Technical Note: Pb-loss-aware Eruption/Deposition Age Estimation
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.
C. Brenhin Keller
Status: open (until 17 Jun 2023)
- RC1: 'Comment on gchron-2023-9', Pieter Vermeesch, 01 Jun 2023 reply
- RC2: 'Comment on gchron-2023-9', Ryan Ickert, 06 Jun 2023 reply
C. Brenhin Keller
Model code and software
C. Brenhin Keller
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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.
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)”