The present-day global geoid and free air gravity anomaly signals induced by Pleistocene deglaciation have been computed, along with their secular variations. A revised Green function has been derived for the free air gravity anomaly, and we find that an Earth model with a lower viscosity moderately larger than the upper mantle value satisfies observations of the anomaly over both Hudson's Bay and Fennoscandia. Using this ''preferred'' Earth model, the predicted global geoid anomaly map is characterized by peak negative values of -36.7, -9.4, and -21.9 m over Hudson's Bay, northern Europe, and Antarctica, respectively, and by a smooth, small amplitude (≲2.5 m) upwarping over the major ocean basins. Although the field has an order of magnitude less power than the observed, there is a significant spatial correlation between the two. Inferences of mantle viscosity based upon comparisons between the observed geoid and the computed deglaciation-induced anomaly are hampered by the large contribution from the convective circulation in the Earth's mantle. We have subtracted a predicted convection signal (based on seismic tomography) from the observed field; however, the ''residual'' geoid thus obtained is still too inaccurate to allow a useful comparison.

In contrast, a filtered version of the observed geoid over Canada, which retains harmonic coefficients in the degree range 10--22, provides a relatively uncontaminated (by convection) datum that is indeed satisfied by the preferred Earth model. Secular variations in the Earth's gravitational field are naturally dominated by the signal from Pleistocene deglaciation. In this respect, we compute zonal harmonics in the expansion of the present day rate of change of the geopotential, and in particular, we predict amplitudes comparable to that for the previously analyzed J˙2 for J˙4, J˙5, J˙7, ND J˙9, all of which reflect, in large part, the response due to the melting of the massive Laurentide ice sheet. This analysis suggests that measurement of these higher-order secular variations of the zonal harmonics based upon analysis of long time series of LAGEOS ranging data could provide very useful additional contraints on the radial variation of mantle viscosity.

These constraints, along with all others described in this paper, are shown to be relatively insensitive to assumptions concerning the deflection, during the glacial isostatic adjustment process, of the 400- and 670-km density discontinuities within the mantle. ¿ American Geophysical Union 1989