Normal mode coupling due to hemispherical anisotropic structure in Earth's inner core

We present illustrative calculations of the effect of hemispherical variation in inner core anisotropy on Earth's normal modes of oscillation. Body wave studies show that the anisotropy in the inner core is not simple cylindrical anisotropy, which is often portrayed in models derived from normal mode data, but varies with longitude. ‘Hemispherical’ or odd degree, structure has to be studied by cross-coupling normal modes, as the self-coupling technique is sensitive only to even degree Earth structure. A completely general definition of inner core anisotropy would require a prohibitive number of degrees of freedom; however, we show that any existing cylindrical anisotropy model can be confined to only one part of the inner core. Using our new theory, we find that hemispherical anisotropy causes significant changes in the frequency and quality factor of several inner core sensitive normal modes. The effect of hemispherical inner core anisotropy can also be seen in synthetic seismograms. Radial, PKIKP and PKJKP modes all respond to the presence of hemispherical variation in inner core anisotropy. If the variations in inner core anisotropy seen in body wave data are part of a gross, large-scale pattern, then this structure should also affect normal mode data on an observable scale.