Abstract
Analytical solutions are presented for the deformation of a three-layered plane earth with elastic—viscoelastic rheology and subject to time-dependent vertical surface loads. The models investigated are: (1) elastic or viscoelastic layers overlying an inviscid fluid; (2) viscoelastic half-space; (3) elastic layer over a viscoelastic layer with different boundary conditions at the base of the second layer. Emphasis is given to the interdependence between the dominant parameters of thickness of the elastic layer, the effective viscosity of the viscoelastic layer, the change in viscosity with depth and the wavelength and duration of loading. The models have been applied to the loading and unloading of the late Pleistocene pluvial Lake Bonneville using the load histories given by Crittenden. The studies differ from earlier analyses of the Bonneville uplift in several important aspects including: a rigorous treatment of the horizontal and vertical coupling between the elastic and viscoelastic media; the mantle is treated as viscoelastic rather than as a viscous medium; the wavelength information has been introduced by using a more realistic model for the load geometry; and the effect of the Wasatch Fault has been considered. The models indicate that the two principal parameters defining the rebound are the effective viscosity of the upper mantle and the effective thickness of the elastic layer and that those two parameters can be separated only if both wavelength and amplitude information of the deformation is available at more than one epoch. Observations of uplift at one epoch are not sufficient to resolve the thickness of the elastic layer and the effective viscosity of the upper mantle but upper bounds for these quantities are well established as 30km and 1.2 × 1021 poise respectively. The uplift results do not confirm or deny the possibility of a low viscosity channel in the upper mantle but this can be resolved only if the uplift data are supplemented with observations of the present uplift rate. The published rates are controversial, but if valid they point to a thin (× 15 km) elastic layer and a relatively narrow (× 200km) low viscosity channel. While the models predict uplift near the centre of the former lake, they also predict that the peripheral regions should be subsiding appreciably if flow is confined into a shallow channel of low viscosity. Observations reported by Anderson & Bucknam suggests such behaviour. Likewise the present rate of uplift changes sign at some distance from the centre of the lake and detailed observations of warping of the shorelines and repeated levelling in the area may yield further constraints on the rebound model.