Robust high-dimensional seismic data interpolation based on elastic half norm regularization and tensor dictionary learning

Abstract

Due to the limitations imposed by acquisition cost, obstacles, and inaccessible regions, the originally acquired seismic data are often sparsely or irregularly sampled in space, which seriously affects the ability of seismic data to image underground structures. Fortunately, compressed sensing provides theoretical support for interpolating and recovering irregularly or undersampled data. Under the framework of compressed sensing, we have adopted a robust interpolation method for high-dimensional seismic data, based on elastic half norm regularization and tensor dictionary learning. Inspired by the elastic net, we first develop the elastic half norm regularization as a sparsity constraint, and we establish a robust high-dimensional interpolation model with this technique. Then, considering the multidimensional structure and spatial correlation of seismic data, we introduce a tensor dictionary learning algorithm to train a high-dimensional adaptive tensor dictionary from the original data. This tensor dictionary is used as the sparse transform for seismic data interpolation because it can capture more detailed seismic features to achieve the optimal and fast sparse representation of high-dimensional seismic data. Finally, we solve the robust interpolation model by an efficient iterative thresholding algorithm in the transform space and perform the space conversion by a modified imputation algorithm to recover the wavefields at the unobserved spatial positions. We conduct high-dimensional interpolation experiments on model and field seismic data on a regular data grid. Experimental results demonstrate that this method has superior performance and higher computational efficiency in noise-free and noisy seismic data interpolation, compared to extensively used dictionary learning-based interpolation methods.