Abstract
The major stochastic elements in the fission track dating method are (i) the number of spontaneous fission tracks (N s ) in a sample, and (ii) the number of induced tracks (N i ) observed when the sample is irradiated with neutrons. The foundations for the statistical uncertainty in these measures are of two kinds: (i) there exists a definite probability of uranium fission by means of natural decay and by neutron activation, and (ii) within a crystal the distribution of uranium is not uniform and perhaps follows something like a Poisson law. In any event, the natural logarithm of the ratio (N s /N i ) is proportional to age. A plausible statistical fission track dating model should, therefore, start by considering the joint distribution of N s and N i . In this paper a joint bivariate normal model is described which allows the rigorous definition of the probability distributions of Ns, N i , the ratio N s /N i , and age itself. A general computer program (FISSION) has been developed to perform all the necessary computations. By accounting for the correlation between N s and N i , the statistical model here ascribes smaller standard errors to N s /N i (and therefore age) than do previous methods. In addition, the error associated with neutron flux is a significant factor in the age relationships and has been incorporated into the model.
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McGee, V.E., Johnson, N.M. Statistical treatment of experimental errors in the fission track dating method. Mathematical Geology 11, 255–268 (1979). https://doi.org/10.1007/BF01034992
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DOI: https://doi.org/10.1007/BF01034992