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 azimuths 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. IntroductionThis paper examines the problem of the deconvolution of source functions from teleseismic recordings. The first step in any deconvolution process is the estimation of the source time function. The next section of this paper deals with this problem.A standard technique in exploration seismology is to decompose the sowce from the seismogram autocorrelation function. This method assumes that the source is minimum phase and that the impulse sequence behaves like white noise (Robinson 1967). Since neither of these assumptions appeared to be generally valid for teleseismic recordings, the technique was not used. Source estimation by homomorphic transformation has also been suggested (Ulrych 1971), and this method is discussed in some detail. However, the low quefrency assumption of this method was found to not be generally valid, and there is also a problem of phase instabilities with the homomorphic transform itself.Both of the above methods attempt to estimate the source from a single seismogram. We decided that on the basis of a single recording of an event it would be difficult, if not impossible, to devise a general method of estimati...

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A method is proposed to obviate the shortcomings of conventional deconvolution approaches applied to vibroseis data. The vibroseis wavelet reduces the time domain resolution of the earth's impulse response by restricting its passband. The spectrum of the wavelet is assumed to be a “low quefrency”phenomenon, and hence it can be estimated by low cut cepstral filtering. The wavelet's amplitude spectrum can then be removed by spectral division. By using an approach which is consistent with the principle of maximum entropy, the undetermined portions of the seismogram's Fourier transform can be filled in by autoregressive prediction. The process of initially deconvolving in a restricted passband reduces the enhancement of noise contaminated parts of the spectrum, and the spectral extension scheme increases the time domain resolution of the process.

A method is presented for enhancing the resolution of impulsive functions which have been degraded by a known convolutional disturbance and by the addition of white noise. An autoregressive model is employed to represent the spectrum of the ideally resolved impulsive function. The method is flexible in that it allows constraints to be incorporated into the resolution scheme. Two quite diverse examples are presented as illustration.