Open AccessCorrection of normal mode frequencies and amplitudes for the effect of spheroidal‐toroidal coupling
Author(s) -
Pollitz F. F.
Publication year - 1990
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1990.tb04470.x
Subject(s) - physics , amplitude , toroid , degenerate energy levels , coupling (piping) , quantum electrodynamics , normal mode , perturbation (astronomy) , perturbation theory (quantum mechanics) , oscillation (cell signaling) , classical mechanics , subspace topology , mathematical analysis , computational physics , quantum mechanics , mathematics , plasma , vibration , mechanical engineering , biology , engineering , genetics
SUMMARY Expressions are developed for the frequencies and amplitudes of spheroidal and toroidal modes, taking into account the rotational coupling between modes n S l ‐ n T l+1 . and n S l ‐ n T l‐1 . Starting from quasi‐degenerate perturbation theory, we derive coupled wave equations which clearly show the additional restoring force due to Coriolis coupling. We employ the subspace projection method to obtain asymptotic expressions for the perturbed amplitudes and frequencies, accurate to first order in coupling strength ε and zeroth order in 1/ l . The resulting expressions may be used to correct free oscillation amplitudes and frequencies in the fundamental Coriolis coupled band for the spheroidal‐toroidal coupling. Data examples using preferentially aligned source‐receiver paths verify the predicted patterns of amplitude and frequency perturbations.