# Seismic Coherent Noise Removal of Source Array in the NSST Domain
## 1 Introduction  
The seismic exploration method is widely used in resource exploration and other fields, and the seismic source, as an important part of the seismic data acquisition, directly affects the exploration effect of the seismic exploration. With the rapid development of vibroseis technology, vibroseis is gradually replacing the traditional dynamite source for seismic data acquisition due to its advantages of safety, environmental protection, high quality, economy, and efficiency. However, limited by its own structure and exploration environment, the single vibroseis has the problems of small output force and limited exploration depth. In order to meet the demand of seismic exploration, the source array based on vibroseis technology is paid more and more attention. In the seismic data acquisition of source array, there are generally more serious coherent noises, such as multiple refraction waves and surface waves of strong energy, strong acoustic interference, and surface direct waves with wide frequency bands, which greatly affect the quality of the seismic data. The removal of coherent noise is essential for the exploration technique of the source array. How to better remove the seismic noise and improve the SNR of the seismic data has been a hot research topic in the seismic exploration field [1; 2; 3]. For coherent noise, scholars of seismic exploration have presented many seismic denoising approaches to suppress it. The traditional noise removal methods mainly suppress coherent noise according to the difference between effective signal and coherent noise in apparent velocity and frequency, such as f-k filter [4; 5], K-L transform [6; 7], Radon transform [8; 9], radial channel transform [10; 11], empirical mode decomposition (EMD) [12; 13], and so on. Wavelet transform [14; 15] is an effective tool for seismic data processing, which has great advantages in one-dimensional data processing, though this advantage cannot be simply extended to two-dimensional or three-dimensional data. Therefore, multi-scale geometric analysis methods such as Ridgelet transform [16; 17], Curvelet transform [18; 19], Contourlet transform [20; 21] and Shearlettransform [22] have been proposed successively. At present, multi-scale geometric analysis has been widely used in seismic data processing and achieved certain effect. [PERSON], [PERSON], and [PERSON] [23] proposed the Shearlet transform based on the basic theory of wavelet transform and the multi-scale analysis theory. Shearlet transform not only has good localization characteristics, scaling characteristics, direction sensitivity, and near-optimal sparse representation performance, but also has a simple mathematical structure and the transformed coefficients have a one-to-one correspondence with the image points. Therefore, compared with other multi-scale geometric analysis methods, Shearlet transform has a more delicate representation of the scale direction and the physical significance of the transformed coefficients is clearer, which is more conducive to the processing of the coefficients. In the process of the conventional Shearlet transform, the subsampling operation is carried out, which leads to spectrum aliasing in the low frequency and high frequency sub-bands decomposed by Shearlet transform. The spectrum aliasing will cause the information of the same direction to appear in several different sub-bands at the same time, which will weaken the direction selectivity. In addition, the subsampling operation makes the Shearlet coefficient low redundancy, resulting in the lack of the translation invariance. If it is used for image denoising, there will be an obvious ringing effect. In order to overcome the shortcomings mentioned above and enhance the directional selectivity and the translation invariance of Shearlet transform, the NSST came into being. NSST is a non-orthogonal transform. The NSST abandons the subsampling operation and combines the non-subsampled Laplacian pyramid transform (NSLP) with the non-subsampled directional filter.