The Interplay of Framelet Transform and lp Quasi-Norm to Interpolate Seismic Data

Missing traces affect the result of subsequent steps, such as migration and amplitude versus offset (AVO) analysis, which harms the understanding of the subsurface structure and hydrocarbon exploration. Framelet transform can sparsely represent seismic data and it can describe data in detail. Compared with the commonly used l(1) norm, l(p) quasi-norm has higher sparsity. In this letter, we establish a new subject with l(p) quasi-norm and framelet transform to reconstruct the seismic record. Instead of a conventional solver, we apply the alternating direction method of multiplier (ADMM) to solve the problem. Both synthetic test and field application prove that our proposed method not only gets a good result with high signal-noise-ratio (SNR) but also costs much less time than the conventional method. This indicates that the interplay of framelet transform and l(p) quasi-norm can do a good job in seismic data reconstruction.