Zonation of H 2 O and F Concentrations around Melt Inclusions in Olivines

Studies of both naturally quenched and experimentally reheated melt inclusions have established that they can lose or gain H 2 O after entrapment in their host mineral, before or during eruption. Here we report nanoSIMS analyses of H 2 O, Cl and F in olivine around melt inclusions from two natural basaltic samples: one from the Sommata cinder cone on Vulcano Island in the Aeolian arc and the other from the Jorullo cinder cone in the Trans-Mexican Volcanic Belt. Our results constrain olivine/basaltic melt partition coefficients and allow assessment of mechanisms of volatile loss from melt inclusions in natural samples. Cl contents in olivine from both samples are mostly below detection limits ( (cid:2) 0 · 03 (cid:3) 0 · 01ppm), with no detectable variation close to the melt inclusions. Assuming a maximum Cl content of 0 · 03 ppm for all olivines, maximum esti-mates for Cl partition coefficients between olivine and glass are 0 · 00002 (cid:3) 0 · 00002. Olivines from the two localities display contrasting H 2 O and F compositions: Sommata olivines contain 27 (cid:3) 11ppm H 2 O and 0 · 28 (cid:3) Sommata melt inclusions before diffusive loss of 6 wt % H 2 O.The findings provide new insights on rapid H 2 O loss during magma ascent and improve our ability to assess the fidelity of the H 2 O record from melt inclusions.

Studies of both naturally quenched and experimentally reheated melt inclusions have established that they can lose or gain H 2 O after entrapment in their host mineral, before or during eruption. Here we report nanoSIMS analyses of H 2 O, Cl and F in olivine around melt inclusions from two natural basaltic samples: one from the Sommata cinder cone on Vulcano Island in the Aeolian arc and the other from the Jorullo cinder cone in the Trans-Mexican Volcanic Belt. Our results constrain olivine/basaltic melt partition coefficients and allow assessment of mechanisms of volatile loss from melt inclusions in natural samples. Cl contents in olivine from both samples are mostly below detection limits ( 0·03 AE 0·01ppm), with no detectable variation close to the melt inclusions. Assuming a maximum Cl content of 0·03 ppm for all olivines, maximum estimates for Cl partition coefficients between olivine and glass are 0·00002 AE 0·00002. Olivines from the two localities display contrasting H 2 O and F compositions: Sommata olivines contain 27 AE11 ppm H 2 O and 0·28 AE 0·07 ppm F, whereas Jorullo olivines have lower and proportionately more variable H 2 O and F (11 AE12 ppm and 0·12 AE 0·09 ppm, respectively; uncertainties are two standard deviations for the entire population). The variations of H 2 O and F contents in the olivines exhibit clear zonation patterns, increasing with proximity to melt inclusions. This pattern was most probably generated during transfer of volatiles out of the inclusions through the host olivine. H 2 O concentration gradients surrounding melt inclusions are roughly concentric, but significantly elongated parallel to the crystallographic a-axis of olivine. Because of this preferential crystallographic orientation, this pattern is consistent with H 2 O loss that is rate-limited by the ' proton^polaron' mechanism of H diffusion in olivine. Partition coefficients based on olivine compositions immediately adjacent to melt inclusions are 0·0007 AE 0·0003 for H 2 O and 0·0005 AE 0·0003 for F. The H 2 O and F diffusion profiles most probably formed in response to a decrease in the respective fugacities in the external melt, owing to either degassing or mixing with volatile-poor melt.Volatile transport out of inclusions might also have been driven in part by increases in the fugacity within the inclusion owing to post-entrapment crystallization. In the case of F, because of the lack of data on F diffusion in olivine, any interpretation of the measured F gradients is speculative. In the case of H 2 O, we model the concentration gradients using a numerical model of three-dimensional anisotropic diffusion of H, where initial conditions include both H 2 O decrease in the external melt and post-entrapment enrichment of H 2 O in the inclusions.The model confirms that external degassing is the dominant driving force, showing that the orientation of the anisotropy in H diffusion is consistent with the proton^polaron diffusion mechanism in olivine. The model also yields an estimate of the initial H 2 O content of the Sommata melt inclusions before diffusive loss of 6 wt % H 2 O. The findings provide new insights on rapid H 2 O loss during magma ascent and improve our ability to assess the fidelity of the H 2 O record from melt inclusions.

I N T RO D UC T I O N
Improvements in in situ analytical methods such as secondary ion mass spectrometry (SIMS), electron microprobe microanalysis (EPMA) and infrared spectroscopy have enabled measurement of the compositions of small volumes of silicate melt enclosed in minerals as melt inclusions (referred to hereafter as MIs) as a tool for magmatic studies. As the host minerals partially isolate MIs from the physical and chemical evolution of their parent melts, MIs can preserve information regarding the origin and evolution of magmas beyond that recorded by the chemistry of erupted lavas (e.g. Anderson, 1975;Sobolev & Shimizu, 1993). In particular, MIs typically preserve higher volatile contents relative to their associated erupted lavas, and thus are commonly used to study the pre-eruptive volatile contents of magmas (e.g. Wallace, 2005) and degassing processes (e.g. Benjamin et al., 2007).
Some studies of naturally glassy (e.g. Watson, 1976;Newman et al., 2000) or experimentally re-heated MIs (e.g. Sobolev et al., 1983) have shown that MIs do not always behave as closed systems, particularly if physical and chemical changes in the melt surrounding the host crystal drive exchange between the MIs and the external melt [either by diffusion through the host crystal (e.g. Watson, 1976) or via cracks (e.g. Anderson et al., 1989)]. Other studies have documented loss or gain of H 2 O in MIs over timescales from hours to days (e.g. Hauri, 2002;Massare et al., 2002;Severs et al., 2007;Portnyagin et al., 2008;Koleszar et al., 2009;Chen et al., 2011Chen et al., , 2013Gaetani et al., 2012;Lloyd et al., 2012). The rapidity of this re-equilibration has been linked to the high rates of hydrogen diffusion through the host olivine (Kohlstedt & Mackwell, 1998;Demouchy & Mackwell, 2006). In many cases H 2 O loss from MIs is examined during heating in the laboratory (e.g. Chen et al., 2011). Although experiments can provide quantitative insights into the transport of H-bearing species through the mineral host, they may not necessarily relate to volatile loss from natural MIs because of ambiguities regarding the pre-eruptive histories of phenocrysts. In addition, several factors, including pressure, temperature, and oxidation state, may differ between experimental and natural magmatic conditions (e.g. Danyushevsky et al., 2002).
As a result of the issues outlined above, we use an alternative approach to investigate volatile loss from MIs in natural samples. Specifically, we measure volatile concentration profiles in host olivine crystals around MIs. Although measurements of H 2 O and other volatiles dissolved in the olivine crystal structure are challenging (e.g. Hauri et al., 2002;Mosenfelder et al., 2011), characterization of such profiles can directly constrain the process of volatile transfer into and out of MIs in natural environments. Variations in the H 2 O, F, and Cl contents of olivines around MIs are determined with high spatial resolution by measurements with a NanoSIMS ion microprobe. This in situ approach allows us to describe the length and crystallographic orientation of volatile element zonation in olivines around MIs. We then use these constraints from natural samples to model H 2 O transfer from MIs using experimentally determined diffusion rates, to assess the timescale and amount of diffusive H 2 O loss from MIs.
The second sample is from a calc-alkaline basaltic tephra fall from the early (Johnson et al., 2008) highly explosive phase of the 1759^1774 eruption of the Jorullo cinder cone in the Trans-Mexican Volcanic Belt (Luhr & Carmichael, 1985). The olivine grains (with Fo 88^91 cores, overgrown abruptly by normally zoned, $50 mm thick rims extending down to $Fo 85 at the crystal edges; Johnson et al., 2008) contain MIs and embayments (regions of glass connected to matrix glass through glassfilled channels or cracks) that are 20^100 mm in diameter, irregular in shape, and sometimes contain a bubble (Johnson et al., 2008(Johnson et al., , 2010. Most of the Jorullo MIs and embayments are glassy, but some contain crystallized daughter minerals (we identified a few olivines, but most daughter minerals were too small to be characterized by EPMA). The glassy MIs are hypersthene-normative, medium-K calc-alkaline basalts to basaltic andesites (49·9^55·2 wt % SiO 2 ; 0·6^1·15 wt % K 2 O; 5·2^10·5 wt % MgO; all values were corrected for 20% post-entrapment olivine crystallization and iron loss; Johnson et al., 2008Johnson et al., , 2009, with a large range in volatile contents (0·55 ·7 wt % H 2 O; 50·005^0·109 wt % CO 2 ; 0·091^0·142 wt % Cl; 0·007^0·207 wt % S; Johnson et al., 2009), suggesting host olivine crystallization over a range of depths from 0·01 to !0·4 GPa (Johnson et al., 2008(Johnson et al., , 2009. The relationship between the Jorullo MIs and the Jorullo matrix glasses has been previously explained by the combined effect of degassing and a two-stage crystallization process (Johnson et al., 2008).

M E T H O D S Sample preparation
Olivine separates were examined in immersion oil (refractive index of 1·678) using an optical microscope. We selected olivine grains containing well-preserved primary MIs, identified based on their random distribution in the centre of the olivine crystal (4 100 mm away from the grain edges) and lack of textural features associated with decrepitation, leakage, or cracking (Roedder, 1984). We also selected a few olivine grains from Jorullo containing embayments. Some of the olivine grains occasionally had matrix glass adhered to their outer edges, which was analysed as well.
The selected olivine grains were mounted in orthodontic resin and polished with alumina papers and/or diamond powder down to 0·25 mm grit size. They were cleaned in successive baths of toluene, acetone, and isopropyl alcohol   Johnson et al., 2008Johnson et al., , 2009, matrix glasses (Johnson et al., 2008) and bulk tephras (for Sommata: De Astis et al., 1997; for Jorullo: Luhr & Carmichael, 1985) are also shown, when available. Major element compositions have been recalculated to 100% on an anhydrous basis. Classifications in (a) are from Peccerillo & Taylor (1976) and Le Ma| OE tre et al. (1989). LK, low-potassium; MK, medium-potassium; HK, high-potassium; UHK, ultrapotassic. Vertical lines distinguish basalt, basaltic andesite, and andesite fields. Arrows in (b) and (c) indicate the general effect of fractional crystallization and degassing. Error bars on H 2 O, F and Cl contents (8% rel., 2SD of repeated measurements in standards of similar composition) are smaller than symbol sizes.  (Aubaud et al., 2007;Mosenfelder et al., 2011), dried overnight at 1158C in a vacuum oven and pressed into indium mounts, oriented in such a way that the polished surfaces were exposed and flush with the surface of the indium.
Finally, the finished mounts were cleaned in successive baths of toluene, acetone, and isopropyl alcohol, dried overnight at 608C in a vacuum oven and coated with an $30^60 nm gold coat for nanoSIMS analysis. After nanoSIMS analysis, the gold coat was removed and replaced by an $15 nm carbon coat for EPMA.

Electron microprobe analyses and electron backscatter diffraction
Major-element compositions of 19 olivines and 37 glasses (including 21 MIs, eight embayments, and eight matrix glasses occasionally adhered to the outer edges of the olivines) were determined with a JEOL JXA-8200 electron microprobe at Caltech using standards and operating conditions similar to those described by Milman- Barris et al. (2008). Olivines were analysed with an accelerating voltage of 15 kV, a 25 or 40 nA beam current, and a focused beam. Glasses were analysed with a lower current (10 or 15 nA) using a beam defocused to 5^20 mm diameter (depending on the sample size). Na was analysed first, to minimize alkali loss. We analysed the VG2 glass standard with variable counting times and beam size, to ensure the absence of alkali loss under such analytical conditions. Because matrix glasses from Jorullo are microcrystalline, we obtained only one analysis that was free from contamination by microcrysts. The major-element compositions of olivines and glasses are reported in Table 1. The crystallographic orientations of 16 olivine grains were determined using an HKL electron backscatter diffraction (EBSD) system on a Zeiss 1550VP scanning electron microscope at Caltech following the procedure described by Ma (2010). EBSD patterns were collected with a 25 kV accelerating voltage, a 6 nA beam current, a focused beam, and a 708 tilted stage. 'Mean angular deviation' statistics given by the HKL software as an indicator of goodness of fit were always better than 1·48.

NanoSIMS analyses
H 2 O, Cl, and F contents of olivines and glasses were determined using the NanoSIMS 50L in the Caltech Center for Microanalysis, following Mosenfelder et al. (2011). Here we describe the analytical procedure and emphasize key settings aiming to minimize volatile background and surface contamination while optimizing beam size resolution. The entire instrument was baked for $24 h prior to the analytical sessions, during which time the sample mounts were kept in the sample exchange airlock. Olivines were analysed during three analytical sessions, and glasses over two separate analytical sessions. During each session, the vacuum pressure in the sample chamber was (1^2) Â 10 À10 torr. To measure precisely the low volatile contents characteristic of natural igneous olivines, we used a 'high current' setting (Saal et al., 2008;O'Leary et al., 2010). A Cs þ primary ion beam of 0·6^1·0 nA accelerated to 8 kV was delivered to the sample surface, with charge compensation provided by an electron flood gun. For the first olivine session we used a 1nA, 5 mm diameter beam rastered over a 10 mm Â10 mm area, electronic gating on the central 5 mm Â 5 mm, and a 20 s presputtering time, with a resulting crater diameter of $20 mm. For the two other olivine sessions we used a lower beam intensity current (down to 0·6 nA), a smaller raster size (5 mm Â 5 mm), a smaller electronic gating (3 mm Â 3 mm), and a longer presputtering time (200^300 s), yielding craters 5^15 mm in diameter. Glasses were analysed using similar procedures (a 5 mm Â 5 mm raster size; a 3 mm Â 3 mm electronic gating; a 200 s presputtering time), except for a lower beam current (50^90 pA). We collected secondary ions counts on seven separate electron multiplier detectors in multi-collection mode, with a counting time of 1s for each mass [ 12 C (used to monitor surface contamination), 16 O 1 H À , 19 F À , 30 Si À , and 35 Cl À ; we also measured one or two of the masses corresponding to 18 O À , 27 Al À , or 24 Mg 16 O À , to monitor the signal stability]. This cycle was repeated 80^200 times for each analysis. The smallest exit slit (No. 3) was selected on the 16 O 1 H À detector to separate 16 O 1 H À from 17 O À (mass resolving power of 13 000^14 000 using Cameca NanoSIMS units; $6000 using ÁM/M in universal unit definition). We performed both single spot analyses and linear profiles. One olivine sample (SOM1) was analysed with a high density of points and the results were interpolated into a concentration contour map. Beam stability degraded at the end of the second analytical session as a result of deterioration of the focus and strong electron gun fluctuations, causing increases of one order of magnitude in the background and in the uncertainty on the calibration slopes, and an unusual scatter in the results. As a consequence, three profiles measured during this period were excluded from this study. However, some of the pits from these analyses are visible in photomicrographs in some of the figures and are appropriately noted.
Although measurements of total hydrogen were made by counting the 16 O 1 H À ion, we report the data as an equivalent concentration (   F, and Cl analyses of glass samples (using volatile contents normalized for SiO 2 ). All calibration curves were based on blank-corrected measurements (H 2 O, Cl, and F blanks were assessed on nominally dry olivine standards; Supplementary Data, Electronic Appendix 2), using leastsquares regression with coefficients (R 2 values) better than 0·97 in all cases (Electronic Appendix 1). Average uncertainties on calibration slopes are 11% relative for the calibration of H 2 O in olivine standards and glass, and 16% rel. for the calibration of F and Cl in glass, which corresponds, once propagated to the final concentrations measured in unknowns, to an uncertainty of 10% rel. for H 2 O and 16% rel. for Cl and F. It should be noted that the use of glass standards to calibrate F and Cl analyses of olivine samples could compromise the accuracy of the reported analyses for these elements owing to matrix effects resulting from differences in major element composition and structure between the olivines and the glass standards. Consequently, the F and Cl contents we report may be systematically inaccurate by an unknown amount (though probably $530% relative or less based on experience with matrix effects in analyses of silicates). We emphasize, however, that relative variations in F and Cl concentrations between olivine analyses are unlikely to be affected by such matrix effects because the olivines we measured span a narrow range in their major element composition (Table 1). For each analysis, raw data were processed following the approach described by Mosenfelder et al. (2011), as follows.
(1) Raw counts were corrected for dead time and blank.
(2) Olivine analyses with anomalously high and/or highly variable 12 C/ 30 Si À were rejected on the assumption of surface contamination (55% of the total analyses). (3) Olivine analyses with 16 O 1 H À / 30 Si À and 19 F À / 30 Si À ratios having large internal analytical uncertainty (s mean 46%; where s mean is 2s standard error over the n counting cycles) or large s mean /s P [s mean /s P 46%; s P is the Poisson counting statistic error; equation (23) of Fitzsimmons et al. (2000)] were rejected (5 1% of the total analyses). This step allows filtering of measurements with poor internal reproducibility relative to other measurements, typical of either surface contamination or the presence of hydrous nano-inclusions in olivine, such as sub-micron-scale fluid or hydrous mineral inclusions, as shown by Mosenfelder et al. (2011). Finally, (4) analyses that visually overlapped an olivine^MI boundary based on the location of the analysed crater, or yielded volatile compositions indicating mixing between adjacent olivine and glass compositions, were rejected (55% of the total analyses; analyses that were rejected for any of the above reasons are appropriately noted in the figures).
Detection limits were assessed by using the calibration slopes to determine the H 2 O, F, and Cl concentrations of the blanks based on the uncorrected ratio of detected ions (e.g. 16 O 1 H À / 30 Si À ). We used the definition for limit of detection (LOD) from Long & Winefordner (1983). For example, the H 2 O detection limit (ppm by weight) is *Partially crystallized glass. All compositions are in wt %. Som, Sommata; Jo, Jorullo; Ol, olivine; MI, melt inclusion; emb, embayment; mx, matrix glass; b.d.l., below detection level; -, not analysed; Fo, forsterite content (%) of olivine; K D , Fe 2þ /Mg of olivine divided by Fe 2þ /Mg of melt, calculated on a molar basis, using Fe 2þ /Fe T ¼ 0·78 (Johnson et al., 2008;Le Voyer, 2009). Uncertainty on H 2 O, F and Cl content of glasses is 8% rel. (2 SD of repeated measurements in standards of similar composition). In the sample names, the number refer to different olivine grains, whereas the letter following the number refer to different MIs, embayments or matrix within/around the same olivine grain.

R E S U LT S
The H 2 O, F, and Cl contents in olivines from Sommata and Jorullo (21 linear profiles and one map), as well as in trapped glass phases (MIs, embayments), and matrix glasses (occasionally found adhered to the outer edges of the olivine grains) are reported in Tables 1^3. Selected data are presented in Figs 1^4.
The Jorullo MIs, embayments and matrix glasses plot within the medium-K calc-alkaline basalt to basaltic-andesite fields of the SiO 2^K2 O classification diagram (Peccerillo & Taylor, 1976;Le Ma| OE tre et al., 1989;Fig. 1a), but the embayments and matrix glass are more evolved than the MIs; that is, the embayments and matrix glass are basaltic andesites with higher SiO 2 and K 2 O contents (55·9^58·1 and 1·0^1·3 wt %, respectively) than the MIs (50·0^53·8 and 0·7^0·9 wt %; Table 1; Fig. 1a). The compositions of Jorullo embayments and matrix glass are similar to those of the matrix glass reported by Johnson et al.   x y These three gradients are also associated with the only three measured gradients in F content (for example, gradient 13 shown in Fig. 2b and Table 2), spanning lengths of 65 to 4125 mm, and with F contents near MIs up to three times greater, relative to measurements 4100 mm from any glass ( Fig. 2b; Table 2). The H 2 O and F contents along and Cl (c) contents in olivines next to two melt inclusions (profile 1, next to SOM1a; profile 13, next to Jo7a) and one embayment (profile 10, next to Jo2eb; profile numbers are from Table 2). Diagonally shaded areas in the lower part of each plot illustrate the respective average detection limits; all measured Cl contents in olivines are below detection limit (0·03 AE 0·01ppm). One maximum error bar is given in each plot (2 SD of repeated measurements in standards of similar composition). (d) Reflected-light photomicrographs of the three profiles, post-analysis. The arrow indicates increasing distance away from the glass. The MIs and embayment are overprinted with a filter (outlined by white dotted line). Data from analytical pits with white crosses have been filtered out of this study (see text for more details).
such profiles are well correlated with each other (R 2 of 0·80^0·89). However, they are not correlated with any variation in major-element or forsterite content of the olivine. One Sommata olivine (SOM1) was analysed with a high density of points distributed roughly evenly across the sample surface near SOM1b MI to determine if there are any spatial patterns in the volatile concentrations of the host olivine (Table 3; Fig. 3a). The core of this olivine (Fo 90 ) is homogeneous in major elements and contains several MIs. EBSD results show that the polished surface is close to the (110) crystallographic face of the crystal (10·58 misorientation; Fig. 3a). Figure 3b shows a map of olivine analytical spots around the 50 mm Â 60 mm cross-sectional SOM1b MI ellipse, which contains 4·0 wt % H 2 O, 0·061wt % F, and 0·218 wt % Cl (Table 1). It should be noted that the elliptical shape of this MI has its long axis approximately parallel to the crystallographic a-axis of the host olivine and its short axis approximately parallel to the b-axis. The exposed part of the inclusion is slightly offset compared with its maximum diameter. In this olivine, 1D profiles indicate that F contents do not show any significant variation (0·29 AE 0·02 ppm; Table 2). In contrast, H 2 O content in the olivine increases from $20 ppm H 2 O far from the MI to 33 ppm next to the MI ( Fig. 3b; Table 3). This variation is not isotropic in two dimensions: when we interpolate between the analytical spots, the resulting contour map is characterized by elliptical concentration contours, elongated along the olivine a-axis, in the same direction as the MI itself, and with a shift of the centroid towards the upper right area (Fig. 3c). Different methods of interpolation (linear, cubic and Matlab V4 function) produce slightly different contour positions but similar contour shape and orientation along the a-axis of the crystal.
Similar to SOM1b, the olivine around Jo1a MI was measured with a high density of spots along two perpendicular directions (Fig. 4) and shows anisotropy in the H 2 O gradients (Table 2; Table 2). Thus, at distances of 540 mm from the edge of the MI, the H 2 O concentrations along the a-axis are greater than those along the c-axis (approximately up to two times greater for measurements taken 20 mm away from the edge; Fig. 4b). Therefore, results from both SOM1b and Jo1a indicate that H 2 O diffusion gradients are longest in the a-axis direction. It should be noted, however, that the Jo1a MI is elongated parallel to the c-axis direction, whereas the SOM1b MI is elongated in the a-axis direction. In principle, this may complicate the interpretation of the length-scales of diffusion gradients. We examine this issue further below by constructing a 3D numerical model that takes into account both inclusion shape and diffusional anisotropy.

H 2 O, F, and Cl partition coefficients between olivine and melt
In natural samples, olivine/melt partition coefficients have frequently been estimated using in situ measurements of olivine and matrix glass, assuming that the matrix glass represents the composition of the melt from which the olivine formed [e.g. see review by Henderson (1982) for trace element partitioning]. This approach may not always be simply extendable to volatiles, especially if the matrix glasses have experienced late-stage degassing. Thus, most known H 2 O, F, and Cl olivine/melt partition coefficients have been determined from experimental studies (e.g. Koga et al., 2003;Aubaud et al., 2004;Hauri et al., 2006;Tenner et al., 2009;Beyer et al., 2012;Dalou et al., 2012, in preparation). Values are reviewed in Table 4. In the previous section we described diffusion gradients in H 2 O and F in olivine adjacent to MI or embayments. Despite the presence of these gradients, the olivine concentrations measured adjacent to the glass are assumed to be a good approximation for the composition of the olivine at equilibrium with the glass. Thus, by pairing each MI or embayment analysis with the olivine analysis performed closest to the glass, our data allow determination of partition coefficients from natural rocks (  Koga et al., 2003;Aubaud et al., 2004;Hauri et al., 2006;1ppm F, Hauri et al., 2006; $10 ppm F, C. Dalou, personal communication). The fact that the distance between each glass (MI or embayment) and the closest olivine analysis (5^40 mm) is not constant (Table 5) might explain part of the scatter in our data. Moreover, the low F contents measured in the olivines (down to 0·06 ppm) are close to the LOD (0·04 AE 0·01ppm F) and this might also enhance the scatter in Fig. 5b. We note that we find the highest F partition coefficient (0·0013, measured next to MI Jo7a) associated with the strongest H 2 O and F gradient we have observed adjacent to an MI (profile 13; Table 2).
Because Cl measurements in olivine are close to or below the LOD (0·03 AE 0·01ppm), we used the single value of 0·03 ppm for all olivines to calculate a maximum value for Cl olivine^glass partition of 0·00002 AE 0·00002 (Table 5). This maximum estimate is consistent with  (profiles 12, 19 and 20) are closer to the c-axis of the crystal and are represented with crosses. One maximum error bar is given (6% rel., 2 SD of repeated measurements in standards of similar composition). The two horizontal profiles overprinted with white crosses were excluded from this study because of instrumental instability (see text for more details). Other isolated analytical pits with white crosses indicate data that have been filtered out of this study (see text for more details).

T R A N S F E R O F VO L AT I L E C O M P O N E N T S B E T W E E N M I s A N D A DJAC E N T O L I V I N E Generation of concentration gradients
The H 2 O and F gradients in olivine adjacent to MIs and embayments reflect transport of volatiles out of the MIs and embayments and into the host olivine. This was probably caused by melts from MIs and embayments that initially had higher volatile contents than the external melt (i.e. the melt from which the matrix glass was quenched). This would have established chemical potential gradients across the olivine that drove diffusion of these components through the olivine until the MIs and embayments had volatile concentrations similar to the external melt. In the following discussion, we use a simplified 1D model to consider two scenarios for generating such chemical potential gradients in volatile compositions (Fig. 6), and assess their implications for the time dependence of volatile-element concentration gradients in the olivines. In both scenarios we use as the initial stage (t 0 in Fig. 6) an olivine that is homogeneous in its volatile content and contains one MI. The volatile composition of the MI is similar to that of the external melt and is in equilibrium with that of the olivine.
In the first scenario we create disequilibrium at the boundary between the olivine and the MI by introducing an increase in volatile content of the MI (Fig. 6). Such a scenario would most probably result from post-entrapment crystallization of volatile-poor phases such as olivine and   Fig. 6 by the black rim on the wall of the melt inclusion). Barring strong changes in the activity coefficients of volatiles during fractionation within the MI, this will lead to increases in their chemical potentials, diffusion through the olivine, and eventual loss to the external melt. At initial time steps (t 1 in Fig. 6), the volatile enrichment is confined to the region adjacent to the MI, but at later steps (t 2^t4 in Fig. 6), volatile diffusion extends progressively deeper into the olivine towards the rim. Eventually, the volatile content of the MI is equilibrated with the external melt. In a second scenario, we create disequilibrium at the boundary between the olivine and the external melt, by introducing a decrease in volatile contents of the external melt (Fig. 6). This scenario represents either degassing of the exterior melt or mixing between the exterior melt and a more volatile-poor magma. Each process could result in a boundary condition at the outer edge of the crystal where the chemical potentials of the volatile components are lower than at the outer wall of the MI. At t 1 (Fig. 6), the volatile loss is confined to the outer edge of the olivine crystal, but with time, it extends progressively deeper (t 42 in Fig. 6), and eventually reaches the MI. At this point, the volatiles will start to migrate out of the MI and through the olivine to the exterior melt. Eventually, the volatile contents of the melt inclusions will be drawn down to values in equilibrium with the external melt. The time it takes for this drawdown will depend on temperature, initial volatile content, size, and depth of the MI within its host olivine, and so will probably vary between MIs even within the same olivine crystal (e.g. Cottrell et al., 2002), consistent with the variable intensity of the measured volatile gradients in this study ( Table 2).
The two scenarios are not mutually exclusive (i.e. some combination of the two may have operated simultaneously), and we seek to discover which mechanism was dominant. To do so, we discuss each scenario for the specific case of H 2 O and F. With regard to increased H 2 O contents in MIs (scenario 1), there are several things to consider in determining whether or not such a configuration may explain the measured H 2 O profiles in olivine. Glassy MIs and embayments (i.e. without any daughter minerals) from both Jorullo and Sommata have undergone a maximum of 9% post-entrapment olivine crystallization (see Results). Based on our established H 2 O partition coefficient between olivine and melt (0·0007 AE 0·0003), such a process would increase the H 2 O content of the MI by only $10% relative to its initial value (i.e. when the MI was trapped), and the H 2 O concentration of olivine adjacent to the MI would also increase by $10% relative to its initial value. However, the measured increase in H 2 O contents of olivines next to glassy MIs or embayments is  Hauri et al., 2006Aubaud et al., 2004Tenner et al., 2009 This study Previous experimental studies Koga et al., 2003Beyer et al., 2012 (a) (b) Fig. 5. H 2 O (a) and F (b) partition coefficients between olivine and melt, for Sommata melt inclusions, Jorullo melt inclusions, and Jorullo embayments. Uncertainty is 8% rel. for H 2 O and F content in glasses, 10% rel. for H 2 O partition coefficients, and 11% rel. for F partition coefficients (2 SD of repeated measurements in standards of similar composition). In each plot the average partition coefficient from our data is represented as a line and the 1 SD as a grey band. Also plotted for comparison are values from experiments (Koga et al., 2003;Aubaud et al., 2004;Hauri et al., 2006;Tenner et al., 2009;Beyer et al., 2012), with the average partition coefficient from these studies indicated as a dotted line and the 1 SD as a stippled band (see the cited studies for uncertainties on single data points). It should be noted that the scales along the axes in (b) are interrupted owing to the large range of the experimental data. much stronger (up to 1·4 times in Sommata olivines, up to four times for Jorullo olivines; e.g. Figs 2^4). In addition, the amount of cooling responsible for post-entrapment crystallization in the MIs should have also resulted in the crystallization of the external melt. If so, this would have increased the volatile concentration in the external melt, and further diminished the chemical potential gradient necessary to drive H 2 O diffusion out of the MI. Thus, although the process defined by scenario 1 could be a contributing factor, it is not likely to be solely responsible for the observed volatile gradients near glassy MIs or embayments (e.g. Chen et al., 2013) vol. Fig. 6. Illustration of spatial and temporal evolution of two scenarios for the evolution of chemical potential gradients responsible for diffusion of volatiles out of an olivine-hosted MI, based on simple 1D forward diffusion model for a 30 mm MI, 1mm olivine, using arbitrary time varying from 1 to 10 4 s and an arbitrary diffusivity of 100 mm 2 s À1 . Both models begin from an initial condition (t 0 ) where concentration in the inclusion equals that in the external melt. The olivine is unzoned and in equilibrium with both melts. In scenario 1 (left), the chemical potential of the volatiles in the MI increases (because of post-entrapment olivine crystallization). In scenario 2 (right), the chemical potential of the volatiles in the external melt decreases (owing to degassing). The lowest panel corresponds to scenarios 1 and 2 combined. For each case, the resulting volatile concentration profile through the olivine (10 mm steps) is represented on the right-hand graph, at four times (in seconds, t 1 ¼100, t 2 ¼ 300, t 3 ¼ 3000, t 4 ¼10000).  (2 AE1ppm) is one order of magnitude lower than those measured in Sommata olivines away from MIs (22^30 ppm; Table 2). This indicates that the H 2 O contents of Sommata olivine are out of equilibrium with those of the matrix glass. This would be consistent with a late H 2 O degassing episode that lowered the H 2 O content of the melt from which the olivine grew. Mixing with a more degassed magma would also result in the same disequilibrium. The fact that Sommata olivine rims are also out of equilibrium with their matrix glass with regard to Fe^Mg partitioning (see Results section) is consistent with both crystallization of the external melt and mixing with a more evolved magma. The mixing hypothesis is also consistent with the hybrid nature of the Sommata basalt described in previous studies (mixture between two magmas, one basaltic and one shoshonitic that is more evolved; e.g. Gioncada et al., 1998). Whatever the cause of the inferred H 2 O disequilibrium between Sommata olivines and matrix glasses, it probably happened shortly before eruption, to retain such disequilibrium (case of t 1 and t 2 of scenario 2 in Fig. 6). In the case of Jorullo, olivine rims are in equilibrium with Jorullo matrix glasses with regard to Fe^Mg partitioning (see Results section). Similarly, the inferred H 2 O content of olivine in equilibrium with matrix glass (2 AE1ppm) is similar to those measured in Jorullo olivines away from MIs (3^12 ppm; Table 2), indicating that the H 2 O contents of olivines are close to equilibrium with those of the matrix glass. Thus, the time between the decrease in H 2 O content of the external melt and the eruption was sufficient for the olivines to re-equilibrate with the low H 2 O content of the external melt (case of t 3 or t 4 of scenario 2 in Fig.  6). This result also implies that the measured H 2 O contents of Jorullo olivines might have been originally higher than those measured 4100 mm away from MIs, and have been strongly affected by diffusive re-equilibration with the external melt. F gradients are present in only one of the Jorullo olivines, near two MIs (Jo7a and Jo7b; Table 2). Because these two MIs are partially crystallized, we infer scenario 1 to have played a significant role in generating such gradients (see discussion related to H 2 O above). With respect to scenario 2, most Jorullo embayments and matrix glasses display similar or higher F contents compared with the MIs (Fig. 1). Fluorine most probably did not strongly partition into the vapor phase, as it is very soluble in silicate melts (up to 10^20 wt %, Carroll & Webster, 1994), and this could explain why the matrix and most embayment glasses are not depleted in F relative to the MIs. However, one of the Jorullo embayments (Jo5ec; 0·006 wt % F, Table 1, Fig. 1) contains significantly less F than the associated MIs (0·019^0·030 wt % F, Table 1). Thus, it might be possible that the Jorullo external melts experienced late-stage degassing. An alternative hypothesis is mixing with an F-poor magma. The mixing scenario is consistent with the results of Johnson et al. (2008), who pointed out the role of shallow assimilation in the evolution of Jorullo lavas. However, none of these hypotheses are very robust, as they are based on a single analysis. Using the partition coefficient from this study, and an approach similar to the one described above for H 2 O, we find that the inferred F contents of olivines at equilibrium with both Jorullo and Sommata matrix glasses (0·15 AE 0·10 and 0·25 AE 0·15 ppm F, respectively) are similar to those measured in olivines 4100 mm away from any MIs (0·070 ·13 and 0·26^0·33 ppm F, respectively ( Table 2). The apparent equilibrium between matrix glasses and olivine from both samples could indicate that there was no F disequilibrium at the boundary between olivines and matrix glasses. Alternatively, it could also reflect the fact that F diffusion was rapid enough to allow homogenization of any pre-existing zoning. This would imply that F could diffuse as rapidly as H. It is also possible that H 2 O and F might interact either through coupled diffusion effects or through the creation of hydrous defects that provide favourable sites for F to occupy or pass through, explaining why the observed F gradients are associated with the strongest H 2 O gradients ( Table 2). The presence of clinohumite in olivine has also been suggested to create pathways for fast F diffusivity (Portnyagin et al., 2008;Koleszar et al., 2009), although no analyses have been performed to establish the presence of clinohumite lamellae in the olivines containing the MIs with anomalously high F contents. It should be noted that all three observed F gradients come from the same olivine grain (Jo7; Tables 1 and 2); thus it is possible that this grain recorded a different magmatic evolution compared with the others. Therefore, both the existence of F gradients and the similarity in the length scales between the F and H 2 O concentration profiles in Jo7 olivine remain puzzling. It is difficult to evaluate the F gradients further because there are no quantitative data that exist (to our knowledge) on F diffusion kinetics in olivine.
Given the issues discussed above, the following section will focus on modelling the combination of the two scenarios outlined previously to reproduce the measured H 2 O gradients. In particular, diffusion driven by H 2 O decrease in the external melt (i.e. scenario 2 of degassing or mixing) is likely to be much more efficient for producing the strong gradients measured in this study because of the contrasting H 2 O contents of the trapped MIs relative to embayments and the matrix glasses. However, as stated above, it is likely that diffusion driven by increase of H 2 O inside the trapped melt (i.e. scenario 1) could also contribute to the measured gradients, especially near partially crystallized MIs or embayments.

Model of diffusive re-equilibration
In this section, we describe the results of a numerical 3D anisotropic diffusion model (Table 6; Fig. 7) to interpret the H 2 O gradients measured in olivines SOM1 and Jo1 (Figs 3 and 4). The goal of the model is to assess whether the anisotropic gradients adjacent to MIs could be understood quantitatively, and to evaluate the relative importance of post-entrapment crystallization and host melt degassing in generating the observed gradients. A forward model of the diffusion process was embedded within a multidimensional optimization algorithm to search for appropriate parameter combinations. Although the results of such an inversion are not unique, there are a number of robust features of the solutions.
The forward model is a finite difference solution of the anisotropic diffusion equation on a Cartesian 3D cubic grid, which is oriented parallel to the crystallographic coordinate system with node spacing of 5 mm. The model domain is defined by a rectangular prism of olivine, with faces assumed normal to the crystallographic a-, b-, and c-axes. The size of the crystal in each direction is a parameter that was held fixed during parameter searches. The size, shape, and position of the SOM1b and Jo1a MIs and the SOM1 and Jo1 olivines were digitized in two dimensions from back-scattered electron images. In the third dimension, normal to the polishing plane, the size of the inclusion, the size of the host olivine, and the position of the inclusion within the olivine were estimated from pre-polishing optical microscope examination. Each cube of the computational grid was taken to be either olivine or MI; certain cube faces were then identified as forming the boundary of the MI. The initial condition was defined by a fixed H 2 O partition coefficient of 0·0007 between olivine and melt, a fixed amount of olivine post-entrapment crystallization (6% for SOM1b and 5% for Jo1a, based on FeM g partitioning between the glass and the MI), and two variable parameters: the initial H 2 O content inside the MI at the moment of trapping (which, together with the partition coefficient, defines the initial uniform H 2 O content throughout the olivine) and the post-degassing but pre-diffusion H 2 O content of the external melt. We conducted a forward model calculation with varying initial conditions to explore the importance of changes in both internal and external H 2 O content on the shape of the diffusion gradient in olivine. The anisotropic threedimensional diffusion equation was stepped forward in time by using an alternating-direction implicit formulation for computational stability and efficiency. The cells on the outer boundary of the olivine were kept in equilibrium with an infinite reservoir of external melt by using the Average over the three orientations min 4 2 5 3 *Using diffusion coefficient of the 'proton-polaron' type of H diffusion in olivine from Kohlstedt & Mackwell (1998), at 10008C. When combined with the number of computational cells defining the inclusion volume, this allowed for monitoring of the changing H 2 O content of the inclusion, which is assumed to be spatially uniform at all times owing to much more rapid diffusion in the melt than in the olivine. There are independent diffusion coefficients along the three crystallographic directions D a , D b and D c ; these were held constant during the run (i.e. no temperature change is explicitly considered). The forward model was run for an arbitrary time t of 10 000 s (in 1s steps), as the output is sensitive only to the products D a t, D b t, and D c t.
Only the ratios D a /D b and D a /D c , and not the absolute values of the diffusion coefficients themselves, are meaningful outputs of the model, barring other constraints on diffusion coefficients or time. Thus, it is assumed that these ratios are independent of temperature (that is, that diffusion along each crystal axis has the same activation enthalpy), such that an isothermal model can stand in for a temperature-dependent model without affecting conclusions about anisotropy.
The results of the forward model (Fig. 7) were evaluated by using a penalty function consisting of the sum of the analytical error-weighted squares of the misfits between each nanoSIMS H 2 O measurement and the modelled H 2 O content in the olivine. The modelled concentrations were interpolated to the positions of analytical craters, which were digitized from BSE images. By Powell's direction-set iteration (Press et al., 1992), the adjustable parameters were varied to obtain a best fit. When one dataset (SOM1b or Jo1a) was modelled separately, with data only on one crystallographic plane, we assumed that D b ¼ D c (labelled D bc ). However, when the two differently oriented crystals were inverted together, all three coefficients were independent and, in addition, the diffusion time of Jo1 was taken as a free parameter. This represents the ratio of the integrals of Ddt for the independent time^temperature histories of each inclusion; only the ratio to the arbitrary time of 10 000 s assumed for SOM1 is meaningful, and expresses some unknown combination of time and temperature differences. To summarize, when one crystal was modelled independently there were four free parameters (D a , D b , initial H 2 O in inclusion, and post-degassing H 2 O in external melt) and all others were fixed (total time, grid spacing, time step, crystal size and inclusion geometry, partition coefficient, degree of post-entrapment crystallization, and D c held equal to D b ). When both crystals were modelled together there were eight free parameters (D a , D b , D c , initial H 2 O in each inclusion, post-degassing H 2 O in each host, and time for one inclusion). The outputs of each realization of the model are the final optimized values for each of the free parameters, the extent of total H 2 O loss from each inclusion, and the final misfit at the end of the calculation (w 2 parameter, used to evaluate the quality of each model fit). When SOM1b and Jo1a datasets were modelled separately, the runs always gave output diffusion coefficients with D a %100D bc (Table 6). When modelled simultaneously, the output diffusion coefficients give the following relationship: D a % 50D c %150D b ( Table 6). Examples of 1D profiles, or 2D maps from the two best results for each dataset run separately, are plotted in Fig. 7 (note that the best result for both datasets run simultaneously would be in agreement with differences of less than 1ppm H 2 O for each point). This model can reproduce the main features shown by the SOM1b and Jo1a datasets (the preferential orientation of the 2D contours of constant H 2 O concentration and 1D gradients, as well as the decrease in H 2 O content away from the MIs; Fig. 7) with less than 5 ppm difference between the modelled and measured H 2 O content for 96% of our data (less than 10 ppm difference for the other 4%; i.e. three data points in Fig. 7b, two of them being the two data points from Fig. 7d with the highest measured H 2 O). The discrepancies between the datasets and the model could be due to (1) the effect of other small MIs in the crystal, not taken into account in the model, or (2) the difficulty in assessing boundary conditions in the model owing to the lack of data closer than 15 mm and further than 130 mm away from the MI. Discrepancies could also arise owing to apparent shift in the high H 2 O content relative to the centre of SOM1b MI (Fig. 3c), which might have been caused by (1) migration of the MI along a temperature gradient during diffusive H loss from the MI (Schiano et al., 2006), or (2) the misorientation between the polished surfaces and the crystallographic faces of each olivine.

Implications for the amount of H 2 O loss from MIs
Although the diffusion model sufficiently fits the measured H 2 O diffusion profiles, it provides only a qualitative assessment of the total amount of H 2 O lost by each MI through diffusion. This is due to the large number of assumptions and poorly constrained parameters in our model, in addition to the misfit between the model output and the measured data (Fig. 7). Nonetheless, values can be calculated, and compared with previous studies. We note that the model yielded similar results regardless of whether the datasets are fitted simultaneously or separately (  Gioncada et al., 1998) and at the upper end of the global range for basaltic MIs (0·2^6·2 wt %; Me¤ trich . This high H 2 O content is also consistent with the high oxidation state of these basalts (NNO þ 0·7) compared with other Italian volcanoes (NNO^0·6 to NNO þ 0·2; Me¤ trich & Clocchiatti, 1996). In the case of Jorullo the predicted initial H 2 O content was not satisfactory as the model rapidly converged to 15 wt % H 2 O, which is the upper limit of the variation interval set for this free parameter. One potential explanation for this outcome is that the initial H 2 O content of Jo1a MI was !15 wt %, which seems highly unlikely; Johnson et al. (2009) estimated that the initial H 2 O content of the Jorullo primary melt was 5·7 AE 0·8 wt %. Overall, this result reminds us that, in addition to the limitations of the data and simplified model applied in this case, the use of hydrogen diffusive profiles to define initial conditions should be considered only a qualitative approach.

Timescales and diffusion mechanism for H 2 O loss from MIs
Our results show that the observed H 2 O gradients are oriented along preferential crystallographic directions. In the sample where the analytical plane is oriented near normal to the c-axis direction and thus approximately contains the aand b-axis directions (SOM1b map, Table 3; Fig. 3), the H 2 O gradients are elongated along the a-axis direction. In the sample where the analytical plane is oriented near normal to the b-axis direction and thus approximately contains the aand c-axis directions, the H 2 O gradients are again elongated along the a-axis direction (profiles around Jo1a, Table 2, Fig. 4). Our 3D diffusion model confirms this preferential orientation, as the output value for D a is approximately one order of magnitude higher than those for D b and D c . Therefore, we conclude that in these natural samples, the diffusion of H out of MIs is fastest along the a-axis of the host olivine. Regarding hydrogen diffusion in olivine, two mechanisms have been suggested to explain the phenomenon. The first is the 'proton^polaron' mechanism, where proton diffusion is coupled with redox exchange (i.e. iron oxidation) to adjust the charge balance (Kohlstedt & Mackwell, 1998;Demouchy & Mackwell, 2006). The second mechanism, known as 'proton^vacancy', consists of moving hydrogen by rearranging the associated point defects (cation vacancies; Kohlstedt & Mackwell, 1998;Demouchy & Mackwell, 2003. These mechanisms differ in their timescales: H would diffuse through a 1mm olivine crystal within minutes to hours using the 'proton^polaron' mechanism, and within hours to days by the 'proton^vacancy' mechanism. Experimentally determined diffusion coefficients for these mechanisms also differ according to crystal orientation: D a 4D b and D c for the 'proton^polaron' mechanism (specifically D a %10D c %100D b , Mackwell & Kohlstedt, 1990), and D c 4D a and D b for the 'proton^vacancy' mechanism (Kohlstedt & Mackwell, 1998;Demouchy & Mackwell, 2006). Our results and model are therefore consistent with the fast, 'proton^polaron' process being the dominant mechanism for H 2 O transport out of natural MIs. This implies very short times for H 2 O diffusive loss from MIs.
In addition to assessing the initial H 2 O contents of MIs, each run of the 3D model gives an estimate of the products D a t, D b t and D c t (Table 6). Thus, by using experimentally determined diffusion coefficients for the proton^polaron mechanism, and petrologically constrained temperatures, we can estimate t, the diffusion time. Specifically, we used the parameters determined by Kohlstedt & Mackwell (1998) at a temperature of 10008C (intermediate between magmatic temperature and quenching temperature, as the diffusion might have taken place during ascent and/or quenching at the surface), to calculate t. In doing so, we find an average diffusion time of 4^5 min for SOM1b H 2 O gradients, and 2^3 min for Jo1a H 2 O gradients (the average is that of the three crystallographic directions; results are similar whether the two datasets were run simultaneously or separately; Table 6). It should be noted that the experimentally determined diffusion coefficients are poorly constrained and have large errors (several orders of magnitude), mainly owing to the imprecision on the activation energy term (Kohlstedt & Mackwell, 1998). Thus the estimated diffusion time ranges from a few seconds to a few hours. Choosing a different temperature will also have a strong influence on the calculated timescales, from seconds at 12008C to hours at 8008C. Finally, other parameters such as the size of the MIs (smaller MIs will reequilibrate faster) or their distance from the olivine edge (MIs closest to the edges will re-equilibrate faster) will also influence diffusion rates (e.g. Cottrell et al., 2002;Lloyd et al., 2012), and thus affect the estimated timescales. As a result of these parameter uncertainties, the timescales of diffusive H 2 O loss from natural samples remain poorly constrained. It is also not clear whether diffusive loss took place during magma ascent, where timescales of a few hours are expected (Turner & Costa, 2007), or during quenching at the surface, where more rapid timescales of minutes or seconds are expected. The upper end of the duration (hours) is consistent with times required to drive significant H 2 O loss from MIs in laboratory experiments (Hauri, 2002;Massare et al., 2002;Severs et al., 2007;Portnyagin et al., 2008;Chen et al., 2011;Gaetani et al., 2012). It is also consistent with previous studies that described H 2 O re-equilibration from natural MIs (e.g. Newman et al., 2000) and modelled timescales of H 2 O loss from natural samples [1·8^19·9 h for Sommata samples modelled by Chen et al. (2013); minutes to hours for Fuego samples, with longer times for larger inclusions (Lloyd et al., 2012)]. Better experimental determinations of hydrogen diffusivities are necessary to quantitatively assess timescales using hydrogen diffusion profiles.

Implications for the fidelity of the H 2 O record in MIs
The issue of H 2 O loss from MIs has been recognized for more than 30 years (e.g. Sobolev et al., 1983Sobolev et al., , 1989Sobolev, 1996;Sobolev & Chaussidon, 1996;Danyushevsky et al., 2002;Hauri, 2002). Since then, caution has been advised when interpreting H 2 O contents from slowly cooled samples such as lava flows. Because H 2 O from MIs can re-equilibrate within less than a few hours at high temperature, MIs would record H 2 O contents reflecting conditions from only the last storage stage (e.g. Newman et al., 2000;Portnyagin et al., 2008;Gaetani et al., 2012;Lloyd et al., 2012;Plank et al., 2013). If the magma undergoes mixing with exotic melt (e.g. assimilation of crustal components) or degassed melts, then it is likely that the H 2 O content recorded in the MI does not represent the primary H 2 O content of the magma (e.g. Portnyagin et al., 2008), but instead represents the H 2 O content of the mixed magma immediately before eruption.
Overall, our model indicates that even rapidly cooled samples such as scoria (Sommata sample) or ash (Jorullo samples) could undergo significant H 2 O loss from MIs within less than a few hours. Thus, for eruptions with slow magma ascent rates, it is possible that part of the pre-eruptive H 2 O content could diffuse out of the MI during ascent. This is in good agreement with results from recent studies on H 2 O loss from natural samples (Lloyd et al., 2012;Chen et al., 2013)

C O N C L U S I O N S
We have determined H 2 O, F and Cl contents of olivines from two basaltic cinder cones (Jorullo, Mexico, and Sommata, Italy), along profiles surrounding MIs and embayments. We show that H 2 O and F contents of olivines generally increase towards the trapped glasses, indicating diffusive re-equilibration between the trapped melt and the olivine, and/or between the trapped melt and the external melt. The generation of chemical potential gradients between the trapped melt and the surrounding environment seems to be dominantly due to the decrease in volatile content of the external melt, caused by degassing or mixing with a volatile-poor melt. Post-entrapment crystallization of the trapped melts might also play a subordinate role. The mass transfer of H 2 O is preferentially oriented along the crystallographic a-axis of the olivines, indicating that H diffusion out of MIs at eruptive pressure, temperature, and timescale conditions occurs preferentially through a 'proton^polaron' mechanism. Three-dimensional anisotropic numerical modelling of the diffusion profiles indicates re-equilibration times of less than a few hours, and confirms that the apparent a-axis dominated 'protonp olaron' pattern observed is not an artefact of the irregular 3D geometry of the inclusion sources. This model allows for qualitatively estimating that Sommata MIs initially contained $6 wt % H 2 O. Diffusive loss of H 2 O probably influences most MIs, even those from rapidly cooled samples, resulting in measured H 2 O values that are lower than the initial contents. Thus, when large suites of inclusions are analysed, the maximum H 2 O contents are best representative of the initial H 2 O content of the MI suite.

AC K N O W L E D G E M E N T S
We thank Chi Ma for help with the electron microprobe and EBSD analyses. Reviews by T. J. Tenner, A. E. Saal, J. D. Webster and Editor W. A. Bohrson helped to improve the paper and were gratefully appreciated.

F U N D I N G
This work was supported by a grant from the Gordon and Betty Moore Foundation to the Caltech Microanalysis Center.

S U P P L E M E N TA RY DATA
Supplementary data are available at Journal of Petrology online.