The effects of noise on minimum‐phase Vibroseis deconvolution

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Ristow and Jurczyk (1975) proposed a mixed‐phase Vibroseis® inverse filter which is the usual minimum phase spiking deconvolution filter convolved with a Weiner‐Levinson minimum phase wavelet having the same amplitude spectrum as the Vibroseis wavelet. A problem exists since (for large time‐bandwidth products) the Vibroseis signal approximates a band‐limited signal and noise may have to be added to ensure convergence of the Wiener‐Levinson algorithm. This processing noise level can alter the resulting minimum phase wavelet. Since the deconvolution filter is influenced by the ambient or environmental noise as well as by the processing noise, the proposed correction to spiking deconvolution may not always yield meaningful results. It is shown that although the Vibroseis wavelet may span several octaves, it is not only band‐limited but can be approximated by a narrow‐band signal representation. In this formulation, the center frequency for the wavelet is considered to be the average of the high and low frequencies. The phase associated with this center frequency is independent of time but depends upon both the signal bandwidth and the deconvolution noise platform. Finally, this paper examines distortions in the deconvolved wavelet arising from both processing and environmental noise‐induced variations in the phase and envelope delay. The reflection sequence is assumed to be white, and a minimum phase, nearly constant Q, earth model is assumed. Curves are presented which show the residual phase error as a function of attenuation, processing noise, and the environmental signal‐to‐noise (S/N) ratio. It was found that although both types of noise will cause some residual phase error, phase compensation can correct for many of the phase distortions and polarity reversals that may be present in the deconvolved data only if the environmental noise is smaller than the processing noise.