Several factors may control the development of a silicic caldera during an eruption: here we match previous studies of caldera forming eruptions with analogue experiments to consider the role of the aspect ratio (thickness/width) of the magma chamber roof. These data suggest that large silicic caldera formation is controlled by: (1) the availability of magma; (2) initial explosive eruption through a conduit connecting the reservoir and the surface; (3) fast depressurization of the reservoir; and (4) chamber roof collapse, with newly-formed fractures connecting the reservoir with the surface and creation of a continuous ring conduit feeding annular vents, capable of sustaining the eruption. The occurrence of the latter condition may depend upon the aspect ratio of the chamber roof: lower ratios (<1.6) form coherent collapse, ensuring connection from the chamber to the surface; higher ratios (>1.6) form incoherent collapse, which may hinder the continuation of the eruption after an initial partial emptying of the chamber. The aspect ratio of the chamber roof should therefore be considered as a further factor, capable of controlling the formation of large silicic calderas.
 Silicic calderas form during explosive eruptions, extruding significant volumes of magma in a short time. The rapid drainage induces a pressure decrease within the magma chamber, below the strength of surrounding rocks, resulting in a collapse [Smith, 1979; Druitt and Sparks, 1984; Lipman, 1997, and references therein].
 Several factors may control the formation of a large silicic caldera during an eruption, including: the volume of available magma (enhancing caldera formation), the dissolved volatile content (enhancing), the volume of extruded magma (enhancing), the depth to the chamber (hindering), the load over the chamber (hindering), the extrusion rate (enhancing) and the possibility to maintain a continuous conduit during the eruption (enhancing) [e.g., Cole et al., 2005, and references therein; Geyer et al., 2006; Lavallèe et al., 2006]. The depth to the chamber seems to be one of the fundamental parameters: this, proportional to the load acting on the reservoir, may control the critical amount of gas required to start the eruption; moreover, shallower chambers may ensure an easier connection with the surface during the eruption, providing higher extrusion rates [Quareni and Mulargia, 1993] or the possibility to develop a caldera [Lavallèe et al., 2006]. Even more representative, to be used in any comparison, is the depth to the chamber normalized to its width, or the dimensionless aspect ratio (thickness/width) of the magma chamber roof.
 This study focuses on the role of such ratio on caldera formation during a silicic eruption. We match previous studies of known caldera forming eruptions with the results of several sets of analogue experiments of calderas, to derive a general model considering the possible role of coherent and incoherent collapses on caldera formation during a silicic eruption.
2. Dynamics of Caldera Forming Eruptions
 In large-scale caldera-forming eruptions, enormous volumes of magma (>101 km3) are extruded, and a substantial fraction (a few tens of %) of the magma chamber volume is evacuated [e.g., Hildreth and Wilson, 2007]. Smith  subdivided caldera structures in central-vent and ring-fracture calderas, suggesting that the former erupt less magma (10–100 km3). Such eruptions may continue after the onset of the collapse of the chamber roof [Smith, 1979], as suggested by the co-eruptive intra-caldera fill at several ring-fracture controlled calderas, including Crater Lake, Long Valley, Valles, Campi Flegrei [Newhall and Dzurisin, 1988, and references therein]. Conversely, other collapses are associated with moderate amounts of erupted magma, compared to that in the reservoir [Smith, 1979]. This usually occurs when the eruptions ceases at the incipient collapse of the chamber roof, as suggested by the deepening of seismicity towards the end of the eruption (Figure 1) [Scandone and Malone, 1985; Mori et al., 1996; Scandone and Giacomelli, 2001]. This association suggests that the pressure decrease in the chamber and conduit, and the incipient chamber collapse may close the conduit, terminating the eruption [Quareni and Mulargia, 1993]. Suitable examples, even though not necessarily related to a caldera, include Pinatubo (in 1991), St. Helens (1980) and Vesuvius (79 AD) [Scandone and Giacomelli, 2001]. Therefore, some eruptions withdraw a limited amount of magma, with weak evidence of a caldera, whereas others extrude a much larger amount of magma, also after the onset of collapse [Geyer et al., 2006].
 A pre-requisite for a sustained explosive eruption is the formation of a conduit, central or peripheral, between the surface and the reservoir. This propagates the fragmentation wave down to the reservoir [Mader et al., 1997], inducing fast drainage and depressurization of the chamber. This, in turn, causes H2O exsolution, bubble nucleation and a temporal increase of the discharge rate [Scandone and Giacomelli, 2001]. The eruption lasts as long as the pressure difference between the magma and host rock equals the rock strength. When this occurs, the fast drainage causes a decompression and seismicity above and around the chamber. The amount of erupted magma is controlled by the interplay between the rock strength, the amount of volatiles and the reservoir volume and depth. In fact, the lower is the lithostatic pressure, the higher is the percentage of exsolved magma in the reservoir and therefore the higher is the fraction of erupted magma (Figure 2). Conversely, higher confining pressures prevent extensive boiling upon decompression and a lower volume increase because of volatile exsolution. Therefore, the hindered exsolution of volatiles at higher depths may partly explain the difficulty in continuing the eruption at the onset of collapse within deeper chambers. However, in presence of moderate-sized chambers, the rapid pressure decrease after the beginning of the eruption may close the conduit, ending the eruption. In fact, an important requisite to continue the eruption is to develop new conduits, ensuring connection between the reservoir and the surface. To understand how new conduits may form during caldera collapse, we consider consistent results of several sets of recent analogue experiments.
3. Development of Ring Fractures During Caldera Collapse
 Analogue models have been widely used to investigate the structure and development of calderas. These, performed under very different boundary conditions, have shown a remarkably consistent deformation pattern, given by reverse (formed first) and peripheral normal faults [e.g., Acocella, 2006, and references therein]. A minor difference lies in the control of aspect ratio of the roof of the chamber analogue [Roche et al., 2000]. With low roof aspect ratios (thickness/width ≤1, type A), coherent piston-like calderas are developed; these are delimited by reverse faults, whereas the gravity-driven normal faults border an outer zone (Figure 3a). For high aspect ratios (>1, type B), multiple reverse faults propagate upwards, forming an incoherent collapse (Figure 3b). Normal faults may be restricted to the upper periphery, where the reverse faults reach surface. These experiments develop funnel-like calderas. Both types, despite the geometric differences, share a consistent mechanism of deformation. In type B, multiple reverse faults are required to propagate the collapse upwards in a thicker crust analogue (Figure 3b). Independently from the roof aspect ratio, all the collapses may display one or more set of reverse faults; if the displacement on the upper ring fault at surface reaches a certain threshold, a normal ring fault may also form.
 The possibility to develop coherent (type A) or incoherent (type B) collapses may control the rise of magma during an eruption. In type A calderas, the reverse ring faults may be intruded during the emptying of the underlying reservoir, transferring magma to the surface. This process in type B calderas is hindered by the incoherent nature of the collapse, where only the lowermost reverse fault may be intruded. Therefore, the aspect ratio of the chamber roof may prevent an efficient and rapid withdrawal of the chamber during caldera collapse. In most experiments the dip of the reverse faults is ∼75° (Figure 3c), in agreement with natural calderas [Mori and McKee, 1987; Mori et al., 1996; Acocella, 2006]. This constraints the theoretically expected largest aspect ratio of the caldera roof (∼1.6), to develop a coherent collapse; this is slightly larger than that (∼1 [Roche et al., 2000]) previously proposed. Beyond a ratio ∼1.6, incoherent collapses form.
4. Discussion and Conclusions
 Some eruptions, extruding magma from a deep chamber, end during the onset of collapse of the chamber roof. Other eruptions extrude larger amounts of magma from a shallower reservoir, even after the collapse onset. These different behaviors may be explained by different factors. Commonly accepted factors are the enhanced exsolution of volatiles at shallower depths and the volume of available magma to be erupted, both enhancing caldera formation. A further factor to consider may be the deformation pattern developed during collapse as a function of the aspect ratio of the chamber roof. In fact, a viable means of formation of new conduits during collapse is to develop reverse faults connecting the chamber to the surface (Figure 4). Because of their inward dip, these may be more easily penetrated and enlarged because of the decreasing pressure in the chamber, and determine the emission of pyroclastic flows and further emptying of the chamber. The amount of erupted magma, representing a large fraction of the eruptible magma, would no longer be controlled by the rock strength only.
 The estimated aspect ratios of the chamber roof for the eruptions of St. Helens (1980) and Pinatubo (1991), based on seismicity data, are ∼6 and ∼1.6 respectively [Scandone and Malone, 1985; Mori et al., 1996]; therefore, incoherent collapse of the chamber roof may be expected for St. Helens, whereas the Pinatubo caldera is related to an aspect ratio to the limit to develop coherent collapse. The seismicity distribution also suggests activity along outward dipping faults, in agreement with the experiments. At other volcanoes, as Huaynaputina (Peru), the incoherent collapse induced by the evacuation of a deep chamber prevented the formation of a caldera during a significant eruption [Lavallèe et al., 2006]. Conversely, the behavior of eruptions from shallower and wider chambers, as that of Mount Mazama, forming the 8x10 km Crater Lake caldera, may be explained by type A collapses. Here the eruption of 30 km3 of magma led to the collapse and further emission of 20 km3 of magma from ring faults [Druitt and Bacon, 1989; Bacon and Lanphere, 2006]. The inferred roof aspect ratio ∼1 [Bacon et al., 1992] and the significant volume of erupted magma may explain, through a coherent collapse, the ring fault-driven phase of the eruption. Other examples with similar behavior include Kumano, Taupo, Reporoa and Rabaul calderas [Saunders, 2001; Spinks et al., 2005].
 In synthesis, silicic caldera formation requires the following conditions. (1) Availability of a large volume of magma. (2) An initial explosive eruption through a conduit (central or inward-dipping ring structure) connecting the reservoir and the surface; (3) fast depressurization of the reservoir; (4) coherent chamber roof collapse, with newly-formed gaping faults connecting the reservoir with the surface and creation of a continuous ring conduit, feeding vents capable of sustaining the eruption. The coherent collapse occurs with aspect ratios (thickness/width) of the chamber roof A < 1.6. While the first 3 points are required for any silicic caldera forming eruption, the catastrophic stage may be most easily triggered, during collapse, connecting the chamber to the surface (condition 4).
 Alternative possibilities to develop a caldera with higher roof aspect ratios must consider, after the initial phase of the eruption: (1) a larger residual magmatic pressure within the reservoir, to start dike propagation as an alternative for the magma to reach the surface, and/or (2) a larger volume of magma to be erupted in the chamber. The aspect ratio of the roof chamber may therefore provide an additional explanation with regard to the established processes (gas exsolution enhanced at shallow depths, volume of available magma) to develop large silicic calderas from shallow reservoirs.
 TH Druitt, J Marti and two anonymous reviewers provided helpful suggestions. RS acknowledges financial support from MIUR-Prin Project 2005 (Risalita dei Magmi e Dinamica delle Eruzioni).