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: M(0) and M(infinity). They correspond to the short- and long-time viscosities, eta(0), and eta(infinity), 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: M(0), L(0), M(infinity), L(infinity). 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 eta(infinity) 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 eta(infinity) cannot be obtained without a priori knowledge of the other parameters of Burgers rheology.