A COMPARISON OF STATISTICAL AND DETERMINISTIC WIENER DECONVOLUTION OF DEEP‐TOW SEISMIC DATA*

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Abstract
Wiener ‘spiking’ deconvolution of seismic traces in the absence of a known source wavelet relies upon the use of digital filters, which are optimum in a least‐squares error sense only if the wavelet to be deconvolved is minimum phase. In the marine environment in particular this condition is frequently violated, since bubble pulse oscillations result in source signatures which deviate significantly from minimum phase. The degree to which the deconvolution is impaired by such violation is generally difficult to assess, since without a measured source signature there is no optimally deconvolved trace with which the spiked trace may be compared.A recently developed near‐bottom seismic profiler used in conjunction with a surface air gun source produces traces which contain the far‐field source signature as the first arrival. Knowledge of this characteristic wavelet permits the design of two‐sided Wiener spiking and shaping filters which can be used to accurately deconvolve the remainder of the trace. In this paper the performance of such optimum‐lag filters is compared with that of the zero‐lag (one‐sided) operators which can be evaluated from the reflected arrival sequence alone by assuming a minimum phase source wavelet. Results indicate that the use of zero‐lag operators on traces containing non‐minimum phase wavelets introduces significant quantities of noise energy into the seismic record. Signal to noise ratios may however be preserved or even increased during deconvolution by the use of optimum‐lag spiking or shaping filters.A debubbling technique involving matched filtering of the trace with the source wavelet followed by optimum‐lag Wiener deconvolution did not give a higher quality result than can be obtained simply by the application of a suitably chosen Wiener shaping filter. However, cross correlation of an optimum‐lag spike filtered trace with the known ‘actual output’ of the filter when presented with the source signature is found to enhance signal‐to‐noise ratio whilst maintaining improved resolution.