Patterns of cooling in basement rocks — A bootstrap method to measure anomalous spatial dispersion of zircon fission-track ages

Thermochronology depends on isotopic systems for which the age is related to the time that a specified mineral cooled through its closure temperature. In tectonic studies, it is often of interest to examine regional variations in cooling age. When the variation in age within a data set exceeds the analytical errors on the age determinations, many options are available to model the spatial variation in age and to correlate it with other data or with the predictions of hypotheses. For example, trend surfaces [e.g. Davis J.C. (1986) Statistics and Data Analysis in Geology, 2nd edn. Wiley, New York] could be used to explain the variation that exceeds experimental error. In the case of interest in this study it may appear that the variations in age originate entirely from random analytical error. We show how geologically significant patterns that may be present in such apparently random data can be detected. Our analysis is based on characterizing how the extreme ages (oldest and youngest) are distributed among the sample localities. In particular, we explore whether the extremes are more dispersed or more clustered than could be expected from a random assignment of ages to the localities, as deduced from bootstrap simulations. This mode of analysis is non-parametric and requires no assumptions about the distributional form of the errors or the ages. The proposed analysis is applied to 34 zircon fission-track ages from the central Appalachian Piedmont, eastern U.S.A. Our results show that the older ages are concentrated near the center of the sample region and are surrounded by younger ages. This age pattern suggests that rocks now at the surface in the central part of the study area cooled first, followed by rocks located toward the periphery of the area.