The Earth's core plays an important role in the formation and chemical differentiation of our planet, in global earth dynamics and earth rotation, and in the generation of the magnetic field. This project focuses on three related objectives, concerning the seismic imaging of the structure and rotation of the inner core and the heterogeneity of the the lowermost mantle. (1) To constrain the inner core rotation using fixed earthquake-station paths, which reduces biases from unmodeled mantle heterogeneities and source mislocation. The project will search for time-dependence of PKP(BC)-PKP(DF) differential times and PKP(CD)-PKP(DF) differential times. Considerable effort will also be made to address uncertainties in determining inner core rotation, in particular errors from potential systematic event mislocation. (2) To model and invert for 3D anisotropic inner core structure using PKP waveforms and differential times. The project will test the recent proposal of a distinct innermost inner core and examine the sharpness and lateral variation of the inner core transition zone from the relatively isotropic upper inner core to strong anisotropy in the lower inner core. (3) To map the heterogeneity of the lowermost mantle from the PKP data collected, in particular, the Central Pacific core-mantle boundary anomaly using abundant PKP samples from the earthquakes and stations in South America and east Asia.