Predictive deconvolution and the zero‐phase source

Predictive deconvolution is commonly applied to seismic data generated with a Vibroseisr® source. Unfortunately, when this process invokes a minimum‐phase assumption, the phase of the resulting trace will not be correct. Nonetheless, spiking deconvolution is an attractive process because it restores attenuated higher frequencies, thus increasing resolution. For detailed stratigraphic analyses, however, it is desirable that the phase of the data be treated properly as well. The most common solution is to apply a phase‐shifting filter that corrects for errors attributable to a zero‐phase source. The phase correction is given by the minimum‐phase spectrum of the correlated Vibroseis wavelet. Because no minimum‐phase spectrum truly exists for this bandlimited wavelet, white noise is added to its amplitude spectrum in order to design the phase‐correction filter. Different levels of white noise, however, produce markedly different results when field data sections are filtered. A simple argument suggests that the amount of white noise used should match that added in designing the (minimum‐phase) spiking deconvolution operator. This choice, however, also produces inconsistent results; field data again show that the phase treatment is sensitive to the amount of added white noise. Synthetic data tests show that the standard phase‐correction procedure breaks down when earth attenuation is severe. Deterministically reducing the earth‐filter effects before deconvolution improved the resulting phase treatment for the synthetic data. After application of the inverse attenuation filter to the field data, however, phase differences again remain for different levels of added white noise. These inconsistencies are attributable to the phase action of spiking deconvolution. This action is dependent upon the shape of the signal spectrum as well as the spectral shape and level of contaminating noise. Thus, in practice the proper treatment of phase in data-dependent processing requires extensive knowledge of the spectral characteristics of both signal and noise. With such knowledge, one could apply deterministic techniques that either eliminate the need for statistical deconvolution or condition the data so as to satisfy better the statistical model assumed in data‐dependent processing.