Response to referee comment RC1 by Samuel Niedermann

We appreciate the thorough and detailed review by Samuel Niedermann and we have made the requested changes to the text as outlined below. Author comments are given in bold. Line numbers refer to the revised version of the manuscript.

General comment

This manuscript proposes a new method to improve the accuracy of comsogenic ³He surface exposure dating using magnetite. The authors have used microCT to screen magnetite grains for the presence of inclusions. They argue that inclusion-free grains should be used for exposure studies, since grains with inclusions have frequently increased ³He concentrations due to several processes. Based on their He analyses of inclusion-free magnetite and a comparison to cosmogenic ¹⁰Be and ²⁶Al concentrations in co-existing quartz, they propose a cosmogenic ³He production rate in magnetite of 116 at/g/a (scaled to sea level and high latitude).

The method proposed by the authors is clearly an important contribution to the wide field of surface exposure dating with cosmogenic nuclides, which has the potential to make some scientific questions accessible to research that have been difficult to treat so far, even though it is unlikely to become a standard method because of the various laborious analyses that are required. For the most part, the paper is written clearly, concisely and in good English. A few points need more explanation, as specified below, and an annoying point is that many references are missing in the reference list. The major flaw is the lack of discussion why some earlier production rate estimates were just about half the new rate (see below). Nevertheless, I recommend this manuscript for publication in Geochronology after minor revision has taken account of the specific and technical comments given hereafter.

Specific comments:

At many places in the manuscript, the authors use expressions such as “cosmogenic production", "cosmogenic exposure", "cosmogenic studies" etc., or similar with radiogenic, nucleogenic. However, "cosmogenic” means “generated by cosmic rays” (“radiogenic" is "generated by radioactive decay" etc.), therefore one can only talk about cosmogenic nuclides, cosmogenic neutrons etc. but not about cosmogenic exposure or studies, and cosmogenic production is a pleonasm. I found such incorrect use of ...genic in the following lines: 16,17,38,45,71,85,87,90,92,309,380,422,425,429,432,440,454,462, 672. 

We consistently replaced “cosmogenic” with “cosmogenic nuclide” or “cosmic-ray” in the Lines mentioned above as well as throughout the rest of the manuscript.

The term “radiogenic ³He" is a bit misleading. Usually, radiogenic means production by α or β decay (or electron capture), while nuclides produces by fission are called fissiogenic. Even thogh fission is a kind of radioactive decay, I would suggest to use that distinction for ³He just like people do for Xe, because it makes clear that it is not about ³He production from ³H. If the authors still prefer radiogenic, they should explain what they mean at the first locations where this appears, i.e line 17 (Abstract) and 69 (main text).

Changed all instances of “radiogenic ³He” to “fissiogenic ³He”.

In lines 85-86, the authors mention a “high-energy muon component of spallogenic production", saying it is negligible. However, they don’t mention slow (negative) muon capture at all. As the reference Nesterenok and Yakubovich 2016 is not shown in the reference list, I could not check whether these authors perhaps say slow muons are generally negligible for ³He. Even if so, this should be mentioned in the text.

Added “by inducing spallation or through μ^- capture reactions” to describe the interactions with the full energy-spectrum of muons, which are the pathways for the muogenic component of ³He production described by Nesterenok and Yakubovich (2016).

In line 112, “high-eU inclusions” are mentioned without an explanation what this means. The explanation follows much later (line 291), but even there no definition of effective uranium is given.

Added a definition of eU along with an appropriate reference at the first occurrence in Lines 115-16.

“high-Ra helium” (line 118) is an incorrect expression. Ra ist the atmospheric ³He/⁴He ratio, which is a fixed value, thus there is no low- or high-Ra helium. If anything like that, it should be high R/Ra, but preferably (and easier to understand for non-experts) I would suggest "helium with high ³He/⁴He ratios".

Changed “high-Ra” to “with high ³He/⁴He ratios”.

In line 132, an exposure age is given with an error shown with 3 significant digits. Even if this is taken from the reference, it is inappropriate to give more than two significant digits for an uncertainty, because uncertainties are not precise numbers but just represent probabilities. Also, values should always be given with the same precision as the corresponding uncertainties. Therefore, this value should be rounded to 54⁺¹⁹_–13 ka. Similarly, in line 391 should be 29.64.6.

The value of 53.9^+19.0_–13.0 ka was stated directly as reported in Owen et al. (2014). We have revised it to 54⁺¹⁹_–13 ka as requested.

On a similar issue, a single 1 as the only significant digit (i.e. such as 1, 0.1, 0.01 etc.) is too little precision to show an error (Tables 2 and 3). E.g., 0.1 could have been rounded from anything between 0.05 and 0.14999, i.e. a factor of 3 difference in the actual precision of the measurement. In such cases it is necessary to give one more digit (for the corresponding value, too; see above).

Added one extra significant digit for all values with 1 as the only significant digit in Tables 2 and 3.

Perhaps some explanation of “isosurface renderings” (lines 224-225) would be appropriate (I don’t know what this means).

Added a sentence explaining how isosurfaces are constructed and rendered (Lines 230-232).

The term “³He excess” in line 258 is misleading. Usually, in cosmogenic ³He literature, it is used for the excess of ³He over a typical He composition, such as mantle He, but here it obviously just means a higher ³He concentration in grains with inclusions. Such equivocal use of terms should be avoided.

Changed “excess ³He” to “³He concentrations significantly in excess of the expected values”.

In line 316, the authors wrote “production of nucleogenic ³He from ¹⁰B is negligible". However, this process wasn't mentioned at all in section 2.1.

Amended the sentence in Line 101 to include ¹⁰Be.

In line 343, I don’t unerstand why the combined RTN production rate is higher than the sum of the individual rates from U and Th.

The sum was given incorrectly and has been corrected to 29 n/g/a. The subsequent numbers are still correct.

The method of correcting for different non-cosmogenic (or better: non-spallation-produced) components is generally clear, but I didn't understand (in lines 348-349) whether for each magnetite sample the nucleogenic ³He contribution was calculated based on its individual ⁴He closure age (but using mean U and Th concentrations) or whether a mean age was used for all samples. Anyway, these corrections have to be documented in a much better way. Rather than just showing uncorrected and corrected ³He concentrations in Table 4, each individual correction applied should be listed for each sample so the reader can retrace what the authors did. Also, there is no discussion at all about the estimated uncertainties of the corrections, though the higher uncertainties for corrected than uncorrected data show that some error estimate has been applied.

The documentation of the corrections was expanded by adding several sentences about the details of the correction process in Section 4.2.

Perhaps the major flaw of this manuscript, there is no discussion nor attempt of an explanation why the production rate of ³He in magnetite obtained here is almost a factor of two higher than previous model results and experimental determinations. Though the agreement with Kober et al. (2005) is excellent, it remains completely mysterious why Bryce and Farley (2002) obtained a much smaller rate (which agreed with Masarik and Reedy’s model calculations). The presence of inclusions in Bryce and Farley's samples can obviously not explain the discrepance, as they would lead to an overestimate rather than an underestimate of the production rate, as shown in this manuscript. Therefore, without any argument why earlier estimates were so much lower, the production rate value reported here cannot really be considered reliable. Just ignoring the lower production rate estimates as done in the Conclusions (line 465) doesn’t help.

We revised parts of Section 4.3 and expanded the discussion on the discrepancies between our production rate value and those of previous publications (Lines 406-430). In short, the modeled production rate of Masarik and Reedy (1996) has been revised based on new element-specific ³He/³H production rate ratios (Leya et al., 2004) producing a modeled production rate of 122 at/g/a (Kober et al., 2005) which is within uncertainty of our estimate. The low production rate calibration of Bryce and Farley (2002) cannot be conclusively explained, but we discuss several factors that might have contributed, such as a revised pyroxene production rate, ³He and ³H ejection differences between magnetite and pyroxene, and possible sample heterogeneity.

 Technical comments: (numbers refer to line numbers in the manuscript)

32 Calling the chemical procedures “dangerous" seems a bit strong. Of course HF (in particular) is a nasty substance, but using the appropriate precautions it can be handled routinely without being in permanent danger. So please, don’t exaggerate!Changed “dangerous” to “involving the use of hydrofluoric acid”

68        Remove comma after “³He data”.

Done.

70 Change “cosmogenic magnetite ³He” to "magnetite cosmogenic ³He" (not the magnetite is cosmogenic, but the ³He).

Changed to “cosmogenic ³He production rate in magnetite”.

236 Change "radiogenic" to "radioactive” (these elements are not products of radioactive decay, but they decay themselves).

Done.

240-241  Something wrong with a sentence; perhaps should be "Combined with … (Fig. 3), these data show ..."

Changed the period to a comma.

313 Should be “production of ³He”

Done.

319 “to yield solely the cosmogenic component”: Obviously what is meant is the component produced by cosmic ray spallation (+ muon interaction perhaps). The cosmogenic thermal neutron component is, however, cosmogenic too!

Changed to “cosmic ray spallation component”.

382 I assume this should be 1.7±0.6 Mat/g rather than at/g!

Yes. Changed to “Mat”.

391-392  It should be stated that ³He is measured in magnetite and ¹⁰Be in quartz, and the ratio labeled ³He_mt/¹⁰Be_qz or similar.

Changed to “³He_mag/¹⁰Be_qtz”.

460 “Knowledge of ... is important ..."

Done.

614 Remove dot after USA

Done.

655 inclusions

Done.

695 “… of ¹⁰Be measured in …” (remove first "in")

Done.

Table 4: Please indicate whether the ³He/⁴He ratio shown is the measured or corrected one. If measured, it would better be shown along with the other measured parameters, not after the corrected ³He.

Expanded the table caption to explain the ratio.

Reference list: There are some inconsistencies in the referencing style (e.g. compare the first two entries). More importantly, the following references cited in the text cannot be found in the reference list:

Blackburn et al. 2007

Amidon et al. 2008

Nesterenok and Yakubovich 2016

Ziegler et al. 2010

Amidon and Farley 2009

Huerta 2017

Phillips et al. 2001

Gayer et al. 2004

In addition, Balbas and Farley 2020 should be before, not after Balco et al. 2008

Thank you for the thorough check of the reference list We corrected the inconsistencies and added the missing references.

Response to referee comment RC2 by Pierre-Henri Blard

We thank Pierre-Henri Blard for his thorough and constructive review, and we especially appreciate the independent calculations confirming the nucleogenic corrections. We have responded to all points and made changes according to the reviewer’s suggestions. Author responses below are given in bold. Line numbers refer to the revised version of the manuscript.

General evaluation

Hofmann et al present here a new pre-screening method based on microCT as a mean to identify the amount and nature of solid inclusions in magnetites. These minerals were collected from a 1.75 m vertical profile below a geological surface that had been exposed for about 54 ka at Earth’s surface. Analyzing the helium isotopes released by melting these prescreen magnetites, they perform a whole inventory of the ³He and ⁴He present in these minerals and compare aliquots that bear inclusions with those that are inclusionfree. Authors notably show that the presence/absence of these inclusions has a major impact on the non-cosmogenic ³He: selecting inclusion-free magnetite thanks to this microCT pre-screening, they show that the inter-sample cosmogenic ³He scatter is reduced. Then, authors compute a spallation ³He production rate (of about 116 at/g/a) from inclusion-free magnetites, after cross-calibration with cosmogenic ¹⁰Be measured in the same vertical profile. This production rate is both in agreement with the previous value reported in iron oxides by Kober et al (EPSL, 2005) and the up-to-date value of 122±12 at/g/a reported for the commonly used olivine and pyroxenes phases (see synthesis by Martin et al., QG, 2017, https://crep.otelo.univ-lorraine.fr/#/productionrate).

            This new pre-screening method has a great potential since it may be very useful to reduce the scatter of cosmogenic ³He concentrations due to “exotic” ³He production process. Authors present convincing observations and perform the main relevant computations to evaluate and hierarchize the different sources of ³He and ⁴He in the analyzed magnetites. This contribution will be of interest for the readership of Geochronology. Several issues however need to be addressed during a revision stage, before the manuscript can become publishable. See more specific comments below.

Major concerns

1 – Calculation of (U-Th)/⁴He* closure ages

To compute (U-Th)/⁴He* closure ages for all magnetites, authors use a mean U and Th concentrations measured from three different samples only. This is a problem since the inter sample variability of U and Th concentrations may be large and mainly controlled by the amounts of bright inclusions (e.g. zircons), as shown and discussed in this manuscript.

(U-Th)/He closure ages and nucleogenic corrections were only calculated for aliquots without inclusions, as confirmed by microCT. Therefore the inter-sample variability of these aliquots is likely not affected by U and Th from inclusions.

I understand that measuring U and Th on the same aliquot than the one used for ³He and ⁴He analysis face technical limitations, but authors should better acknowledge their assumption of using U-Th measured in 3 samples. They should also better propagate the uncertainty arising from this calculation. Unrecognized U and Th variations may indeed affect the accuracy of the closure age calculation for a specific sample, and also, affect the accuracy and precision of the nucleogenic ³He correction.

We added uncertainties and a statement about the number of datapoints in Line 337. We also added several sentences about external uncertainties in Lines 338-345 to emphasize the limitations, and we provide additional details about the propagation of error due to the uncertainty in the closure ages in Lines 361-367. All uncertainties were propagated to the final corrected ³He concentrations. We added the individual corrections (with uncertainties) to Table 4 and added text to Section 4.2 to explain the intermediate steps involved in making the corrections. While the measurement procedure employed here did not allow sample recovery, we are planning on adjusting the procedure in the future to be able to recover degassed samples and measure Li/U/Th concentrations in the same aliquot, which should improve the accuracy of this method.

Please display the individual (U-Th)/⁴He* closure age of each sample adding a new column in Tables 2, 3 and 4, or at least in Table 4, the one presenting the unscreened magnetites.

We added (U-Th)/He closure ages and individual corrections to Table 4 which contains data for aliquots without inclusions. Closure ages and corrections for nucleogenic/CTN concentrations were not calculated for unscanned aliquots and aliquots with confirmed inclusions; therefore Tables 2 and 3 were not amended.

 2 – Nucleogenic ³He corrections

The amplitude and the uncertainty arising from the nucleogenic 3He correction should be better presented and discussed, notably taking into account the variance of the helium closure ages due to potential inter-samples and inter-aliquots variability of U and Th concentrations. Adding a column in the Tables with the sample specific nucleogenic ³He corrections (and attached uncertainty) could be useful.

We added separate columns for nucleogenic ³He and CTN corrections to Table 4.

More specifically, the computed nucleogenic ³He contributions reported at lines 348 are not in agreement with the nucleogenic production rates and closure ages given two lines above. Although I find the same nucleogenic production rate using my own code (based on reported major and trace, Li compositions for these rocks), multiplying these production rates with the given closure ages of 15 Ma and 130 Ma yield 0.3 Mat/g and 2.3 Mat/g, respectively (not 1 Mat/g and 7 Mat/g as stated lines 348). Please carefully check these calculations.

Thank you for double-checking our calculations. The nucleogenic corrections were incorrectly given in the text, but correctly applied to the data. We corrected the average nucleogenic concentrations in the manuscript and added several sentences describing the details of how the corrections were calculated and applied (Lines 362-367 and Lines 379-381).

3 – Data presentation in the online open access table

The online spreadsheet presenting the data as open format in the NSF website bears mistakes: for some samples, notably 17WW-01 aliquots, reported ³He concentrations are not similar to those reported in the Tables of the Geocrhonology paper. Please check all samples. Moreover, analytical uncertainties and helium blanks are not presented in this open database. I think they should be provided.

Thank you for spotting this inconsistency. The labels for sample 01 were shifted downwards by two places. We have corrected this error and checked the rest of the datapoints, which remained unaffected. Uncertainties and helium blank analyses were added to the dataset. An update of the EarthChem record has been requested.

Finally, I find quite strange to report ³He in at/g while ⁴He concentrations are given in nmol/g. My comment is here about the open database, but also for all sections, figures and Tables of the main article. Why not homogenizing these units?

See detailed comments below.

4 – Citation of many abstract conferences

Authors quote at least 4 conference abstracts (Bryce and Farley, 2002; Cox et al., 2017; Matsumara et al., 2014; Rogers et al., 2013) and one M.S. dissertation (Moore, 2017). Since those materials are not strictly peer reviewed, I wonder if this is compatible with the editorial policy of the Geochronology journal. If not, please, remove these references.

After conferring with the editors, we decided to keep the citations of conference abstracts in order to acknowledge previous work on the topic, even if not published in peer-reviewed sources. Such citations are permissible as per the journal’s editorial policy. We also kept Bryce and Farley (2002) since it provides the only other reference to a cosmogenic ³He production rate in magnetite besides Kober et al. (2005), and is needed in order to discuss the possible reasons for the divergence between our production rate estimate and that of Bryce and Farley (2002), as requested by the other reviewer.

5 – Price of microCT

What is the price and accessibility of such microCT analytical sessions?

We added the total time required to perform the scans (9 hr) to the Results (Line 212), which can be used by readers to estimate the amount of time required for their own samples. Rates vary widely based on the scan parameters, facility, and user, and they might change over time. Therefore, we do not want to report prices in the manuscript, which might not be applicable to every user or which might be out of date in the future.

Other concerns and suggestions

Line 15: indicate whether this “excess ³He” is due to magmatic ³He, inherited cosmogenic ³He or other sources of ³He.

Clarified as “in excess of the expected spallation production”.

Line 25: Give the uncertainties attached to this 53.5 ka ¹⁰Be exposure age.

Added the uncertainty of “±2.2” to the exposure age.

Line 29: “Since” implies causality, and this is strange to use this word here, no? If you agree, I suggest replacing “since” by “while”.

Deleted “Since” and added “therefore” to the subordinate clause.

Line 32: Helium measurement may also involve “dangerous task” and use of chemical products. I would remove this quite subjective statement.

Changed to “involving the use of hydrofluoric acid”.

Line 34: The necessary amount of quartz for ¹⁰Be analysis may be as low as 1 g, in the case of ¹⁰Be rich samples (> 10⁵ at/g) (e.g. Blard et al., EPSL 2013).

Changed to “require at least gram quantities and typically hundreds of grams”.

Line 67: “same soil samples…” Quote the previous ¹⁰Be study here.

Done.

Line 131: Given the uncertainties, 53.9 ka should be rounded to 54 ka. There are too many significant numbers.

Changed the value and the uncertainties to two significant digits.

Line 137: Did Owen et al., 2014 also compute an erosion rate from the ¹⁰Be profile inversion? If so, it can be useful to state this number here.

Added the erosion rate of 0.42 cm/ka reported in Owen et al. (2014).

Line 139-141: State here that you collected 12 samples in this vertical profile.

Done.

Line 150: Why disgarding the 100-250 microns fractions? Some studies (Williams et al., QSR, 2004; Puchol et al., Chem. Geol, 2017) demonstrated that the 100-250 microns granulometry bear much less magmatic ³He than larger fractions.

Since we did not find significant amounts of magmatic ³He in our samples (Sections 3.3.4 and 4.4) this was not a primary concern. We have made the observation that smaller grain size fractions have fewer inclusions (Lines 224-228). However, too many individual grains would have to be scanned in this grain size range to obtain any appreciable amount of sample material since mass scales to the third power with grain diameter (see also Section 4.1). In addition, small grain sizes might have the potential to adsorb atmospheric helium (Protin et al., 2016 GCA), which could lead to overestimation of the helium concentrations, as discussed in Lines 193-195.

Line 166-167: If possible, why not stating here the correspondence between these inclusions colors characterized by the microCT scan and the real nature of the inclusions?

A characterization of bright inclusions as apatite/zircon and dark inclusions as quartz/silicates is an interpretation based on multiple observations. We present this interpretation in the Discussion (Section 4.1).

Line 179-180: Does this statement imply that some elements that are abundant in zircons, such as U and Th, could have been underestimated?

These measurements likely represent elemental concentrations close to those of pure magnetite since the contribution from chemically resistant high-eU inclusions, such as zircon, is suppressed. The goal was to establish the elemental concentrations of magnetite, which are important for the corrections. We did not measure the U and Th concentrations of inclusions specifically. Calculations of the contributions of ³He from inclusions are based on assumed average values for apatite, zircon, quartz, and silicates (see Section 4.4).

Line 204: Did you analyze the ³He and  He concentrations in a solid standard, such as CRONUS-P?

No reference materials were analyzed in the same runs as the samples. Measurements were made relative to an air standard, which is regularly calibrated against a Caltech-internal gas standard. This is the same calibration as was used for the CRONUS interlaboratory comparison (Blard et al., 2015).

Line 250: Why not homogenize ³He and ⁴He units? Reporting both isotopes in atoms/g (or mol/g) is better.

The most useful and intuitive units for ³He in this context are at/g since this is the standard used for cosmogenic nuclides. Besides this exception, all other units are given in SI units or relative to a standard (R/Ra).

Line 271 to 276, lines 301 to 304, and Fig 11: 4 crushed aliquots (among 6) have higher samples used for ⁴He analysis.

It is not clear what this comment means.

Line 328: State here that these U and Th concentrations are average of 3 samples only, report the standard deviation (that is at least 30%) and propagate this uncertainty into closure ages (if not done).

Added uncertainties to the values in Line 337. This uncertainty was already propagated to the closure ages.

Line 328 to 330: Presentation of (U-Th)/⁴He* closure ages: as it is well shown by Fig. 9 and discussed latter, the inter-samples 4He variability is also controlled by the proportion of bright inclusions (zircons) and hence the eU of each aliquot. So, you should better acknowledge and discuss the limitation of your approach that consider mean U-Th concentrations from only 3 samples to compute individual (U-Th)/4He* closure ages.

We expanded the explanation and discussion of the (U-Th)/He closure ages and added ages to Table 4, as discussed above.

Line 390: The most up-to-date ¹⁰Be world average SLSHL production rate in 2021 is 4.11+-0.19 at/g/a with the time-dependent Lal/Stone factor (Martin et al., QG, 2017) https://crep.otelo.univ-lorraine.fr

Exchanged the value and reference and recalculated the ³He/¹⁰Be production ratio.

Line 397: The most up-to-date ³He world average SLSHL production rate in 2021 is 122+-12 at/g/a with the time-dependent Lal/Stone factor (Martin et al., QG, 2017) https://crep.otelo.univ-lorraine.fr. Contrary to the value reported in (Goehring et al., 2010), this updated P3 average includes radiogenic ⁴He corrections and new calibration sites published during the last 10 years.

Added the requested comparison and reference.

Line 400-401: In this discussion, the “hence” followed by a “consequently” seems to be a sort of circular reasoning.

Both sentences represent a progression of thought, so this does not reflect circular reasoning. The second sentence was revised to clarify this progression of ideas.

Line 405: “large”? What is the typical ejection distance of this reaction?

The value of 121 µm from Line 117 was inserted here and the sentence was expanded to include this number and clarify the relative length scales.

Line 414: Remove “and CTN” since you only discuss the nucleogenic ³He in this paragraph.

Done.

Line 425: Most of pyroxene have Li concentrations lower than 20 ppm.

Qualified the statement about potentially high Li concentrations in silicates.

Line 455: Shouldn’t you mention here the impact of nucleogenic ³He?

Done.

Line 460: I suggest you mention that this best granulometric window of 400-800 microns is the convolution of two opposites necessity: < 300 microns grains have the lowest inclusion amounts, while 600-800 microns are the biggest contributors of analyzed material (in volume).

Reworked the sentence to include these details.

Line 465: I suggest adding here than the computed P3 for magnetite is also compatible with the 122+-12 at/g/a production rates reported for the commonly used silicates (olivines and pyroxenes; Martin et al., QG, 2017) https://crep.otelo.univ-lorraine

Added as requested (Line 514).