On the diurnal and nearly-diurnal free modes of the Earth

Abstract : computations concerning the motions of the solid inner core of a slowly rotating, ellipsoidal earth model can be explained by the fact that Smith neglected in the equations of motion second-order terms in the ellipticity. We demonstrate this statement by calculating the eigenfunctions associated with the diurnal tilt-over mode (TOM) and inserting them into the equations of motion. Next, we compute the free core nutation (FCN) and the free inner core nutation (FICN) for various realistic earth models. We ®nd that their respective periods are in good agreement with the results of Mathews et al. (1991b) and de Vries & Wahr (1991), who have computed these modes by other means.