Reply to comment by W. Fjeldskaar ‘What about the asthenosphere viscosity? Sea-level change, glacial rebound and mantle viscosity for northern Europe’

Abstract

viscosity profiles that best match the observational database. include a low-viscosity channel in the upper mantle (Fjeldskaar Neither point to a well-developed low-viscosity channel in the 2000). In our paper we clearly noted that we examined only a upper mantle, and the second model compares well with the part of the possible earth-model space and that we restricted results from the sea-level analysis only. ourselves to a three-mantle-layer model comprising a lithoThe second reason for not pursuing the more detailed sphere, an upper mantle extending from the base of the solutions for the Scandinavian region is that a major limitation lithosphere down to the 670 km seismic discontinuity, and a in the modelling is the inadequate knowledge of the temporal lower mantle. A broad range of parameters defining these three and spatial distribution of the ice cover over the region, and, layers was explored and no a priori values were attached to based on tests with different ice models, we concluded that this any one layer. This is important in that considerable trade-off was more important than differences in predictions between between parameters can result. We were careful to note that the threeand five-layer mantle models: unless some modification analysis yielded only first-order results and that the resulting of the ice sheet was permitted in the inversion, this would earth-model parameters are effective values that, while they result in a very considerable dependence of earth-model results appear to give an adequate description of the rebound evidence on the adopted ice model (for example, compare Figs 16(a) (the relative sea-level change and shoreline migration), may and (b) and Fig. 33(b) in LSJ). We concluded that further not be a true reflection of the actual physical layering within the improvements in the knowledge of the spatial and temporal Earth. We also noted that further work is required to examine distribution of the ice are required before it becomes worthwhile whether a higher degree of mantle layering is appropriate to explore the earth structure in greater detail. Subsequent (e.g. p. 135). inversions in LSJ therefore placed greater emphasis on the ice The reason we did not conduct a more exhaustive search of model than on the detailed earth structure, although care was the model space was two-fold. The first was that our earlier taken at all times to ensure that an adequate separation of the experience with the British rebound modelling (Lambeck et al. earthand ice-model parameters occurred. 1996) led to the conclusion that five-layer mantle models, Three inversions of independent sea-level data for ice-sheet including the low-viscosity asthenosphere option, yielded only parameters and (three-layered) mantle parameters led to a marginal improvement in the overall comparison of preconsistent conclusions about likely ice thicknesses during Latedictions of sea-level change with observations. Fig. 1 illustrates glacial times. These data sets are the Lateand postglacial the two sets of effective earth-model parameters that were geological evidence for sea-level change across the region found to be optimal for the threeand five-layer models. The (LSJ), the tide-gauge data for the region (Lambeck et al. five-layer model is physically more intuitive but, in the British 1998b), and the timing and elevation data of various Baltic lake Isles case, it does not lead to a significant improvement in the stages (Lambeck 1999). In all cases, thick, quasi-parabolic ice ability to predict Lateand postglacial sea levels and shoreline models, in which ice thickness increases rapidly with distance locations compared to the three-layer model. In this particular from the ice margin, yield predictions that are inconsistent case the observational database has only limited resolving with the sea-level and shoreline observations for the southern power for isolating the higher-resolution structure in the mantle, and southeastern Scandinavia and Baltic regions (see also and for ‘all predictive purposes of sea-level change and shoreTushingham & Peltier 1991 and Lambeck et al. 1990). With line evolution, three-layer or five-layer models are essentially the exception of some of the Norwegian coastal zones, the