The very base of the mantle is investigated with core-diffracted P wave (P-diff) travel times published by the International Seismological Centre (ISC) for the period 1964-1987. Apparent slownesses are computed for two-station profiles using a difference method. As the short-period P-diff mostly sample a very thin layer above the core-mantle boundary (CMB), a good approximation of the true velocity structure at the CMB can be derived from the apparent slownesses. More than 27 000 profiles are built, and this provides an unprecedented P-diff sampling of the CMB. The overall slowness distribution has an average value of 4.62 s/deg, which corresponds to a velocity more than 4% lower than that of most mean radial models. An analysis of the residuals of absolute ISC P and P-diff travel times is independently carried out and confirms this result. It also shows that the degree of heterogeneities is significantly higher at the CMB than in the lower mantle. A search for lateral velocity variations is then undertaken; a first large-scale investigation reveals the presence of coherent slowness anomalies of very large dimensions of the order of 3000 km at the CMB. A tomographic inversion is then performed, which confirms the existence of pronounced (+/-8-10%) lateral velocity variations and provides a reliable map of the heterogeneities in the northern hemisphere. The influence of heterogeneity in the overlying mantle, of noise in the data and of CMB topography is evaluated; it seemingly proves minor compared with the contribution of heterogeneities at the CMB. Our results support the rising idea of a thin, low-velocity laterally varying boundary layer at the base of the D '' layer. The two principal candidate interpretations are the occurrence of partial melting, or the presence of a chemically distinct layer, featuring infiltrated core material. (C) 1997 Elsevier Science B.V.