Post‐Glacial Relaxation of A Viscously Stratified Compressible Mantle

We investigate the post‐glacial relaxation phenomenon of a viscously compressible, non‐self‐gravitating, spherical‐shell model. We have developed analytical solutions to an exponentially depth‐dependent viscosity with various types of compressible density models such as those with an exponential dependence of the radius and an algebraic‐root dependence of the radius. the solutions of a viscously compressible, multilayered model with constant thermodynamic properties and viscosity are developed by the propagator matrix method. Our results show that inferences of deep mantle viscosity from post‐glacial rebound would be hampered by mantle compressibility for long‐wavelength harmonics because of the smaller excitation of compressible eigenfunctions in the lower mantle. the relaxation times and velocity fields are more sensitive to higher viscosity contrast for the exponentially varying viscosity than for models with discrete jumps in the viscosity structure. Stress fields associated with deglaciation are extremely sensitive to the underlying mantle viscosity structure. Large stresses, O(10² bar), can still remain at the deglaciated region, if the lower mantle viscosity is O(10²³P). the presence of a hard garnet layer in the transition zone will induce a smaller viscosity in the lower mantle in the viscosity trade‐off with the standard two‐layer model.