DFENS: Diffusion Chronometry using Finite Elements and Nested Sampling

In order to reconcile petrological and geophysical observations of magmatic processes in the temporal domain, the uncertainties in 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 that uncertainties in the parameters contributing to diffusion timescale estimates can be obtained and that observations from multiple elements can be used to better constrain individual timescales. Uncertainties associated with diffusion timescales can be reduced by accounting for covariance in the uncertainty structure of diffusion parameters rather than assuming that they 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 towards 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, initial conditions, crystal growth, and the petrological context of diffusion timescales.