Fast 3D Blind Seismic Deconvolution via Constrained Total Variation and GCV

When improving the Earth's description of seismic data via deconvolution, the spatial coherency of the information that can be extracted may be damaged through suboptimal trace-by-trace processing. Furthermore, the source function is usually not known or is known only approximately. This article presents an efficient multichannel blind deconvolution for addressing these problems and restoring three-dimensional (3D) seismic data based on a variational approach. To overcome the ill-posedness of the deconvolution problem, appropriate regularizers are used for the reflectivity and source. A new sparsity and continuity-promoting regularizer is introduced which is able to promote temporal sparsity and at the same time continuity along 3D singularities in reflectivity space. Sparsity in a wavelet domain is used as source prior. To find a solution for the overall problem, we alternate between two subproblems: 3D reflectivity estimation and updating the source. Each subproblem consists of solving a convex constrained optimization which is carried out very fast and efficiently via the alternating split Bregman iteration. We use the generalized cross validation criterion for determining the optimum number of Bregman iterations. We illustrate the performance and optimality of our blind deconvolution with simulated and field seismic data.