Wavelet Model of Geomagnetic Field Variations and Its Application to Detect Short-Period Geomagnetic Anomalies
Round 1
Reviewer 1 Report
The article considers the application of wavelet analysis to highlight the effects of non-stationary behavior in the time series of monitoring the Earth's electromagnetic field. As a measure of non-stationary behavior, we consider the standard deviation from the observation results from the so-called Sq-signal, which is considered as the standard for the "calm" behavior of the geomagnetic background. The standard deviation is calculated in a time window with a length of 1 month for the values ​​of the wavelet coefficients of 5 levels of detail of the orthogonal wavelet decomposition (formula (3)). The problem of choosing the optimal number of the level of detail from the condition of the minimum square deviation from the standard Sq-signal is considered, subject to the restriction on the square deviation from the decomposition of the Sq-signal for the next number of the level of detail. The value of the constant limitation is determined by an expert assessment for each station based on the results of observations in quiet months when there are no electromagnetic storms. At the same time, the problem of determining the best orthogonal wavelet basis for which the found minimum of the square deviation is minimal is solved.
The presentation of the use of orthogonal wavelet analysis is supplemented by the results of using continuous wavelets in Chapter 2.2. In this case, the hard thresholding operation is used for continuous wavelet coefficients (formula (6)).
The article should be commented on.
- Figure 1 is presented for observations lasting 2 days. At the same time, the article says that the analysis is carried out for fragments 1 month long. Therefore, it is logical that Figure 1 be presented for the analysis of 1 month long data.
- The article does not specify a set of orthogonal wavelet bases for which problem (5) is being solved. Figure 2 shows the results of using only 3 bases. This is not enough, considering that there are only 17 Daubechies wavelets with the minimum support length and the number of vanishing moments from 1 to 10. The choice of the optimal basis is critically important, since it allows one to adapt to the smoothness of the perturbation being distinguished.
- When choosing the optimal basis, there should be a dependence on the analyzed data fragment. That is, for each piece of data, its optimal basis must be determined. The presentation of the method should be accompanied by information on how the optimal basis changes, for example, how the number of vanishing moments changes. This point is not reflected in the article at all.
- Traditionally, in wavelet analysis, the choice of the optimal basis is carried out from the condition of the minimum entropy of the distribution of squared values ​​of the coefficients [Mallat]. It is necessary to compare the results of determining the optimal basis from the condition of minimum entropy and method (5).
- There is no information in the article about which smoothing kernel of the continuous wavelet transform was used in the formula after line 199 - what exactly: Mexicat hat, Morlet or something else. I couldn't find any mention of this in the article. This information should be placed in clause 2.2. The choice of the smoothing kernel of the continuous wavelet transform is as critical as the choice of the optimal orthogonal wavelet basis.
- In paragraph 2.2, it is necessary to state the considerations regarding the choice of hard thresholding thresholds in formula (6). Now it is completely unclear how this choice occurs and to what extent it is adapted to changes in the properties of the analyzed signals.
- The hard thresholding operation is traditionally used in orthogonal wavelet analysis to suppress noise and highlight significant anomalies since the classical work [Donoho D., I. Johnstone (1994) Ideal spatial adaptation via wavelet shrinkage. Biometrika, vol. 81, pp. 425-455, https://doi.org/10.1093/biomet/81.3.425]. Explanations are needed why the authors refused to use a carefully designed denoising apparatus in orthogonal wavelet analysis, where the choice of thresholding thresholds is mathematically justified and adapted to changing signal properties [Berger J., R. Coifman, and M., Goldberg (1994) Removing noise from music using local trigonometric bases and wavelet packets. J.AudioEng. Soci., Vol. 42, no. 10, pp. 808-818.] see also [Mallat].
Author Response
Dear Reviewer!
Comments are in the attached file.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The work concerns using a particular analysis technique for the detection of geomagnetic pulsations. The method used and examples of its application are adequately illustrated, which is sufficient for the work to be published. Its application to a limited number of cases does not support the use of such observations as precursors of geomagnetic storms, but this does not diminish the importance of the work. I hope that the authors will apply the method to a more extensive set of observations to demonstrate its effectiveness in different situations so that it will be helpful for space weather applications.
I have attached a pdf copy with comments, suggestions and corrections to English.
Comments for author File: Comments.pdf
Author Response
Dear Reviewer!
Comments are in the attached file.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The authors took into account all remarks from the first version of the paper
