DECOMPOSITION OF FISSION-TRACK GRAIN-AGE DISTRIBUTIONS

The external-detector method of fission-track (FT) dating is capable of providing FT ages for individual mineral grains. As a result, this method when applied to dating detrital zircons in unreset sandstone samples has much potential for resolving the depositional age and provenance of the samples. One problem is that individual FT grain ages for detrital zircons usually have fairly low precision, with an average relative standard error of about 13 percent. As a result, it is necessary to find related groups of grain ages in order to improve the precision of the age estimates. This paper introduces two new methods for decomposing a FT grain-age distribution from a single sandstone sample into component grain-age populations. The FT grain ages from a sample of unreset detrital zircons reflect the cooling and/or magmatic history of the source region from which they were eroded. The sample grain-age distribution can be viewed as a mixture of component populations, each of which is related to a FT source terrain with a characteristic FT age. The first decomposition method, the chi2 age method, isolates the youngest fraction of "plausibly related" grain ages and assigns an age to this fraction, called the chi2 age. This age estimate is useful in that it provides a maximum limit for the depositional age of the sandstone sample. The second method, the Gaussian peak-fitting method, decomposes the entire grain-age distribution into a finite set of component Gaussian distributions, each of which is defined by a unique mean age, a relative standard deviation, and an estimated number of grain ages in the component distribution. A series of simulation experiments indicates that both these methods will produce satisfactory results given a sufficient number of grain ages for each peak and adequate separation between adjacent peaks. A practical application of these methods is given in a companion paper (Brandon and Vance, this issue).