Multichannel Semi-blind Deconvolution (MSBD) of seismic signals

Seismic deconvolution is a general problem associated with recovering the reflectivity series from a seismic signal when the wavelet is known. In this paper, we solve the problem of semi-blind seismic deconvolution, where the wavelet is known up to some error. The Multichannel Semi-blind Deconvolution (MSBD) model was developed for cases where there is some uncertainty in the assumed wavelet. We present a novel, two-stage iterative algorithm that recovers both the reflectivity and the wavelet. While the reflectivity series is recovered using sparse modeling of the signal, the wavelet is recovered using L2 minimization, exploiting the fact that all channels share the same wavelet. The L2 minimization solution is revised to suit the multichannel case. An analysis is made for each wavelet uncertainty according to the parameters of the respective recovery method. We show that our algorithm outperforms the straightforward method of assuming the initial wavelet. As a side result, we also show that the final estimated wavelet fits the true wavelet better than the initial one.