Seiji Tsuboi

Variational free oscillation computations for three laterally heterogeneous Earth models

Abstract 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 Earths 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 0 S 32 and 0 T 31 , 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 Earths lateral heterogeneity is thus likely to require the processing of large amounts of data in order to overcome the effects of anelasticity.

Analysis of short-period P waves from the 1989 Macquarie Ridge Earthquake using a broadband array in Japan

We have developed a simple method of array analysis, enabling to find out apparent radiation centers of teleseismic waves. Applying this method to short-period P waveforms from the 1989 Macquarie Ridge earthquake recorded at 7 stations of the Pre-POSEIDON network in Japan, we obtained a pattern of apparent radiation center migration that is more compatible with a bilaterally propagating source model than with a unilateral one.

Amplitude anomalies of surface waves from the July 16, 1990, Philippine Islands Earthquake

Love waves from the 1990 Philippine Islands earthquake show large amplitude anomalies at broadband seismograph stations in Japan, while Rayleigh waves do not. We calculate synthetic seismograms using the fully coupled eigensolutions obtained by a variational method to see if this anomalous behavior of surface waves is explained by the laterally heterogeneous earth model M84A of Woodhouse and Dziewonski. We show that the anomalous long-period surface wave amplitude behavior can be reproduced relatively well by M84A.

Free Oscillations of a Laterally Heterogeneous and Anelastic Earth

We calculate normal modes of the laterally heterogeneous and anelastic earth model by using the variational method to include the coupling of the modes due to the asphericity of the earth. If the aspherical anelasticity correlates with the heterogeneity of elastic velocity structure, the quality factor Q of the split singlets has a correlation with the eigenfrequency. This can cause a center frequency shift of the spectral peak with time. We perform a synthetic experiment to examine whether the magnitude of the shift can become an observable for the realistic lateral heterogeneity model of anelasticity. The result of the experiment reveals that the shift of the center frequency is consistent with the initial estimate for the fundamental spheroidal modes used in the experiment. We then examine the actual seismograms of the June 9, 1994, Bolivian earthquake to determine if this shift of center frequency can be observed. Although the amount of the center frequency shift of each multiplet is large, there is no consistent shift of the center frequency that is predicted in the synthetic experiment.