Spatial and temporal variations in sea-level are produced by the melting of the Late Pleistocene ice and by the Earth's response to the redistribution in surface loads. By examining different parts of the sea-level curves of the past 20 000 yr from geographically widely distributed regions it becomes possible to constrain models of the melting history of the ice sheets and of the Earth's rheology. Observations from sites away from the former Arctic ice sheets, such as the Australian and South Pacific region, are particularly important for constraining the total meltwater volumes added into the oceans in the past 20 O00 yr and the rates at which this occurred. These observations indicate that the Antarctic ice sheets provided a significant contribution to the sea-level rise at a rate that was approximately synchronous with the melting of the Laurentide ice sheet, except for the interval 9OOO-6ooo yr ago when it may have lagged behind. Minor melting of the Antarctic ice sheet appears to have continued throughout the Late Holocene. Differential observations of the Late Holocene sea-level change recorded at sites in the same region are particularly useful for estimating parameters describing the Earth's non-elastic response to surface loading. The effective parameters used here are a lithospheric thickness, an upper mantle viscosity, and a lower mantle viscosity describing the response below 670 km depth. With the observations used here, it is not possible to separate the lithospheric thickness H from the upper mantle viscosity and the viscosity results are based on the assumption that 50 5 H s 100 km. Neither do these observations provide a resolution of the depth dependence of viscosity in the upper mantle and the resulting estimates are effective parameters only. Differential sea-levels along continental margins and along the shores of large gulfs and bays constrain the effective upper mantle viscosity to be about (1-2) x Ido Pa s-' while differential values from islands of different sizes are suggestive of a somewhat lower value. The lower mantle (taken to be below 670 km depth) viscosity is about two orders of magnitude greater than this. The estimated ice and rheological models explain many of the Holocene sea-level observations throughout the Australian and southern Pacific region. The tilting of continental margins, as exemplified by observations of variable amplitudes of the Holocene high-stands and the variable times at which sea-levels first reached their present level along the north Queensland coast and Great Bamer Reef, is well represented by these models. Differential Holocene sea-levels observed along the narrow Spencers Gulf of South Australia are also well explained by the models and in neither case is it necessary to invoke tectonic motions. Predicted Late Holocene sea-levels at small-to medium-sized islands are characterized by small amplitude high-stands that reached their maximum values about 4000-2000 yr ago, consistent with observations from the Society, Cook and Tuamotu Islands.

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levels at sites in both the near-and far-field places an upper limit of about 50-80 km on the effective lithospheric thickness. These sea-level observations are also consistent with an upper mantle viscosity of about lo2' Pa s with a lower mantle viscosity in the range of 102'-1023Pa s.

S U M M A R Y Observations of Late Pleistocene and Holocene sea-level change relative to the crust exhibit very considerable variations across NW Europe in consequence of the response of the Earth's crust to the deglaciation of Fennoscandia and of the water added to the oceans from the melting of all Late Pleistocene ice sheets. Inversion of sea-level observations from a site near the centre of the Fennoscandian ice sheet and from three sites located beyond the margin of the ice sheet at the time of maximum glaciation yield a range of plausible models for the Earth's response and for the ice models. Further constraints on this range of models is placed by a comparison of observed sea-levels with predicted values at other sites near the former ice sheet margins. The resulting mantle parameters are: upper mantle viscosity (3-5) X 10'' Pa s; lower mantle viscosity (2-7) X loz1 Pa s; lithospheric thickness 100-150 km. These values represent effective parameters that describe the response of the Earth to surface loading of short to intermediate wavelengths on a time-scale of 104yr. The lower mantle viscosity is poorly constrained but the marked increase from upper to lower mantle is a characteristic of all plausible solutions. The inversion places a constraint on the total volume of ice in the Fennoscandian ice sheet such that the equivalent sea-level rise from this contribution is about 13-14 m. A less well-determined constraint of about 10 m equivalent sea-level rise is suggested for the Barents-Kara ice sheet. The inversion also indicates that a small amount of melt-water, from ice sheets far away from Europe, continued to be added into the oceans during Late Holocene time so as to raise the equivalent sea-level by about 3 m during the past 6000 yr, consistent with similar inversions of data from sites in the Australian and Pacific regions.

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...

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