Deconvolution by autocepstral windowing

Abstract

The autocepstrum of a reflection seismogram is defined by the cepstrum of its autocorrelation function. Using the autocepstrum extends the basic deconvolution method for removing a minimum‐phase source wavelet to unmask subsurface reflectivity. When we record only the seismic trace and assume a minimumphase source wavelet, deconvolution reduces to estimating the wavelet autocorrelation. In practice, a portion of the seismic trace autocorrelation is used as an estimate of the wavelet autocorrelation. This can be justified by assuming a random reflectivity series with a white power spectrum. However, in cases where the reflectivity spectrum is not white, a preferred wavelet autocorrelation may be obtained by low‐pass windowing the trace autocepstrum. This approach liberates the selection of various deconvolution parameters such as filter length and design window length that are typically chosen to reinforce the assumption of a white reflectivity spectrum. For problems that require short, deconvolution‐filter design windows, and thus nonwhite reflectivity spectra, windowing the trace autocepstrum is an appropriate alternative to the conventional practice of windowing the trace autocorrelation.