### Abstract:

Isotropic shear-wave velocities from the Ekström/Dziewonski S20 global tomographic model and residual `crust-free' gravity are used to determine density-velocity relations for various mantle layers by inversion. The residual gravity field was obtained by subtracting the crustal density inhomogeneities from the observed surface gravity. The residual field is dominated by upper mantle signatures. As the effect of dynamic topography is also reduced from the gravity field before-hand, the gravity-seismic inversion is almost independent of the viscosity distribution within the Earth. There exists a reliable correlation between residual gravity and shear-wave velocities in the upper mantle under oceans but not under continents. This result supports the idea that lateral density variations in the oceanic upper mantle are mostly driven by the temperature distribution, while under the continents temperature- and composition-induced density anomalies are superimposed. The inversion is therefore restricted to the oceanic area and was done by a least-squares adjustment in the spatial domain. The density/velocity ratios obtained for the subcrustal layer (down to 75km) and for the deep part of the oceanic upper mantle (below 225km) are very close to the ones predicted from mineral physics analyses. However, for the oceanic layer from 75 to 225km depth, a significantly lower density/velocity ratio is obtained. This may be explained by a compositional layering: dry, partially depleted peridotite residuum underlain by `damp' fertile peridotite and separated by the G discontinuity at a depth of about 70km. For the mantle transition zone and for the lower mantle the results obtained are less reliable, but relative minima in the density/velocity ratio are found for the layers around the phase transition discontinuities and for the depth interval from about 900 to 1100km. Applying the adjusted velocity-to-density relations to the seismic tomography model, a mantle density distribution under the oceans is found which explains about 85 per cent of the longest-wave `crust-free' gravity field (degrees 1-5) and 70 per cent of the overall field up to degree 20, which was the limit of this investigation.