Postglacial rebound and sea level contributions to changes in the geoid and the Earth's rotation axis

The rate of change of the spherical harmonic degree 2 component of the Earth's gravitational potential (<((C) over dot)over bar>(20)) and polar wander velocity are two signals which are sensitive to Late Pleistocene deglaciation, current changes in sea level and deep mantle viscosity. Different load and earth models have been used in earlier papers to predict the component of these geophysical signals caused by the collapse of the last great ice sheets and recent melting of polar ice caps. In this paper, we present a systematic analysis of the dependence of the predictions on parameters of the ice and earth model. We show that the key parameters of the ice model which govern the predictions are the mass, the location of the centre of mass and the midpoint of the deglaciation phase. Of secondary importance is the length of the deglaciation phase and the mean ice load prior to the Last Glacial Maximum. These conclusions enable us to make a more robust inference of mantle viscosity than has been made before, allowing for the uncertainties in the model of Late Pleistocene and present deglaciation. As previous authors have shown, the lower-mantle viscosity is the most important rheological parameter and therefore the <((C) over dot)over bar>(20) observation complements sea level observations, which are primarily sensitive to lithospheric thickness and the viscosity of the upper part of the mantle. Using realistic constraints on the sizes, locations and timing of deglaciation of the Late Pleistocene ice sheets and current changes in polar ice caps, the observation of <((C) over dot)over bar>(20) is used to infer lower-mantle viscosity as a function of the present rate of sea level change. If the present rate of non-steric sea level change is 1 mm yr(-1) and that change has been occurring for less than 1000 years, then the lower-mantle viscosity satisfies log(10) eta(lm) = 21.82 +/- 0.15, which is consistent with inferences drawn from recent sea level analyses and confirms other analyses of the <((C) over dot)over bar>(20) observation. If the polar wander signal is produced entirely by postglacial rebound and current sea level change, no more than 20 per cent of the present contribution to global sea level change comes from Greenland. The above conclusions also hold if the density discontinuities at 420 and 670 km are modelled as phase boundaries rather than material (chemical) boundaries.