Postglacial rebound in a power-law medium with axial symmetry and the existence of the transition zone in relative sea-level data

Abstract

This work is a continuation of the investigation of Wu (1992a) into understanding the effect of non-linear rheology on postglacial rebound. As in the previous study, the finite element method is used to study the deformation of incompressible flat-earth models with power-law rheology. However, unlike the previous study where the unrealistic assumption of plane strain was used, here the loads are assumed to be axially symmetrical. T1 characteristic deformation pattern of some simple earth models due to these axially symmetrical loads are studied. The effects of load distribution and a time-dependent contracting ice model are also investigated in this paper. From the characteristic deformation patterns of non-linear half-spaces or channels that do, or do not, have elastic lithospheres, it is demonstrated that non-linear earth models cannot explain the existence of the ‘transition zone’ in the sea-level data. This cannot be achieved by varying the stress exponent n because increasing n only makes the effect of non-linearity more prominent and will not significantly alter the pattern of deformation. It is also demonstrated that a contracting parabolic ice load with diminishing load cannot explain the sea-level data in the ‘transition zone’ either. When the observed sea-level data near the centre of rebound in Fennoscandia or Laurentia are compared with the predicted uplift curves, it is demonstrated that power-law rheological models with instantaneous melting histories can fit the relative sea-level (RSL) observations near the centre of rebound. However, no earth model with a completely non-linear mantle that is able to match the data simultaneously in the centre, near the edge or outside the ice sheet has been found. Thus, although the rheology of the mantle maybe non-linear, postglacial rebound probably sees the rheology of the mantle as linear.