Average long-wavelength shear velocity structure in several regions at the base of the mantle is determined using the profiles of core-diffracted SH waves (SHdiff). There is significant lateral variation in the Sdiff apparent ray parameters, suggesting considerable lateral shear velocity anomalies in D″, the region just above the core-mantle boundary (CMB). Apparent ray parameters are determined by least squares fits through the pulse maxima of the instrument-deconvolved ground displacements, and heterogeneities are quantified through comparisons with reflectivity synthetic ray parameters. Corrections are applied to the data to account for the effects of the Earth's ellipticity and of mantle heterogeneities along the SHdiff upswing paths. A total of 161 SHdiff profiles were obtained, greatly expanding the number of ray parameter measurements reported in previous studies. Most of the observed slowness fall in the range between 8.2 and 8.8 s/deg. These correspond to slowness anomalies of ¿3.5%. The most robust and extensive feature resolved is under the northern and northeastern Pacific Ocean. The slowest values (Δp=+4%) occur toward the southeast, and there is a trend toward fast velocities moving to the northern and eastern rims of the Pacific. A model of D″ shear velocities is obtained by converting the slowness to velocity anomalies, superposing the D″ path profiles onto the CMB, and applying a weighted moving cap spatial average. This model agrees well with many current tomographic models, both at large (~5000 km) and intermediate (~1000 km) scales. The fact that this occurs with a different type of data and technique of analysis suggests that we are now able to recognize some of the smaller-scale lateral variations at the base of the mantle. Locations of fast and slow velocity anomalies at the CMB are consistent with the model of cold paleoslabs ponding at the CMB and forcing D″ rock laterally to form hot aggregates that give rise to plumes in the mantle and hot spots at the surface. ¿ 2000 American Geophysical Union