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The power spectra of four recent global tomographic models are shown in Figure 1.5. While S362ANI+M contains little power above spherical harmonic degree 20 due to its long‐wavelength lateral parameterization with 362 evenly spaced spline knots, the other models contain significant power at shorter wavelengths that are beyond the scope of this study. In general, the models are dominated by longer wavelengths at all depths. The spectral slope for each model (up to degree 20) is shown in the rightmost panel of Figure 1.5. Increasingly negative spectral slopes indicate that heterogeneity is dominated by long‐wavelength features. All of the models generally show a more negative spectral slope in the transition zone than in the upper mantle or the shallow lower mantle, indicating the presence of more long‐wavelength V_S heterogeneity within the transition zone and just below the 650 km discontinuity, which we attribute to the lateral deflection of slabs.

Figure 1.5 Power spectra of four recent global V_S tomographic models. Because our focus is on long‐wavelength structure, and to ensure a more equitable comparison, we show only spherical harmonic degrees 1–20, though SEMUCB‐WM1, SEISGLOB2, and GLAD‐M15 contain significant power at shorter wavelengths. At the right, we show spectral slopes (defined in the text) for the four models. Here, increasingly negative values indicate a concentration of power in longer wavelengths/lower spherical harmonic degrees.

Figure 1.3 shows radial correlation plots for the four tomographic models. Here, the spherical harmonic expansions are truncated at degrees 2 (lower left triangle) and 4 (upper right triangle). At degrees 1–2 and 1–4, both SEMUCB‐WM1 and SEISGLOB2 show a clear change in the correlation structure near 1,000 km depth. On the other hand, S362ANI+M and GLAD‐M15 both show a change in correlation structure at 650 km.

We compared the character of heterogeneity in the geodynamic models with mantle tomography by calculating the power spectrum and spectral slope of each of the five geodynamic models. Because the depth‐variation of power in the geodynamic models does not have as straightforward an interpretation as the V_S power spectra shown for tomographic models, we focus on the spectral slope of the geodynamic models, shown in Figure 1.4. We computed correlation coefficients between each of the geodynamic models and SEMUCB‐WM1, shown in Figure 1.4C.

For both of the tomographic models used to infer mantle viscosity, we carried out viscosity inversions (Figure 1.6) constrained by spherical harmonic degree 2 only, degrees 2 and 4 only, and degrees 2–7. The viscosity profiles are quite similar, regardless of which spherical harmonic degrees are used to constrain the inversion. However, we observe an increase in the overall complexity of the viscosity profile as more spherical harmonic degrees are included, as well as a tendency towards developing a low‐viscosity region below the 650 km discontinuity (red curves in Figure 1.6), considered in the context of parsimonious inversions, this tendency toward increased complexity can be attributed to the progressively greater information content of the data. The posterior ensembles from the viscosity inversions contain significant variability among accepted solutions, and the solid lines in Figure 1.6 indicate the log‐mean value of viscosity present in the ensemble at each depth while the shaded regions enclose 90% of the posterior solutions. We note that while the individual solutions in the posterior ensemble produce an acceptable misfit to the geoid, the ensemble mean itself may not. Therefore, potential applications in the future need to account for all samples of viscosity models in our ensemble rather than employ or evaluate the ensemble mean in isolation.