We are thankful to Prof. Michel Condomines for his pertinent comments and corrections. We are going to modify the manuscript accordingly. Please find below the detailed response to the comments:

Reviewer Comment (RC)

This paper presents an interesting comparison of various methods to date cave calcite. Its main interest resides in the demonstration of the coherence between ages obtained by the very precise U-Th dating method through liquid MC-ICP-MS and the new LA-SC-ICP-MS (laser-ablation, single collector, ICP-MS) method. This latter, although far less precise, offer the significant advantage of allowing a mapping of the different nuclides needed to calculate and correct an U-Th age (i.e. ²³⁸U, ²³⁴U, ²³⁰Th, ²³²Th). It is thus possible to select the most favourable zones for dating (e.g. those devoid of detrital contamination, with the highest ²³⁸U/²³²Th ratio).

answer: The paper is well written and clearly deserves publication in egusphere. I only have some minor comments that should easily be addressed by the authors.

- Section 2.4.2: Although the complete procedure for LA-SC-ICP-MS analyses is described in the previous article by Martin et al. (2022), a few more details would be welcome in this paper. In particular, the authors should explain their method to correct for instrumental isotope and U/Th fractionations.

answer: These details will be added to the manuscript:

“fsLA allows the use of liquid standard for calibration. A U standard solution (USS) of 0.02 μg·L⁻¹ was used for the calibration of the measurement. It was prepared from IRMM 184 SRM (IRMM, Geel, Belgium) in 2% HNO3 (Ultrex, Baker) diluted in ultrapure water (Milli-Q, Millipore) with 0.1% CaCO3 (Suprapur, Merck Darmstadt, Germany). This solution contained a certified 235U/238U isotope ratio of (7.2623 ± 0.0022) × 10⁻³ and was used to correct mass bias. U/Th fractionation has been tested to be negligible with fsLA (Martin et al. (2022).”

- In Table 1, there is a problem with the data for SOY 19-01 int and ext. Apparently, the ²³²Th contents have been reversed between int and ext samples. Int should have 198 ppb ²³⁸U and 4.16 ppb ²³²Th, and ext 218 ppb ²³⁸U and 0.257 ppb ²³²Th, in order to find the correct activity ratios reported in the Table.

answer: This will be corrected.

The authors should also report in the caption the half-lives used to convert atomic or weight ratios to activity ratios. U and Th contents are reported in columns 4 and 5. Activity ratios are reported in columns 7-8. Instead of using the d²³⁴U notation, ²³⁴U/²³⁸U activity ratios could also be reported in columns 6 and 10. Otherwise, d²³⁴U should be defined in the caption.

answer: The half live used are taken from Cheng et al. (2013) and Jaffey et al. (1971): (4.4683±0.0024) × 10⁹ a for ²³⁸U , 245620 ± 260 a for ²³⁴U and 75584 ± 110 a for ²³⁰Th. We will add them in the caption, along with the following references:

Cheng, H., Lawrence Edwards, R., Shen, C.-C., Polyak, V. J., Asmerom, Y., Woodhead, J. D., Hellstrom, J., Wang, Y., Kong, X., Spötl, C., Wang, X., & Calvin Alexander, E. (2013), Improvements in 230Th dating, 230Th and 234U half-life values, and U–Th isotopic measurements by multi-collector inductively coupled plasma mass spectrometry, Earth Planet. Sci. Lett., 371-372, 82–91

Jaffey, A.H., Flynn, K.F., Glendenin, L.E., Bentley, W.C., & Essling, A.M. (1971), Precision measurements of half-lives and specific activities of ²³⁵U and ²³⁸U. Phys. Rev. C, 4(5), 1889–1906.

The definition of d²³⁴U will be added to the caption.

- lines 36-37: opening of the U-Th system (gain or loss of one or more of the three needed nuclides from the calcite) is different from detrital contamination, which can occur at the time of calcite formation.

answer: We thank the reviewer for attracting our attention to this mistake: there should have been a comma between “opening of the geochemical” and “in the event of detrital contamination”. The sentence will be rewritten to correct this and to be clearer:

 “However, with the latter, the main difficulty lies in the possible opening of the geochemical system, in the event of detrital contamination by the surrounding sediments during the carbonate formation, or in the event of carbonate alteration accompanied by leaching of uranium (Perrin et al., 2014; Scholz et al., 2014, Pons-Branchu et al., 2020).”

- line 129: ^230Th

answer: This will be corrected.

- line 175: …linked to divalent cation substitution.

answer: This will be corrected.

- line 211: … ²³²Th contents range from 0.257 to 140 ppb (not ppt).

answer: This will be corrected.

We thank the reviewer for these relevant comments which have helped us improve the manuscript. Our detailed responses are given below.

Reviewer:

This paper reports on an innovative approach to dating cave carbonates that emphasizes using laser ablation ICP-MS techniques to construct elemental maps of small samples and date them via the U-Th technique. Those results are combined with sample characterization by other methods including transmitted light microscopy, cathodoluminescence microscopy, and Fourier Transform Infrared spectroscopy, and with bulk U-Th ages determined by solution ICP-MS and 14C dating. These approaches are applied to carbonate deposits from the wall and ceiling of the cave of the Trou du Renard (Soyons, France). Although the U-Th ages determined by laser ablation are of relatively low precision (relative errors generally >10%, 2s), they can be used to reveal age differences across layered carbonates on the sub-mm-scale, making the approach useful in determining limiting ages for rock art associated with carbonate coatings. Laser ablation results can also be used to guide sampling for more precise solution ICP-MS analyses.

This is an interesting, innovative paper but it would benefit from several improvements prior to publication. These include improving the quality of figures, better explaining aspects of the relatively novel fsLA-single collector-ICPSFMS technique and the STRUT approach to initial 230Th correction, more accurately characterizing relations between the laser ablation and solution U-Th results, and more fully citing previous relevant work by others.

Specific comments, keyed to figures and text are provided below.

Introduction

Line 36. Several other important studies have employed U-Th dating of carbonate coatings; they should be cited (e.g., Pike et al, 2012, Science 336:1409-1413; Aubert et al, 2015 Nature 514:223-227;  Hoffmann et al, 2017, Quat. Int. 432:50-58.)

Answer: As U-Th dating of carbonate coatings is fairly common, rather than providing an extensive list of citations, we preferred to cite a multi-method study (Valladas et al.  2017) which, we felt, was more relevant to this paper. However, we have added the references proposed by the reviewer to the revised manuscript. (Pike et al. (2012) is already cited and discussed in the manuscript).

Material and Methods

Fig. 1(a) Needs a scale, label host rock and coatings in photo. Can a similar photo of SOY-19-01 be provided?

Answer: The scale and additional labels have been added. Unfortunately, no similar photo of SOY-19-01 was taken, but we have added to fig.1 in the revised manuscript a photo of the area where the sample was found with an indication of its probable area of origin on the roof of the room.

Line 121. The locations of the large samples (weighing 67-167 mg) analyzed by solution MC-ICPMS need to be shown on Figs. 4 and 5 (for SOY19-02 endo and -exo) so their positions may be compared to the regions of the samples dated by laser ablation.

Answer: We have indicated the position of the large samples in the text of the revised manuscript as well as on Fig.B1b and Fig. B2b. For the exo part of SOY-19-02, the large sample corresponds to the bulk (as mentioned in the text, in Fig.6 and Table 1) so there is no point adding a position on the figures.

LIne 129. I agree with M. Condomines, who notes that although the author's LA-ICP-MS method has been described elsewhere, an overview would be appropriate here.

Answer: The following details have been added to the revised manuscript:

“A 10 μm laser beam diameter delivered at a repetition rate of 1 kHz was continuously and rapidly moved (1 mm.s-1) according to a vertical back and forth movement of 40 μm while the sample was moved horizontally at a speed of 50 μm.s^-1, resulting in 50 μm wide ablation lines. The accumulated counts were read every 1 s. This resulted in mappings with a resolution of 50 µm in both X and Y direction. Each mapping includes the measurement of a blank for 30 minutes before and after sample ablation. A High Resolution ICPMS (Element XR, Thermo Fisher Scientific^TM) fitted with the Jet Interface was used for detection. The laser was coupled to the ICPMS in a wet plasma configuration by means of a modified three-inlet cyclonic spray chamber that allows the dry aerosol from the ablation cell to be mixed axially upstream of the injector with the wet aerosol from the nebulization. The third inlet, tangential to the position of the nebulizer, was used to introduce a 10 ml nitrogen flow into the argon stream to obtain the best performance from the jet interface option. During ablation, a solution containing 2% HNO3 diluted in ultra-pure water was nebulized in the spray chamber, while during the mass bias calibration procedure, the laser was stopped and the USS was nebulized in the spray chamber The fsLA-ICPMS coupling was tuned daily with a NIST 612 glass sample in order to obtain the best sensitivity while keeping a U/Th ratio of 1.00±0.05, thus ensuring similar U and Th atomization and ion transmission. This stoichiometric detection of U and Th was checked prior to each image acquisition. fsLA allows the use of liquid standard for calibration. A U standard solution (USS) of 0.02 μg·L⁻¹ was used for the calibration of the measurement. It was prepared from IRMM 184 SRM (IRMM, Geel, Belgium) in 2% HNO₃ (Ultrex, Baker) diluted in ultrapure water (Milli-Q, Millipore) with 0.1% CaCO₃ (Suprapur, Merck Darmstadt, Germany). This solution contained a certified ²³⁵U/²³⁸U isotope ratio of (7.2623 ± 0.0022) × 10⁻³ and was used to correct mass bias. U/Th fractionation was tested with fsLA and found to be negligible (Martin et al., 2022).”

LIne 130. LA-ICP-Ms samples range from ~7 to 20 mm2; give thickness, which will allow the weights of the mounted samples to be estimated.

Answer: The approximate masses (1 to 3 mg per mapping) are indicated in the discussion. We have added them in the LA-ICPMS methodology in section 2.4.2 in the revised manuscript. Please note that these masses depend on the material density and on the depth of ablation, which vary between and within samples. Therefore, they can only be calculated approximately. A measure of the mass before and after ablation would have enabled accurate mass values to be obtained, but this was not done in the present study as it is not critical for the results.

LIne 132. Spatial variations in 238 and 232Th/238U were used to define "Regions of Interest" (ROI). The authors suggest these may correspond to different periods of calcification; however, they do not return to evaluate this suggestion after they present the U-Th ages.

Answer: In addition to having been demonstrated in Martin et al. (2022), the results of this method of defining ROIs are discussed at the beginning of the results sub-section 3.2.2 relative to fsLA-single collector-ICP-SFMS analysis. In addition, the ROI and age results for the sample SOY-02Exo can be directly compared on Fig.5 and Fig.6.

Line 136. The authors say they use three approaches to correct for detrital Th but seem to discuss only two.

Answer: We thank the reviewer for pointing out this mistake. Initially a third approach by an isochronal method was also tested (as in Martin et al., 2022), but it was abandoned because the areas of the same age in SOY-01Exo and SOY-02Exo were too small to provide precise results, and both SOY-01 and SOY-02endo were too homogeneous for precise isochronal analysis. There were also no isochronal analysis results from the liquid protocol that would have allowed a comparison, while comparison of the method is a major point of the study. Therefore, only the two approaches mentioned were kept, the “three” at the beginning of the sentence is a remnant of the first draft of the manuscript and has been replaced by “two”. We have added a brief discussion about the potential of the isochronal approach and why it was dismissed in this study.

The first approach assumes a value for (230Th/232Th)A0 for detritus of 1.50 ± 0.75. This is attributed to Hellstrom (2006). But that paper (Quat. Geochron. 1:289) explicitly recommends against the use of such a value and uncertainty, saying,

Where no information is available on the likely initial 230Th/232Th ratio in a speleothem (such as from an isochron, stratigraphical constraint or other independent means), a choice of initial ratio and uncertainty for (230Th/232Th)A0 of 1.0 ± 0.5 (±50%) is potentially incorrect (Richards and Dorale, 2003) because the reported range in speleothems is much larger than this, from at least  0.2 (Drysdale et al., 2006) to ~18 (Beck et al., 2001).

and then,

A median value of 1.5 with a log-normal distribution corresponding to a 95% confidence interval of plus or minus a factor of 10 (my emphasis) adequately covers the distribution of all reported speleothem (230Th/232Th)A0 ...

While few workers adopt such wide uncertainties, the point is that arbitrary choices of (230Th/232Th)A0  are probably not appropriate for the Trou du Renard samples, which have (230Th/232Th)A, Measured  of as low as 2.7, and where more than third of the samples have (230Th/232Th)A, Measured  <10.

Answer: We thank the reviewer for this very detailed comment, with which we agree. Indeed, this is the reason why we used several approaches for age correction. We have modified the text slightly in order to be more precise and have added 2 references.

The beginning of the paragraph “2.4.3 Detrital corrections” is now “Two approaches were used for U-Th age corrections. The first one was based on an a priori ²³⁰Th/²³²Th value for the detrital fraction, here an activity ratio of 1.50 ± 0.75. This value of 1.50 has been identified as the median value for the (230Th/232Th)A0  of the detrital phase for the dating of speleothems (Hellstrom et al., 2006) and  is a commonly used value used for speleothem age correction (Martín-García., 2019, Genuite et al., 2022, Pons-Branchu et al., 2022).”

Here, the value for (230Th/232Th)A0 determined using STRUTages routine is more precise but within the range of the correction using the common a priori value of 1.5 +/- 0.75. If the values of (230Th/232Th)A0 determined by STRUTages had been significantly different, the detrital correction would have been discussed in greater depth, and it is likely that we would have chosen to discard the results from the (230Th/232Th)A0 = 1.50 ± 0.75 correction. This approach is thus validated in our case.

The second approach used to correct for detrital Th results in "corrected ages modelled using stratigraphic constraints" via the STRUTAge routine. The latter approach should be described, including its assumptions. See comment for Line 245.

Answer: The following paragraph has been added to the revised manuscript: “The “STRUTAge routine consists of a script, available as supplementary material in the initial article, that can be used with Gnu Octave freeware (http://www.gnu.org/software/octave/). Basically, this routine combines stratigraphical constraints as proposed by Hellstrom 2006 and coevality constraints as in the isochronal approach, but without requiring a single (²³⁰Th/²³²Th)A₀ initial. This method tests a large range of correction (Monte Carlo simulation) for detrital thorium and gives the best estimate of the initial ²³⁰Th/²³²Th ratio and the corrected age of each sample. With this routine, the estimated variability of the ²³⁰Th/²³²Th)A₀ can be set”

What is third approach to detritus correction?

Answer: See answer to comment on Line 136

In samples with low (230Th/232Th)A, Measured  and high, variable 232Th/238U, an isochron approach might be used to determine the initial 230Th/232Th of detritus, rather than assuming or modeling it. In presenting the LA-ICP-MS approach used here, Martin et al. (2022) used such isochrons. Was this tried on the Trou du Renard samples? If so, what was the result?

Answer: See answer to comment on Line 136

General comment. For many samples in this paper the detritus correction has a defining effect on the value of the final U-Th age and its calculated precision. (For example, in Table 1, compare ages uncorrected for detritus (col. 9) with detritus-corrected ages (col. 11)). Hence the detritus correction and its impact on the ages needs to be discussed more fully in the text.

Answer: An extended discussion about the different methods of detrital correction used and their impact on the dating has been added in section 3.3.

Petrography and mapping results

Line 160. The authors state that "The CL image confirms this relative homogeneity..." However, the samples appear to be far from homogeneous. Can the authors provide more informative interpretations of the optical and CL images?

Answer: The following details have been added relative to the CL images:

“The CL image shows a high degree of homogeneity for the endo sample, with luminescence in the blue hues characteristic of low-luminescent carbonates. The luminescence is more variable for the exo sub-sample, showing some more luminescent levels, mainly towards the outside, with a red luminescence hue. These levels are relatively continuous and can be interpreted as the consequences of a change in water chemistry or the incorporation of trace elements into the carbonates, such as Mn, which is the main activator of carbonate luminescence (Machel et al., 1991).”

Line 178. The authors state that the LA-ICP mappings indicate "good homogeneity". This does not seem to be an accurate (or informative) description of the element maps presented, which show factor-of-four variations in the signal intensity of the analyzed elements.

Answer: This statement only concerns the endo part and excludes the exo part and the basal part of the sample:

“The fsLA-single collector ICP-SFMS mappings of SOY19-02 Endo indicate a good homogeneity of the distribution of the chemical elements investigated (²⁴Mg, ²⁷Al, ²³⁸U, ²³²Th and ⁴³Ca), apart from the basal part”

In this endo part, the signal intensity varies by a factor of less than 2.

Some figures need to be improved.

1) In Fig. 1, can host rock, "endo", and "exo" layers should be delineated.

Answer: The endo and exo layers have different colors and clearly distinguishable textures, which can be differentiated even in black and white. Delineating them on this image could give the false impression that these layers are next to each other instead of being on top of each other, which would confuse the reader.

2) A uniform orientation of samples should be adopted. In Figs. 2, 3, and 4, samples are oriented with crystal growth upwards while in Fig. 5 and Fig. B2 the same samples are shown oriented with crystal growth down. This makes it difficult to relate the different types of observations made on each sample. Make sure captions accurately describe orientations.

Answer: All the figures have been shown in the same orientation in the revised manuscript, and a description of the orientation has been added to the captions.

3) In the figures with color ramps, sample outlines need to be highlighted using a bold line in a contrasting color. At present, colors designating low count rates merge into the background color of some images, making it hard to see the outlines of the samples.

Answer: The color ramp used was chosen w.r.t. the editor’s chart (i.e. it must be visible and understandable for color blind people as well as in black and white). Most color ramps using sharply contrasting colors do not comply with this chart, but we are open to suggestion if the reviewer knows a color ramp that would allow both sharp contrast with the background and comply with the journal’s requirement.

It would also be possible to modify the range of values displayed in order to obtain a better contrast with the background, but this would be at the cost of saturating the highest values, which often represent regions of interest for the study, such as high heterogeneity areas. We chose this range of displayed values in order to enable the visibility of both the highest signal area and the low signal area, which unfortunately means that the low values may have low contrast with the background.

3) Switch positions of Fig. 3 and Fig. B2. Fig. 3 shows FT-IR analyses for SOY19-03, however, since no U-Th data are reported for this sample, the significance of the FT-IR results for U-Th dating are unclear. On the other hand, key U and 232Th/238U maps for SOY19-02 Endo and for SOY19-02 Exo, the samples with the most intensively studied U-Th systems, are relegated to Fig. B2 in the Appendix.

Answer: We highlighted in part 2.1 the similarity between SOY19-02 and SOY19-03, which could in fact be considered as two sub-samples of the same deposit. The FT-IR results presented on Fig.3 indicate no evidence of different mineralization (calcite and aragonite for example) or of diageneses, which would both have significant consequences on the validity of U-Th ages. On the other hand, the mappings presented on Fig.B2 are redundant with the mappings of Fig.4 and Fig.5. Even if the ²³²Th/²³⁸U mapping highlights relevant data for the U-Th dating, the usefulness of the Endo part mapping for the age calculation was limited in view of its homogeneity and the Exo part mapping is provided on Fig.5. We also believe that the accumulation of the LA-ICPMS mappings within the manuscript creates problems of readability, and therefore we maintain our decision to place these data in the Appendix, where they can still be accessed by the reader.

4) Positions of samples analyzed by solution ICP need to be shown on figures to make clear their locations relative to laser ablation ROIs.

Answer: Endo 1 was sampled in the first third of the endo part (from the base), Endo 2 was sampled in the last third. These positions are now indicated in the text of the revised manuscript and have been added to Fig.B2b. Please note that they are approximate positions, as the sub-sample used for the liquid ICPMS protocol is not the same as the one used for the LA-ICPMS protocol.

5) In Fig. 6, error bars for the different types of ages for each sub-sample commonly overlap, making them hard to see. An easy fix for this would be to offset the different ages for each sample by small amounts along the X-axis.

Answer: In fact, there is no X-axis, as this is not a scatter-plot. This made it quite difficult to offset the different points corresponding to the same sub-sampling. We have changed the colors of the points in the revised manuscript (lighter colors for the uncorrected ages and associated uncertainty bars) in order to make the figure easier to read.

Line 185. Call out for Fig. 9; there seems to be no such figure.

Answer:  We apologize for this mistake; it should be fig.6, not 9. This has been corrected.

Line 202. The authors state, "In conclusion, data from different analytical methods converge towards a coherent description of the samples. They all are composed of successive layers of pure calcite, without any evidence of diagenesis (Fig 2 and Fig 3)." (Boldface added.) How do they conclude this? It would be helpful if they commented on salient features of their data. For example, what is the significance of the factor-of-four co-variation in Mg and 238U count rates observed for the Endo part of SOY-19-02?

Answer: This salient feature is not part of the endo part but corresponds to the basal part on which the calcite deposed. We apologize for the confusion; the following sentences have been added to the caption of Fig.4 in the revised manuscript:

“The bottom part of the image corresponds to the Jurassic Kimmeridgian karst basal part. It can be easily identified by the highest signal area for ²⁴Mg, ²⁷Al ²³⁸U, ²³²Th as well as a different texture on the ⁴³Ca mapping.”

Line 211. ppm, not ppt, for 232Th. Add median values for concentrations, ratios, which are more informative.

Answer: It is actually ppb for the ²³²Th. We find that the range of values makes more sense here, as the precision of the analysis and that of the detrital correction are directly related to these and because the study focuses on investigating the sample variability. However, we agree that adding the ²³²Th/²³⁸U ratio would be more informative than the ²³²Th and ²³⁸U values alone, so we have added this ratio range to the revised manuscript.

Line 214. State confidence level of errors here.

Answer: All quantitative results and ages are provided with uncertainties at 95% confidence level. This has been added at the beginning of the dating results part in the revised manuscript.

Line 216. The authors state that, "The fsLA-single collector-ICP-SFMS provided qualitative mappings of 230Th, 232Th, 234U and 238U with relative variations." Can maps of 230Th and 234U (or 230Th/238U and 234U/238U ratios) be shown to illustrate their variation within and between ROIs? The number of counts obtained for 230Th and 234U in each ROI should be provided.

Answer: We find the ²³⁰Th and ²³⁴U maps redundant with the ²³⁴U map: the distribution of counts is very similar, but with more scatter due to the lower count rate. We have attached those of SOY19-02 exo to this response as an illustration. Therefore, they are not useful for the understanding of the results and of the paper. The ²³⁰Th and ²³⁴U count ranges have been added to the revised manuscript at the beginning of the results part relative to LA-ICPMS dating:

“Depending on the size, ²³⁸U content and age of the ROI, the number of ²³⁰Th counts ranged from about 3.3x10³ to 2.6x10⁵ and the number of ²³⁴U counts ranged from about 1.5x10⁴ to 1.0x10⁶.”

No information on U content in the laser ablation samples is given in Table 1. Some measure of relative U contents should be provided. For example, a histogram of U count rates could be provided for each ROI, or U count rates at the 10th, 50th, and 90th percentiles could be given. Martin et al. (2022) estimate U concentrations by estimating ablated mass using 43Ca signal levels and by comparing profiles of samples before and after ablation. Can that be done here?

Answer: The ⁴³Ca signal was not measured during the LA-ICPMS analysis from which the data of table 1 were obtained, in order to maximize the counting time on the isotope necessary to the dating. Therefore, no quantification can be done. The rate of ablation, which can be estimated by the variability on the ⁴³Ca image of fig.4.e, is highly variable and therefore the U count rate is not a good estimation of the U content. It would have been possible to estimate the U content of the different layers used for the dating by using their correspondence with the layers observable in Fig.4 by analysing an area nearby in the same sample. However, the analyses presented on Fig.4 were qualitative and no quantitative calibration of the ICPMS was done. Therefore, no quantification based on this analysis can be done.

Line 217-218. The authors state that, "SOY-19-02 Endo and SOY-19-01 appear relatively homogeneous, while distinct successive layers can be observed on SOY-19-02 Exo." But in Fig. B2, SOY-19-02 Endo shows clear layering defined by three-fold variations in 238U count rates and 232Th/238U ratios. Likewise, SOY-19-02 Endo shows well developed layering in optical microscopy (Fig. 2) and in Mg counts (Fig. 4a). Can the authors quantify what is meant by relatively homogeneous?

Answer: As explained in response to the comment on line 202, the high variation area at the bottom of the SOY-19-02 Endo images is the basal part, which is not part of the endo part. The same sentence as for Fig.4 has been added to the caption of Fig.B2. Concerning the layering observable on optical microscopy, the fact that the different layers are visible does not mean that their composition or content in U and Th are significantly different.

Dating results

Line 245. Table 1 caption, referring to results using STRUTAge, the authors say, " Results are given for strict coeval constraints, with 30% variability for Ri = (230Th/232Th)det determined here at 1.72 ± 0.3." For readers unfamiliar with the STRUT algorithm, some explanation/context needs to be provided in the text.

Answer: At the reviewer's request, we have added an explanation in the Results section of the revised manuscript.

lines 220-224 (move to line 250?). The solution and laser ablation results obtained for SOY-19-02 Endo do not agree well (see Table 1). Despite the relatively large uncertainty (~10%) of the detritus-corrected age for “Endo bulk” determined by laser ablation, its detritus-corrected age and that of Endo-1 (determined by solution) are distinct outside of their 2 sigma errors. Detritus-corrected ages for Endo bulk and Endo-2 (a second sub-sample determined by solution) are closer but remain distinct at the 1 sigma level, making the probability that the two ages agree rather low (<5%).

Answer: There is a mistake in table 1, for which we apologize: the age of the LA-ICPMS Endo bulk subsample is 171 +17/-15 ka, not 163 +17/-15 ka (i.e. the age in table 1 is wrong, the age displayed on Fig.6 is right). The data of the graph on Fig.6 are right, and it can be seen that the LA-ICPMS age is consistent with the solution ages within the 95% confidence level. This has been corrected in the revised manuscript.

Beyond that, we would like to highlight here a phenomenon related to the spatial resolution of the analysis (which is discussed in the sub-section “3.3.4 Summary of ages obtained by comparing the two techniques”): the uncertainty associated with the bulk age mostly reflects the uncertainty on the measurement and not on the extent of time during which the carbonate deposit accumulated. The ages for Endo 1 and Endo 2 are the ages for distinct parts of the deposit, with relatively small uncertainties relative to the protocol used for age determination. The bulk age corresponds to the age of mixed material in various quantities between the different layers of the Endo part, including the parts corresponding to the Endo 1 and Endo 2 ages. The larger uncertainty here is due to the LA-ICPMS protocol, and not to the variation of ages between the layers of the Endo part. Therefore, if we can expect the bulk age to be close to the Endo 1 and Endo 2 ages, ideally between those two ages if the measurement uncertainty is small enough, incompatibility between these different ages does not necessarily mean a measurement or protocol error, as it is not the same parts that are dated. It simply means that a bulk measurement is not capable of providing information about the time extent of the carbonate part that it dates, while spatially resolved measurement can. Therefore, comparing the compatibility within the uncertainty of the different ages (Endo 1, Endo 2 and bulk) is not a relevant approach here.

The detritus-corrected age for Endo bulk calculated using the STRUT algorithm is distinct outside of 2 sigma errors from both Endo-1 and Endo-2 ages determined via solution analyses. The clear discordance between the laser ablation ages calculated using the STRUT algorithm and the Endo-1 and -2 ages from solution analyses raises the question of whether STRUT is suitable for these samples.

Since comparing results obtained using conventional solution analyses with those obtained using laser ablation is one of the salient features of this paper, these differences need to be noted and possible reasons for them discussed (e.g., underestimating errors, sampling bias, inconsistent analytical and data reduction protocols, etc.). As mentioned above, the positions of the samples analyzed by solution need to be shown in the relevant figures. For example, what are the relations among SOY19-02 Exo Bulk (analyzed by solution) and the seven layers of SOY19-02 Exo (analyzed by LA)?  How was the "bulk" sample for solution analysis prepared? Is it a representative aliquot? If so, of what portion of SOY19-02 Exo? That is, were equivalent materials analyzed by solution and laser ablation? If so, do the results agree?

Answer: An extended discussion of the detrital correction and the STRUTage model has been added to section 3.3 in the revised manuscript:

“The detrital correction has a significant impact on the final U-Th ages, especially for the spatially resolved fsLA-single collector-ICP-SFMS results of the SOY-19-02 Exo part: the layers 1, 3 and 7 present considerable amounts of detrital Th associated with stratigraphic inversion of the uncorrected ages (Fig. 6, Table 1). We used two independent methods for detrital correction: a correction using an a priori value and the STRUTage model. It is noticeable that the results of these two methods agree within the uncertainties and provide ages in stratigraphical order (Fig. 6, Table 1). This seems to indicate that the results of the two correction methods are coherent.

The accuracy of the correction by an a priori value is discussed by Hellstrom et al. (2006) because the initial detrital Th ratio (230Th/232Th)A0 of some samples can be beyond the range covered by the a priori value of 1.50 ± 0.75. However, this does not seem to be the case for the sample investigated here as the correction provided coherent results and the STRUTage model calculated a compatible average value of (230Th/232Th)A0 of 1.72 ± 0.30. Of course, this does not mean that this method of detrital Th correction is valid for every sample, as highlighted by Hellstrom et al. (2006), only that it is possible to check its relevance by comparing it with other methods and therefore that a multi-method approach is also advisable for detrital correction in order to ensure the reliability of the dating.

The STRUTage model provides a more precise detrital corrected age than the correction by the a priori detrital value. This is made possible by the use of the stratigraphy by these models to constrain the results. Therefore, the use of this model with high spatial resolution analysis such as fsLA-single collector-ICP-SFMS imaging seems particularly appropriate and is likely to be developed further in the future. It is noticeable that the results of the STRUTage model for layer 1 of SOY-19-02 exo are significantly older than the detrital corrected ages of layer 2 and almost incompatible, within the uncertainty, while the STRUTage result for SOY-19-02 endo is significantly younger than the age determined by Liq-MC-ICPMS for the endo 2 part. This may be the result of a gap within the carbonate stratigraphy between SOY-19-02 endo and SOY-19-02 exo, corresponding to a period where the wall was covered by clay (as stated in part 2.1, a clay layer is observed between the endo and exo part of SOY-19-02 and SOY-19-03) and no carbonate was deposited at its surface. However, other explanations, such as measurement errors or a detrital Th value beyond the usual range, cannot be completely dismissed, and more work is needed in order to determine the cause of this potential mismatch of ages.

Martin et al. (2022) took advantage of fsLA-single collector-ICP-SFMS imaging in order to refine another method of detrital Th correction, the isochronal method. This method was considered for this study as part of the multi-method approach; however it was dismissed for several reasons: the SOY-19-02 endo and SOY-19-01 detrital Th distributions were too homogeneous to provide accurate results with this method, and the areas of the same age as SOY-19-02 exo were too small to obtain enough counting statistics to be able to calculate a sufficiently precise correction. This only led to an average value of (230Th/232Th)A0 of 1.3 ± 0.8, which is compatible with the a priori value used and with the average value determined by STRUTage but cannot provide precise detrital corrected ages. Although it is not appropriate for this sample, this method of detrital correction still presents a strong potential for more heterogeneous samples, or with an increase in measurement accuracy with fsLA-single collector-ICP-SFMS, by accumulating the counts over several successive imagings of the same area or sample for example, as done by Martin et al. (2022).”

 The position of the different samples has been added in the text and in Fig.B1 and Fig.B2.

The relations among SOY19-02 Exo Bulk (analyzed by solution) and the seven layers of SOY19-02 Exo are discussed in section 3.3.4. The preparation of the sample is described in section 2.4.1 and in Pons-Branchu et al. (2014). Bulk means all the layers of the exo part; this seems self-evident so is not explained in the paper. The representativity of the bulk measurement compared to the measurement of the 7 layers by LA-ICPMS is discussed in section 3.3.4.

Same comment for SOY19-01 with regard to samples designated int, ext, and bulk. The positions of these samples should be shown on the relevant figures.

Answer: The int part was sampled in the first third of the sample (starting from the centre), the ext part was sampled in the last third. These positions have been indicated in the text of the revised manuscript and added to Fig.B1b. Please note that they are approximate positions, as the sub-sample used for the liquid ICPMS protocol is not the same as the sub-sample used for the LA-ICPMS protocol.

The authors suggest that regions of Interest (ROI) defined on the basis of 232Th/238U ratios have age significance but the data in Table 1 do not seem to support that interpretation. For example, SOY-19-02Exo layers 1, 2, and 3 have indistinguishable detritus-corrected ages (Table 1) although the values and patterns of  their 232Th/238U ratios are distinct (Fig. 5). Likewise with SOY-19-02 layers 6 and 7. Indeed, the detritus-corrected U-Th ages of SOY-19-02 support dividing the sample into just three age-groups, consisting of layers 1 to 3, layers 4 and 5, and layers 6 and 7. An obvious question is whether these ROIs actually have age significance.

Answer: The corrected ages are compatible within their uncertainty, but it is impossible to tell if it is because their age is the same or simply because of the lower precision of LA-ICPMS analysis and of the additional uncertainty introduced by the detrital correction. It is certain that the layers were deposited one after the other, so in that case it may simply indicate that the current precision of the method cannot resolve their ages. Improvements in measurement and in detrital correction may in the future make it possible to resolve such small age differences. Despite these ages being compatible within their uncertainties, we can observe a clear decreasing trend of the ages of the different ROIs within the SOY19-02 sample, which provides information about the rate of carbonate deposit and can be exploited by a stratigraphical constraint model such as STRUTage to improve the chronology.

Would the results have been different with a different ROI set? Because of the limited precision of the method, smaller ROIs would likely only provide low precision ages. Larger ROIs would lead to more precise results, but with a lower spatial resolution, which could have made us miss the age gap between layer 5 and layer 6, or made the global age decrease from layer 1 to layer 7 less obvious. The average ages would still be the same with smaller or larger ROIs, but we need to find a balance between age precision and spatial resolution. Defining the ROI by the ²³²Th/²³⁸U, in addition to having proved to be a successful method in Martin et al. (2022), seems a good compromise and made some of the variation of this isotopic ratio correspond with a significant age variation (such as the age gap mentioned before between layer 5 and 6).

Another advantage of this method of ROI definition is in the event of problems with the detrital correction: if the detrital correction method had led to incoherent results (because, for example, of an unusual ²³⁰Th/²³²Th detrital ratio, or other incompatibility with the base hypothesis of the correction), it would have been possible to exclude the ROIs with high detrital content and to keep only the ages of the ROIs with low detrital content. This advantage was not required in this study as the detrital correction seems to lead to a coherent chronology.

Looking at col. 11 in Table 1, the central values of the STRUT ages for SOY-19-02 sub-samples may be either older or younger than ages corrected assuming (230Th/232Th)detritus = 1.5 ± 0.75. However, if the STRUT algorithm determines 230Th/232Th)detritus = 1.72 ± 0.3, as stated in the caption, it seems to me that STRUT ages should be younger because STRUT attributes more 230Th to detritus and less to in situ decay. That is, why don't the two types of ages maintain a consistent older/younger relation?

Answer: With the STRUTages correction, initial ²³⁰Th/²³²Th can vary by 30% as explained in the previous section (and specified in the revised version of the article), so corrected values can vary. Please note that corrected ages assuming one or the other correction method for SOY-19-02 sub-samples are always in agreement taking into account error bars.

There appear to be discrepancies between Fig. 6 and Table 1. For example, the old-side error bar for the detritus-corrected age for Endo bulk, 163 +17/-15 ka, should coincide with the corresponding error bar for the Endo-1 age, 177.2±3 ka. However, in Fig. 6, the error for the LA analysis extends to an older age, providing a misleading visual impression of the relation between them. Please check for consistency between Table 1 and Fig. 6.

Answer: We thank the reviewer for pointing out this mistake: the age of the LA-ICPMS Endo bulk subsample is 171 +17/-15 ka, not 163 +17/-15 ka (i.e. the age in table 1 is wrong, the age displayed on Fig.6 is right). This has been corrected in the revised manuscript; We double checked the other values in the table.

Line 260-261. The authors attribute the age gap between layer 5 (84±6 ka) and layer 6 (33±6 ka) to "drier conditions in the cave during ... MIS 4". But MIS 4 (~71-59 ka) coincides with only part of this gap. Likewise, the authors attribute calcite deposition in layers 6 and 7 at c. 33 ka to "a higher calcite deposition during MIS3". But layers 6 and 7 likely occupy only a small fraction of the MIS 3 interval (~59-28 ka). Such mismatches suggest that relating calcite deposition to marine isotope stages is overly simplistic.

Answer: The reference to marine isotope stages has been removed from the revised manuscript.

Line 265. Is this an error-weighted mean age? That is not a meaningful quantity when determined from two ages that are distinct outside 2-sigma errors, as these are. The utility of the 14C analysis of SOY 19-01 is limited since the calculated age can vary from >2.3 ka to <0.6 ka depending on the percent dead carbon, which is not independently known.

Answer: We again thank the reviewer for bringing our attention to this mistake. We agree, an error-weighted mean age makes no sense here as the two values are the ages of different parts of the sample. This has been replaced by a mean value with an uncertainty covering the range of possible values (mean age 2.1 +1.3/-0.8 ka BP). Concerning the proportion of C14 age depending on the proportion of dead carbon, we wanted to highlight that the results are compatible with C14 ages assuming a common dead carbon content between 0 and 20% if sites above peat bogs are excepted (Genty et al. 2001).

Summary of ages obtained by two techniques

Line 293. "Uranium leaching can also be highlighted, and areas affected by these changes can be excluded from the age calculation." No results supporting this claim have been presented in this paper. Elsewhere, some of the current authors have claimed that U loss may be recognized based on associated anomalous 234U/238U ratios, however, such claims need to be justified in light of the relatively low analytical precision achievable for d234U by laser ablation (e.g., d234U values with ± 10 to 20% errors; Table 1). Further, significant primary variation is observed in the cave (e.g., d234U of <90 to >290 ‰; Table 1). In light of these factors, the threshold for detecting U loss by this approach must be rather high.

Answer: This possibility of detecting and excluding uranium leached areas is detailed and was used in Martin et al. (2022). This reference has been added to this sentence. Without going into too much detail, potential U leached areas can be identified by different factors: a significantly anomalous ²³⁴U/²³⁸U ratio, a significantly lower U content and a significantly higher apparent age. Any of these factors alone may not be good enough evidence of U leaching, but areas presenting at least two of the factors can be reasonably suspected and their reliability for dating discussed, which could lead to excluding them from the analysis. It is noticeable that anomalous ²³⁴U/²³⁸U ratios beyond the uncertainty range were detected in Martin et al. (2022). That was not the case in this study, therefore no area was excluded from the analysis, but this advantage of the method needs to be highlighted considering the frequency of U leaching in carbonates.

Implications for rock art studies

Line 301. The authors assert that "no attention was paid to the uranium behavior" in previous studies. However, this is an incomplete and inaccurate characterization of prior research on dating carbonate coatings on rock art. For example,  Hoffmann et al. 2017 (Quat. Int. 432:50-58) and Hoffmann et al. 2018 (Science 359: 912-915) evaluated preservation of stratigraphic order in carbonate layers coating cave paintings, thereby testing for intact U-Th systems and appropriate initial Th corrections. Their approach employed micro-sampling techniques and relatively precise solution ICP analyses with which they evaluated U-Th ages from a series of milligram-size samples scraped from progressively greater depths within coatings. In most cases, they produced impressive sequences of ages that progressively increased inwards, as expected, and were associated with coherent initial 234U/238U ratios. See also the discussion of "U-Th dating: open system issues..." in Pike et al. (2017). These references need to be cited and considered.

Answer: We had no intention of implying that no study had paid attention to uranium behaviour, but rather that some studies did not consider it. To avoid confusion, we have removed this sentence, which could be misinterpreted.

Line 312. The authors say, "The control of the basic hypothesis on which the dating is based, such as the absence of diagenesis and the application of detrital correction, is a key element that only the approach we have implemented in this case study allows..." Considering the research mentioned above, this statement seems overreaching and should be qualified or deleted.

Answer: The sentence has been rewritten as follows:

“The control of the basic hypothesis on which the dating is based, such as the absence of diagenesis and the application of detrital correction, reinforces the reliability and robustness of the chronology.”

Line 318. The authors say, "However, the total mass required for petrographic analysis and dating is only a fraction of this amount, less than one gram." Then, further below, they say,

Line 324. "If discussed in relation to the archaeological, geological and preservation expertise, such results would probably allow the identification of sampling points closest to the decoration that would maximize the chronological data for a minimum of sampled mass, i.e. 1 to 10 mg of sample taken with a micro-drill tool."

Although only several milligrams are consumed in the laser ablation analyses, significantly larger amounts of material are required to fabricate the various mounts used in the current study. Further, it is a non-trivial problem to devise a protocol that would allow gram-size, or milligram-size, quantities of thin carbonate coatings to be recovered intact so that they may be analyzed by laser ablation as in this study, without damaging underlying art, if present. Since the current study used cm-scale blocks chiseled from the outcrop (e.g., Fig. 1 and 2), it's probably appropriate to qualify these statements until they have demonstrated such capabilities.

Answer: The paragraph from which these different sentences are taken is a discussion, in which we clearly state at the beginning that the current analyses are not, in their present form, suitable for the direct dating of decorated areas:

“In the present study, the initial size of the samples (a few cm) is not compatible with the preservation requirements for decorated caves”

In the same paragraph, we recommend applying it only outside decorated areas in view of the quantity necessary for the analysis, in order to provide guidance for smaller targeted samplings:

 “Similar analyses to this study can be carried out in non-decorated areas, or on small or naturally fallen pieces of calcite to establish a chronology of calcite deposition in the cave and to highlight any difficulties for dating methods”

In addition, we never claim that we are already capable of performing these mg sized samplings (although we are working on it), as highlighted by the use of hypothetical form through this whole paragraph.

Line 340. Since U-Th dating by ICP-MS (by laser or solution analyses) is limited by counting statistics on the minor isotopes (especially 230Th), it's not actually possible to "improve the age precision and spatial resolution" simultaneously. This is shown by the laser ablation ages in this paper, which generally have relative errors of 10% or more. As the authors say earlier, laser ablation can probably best be used to provide a framework to guide sampling of larger, multi-milligram quantities of carbonate for precise analysis by solution techniques.

Answer: It is actually perfectly possible to improve LA-ICPMS by various means, such as taking successive images of the same area in order to improve the counting statistic at the expense of a longer analysis time.  In addition, recent analysis showed that dry plasma conditions can improve the background, leading to a greater precision of the measurements. The remaining instrumental challenges consist in the design of instruments with even less background and a better ion transmission.