Experimental setup and scaling
We follow previous experimental investigations (e.g. Roche et al. 2000), simulating caldera subsidence and shear localization in a granular material that approaches a Mohr-Coulomb friction law (Schellart 2000). Our new results comprise application of a digital image correlation (DIC) technique that allows strain studies with spatial and dynamic resolutions in sub-millimeter and microstrain range, respectively (Adam et al. 2005). A monochrome CCD (charge-coupled device) digital camera was used to acquire images at high resolution (12 megapixels). Calculation of displacements at precisions of <0.1 pixels (White et al. 2001) was achieved by the application of a multi-pass cross correlation algorithm (LaVision 2002), allowing us to compare successive images. We compared the particle distribution of two subsequent images in order to derive the deformation-vector field and the strain field in each granular flow experiment (Fig. 4). For the adopted distance to the experiment box and camera parameters, we obtained spatial resolutions of about 0.2 mm and a temporal resolution between successive images of 5 Hz. Further details about the DIC method are provided in the Electronic Supplementary Material (S3).
The experiments were performed in a sand box, and cross-sectional development could be investigated through two glass panes set up at a distance of 10 cm (Fig. 4). To simulate reservoir deflation, we used a retractable piston with an area of 10 × 10 cm2 emplaced within a cut-out of the same size in the basal plate. At the beginning of the experiment, the piston was located at the level of the basal plate, which was overlain by the analogue crustal material. Using a computer-controlled motor, we set piston retraction at a subsidence rate of 0.015 cm s-1 for 120 s, to a total subsidence of 1.8 cm. In systematic experimental tests, we varied the chamber depth to evaluate the influence of the roof aspect ratio (AR), which ranged from 0.41 to 3.01 in eleven individual experiments. This AR range also covers the geometric configuration of the Miyakejima caldera system, to which the results are compared in section “Comparison of experimental structures to Miyakejima chronology”.
The experiments were geometrically and partially dynamically scaled (cf. Hubbert 1937; Sanford 1959) to fit the configuration of natural calderas regarding roof aspect ratio and subsidence. The geometric scaling factor was 2.5 × 10-5, so that 1 cm in the experiments corresponds to approximately 400 m in nature. As a crustal analogue material, we used a 1:5 mixture of wheat starch (cf. Donnadieu and Merle 1998) and dry quartz sand (Cobbold and Castro 1999). We determined the coefficient of internal friction μF for the starch-sand mixture with the ring shear test; the angle of internal friction φF is ~28° and thus comparable to natural systems. The natural cohesion of crustal materials is in the range of 105 to 107 Pa (e.g. Hoshino et al. 1972), while the cohesion of the analogue material is 70 Pa. Considering a scaling factor of 2.5 × 10-5, cohesion in our experiments is thus properly scaled. A comparison of experiments with pure sand and the mixed sand-starch material showed similarly oriented structures, although the structural resolution obtained in the sand-starch mixture is considerably higher and provides additional details. Particulars of ring-shear granular material tests and the scaling procedure are provided in the Electronic Supplementary Material.
Time-dependent viscosities of the magma analogue were not considered in these experiments, since we focused our investigation on brittle fracturing only. Other limitations of our experiments include the simplified geometry, rheology, and sidewall effects. The subsiding magma chamber roof is simulated by a retracting undeformable piston that induced stresses at the base of the overlying roof. In nature, the pressure within the magma chamber should be different from lithostatic, so that the distribution and relative intensity of stresses within the roof could be different from those in the experiment. We note however, that the chamber geometry is in agreement with plutons that are often nearly flat-roofed (e.g. Pitcher 1993, Zak and Paterson 2006). Furthermore, subsidence occurred along panes of glass that might influence experimental results by friction. However, the structures produced during the experiments were the same in the vicinity and away from the glass panes. In addition, our results broadly mimic those of other studies, yielding geometric similarity even though different materials and apparatus were used (cf. Acocella 2008).
Digital image processing results
From the DIC analysis of the individual experiments, we reconstructed a temporal sequence of fault propagation and interaction. Each experiment simulated up to ~700 m of subsidence in nature. About 600 successive digital images were recorded for each experiment and postprocessed in order to constrain the structural evolution in detail. A photo sequence showing the computed fault initiation, propagation, and interaction is illustrated in Fig. 5 for a magma chamber roof aspect ratio (AR, ratio depth-to-width) of AR = 0.6, and in Fig. 6 for a roof aspect ratio of AR = 1.5. Supplementary movies of the experiment development are provided in the Electronic Supplementary Material.
For AR < 1, shear zones first appear at depth. A first set of outward-dipping reverse faults initiates underground at the sides of the retracting piston (Fig. 5a). These reverse faults propagate in tandem upwards and reach the surface at outward-dips of ~50° near the surface and 80° at depth. When they reach the surface after ~0.2 cm (~80 m in nature) of subsidence, a second, steeper reverse-fault set forms and propagates upward, while the first set of faults becomes inactive. Then, in the caldera periphery, extensional fractures commence to propagate downwards and develop into inward-dipping normal faults (Fig. 5h, i). After subsidence of ~0.6 to 0.7 cm (~250 m in nature) these peripheral normal faults join with the reverse faults at depth (Fig. 5j). This fault linkage affects the activity of the former dominant reverse faults; they become inactive for most of the ensuing experiment duration. Occasionally near-surface segments of the reverse ring-fault reactivate. Overall, however, subsidence exceeding 0.7 cm is accommodated almost entirely by displacement along faults that are inward-dipping near the surface and subvertical to steeply outward-dipping at depth (Fig. 5l).
For roof aspect ratios >1, faulting is initially asymmetric, with laterally alternating propagation and activity of individual faults which develop at larger numbers and different scales compared to low-AR calderas (Fig. 6). The period of downsag observed at the surface lasts up to ~0.26 cm of subsidence, during which a sequence of faulting occurs beneath the surface. First, reverse faults develop near the magma chamber margin at about 0.1 cm of subsidence in a symmetric fashion (similar as in AR = 0.6 experiment; Fig. 6a, b). Then a second, steeper reverse fault develops on one side of the chamber roof (here to the right of the chamber; Fig. 6b) propagating upwards to the center of the magma chamber roof. When another fault on the opposite side of the chamber (here to the left) develops, displacement transfers from the second to the newly formed fault (Fig. 6d). This is the first fault that reaches the surface with a dip of about 30°, increasing to 45° in the upper part of the chamber roof and then steepening to 70° for most of the fault length down to its base at the chamber side. Further sets of faults may develop in alternating patterns, broadening the structural caldera diameter at the surface. In general, the simultaneous activity of two successive reverse-fault pairs on each side of the magma chamber is short-lived, so that displacement is generally focused on one reverse-fault pair. With about 1.2 cm of subsidence (Fig. 6f), the first inward-dipping reverse faults develop at the caldera periphery. A clear propagation direction, however, is not always recognizable; thus, the periphery faults appear to localize contemporaneously over their entire length. Immediately after interlinkage of the normal and reverse ring-fault segments, the upper parts of the outward-dipping faults become inactive (Fig. 6i, j). However, at greater subsidence, they can sporadically become reactivated allowing faulting in the upper part of the subsiding roof.
High-AR caldera formation includes a series of reverse ring faults that lead to a continued disintegration of the subsiding piston. Consequently, collapse of high-AR calderas tends to occur in a segmented (piecemeal) fashion, whereas low-AR calderas are characterized by the subsidence of a more or less coherent piston.
Thus, our experiments reveal complexly propagating and interacting ring faults that develop sequentially, which may help explain the chronologic and geometric patterns observed at Miyakejima during the 2000 caldera collapse.
Comparison of experimental structures to Miyakejima chronology
The 2000 Miyakejima collapse is probably the best instrumentally recorded caldera-forming event, since it was observed in detail at the surface and monitored with many geophysical methods. Seismic activity below the summit was distributed in a 2 km wide, columnar swarm, the top of which migrated to shallower depths (Fig. 3; Propagation Phase), while the summit of Miyakejima was initially deflating before caldera collapse occurred at the surface on 8 July. Based on the collected data, Geshi et al. (2002) developed a conceptual model for the structural evolution of the collapse caldera including upward propagation of reverse ring faults. Our experimental results bear a striking resemblance to the model by Geshi et al. (2002). With detailed information about the kinematics of ring fault evolution, the experiments contribute to an understanding of events prior to and during collapse in July and August 2000, especially to the Propagation Phase indicated in Fig. 3.
The effective subsidence achieved during the 40 days of caldera formation was 1.6 to 2.1 km. The aspect ratio of the Miyakejima caldera, constrained by a 3 km deep reservoir and maximum 1.5 km diameter structural diameter above (Geshi et al. 2002), was about AR = 2.5. In Fig. 7, results of an experiment with AR = 2 is illustrated and compared to the development of seismic activity in Miyakejima during the Propagation and Subsidence Phase. Although the scaled subsidence at Miyakejima (>40 mm when scaled down) exceeds the subsidence in our experiments and we neglected the influence of topography, there are clear analogies between our experimental results and caldera collapse at Miyakejima. Similar to the upward-directed propagation of seismicity observed at the volcano (Fig. 3a), our scaled Miyakejima experiments are characterized by more than three sets of reverse faults that progressively propagate upward to shallower depths so that surface collapse only occurs after subsidence of 4 mm for AR = 2 (~160 m in nature). This sequence of successively active reverse ring faults produced in the experiments for high-AR calderas corresponds to the “stoping column” below the summit of Miyakejima (Geshi et al. 2002), a cylindrical area of underground faulting that could be traced by seismicity before surface collapse occurred. In the experiments, surface collapse is thus delayed relative to magma chamber deflation (cf. Walter and Troll 2001). In the case of Miyakejima, the delay between lateral dike intrusion and surface caldera collapse was 12 days (Geshi et al. 2002; Nakada et al. 2005). In addition, our experimental results indicate that with increasing subsidence, larger faults are active and propagate over longer times. This may explain why largest earthquake energy releases did not occur at initial caldera stages, but rather increased during the Propagation and Subsidence Phases on Miyakejima (Fig. 3c). After ring faults have connected to the surface in the experiments, the fault configuration of the inner reverse ring faults remains nearly stable. Furthermore, the experiments show that with increasing subsidence, displacement is transferred from inner reverse ring faults to newly-formed outer normal ring faults (Figs. 5, 6 and 7). This is in accordance with observations at Miyakejima, where the peripheral normal faults play an increasingly important role for successive subsidence after the manifestation of the caldera at the surface (Geshi et al. 2002). In the experiments, the process of displacement transfer is characterized by a transitional phase, during which the peripheral normal faults propagate downward while the reverse faults remain active. The upper segments of the reverse faults become inactive only after the normal faults have linked with the reverse faults at depth (Fig. 6f, j). Hence, the structural diameter of the caldera at the surface increases successively, as was observed at Miyakejima, which increased its diameter by more than 50% from July to August (Fig. 1). The location of a major normal fault connecting at the base of the present caldera wall outside the initial caldera, as described by Geshi (2009), indicates the outward migration of ring faulting. In the case of Miyakejima, the caldera diameter also increased as a consequence of landslide processes (Geshi et al. 2002).
Our experimental results also provide a possible explanation for vent migration and the location of geothermal activity during caldera collapse. According to Geshi and Oikawa (2008), the first phreatomagmatic eruptions at the beginning of collapse occurred near the caldera centre, whereas subsequent eruptions took place at the marginal areas of the caldera. In addition, geothermal activity in the post-caldera stage was concentrated along the rim of the caldera floor. Displacement transfer from inner reverse ring faults that first reach the surface near the centre of the caldera to outer ring faults accompanied by the inactivation of the earlier ring faults, as observed during the experiments, offers a possible explanation for these observations.