**5. Discussions**

The proposed de-noising method is based on sparse representation of periodic noise. The key to our method is the construction of the noise dictionary. Because ambient noise contains no seismic waves but dominant periodic noise and other random noise, periodic noise can be estimated without the influence of seismic reflections. Therefore, our method is useful regardless of whether the seismic waves are strong or weak. A scanning method is used to estimate the noise period. The accuracy of the noise period largely influences our de-noising result. To obtain an accurate noise waveform, the waveforms in the time domain and the space domain are stacked shown as the Equations (5) and (6), respectively. It must be emphasized that our de-noising method is only applicable to stationary noise with a constant period, waveform and amplitude. It can be used to attenuate power line harmonic noise, pump jack noise and engine operation noise in land or oceanic seismic exploration.

Based on the proposed method, ambient noise detection is urged for noise estimation. However, ambient noise has not specifically been detected in oil exploration. Therefore, we suggest that ambient noise should be acquired for one second before source excitation. Long-term ambient noise will be helpful for building a perfect noise dictionary.

Wind- or water-induced noise is not strictly stationary, and the stationarity becomes weak with increasing recording time [22,23]. Our method cannot be used to attenuate this kind of noise. To broaden the method for non-stationary noise, higher-order statistics [24] need to be considered further. In addition, methods of noise feature extraction from ambient noise based on machine learning [25] will draw increased attention in the future.

### **6. Conclusions**

A new method is proposed to attenuate periodic noise based on sparse representation. The novelty is the construction of a noise dictionary based on ambient noise. Our method can attenuate monochromatic or multitoned periodic noise automatically without preknown noise frequencies. The noise is assumed to be stationary noise with a constant period, waveform and amplitude. Synthetic and field tests show the effectiveness of the proposed method. Compared with the conventional notch filtering method, the proposed

method can obtain de-noised data with no distortion in the time and frequency domains. Therefore, our method can attenuate periodic noise without damaging the seismic events.

**Author Contributions:** Conceptualization, Y.W.; investigation, C.W.; writing—original draft preparation, L.S.; writing—review and editing, L.S. and X.Q.; visualization, X.Q. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the National Natural Science Foundation of China (62127815) and Guizhou Science and Technology Cooperation Platform Talents Program: [2021] 5629.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** We thank Yijun Yuan for providing the field data.

**Conflicts of Interest:** The authors declare no conflict of interest.
