We derive poloidal flow internal loading Green functions for incompressible fluid models of the mantle consisting either of a single constant viscosity spherical shell or of two adjacent spherical shells having different viscosities. From the Green function we obtain kernels connecting the surface divergence, the geoid, and the surface topography fields to the lateral density heterogeneity inferred on the basis of the application of seismic tomographic imaging techniques, and with these kernels we argue that both the surface divergence and geoid fields, consisting of harmonic degrees 2--5, may be reasonably fit with only a factor of 8 viscosity increase at a depth of 1200 km. We point out, however, that the coupling from poloidal to toroidal flow which is required to understand surface velocity spectra, may allow these observations to be understood in terms of a viscosity increase at depth which is smaller than required by nonhydrostatic geoid data in the context of pure poloidal models. Using the observed kinetic energy in the surface plate motions as a constraint allows us to infer a value for the steady state upper mantle viscosity of (2.0¿0.5)¿1021 Pa s. We comment on the implication of the differcnce between this number and the somewhat lower value (1¿1021 Pa s) which has been derived on the basis of analyses of signatures of the glacial isostatic adjustment process. ¿American Geophysical Union 1987