Three-dimensional finite-element modelling of Earth's viscoelastic deformation: effects of lateral variations in lithospheric thickness

We have developed a 3-D spherical finite-element model to study the dynamic response to surface loads of a self-gravitating and incompressible Earth with 3-D viscoelastic structure. We have forced our model with the ICE-3G deglaciation history of Tushingham & Peltier to study the effects of laterally varying lithospheric thickness on observations of post-glacial rebound (PGR). The laterally varying lithospheric thicknesses are derived from estimates of the thermal structure of the oceanic lithosphere and from elastic thicknesses on continents as estimated from studies of long-term geological loads. Our calculations show that the effects of lithospheric structure on the relative sea level change (RSLC) depend on the locations of the observation sites and on the size of loads. The RSLC at the centre of the North American ice sheet is significantly less sensitive to lithospheric thickness, compared with the RSLC at the centre of the Fennoscandian ice sheet. At the peripheral bulges the RSLC tends to be more sensitive to lithospheric thickness. The RSLC is controlled by local lithospheric thickness. The RSLC at a given location, as predicted using models with laterally varying lithospheric thickness, can be reproduced using a 1-D model with a uniform lithospheric thickness equal to the local lithospheric thickness. Coupled with efficient parallel computing, we believe that the finite-element model that we present here can be used to address a variety of viscoelastic deformation problems in geodynamics.