Extraction of multiple ages from <i>c</i> -axis projected fission tracks

Abstract. It is generally accepted that the commonly used fission track age equation accurately calculates the cooling age for apatite minerals when the cooling rate is fast. Nevertheless, it is used when the cooling rate is gradual, for example when the age of transition through the partial annealing window is to be estimated. Added age information is here obtained by inclusion of the length distribution of fully included near horizontal tracks. The tendency that the shortest tracks are the oldest ones, and the longest ones are the youngest enables the age dating of a given track by counting the number of shorter tracks, adding one, and dividing by the volumetric track generation rate. The difficulty is that the track length–age relation is blurred by the spread in lengths due to the inherent spread in fission decay energies, crystallographic anisotropy and observational uncertainties. The blurring can be reduced by mathematical deconvolution in which the blurring of tracks in annealing experiments is used. A previously given equation for the oldest track in each histogram column is mathematically further reduced. This paper presents a method where deblurring is first performed by projecting the observed track lengths on the mineral c-axis and then by deblurring using probabilistic least squares inversion. This leads to the extraction of several track ages with deviations for each deconvolved track length histogram. This information may be used to constrain the timing of tectonic events and provide the basis for calculation of past temperature.