Bias in detrital fission track grain-age populations: Implications for reconstructing changing erosion rates

https://doi.org/10.1016/j.epsl.2015.04.020Get rights and content

Highlights

  • Interpreting detrital fission track data: Distinguishing changing exhumation rates and inversion artefacts.

  • Identification of bias in detrital fission track age dating.

  • Monte-Carlo bootstrapping of true closure age synthetics to find measurable population ages.

Abstract

The sedimentary record is our principal archive of mass transfer across the Earth's surface in response to tectonic and climatic changes in the geologic past. The thermochronology of individual sediment grains (detrital thermochronology) has emerged as a critical tool to infer erosion rates and track mountain belt evolution. Such inferences are reliant upon the statistical inversion of detrital grain ages to unbiasedly approximate the cooling history of the source areas from which the sediment originated. However, it is challenging to critique the reliability and consistency of modelled ages. These arise both from fundamental measurement uncertainties and the assumptions we employ in inverting the data. For detrital fission track modelling of young detrital samples, this problem is particularly acute since the uncertainty on the track counts produces uncertainty in the age estimates. We apply Monte-Carlo modelling to generate synthetic detrital data conditioned on known closure age models, and then invert the grain data to assess the reliability of different inversion schemes. The results clearly demonstrate that existing practice can be subject to large uncertainty, to systematic bias and to non-uniqueness of interpretation. We then show how to map such regions of systematic bias in the population modelling as a function of the true closure ages, and how this bias propagates through into the lag-time modelling. Applying the method to real data from the Siwalik group sediments in western Nepal, we find no evidence for a change in the underlying climate or tectonic processes, since the apparent change in lag coincides with a thresholded change in the resolution of the population modelling. This paper shows how to map regions of systematic bias in the population modelling as a function of the true closure ages, and how this bias propagates through into the lag-time modelling and can be applied retrospectively to existing studies. However, it is equally applicable to other age inversion schemes such as minimum age modelling. The application of these methods will enhance current practice and facilitate more robust interpretation of grain ages, in particular in discriminating between stationary and non-stationary geological and climatic processes.

Introduction

The reconstruction of past erosion rates is critical in determining the evolution of past sediment fluxes (Allen et al., 2013), the development of active mountain ranges (Jamieson and Beaumont, 1989) and evolving surface topography (England and Molnar, 1990). Erosion records the interplay of climate, lithology and tectonics, and so past erosion rates are also commonly interpreted in terms of these controls. Methodologies for reconstructing erosion over millions of years are dominated by measurements of sediment volumes and measuring the cooling history of rocks (thermochronology) where cooling is used as a proxy for exhumation of rock through erosion (Reiners and Brandon, 2006).

Bedrock thermochronology analyses the cooling history of a number of crystals from a single rock sample where all the grains have experienced the same history. In order to reconstruct the cooling history of a bedrock sample, multiple thermochronometers that record the time of passage through a range of closure isotherms are required. For regional analyses, multiple samples have to be collected, ideally from a range of different elevations (e.g. Fitzgerald et al., 1995); spatial interpolation may then enable regional erosion histories to be reconstructed (e.g. Vernon et al., 2008). Bedrock thermochronology often misses the early, now substantially eroded part of the exhumation history.

An alternative to regional bedrock sampling is to analyse the sediment sourced from river catchments that drain the region over variable timescales; this approach is termed detrital thermochronology (Garver et al., 1999). In this method, grains originate from erosion of a source area that covers a broad region where exhumation rates are likely to vary, and hence the age distributions should record that variability. For sediment samples taken from the stratigraphic record, the age distributions record exhumation rates averaged over the time intervals for each grain to pass from its closure depth to the surface; these intervals will be different for the different populations. This ability to reconstruct ancient exhumation rates of the upper few kilometres of the crust for different stratigraphic time intervals using a single technique has increased understanding of the evolution of mountain chains such as the Alps (Bernet et al., 2009, Glotzbach et al., 2011) and the Himalaya (e.g. van der Beek et al., 2006).

A widely used thermochronometer is fission-track (FT) analysis of apatite and zircon grains (e.g., Gallagher et al., 1998, Tagami and O'Sullivan, 2005). In contrast to noble-gas based methods (e.g. Ar–Ar, (U–Th)/He), FT analysis is relatively insensitive to abrasion of grains during sediment transport and so is most suited to detrital thermochronology. In the simplest case, the FT method takes grains of apatite or zircon, measures the density of spontaneous fission tracks that have damaged the crystal lattice of the grain, and uses independent information of the amount of uranium in the grain to estimate a duration since the grain started accumulating tracks (Fleischer et al., 1975, Price and Walker, 1963). The detrital fission-track (DFT) method is similar to bedrock FT up to the point where individual grain ages are estimated. Since detrital samples contain grains from multiple bedrock sources that were exhuming at different rates, we cannot assume that a common pooled age is a useful measure for characterising the composite cooling histories recorded in the detrital sample.

There are two commonly applied methods used to analyse detrital grain age data. The first uses population modelling to invert samples with up to ∼120 grains sampled from modern river sediments or the stratigraphic record to find a parsimonious set of population ages that explain the variance in the observed grain ages (Brandon, 1992, Brandon, 2002; Galbraith, 1988, Galbraith and Green, 1990, Galbraith and Laslett, 1993). These populations, especially the youngest P1 population, are then interpreted to make inferences about the evolution of regional erosion rates, as well as sediment provenance and catchment reorganisation (e.g., Bernet et al., 2001, Bernet et al., 2009; Glotzbach et al., 2011, Kirstein et al., 2010). The second method uses one of several methods to invert for a minimum age consistent with the population of ages (e.g. Galbraith and Laslett, 1993, Galbraith, 2005).

This paper considers how the component age populations in detrital fission-track analysis are estimated, and how they relate to “true” closure ages experienced by the grains. We explore issues of bias, uniqueness, and uncertainty when identifying component populations within detrital samples. Monte-Carlo sampling is used to generate synthetic DFT samples where the underlying closure age distribution is specified and our ability to recover the known closure age(s) in multiple random samples is tested. In these samples, the only sources of uncertainty are the probabilistic assignment of closure ages to each grain and Poisson counting errors on the number of spontaneous tracks. We then apply these methods to facilitate a more robust reinterpretation of detrital data from the Siwaliks (van der Beek et al., 2006). The power of this computational method comes in the scale of the samples that can be analysed; we have typically run ∼500,000 synthetic detrital samples which take ∼2 days on a desktop computer. This allows us to critique previous interpretations of data in a transparent and systematic manner. Specifically, the method quantifies the emergence of artefacts as the resolution of population modelling degrades.

Section snippets

Fission track theory and age models

Fission tracks in crystals, such as apatite and zircon, are the record of lattice damage generated by the spontaneous decay of 238U or the induced decay of 235U. These tracks become visible under a microscope when the crystals are mounted, cut, polished and etched (Fleischer et al., 1975, Price and Walker, 1963). Annealing of the crystals removes fission tracks at a rate that increases with temperature; above some mineral-specific closure temperature all tracks are rapidly lost and below that

Quantifying uncertainty and bias using the Monte-Carlo bootstrap

The basis of the bootstrap method (Fig. 1) is to (i) forward model a synthetic detrital fission track sample using a known closure age model and (ii) invert the resulting dataset to quantify how well we can recover information about the original closure age model. By repeating this many times for the same age distribution, we identify systematic bias and determine uncertainty as a result of: 1) stochastic uncertainty on the number of observed tracks and, 2) fundamental limitations in the

Results using discrete closure age models

We determine what closure age models are resolvable in principle using population modelling for a specific detrital sample. By specific, we mean a finite set of n grains with some measured uranium content, likely determined through the external detector method.

When discussing the results, the term “closure age” is reserved to refer to the ages that are probabilistically assigned when generating the synthetic track data; in this sense, they are the “true” ages on which the synthetic data are

Case study: Karnali Apatite FT (AFT) data

To make the studies relevant to real data requires the synthetics to be calibrated against the properties of the dataset under consideration. For example, the synthetics should be conditioned on the measured induced track data. In this case study, we demonstrate how to interrogate a detrital apatite fission-track dataset in order to test whether a specific interpretation is robust.

We consider a detrital AFT dataset from van der Beek et al. (2006). The samples come from a Mio-Pliocene (<15 Ma)

Discussion

This study starts to address problems that are known to exist with common practice in the analysis of detrital fission track data. For example, Galbraith (2005) points out that “A finite mixture model is sometimes reasonable in fission-track dating applications when not all grains have the same true age,” and goes on to say “However, it will not always be an appropriate model … for heterogeneous ages,” and that “the mixing ages may sometimes have a rather artificial meaning.” These points are

Conclusions

Through the application of the Monte-Carlo bootstrap method, we have demonstrated that it is possible to quantify systematic bias and uncertainty in detrital fission track modelling. Understanding these sources of bias is essential if methodologies for rigorously interpreting detrital fission-track data to understand geological process and history are to be developed.

Computationally bootstrapping the behaviour of synthetic DFT samples based on real FT data is an efficient way to improve the

Acknowledgments

MN was funded by a Royal Society of Edinburgh and Scottish Government Personal Research Fellowship. A visit to Grenoble to further collaboration was supported by Marie Curie Actions. For access to the code contact [email protected].

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