Craters at many volcanoes, including most maars, are formed by multiple subsurface explosions. Experiments compared the crater formed by a single large, buried explosion, with craters formed by multiple explosions with the same cumulative energy. Explosive charges were detonated in pads composed of layered aggregates, in three configurations: (1) a single large charge buried near its optimal crater excavation depth; (2) three charges, each with 1/3 the energy of the first one, buried at approximately the same depth with respect to the original pad surface; (3) the same three charges buried successively deeper. Final crater size in the multiple explosion cases is not a good indicator of the energy of individual explosions. However, crater morphology, and ejecta volume and distribution can be good indicators of explosion energy and depth. These results directly impact the estimate of the energy released by past maar eruptions and future hazard assessments.
 Many volcanic craters are formed by multiple explosions. In particular, maar volcanoes are formed by many subsurface explosive interactions of magma with groundwater. The resulting landform is a deep crater with a bottom below the pre-eruption ground surface, surrounded by a low profile tephra (ejecta) ring. Beneath the maar is a funnel-shaped body (diatreme) of fragmented country rock, juvenile volcaniclastic material, and intrusions [Lorenz, 1986; White and Ross, 2011; Valentine and White, 2012]. Maars are typically 100s of meters to >1 km in diameter, and diatremes can extend as deep as ∼2 km.
 Recent work [Taddeucci et al., 2010; Valentine et al., 2011] has opened the question: Can features such as maar crater diameter be used to estimate explosion energy, which in turn can be used for hazard assessment? For a given explosion energy there is an optimal depth of burial that will result in excavation of a maximum diameter crater [e.g., Goto et al., 2001; Yokoo et al., 2002]. Empirical scaling relationships show that both optimal depth and crater diameter vary proportionally with E1/3, where E is the energy released by an explosion [e.g., Sato and Taniguchi, 1997]. However, the scaling relationships were developed for craters produced by single explosions, rather than by multiple explosions as at a maar volcano. It is not clear whether maar crater diameter can be related to explosion energy in the same way that crater diameter relates to the energy of a single explosion. Here we compare experimental data from a single explosion crater with craters produced by multiple explosions. In all of the cases, the total explosive energy was the same, but in the multiple-explosion cases it was divided into three smaller explosions.
2. Experiment Setup
 Three pads, each ∼4 m × 4 m in plan view and with their bases ∼30 cm below the surrounding ground surface, were constructed outdoors with layers of aggregates. In Pads 1 and 2, the basal layer was ∼30 cm of light brown gravel (median grain size ∼5 mm) and the middle layer was ∼30 cm of medium to coarse, light gray sand (median grain size 1 mm). The layers were mechanically compacted, which reduced the layer thicknesses by 1–2 cm, and were dampened slightly with water to provide some cohesion for post-explosion excavation. The top layer was composed of crushed asphalt product that formed a dark gray, poorly sorted bed (median grain size ∼4 mm). This layer was not mechanically compacted, but developed some strength because many asphalt particles stuck together in the daytime heat (this also produced several-cm sized composite “clasts” that are not reflected in granulometric data). Pads 1 and 2 each had a total thickness of 85–90 cm. Pad 3 had the same structure but the layer of sand beneath the crushed asphalt product was ∼35 cm thick, and there was an additional ∼45 cm thick layer of the light gray sand below the three layers described above.
 The charges consisted of a mixture of trinitrotoluene (TNT) and pentaerythritol tetranitrate (PETN), with an approximate explosive energy density of ∼6 × 106 J/kg. Charges were emplaced in holes with diameters of ∼15 cm, which were refilled with aggregate and tamped prior to detonation. Note that the energy release by these chemical explosives is likely more rapid than would be expected for a volcanic explosion, which would affect coupling between the explosions and surrounding media. However, our focus here is on the relative variations from single versus multiple explosions, rather than the quantitative details of crater dynamics.
 Explosive charges were emplaced in different configurations in the pads (Table 1). Pad 1, a reference case, had a single charge of 0.45 kg at a depth of 50 cm, approximately the depth for optimal crater excavation (∼55 cm, based upon Goto et al. ). In Pad 2, the explosive energy was divided into three charges, each 0.15 kg. Each of the three explosions occurred at approximately the same depth (∼50 cm) with respect to the original pad surface, thus testing the effects of dividing the explosive energy into discrete bursts but without variations in the location of the bursts. In Pad 3, the three charges (each 0.15 kg) were emplaced at different depths. Charge 1 was emplaced 50 cm below the pad surface (as in the explosions for Pads 1 and 2). Charge 2 was emplaced between 40–50 cm deeper than the lowest point in the crater that was produced by Charge 1; depth was less well constrained for this charge because of failure of the walls of the emplacement hole (material had been weakened by the Charge 1 explosion). Charge 3 was emplaced 50 cm deeper than the deepest part of the crater that was produced by Charge 2. This configuration simulates a maar-diatreme volcano in which explosions are progressively deeper as an eruption proceeds [Lorenz, 1986]. In all cases, charges were emplaced beneath the center of the pads in plan view. Explosions were separated in time by 30–45 minutes, allowing crater diameter, depth, and morphology to be recorded after each explosion.
Table 1. Charge (explosion) depths and crater geometry
Cone shaped crater, outer rim developed during Charge 2 explosion, steep inner crater with 1.3 m diameter (similar to Charge 2 crater). Relatively smooth ejecta blanket and rim. Concentric cracks opened around rim during several minutes after blast.
Poorly defined shallow crater, subdued rim, hummocky interior with central mound of crushed asphalt nearly as high as the raised rim. Crushed asphalt deposited in patches around crater, extending ∼1 m from rim.
Cone shaped crater with gentle slopes on inner 20–30 cm diameter floor. Hummocky rim with sand from second layer down deposited in a fan around ∼2/3 of the ejecta blanket.
Bowl shaped crater with hummocky central floor. Hummocks in rim more subdued than after previous shot. Sand from second layer down asymmetrically deposited in one quadrant of crater and ejecta blanket.
 Explosions were recorded with a high-speed (600 frames/s) video camera located about 50 m from the test pads on an elevated surface. Ejecta deposits were sampled on plastic mats situated at regular radial distances along a single line from each of the explosion sites, beginning 2.5 m from ground zero (4.2 m at Pad 3). Only the explosions at Pads 1 and 2 resulted in significant quantities of ejecta reaching these sample collection sites; the samples for Pad 2 were collected at the end of the three-explosion sequence there. The pads were excavated after all explosions were completed in order to document the subsurface structures, and the excavation results will be presented elsewhere.
3. Crater Characteristics
 The single 0.45 kg explosion (∼3 × 106 J) at Pad 1 produced a 1.92 m diameter, 47 cm deep crater (Table 1 and Video 1; compare with predicted diameter of 1.9 m using the relationships in Goto et al. ). The explosion took place in the sand layer beneath the topmost layer of crushed asphalt; most of the ejected material was crushed asphalt but finer grained, lighter colored sand was ejected in streaks that are preserved in crater wall and rim deposits (Figure 1a). The crater was cone shaped with walls sloping inward at ∼26°, surrounded by a rim of ejecta with a hummocky surface.
 The first explosion at Pad 2 (Table 1) occurred beneath ∼50 cm of overburden (compare with the optimum depth of burial of ∼35 cm; Goto et al. ). The resulting crater diameter was 1.5 m (compare to predicted ∼1.35 m; Goto et al. ), but it had a very subdued, shallow shape with a hummocky floor rather than a conical shape. This is because much of the ejected material (mainly crushed asphalt and some sand) was disaggregated and lifted only ∼2 m or so in a low vertical jet before falling back into the crater; only a small amount fell outside the crater (see Video 2). The second charge (Video 3) was placed near the same level as the first, with respect to the original pad surface, but the overburden (measured from the low point of the Charge 1 crater) was similar to the optimum burial depth for the 0.15 kg charge. As a result, Charge 2 efficiently ejected material already loosened by the previous explosion, destroying the hummocky structures in the Charge 1 crater and producing a deeper (53 cm) and wider (1.8 m diameter) crater. The crater was cone shaped, with a steeper-sloped inner part (1.3 m diameter) that we infer corresponded to the edge of the damage zone from Charge 1. The average slope of the Charge 2 crater was ∼30°, steeper than the crater in Pad 1, because of the pre-damaged aggregate. In order to maintain an approximately constant detonation location, Charge 3 was buried in the bottom of the Charge 2 crater, so that the top of the cylindrical (∼12 cm long) charge was even with the crater bottom. Most of the energy of the Charge 3 blast was transmitted into air shock, although a small amount of crushed asphalt was sheared off the walls of the Charge 2 crater and ejected onto the surrounding pad surface (Video 4). Although Charge 3 did not widen the existing crater significantly (Figure 1b), it did further weaken the material around it. Within ∼10 minutes after the detonation, concentric tension fractures opened up around the crater to distances of ∼30 cm from its rim, as the weakened pad material responded to the open crater topography. However, when the crater was re-examined two days later these fractures had “healed” without significant slumping into the crater.
 The crater produced by Charge 1 at Pad 3 had a smaller diameter than, but was otherwise similar to, the Charge 1 crater at Pad 2, because of the essentially identical blast conditions (Table 1 and Video 5). Charge 2 was placed between 40–50 cm lower than the lowest level of the Charge 1 crater, such that it was also beneath its optimum depth in terms of overburden, but not as much as was Charge 1. This fact, plus the pre-weakened aggregate (due to the Charge 1 detonation), resulted in further excavation of the crater (Video 6) and destruction of the hummocky surface and development of a conical new crater with inner slopes of ∼26°. Charge 3 was detonated 45 cm beneath the Charge 2 crater, in the crushed gravel layer. Ejection of material was quite limited; most material (dominated by crushed asphalt, less sand, and a minor amount of gravel) rose <2 m above the crater rim and simply fell back into the crater or onto its rim (Video 7), depositing hummocks of debris several cm high on the crater floor (Figure 1c), and slightly reducing the crater diameter from 1.80 m (after Charge 2) to 1.78 m. The slopes of the crater walls were, however, steepened by the Charge 3 explosion. This, plus the additional accumulation of ejecta rim deposits, meant that the crater volume increased slightly.
 To summarize, the single explosion case produced a crater diameter of 1.92 m, while the multiple explosion cases (but adding up to the same total energy for each pad) resulted in crater diameters of 1.78–1.80 m (a difference of ∼7%), regardless of the location of the explosions for the configurations tested here. Similarly, the final volumes of each of the craters were essentially the same when measured from the high point of the ejecta rim to the crater bottoms (but see below; Table 1). Final crater size appeared to reflect the cumulative energy released, although the generality of this conclusion must be tested with a wider range of configurations. Crater size is not a good indicator of the energies of individual explosions at a multi-explosion crater. However, the shape of a crater, especially the presence of hummocks and departure from conical geometry (steeper walls and broader floor), is an indicator of relatively weak or/and too-deeply-buried explosions.
4. Ejecta Dynamics
 Although the final crater volumes produced at each pad, when measured from the tops of the ejecta rims, were similar (Table 1), the ejected volumes (based upon the crater volumes measured from the original pad surfaces rather than ejecta rims) and dispersal of the ejecta were sensitive to the explosion energies and depths (Figure 2). The single large explosion at Pad 1 dispersed ballistic ejecta radially away from the explosion epicenter to distances exceeding 16 m. The ratio of the thickness of ejecta at the crater rim to the total crater depth (R) was 0.2. The explosion sequence in Pad 2 ejected about 10% less volume and resulted in much less ejecta reaching the sampling locations, with most of the ejecta mass falling within ∼7 m of the epicenter. At the end of the explosion sequence at Pad 2, R = 0.2, similar to that at Pad 1. The Pad 3 explosion sequence ejected ∼20% less material than the Pad 1 case, and produced no deposits on the sample pads which began about ∼2.5 m from the epicenter at Pad 2, and ∼4.2 m from the Pad 3 epicenter. At Pad 3 the final crater had R = 0.4, illustrating how the deepening explosions were progressively less able to disperse material far from the explosions' epicenter. Material from the crushed asphalt (topmost) layer was ejected with a range of clast sizes up to several cm, but many of these were composite clasts that tended to break apart upon landing, which complicates any detailed interpretation of the granulometry of the ejecta deposits.
 The experiments demonstrated processes related to the formation of dilute pyroclastic density currents at maars. Most of the explosions took place in the sand layer that was overlain by coarser crushed asphalt, and this sand included a small fraction of fine silt. At Pad 1, material was ejected very energetically to a maximum height of ∼15 m, with coarse clasts (“lapilli”) following ballistic trajectories. As the ballistic material traveled away from the explosion site, fine silt, which has high particle drag with the gas phase, remained over the epicenter in a dilute plume that slowly diffused into the atmosphere and a weak density current developed due to the slightly higher density of the dusty gas relative to ambient air (Figure 3a and Video 1). In contrast, the lower energy bursts that were detonated below their optimal excavation depths (Charge 1 at Pad 2, and all the charges at Pad 3) ejected material only a few meters above the epicenters and most of that material simply collapsed back into the craters or within ∼2–4 m of the crater rims. As the high-particle-concentration jet collapsed, coarse clasts fell relatively directly to the ground while the dusty gas component of the mixture, along with new silt propelled from the crater floor by coarse-clast impacts, was expelled laterally outward, in turn forming dilute density currents that traveled up the craters' walls and outward beyond the rims (Figure 3b and Video 7). At Pad 1, the slightly higher density of the dusty gas initiated the current, whereas at Pad 3, explosion 3, the density current was initiated by the effects of the wide range of particle-gas coupling in the multiphase mixture of the jet. These processes, when occurring on a larger scale in Nature, could contribute to the formation of fine-grained deposits in tephra rings with evidence of having been emplaced by lateral currents (e.g., dune bedding). They are discrete-explosion variants of column collapse, and are base surges in the original sense used for buried (or underwater) nuclear and phreatomagmatic explosions [seeFisher and Schmincke, 1984].
 For the configurations tested here the crater size (diameter, total volume) is not a good indicator of the energy of individual explosions. Hazards associated with explosions at maars and other multi-explosion volcanic craters may be overestimated if crater diameter is used to estimate individual explosion energy. Crater morphology can provide some evidence of the relative strength or/and depth of explosions, in that ejecta from weak or too-deeply buried explosions will not rise very high and much of it falls back into the crater. This results in a departure from a simple cone-shaped crater that forms when material is effectively excavated by explosions that occur close to their optimal depths. The most sensitive indicator of the strength of individual explosions is ejecta dispersal; an indicator of this is the ratio of the thickness of ejecta deposits on the crater rim to the total crater depth. The experiments provide clues about the sources of pyroclastic surges that are commonly evidenced in tephra ring deposits; even relatively weak or too-deeply-buried explosions can drive surges as proximal fallback of coarse material expels the fine ash-gas (dusty gas) mixture and forces it radially outward. Future experiments will explore a wider range of geometries and will focus on ejecta dynamics and relationships between experimental ejecta deposits with known source conditions, and those found in nature where source conditions are less well constrained.
 We thank D. Schonwalder, S. Pansino, J. Ball, D. Ruth, M. Bursik, P. Scarlato, G. Babonis, S. Ogburn, and R. Andrews for assistance in preparing the site and during the experiments. D. Goralski provided invaluable logistics support. Comments by P. Dellino and an anonymous reviewer improved the manuscript. The experiment was funded by the University at Buffalo, through the Center for Geohazards Studies. We also acknowledge support from NSERC (Discovery grant to P.S.R.), the New Zealand Ministry for Business, Innovation, and Employment (to J.D.L.W.), and INGV (to J.T.).
 The Editor thanks Bernd Zimanowski and Pierfrancesco Dellino for their assistance in evaluating this paper.