A revised relaxation-time spectrum for Fennoscandia

Abstract

The Fennoscandian relaxation-time spectrum (RTS), first derived by McConnell (1968), is a classic data set in studies of glacial isostatic adjustment (GIA). We outline a new method for estimating an RTS from a set of strandline data, which is based on a damped least-squares solution for spherical harmonic coefficients associated with the strandline heights. In contrast to the Hankel transform approach outlined by McConnell (1968), the method does not require interpolation or extrapolation of the data, nor does it use the assumption that peripheral deformation are zero. We begin by applying the new approach to a suite of synthetic strandlines. These synthetic calculations quantify the effect on the RTS estimates of the common assumptions of free-decay uplift, an axi-symmetric Fennoscandian deformation field, and the uncertainty introduced by limited spatial and temporal sampling of this field. Recently, the accuracy of the Sauramo (1958) strandline data upon which the McConnell (1968) RTS was based has been questioned (Wolf 1996); accordingly, we apply our new approach to a set of more robust strandline data published by Donner (1964, 1969, 1980, 1995) to compute a revised RTS for Fennoscandia. At high harmonic degree (above 50), our new RTS is characterized by weak constraints, whereas McConnell's (1968) RTS suggest a significant reduction in relaxation times relative to the values at low degrees. This reduction was the basis for McConnell's (1968) inference of an elastic lithosphere. In contrast to this, we conclude that the trend is an artefact of the observational data set he adopted. At lower degrees, McConnell's (1968) relaxation-time estimates lie at the lower end of the range implied by the present analysis. To complete our study, we apply the techniques of linearized Bayesian inference to invert our newly derived RTS for mantle viscosity. We find that the RTS provides an estimates ~ 5 x 1020 Pa s for the volumetric mean viscosity in a region extending from the base of the lithosphere to about 550 km depth. Target regions which extend from the transition zone to ~ 1200 km depth are less well constrained; however, the average viscosity from the base of the lithosphere to 1200 km depth is consistent with the classic Haskell (1935) value of 1021 Pa s for mantle viscosity. Finally, we demonstrate that viscosity models within the class inferred by Mitrovica and Forte (1997) from joint inversions of postglacial relaxation times associated with GIA and mantle convection observables simultaneously fit the revised Fennoscandian RTS.