Computations of the viscoelastic response of a 3-D compressible Earth to surface loading: an application to Glacial Isostatic Adjustment in Antarctica and Canada

We develop a 3-D finite-element model to study the viscoelastic response of a compressible Earth to surface loads. The effects of centre of mass motion, polar wander feedback, and self-consistent ocean loading are implemented. To assess the model's accuracy, we benchmark the numerical results against a semi-analytic solution for spherically symmetric structure. We force our model with the ICE-5G global ice loading history to study the effects of laterally varying viscosity structure on several glacial isostatic adjustment (GIA) observables, including relative sea-level (RSL) measurements in Canada, and present-day time-variable gravity and uplift rates in Antarctica. Canadian RSL observations have been used to determine the Earth's globally averaged viscosity profile. Antarctic GPS uplift rates have been used to constrain Antarctic GIA models. And GIA time-variable gravity and uplift signals are error sources for GRACE and altimeter estimates of present-day Antarctic ice mass loss, and must be modelled and removed from those estimates. Computing GIA results for a 3-D viscosity profile derived from a realistic seismic tomography model, and comparing with results computed for 1-D averages of that 3-D profile, we conclude that: (1) a GIA viscosity model based on Canadian relative sea-level data is more likely to represent a Canadian average than a true global average; (2) the effects of 3-D viscosity structure on GRACE estimates of present-day Antarctic mass loss are probably smaller than the difference between GIA models based on different Antarctic deglaciation histories and (3) the effects of 3-D viscosity structure on Antarctic GPS observations of present-day uplift rate can be significant, and can complicate efforts to use GPS observations to constrain 1-D GIA models.