A computer-aided, algebraic approach to the post-glacial rebound problem

We present an analytical approach, based on computer algebra using Mathematica, to solve for the time-dependent responses of the earth's surface to the melting of the last ice age. The mathematical formulation, based on the correspondence principle for viscoelasticity, allows for the analytical determination of the relaxation times and of the associated Green's functions describing the temporal responses of the unloading event. By using Mathematica, we have developed an efficient means for evaluating the Green's functions of a multilayered model, which would be difficult by the usual analytical methods. We thus obtain an explicit closed-form analytical solution for a five-layer earth model, which facilitates the variations of parameters in different parts of the mantle.