How flat is the lower-mantle temperature gradient?

The temperature gradient in the lower mantle is fundamental in prescribing many transport properties, such as the viscosity, thermal conductivity and electrical conductivity. The adiabatic temperature gradient is commonly employed for estimating these transport properties in the lower mantle. We have carried out a series of high-resolution 3-D anelastic compressible convections in a spherical shell with the PREM seismic model as the background density and bulk modulus and the thermal expansivity decreasing with depth. Our purpose was to assess how close under realistic conditions the horizontally averaged thermal gradient would lie to the adiabatic gradient derived from the convection model. These models all have an endothermic phase change at 660 km depth with a Clapeyron slope of around -3 MPa K^-1, uniform internal heating and a viscosity increase of 30 across the phase transition. The global Rayleigh number for basal heating is around 2 × 10⁶, while an internal heating Rayleigh number as high as 10⁸ has been employed. The pattern of convection is generally partially layered with a jump of the geotherm across the phase change of at most 300 K. In all thermally equilibrated situations the geothermal gradients in the lower mantle are small, around 0.1 K km^-1, and are subadiabatic. Such a low gradient would produce a high peak in the lower-mantle viscosity, if the temperature is substituted into a recently proposed rheological law in the lower mantle. Although the endothermic phase transition may only cause partial layering in the present-day mantle, its presence can exert a profound influence on the state of adiabaticity over the entire mantle.