High-resolution seismic processing by Gabor deconvolution

Since viscoelastic attenuation effects are ubiquitous in subsurface media, the seismic source wavelet rapidly evolves as the wave travels through the subsurface. Eliminating the source wavelet and compensating the attenuation effect together may improve seismic resolution. Gabor deconvolution can achieve these two processes simultaneously, by removing the propagating wavelet which is the combination of the source wavelet and the attenuation effect. The Gabor deconvolution operator is determined based on the Gabor spectrum of a nonstationary seismic trace. By assuming white reflectivity, the Gabor amplitude spectrum can be smoothed to produce the required amplitude spectrum of the propagating wavelet. In this paper, smoothing is set as a least-squares inverse problem, and is referred to as regularized smoothing. By assuming that the source wavelet and the attenuation process are both minimum phased, the phase spectrum of the propagating wavelet can be defined by the Hilbert transform of the natural logarithm of the smoothed amplitude spectrum. The inverse of the complex spectrum of the propagating wavelet is the Gabor deconvolution operator. Applying it to the original time-frequency spectrum of the nonstationary trace produces an estimated time-frequency spectrum of reflectivity series. The final time-domain high-resolution trace, obtained by an inverse Gabor transform, is close to a band-pass filtered version of the reflectivity series.