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Improvement of Lunar Surface Dating Accuracy Utilizing Crater Degradation Model: A Case Study of the Chang’e-5 Sampling Area

Remote Sens. 2023, 15(9), 2463; https://doi.org/10.3390/rs15092463

by Feiyue Zhao^1,2

, Wei Zuo^1,2,*

and Chunlai Li^1,2

Reviewer 1:

Aisha Alderremy

Reviewer 2:

Ekaterina Feoktistova

Reviewer 3:

Zongyu Yue

Remote Sens. 2023, 15(9), 2463; https://doi.org/10.3390/rs15092463

Submission received: 2 April 2023 / Revised: 29 April 2023 / Accepted: 5 May 2023 / Published: 8 May 2023

(This article belongs to the Special Issue Future of Lunar Exploration)

Round 1

Reviewer 1 Report

What is the main contribution of this paper to the field of lunar research?

How does the proposed three-part crater degradation model improve the accuracy of the CSFD dating method for lunar surface geological units?

Can you provide more detail on the method proposed to simulate the degradation process of the craters and how it helps determine the crater degradation experience and screen out the craters suitable for CSFD analysis?

How was the accuracy of the proposed method evaluated, and what were the results of this evaluation?

What are the limitations of the proposed method, and how might they impact its use in future lunar exploration missions or the development of lunar resource utilization strategies?

Could the proposed method be applied to other geological units on the Moon, or is it specific to the CE-5 sampling area?

How does the paper's proposed method advance our understanding of the evolutional history of the geological units of the study area?

Are there any potential ethical considerations associated with the use of the proposed method in future lunar exploration missions or resource utilization strategies? If so, how might these be addressed?

The following papers are selected from various scientific disciplines and provide a glimpse into the breadth of research being conducted in diverse fields. The first paper, a review article by Zhang et al. (2022), discusses radionuclide transport in multi-scale fractured rocks, which has significant implications for nuclear waste disposal. The second paper by Zhang et al. (2022) focuses on plutonium reactive transport in fractured granite, and presents experimental and simulation results. Liu et al. (2022) explore the use of full polarimetric radar to discriminate between dry and water ices for China's first Martian exploration. Li et al. (2023) investigate the effects of carbonate minerals and exogenous acids on carbon flux from the chemical weathering of granite and basalt. Xu et al. (2022) propose a forecasting model for urban land use change based on cellular automata and the PLUS model, while Qin et al. (2022) present a user OCEAN personality model construction method using a BP neural network. Together, these papers demonstrate the diversity and depth of scientific inquiry in various fields. doi: 10.1016/j.jhazmat.2021.127550; doi: https://doi.org/10.1016/j.watres.2022.119068

doi: 10.1109/TGRS.2022.3228684; https://doi.org/10.1016/j.gloplacha.2023.104053; doi: 10.3390/land11050652; https://doi.org/10.3390/electronics11193022

"constructed a three-part" should be "constructed a three-parted"

"that can improve the CSFD dating accuracy was also proposed" should be "that can improve the accuracy of CSFD dating was also proposed"

"to help determine the crater degradation experience" should be "to help determine the crater degradation process"

"The determined age for CE-5 sampling area is 2.0 ± 0.2 Ga" should be "The age determined for the CE-5 sampling area is 2.0 ± 0.2 Ga"

"fully demonstrated" should be "fully demonstrates"

"describing and distinguishing the degradation state of crater over time due to the cumulative effects of small craters" should be "describing and distinguishing the degradation state of craters over time due to the cumulative effects of small craters"

"naturally degraded (which conform to the degradation model)" should be "naturally degraded (which conforms to the degradation model)"

"advances our understanding of the evolutional history" should be "advances our understanding of the evolutionary history"

"for the in-depth study of the formation and evolution of the Moon" should be "for the in-depth study of the formation and evolution of the moon"

"especially for the lunar chronology" should be "especially for lunar chronology"

Author Response

Dear Reviewer,

On behalf of my coauthors, we appreciate your insightful comments and suggestions for our manuscript entitled “Improvement of Lunar Surface Dating Accuracy Utilizing Crater Degradation Model: A Case Study of Chang'E-5 Sampling Area” (No.: remotesensing-2352384). According to the last round comments and suggestions, all the corrections have been addressed. We have made careful revisions and all changes are marked in red. We hope that the revised manuscript is now acceptable for publication.

Once again, we are grateful for the reviewer’s constructive comments and suggestions, which are very valuable for improving our manuscript. 

Below are our point-by-point responses to the reviewer’s comments. Our response is in red.

Reviewer's comments and suggestions:

Reviewer #1:

What is the main contribution of this paper to the field of lunar research?

This is a very good question. The crater degradation model used in this paper can model the experience of crater degradation to judge the evolution of craters and provide reference information for the study of the evolution of geological units on the lunar surface. At the same time, the proposed method can efficiently select craters to improve the accuracy of the CSFD method and provide methodological support to accurately determine the geologic age of the lunar surface in unsampled regions of the moon, which can then be used to obtain more accurate geologic evolution of the moon.

Corresponding contents have been modified and presented in the section 5

New lines: 474-478.

How does the proposed three-part crater degradation model improve the accuracy of the CSFD dating method for lunar surface geological units?

The crater degradation state can be modeled by the proposed three-part crater degradation model. By comparing the crater degradation state simulated by the crater degradation model with the existing degradation state, we can distinguish the diffusively degraded craters and non-diffusively degraded craters, achieve the selection of craters, and filter out the craters with the same degradation experience, thus obtaining more "exact" crater data, improving the accuracy of crater extraction in the CSFD method, and thus improving the accuracy of the CSFD method in determining the age of geological units on the lunar surface.

The diffusion degradation process of the crater can be obtained by solving the diffusion equation (1) by setting the initial boundary conditions and the final boundary conditions. The initial boundary condition is the initial state of the crater (for a crater of arbitrary diameter, Eqs. (2) and (3)can simulate the initial profile model of the crater, as shown in (Fig. 4a)), and the final boundary condition is the crater degradation to unrecognizable (the elevation of all points on the crater profile is 0), and using these two boundary conditions to solve Eq. (1), the crater degradation from the initial crater rim height H₀ to the crater rim height H_D after t years of degradation (Fig. 4b), thus obtaining the change of the diffusion degradation state of the crater with time.

The crater degradation model simulates the diffusion degradation process of craters. In this paper, the model is used to distinguish two types of craters in the CE-5 landing area that conform to the crater degradation model (diffusively degraded craters) and those that do not conform to the crater degradation model (non-diffusively degraded craters). The age of the CE-5 landing area is determined by selecting craters on homogeneous units for dating based on the CSFD method.

Corresponding contents have been modified and presented in the section 2.3.1

New lines: 230-239.

How was the accuracy of the proposed method evaluated, and what were the results of this evaluation?

The accuracy of the method is assessed by comparing the age of the CE-5 landing area counted by the method of this paper with radiometric age of the CE-5 sample. The age of the CE-5 landing area obtained by the CSFD method for the crater screened in this paper is 2.0 ± 0.2 Ga, which is close to radiometric age of the sample returned from the CE-5 mission (2.03 ± 0.004 Ga), and therefore the method proposed in this paper is considered to be effective in improving the accuracy of the CSFD method.

What are the limitations of the proposed method, and how might they impact its use in future lunar exploration missions or the development of lunar resource utilization strategies?

The initial model of this approach was constructed in an idealized model, and the morphology of the craters was simplified. Future lunar resource utilization strategies are aimed at the whole moon and will face different types of craters. A single initial model of the crater will affect the accuracy of the crater dating results and the evolutionary history of the regional geological units inferred from the crater degradation process. Future work will establish corresponding initial models of craters based on different types of lunar surface features to ensure that crater dating results and the evolution of regional lunar geological units can provide reliable information for future lunar exploration missions and lunar resource utilization strategies.

Could the proposed method be applied to other geological units on the Moon, or is it specific to the CE-5 sampling area?

The idea of screening craters with the same evolutionary experience according to their degradation process for the CSFD method to determine the age of stratigraphic units is applicable to additional stratigraphic units on the moon. However, these experiments have only been conducted in the CE-5 landing area, and future work is planned to select different landing areas on the moon to validate the method proposed in this paper.

How does the paper's proposed method advance our understanding of the evolutional history of the geological units of the study area?

The method in this paper simulates and determines the evolutionary experience of craters through the crater degradation model, which can then be used to determine the geological evolution of the geologic unit where the craters are located, and provides a detailed understanding of the evolutionary history of geological units in the lunar surface area. In addition, this method uses the degradation model to screen out craters that conform to the degradation model and those that do not, so as to improve the accuracy of the crater dating method, obtain accurate ages of the geological units in the study area, determine the exact period of volcanic activity in the study area, and facilitate the understanding of the regional geological history of the lunar surface.

Corresponding contents have been modified and presented in the section 5

New lines: 474-478.

The methods used in this paper do not have any potential ethical risks to consider in future lunar exploration missions or resource utilization strategies.

Thank you for recommending excellent paper. Our paper only focuses on the realization and improvement of technical methods and does not use the proposed methods to explore deep scientific problems. In the future work, we will refer to these papers, explore the ideas of scientific problems, learn the research methods of these documents, and carry out research from multiple angles and in an all-round way.

Comments on the Quality of English Language:

We are truly sorry for our wrong writing. All the following corrections we have made in the corresponding place in the text. Thank you for your corrections.

"constructed a three-part" should be "constructed a three-parted"

Corresponding contents have been modified, new line:12

"that can improve the CSFD dating accuracy was also proposed" should be "that can improve the accuracy of CSFD dating was also proposed"

Corresponding contents have been modified, new line:15.

"to help determine the crater degradation experience" should be "to help determine the crater degradation process"

Corresponding contents have been modified, new line:18.

"The determined age for CE-5 sampling area is 2.0 ± 0.2 Ga" should be "The age determined for the CE-5 sampling area is 2.0 ± 0.2 Ga"

Corresponding contents have been modified, new line:18-19.

"fully demonstrated" should be "fully demonstrates"

Corresponding contents have been modified, new lines:22-23.

Corresponding contents have been modified, new lines:23-25.

"naturally degraded (which conform to the degradation model)" should be "naturally degraded (which conforms to the degradation model)"

Corresponding contents have been modified, new line:26-27.

"advances our understanding of the evolutional history" should be "advances our understanding of the evolutionary history"

Corresponding contents have been modified, new lines:30-31.

"for the in-depth study of the formation and evolution of the Moon" should be "for the in-depth study of the formation and evolution of the moon"

Corresponding contents have been modified, new lines:31-32.

"especially for the lunar chronology" should be "especially for lunar chronology"

Corresponding contents have been modified, new line:32.

Author Response File: Author Response.docx

Reviewer 2 Report

In equations 2) and 3) the authors use a single dependence for the height of crater rim on the diameter. However? this parameter depends on the characteristics of the impactor, such as dencity, velocity and angle of incidence, and target.

Line 340: The title of the section contains the wors @Dating result analysis@ twice.

pp 14-15:

Figure 12 caption is on page 15, Figure 12 is on page 14.

Author Response

Dear Reviewer,

Once again, we are grateful for your constructive comments and suggestions, which are very valuable for improving our manuscript. 

Below are our point-by-point responses to the reviewer’s comments.

Reviewer's comments and suggestions:

Reviewer #2:

That's a very good question. The diameter and size of craters at the moment of formation depend on the characteristics of the impactor (density, velocity, and incidence angle) and the characteristics of the target surface. After formation, most fresh, primitive, and simple craters have a consistent shape profile (pike 1977). Based on this research conclusion, Fassett et al.(2014) used the diffusion equation to build a degradation model to simulate the change laws of the characteristic state of crater. Xie et al.(2017) and Du et al.(2019) respectively, modified the initial profile equation of impact crater established by Fassett .,(2014). In this paper, formula (2) and formula (3) directly refer to the initial impact crater profile equations established by Xie et al.(2017) and Du et al.(2019), which are used to describe the initial morphology of impact craters with D < 1km and D≥1km, respectively.

Corresponding contents have been modified and presented in the section 1

New lines:61-64.

Line 340: The title of the section contains the wors @Dating result analysis@ twice.

We are sorry for our carelessness. Thanks for the reviewer's careful correction.

Corresponding contents have been modified and presented in the section 4.1

New lines:372.

pp 14-15:

Figure 12 caption is on page 15, Figure 12 is on page 14.

Thanks for the reviewer's careful correction.

The question has been modified on page 16 of the text.

Author Response File: Author Response.docx

Reviewer 3 Report

Comments for author File: Comments.pdf

see the attachment.

Author Response

Dear Reviewer,

Once again, we are grateful for your constructive comments and suggestions, which are very valuable for improving our manuscript. 

Below are our point-by-point responses to the reviewer’s comments.

Reviewer's comments and suggestions:

Reviewer #3:

Major revisions:

The authors should explain why the diffusion equation can model the “natural” degraded craters’ morphology, and why the diffusion equation can’t describe the “unnatural” degraded craters’ morphology. What is the morphologic difference between the two classes of craters? Are there craters that suffered from the “unnatural” degradation process yet their morphologies satisfy the “natural” degradation process (i.e., Figure 9)? This is the key point that should be explained.

It's a good question, our step-by-step answers are as follows:

Using diffusion equation to study the degradation of crater model is an accumulated result of different researchers' work. Culling (1960) established diffusion equations to model the elevation of typical landforms on the lunar surface as a function of time, and Soderblom (1970) considered that diffusion equations can be used to model the diffusion of craters caused by the cumulative effect of small craters generated by micrometeoroids. Fassett et al.(2014) studied the craters with diameters ranging from 0.8-5km in the lunar mare, which covers 30% of the lunar surface, and verified that the diffusion equation represents the degradation process of craters caused by the impact of micrometeoroids. This process is referred to as diffusively degradation in the paper. In addition to the diffusive process caused by the impact of small craters, there are also non-diffusively processes such as lava flow coverage and ejecta blanket coverage that cause the reduction of crater rim height in the non-diffusively degraded craters mentioned in the paper, so the diffusion equation cannot be used to model the degradation process of non-diffusively degraded craters.

（2）Whether diffusively degraded craters and non-diffusively degraded craters differ in morphology needs to be categorized and discussed. (a) diffusively degraded craters and non-diffusively degraded craters differ in morphology: for small-diameter craters (D < 1 km), the relationship between the diameter D₀ and the initial height h₀ of the crater rim is h₀ = 0.024D₀^1.058 (Stopar et al., 2017). Small-diameter crater rim heights are smaller and subject to non-diffusively effects, the rim height varies significantly, and there is a clear difference in the morphology of diffusively degraded craters and non-diffusively degraded craters. (b) There is no difference in the morphology of diffusive degraded craters and non-diffusive degraded craters: for some large impact craters (D > 1 km), the crater rim can be clearly identified on the image, and the height of the rim is large, the rate of change of the rim is smaller than that of small craters when subjected to non-diffusively effects (Fassett et al., 2014). For example, in some partially buried craters, the crater rims remain visible after experiencing lava flow coverage (du et al., 2019). Compared to craters that have not undergone non-diffusively degradation, there is no significant difference in crater morphology between partially buried craters that have undergone diffusively degradation and non-diffusively degradation, so a crater degradation model needs to be used to distinguish whether craters have undergone non-diffusively degradation.

（3）The question of whether there are craters that suffered a non-diffusively degradation process but whose morphology satisfies the diffusively degradation process can be understood as craters that underwent non-diffusively degradation but are not morphologically identifiable as having undergone a non-diffusively degradation process. This situation can be explained by the partially buried crater mentioned in (2). For example, for a crater with D = 10 km, the initial crater rim height is calculated to be about 363.08 m using the initial crater profile model. After this crater has experienced volcanic activity, the crater rim is covered by lava flow (assuming a lava flow thickness of about 50 m), and a clear crater rim can still be recognized from the image, but the reduced height of the crater rim cannot be seen from the image. This is an example of an crater that has suffered a non-diffusively process but is not morphologically identifiable as having undergone a non-diffusively process.

Minor suggestions:

Line 15: it: which

Corresponding contents have been modified, new lines:16.

Line 18: remove “geological”

Corresponding contents have been modified, new line:19.

Line 25 and 26: I suggest to use another word instead of “naturally” and “non-naturally”

This is a very good suggestion. After careful consideration, we decided to replace natural and unnatural degradation with diffusively degradation and non-diffusively degradation. And the corresponding place in the full text is replaced.

Line 27~29: “This not only provides an effective solution to the problem of obtaining more "exact" frequency distribution of craters, which has long plagued the practical application of the CSFD method in dating lunar surface …” The CSFD is

Corresponding contents have been modified, new lines:28-30.

Line 36~39: They can be preserved for long period because of the absence of atmosphere and water on the lunar surface and weak geologic activities; however, they could be degraded by coverage from later impact ejecta or terrain relaxation over time.

Corresponding contents have been modified, new lines:36-39.

Line 43~44: the sentence is incomplete

Corresponding contents have been modified and presented in the section 1.

New lines:41-44.

Line 64: varies: is different

Corresponding contents have been modified, new line:69.

Line 86~88: the age difference is also caused the different counting areas, different images, and even different counting crater methods.

We have considered the influence of different counting areas, different images, and different crater counting methods on the dating results, but these factors are unavoidable in practice, so in this paper we focus on the problem of ignoring the complex geological effects experienced in the study area when counting craters.

Corresponding contents have been modified and presented in the section 1.

New lines:93-96.

Line 90: what do the authors want to say by “recreated by new impacts”? Do you want to say that the geologic units that include new craters always include the old craters?

It’s very sorry that we didn't articulate the idea of solving the problem clearly.

What we're trying to say is: For craters in the same degradation state, a larger crater will appear substantially fresher than its smaller counterparts, and some of the large craters on older geologic unit are preserved because the morphological change rate is smaller than that of smaller craters (Fassett et al., 2014). This results in the coexistence of old craters on old geologic unit and young craters on young geologic unit, thus making the crater statistics include craters formed on different geologic unit with different evolutionary experiences. This makes it difficult to obtain "exact" crater statistics when using CSFD statistics for dating. In this study, we use the degradation model to simulate the degradation of craters, and screen out two types of craters with different evolutionary processes: diffusively degraded craters that conform to the crater degradation model represent young craters formed on young geological unit, and non-diffusively degraded craters that do not fit the crater degradation model represent old impact craters formed on old geological unit. The degradation process of craters is used to infer the geological activity experienced in the region, and for different geologic unit, all craters accumulated on that geologic unit are selected for CSFD dating.

Corresponding contents have been modified and presented in the section 1.

New lines: 98-112.

Line 91: Actually, different degradation stages of craters are also included during establishing the crater production function and chronology function.

We agree with the reviewer that the CSFD method calculates the age of geologic unit by counting the craters accumulated on the geologic unit since their formation until now, and the craters used for counting include those at different stages of degradation, but they all formed after the formation of the geologic unit. In contrast, this paper uses the degradation model to simulate the degradation process of craters and finds that there is a coexistence of old craters on old geologic unit and young craters on young geologic unit in the counted craters, and the craters formed on old geologic unit cannot be used to calculate the age of young geologic unit.

Line 102~103: I am afraid that the authors were confused with the method of surface dating based on CSFD. All the craters on the geologic unit should be identified to date the surface.

It’s very sorry that we didn't articulate the idea of solving the problem clearly.

Corresponding contents have been modified and presented in the section 1.

New lines: 120-121.

Line 104: remove “dating”

Corresponding contents have been modified.

Line 113~114: again, all the craters should be identified to date the surface age

Corresponding contents have been modified and presented in the section 1.

New lines:131-132.

Line 126: morphological: distributional

Corresponding contents have been modified , new line:145.

Line 127: insert “in diameter” after 350 m

Corresponding contents have been modified, new line:146.

Line 128: what does it mean “the total area of these craters”? Do the authors want to say “the total area of the surface”?

Corresponding contents have been modified, new line:146-147.

Line 132: remove “being”

Corresponding contents have been modified.

Line 139: “between each point are independent” should be “are randomly distributed within the region”. And remove “which is also … of craters”

Corresponding contents have been modified, new line:158.

Line 144: between craters: of craters’ distribution

Corresponding contents have been modified, new line:162.

Line 155: craters: craters’ distribution

Corresponding contents have been modified, new line:185.

Line 157: Figure 4a seems should be Figure 3a

Corresponding contents have been modified, new line:176.

Line 161: Figure 4b seems should be Figure 3b

Corresponding contents have been modified, new line:180.

Line 162: Figure 4c seems should be Figure 3c

Corresponding contents have been modified, new line:182.

Line 162: less clustered: ordered

Corresponding contents have been modified, new line:181.

Line 171: remove “crater”

Corresponding contents have been modified, new line:192.

Line 176: first, the larger craters of the old geologic unit can be used to date the old surface, which is called the resurface process and you can find it in many published papers. Second, what does it mean “some craters with different experiences caused by other erosion mechanisms”? Do you think if they can be used in dating the geologic unit?

We quite agree with you on these points, Our lack of clarity has caused you a misunderstanding. Here we mean that larger craters on geologic units are formed on older geologic units and cannot be used to determine the age of younger geologic units overlying older geologic units.

Line 188: why use 1 km as the division? Is there any particular sensing?

There is no special meaning in using D = 1 km as the division, just because the initial crater profile model and the diffusion equation used to model the crater degradation process (fassett et al., 2014) are only applicable to craters with 0.8 km ≤ D ≤ 5 km, while the diameter of craters in our study area is in the range of 0.35 km ≤ D ≤ 6.36 km. The crater profile models covering this diameter range are the initial crater profile models established by xie et al., (2017) for small diameter craters (D < 1 km) and du et al., (2019) for craters with D ≥ 1 km, so we chose these two models to represent the initial profile models for all craters in the study area.

Line 197: H seems not the height of the crater rim, it seems that is the height of the terrain with the distance of r to the crater center. Please the authors verify this

We are very sorry for our unclear description, H is the elevation of the point on the crater profile at a distance r from the center of the crater.

Corresponding contents have been modified and presented in the section 2.3.1.

New lines:214-215 and 218-219.

Line 206: Eq.2 should be Eq.3

Corresponding contents have been modified, new lines:228-229.

Line 208: For craters with the diameters less than 15 km, the original ….

Corresponding contents have been modified, new line:230.

Line 228: remove “it indicates that”

Corresponding contents have been modified.

Line 238: 7 m: 7 m/pixel

Corresponding contents have been modified, new line:266.

Line 280: number: frequency

Corresponding contents have been modified, new line:307.

Line 282: remove “per Ga”. So I doubt if the authors have really understood the principle of the surface dating method based on CSFD

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Line 291: age: chronology

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Line 293: Here, : where

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Line 301: remove “distributed”

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Line 314: remove “years’”

Corresponding contents have been modified, new line:342.

Line 314: the variable of “Hfin” should be written as “”, and there are similar problems in other places

Corresponding contents have been modified, new line:342;346; 348; 349.

Line 321~322: there is a grammar mistake in this sentence, and what is “ti”? That confuses me and I don’t know how to correct this sentence

Corresponding contents have been modified, new line:349-350.

Line 327: insert “been” before “accumulated”. And does the sentence mean that other five craters are not accumulated on the surface of the geological unit?

We are very sorry for our unclear description, the implication here is that the degradation process of these five craters is different from that of the other 107 craters, and the process of decreasing elevation of the crater rims does not conform to diffusively degradation process. It is inferred that the five craters that do not conform to the degradation model were formed in the old geological unit and the 107 craters that conform to the degradation model were formed in the young geological unit.

Corresponding contents have been modified and presented in the section 3.2.

New lines:353-359.

Line 333: Did the authors use the lunar crater chronology function by Neukum (1983) to derive the ages of 2.0 Ga and 1.99 Ga? Why they don’t use the chronology function by Yue et al. (2022), which has updated the chronology function with the CE-5 samples’ radiometric age?

Yes, we use the lunar crater chronology function by Neukum (1983) to derive the ages of 2.0 Ga and 1.99 Ga. The reason why we did not use the chronology function of Yue et al. (2022) is that previous research results were calculated based on the lunar crater chronology function by Neukum (1983), in order to facilitate comparative analysis.

Line 336: crater: craters; I am really astonished that the error bars are so regular in the CSFD. Please authors verify it is correct. In addition, please provide the saturation functions for the figure or list the reference(s)

The error formula is ±(Michael et al.,2010), confirming that there is no problem. It may be that the error bars are more regular when looked at visually due to the dense segmental interval of the crater diameter. In this paper, the 5% saturation line and 3% saturation line are plotted in the figure with reference to Robbins (2014), and the saturation function formula applied is N_eq(D)=1.54D^-2(Riedel et al., 2020).

Corresponding contents have been modified, new lines:370 and 406.

Line 337: blue: Blue; insert “and” before “orange”

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Line 340: remove “Dating result analysis”

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Line 344~347: I am really confused with the derived ages with only two or three more unnaturally degraded craters. If the authors use the CSFD to derive the N(1), and then obtain the AMA through the crater chronology function, the difference of the results are unbelievably large! The important is, how did the authors derive the N(1)? If they directly measured the N(1) through the frequency of the observed craters larger than 1.0 km in diameter, it is probably the case. However, the question is such calculation would be very uncertain and be questionable, and this is also the reason that we usually use PF – derive N(1) with different diameters and select the best value.

The age estimation using three non-diffusively degraded craters in this paper is only to make a rough estimate of the time when these craters were created, and indeed there is a large uncertainty, but this age is only used as a reference value in this paper.

In this paper, N(1) is calculated based on the N_cum values for each diameter interval range, and N(1) is derived after applying the least-squares fitting method to a₀ by combining the yield functions NPF1983 and NPF2001. Such an approach integrates the overall situation of all craters and avoids the limitation of using only a single diameter of crater measurements to find N(1).

Fig.11: I guess the authors derived the age of 3.96 Ga only based on the three large craters. If this is the case, there would be large uncertainty.

Due to the small study area, there are only three large craters with diameters greater than 4 km. It is indeed uncertain to calculate the age of only three craters just like the reviewer said. However, in this paper, we only use these three craters to make a rough prediction of the age of the old geologic units.