Application of the Fourier Series Expansion Method for the Inversion of Gravity Gradients using Gravity Anomalies

Round 1

Reviewer 1 Report (Previous Reviewer 3)

The authors have addressed my comments well during the revison. I recommend this paper to be published as soon as possible.

Reviewer 2 Report (Previous Reviewer 4)

The present manuscript was already submitted to Remote Sensing and judged worth for publication by this reviewer. The judgement is renewed in this new version.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

The manuscript is devoted to the calculation of gravity gradients by gravitational anomalies. Fourier series expansion is used for these calculations. The paper presents both the theoretical decomposition and the application of this method on satellite images.

There are some shortcomings in the manuscript:

1. The abstract should describe what was done in the work itself, without justification. It is better to remove the first two sentences.

2. There is very little description in section 3.2. If the section itself occupies 1.5 pages, then removing the figures and tables we get only 6 lines of description. A description of the figures and tables should be added.

3. There is subsection 4.1, but there is no subsection 4.2. Can I remove subsection 4.1 altogether?

4. Subsection 4.1 also lacks descriptions of figures and tables.

5. The quality of the drawings is very low. If Figures 1 and 2 can still be cured, then the signatures on them are poorly readable. Figure 3 is better to reduce. Figures 4 and 5 are of very poor resolution. It is impossible to read the captions on these drawings. It needs to be redone.

Reviewer 2 Report

This paper entitled “Application of Fourier Series Expansion for the Determination of Gravity Gradients by Gravity Anomalies” mainly studied the Fourier series expansion of gravity anomalies and gravity gradients. The methodology used in the paper is not new and based on already well-known methods. Therefore, the study lacks innovations. On the other hand, the method described is very simple in many places, and readers obviously can not understand the content based on the current draft. In addition, the figures have very low quality, and the English language should be seriously improved before submission. At last, the paper doesn’t present any analysis of the calculation efficiency.

Reviewer 3 Report

This paper gives a new method for recovering the gravity field from gravity anomalies using the Fourier series transform. The article has important theoretical significance and practical value.

The suggestions are listed below.

(1) The title is too common, inaccurate, and easily ambiguous. Fourier Series Expansion is only a process of Fourier Transform. We cannot use the processes as a method to name the topic. The title needs to be adjusted.

(2) Line 45-48, author summarized the theoretical method of gravity gradient forward modeling into two categories: gravity gradient forward modeling based on regular volume division and gravity gradient forward calculation based on the finite element method. I think this category is inaccurate. Please consult the recent years and revise this part.

(3) The authors conclude in the introduction that the previous gravity gradient orthorectification methods have high computational efficiency mantle and memory consumption, and I think this conclusion is also inaccurate. At present, there are already very many excellent algorithms for orthogonal gravity gradient with outstanding advantages of fast computational efficiency and small memory occupation.

(4) Line 45-64, the authors summarize the problems of previous research results with too few citations and unclear conclusions. Problems with the computational efficiency and effectiveness of previous methods are noted in this paper, and the paper attempts to address them. However, there is no mention of efficiency in the main text of the paper and the effectiveness section is not adequate. The authors are requested to explain and add both the efficiency and effectiveness sections to the text.

(5) Figure3 does not provide much useful information and is not necessary to show at all. Please delete this figure.

(6) In section 4.1, does UCSD also provide gravity gradient data? Unfortunately, I haven't seen any plots about gravity gradient in the text, nor do I see plots comparing the method of this paper with known gravity gradient data. Please add relevant comparison plots as well as error plots for both.

(7) When we use UCSD data for geological interpretation, the order is usually at least 90. but the orders tested in this paper are all less than 40, which is not enough. It does not reflect the real regional gravity anomaly and gravity gradient.

(8) This paper only uses UCSD satellite gravity data for testing, and does not use high-precision ship gravity gradient data to verify the validity and correctness of the method, which reduces the persuasive power of the paper. I suggest that the authors add more high-precision ship gravity gradient data and compare them with the gravity gradient data calculated by this paper, and list the comparison results.

Reviewer 4 Report

General comments

The paper entitled “Application of Fourier Series Expansion for the Determination of Gravity Gradients by Gravity Anomalies” treats about a topic of the highest interest in gravitational gradient modelling scope. By visiting the UCSD website it can be derived that the gravity dataset there contained has been evaluated from CryoSat-2 and Jason-1 satellites; therefore, the topic clearly falls under the journal scope.

The declared objective of the manuscript is to provide explicit analytical equations for the estimation of the gravity gradient field from gravity anomaly data. The experimental areas are located in vast portions of China country. The aim is very interesting considering the many application sectors of these results.

 

1.       What is the main question addressed by the research: The declared objective of the manuscript is to provide explicit analytical equations for the estimation of the gravity gradient field from gravity anomaly data.

2.       Do you consider the topic original or relevant in the field, and if so, why: The aim is very interesting considering the many application sectors of these results.

3.       What does it add to the subject area compared with other published material: In the manuscript, Authors claim the novelty of the proposed methodology.

4.       What specific improvements could the authors consider regarding the methodology: the reduction of complexity of the equations.

5.       Are the conclusions consistent with the evidence and arguments presented and do they address the main question posed: the statistic accuracy assessment is slightly poor and no mention is done about improvements of the computational effort of the new methodology in comparison with earlier ones.

6.       Are the references appropriate: The References are good with recent citations.

7.       Please include any additional comments on the tables and figures: Graphic representations are generally fine and explicative and Tables very readable.

 

Concerning the manuscript, the typographical outline is nearly satisfactory. The used language is fluent apart some passages. Abstract and Introduction introduce the reader into the treated topic very well, clarifying very well the aims of the manuscript. Keywords are pertinent to paper content and appropriate. The highlights are missing. Materials and Methods are good. The References section is rich with recent citations. Graphic representations are generally fine.

Entering in the very merit of the paper is opinion of this reviewer that the manuscript is substantially well written and the experimental part is well conducted. This reviewer deems that the accuracy section is slightly poor and no mention is done concerning computational improvements that are claimed in the Introduction section.

In conclusion, this reviewer recommends considering the paper after “minor revisions”.