In examining the slownesses of linear profiles of diffracted P arrivals, we have discerned regional variations in the compressional velocity structure of D, the base of hte mantle. Three methods of determining the slownesses were tested, concluding that the waveform cross-correlation (XC) technique is more reliable over a wide range of epicentral distances than methods involving a linear regression through either the first motion or first peak arrival times. XC slownesses suggest a statistically conservative range in D average velocities of 3.1%m and reveal regions of very fast velocities under Asia and the eastern Pacific basin and of very slow velocities under the New Guinea/Solomon Islands region. Slownesses were found to correlate well with the tomographic model V3 of Morelli and Dziewonski [1986>, derived from a different technique and data set. Synthetic seismograms were generated using a summation of spheroidal normal modes, and at periods greater than 45 s the diffracted waves show much less variation and are very well modeled by PREM. ¿ American Geophysical Union 1989