Viscosity profile of the lower mantle

Summary. We determine the variation of effective viscosity η across the lower mantle from models of the Gibb's free energy of activation G * and the adiabatic temperature profile. The variation of G * with depth is calculated using both an elastic strain energy model, in which G * is related to the seismic velocities, and a model which assumes G * is proportional to the melting temperature. The melting temperature is assumed to follow Lindemann's equation. The adiabatic temperature profile is calculated from a model for the density dependence of the Grüneisen parameter. Estimates of η depend on whether the lower mantle is a Newtonian or power law fluid. In the latter case separate estimates of η are obtained for flow with constant stress, constant strain rate, and constant strain energy dissipation rate. For G * based on the melting temperature, increases in η with depth range from a factor of about 100 for Newtonian deformation or power-law flow with constant stress to about 5 for non-Newtonian deformation with constant strain rate. For G * based on elastic defect energy, increases in η with depth range from a factor of about 1500 for Newtonian deformation or power-law flow with constant stress to about 10 for non-Newtonian deformation with constant strain rate. Among these models, only a non-Newtonian lower mantle convecting with constant strain rate or constant strain energy dissipation rate is consistent with recent estimates of mantle viscosity from post-glacial rebound and true polar wander data.