Coefficients of a spherical harmonic expansion, up to angular order 3, of velocity anomalies in five shells within the earth's mantle were obtained from an analysis of nearly 700,000 P wave travel time residuals. The results for depths less than 1100 km are unreliable; on the basis of tests and numerical experiments we infer that lateral heterogeneities in this depth interval are dominated by velocity perturbations of lateral dimensions less than 5000 km. Relatively large wavelength features were resolved below 1500-km depth; the average perturbation level increases in the lowermost mantle. The region betwen 1100 and 1500 km may represent a transition zone with respect to the dimensions of anomalies. We present statistical evidence for a negative correlation between the long wavelength gravity anomalies observed at the surface and those computed from velocity anomalies at depths greater than 1100 km under the assumption of proportionality between velocity and density perturbations. The proportionality coefficient Δv/Δ&rgr; has been determined by using two different methods: the values are -4.45 and -6.02 (km/s)/(g/cm3). Only minor changes in the velocity distribution are needed to satisfy the long wavelength gravity field exactly. Possible origins of the correlation are (1) sinking of eclogite-rich material into the lower mantle from regions of lithospheric subduction, (2) chemical plumes of light high-velocity material originating near the core-mantle boundary, (3) temperature differences and perturbations of the core-mantle boundary and the earth's surface associated with mantle-wide convection, or (4) static chemical heterogencities in a nonconvecting mantle. The first three alternatives, all involving flow in the lower mantle, may be complementary but act on a different time scale. There appears to be a westward or northwestward translation of some anomalies with respect to the pattern obtained for the innermost shell. In particular, the direction of translation of large negative anomaly under the Pacific is in agreement with the sense of motion of the Pacific plate. We must caution the reader, however, that this is a highly speculative interpretation. If correct, it would favor the convective hypotheses.