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

SUMMARY 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 o and M ∞ . They correspond to the short‐and long‐time viscosities, η o 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: M o , L o , 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.