Statistical treatment of experimental errors in the fission track dating method |
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| Authors: | Victor E McGee and Noye M Johnson |
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| Institution: | (1) Amos Tuck School of Business, Dartmouth College, 03755 Hanover, New Hampshire, USA;(2) Department of Earth Sciences, Dartmouth College, 03755 Hanover, New Hampshire, USA |
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| 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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| Keywords: | fission track dating statistical model |
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