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Significant zonation in major, minor, trace, and volatile elements has been documented in naturally glassy olivine-hosted melt inclusions from the Siqueiros Fracture Zone and the Galapagos Islands. Components with a higher concentration in the host olivine than in the melt (e.g., MgO, FeO, [Cr.sub.2][O.sub.3], and MnO) are depleted at the edges of the zoned melt inclusions relative to their centers, whereas except for CaO, [H.sub.2]O, and F, components with a lower concentration in the host olivine than in the melt (e.g., [Al.sub.2][O.sub.3], Si[O.sub.2], [Na.sub.2]O, [K.sub.2]O, Ti[O.sub.2], S, and Cl) are enriched near the melt inclusion edges. This zonation is due to formation of an olivine-depleted boundary layer in the adjacent melt in response to cooling and crystallization of olivine on the walls of the melt inclusions, concurrent with diffusive propagation of the boundary layer toward the inclusion center. Concentration profiles of some components in the melt inclusions exhibit multicomponent diffusion effects such as uphill diffusion (CaO, FeO) or slowing of the diffusion of typically rapidly diffusing components ([Na.sub.2]O, [K.sub.2]O) by coupling to slow diffusing components such as Si[O.sub.2] and [Al.sub.2][O.sub.3]. Concentrations of [H.sub.2]O and F decrease toward the edges of some of the Siqueiros melt inclusions, suggesting either that these components have been lost from the inclusions into the host olivine late in their cooling histories and/or that these components are exhibiting multicomponent diffusion effects. A model has been developed of the time-dependent evolution of MgO concentration profiles in melt inclusions due to simultaneous depletion of MgO at the inclusion walls due to olivine growth and diffusion of MgO in the melt inclusions in response to this depletion. Observed concentration profiles were fit to this model to constrain their thermal histories. Cooling rates determined by a single-stage linear cooling model are 150-13,000°C [h.sup.-1] from the liquidus down to ~ 1,000°C, consistent with previously determined cooling rates for basaltic glasses; compositional trends with melt inclusion size observed in the Siqueiros melt inclusions are described well by this simple single-stage linear cooling model. Despite the overall success of the modeling of MgO concentration profiles using a single-stage cooling history, MgO concentration profiles in some melt inclusions are better fit by a two-stage cooling history with a slower-cooling first stage followed by a faster-cooling second stage; the inferred total duration of cooling from the liquidus down to ~ 1,000°C ranges from 40 s to just over 1 h. Based on our observations and models, compositions of zoned melt inclusions (even if measured at the centers of the inclusions) will typically have been diffusively fractionated relative to the initially trapped melt; for such inclusions, the initial composition cannot be simply reconstructed based on olivine-addition calculations, so caution should be exercised in application of such reconstructions to correct for post-entrapment crystallization of olivine on inclusion walls. Off-center analyses of a melt inclusion can also give results significantly fractionated relative to simple olivine crystallization. All melt inclusions from the Siqueiros and Galapagos sample suites exhibit zoning profiles, and this feature may be nearly universal in glassy, olivine-hosted inclusions. If so, zoning profiles in melt inclusions could be widely useful to constrain late-stage syneruptive processes and as natural diffusion experiments. Keywords Melt inclusions * Chemical zonation * Diffusion * Geospeedometry, Introduction It is often implicitly assumed that glassy melt inclusions in phenocrysts are homogeneous and thus that analyses from near the center of an inclusion are representative of the inclusion [...]