Back to the subseismic approximation for core undertones

The problem of the long-period gravity modes of the Earth outer fluid core is investigated using either the subseismic or the anelastic approximation These two approximations aim at filtering out the uninteresting short-period seismic or acoustic oscillations while taking into account the density variations across the core However, they differ on the form of the equation of mass conservation since the density perturbations do not contribute to the mass balance in the anelastic case Here we show that these two approximations lead to the almost same results because of the weakness of the core stratification due to the convective mixing The anelastic approximation should be however preferred because it is simpler, mathematically self-consistent and is the only one which can be applied to problems with a stronger stratification such as the ones encountered in radiative zones of stars