Evaluation of Electromagnetic Fields of Extremely Low-Frequency Horizontal Electric Dipoles at Sea–Air Boundaries
Round 1
Reviewer 1 Report
The authors proposed a quasi-static approximation method using horizontal electric seven dipoles as a model. The work is well-written and well-divided. Despite its brevity, it is clear and objective. However, I have a few comments.
- In Figure 2, why did the authors choose the frequencies 3 and 30 Hz? Please add it to the text. Depending on the reader's knowledge, it's helpful to emphasize this information.
- I believe the results in graphs 5 and 6 have not been explored and explained in sufficient depth. The attenuations of E0p and B0p have not been sufficiently explained, and the conclusion regarding these observations has not been presented.
- Since there was no practical test, the authors could have presented better quantitative results. No statistical indexes or values were presented to justify the application of the technique. At least some values could be presented in the conclusions.
Author Response
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Reviewer 2 Report
In this paper, a quasi-static approximation method is proposed using horizontal electric dipoles (HED) as a model. The experimental results show that lateral wave is the main mode of electromagnetic wave propagation at the boundary between sea and air. The topic of this paper is interesting to the readers, within the scope of the journal. However, before its publication changes must be done.
1. The use of English must be improved. The paper includes several grammatical and syntax errors.
2. Keywords should be placed in alphabetical order.
3. In the Introduction section the authors need to point out how this study is different from other ones. The contribution of this work is limited since exist many survey/review articles that targeted the same topic. The authors should highlight their contributions in a proper manner by emphasizing on how their review is different from other review articles. Please, add at least 10 references to support your points for example:
· https://doi.org/10.3390/electronics12122577
· 10.1049/iet-smt:20060137
4. In your text there are plenty of equations. Perhaps some of them could be inserted in a separate Appendix.
5. In Section 4 you present a simulation and analysis in the near field. What about the far field? Can you make a comparison and further analysis between far and near field in your manuscript, giving more details and remarks?
6. Increase the size of the figures in the manuscript to be easy to be read.
7. Can you refer in your manuscripts how your research can help in practical problems (if there are)?
8. A separate discussion section before conclusions must be added. This must replace results section.
9. Add at the end a section named “Conclusions”. This section must summarize the work presented within the paper. Please expand it and add limitations of your work.
10. An abbreviation list should be added in the manuscript.
The use of English must be improved. The paper includes several grammatical and syntax errors.
Author Response
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Author Response File: Author Response.pdf
Reviewer 3 Report
This paper proposes a quasi-static approximation method using horizontal electric dipoles as a model. A numerical integral approximation of Sommerfeld's expression for an extremely low-frequency electromagnetic field excited by horizontal electric dipoles in seawater is obtained near the sea-air interface where the wavenumber relation does not hold. The correctness of the proposed method is verified by comparison with the approximate Pan expression and the exact Margetis expression. In addition, through modeling and calculation, the variational characteristics of the electromagnetic field in sea water at different frequencies, the height of the source and the height of the observation point were obtained, and their influence on the propagation of electromagnetic waves was analyzed. The authors show the simulation results that the lateral wave is the main propagation mode of ELF HED at the sea-air interface, and the electromagnetic wave is more influenced with increasing seawater mean field source height, observation point height, and propagation distance. The experimental results show that the lateral wave is the main method of propagation of electromagnetic waves at the sea-air interface.
However, the article does not provide an analysis of previous studies devoted to the problem, expanding the analysis of studies and comparative analysis of various methods will make the article better. It is desirable to expand the justification of the research methods used. Separately, it would be good for readers to understand the practical value of the described research.
needs editorial corrections
Author Response
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Author Response File: Author Response.pdf
Reviewer 4 Report
My review
Calculation and analysis of electromagnetic fields of ELF horizontal electric dipoles in the sea-air boundary
The propagation of an electromagnetic wave involves the propagation of vibrations of electric and magnetic field strength vectors in space. Light, interacting with matter, causes the charges contained in it to vibrate and emit secondary electromagnetic waves.
Propagation takes place thanks to ionospheric refraction, the propagation depends on the route, time of day, year and solar activity. Multiple reflections from the ionosphere and the Earth's surface allow it to propagate over very long distances, with a global range.
Over the last few decades, the propagation of electromagnetic waves in key layers has gained great importance and interest.
In the reviewed work Calculation and analysis of electromagnetic fields of ELF horizontal electric dipoles in the sea-air boundary based on the HED model, the problem of ELF electromagnetic field propagation near the "sea-air" interface was examined and a quasi-static approximate numerical integration method was proposed. Sommerfeld.
A model for the propagation of the HED-induced ELF near field in the sea-air half-space is shown in Figure 1, using cylindrical coordinates as a coordinate reference system.
The solution of the "quasi-static" approximation was analysed, since the simplified expression of each electromagnetic field component contains an infinite integral term of the Bessel function, the integral expression of each field component can be further simplified.
In order to check the correctness of the proposed method, the approximate Pan expression and the exact Margetis expression were simplified in the work carried out. Using Maclaurin's progressive formula, the calculation results of the corresponding approximate expressions were compared with the method proposed in the current work.
In the work, Figure 2a, b show a comparison of the results calculated by the proposed method with the existing results for the electric field component (E0ρ).
The electric field component in the ρ direction decreases with increasing propagation distance. However, when the frequency is the same, the amplitude E0ρ obtained by the approximation method (approximating the function using a "simpler" Pan function belonging to a specific class) decreases the most with distance. In the case when the amplitude E0ρ (obtained using the exact Margetis expression) is in the middle of the two approximation algorithms, the amplitude obtained by the method proposed in this article decreases the most gently.
To further investigate the distribution of HED in the ELF near field near the sea-air interface, the relative dielectric constants of seawater and the air above were observed to remain unchanged. The obtained results from simulation and near-field analysis are respectively presented in Figures 3 - 6 and carefully discussed.
Based on quasi-static assumptions (ω→0, k1ρ<<1, k1<<k0), in the reviewed work Calculation and analysis of electromagnetic fields of ELF horizontal electric dipoles in the sea-air boundary, a model of HED propagation at the boundary " sea-air.” An integral expression of the near-field electromagnetic field excited by ELE HED in seawater is derived. It should be emphasized that using this method, the propagation characteristics of the electromagnetic field in the close ELF region are studied at different frequencies, source height and observation point height.
The simulation results show that the main form of ELF HED propagation at the sea-air interface is a side wave. The electromagnetic wave is more influenced by the increase in the height of the seawater centre field source, the height of the observation point and the propagation distance.
What is important in the research being carried out is the fact that the calculated results of the proposed method were compared with the results of the works of Mr. and Margetis, respectively. It was found that the calculated results are consistent, which verifies the correctness of the proposed method.
To sum up, the reviewed work Calculation and analysis of electromagnetic fields of ELF horizontal electric dipoles in the sea-air boundary presents interesting research on the calculation and analysis of electromagnetic fields of ELF horizontal electric dipoles at the sea-air boundary.
The research is carried out correctly, the discussion of the work carried out and their results documented with carefully prepared drawings (6) confirms the validity of the work carried out regarding the calculations and analysis of horizontal electric dipoles.
The references cited in the work (25) are consistent with the research topic and confirm the validity of the undertaken scientific task.
Taking into account the results of the conducted research, I believe that they should find practical application. This fact should be particularly emphasized and discussed in the summary of the task being performed.
According to the reviewer, the work Calculation and analysis of electromagnetic fields of ELF horizontal electric dipoles in the sea-air boundary, after careful justification of the purpose and importance of the research conducted and their practical importance for science/economy, as well as after linguistic correction of the text, is suitable for printing.
My review
Calculation and analysis of electromagnetic fields of ELF horizontal electric dipoles in the sea-air boundary
The propagation of an electromagnetic wave involves the propagation of vibrations of electric and magnetic field strength vectors in space. Light, interacting with matter, causes the charges contained in it to vibrate and emit secondary electromagnetic waves.
Propagation takes place thanks to ionospheric refraction, the propagation depends on the route, time of day, year and solar activity. Multiple reflections from the ionosphere and the Earth's surface allow it to propagate over very long distances, with a global range.
Over the last few decades, the propagation of electromagnetic waves in key layers has gained great importance and interest.
In the reviewed work Calculation and analysis of electromagnetic fields of ELF horizontal electric dipoles in the sea-air boundary based on the HED model, the problem of ELF electromagnetic field propagation near the "sea-air" interface was examined and a quasi-static approximate numerical integration method was proposed. Sommerfeld.
A model for the propagation of the HED-induced ELF near field in the sea-air half-space is shown in Figure 1, using cylindrical coordinates as a coordinate reference system.
The solution of the "quasi-static" approximation was analysed, since the simplified expression of each electromagnetic field component contains an infinite integral term of the Bessel function, the integral expression of each field component can be further simplified.
In order to check the correctness of the proposed method, the approximate Pan expression and the exact Margetis expression were simplified in the work carried out. Using Maclaurin's progressive formula, the calculation results of the corresponding approximate expressions were compared with the method proposed in the current work.
In the work, Figure 2a, b show a comparison of the results calculated by the proposed method with the existing results for the electric field component (E0ρ).
The electric field component in the ρ direction decreases with increasing propagation distance. However, when the frequency is the same, the amplitude E0ρ obtained by the approximation method (approximating the function using a "simpler" Pan function belonging to a specific class) decreases the most with distance. In the case when the amplitude E0ρ (obtained using the exact Margetis expression) is in the middle of the two approximation algorithms, the amplitude obtained by the method proposed in this article decreases the most gently.
To further investigate the distribution of HED in the ELF near field near the sea-air interface, the relative dielectric constants of seawater and the air above were observed to remain unchanged. The obtained results from simulation and near-field analysis are respectively presented in Figures 3 - 6 and carefully discussed.
Based on quasi-static assumptions (ω→0, k1ρ<<1, k1<<k0), in the reviewed work Calculation and analysis of electromagnetic fields of ELF horizontal electric dipoles in the sea-air boundary, a model of HED propagation at the boundary " sea-air.” An integral expression of the near-field electromagnetic field excited by ELE HED in seawater is derived. It should be emphasized that using this method, the propagation characteristics of the electromagnetic field in the close ELF region are studied at different frequencies, source height and observation point height.
The simulation results show that the main form of ELF HED propagation at the sea-air interface is a side wave. The electromagnetic wave is more influenced by the increase in the height of the seawater centre field source, the height of the observation point and the propagation distance.
What is important in the research being carried out is the fact that the calculated results of the proposed method were compared with the results of the works of Mr. and Margetis, respectively. It was found that the calculated results are consistent, which verifies the correctness of the proposed method.
To sum up, the reviewed work Calculation and analysis of electromagnetic fields of ELF horizontal electric dipoles in the sea-air boundary presents interesting research on the calculation and analysis of electromagnetic fields of ELF horizontal electric dipoles at the sea-air boundary.
The research is carried out correctly, the discussion of the work carried out and their results documented with carefully prepared drawings (6) confirms the validity of the work carried out regarding the calculations and analysis of horizontal electric dipoles.
The references cited in the work (25) are consistent with the research topic and confirm the validity of the undertaken scientific task.
Taking into account the results of the conducted research, I believe that they should find practical application. This fact should be particularly emphasized and discussed in the summary of the task being performed.
According to the reviewer, the work Calculation and analysis of electromagnetic fields of ELF horizontal electric dipoles in the sea-air boundary, after careful justification of the purpose and importance of the research conducted and their practical importance for science/economy, as well as after linguistic correction of the text, is suitable for printing.
Author Response
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Author Response File: Author Response.pdf
Reviewer 5 Report
In this study, the authors proposed a quasi-static approximation for calculating low-frequency EM wave propagation at sea-air interfaces. Overall, the manuscript is well-structured and written, but there are several issues that need to be addressed before published.
1. In Equation (4), are values of n supposed to be only 1,2 instead of 1,2,....?\
2. The conclusion in line 137: "The superiority of the proposed method compared with Pan approximation is demonstrated" is not clear to me: From Figure(2), the error of proposed methods is not significantly less than Pan's results.
Author Response
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Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
The authors have revised their manuscript according to my review in most points. However, before publication they must replace some references with newer ones. References 23-31 are dated from 1954-1981. They are very old! Please, replace references 23-31 with newer ones (of the last 5-8 years).
Englsih language has significantly improved in the revised version.
Author Response
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Reviewer 3 Report
These amendments do not fully respond to the reviewers' previous recommendations. The article needs revisions.
editorial corrections required
Author Response
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Reviewer 4 Report
The work "Calculation and analysis of electromagnetic fields of ELF horizontal electric dipoles in the sea-air boundary" has been corrected in accordance with the comments reviewer is suitable for publication.The work has been corrected in accordance with the comments reviewer is suitable for publication.
Let me explain that, in my opinion, the work "Calculation and analysis of electromagnetic fields of ELF horizontal electric dipoles in the sea-air boundary" after justifying the purpose and importance of the research conducted and their practical significance for science has been carefully explained. The linguistic correction of the text has been corrected.
In summary, research on the calculation and analysis of electromagnetic fields of horizontal ELF electric dipoles at the sea-air boundary should be published.
Author Response
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Author Response File: Author Response.pdf
Round 3
Reviewer 2 Report
The authors revised their manuscript according to my suggestions. In my opinion the manuscript can be published in its current form.
The quality of English in the manuscript has been significantly improved.
