seismic wave speed as only a small portion of the mantle may be highly oxidized.
While increasing water content can drastically reduce the peridotite solidus, tholeiitic (dry) magmas are observed in the western United States (Till, 2017). Melting experiments on dry peridotite compositions require temperatures >1300°C at 60 km depth, greater than nearly all our temperature results (Hirschmann, 2000). Given the existence of Holocene age tholeiitic magmas, the reported uncertainty in magmatic thermobarometry (11–43°C, 0.1–0.4 GPa) cannot explain the temperature discrepancy present at 60 km.
Miscalculation in the forward calculation of seismic wave speeds in WISTFUL is also unlikely to explain the temperature estimate discrepancy. As we incorporate expected non-systematic uncertainty from our forward calculations into the error allowed for fitting and utilize current experimental moduli for most mineral endmembers, the only systematic error from this could be due to a difference in mixing assumptions, e.g. anisotropy. WISTFUL calculates the isotropic wave speeds, so comparing with the fast direction wave speeds would produce colder than realistic temperature estimates. As MITPS_20 inverts isotropic wave speed from combination of teleseismic body waves and surface wave arrival times, a systematic increase in recovered wave speed due to anisotropy beneath all regions with magmatic temperature estimates is unlikely.
Lastly, WISTFUL does not incorporate any effect of melt and hydrous phases, both of which would decrease the predicted temperature. Melt strongly reduces Vs (e.g., Hammond and Humphreys, 2000), but the exact wave speed reduction is heavily dependent on the melt content and the melt connectivity (Zhu et al., 2011). Thus, incorporating the effect of melt would make supersolidus temperatures require even lower wave speeds than observed. Similarly, pargasitic amphibole, (NaCa2(Mg4Al)(Si6Al2)O22(OH)2), the most common hydrous phase predicted for the shallow mantle (Dawson and Smith, 1982), has Vs =3.85 km s-1 andVp/Vs =1.83 at 60 km pressure and 1200°C assuming the same anelasticity described in Section 3 and moduli from Abers and Hacker (2016). At the same conditions, diopside (MgCaSi2O6) hasVs =4.35 km s-1 andVp/Vs =1.78. Replacing clinopyroxene at the same temperature with pargasite would decreaseVs and increaseVp/Vs (shifting all forward calculations to the upper left in Figure 2). Therefore, the addition of melt and/or hydrous phases would decrease the predicted temperature for the same seismic wave speed. Despite amphibole dikes and peridotites being hypothesized as a significant source of volatiles for alkaline and ocean-island basalts (Harry and Leeman, 1995; Pilet et al., 2011), the volume required to have a geochemical impact is unlikely to have a noticeable impact on seismic wave speed of the shallow mantle on the scale we are can interpret with MITPS_20 (~1.5°).
In summary, our results agree within error of recent (<10 Ma) xenolith compositions, predict temperature greater or equal temperature to spinel-bearing and garnet-bearing xenoliths, but underpredict magmatic temperature estimates, especially at 60 km. The systematic difference between our best-fit temperature estimates with magmatic temperature estimates are best explained by a difference in the scale of the estimates, smearing in the tomographic models at shallow depths along a steep geotherm, and/or errors in anelastic corrections. Further experimental work on anelasticity is required to better interpret high temperature mantle regions like the western United States.
Supplementary Table 1: Compiled xenolith thermobarometry and compositional data. Empty cells represent data that was not reported or measured. All compositional data is in wt. %. References listed at the bottom of the table.
Supplementary Table 2: Locations, sources, and primary magma thermobarometry data utilized for Figure S1. Full references listed at bottom of table.
Supplemental Data File 1: This data file contains the MITPS_20 model used to produce the results presented in the paper of temperature, Mg #, and density with uncertainties at 60, 80, and 100 km depth. Variables are named following the table below.