THE ANALYSIS OF PROJECTED FISSION-TRACK LENGTHS

The lengths of fission tracks in an apatite crystal reflect its therma l history. This article deals with the question of how features of the thermal history can be estimated from projected track length measurem ents, i.e. lengths of the remaining parts of tracks that have intersec ted a surface, projected onto that surface. The appropriate mathematic al theory is described and used to provide a sound basis both for unde rstanding the nature of projected length measurements and for analysin g observed data. The estimation of thermal history parameters correspo nding to the current temperature, the maximum palaeotemperature and th e time since cooling, is studied using laboratory data and simulations . Among the questions addressed are: what parameter values can be esti mated in practice, what sample sizes are necessary, how useful are mea surements of angles (in addition to lengths), how do estimates from pr ojected track measurements compare with those from confined tracks, an d how do simple ad hoc methods compare with maximum likelihood estimat ion? 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 o f confined tracks, though we identify some circumstances when such mea surements may be useful. Also it is not straightforward to extract the information and simple ad hoc estimation methods are generally inadeq uate.