of geodynamic models with the δVS spectrum in tomographic models, and this is most appropriate at depths where long‐wavelength VS variations are primarily controlled by temperature. For all of the mantle tomographic models considered, there is a local minimum in spectral slope centered on (or slightly above for SEMUCB‐WM1) 650 km, reflecting the dominance of long‐wavelength structures noted above. Below the base of the transition zone, the spectral slope increases, suggesting the presence of shorter‐wavelength velocity heterogeneity. In the lowermost mantle, all of the tomographic models are again dominated by very long‐wavelength structures, indicated by a decrease in the power spectral slope. We note that the slope for SEISGLOB2 is quite different from the other models due to the limited power at spherical harmonic degrees above 8 in this model, which may be due to regularization choices and limited sensitivity of their data to short‐wavelength structure.
In analyzing the changes in spectral content of tomographic models, we assume that the model spectral content is an accurate reflection of the true spectrum of mantle heterogeneity. A geodynamic study has suggested that there could be substantial aliasing from shorter to longer wavelengths due to model regularization, limited data sensitivities and theoretical assumptions (Schuberth et al., 2009), potentially influencing our inferences of spectral slopes in the transition zone. However, aliasing is likely to be very limited at the wavelengths considered here for three reasons. First, aliasing is expected to be small if the model parameterization is truncated at a spherical harmonic degree where the power spectrum has a rapid falloff with degree (e.g., Mégnin et al., 1997; Boschi and Dziewonski, 1999). Second, a recent model like S362ANI+M uses diverse observations – normal modes, body waves (S, SS, SS precursors), long‐period surface waves, and overtone waveforms – whose data variance are dominated by the longest wavelength components and show a clear falloff in power above a corner wave number (e.g., Su and Dziewonski, 1991, 1992; Masters et al., 1996). Third, we note that the spectral slope minimum in the lower part of the transition zone is recovered with models that employ various theoretical approximations.
The geodynamic models all produce long‐wavelength structures that are quite similar to tomographic models at the surface and in the lowermost mantle, but there are some distinct differences in the mid‐mantle that arise from differences in the viscosity profiles and inclusion or omission of phase transitions. In Figure 1.4c, we show the correlation between each of the convection models and SEMUCB‐WM1 as a function of depth, for spherical harmonic degrees 1‐4. All of the models produce structures that are highly correlated with SEMUCB‐WM1 in the lithosphere and and lowermost mantle. The former is entirely expected because the lithospheric temperature structure is entirely determined by plate cooling in response to the imposed plate motions, which are well‐constrained for the recent past. Similar models have successfully predicted the long‐wavelength lowermost mantle structure, which is shaped largely by subduction history (e.g., McNamara and Zhong, 2005; Zhang et al., 2010). Recently, Mao and Zhong (2018; 2019) demonstrated that the inclusion of an endothermic phase transition at 660 km in combination with a low viscosity channel below the transition zone can produce slab behaviors consistent with tomographically imaged structures beneath many subduction zones.
Our Case 40 includes a low‐viscosity channel below 660 km and a phase transition but differs from the models shown in Mao and Zhong (2018) in that we use a longer plate motion history and a different plate reconstruction. We find that relative to the other models considered, this model produces the best correlation in long‐wavelength structure within and immediately below the mantle transition zone (Figure 1.4c), but poorer overall correlation between c. 800–1,000 km than the other models considered. Intriguingly, the power spectral slope in Case 40 is more similar to the pattern seen in the tomographic models (Figure 1.5) than any of the other cases, showing an increase in the slope of the power spectrum below the base of the transition zone, similar to the feature observed in SEISGLOB2 (Durand et al., 2017). The key parameter that distinguishes this model from the others is the inclusion of the low‐viscosity channel, which can have a “lubrication” effect on slabs, allowing them to move laterally below the base of the transition zone. Among the other cases, we can see that there is limited sensitivity of the power spectral slope to whether viscosity is increased at 660 km or 1,000 km depth. Indeed, in Cases 18 (viscosity increase at 1,000 km) and 9 (viscosity increase at 660 km depth), the most significant change in spectral slope is at a depth of 660 km, coincident with the included phase transition. We note that Case 9 has the best overall correlation with the tomographic model due to high values of correlation throughout much of the lower mantle, but does not reproduce structure in the transition zone or shallow lower mantle as well as some of the other models.
In previous work (Rudolph et al., 2015), we presented evidence for an increase in viscosity in the mid‐mantle based on inversions constrained by the long‐wavelength geoid. The viscosity inversions shown in Figure 1.6 are quite similar to what we found previously, despite different choices in parameterization (piecewise linear variation of viscosity vs. piecewise constant), and the use of a different tomographic model (the density model ME16‐160, for which results are shown in Figure 1.6b). There are key differences in the parameterizations of SEMUCB‐WM1 versus the density model ME16‐160, especially near the transition zone. SEMUCB‐WM1 uses a continuous parameterization in the radial direction using splines, whereas ME16‐160, which adopts the same radial parameterization as S362ANI and S362ANI+M (e.g., Kustowski et al., 2008; Moulik and Ekström, 2014), allows a discontinuity in the parameterization at 650 km depth. Moreover, S362ANI+M includes data particularly sensitive to these depths such as normal modes and the precursors to the body wave phase SS that reflect off transition‐zone discontinuities. As a result, the change in the pattern of heterogeneity from the transition zone to the lower mantle across the 650‐km discontinuity is more abrupt in ME16‐160 compared to SEMUCB‐WM1. The depth and abruptness of changes in structure are exactly the features reflected in the plots of the radial correlation function in Figure 1.3. SEMUCB‐WM1 shows a clear decorrelation at 1,000 km depth and a minimum in correlation length at 650 km. On the other hand, S362ANI+M and GLAD‐M15 show the most substantial change in correlation structure at 650 km depth and a minimum in correlation at shallower depths in the upper mantle. Given the differences in the depths at which major changes in lateral structure occur in SEMUCB‐WM1 vs. ME16‐160, one might expect to recover a somewhat different preferred depth of viscosity increase between the upper mantle and lower mantle, because the preferred depth of the viscosity increase is typically very close to the crossover depth from positive to negative sensitivity in the geoid kernel. The fact that viscosity inversions with both tomographic models yield a viscosity increase substantially deeper than 650 km and closer to 1,000 km may therefore be significant.
Some of the inferred viscosity profiles contain a region with reduced viscosity below the 650 km phase transition (Figure 1.6b). The low‐viscosity channel emerges as a feature in our ensemble solutions as additional data constraints are added to the inversion, justifying more complex solutions. The low‐viscosity region is a pronounced feature in the viscosity profiles based on ME16‐160 and there also appears to be a more subtle expression of this feature in the viscosity profiles based on SEMUCB‐WM1. Such a feature has been suggested on the basis of several lines of evidence. First, the transition from ringwoodite to bridgmanite plus ferropericlase involves complete recrystallization of the dominant phases present, and multiple mechanisms associated with the phase transition could modify the viscosity. In convective downwellings, the phase transition could be accompanied by a dramatic reduction in grain size to ∼μm size (Solomatov and Reese, 2008). On theoretical grounds, it might be expected that transformational superplasticity could reduce viscosity by two to three orders of magnitude within 1.5 km of the 650 km phase transition (Panasyuk and Hager, 1998). Second, inversions for the viscosity profile constrained by the global long‐wavelength geoid allowed