Effects due to compressional and compositional density stratification on load-induced Maxwell viscoelastic perturbations

Abstract

SUMMARY Calculations of viscoelastic perturbations of an incompressible £uid earth initially in hydrostatic equilibrium have been conventionally based on models consisting of isocompositional layers. A special case is the incompressible, isocompositional half-space, for which the initial density distribution is spatially uniform. One of the de¢ciencies of this model is that it ignores the increase of the initial density with depth in the earth’s interior due to compressional and compositional strati¢cation. The presentstudy is concernedwith load-induced Maxwellviscoelastic perturbations of a half-space with a compressional and compositional initial density gradient. Analytic solutions to this problem are deduced for the limiting cases of purely compressional strati¢cation (earth model P) and purely compositional strati¢cation (earth model C). The comparison of the solutions for these earth models with that for the special case of no density strati¢cation (earth model R) shows that eiects due to the initial density gradient become important for perturbations whose lateral scale length exceeds about 10 3 km. Using axisymmetric models of the Pleistocene Fennoscandian and Canadian ice sheets and considering the vertical surface displacements near the load axes, the maximum diierences are found to be about 10 m (Fennoscandia) or 35 m (Canada) at the beginning of relaxation for earth models P and R and about 50 m (Fennoscandia) or 150 m (Canada) at intermediate times of relaxation for earth models C and R.