Calculation of associated mass tensor in the problem of the Earth's hard core motion

We have calculated the associated mass tensor for harmonic oscillations of the Earth's hard core. The consideration of this tensor causes free oscillation periods of the Earth's inner core to increase by approximately an hour. For some values of the core density, the periods of oscillation are close to the experimental ones obtained by D. E. Smylie. The splitting of experimental frequencies can well be interpreted as the splitting of the equatorial mode of free oscillations of the inner core in the gravity field of the asymmetric shell, provided that the latter possesses a corresponding quadrupole moment.