POCS high‑efficient reconstruction method of seismic signals based on regional threshold model

Most of the projection onto convex sets（POCS）algorithms widely used for seismic signal reconstruction use linear or exponential threshold models，which have high computational efficiency，but have poor reconstruction effect due to the difficulty in eliminating the noise caused by the leakage of missing signals. Therefore，this paper proposes a POCS seismic signal reconstruction method based on the regional threshold model，which transforms the numerical threshold into a regional threshold，and the regional filtering window is iteratively updated as the threshold. The core idea is to reserve the transform coefficients of effective signal as much as possible by selecting a rectangular or a sectorial region of fixed size as a threshold according to a certain law in each POCS reconstruction iteration based on the frequency-wavenumber（F-K）spectrum distribution range of missing seismic signal in the spatiotemporal domain，and reserving and zeroing the transform coefficients inside and outside the region respectively. The rectangular and sectorial threshold models for POCS reconstruction of seismic signals are thus constructed. The numerical results demonstrated that compared with the POCS reconstruction of the exponential threshold model in the F-K domain，the regional threshold model in the F-K domain has a higher reconstruction accuracy for continuous missing signals. Compared with the sectorial region threshold model，the reconstruction accuracy and computational efficiency of the rectangular region threshold model are slightly higher. Compared with the exponential threshold model reconstructed by POCS in the curvelet domain，the reconstruction accuracy of the regional threshold model in the F-K domain is similar，but the computational efficiency is increased by about 90%. © 2024 Editorial office of Oil Geophysical Prospecting. All rights reserved.