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

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:



1) Evaluating counting data with the program Zetaage


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

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 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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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.