GLACIAL REBOUND OF THE BRITISH-ISLES .2. CONSTRAINTS ON MANTLE VISCOSITY

Observations of sea-level change since the time of the last glacial ma ximum provide important constraints on the response of the Earth to ch anges in surface loading on time-scales of 10(3)-10(4) years. This res ponse is conveniently described by an effective elastic lithospheric t hickness and effective viscosities for one or more mantle layers. Cons iderable trade-off between the parameters describing these layers can occur, and different combinations can give rise to comparable predicti ons of sea-level change. In particular, the trade-off between lithosph eric thickness and upper-mantle viscosity can be important, and for an y reasonable value for the lithospheric thickness a corresponding mant le viscosity structure can be found that gives a plausible comparison of sealevel predictions with observations. In particular, thin-lithosp here 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 para meter space, and may not correspond to the optimum solution. It become s important, therefore, that in the inversion of observational data, a comprehensive search is conducted throughout the entire model-paramet er space, to ensure that the solution identified does indeed correspon d to the optimum solution. The sea-level data for the British Isles le nd themselves well to such an inversion because of the relatively high quality of the data, the good geographic distribution of the data rel ative to the former ice sheet, and reasonable observational constraint s on the dimensions of the former ice sheet and on its retreat. Furthe rmore, because of the contribution to the sea-level signal from the di stant ice sheets, as well as from the melt-water load, the observation al data base for the region also has some resolving power for the visc osity of the deeper mantle. The parameter space explored is defined by up to five mantle layers, the lithosphere of effective elastic thickn ess D-1, and a series of upper-mantle layers, i = 2-4, extending down to depths of 200, 400 and 670 km, respectively, each of viscosity eta( i), and a lower-mantle layer of viscosity eta(im) extending down to th e core-mantle boundary. The range of parameters explored is 30 less th an or equal to D-1 less than or equal to 120 km, 3 x 10(19) less than or equal to eta(i) (i = 2, 3, 4) less than or equal to 5 x 10(21) Pa s , 10(21) less than or equal to eta(lm) less than or equal to 10(23) pa s with eta(2) less than or equal to eta(3) less than or equal to eta( 4) less than or equal to eta(lm) g. Simple models comprising three lay ers with D-1 similar to 70 km, D-2 similar to 670 km, eta(2) similar t o (4-5) 10(20) Pa s, and eta(3) > 10(22) Pa s describe the sea-level r esponse 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 solu tion for the mantle viscosity leads to a low-viscosity (<10(20) Pa s) channel. Such a model does not, however, represent the overall least v ariance solution that would be obtained if D-1 were also introduced as an unknown. Likewise, if a thick lithosphere (>120 km) is imposed, th en the solution points to a considerably higher value for the upper-ma ntle viscosity (similar to 10(21) Pa s). But this also represents only a local minimum solution. The observational data do point to some str atification in the viscosity of the upper mantle, and the optimum solu tion is for a five-layer model with the following effective parameters : 55 < D-1 < 60 km (2 < eta(2) < 4) x 10(20) Pa s for (D-1 < D less th an or equal to 200) km (4 < eta(3) < 6) x 10(20) Pa s for (200 < D les s than or equal to 400) km eta(4) similar to 2 x 10(21) Pa s for (400 < D less than or equal to 670) km eta(lm) greater than or similar to 1 0(22) Pa s for (670 < D < D-cmb) km