The Importance of a High Viscosity Peak at 2000 km Depth for Time-Dependent Convection Dynamics: An Explanation for the Dominance of Degree-2 Structure in the Lower-most Mantle.

In a recent study of the viscosity and thermochemical structure in the deep mantle, Forte and Mitrovica [Nature, 2001] carried out nonlinear, iterative inversions of all available global geophysical data associated with thermal convection in the mantle. These inversions were performed using a new viscous flow model based on recent high-resolution tomographic models of S-wave velocity anomalies. The radial viscosity profiles delivered by these inversions are characterized by a strong peak in viscosity near 2000 km depth, with viscosity then decreasing rapidly towards the core-mantle boundary. Forte and Mitrovica found that this viscosity peak has a profound impact on the pattern of present-day flow in the lower-most mantle, effectively suppressing all but the longest wavelengths of flow (characterized by harmonic degrees less than about l = 6). They argued that such a viscosity-induced low-pass filtering effect provides a simple explanation for the `red' spectrum of heterogeneity in the bottom 1000 km of the mantle. Such tomography-based flow modelling is limited, however, because it only provides an instantaneous `snapshot' of present-day convection dynamics. To confirm the impact of the high-viscosity peak on the time-dependent evolution of the thermal structure in the lower mantle, we developed a numerical model of high Rayleigh number thermal convection in 3-D spherical geometry [Espesset and Forte, 2001]. The model is compressible (in the anelastic approximation), it incorporates surface tectonic plates, depth dependent thermal expansivity and thermal conductivity, and it includes the geodynamically constrained radial viscosity profile inferred by Forte and Mitrovica [Nature, 2001]. As a starting point for the convection simulations we employ the temperature anomalies Forte and Mitrovica derived from the high-resolution seismic tomography models. The convection simulations at high Rayleigh numbers reveal the development and persistence of a pattern of thermal heterogeneity in the bottom 1000 km of the lower mantle which is strongly dominated by spherical harmonic degree l = 2. Comparisons with convection models using a constant viscosity or using a simple two-layer viscosity profile show that this dominance of degree-2 heterogeneity is due to the geodynamically-inferred high viscosity peak at 2000 km depth. The stability and dominance of this quadrupolar pattern of thermal heterogeneity over long times provides a straightforward explanation for the `red' spectrum of deep mantle heterogeneity which has long been observed in the global seismic tomographic models.