Inverse modeling of annealing of fission tracks in apatite 1: A Controlled Random Search method

A model of thermal annealing of fission tracks in apatite is described and used in a Controlled Random Search (CRS) algorithm to estimate a set of thermal histories consistent with fission track age and track length data, The CRS algorithm starts from an initial set of random temperature histories. New temperature histories are generated in the neighborhood of the current set, tested for fit to observed fission track data, then discarded or added to the set, based on the quality of the fit, The number of solutions in the set remains constant; so that the average quality of fit of the set improves as the process continues, Eventually, all members of the set converge to the global minimum of the objective function, but the more valuable information comes from the set of solutions that fit the data at the limit of statistical acceptance, If the search process has adequately sampled the parameter space, this set gives the range of temperature histories consistent with the data, Advantages of the CRS algorithm include: an efficient and effective parameter-space search scheme, the ability to find a global minimum in the presence of local minima, and the ability to include explicit and implicit constraints on thermal histories. Synthetically generated data are used to analyse the technique. The importance of rate constraints in resolving temperature is demonstrated for continuous cooling histories, An example of synthetic data generated from a temperature history with a second heating event provides a difficult test and shows the value of applying cluster analysis to the generated solution set, Timing of a second heating event is difficult to resolve; prior knowledge of the timing greatly improves the ability to estimate accurately the magnitude of a second heating event.