Coupled free oscillations of an aspherical, dissipative, rotating earth - Galerkin theory

Details Coupled free oscillations of an aspherical, dissipative, rotating earth - Galerkin theory Coupled free oscillations of an aspherical, dissipative, rotating earth - Galerkin theory

Jun 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986jgr....91.7241p&link_type=abstract

Journal of Geophysical Research (ISSN 0148-0227), vol. 91, June 10, 1986, p. 7241-7260. Research supported by the University of

Statistics

Applications

59

Earth Rotation, Galerkin Method, Oscillations, Seismology, Coriolis Effect, Eigenvalues, Pendulums, Variational Principles

Scientific paper

A study is described that is intended to show how free oscillation coupling calculations can be incorported into a search for global lateral structure in the deep earth. A discussion of the methods of performing coupling calculations is given, followed by recipes and examples of the construction of synthetic seismograms. Using matrix algebra, the coupling and attenuation properties are modeled. The Galerkin formalism is outlined for calculating coupled modes from a fixed basis Lagrangian interaction. Nearly all applications can be adequately modeled as a quadratic eigenvalue problem, which is shown to be reducible to a more tractible linear eigenvalue problem using an approximation to the term linear in oscillation frequency omega. Numerical examples of coupling interaction on rotating, attenuative, earth models with lateral structure are presented, and the importance of considering nonorthogonality of free oscillation modal singlets when calculating synthetic seismograms is emphasized.

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