A different take on fission-track annealing in apatite

Jonckheere, Raymond; Trilsch, Florian; Härtel, Birk; Nagel, Thorsten

doi:10.5194/egusphere-2026-1924

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https://doi.org/10.5194/egusphere-2026-1924

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14 Apr 2026

| 14 Apr 2026

A different take on fission-track annealing in apatite

Raymond Jonckheere, Florian Trilsch, Birk Härtel, and Thorsten Nagel

Abstract. This work discusses a model for calculating the mean-lengths of confined fission tracks in apatite after isothermal heating. We derive separate equations for gradual and accelerated high-temperature annealing, and for ambient-temperature annealing. A three-parameter fanning Arrhenius model describes the initial gradual length reduction in all apatites. A linear equation corrects for the different rates of length reduction in different apatite compositions during subsequent accelerated annealing. Another linear equation describes ambient-temperature annealing at lab and geological timescales. At present, these equations give the mean track length in the most and least resistant apatites over their full annealing ranges, at all time-temperature conditions. The aim is not to achieve greater precision or accurateness than existing equations. Instead, we made some choices and concessions in order to combine different datasets, and construct an annealing model that aims to be a reasonable approximation across different apatites and measurement protocols. The calculated age-vs.-depth profile for the Kontinentale Tiefbohrung fits the data almost without compromise for a cooling path constrained by independent geological and thermochronological evidence. In contrast, the mean-length-vs.-depth profile is offset to higher values than the length data. Experimental factors and ambient-temperature annealing could in part be responsible. The inconclusive fit to geological data emphasizes the need for a consensus on a set of reliable geological benchmarks.

Received: 04 Apr 2026 – Discussion started: 14 Apr 2026

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Raymond Jonckheere, Florian Trilsch, Birk Härtel, and Thorsten Nagel

Status: final response (author comments only)

RC1:
'Comment on egusphere-2026-1924', Anonymous Referee #1, 25 May 2026
General Comments
This manuscript proposes a novel multi-stage empirical model for fission-track (FT) annealing in apatite. By distinguishing between initial gradual shortening, subsequent accelerated shortening (segmentation), and ambient-temperature annealing, the authors aim to build a robust approximation rather than absolute mathematical precision.
The approach of explicitly separating the gradual and accelerated stages of annealing is a strong point, effectively building on earlier mechanistic insights that track shortening and track segmentation are kinetically dissimilar processes. The manuscript helpfully addresses the common failure of high-temperature models to accurately predict track shortening at geological time scales by integrating short-term, low-temperature data.
However, the resulting model introduces a quasi-fanning Arrhenius equation with three fitting parameters (plus L_0 and a unit-correcting scale parameter), relying on empirical thresholds rather than a unified kinetic theory. For model validation, the authors compare calculated FT lengths and ages with KTB borehole profiles. To fully assess the model’s utility for thermal history inversion, the validation needs to be expanded. Currently, it is unclear how the model performs under variable temperatures. Calculating closure temperatures to allow for a direct comparison with existing models, as well as presenting calculated track length distributions, would significantly strengthen the manuscript.
Specific Points
Using absolute shortening (S) instead of the normalized length ratio (r) implicitly assumes that all apatites shorten at the same absolute rate regardless of their initial length (L_0). This appears to contradict existing experimental findings where unannealed length correlates more strongly with etching rates (D_par) than with latent track properties. The authors should justify this choice.

The text relies too heavily on frequent references to tables and figures in the supplementary material, which hinders readability. I recommend moving the most critical data and figures into the main text, while keeping within the journal's length limits.

The presentation in Figure 1 could be improved. It would be highly beneficial to include error bars so readers can fully appreciate the degree of agreement between the experimental data and the model curves. Additionally, please clarify the origin of the parallel lines; are they directly fitted to the data?

Lines 103–104: The Ravenhurst et al. (2003) dataset is fundamentally a study on chemical etching, as samples were etched under varying conditions depending on their chemical compositions. Combining this dataset with those of Carlson et al. and Barbarand et al. may introduce inconsistencies and could explain the discrepancies observed in Figure 4. The authors should address this potential compounding factor.

Lines 115–118: The rationale behind the "zero-length" logic requires further clarification. While it is clear that S approaches A_1 as T_0 approaches zero Kelvin, it is less clear why L should be forced to be greater than L_0 if the data fit yields an A_1 value less than zero. This might suggest that the empirical formula does not fully capture the physical reality of the process.

Lines 118–119: Please explicitly clarify if your definition of C_1 corresponds directly to that of a fanning point temperature.

Lines 128–130: Dimensional units are critical here. While the authors establish a connection between B_1 and C_1, a third parameter is not truly eliminated; rather, it appears to be made arbitrary. For instance, C_2 is effectively set to 1 micrometer. If a different unit of length had been chosen, C_2 would simply change to reflect that unit. Please clarify this parameterization.

Equations 3 and 4 and Lines 131–141: This formulation resembles a modified fanning model. It appears that a moving fanning point will cause a significant departure from standard models when applied to long-time, low-temperature data (i.e., geological timescales). Expanding the discussion on the implications of this departure would be valuable.

Figure 9 and age calculations: The agreement between the calculated FT ages and the KTB profile ages seems to be a direct consequence of the arbitrary choice of the bias model. Furthermore, the methodology behind the FT age calculation needs transparency. It appears a simple length correction was applied rather than calculating the cumulative reduction across multiple track populations generated at different times, as is standard in thermal history inversion software. Please clarify this procedure.

Lines 351–353: At the laboratory timescale, the proposed model behaves essentially like a standard fanning model. The text should explicitly highlight what unique insights or advantages this model provides at this scale compared to existing frameworks.

Conclusion
Recommendation: Revisions Required (Major Revisions)
In summary, this manuscript possesses high scientific significance for the geochronology community, offering a thought-provoking and valuable discussion on fission-track annealing mechanisms. The effort to bridge laboratory data with geological timescales is highly relevant. However, the exact calculation methods require greater clarification, the validation process needs to be expanded (specifically regarding closure temperatures and length distributions), and the overall presentation needs some polish to improve readability. I recommend publication after the authors have addressed these substantial concerns.
Citation: https://doi.org/10.5194/egusphere-2026-1924-RC1
- AC1: 'Reply to RC1', Raymond Jonkheere, 11 Jun 2026
  
  Please find our replies in the attached document. The authors.
  
  Citation: https://doi.org/10.5194/egusphere-2026-1924-AC1
RC2:
'Comment on egusphere-2026-1924', Maria-Laura Balestrieri, 29 Jul 2026

Dear Authors and Editor,
The manuscript titled “different take on fission-track annealing in apatite” by Jonckheere et al., presents an original and provoking re-interpretation of apatite fission-track annealing. The proposal that compositional effects are primarily expressed through the onset of accelerated shortening rather than through different overall annealing rates is novel and deserves consideration.
The central assumption of the manuscript is that all apatite compositions share a common gradual annealing trajectory and differ primarily in the onset of accelerated annealing: compositional differences do not primarily control the rate of track shortening; rather, they control the point at which accelerated annealing begins.In this framework, fission tracks in all apatites undergo an initial stage of gradual shortening, followed by a stage of accelerated shortening, with the transition occurring at different mean track lengths depending on apatite composition.
The core hypothesis of the manuscript is that compositional differences among apatites are more appropriately described by a threshold mean length for the onset of accelerated shortening than by composition-dependent annealing rates as implemented in existing models. However, the procedure used to distinguish data belonging to the gradual and accelerated regimes appears largely empirical. A sensitivity analysis showing how the model parameters vary when different transition thresholds are adopted would considerably strengthen the argument.
A critical point is that the high-temperature annealing model fails to reproduce the observed low-temperature behaviour, and a separate logarithmic time-dependent relationship is introduced to reconcile laboratory and geological observations. However, the physical basis for this additional process remains unclear. The introduction of a separate ambient-temperature annealing mechanism appears largely phenomenological.
The KTB benchmark represents a key test of the proposed model. But the geological validation remains inconclusive. While the calculated age-depth profile reproduces the observed apatite fission-track ages reasonably well, the predicted mean track lengths show a systematic offset relative to observations. The authors attribute this discrepancy partly to experimental biases and partly to ambient-temperature effects.However, mean track lengths constitute one of the principal observables used to calibrate and test annealing models. Therefore, the mismatch should probably receive greater emphasis in the conclusions. At present the manuscript gives the impression of stronger validation than is actually demonstrated.
In conclusion, several key assumptions remain insufficiently demonstrated, particularly regarding the identification of the transition between annealing regimes, the treatment of ambient-temperature annealing, and the geological validation of the model. I recommend a more cautious presentation of the conclusions, clearly distinguishing between observations directly supported by the data and interpretations that remain speculative.
I view the proposed model not yet as a replacement for established annealing formulations (the current evidence does not demonstrate that this framework provides a superior explanation compared with established rmr0-based approaches) but rather as an interesting working hypothesis. What is lacking is a quantitative comparison between the predictive performance of the proposed approach and established rmr0-based model. Without such a comparison, it is difficult to assess whether the new parameterization provides a genuine improvement over existing formulations or simply represents an alternative description of the same observations.
While several aspects of the model remain incompletely validated and require further testing against both experimental and geological datasets, I see clear value in sharing this hypothesis with the fission-track community. The manuscript raises important questions regarding the interpretation of compositional effects on annealing and may stimulate further discussion and investigation of these processes.
Regards,
Maria Laura Balestrieri

Citation: https://doi.org/10.5194/egusphere-2026-1924-RC2
- AC2: 'Reply to RC2', Raymond Jonkheere, 09 Aug 2026
  
  Thank you for your comments. Please find our replies in the attached pdf. The authors.
  
  Citation: https://doi.org/10.5194/egusphere-2026-1924-AC2
CC1:
'Comment on egusphere-2026-1924', Jocelyn Barbarand, 12 Aug 2026

The study by Jonckheere et al. examines the model for the annealing of fission tracks in apatite. They propose a new model based on existing data obtained from laboratory experiments on the fission track annealing. The three aspects that have been debated for over 40 years are the role of apatite chemistry, low-temperature annealing over geological timescales, and extrapolation to geological annealing processes.
The new model is based on a strong assumption: only the mean length is used to simulate annealing, taking into account the difference between the length after the experiment and the initial length. This deliberately simplified approach is intended to be more realistic, particularly by taking into account the variations that may exist between analysts in the measurement of average lengths. This assumption, however, disregards the strong influence of crystallographic orientation on the annealing kinetics of fission tracks, which has been well known since the pioneering work of Green and Durrani (1977). This assumption results in the shape of the histogram of average track lengths not being utilised; this shape is partly controlled by crystallographic orientation, the user’s choice, and also the thermal history, which is central to the application of this method. I find this somewhat regrettable.
The abstract and introduction lack an explanation of the rationale for developing this new model: what are the shortcomings of the previous models? Are these shortcomings addressed by this new model? Why develop this new model based on the same data as the previous models?
Page 2, first paragraph: add the references to Ketcham et al. 1999 and Ketcham et al. 2007, which present the annealing models
L78: use a term other than ‘break in slope’ as this refers to something else in fission track terminology (shape of the length versus age distribution)
L147–161: Is the distribution of the residuals the same if we consider only the data corresponding to the first plateau, for which the analysts’ choices are not, a priori, very different?
Paragraph on ambient temperature: the conclusions are fairly similar to what was already known, and the question remains as to the very precise definition of the thermal history of samples described as volcanic but which may have been slightly heated by the overlying layer.
L321: The suggestion that the experimental data are not robust enough is an interesting point and could easily be resolved, given that the samples must exist. The text mentions that measurements are currently being carried out. It would be worth including these.
L355: We can read that “the annealing model is incorrect”. Why, then, should the readers use this new model ?

Citation: https://doi.org/10.5194/egusphere-2026-1924-CC1
- AC3: 'Reply to CC1', Raymond Jonkheere, 14 Aug 2026
  
  Thank you for your comments. Please find our replies in the attached document. The authors.
  
  Citation: https://doi.org/10.5194/egusphere-2026-1924-AC3

Raymond Jonckheere, Florian Trilsch, Birk Härtel, and Thorsten Nagel

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Raymond Jonckheere, Florian Trilsch, Birk Härtel, and Thorsten Nagel

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Short summary

Fission-track modelling rest on empirical equations fitted to lab datasets. It is therefore doubtful that a specific set applies to all samples, protocols, and analysts, while there also remain unresolved issues. We propose a different take on the data. Our aim is not to improve existing equations, but to construct the basis of an alternative approach, as a reference for interrogating current assumptions, and perhaps as the beginnings of a model that can connect with the latent-track properties.


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