Study of inner core differential rotation detected from earth's free oscillation

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The anisotropic structure of the inner core is retrieved from interaction coefficients of splitting functions of the inner core modes. Five elastic constants are determined assuming that the inner core has anisotropic properties of hexagonal symmetry. If the seismic anisotropy is dependent on radius, ε, which denotes fractional difference between P-wave velocities propagating along the earth's rotation axis and equatorial plane, becomes positive and its radial dependence has a minimum at 230 km depth from the inner core boundary. The effect of inner core anisotropy on free oscillations spectra is investigated using the retrieved anisotropy structure. Because the strain energy due to the elastic anisotropy is usually small in the inner core, the inner core anisotropy and inner core differential rotation are hard to have a large influence on the amplitude spectrum of core modes. Thus it is not easy to detect the inner core differential rotation and to show that the inner-core anisotropy is restricted to the east hemisphere of the inner core. But the inner core rotation is possibly detected from systematic change in amplitude spectra even if the spectral changes are small, when a lot of spectral data are used for the analysis. We try to estimate a rate of the inner core rotation from time variations of splitting functions of seven inner-core modes. The splitting functions are corrected for the effect of mantle heterogeneity to obtain splitting functions that reflect only the inner-core structure. From time variation of the corrected splitting functions, a mean rate of the inner-core rotation is estimated to be as small as 0.03 ± 0.18° per year westward.Although our estimate shows a slightly westward rotation, the rotation rate is insignificantly different from zero.Therefore we conclude that the inner core is not rotating at a significant rate relatively to the crust and mantle.