**3. Results**

### *3.1. Synthetic Example*

In order to verify the validity of the coherent noise removal method based on the NSST, the synthetic data example is tested in this article. The synthetic seismic data is shown in Figure 4a. The seismic data to be tested includes 100 channels, each channel contains 1000 sampling points, and the sampling interval is 1 ms.

**Figure 4.** The processing results of the synthetic seismic data by the proposed method. (**a**) The original synthetic seismic data. (**b**) The removed noise. (**c**) The seismic data after the denoising.

As can be seen from Figure 4a, the effective signal with weak energy in the in-phase axis of the seismic record is covered by the coherent noise, which brings the interference to the subsequent processing of the seismic data. We apply the denoising method to the synthetic seismic data. Among the process, the decomposition scale of the NSST is 2, and the direction matrix is [12]. Figure 5 shows the coefficients after the decomposition of the NSST. There is an overlap of the frequency band between the effective signal and the noise. NSST can map the data into several sub-domains, which can represent the data sparsely, so that the noise and the signal can be separated better and the processing effect is better. Figure 4b shows the removed noise. Figure 4c is the result of the denoising method in this article. This method removes most of the coherent noise. This method can not only suppress the coherent noise but can also protect the effective signal to a great extent, restore the in-phase axis of the seismic record, enhance the continuity of the seismic record, and improve the SNR of the seismic record. The denoising results proves the feasibility of the denoising method in this article.
