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.
1.4 DISCUSSION
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 VS 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 VS/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