Northwestern Europe remains a key region for testing models of glacial isostasy because of the good geological record of crustal response to the glacial unloading since the time of the Last Glacial Maximum. Models for this rebound and associated sealevel change require a detailed knowledge of the ice-sheet geometry, including the ice thickness through time. Existing ice-sheet reconstructions are strongly model-dependent, and inversions of sea-level data for the mantle response may be a function of the model assumptions. Thus inverse solutions for the sea-level data are sought that include both ice-and earth-model parameters as unknowns. Sea-level data from Fennoscandia, the North Sea, the British Isles and the Atlantic and English Channel coasts have been evaluated and incorporated into the solutions. The starting ice sheet for Fennoscandia is based on a reconstruction of a model by Denton & Hughes (1981) that is characterized by quasi-parabolic cross-sections and symmetry about the load centre. Both global (northwestern Europe as a whole) and regional (subsets of the data) solutions have been made for earth-model parameters and ice-height scaling parameters.The key results are as follows. (1) The response of the upper mantle to the changing ice and water loads is spatially relatively homogenous across Scandinavia, the North Sea and the British Isles. (2) This response can be adequately modelled by an effective elastic lithosphere of thickness 65-85 km and by an effective upper-mantle viscosity (from the base of the lithosphere to the 670 km depth seismic discontinuity) of about 3-4×1020 Pa s. The effective lower-mantle viscosity is at least an order of magnitude greater. (3) The ice thickness over Scandinavia at the time of maximum glaciation was only about 2000 m, much less than the 3400 m assumed in the Denton & Hughes model. ( 4) The ice profiles are asymmetric about the centre of the ice sheet with those over the western part being consistent with quasi-parabolic functions whereas the ice heights over the eastern and southern regions increase much more slowly with distance inwards from the ice margin.

Observations of sea-level change since the time of the last glacial maximum provide important constraints on the response of the Earth to changes in surface loading on time-scales of 103-104 years. This response is conveniently described by an effective elastic lithospheric thickness and effective viscosities for one or more mantle layers. Considerable trade-off between the parameters describing these layers can occur, and different combinations can give rise to comparable predictions of sea-level change. In particular, the trade-off between lithospheric thickness and upper-mantle viscosity can be important, and for any reasonable value for the lithospheric thickness a corresponding mantle viscosity structure can be found that gives a plausible comparison of sealevel predictions with observations. In particular, thin-lithosphere models will lead to low estimates for the upper-mantle viscosity, while thick-lithosphere models lead to high viscosity values. However, either solution may represent only a local minimum in the model parameter space, and may not correspond to the optimum solution. It becomes important, therefore, that in the inversion of observational data, a comprehensive search is conducted throughout the entire model-parameter space, to ensure that the solution identified does indeed correspond to the optimum solution. The sea-level data for the British Isles lend themselves well to such an inversion because of the relatively high quality of the data, the good geographic distribution of the data relative to the former ice sheet, and reasonable observational constraints on the dimensions of the former ice sheet and on its retreat. Furthermore, because of the contribution to the sea-level signal from the distant ice sheets, as well as from the melt-water load, the observational data base for the region also has some resolving power for the viscosity of the deeper mantle. The parameter space explored is defined by up to five mantle layers, the lithosphere of effective elastic thickness D,, and a series of upper-mantle layers, i = 2-4, extending down to depths of 200, 400 and 670 km, respectively, each of viscosity qi, and a lower-mantle layer of viscosity qlm extending down to the coremantle boundary. The range of parameters explored is 30 < D, I 120 km, 3 x lOI9 I q i (i = 2, 3, 4) I 5 x 10, ' Pa s, 1021 I qlm I Pa s with q2 I q3 I q4 I qlm. Simple models comprising three layers with D, -70 km, D, -670 km, q, -(4-5) 10,' Pa s, and qj > lo2, Pa s describe the sea-level response to the glacial unloading well. Earth models with low-viscosity channels immediately beneath the lithosphere are not required, but if a thin lithosphere (<50 km) is imposed in the inversion then the solution for the mantle viscosity leads to a low-viscosity (< 10,' Pa s) channel. Such a model does not, however, represent the overall least variance solution that would be obtained if D,were also introduced as an unknown. Likewise, if a thick lithosphere (> 120 km) is imposed, then the solution points to a considerably higher value fo...

Evidence for changing sea levels in northwestern Europe related to glacial rebound is found in both the geological record of the past millennia and in the instrumental records of the past two centuries. The latter records are of two types: records of sea‐level change, primarily from the Baltic and the Gulfs of Finland and Bothnia, and records of the tilting of some of the larger lakes in both Finland and Sweden. The sea‐level records are particularly important because of their long duration and high quality, their large number and good spatial distribution, and the spatially coherent background noise. The two instrumental data types are complementary and provide constraints on the upper‐mantle rheology and on the distribution of ice during the late glacial stage. Comparisons of the observed rates of change of the water levels with models for glacial rebound yield earth models with a lithospheric thickness of 80–100 km and an upper‐mantle viscosity of (4–5) × 1020 Pa s, effective parameters that are consistent with those obtained from the analysis of the geological evidence for the same region. The mareograph results support ice‐sheet models in which the Late Weichselian ice thickness over the eastern and southern parts of Fennoscandia is relatively thinner than that for the western region, also consistent with the interpretation of the geological evidence for sea‐level change. In addition, the instrumental records provide constraints on the eustatic sea‐level change for about the past 100 years. A satisfactory separation of the earth rheology parameters from this rate of change can be achieved by estimating the latter only from those records for which the predicted isostatic effects are small. A check on these results is possible by using the lake‐level records to establish constraints on the earth‐model parameters and the sea‐level records to constrain also the eustatic change. All approaches lead to an average eustatic sea‐level rise for the past century of about 1.1 ± 0.2 mm yr−1.

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