Controls on caldera structure: Results from analogue sandbox modeling
Ben Kennedy† John Stix Department of Earth and Planetary Sciences, McGill University, 3450 University Street, Montreal, Quebec H3A 2A7, Canada
James W. Vallance‡ Department of Civil Engineering and Applied Mechanics, McGill University, 817 Sherbrooke Street West, Montreal, Quebec H3A 2K6, Canada
Yan Lavalle´e Marc-Antoine Longpre´ Department of Earth and Planetary Sciences, McGill University, 3450 University Street, Montreal, Quebec H3A 2A7, Canada
ABSTRACT We conducted scaled analogue sandbox models of caldera formation in order to understand the effects of chamber depth and orientation on the spatial and temporal development of calderas. Dry sand contained in a 1-m-diameter cylinder served as a crustal rock analogue, and a water-filled 0.6-m-diameter rubber bladder served as an analogue magma chamber. Scaling parameters included a length ratio (L*) of 2.5 3 10–5 and a stress ratio (s*) of 1.8–2.4 3 10–5. In contrast to some previous analogue models, the viscosity of the fluid in the chamber and its withdrawal rate were properly scaled. Generally, deformation began with broad sagging, followed by an arcuate or linear outward-dipping fault that formed on one side of the caldera. This fault propagated laterally around the caldera in both directions, sometimes joining other faults, and typically forming an overall polygonal structure. As subsidence continued, the caldera grew incrementally outward and progressively formed a series of concentric outward-dipping faults. Lastly, a peripheral zone of extension and pronounced sagging, and commonly an inwarddipping outer fault related to extension, developed at the surface. As the depth of the chamber increased, (1) the area of faulting E-mail:
[email protected]. Present address: U.S. Geological Survey, 1300 SE Cardinal Court, Building 10, Suite 100, Vancouver, Washington 98683-9589, USA.
decreased, (2) the symmetry of the caldera was affected, and (3) the coherence of the subsiding block decreased. Tilting the chamber caused highly asymmetric subsidence to occur. In this case, faults formed first where the bladder was shallowest. Subsidence then shifted rapidly to where the bladder was deepest, producing an elongate trapdoor caldera that was deepest where the bladder was deepest. Our experiments highlight the roles of sagging and faulting during caldera subsidence. Surface fault patterns both in our experiments and at natural calderas are frequently not circular. The aspect ratio of the block above the magma chamber controls the shape of the caldera, which is frequently polygonal. The faults at natural calderas determine locations and migration of eruptive vents, the degree of subsidence, the style of postcaldera resurgent magmatism, and the extent of hydrothermal circulation. Our experiments reveal details of how calderas grow outward incrementally and demonstrate that asymmetric subsidence along linear and arcuate faults is common to many calderas. Keywords: caldera, modeling, structure, faults, collapse, subsidence. INTRODUCTION
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Hundreds of calderas, ranging in diameter from 2 km to more than 100 km, exist on Earth and other planets. These large volcanic
depressions vary widely in morphology and formation, and they record some of the most catastrophic events in Earth’s history. Although definitions of calderas vary, we consider calderas to be volcanic topographic or paleotopographic features formed by the removal of magma from a subvolcanic magma chamber (Williams, 1941; Kokelaar and Branney, 1999). Scientists have never directly observed the formation of a large caldera because of the infrequency of their occurrence and the violence of the associated eruptions. Some authors have linked the caldera-forming eruptions at Santorini caldera, Greece, and Ilopango caldera, El Salvador, to the demise of the Minoan and Mayan civilizations, respectively (Heiken and McCoy, 1984; Sheets, 1979). The large volumes of ash and volcanic gases that are associated with caldera-forming eruptions can cause global climate changes (Mills, 2000). Caldera structure influences locations of eruptive vents, formation of debris avalanches, and emplacement of intracaldera and extracaldera ignimbrites, as well as the nature and location of postclimactic activity. Although few calderas have formed during historical times, there have been ;1300 episodes of historical unrest recorded at 138 calderas (.5 km diameter) (Newhall and Dzurisin, 1988). The frequency of this postclimactic activity illustrates the importance of calderarelated hazards. Caldera faults also provide pathways necessary for the circulation of postcollapse hydrothermal systems, which are use-
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ful geothermal energy resources and which deposit economically important epithermal and volcanogenic massive sulfide mineral deposits. In this paper we describe carefully controlled analogue experiments designed to address the nature and variability of caldera structure. These experiments are a continuation of previous work (Komuro et al., 1984; Komuro, 1987; Martı´ et al., 1994; Roche et al., 2000, 2001; Acocella et al., 2001; Walter and Troll, 2001; Troll et al., 2002) and attempt to achieve a more realistic approximation of caldera subsidence. Two crucial improvements were made for our experiments. (1) Magma viscosity and chamber-evacuation rate were correctly scaled. (2) The length scale was significantly larger than previous models, which proved important because fault geometries changed as they propagated through the sand. This improved experimental approach showed that caldera growth was incremental, revealing previously unrecognized planar faults and unusual asymmetries. Previous Experimental Work Results from early experiments showed that collapse basins could be produced by doming or evacuation (Komuro et al., 1984; Komuro, 1987; Martı´ et al., 1994). Komuro (1987) simulated the total evacuation of a magma chamber by using an evaporating block of dry ice. Martı´ et al. (1994) performed their experiments by using a spherical air-filled balloon that was inflated and deflated to simulate tumescence, evacuation, and resurgence. In these experiments, tumescence-related faults were reactivated during subsidence, and subsidence-related faults were reactivated during resurgence. More recently, experimental studies using a piston-like subsiding cylinder of silicone revealed that ring faults, resulting from chamber evacuation, are outward dipping and steepen with depth. Peripheral normal faults also form in response to the inner faults (Odonne et al., 1999; Roche et al., 2000, 2001). These experimental results are consistent with field observations made by Branney (1995). The experiments performed by Roche et al. (2000) also illustrate that the aspect ratio (thickness/ diameter) of the subsiding block controls the style of collapse. Subsiding blocks of low aspect ratio promote piston-style collapse. As the aspect ratio increases, the collapse style becomes more complex, because the subsiding block is increasingly incoherent (Roche et al., 2000, 2001). These experiments also showed that subsidence is generally asymmetric in
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Figure 1. (A) Experimental setup, with a video camera mounted on a ladder above the cylinder containing sand. (B) Measuring the morphology of the experimental calderas by using a dipstick and a grid. cross section. Further work using a similar experimental system supports these subsidence observations and illustrates that the style of resurgence depends on the aspect ratio of the crustal block (Acocella et al., 2001). Analogue caldera experiments also have been applied to the Tejeda caldera on Gran Canaria, indicating that this caldera underwent several episodes of collapse and inflation (Troll et al., 2002). METHODOLOGY Experimental Setup Our experimental apparatus consisted of a cylinder 0.9 m in diameter and 1 m in height (Fig. 1). The cylinder was filled with poorly sorted dry sand. Buried within the sand was a
0.6-m-diameter rubber chamber filled with water to a capacity of 45 L. We chose to model the crust as a Coulomb material. Coulomb behavior governs deformation in the upper crust, where calderas form (Davis et al., 1983). Deviatoric stresses associated with caldera collapse are high and promote brittle failure with limited elastic bending. Because sand exhibits Mohr-Coulomb behavior and fractures in a brittle manner (Sandford, 1959), it is an appropriate choice of material. The full rubber chamber was circular in plan view and had convex upper and lower surfaces, so that it was the shape of an oblate or flattened sphere. This form is a reasonable approximation of a shallow crustal magma chamber. For example, the magma chamber at Long Valley caldera, California, has been es-
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timated to have been over 5 km thick, with a convex top (Wallace et al., 1999). The rubber chamber was filled and evacuated from a tube attached centrally to its underside. A flow meter controlled and measured the evacuation rate of water out of the chamber. During the experiments, a constant evacuation rate of 0.0016 m3·min21 over a period of 5 min resulted in the removal of 0.008 m3. We simulated an overpressured, closed-system magma chamber maintaining a stress field relevant to a natural system. Within a closed magma chamber, pressure builds up and is then released suddenly during eruption (Druitt and Sparks, 1984); this pressure release may induce an elastic response from the crust (contraction) before the mass of the crust imposes a deformation upon the chamber and the chamber roof fails in a brittle manner. Our analogue magma chamber reproduces this response by contracting elastically before deforming in response to the mass of the overlying sand. The depth and orientation of the chamber were variable. The depth to the top of the chamber varied between 0.06 and 0.24 m. Because the width of the chamber was constant, changing the depth to its top could be treated as changing the aspect ratio of the subsiding block over the chamber. The aspect ratio is the height/diameter ratio of the subsiding block (h/r). Aspect ratios in our experiments varied from 0.10 to 0.40. The chamber could be tilted in order to test hypotheses regarding asymmetric collapse (Lipman, 1997). The orientation and depth of the chamber were monitored by using a dipstick and grid (Fig. 1B). Certain experiments were repeated with layered sand of different colors; after collapse, the subsidence structures were refilled with sand and soaked with water, allowing vertical cross sections to be cut and examined. Scaling of Variables An appropriate analogue model requires the geometric and dynamic similarity between the model and the natural system to be maintained. Scaling ratios help maintain this similarity (Sandford, 1959). Therefore, we carefully scaled the experimental parameters on which the collapse process depends. Calderas on Earth have diameters varying from more than 50 km to 2 km (Lipman, 1984). For practical considerations, the experimental setup could be no larger than 1 m in total diameter and 1 m deep, because of the substantial mass of this large volume of sand. To minimize edge effects of the model, the diameters of our experimental calderas were
kept within 50% of the diameter of the cylinder. Thus, an experimental caldera of 0.5 m diameter represents a 20-km-diameter caldera in nature, i.e., the length ratio (L*) is equal to the maximum diameter of the model (0.5 m) divided by the maximum diameter of a caldera (20,000 m) 5 2.5 3 10–5. This length ratio is significantly larger than the length ratios used in previous caldera models (Komuro et al., 1984; Komuro, 1987; Martı´ et al., 1994; Odonne et al., 1999; Roche et al., 2000, 2001). Caldera dimensions and chamber depths were scaled by using this ratio. Therefore, the length ratio is equal to the depth ratio (H*). The time required for a large caldera to form is not known. Wilson and Hildreth (1997) estimated that the eruption of the Bishop Tuff that formed Long Valley caldera lasted about 4 days. The climactic eruption of Krakatau in 1883 continued for ;24 h (Simkin and Fiske, 1983), whereas the calderaforming phase of the 1991 Pinatubo eruption occurred over ;9 h (Wolfe and Hoblitt, 1996). For our scaling, we selected a 17 h eruption for a natural caldera and a 5 min evacuation time for our experiments, i.e., the evacuation time ratio (T*) is ;5 min (5 300 s) divided by 17 h (5 61,200 s) equals 4.9 3 1023. In order to correctly scale the cohesion and viscosity of the experimental materials, the density ratio and gravity ratio were first considered. The density ratio (r*) of sand to rock 5 1890 kg·m23 divided by 200022700 kg·m23 5 0.9520.70. The density ratio for the fluids in the experiments is also within the same order of magnitude (density of water to density of silicic magma 5 1000 kg·m23/ ;2200 kg·m23). Our experimental calderas and natural calderas form under the same gravitational conditions. This is appropriate because the units of gravity are m·s22 and the gravity ratio is a product of L*/(T*)2, giving a gravity ratio of ;1.04. Sand cohesion was scaled to rock strength by using the stress ratio (*), which is a product of the density ratio (r*), the gravity ratio (g*), and the depth ratio (H*): s* 5 r*g*H* 5 1.822.4 3 10–5. The tensile strength of volcanic rock (equivalent scaling ratio to s*) is on the order of 107 Pa (10 MPa). However, on a larger scale, jointing and fracturing reduce the tensile strength of volcanic rock to ;106 Pa (Schultz, 1996), so the model should have a tensile strength (cohesion) of 18–240 Pa. Theoretically, well-sorted dry sand has no cohesion. However, the sand used in the experiments was poorly sorted and contained some moisture absorbed from the air. Attempts were made to measure the cohesion by using shear-
box tests, but it was difficult to accurately determine such low cohesion values. As a result, the sand can only be said to have cohesion of 0–100 Pa, which is appropriate to the scaled cohesion of volcanic rock containing some fractures. As sand and rock are in theory Coulomb materials, varying time scales should not affect the deformation. The preliminary shearbox tests on the sand and some of our early experiments showed that time may, in fact, influence the resultant deformation in pure dry sand. For this reason, we thought it was essential to scale time and viscosity. A simple definition of the viscosity ratio is m* 5 s*T* 5 5.8 3 10–8. Our analogue magma is scaled by using a viscosity of 1 3 10–7 Pa·s for natural magma, which represents a rhyolitic melt with 6 wt% dissolved water at 800–900 8C (Hess and Dingwell, 1996). This value indicates that a very low viscosity is required for the analogue model. The water in our experimental chamber has a viscosity of 10–3 Pa·s, which is scaled appropriately. Our scaling thus requires a comparatively low viscosity and rapid evacuation rate, resulting in a more irregular style of subsidence. This may be the case in nature, as well. On the other hand, the rubber bladder that contains the water may mask the rheological properties of the water. However, the partially crystallized chamber margin and the hot rocks surrounding a real magma chamber are also likely to have unusual elastic or viscoelastic properties and therefore may not deform in a simple brittle manner (Newman et al., 2001). Analogue experimental calderas cannot fully reproduce the complex processes involved in caldera formation. However, the experiments do provide insights into the manner by which a block of homogeneous crust may deform when subsiding into a shallow oblate magma chamber. A large proportion of the structures seen at calderas are associated with this process. We note that many calderas have undergone a complex collapse history and sometimes represent several caldera cycles, with multiple collapse and intrusion episodes (Smith and Bailey, 1968; Moore and Kokelaar, 1998). Our experiments represent only a single collapse event with no intrusion events. Our objective is not to reproduce all the complexities of a natural system but instead to isolate variables and assess their importance on the system as it deforms. However, many aspects of the structures seen in our experiments are still relevant to these complex natural systems. RESULTS From the many experiments undertaken, we have chosen representative examples to illus-
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Figure 2. A series of photographic sequences showing the temporal evolution of faults at the surface after 3, 4, and 5 min. (A) Experiment 7B shows trapdoor subsidence partially controlled by downsag above a shallow analogue magma chamber (depth to top of chamber 0.06 m; scaled to 2.4 km). (B) Experiment 33A shows piston collapse along a polygonal ring fault above a chamber, the top of which is
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trate five different styles of subsidence. We investigated two principal controls on the nature of the subsidence process: aspect ratio of the subsiding block and chamber orientation. We found that the dominant control on collapse style was the aspect ratio. We therefore describe the surface expressions of the different styles of subsidence in terms of increasing aspect ratio. These five styles (Fig. 2) are (1) trapdoor subsidence along an arcuate fault, partially controlled by subsidence; (2) polygonal piston subsidence along a series of connected linear and arcuate faults; (3) incremental collapse along a series of interconnected, concentric, linear, and arcuate faults; (4) complex collapse along a series of interacting faults, frequently without a central piston; and (5) trapdoor subsidence along linear faults that was produced when the chamber was tilted. Trapdoor Subsidence Partially Controlled by Sagging (Experiment 7E; Depth 0.06 m) This deformation style occurred only when the aspect ratio (h/r) of the subsiding block was less than 0.15 (e.g., a 0.6-m-diameter chamber at a depth of less than 0.09 m) with a horizontal chamber (Fig. 2A). Higher aspect ratios produced this style of deformation if the chamber was tilted. Trapdoor deformation began with a symmetric sag centered above the chamber (Fig. 2A, panel i). This sag became asymmetric, and a fault began to develop where subsidence was greatest. Away from the fault, sagging was the predominant form of subsidence. The principal fault propagated curvilinearly outward from the area of maximum subsidence (Fig. 2A, panel ii). Next, a second concentric fault developed outside the first. The second fault grew outward like the first (Fig. 2A, panels ii and iii). The final result was a highly asymmetric subsidence structure (Fig. 2A, panel iii). Sagging dominated subsidence in the shallower half of the depression, whereas concentric arcuate faults dominated in the deeper half.
was intermediate (h/r ø 0.20). Surface deformation began with symmetrical sagging. With time, the sag became asymmetric, and a series of linear faults began to form on the side of greatest subsidence. Next, the linear faults connected and began to propagate toward the side of least subsidence (Fig. 2B, panel i). The faults joined to form an irregular horseshoeshaped fault with distinct corners (Fig. 2B, panel ii). At one of the corners, an inner fault typically propagated outward to become part of an outer fault (Fig. 2B, panel iv). This outer fault also propagated away from the area of maximum subsidence but formed a more curved structure (Fig. 2B, panel iii). Neither the outer nor the inner ring faults formed fully. Sagging was important in areas of least subsidence. These experiments produced subsidence structures with a main ring fault, consisting of interconnected linear faults. Incremental Collapse Along Linear Faults (Experiment 14B; Depth 0.139 m) Incremental collapse occurred along predominantly linear faults when aspect ratios of the subsiding block were intermediate to high (h/r 5 0.23–0.30). Surface deformation began with symmetrical sagging and continued with formation of linear faults perpendicular to each other. Two more linear faults formed outside and concentric to the initial faults (Fig. 2C, panel i), then joined with the first-formed faults to produce a fault-bounded subsiding block. Another linear fault propagated outside this new subsiding block from its corner. This pattern of fault formation and propagation repeated itself several times and created multiple rectilinear blocks, thereby increasing the plan-view symmetry of the depression and forming terraces or benches between faults (Fig. 2C, panels i–iii). An outer fault never clearly developed. These experiments produced subsidence structures that were composed of a series of interconnected linear faults. These faults connected in different ways, so that they formed triangular or rectangular subsiding blocks (Fig. 2C).
Piston Collapse Along a Polygonal Ring Fault (Experiment 33A; Depth 0.116 m)
Complex Collapse (Experiment 18A; Depth 0.24 m)
Polygonal ring faults formed in experiments where the aspect ratio of the subsiding block
Complex collapse occurred when the aspect ratio of the subsiding block was high (h/r .
0.3). Initially, the surface exhibited only a broad symmetrical sag. Faults began to form at the edge of the main sag, but never developed fully into a ring-fault system. Sagging at the surface continued, and two intersecting arcuate faults formed in the center (Fig. 2D, panel ii). In this central region, arcuate faults developed and intersected one another, producing a series of overlapping faults. These structures formed two fault blocks in the center of the depression, both of which were highly asymmetric in plan view. Sagging continued in peripheral parts of the depression (Fig. 2D, panel iii). These experiments produced calderas with individual fault-bounded blocks that tended to be small and irregular in shape and that varied from one experiment to another in an apparently unpredictable way (Fig. 2D). Trapdoor Collapse Along Linear Faults (Experiment 22B; Tilted) Trapdoor collapse along predominantly linear faults occurred at chamber depths of ;0.1 m, or when the chamber was deliberately tilted so that one edge was 0.1 m higher than the other. These experiments illustrated the effect of magma-chamber orientation on caldera formation. Surface deformation began with sagging above the shallowest part of the chamber (Fig. 2E, panel i). A series of faults formed, but little subsidence occurred on these structures. Sagging rapidly shifted to the other side of the depression where the chamber was deepest, and new linear faults formed. These faults joined up with the earlier-formed faults to create a rapidly subsiding rectangular block (Fig. 2E, panel i). A second fault set formed parallel to the original faults, creating terraces, enlarging the area of faulting, and preserving the rectangular shape of the subsiding area. A semicircular outer fault developed quickly and joined with a linear fault to form an elongate outer ring. During the last stages of the experiment, a small curved graben developed, associated with the ‘‘hinge’’ area of the trapdoor (Fig. 2E, panel iv). These experiments produced elongate calderas in plan view. Inner faults were largely linear, individual fault blocks were generally rectangular, and the outer faults tended to be more curved.
at moderate depth (0.116 m; scaled to 4.6 km). (C) Experiment 14B shows incremental collapse along linear faults above a deeper, but still moderate-depth chamber (0.139 m to top of chamber; scaled to 5.5 km). (D) Experiment 18A shows complex collapse above a deep chamber (0.24 m to top of chamber; scaled to 9.6 km). (E) Experiment 22B shows trapdoor collapse along linear faults when the chamber was tilted (high in northeast, minimum depth to top of chamber is 0.104 m; scaled to 4.2 km).
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Cross Sections The vertical cross sections (Figs. 3 and 4) clearly show that the inner faults have the largest displacements, are outward dipping, and become steeper with depth. Some dips are as low as 408 near the surface and can reach 908 at depth. These faults propagate upward through the sand, exhibiting larger displacements at depth than at the surface. Some of these faults were initiated from the same position at the chamber margin and splay upward into separate faults (Fig. 4C), as seen in the majority of experiments of Roche et al. (2000). However, most multiple inner faults propagated from distinctly separate positions on either side of the analogue chamber roof (Figs. 3 and 4D). The faults closest to the center of the subsidence structure dip outward at shallow angles (Fig. 3D). In cross section, some inner faults never reach the surface (Figs. 3B–3D and 4D); these commonly occur in the central area of the subsidence structure. These faults probably formed at an early stage and then became inactive as subsidence was accommodated on faults farther away from the structure’s center. The faults that formed later tend to be steeper, occurred farther from the center of the caldera, and remained active until the end of the experiment. Inward-dipping faults sometimes formed outside the inner faults. These are usually planar with more displacement at the surface than at depth (Fig. 4C). Some outward-dipping faults also propagated downward in a similar fashion. We were able to make multiple cross sections of a caldera that allowed us to observe how the orientation of a single fault varied spatially within the caldera. Some ring faults were outward dipping in one area of the caldera but inward dipping in other areas (Fig. 4E). Such faults are transitional between inner and outer faults and show characteristics of both. DISCUSSION Our experimental results are striking in their complexity; they exhibit both circular and linear fault patterns, crisscrossing faults, circular and rectilinear subsiding blocks, incremental outward growth by terrace formation, and strong asymmetry. The patterns contrast with the comparatively simple, circular patterns of caldera growth documented by previous experiments (Roche et al., 2000, 2001). This difference is interesting and may be the result of contrasting magma-chamber analogues, time scales, and length scales.
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Figure 3. Cross sections across experimental calderas as they vary with increasing aspect ratio of the subsiding block. (A) Experiment 10C shows trapdoor subsidence partially controlled by downsag above a shallow chamber (top of chamber at 0.06 m; scaled to 2.4 km). In this example, an outward-dipping fault is seen on both sides of the caldera, whereas in other experiments, downsag controlled the subsidence on one side of the caldera. (B) Experiment 3C shows symmetric piston collapse along a polygonal ring fault above a shallow- to moderate-depth chamber (top of chamber at 0.1 m; scaled to 4 km). (C) Experiment 7C shows incremental collapse along linear faults above a moderate-depth chamber (top of chamber at 0.15 m; scaled to 6 km). (D) Experiment 5C shows a complex collapse pattern above a deep chamber (top of chamber at 0.2 m; scaled to 8 km). (E) Experiment 11C shows trapdoor collapse along linear faults above a tilted shallow- to moderate-depth chamber (minimum depth to top of chamber is 0.1 m on the right; scaled to 4 km).
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Figure 4. (A) Detailed plan view of the periphery of experiment 6C; complex fault interactions can be seen. (B) An outward-dipping inner fault with an associated grain-flow deposit. (C) Two outward-dipping faults and an inward-dipping fault splay from a similar position at the chamber margin. (D) A shallow-dipping inner fault that propagated up through the sand, a steeper inner fault that never reached the surface, and an outwarddipping inner fault that propagated down.
The results of our experiments provide insights into the mechanisms responsible for a variety of morphologies seen at real calderas. Different mechanisms can create similar caldera morphologies; as an example, trapdoor calderas might form from a subsiding block with a low aspect ratio or from a tilted chamber with a higher aspect ratio. Faults Two main types of faults exist in a caldera: (1) the inner faults, which are outward dipping and upon which the majority of displacement occurs, and (2) the outer, inward-dipping faults that form in response to the inner faults (Branney, 1995; Roche et al., 2000, 2001). Our experiments clearly show that subsidence rarely occurs upon a single, circular ring fault. Instead, the inner fault patterns observed at the surface include (1) semicircular arcuate faults, (2) polygonal ring faults, (3) a series of
rectilinear block faults, and (4) complex surface faults. Outer faults show less variation in style and usually appear as a series of arcuate structures at the surface, but they are not always observed. The types of caldera-related faults documented in our experiments also have been observed at natural calderas, and we cite some relevant examples at the end of this section. Semicircular arcuate faults formed within trapdoor subsidence structures when the aspect ratio of the subsiding block was small, between 0.10 and 0.18 (Figs. 2A and 3A). In this case, a low lithostatic load upon the chamber allowed asymmetric subsidence and lateral displacement of fluid within the chamber. These structures were significantly more asymmetric than any seen in previous experiments (Roche et al., 2000, 2001) and are probably caused by the increased mobility of the low-viscosity fluid within the chamber. A related factor is the shallow depth of the
chamber above which the faults are initiated. They propagated only short distances upward and maintained an arcuate form. Polygonal ring faults formed in blocks with moderate aspect ratios, between 0.18 and 0.23. These ring faults consist of a series of planar faults and curved faults that developed simultaneously and joined up to form the ring-fault system. Inner faults became more linear as the chamber depth was increased. We propose that an initially curved fault tends to become planar to reduce friction as it propagates up through the sand, producing a linear structure at the surface. The different segments of the ring fault formed separately, yet joined to form a coherent subsiding block. Faults crossed and extended beyond the ring fault (Fig. 4A), indicating that different segments of the overall polygonal ring structure were active individually, rather than the ring structure behaving as a single fault, as seen in previous experiments (Roche et al., 2000, 2001). We think that the low viscosity of the fluid in the chamber allows this behavior. Rectilinear fault and irregular fault blocks formed at high aspect ratios, between 0.23 and 0.30. In this case, planar faults and curved faults joined to form fault blocks. The cross section revealed that progressively steeper faults developed outside the initial blockforming terraces (Fig. 3C). In this area, faults may cross, bifurcate, and change orientation (Fig. 4A). A tilted chamber also promoted rectangular fault blocks at all but the lowest aspect ratios. This type of caldera faulting is sometimes referred to as piecemeal (Moore and Kokelaar, 1998). We again attribute the planar faulting and piecemeal subsidence to the increased depth, and we interpret the low viscosity and convex nature of our magma analogue to allow the subsidence centers to shift. In our experiments, there are clear differences between structures that form in subsiding blocks with low aspect ratios and those that develop in subsiding blocks with high aspect ratios. Similar differences are seen at natural calderas. For example, Kumano caldera, southwest of Honshu, Japan, which has a shallow magma chamber (only 2.5 km deep) and hence a subsiding block with a low aspect ratio, has semicircular arcuate faults (Miura, 1999). Ishizuchi caldera, Japan, which has a deeper magma chamber (its top is located at 5–6 km depth) and a higher aspect ratio for its subsiding block (Yoshida, 1984), clearly shows a polygonal ring dike. Ishizuchi caldera also illustrates multiple inner faults, bifurcating faults, terraces, and ring faults that change orientation from inward dipping to outward dipping, very similar to the structures seen in
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our experiments. Linear structures are seen at many calderas, e.g., Glencoe caldera, Scotland (Moore and Kokelaar, 1998), and Tengger caldera, Indonesia (Rowland et al., 2000), and both examples show subsidence controlled by rectangular fault blocks that are attributed to the reactivation of regional faults. Our experiments, however, show that rectangular fault blocks also can be produced without the need for regional structures. Incremental Caldera Growth As our experimental calderas subsided, they first grew incrementally by developing concentric inner faults that propagated outward from the central part of the caldera structure (Fig. 2). In turn, these inner faults generated an area of extension that was peripheral to the first-formed faults (Fig. 4A) (Branney, 1995; Roche et al., 2000). This area of extension showed features such as a series of arcuate, inward-dipping normal faults, a single inwarddipping fault, and an area of grain flow of the sand. The extensional zone underwent bending and tilting, and new faults developed, causing further incremental growth of the caldera. Thus, the outer faults are secondary and formed in response to movement on the inner faults. In cross section, these outer faults propagated from the surface downward; they show progressively less displacement with depth (Fig. 3E). This pattern is consistent with the observations of Odonne et al. (1999) and Roche et al. (2000). When there were multiple outward-dipping inner faults, a clear pattern of outward incremental growth of the subsidence structure also appeared within the main subsiding area. We attribute this process to the convex nature of the upper surface of the analogue magma chamber, and not to peripheral extension and sagging. As magma is progressively removed from the chamber, a foam layer of increasing volume may form at the top of the chamber. Faults are likely to form at the interface between the compressible foam and the incompressible magma (Fig. 5). In plan view, outward migration of the deformation front on the roof of the magma chamber caused incremental outward growth of subsidence. At the surface, inner faults formed progressively farther from the center of the caldera (Fig. 2). In experiments performed by Roche et al. (2000), inner faults were generally initiated at the same point at the silicone-chamber margin. However, in their experiments with a convex roof (their Fig. 8C), faults were initiated progressively farther from the chamber center in
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Figure 5. As magma is progressively removed from the chamber, a foam layer of increasing volume may form at the top of the chamber. Faults are likely to form at the interface between the compressible foam and the incompressible magma. (A) Owing to the convex nature of the upper surface of the chamber, the position of ring faults shifts progressively outward, producing a caldera that grows outward in an incremental fashion. (B) With a flat-topped chamber, only one ring fault forms.
a manner similar to our experiments, although this point is not discussed in their paper. In natural calderas, incremental collapse is often observed (Skilling, 1993; Hallinan, 1993; Hallinan and Brown, 1995), and we therefore postulate that subsidence of this type can occur above a magma chamber whose roof is convex. More generally, we concur with Branney (1995) that calderas showing nested ring faults can form during one cycle, without requiring multiple collapse episodes. Caldera Asymmetry Natural calderas exhibit asymmetry in both cross section and plan view, a fact that is often attributed to external tectonic stresses or preexisting fault systems (Lipman, 1997). Yet our subsidence structures exhibited significant degrees of asymmetry despite a homogeneous crust and no imposed external stresses. In our experiments, plan-view asymmetry commonly corresponds with cross-sectional asymmetry. This correspondence is also common in nature, i.e., a caldera that is elongate in plan view is likely to show trapdoor subsidence along its long axis. For example, Long Valley and Kumano calderas are elongate structures
that show distinct trapdoor-style subsidence in cross section (Bailey et al., 1976; Miura, 1999). Our experiments illustrate plan-view asymmetry in several ways. First, trapdoor subsidence structures were produced by inner, outward-dipping faults on one side of the structure. Asymmetry of this type occurred when the analogue magma chamber was at shallow depths (so that h/r of the subsiding block was ,0.15) and when small volumes were evacuated from the analogue magma chamber. Asymmetry early in collapse also was noted by Branney (1995), Branney and Gilbert (1995), and Roche et al. (2000). However, our experiments show a greater degree of asymmetry than previously described. Kumano caldera is associated with a shallow magma chamber and exhibits asymmetry that is largely controlled by a single arcuate fault (Miura, 1999). Asymmetric subsidence can result when a principal fault occurs on one side and multiple faults step down on the other side. In cross section, the amount of displacement upon the individual faults can vary considerably. Drilling into the Valles caldera, New Mexico, revealed this type of asymmetry; multiple step-down faults were documented to the west, and a principal fault was inferred to the east (Nielson and Hulen, 1984). A caldera may be bounded entirely by faults, yet still be elongate and trapdoor in cross section. Our experiments simulated this configuration by using a tilted chamber. These elongate structures were highly asymmetric in cross section; maximum subsidence occurred above the deepest area of the analogue magma chamber. Our results contrast with the model of Lipman (1997, 2000), who proposed that maximum subsidence occurs above the shallowest area of the magma chamber, but agree with the observations of Roche et al. (2000). Lastly, a caldera may have a roughly circular topographic rim but show an irregular fault pattern of mixed linear and arcuate faults within the area of subsidence (Fig. 2). Experimental simulations that exhibit the most complex asymmetry have analogue magma chambers with deeper tops (i.e., the aspect ratio h/r of the subsiding block is .0.3) (Fig. 2D). In summary, our experimental results indicate that collapse asymmetry is promoted by (1) collapse due to a small-volume eruption from a large magma chamber, (2) collapse into a shallow, large-diameter magma chamber, and (3) collapse into a tilted magma chamber. Other causes of asymmetry, which we have not addressed, include heterogeneity in the tensile strength of the rock that composes the subsiding block, preexisting structure and to-
Geological Society of America Bulletin, May/June 2004
CONTROLS ON CALDERA STRUCTURE: RESULTS FROM ANALOGUE SANDBOX MODELING
pography, and the influence of regional tectonics. CONCLUSIONS Our analogue models demonstrate some important controls on caldera collapse. Sagging controls early caldera subsidence and remains an important process throughout subsidence; this result supports the work of Branney (1995), Branney and Gilbert (1995), and Roche et al. (2000). Inner faults are outward dipping to vertical and manifest themselves at the surface in a variety of differing caldera structures that are largely controlled by the aspect ratio of the subsiding block, but that are also sensitive to chamber orientation. As the aspect ratio increases, the structural manifestation of deformation evolves from semicircular arcuate faults through linear faults and rectilinear fault blocks, to complex surface fault patterns. Inner faults commonly cross, bifurcate, and change orientation. Outer, inward-dipping faults form late as a result of subsidence along the inner faults. In plan view, these outer faults were generally curved, except where they joined inner faults. Both inner faults and outer faults generally propagated away from the area of initial maximum subsidence and joined or crossed other faults. Thus, the analogue caldera structures grew incrementally outward, as do many real calderas, which we attribute to the convex shape of our analogue magma-chamber roof. Asymmetry in both plan view and cross section, a feature common to experimental and natural calderas, was promoted by subsiding blocks with low aspect ratios and by tilted chambers. Deformation during caldera collapse is a product of the stress field that exists between the chamber and the surface (Gudmundsson et al., 1997). The stress field is controlled by the geometry of the magma-chamber roof and the surface. A change in the depth or orientation of the chamber will alter this stress field and as a result affect fault development. During an experiment, the chamber deforms and faults form, which also modify the stress field. The variety and complexity of the structures seen in our experiments are a result of the intricate manner in which a stress field develops. Our experiments are useful approximations of the initiation, evolution, and interaction of faults during caldera-forming eruptions. These structures may act as vents from which pyroclastic material is erupted. The experiments thus provide a model for predicting the initial locations and migration of vents during caldera-forming eruptions. One or more inner faults control the areas of maximum subsi-
dence within the caldera. These areas will dictate the location of intracaldera ponding and extracaldera outpourings of pyroclastic material. Furthermore, the orientation of the magma chamber can help determine where the first caldera faults develop and in which directions they propagate. Our experiments also illustrate some important structural constraints on calderacollapse processes. The experiments show that piston-style collapse occurs only under certain conditions and that other collapse geometries are likely. These structural alternatives provide powerful alternate hypotheses for geologists mapping young calderas where the internal structure is hidden. Fault interactions also may create structurally permeable pathways beneath the caldera. Understanding the controls on these pathways is critical to the mining industry, as caldera-related volcanogenic massive sulfide and epithermal mineralization can be focused by these structures (Stix et al., 2003). Our observations show that fault distributions vary considerably among the different caldera types, which could explain why hydrothermal activity is rarely restricted to the area of the ring fault. We recognize that there are still many important parameters that have not, as yet, been experimentally tested. These include the influence of preexisting structures, active tectonics, precursory tumescence related to intrusion, and heterogeneities in the crust. These are appropriate issues to address in future experiments. ACKNOWLEDGMENTS We thank Mike Branney, Tim Druitt, Joan Martı´, Jim Cole, and Scott Baldridge for very thorough and constructive reviews that allowed us to improve the paper immeasurably. We also thank Andrew Hynes and Ronald Doig of McGill University for useful discussions throughout the study. Conversations with Olivier Roche, Valerio Acocella, and Ewan Garel also provided us with ideas and help for this paper. Financial support was provided to Kennedy by funds from the Department of Earth and Planetary Sciences, McGill University, and from GEOTOP, Universite´ du Que´bec a` Montre´al, and by a research grant to Stix from the Natural Sciences and Engineering Research Council of Canada. We also acknowledge support from National Science Foundation grant EAR-0125631. REFERENCES CITED Acocella, V., Cifelli, F., and Funiciello, R., 2001, The control of overburden thickness on resurgent domes: Insights from analogue models: Journal of Volcanology and Geothermal Research, v. 111, p. 137–153. Bailey, R.A., Dalrymple, G.B., and Lanphere, M.A., 1976, Volcanism, structure, and geochronology of Long Valley caldera, California: Journal of Geophysical Research, v. 81, p. 725–744.
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