Self-Organization Characteristics of Lunar Regolith Inferred by Yutu-2 Lunar Penetrating Radar

Round 1

Reviewer 1 Report

I have appreciated the effort of the authors to reply to my challenging questions and now the manuscript has been improved.

Unfortunately, several significant issues remain, few of them related to the questions of the above review stages.

First of all, again no satisfyingly geological justification at the basis of the choice of the models is reported.

Several definitions are missing to fully assess the validity of the results, see correlation coefficient and RMS perturbation.

It is necessary to add the colorbar to all the figures.

 The main new result of the present version is the Table1. By observing this table, it seems that the result is not dependent on the correlation length and the RMS perturbation. This would mean that the results are largely dominated by the reflection of the rocks and pose significant issues about the models used for the regolith. It is necessary to address very carefully this issue.

Finally, I request to add the reference C. LI et al. The Moon’s farside shallow subsurface structure unveiled by Chang’E-4 Lunar Penetrating Radar published on Science Advances, DOI 10.1126/sciadv.aay6898

Author Response

1. First of all, again no satisfyingly geological justification at the basis of the choice of the models is reported.

##### Response:

Thank you for your challenging questions, which greatly improve the quality of the manuscript.

As shown in the first paragraph in Introduction, we mentioned that

“The structure of lunar shallow surface is complex due to long-term impact, sputtering and stacking process. The remote-sensing spectrum and radar detection results show that there is a ~12m-thick regolith layer on the top of Von Kármán crater, which provides an excellent opportunity for us to detect the structural characteristics and stacking mode of lunar regolith, which are critical for understanding the formation process of the lunar regolith. However, in the past, the lunar regolith is usually assumed to be a uniform layered medium. A series of recent studies have shown that the lunar regolith is essentially inhomogeneous but the specific structural characteristics of the lunar regolith are still unclear.”

We think this could be a geological justification, even although not satisfying at this stage.

2. Several definitions are missing to fully assess the validity of the results, see correlation coefficient and RMS perturbation.

##### Response:

Correlation distance and RMS perturbation are two key parameters to describe the self-organization random media. We have to concentrate on these two parameters after a careful selection on controlling parameters to avoid unaffordable computational cost in high dimensions, as described in Discussion. In addition, these two parameters have relatively clear physical meaning: the correlation distance could well constrain the variation range of regolith permittivity and the RMS perturbation can well present the extent of regolith permittivity variation. Of course, more factors should be considered and discovered in future works.

3. It is necessary to add the colorbar to all the figures.

##### Response:

Thank you for your helpful comments. We added color bar to each figure.

4. The main new result of the present version is the Table1. By observing this table, it seems that the result is not dependent on the correlation length and the RMS perturbation. This would mean that the results are largely dominated by the reflection of the rocks and pose significant issues about the models used for the regolith. It is necessary to address very carefully this issue.

##### Response:

Table 1 shows 9 cases of the two parameters (i.e., correlation distance and the RMS perturbation). Obviously, the peak correlation coefficients between Yutu-2 radar data and synthetic data appear at 3% RMS perturbation and 5-10 cm correlation distance. Similarly, we can draw the same conclusion from the square errors between Yutu-2 radar data and synthetic data, as shown in Table 2. This indicates that the correlation distance and the RMS perturbation can well reflect the basic property of the lunar regolith. Additionally, the RMS perturbation in our experiments can be well constrained, since it has a relatively deterministic value of 3%; meanwhile, the correlation distance has a relatively large range around 5-10 cm. Nevertheless, to the best of our knowledge, the correlation distance is still well constrained for the first time.

5. Finally, I request to add the reference C. LI et al. The Moon’s farside shallow subsurface structure unveiled by Chang’E-4 Lunar Penetrating Radar published on Science Advances, DOI 10.1126/sciadv.aay6898

##### Response:

This reference has been added during the revision.

Reviewer 2 Report

Dear Editors and Authors,

GENERAL COMMENTS

It is a great satisfaction for me to collaborate in the process of revising this manuscript.

The theme of the manuscript is relevant since it uses self-organization to study the heterogeneities of the lunar regolith. I understand that the manuscript is already in a mature research phase, having implemented highlighted adjustments in the text.

A few specific comments and notes will be dealt with in the following topic.

SPECIFIC COMMENTS

Figures 4, 5, 6, 7, 8, 9, and 10: I think it is more appropriate to replicate the color bars in all figures. It is not practical to go back to an earlier figure to understand the meaning of colors.

Pages 10 and 11 - Figures 11 and 12: Insert the amplitude unit in the figures.

Page 11 - Figure 12: I suggest discussing the greatest variations between the value of Yutu-2 and the three different correlation distances (20, 10, and 5 cm) in the range of amplitude between 0.5 and 1 and time 0.15 and 0.2. I understand that it is in this specific area (the lower part of the image) that the biggest differences between the radar data and the simulated data are concentrated. I understand that the manuscript could briefly discuss, in one paragraph, why these major differences are made.

I hope that my comments can contribute to the improvement of the manuscript.

Sincerely,

Reviewer

Author Response

1. Figures 4, 5, 6, 7, 8, 9, and 10: I think it is more appropriate to replicate the color bars in all figures. It is not practical to go back to an earlier figure to understand the meaning of colors.

##### Response:

Thank you for your helpful suggestions. We added color bar to each figure.

2. Pages 10 and 11 - Figures 11 and 12: Insert the amplitude unit in the figures.

##### Response:

We did not add unit because the amplitude was normalized. We mentioned in the figure caption that “The amplitude is normalized for each stacked envelope.”

3. Page 11 - Figure 12: I suggest discussing the greatest variations between the value of Yutu-2 and the three different correlation distances (20, 10, and 5 cm) in the range of amplitude between 0.5 and 1 and time 0.15 and 0.2. I understand that it is in this specific area (the lower part of the image) that the biggest differences between the radar data and the simulated data are concentrated. I understand that the manuscript could briefly discuss, in one paragraph, why these major differences are made.

##### Response:

Thank you for your valuable advices. We added a new paragraph to enhance the discussions.

Reviewer 3 Report

The article is very clear and understandable, well illustrated, and may be published. The limitations of the used modeling method are indicated and discussed. I did not notice any fundamental mistakes in it, there are only the following technical notes and questions.
1. The quantity \xi in formula (1) is not defined.
2. Figures 2abc, 5abc - what is the peak at depth ~13 m? This depth does not correspond to the position of the boundary between the regolith and the ejecta layer.
3. In Figures 2def at depth > 12 m, points with \eps ~ 5 are observed. There are no such values ​​on the curves in Figures 2abc. Are these fluctuations? If not, what is their origin?
4. There are no color bars in figures 4def, 5def and later. It is very uncomfortable. I recommend that the authors put them on all drawings.

Author Response

1. The quantity \xi in formula (1) is not defined.

##### Response:

Thank you for your helpful comments. We've added the definition of \xi.

2. Figures 2abc, 5abc - what is the peak at depth ~13 m? This depth does not correspond to the position of the boundary between the regolith and the ejecta layer.

##### Response:

The peak at depth ~13m is a rocky block, whose relative dielectric permittivity is of 5. The spatial density of rocks is very low (as mentioned in the late experiments); thus, we can only have one block in one trace that are at the center of Figures 2 or 5.

3. In Figures 2def at depth > 12 m, points with \eps ~ 5 are observed. There are no such values on the curves in Figures 2abc. Are these fluctuations? If not, what is their origin?

##### Response:

We added some small rocky blocks with a relative dielectric permittivity of 5 below the 12m in Figure 2def. They are not fluctuations. Because the section in Figure 2abc passes through only one rock, we can only see a peak. We added some more explanation in the corresponding captions.

4. There are no color bars in figures 4def, 5def and later. It is very uncomfortable. I recommend that the authors put them on all drawings.

##### Response:

Thank you for your helpful comments. We added color bar to each figure.

Reviewer 4 Report

some suggested modifications:

pag. 1. Introduction , 3rd line, change from "....strong cementation due to lacking of liquid water." to " strong cementation due to absence of interstitial water."  Because it is not necessary that the water be liquid to induce cementation or particle bonding.

pag 2 , 11th line, the sentence " ......accumulation under weak dynamic mechanism. " needs a some explanation/ justification text.

pag. 8, 7th line,  modify the sentence " For the convenience of readers to catch the main idea of this work, .......". You could say, as an example, " for the sake of simplicity ....." but this is a scientific paper that possibly goes to other scientists that should be able to understand also complex explanations and I do not think that the word " convenience2 in this context is adequate.

Author Response

1. pag. 1. Introduction , 3rd line, change from "....strong cementation due to lacking of liquid water." to " strong cementation due to absence of interstitial water."  Because it is not necessary that the water be liquid to induce cementation or particle bonding.

##### Response:

Thank you for your helpful comments. We have modified it accordingly.

2. pag 2 , 11th line, the sentence " ......accumulation under weak dynamic mechanism. " needs a some explanation/ justification text.

##### Response:

Thank you for your helpful comments. We rewrote this part.

3. pag. 8, 7th line,  modify the sentence " For the convenience of readers to catch the main idea of this work, .......". You could say, as an example, " for the sake of simplicity ....." but this is a scientific paper that possibly goes to other scientists that should be able to understand also complex explanations and I do not think that the word " convenience2 in this context is adequate.

##### Response:

Thank you for your helpful comments. We have modified it accordingly.

Round 2

Reviewer 1 Report

The manuscript has been improved with respect to the version originally submitted. I only request the authors to state that the proposed model is one among the possible and is not fully justified by the point of view of the geology.

Author Response

I only request the authors to state that the proposed model is one among the possible and is not fully justified by the point of view of the geology.

##### Response:

Thank you for your helpful comments. We added a new paragraph on request.

Round 3

Reviewer 1 Report

Ok for the publication.