Modelling post-glacial rebound with lateral viscosity variations

Observations of isostatic adjustment of the Earth's surface due to glacial loading provide important constraints on mantle viscosity structure. We solve the forward problem of glacial isostatic adjustment in two complementary ways: a spectral method for strictly 1-D (spherically symmetric) earth models, and a finite element method that can accommodate 3-D viscosity structure. We discuss how each method may be augmented in three ways: to accommodate motion of the centre of mass, to implement a gravitationally self-consistent ocean load via the sea level equation and to include the influence of polar wander. With all these effects implemented, the two methods are benchmarked against each other. We also study the influence of lateral viscosity variations upon measurements of post-glacial rebound (PGR) in two ways: first by observing the effect of viscosity perturbations in an idealized model and second by developing a realistic 3-D viscosity model and comparing it with results of related 1-D (spherically symmetric) models. The 3-D viscosity structure is derived starting from seismic tomography models. We conclude from both approaches that PGR observations are sensitive to both the local viscosity structure and to the viscosity structure beneath the loaded region, even if it is removed from where the observations are made. In particular, PGR measurements made at Hudson Bay tend to reflect the local viscosity structure beneath Hudson Bay; PGR measurements made along the east coast of North America, being sensitive to both the local (east coast) viscosity structure as well as the loaded (continental) viscosity structure, are not reproducible with a 1-D viscosity model.