Time-Domain Electromagnetic Noise Suppression Using Multivariate Variational Mode Decomposition

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors propose a novel TDEM signal denoising method based on MVMD by take full use of the correlation between multiple-channel signals, and use MDFA to select useful IMFs to improve the automation of data processing and reduce subjective bias. The effectiveness and superiority of the proposed method are verified through measured and synthesized data. The manuscript has sufficient innovation and practicality and is well-structured with fluent language. It can be accepted after minor revisions:

(1)MVMD has been successfully applied in denoising geomagnetic data, please cite relevant literature:  Chinese J. Geophys. (in Chinese), 2023, 66(8), 3540–3556.

(2)As to the TDEM signals, how many channels can the proposed method process simultaneously? How many IMFs is a signal typically decomposed into? Please conduct some experimental tests or provide some guiding descriptions.

(3)The variables in the main text should also be italicized, such as Line 97, "K"; Lines 102&108, "c". Please check the entire manuscript.

(4)Add a comma or period after all equations

(5)Figures 2, 9, and 10, an additional subfigure should be added to display the decomposed signal, in order to observe the difference between the decomposed signal and IMF, and to evaluate the decomposition effect.

(6)The font size of the coordinates in Figures 8 and 12 is too large, and the font is different from other Figures

(7)Figure 11 only has two subfigures, but there are three image introductions in the caption. Please make necessary modifications.

(8)MVMD and MDFA are both time-consuming, but this is not a problem for modern computers. It is recommended to display the time consumption of the proposed method and indicate the advantages and disadvantages of the method in the conclusion.

Comments on the Quality of English Language

none.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Interesting paper.

Some suggestions:

- The quality of some figures must be improved and some labels and captions must be inserted to help the understanding about you want to show to the reader. The captions must have some explanations and comments about what you want to show.

- Discussion must be improved to be more detailed.

 

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

In this work, the authors present a noise reduction method for multichannel time-domain electromagnetic (TDEM) method data. The proposed method consists of two stages: decomposing 2-D TDEM data into a series of intrinsic mode functions (IMFs) using the Multivariate Variational Mode Decomposition (MVMD) algorithm; applying the multivariate detrended fluctuation analysis (MDFA) to distinguish between IMFs containing mainly signal or noise. The authors present the results of an artificial test and a real-life one.

The work is original and the results presented are sound in my opinion. I suggest only fixing a few minor things listed in the following. Besides them, I believe the paper is ready for publication.

Minor comments

1) I suggest using the EPS format for figures 1-5 and 8-12. Current images are of low resolution.

2) I invite the authors to add in Table 1 a column reporting the computational time of all different methods tested.

3) I invite the authors to mention in the conclusion that other methods can be explored in the future for the decomposition of multichannel signals that are alternatives to EMD and VMD. Such methods do not require the a priori selection of the number of IMFs to be extracted, like in EMD, and, at the same time, have stability to noise like VMD. For instance, we have Multivariate Iterative Filtering (MvFIF) [1], Multi-channel Adaptive Fourier decomposition (MAFD) [2], multi-channel Fourier decomposition method (MFDM) [3], multivariate nonlinear chirp mode decomposition (MNCMD) [4]

[1] Cicone, A., & Pellegrino, E. (2022). Multivariate fast iterative filtering for the decomposition of nonstationary signals. IEEE Transactions on Signal Processing, 70, 1521-1531.
[2] Wang, Z., Wong, C. M., Rosa, A., Qian, T., & Wan, F. (2022). Adaptive Fourier decomposition for multi-channel signal analysis. IEEE Transactions on Signal Processing, 70, 903-918.
[3] Singh, P. (2018). Novel Fourier quadrature transforms and analytic signal representations for nonlinear and non-stationary time-series analysis. R. Soc. Open Sci., 5(11), 181131.
[4] Chen, Q., Xie, L., & Su, H. (2020). Multivariate nonlinear chirp mode decomposition. Signal Processing, 176, 107667.

4) On page 8, the caption of Figure 4, I suggest rephrasing "Results of different methods for channel 2 and 14 (a) channel 2;(b) channel 14" to read something like "Results of different methods for channel 2 (a); and channel 14 (b)"

5) Page 2, line 64, trend -> tend

Author Response

Please see the attachment.

Author Response File: Author Response.pdf