On the viability of detrital Rb-Sr geochronology

Larson, Kyle Patrick; Dyck, Brendan; Shrestha, Sudip; Button, Mark; Najman, Yani

doi:https://doi.org/10.31219/osf.io/xhbj6

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https://doi.org/10.31219/osf.io/xhbj6

Preprints

20 Feb 2024

| 20 Feb 2024

On the viability of detrital Rb-Sr geochronology

Kyle Patrick Larson, Brendan Dyck, Sudip Shrestha, Mark Button, and Yani Najman

Abstract. Re-examination of sediment samples collected from the Bay of Bengal via laser-ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) Rb-Sr geochronology demonstrates the viability of the Rb-Sr system for use as a detrital chronometer. The age population defined by the Rb-Sr dates essentially reproduces that previously published for detrital ⁴⁰Ar/³⁹Ar dates. The assumed initial ⁸⁷Sr/⁸⁶Sr on the calculated population has some influence on the age of the final population, but that influence can be ameliorated by filtering for higher ⁸⁷Rb/⁸⁶Sr ratios. The ⁸⁷Rb/⁸⁶Sr ratio cut-off used for such filters to minimize the effect of initial ⁸⁷Sr/⁸⁶Sr on the final population is strongly dependant on the age of the material being analysed (i.e. ~> ⁸⁷Rb/⁸⁶Sr = 500 @ 250 Ma and ~>⁸⁷Rb/⁸⁶Sr = 50 @ 2500 Ma). Finally, Ti-in-biotite temperatures calculated based on data collected during LA-ICP-MS overlap with those calculated for the same material based on electron probe microanalyzer data demonstrating the potential for petrochronolgy based on the Rb-Sr system.

Received: 14 Feb 2024 – Discussion started: 20 Feb 2024

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Journal article(s) based on this preprint

02 Jul 2024

On the viability of detrital biotite Rb–Sr geochronology

Kyle P. Larson, Brendan Dyck, Sudip Shrestha, Mark Button, and Yani Najman

Geochronology, 6, 303–312, https://doi.org/10.5194/gchron-6-303-2024,https://doi.org/10.5194/gchron-6-303-2024, 2024

Short summary

Kyle Patrick Larson, Brendan Dyck, Sudip Shrestha, Mark Button, and Yani Najman

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2024-443', Stijn Glorie, 25 Mar 2024

This is a welcome contribution for the Rb-Sr geochronology community. The manuscript is generally clearly written and illustrated. However, I think some parts need to be expanded a bit for added clarity. I have a number of comments and suggestions in the attached pdf, but arguably most of these are minor edits. Below I summarize my more major comments:
1) This manuscript solely deals with biotite and I think this should be reflected in the title and abstract. Other (lower radiogenic) minerals might need different approaches.
2) A strategy of filtering based on high radiogenic nature is suggested. This indeed removes the reliance on an initial anchor. However, filtering in provenance studies likely creates bias (as different populations might have different degrees of radiogeneity). In my opinion, this needs to be better acknowledged (see comment in pdf).
3) Sample preparation: it is not specified how the micas were mounted. It is well known that mica-orientation has an influence on the apparant Rb-Sr dates. Were samples and standards both mounted parallel to ablation? If not, how did you deal with this issue?
4) Rb-Sr Method section: There is some information missing here. It`s written a bit too concise in my opinion. See the relevant section in the pdf, but generally: What was fluence and rep rate for NIST? Can you demonstrate similar enough DHF between NIST and biotite? It is not clear to me how the matrix correction was handled. I suggest you add some more description and use the terminology by Glorie et al. 2023, same journal. How confident are you that you can use Ar-Ar reference ages for your RMs? Some RMs return too high MSWDs (this is not acknolwedged/discussed). Which initial did you use for your RMs (cogenetic phase)? And finally, I missing a table that details instrumental conditions.
5) Thermometry method section: The assumed SiO2% is probably OK, but I think it`s good to evaluate the assumption. Our probe standard in Adelaide has 40% SiO2, Webmineral has 42% SiO2. And I`m sure you can find an even wider range. What is the effect of 7-8% difference on your internal standard to the calculated temperatures?
6) Thermometry tables: Looking at the EPMA data, some of your totals are very low. This is partly due to the inability of the probe to measure H (which might be high for the most weathered grains), but I`m also surprised that F wasn`t measured (which can be up to wt%). In any case, I think it`s difficult to make a case for the robustness of the Ti concentration when totals are low. Filtering for the most altered grains helps, but it`s probably not good enough (as nearly all totals are low). What might be good to do here, in my opinion, is to evaluate the sensitivity of the thermometer to the Ti concentration. From what I can see, temperatures don`t change much over the range of reported Ti concentrations, hinting that it`s rather insensitive to the Ti concentration over a natrual range in biotite. What I mean here is that the possible inaccuracy due to low totals might be within error considering the temperature derived from the Ti concentration. I think it would be good to add a few lines on this so that the reader has confidence in your approach, even though totals are low.
7) This is probably my biggest concern: The use of a bulk regression initial in a detrital sample. I understand you want to compare functions, but option 2 is just not valid as a start in my opinion. As you say above, you overconstrain the degree of freedom, based on a meaningless average of initial values from grains that might have come from different sources. I suggest to write that this method is not valid for detrital studies and not report results for it (including figure 2). The main reason why I think you shouldn`t report on that approach, even though you try to make a point with it in the discussion, is that other might copy that approach and think it`s OK to do. I think we need to avoid that opportunity.
8) Some lines are long and convoluted and somewhat difficult to read. I highlighted those in the pdf. Consider splitting up for more clarity.
9) The text related to plot 4 is a bit confusing in places. It might help to add your examples directly onto the figure to demonstrate how the reader should interpret the figure.
10) Lastly, there are several places where vague terms such as `high`, `low`, `younger` are used. I suggest to quantify those measures (see pdf).
I hope this is useful for the revisions. I`m available to the authors should they want to discuss anything during the revision.
Best wishes
Stijn Glorie

Citation: https://doi.org/10.5194/egusphere-2024-443-RC1
- AC2: 'Reply on RC1', Kyle Larson, 26 Apr 2024
  
  We thank the reviewer for their careful assessment of our study. Below we outline how we have incorporated their suggestions in our revised work.
  1) We have modified the title to be more specific to biotite (new text is bold):
  
  “On the viability of detrital biotite Rb-Sr geochronology”
  2) As noted by the reviewer, filtering of data is discussed and the effects of the filtering on the dataset collected and presented in this work is shown (Fig 2 – lower curves). The possibility of introducing bias through filtering is now acknowledged in various places in the study, for example (new text is bold):
  
  “Such filtering, however, could introduce bias toward more radiogenic populations, especially in younger material that has not had time to accumulate radiogenic child product (e.g. limiting the effect of initial ⁸⁷Sr/⁸⁶Sr to ~<5% requires filtering of ⁸⁷Rb/⁸⁶Sr > 500 @ 250 Ma and ⁸⁷Rb/⁸⁶Sr > 50 @ 2500 Ma).”
  3) We have added further information about sample preparation (new text is bold):
  
  “The biotite grains were either manually picked from sediment separates and mounted in epoxy, or the sediments were poured directly into an epoxy mount. Grains were not mounted with a preferred orientation resulting in a semi-random c-axis orientation (the natural shape of a mica lath favours a c-axis normal to the mounting surface). Mixed c-axis orientations may help avoid less optimal signal stability ablating parallel to the mica c-axis (Rösel and Zack 2022) that may effect the final Rb-Sr date calculated (Lloyd et al. 2023).”
  
  With regard to the reviewer’s comment “It is well known that mica-orientation has an influence on the apparant [sic] Rb-Sr dates.” So far as we are aware, the only published work to comment on the effect of grain orientation is Rösel and Zack (2022) wherein it is noted that mounting grains with c-axes perpendicular to the laser typically resulted in more stable signal than mounting grains with the c-axes parallel to the laser path. They do not, however, indicate that the orientation affects the final Rb-Sr date. That conclusion is mirrored by anecdotal experience in our lab. We do, however, acknowledge that a recent abstract was presented at the 2023 Goldschmidt meeting (Lyon) that does outline an affect of mica orientation on the resulting Rb-Sr date.
  4) We have included additional details in the method section as suggested by the reviewer including detailed instrument settings in the supplementary materials. Contrary to the reviewer’s comment, all reference dates cited are Rb-Sr dates, not Ar-Ar, and, as in the original text, the initial 87Sr/86Sr values are listed with the appropriate reference for further information. Yes, some of the materials of known age return MSWDs that are consistent with some degree of heterogeneity. We now refer to one of these (Mica 1B) as an ‘in-house’ reference material to help avoid implying it is perfectly homogeneous. It is important to note that MSWD is only one measure of population dispersion with some significant limitations related to the effect of outliers etc. Using an alternative statistical method, such as the ‘Robust Regression’ of Powell et al. (2020 – Geochronology), which better accommodates potential geologic dispersion, yields a single population isochron for all materials of known age, including using all 20 analyses of Mica 1B from the second run (992 ± 6 with a spine (s) = 1.12; max s for a single population of 20 analyses = 1.37).
  
  5) The SiO₂ assumption has little effect on the Ti-in-biotite temperatures calculated. Recalculating using 40 wt % SiO₂ yields Ti-in-biotite temperatures that are ~5 ˚C less than those calculated using 35 wt % SiO₂, well within the expected uncertainty of the method. This is now mentioned in the text (new text bold):
  
  “Ti-in-biotite temperatures calculated via LA-ICP-MS data generally range between ~ 650 and 725 ˚C for most samples (Fig. 3). The SiO₂ content used in the calculations has little effect on temperature. Increasing the SiO₂from 35 to 40 wt. % results in only a ~ 5 ˚C temperature change (Fig. S2), well within the expected uncertainty of the method (Henry, Guidotti, and Thomson 2005).”
  
  This relationship is also shown as a new supplementary figure (Fig. S2).
  
  6) In a newly added Fig. S1 we now show the potential effect of low totals on the Ti-in-biotite temperature. Changing the wt. % from 96 to 88 (the cut-off wt. % used in this study – now noted in the methods), while maintaining Mg# results in a commensurate change in calculated Ti-in-biotite temperature from ~680 to 695 ˚C. In addition, we now colour the biotite electron probe data in Fig. 3A and B by the totals to further demonstrate the apparently limited effect that the total wt. % has on calculated temperature.
  
  7) We recognize the potential unintended misuse of including the bulk regression-derived dates in the study. As suggested by both reviewers, we have removed dates calculated in this way from the study.
  
  8) We have attempted to improve the flow of these sections (highlighted in the reviewer’s marked up PDF).
  
  9) We have added additional annotations to help match the text in the discussion.
  
  10) Noted, and modified throughout.
  
  Citation: https://doi.org/10.5194/egusphere-2024-443-AC2
RC2:
'Comment on egusphere-2024-443 by Hugo Olierook', Hugo Olierook, 26 Mar 2024

I thank Larson and others for writing a stimulating contribution on the use of Rb-Sr geochronology for detrital mica studies, with a case study focussed on the Bay of Bengal. To my knowledge, this is the first study that obtains a statistically-sufficient number of analyses per sample (>100) on detrital K-bearing minerals, although I will add that our group also has a similar paper currently under review. Nevertheless, it is fantastic to see the field of detrital K-bearing minerals move forward so as to understand single-stage transport cycle processes (where mineral like zircon fail). I have three minor comments, the latter which is perhaps the most significant, for the authors to consider to improve their paper.

1. Filtering the data based on 87Rb/86Sr ratios. The issue with filtering in detrital mica datasets is that you may be inadvertently biasing your selection towards specific sources that have higher 87Rb/86Sr ratios. Whilst it is not possible to get precise dates for these lower 87Rb/86Sr grains, it would be less biased to keep these but propagating the uncertainty that results from the uncertainty on the initial 87Sr/86Sr ratio. A simple way of computing this would be to calculate the age with an initial ratio of 0.700 and 0.730 (or 0.760 for extreme cases), where the difference in age can be expressed as the uncertainty.

2. The totals measured on the EPMA data are very low (almost always <95%, and often much lower). What is missing here? I can see F and Cl were not measured, but I wouldn’t expect these to account for more than 1-2 wt. %. I normally achieve 93-97% (with F and Cl measured as extras), so I’m surprised that you’re averaging at around 90 wt.%. These low totals, and scaling up to 100% changes the Ti concentrations by ~10% on average. What are the ramifications on calculated temperatures?

3. The computation of isochron from multiple samples in a detrital sample is statistically invalid – it would only work if you had multiple spots from single grains where you build up individual isochrons per grain. It’s much better to use an approach like Rosel & Zack in their 2022 paper use on single grains by computing individual grain model dates with an assumed initial 87Sr/86Sr (like your approach 1 you suggest in L121). Option 2 (in L122) assumes that most of the detritus comes from a single population; whilst that may be true, it’s not something that would be applicable to all situations. Thus, I’m far more in favour of staying conservative, and using a conservative initial 87Sr/86Sr ratio. Something like 0.715 +/0.015 would work as that takes into account most natural crustal Sr compositions, although something skewed like 0.715 +0.045/-0.015 is also possible to take into a wider range of possibilities (but would yield non-Gaussian model dates). The key here, particularly with young grains that you have, is to propagate this uncertainty through. Perhaps the simplest way to do this is to compute what each grains’ date is using the higher, centroid and lower 87Sr/86Sr initials, use the centroid as the model date, and then compute the difference older and younger generates by the dates calculated using the lower and higher 87Sr/86 initials. If that’s a bit confusing, let me know, and we can chat more about it together.

Other minor comments that I think improve the paper – take or leave these as you like:
L7: Spelling error in “petrochronology”

L34-35: I would also consider the authors citing and incorporating a recent study that uses total fusion 40Ar/39Ar dating of micas that came out in mid-March (after Larson and others submitted their paper). They have a very low number of analyses per sample that clearly highlights the inefficiency of Ar/Ar for detrital studies: https://www.tandfonline.com/doi/full/10.1080/08120099.2024.2319105. I would also briefly discuss the issues of undetectable excess 40Ar in spot-based 40Ar/39Ar analyses, with Rb-Sr being superior in accuracy.

L36. “allows” rather than allow (The development allows)

L43. Switch the references around so they are in the correct order for the Lu-Hf and Rb-Sr ratios.

L80. This additional reference material is rather overdispersed (17 analyses with an MSWD of 3.7). In inverse space (albeit without the error correlations), I also get a much younger age at ~840 Ma. Could you check what the issues are here? Or is it simply that this other reference material isn’t quite great as a reference material?

L180. One of the aspects that’s not covered here is the limited number of white mica analyses that Yani and others collected per sample (~40-50); the sheer volume of analysis throughput of in situ Rb-Sr is just so superior to Ar-Ar data! Don’t get me wrong, I commend Yani for going to the effort of getting ~40-50 Ar-Ar analyses per sample – a significant effort – but it’s important to stress that biotite Rb-Sr is the way of the future for detrital studies. With multicollectors collision cell technologies for Rb-Sr (and K-Ca), I expect we’ll also see white mica become more of a staple as well.

L217. I really like the Ti-in-biotite approach, but would like to see more discussion around some of the lower temperature outliers earlier in the paper. Are these outliers because they are cooler, metamorphically-grown biotite (either during prograde or retrograde paths) or are they analytically problematic?

Fig. 1. I like the approach of trying to bracket the oldest and youngest grains but please label these age extremities on Fig. 1.

Fig. 3. Superscript the 22 in 22O in the figure caption. Change XMg to Mg# in the axis of panel B (given that’s what you refer to it in the rest of the text). In the caption, change whisker and box plot to box and whisker plot. On panel D, could you add error bars to evaluate whether the EPMA and laser based thermometry data overlap within uncertainty of the 1:1 line? I appreciate this may look cluttered though, but it would still be interesting to test this mathematically.

Hugo Olierook
26 March 2024

Citation: https://doi.org/10.5194/egusphere-2024-443-RC2
- AC1: 'Reply on RC2', Kyle Larson, 26 Apr 2024
  
  We thank the reviewer for their time and efforts in helping improve our study. Below we demonstrate how we have incorporated their suggestions.
  
  1) We appreciate the reviewers comments on filtering the data by 87Rb/86Sr. In Larson et al. 2023 (EPSL) of the hundreds of biotite analyses reported only a single analysis was <3. Similarly, in Qui et al. 2024 (JGSL), Camacho et al. 2020 (Geo. Cosmo. Acta), Camacho et al. 2012 (EPSL), and Rosel and Zack, 2022 (Geostandards and Geoanalytical Research) no biotite analyses had 87Rb/86Sr < 3. As such, the analyses excluded in the present work are most likely not biotite or have significant inclusions.
  
  Including analyses with lower ratios may not only include non-biotite material (which was not the target of the current study), but also would have very minimal statistical impact on the final interpretations. The two-point date calculated from an 87Rb/86Sr = 3 (± 5%) and an 87Sr/86Sr = 0.7156288 (± 5% - as calculated from a 15 Ma isochron through 0.715) with an intercept of 0.715 ± 0.015 (as suggested by the reviewer) would be 15 ± 840 Ma. Similarly, for 87Rb/86Sr = 2 (± 5%) and 1 (± 5%) along a 15 Ma isochron through 0.715, the uncertainties would be 1250 and 2510 Ma, respectively. If, however, the actual initial of the analyses was 0.730, the dates calculated based on the same 87Sr/86Sr intercept (0.715 ± 0.015) would be 370 ± 850 Ma, 550 ± 1270 Ma and 1080 ± 2523 Ma for 87Rb/86Sr = 3, 2, and 1 (±5%), respectively.
  
  Given the likelihood for analyses with 87Rb/86Sr <3 to not be biotite, and given the limited statistical effect on the age distributions, we have chosen to leave these analyses out.
  
  With respect to filtering for highly radiogenic analyses, e.g. 87Rb/86Sr <2500, we now include text that recognizes the potential bias (new text bold):
  
  “Such filtering, however, could introduce bias toward more radiogenic populations, especially in younger material that has not had time to accumulate radiogenic child product (e.g. limiting the effect of initial 87Sr/86Sr to ~<5% requires filtering of ⁸⁷Rb/⁸⁶Sr > 500 @ 250 Ma and ⁸⁷Rb/⁸⁶Sr > 50 @ 2500 Ma).”
  
  Moreover, as before, we show the effect of filtering in Fig. 2 (lower curves).
  
  2) As noted in the manuscript, the biotite, which were separated from samples collected in the Bay of Bengal, are affected by at least some degree of alteration/weathering leading to low totals. We now quantify the potential effect on Ti-temperatures in a new Fig. S1 and have modified Fig. 3 to be coloured by total wt% to show the net effect on our data specifically.
  
  3) The reviewer makes a valid point about how the dates calculated using the 2nd calculation method (bulk regression) as presented in the original paper. This same issue was raised by the other reviewer and, as such, we have removed it from the revised version of the study.
  
  All dates calculated using the two-point isochron method (as implemented in IsoplotR – Vermeesch, 2018 (GSF)) have full uncertainties propagated and presented in the supplementary information.
  
  L7) Fixed, thank you
  
  L34-35) We appreciate the reviewer’s comments. We have added the citation suggested (new text bold):
  
  “The coincidence of the isochron and spot-dates derived independent of the measured initial ⁸⁷Sr/⁸⁶Sr indicates that detrital Rb-Sr geochronology may be a viable alternative or addition to detrital ⁴⁰Ar/³⁹Ar geochronology (e.g. Crossingham et al. 2024), eliminating the potential time-consuming step of irradiation and permitting increased numbers of analyses.”
  
  With regard to excess 40Ar, this is discussed elsewhere in the manuscript and, as such, is not added here.
  
  L36) Fixed
  
  L43) Fixed
  
  L80) The material is a phlogopite of known age. It has not been demonstrated to be fully homogeneous at the scale of analysis. It is now referred to as an ‘in-house reference material’ to avoid confusion. Moreover, the assessment of over dispersion is just in the statistical context of MSWD. If an isochron is calculated with the robust regression of Powell et al. 2020 (Geochronology) using all of the analyses from MICA 1B, it defines a single population isochron at 992 ± 6 Ma – which overlaps the expected dates of 990 ± 6 Ma (Camacho et al. 2012 – EPSL)
  
  L180) We understand the reviewer’s comment. This advantage of detrital LA-ICP-MS Rb-Sr is now noted in the introduction (new text bold):
  
  “The coincidence of the isochron and spot-dates derived independent of the measured initial ⁸⁷Sr/⁸⁶Sr indicates that detrital Rb-Sr geochronology may be a viable alternative or addition to detrital ⁴⁰Ar/³⁹Ar geochronology (e.g. Crossingham et al. 2024), eliminating the potential time-consuming step of irradiation and facilitating increased numbers of analyses.”
  
  L217) We appreciate the reviewer’s interest in this. As noted previously in response to R1 we have now modified our Figure 3, which shows Ti-in-biotite temperatures, to include total weight % information. In the new figure, it is apparent that the majority of the lower T outliers have low total weight %.
  
  Fig 1) Done
  
  Fig 3) The 22O refers to the number of oxygen in the normalized biotite mineral formula, not an isotope. Changed to Mg# and box and whisker plot. We have not added the uncertainties in panel D as suggested. The calculated mean Euclidean distance is essentially a measure of the average distance away from the 1:1 line and, as noted in the text, it is suggested that such an uncertainty should be added to the temperature estimate.
  
  Citation: https://doi.org/10.5194/egusphere-2024-443-AC1

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2024-443', Stijn Glorie, 25 Mar 2024

This is a welcome contribution for the Rb-Sr geochronology community. The manuscript is generally clearly written and illustrated. However, I think some parts need to be expanded a bit for added clarity. I have a number of comments and suggestions in the attached pdf, but arguably most of these are minor edits. Below I summarize my more major comments:
1) This manuscript solely deals with biotite and I think this should be reflected in the title and abstract. Other (lower radiogenic) minerals might need different approaches.
2) A strategy of filtering based on high radiogenic nature is suggested. This indeed removes the reliance on an initial anchor. However, filtering in provenance studies likely creates bias (as different populations might have different degrees of radiogeneity). In my opinion, this needs to be better acknowledged (see comment in pdf).
3) Sample preparation: it is not specified how the micas were mounted. It is well known that mica-orientation has an influence on the apparant Rb-Sr dates. Were samples and standards both mounted parallel to ablation? If not, how did you deal with this issue?
4) Rb-Sr Method section: There is some information missing here. It`s written a bit too concise in my opinion. See the relevant section in the pdf, but generally: What was fluence and rep rate for NIST? Can you demonstrate similar enough DHF between NIST and biotite? It is not clear to me how the matrix correction was handled. I suggest you add some more description and use the terminology by Glorie et al. 2023, same journal. How confident are you that you can use Ar-Ar reference ages for your RMs? Some RMs return too high MSWDs (this is not acknolwedged/discussed). Which initial did you use for your RMs (cogenetic phase)? And finally, I missing a table that details instrumental conditions.
5) Thermometry method section: The assumed SiO2% is probably OK, but I think it`s good to evaluate the assumption. Our probe standard in Adelaide has 40% SiO2, Webmineral has 42% SiO2. And I`m sure you can find an even wider range. What is the effect of 7-8% difference on your internal standard to the calculated temperatures?
6) Thermometry tables: Looking at the EPMA data, some of your totals are very low. This is partly due to the inability of the probe to measure H (which might be high for the most weathered grains), but I`m also surprised that F wasn`t measured (which can be up to wt%). In any case, I think it`s difficult to make a case for the robustness of the Ti concentration when totals are low. Filtering for the most altered grains helps, but it`s probably not good enough (as nearly all totals are low). What might be good to do here, in my opinion, is to evaluate the sensitivity of the thermometer to the Ti concentration. From what I can see, temperatures don`t change much over the range of reported Ti concentrations, hinting that it`s rather insensitive to the Ti concentration over a natrual range in biotite. What I mean here is that the possible inaccuracy due to low totals might be within error considering the temperature derived from the Ti concentration. I think it would be good to add a few lines on this so that the reader has confidence in your approach, even though totals are low.
7) This is probably my biggest concern: The use of a bulk regression initial in a detrital sample. I understand you want to compare functions, but option 2 is just not valid as a start in my opinion. As you say above, you overconstrain the degree of freedom, based on a meaningless average of initial values from grains that might have come from different sources. I suggest to write that this method is not valid for detrital studies and not report results for it (including figure 2). The main reason why I think you shouldn`t report on that approach, even though you try to make a point with it in the discussion, is that other might copy that approach and think it`s OK to do. I think we need to avoid that opportunity.
8) Some lines are long and convoluted and somewhat difficult to read. I highlighted those in the pdf. Consider splitting up for more clarity.
9) The text related to plot 4 is a bit confusing in places. It might help to add your examples directly onto the figure to demonstrate how the reader should interpret the figure.
10) Lastly, there are several places where vague terms such as `high`, `low`, `younger` are used. I suggest to quantify those measures (see pdf).
I hope this is useful for the revisions. I`m available to the authors should they want to discuss anything during the revision.
Best wishes
Stijn Glorie

Citation: https://doi.org/10.5194/egusphere-2024-443-RC1
- AC2: 'Reply on RC1', Kyle Larson, 26 Apr 2024
  
  We thank the reviewer for their careful assessment of our study. Below we outline how we have incorporated their suggestions in our revised work.
  1) We have modified the title to be more specific to biotite (new text is bold):
  
  “On the viability of detrital biotite Rb-Sr geochronology”
  2) As noted by the reviewer, filtering of data is discussed and the effects of the filtering on the dataset collected and presented in this work is shown (Fig 2 – lower curves). The possibility of introducing bias through filtering is now acknowledged in various places in the study, for example (new text is bold):
  
  “Such filtering, however, could introduce bias toward more radiogenic populations, especially in younger material that has not had time to accumulate radiogenic child product (e.g. limiting the effect of initial ⁸⁷Sr/⁸⁶Sr to ~<5% requires filtering of ⁸⁷Rb/⁸⁶Sr > 500 @ 250 Ma and ⁸⁷Rb/⁸⁶Sr > 50 @ 2500 Ma).”
  3) We have added further information about sample preparation (new text is bold):
  
  “The biotite grains were either manually picked from sediment separates and mounted in epoxy, or the sediments were poured directly into an epoxy mount. Grains were not mounted with a preferred orientation resulting in a semi-random c-axis orientation (the natural shape of a mica lath favours a c-axis normal to the mounting surface). Mixed c-axis orientations may help avoid less optimal signal stability ablating parallel to the mica c-axis (Rösel and Zack 2022) that may effect the final Rb-Sr date calculated (Lloyd et al. 2023).”
  
  With regard to the reviewer’s comment “It is well known that mica-orientation has an influence on the apparant [sic] Rb-Sr dates.” So far as we are aware, the only published work to comment on the effect of grain orientation is Rösel and Zack (2022) wherein it is noted that mounting grains with c-axes perpendicular to the laser typically resulted in more stable signal than mounting grains with the c-axes parallel to the laser path. They do not, however, indicate that the orientation affects the final Rb-Sr date. That conclusion is mirrored by anecdotal experience in our lab. We do, however, acknowledge that a recent abstract was presented at the 2023 Goldschmidt meeting (Lyon) that does outline an affect of mica orientation on the resulting Rb-Sr date.
  4) We have included additional details in the method section as suggested by the reviewer including detailed instrument settings in the supplementary materials. Contrary to the reviewer’s comment, all reference dates cited are Rb-Sr dates, not Ar-Ar, and, as in the original text, the initial 87Sr/86Sr values are listed with the appropriate reference for further information. Yes, some of the materials of known age return MSWDs that are consistent with some degree of heterogeneity. We now refer to one of these (Mica 1B) as an ‘in-house’ reference material to help avoid implying it is perfectly homogeneous. It is important to note that MSWD is only one measure of population dispersion with some significant limitations related to the effect of outliers etc. Using an alternative statistical method, such as the ‘Robust Regression’ of Powell et al. (2020 – Geochronology), which better accommodates potential geologic dispersion, yields a single population isochron for all materials of known age, including using all 20 analyses of Mica 1B from the second run (992 ± 6 with a spine (s) = 1.12; max s for a single population of 20 analyses = 1.37).
  
  5) The SiO₂ assumption has little effect on the Ti-in-biotite temperatures calculated. Recalculating using 40 wt % SiO₂ yields Ti-in-biotite temperatures that are ~5 ˚C less than those calculated using 35 wt % SiO₂, well within the expected uncertainty of the method. This is now mentioned in the text (new text bold):
  
  “Ti-in-biotite temperatures calculated via LA-ICP-MS data generally range between ~ 650 and 725 ˚C for most samples (Fig. 3). The SiO₂ content used in the calculations has little effect on temperature. Increasing the SiO₂from 35 to 40 wt. % results in only a ~ 5 ˚C temperature change (Fig. S2), well within the expected uncertainty of the method (Henry, Guidotti, and Thomson 2005).”
  
  This relationship is also shown as a new supplementary figure (Fig. S2).
  
  6) In a newly added Fig. S1 we now show the potential effect of low totals on the Ti-in-biotite temperature. Changing the wt. % from 96 to 88 (the cut-off wt. % used in this study – now noted in the methods), while maintaining Mg# results in a commensurate change in calculated Ti-in-biotite temperature from ~680 to 695 ˚C. In addition, we now colour the biotite electron probe data in Fig. 3A and B by the totals to further demonstrate the apparently limited effect that the total wt. % has on calculated temperature.
  
  7) We recognize the potential unintended misuse of including the bulk regression-derived dates in the study. As suggested by both reviewers, we have removed dates calculated in this way from the study.
  
  8) We have attempted to improve the flow of these sections (highlighted in the reviewer’s marked up PDF).
  
  9) We have added additional annotations to help match the text in the discussion.
  
  10) Noted, and modified throughout.
  
  Citation: https://doi.org/10.5194/egusphere-2024-443-AC2
RC2:
'Comment on egusphere-2024-443 by Hugo Olierook', Hugo Olierook, 26 Mar 2024

I thank Larson and others for writing a stimulating contribution on the use of Rb-Sr geochronology for detrital mica studies, with a case study focussed on the Bay of Bengal. To my knowledge, this is the first study that obtains a statistically-sufficient number of analyses per sample (>100) on detrital K-bearing minerals, although I will add that our group also has a similar paper currently under review. Nevertheless, it is fantastic to see the field of detrital K-bearing minerals move forward so as to understand single-stage transport cycle processes (where mineral like zircon fail). I have three minor comments, the latter which is perhaps the most significant, for the authors to consider to improve their paper.

1. Filtering the data based on 87Rb/86Sr ratios. The issue with filtering in detrital mica datasets is that you may be inadvertently biasing your selection towards specific sources that have higher 87Rb/86Sr ratios. Whilst it is not possible to get precise dates for these lower 87Rb/86Sr grains, it would be less biased to keep these but propagating the uncertainty that results from the uncertainty on the initial 87Sr/86Sr ratio. A simple way of computing this would be to calculate the age with an initial ratio of 0.700 and 0.730 (or 0.760 for extreme cases), where the difference in age can be expressed as the uncertainty.

2. The totals measured on the EPMA data are very low (almost always <95%, and often much lower). What is missing here? I can see F and Cl were not measured, but I wouldn’t expect these to account for more than 1-2 wt. %. I normally achieve 93-97% (with F and Cl measured as extras), so I’m surprised that you’re averaging at around 90 wt.%. These low totals, and scaling up to 100% changes the Ti concentrations by ~10% on average. What are the ramifications on calculated temperatures?

3. The computation of isochron from multiple samples in a detrital sample is statistically invalid – it would only work if you had multiple spots from single grains where you build up individual isochrons per grain. It’s much better to use an approach like Rosel & Zack in their 2022 paper use on single grains by computing individual grain model dates with an assumed initial 87Sr/86Sr (like your approach 1 you suggest in L121). Option 2 (in L122) assumes that most of the detritus comes from a single population; whilst that may be true, it’s not something that would be applicable to all situations. Thus, I’m far more in favour of staying conservative, and using a conservative initial 87Sr/86Sr ratio. Something like 0.715 +/0.015 would work as that takes into account most natural crustal Sr compositions, although something skewed like 0.715 +0.045/-0.015 is also possible to take into a wider range of possibilities (but would yield non-Gaussian model dates). The key here, particularly with young grains that you have, is to propagate this uncertainty through. Perhaps the simplest way to do this is to compute what each grains’ date is using the higher, centroid and lower 87Sr/86Sr initials, use the centroid as the model date, and then compute the difference older and younger generates by the dates calculated using the lower and higher 87Sr/86 initials. If that’s a bit confusing, let me know, and we can chat more about it together.

Other minor comments that I think improve the paper – take or leave these as you like:
L7: Spelling error in “petrochronology”

L34-35: I would also consider the authors citing and incorporating a recent study that uses total fusion 40Ar/39Ar dating of micas that came out in mid-March (after Larson and others submitted their paper). They have a very low number of analyses per sample that clearly highlights the inefficiency of Ar/Ar for detrital studies: https://www.tandfonline.com/doi/full/10.1080/08120099.2024.2319105. I would also briefly discuss the issues of undetectable excess 40Ar in spot-based 40Ar/39Ar analyses, with Rb-Sr being superior in accuracy.

L36. “allows” rather than allow (The development allows)

L43. Switch the references around so they are in the correct order for the Lu-Hf and Rb-Sr ratios.

L80. This additional reference material is rather overdispersed (17 analyses with an MSWD of 3.7). In inverse space (albeit without the error correlations), I also get a much younger age at ~840 Ma. Could you check what the issues are here? Or is it simply that this other reference material isn’t quite great as a reference material?

L180. One of the aspects that’s not covered here is the limited number of white mica analyses that Yani and others collected per sample (~40-50); the sheer volume of analysis throughput of in situ Rb-Sr is just so superior to Ar-Ar data! Don’t get me wrong, I commend Yani for going to the effort of getting ~40-50 Ar-Ar analyses per sample – a significant effort – but it’s important to stress that biotite Rb-Sr is the way of the future for detrital studies. With multicollectors collision cell technologies for Rb-Sr (and K-Ca), I expect we’ll also see white mica become more of a staple as well.

L217. I really like the Ti-in-biotite approach, but would like to see more discussion around some of the lower temperature outliers earlier in the paper. Are these outliers because they are cooler, metamorphically-grown biotite (either during prograde or retrograde paths) or are they analytically problematic?

Fig. 1. I like the approach of trying to bracket the oldest and youngest grains but please label these age extremities on Fig. 1.

Fig. 3. Superscript the 22 in 22O in the figure caption. Change XMg to Mg# in the axis of panel B (given that’s what you refer to it in the rest of the text). In the caption, change whisker and box plot to box and whisker plot. On panel D, could you add error bars to evaluate whether the EPMA and laser based thermometry data overlap within uncertainty of the 1:1 line? I appreciate this may look cluttered though, but it would still be interesting to test this mathematically.

Hugo Olierook
26 March 2024

Citation: https://doi.org/10.5194/egusphere-2024-443-RC2
- AC1: 'Reply on RC2', Kyle Larson, 26 Apr 2024
  
  We thank the reviewer for their time and efforts in helping improve our study. Below we demonstrate how we have incorporated their suggestions.
  
  1) We appreciate the reviewers comments on filtering the data by 87Rb/86Sr. In Larson et al. 2023 (EPSL) of the hundreds of biotite analyses reported only a single analysis was <3. Similarly, in Qui et al. 2024 (JGSL), Camacho et al. 2020 (Geo. Cosmo. Acta), Camacho et al. 2012 (EPSL), and Rosel and Zack, 2022 (Geostandards and Geoanalytical Research) no biotite analyses had 87Rb/86Sr < 3. As such, the analyses excluded in the present work are most likely not biotite or have significant inclusions.
  
  Including analyses with lower ratios may not only include non-biotite material (which was not the target of the current study), but also would have very minimal statistical impact on the final interpretations. The two-point date calculated from an 87Rb/86Sr = 3 (± 5%) and an 87Sr/86Sr = 0.7156288 (± 5% - as calculated from a 15 Ma isochron through 0.715) with an intercept of 0.715 ± 0.015 (as suggested by the reviewer) would be 15 ± 840 Ma. Similarly, for 87Rb/86Sr = 2 (± 5%) and 1 (± 5%) along a 15 Ma isochron through 0.715, the uncertainties would be 1250 and 2510 Ma, respectively. If, however, the actual initial of the analyses was 0.730, the dates calculated based on the same 87Sr/86Sr intercept (0.715 ± 0.015) would be 370 ± 850 Ma, 550 ± 1270 Ma and 1080 ± 2523 Ma for 87Rb/86Sr = 3, 2, and 1 (±5%), respectively.
  
  Given the likelihood for analyses with 87Rb/86Sr <3 to not be biotite, and given the limited statistical effect on the age distributions, we have chosen to leave these analyses out.
  
  With respect to filtering for highly radiogenic analyses, e.g. 87Rb/86Sr <2500, we now include text that recognizes the potential bias (new text bold):
  
  “Such filtering, however, could introduce bias toward more radiogenic populations, especially in younger material that has not had time to accumulate radiogenic child product (e.g. limiting the effect of initial 87Sr/86Sr to ~<5% requires filtering of ⁸⁷Rb/⁸⁶Sr > 500 @ 250 Ma and ⁸⁷Rb/⁸⁶Sr > 50 @ 2500 Ma).”
  
  Moreover, as before, we show the effect of filtering in Fig. 2 (lower curves).
  
  2) As noted in the manuscript, the biotite, which were separated from samples collected in the Bay of Bengal, are affected by at least some degree of alteration/weathering leading to low totals. We now quantify the potential effect on Ti-temperatures in a new Fig. S1 and have modified Fig. 3 to be coloured by total wt% to show the net effect on our data specifically.
  
  3) The reviewer makes a valid point about how the dates calculated using the 2nd calculation method (bulk regression) as presented in the original paper. This same issue was raised by the other reviewer and, as such, we have removed it from the revised version of the study.
  
  All dates calculated using the two-point isochron method (as implemented in IsoplotR – Vermeesch, 2018 (GSF)) have full uncertainties propagated and presented in the supplementary information.
  
  L7) Fixed, thank you
  
  L34-35) We appreciate the reviewer’s comments. We have added the citation suggested (new text bold):
  
  “The coincidence of the isochron and spot-dates derived independent of the measured initial ⁸⁷Sr/⁸⁶Sr indicates that detrital Rb-Sr geochronology may be a viable alternative or addition to detrital ⁴⁰Ar/³⁹Ar geochronology (e.g. Crossingham et al. 2024), eliminating the potential time-consuming step of irradiation and permitting increased numbers of analyses.”
  
  With regard to excess 40Ar, this is discussed elsewhere in the manuscript and, as such, is not added here.
  
  L36) Fixed
  
  L43) Fixed
  
  L80) The material is a phlogopite of known age. It has not been demonstrated to be fully homogeneous at the scale of analysis. It is now referred to as an ‘in-house reference material’ to avoid confusion. Moreover, the assessment of over dispersion is just in the statistical context of MSWD. If an isochron is calculated with the robust regression of Powell et al. 2020 (Geochronology) using all of the analyses from MICA 1B, it defines a single population isochron at 992 ± 6 Ma – which overlaps the expected dates of 990 ± 6 Ma (Camacho et al. 2012 – EPSL)
  
  L180) We understand the reviewer’s comment. This advantage of detrital LA-ICP-MS Rb-Sr is now noted in the introduction (new text bold):
  
  “The coincidence of the isochron and spot-dates derived independent of the measured initial ⁸⁷Sr/⁸⁶Sr indicates that detrital Rb-Sr geochronology may be a viable alternative or addition to detrital ⁴⁰Ar/³⁹Ar geochronology (e.g. Crossingham et al. 2024), eliminating the potential time-consuming step of irradiation and facilitating increased numbers of analyses.”
  
  L217) We appreciate the reviewer’s interest in this. As noted previously in response to R1 we have now modified our Figure 3, which shows Ti-in-biotite temperatures, to include total weight % information. In the new figure, it is apparent that the majority of the lower T outliers have low total weight %.
  
  Fig 1) Done
  
  Fig 3) The 22O refers to the number of oxygen in the normalized biotite mineral formula, not an isotope. Changed to Mg# and box and whisker plot. We have not added the uncertainties in panel D as suggested. The calculated mean Euclidean distance is essentially a measure of the average distance away from the 1:1 line and, as noted in the text, it is suggested that such an uncertainty should be added to the temperature estimate.
  
  Citation: https://doi.org/10.5194/egusphere-2024-443-AC1

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

ED: Publish subject to technical corrections (11 May 2024) by Axel Schmitt

ED: Publish subject to technical corrections (11 May 2024) by Klaus Mezger (Editor)

Dear authors
the paper is now accepted for publication in GEOCHRONOLOGY. The content is fine, however the presentation is wanting.
As pointed out by the AE some corrections are needed. I have a few addtional ones.
As it is obvious from the text, the first or native language of the authors is not English. This may account for the numerous grammar, style and wording mistakes. I understand that it is always a challenge to write text in a foreign languaage (I can relate to this "problem" very well) , but English is the language of communication in GEOCHRONOLOGY. I recommend two options: ask someone with a good command of the English language to read the paper and make corrections, or just run the the text through DEEPL.
l 14 dependent (adjective) not dependant (noun)
l 37 a non-radiogenic intercept: awkward wording, do you mean: initial isotope composition?
l 39: can be regressed through : do you mean: can be regressed to define...
l 40: an initial, non radiogenic intercept. Tautology, the intercept is by definition unradiogenic. (non radiogenic: not a proper term)
54 Ti, like in the rest of the text
l 56 test the viability of detrital Rb-Sr, : word missing after Rb-Sr, there is not such thing as detrital Rb-Sr, may be the Rb-Sr systematics of detrital biotite...
l67 and Hogmalm et al. (Hogmalm et al. 2017) : should be and Hogmalm et al. 2017)
l 86: granulite grade : there is no such thing as granulite grade, you mean granulite facies.
l 87 .. to molar weight per cation TiO2 equivalent : TiO2 is not a cation, Ti is, what do you mean here?
l 88 MTiO2 = molar weight per cation: TiO2 is not a cation
l 110 kaolinite, you mean the mineral not the rock.
l 136 ashed grey lines : they are black
l 160 Tautology, value of the initial intercept can : either: value of the initial isotope composition or value of the intercept can
l 184 Larson, Button, et al. 2023) : correct reference
l 189 (Jager, Niggli, and Wenk 1967; Armstrong, Jäger, and Eberhardt 1966: correct references, only one author and then et al!
l 191: this variability or the variability
l 210 the temperature is not measured in, it is derived from or estimated from.

You might consider looking at the following studies that show nicely that your Rb-Sr dating of biotite gives more robust ages than Ar-Ar. This makes your study even more significant when applying your method to detrital biotite. (no need to cite these paper, just look at them)
Willigers, B.J.A., Mezger, K. and Baker, J.A., 2004. Development of high precision Rb–Sr phlogopite and biotite geochronology; an alternative to 40Ar/39Ar tri-octahedral mica dating. Chemical Geology, 213(4), pp.339-358.
Scibiorski, E., Jourdan, F., Mezger, K., Tohver, E. and Vollstaedt, H., 2021. Cryptic excess argon in metamorphic biotite: Anomalously old 40Ar/39Ar plateau dates tested with Rb/Sr thermochronology and Ar diffusion modelling. Geochimica et cosmochimica acta, 315, pp.1-23.

This is a nice study that will be of interest to many geologists! Thank you for submitting it to GEOCHRONOLOGY.

Klaus Mezger

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AR by Kyle Larson on behalf of the Authors (13 May 2024) Author's response Manuscript

Journal article(s) based on this preprint

02 Jul 2024

On the viability of detrital biotite Rb–Sr geochronology

Kyle P. Larson, Brendan Dyck, Sudip Shrestha, Mark Button, and Yani Najman

Geochronology, 6, 303–312, https://doi.org/10.5194/gchron-6-303-2024,https://doi.org/10.5194/gchron-6-303-2024, 2024

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Kyle Patrick Larson, Brendan Dyck, Sudip Shrestha, Mark Button, and Yani Najman

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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.

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This study demonstrates the utility of the recently developed laser ablation-based Rb-Sr geochronology methodology to investigate the rates of exhumation and burial in active mountain building systems. It is further demonstrated that additional chemical data collected during spot analyses can be used to determine temperatures recorded in biotite. The method used has advantages over traditional methods in speed, ease of acquisition and the ability to collect additional chemical information.


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