Edge-preserving traveltime tomography with a sparse multiscale imaging constraint

•Improve the imaging quality of near-surface•Edge-preserving first-arrival traveltime tomography•Solving tomography problem by taking the advantages of multiscale representation•Apply sparse promotion to nonlinear tomography problem

Solving the near-surface statics problem is often the first step in land or shallow marine seismic data processing. Near-surface velocity structures can be very complex, with large velocity contrasts within a small depth range. First-arrival traveltime tomography is a common approach for near-surface imaging. However, first-arrival traveltime tomography generally produces smooth model solutions due to the Tikhonov regularization, which constrains the model for minimum structures. Failing to resolve high velocity contrasts may result in inaccurate static values for reflection imaging. In this study, we develop a sparse multiscale imaging constraint for traveltime tomography to address this issue. In this method, we assume that the velocity model is sparse under a known wavelet basis. According to the model sparse representation, we first obtain the low wavenumber velocity structures, followed by the finer features, by alternately solving two sets of inversion problems. The synthetic tests and two real data applications show that this method exhibits better performance in reconstructing near-surface models with high velocity contrasts.