Statistics for Fission-Track Thermochronology

This chapter introduces statistical tools to extract geologically meaningful information from fission-track (FT) data using both the external detector and LA-ICP-MS methods. The spontaneous fission of 238U is a Poisson process resulting in large single-grain age uncertainties. To overcome this imprecision, it is nearly always necessary to analyse multiple grains per sample. The degree to which the analytical uncertainties can explain the observed scatter of the single-grain data can be visually assessed on a radial plot and objectively quantified by a chi-square test. For sufficiently low values of the chi-square statistic (or sufficiently high p values), the pooled age of all the grains gives a suitable description of the underlying ‘true’ age population. Samples may fail the chi-square test for several reasons. A first possibility is that the true age population does not consist of a single discrete age component, but is characterised by a continuous range of ages. In this case, a ‘random effects’ model can constrain the true age distribution using two parameters: the ‘central age’ and the ‘(over)dispersion’. A second reason why FT data sets might fail the chi-square test is if they are underlain by multimodal age distributions. Such distributions may consist of discrete age components, continuous age distributions, or a combination of the two. Formalised statistical tests such as chi-square can be useful in preventing overfitting of relatively small data sets. However, they should be used with caution when applied to large data sets (including length measurements) which generate sufficient statistical ‘power’ to reject any simple yet geologically plausible hypothesis

The Parameters That Govern the Accuracy of Fission-Track Age Determinations: A Re-Appraisal

Since the generalized use of the zeta-calibration method, research on fission-track age calibration and the parameters that govern the accuracy of fission-track ages has become limited to a few laboratories. The present paper gives a review of the research that has been carried out on these problems in our laboratory during the last decade. The results of these investigations demonstrate that absolute thermal neutron fluence measurements and the determination of the U-235 fission rate during sample irradiation no longer present a problem. The only parameter that would seem to remain to be determined is therefore the spontaneous fission decay constant of U-238 (lambda(f)). However, the results of our experiments also re-emphasize the importance of the techniques of track analysis that are used in an FT age determination, They can be responsible for systematic differences up to 15-20% in the final age result if the absolute approach is used. The parameters that play a role are the track registration efficiency and the combined etching-observation efficiency. These parameters have to be properly dealt with if hf is determined through the analysis of samples of known age. By applying the same analytical techniques to the age standards and the unknown samples, the zeta-method eliminates the systematic effects of these parameters and intrinsically ensures accurate ages. When a value of lambda(f) is agreed by consensus and/or as a result of new experimentation, it will still be essential to perform age standard analyses for determining a procedure factor (Q) that yields direct information on the systematic effect of the technique of track analysis. This routine will nevertheless be a significant improvement on the calibration based on the determination of the all-embracing zeta-factor

Cenozoic granitoids in the Dinarides of southern Serbia: age of intrusion, isotope geochemistry, exhumation history and significance for the geodynamic evolution of the Balkan Peninsula

Two age groups were determined for the Cenozoic granitoids in the Dinarides of southern Serbia by high-precision single grain U–Pb dating of thermally annealed and chemically abraded zircons: (1) Oligocene ages (Kopaonik, Drenje, Z ˇ eljin) ranging from 31.7 to 30.6 Ma (2) Miocene ages (Golija and Polumir) at 20.58–20.17 and 18.06–17.74 Ma, respectively. Apatite fission-track central ages, modelling combined with zircon central ages and additionally, local structural observations constrain the subsequent exhumation history of the magmatic rocks. They indicate rapid cooling from above 300°C to ca. 80°C between 16 and 10 Ma for both age groups,  induced by extensional exhumation of the plutons located in the footwall of core complexes. Hence, Miocene magmatism and core-complex formation not only affected the Pannonian basin but also a part of the mountainous areas of the internal Dinarides. Based on an extensive set of existing age data combined with our own analyses, we propose a geodynamical model for the Balkan Peninsula: The Late Eocene to Oligocene magmatism, which affects the Adria derived lower plate units of the internal Dinarides, was caused by delamination of the Adriatic mantle from the overlying crust, associated with post-collisional convergence that propagated outward into the external Dinarides.  Miocene magmatism, on the other hand, is associated with core-complex formation along the southern margin of the Pannonian basin, probably associated with the W-directed subduction of the European lithosphere beneath the Carpathians and interfering with ongoing Dinaridic–Hellenic back-arc extension