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Primary data, model initial conditions, model results, a compiled database of olivine diffusivity experiments and supplementary tables used in the paper: 'Mutch, E. J. F., Maclennan J., Shorttle, O., Edmonds, M. & Rudge, J. F., (2019), Rapid trans-crustal magma movement under Iceland, Nature Geoscience'. Data_S1 contains electron probe microanalysis (EPMA) profile data of olivine crystals used in this study. This file also includes all of the initial conditions for forsterite content (XFo), Ni and Mn used in the diffusion modelling. Standard deviations are averaged values of standard deviations from counting statistics and repeat measurements of secondary standards. Data_S2 is a compiled database of olivine diffusion experiments used to derive multiple linear regressions for diffusion coefficients and associated covariance matrices. Regressions were only made through  data. Data_S3 contains median values for all of the inverted parameters estimated for each crystal profile from the Nested Sampling Bayesian inversion for each type of initial condition and model equation. All of the Monte Carlo realisations for each model are also included in this file. Table_S1 is a supplementary table that contains olivine diffusion equation regression parameters derived and used as part of this study. Table_S2 is a supplementary table that contains covariance matrices for olivine diffusion equations derived in this study. Table_S3 is a supplementary table that contains covariance matrices for aSiO2 (silica activity) dependent olivine diffusion equations derived in this study. Table_S4 is a supplementary table that contains angles between the EPMA profile and the main crystallographic axes in olivine as measured by EBSD. These angles are incorporated into the anisotropy calculation used to determine the apparent diffusivity parallel to the measured profile. angle100P, angle010P and angle001P are the angles between the profile and ,  and  respectively. Table_S5 is a supplementary table that contains ,median timescales and 1 sigma errors obtained from the posterior distributions of the Nested Sampling Bayesian inversion conducted on each olivine profile. The results using Al-based initial conditions, constant initial conditions (diffusion only), and aSiO2 based equations using Al-based initial conditions are presented here. The classification of each profile (growth-dominated vs. Al-decoupled) is also shown. See paper (Mutch, E. J. F., Maclennan J., Shorttle, O., Edmonds, M. & Rudge, J. F., (2019), Rapid trans-crustal magma movement under Iceland, Nature Geoscience) for more details.