Open AccessFree Oscillations of the Laterally Inhomogeneous Earth: Quasi‐degenerate Multiplet Coupling
Author(s) -
Luh Peter C.
Publication year - 1973
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1973.tb06526.x
Subject(s) - multiplet , toroid , physics , classical mechanics , degenerate energy levels , coupling (piping) , spherical harmonics , tensor (intrinsic definition) , harmonics , quantum electrodynamics , quantum mechanics , geometry , mathematics , mechanical engineering , plasma , engineering , spectral line , voltage
Summary The scheme leading to the computation of the normal mode eigen‐frequencies of the laterally inhomogeneous Earth is derived. Rayleigh's variational principle is used to calculate the first‐order corrections to the eigenfrequencies of a spherically symmetric, non‐rotating and elastic Earth model due to the lateral variations in the real Earth. The Wigner‐Eckart theorem is used, whenever applicable, to simplify many complicated angular integrals involving the strain deviator tensor to more basic and manageable integrals involving three spherical harmonics. In particular, near‐resonance multiplet coupling for spheroidal‐spheroidal, spheroidal‐toroidal and toroidal‐toroidal multiplets is presented along with the uncoupled case of a single arbitrary spheroidal or toroidal multiplet.