Computing core oscillation eigenperiods for the rotating Earth: a test of the subseismic approximation

Abstract

The liquid outer core (OC) density profile of the preliminary reference Earth model (PREM) is modified to have various values of the Brunt-Väisälä frequency N in order to study long-period gravity modes modified by rotation. The eigenperiods of gravity modes of both non-rotating and rotating, self-gravitating, stably and spherically stratified, compressible OC models with rigid-fixed boundaries are obtained by solving the exact two-potential description (TPD) of core dynamics and the subseismic wave equation (SSWE) respectively, so as to test the subseismic approximation (SSA). Comparison of the resulting eigenperiods shows the high accuracy of the SSA: (1) the eigenperiods computed from the SSWE differ from those calculated from the TPD by at most 0.8% for a non-rotating core with 2π N = 6 h ; (2) the weaker the stability of the OC, the smaller the difference; (3) the more complex the spatial variation of the eigenfunction, the smaller the difference; (4) the SSA gives the eigenperiods more accurately for a rotating Earth than for a non-rotating model. The results also show that the SSA always shortens the eigenperiods. Convergence of the truncated series of trial functions in the Galerkin method used in the calculations is carefully checked to guarantee reliability of the numerical results.