Seismic data interpolation using generalised velocity‐dependent seislet transform

Data interpolation is an important step for seismic data analysis because many processing tasks, such as multiple attenuation and migration, are based on regularly sampled seismic data. Failed interpolations may introduce artifacts and eventually lead to inaccurate final processing results. In this paper, we generalised seismic data interpolation as a basis pursuit problem and proposed an iteration framework for recovering missing data. The method is based on non‐linear iteration and sparse transform. A modified Bregman iteration is used for solving the constrained minimisation problem based on compressed sensing. The new iterative strategy guarantees fast convergence by using a fixed threshold value. We also propose a generalised velocity‐dependent formulation of the seislet transform as an effective sparse transform, in which the non‐hyperbolic normal moveout equation serves as a bridge between local slope patterns and moveout parametres in the common‐midpoint domain. It can also be reduced to the traditional velocity‐dependent seislet if special heterogeneity parametre is selected. The generalised velocity‐dependent seislet transform predicts prestack reflection data in offset coordinates, which provides a high compression of reflection events. The method was applied to synthetic and field data examples, and the results show that the generalised velocity‐dependent seislet transform can reconstruct missing data with the help of the modified Bregman iteration even for non‐hyperbolic reflections under complex conditions, such as vertical transverse isotropic (VTI) media or aliasing.