In this paper, we investigate the perturbations induced by the nearly-diurnal luni-solar tidal potential on the surface gravity changes and on the spatial nutations. The effects of the magnetic friction at the inner core boundary (ICB) and on the inner core viscosity at this time scale are studied. We show that very precise very long baseline interferometry (VLBI) observations of the in-phase and out-of-phase components of some nutations can give information on the Earth's deep interior, especially on the effective viscosity of the inner core and on the amplitude of the radial component of the magnetic field at the ICB.