The investigator proposes to map out detailed structural and velocity features of the two prominent low-velocity anomalies in the lower mantle beneath Africa and the Pacific. He will use extensive waveform modeling by the 2D hybrid methods to constrain the seismic velocities, geometry, and length-scale of the seismic anomalies from various directions using various seismic phases. The PI also proposes to develop a three-dimensional hybrid seismic code along the course of this research program. The three-dimensional hybrid code will be used to forward verify the validity of the seismic results obtained from the 2D-hybrid method waveform modeling. The intellectual merits of the proposal include both observational and theoretical aspects of seismology. The observational aspect of the proposal includes collection, identification, interpretation and modeling of high-quality anomalous seismic data, with a scientific goal of mapping detailed features of the two prominent low-velocity anomalies in the lower mantle. The theoretical aspect of the proposal includes systematic studies of seismic wave propagation in a heterogeneous mantle, detailed modeling of the anomalous seismic data, and the development of a 3D hybrid method. The proposed research has broad impacts on our further understanding of the formation and evolution of the Earth, thermal-chemical convection in the mantle, the nature of the core-mantle boundary, and the origin of some geochemical reservoirs, such as "the DUPAL anomaly". The new 3D code will have broad applications in the seismology community.