Observational study of terrestrial eigenvibrations

A comprehensive analysis has been made of analog and digital recordings of eigenvibration ground motion obtained following four great earthquakes; August 1976 (Philippines), August 1977 (Indonesia), September 1979 (West Irian), and December 1979 (Colombia). The time series (ranging in length from ～28 to ～140 h) are assumed to be linear combinations of damped harmonics in the presence of noise. Tables are calculated from values of the four parameters: Θ, used in describing eigenvibrations, period of oscillation, amplitude, damping factor Q, and phase together with their statistical uncertainties (53 spheroidal modes, ${}_0\text{S}{}_4\text{to}{}_0\text{S}{}_{48}$, and 13 torsional modes, ${}_0\text{T}{}_8\text{to}{}_0\text{T}{}_{45}$). The estimation procedures are by the methods of complex demodulation and non-linear regression that specifically incorporate into the basic model the decaying aspect of the oscillations. These methods, extended to simultaneous estimations of groups of modes, help to eliminate measurement error and measurement bias from estimations of Θ. The result is that overtone modes very near in frequency to fundamental modes can, under certain conditions, be resolved through a non-linear regression technique, although parameter uncertainties are underestimated in general.Of the time series analyzed, 17 were from a northern California regional network of ultra-long period seismographs at Berkeley (three components), Jamestown (vertical component), and Whiskeytown (vertical component) following the four listed earthquakes. The other 7 time series were recorded digitally by the worldwide IDA network following the 1977 Indonesian earthquake. Weighted regional and worldwide averages were made for period and Q of each eigenvibration mode.From the theoretical viewpoint, comparisons of measured period, Q, amplitude, and phase for all modes analyzed led to five conclusions. First, there are no detectable systematic shifts in period, Q, or phase of eigenvibrations within a region whose dimensions are less than a wavelength. Second, though not conclusive, there may be slight systematic shifts in period (<0.65 s) and relative amplitudes within the California regional network due to different source positions and mechanisms. Differences in Q values are not statistically significant. Third, even though differences in period obtained worldwide were as great as 1.33 s (≈0.33%), differences between Q values (as great as 20%) for the same mode were not significant. The conclusion is that the damping characteristics of singlet eigenfunctions are not observed to be significantly different. Fourth, the assumption that a multiplet ${}_{\mathrm{n}}\text{S}{}_{\mathrm{l}}$ behaves as a single oscillation is valid from at least ${}_0\text{S}{}_7$ through ${}_0\text{S}{}_{30}$. Fifth, no systematic pattern emerged for the shift of eigenperiod as a function of order / or posit on the Earth.