Electronic Supplementary Material
- Additional Descriptions -
Supplement Material “S-1”:
Previous experiments on inward or outward dipping ring faults
The geometry of caldera ring faults has been intensely debated for more than 20 years. However, there
exists no consensus if caldera ring faults are inward or outward dipping, upward or downward
propagating. The table provides a summary of experimental work that have tried to solve these
questions.
Author
Method
Reverse fault propagation
Normal fault propagation
Komuro, 1987
sand box
upward
upward
Marti et al., 1994
sand box
upward
upward
Gudmundsson et al., 1997
numerical
-
downward
Burov and Guillou-Frottier, 1999
numerical
-
upward
Acocella et al., 2000
sand box
upward
upward
Roche et al., 2000
sand box
upward
upward
Walter and Troll, 2001
sand box
upward
upward
Kusumoto and Takemura, 2003
numerical
upward
upward
Folch and Marti, 2004
numerical
-
downward
Gray and Monaghan, 2004
numerical
-
downward
Kennedy et al., 2004
sand box
upward
upward
Pinel and Jaupart, 2005
numerical
-
downward
Geyer et al., 2006
sand box
upward
downward
Hardy 2008
numerical
upward
downward
S-1 Table 1. Analogue experiments suggest both inward or outward dipping caldera ring-faults
Supplement Material “S-2”:
Experimental scaling
Analogue experiments were geometrically and dynamically scaled. A scaling ratio of 2.5 ×10-5 was
applied in all experiments. Gravity and density were constant, so that the stress ratio is 1.25 × 10 -5. The
scaling procedure described in earlier studies (see Supplement S-1) was applied:
Length ratio
L*  Lexp / Lnature  2.5 10 5
Gravity ratio
g*  1
Density ratio
 *  0 .5
Stress ratio
 *   * g * L*  1.25  10 5
Results of Ring Shear Test
starch-sand mixture
Material
1:5
Cohesion
70.36 Pa
Angle of internal friction
27.6°
S-2 Table 1: Result of Ring shear test.
S-2 Figure 1: Result of Ring shear test.
Material properties were tested in a ring shear apparatus at the Geodynamics Lab of GFZ Potsdam. The
results for a starch-sand mixture of 1:5 yield a cohesion of about 70 Pa and an angle of internal friction
of 28 °. Cohesion is inferred from a linear fit; there is no data for low critical forces.
Loading cycle
1
critical force [kg]
0,487
tau krit [Pa]
340,41
2
0,867
606,02
7
0,511
357,18
8
0,843
589,24
13
0,426
297,77
14
0,836
584,35
S-2 Table 2: Result of Ring shear test.
Supplement Material “S-3”:
Digital Image Correlation (DIC) method details
The DIC method correlates two successive images recorded at t1 and t2. During postprocessing the
recorded images to be compared are analyzed successively in interrogation windows, small quadratic or
circular areas, some pixels in diameter, in which the pixel pattern of both images is compared by fast
Fourier transformation. From the results, a displacement vector is calculated for the area of the
interrogation window. Then the interrogation window is moved. An overlap between successive
interrogation windows enhances the spatial resolution of the vector calculation. A further enhancement
of the spatial resolution can be achieved by adaptive multi-pass correlation (Fincham and Spedding,
1997; Scarano and Riethmuller, 2000; Wienecke, 2001) and by decreasing the size of the interrogation
windows. In adaptive multi-pass correlation, the results of each pass are used to adapt the shift of the
interrogation window.
The spatial resolution of the calculated results thus depends on the optical resolution of the camera
used and the parameters of the postprocessing, including the size of the interrogation windows and the
parameters of the multi-pass correlation.
For the complete displacement vector field, the displacement vectors of all interrogation windows are
combined. From the calculated vector field, information about particle paths in x- or x-direction, particle
velocity, or strain tensor components can be derived. From the components of the strain tensor,
rotational shear strain around the z-axis (perpendicular to x and y), Poisson’s ratio, and the shear
strength can be deduced.
Supplement Material “S-4”:
The influence of the chamber aspect ratios
In general, the sequence of ring fault formation and propagation observed in our experiments was
observed in detail (S-4 Figs. 1 & 2) and independent of the roof aspect ratio AR (S-4 Fig. 3). Hence, the
final configuration for all experiments was very similar: a central subsiding piston bounded by ring faults
that are steeply inward-dipping near the surface and subvertical to very steeply outward-dipping at
depth. The amount of subsidence controls when this final (or any other) stage in the sequence is
reached. However, there is no linear trend between subsidence and the occurrence of a certain stage.
We therefore propose that ring fault evolution is a continuum rather than a stepwise process as shown
below.
S-4, Figure 1. Sequence of propagating ring
faults for shallow chamber.
Interpretation of the results of experiment
2D_15-110 and Movie 1. The results are
representative for all experiments with roof
aspect ratios <1. Solid, black lines represent
active faults, whereas dashed, grey lines
represent inactive faults. Black arrow heads
represent propagation direction. Reverse
faults - dashed, grey lines.
The interpretation of the results of experiment 2D_15-110 is provided in the S-4 Figure 1 and Movie 1.
The results are representative for all experiments with roof aspect ratios <1. It is shown that a first set of
reverse faults propagates to the surface (A), followed by a second set of reverse faults (B). Normal faults
start to propagate downwards from extension fractures at the surface. The first set of reverse faults is
inactive. C) The piston is bounded by inward-dipping normal faults close to the surface and steeply
outward-dipping to subvertical faults at depth. Both the first and the second set of reverse faults are
inactive.
Experiments with a roof aspect ratio of 1.54 are shown in the next figure, and show that individual fault
segments can be reactivated at higher subsidence rates.
S-4, Figure 2. Sequence of propagating ring faults for deeper chamber.
Interpretation of the results of experiment 2D_15-118 with a roof aspect ratio of 1.54. Dashed, grey lines
represent inactive faults, whereas the dashed, black lines in E) indicate that these fault segments can be
reactivated at higher subsidences. Black arrow heads represent propagation direction.
Correlation between the achievement of individual ring-fault configurations and the subsidence for ten
experiments with different roof aspect ratios further supports the hypothesis that a general sequence of
events is given for different chamber depths or widths. The sequence of events is similar for all aspect
ratios; the required subsidence, however, depends on the aspect ratio.
S-4, Figure 3. Synthesis of all experiments.
Correlation between the achievement of
individual
legend)
ring-fault
and
the
configurations
subsidence
for
(see
ten
experiments with different roof aspect
ratios. Stage 1: Downsag; Stage 2: reverse
ring-fault; Stages 3 & 4: peripheral normal
faulting. Background coloring indicates the
continuous nature of the realization of
individual stages.
References of Electronic Supplementary Material S1, S2, S3, S4
Acocella V, Cifelli F, Funiciello R (2000) Analogue models of collapse calderas and resurgent domes. J
Volcanol Geotherm Res 104:81-96
Burov EB, Guillou-Frottier L (1999) Thermomechanical behaviour of large ash flow calderas. J Geophys
Res 104:23, 081-23, 109
Fincham AM, Spedding GR (1997) Low cost high resolution DPIV for measurement of turbulent fluids.
Exp in Fluids 23:449-462
Folch A, Marti J (2004) Geometrical and mechanical constraints on the formation of ring-fault calderas
Earth Planet Sci Lett 221:215-225
Geyer A, Folch A, Martí J (2006) Relationship between caldera collapse and magma chamber withdrawal:
An experimental approach. J Volcanol Geotherm Res 157:375-386
Gray JP, Monaghan JJ (2004) Numerical modelling of stress fields and fracture around magma chambers.
J Volcanol Geotherm Res 135:259-283
Gudmundsson A, Martí J, Turon E (1997) Stress field generating ring faults in volcanoes. Geophys Res
Lett 24:1559-1562
Hardy S (2008) Structural evolution of calderas: Insights from two-dimensional discrete element
simulations. Geology 36:927-930
Kennedy BM, Stix J, Vallance JW, Lavallee Y, Longpre MA (2004) Controls on caldera structure: results
from analogue sandbox modeling. Bull Geol Soc Am 106:515-524
Komuro H (1987) Experiments on cauldron formation: a polygonal cauldron and ring fractures. J
Volcanol Geotherm Res 31:139-149
Kusumoto S, Takemura K (2003) Numerical simulation of caldera formation due to collapse of a magma
chamber. Geophys Res Lett 30:2278
Marti J, Ablay GJ, Redshaw LT, Sparks RSJ (1994) Experimental studies of collapse calderas. J Geol Soc
London 151:919-929
Pinel V, Jaupart C (2005) Caldera formation by magma withdrawal from a reservoir beneath a volcanic
edifice. Earth Planet Sci Lett 230:273-287
Roche O, Druitt TH, Merle O (2000) Experimental study of caldera formation. J Geophysi Res 105:395416
Scarano F, Rietmuller ML (2000) Advances in iterative multigrid PIV image processing. Exp in Fluids
(Supplements) 29:51-60
Walter TR, Troll VR (2001) Formation of caldera periphery faults: An experimental study. Bull Volcanol
63:191-203
Wienecke B (2001) PIV adaptive multi-pass correlation with deformed interrogation windows. PIV
Challenge 2001, 1-6