Scaling relationships for chemical lid convection with applications to cratonal lithosphere

We obtain scaling relationships for convection beneath a chemically distinct conducting lid and compare this situation with isochemical stagnant lid convection. In both cases, the vigor of convection depends upon the small temperature contrast across the actively convecting rheological boundary layer, that is, Delta T(rheo), the temperature difference between the base of the lid and the underlying half-space. The laterally averaged convective heat flow beneath a chemical lid scales as q alpha Delta T(rheo)(4/3). Heat flow through a chemical lid approaches a stagnant lid value where the lid does not impact the rheological boundary layer. Such a condition is met when Delta T(rheo)/T(eta) approximate to 3.6, where T(eta) is the temperature change required to change viscosity by a factor of e. We apply our scaling relationships to the slow vertical tectonics of continental interiors: We find that whereas chemical lid convection governs the mantle heat flow to the base of cratons that are underlain by chemically buoyant lithosphere, classical stagnant lid convection governs heat flow into platforms. The laterally averaged heat flow supplied by isochemical stagnant lid convection to platforms has waned as the Earth's mantle cooled. Consequently, the thickness of platform lithosphere, in thermal equilibrium with isochemical stagnant lid convection, has increased over time. Thermal contraction of the thickening platform lithosphere is expected to produce similar to 300 m subsidence relative to cratons beneath air. This prediction explains why cratons tend to outcrop and platforms tend to be sediment covered.