Conclusions

The rank-reduction method for seismic noise suppression based on the nuclear norm minimization requires a carefully selected threshold value. We have developed an optimal weighting strategy to obtain better shrinkage of the singular-values, bypassing the need for manual selection of the rank as a priori information. Considering the issue of residual noise after the optimal rank-reduction method, we further introduce an optimal way to damp the remaining noise. The proposed method can separate the noise subspace and the signal subspace in an optimal way. Detailed analyses on the proposed algorithm via two synthetic datasets and one field example demonstrate that the proposed method can obtain better denoising performance regarding the noise removal and signal preservation than the widely used methods in terms of SNR and local similarity measurements. More importantly, because of the optimally damped singular-values, the proposed method is an adaptive method, i.e., the performance is not sensitive to the predefined rank parameter.