Noise suppression for microseismic data by non-subsampled shearlet transform based on singular value decomposition

The existence of strong random noise in surface microseismic data may decrease the utility of these data. Non-subsampled shearlet transform can effectively suppress noise by properly setting a threshold to the non-subsampled shearlet transform coefficients. However, when the signal-to-noise ratio of data is low, the coefficients related to the noise are very close to the coefficients associated with signals in the non-subsampled shearlet transform domain that the coefficients related to the noise will be retained and be treated as signals. Therefore, we need to minimise the overlapping coefficients before thresholding. In this paper, a singular value decomposition algorithm is introduced to the non-subsampled shearlet transform coefficients, and low-rank approximation reconstructs each non-subsampled shearlet transform coefficient matrix in the singular value decomposition domain. The non-subsampled shearlet transform coefficients of signals have bigger singular values than those of the random noise, which implies that the non-subsampled shearlet transform coefficients can be well estimated by taking only a few largest singular values. Therefore, those properties of singular value decomposition may significantly help minimise overlapping of noise and signals coefficients in the non-subsampled shearlet transform domain. Finally, the denoised microseismic data are obtained easily by giving a simple threshold to the reconstructed coefficient matrix. The performance of the proposed method is evaluated on both synthetic and field microseismic data. The experimental results illustrate that the proposed method can eliminate random noise and preserve signals of interest more effectively.