Geoid Inversions

A study by King and Masters [1992] inverted for radial viscosity models that best fit the observed l = 2-8 geoid using several published S-wave velocity models as the density anomalies: model MDLSH [ Tanimoto, 1991]; model SH425.2 [ Su and Dziewonski, 1991]; and model MODSH.C [ Masters and Bolton, 1991]. All three of the seismic velocity models predict a low viscosity between 400-670 km depth. The pattern of viscosity with depth for the three models is strikingly similar: a high viscosity from 0 to 400 km depth, a low viscosity between 400 and 670 km, and a high viscosity below 670 km. The largest difference between the viscosity models is a factor of two difference in the viscosity of the 400-670 km layer. It is interesting to note that the viscosity in the lower mantle increases by a factor of five below 1022 km in addition to an increase at 670 km. This resembles the two-layer model of Forte and Peltier [1991].

Forte et al. [1993] determined the viscosity profile required to fit the geoid using S-wave model SH8/U4L8, which they describe. Their preferred viscosity model, which contains a thin, low-viscosity zone at the base of the upper mantle and an increase in viscosity in the lower mantle, is quite similar in gross features to the preferred model of King and Masters [1992]. Forte et al. obtain a 65% variance reduction for the observed geoid (l = 2-8), in addition to a reasonable fit to the plate velocities with these viscosity and density models. They also point out that their viscosity model is consistent with recent post-glacial uplift analyses and mineral physics. It may be beyond the limit of the data to constrain the thickness of the layer at the base of the mantle because, layer thickness and viscosity contrast trade-off directly. It is possible that the geoid alone can not discriminate between the models from Forte et al. and King and Masters.

Using a genetic algorithm (GA), King [1994b] identified several families of radial mantle viscosity models that fit the observed geoid. GA's are a relatively new class of optimization techniques that exploit the analogy between functional optimization and the biological process of evolution. The detailed theory behind GA's can be found elsewhere [ Goldberg, 1989]. One family of models is characterized by a low viscosity transition zone with a viscosity 30 to 65 times smaller than that of the deep lower mantle. This family of models is consistent with preferred models from other inversion studies of mantle viscosity discussed above. A new family of viscosity models, characterized by a high viscosity transition zone that is a factor of 1.5 to 2.5 smaller than the lower mantle, but surrounded by low viscosity layers in the upper mantle and upper 200 km of the lower mantle, fits the observed geoid data equally well. Inspection of the Green's functions shows that both families of models can produce identical Green's functions, hence, the geoid cannot be used to rule out one of the families of models.