Isostatic recovery and the strain rate dependent viscosity of the Earth's mantle

This paper is concerned with the interpretation of isostatic recovery data in terms of the flow properties of the earth's mantle. A hydrodynamic analysis is first presented that allows straightforward calculation of the relaxation time for isostatic recovery within a mantle in which the viscosity varies continuously with depth. However, it transpires that no curve of this type (i. e. , choice of a reference viscosity and a rate of change of viscosity with depth) can of itself adequately explain the available observational data from the Fennoscandian and Laurentide ice sheets and the pluvial Lake Bonneville. Proceeding onward it is then demonstrated that the strain rates within such flows are in fact greater than the critical strain rate envisaged by Weertman (1970) in his theoretical rheological model of the mantle. Below this critical value, diffusion creep is the dominant flow process, and the flow can be modeled by a Newtonian viscosity. But above this value, dislocation glide takes over, and the viscosity exhibits a decrease with increasing strain rate. This feature is then incorporated into the theoretical model, and the isostatic recovery data are interpreted in such a way as to provide experimental values of the strain rate dependent viscosity that can be compared with the values in Weertman's rheological model. It is demonstrated that the data become most self-consistent and exhibit the most satisfactory agreement with Weertman's model when the increase of mantle viscosity with depth is given roughly by exp (5 × 10^ (−4) z), where z is the depth in kilometers. Thus in addition, the analysis would appear to provide some verification of Weertman's model of the mantle flow properties. It is further demonstrated that the much larger increase of viscosity with depth predicted by McConnell (1968) and others from previous analyses of isostatic recovery data is an artifice induced by the nature of such flows in which the strain rate decreases with depth; this led to an apparent increase of viscosity that is much larger than the actual variation.