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A stochastic sampling approach to zircon eruption age interpretation

C.B. Keller1,2,

1Berkeley Geochronology Center, Berkeley, CA 94709, USA
2Department of Earth and Planetary Science, University of California, Berkeley, CA 94720, USA

B. Schoene3,

3Department of Geosciences, Guyot Hall, Princeton University, Princeton, NJ 08544, USA

K.M. Samperton4

4Nuclear and Chemical Sciences Division, Lawrence Livermore National Laboratory, Livermore, CA 94550, USA

Affiliations  |  Corresponding Author  |  Cite as  |  Funding information

C.B.K. partially supported by U.S. DOE CSGF under contract DE-FG02-97ER25308.

Geochemical Perspectives Letters v8  |  doi: 10.7185/geochemlet.1826
Received 5 February 2018  |  Accepted 13 September 2018  |  Published 2 October 2018
Copyright © The Authors

Published by the European Association of Geochemistry
under Creative Commons License CC BY 4.0

Figure 1 Zircon distributions. (a) Theoretical and empirical relative zircon crystallisation distributions f(tr), scaled from initiation to termination of zircon crystallisation. 1: Kinetic model of Watson (1996)

Watson, E.B. (1996) Dissolution, growth and survival of zircons during crustal fusion: kinetic principles, geological models and implications for isotopic inheritance. Transactions of the Royal Society of Edinburgh: Earth Sciences 87, 43–56.

, based on zirconium diffusion constraints. 2: Thermodynamic model of Keller et al. (2017)

Keller, C.B., Boehnke, P., Schoene, B. (2017) Temporal variation in relative zircon abundance throughout Earth history. Geochemical Perspectives Letters 3, 179–189.

using MELTS calculations. 3: Observed zircon crystallisation distributions of Samperton et al. (2017)

Samperton, K.M., Bell, E.A., Barboni, M., Keller, C.B., Schoene, B. (2017) Zircon age-temperature-compositional spectra in plutonic rocks. Geology 45, 983–986.

, shown as a kernel density estimate for all autocrystic zircons, truncated at +/- 1 kernel bandwidth. (b-d) Representative synthetic zircon age datasets for a variety of ∆t/σ at N = 10. (e) Example dataset with N = 100 at ∆t = 1σ; note the range is greater than in c despite lower ∆t. (f) Schematic illustration of the three most common volcanic zircon age interpretations.
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Figure 2 Performance of each age interpretation as a function of N and ∆t/σ. (a-d) Mean absolute error is the mean absolute deviation of the model result from the true value; lower absolute errors are better. (e-h) Accuracy of the model uncertainty for each age interpretation. A value greater than 1.0 indicates an under-estimation of the model uncertainty (i.e. over-precision), while a value lower than 1.0 indicates an over-estimation of the model uncertainty. MSWD in each panel is the average mean square of weighted deviation (also known as the reduced chi squared statistic) for that ∆t/σ over all N. Each datum reflects the mean of 1200 synthetic dataset tests; standard error of the mean is on the order of the line width.
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Figure 3 Bayesian eruption age estimates for two well known volcanic zircon populations. For age spectra with well-resolved dispersion (a), a kernel density estimate may recover a close approximation of f(tr), obviating the need to identify and reject antecrysts. However, for age spectra where igneous dispersion is not well resolved (b), assuming a uniform f(tr) may be more parsimonious.
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