Compressible vs. incompressible in glacial isostatic adjustment models: Does it matter?

Glacial isostatic adjustment (GIA) models provide estimates of velocity, gravity, stress, and sea-level change based on ice-loading scenarios from past glaciations. These models require extensive input, including ice histories and a variety of Earth model parameters that describe the 3D structure and rheology. Different assumptions can be made regarding material parameters, particularly in terms of compressibility, which is described by the Poisson’s ratio. Incompressible materials (Poisson’s ratio equal to 0.5) do not change volume under deformation. However, seismological observations indicate that the Poisson’s ratio in the lithosphere and mantle deviates from 0.5, typically being much smaller, which reflects the presence of compressible materials. Consequently, GIA models must account for compressibility in their material parameters as well as in the solved equations. Despite this, some GIA model codes consider only incompressible materials.

Here, we will show the effect of compressible versus incompressible Earth models on changes in sea level, velocity, gravity, and stress using a newly developed compressible finite-element code. The new GIA model code incorporates the sea-level equation with moving coastlines and rotational feedback, accounts for both grounded and floating ice, removes rigid-body rotation, and calculates deformation in the centre-of-mass frame. Importantly, this global-scale analysis, using the new code, is the first to explore how glacially induced stresses obtained from a spherical GIA model are affected by assumptions about compressibility.