Cooling of the Earth: A parameterized convection study of whole versus layered models

Compositionally layered mantle models have often been invoked in order to explain the geochemistry observed at the Earth's surface, specifically the discrepancy between ocean island basalt and mid-ocean ridge basalt compositions. One disadvantage of layered models is the reduction in cooling efficiency compared to whole-mantle convection as a direct result of the insulating nature of the thermal boundary layer that develops between the two convecting layers. This may pose a significant problem for layered models in which the bottom layer is enriched in heat-producing radioactive elements with respect to the top layer. One may expect that the bottom layer would become superheated over the lifetime of the Earth. We perform this study in order to test whether layered models are thermally feasible. We are interested in discovering whether it was possible, within Earth-like constraints, to produce a bottom layer temperature that remains below the solidus without simultaneously producing a top layer that is too cool. We use parameterized convection to explore a wide parameter range of input values for several layering configurations. We study both a whole mantle convection model and the recently proposed layered convection model, which places the boundary between the layers at 1600-km depth [Kellogg et al., 1999]. We use the present-day heat flow and mantle viscosity as primary constraints and use the resulting average temperature as a test for the feasibility of the models. Our results reveal that for whole mantle convection, a wide parameter range produces results that satisfy our constraints. This is in contrast to the layered convection model in which we find that the parameter range that satisfies constraints is significantly reduced or perhaps, nonexistent.