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 (>1600m 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
1
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
WholeRock
Chemistry
Lab
L-Mgt
L-Mgt
U-Mgt
Sw
Sw
Oru
Oru
Oru
Okp
Okp
Okp
Okp
Okp
IX-1b-1b
IX-1b-2a
IXe-1
Sw-5b-2b
Sw-5b-4
M-Oru-2a
M-Oru-3a
M-Oru-4a
Ph-16a-5a
B13-Ph-16a-1c
B50-Ph-16b-3a
B50-Ph-16b
Ph-2-1d-5x
Yes
No
No
NP-3
Yes
Yes
No
No
Yes
No
No
No
No
No
NP-75
NP-22
NP-38
NP-40
No
No
NP-52
No
NP-60
No
LBNL
LBNL
ISTO
LBNL
ISTO
ISTO
ISTO
ISTO
ISTO
ISTO
ISTO
ISTO
LBNL
Processed
tomographic
images (#) x
sub-volume
636
666
879
529
1261
600
600
600
600
600
600
600
1750
Pixel
Size
(m)
Sample field of
view (pixel×pixel)
( × # images)
4.4
4.4
3.6
4.4
4.4
3.5
3.5
4.2
4.2
4.0
4.2
2.0
2.0
2961×2805 (×420)
3526×3505 (×667)
1911×1983 (×879)
3552×3636 (×591)
1958×1934 (×1261)
1878×1953 (×1398)
1948×1978 (×1817)
2024×1650 (×1428)
1938×1992 (×1952)
2055×2016 (×1953)
1989×1926 (×2023)
1929×1932 (×1617)
3216×3500 (×1768)
Subvolume
size (mm3)
(× # subvolumes)
9-21 (×4)
10-34 (×4)
9-10 (×4)
11-17 (×5)
16-18 (×4)
5-9 (×4)
5-7 (×4)
9-11 (×4)
11 (×20)
14 (×4)
13-14 (×3)
2 (×4)
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
Microvesicular
Dense
Microfibrous
2961 × 2805; 4.4 m
1958 × 1934; 4.4 m
1958 × 1934; 4.4 m
3200 × 3500; 2.0 m
600 × 1228
600 × 600
500 × 500
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.
2
Groundmass crystallinity (), defined as the microlite content (%), and the microlite area
number density (𝑁𝑥𝑎 ) 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 = ( × 𝑁𝑥𝑎 )1/2]
was used to convert 𝑁𝑥𝑎 into volumetric number density (𝑁𝑥𝑣 ) (Table SM 3.3), following
Underwood (1970), where:
𝑁𝑥𝑣 =
𝑁𝑎
𝑑
[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 intersection-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 distributions 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 preexisting 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:
3
𝑁𝑣𝐶𝑜𝑟𝑟 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑣𝑒𝑠𝑖𝑐𝑙𝑒𝑠⁄(𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑣𝑒𝑠𝑖𝑐𝑙𝑒𝑠 + 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑚𝑒𝑙𝑡) [Eq. 2]
Similarly, the crystal number density (Table SM 3.5) calculated for the mafic phases (𝑁𝑃𝑥 ,
for pyroxene and 𝑁𝑀𝑡 , 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.
Microlite Texture
Glass SiO2
3LD =
mode of
the
volumebased
CSD
n˚ (mm-3)
Nxt = total
number of
crystals per
unit volume
(mm )
(mm )
Vesicle-Free
crystallinity [%]
Thin
Pumice Texture
section
Unit
LD = average size
from CSD
[mm]
d (mm)
(mean
size)
12148
1.4 × 107
9.6
0.001
0.001
0.002
5.3 × 1010
3.6 × 107
22332
2.3 × 107
20.2
0.001
0.001
0.003
2.5 × 1010
2.2 × 107
1313
7.2 × 105
4.4
0.001
0.001
0.003
2.7 × 109
3.0 × 106
283
1.2 × 105
1.7
0.002
0.002
0.006
7.1 × 107
1.5 × 105
Nxa
-2
Nxv
-3
wt%
±
Sw
D3
Microvesicular
Spiky
62.40
0.27
Sw
D5
Dense*
Spiky
70.70
L-Mgt
C11
Foamy
Subhedral
60.19
L-Mgt
C12
Sheared*
Subhedral
57.38
U-Mgt
D2
Microsheared
Spiky
64.15
0.63
14462
1.6 × 107
11.9
0.001
0.001
0.004
8.8 × 109
1.1 × 107
Oru
D12
Dense
Subhedral-Euhedral
72.18
1.34
26226
2.9 × 107
21.9
0.001
0.001
0.002
2.0 × 1011
1.2 × 108
Okp
E5
Fibrous*
Subhedral-Euhedral
68.76
15754
1.5 × 107
17.5
0.001
0.002
0.005
1.3 × 1010
2.0 × 107
0.25
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.
Correction for microlite-rich groundmass composition
Groundmass crystallinity
25.0
y = 1.392x - 78.21
R² = 0.980
20.0
Microvesicular
15.0
Dense*
Foamy
10.0
Sheared*
5.0
Microsheared
Dense
0.0
Figure SM 3.1 Samples not marked with “*” follow
a linear consistent with increasing glass SiO2 with
groundmass crystallinity. The fitting line equation
was used to extrapolate SiO2 for the crystallinities
calculated for samples marked with “*”.
Fibrous*
Glass SiO2
4
Table SM 3.4. Vesicularity results complementary of Table 1 in the manuscript.
Unit
Sample
Steady column:
Sw-b
Sw-2b
Sw-5b
Oscillatory column:
IX-1b-1
L-Mgt
IX-1b-2a
U-Mgt IX-1e-2
Collapsing column (wet):
Texture
Tot
Vol
[mm3]
Tot.
Ves.
Vol.
[mm3]
Ves.
Free
Vol.
[mm3]
no Ves.
Ves.
[%]
Melt
Vol.
[mm ]
[mm3]
Nv
-3
VVD Corrected
1
[m]
Peaks
2
VSD Corrected
3
CVSDCorrected
n0
-L/GT
L(mm)
Nt
Microvesicular
Dense
71
68
42
35
29
33
37811
10980
59
52
535
162
26
26
Skewed
~Unimodal
316
40
200
2.E+04
7.E+05
146
914
0.068
0.011
3.E+06
7.E+08
Exponential
Power-law (d =-6.4)
Foamy
Sheared
Microsheared
66
68
38
49
47
20
18
20
19
20142
21170
12068
73
70
51
304
312
316
17
20
16
Skewed
Polymodal
Unimodal
794 1259
794 316
40
5.E+04
7.E+04
1.E+06
172
224
986
0.006
0.045
0.010
9.E+06
2.E+07
1.E+09
Exponential
Power-law (d =-2.52)
Exponential
Oru2a
Microsheared
33
16
16
17403
50
533
13
Unimodal
40
2.E+06
980
0.020
1.E+09
Exponential
Oru 3a
Oru 4a
Fibrous
Dense
24
42
12
22
12
20
12415
9449
51
52
518
226
10
16
Unimodal
~Bimodal
32
32
126
1.E+06
1.E+06
1181
1167
0.085
0.009
2.E+09
1.E+09
Exponential
Exponential
Collapsing column (dry):
L-Okp Ph16a-5a
Microvesicular A
Microvesicular B
Microvesicular C
58
75
38
30
28
15708
15970
17843
52
55
49
271
22
~Bimodal
Polymodal
~Bimodal
40
32
40
10
79
158
2.E+06
6.E+05
1.E+06
1336
1130
916
0.075
0.009
0.011
2.E+09
6.E+08
9.E+08
Exponential
Power-law (d =-4.94)
Exponential
Microvesicular D
43
21211
62
~Bimodal
79
10
6.E+05
782
0.013
5.E+08
Exponential
5.E+05
599
0.017
3.E+08
Power-law (d =-4.67)
6.E+04
896
0.011
5.E+07
Power-law (d =-3.78)
Oru
U-Okp
10
Average
215
70732
54
B13-Ph16-1c-6a
Microvesicular
55
17
38
41805
32
756
30
Unimodal
79
B50 Ph16b-3a
Fibrous
41
25
16
1252
61
31
13
~Bimodal
79
B50Ph16b_1
Fibrous
7
3
4
7883
43
1185
3
Polymodal
25
40
6
Ph-2-1d-5x
Fibrous
2
1
1
10032
41
5280
1
Polymodal
79
251
141
158
Power law (d =0.31)
2.E+07
556
0.018
Exponential
1.E+10
~Exponential
Tot. Vol.: total volume analysed; Ves: vesicularity data; n 0 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.
5
Table SM 3.5. Vesicle-Free, mafic-crystallinity results, complementary to Table 1 in the manuscript.
Unit
Sample
Steady column:
Sw-2b
Sw-b
Sw-5b
Oscillatory column:
IX-1b-1
L-Mgt
IX-1b-2a
IX-1e-2
U-Mgt
Collapsing column (wet):
Oru2a
Oru
Oru 3a
Oru 4a
Collapsing column (dry):
Ph16a-5a
L-Okp
U-Okp
B13-Ph16-1c-6a
B50 Ph16b-3a
B50Ph16b_1
Ph-2-1d-5x
Nmafics-Corr.
All
mafics
[mm-3]
All mafics-CVD
[mm-3]
All mafics-CCSD
Interpretation of mafic crystal volume and size
distributions
[%]
±
7432
622
20.2
11.8
2.3
4.8
8322 Polymodal
642 Polymodal
631
316
40
50
251
126
Power-law (d = -3.37)
Power-law (d = -4.66)
Multiple stages of nucleation and growth (3)
Multiple stages of nucleation and growth (3)
3.5
3.0
1.6
3713
4075
1326
17.0
37.2
9.5
3.5
2.6
1.3
3713 Polymodal
2603 Unimodal
Skewed
88
398
40
479
251
794
Power-law (d = -2.20)
Power-law (d = -4.15)
Power-law (d = -2.79)
Multiple stages of nucleation and growth (4)
One stage of nucleation and growth
One stage of nucleation and growth
2.1
7.3
8.2
1392
3349
1297
5.9
7.4
21.9
1.5
2.8
11.7
1689 Polymodal
1774 Polymodal
2186 Polymodal
794
398
63
316
50
100
63
200
251
Power-law (d = -2.82)
Power-law (d = -3.85)
Power-law (d = -3.82)
Multiple stages of nucleation and growth (3)
Multiple stages of nucleation and growth (3)
Multiple stages of nucleation and growth (3)
1700
550
380
760
7.4
2.9
7.8
8.7
6.7
14.9
49
21
29.5
8
7
4
12
Polymodal
Polymodal
Polymodal
Polymodal
794
1000
501
794
100
398
794
398
251
100
100
200
Power-law (d = -3.21)
Power-law (d = -2.97)
Power-law (d = -3.4)
Power-law (d = -2.79)
Multiple stages of nucleation and growth (3)
Multiple stages of nucleation and growth (3)
Multiple stages of nucleation and growth (3)
Multiple stages of nucleation and growth (3)
400
626
3500
8500
Polymodal
Polymodal
Polymodal
Unimodal
79
79
63
40
501
794
126
316
251
200
Power-law (d = -3.5)
Power-law (d = -3.5)
~Exponential
Power-law (d = -3.7)
Multiple stages of nucleation and growth (3)
Multiple events of nucleation and growth
Multiple events of nucleation and growth
One stage of nucleation and growth
[%]
±
21.5
15.6
2.4
6.5
17.0
36.7
33.7
6.4
19.5
22.4
10.5
10.7
30.1
10.3
27.7
54.7
23.2
29.5
NPx-Corr
PxCorr
9.8
9.3
3.8
2.8
5.9
2000
2400
5500
8500
2.6
5.3
0.9
4.6
2.9
[mm]
Peak 1 Peak 2 Peak 3
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.
6
SM 3.3 Decompression rates:
Toramaru’s (2006) method was used to calculate the absolute values of magma
decompression rate (𝑑𝑃⁄𝑑𝑡), using: the groundmass glass silica content (𝐶𝑠 , in wt%), the
average vesicle number density of pumice clasts within each unit (non-corrected N, given in
m-3), the initial water content (𝐶𝑤 , in wt%), and the corresponding initial water saturation
pressure (𝑃𝑤 ) (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:
𝑑𝑃
𝑑𝑡
= 𝑎 × 𝐷 × 𝜎 2 × 𝑃𝑤 −1/3 × 𝑇 −1/2 × 𝑁 2/3
[Eq. 3]
Where 𝑎 is a constant (1.5 × 1015), 𝐷 is the water diffusivity in a silica melt (m2/s), calculated
following equation 4-6 of Toramaru (2006) and assuming P = 𝑃𝑤 ;  is the supercritical water
fluid/silica melt interfacial surface tension (N/m), calculated from:
𝜎 = 0.2366 × 𝑒
1
1
)/𝑅]}
𝑇 1273
{[(−0.35 × 10−8 )−(11 × 103 )]× [( −
[Eq. 4]
R is the gas constant 8.3 J/K and 𝑇 is the magma temperature (in K), following Toramaru
(1995):
1000
𝑇 = 0.16+0.01𝐶
𝑠
[Eq. 5]
In this study, a constant 𝐶𝑤 of 5.3 wt% was assumed for all eruptions, obtained from the
average of the maximum contents measured by the Fourier Transform infra-red technique
7
(micro-FTIR) in pyroxene-antecrysts melt inclusions (10 inclusions per eruption unit; Pardo,
2012). This 𝐶𝑤 corresponds to a 𝑃𝑤 of 191 MPa (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 with the magma storage region (2-9
km) proposed for Ruapehu from similar inclusions in recent eruptives (Kilgour et al., 2013)
and with 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):
𝜎𝐸𝐹𝐹 = 𝜎𝜑1/3 [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.
Unit
SiO2
EFF
teo

-3
T (K)
D (m2/s) Nv (m )
(N/m) (N/m) (N/m)
wt%
dP/dt [Pa/s]
[EFF]
[teo]
Sw
62.02
1280
0.122
0.094
0.083
2.3E-11
4.2E+11
5.9E+05
4.6E+05
L-Mgt
61.63
1288
0.123 0.0946
0.083
2.5E-11
3.5E+11
5.5E+05
4.3E+05
U-Mgt
64.15
1246
0.118 0.0914
0.083
1.9E-11
3.8E+11
4.2E+05
3.5E+05
Mgt
61.88
1267
0.120
0.093
0.083
2.2E-11
3.6E+11
4.9E+05
3.9E+05
M-Oru
73.34
1125
0.106 0.0815
0.090
1E-11
4.8E+11
2.2E+05
2.7E+05
M-Oru-a
73.34
1125
0.106 0.0815
0.090
1E-11
1.4E+12
4.6E+05
5.6E+05
M-Oru-b
73.34
1125
0.106 0.0815
0.090
1E-11
2.4E+12
6.5E+05
7.9E+05
L-Okp
71.69
1147
0.108 0.0834
0.090
1.1E-11
1.0E+12
4.1E+05
4.8E+05
U-Okp
71.69
1173
0.111 0.0856
0.090
1.3E-11
1.3E+12
5.7E+05
6.3E+05
Okp
71.69
1160
0.109 0.0845
0.090
1.2E-11
1.1E+12
4.9E+05
5.5E+05
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.
8
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