Caldera subsidence in areas of variable topographic relief ... - UQAM

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Journal of Volcanology and Geothermal Research 129 (2004) 219^236 

www.elsevier.com/locate/jvolgeores 

Caldera subsidence in areas of variable topographic relief: 

results from analogue modeling 

Yan Lavalle¤e a; , John Stix b , Ben Kennedy b , Mathieu Richer b , 

Marc-Antoine Longpre¤ b 

b 

a 

Department of Space Studies, University of North Dakota, Grand Forks, ND 58202, USA 

Department of Earth and Planetary Sciences, McGill University, 3450 University Street, Montreal, Qc, Canada H3A 2A7 

Received 16 July 2002; accepted 17 March 2003 

Abstract 

Calderas form in volcanic areas commonly associated with topographic relief. Pre-existing topography plays an 

important role in the style of the caldera subsidence; topography increases the load and affects the principle stress 

trajectories located between the roof of the magma chamber and the surface. The morphology, internal structure, and 

temporal evolution of calderas are therefore sensitive to the local topography. We carried out scaled analogue 

experiments to investigate the effect of pre-existing topographic relief on caldera subsidence by modeling the presence 

of stratocones and plateaus, of variable mass, diameter and positions, prior to collapse. We induced collapse in 

sandbox experiments by withdrawing water from a rubber bladder to simulate caldera collapse into a large, shallow 

reservoir. Deformation was first manifested by sagging of the sand at the surface, followed by the upward 

propagation of a set of subsidence-controlling faults from the bladder. In experiments with no topography, these 

faults usually reached the surface near the centre of the cylinder. As evacuation and incremental growth progressed, a 

second outer set of subsidence-controlling faults developed; this outer set dominated the subsidence. By increasing the 

topographic load by 6%, the subsidence efficiency increased, producing calderas up to approximately 20% deeper. The 

inner set of subsidence-controlling faults steepened and controlled most of the collapse, by contrast to the experiments 

without topography. Adding load also reduced outward growth of peripheral sagging and development of extensional 

faults; leading to a diameter of sagging 20% smaller than with no topography. A comparative analysis of our results 

with Mount Mazama at Crater Lake, Oregon, and Glass Mountain at Long Valley, California, supports the 

interpretation that the addition of topographic load modifies the evolution of the major caldera faults. 

ß 2003 Elsevier B.V. All rights reserved. 

Keywords: caldera subsidence; analogue modeling; ring fault; topography 

1. Introduction 

* Corresponding author. Tel.: +1-701-777-3460; 

Fax: +1-701-777-3711. 

E-mail address: yanlavallee@hotmail.com (Y. Lavalle¤e). 

Despite many years of research on large silicic 

caldera systems, we do not yet have a comprehensive 

understanding of the formation of these calderas 

for several reasons. First, ¢eld observations 

at young calderas are limited because the depres- 

0377-0273 / 03 / $ ^ see front matter ß 2003 Elsevier B.V. All rights reserved. 

doi:10.1016/S0377-0273(03)00241-5

220 

Y. Lavalle¤e et al. / Journal of Volcanology and Geothermal Research 129 (2004) 219^236 

sions are ¢lled with large accumulations of ignimbrite 

and therefore conceal the deeper internal 

structures. Second, the rare occurrence and the 

violent nature of large ignimbrite eruptions during 

caldera subsidence make it di⁄cult or impossible 

to directly view the mechanisms of caldera formation. 

Third, complexities such as pre-existing 

faults and other crustal heterogeneities appear to 

play an important role during the process of caldera 

subsidence (e.g. Riller et al., 2001), but these 

factors are as yet poorly constrained. 

Calderas have been the subject of numerous 

¢eld studies (e.g. Smith and Bailey, 1968; Walker, 

1984; Lipman, 1984; Branney, 1995; Moore and 

Kokelaar, 1998), and their formation also has 

been studied theoretically (Druitt and Sparks, 

1984; Gudmundsson, 1988, 1998; Gudmundsson 

et al., 1997; Scandone, 1990). The temporal evolution 

of calderas recently has been investigated 

using scaled physical models (Komuro et al., 

1984; Komuro, 1987; Mart|¤ et al., 1994; Roche 

et al., 2000; Acocella et al., 2000, 2001; Kennedy 

et al., in press). These models have used a £at 

horizontal topography, despite the fact that this 

is rarely the case in nature. Instead, calderas form 

in volcanic ¢elds which usually are associated 

with signi¢cant topographic relief. Topographic 

relief is expressed as a mass dispersed over a given 

area, which a¡ects the load imposed on the underlying 

magma chamber (Kennedy, 2000). 

At some volcanic complexes such as Crater 

Lake caldera, Oregon, the topographic load is 

the dominant upper-crustal stress ¢eld (Bacon, 

1983). Scaled experiments have shown that volcano 

loading modi¢es the regional fault patterns, 

increases the fault throw and induces extension 

(Van Wyk de Vries and Merle, 1996, 1998; Merle 

and Borgia, 1996). These researchers model and 

explain these volcano-loading e¡ects by a ductile 

layer which spreads outward below the volcano. 

There has been recent interest in the e¡ects of 

pre-existing topographic relief upon the dynamics 

of caldera subsidence (Kennedy, 2000; Walter 

and Troll, 2001; Troll et al., 2002; Kennedy et 

al., in press). The presence of relief increases the 

load and shifts stress trajectories located between 

the roof of the magma chamber and the ground 

surface (Fig. 1). Principal stress trajectories are 

oriented perpendicular to the free surfaces (Jaeger 

and Cook, 1969) and therefore are a¡ected by 

topography. Stress trajectories are concentrated 

where the curvature of the free surface is greatest, 

in this case at the basal margin of the topography 

and where the magma chamber roof becomes 

curved. Hence, the morphology, internal structure 

and temporal evolution of caldera subsidence can 

be a¡ected by topography. 

With this in mind, our objectives were to understand 

the consequences of varying the initial load 

using various geometric forms similar to volcanic 

edi¢ces, such as cones and plateaus. Speci¢cally, 

the present study aims to elucidate several aspects 

of pre-existing topographic relief on the behaviour 

of caldera subsidence. Three variables were investigated 

for this study: (1) topographic mass, (2) 

topographic diameter, and (3) volcanic construct 

positioning relative to the centre of the analogue 

magma chamber. 

2. Methodology 

2.1. Scaling relationships 

In order to model natural processes, we scaled 

down experimental parameters by adhering to the 

principles of similitude (Hubbert, 1937). This scaling 

validated that our model is mechanically, kinematically 

and dynamically comparable to the 

natural case (Sanford, 1959). 

Calderas are large volcanic depressions ranging 

from 2 to more than 50 km in diameter (Lipman, 

1984). The cylinder used in our experiments has a 

diameter of 1.0 m, so we assume that a 0.50-mdiameter 

experimental caldera is equivalent to a 

20-km-diameter natural caldera: 

L ¼ d D ¼ 

0:5 m 

20000 m ¼ 2:5U1035 

where d is the diameter of the experimental caldera, 

D is the diameter of the natural caldera, and 

L* is the length ratio. L* is relevant for the dimensions 

of topography, caldera and magma 

chamber aspect ratio (depth/diameter ratio of 

the roof of the analogue chamber). Thus, the 

8.5-cm depth of the analogue chamber constantly

Y. Lavalle¤e et al. / Journal of Volcanology and Geothermal Research 129 (2004) 219^236 221 

Fig. 1. Stress trajectories between a pressurised magma chamber and the surface, where the vertical load (c 1 ) is the sole stress applied. 

(a) No topographic relief. (b) In the presence of a plateau. (c) In the presence of a cone. (d) In the presence of a cone located 

above the edge of the analogue chamber. The ¢gures are purely qualitative and designed to illustrate how the orientation 

of the free surface alters the orientation of the stress trajectories. Faulting is most likely where stress trajectory concentrations 

are highest; these regions are marked by a X. Modi¢ed from Jaeger and Cook (1969). 

used in our experiments corresponds to a 3.4-kmdeep 


Time is another fundamental parameter that 

needs to be scaled (Hubbert, 1937). Shear box 

tests and some preliminary experiments have demonstrated 

that time is an important factor, as sand 

deformation may be partially time-dependent. 

The duration of caldera formation is poorly constrained. 

While Wilson and Hildreth (1997) estimated 

that the collapse of Long Valley caldera 

took approximately 98 h, the caldera-forming 

eruption of Pinatubo in 1991 lasted approximately 

9 h (Wolfe and Hoblitt, 1996). For our 

scaling, we chose a mean value of 17 h for a 

natural caldera and a 5-min evacuation time for 

the experiments (t). The time ratio, d*, is: 

d ¼ t T ¼ 

5 min 

1020 min ¼ 4:9U1033 

The appropriate experimental material is determined 

by scaling the shear strength of crustal 

rocks. The stress ratio, c*, can be used for this 

and is equivalent to the density ratio, b*, multiplied 

by the gravity ratio, g*, and L*: 

c ¼b g L ¼1:8U10 35 to 2:4U10 35 

where b* = 0.70^0.95 (density of partially compacted 

sand 1890 kg m 33 , density of rocks 

2000^2700 kg m 33 ) and g* = 1. The gravity ratio 

obtained from our scaling ratios (units of m/s 2 

and therefore L*/T* 2 ) is approximately 1, supporting 

the gravitational conditions under which 

the experiments were performed. 

Crustal rocks have a cohesion on the order of 

10 6 to 10 7 Pa depending on fracturing (Schultz, 

1996). Scaling cohesion using the stress ratio 

therefore requires the use of material with a 

very low cohesion (18^240 Pa). In theory, sand 

consists of cohesionless particles held by static 

friction (Krantz, 1991; Wittmer et al., 1996). We 

used poorly-sorted, partially compacted sand that 

has absorbed some moisture from the air. Due to 

its poor sorting and slight humidity, the sand has 

acquired a small amount of cohesion which is 

appropriate for our experiments. Attempts to es-

222 


timate the cohesion were made using shear box 

tests, but the low cohesion values were di⁄cult 

to estimate. We concluded that a value of 0^100 

Pa was reasonable, which is equivalent to the 

scaled strength of crustal rocks in nature. 

The viscosity of the magma also needs to be 

considered in the scaling process, since it is an 

important variable dependent on three fundamental 

parameters: mass, length and time. The viscosity 

ratio, R*, is thus: 

R ¼d c ¼8:8U10 38 to 1:2U10 37 

The viscosity of magmas varies from 10 2 Pa s 

for basaltic melts up to 10 18 Pa s for anhydrous 

granitic melts (Murase and McBirney, 1973; Hess 

and Dingwell, 1996). We decided to scale our analogue 

material using a magma viscosity of 10 4^10 5 

Pa s, as this viscosity spans a wide range of magma 

compositions (e.g. dry andesitic melt to granitic 

melt containing 4 wt% H 2 O at 900‡C; Hess 

and Dingwell, 1996). We used water with a viscosity 

of 10 33 Pa s as our analogue material, because 

it is consistent with our scaling factor. 

2.2. Experimental setup 

The apparatus comprised a cylinder 1.0 m in 

diameter and 1.0 m in height, ¢lled with poorlysorted, 

partially compacted sand, which represents 

brittle crustal rock (Fig. 2a). A 45-l water- 

¢lled rubber bladder was buried within the sand 

to represent a magma chamber. The analogue 

chamber, circular in plan view and oblate in section, 

deformed in two di¡erent ways during the 

experiments. When ¢lled with water to its maximum 

capacity, the analogue chamber de£ated 

elastically and contracted due to overpressure decrease 

(Fig. 2b). At lower water capacities, however, 

the roof subsided vertically as the water was 

evacuated (Fig. 2c). These two mechanisms of 

analogue chamber deformation represent initially 

elastic behaviour of the crust and the crystal mush 

around the chamber during contraction as the 

pressure in the magma chamber was decreased, 

followed by brittle failure of the roof when the 

deviatoric stress reached the Mohr^Coulomb criterion 

curve (Hubbert, 1951; Mandl, 1988). 

Fig. 2. (a) Experimental setup showing a cylinder containing sand. The cylinder has a diameter of 1.0 m, a height of 1.0 m, and 

is ¢lled with poorly-sorted, compacted sand. The rubber bladder, buried at a depth of 0.085 m, has a diameter of 0.60 m and is 

¢lled initially with 45 l of water. Two lasers are inclined at an angle of 30‡; they produce two perpendicular lines on the surface. 

(b) Deformation of the bladder during initial withdrawal. The bladder contracts, similar to a magma chamber losing volatiles as 

the gas-rich magma erupts. (c) Schematic representation of the bladder deformation at a later stage, where the roof subsides vertically. 

This stage represents the subsidence of the roof into the magma chamber.


Magma withdrawal was simulated using a tube 

attached to the underside of the analogue chamber, 

with a £owmeter to control the rate of water 

evacuation. Subsidence was thus a consequence of 

depressurisation in the magma chamber; after the 

initial contraction, the weight of the overlying 

sand was the only stress acting on the system 

(no far-¢eld stress was present). Two lasers positioned 

at right angles to each other and inclined 

at 30‡ produced two initially perpendicular 

straight lines on the surface of the sand. As water 

was evacuated, the subsidence of the caldera £oor 

was revealed by curvatures and o¡sets of the 

lines. To clearly see the di¡erent structures forming 

at the surface, the sand was kept as smooth 

as possible, and the relief was well de¢ned. Before 

each experiment, the sand was mixed and 

compacted, by moderately tamping the entire 

surface, to keep it homogeneous and to erase 

traces of any pre-existing fractures from previous 

experiments. 

In order to investigate the role of pre-existing 

topographic relief, all complementary variables 

were kept constant. The 45-l analogue chamber 

was leveled and buried at a depth of 0.085 m 

and evacuated at a rate of 1.6 l min 31 for 5 min. 

For some experiments, the evacuation rate was 

600 l min 31 for 13.3 min. In both cases the 

evacuation totalled 8000 l. With the evacuation 

of this volume, the sand subsided by approximately 

0.05 m, which represents about 2000 m 

of subsidence according to our scaling ratio (see 

below). This value corresponds to the amount of 

subsidence at large calderas (e.g. Long Valley caldera; 

Wallace et al., 1999). 

Temporal evolution of the subsidence was 

monitored using a video camera centred above 

the apparatus. To allow the observation of surface 

structures, a low-angle light was used to de- 

¢ne fault scarps. Interruption of the power every 

10 s allowed the camera to monitor the evolution 

of the curves produced by the lasers. To validate 

our observations, we made cross-sections for selected 

experiments. For these, we used alternating 

layers of white and brown sand. After an experiment, 

the dry sand was saturated with water, 

which raised the cohesion and allowed cross-sectioning 

in order to perform fault analysis. 

2.3. Description of the experiments 

The e¡ect of adding topography was studied by 

performing two sets of experiments with centred 

sandpiles of similar basal diameters, but di¡erent 

masses. We ran an initial set of experiments with 

no pre-existing topographic relief, followed by experiments 

with 0.17-m-diameter constructs: small 

plateaus of 0.25 kg, thicker plateaus of 0.5 kg, 

and 1-kg cones (sand at the angle of repose) (Table 

1). The presence of these volcanic constructs 

increased the average load by about 4, 7 and 14%, 

respectively. The second set of experiments was a 

repetition of the ¢rst, but the masses were all 

doubled, and the resulting basal diameter of the 

topography was 0.25 m instead of 0.17 m. This 

second set thus consisted of experiments with 

0.5- and 1-kg plateaus and a 2-kg cone, which 

increased the load by 3, 6 and 12%, respectively. 

Even though the masses of the sandpiles 

were doubled in the second set of experiments, 

the increase in load was less because the area 

of sand distribution increased more than did the 

mass. 

The same two sets of experiments also were 

used to investigate the e¡ect of changing the diameter 

of topographic relief on the behaviour of 

caldera collapse. We compared experiments with 

no topographic relief and experiments with 0.5-kg 

plateaus having a basal diameter of 0.17 and 0.25 

m. We also compared experiments with no topography, 

experiments with 1-kg cones 0.17 m in diameter, 

and 1-kg plateaus 0.25 m in diameter. 

Lastly, the e¡ect of topography positioning on 

caldera subsidence was studied by building a 

1-kg conical sandpile, 0.17 m in diameter, above 

the edge of the magma chamber. The o¡-centred 

topography experiments were compared with 

those done using a 1-kg cone centred above the 


To verify the consistency of our results, one 

experiment with no topography was performed 

between each set of topography experiments. 

This acted as a reference to compare with experiments 

having pre-existing topographic relief. Each 

type of experiment was performed three times, 

which allowed some quantitative analysis in addition 

to the qualitative interpretation.

224 


Table 1 

Quantitative and qualitative results obtained from the experimentS 

Experiment 

number 

Topographic variation 

Results 

Type Size Mass Depth Diameter of 

inner faults 

Diameter of 

outer faults 

Diameter of 

sagging 

Caldera type Set of faults 

controlling the 

subsidence 

(m) (kg) (cm) (cm) (cm) (cm) 

10 no topography 0 0 4.5 10 21 63 trapdoor outer set of faults 

11 no topography 0 0 4.5 18 30 56 asymmetric outer set of faults 

piston 

15 no topography 0 0 4.1 13U17 29U32 63 asymmetric outer set of faults 

piston 

19 no topography 0 0 4.7 20 32 52U60 trapdoor outer set of faults 

24 no topography 0 0 5 15 23 64 trapdoor outer set of faults 

27 no topography 0 0 4 20 38 58 trapdoor outer set of faults 

33 no topography 0 0 4 18U22 36 65U68 trapdoor outer set of faults 

3 b no topography 0 0 4.2 16U18 37U42 52U58 piston outer set of faults 

18 plateau 0.17 0.25 4 17 27 60 trapdoor both controlled 

equally 

20 plateau 0.17 0.25 5 24 51 70 trapdoor outer set of faults 

16 plateau 0.17 0.5 5 17U23 30U37 60 trapdoor inner set of faults 

17 plateau 0.17 0.5 5 17U26 38 57 trapdoor inner set of faults 

12 cone 0.17 1 5 13U31 46 50 asymmetric inner set of faults 

piston 

13 cone 0.17 1 5 22U33 46 50 piston inner set of faults 

14 cone 0.17 1 4.7 17U24 36 56 piston inner set of faults 

2 b cone 0.17 1 4.6 30 36 55 piston inner set of faults 

4 b cone 0.17 1 6 26 34 56 asymmetric inner set of faults 

piston 

21 plateau 0.25 0.5 5.2 25 31 64 trapdoor outer set of faults 

22 plateau 0.25 0.5 4.4 12 28 69 trapdoor outer set of faults 

23 plateau 0.25 0.5 5.2 28 32 65 trapdoor both controlled 

equally 

28 plateau 0.25 1 5.1 25 38 63 trapdoor inner set of faults 

29 plateau 0.25 1 4.7 18 28 50 asymmetric inner set of faults 

piston 

30 cone 0.25 2 5.3 25 none 47 trapdoor inner set of faults 

31 cone 0.25 2 4.7 25 33 52U46 trapdoor inner set of faults 

2.4. Relevance and limitations 

Physical modeling of caldera formation provides 

useful insights into the intricate process of 

caldera formation. Although the granular nature 

of sand allows it to £ow, it behaves according to 

the Mohr^Coulomb failure criterion as a brittle 

material similar to the upper few kilometres of 

the crust ( 6 10 km; Sanford, 1959). Our model 

uses a water-¢lled rubber bladder with a convex 

roof as an analogue chamber; the average roof 

aspect ratio is approximately 0.3. We used such 

a geometry because it appears to be representative 

of large magma chambers (e.g. Long Valley caldera; 

Wallace et al., 1999). The rubber bladder is 

the boundary between the water and the sand and 

may represent the crystal-mush transition between 

the magma and the rock. However, this boundary 

is not scaled and constitutes a barrier preventing 

the occurrence of physical processes such as intrusion 

and the collapse of crustal blocks into a magma 

chamber. Such processes may a¡ect the magmatic 

pressure and could play a role during the 

process of caldera formation. However, the cor-


rectly scaled low-viscosity water allows for irregular 

styles of subsidence due to relatively rapid 

£uid £ow within the bladder, as is the case in 

nature. However, in contrast to a magma carrying 

bubbles, water is not compressible, which may 

distort the fashion by which the magma chamber 

responds to subsidence of the overlying crustal 

block. 

Fig. 3. Plan view images of analogue calderas during the experiments. The sets of subsidence-controlling faults are represented by 

dashed lines (f 1 and f 2 ). The thicker lines indicate the faults with greater displacement. The extensional faults are represented by 

a solid line (e 1 ). (a^c) Fault propagation in the absence of pre-existing topographic relief: after 2.5 min (a); after 4 min (b); after 

5 min (c). (d^f) Fault development when a centred 0.25-kg plateau of 0.17 m basal diameter is present: after 2.5 min (d); after 

4 min (e); after 5 min (f). (gî) Fault propagation when a centred 1-kg cone of 0.17 m basal diameter is present: after 2.5 min 

(g); after 4 min (h); after 5 min (i). The ¢rst faults are initiated at the surface at the margin of the cone, and they propagate 

away from the area of maximum subsidence. The faults are curvilinear, forming a polygonal-shaped caldera. Note the localised 

development of faults in the periphery when pre-existing topography is present. In (d^f) a fault cuts through topography.

226 


3. Results 

We now describe our experimental caldera development 

in plan view. The results are presented 

in four sections (Table 1). First we describe our 

experiments with no pre-existing topography. 

Then we describe the changes caused by: (1) adding 

topographic mass, (2) increasing the diameter 

of the topography, and (3) moving the topography 

from above the centre to above the edge of 

the magma chamber. 

3.1. No topographic relief 

In the absence of pre-existing topography, the 

evacuation of water was immediately manifested 

near the centre of the free surface by downsagging 

of the sand, which is de¢ned as the tilting of the 

strata towards the centre of the caldera (Branney, 

1995). This was followed by the propagation of a 

subsidence-controlling fault (f 1 ) from the analogue 

chamber roof in the area of maximal curvature 

(see Fig. 1) which reached the surface near 

the centre of the cylinder (Fig. 3a). As evacuation 

continued and vertical displacement increased, f 1 

propagated laterally in a curvilinear fashion away 

from the location of fault initiation at the surface 

(Fig. 3a^c). Midway during the experiment, a second 

set of subsidence-controlling faults (f 2 ) usually 

formed outside the ¢rst set (although in a few 

rare cases f 1 and f 2 intersected), re£ecting incremental 

growth of the caldera as it subsided. As f 2 

developed, the area of sagging increased away 

from the centre. Once it reached its maximum 

extent, extensional faults (e 1 ) developed in peripheral 

regions, and the inwardly tilted sand began to 

slump and slide slowly into the caldera. The end 

result typically consisted of a trapdoor-style caldera, 

faulted on only one side, with an elliptical 

area of sagging aligned with the trapdoor 

(although pistons with complete ring faults sometimes 

developed). As previously observed (Kennedy, 

2000; Kennedy et al., in press), the position 

of fault initiation was generally found to be the 

point of maximum subsidence at the end of the 

experiment, even though f 2 displayed greater vertical 

displacement than f 1 . 

3.2. The addition of topographic mass 

The addition of a small 0.25-kg plateau of 0.17 

m diameter did not a¡ect the development of the 

subsidence-controlling faults signi¢cantly. Two 

sets of subsidence-controlling faults (f 1 through 

the plateau and f 2 around its margin) developed, 

with their initial positions similar to experiments 

with no topography (Fig. 3a). Although in this 

example f 1 and f 2 intersected (Fig. 3b), the subsidence 

was still mainly controlled by the outermost 

portions of the faults (see displacements on 

Fig. 4. Average depth of calderas as a function of mass added at the surface. The range of depth variation is þ 0.3 cm for experiments 

with topography, and þ 0.5 cm for experiments without topography.


Fig. 5. A schematic view showing slumping of topography, 

induced by asymmetric collapse. The thick line represents the 

fault with greatest vertical throw. 

Fig. 3f). Similar to experiments with no topography, 

an extensional peripheral fault (e 1 ) formed 

near the end of the experiment. 

With increased sandpile masses (0.5 kg, 1 kg), 

the ¢rst set of subsidence-controlling faults (f 1 ) 

developed at the basal margin of the sandpile 

(Fig. 3g). In contrast to experiments without topography, 

a complete second set of subsidencecontrolling 

faults (f 2 ) rarely developed; when f 2 

did develop, the subsidence generally remained 

focused along f 1 (Fig. 3gî). The main set of subsidence-controlling 

faults always had a smaller 

Fig. 6. Development of sagging in terms of time as the subsurface bladder is evacuated progressively. The data in (a) show sagging 

for topographic elements with 0.17 m basal diameters and variable masses compared to sagging in the absence of topography. 

The sagging growth rate is similar for all experiments during the ¢rst 3 min. (b) The data for the di¡erent topographic 

masses from (a) above are normalised to the data in the absence of topography. Compared to experiments without topography, 

the extent of sagging is signi¢cantly smaller when topography is present, even for masses as small as 0.25 kg. The accuracy of 

the sagging diameter is þ 1 cm.

228 


diameter than experiments with no pre-existing 

topography. With increased topographic mass, 

the resultant calderas were on average 20% deeper 

(Fig. 4), although there is some scatter in the 

data, since the maximum depth of the caldera 

£oor was sometimes di⁄cult to estimate due to 

the presence of topography. The subsidence asymmetry 

was una¡ected by the presence of additional 

mass, and asymmetric subsidence caused 

slumping to occur on the £anks of the topography. 

In one extreme case, a normal fault developed 

within a subsiding cone, leading to slumping 

of the entire construct (Fig. 5). 

Sagging also was a¡ected by the presence of 

additional mass. The presence of topography decreased 

the diameter of sagging by about 20% 

(Fig. 6a). This di¡erence appears to be related 

to slower outward propagation of the sagging 

for experiments with topography. During the ¢rst 

2 min, the rate of sagging propagation was similar 

for all experiments (Fig. 6). Beyond this point, 

however, the rate slowed when topography was 

present. For experiments with large masses, the 

e¡ects are most evident near the end of the experiments, 

but even a small addition of mass greatly 

a¡ected the ¢nal diameter of sagging (Fig. 6b). 

The pre-existing topographic relief also appeared 

to in£uence the shape of the sagging 

area. In the absence of topography, sagging was 

often found to be more elongate parallel to the 

trapdoor, creating an elliptical shape in plan view. 

The addition of a sandpile on the surface appeared 

to increase the circularity by about 4% 

(Fig. 7). 

In summary, for small sandpile masses, the resulting 

calderas were typically all trapdoor struc- 

Fig. 7. (a) Evolution of the ellipticity of calderas with no topography, compared to calderas with di¡erent topographic masses 

but similar basal diameter (0.17 m). (b) Evolution of the ellipticity for calderas of variable mass and diameter. The ellipticity is 

de¢ned as the ratio of the smallest diameter of sagging over the largest diameter of sagging (ellipticity = 1 for a perfect circle).


tures, similar to the experiments with no topography. 

With larger topographic masses, the subsidence 

was focused on a smaller-diameter inner 

set of subsidence-controlling faults, which were 

fully developed around the entire caldera. The 

calderas formed were piston-type and they tended 

to be deeper with a smaller peripheral area of 

sagging. 

Fig. 8. Development of sagging as a function of time for di¡erent basal diameters. (a) Topographic elements with a mass of 0.5 

kg and diameters of 0.17 m and 0.25 m, both plateaus. (b) Topographic elements with a mass of 1.0 kg and diameters of 0.17 m 

(cone) and 0.25 m (plateau). (c) The sagging data for two 1-kg topographic elements, the ¢rst a cone of 0.17 m basal diameter 

and the second a plateau of 0.25 m basal diameter, are normalised to sagging in the absence of topography.

230 


3.3. Varying the diameter of the topography 

Varying the basal diameter of the topography 

for a given mass also a¡ected the morphology of 

calderas. Small-diameter sandpiles typically were 

bounded by the main subsidence-controlling 

faults at the edge of the basal margin of topography, 

whereas large-diameter sandpiles typically 

were intersected by faults. The subsidence of these 

latter experiments was concentrated primarily 

along the outer set of subsidence-controlling 

faults. 

In terms of sagging, small-diameter sandpiles 

produced calderas with a diameter of sagging approximately 

12% less than large sandpiles (Fig. 

8a,b). The rate at which sagging expanded outward 

also was a¡ected by varying the topographic 

basal diameter. Calderas with small-diameter topography 

had signi¢cantly lower rates, particularly 

in the latter stages of experiments, compared 

to experiments with large-diameter topography 

(Fig. 8c). 

3.4. Changing the position of the topography 

When compared to experiments without topography, 

experiments where the topography was 

moved from above the centre of the analogue 

chamber to above its edge appeared to have little 

in£uence on the behaviour of caldera subsidence. 

For o¡-centred cones of 1 kg, faults initially did 

not reach the edge of the topography, but instead 

reached the centre of the free surface, as seen for 

experiments without topography. With o¡-centred 

topography, propagation of the subsidence-controlling 

faults did not follow a clear pattern. 

They either propagated away from or toward 

the o¡-centred cone. The late-stage extensional 

faults associated with the area of peripheral sagging 

always reached the basal margin of the construct. 

The asymmetry of subsidence was not a¡ected 

signi¢cantly by changing the location of the sandpile. 

The trapdoor was formed in the same direction 

as the experiments performed with no topography, 

and the location of the cone did not cause 

the caldera to be deepest at that location. In fact, 

the caldera £oor was more symmetric than for 

experiments without topography. The area of 

maximum subsidence was still located where the 

¢rst fault initiated but did not coincide with the 

basal margin of the topographic relief. The depth 

of the caldera also did not increase when a cone 

was added above the edge of the magma chamber. 

Lastly, sagging was not a¡ected by varying the 

position of the topography. The shape of the sagging 

area was nearly circular for both experiments 

with centred and o¡-centred topographic relief. 

4. Discussion 

4.1. Variations of load 

Our experimental results demonstrate that increasing 

the mass or decreasing the diameter of 

the topography have the same e¡ects. This fact 

reveals that deformation at calderas is sensitive 

to variations in load. The load (expressed as c 1 , 

since it is the principal stress) is a force per unit 

area which is dependent on the mass of the overlying 

material covering a particular area (Gudmundsson, 

1998): 

c 1 ¼ b g h ¼ 

mass gravity 

area 

where b is the density of the sand (1890 kg m 33 ), 

g is the gravity (9.81 m s 32 ), and h is the averaged 

depth of the overall analogue chamber (0.2 m). 

The depth at the centre of the analogue chamber 

is 0.085 m, but due to the convex geometry of the 

roof, the depth increases in the periphery. With 

no pre-existing topography, the average load 

upon the analogue chamber is 3708 Pa. 

The ¢rst set of experiments consisted of sandpiles 

of 0.25, 0.5 and 1 kg distributed over a basal 

diameter of 0.17 m. The addition of these masses 

increased the load by 122, 244 and 488 Pa, respectively. 

The second set of experiments consisted of 

sandpiles of 0.5, 1 and 2 kg with a basal diameter 

of 0.25 m. These masses represent loads of 100, 

200 and 400 Pa, respectively. Even though the 

masses of the sandpiles were doubled in the second 

set of experiments, the relative load increase 

was less because the area of sand distribution increased 

more than did the mass.


The main e¡ects of increasing the load above 

the analogue chamber are the following: (1) the 

¢rst fault forms at the topographic margin; (2) 

the subsidence is concentrated along the inner 

set of subsidence-controlling faults; (3) the diameter 

of main subsidence-controlling ring faults is 

smaller; (4) the depth of the caldera increases by 

up to 20%; (5) the outward growth rate of sagging 

decreases; (6) the diameter of sagging decreases 

by 20%; and (7) the ellipticity of the 

area of sagging decreases. 

These seven consequences appear to be closely 

related to each other. Adding topography above 

the magma chamber increases the load by up to 

13% and shifts the stress trajectories, which concentrate 

at the basal margin of the topography 

(Fig. 1). An increased deviatoric stress is produced 

below the basal margin of the topography, 

favouring the development of faults in this area. 

This may explain the concentration of subsidence 

along the inner set of subsidence-controlling faults 

that are found at the margin of large topographic 

masses (Fig. 9a). Because the subsidence mainly 

occurs along the inner set of faults, the displacement 

along the outer set of faults is smaller, and 

thus the tension created in the periphery is smaller 

as well, creating a smaller-diameter sagging 

area. 

Fig. 9. Cross-section and plan view photographs for two types of experiments. (a,b) For the heaviest topographic masses, the 

subsidence concentrates along f 1 , which propagates at the margin of the topography. The displacement can be seen to be greatest 

at depth, showing that the subsidence-controlling fault propagated upward. (c,d) In the absence of topography, the subsidence is 

focused along f 2 . Although f 1 only shows slight displacement at depth, a close-up view of the cross section coupled with plan 

view information indicates the complete development of f 1 . On the plan view photographs, the cross sections are marked as thin 

lines with a dot at each end. In the sketches, the thicker lines represent faults with the greatest vertical throw.

232 


4.2. The nature of faulting and sagging during 

caldera development 

Knowledge of fault orientations is important to 

the understanding of caldera subsidence processes. 

Experimental work has shown that subsidencecontrolling 

faults (often referred to in the literature 

as ring faults) are steeply outward dipping 

Fig. 10. Relationships between angles of the outward dipping fault and the peripheral inward dipping fault. (a) For vertical inner 

faults (left), no space is created during subsidence, hence only the sand on the topographic rim slumps. For a steep outward dipping 

fault (right), a small space can be created at shallow depth during caldera collapse. The resulting peripheral extensional fault 

thus only reaches a shallow depth, and a comparatively larger area at the surface will be a¡ected by peripheral extension and 

slumping. (b) For low-angle outward dipping faults, the space created is much larger and deeper, allowing more sand in the periphery 

to subside inside the caldera. The peripheral faults have the same angle, but the area of peripheral extensional slumping 

becomes larger due to the greater fault extent. The ¢gures are all drawn to the same scale. (c) Photograph of a steep arcuate outward 

dipping fault, which developed a small area of peripheral extension. This extensional area coupled with a small kink in the 

second layer of white sand appear to delineate a shallow peripheral inward dipping fault (the minimal fault displacement is 

shown by a thin dashed line). (d) Photograph of a low angle arcuate outward dipping fault bounded by a deep peripheral inward 

dipping fault.


(Sanford, 1959; Acocella et al., 2000; Roche et 

al., 2000). The displacement which we have observed 

in cross-sections is greater at depth (Fig. 

9), indicating that subsidence-controlling faults 

propagate upward from the roof of the analogue 

chamber to the surface. Upon subsidence along 

an outward dipping fault, tension is created in 

the hanging wall, producing extensional faults at 

the surface (Branney, 1995; Roche et al., 2000; 

Acocella et al., 2000, 2001; Kennedy et al., in 

press). Our results demonstrate that a steepening 

of the arcuate outward dipping fault creates less 

space at depth, which reduces the extent of the 

peripheral extensional faults (Fig. 10). 

Increasing the load by 6% caused the subsidence 

to be concentrated along the inner set of 

outward dipping faults (f 1 ) at the margin of the 

topography, rather than along f 2 (Fig. 9). As a 

result, f 1 is active over a longer period of time 

than f 2 . This may explain the fact that the addition 

of load reduces the growth rate of sagging 

during the second half of the experiments (Fig. 6); 

for experiments with topography, the subsidence 

is primarily controlled by f 1 , producing an area of 

sagging which is 20% smaller (Figs. 6 and 8). Furthermore, 

in the presence of topography, steeper 

f 1 faults appear to enhance subsidence, as fault 

displacement increased by up to 20% (Figs. 4 

and 9). These changes in the dimensions of the 

caldera appear to be strongly linked to the subsidence-controlling 

faults, their dips and their duration 

of activity. 

The evolution of sagging ellipticity appears 

non-systematic but may re£ect complex episodes 

of fault propagation (Fig. 7b). Faults propagate 

laterally and vertically, tending to de¢ne a 

roughly circular shape. However, the way in 

which this is achieved is not necessarily straightforward. 

Faults propagate dominantly in one direction 

or in one area for a period of time, accompanied 

by sagging. The direction or the area 

of faulting then can change, and the area of active 

sagging follows accordingly. This relationship 

supports the observation that the area of sagging 

is a direct response to movement on the subsidence-controlling 

faults (Branney, 1995; Roche 

et al., 2000). 

Lastly, the e¡ects of placing the sandpiles 

above the margin of the analogue magma chamber 

are small compared to experiments without 

topography, since the region of increased load 

only partly overlies the area where the analogue 

chamber is evacuated (Fig. 1d). As a result, the 

subsidence process is generally una¡ected by this 

topographic con¢guration. The resulting calderas 

are thus similar to those produced without preexisting 

topography. 

5. Application to natural caldera systems 

The data we have presented suggest that topography 

has important e¡ects on caldera subsidence. 

The basement rock beneath calderas frequently is 

faulted and broken into blocks. These structures 

commonly are interpreted as either the caldera 

£oor fragmented by subsidence-controlling faults 

or megabreccias which slid o¡ the caldera walls 

during subsidence (Fig. 10; Lipman, 1984; Troll 

et al., 2000). Our experiments suggest that these 

subsurface structures also could represent topographic 

failure. Such failure would be expected, 

since caldera subsidence is generally asymmetric. 

In our experiments, asymmetric subsidence caused 

tilting and induced slumping of the volcanic construct 

towards the area of maximum subsidence 

(Fig. 5). This could explain why megabreccias are 

observed at some distance inward from the caldera 

ring dyke, as seen at Lake City caldera, Colorado 

(Lipman, 1984). 

The presence of Mount Mazama prior to the 

6845 þ 50 yr BP climactic eruption which formed 

Crater Lake caldera, Oregon, is a good example 

of a pre-caldera topographic stratocone. Bacon 

(1983) has proposed that the pre-collapse summit 

of the volcano was located in the south-central 

part of the present caldera. Crater Lake is thus 

a case of topography centred above the pre-collapse 

magma chamber. Bacon (1983) estimated 

the volume of Mount Mazama at between 40 

and 52 km 3 , which corresponds approximately 

to a sandpile of between 1.25 and 1.62 kg. In 

our experiments for such masses, the entire sandpile 

is downfaulted, so that only the very edge of 

the topography remains at the surface after collapse, 

and most of the topography lies at the bot-

234 


tom of the caldera £oor. Our work further shows 

that the addition of topography increases the load 

and promotes subsidence along an inner set of 

subsidence-controlling faults. Interestingly, Bacon 

(1983) raised the possibility that Crater Lake is a 

coherent piston which subsided along a steeply 

dipping ring fault. As shown by our experiments, 

an important consequence of pre-existing topographic 

relief is the initiation and development 

of the ¢rst caldera fault at the basal margin of 

the topography. At Mount Mazama, vent locations 

of pre-collapse eruptions were clustered on 

its northern £ank near the base of the volcano 

and may de¢ne a semi-circular pattern from the 

northwest to the east (Bacon, 1983; Kamata et 

al., 1993). It is possible that these pre-caldera 

magma leaks de¢ne an arcuate fracture, or an 

outer set of subsidence controlling faults (Williams, 

1942), which was developing around the 

main subsidence-controlling fault, although Bacon 

(1983) suggested that these vents may also 

be radial in nature. By contrast, the climatic eruption 

at Mount Mazama was initiated from a single 

vent north of the volcano’s summit but within 

the ring structure. With the development of the 

ring fracture during subsidence, ignimbrites were 

erupted from multiple vents along this fracture 

system, cutting the £ank of the volcano (Bacon, 

1983). In our experiments, the ring fault was of 

a greater diameter relative to the topography, 

whereas at Crater Lake the ring fault developed 

within the topography; this may be due to the 

higher roof aspect ratio of the chamber at Crater 

Lake (0.8) than in our experiments (0.3). A higher 

roof aspect ratio promotes smaller-diameter subsidence-controlling 

faults which may intersect topography 

(Roche et al., 2000; Roche and Druitt, 

2001; Kennedy et al., in press). 

Long Valley is a caldera showing evidence of 

signi¢cant pre-existing topography above a magma 

chamber with a V0.25 roof aspect ratio (Wallace 

et al., 1999). While the western half of the 

caldera originally comprised mountains of the Sierra 

Nevada batholith, the northeastern margin of 

the depression is occupied by Glass Mountain 

(Metz and Mahood, 1985; Bailey et al., 1989). 

Glass Mountain represents an example of o¡-centred 

topographic relief. The southwestern part of 

Glass Mountain was downfaulted into the caldera 

during its collapse (Bailey et al., 1976). The exact 

volume of Glass Mountain is unknown because 

the amount buried beneath thick accumulations 

of Bishop Tu¡ and post-caldera rocks has not 

been estimated. Based on an area estimate from 

Metz and Mahood (1985), we estimate the volume 

of Glass Mountain to be approximately 70 km 3 . 

Scaled to our model, this represents a large 2-kg 

cone with a 0.25-m basal diameter. A detailed 

study of the Bishop Tu¡ eruption by Wilson 

and Hildreth (1997) revealed that vents propagated 

to Glass Mountain during the latter parts 

of the eruption. Their analysis shows that the 

vents propagated from both the north and south 

sides of the caldera, converging on Glass Mountain. 

A similar phenomenon was observed in our 

experiments with o¡-centred topography, where 

subsidence along late-forming faults propagated 

towards the basal margin of the o¡-centred sandpile. 

On the other hand, the location of Glass 

Mountain appears to be coincident with, or close 

to, the area of maximum subsidence (Jachens and 

Roberts, 1985). 

This study has shown that pre-existing topographic 

relief has important consequences on the 

morphology of calderas if the topography is located 

above the central area of the underlying 

magma chamber. In the presence of small and 

medium-sized magmatic systems, a volcano may 

be more likely to directly overlie the magma 

chamber, unless the source was displaced laterally 

with time or magma ascent occurred through an 

oblique plumbing system. On the other hand, 

large magmatic systems (e.g. Long Valley) may 

favour the development of o¡-centred topographic 

constructs, which partially reduce their 

e¡ects. Hence, the size of the magma chamber 

may a¡ect the distribution of overlying topography 

and caldera collapse. 

6. Conclusions 

This study has demonstrated that the style of 

caldera subsidence may be a¡ected by the load. 

By adding mass (for a given diameter of topography) 

or by decreasing the diameter of topography


(for a given mass), the load increased locally. A 

6% increase in load results in: (1) steepening of 

the inner set of subsidence-controlling faults, 

which controls the development of subsidence; 

(2) an increase in subsidence e⁄ciency, leading 

to calderas up to 20% deeper; (3) a slowing of 

the expansion rate of sagging during magma evacuation, 

hence a decrease of the sagging area; (4) a 

decrease of the ellipticity of the sagging area; and 

(5) the development of smaller piston-type calderas. 

Moving the sandpile from above the centre to 

above the edge of the magma chamber reduces 

the loading e¡ect on the system. Therefore, moving 

the topographic relief to an o¡-centred position 

has similar e¡ects as having no pre-existing 

relief. 

Acknowledgements 

We are grateful to Jim Vallance and Ron Doig 

for assistance during various aspects of this research, 

and we thank Shanaka de Silva and Robert 

Andres for useful discussions and earlier reviews 

of the manuscript. We are indebted also 

to Valerio Acocella, Charles Bacon and Takehiro 

Koyaguchi for thorough reviews of the manuscript. 

This work has been supported by the Natural 

Sciences and Engineering Research Council 

of Canada and by the ‘Fonds pour la formation 

de chercheurs et l’aide a' la recherche of Que¤bec’. 

Lastly, support from NSF grant EAR-0125631 is 

gratefully acknowledged. 

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