Multichannel seismic attenuation compensation and interpolation with curvelet sparse constraint of frequency-wavenumber spectrum

High-resolution exploration is hampered by seismic attenuation, caused by the viscosity and heterogeneity of underground media. Conventional single-channel attenuation compensation methods can increase the corresponding vertical resolution partially. However, the lateral continuity of compensated seismic data is always ignored and the noise resistance can be improved. Therefore, multichannel attenuation compensation methods were proposed, including the algorithm with sparse curvelet coefficient constraint of the time-space (t-x) data. However, nonstationary seismic data may be affected by irregular missing traces in field cases, which severely degrades its lateral continuity and negatively affects the performance of multichannel attenuation compensation. Therefore, we concentrate on simultaneous multichannel attenuation compensation and missing trace interpolation in a unified framework. Based on the inversion framework of sparsity promotion, we propose an approach for simultaneous multichannel compensation and interpolation, utilizing sparse curvelet coefficient constraint of the recovered principal frequency-wavenumber (f-k) spectrum. The size of the principal f-k spectrum is reduced by at least half compared with that of the corresponding t-x band-limited data. It significantly reduces the computational expense of curvelet transform-based processing. Synthetic and field data experiments validate the effectiveness of the proposed method in efficiency improvement with consistent performance when compared to the multichannel method with sparse curvelet coefficient constraint of the t-x data in improving the vertical resolution and lateral continuity. Furthermore, we have discussed a potential acceleration strategy based on random sampling in the normal compensation issue.