Small-scale convection beneath oceans and continents

Small-scale convection supplies heat flow of ∼17 mW m⁻² to the base of stable continents where xenolith studies resolve the geotherm. However, effects of small-scale convection are difficult to resolve in ocean basins. On first pass, most seafloor appears to subside to an asymptote compatible with ∼40 mW m⁻² convective heat flow. These common regions are tracked by hotspots so uplift associated with ponded mantle material is an attractive alternative. Unaffected seafloor in the North and South Atlantic continues to subside with the square root of age as expected from pure conduction. The theory of stagnant-lid convection provides good scaling relationships for heat flow. For linear viscosity, heat flow is proportional to the underlying “half-space” viscosity to the −1/3 power and the temperature to change viscosity by a factor of e to the 4/3 power. The formalism is easily modified to represent convection beneath a lid of highly viscous and buoyant cratonal lithosphere and to represent transient convection beneath thickening oceanic lithosphere. Asthenospheric mantle with linear, strongly temperature-dependent, and weakly depth-dependent viscosity is compatible with both oceanic and continental data. More complicated rheology may allow vigorous small-scale convection under most but not all old ocean basins. Still viable hypotheses require poorly understood global features, including lateral variations of asthenospheric temperature. Seismological studies have the potential to resolve the lithosphere-asthenosphere boundary, including local variations of its depth associated with small-scale convection.