Stability and Motion of the Asthenosphere

Abstract

After a discussion of the equations of motion of the asthenosphere, the physical properties of the lithosphere are considered, with particular reference to the boundary condition at the interface of the two regions. A linear instability problem is then derived for the lithosphere/asthenosphere system regarded as a plane layer. This problem is similar to that obtained for the convective instability of a plane layer with surface tension variations, and a new method of solution for problems of this type is demonstrated. For the asthenosphere the presence of the lithosphere has a similar effect to that of surface tension. The results for different values of lithosphere thickness and asthenosphere depth are discussed. It is shown that the presence of surface forces tends to increase the wave-length of the motion at instability. The equations for linear convective instability within a spherical annulus are derived in a simplified form, and the combined buoyancy/surface tension problem on a sphere is solved. The relevance of this problem to that of convection within the asthenosphere is discussed, with emphasis on the effect that surface forces have on the flow pattern realised. Finally, a subduction zone is modelled as a two-dimensional semi-infinite strip with moving walls. The Stokes' flow problem for all regions of this type is solved by means of an eigenfunction expansion.