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Zero-phasing the zero-phase source

CGG

Corresponding author: gcambois@cgg.com

The first 20% of the full text of this article appears below.

This paradoxical title is in fact a tribute to the classic paper by Gibson and Larner, "Predictive deconvolution and the zero-phase source" (GEOPHYSICS, 1984). Their work was originally presented at the 1982 SEG Annual Meeting, which means that it has been almost 20 years since they exposed the problems associated with controlling the phase of vibroseis records, and we are still struggling with them. The main issue is not related to the zero-phase Klauder wavelet itself but rather with the rest of the recording chain which contains a series of minimum-phase filters (such as the geophone response and possibly the coupling conditions). The resulting seismic wavelet is therefore mixed phase, thus making it virtually impossible to process correctly and obtain final zero-phase records with standard deconvolution processing.

To circumvent this problem, Gib-son and Larner recommended transforming the vibroseis data into minimum-phase records by applying a deterministic filter based on the known Klauder wavelet. The resulting records can then be processed within a controlled-phase sequence similar to that used for dynamite data. However, there is no clear minimum-phase equivalent for the vibroseis wavelet, and Gibson and Larner suggested that such a "beast" might not even exist. Figure 1, taken from their paper, shows four different minimum-phase equivalents of a Klauder wavelet, corresponding to four values of an obscure parameter in the minimum-phase transform. If the minimum-phase equivalent of the vibroseis source is nonunique, how can we guarantee a final zero-phase result?

View larger version (16K): [in this window] [in a new window]   Figure 1. Klauder wavelet (top) and four minimum-phase equivalent wavelets generated using the indicated amounts of white-noise. (From Gibson and Larner.)