Postglacial rebound and lateral viscosity variations: a semi-analytical approach based on a spherical model with Maxwell rheology

A spectral method is employed to study the response to surface loads of a Maxwell earth including lateral viscosity variations. In particular, we focus on the effects of lithospheric cratons on the long-wavelength time-dependent displacement field for simple earth models. The viscosity contrast of the craton with respect to the surrounding mantle is kept fixed, whereas its thickness is allowed to vary. We show that the long-wavelength vertical displacement is not greatly affected by the presence of a lithospheric craton, while the tangential displacement is severely modified for the case of a homogeneous mantle. With increasing harmonic degree and thickness of the craton, the load-deformation coefficients deviate from those pertaining to a homogeneous mantle with a viscosity of 10²¹ Pa s. These deviations are particularly enhanced on timescales larger than a few hundred years. These findings indicate that the interpretation of the viscosity structure of the mantle inferred from postglacial rebound signatures based on radially stratified models is affected by the presence of lateral viscosity variations.