| Since the removal of the large glaciers of the last ice age, the Earth has been viscoelastically relaxing from the depression formed of their weight. This process, called post-glacial rebound (PGR), is measurable in changing sea levels, gravitational field anomalies and changes in the Earth's moments of inertia. Since these effects are sensitive to the viscosity of the mantle and thickness of the lithosphere, computational models of these Earth properties can provide important constraints on the structure of the solid Earth. In this thesis I develop a realistic computational model of PGR and apply it to study what can be inferred of the mantle's viscosity structure.; Two computational methods for the solution for viscoelastic deformation are developed that include the effects of center of mass motion, a gravitationally responsive ocean, and a new model for the interaction of polar wander with the solid Earth. With these codes and a realistic model of the Earth's three dimensional viscosity structure, I study the sensitivities of PGR to lateral viscosity variations and study how 1D viscosity models, inferred from PGR data, are likely to be related to the true 3D structure.; I next apply these codes to investigate how well PGR observations are able to constrain the spherically symmetric (1D) viscosity structure of the Earth. With synthetic PGR data generated from the 3D model, I attempt to invert for 1D viscosity. I find that the PGR data cannot resolve more than two layers of mantle viscosity.; Finally, I perform an inversion for mantle viscosity from relative sea levels and GRACE data. I find that well-constrained values for the upper and lower mantle viscosities can be obtained together with knowledge of the viscosity contrast between those two layers. The viscosities of three layers cannot be well-constrained by the PGR data. |
