Mantle Convection and Surface Expressions. Группа авторов

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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 СКАЧАТЬ