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

利用内核模式分裂函数的相互作用系数反演内核的各向异性结构。假设内核具有六方对称的各向异性，确定了五个弹性常数。如果地震各向异性依赖于半径，则ε（表示沿地球旋转轴和赤道平面传播的纵波速度差的分数）变为正值，其径向相关性在距内核边界230 km处最小。利用反演的各向异性结构，研究了内核各向异性对自由振荡谱的影响。由于内核中弹性各向异性引起的应变能通常较小，因此内核各向异性和内核微分旋转很难对内核模态振幅谱产生较大的影响。因此，不容易检测到内核的微分旋转，也不容易表明内核的各向异性仅限于内核的东半球。但是，当使用大量的光谱数据进行分析时，即使光谱变化很小，也有可能从系统的振幅光谱变化中检测到内核的旋转。我们试图从七个内核模式的分裂函数的时间变化中估计内核的旋转速率。对地幔非均质性对分裂函数的影响进行校正，得到只反映内核结构的分裂函数。根据修正后的分裂函数的时间变化，估计内核的平均自转速率为每年向西0.03±0.18°。虽然我们的估计显示了轻微的向西旋转，但旋转速率与零没有显著差异。因此，我们得出结论，相对于地壳和地幔，内核的旋转速度并不显著。

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.