Mantle viscosity from postglacial rebound

Relative Sea-level Data (RSL) in the Hudson Bay during the postglacial rebound are used to infer the Earth's mantle viscosity profile. These data are inverted by the Metropolis algorithm together with an annealing schedule. The forward model is based on a self gravitating multi-layered viscoelastic incompressible planet. Preliminary results, computed by a five layer model, suggest that the best fitting viscosity profile is characterized by a shallow upper mantle with viscosity of 3 x 10²⁰ Pa.s and a lower mantle with viscosity close to 10²¹ Pa.s. The main finding is the presence of a stiff transition zone, with viscosity close to 10²². This solution agrees with previous findings concerning postglacial rebound observables and global geodynamic signatures. The inversion can be improved increasing the number of the viscoelastic layers to test the sensitivity of the RSL data to more complex viscosity profiles. The results of these inversions can be interpreted as mean viscosities of the layers considered: the linear viscoelastic rheology seems to provide a good description of the relaxation process due to postglacial rebound. However, experimental studies of the mantle minerals suggest nonlinear relaxation mechanisms. A step forward in the interpretation of the observed sea level changes can be achieved by a more realistic rheology for the lithosphere and mantle, and also considering the variations of crust and lithosphere thicknesses beneath the Hudson Bay area. We present a finite element model to study the postglacial deformations of the northern America, with a composite rheology for the mantle, in which the transition between diffusion and dislocation creep is self-consistently determined by the deviatoric stress. Our aim is to provide an alternative fit to observed RSL data by a more realistic model.