Anelastic attenuation of seismic energy is considered to be a minimum phase process. Gabor deconvolution aims at the simultaneous elimination of both the attenuation effects and the source wavelet, which in the case of explosive sources is also considered to be minimum phase. In the absence of an accurate estimation of Q, the phase component of the Gabor deconvolution operator is designed with the help of the digital Hilbert transform. The digital Hilbert transform, however, may suffer serious distortions when the seismic trace presents a poor signal to noise ratio. As redundancy is the best protection against the harmful effects of random noise, a more robust implementation of the Gabor deconvolution method can be obtained through the use of the surface consistency assumption. In this work, the nonstationary convolutional model for the seismic trace is slightly modified and converted into a surface-consistent model. The resulting surface-consistent Gabor deconvolution method is less sensitive to the presence of random and coherent noise, and surface consistent variations in the near-surface effects.
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