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UBC Theses and Dissertations

The deconvolution of teleseismic recordings Clayton, Robert W.

Abstract

A method is presented for the deconvolution of a suite of teleseismic recordings of the same event. The suite must be restricted in azimuthal and delta ranges in order that the assumption of source stationarity can be made. The source is estimated by averaging the log amplitude and phase spectra of the recordings. This method of source estimation uses the redundant source information contained in secondary arrivals. The necessary condition for this estimator to resolve the source wavelet is that the travel times of the various secondary arrivals be evenly distributed with respect to the initial arrivals. The actual deconvolution of the seismograms is done by spectral division with two modifications. The first is the introduction of a minimum allowable source spectral amplitude termed the waterlevel (Helmberger and Wiggins, 1971). This parameter constrains the gain of the deconvolution filter in regions where the seismogram has little or no information, and also trades-off arrival time resolution with arrival amplitude resolution. The second modification, designed to increase the time domain resolution of the deconvolution, is the extension of the transmission path impulse response spectrum beyond its optimal passband (the passband of the seismograms). The justification for the extension lies in the fact that the impulse response is "impulsive" by nature which means its spectrum is not band-limited. Thus, the impulse response is best represented by a continuous spectrum rather than one which is set to zero outside the optimal passband. The actual prediction is done by an recursive application of a unit-step prediction operator determined by Burg's maximum entropy algorithm (Burg, 1967). The envelopes of the deconvolution are used to detect the presence of phase shifted arrivals. The source estimator and deconvolution method are applied to three examples: Kern County (16/10/62) , West Australia (24/3/70) , and Novaya Zemlya (14/10/69). Source estimation by homomorphic transforms (Ulrych, 197 1) is also discussed in this thesis. This method of source estimation was found to be of limited use because of the invalidity of the low quefrency [sic] assumption that must be applied (Ulrych, 1971), and the phase instabilities of the transform itself.

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