DFENS: Diffusion Chronometry Using Finite Elements and Nested Sampling. (22nd April 2021) - Mutch, Euan J. F.; Maclennan, John; Shorttle, Oliver; Rudge, John F.; Neave, David A.
Abstract: 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 toward 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. Plain Language Summary: Diffusion acts to smooth out compositional changes in minerals, such as olivine and plagioclase, when they try to equilibrate with new magmatic environments. Modeling this diffusion process has proven to be a powerful tool for estimating the timescales of magmatic processes: an expanding field known as diffusion chronometry. This method, however, is typically associated with large errors due to uncertainties in physical parameters (e.g., temperature and pressure) and the experimentally derived diffusion coefficients. Here, we present a new diffusion chronometry method called Diffusion chronometry using Finite Elements and Nested Sampling (DFENS). This method uses Bayesian statistics to account for all of the uncertainties in the physical and diffusion coefficient parameters, meaning the uncertainties in diffusion timescales can be robustly accounted for. We applied the DFENS method to olivine and plagioclase crystals from the Skuggafjöll eruption, Iceland. These minerals appear to have shared a common magmatic history. We found that the plagioclase and olivine crystals gave broadly consistent pre‐eruptive residence timescales of less than 1 year. This could have important implications for volcanic hazard assessment and volcano monitoring in the Bárðarbunga volcanic system, Iceland. Key Points: New diffusion chronometry method that combines finite elements and Bayesian statistics to robustly account for timescale uncertainties Agreement between olivine and plagioclase chronometers when applied to samples from the Bárðarbunga volcanic system, Iceland Magma mixing timescales prior to the Skuggafjöll eruption are estimated to be less than 1 year