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The Earth's inner core has this remarkable property: Compressional waves travel faster along its spin axis than in the equatorial plane. Such a directional dependence of wave propagation, together with the anomalous splitting of core-sensitive normal modes, was explained by an anisotropic inner core model first proposed by Harvard Seismology Group in 1986. Since then, we have further investigated its anisotropy extensively using both travel-time anomalies and the normal modes splitting.