Some effects of lateral viscosity variations on geoid and surface velocities induced by density anomalies in the mantle

We present 3-D solutions for buoyancy-driven flow with variable viscosity in a spherical shell. A hybrid finite difference and spectral method is used to assess the influence of lateral-viscosity variations (LVV) on the long-wavelength (ℓ = 1–6) observable features of mantle convection: geoid anomalies, topography anomalies and surface velocities. The non-linear coupling of the various spherical harmonic modes is calculated by an interative technique. The density anomalies δp</it> that drive the flow are taken to be proportional to the anomalies of seismic velocity from several tomographic models. Two viscosity models are used: a Newtonian ‘temperature dependent’ model in which the viscosity varies exponentially with δp</it>, and a non-Newtonian model in which the viscosity varies with strain rate. Our calculations show that the effects of LVV on the geoid are of second order relative to those due to changes in radial-viscosity structure. The geoid is hardly affected by LVV if the mantle viscosity is radially uniform, but the effect on the higher order (δ > 3) modes of the geoid can be significant if the viscosity is radially stratified. However, for the models tested neither temperature-dependent viscosity nor non-linear rheology is found to reduce the misfit between the observed and the modelled geoid. Toroidal motion is generated by lateral viscosity differences inferred from the tomography results, but the toroidal-to-poloidal ratio is small (<20 per cent).