The influence of rotation on the free oscillations of the earth

Details The influence of rotation on the free oscillations of the earth The influence of rotation on the free oscillations of the earth

Sep 1975

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975rspta.279..583d&link_type=abstract

Royal Society (London), Philosophical Transactions, Series A, vol. 279, no. 1292, Sept. 25, 1975, p. 583-624.

Physics

29

Earth Rotation, Eigenvectors, Elastic Deformation, Free Vibration, Gravitational Effects, Boundary Value Problems, Equations Of Motion, Gyroscopic Stability, Isentropic Processes, Perturbation Theory, Stress Tensors, Transient Response, Traveling Waves, Vibration Mode

Scientific paper

The paper is an abstract, systematic investigation of the properties of the isentropic elastic-gravitational free oscillations of a general rotating, self-gravitating, perfectly elastic earth model. It is found that the displacement eigenfunctions of a rotating earth model are not in general mutually orthogonal, and they cannot be considered disjointly in seeking to determine at least the static part of the response to an imposed body force distribution. The Rayleigh-Schrodinger perturbation theory is used to show how the eigenfrequencies associated with any pair of predominantly elastic oppositely directed generalized traveling waves are split apart by the influence of rotation by an amount of certain order. The two zero-frequency equatorial rotational modes of any nonrotating earth are split by rotation into two oppositely directed generalized traveling waves, whose eigenfrequencies are again separated by an amount of the same order.

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