ANALYTICAL METHODS/Fission Track Analysis 49 Thermal History Modelling Figure (A) Radial plot for a sample with two clearly defined age populations (red and blue) More precise fission track ages plot further from the origin of the x axis (precision) The y axis gives the fission track age and its error The two populations have ages of $90 Ma (red) and $225 Ma (blue) and a combined age of 142 Ma (B) Histogram of the individual crystal ages in the radial plot of fission tracks depends on the orientation of the fission tracks with respect to the crystallographic orientation of the apatite crystal (Figure 1) Tracks perpendicular to the c-axis anneal slightly faster than those parallel to it For weakly annealed samples, this effect will be very small and usually it is ignored For samples that experienced higher degrees of annealing, ignoring the orientation dependency of the track length will introduce some error Anisotropy of annealing can, however, easily be taken into account by measuring y, the angle of the fission track with the crystallographic c-axis, when the track length is measured Tracks that are revealed by etching because they intersect cracks (track-in-cleavage, TINCLE Figure 2), tend to be longer than tracks that are revealed because they intersect other tracks (track-in-track, TINT; Figure 2) Several explanations have been proposed, such as widening of cracks during polishing, increased etch rates along cracks, and the smaller likelihood for shorter tracks to intersect a crack Because of their bias towards longer track lenghts, TINCLEs tend to conceal the anisotropy of annealing It is recommended to measure only TINTs Fission tracks are produced continuously throughout the thermal history of a sample Older fission tracks will, therefore, always have experienced a longer and older part of a sample’s thermal history than younger fission tracks This results in variation of fission track lengths within a sample and within single crystals In the case of a purely cooling history, the older tracks will have experienced higher temperatures than younger tracks and so the older tracks will be annealed more, and thus will be shorter, than younger tracks Track length reduction within the PAZ results in a mean length shorter than the initial length (l0) and a skewed track length distribution Different cooling histories and their resulting apatite fission track age and track length distributions are displayed in (Figure 8) Thermal history modelling makes use of annealing models to calculate the apatite fission track age and track length distribution that would result from a particular thermal history This synthetic modelling result can be compared to the fission track age and track length distribution obtained from a sample and the degree of fit can be assessed By doing this for many different thermal histories, a range of thermal histories with a good degree of fit can be obtained A geological interpretation can then be based on these thermal histories Independent geological observations and also additional age data such as those from (U-Th)/He dating can be used to constrain the range of thermal histories that a modelling program has to go through For example, a time–temperature point with surface temperature at 100 Ma can be used as a constraint when modelling fission track data from a sedimentary sample of 100 Ma old (or data from a sample of the basement just below the sediment), because at the time of deposition the sediment (and the basement immediately below) must have been experiencing surface temperatures Thermal history modelling is a popular tool to retrieve a time–temperature path from apatite fission track data However, in the absence of independent geological constraints, it cannot constrain anything other than cooling The fission track age and fission track length distribution resulting from a thermal history that includes a reheating event will be virtually identical to that resulting from the same thermal history without the reheating event (Figure 9) Fission tracks essentially record cooling, and even in a thermal history that has included reheating, most of the record will come from the cooling segments A very common characteristic of thermal histories obtained from modelling of fission track data is that they include a late cooling event The annealing