Simultaneous source shooting, also known as blending, is now an accepted practice in seismic acquisition. Most seismic processing algorithms, however, can still not handle blended data directly as input. Deblending, a procedure which separates the wavefields from each individual source, becomes then necessary. Deblending is an ill-posed problem, but often prior information can be incorporated to the problem in the form of constraints. The proposed algorithm utilizes the fact that the deblended data are expected to have a sparse representation in the focal transform domain, by casting deblending as a basis pursuit denoising problem. The novelty of the algorithm lies on the fact that by means of the focal transform, available subsurface information is used to construct the sparsifying basis. The algorithm is assessed by testing its ability to deblend numerically blended synthetic data, in both cases of exact and inexact knowledge of subsurface information.


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