Sparse Multichannel Blind Deconvolution of Seismic Data via Spectral Projected-Gradient

In this paper, an efficient numerical scheme is presented for seismic blind deconvolution in a multichannel scenario. The proposed method iterate with two 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.