General Comments:

This manuscript presents an approach to reduction of large quantities of spatially characterized isotopic data obtained by raster scans of samples using LA-ICPMS. Image reduction programs already exist. The main novel feature of this one seems to be the ability to average data from virtual spots in order to achieve an optimal balance between precision and spatial resolution. As such, it is of potential use to a large number of geochemists and geochronologists. I found it to be very interesting, although I have no experience in using a femtosecond laser and have never tried elemental imaging.

Specific Comments:

The manuscript could use a more extensive and clearer discussion of limitations and how these might be improved. The authors use a single collector mass spectrometer so masses are measured at different times. The lateral movement between mass scans is about 1.4 mic while the pulse separation is about 0.05 mic. However, spatial resolution of data should be mainly limited by the ca. 0.6 sec transfer function (washout time) of ablated material into the plasma (in contrast to line 465), which covers a range of about 15 mic of beam movement along a scan. The observed distribution of isotopic ratios in the direction of a scan should be the actual distribution convoluted with the transfer function of the instrument. This would cause data variations along a scan at a scale lower than about 15 mic to be smeared together by the response time of the instrument, which is much broader than the distance covered by a mass sweep (1.4 mic). Therefore, defining the mass sweep as a pixel seems a bit misleading. Pixels, in the sense of a fundamental area scale at which independent values can be measured, are really more like the size of the spots but they vary along a continuum so it might be better to avoid the term pixel altogether. The relatively slow instrument response time is largely the result of using a nebulizer chamber where carrier He and makeup Ar are mixed before injection into the plasma. Response time can be significantly lowered by the use of a modified, commercially available, quartz injection tube where mixing between the He carrier gas and Ar occurs within the plasma. Further improvement would require the use of a multi-collector or time of flight mass spectrometer in which signals for different masses are effectively measured simultaneously. The scale of observable compositional variations across (rather than along) scans will be limited by the beam size (25 mic). It should also be noted that although the scan line is claimed to have a depth of 40 mic at 500 Hz, the troughs should have a V-shaped profile for non-overlapping lines so the average depth would be 20 mic. One should therefore be mapping triangular segments beneath the surface. This should of course affect ablation bias so standards need to be analyzed the same way.

A more fundamental problem is the fact that regression of relatively imprecise ratios produces ages that can be significantly different using the Wetherhill plot and the more commonly used Tera-Wasserburg (T-W) plot. I assume the reason is that one measures counts on the masses but one plots and calculates with ratios of these counts. Errors in the numerator mass count will propagate linearly whereas those in the denominator mass count will only propagate linearly to first order so second order effects become important when the relative error is large. This was the main reason that I developed the approach of regressing signals in a 3D space where the Wetherhill solution generally agrees most closely with the 3D solution for poorly radiogenic data sets and both disagree for highly radiogenic data sets (see Davis and Rochan-Banaga, 2021, Fig. 5). The reason can be visualized by considering that non-linear variations in the denominator isotope in T-W plots (²⁰⁶Pb) will bias data along a diagonal, which usually is at a high angle to the mixing line (isochron), whereas in the Wetherhill plot the denominator isotopes are from U, which is usually the largest peak (lowest error) and the common Pb end member is at infinity so non-linear variations will tend to be sub-parallel to the mixing line unless the datum is very radiogenic. The manuscript demonstrates this clearly but does not offer any discussion on how to effectively deal with it. One way would be to do regressions in 3D but there may be ways of correcting for it in 2D.

The best application that I can think of for this method would be WC1. This is an excellent standard because of its relatively old age and high U concentration but shows evidence of not being homogeneous in age based on the high ID-TIMS age error (2.7%) and the work of Guilong et al (2020, https://doi.org/10.5194/gchron-2019-20). If it were possible to isolate the predominate phase, this would be a much more useful standard.

Technical corrections:

If one choses not to indent paragraphs there should be a space left between them, as well as between references.

In some places I found the phasing unclear or ambiguous. Suggestions for improvement are made on an annotated copy.

The authors refer to Wetherhill Concordia plots as ‘concordia’ and the inverse (but more commonly used in this application) Tera-Wasserburg concordia plot as T-W. This is confusing because both are concordia plots. It would be better to refer to T-W and W plots.

Line 62:

Presumably the authors mean 207Pb/235U, but why would one want to use this ratio, rather than the more precise 206Pb/238U ratio as a criterion for sorting? They both encode the same information (age and radiogenicity).

Line 73:

The 3D regression also allows for editing outliers. This aspect is a separate problem from the best regression approach as discussed above.

Lines 125, 129, Table 1:

A better use of English would be to refer to line width (rather than height) as the diameter of the laser beam and line length (rather than width)  as the scanning distance. Otherwise it can be confusing to the reader.

Don Davis

General Comments:

The manuscript presents a novel approach to obtaining U-Pb ages of carbonates using isotopic maps and guided by statistical approaches to obtain the best age in what can be considered virtual spots. This is an interesting approach, and we can see the benefits the approach can have. The authors present a large amount of data from a number of samples (some of which have been previously dated for comparison).

Specific Comments:

• In the introduction, the manuscript heavily relies on references and comparison with other studies, which when one isn’t familiar with all of them makes reading and following the arguments a bit difficult. Particularly as the reader doesn’t know the details of the approach this paper takes at that point in the text. Therefore, we wonder if some of this might be better suited for the discussion instead of the introduction. We would welcome it if the abstract and the introduction would focus a bit more on the rationale for using this approach. Why is this new method needed, what is the overall problem, that justifies using the approach the authors present? The text says that the ages are similar to the traditional approach but that the uncertainties can be worse. So, the authors should be clearer what the advantage of this method over the other methods is.
• After stating here in the methods that some samples have been treated differently none of this is mentioned afterwards in the results of discussion. Even if it doesn’t make a difference. It would be important to mention that explicitly. If it does make a difference could some of the results be influenced by this and if yes how?
• Line 128: Why was the laser frequency changed from 100 to 500 Hz, please explain this change and the advantage of using one over the other. Additionally, can you detail if and what change this has on the results?
• Line 137: For sample BH14 only Ar was used as a carrier gas. It has been shown by Eggins et al., 1998​ that Ar and He have quite different transport qualities. How did the use of only Ar as a carrier gas influence the results?
• Line 149: Why was NIST SRM 614 used after 2020 and 612 before 2020? Are there any differences in the results or uncertainties?
• Use of rainbow colour maps. Jet or rainbow colour maps have been shown to be not a good choice. Both in terms of accessibility (colour blind and other sight impairments) the rainbow scheme is also misleading normal normal-sighted people due to a higher sensitivity of the human eye for certain colours which leads to a visual bias. Therefore, it should not be used:
  
  https://blogs.egu.eu/divisions/gd/2017/08/23/the-rainbow-colour-map/
  
  Have a look here for alternative suggestions https://www.fabiocrameri.ch/colourmaps/
• The comparison of the ages already determined by other studies (AUG-B6, BH14, DBT, Senz7) and this manuscript isn’t very clear. In section 5.1.1. it is mentioned, but in none of the tables or figures (despite a reference to it) is it shown clearly.
• A lot of the ages are quoted without external error propagation. How much would external uncertainty add? I assume a good amount of external uncertainty comes from the standards? What other sources are there and what is the justification to ignore them? When comparing ages from previous studies with this one external error propagation would be needed to understand the full extent of how they compare to each other.
• In section 5.2 the choice of data processing approach shows large (up to 50 Ma) variations in age (shown in figure 6 as well). How should a user choose which one to use? In the text, the authors mention that they chose the one closer to the expected age. But what if one doesn’t know the expected age? Wouldn’t this also mean that people might reject the ‘true’ age because they didn’t expect it?
• In section 5.3.1 line 348 the authors refer to a map of sample Cot02a that has more precise ages, but then say it isn’t presented here? Why is that? Why not at least provide this in the supplement?
• In lines 427-428: The sentence ‘In the case of reliable samples, it is expected that the position of the spots does not influence the calculated ages.’ What would you consider a reliable sample? What if your sample isn’t reliable, can you still use the approach? We would appreciate it if the authors could provide a bit more information on the limitations of this method. Particularly as carbonates can be complex in their formation and thereby age pattern. We would also appreciate it if the authors would touch on potential user biases that could be introduced when choosing one approach over another. It has been shown that data reduction and the choice of approach can make a difference in the final result. Particularly here with the possibility of choosing many virtual spots and statistical approaches, some clear guidelines for the reader would be helpful.
• A number of studies (e.g., van Elteren et al., 2018, Norris et al., 2021) have shown that aliasing and other artefacts can be created by LA-ICP-MS mapping. Have you observed any such effects, how are you mitigating such effects and how would this influence your ages?

Technical Comments:

• Use of the word ‘image’ when referring to the laser map, in many cases even using ‘image map’. Images imply that pixels are acquired simultaneously, which is not the case for LA-ICP-MS. Therefore, the word map should be used in this case. Please change this throughout the manuscript.
• Line 55 & 62: use 238U/208Pb, we were wondering if this is a typo and should say 238U/206Pb.
• Line 76/77: ‘Both allowed to obtain highly spatially resolved image maps (25 μm rasters) and with a good analytical sensitivity.’ What is good analytical sensitivity in this case, can you please quantify this?
• Line 169: ‘This script as well as the ones described below are publicly available (Hoareau et al., 2024).’ Instead of saying it is publicly available and referring to another paper it should say where the code is available. Good practice is to publish the code on GitHub and then provide the link here. Make it easy for people to find and use!
• Line 172 should say virtual spot
• Inconsistent use of NIST glass names, sometimes NIST SRM 612/614 other times NIST 612/614. We suggest to always use the same labelling.
• The use of the word spot height is a bit confusing, we suggest using width instead when talking about the vertical extent and then speaking about line length when speaking about the horizontal extent.
• Line 183-185: “To achieve this, it may be necessary to adjust the size of the virtual spots very slightly (e.g., 51 μm x 50 μm instead of 50 μm x 50 μm) to ensure an integer number of pixels per spot.”
• Why is it, is it because of the Python language/computing characteristics?
• Fig 1. The use of the arrows from A to B&C is confusing as they are not derived from A. They simply show a different configuration or the grid. Therefore, we suggest deleting the arrows. Furthermore, it would be good to provide the information on what map is shown. Is that a raw map? What element/ratio does it show? What sample is it?
• Fig 2. This figure is quite busy, are all images needed? Could some of them go into the supplement?
• In the caption of Fig 2, it says that concentrations were estimated from NIST SRM. First of all, which NIST was used for which sample? And secondly, what do you mean by estimates? Why not do a proper calibration of them?
• Fig. 7: The maps at the top have two areas highlighted that represent two calcite generations. What is the rest of the map? Nowhere does it say what it is and based on what the areas highlighted have been chosen.
• All isotope maps would benefit from a scale bar
• The labelling of the elements and isotope ratios next to the maps in the figures is very small and not well-readable. Suggest increasing the font size.

This is a co-review from Barbara Kunz & Igor Figueiredo