THE SLICHTER MODES OF THE ROTATING EARTH - A TEST OF THE SUBSEISMIC APPROXIMATION

The eigenperiods of the principal translational (Slichter) mode of fre e oscillation of the solid inner core (split into a triplet by the Ear th's rotation) are computed by a variational principle based on the su bseismic approximation, neglecting ellipticity but taking Coriolis cou pling into account to high order in the liquid core. First-order Corio lis coupling is retained in the solid parts of the Earth to compute th eir dynamical response (represented by load Love numbers) to disturban ces of the outer core. A simple analytical model explains the presence of a low-frequency resonance in the Love numbers of degree 1 for the inner core boundary, which renders them highly frequency dependent nea r the Slichter eigenfrequencies. For PREM, with the outer core density profile slightly modified so as to be exactly neutral, the Slichter p eriod neglecting Earth's rotation is 5.4119 hr. Fifth-order Coriolis c oupling in the outer core is more than adequate to ensure convergence of the computed eigenperiods: we obtain 5.9697 hr, 5.3017 hr and 4.759 4 hr for the prograde equatorial, axial and retrograde equatorial mode s respectively. We draw attention to some shortcomings of the subseism ic approximation encountered in this study.