Seismic Data Interpolation by Shannon Entropy-Based Shaping

The undersampled seismic data may surfer from degraded quality and pose negative impacts on subsequent processing procedures. Seismic data interpolation is a cost-saving technique to obtain regular and high-density data in modern seismological community. In this study, I present a seismic data interpolation technique which is based on the Shannon entropy and shaping regularization. I consider seismic data interpolation problem as a process of improving the orderliness of a system. A seismic section with clean and completely-sampled signals can be treated as an orderly data system while the added noise or decimation will destruct such orderliness. Therefore, we can recover the missing signals as the orderliness of the seismic data section is improved. The wave field is predicted by a regularized least-squares matching with the assumption of local plane-wave. The orderliness-improving process is packaged as a shaper and incorporated into the shaping regularization framework to iteratively solve the seismic interpolation problem. Unlike the conventional methods, such as prediction-based, sparsity-promoting-based or rank-reduction-based methods, which generally assume the observed data are regularly or irregularly undersampled, the presented Shannon entropy shaping-based method has no requirement on the distribution pattern of missing traces and hence can be applied to interpolate both regular and irregular seismic data. I use both synthetic and field seismic data to test the performance of the proposed algorithm on both regular and irregular seismic data interpolation problems. The results demonstrate that the presented approach can achieve a superior performance compared with the widely-used techniques.