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

Abstract

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.

Random Noise Reduction in Seismic Data by Using Bidimensional Empirical Mode Decomposition and Shearlet Transform

“…Therefore, we can suppress random noise by threshold method to achieve the separation of signals and noise. As shown in expression (19): where S denotes Shearlet transform, S T denotes inverse Shearlet transform, T denotes the threshold function. Since random noise and seismic data are different in the Shearlet domain, we can separate them by this property.…”

“…Kong and Peng [18] proposed an effective denoising method based on shearlet and total generalized variation (TGV) regularization. Liang et al [19] introduced the singular value decomposition algorithm to non-subsampled shearlet transform, which get the effect of the microseismic data denoising. To find the optimal solution of image denoising based on sparse representation, Liu et al [20] proposed a novel denoising method via sparse representation in Shearlet domain based on continuous cycle spinning.…”

Prestack seismic random noise attenuation using the wavelet-inspired invertible network with atrous convolutions spatial pyramid

“…The high SNR reconstruction results demonstrate the feasibility of this method. Liang et al (2018) proposed a denoising method based on the non-subsampled shearlet transform. The results show that the non-subsampled shearlet transform can suppress random noise and retain effective signals.…”

Optimization Algorithm for Delay Estimation Based on Singular Value Decomposition and Improved GCC-PHAT Weighting

“…The singular value decomposition [ 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 ] method is referred to as the SVD method, which is an important matrix decomposition method when dealing with mathematical problems. The noise reduction principle is to decompose the matrix on the basis of phase space reconstruction, set the singular value corresponding to the noise to zero, and then use the inverse operation to reconstruct the signal, so as to achieve the purpose of noise reduction.…”