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The development of quantitative models for fission track annealing (Laslett et al. 1987; Carlson 1990; Laslett and Galbraith 1996; Ketcham et al. 1999) and more recently, helium diffusion in apatite (Wolf et al. 1996; Farley 2000), has allowed direct inference of the temperature history of the host rocks, and a more indirect inference of denudation chronologies (see Kohn et al. this volume, and references therein). An example of a model prediction of AFT parameter and (U-Th)/He age for a specified thermal history is given in Figure 1⇓. Various approaches exist to extract a thermal history model directly from the data, and these focus around inverse modeling (Corrigan 1991; Gallagher 1995; Issler 1996; Willett 1997; Ketcham et. al. 2000). The user specifies some constraints on the thermal history (e.g., upper and lower bounds on the temperature time, and heating/cooling rate), and then typically some form of stochastic sampling is adopted to infer either the most likely thermal history (ideally with some measure of the uncertainty of the solution), and/or a family of acceptable thermal histories. In both the forward and inverse approaches, the thermal history is typically parameterized as nodes in time-temperature space, with some form of interpolation between the nodes.
Over recent years, one of the major applications of low temperature thermochronology has been the study of long term denudation as recorded in the cooling history of surface samples. More recently, some studies have specifically tried to …