*3.2. Field Data Example*

The above section has verified the feasibility and validity of the proposed method using the synthetic data example. Now, we further verify the effectiveness and practicality of the proposed method from the field data example.

In this article, the field seismic data of source array in Chaganhua area is selected. The overview of the field exploration area is shown in Figure 6. The field exploration area is located in a grassland near Chaganhua Town, Qianguerroth Mongolian Autonomous County, Songyuan City, Jilin Province, China. The terrain of the exploration area is flat and the diving surface of the exploration area is relatively shallow. Table 1 shows the field seismic data parameters.

**Figure 5.** The NSST coefficients after the decomposition of the NSST. (**a**) The approximate NSST coefficients. (**b**) The detail NSST coefficients at scale 2, 2 directions. (**c**) The detail NSST coefficients at scale 1, 4 directions.

**Figure 6.** The overview of the field exploration area.


**Table 1.** Field seismic data parameters.

Figure 7a shows the field seismic gather. From Figure 7a, we can see that the seismic gather contains obvious coherent noise, including surface wave, acoustic wave, and direct wave. The coherent noise seriously affects the SNR of the seismic gather and bring certain difficulties to the subsequent seismic processing and interpretation. The SNR of the seismic gather in this work area is low, which is suitable for testing the effectiveness and adaptability of the proposed method in this article. We apply the method in this article to remove the coherent noise from this seismic data. Among the processes, the decomposition scale of the NSST is 3 and the direction matrix is [4 5 5]. Figure 8 shows the main NSST coefficients containing the coherent noise after the decomposition of the NSST. Figure 7b shows the removed noise. Figure 7c shows the seismic data after noise removal using the method in this article. From the denoising results in Figure 7, the coherent noise in Figure 7a is effectively removed by this method, and the effective information of the seismic data is greatly protected. The coherent noise removed in Figure 7b is obvious, including surface wave, acoustic wave, and direct wave. The SNR of the seismic data in Figure 7c is greatly improved, the effective reflection signal is well recovered, and the seismic lineups becomes very clear and continuous, which can provide the better basic data for the subsequent seismic processing and interpretation. In order to show the ability of the proposed method, we use the conventional coherent noise suppression method—FK filtering—to compare with this method. As shown in the Figure 7d,e, FK filtering can cause certain damage to the effective signal while suppressing the coherent noise and have certain noise residue. To sum up, the method proposed in this article has a good effect on the removal of the coherent noise in various kinds of the field seismic data.

We analyzed the average amplitude spectrum, the single-channel amplitude spectrum, and the f-k spectrum of the original data and the denoised data after processing using this method. The frequency spectrum of the original data and the denoised data in Figures 9 and 10 shows that the effective signal is distributed in the frequency range of 25–40 Hz and the coherent noise is mainly distributed in the frequency range of 5–20 Hz, and 70–85 Hz. The spectrum analysis in Figure 9 shows that the noise signal in the frequency range of coherent noise is well suppressed after the denoising by this method. The deviation of the signal waveform outside the coherent noise frequency range is very small compared with the original signal. The spectral analysis of the f-k spectrum in Figure 10 also shows that the coherent noise is significantly suppressed. The spectral analysis of Figures 9 and 10 further illustrate that the proposed method in this article has good removal ability for coherent noise and can protect the effective signal well.

**Figure 7.** The processing results of the field seismic data using the proposed method. (**a**) The field seismic data. (**b**) The removed noise by NSST. (**c**) The seismic data after the NSST. (**d**) The removed noise by FK filter. (**e**) The seismic data after the FK filter.

**Figure 8.** The main NSST coefficients containing the coherent noise. (**a**) The detail NSST coefficients at scale 2, 2 directions. (**b**) The detail NSST coefficients at scale 1, 3 directions.

**Figure 9.** Waveform and amplitude spectra of the seismic data. (**a**) The waveform of trace 80 of the original seismic data (the green curve), the denoised seismic data by the NSST (the blue curve), and the denoised seismic data by the FK filter (the red curve). (**b**) The amplitude spectra of trace 80 of the original seismic data (the green curve), the denoised seismic data by the NSST (the blue curve) and the denoised seismic data by the FK filter (the red curve). (**c**) The average amplitude spectra of the original seismic data (the green curve), the denoised seismic data by the NSST (the blue curve) and the denoised seismic data by the FK filter (the red curve).

**Figure 10.** The results of applying f-k transform in the original seismic data and the denoised seismic data. (**a**) The original data. (**b**) The seismic data after the NSST. (**c**) The seismic data after the FK filter.

### **4. Discussion**

As described in Sections 3.1 and 3.2, we used synthetic data examples and field data examples to analyze the denoising performance of the proposed method in this article. We mainly used the difference in the distribution of noise and signal in the scale and direction through NSST, a multi-scale and multi-directional analysis method, to suppress the noise. The denoising results show that this method can effectively remove the coherent noise from the source array seismic data, especially surface wave, and it can greatly protect the effective information of the seismic data from being lost and greatly improve the SNR of the seismic data. The proposed NSST method is not only a method to suppress noise, but also a beneficial tool for signal analysis. The accurate data analysis, targeted strategy, and sparse representation make NSST have more desirable denoising results. There are some limitations to the proposed method: we need to artificially select the scale, direction, and threshold zone according to the seismic data, which is not adaptive enough, and then we will study further to simplify the process.
