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.