Sublithospheric convection, `steady-state' heat flow, and the rheology of oceanic mantle

The dynamic state of oceanic asthenosphere is poorly known. Assuming that it is convecting, however, we can relate surface observables to mantle rheology using scaling laws for thermal convection. Inferred rheology can then be compared with other types of constraints to verify the initial assumption. Surface heat flow is relatively constant at old ocean basins (40-50 mW~m^-2), and this so-called steady-state heat flow has been used as a constraint on the viscosity of asthenospheric mantle. Most of previous attempts have used a heat flux scaling law derived for steady-state convection (in a time-averaged sense), and their estimates are consistently within the range of 10^18}-10{19~Pa~s. Even if asthenospheric mantle is convecting, however, whether or not the convection is at a statistically steady state is another question, which depends on the onset time of convection as well as the size of a convection system. On the basis of recently established scaling laws for sublithospheric convection [Korenaga and Jordan, 2002, JGR, submitted], it can be shown that steady-state convection is quite unlikely to be realized beneath oceanic lithosphere. An alternative approach based solely on a scaling law for the onset of convection thus appears to be potentially more robust. The range of asthenospheric viscosity estimated by this approach is 8*E^18}-3*E{19~Pa~s if the activation energy is 300 kJ~mol^-1, and 2*E^19}-9*E{19~Pa~s if the activation energy is 100 kJ~mol^-1. The former range is consistent with laboratory data as well as geodynamic inference based on the geoid. The latter is consistent with geodynamic inference based on seamount loading history. Different activation energies predict different temperature contrasts in convecting mantle. Seismic tomography has the potential to discriminate between these possibilities.