Sparsity- and continuity-promoting seismic image recovery based on split Bregman method

Recovering the subsurface reflectivity from the surface recorded seismic data is necessary to improve the resolution of a seismic image. However, this inversion process is ill-posed by nature. To tackle the ill-posedness, we assume the reflectivity series is sparse in the time domain but continuous in the space domain, and encode such information in the form of l₁-norm constraints within the trace and spatial smoothing constraints across the trace in the inverse problem. In particular, split Bregman method is used to solve this constrained optimization problem. Theoretical simulations are performed to verify the validity and feasibility of our method.