Geoid anomalies in the wavelength range corresponding to spherical harmonics 6 to 30 are used to bring new constraints on the deep structure of the continental lithosphere, on the nature of upper mantle seismic anomalies, and on the thermal evolution of the oceanic lithosphere. For the shallow lithospheric density anomalies considered here, the geoid anomaly is shown to follow approximately the moment law derived from isostasy. By a procedure of least squares inversion, the geoid over old cratons is found to be equal to that over relatively young (50 Myr) oceanic lithosphere. The oceanic geoid as a function of age follows the expected linear trend with flattening at old ages. These results are independent of the degree at which the spherical harmonics are truncated. If the tectosphere consisted only of a thick thermal boundary layer, marked geoid lows, with an amplitude larger than 20 m, should be present over cratons, is disagreement with the present observation. The predicted geoid agrees with the observations if the negative density anomalies associated with a depleted peridotitic layer are present to the bottom of the lithosphere. This analysis of the geoid confirms the petrological inferences that the deep roots observed seismically in the top upper mantle form a chemically differentiate reservoir. The density of these cold roots is similar to that of mantle material elsewhere, because the increase in density resulting from their lower temperature is largely balanced by the decrease in density caused by their depletion. Analysis in wavelength range corresponding to harmonics 6 to 30 in the oceans confirms that the geoid flattens at old ages, and thus supports the view that an important amount of heat is transfered at the base of the lithosphere by small-scale convection. ¿ American Geophysical Union 1996