The inverse problem for mantle viscosity

The site-specific relaxation-time parametrization of relative sea level histories, for sites that were ice covered at the last glacial maximum, is herein applied in the context of formal inversions of the highest quality fraction of such data in order to infer the depth dependence of mantle viscosity. These data are jointly inverted together with additional relevant information that includes the relaxation spectrum for Fennoscandian rebound, originally derived by McConnell and two data derived from observed anomalies in the Earth's present rotational state. The latter include both the so-called 'nontidal' component of the observed axial acceleration of rotation and the ongoing motion of the north pole of rotation relative to the surface geography at a rate near 0.95 degrees per million years that is directed southwards along the 76 degrees west meridian of longitude. The formal inversion of the totality of these data is based upon the Bayesian methodology of Tarantola and Valette, Jackson and Matsu'ura, and Backus. Both the preparation of the data that is required for the formal analysis and the derivation of the Frechet kernels for the individual data types are discussed in some detail. The results obtained in these analyses, preliminary versions of which were recently described in abbreviated form elsewhere, appear to be rather significant. The variation of mantle viscosity with depth deduced from the glacial isostatic adjustment data is found to agree, within a constant scale factor and then rather precisely, with a model previously inferred on the basis of nonhydrostatic geoid anomalies related to the mantle convection process. Since the latter data are insensitive to a constant rescaling, this implies that the rheology of the bulk mantle may exhibit no significant transient behaviour and thus may well be Newtonian.