Supplementary Material ESM-3: X-ray synchrotron and computed microtomography
SM 3.1 Methodology details:One of the key problems in Volcanology, and particularly in tephra analyses, is the 3D extrapolation from 2D information. Stereological assumptions are common and have been used to obtain volumetric measurements for bubble and crystal size distributions, and volumetric number density (e.g. Underwood, 1970; Toramaru, 1995; Higgins, 2000; Blower et al., 2001; Proussevitch et al., 2007). By contrast, X-ray computed microtomography (Ketcham and Carlson, 2001; Song et al., 2001; Gualda and Rivers, 2006; Polacci et al., 2006; Degruyter et al., 2010; Giachetti et al., 2010; 2011) provides 3D representations of the bubble network in pumice samples, which allows for direct quantification of parameters such as the permeability, hydraulic tortuosity, and pore-size and throat aperture size distributions, which are crucial to constrain the state of magma prior to fragmentation (Saar and Manga, 1999; Blower et al., 2001; Costa, 2006).
Limitations of the microtomography technique include the resolution of the synchrotron and CT cameras used in this study (~2 or 4 m), causing some smaller features (e.g., bubble walls) to be lost. The small 5 mm diameter sample sizes may truncate large features (e.g., vesicles and crystals). In addition, all studied samples show a few irregularly shaped, anomalously large vesicles (>1600m in maximum diameter) that could not be included in the image analysis. However, these are not important for interpretation of degassing mechanisms, since they likely result from pre-eruptive nucleation and growth within the deeper magma chamber (c.f., Orsi et al., 1992).
The analytical details for tomographic images of each analyzed sample can be seen in Table SM 3.1. Each sample was cored to 5 or 10 mm diameter cylinder (up to 10 mm high) and imaged over a volume indicated as “Sample field of view”. Sample sub-volume refers to the virtually cropped portion of each sample that could be uploaded (limited by a windows-64 bit computer power) and used for 3D image processing and quantification. Pixel size refers to the resolution limit [voxel size = (pixel-size)3].
Table SM 3.1. Details on m-CT analyses for samples processed at the Lawerence berkely National laboratory (LBNL) with x-Ray synchrotron energy; and at the Institut des Sciences de la Terre d’Orléans (ISTO) with Computed m-CT. Slice interspacing is equal to the pixel-size.
Unit / Sample / Glass Chemistry / Whole-Rock Chemistry / Lab / Processed tomographic images (#) x sub-volume / Pixel Size (m) / Sample field of view (pixel×pixel) ( × # images) / Subvolume size (mm3) (× # sub-volumes)L-Mgt / IX-1b-1b / Yes / No / LBNL / 636 / 4.4 / 2961×2805 (×420) / 9-21 (×4)
L-Mgt / IX-1b-2a / No / NP-3 / LBNL / 666 / 4.4 / 3526×3505 (×667) / 10-34 (×4)
U-Mgt / IXe-1 / ISTO / 879 / 3.6 / 1911×1983 (×879) / 9-10 (×4)
Sw / Sw-5b-2b / Yes / NP-75 / LBNL / 529 / 4.4 / 3552×3636 (×591) / 11-17 (×5)
Sw / Sw-5b-4 / Yes / NP-22 / ISTO / 1261 / 4.4 / 1958×1934 (×1261) / 16-18 (×4)
Oru / M-Oru-2a / No / NP-38 / ISTO / 600 / 3.5 / 1878×1953 (×1398) / 5-9 (×4)
Oru / M-Oru-3a / No / NP-40 / ISTO / 600 / 3.5 / 1948×1978 (×1817) / 5-7 (×4)
Oru / M-Oru-4a / Yes / No / ISTO / 600 / 4.2 / 2024×1650 (×1428) / 9-11 (×4)
Okp / Ph-16a-5a / No / No / ISTO / 600 / 4.2 / 1938×1992 (×1952) / 11 (×20)
Okp / B13-Ph-16a-1c / No / NP-52 / ISTO / 600 / 4.0 / 2055×2016 (×1953) / 14 (×4)
Okp / B50-Ph-16b-3a / No / No / ISTO / 600 / 4.2 / 1989×1926 (×2023) / 13-14 (×3)
Okp / B50-Ph-16b / No / NP-60 / ISTO / 600 / 2.0 / 1929×1932 (×1617) / 2 (×4)
Okp / Ph-2-1d-5x / No / No / LBNL / 1750 / 2.0 / 3216×3500 (×1768) / 0.5-1 (×3)
After applying the median smoothing filter, a subset of image stacks of some of the most contrasting textures was imported in ImageJ and saved as .avi to produce videos showing the texture across each sample (see Video 1; Table SM 3.2).
Table SM 3.2. Details of 2D images (.tiff) illustrated in video format (.mov)
Texture illustrated in video 1 / Whole-diameter image stacks:Used image resolution (pixel×pixel; pixel size) / Zoomed texture image stacks(pixel× pixel)
Fluidal / 2961 × 2805; 4.4 m / 600 × 1228
Microvesicular / 1958 × 1934; 4.4 m / 600 × 600
Dense / 1958 × 1934; 4.4 m / 500 × 500
Microfibrous / 3200 × 3500; 2.0 m / 1600 × 1750
SM 3.2 Groundmass crystallinity, corrected vesicularity and mafic crystallinity:
Microlites include plagioclase, pyroxene, and titanomagnetite, and were defined as those crystals with maximum length L <35 m. Figure 4, in the main manuscript, shows examples of the microlite content variation in each pumice texture.
Groundmass crystallinity (), defined as the microlite content (%), andthe microlite area number density () were calculated from binary images of thin sections. Truncated crystals along the edges of the images were excluded from the analysis and the resulting was normalized to the vesicle-free area (corrected). The microlite mean size [d;d = ( × )1/2] was used to convert into volumetric number density () (Table SM 3.3), following Underwood (1970), where:
[Eq. 1]
Errors in the conversion of 2D measurements to 3D arise from: (1) the sectioning of crystals along dimensions smaller than their greatest length (cut-section effect), and (2) the inter- section-probability effect whereby small crystals are intersected less often than large crystals. Similarly to Castro et al., (2003) we did not use the stereological conversion of Sahagian and Proussevitch (1998) because their technique was developed for measuring vesicles with small aspect ratios and a limited range of shapes. It also requires particle counts of more than 102 for each size class and total counts of about 104 to ensure accurate tailing corrections. The thin section data included in this study contain too few measurements (total counts=820-2150 in all cases except Mgt, where only 23-145 microlites where found). Castro et al., (2003) found that CSD calculated in 3D with the stereological approache of Underwood (1970), compare to the real 3D distribution if the extreme large and small sizes of the given distribu- tions are not incorporated into the analysis.
Vesicle number densities and proportions (Table SM 3.4) were normalized to melt volume to minimize the influence of bubble expansion as well as the volumetric participation of pre-existing phenocryst phases (e.g., Gurioli et al. 2005; Shea et al., 2012). Firstly, the groundmass crystallinity was substracted from the total vesicle-free volume analyzed in 3D. The melt-referenced vesicle number density then follows as:
[Eq. 2]
Similarly, the crystal number density (Table SM 3.5) calculated for the mafic phases ( , for pyroxene and , for titanomagnetite) as digitally separated using the tomography data (including crystals with L >35 m), were also normalized to the vesicle-free volume. The fitting line used to correct microlite-rich samples with microlites smaller than the EMPS beam-size is shown in Fig. SM 3.2.
Table SM 3.3. Groundmass crystallinity results.
Nxa: areal microlite number density; Nxv: microlite volume number density calculated following Underwood (1970). Eruption units: Sw: Shawcroft; L/U-Mgt: Lower/Upper-Mangatoetoenui. M-Oru: Oruamatua; L/U-Okp: Lower/Upper Okupata Samples marked with “*” were corrected due to the large EMPA beam size compared to microlite size.
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Table SM 3.4. Vesicularity results complementary of Table 1 in the manuscript.
Tot. Vol.: total volume analysed; Ves: vesicularity data; n0 Ves: number of vesicles. Nv: vesicle number density (un-corrected). VVD: vesicle volume distribution; VSD: vesicle size distribution; CVSD (Cumulative vesicle size distribution).
Eruption units: Sw: Shawcroft; L/U-Mgt: Lower/Upper-Mangatoetoenui; M-Oru: Oruamatua; L/U-Okp: Lower/Upper Okupata.
Table SM 3.5. Vesicle-Free, mafic-crystallinity results, complementary to Table 1 in the manuscript.
Nmafics-Corr.: total mafics number density (vesicle-free). Px%: pyroxene content; NPx-Corr.: pyroxene number density (vesicle-free). CVD: mafic crystals volume distribution; CCSD: mafic crystals cumulative size distribution. Eruption units: Sw: Shawcroft; L/U-Mgt: Lower/Upper-Mangatoetoenui; M-Oru: Oruamatua; L/U-Okp: Lower/Upper Okupata.
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SM 3.3 Decompression rates:
Toramaru’s (2006) method was used to calculate the absolute values of magma decompression rate (),using: the groundmass glass silica content (, in wt%), the average vesicle number density of pumice clasts within each unit (non-corrected N, given in m-3), theinitial water content (, in wt%), and the corresponding initial water saturation pressure () (Table SM 3.6). Note that several typographical errors appeared in the original version of Toramaru (2006); these errors are corrected here. Toramaru’s (2006) decompression meter establishes that:
[Eq. 3]
Where is a constant (1.5 × 1015), is the water diffusivity in a silica melt (m2/s), calculated following equation 4-6 of Toramaru (2006) and assuming P = ; is the supercritical water fluid/silica melt interfacial surface tension (N/m), calculated from:
[Eq. 4]
R is the gas constant 8.3 J/K and is the magma temperature(in K), following Toramaru (1995):
[Eq. 5]
In this study, a constantof 5.3 wt% was assumed for all eruptions, obtained from the average of the maximum contents measured by the Fourier Transform infra-red technique (micro-FTIR) in pyroxene-antecrysts melt inclusions (10 inclusions per eruption unit; Pardo, 2012). This corresponds to aof 191MPa (7 km depth) using the solubility model of Newman and Lowenstern (2002).Although melt inclusions have been only found within antecrysts, the estimated saturation depth is consistent withthe magma storage region (2-9 km) proposed for Ruapehu from similar inclusions in recent eruptives (Kilgour et al., 2013) andwith existing geophysical data (Ingham et al., 2009; Rowlands et al., 2005). Therefore, values considered here are realistic approximations.
A correction factor = 0.46 for heterogeneous nucleation (Cluzel et al., 2008) was used to convert the calculated to an “effective” surface tension (EFF), following Shea et al. (2011):
[Eq. 6]
For comparison, a theoretical surface tension value of 0.083 N/m for dacitic melts and one of 0.090 N/m for rhyolitic melts were used, based on the experimental data of Gardner and Ketcham (2011).
Table SM 3.6 Magma decompression rate (dP/dt) calculated for each unit.
T (K): Magma temperature calculated with equation Eq. 5 (Toramaru, 1995)
: supercritical water fluid/silica melt interfacial surface tension.
EFF: effective surface tension.
teo: theoretical surface tension, based on experimental data reported by Gardner and Ketcham (2011)
dP/dt: decompression rate calculated following Toramaru (2006), and considering the different surface tensions.
Eruption units: Sw: Shawcroft; L/U-Mgt: Lower/Upper-Mangatoetoenui. M-Oru: Oruamatua (suffix “a” and “b” denote two alternative calculations for Oru using different combinations of Nv data of fibrous textures (see Fig. 7 in the manuscript); L/U-Okp: Lower/Upper Okupata.
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