3D high‐order sparse radon transform with L₁–₂ minimization for multiple attenuation

Among many multiple attenuation methods, parabolic Radon transform has been widely used due to its efficiency and effectiveness. However, there are two factors that restrict the application of Radon transform: (1) the smearing caused by finite seismic acquisition aperture and discrete sampling of seismic data and (2) the destruction of the amplitude versus offset signature in seismic data. Therefore, a high‐order sparse Radon transform in the mixed frequency–time domain with L 1–2 minimization is proposed. The L 1–2 metric has been proved an unbiased approximation to L 0 norm, which helps improve the sparsity and resolution of the Radon model. By combining the orthogonal polynomial transform, which can fit the amplitude variations of seismic data, the amplitude versus offset signature is also considered. Furthermore, the 2D Radon transform is extended to 3D by modifying the augmented Lagrangian in the alternating direction method of multipliers algorithm. Compared with the 2D algorithm, 3D Radon transform considers seismic wave propagation in three dimensions, which can describe the wavefield more accurately. The proposed method is applied to multiple attenuation examples based on both synthetic and real 3D data examples to demonstrate its effectiveness, compared with some existing high‐resolution techniques and the corresponding 2D algorithm.