Testing the Consistency of Diffusion Modelling in Multiple Crystal Phases: A Case Study from the Bishop Tuff, California

Diffusion modelling of elemental gradients across compositional zones within crystals is frequently used to investigate timescales of various magmatic processes. In most cases, however, only a single crystal phase is used for this modelling. The ~0.76 Ma Bishop Tuff (Long Valley, eastern California) in later parts of its eruptive sequence has zoned orthopyroxene, quartz and sanidine. It thus provides an unusual opportunity to compare the modelled timescales from each phase, and assess the limitations of single-phase diffusion modelling in lower-temperature, rhyolitic volcanic systems. The presence of a late-stage compositionally distinct melt (the 'bright-rim' melt) mixing into the lower parts of the Bishop magma chamber has been noted by many authors [e.g. Wark et al. 2007, Geology 35, 235; Roberge et al. 2013, CMP 165, 237; Chamberlain et al. 2014, J Petrol 55, 395] in later-erupted material discharged from vents along the northern ring fracture of the caldera. Here we present the results of 1D diffusion modelling of Ba and Sr in sanidine, Ti in quartz and Fe-Mg interdiffusion in orthopyroxene in samples from later-erupted ignimbrite packages in the tuff. Timescales from diffusion modelling of Fe-Mg interdiffusion in orthopyroxene are <20 years; Ti in quartz <150 years and from Ba and Sr in sanidine <10000 years. The orders of magnitude variance between different crystal phases can be attributed to either distinct differences in the timing of interaction with the 'bright-rim' melt, or to uncertainties in the diffusion coefficient (orthopyroxene) and incorrect assumptions about the initial conditions for diffusion modelling (sanidine), or some combination of these factors. By combined modelling of Ba and Sr diffusion in sanidine the diffusion timescales are reduced to <1000 years, implying that interaction of the 'bright-rim' melt may have occurred over more extended timescales, and was not necessarily a direct eruptive trigger for the Bishop Tuff eruption. We highlight the importance of having a good understanding of the assumptions made and uncertainties in diffusion coefficients when undertaking such modelling, especially in examples where only one phase is available for diffusion modelling.