Thermal response of a moving lithosphere over a mantle heat source

Abstract

The mid‐ocean bathymetric swells observed around some volcanic island chains can be modeled using the thermal conduction equations of an oceanic lithosphere moving over a heat source located at the base of the plate. Some previous studies of this problem have suggested that the heat source must lie well within the lithosphere in order to explain the observed bathymetry and surface heat flow. These conclusions are based on an isothermal boundary condition at the base of the lithosphere, but this choice requires that the heat source is maintained above this boundary and can actually lead to a flux of heat back into the mantle, particularly in the vicinity of the heat source. If the lower boundary is insulated insofar as the anomalous temperature field is concerned, flux from the heat source back into the mantle is prevented, resulting in a more rapid uplift of, and in an increased heat flow across, the seafloor. Previous solutions have considered only the steady state solutions, whereas the present model also evaluates transient solutions. For rapidly moving oceanic plates the transient effects can be neglected provided that the heat source has been active for at least 107 years and that the direction of motion and the intensity of the heat source have remained constant in this interval. Solutions, with the heat source located near the base of the conductive layer, of the conduction equations for heat flow, bathymetry, and geoid heights in the spatial domain reproduce the principal observational characteristics of the Hawaiian swell at distances away from the immediate origin of the swell, and this part of the swell can be used to estimate the thermal conduction model parameters. The model does not wholly explain the observations near the origin and the mismatch may reflect a dynamic component in the support of the swell.