**DETRITAL FT DATA ANALYSIS: **

**GETTING
RESULTS FROM **

**SINGLE
GRAIN AGES**

**Matthias
Bernet**

**Yale University,
Department of Geology & Geophysics**

**210 Whitney Ave.**

**New Haven, CT 06520-8109,
USA**

**Phone: (203) 432 5686, fax:
(203) 432 3134**

email: matthias.bernet@yale.edu

Detrital fission-track grain age (FTGA) populations can usually be decomposed
into several grain age components, using binomial peak fitting (Galbraith and
Green, 1990). Probability density (PD) plots are a convenient way to show the
observed grain age distribution and the binomial fitted peaks. The statistical
background for constructing PD plots is given in Brandon (1996). This chapter
only explains the data handling after counting, including all the steps using
various programs from Brandon, to create PD plots in Sigma Plot All programs are
by M.T. Brandon
(Zetaage, Zetafactor, Binomfit, Chi2comp, etc.) and currently available free of
charge at:

http://www.geology.yale.edu/~markb/Software/FT_PROGRAMS/

**1) Evaluating counting data
with the program Zetaage**

Using
the zeta factor method, to get started one needs to know:

- Effective track
density (tr/cm
^{2}) - The relative
standard error (%) for the fluence monitor
- The effective
uranium concentration (ppm) of the monitor standard
- Zeta factor (yr cm
^{2}/tr) - Standard error of
zeta factor (yr cm
^{2}/tr) - Counter square size
(cm
^{2}) - Spontaneous track
density
- Induced track
density
- Number of squares
counted

Data input is usually done in a simple text editor like Notepad, Ultra edit, Word pad etc, where it is possible to save the text files. ATTENTION: the extension *.ftz (zircon) or *.fta (for apatite) should be used instead of *.txt. Figure 1 shows a typical data file.

Fig. 1

__Explanations to Fig.1__

Information about Sample - this line is for
indentifying the sample, it is not used in the calculations, but it is printed
at the top of the results.

_____________________

Effective track density - this is the track density of the fluence monitor, not
that because this is the first line of the the data file, it is preceded by a
negative sign.

Relative Standard Error for the fluence
monitor, give here as percent. This value can be calculated manually, but it is
given in the program "Fluence."

________________________

Zeta Factor - regardless of monitor glass, enter Zeta value here, the glass value
appears on the previous line. Standard Error of Zeta Factor - Give as 1
SE

Counter Square size. - given in square
centimeters. Most microscopes are fitted with a 10 x 10 grid - a total of
100 squares. This is the value of one square.

________________________

Spontaneous tracks - the number of tracks counted on a grain.

Intuduced tracks - the number of tracks
counted on a grain image on the mica.

Counted Squares - number of squares counted
for that grain.

________________________

The file should end with the last grain analyzed, do not leave blank lines after
the last data set.

Files from the same sample, but from different
mounts can be put together in this file. to do this, start the new mount
information from line two onwards. The negative sign flags the data and
tells the program that these are new parameters.

**2) Getting results**

After
the data are entered correctly it is possible to evaluate them with Zetaage.
The first step it to start zetaage and change to the appropriate directory, if
it is not in the same one as the Zetaage program. Because Zetaage is a
DOS-based program it is necessary to change the directory in Zetaage using DOS
commands like ..\ to get one level up and so on. To facilitate file
transfers in the DOS shell, it is helpful to keep file names under 8 characters
(not including extension).

When
the correct directory is found and the right *.ftz files are listed, type in
the complete file name (e.g. "99_23.ftz") and hit return. Next
follows a selection between different output options. In general only
"F" for full output and "P" for probability density data
are used. "F" should be selected and the output can be given in an
*.asc file (e.g. 99_23.asc) and viewed in Notepad etc.

**3) Binomial peak-fitting**

Using the information from the new *.asc file it is
possible to proceed to the peak-fitting procedure. First start the Binomfit
program and change into the directory where the *.ftz files reside. Type in the
filename (e.g. 99_23.ftz) and hit return.

The program asks how many peaks should be fit.
It is good always to start with one peak and in the next iteration add the next
peak and so on, up to ten peaks. In general it is not necessary to fit more
then 3-4 peaks (when 50-100 grains were dated). To get an idea where to start with
the peak fitting the zetaage output gives some help because it already provides
information about Gaussian-fitted peaks. These help as an orientation, which
peak ages could be entered. Furthermore the plot (histogram and PD plot) given
at the very end of the *.asc file can help to estimate the ages. The program
evaluates the data, it just needs a starting point but not the exact peak age.

It is useful to have the output in file form, which
comes with the extension *.bft, and each new iteration (adding another peak)
can be attached to the previous data file. The *.bft file can be viewed in
Notepad, Word, etc. We typically fit peaks successively (i.e. 1-5 peaks),
and then evaluate the results (see below).

After all peaks are fitted, it is necessary to evaluate,
which is the optimal solution. Do 3 peaks better represent the data than 4
peaks or the other way around? Sometimes it is obvious because you want to
choose the optimal log-likelihood value, but in general the "F test"
should be run, using the Chi2comp program. This program asks for the Chi^2
value and the degrees of freedom for the first fit. This information is
available form the *.bft file. The program then compares the first fit against
the second and evaluates if adding another peak improves the model. If
"F" is large and "P(F)" small, it indicates that more peaks
better fit the data. This has to be tested for all peaks and in the next step
the Chi^2 value and degrees of freedom of 2 peaks have to be compared to 3
peaks and so on. When "F" gets small (less then 5) and
"P(F)" >10 it is a good indication that fitting another peak didnt
improve the model anymore and the previous solution should be used.

Lets say 3 peaks were the best solution and fitting 4
peaks wasnt an improvement, one can go back to the binomfit results and check
the data for the 3 peak solution. This data includes the mean peak age for each
peak, the peak width W, and the fraction of grains belonging to each peak. This
information is necessary to generate the data for creating the PD plot in Sigma
Plot.

**3)
PD plot data**

Knowing the mean peak age, peak width, and grain
fraction of the best fitted peaks it is necessary to run the zetaage program
again and select the appropriate *.ftz file again. This the P for probability
density data should be selected and printed to a file that will have the
extension .prb. When the program asks how many peak should be included, enter
the best-fit solution (e.g. 3 peaks) and then the mean peak age, peak width and
grain fraction, for each peak.

**4)
PD plots in Sigma Plot**

To generate the PD plots in Sigma Plot example Sigma
Plot notebook files are available from matthias.bernet@yale.edu
on request. It is necessary to import the *.prb file that contains the PD data
into Sigma Plot. This is done by clicking on file in the taskbar and selecting
import. The next step is to select , as the delimiter and skip the rows that
contain text. This is all, if using an example notebook file, because than the
PD plot is already set up.

**5) References**

Brandon, M. T. (1996) Probability density plot
for fission-track grain-age samples. *Radiation Measurements*, Vol. 26, No.5, 663-676.

Galbraith, R. F., & Green, P. F. (1990)
Estimating the component ages in a finite mixture. *Nuclear Tracks and
Radiation Measurements*, Vol. 17, No.
3, 197-206.

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Garver

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All rights reserved. No part
of the document can be copied and/or redistributed, electronically or otherwise, without written permission
from: J.I.Garver, Geology
Department, Union College, Schenectady NY, 12308-2311, USA.

Last
Revised: 3 January 2003

Some of this
material is based upon work supported by the US National Science Foundation
under Grant No. 9614730. Any opinions, findings, and conclusions or
recommendations expressed in this material are those of the author(s) and do
not necessarily reflect the views of the National Science Foundation.