The long wavelength geoid height undulations are the result of density variations inside the Earth and the dynamic response of the viscous mantle due to the buoyancy forces resulting in dynamic topography, plus the contribution of isostatic topography due to crustal and lithospheric structure. The dynamic topography is a function of the effective stress transmission inside the earth and is linked to the viscosity of the mantle. We solve the equation of motion for a viscous Earth's mantle assuming an incompressible 6-layer shell model and determine the dynamic response function for geoid, dynamic topography, and (poloidal) surface velocity. The internal density distribution can be estimated from seismic tomography, but since density variations might be of thermal and chemical nature, the s-wave velocity to density conversion factor,
, varies throughout the mantle. Based on CHAMP gravity field coefficients and four new seismic s-wave tomography models we search for ranges of radial profiles of viscosity and
, resulting in a correlation to better than 0.85 to the long wavelength hydrostatic geoid, and to a fit better than 0.6 for gravity, dynamic topography and (poloidal) plate velocity. For purely thermal origin
should be between 0.2 and 0.4. Successful models however, show a small or even negative value for
, between 100 and 300 km depth and a low value of ∼ .1 between 700 and 1200 km, but is otherwise roughly constant with values of ∼ .28. The viscosity is slightly reduced in the asthenosphere and even stronger decreased in the mantle transition zone between 410 and 670 km. Resolution for both, viscosity and conversion factor, is poor below the transition zone down to ∼ 1500 km, but well confined in deeper parts of the mantle, where a viscosity between 30 to 40 1021 Pa s and a conversion factor of 0.28 to 0.32 is found.