*Article* **Sparse Parabolic Radon Transform with Nonconvex Mixed Regularization for Multiple Attenuation**

**Qiuying Wu, Bin Hu \*, Cai Liu \* and Junming Zhang**

College of GeoExploration Science and Technology, Jilin University, Changchun 130026, China

**\*** Correspondence: binhu@jlu.edu.cn (B.H.); liucai@jlu.edu.cn (C.L.)

**Abstract:** The existence of multiple reflections brings difficulty to seismic data processing and interpretation in seismic reflection exploration. Parabolic Radon transform is widely used in multiple attenuation because it is easily implemented, highly robust and efficient. However, finite seismic acquisition aperture of seismic data causes energy diffusion in the Radon domain, which leads to multiple residuals. In this paper, we propose a sparse parabolic Radon transform with the nonconvex *Lq*<sup>1</sup> − *Lq*<sup>2</sup> (0 < *q*1, *q*<sup>2</sup> < 1) mixed regularization (SPRT*Lq*<sup>1</sup> − *Lq*<sup>2</sup> ) that constrains the sparsity of primary and multiple reflections to overcome the energy diffusion and improve the effect of multiple attenuation, respectively. This nonconvex mixed regularization problem is solved approximately by the alternating direction method of multipliers (ADMM) algorithm, and we give the convergence conditions of the ADMM algorithm. The proposed method is compared with least squares parabolic Radon transform (LSPRT) and sparse parabolic Radon transform based on *L*<sup>1</sup> regularization (SPRT*L*1) for multiple attenuation in the synthetic data and field data. We demonstrate that it improves the sparsity and resolution of the Radon domain data, and better results are obtained.

**Keywords:** multiple attenuation; parabolic Radon transform; *Lq* regularization; sparse inversion
