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

Calculations of viscoelastic perturbations of an incompressible fluid 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 deficiencies 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 stratification. The present study is concerned with load-induced Maxwell viscoelastic 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 stratification (earth model P) and purely compositional stratification (earth model C). The comparison of the solutions for these earth models with that for the special case of no density stratification (earth model R) shows that effects due to the initial density gradient become important for perturbations whose lateral scale length exceeds about 10 km. Using axisymmetric models of the Pleistocene Fennoscandian and Canadian ice sheets and considering the vertical surface displacements near the load axes, the maximum differences 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.