We have studied the problem concerning the onset of convective instabilities below the oceanic lithosphere. A system of linear partial differential equations, in which the background temperature field is time-dependent, is integrated in time to monitor the evolution of incipient disturbances. Two types of rheologies have been examined. One depends strongly on temperature. The other involves a viscosity which is both temperature- and pressure-dependent. The results from this initial-value approach, in which the viscosity profiles migrate downward with time, reveal the importance of considering temperature- and pressure-dependent rheology in issues regarding the development of local instabilities in upper mantle convection. For temperature-dependent viscosity, viscosities of 0(1020P) are required to produce instabilities with growth-rates of 0(.1/Ma). In contrast, these same growth rates can be attained for a temperature- and pressure-dependent viscosity profile with a mean value close to 0(1020P) in the upper mantle, owing to the presence of a low viscosity zone, 0(1020P), existing right below the lithosphere. Unlike the results of temperature-dependent viscosity, whose growth-rates increase with time, the amplification of disturbances in a fluid medium with temperature- and pressure-dependent rheology reaches a maximum at an early age, < 50 Ma, and decreases thereafter with time. This suggests the potential importance played by initial disturbances in the evolution of the oceanic lithosphere.
Bibliographical noteFunding Information:
We thank Dr. Granville Sewell of Univ. Texas for helpful numerical advice. We are especially grateful to C. Jaupart for giving us a copy of his preprint. It is also a pleasure for us to acknowledge the thoughts that Uli Christensen, H.C. Nataf, and S.H. Davis have so generously shared with us. This research has been supported by N.S.F. grants EAR-8117439 and EAR-8214094, by Petroleum Research Foundation grant 13550-G2, administered by the American Chemical Society, and by a N.A.T.O. research award (grant no. 27681), and by the "Institut National d'Astronomie et de G6ophysique" (INAG) in the framework of the A.T.P. "Sismog6n6se". (Decision No. 1150.)