Regional perturbations in a global background model of glacial isostasy

In Schotman and Vermeersen (2005, Earth Planet. Sci. Lett. 236), the effect of crustal and asthenospheric low-viscosity zones (LVZs) on geoid heights was shown, as predicted by models of glacial-isostatic adjustment (GIA). The governing equations were solved analytically in the spectral domain, which makes the method used accurate and fast. However, it does not allow for (large) lateral variations in earth stratification. As the properties of shallow LVZs can be expected to vary laterally, we have developed a finite-element model based on Abaqus. Global (spherical-3D) finite-element models are currently not capable of providing high-resolution predictions, which we expect due to the shallowness of the LVZs. We therefore use a regional (flat-3D) model and compute geoid heights from the predicted displacements at density boundaries by solving Laplace’s equation in the Fourier-transformed domain. The finite-element model is not self-gravitating, but we compare the results with a self-gravitating spectral model under the assumption that the lack of self-gravitation is partly compensated by the lack of sphericity, and that long-wavelength differences largely cancel out when using perturbations, which are the difference between a model with and without an LVZ. We show that geoid height perturbations due to an LVZ can be computed accurately, though the accuracy deteriorates somewhat with the depth of the LVZ. Moreover, we show that horizontal rates of displacement, though not accurate for total displacements, are accurate for perturbations in the near field. We show the effect of lateral variations in the properties of the LVZ and in lithospheric thickness, and compute geoid height perturbations for Northern Europe based on a simple laterally heterogeneous model. The model is forced with a realistic ice-load history and a eustatic ocean-load history. The errors introduced by using a eustatic ocean-load history instead of realistic oceans are generally smaller than 10%, but might be critical for perturbations due to crustal LVZs.