Deformation of an incompressible viscoelastic flat earth with powerlaw creep: a finite element approach

SUMMARY Extrapolating experimental creep data to mantle conditions indicates that the upper mantle may deform as a power‐law medium. In all of the previous models of loading/unloading in a power‐law medium, some simplifying assumptions were made to keep the calculation tractable. Unfortunately, some of these assumptions are invalid while others are too restrictive. In this paper, the finite element method is used to study the deformation of incompressible linear and non‐linear rheological earth models that are subject to constant gravitational acceleration. The advantage of this new approach is that none of these simplifying assumptions has to be made—thus the solution is much more rigorous. The deformation of a non‐linear half‐space due to Heaviside loading and unloading of a boxcar load is shown to be characterized by: (i) ubiquitous updoming/sinking outside the load; (ii) a very high initial rate of deformation followed by a much slower rate inside the load; and (iii) the load history is fully coupled with the rheology of the earth because the state of stress, caused by the magnitude of the load and the sequence of loading or unloading events, determines the effective viscosity and thus the deformation. It is also demonstrated that the usual assumption of ‘self‐similarity’ and ‘proportional relaxation’ are invalid. Moreover, the relaxation time is a function of both space and time. The effect of an elastic lithosphere on a linear or non‐linear channel is shown to be much larger than that for a half‐space even at small t . The effects of a non‐linear channel, a parabolic load and a depth‐dependent creep parameter A are also studied. When the observed uplift data near the rebound centre in Fennoscandia are compared to the predicted uplift curves, it is demonstrated that for the instantaneous removal of a 15 MPa boxcar load, power‐law rheological models cannot fit the observations as well as the linear models can. However, more work has to be done before one can decide whether the rebound process actually involves a mantle with linear rheology or power‐law rheology.