Recent studies of SKS waveform modeling emphasize the strong variation of seismic properties at the core-mantle boundary (CMB) and the need for two-dimensional and three-dimensional waveform modeling capabilities. In particular, the bifurcation of SKS into SPdKS and SKPdS near 110¿ shows strong regional variations. The first of these phases has a P wave diffraction along the bottom of the mantle near the source, while the latter phase occurs at the receiver end. Generalized ray theory proves effective in generating theoretical seismograms in this type of problem because each of these diffractions is associated with a particular transmission coefficient: Tsp which transmits shear waves into primary waves when crossing the CMB and Tps which transmits the primary waves back into shear waves at the receiver end. Each region can then be isolated and have its separate fine structure, sharp or gradational. Two classes of boundaries are explored: the CMB as a simple, sharp interface and the CMB with a very low velocity transition layer (10% slower than reference models). The two diffractions produced by these structures have diagnostic arrival times and wave shapes and when combined with the geometric SKS produce distinct waveform characteristics not easily generated by other means. Since the ray paths associated with these three phases are virtually identical in the mantle and only differ along a short sample of CMB and in the one-dimensional fluid core, we can isolate the small localized CMB region sampled. Thus the waveform character of the extended SKS in the range of 105¿ to 120¿ becomes an excellent CMB probe which we demonstrate on a small sample of observations from the Fiji-Tonga region as recorded in North America. ¿ American Geophysical Union 1996