16.4 Detrital populations

An advantage of the external detector method of fission track counting is the ability to determine a separate age from each grain of the population (this also applies to the less-widely used re-polishing method). This capability is useful if a heterogeneous age population is suspected in the sample, as in the case of sedimentary rocks with mixed provenance (e.g. Hurford and Carter, 1991). However, the scatter of analysis points generated by these kinds of sample can be a challenge when it comes to data presentation.

Fission track results for individual detrital grains may be presented in histogram form. However, a more quantitative age estimate is possible if errors are assigned to each individual grain determination, so that the data can be presented as a probability density function (Hurford et al., 1984). This function is simply the summation of the Poisson age distributions for each of the individual grain determinations. Fig. 16.9 shows such a plot for zircons from the re-worked El Ocote tephra deposit in Mexico, which displays a bimodal age distribution (Kowallis et al., 1986). The younger peak places a maximum age on the time of sedimentary re-working, and is in agreement with the estimated biostratigraphic age of associated fossil material. These results show that application of the population method to fission track dating of this tephra would yield a meaningless average of the two age populations.

Fig. 16.9. Plot of probability density as a function of age for fission track data on detrital zircons from the re-worked El Ocote tephra from Mexico. After Kowallis et al. (1986).

A problem with the probability density plot is that individual data points cannot be distinguished, so that some important but small components in the data distribution can be buried under the other data. To avoid these problem, Galbraith (1988) introduced a kind of isochron diagram for the presentation of fission track data measured on individual grains of a heterogeneous sample. This ‘radial’ plot is designed for fission track data sets with a high degree of scatter, either due to mixed detrital ages or variable cooling ages.

This diagram differs from other isochron plots used in geology because the two variables plotted are the apparent fission track age of each grain, and the standard error of each grain age (F). These quantities are plotted in the form of age/F against 1/F (Fig. 16.10a). In this plot, the slope of an array indicates the average age of the suite of grains analysed, and this age can be indicated on a calibrated arc. In practice, Galbraith argued, it is more convenient to normalise the average slope to a horizontal, and plot the y axis on a log scale from +2 to –2 (Fig. 16.10b). The age of any individual point is then determined by projecting from the zero point on the y axis, through the data point, to the calibrated arc of ages (on a log scale).

Fig. 16.10. Variations on the radial plot for presentation of single grain fission track data on heterogeneous samples; a) raw data; b) normalised. After Galbraith (1988).

An alternative data presentation of this type was proposed by Walter (1989). He suggested that additional assessments could be made of the quality of detrital fission track ages if the raw data (spontaneous- versus induced-track densities) were plotted for each grain. This also yields an isochron diagram (Fig. 16.11) where the slope of each correlation line is proportional to age. These lines should pass through the origin, corresponding to a grain with zero uranium content. The linearity of each correlation line can be used to assess the influence of systematic analytical errors or geological disturbance on the reliability of the best-fit ages. However, this presentation has not been as popular as the isochron diagram of Galbraith, which has found wide application to complex fission track data sets, including partially annealed systems as well as detrital systems.

Fig. 16.11. Spontaneous- versus induced-track isochron diagram showing data for individual zircon grains from the El Ocote tephra. After Walter (1989).

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