Steven Kamal

Date of Award


Degree Type


Degree Name

Doctor of Philosophy


Free oscillations of the earth (also called normal modes) depend on the shape and structure of the earth. Each mode is a decaying sinusoid, and the modal parameters (frequency, phase, Q and relative amplitudes) may be determined from seismic records of large earthquakes. The observed modal parameters act as constraints on possible earth models. The fine structure of the free oscillation peaks, such as multiplets and split peaks, are a source of information and speculation on second order variations of earth shape and structure, such as departure from sphericity and local homogeneities.;The normal mode parameters have traditionally been estimated through the Short Time Fourier Transform (STFT) method. It is well known, and we demonstrate here, that the STFT method gives the correct frequency (to the nearest Fourier component) but an incorrect amplitude spectrum for decaying sinusoids. We propose an alternative approach for modal parameter determination through a non-linear least-squares fit of wavelets, customized for the normal modes of the earth. Iterative minimization of the error function is carried out through Marquardt's method to obtain the normal mode parameters. This direct computation of parameters through modal fitting is tested with synthetic noise free data and several data sets with varying levels of random Gaussian noise. The values for the noisy data using this method are found to be much closer (within 10%) to the true parameter values than those obtained using the STFT method (which may be off by as much as 500%) for signal to noise ratios as low as 1.3. The method is then tested on the record of the Minahasa Peninsula earthquake of April 18, 1990 {dollar}(M\sb S{dollar} = 7.4). The results obtained for the real data give reasonable values for 50% of the modes only. The possible cause for this may be the splitting of modes and/or source generated nonmodal seismic noise.;The second part of the dissertation reports on the discovery of at least two normal mode periodicities (55.38 minutes, {dollar}\sb0S\sb2{dollar} and 43.2 minutes, {dollar}\sb0T\sb2){dollar} in the aftershock sequence of the Loma Prieta, California, earthquake (October 18, 1989; {dollar}M\sb S{dollar} = 7.1). The evidence for the presence of these two periods has been corroborated by two different methods. A third period, corresponding to {dollar}\sb0S\sb3{dollar} is visible, though the evidence is not as compelling as the former two periods. It is apparent that the normal modes generated by the earthquake are triggering small aftershocks {dollar}(1\leq M\sb L\leq2).{dollar} Strong evidence of the triggering of low magnitude aftershocks by normal modes is seen during the first 6 days following the mainshock. After 6 days, the decay of the normal modes and the decrease in number of aftershocks make it difficult to detect such an effect. We speculate on possible mechanisms. A clear understanding of this triggering will enhance our knowledge of focal processes in general.;Large aftershocks {dollar}(M\sb L\geq3),{dollar} both in Loma Prieta earthquake sequence and in a catalog of the aftershocks of all {dollar}M\sb S\geq7{dollar} earthquakes around the world during the period 1970 to 1990, do not appear to be triggered by normal modes. However, this may simply reflect the fact that there are only a small number of large aftershocks, making the detection of periodicities difficult.



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