Seismic imaging of the D'' and constraints on the core heat flux

Recent seismic imaging of the deep mantle has revealed lens-shaped layers near the bottom of the mantle. The morphology of this layering has been attributed to the crossing of the post-perovskite phase boundary by the local geotherm. We have developed a technique for quantifying the relationships between the depths of the double crossings of the post-perovskite transition developed in 3D spherical mantle convection, as a means for testing the viability for using the Clapeyron slope of the phase transition to put bounds on the heat flux from the core. We have argued from the probability distribution of the local heat flow at the core-mantle boundary that there are intrinsic problems in using error function from half-space cooling curves for constraining the core heat flux because of the non-Gaussian shape of the probability distribution of the core heat flow in realistic 3D convection models. In order to constrain better the core heat flux with the above arguments, we need to know much better the mantle viscosity stratification and the pressure dependence of thermal conductivity in the deep mantle. Only then can we put together enough constraints to discuss with greater certainty about the core heat flux.