Review Reports

Round 1

Reviewer 1 Report

The paper fits well in the scope of this journal as it introduces a new fast iterative method of deriving subsurface densities from gravity data for mineral exploration. Overall, the paper is good and deserves publication after some minor revisions. Here are my comments and recommendations for the authors to take into account while they revise this manuscript:

1. English must be checked carefully – I wish the authors provided me with the word copy of the manuscript, so I can run the first round of English corrections for them. I suggest the authors avoid complex sentences to make the text a bit more reader-friendly. I also suggest utilizing some English-checking software that can help them with grammar (I use a free version of Grammarly, and it does a good job cleaning my non-native English).
2. Please verify that your figures and equations are tied to the main text. For example, in Figure 1 the observation point is denoted as D, while in the text it is P (line 115). Some equations use the notations that are not explained in the text, such as e in Equation 15.
3. Your Figures are great! However, I suggest adding titles to each panel of Figures 2 through 4, such as “Vertical cross-section”, “Horizontal cross-section”. “Conventional iterative migration”, “3D regularized focusing migration”, etc. While this information is provided in the captions, this will help your reader to comprehend figures better. I also suggest adding the planes for vertical and horizontal cross-sections in the figures of your synthetic models, namely in Figures 2a, 3a, and 4a, to help your readers to visualize the locations of your cross-sections. This is just a suggestion, but this will be appreciated by your readers for sure.
4. Please include a statement addressing the obvious discrepancy between the true and recovered density contrasts for your synthetic examples – your recovered densities are half of the true ones! This must be explained.  
5. I suggest replacing the term “residual density” with “density contrast”
6. Figure 7 will benefit from the inset map with the regional figure (Maybe, move the left portion of Figure 9 here?).
7. The last paragraph of the conclusion appears confusing – you have not used magnetic data in your analysis. I encourage you to rephrase that to clarify that the next step of the geophysical analysis intends to analyze magnetic data in addition to gravity, as the ore bodies are known to be highly magnetic.

I include the pdf with my markups and comments. Please let me know if you have any questions.

 

Comments for author File: Comments.pdf

Author Response

Response to Reviewer 1 Comments

 

We would like to thank you for the time and efforts put into reviewing the draft manuscript. Your professional comments and suggestions are very helpful in improving our manuscript. We have carefully considered the valuable comments and thoughtful suggestions, responded to these suggestions in a point-by-point manner, and revised the manuscript accordingly.

 

Point 1: English must be checked carefully – I wish the authors provided me with the word copy of the manuscript, so I can run the first round of English corrections for them. I suggest the authors avoid complex sentences to make the text a bit more reader-friendly. I also suggest utilizing some English-checking software that can help them with grammar (I use a free version of Grammarly, and it does a good job cleaning my non-native English).

 

Response 1: We are really touched by your meticulous modification. Your suggestions will be of great help to our writing in the future. We feel sorry for wasting your time because of English errors in our manuscript. We have studied your marks and comments in the pdf carefully and have made revisions accordingly. All changes have been highlighted using the Track Changes function in the word document called “Revised Version”. We also replied to all of your comments in the pdf document (please see the attachment).

 

Point 2: Please verify that your figures and equations are tied to the main text. For example, in Figure 1 the observation point is denoted as D, while in the text it is P (line 115). Some equations use the notations that are not explained in the text, such as e in Equation 15.

 

Response 2: Thank you very much for your careful check. We changed P to D (page 4, line 122), and checked the manuscript to make sure there were no similar errors. We explained the value of e in Equation (15) (page 5, line 161).  We reedited the notations in Equations (7-9) and added the interpretation of the meaning of each notation (page 4, lines 137-142).

 

Point 3: Your Figures are great! However, I suggest adding titles to each panel of Figures 2 through 4, such as “Vertical cross-section”, “Horizontal cross-section”. “Conventional iterative migration”, “3D regularized focusing migration”, etc. While this information is provided in the captions, this will help your reader to comprehend figures better. I also suggest adding the planes for vertical and horizontal cross-sections in the figures of your synthetic models, namely in Figures 2a, 3a, and 4a, to help your readers to visualize the locations of your cross-sections. This is just a suggestion, but this will be appreciated by your readers for sure.

 

Response 3: Your suggestion is quite reasonable. We have added titles to each panel of Figures 2 through 4, and added the planes for vertical and horizontal cross-sections of the synthetic models (page 7, line 204; page 8, line 218; page 11 line 258). We are not sure whether these titles could convey the exact meaning. If this change is not to your requirements, or you have any other suggestions, please let us know and we will make further revisions as soon as possible.

 

Point 4: Please include a statement addressing the obvious discrepancy between the true and recovered density contrasts for your synthetic examples – your recovered densities are half of the true ones! This must be explained. 

 

Response 4: Thank you for this valuable feedback. Gravity anomaly is the comprehensive response of subsurface density distribution. Observations are two-dimensional, while the subsurface model is three-dimensional. Extrapolating subsurface structures from finite observation data is mathematically a matter of finding a solution to an underdetermined equation. As stated in lines 33-38 of the manuscript: “However, from the perspective of classical theory, all geophysical inversions including gravity inversion are ill-posed for their solutions are either non-unique or unstable. Nevertheless, geophysicists can solve this problem to some extent by adopting different types of regularization algorithms”. The proposed method can reduce non-uniqueness, but cannot eliminate it completely. Therefore, recovered densities are not equal to the true ones. This is explained mathematically in reference [1] (page 1, line 36), so we did not expand on this issue. We are not sure if it is clear. If we misunderstand your meaning, please feel free to contact us, and we will make further modification as soon as possible.

 

Point 5: I suggest replacing the term “residual density” with “density contrast”.

 

Response 5: Sorry for our unidiomatic expressions. We replaced the term “residual density” with “density contrast” (page 6, line 200; page 9, line 237)

 

Point 6: Figure 7 will benefit from the inset map with the regional figure (Maybe, move the left portion of Figure 9 here?).

 

Response 6: We moved the left portion of Figure 9 to the left of Figure 7 (page 14, line 336).

 

Point 7: The last paragraph of the conclusion appears confusing – you have not used magnetic data in your analysis. I encourage you to rephrase that to clarify that the next step of the geophysical analysis intends to analyze magnetic data in addition to gravity, as the ore bodies are known to be highly magnetic.

 

Response 7: We are very sorry for the misrepresentation in the last paragraph. We rephrased the last paragraph (page 21, lines 463-465).

Author Response File: Author Response.pdf

Reviewer 2 Report

Good Work!

A few suggestions:

1. page 1, line 39~40, 'inversion inversion' -> 'inversion'
2. page 10, line 266, 'Blue solid line' -> 'Blue dash line'
3. page 10, line 268, 'took 224 s', The computer type and the configuration need be mentioned to make sense to compare.
4. For using a focusing, the e value (in the equation 15) is important, what is the value in the Synthetic Examples, and in the Yucheng data migration?
5. What is the convergence curve looks like in the Yucheng data migration?

Author Response

Response to Reviewer 2 Comments

 

We would like to thank you for the time and efforts put into reviewing the draft manuscript. Your professional comments and suggestions are very helpful in improving our manuscript. We have carefully considered the valuable comments and thoughtful suggestions, responded to these suggestions in a point-by-point manner, and revised the manuscript accordingly.

 

Point 1: page 1, line 39~40, 'inversion inversion' -> 'inversion'

 

Response 1: We are really sorry for these silly mistakes. We deleted the repeated 'inversion' (page 1, line 39).

 

Point 2: page 10, line 266, 'Blue solid line' -> 'Blue dash line'

 

Response 2: We changed 'blue solid line' to 'blue line' and 'red solid line' to 'red line' (page 13, lines 295-296).

 

Point 3: page 10, line 268, 'took 224 s', The computer type and the configuration need be mentioned to make sense to compare.

 

Response 3: We are very sorry that we did not provide this important information. We supplemented the computer type and the configuration. ‘All tests were run on an Intel Xeon E5-2650 with 2.2Ghz, 64GB of main memory’ (page 11, line 266-267).

 

Point 4: For using a focusing, the e value (in the equation 15) is important, what is the value in the Synthetic Examples, and in the Yucheng data migration?

 

Response 4: The e value is selected as 0.08 by trial and error. We added ‘where e is selected as 0.08 by trail and error’ on page 5, line 161.

 

Point 5: What is the convergence curve looks like in the Yucheng data migration?

 

Response 5: This is a very valuable suggestion. We added convergence curve map, as shown in Figure (11) (page 18, lines 409-410).

Reviewer 3 Report

Dear authors.
This is a very good manuscript, very well written and all figures express in a good way your achievements. U fully support its publication after a minor review - few comments I have listed here:
- In the Introduction part, it would be good to mention also a very   interesting contribution from Liu et al. (2020), which I give here   in the end of this review.
- In page 2, line 69 you cite the paper from  Portniaguine and Zhdanov [24],   but in your references list is under the number [24] given the paper   Zhdanov et al. (2004). Please, check this.
- In page 3, line 115, there is named the observation point with letter P,   but in both parts of Fig. 1 is used the letter D. Please, unify this.
- In page 4, equation (9), there is a matrix A (with subscript "alpha" and   superscript "omega", but its meaning is explained later in equation (12).   It would be good to mention it immediately below Eq. (9).
- In page 6, line 198 you write about a "dike complex and a rectangle".   Dike is a 3D body and it is OK. But rectangle is just a projection of a real   3D body. So, in my opinion, it should be used the word "prism" instead   of "rectangle".
- In page 9, in Figure 5 you bring results also for a third method, which you   call generally as "Regularized inversion method". This is too general,   in the main text you should exactly describe (also with appropriate
  reference) which is this third method.
- In page 13, in the caption to figure 9 is would be good to give the precise   source of the used aerial photo. I wish good luck in your scientific activities. Reference (mentioned in this review):
Liu, S.; Baniamerian, J.; Fedi, M. Imaging Methods Versus Inverse Methods:     An Option or An Alternative? IEEE Transactions on Geoscience and remote     sensing 2020, 58, 5, 3484-3494.

Author Response

Response to Reviewer 3 Comments

 

We would like to thank you for the time and efforts put into reviewing the draft manuscript. Your professional comments and suggestions are very helpful in improving our manuscript. We have carefully considered the valuable comments and thoughtful suggestions, responded to these suggestions in a point-by-point manner, and revised the manuscript accordingly.

 

Point 1: In the Introduction part, it would be good to mention also a very interesting contribution from Liu et al. (2020), which I give here in the end of this review.

 

Response 1: We are very sorry that we missed this important article in our previous research. It points out the high efficiency and high resolution of the imaging method. We added this reference to give readers a better understanding of the imaging method (page 2, line 51).

 

Point 2: In page 2, line 69 you cite the paper from Portniaguine and Zhdanov [24], but in your references list is under the number [24] given the paper Zhdanov et al. (2004). Please, check this.

 

Response 2: Thank you so much for your careful check and we apologize for our carelessness. We moved this reference to page 5, line 160.

 

Point 3: In page 3, line 115, there is named the observation point with letter P, but in both parts of Fig. 1 is used the letter D. Please, unify this.

 

Response 3: We changed P to D in page 4, line 122, and checked the manuscript to make sure there were no similar errors.

 

Point 4: In page 4, equation (9), there is a matrix A (with subscript "alpha" and   superscript "omega", but its meaning is explained later in equation (12).   It would be good to mention it immediately below Eq. (9).

 

Response 4: Thank you for underlining the irrationality. We reedited the notations in Equations (7-9) and added the interpretation of the meaning of each notation (page 4, lines 137-142).

 

Point 5: In page 6, line 198 you write about a "dike complex and a rectangle".   Dike is a 3D body and it is OK. But rectangle is just a projection of a real   3D body. So, in my opinion, it should be used the word "prism" instead   of "rectangle".

 

Response 5: Sorry for our unidiomatic expressions. We replaced the word ‘rectangle’ with ‘prism’ (page 7, line 216).

 

Point 6: In page 9, in Figure 5 you bring results also for a third method, which you call generally as "Regularized inversion method". This is too general, in the main text you should exactly describe (also with appropriate reference) which is this third method.

 

Response 6: Thank you for this valuable feedback. We are sorry that we didn't make it clear. The third method is the regularized focusing inversion method based on conjugate gradient. The method is described in detail in Chapter 7 of Geophysical Inverse Theory and Regularization Problems, so we added this reference in page 12, line 269.

 

Point 7: In page 13, in the caption to figure 9 is would be good to give the precise source of the used aerial photo.

 

Response 7: We gave the precise source of this photo. ‘The aerial photo is culled from Google Maps’ (page 16, line 372).

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

Page	Line	Comment
1	11	, we propose “a”
1	15	…which effectively “improves” (you are mixing tense)
1	19	…method developed is applied to interpret gravity survey data collected in a skarn type…
1	28	…is an important method in…
1	40	Capitalise “on”
2	52-53	For gravity and its gradient field, migration imaging
2	60	…adopted as the final result.
2	61	Accuracy implies you know the answer.  Also the sentence should read “imaging accuracy is improved to a certain extent”.  “Improved to a certain” is incorrect english
2	72	...problem of minimizing…
2	80	…we propose is efficient and stable, and can provide…
2	90	We discuss the …area, interpret the geophysical… (current sentence is mixing past and present tense)