The Projection onto Convex Sets (POCS) interpolation algorithm is widely adopted in seismic data processing, benefiting from its low computational complexity and strong data adaptability. However, the conventional POCS method fails to fully explore the inter-trace correlation information of seismic data, which leads to interpolation results with poor lateral continuity and high interpolation noise. To address this issue, this paper takes the traditional alternating projection framework for biconvex sets as the foundation, introduces a laterally constrained convex set, and thus effectively improves the interpolation quality of seismic data in terms of lateral continuity, signal-to-noise ratio (SNR) and interpolation accuracy. The specific research work is outlined as follows: First, the triple convex sets are defined in detail, the projection formula of the lateral constrained set is derived, and the triple convex set interpolation workflow is established. Second, the convergence of the new algorithm is theoretically proven, and its computational efficiency is compared and analyzed, which provides a reliable theoretical foundation for the stability of the algorithm. Finally, to verify the effectiveness of the proposed method, experiments are conducted on both synthetic seismic data and field seismic data, with a quantitative comparison of the interpolation accuracy between the two algorithms. The results demonstrate that the proposed algorithm significantly enhances interpolation accuracy while ensuring reconstruction efficiency, and therefore possesses excellent practical value.
Qin et al. (Sun,) studied this question.