A singularity free approach to post glacial rebound calculations

Calculating the post glacial response of a viscoelastic Earth model using the exponential decay normal mode technique leads to intrinsic singularities if viscosity varies continuously as a function of radius. We develop a numerical implementation of the Complex Real Fourier transform (CRFT) method as an accurate and stable procedure to avoid these singularities. Using CRFT, we investigate the response of a set of Maxwell Earth models to surface loading. We find that the effect of expanding a layered viscosity structure into a continuously varying structure is to destroy the modes associated with the boundary between layers. Horizontal motion is more sensitive than vertical motion to the viscosity structure just below the lithosphere. Horizontal motion is less sensitive to the viscosity of the lower mantle than the vertical motion is. When the viscosity increases at 670 km depth by a factor of about 60, the response of the lower mantle is close to its elastic limit. Any further increase of the viscosity contrast at 670 km depth or further increase of viscosity as a continuous function of depth starting from 670 km depth is unlikely to be resolved.