NORMAL-MODE SPLITTING DUE TO INNER-CORE ANISOTROPY

There is a collection of core-sensitive normal modes that is split muc h more than predicted from the Earth's rotation, ellipticity, and late ral heterogeneity, PKIKP traveltime observations suggest that the Eart h's inner core exhibits cylindrical anisotropy about a nearly corotati onal axis, We investigate the effect of transverse isotropy, which is the simplest type of anisotropy that exhibits cylindrical symmetry, on the free oscillations of the Earth. We demonstrate that transverse is otropy with a symmetry axis parallel to the rotation axis produces spl itting of the form delta omega(m), = omega(a' + c'm(2) + dm(4)), where m denotes the azimuthal order of a specific singlet within a given mu ltiplet with degenerate eigenfrequency omega; the scalars a', c', and d represent the effects of transverse isotropy on a particular normal mode, The effect of a tilt in the anisotropic symmetry axis relative t o the axis of rotation can be easily incorporated and leads to non-zon al splitting.