Age dispersion is a common feature of apatite fission track (AFT) and
apatite (U–Th)

The works published in this journal are distributed under the Creative Commons Attribution 4.0 License. This licence does not affect the Crown copyright work, which is re-usable under the Open Government Licence (OGL). The Creative Commons Attribution 4.0 License and the OGL are interoperable and do not conflict with, reduce or limit each other. The co-author Dale R. Issler is an employee of the Canadian Government and therefore claims Crown copyright for the respective contributions. © Crown copyright 2021

Studies focusing on upper crustal tectonics, landscape evolution, and
sedimentary basin analysis often rely on apatite fission track (AFT) and
apatite (U–Th)

The canonical temperature sensitivity for AFT dating is

There is clear experimental documentation that AFT annealing is influenced
by composition (e.g., Gleadow and Duddy, 1981; Green et al., 1986; Carlson
et al., 1999; Barbarand et al., 2003; Ravenhurst et al., 2003). While the
use of track annealing kinetic models based on different apatite
compositions is not a new concept (e.g., Green, 1992), there has been
limited application within the broader thermochronology community over the
years in terms of fully exploiting detailed apatite elemental analyses
rather than kinetic proxy data. The work of Carlson et al. (1999) remains
one of the most detailed studies of fission track annealing with respect to
apatite chemistry. They derived the empirical

The main purpose of this paper is to show that multikinetic AFT samples with
significantly different annealing characteristics carry far more thermal-history information than single AFT populations with typical annealing
temperatures (

We chose a deep-time problem involving slow cooling and multiple reheating events because it is harder to deal with than a Phanerozoic case that may have more geological constraints available. In general, deep-time problems suffer from greater uncertainty that could be addressed by having thermochronometers with a broad range of temperature sensitivity (McDannell and Flowers, 2020). This is a synthetic resolution test and a single example drawn from a nearly infinite number of possibilities. These exercises were performed assuming that we knew the true thermal history, which is almost always not the case, and they are ultimately meant to encourage users of low-temperature thermochronology to thoroughly interpret data and explore kinetics before undertaking thermal-history simulations.

For natural samples, complicated thermal-history information may be retained
in multikinetic AFT data. Consideration of kinetics is most important for
histories involving persistence at, or reheating to, a temperature range
that differentiates the thermal response of the grains present, and thus the
apparent ages and lengths recorded. Our ability to resolve kinetic
populations depends on the number of AFT age and length measurements and
their distribution across different populations. For example, multikinetic
AFT data with low-U apatite grains can pass the

Unlike AFT, there is limited empirical evidence to suggest

Many modern studies include both AFT and AHe data, and reconciliation of
these complementary datasets is often difficult in slowly cooled settings.
In situations where this occurs, AHe apparent age scatter is often
attributed to the effects of radiation damage (or secondarily grain size),
yet unexplained dispersion often persists even when these variables are
considered. The commonly implemented kinetic models for the AHe system
(Flowers et al., 2009; Gautheron et al., 2009) utilize fission track
annealing as a proxy for radiation damage annealing – therefore it is
unclear whether chemistry truly affects He diffusion or if this is illusory
due to the use of a composition-based fission track kinetic model. The
assumption here is that apatite chemistry

Synthetic AFT data were generated from forward modelling a two-pulse heating
history over 2000 Myr using the QTQt software v. 5.7.3 (Gallagher, 2012)
implementing Ketcham et al. (1999) annealing kinetics (Fig. 1), with one
maximum heating event occurring at 1000 Ma (110

Thermal history used to predict synthetic AFT and AHe data. This

Predicted synthetic AFT data from the thermal history in Fig. 1.
Multikinetic age populations were individually predicted using distinct

We attempted to recover the true thermal history used to predict the
synthetic data from Sect. 3.1 using the QTQt software. QTQt implements a
reversible jump Markov chain Monte Carlo algorithm to systematically search

The

The data were formulated with identical EDM parameters, including, a

We ran QTQt in multiple stages to tune the parameters for sampling and to
ensure the acceptance rates for time and temperature were between

The long time interval for these model inversions are styled after a typical
cratonic history, and the only constraint that was consistently enforced was
starting the model at 300

For all models presented hereafter, we show the QTQt maximum likelihood (ML;
i.e., usually more complex, best fit

QTQt inversion results are shown in Fig. 3 and illustrate the implications
of multikinetic AFT-only, joint models with multikinetic AFT and AHe grains
using the correct kinetics (i.e., the kinetics implemented during forward
modelling to predict AHe ages), and different combinations of incorrect
monokinetic AFT models where the three multikinetic populations were
combined and treated as a single AFT sample, and/or AHe ages were assumed to
have the endmember fluorapatite

Thermal-history inversion results from QTQt under different
imposed kinetic and

QTQt inversion predictions compared to “observed” synthetic
thermochronology data generated during forward modelling. Panel letters
correspond to counterpart

The first model was setup to simultaneously invert each AFT kinetic
population without AHe data for scenarios with a “no constraint” model, a
“single

The addition of the three AHe ages using their

In our experience, multikinetic behaviour is not uncommon for basement
samples characterized by complicated burial histories and nearly always
present for detrital apatite samples derived from complex source areas that
experience multiple heating events. In our “monokinetic” scenario, the
multikinetic AFT data were incorrectly treated as a single population and
modelled using the central age, MTL, and average eCl (or

The AFT and AHe modelling results presented here may seem intuitive based on the implemented kinetics and modelling exercises using synthetic data but are worth discussing, since situations where variable apatite compositions could influence thermochronometric ages are likely to be encountered in natural samples. The results indicate the benefits offered by interpreting intrasample AFT kinetic populations for inverse modelling and show how inappropriate assumptions regarding kinetic parameters can greatly influence model outcome. Our examples were determined for a single, distinct thermal history, and yet they establish that apatite composition and multikinetic interpretation (when appropriate) provide valuable information for thermal-history modelling – and they are mostly unexplored, or at least underutilized, by routine AFT studies.

Collection of elemental data and interpretation of multikinetic samples is
particularly important for providing greater

The overall temporal and thermal resolution contained in multikinetic AFT
data is influenced by multiple factors, such as the amount and distribution
of the data (i.e., if most of the data are contained in one population
versus distributed more equally), thermal history (i.e., the magnitude and
sequence of heating-cooling events), and kinetics (i.e., the range of
temperature sensitivity). A greater number of different kinetic groups are
sensitive to an expanded

However, enforcing constraints do not provide a remedy if AFT kinetic
relationships are ignored. The main region of

QTQt models of each individual AFT kinetic population plotted with
respect to the true thermal history.

Figure 3e shows the ideal case with the most accurate thermal-history
recovery (nearly identical to the true history) when two constraint boxes
are implemented with three interpreted AFT kinetic populations and three AHe
grains modelled using the proper kinetics. Importantly, this applies in the
case of integrating multiple low-temperature thermochronometers and/or
multikinetic AFT data, especially multikinetic populations that
progressively diverge in kinetics, therefore increasing thermal resolution.
However, constraint boxes provide no obvious advantage when the three
multikinetic populations are ignored and only the overall central AFT age is
modelled (Fig. 3h). We show additional QTQt models in Fig. 5 to further
establish the utility of modelling AFT grain populations with different
annealing kinetics and the distinct temperature sensitivity provided by each
kinetic group. These simulations were carried out for each kinetic
population individually to demonstrate the sensitivity of each population to
the multiple heating and cooling events present in the true forward history.
The model in Fig. 5a shows that population one is only sensitive to
post-1 Ga cooling and the second reheating event, whereas the model in
Fig. 5b shows that population two is most sensitive to peak temperatures
achieved during the first heating event. Population three is sensitive to
the initial cooling from high temperature and requires some poorly resolved
reheating to partially reset the AFT age and match the track length
distribution. The high retentivity of population 3 makes it mostly
insensitive to the two heating and cooling cycles. Each of these simulations
illustrates that a single AFT population lacks sufficient

Recently, Green and Duddy (2020) stated that “thermochronology data in isolation cannot define periods when samples were cooler and subsequently reheated. This can only be defined with the aid of constraints from geological evidence.” Their comment alludes to the non-uniqueness of

Multikinetic AFT data may record complicated thermal histories that are
difficult to simulate using classical randomized MC algorithms, and model
success can depend strongly on the choice of boundary conditions that are
used to limit the model search space. The synthetic AFT data were inversely
modelled using the newest version of AFTINV v. 6.15 (Issler, 1996), a
derivative of the Willett (1997) model that is similar to the HeFTy software
(Ketcham, 2005) in using a nondirected MC scheme and

Model sensitivity runs were undertaken to determine the boundary conditions
needed to obtain close fitting solutions, and Fig. 6 shows the final
preferred model results obtained from the CRS calculations. We assumed two
random reheating events with two accompanying thermal minima randomly
selected between 1700–1200 and 700–400 Ma for the model

Unlike the QTQt model results of Fig. 3, all individual thermal histories
in Fig. 6a provide statistically significant fits to the AFT data. The
minimum objective function solution (green curve; Fig. 6a) provides the
closest fit to the AFT age and length data (Fig. 6c). The exponential mean
of all 300 solutions (blue curve; Fig. 6a) provides acceptable fits for
kinetic populations two and three but fails to fit population one lengths
due to insufficient annealing; the wide range of permissible solutions for
the low-temperature peak results in an exponential mean peak temperature
that is lower than each of the individual solutions. Retention ages (Fig. 6b) are model ages representing the oldest track (the shortest retained
track length of

Using synthetic multikinetic AFT (and AHe data) derived from forward
modelling, we show that, under favourable conditions, it is possible to
extract multi-cyclic heating and cooling history information using inverse
modelling methods when kinetic parameters for AFT annealing are correctly
specified. Essential details of a two-phase heating and cooling history are
reproduced using AFT multikinetic data alone without imposing constraint
boxes, but the closest fit to the true solution is achieved using all the
synthetic data with constraint boxes. Alternative monokinetic
interpretations that ignore multikinetic behaviour generate solutions that
significantly depart from the true solution while providing close fits to
the interpreted AFT data; under these conditions, imposing constraint boxes
does not improve modelled

We recommend the routine collection of elemental data for apatite dated
using the fission track method to better quantify sample compositional
variation and relate this to kinetic behaviour for thermal-history analysis.
Elemental data may also prove useful to characterize first-order chemical
variation in AHe datasets. The use of

The Supplement contains the true thermal history and the synthetic AFT dataset. See the main text for further details.

The supplement related to this article is available online at:

KTM designed research and performed QTQt modelling. DRI performed AFTINV modelling and was involved in conceptual discussions and model evaluation. KTM and DRI wrote the paper.

The authors declare that they have no conflict of interest.

These ideas were developed while Kalin T. McDannell was a postdoc at the Geological Survey of Canada and supported by the Natural Resources Canada Geo-mapping for Energy and Minerals (GEM) program. The authors graciously thank Kerry Gallagher, Rich Ketcham, and an anonymous reviewer for thoughtful comments to improve the clarity of this article and Noah McLean for efficient editorial handling and correspondence. Kerry Gallagher is also acknowledged for making changes to QTQt specifically for these modelling exercises. Kalin T. McDannell thanks his partner Jennifer for her help during the writing of this article. This is NRCan contribution number 20200758.

This paper was edited by Noah M. McLean and reviewed by Kerry Gallagher, Richard A. Ketcham, and one anonymous referee.