In order to reconcile petrological and geophysical observations in the
temporal domain, the uncertainties of diffusion timescales need to be
rigorously assessed. Here we present a new diffusion chronometry method:
Diffusion chronometry using Finite Elements and Nested Sampling (DFENS).
This method combines a finite element numerical model with a nested
sampling Bayesian inversion meaning the uncertainties of the parameters
that contribute to diffusion timescale estimates can be rigorously
assessed, and that observations from multiple elements can be used to
better constrain a single timescale. By accounting for the covariance in
uncertainty structure in the diffusion parameters, estimates on
timescale uncertainties can be reduced by a factor of 2 over assuming
that these parameters are independent of each other. We applied the
DFENS method to the products of the Skuggafjöll eruption from the
Bárðarbunga volcanic system in Iceland, which contains zoned macrocrysts
of olivine and plagioclase that record a shared magmatic history.
Olivine and plagioclase provide consistent pre-eruptive mixing and mush
disaggregation timescales of less than 1 year. The DFENS method goes
some way to improving our ability to rigorously address the
uncertainties of diffusion timescales, but efforts still need to be made
to understand other systematic sources of uncertainty such as crystal
morphology, appropriate choice of diffusion coefficients, growth, and
the petrological context of diffusion timescales.