In an attempt to map lateral velocity variations in the D'' zone of the lowermost mantle of the Earth, long-period Pdiff ray parameters are determined from digital data of the Global Seismic Network. Twenty-six earthquakes between 1981 and 1986 provided 37 profiles in North America and Europe. Average profile length is 18¿, and the number of stations per profile is 3 or 4. For accurate travel time determination of the Pdiff wave group peaks, seismograms are equalized to the same instrument characteristic. Ray parameter interpretation in terms of the velocity along the D'' path of each profile requires correction of Pdiff travel times for mantle heterogeneity above D'' on the upgoing Pdiff paths. The finite difference method of Podvin and Lecomte <1991> in two dimensions is used to calculate Pdiff travel time curves for the global tomography model of Inoue et al. <1990> and for related models, having lateral heterogeneity only in D'' or only above D''. From these calculations, Pdiff ray parameter corrections of up to 1.5% are found. Maps with uncorrected and corrected ray parameters are shown. Conflicting ray parameters on close D'' profiles continue to exist after correction, which points to insufficient correction. Global tomography models underestimate upper mantle heterogeneity, which, according to regional tomographic studies, has scale lengths of a few hundred kilometers and velocity variations of up to ¿3%. Such upper mantle structures are modeled by Gaussian random media with correlation distances of 250--1000 km and standard deviations of 0.5--1% of their slowness fluctuations. Pdiff ray parameter corrections for such structures can reach 3%. The results of this study show that regionalization of D'' with Pdiff requires detailed knowledge of mantle heterogeneity, in particular of heterogeneity in the upper mantle. Currently, this information is only rarely available.¿ 1997 American Geophysical Union