Off-the-grid seismic data reconstruction approach based on a combined sampling operator and fast sparse inversion

Abstract

Summary Compressive sensing (CS) acquisition realizes the irregular sample along one or two spatial directions, and reconstruct the missing samples in the processing stage, which brings much attention to industry. However, the major challenge of CS acquisition is the missing data reconstruction, especially the reconstruction speed and accuracy. In addition, field construction conditions can also disrupt the sampling geometry, resulting in missing samples and samples off-the-grid to the designed grid, which will affect the reconstruction accuracy. In order to simultaneously regularize off-the-grid samples and interpolate missing data for off-the-grid CS seismic data, a new mathematical model that combines a 3D curvelet transform, a fast sparse inversion algorithm, and a new combined sampling operator is proposed. The combined sampling operator includes a binary mask for interpolating on-the-grid samples and a barycentric Lagrangian operator for regularizing off-the-grid samples. The fast sparse inversion algorithm efficiently solves the inversion problem and improve computational efficiency compared with the conventional inversion algorithms. Finally, we demonstrate the effectiveness of the proposed approach by a field dataset.