A P-SV hybrid method is developed for calculating synthetic seismograms involving two-dimensional localized heterogeneous structures. The finite difference technique is applied in the heterogeneous region and generalized ray theory solutions from a seismic source are used in the finite difference initiation process. The seismic motions, after interacting with the heterogeneous structures, are propagated back to the Earth's surface analytically with the aid of the Kirchhoff method. Anomalous long-period SKS-SPdKS observations, sampling a region near the core-mantle boundary beneath the southwest Pacific, are modeled with the hybrid method. Localized structures just above the core-mantle boundary, with lateral dimensions of 250 to 400 km, can explain even the most anomalous data observed to date if S velocity drops up to 30% are allowed for a P velocity drop of 10%. Structural shapes and seismic properties of those anomalies are constrained from the data since synthetic waveforms are sensitive to the location and lateral dimension of seismic anomalies near the core-mantle boundary. Some important issues, such as the density change and roughness of the structures and the sharpness of the transition from the structures to the surrounding mantle, however, remain unresolved due to the nature of the data. ¿ 1998 American Geophysical Union