Conclusions

We have introduced a new rank-reduction (RR) method for interpolating and denoising five-dimensional seismic data based on a cascaded optimal weighting and damping operations. The proposed optimally damped rank-reduction (ORR) method can further improve the damped rank-reduction (DRR) method in causing less residual noise and making the result smoother. The proposed ORR method works effectively in various data examples including data with linear/planar events, data with hyperbolic events, and field data. While in the case of low SNR, all rank-reduction methods tend to damage some useful energy, the proposed ORR method does not cause extra damage but can remove more noise than the other rank-reduction methods. The waveforms reconstructed from the proposed method are more similar to the ground-truth solution in the synthetic tests. The block Hankel matrix from the proposed method in each frequency slice is smoother than other rank-reduction method, which accounts for why it is more capable of suppressing residual noise. The proposed method outperforms the other rank-reduction methods more in stronger noise and higher sampling ratios. The effectiveness is almost unchanged for different predefined ranks, meaning that the proposed method is almsot parameter-free. One drawback of the proposed method is that the computational cost is 2-5 times higher than the other rank-reduction methods, which can be potentially tackled in future research.