A procedure for quantifying thermal histories from apatite fission-track data is presented. Given an appropriate annealing algorithm, or forward model, the problem is to determine a best-fit thermal history and quantify the resolution of this solution. Also, a priori geological information should be readily incorporated. Due to the non-linear nature of the problem, conventional inversion methods such as iterative least squares are inappropriate. The procedure described here relies on an initial stochastic search of a broad range of potential thermal histories using a genetic algorithm (GA). These techniques are extremely efficient in defining the regions of time-temperature space where good data-fitting solutions occur. However, the best model found with a genetic algorithm is generally non-optimal. Therefore, a multi-dimensional direct search method is used to update the best GA solution. A variety of standard statistical methods are considered to define confidence regions around this refined best thermal history. © 1995.
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