The analysis of projected fission track lengths

Abstract

The lengths of fission tracks in an apatite crystal reflect its thermal history. This article deals with the question of how features of the thermal history can be estimated from projected track length measurements, i.e. lengths of the remaining parts of tracks that have intersected a surface, projected onto that surface. The appropriate mathematical theory is described and used to provide a sound basis both for understanding the nature of projected length measurements and for analysing observed data. The estimation of thermal history parameters corresponding to the current temperature, the maximum palaeotemperature and the time since cooling, is studied using laboratory data and simulations. Among the questions addressed are: what parameter values can be estimated in practice, what sample sizes are necessary, how useful are measurements of angles (in addition to lengths), how do estimates from projected track measurements compare with those from confined tracks, and how do simple ad hoc methods compare with maximum likelihood estimation? The answers to these questions are inter-related. In general the information contained in projected track lengths and angles is fairly limited, compared, for example, with that from a much smaller number of confined tracks, though we identify some circumstances when such measurements may be useful. Also it is not straightforward to extract the information and simple ad hoc estimation methods are generally inadequate.