  In this work, an efficient numerical scheme is presented for seismic blind
deconvolution in a multichannel scenario. The proposed method iterate with wo
steps: first, wavelet estimation across all channels and second, refinement of
the reflectivity estimate simultaneously in all channels using sparse
deconvolution. The reflectivity update step is formulated as a basis pursuit
denoising problem and a sparse solution is obtained with the spectral
projected-gradient algorithm - faithfulness to the recorded traces is
constrained by the measured noise level. Wavelet re-estimation has a closed
form solution when performed in the frequency domain by finding the minimum
energy wavelet common to all channels. Nothing is assumed known about the
wavelet apart from its time duration. In tests with both synthetic and real
data, the method yields sparse reflectivity series and stable wavelet estimates
results compared to existing methods with significantly less computational
effort.
