Technical Note: Pb-loss-aware Eruption/Deposition Age Estimation

Keller, C. Brenhin

doi:https://doi.org/10.5194/gchron-2023-9

Preprints

https://doi.org/10.5194/gchron-2023-9

Preprints

02 May 2023

| 02 May 2023

Status: this preprint is currently under review for the journal GChron.

Technical Note: Pb-loss-aware Eruption/Deposition Age Estimation

C. Brenhin Keller

Abstract. Interpreting overdispersed crystallization and closure age spectra has become a problem of significant import in high-precision geochronology. While Bayesian eruption age estimation appears to provide one promising avenue for the statistical interpretation of such dispersed datasets, existing methods critically hinge on an assumption of fully closed-system behavior after the time of eruption. However, given the presence of two independent decay systems with distinct responses to open-system behavior, the U/Pb system provides in principle the possibility of quantifying and potentially even constraining the timing of Pb-loss. Here we present a method for Pb-loss-aware eruption age estimation, that explicitly models not only the duration of crystallization but also the timing and magnitude of Pb-loss given accurate ²⁰⁶Pb/²³⁸U and ²⁰⁷Pb/²³⁵U isotopic ratios and covariances, leading to eruption age estimates that are potentially robust to post-eruptive Pb-loss. Further applications to detrital zircon data are considered.

Received: 12 Apr 2023 – Discussion started: 02 May 2023

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C. Brenhin Keller

Status: final response (author comments only)

RC1:
'Comment on gchron-2023-9', Pieter Vermeesch, 01 Jun 2023

This manuscript modifies the eruption age estimation algorithm of Keller et al. (2018) to accommodate Pb-loss. The Keller et al. (2018) model uses a Markov Chain Monte Carlo (MCMC) inversion algorithm to estimate the onset (saturation) and termination (eruption) of zircon crystallisation, as parameterised by either a theoretical or an empirical magma evolution model. The new paper adds a third parameter to the inversion, namely the time of partial Pb loss. The topic of the manuscript is suitable for a technical note in GChron. However, I do have a number of substantive comments.
The manuscript provides surprisingly little technical detail for a technical note. It does not contain a single equation. Perhaps this is because the maths are similar to Keller et al. (2018)? Nevertheless, the lack of detail left me unable to answer a number of important questions.
From the examples, it appears that the algorithm works in “Wetherill space”, and does not use 204Pb or 208Pb as a proxy for common Pb. Is this correct? If so, why is the full Pb composition not taken into account?
Line 60 of the manuscript explains that the algorithm “Project[s] along a Pb-loss array from your proposed time of Pb loss, through each analysis, back to Concordia”. This does not look right to me. It implies that the measured isotopic ratios are equal to the true ratios. In reality, the true isotopic ratios are unknown and must be estimated from the data. As a counter example, suppose that:
a) the crystallisation sequence follows a uniform distribution between 1050 and 1000 Ma.
b) we set the prior distribution for the crystallisation history equal to this true solution (in the real world this is impossible, but in a thought experiment we should be able to do so).
c) 50% of the radiogenic Pb was lost at 0 Ma.
then the true Pb207/U235 and Pb206/U238 ratios of the youngest (syn-eruptive) age should be 0.8387 and 0.0839, respectively. Now suppose that the measured Pb207/U235 and Pb206/U238 ratios are 0.8380 and 0.0839. Then a line through these measurements and the origin of the Wetherill diagram (t=0 Ma) would project outside the prior distribution. In other words: the measurements are impossible! As a result, the true geological history would be excluded from the collection or posterior solutions.
My intuition tells me that any mixing line between any point within the prior distribution of Pb loss and the prior distribution of zircon crystallisation should be allowed. In the counter example, a mixing line between the origin and the composition at 1000 Ma would not go right through the measurement, but it would pass by it close enough to be retained within the posterior ensemble of solutions.
Other comments:
Line 8: I would suggest changing “covariances” to “(co)variances”.
Line 9 of the abstract should be expanded. To paraphrase K.K. Landes: an abstract is not an outline but a summary of a paper.
Figure 1: there are duplicate tick marks on the concordia line. Figures 2a and 4a have the same problem.
Figure 1, third line of the caption: typo (“uncertaities”)
Lines 44-45: “While a traditional discordia array could be fitted to the entire dataset, potentially eliminating the problem of Pb loss, this would be as statistically invalid as a traditional weighted mean given the geologic dispersion of the data”
-> this comment does not apply to “non-traditional” discordia regression. For example, IsoplotR implements a “model-3” regression model that parameterises overdispersion using an excess variance component of the lower age intercept. A similar solution could be formulated for the partial Pb-loss problem.
Line 66: it would be useful to show the actual likelihood function, perhaps in an appendix.
Line 68: please remove the double brackets here and elsewhere in the manuscript.
Line 71: missing references for Julia and Isoplot.jl
Lines 96-97: duplication of “broad”.
Line 114: are decay constant uncertainties accounted for in the MCMC model?
Line 144: “in summary”?
Figure 5: This case study raises all kinds of new questions:
1. I am not sure if this is the best example, as there is hardly any discordance visible in it.
2. What does a “Normal prior of 0 +/- 30% Pb-loss extent” mean? Is it possible that some grains have gained 30% Pb?
3. The cloud of discordia lines implies that only the youngest grains experienced Pb loss. Why would this be?
4. Following up on 3, if all grains are allowed to have experienced Pb loss, then each should be allowed to have a different common-Pb loss intercept. This problem is unsolvable. If only modern Pb loss is allowed, then the MCMC solution is no different than projecting the data onto concordia and applying a conventional MDA algorithm to the projected data.
In conclusion, I do not think that the MCMC algorithm is ready to be used in detrital geochronology.
Line 150: should be “interpreted by Karlstrom et al. (2018)”

Citation: https://doi.org/10.5194/gchron-2023-9-RC1
- AC1: 'Reply to RC1', Brenhin Keller, 14 Nov 2023
  
  Many thanks for the detailed and thoughtful review! Among other points, you are quite correct that more equations would do well in a paper of this style. In addition, I will also attempt to
  
  1) Better explain the proposed method and how it would deal with the thought experiment you outline, particularly including graphically
  
  2) Attempt to compare the results given with the present method with a more exact (but more computationally expensive) method integrating the probability density of all the bivariate Gaussians over the relevant wedge of Concordia space for each proposal, and/or other possible implementations
  
  as well as
  
  3) Remove the section on application to detrital age spectra
  
  4) Implement all suggested line-by-line comments
  
  Citation: https://doi.org/10.5194/gchron-2023-9-AC1
RC2:
'Comment on gchron-2023-9', Ryan Ickert, 06 Jun 2023
Review of “Technical Note: Pb-loss-aware Eruption/Deposition Age Estimation” by Keller for Geochronology.

This review by Ryan Ickert (Purdue University)

This short manuscript is an extension of the Keller et al. (2018; hereafter K18) method for estimating age distributions from geochronological data (most often U-Pb ID-TIMS zircon). The portion of the age distribution that is typically of interest is the end of zircon crystallization (“eruption” age). In K18, the model required the ages and uncertainties, and some way to estimate the relative crystallization distribution (e.g., a uniform, truncated normal, saturation, bootstrapped distribution etc.). However, in some U-Pb datasets there is evidence for unmitigated Pb-loss, even after chemical abrasion.

The novel extension in this technical contribution is that the model now can take into account single-stage Pb-loss for the coupled ²³⁸U-²⁰⁶Pb and ²³⁵U-²⁰⁷Pb systems. This likely is relevant for only a small subset of U-Pb data, but nevertheless it is an important one. The technique is straightforward and relatively flexible, hopefully amenable to most datasets with small amounts of Pb-loss.

I like that this is a short contribution, though it can be tightened a bit, and I have some concerns about one critical element that is only lightly addressed. These are detailed below, followed by more minor points that are detailed line-by-line.

Length:
For reasons detailed below, the entire detrital zircon section can probably be eliminated. Multi-stage Pb-loss is probably common in discordant DZ data. I don’t think that hurts the manuscript.
The figures can be significantly condensed. Figure 3 is not necessary – the typical reader of Geochronology will trust the author if he says the Markov chain has a short burn in and is usually stationary. Figure 1, 2a, and 4 are almost identical and could easily be condensed into one, physically larger, figure. This would have the added benefit of a reader being able to more easily see the differences (or lack thereof) instead of having to flip back and for, as I did.
Choice of decay constants:
This is given very short treatment in the manuscript. I think this needs to be expanded, for two reasons.
This model will generate inaccurate results with the Jaffey decay constants, and this is not clearly stated in the paper. High-precision zircon U-Pb datasets almost always generate U-Pb data that clusters to the right of the Jaffey-concordia central estimate, but within uncertainty. Although not often made explicit, the interpretation is generally that these represent accurately measured, closed-system domains, and the systematic offset is simply because high-precision U-Pb data provides a more precise measurement of the decay constant ratios than those in Jaffey. If this is true, then using the Jaffey decay constants, this model will infer that *every* zircon dataset that is currently interpreted as closed system has had a small but consistent amount of Pb-loss, and (if I understand the model correctly) will increase the amount of apparent age dispersion by “overprojecting” the data through the concordant cluster back to the Jaffey concordia. I’m not sure if this is significant or not, but it certainly is inaccurate, assuming our understanding of zircon U-Pb systematics is correct (ie, that there is no other reason for the offset).

Despite the well documented datasets from the Schoene et al. and the Mattinson papers, no one uses the revised decay constant ratio and this may generate confusion. A large part of the reason is that we can’t get away from Jaffey – we only have information on the ratios, so we either need to pin one on the other or use some combination of both Jaffey constants and the ratio, and Jaffey is indistinguishable from the geochronologically determined ratio (just less precise) so the dates change very little, if at all. Most recommendations are to keep the lambda-238, so very few ages actually change. Adding this changed suite of decay constants into the mix threatens to throw U-Pb geochronology into the chaos that Ar/Ar geochronology seems to relish. I don’t object to it, but it certainly warrants some discussion in the manuscript because this is something that many geochronologists will be wary of.

(I repeat myself below but it’s worth emphasizing that there is little or no evidence that the Jaffey decay constants are inaccurate. Evidence suggests that high-precision U-Pb data can measure the decay constant ratios at a higher precision than Jaffey, but the quantity estimates are indistinguishable. If Jaffey were inaccurate, then the ratios would differ outside of uncertainty. I’m 100% sure that the author knows this and perhaps wrote inaccurately (hah!) due to length constraints. That should be made more clear in the manuscript because it’s easy for someone to misunderstand.)

L8: “Covariance” alone is probably not correct because it does not include the variances? (Maybe it’s short for covariance structure or covariance matrix, but some readers may find this confusing)

L8: I’m not sure what “potentially robust” means here? Perhaps just eruption age estimates for which Pb-loss is explicitly accounted for?

L26: For consistency with line 19 use U/Th instead of U-Th.
L30: Consider mentioning that the weighted-mean is the gold standard of geochronological statistical tools.

L33: This is a rather bold statement that requires some evidence. There’s plenty of suspicion in the community that unmitigated Pb-loss might be responsible for some overdispersion and it is very hard to test.

L53: What does “dispersed” mean here? Typically one would refer to data being either overdispersed and underdispersed, which implies “dispersed” means the analytical uncertainties account for the scatter in the data. But I don’t think that’s the meaning implied?

L111: Here, the term “accuracy” is used in a way that is confusing. The Jaffey, Mattinson, and Schoene decay constant ratios are all mutually consistent. The Jaffey decay constant ratios are less precise, but as far as I’m aware, there is no evidence to suggest that they are inaccurate. Obviously, this is not a misunderstanding by the author – who himself has worked on improving the decay constants - but I think the problem is that the issue here is rather nuanced and is done a disservice by condensing it into a short 7 line paragraph.

L114: Please also cite Mattinson (2010) for the decay constant ratios.
L115: Following Holden et al., (2011), please use a consistent unit for time (preferably Ma). Please also specify the confidence level.
Section 3: I appreciate the effort here but I’m not sure this is the right tool for detrital zircon. For chemically abraded ID-TIMS zircon dates from igneous rocks with simple histories, most sample suites tend to be very close to concordant and in many cases (particularly very old ones) have consistent “zero age Pb-loss 207/206 dates” that are consistent with the unmitigated Pb-loss being consistent with a single-stage event. However, this is not the case for grains that are not chemically abraded. My experience is that many unabraded zircon from the Proterozoic and Archean of northern Canada have multi-stage Pb-loss, and I expect that to be the case for Pb-loss in many suites of detrital grains, violating the assumptions in the model here. I recommend this section be eliminated.
Citation: https://doi.org/10.5194/gchron-2023-9-RC2
- AC2: 'Reply to RC2', Brenhin Keller, 14 Nov 2023
  
  Many thanks for the detailed and thoughtful review! Better justifying and explaining the choice of decay constants is a quite good point. Among other changes I will attempt in revision, I will implement all line-by-line comments and (as suggested by multiple reviewers) remove the section on application to detrital geochronology.
  
  Citation: https://doi.org/10.5194/gchron-2023-9-AC2
RC3:
'Comment on gchron-2023-9', Jahandar Ramezani, 12 Jul 2023

The chemical abrasion pre-treatment procedure for mitigating the effects of Pb loss in zircon, developed after the pioneering work of Mattinson (2005), has revolutionized U-Pb geochronology by the ID-TIMS technique. However, it has proven imperfect in cases where persistent Pb loss cannot be completely eliminated. The proposed age interpretation scheme of this manuscript builds upon the earlier Bayesian eruption age estimation method of Keller et al. (2018), which deals with excess geologic age scatter due to prolonged crystallization histories of analyzed zircons. The added functionality of the new algorithm involves constraining the timing of the apparent Pb loss and thereby attempting to model its magnitude.
The manuscript is good in laying out the limitations and potentials pitfalls of the proposed statistical data treatment. However, I feel some of the mentioned issues need a more detailed scrutiny, as stated below.
The recognition of Pb loss for the purpose of eruption age estimation here is based solely on the observed discordance, which itself is a function of the precision and accuracy of the measured ²⁰⁷Pb/²³⁵U dates. In high-precision and low-blank U-Pb measurements, the latter date is highly sensitive to common Pb correction and thus reliable measurements of ²⁰⁴Pb. Measuring less than 30 counts per second of mass 204 signal requires a well-tuned ion counting system with a superb control on isobaric interferences and baseline (even the way mass spectrometer software does baseline correction can significantly affect measured ²⁰⁴Pb ratios). Accurate measurement of ²⁰⁷Pb in small Phanerozoic zircons has its own difficulties, with a host of known and perhaps not well understood isobaric interference issues. A survey of modern published U-Pb ages would show that even among analyzed zircons with tight ²⁰⁶Pb/²³⁸U dates, the corresponding ²⁰⁷Pb/²³⁵U dates may vary from normally to reversely discordant, with dispersions often beyond analytical uncertainty. Therefore, I believe the problem of poor constraints on discordance as an indicator of Pb loss extends far beyond the “less than ~100 Ma” old samples and is a much more serious hindrance to tackle.
Another potential complication arises from zircon xenocrysts. The age estimation method of Keller et al. (2018) requires advance exclusion of analyses identified as xenocrystic. In cases where only a small inherited component is present, or inheritance stems from an only slightly older source(s), the distinction between a xenocryst and an early forming zircon (and hence the magnitude of age dispersion) becomes a subject of interpretation. Naturally, the same issue exists with the proposed age estimation method of this manuscript.
Given the above limitations, I would suggest that the proposed statistical method will be suitable only in case of ‘ideal data sets’ in ID-TIMS geochronology, with its applicability decreasing with younger zircon ages. I do not believe the method is ready to handle the many complexities of LA-ICPMS detrital zircon age spectra. My recommendation is that the section on ‘Application to depositional age estimation’ be removed or substantially shortened. Also, more non-ideal ID-TIMS cases from a range of sample ages should be examined to test the applicability of the method. Particularly useful cases would be those for which air-abraded (showing Pb loss) and CA-TIMS data exist in the literature.
As a final note, I would argue that chemical abrasion would be more effective (and less need for statistical manipulation methods) if researchers abandon their one-size-fit-all approach to chemical abrasion and try to optimize the partial dissolution temperature and duration, at least for problematic samples exhibiting persistent Pb loss. I agree that there is a legitimate concern about old/U-rich/metamict zircons being decimated under intensive chemical abrasion. On the other hand, careful selection of least damaged zircons through CL imaging can significantly increase the chance of survival of these types of samples. Recent geochronological works (e.g., Swanson-Hysell et al., 2019; Hoffman et al., 2023) have demonstrated that Proterozoic or even Archean zircons are capable of producing statistically valid ages derived from the ²⁰⁶Pb/²³⁸U chronometer free of Pb loss effects (outside analytical uncertainty), given the optimum chemical abrasion conditions.
I would also suggest that there are better prospects in the future for quantifying Pb loss by developing proxies based on zircon chemical and/or spectroscopic characteristics, rather than taking a purely statistical approach. The recent study of Su et al. (2023) serves as a good example.
Jahan Ramezani

References:
Hoffman P.F., Macdonald F.A., Bowring S.A., Ramezani J., Buchwaldt R., Hildebrand R.S., and Whalen J.B. (2023) Crustal eduction and slab-failure magmatism in an Orosirian (2.05–1.80 Ga) postcollisional cratonic foredeep: geochronology of Seton volcanics and Compton laccoliths, Tu Cho (Great Slave Lake), NWT, Canada. Canadian Journal of Earth Sciences, (in press), doi: https://doi.org/10.1139/cjes-2023-0011.
Mattinson J.M. (2005) Zircon U-Pb chemical abrasion ("CA-TIMS") method: Combined annealing and multi-step partial dissolution analysis for improved precision and accuracy of zircon ages. Chemical Geology, 220(1-2), 47-66, doi: https://doi.org/10.1016/j.chemgeo.2005.03.011.
Su K., Zhang S.-B., Hanchar J., Zhen-Xin L., Sun F.-Y., Liang T., and Gao X.-Y. (2023) Quantification of radiation damage in natural and synthetic zircon by Raman spectroscopy: application to low-temperature thermochronology. Acta Geochimica, 42, doi: https://doi.org/10.1007/s11631-023-00606-w.
Swanson-Hysell N.L., Ramezani J., Fairchild L.M., and Rose I.R. (2019) Failed rifting and fast drifting: Midcontinent Rift development, Laurentia's rapid motion and the driver of Grenvillian orogenesis. Geological Society of America Bulletin, 131(5-6), 913-940, doi: https://doi.org/10.1130/B31944.1.

Citation: https://doi.org/10.5194/gchron-2023-9-RC3
- AC3: 'Reply to RC3', Brenhin Keller, 14 Nov 2023
  
  Many thanks for the detailed and thoughtful review! I do not disagree that the ultimate solution will likely be analytical, and particularly regarding improved CA procedures. That said, for now there are many cases where it falls to us to do the best we can with the data we have. The complications regarding xenocrysts/xenocrystic cores, etc., have not escaped me, and are not discussed in the current manuscript, so I will attempt to expand on this in the revised manuscript.
  As suggested by multiple reviewers, I will remove the section on application to detrital geochronology.
  
  Citation: https://doi.org/10.5194/gchron-2023-9-AC3

C. Brenhin Keller

Model code and software

Isoplot.jl C. Brenhin Keller https://doi.org/10.17605/OSF.IO/Z37WE

C. Brenhin Keller

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Short summary

As a result of increasing precision and accuracy in geochronology, interpreting complicated age spectra has become increasingly important, since individual mineral ages often do not directly date the actual geologic process of interest. Here we propose a method for estimating the age of eruption or deposition of a set of minerals dated by the U-Pb system which, in contrast to previous approaches, remains accurate even when the dated minerals have experienced loss of the daughter product Pb.


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