Interpolation of irregularly sampled seismic data via non-convex regularization

Abstract

Seismic data interpolation is necessary for high-resolution imaging when the field data are not adequate or when some traces are missing. Sparse inversion is an important interpolation method for seismic data, which requires sparse transformation to build an inversion model. Most existing sparsity-promoting interpolation methods are generally based on convex function regularization, especially the L1 norm. Some studies suggest that non-convex regularization with non-convex functions can achieve better sparsity than L1 norm, and produce faster and better results. But this approach is only suitable for noise-free data interpolation, as it is less stable than convex regularization. To overcome the noisy data interpolation problem and improve the stability of non-convex regularization, we propose a novel non-convex function, called arc-tangent function, to construct the inversion model. We also present a gradient-based prediction-projection method to solve the proposed models. We used a prediction-projection method to solve the proposed models. In each iteration, we first obtained a predictive solution by gradient update algorithm and then projected it onto a convex set to update the iterative solution, and the predictive solution instead of the projection solution was output as the final results. Tests on synthetic and field data demonstrated that our non-convex regularization method performed well for both noise-free and noisy data interpolation.