Glacial-Isostatic Adjustment-I. The Forward Problem

The isostatic adjustment of a radially stratified visco-elastic spheroid is treated using space-time Green functions for the associated surface mass load boundary value problem. These impulse response functions are convolved with a Heaviside function to give the time dependent deformation of the planet which would be produced by a unit point mass brought up from infinity at t= 0 and allowed to remain on the surface. The resulting 'Heaviside Green functions' can be employed to simulate all of the important signatures of glacial isostatic adjustment. Given a space-time dependent surface mass load consisting of ice sheet ablation histories and a model of the simultaneous filling of the ocean basins, these source terms are simply convolved with the Heaviside Green function appropriate to a specific response signature. A realistic model of the spatial distribution of the main late Pleistocene ice loads and of their temporal disintegration is constructed. The response of two visco-elastic earth models is computed and compared to a global set of relaxation data (relative sea-level curves). On the basis of this initial comparison of theory and observation the possibility that the lower mantle has a viscosity which is significantly in excess of the viscosity of the upper mantle is excluded. In addition, clear evidence of the presence of the lithosphere has been found in relaxation data from sites which were near the edge of the Laurentide ice sheet. Such data should therefore prove useful as a basis for analysis of lateral variations in lithosphere thickness. Further extensions of the calculation are suggested.