Residual static estimation in complex areas is one of the main challenging problems in seismic data processing. Inappropriate estimation of residual statics affects the quality of seismic images dramatically. In this paper, I propose a novel method for residual static estimation based on sparsity maximization. If pre-stack data have a sparse representation in a known transform domain (e.g. Fourier or Curvelet), then short-wavelength time shifts are incoherent in that transform domain (i.e. produce noise like artifacts). Thus, the time shifts can be estimated by a sparsity-promoting non-linear problem. A fast algorithm is presented to solve the problem. The performance of the method is illustrated by synthetic and real numerical experiments.


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