| 14 Apr 2026
A different take on fission-track annealing in apatite
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.
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
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.