Suppression of Strong Cultural Noise in Magnetotelluric Signals Using Particle Swarm Optimization-Optimized Variational Mode Decomposition
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsAuthors deal with the strong cultural noise as it impacts magnetotelluric signals using the signal processing based on the particle swarm optimization and variational mode decomposition. The proposed results demonstrate advantages over several other algorithms by means of normalized cross-correlation and signal-to-noise ratio. In general, the study provides a scientific and technical background and provides an argumentative alternative to the traditional signal processing methods, thus providing an interesting solution; however, several comments must be addressed:
1. While authors deal with the strong cultural noise, in row 98 the term “anthropogenic noise” is used. If it is the same, use the same term, if not, provide an explanation.
2. In Figure 1, four types of strong cultural noise are provided. Explain why are such waveforms and such signal parameters used. Maybe, it can be explained with referencing some previous works?
One more thing, the caption of Figure 1 misses the word “noise”.
3. While the two parameters of the VMD algorithm are K and α, K is missed in the equations. As for me, it would be more illustrative if it is provided in the equations.
4. In Table 2, the symbol α is missing.
5. In Figure 4, provide the axes explanation for the three waveforms for (a), (b), (c) and (d). The same for Figure 5, and Figure 1.
6. Zxy and Zyx are not explained in the text.
7. Can there be in practice that the different noise waveforms (Figure 1) overlap? Will the proposed algorithm be suitable?
Author Response
Comments 1: While authors deal with the strong cultural noise, in row 98 the term “anthropogenic noise” is used. If it is the same, use the same term, if not, provide an explanation.
Response 1: Thank you for pointing this out. We agree with this comment. We misspelled “cultural” as “anthropogenic” before. Therefore, we have made changes in row 98 on page 2.
Comments 2: In Figure 1, four types of strong cultural noise are provided. Explain why are such waveforms and such signal parameters used. Maybe, it can be explained with referencing some previous works? One more thing, the caption of Figure 1 misses the word “noise”.
Response 2: Through detailed analysis of the time-domain waveforms of our measured 156 measurement points, combined with the previous research on the classification of cultural noise that often appears in magnetotelluric time series signals (Ref. 2, Ref. 9, and Ref. 23), we classified the cultural noise into these typical four types, which are impulse noise, square noise, triangular noise and periodic noise. We missed “noise” in the caption of Figure 1 before. Therefore, we have made changes in row 147 on page 4.
Comments 3: While the two parameters of the VMD algorithm are K and α, K is missed in the equations. As for me, it would be more illustrative if it is provided in the equations.
Response 3: K is actually the k of the above equation, and when we extract k as a parameter for optimization, we refer to it as K (Refs. 26 to 30). We still illustrate K in the text. Therefore, we have made changes in row 195 on page 5.
Comments 4: In Table 2, the symbol α is missing.
Response 4: Thank you for pointing this out. We agree with this comment. We forgot to change “K” to “α” before. Therefore, we have made changes in Table 2 on page 6.
Comments 5: In Figure 4, provide the axes explanation for the three waveforms for (a), (b), (c) and (d). The same for Figure 5, and Figure 1.
Response 5: Thank you for pointing this out. We agree with this comment. Due to the complexity of the diagrams in Figure 1, Figure 4, and Figure 5, and in order to keep the diagrams looking nice, we give our axes explanation in the captions of these figures, in row 147 on page 4, row 367 on page 10, and row 416 on page 12, respectively.
Comments 6: Zxy and Zyx are not explained in the text.
Response 6: Thank you for pointing this out. We have added to the text based on this comment. For Zxy and Zyx, we have carried out the meaning and description of magnetotelluric impedance on page 12, second paragraph, and explained in row 434, row 438, row 440 on page 13, respectively.
Comments 7: Can there be in practice that the different noise waveforms (Figure 1) overlap? Will the proposed algorithm be suitable?
Response 7: In practice that the different noise waveforms (Figure 1) can overlap. However, for clarity and accuracy of our study, we categorized the noise waveforms, simulated them separately and performed denoising studies. And we show the processing of the noise for the field data in Figure 5 on page 12, and the effect is good, so we can say that the proposed algorithm is suitable. In response to this comment, our next step will be to study in depth how to perform signal-to-noise separation in the case of overlapping noise waveforms.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsDear authors,
In this study, the PSO-optimized VMD approach for processing geomagnetic time series signals with high cultural noise is developed by combining artificial intelligence with the VMD method. In order to thoroughly assess the denoising performance of this approach, the research examines two parameters, NCC and SNR, using simulated tests on four different kinds of typical strong cultural noise signals. The findings show that this technique successfully eliminates impulse, square wave, triangle wave, and periodic sounds from the geomagnetic time series signals while extracting the profile characteristics of strong cultural noise.
Overall, I believe that the paper can be published after a careful review by the authors and the correction of some technical errors (please double-check the header rows of Tables 1 and 2).
Author Response
Comments 1: Please double-check the header rows of Tables 1 and 2.
Response 1: Thank you for pointing this out. We agree with this comment. We reversed the results for NCC and SNR in Table 1 and Table 2. Therefore, we have made changes in Table 1 and Table 2 on page 6.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsThe paper “Suppression of Strong Cultural Noise in Magnetotelluric Signals Using PSO-Optimized VMD”, by Zhongda Shang, Xinjun Zhang, Shen Yan and Kaiwen Zhang, works on the problem of separating strong cultural noise in Magnetotelluric signals under strong interference conditions. It has the goal of restoring the true forms of apparent resistivity and phase curve. To do this, it is proposed an improved method for suppressing strong cultural noise based on Particle Swarm Optimization and Variational Mode Decomposition. The results show good results when compared to several traditional algorithms.
The paper approaches an important problem and gives interesting results. The language is good; the text just needs some new checks to correct small errors. The figures have good quality.
Besides being an interesting paper, I have some suggestions to improve the text, as shown below.
1) The paper mention that “Therefore, this paper will not delve deeply into geological noise and source noise, but will focus on the analysis and processing of strong cultural noise in MT signals.” Can you explain better the consequences of this fact?
2) The paper uses a parameter convergence tolerance of 1 × 10−7, and a penalty factor α of 2000. How those parameters are selected? How this choice influences the results?
3) The optimization method looks very important in this problem. The paper mentions some of its advantages, but I would like to see some more explanations about this crucial point. Would be possible to use a different optimization method?
4) The results simulated show good results, but I would like to see some explanations about the range of applicability of the method. How far can we go from the cases simulated and still get good results?
5) So, the conclusions should: i) mention some key numbers of the results obtained, emphasizing the advantages of the method; ii) explain better the limitations of the work presented; iii) show the next steps for future research.
Considering the above comments, I suggest just some more explanations in the text to publish the paper.
Author Response
Comments 1: The paper mention that “Therefore, this paper will not delve deeply into geological noise and source noise, but will focus on the analysis and processing of strong cultural noise in MT signals.” Can you explain better the consequences of this fact?
Response 1: Sourse noise and geological noise are caused by natural factors, by the previous research know that both them these can be corrected and eliminated using various calibration methods (Refs. 21, 22). But the cultural noise is caused by human factors, this kind of noise is more complex, the previous research denoising methods can not remove the cultural noise in our field data. Therefore, this paper is focus on the analysis and processing of strong cultural noise in MT signals.
Comments 2: The paper uses a parameter convergence tolerance of 1 × 10−7, and a penalty factor α of 2000. How those parameters are selected? How this choice influences the results?
Response 2: Thank you for pointing this out. The paper uses a parameter convergence tolerance of 1 × 10−7, because decreasing this value can make the algorithm converge to more accurate results, but will also increase the computation time, by the previous research is known to be generally set at 1 × 10−7 the most appropriate (Refs. 26 to 30). However, through previous research (Refs. 26 to 30) and our study of α as a control variable experiment in Table 2, we learned that α has a wide range of values and seriously affects the effectiveness of data processing, so we need to optimize this method with PSO to select the appropriate α. One more thing, we forgot to change “K” to “α” before. Therefore, we have made changes in Table 2 on page 6.
Comments 3: The optimization method looks very important in this problem. The paper mentions some of its advantages, but I would like to see some more explanations about this crucial point. Would be possible to use a different optimization method?
Response 3: On the one hand, due to the characteristics of MT signals with wide bandwidth and long sampling time, and the complexity of the noise in MT signals, combining the previous research we learned that using the global optimization algorithm PSO to optimize VMD is more mature and effective. On the other hand, in the future, we will study more applicable algorithms for denoising MT signals for optimization.
Comments 4: The results simulated show good results, but I would like to see some explanations about the range of applicability of the method. How far can we go from the cases simulated and still get good results?
Response 4: Regarding the range of applicability of this method, no scholar can give a clear range of applicability in the field of magnetotelluric signal processing for the time being, but we have also given in Figure 5 on page 12 that the denoising effect is still reliable in the case of very complex or even overlapping noise waveforms of the field data.
Comments 5: So, the conclusions should: i) mention some key numbers of the results obtained, emphasizing the advantages of the method; ii) explain better the limitations of the work presented; iii) show the next steps for future research.
Response 5: Thank you for pointing this out. We agree with this comment. Therefore, we have mentioned the key numbers of the results obtained in row 453 on page 14. The limitations of the work presented and the next steps for future research are in the last paragraph of the conclusion.
Author Response File: Author Response.pdf
