Viscoelastic relaxation of a Burgers half-space: implications for the interpretation of the Fennoscandian uplift

We investigate the load-induced response of a Burgers earth model. In particular, using the incremental field equations and interface conditions of viscoelastodynamics, we give closed-form solutions for a two-layer half-space subjected to surface loading. In the special case of homogeneity, the solution shows that the Burgers half-space is characterized by two fundamental normal modes: Mo and M∞. They correspond to the short-and long-time viscosities, ηo and η∞, which describe the creep behaviour of the transient Burgers rheology at short and long times after the onset of loading. In the more general case of a Burgers substratum overlain by an elastic layer, the number of normal modes increases to four: Mo, Lo, M∞, L∞. Values of the parameters specifying the Burgers substratum are estimated by predicting the observed post-glacial uplift in Fennoscandia with a simple model of the Pleistocene glaciation history. The calculations return the following results: (1) an upper bound on η∞ cannot be determined; (2) a comparison with uplift curves for a steady-state Maxwell substratum shows that the marginal and peripheral regions of the Fennoscandian ice sheet are most sensitive to transient creep in the Earth's mantle; and (3) an estimate of η∞ cannot be obtained without a priori knowledge of the other parameters of Burgers rheology.