Physics
Scientific paper
Aug 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987pepi...47..288m&link_type=abstract
Physics of the Earth and Planetary Interiors, Volume 47, p. 288-318.
Physics
17
Scientific paper
The eigenfrequencies and eigenfunctions of the modes of three laterally heterogeneous, anelastic, elliptical, rotating models are calculated using the variational method. The basis set consists of the degenerate singlets of 11 multiplets of a spherically symmetric model (four toroidal and seven spheroidal multiplets), giving a total of 351 trial functions. The eigenfrequencies of the degenerate multiplets are clustered in a narrow frequency band around 250 s. The solution of the resulting 351 × 351 complex, non-hermitian eigenvalue problem required about 30 s of CPU time on the Hitachi S-810/20 supercomputer at the Computer Centre of Tokyo University. The power of present computational facilities thus makes the variational method a practical approach for studying the Earth's lateral heterogeneity. Using results presented elsewhere, the variational method can be used to obtain the partial derivatives of the eigenfrequencies with respect to a change in an initially laterally heterogeneous model.
The eigenfrequencies and eigenfunctions of the more accurate variational calculation substantially differ from those of first order degenerate perturbation theory, which does not include coupling between multiplets. Our basis set includes 0S32 and 0T31, which are well-known to be coupled by Coriolis terms. However, the results of the variational calculations show that the degree of coupling between these two fundamental mode multiplets is comparable to their coupling with nearby overtone multiplets that results from lateral heterogeneity.
Synthetic line spectra (without anelastic attenuation) are calculated for two earthquakes: the 1977 Indonesia event and a 1978 deep event of Honshu, Japan, for the three laterally heterogeneous Earth structure models. There are marked differences between the line spectra for three Earth models, and between the line spectra for the variational method and those from first order degenerate perturbation theory for a given Earth model. In contrast, when anelastic attenuation is included in the calculation of the synthetic spectra, the differences between Earth models, and between perturbation theory and the variational method, become much less distinct. Resolving the Earth's lateral heterogeneity is thus likely to require the processing of large amounts of data in order to overcome the effects of anelasticity.
Geller Robert J.
Kawakatsu Hitoshi
Morris Sandra P.
Tsuboi Seiji
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