A global map of shear velocity in the D″ layer results from the inversion of 340 differential travel times of diffracted S(SH) minus SKS(SV)(Sd-SKS), from long-period records of global seismic networks. The two-phase design reduces contamination from upper mantle heterogeneities and errors in location and origin time of the events. Additional corrections are made for (1) azimuthal anisotropy at stations where shear wave splitting parameters are available and for (2) travel time perturbations due to lower mantle asphericity, although both effects are minor compared with the observed residuals with respect to the preliminary reference Earth model (PREM) <Dziewonski and Anderson, 1981>. The corrected residuals, ranging from -16 to 18 s, are attributed to anomalies in D″ sampled by both phases. Taking these residuals as data and assuming a constant, 250-km-thick D″ layer, we invert for a lateral velocity variation model of D″ using spherical harmonics. In parameterizing D″ velocities, a high degree expansion (L=14) avoids aliasing, but only the reliably determined, low degree components (L1 produce optimal models. The optimal model L1=6 achieves a variance reduction of 56% and mean error 0.019 km/s, and the velocity is insensitive to the thickness of the D″ layer assumed. A baseline shift of -0.022 km/s from PREM is resolved. The magnitude of variation (~0.2 km/s or 3%) is nearly twice as large as that of Tanimoto <1990> and Su et al. <1994>, while comparable to that of Liu and Dziewonski <1994> which includes S-SKS data and Li and Romanowicz <1996>. Degree 2 variation dominates the D″ with positive anomalies beneath the Asian, Australian, and American continents and southernmost Pacific and negative anomalies beneath the Pacific, western Africa, Atlantic, and the southern Indian Ocean. This pattern is similar to that found in previous tomographic models; significant discrepancies in nondegree 2 features are discussed in terms of the constraints from Sd. The fast and slow regions of D″ correlate with the inferred paleoslab positions and the major hotspot distribution, respectively, both at the 99% confidence level. Implications of these correlations for mantle dynamics are suggested. The global model agrees reasonably well with the velocities determined regionally from the Sd slowness measurement and the ScS-S residuals in other studies. The latest radial models of D″ constrained from S triplications at distances of 75¿--90¿ provide a completely independent benchmark; models for Eurasia, Alaska, and the Caribbean predict Sd travel times corresponding to 0.03--0.08 km/s anomalies, consistent with our lateral variation model in respective regions. These vertical structures are also consistent with this study in ScS times, indicating that they agree in a vertically averaged sense. Major inconsistency exists for the India model SYL1 <Young and Lay, 1987b>, which predicts Sd and ScS arrivals much slower than those expected from the 0.1 km/s fast anomaly we found, suggesting either the presence of strong lateral heterogeneities or the need for further mapping in this area.¿ 1997 American Geophysical Union