On Convection in the Upper Mantle

Present estimates of viscosity and other pertinent parameters make it unlikely that thermal convection exists in the lower mantle. Convection may be considered from the point of view of an instability process for the upper mantle but the probable non-Newtonian nature of viscosity in the upper mantle makes this problem difficult to solve. Criteria are suggested which evaluate the pertinence of the convection current hypothesis to the upper mantle, and which are formally independent of the viscosity. Estimates of these quantities can be obtained from the model in which Newtonian viscosity is used. The postulate is introduced that, since these quantities are independent of the viscosity, their estimates will apply, to order of magnitude, to other models of viscosity. The estimates of (1) the time necessary to set up stable convection and (2) the gravity anomaly expected over a convecting mantle are consistent with the hypothesis of convection in the upper mantle. The estimates (3) of the depression of the geoid over a rising current and (4) of the horizontal scale of the convection cells appear to yield results inconsistent with convection in the upper mantle.