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The recent tomographic models considered here show substantial discrepancies in the large‐scale variations within the mid mantle. The low overall RMS of heterogeneity (with the consequent small contribution to data variance) and a reduction in data constraints at these depths (e.g., normal modes, overtone waveforms) exacerbates the relative importance of a priori information (e.g., damping) in some tomographic models. The RCF plots shown in Figure 1.3 show that even at the very long wavelengths characterized by spherical harmonic degrees 1–2 and 1–4, there is rapid change in the RCF near 1,000 km in SEMUCB‐WM1 and SEISGLOB2. On the other hand, S362ANI+M and GLAD‐M15 both show more evidence for a change in structure near 1,000 km at degrees 1–2 but closer to the 650 km discontinuity for degrees up to 4. In order to understand the changes in the RCF, spatial expansions of the structures in the four tomographic models are shown for degrees 1–4 and at depths within the lithosphere, transition zone, and lowermost mantle are shown in Figure 1.2. We previously examined the long‐wavelength structure of SEMUCB‐WM1 and suggested that the changes in its RCF at 1,000 km depth are driven primarily by the accumulation of slabs in and below the transition zone in the Western Pacific (Lourenço and Rudolph, in review).

Figure 1.6 Results from transdimensional, hierarchical, Bayesian inversions for the mantle viscosity profile, using two different models for density. (a) Density was scaled from Voigt V_S variations in SEMUCB‐WM1 using a depth‐dependent scaling factor computed using HeFESTo (Stixrude and Lithgow‐Bertelloni, 2011). (b) Density variations from a joint, whole‐model mantle of density and seismic velocities (Moulik and Ekström, 2016)

The shift in pattern of mantle heterogeneity within and below the transition zone is influenced by changes in the large‐scale structure of plate motions. In Figure 1.7, we show the long‐wavelength structure of plate motions at 0, 100, and 200 Ma. We expanded the divergence component of the plate motion model by Matthews et al. (2016) using spherical harmonics and show only the longest‐wavelength components of the plate motions. This analysis is similar in concept to the multipole expansion carried out by Conrad et al. (2013) to assess the stability of long‐wavelength centers of upwelling, as a proxy for the long‐term stability of the LLSVPs. These long‐wavelength characteristics of the plate motions need to be interpreted with some caution because the power spectrum of the divergence of plate motions is not always dominated by long‐wavelength power, and power at higher degrees may locally erase some of the structure that overlaps with low spherical harmonic degrees (Rudolph and Zhong, 2013). However, for the present day (Figure 1.7, right column), the long‐wavelength divergence field does show a pattern of flow with centers of long‐wavelength convergence centered beneath the Western Pacific and beneath South America, where most of the net convergence is occurring. On the other hand, at 100 and 200 Ma, the pattern of long‐wavelength divergence is dominated by antipodal centers of divergence, ringed by convergence. The mid‐mantle structures seen in global tomographic models (Figure 1.2) closely resemble the long‐wavelength divergence field for 0 Ma, while the lowermost mantle structure is most correlated with the divergence field from 100 and 200 Ma (Figure 1.7). This analysis of the long wavelength components of convergence/divergence and the long‐wavelength mantle structure is consistent with analyses of the correlation between subduction history with mantle structure that include shorter wavelength structures (Wen and Anderson, 1995; Domeier et al., 2016). In particular, Domeier et al. (2016) found that the pattern of structure at 600–800 km depth is highly correlated with the pattern of subduction at 20–80 Ma. This suggests a straightforward interpretation of the changes in very long wavelength mantle structure, and the associated RCF, because the present‐day convergence has a distinctly different long‐wavelength pattern from the configuration of convergence at 50–100 Ma, and the mid‐mantle structure is dominated by the more recently subducted material. We note, however, that this explanation addresses only the seismically fast features and does not capture additional complexity associated with active upwellings.

Figure 1.7 Divergence component of plate motions computed for 0, 100, and 200 Ma. In the top row, we show the divergence field up to spherical harmonic degree 40. Red colors indicate positive divergence (spreading) while blue colors indicate convergence. The second row shows only the spherical harmonic degree‐1 component of the divergence field, which represents the net motion of the plates between antipodal centers of long‐wavelength convergence and divergence. The third row shows the spherical harmonic degree‐2 component of the divergence, and the bottom row shows the sum of degrees 1 and 2. The white diamonds in the bottom two rows indicate the locations of the degree‐2 divergence maxima (i.e., centers of degree‐2 spreading).

The power spectra of mantle tomographic models contain information about the distribution of the spatial scales of velocity heterogeneity in the mantle, and this can be compared with the power spectra of geodynamic models. Interpreting the relative amounts of power at different wavelength but at a constant depth is more straightforward than the interpretation of depth‐variations in power spectral density. In mantle tomography, decreasing resolution with depth as well as the different depth‐sensitivities of the seismological observations such as surface wave dispersion, body wave travel times, and normal modes used to constrain tomographic models can lead to changes in power with depth that may not be able to accurately reflect the true spectrum of mantle heterogeneity. The geodynamic models presented here have only two chemical components – ambient mantle and compositionally dense pile material. The models are carried out under the Boussinesq approximation, so there is no adiabatic increase in temperature with depth, and the governing equations are solved in nondimensional form. Therefore, to make a direct comparison of predicted and observed shear velocity heterogeneity, many additional assumptions are necessary to map dimensionless temperature variations into wavespeed variations. The effective value of d ln V_S/d ln T at constant pressure is depth‐dependent, with values decreasing by more than a factor of two from the asthenosphere to 800 km depth (e.g., Cammarano et al., 2003), and compositional effects become as important as temperature in the lowermost mantle (Karato and Karki, 2001). Here, we compare the temperature spectrum of geodynamic models with the δV_S spectrum in tomographic models, and this is most appropriate at depths where long‐wavelength V_S 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 for the presence of a low‐viscosity channel at the base of the upper mantle (Forte et al., 1993), and a similar “second asthenosphere” was recovered in inversions constrained by regional (oceanic) geoid anomalies (Kido et al., 1998). The effect of the low‐viscosity channel can modify predictions associated with GIA observables Milne et al. (1998), and in joint inversions of GIA, misfits can be significantly reduced for models that include such a low‐viscosity notch (Mitrovica and Forte, 2004). Finally, in global geodynamic models with prescribed plate motions, the behavior of slabs is broadly consistent with observations of stagnation when such a feature is included (Mao and Zhong, 2018; Lourenço and Rudolph, in review).

An increase in viscosity in the mid‐mantle or viscosity “hill,” which is a feature common to all of our viscosity inversions, has been suggested on the basis of geophysical inversions, and several potential mechanisms exist to explain such a feature. An increase in viscosity below 650 km depth has been recovered in many inversions constrained by the long wavelength geoid and GIA observables (e.g., King and Masters, 1992; Mitrovica and Forte, 1997; Forte and Mitrovica, 2001; Rudolph et al., 2015). An increase in viscosity would be expected to slow sinking slabs (Morra et al., 2010) and affect the dynamics of plumes. The correlation between subduction history and tomographic models has been used to test whether slabs sink at a uniform rate in the lower mantle. A recent study of the similarity between convergence patterns in plate reconstructions and patterns of mantle lateral heterogeneity from an average of V_S tomographic models suggests that the data can neither confirm nor reject the possibility of a change in viscosity below 600 km (Domeier et al., 2016). On the other hand, an analysis of a catalog that relates imaged fast anomalies to specific subduction events does find evidence that the rate of slab sinking decreases across a “slab deceleration zone” between 650–1500 km (van der Meer et al., 2018); one explanation for such a deceleration zone is the increase in viscosity in the shallow lower mantle seen in all of our inverted viscosity profiles.

Several mechanisms exist that could produce an increase in viscosity in the mid‐mantle. Marquardt and Miyagi (2015) measured the strength of ferropericlase at pressures of 20–60 GPa (600–1,000 km) and observed an increase in strength across this range of pressures. Though ferropericlase is a minor modal component of the lower mantle, it could become rheologically limiting if organized into sheets within rapidly deforming regions, an idea supported by experiments with two‐phase analog materials (Kaercher et al., 2016) and with bridgmanite‐magnesiowüstite mixtures (Girard et al., 2016). If the lower mantle rheology is determined by the arrangement of distinct mineral phases, we expect history‐dependence and anisotropy of viscosity (Thielmann et al., 2020), further confounding our interpretations of viscosity in inversions. An increase in the viscosity of ferropericlase is also supported by experimental determinations of the melting temperature at mantle pressures (Deng and Lee, 2017), which show a local maximum in melting temperature for pressures near 40 GPa (1,000 km). Changes in the proportionation of iron could also alter the viscosity of bridgmanite across a depth range consistent with the inferred mid‐mantle viscosity increase. Shim et al. (2017) suggested that at depths of 1,100–1,700 km, an increase in the proportionation of iron into ferropericlase could depress the melting point of bridgmanite, increasing the viscosity predicted using homologous temperature scaling. These various mechanisms are not mutually exclusive and could operate in concert to produce an increase in viscosity near 1,000 km. Finally, we note that the deformation mechanisms of even single phases within the lower mantle remain uncertain. While the lower mantle has long been thought to deform by diffusion creep due to absence of seismic anisotropy at most lower mantle depths, recent calculations suggest that another deformation mechanism – pure climb creep, which is insensitive to grain size and produces no seismic anisotropy – may be active in bridgmanite at lower mantle conditions (Boioli et al., 2017).