Annex: Lava flow rheology: A comparison of morphological and petrological methods

Equation Reference Notes(1) τ0=1.26ρg(Dp/(φm-φ))(φm/(1-φm))2

(1/(ξ1.5-σ2))

Gay et al., 1969 ρ is the density of the lava (2600 kg.m-3); Dp is the mean diameter of particles; ξ is the shape factor defined as the ratio of the surface area of a sphere of equivalent volume to the surface area of the particle, σ is the geometric standard deviation that is estimated from a plot of particle diameter versus the cumulative proportion of particles less than a given size. The values used here are similar to Pinkerton and Stevenson (1992); Dp=100µm, ξ=0.5; σ =1.5

(2) τ0=6500φ2.85 Ryerson et al., 1988 Experimental fit obtained from crystalisation of picritic lava

(3) τ0=a(exp(b(Tl-T))-1) Dragoni, 1989

Tl is the liquidus temperature, a et b are fitting parameters given byDragoni et al., 1989: a=0.01 and b=0.08. This equation is based on alinear relationship between temperature and crystallization.

(4) τ0= τc (((φ/φc)-1)/(1-(φ/φm)))1/p Zhou et al., 1995; Saar et al., 2001

τc reflects the total inter-particulate cohesion resisting tohydrodynamic forces and p may reflect the response of the aggregatestate to shearing; φc is the critical minimum particles concentration atwhich the suspension can sustain some external stress (onset of yieldstrength). The values used here are similar to Hoover et al., 2001, forprism with p=1 and A=6.9, however the absolute value of this last isnot meaningful for geological material.

(5) τ0= τ* ((1-(φ/φm))-2 -1)Mueller et al., 2010; Heymann et al., 2002

τ∗ is a fitting parameter related to the size of the particles. The valuesused here are similar to Mueller et al., 2010 with τ*=0.234 forspheres and = 0.087 for needles.

M.O. Chevrel et al. / Earth and Planetary Science Letters 384 (2013) 109-120

1

Measurements across individual profiles

Flow_width W

1 2 3 4 5 6 7 8 91 251.36 221.85 166.88 130.37 359.21 295.50 218.00 142.82 148.832 250.91 220.32 165.94 124.18 360.43 295.40 249.82 142.73 148.543 251.89 218.32 167.94 124.18 359.45 294.43 253.80 142.71 149.554 255.85 220.31 165.93 121.99 359.45 296.38 251.82 142.71 149.545 254.88 222.29 167.93 126.00 361.46 296.40 248.80 142.71 151.526 254.90 221.30 166.93 126.00 360.45 298.38 246.81 144.71 152.527 254.88 221.31 166.92 131.13 359.45 299.39 247.78 143.71 152.538 253.87 222.30 166.92 130.14 359.45 299.39 246.82 144.71 154.519 255.88 222.30 165.93 129.99 359.45 300.38 245.79 142.71 154.47

10 255.88 226.29 167.92 129.99 358.46 300.39 246.81 141.72 155.51

number of profiles 9

mean X [m] 254.03 221.66 166.92 127.40 359.73 297.60 245.63 143.12 151.75standard deviation sX [m] 0.6 0.6 0.3 1.0 0.3 0.7 3.2 0.3 0.8

mean of flow width W [m] 218.6

0.41

Flow width W [m] = 218.6 ± 0.41

standard deviation SW of mean flow width X [m]

number of measurements per profile

Each profiles consists of 10 sub-profiles spaced 1 m apart. In 8 profiles no channel development is observed. Only profile 6 shows a flow channel (see illustration above).

Profile j


2

Flow-channel_width w

1 2 3 4 5 6 7 8 91 104.822 108.783 108.794 107.785 106.786 95.807 99.808 99.809 101.79

10 97.80


mean X [m] 103.2standard deviation sX [m] 1.5

Flow width w [m] = 103.2 ± 1.5

Flow_length L

number of measurements

123456789

10

mean L [m]standard deviation sL [m]

Flow length L [m] = 2044.66 ± 0.82

Flow_height H

maximum surface height

1 2 3 4 5 6 7 8 91 305.8 310.1 316.1 321.9 336.9 339.5 344.6 351.1 355.22 305.8 310.1 316.2 321.9 336.9 339.5 344.6 351.1 355.23 305.8 310.1 316.1 321.8 336.9 339.5 344.5 351.1 355.24 305.8 310.0 316.1 321.8 336.9 339.5 344.6 351.0 355.25 305.8 309.9 316.1 318.4 336.8 339.5 344.6 351.1 355.26 305.7 309.9 316.1 321.6 336.8 339.4 344.7 351.1 355.27 305.7 309.9 316.1 321.5 336.9 339.4 344.7 351.2 355.28 305.6 309.9 316.2 321.5 336.9 339.5 344.6 351.1 355.29 305.6 309.8 316.2 321.5 336.9 339.5 344.6 351.1 355.1

10 305.6 309.7 316.2 321.4 336.9 339.6 344.5 351.0 355.1


mean upper flow height A [m] 305.7 309.9 316.1 321.3 336.9 339.5 344.6 351.1 355.2standard deviation sA [m] 0.09 0.12 0.05 0.99 0.04 0.06 0.05 0.05 0.04


Length [m]

2043.002046.002046.202046.90

2044.66

Profile j


Note the length was measured from the last major break in slope to the distal portion of the lava flow.

2048.502043.902042.102042.90

0.82

2040.302046.80

Profile j


3

lower basal height B1

1 2 3 4 5 6 7 8 91 300.7 305.0 312.3 318.5 331.0 333.010 341.8 348.2 353.22 300.7 305.0 312.3 318.7 331.0 333.003 340.9 348.1 353.23 300.6 305.1 312.3 318.6 331.0 333.025 340.7 348.2 353.24 300.5 305.0 312.3 318.7 331.0 333.187 340.6 348.2 353.35 300.4 304.9 312.3 318.4 330.9 333.291 340.4 348.3 353.46 300.3 304.9 312.3 318.4 330.9 333.368 340.2 348.3 353.57 300.2 304.9 312.3 318.2 330.9 333.403 340.1 348.4 353.78 300.2 304.9 312.3 318.2 330.9 333.445 340.0 348.4 353.79 300.2 304.9 312.3 318.1 330.9 333.445 339.9 348.4 353.8

10 300.2 304.8 312.3 318.1 330.9 333.411 339.9 348.5 353.9

mean lower basal height B1 300.4 304.9 312.3 318.4 331.0 333.3 340.5 348.3 353.5standard deviation sB1 0.20 0.08 0.00 0.21 0.04 0.18 0.55 0.13 0.26

lower basal height B2

1 2 3 4 5 6 7 8 91 300.6 305.0 311.4 317.7 327.9 332.8 338.0 347.4 352.02 300.6 305.0 311.7 317.7 327.9 332.8 337.8 347.5 352.13 300.6 305.0 311.6 317.8 327.9 332.8 337.5 347.6 352.34 300.3 304.9 311.6 318.0 327.9 332.8 337.5 347.7 352.55 300.3 304.9 311.5 317.9 327.9 332.8 337.6 347.7 352.76 300.3 304.9 311.4 317.9 327.8 332.8 337.7 347.8 352.97 300.2 304.9 311.4 317.7 327.7 332.7 337.5 347.9 353.08 300.3 304.9 311.4 317.8 327.6 332.6 337.5 347.9 353.19 300.2 304.9 311.4 317.8 327.6 332.5 337.5 348.0 353.2

10 300.2 304.7 311.3 317.9 327.5 332.5 337.3 348.0 353.2

mean lower basal height B2 [m] 300.4 304.9 311.5 317.8 327.8 332.7 337.6 347.8 352.7standard deviation sB2 [m] 0.15 0.08 0.13 0.10 0.15 0.13 0.19 0.19 0.43

mean of B1 and B2 [m] 300.4 304.9 311.9 318.1 329.4 333.0 339.0 348.0 353.1standard deviation sB1,B2 [m] 0.03 0.01 0.43 0.29 1.59 0.27 1.43 0.27 0.40

resolution of HRSC-DTM [m] 0.20systematic deviation

for A, B1, B2 [m] 0.35

H [m] 5.3 5.0 4.2 3.2 7.5 6.5 5.6 3.1 2.1standard deviation [m] 0.35 0.35 0.55 0.45 1.63 0.44 1.47 0.44 0.53

mean flow height H [m] 4.73

0.28

Flow_height H [m] = 4.73 ± 0.28

standard deviation of mean flow height H [m]

number of measurements per profileProfile j

number of measurements per profileProfile j


4

Flow_gradient α

Height difference

1 2 3 4 5 6 7 8 9 #Ch 316.0 306.8 317.4 310.3 320.4 336.0 337.8 338.1 339.98 #Dh 294.0 293.3 291.9 294.3 295.8 333.0 336.1 337.1 338.22 #


resolution of HRSC-DTM [m] 0.20systematic deviation [m] 0.28

height difference [m] 22.0 13.5 25.5 16.0 24.6 3.0 1.7 1.0 1.8 #+/- 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 #

length lnumber of measurement

1 2 3 4 5 6 7 8 9 #1 685.91 391.05 739.73 361.44 594.17 115.37 102.56 113.09 102.38 #

topographic gradient αα [°] 1.8380 1.9803 1.9769 2.5340 2.3754 1.4823 0.9538 0.5059 0.9820 #

1.5E-03 2.6E-03 1.4E-03 2.8E-03 1.7E-03 8.7E-03 9.8E-03 8.8E-03 9.8E-03 #-4.7E-05 -8.8E-05 -4.7E-05 -1.2E-04 -7.0E-05 -2.2E-04 -1.6E-04 -7.8E-05 -1.7E-04 #

standard deviation α [°] 0.0004 0.0007 0.0004 0.0008 0.0005 0.0025 0.0028 0.0025 0.0028 #

mean of α [°] 1.6603standard deviation

of mean α [°] 0.0006

Flow_gradient α [°] = 1.66 ± 0.006

Profile j

Profile j

Profiles were drawn parallel to flow direction either on the lava flow surface or adjacent to the flow.


5

Calculation of rheological parameters

W [m] 218.6 0.4055 0.19% 2600 +/- 100

w [m] 103.2 1.5195 1.47% 9.80665

L [m] 2044.7 0.8199 0.04% 300

H [m] 4.7 0.2775 5.87%

α [°] 1.66 0.0006 0.04% 7.00E-07

Yield strength τ0,flow

τ0,flow,1 [Pa] = ρ × g × sinα × H

mean τ0,flow,1 [Pa] = 3492first order derivation: 1.343 120476.038 738.736 (error propagation)

τ0,flow,2 [Pa] = 3492+/- 240.42

τ0,flow,2 [Pa] = ρ × g × sin2α × (flow_width - levee_width)

mean τ0,flow,2 [Pa] = 4680 if W=w then ==>first order derivation: 1.800 322912 21.40 -21.40 (error propagation)

τ0,flow,2 [Pa] = 4680 4680+/- 271.7 271.7

τ0,flow,3 [Pa] = ρ × g × sin2α × (flow_width - levee_width) (for profile 6 with channel development)

mean τ0,flow,3 [Pa] = 2100.8first order derivation 0.80798 204047.82 10.81 -10.81 (error propagation)

τ0,flow,3 [Pa] = 2100.8+/- 264.7

Effusion rate QQ [m3s-1] = (Gz × κ × W × L)/H

mean Q [m3s-1] = 19.9first order derivation: 0.091 0.0046 -1.983 (error propagation)

Q [m3s-1] = 19.9 1.99E+01+/- 0.6 5.67E-01

Q [m3s-1] = (Gz × κ × W × L)/H (for profile 6 with channel development)mean Q [m3s-1] = 6.8

first order derivation: 0.066 0.0033 -1.047 (error propagation)Q [m3s-1] = 6.8

+/- 0.4

percentage

density ρ [kgm-3]

gravity g [ms-2]

physical parametermeasured parameters

mean value standard deviation

Grätz number Gz [-]

thermal conductivity κ [m2s-1]


6

Viscosity ηflow

ηflow,1 [Pa·s] = (ρ × g × H3 × W × sinα)/nQ (n=3 for wide, n=4 for narrow lava flows [-])n = 3

mean ηflow,1 [Pa·s]= 2.86E+05first order derivation 1.10E+02 1.82E+05 1.31E+03 9.88E+06 -1.44E+04 (error propagation)

η flow,1 [Pa·s]= 286341 2.86E+05+/- 51191 5.12E+04

ηflow,2([Pa·s] = (ρ ×(g × H4)/Qmean ηflow,2 [Pa·s]= 6.410E+05

first order derivation 2.465E+02 5.424E+05 -3.227E+04 (error propagation)η flow,2 [Pa·s]= 640991 6.41E+05

+/- 153637 1.54E+05

ηflow,3 [Pa·s] = (w3τ0,flow,3 × sin2α)/24Q 0<R<1 (R = w/(W-w) [m]) (for profile 6 with channel development)R = 0.53

mean ηflow,3 [Pa·s]= 5.98E+03first order derivation 1.74E+02 2.8 5.81E+05 -878.7 (error propagation)

η flow,3 [Pa·s]= 5.98E+03+/- 1.12E+03

Summary of rheological parameters

τ0,flow,2 [Pa] 3.49E+03 2.40E+02 6.88% based on flow width τ0,flow,2 [Pa] 4.68E+03 2.72E+02 5.81% based on flow width τ0,flow,3 [Pa] 2.10E+03 2.65E+02 12.60% based on channel widthQ [m3s-1] 1.99E+01 5.67E-01 2.86% based on flow widthQ [m3s-1] 6.81E+00 3.62E-01 5.31% based on channel width

η flow,1 [Pa·s] 2.86E+05 5.12E+04 17.88% based on flow widthη flow,2 [Pa·s] 6.41E+05 1.54E+05 23.97% based on flow widthη flow,3 [Pa·s] 5.98E+03 1.12E+03 18.70% based on channel width

rheological parameter

mean error error % Comment


7

Appendix A. 3: Representative chemical composition of the minerals. Analysis were carried out using a CAMECA SX100 Electron MicroProbe Analyser at the University of Munich according to the PAP procedure (Pouchou and Pichoir, 1985). Oxide abundances in wt.% and FeOtot is the total Fe expressed as FeO. An accelerating voltage of 15 kV and a 5µm size defocused beam with a current of 20 nA was used to minimize alkali loss (Platz et al., 2007). The olivine phenocrysts have a homogeneous composition of 84 % forsterite. Thin rims of less than 20 mm, as well as olivine microlite in the groundmass, have lower forsterite contents (Fo76). This more ferrous composition is associated with a lower temperature and late post eruption crystallisation (in agreement with Eason and Sinton, 2009). The plagioclase (phenocrysts and microlites) is 70 to 80 % anorthitic and the pyroxene belongs mainly to the Ca-rich group (augite) with approximately 37% wollastonite.

Olivine Olivine Plagioclase Pyroxene

phenocryst rim/groundmass

40.12 38.92 50.61 50.31

- - 29.97 2.68

FeO 14.43 21.58 1.13 14.37

MgO 43.46 39.53 - 14.023

CaO 0.30 0.33 14.47 17.24

- - 3.37 0.23

Fo a 84.3 76.6 - -

An - - 70.4 -

Woc

- - - 36.9

a Forsterite %= Mg100 / (Mg + Fe)

Anorthite %= Ca100 / (Ca + Na)

c Wollastonite %= Ca100 / (Ca + Mg +Fe)

SiO2

Al2O

3

Na2O

b

b


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Annex: Lava flow rheology: A comparison of morphological and petrological methods

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