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number of simulation runs and the modelled output parameters are compared with the
input parameters. The correlation of input and modelled output data is statistically
evaluated with the Kolmogorov-Smirnov test. The program provides a graphic display
of the modelling results showing the best fit thermal evolution and statistically
acceptable limits. The best fit thermal history may neither be geologically meaningful
nor unique. The annealing model of Ketcham et al. (2000) was chosen with the
measured chlorine data as input for the chemical composition. None of the modelled
samples defined selected kinetic populations as all apatites were fluorapatites. Each
sample was modelled in 50.000 simulation runs. The modelled time-temperature paths
are shown in Appendix C, Fig. C3.
2.13 Decomposition of zircon fission track grain age distributions
Single fission track grain age spectra of sedimentary samples that are not thermally
overprinted or reset, mirror the provenance ages of their source area. The
decomposition of the mixed fission track grain age distribution of a sample yields age
populations. These populations reflect low-temperature cooling phases during the
geological history of the hinterland from which the sediment was eroded. The
decomposition of the age spectra can be approximated statistically. The computer
program BINOMFIT (Brandon 2002) was used, which is based on the binomial peakfitting
method of Galbraith and Green (1990). The binomial peak-fitting method is
based on the maximum likelihood method which determines the best-fit solution by
directly comparing the distribution of the grain data to a predicted mixed binomial
distribution (Brandon 2002). The entire grain age distribution is decomposed into a
finite set of component binomial distributions, each of which is defined by a unique
mean age, a relative standard deviation, and an estimated number of grains in the
component distribution. The initial guesses for peak ages are generated from the
probability density plot for the fission track grain age distribution. The quality of the fit
for each solution is scored using the � 2 test (Brandon 2002). To test the number of
underlying distributions and to define the minimum number of binomials needed, an Fratio
test (Bevington 1969) is introduced to judge whether the reduction of � 2 , due to
the addition of a new peak, is only by chance. When F is large the improvement in fit,
associated with the additional peak is considered significant. The F distribution is used
to assign a probability P(F), which is the probability that random variation alone could
produce the observed F statistics. Brandon (2002) considers P(F) < ~5% to indicate
that the improvement in fit is significant. Thus, the optimal number of significant peaks
can be found by adding peaks until one gets a value of P(F) > ~5%. Results of fission
track data and calculated age clusters using the computer program BINOMFIT are
illustrated in Appendix C, Tab. C7 and the decomposed fission track age spectra in
Appendix C, Fig. C5.