Normal‐mode splitting due to inner‐core anisotropy

There is a collection of core‐sensitive normal modes that is split much more than predicted from the Earth's rotation, ellipticity, and lateral heterogeneity. PKIKP traveltime observations suggest that the Earth's inner core exhibits cylindrical anisotropy about a nearly corotational 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 isotropy with a symmetry axis parallel to the rotation axis produces splitting of the form δω_m=ω(a′+c′m²+dm⁴), where m denotes the azimuthal order of a specific singlet within a given multiplet with degenerate eigenfrequency ω; 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 to the axis of rotation can be easily incorporated and leads to non‐zonal splitting.