Source shape estimation and deconvolution of teleseismic bodywaves

We consider the deconvolution of a suite of teleseismic recordings of the same event in order to separate source and transmission path phenomena. The assumption of source uniformity may restrict the range of muths and distances of the seismograms included in the suite. The source shape is estimated by separately averaging the log amplitude spectra and the 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 subsequent deconvolution of the seismograms is carried out by spectral division with two modifications. The first is the introduction of a minimum allowable source spectral amplitude termed the waterlevel. 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 frequency range of the transmission path impulse response spectrum beyond the optimal passband (the passband of the seismograms). The justification for the extension lies in the fact that the impulse response of the transmission path is itself a series of impulses 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. This continuity is achieved by a recursive application of a unit-step prediction operator determined by Burg's maximum entropy algorithm. The envelopes of the deconvolution are used to detect the presence of phase shifted arrivals.

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