Corresponding author: J. Taddeucci, Istituto Nazionale di Geofisica e Vulcanologia (INGV), Via di Vigna Murata, 605-00143 Roma, Italy. (email@example.com)
 Most volcanic eruptions occur in craters formed by previous activity. The presence of a crater implies specific confinement geometries, variably filled by loose fragmental deposits, which are expected to exert a strong, yet poorly studied, control on the violent gas expansion that drives the eruption. Here we analyze patterns of ejection from buried explosions in analog experiments, in order to investigate how the presence of a crater and changes in explosion depth and intensity may affect the formation of eruptive ejecta jets. Results show that scaled depth (charge burial depth divided by the cubic root of charge energy) controls the velocity and, partly, spread angle of eruptive jets independently of the presence of a pre-existing crater. Conversely, for a fixed scaled depth, the presence of a pre-existing crater limits the development of a laterally expanding annulus of the jet. These results are directly applicable to interpretation of volcanic explosions.
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 Explosive volcanic eruptions are commonly associated with the creation of a crater, the characteristics of which are determined by a combination of lofting and erosion of host rocks during rapid expansion of a pressurized gas-pyroclast mixture, and by proximal sedimentation of pyroclasts and talus that might partly fill the crater. Many, perhaps most, volcanic explosions occur at pre-existing craters, be they long-lived central craters at stratovolcanoes or newly-formed from short-lived explosive activity at maar volcanoes and scoria cones. Despite the pervasive presence of volcanic craters, studies investigating the effect of a pre-existing crater on the expansion of gas-particle mixtures are surprisingly scarce.
 The presence of a crater has at least two important implications for eruptions. First, the mixture expanding at the vent is initially confined in a well-defined geometry, i.e., a concave or cone-shaped depression with a specific profile that can influence its expansion and interaction of the eruptive jet with the atmosphere [e.g., Woods and Bower, 1995]. Second, the crater is a depression that collects deposits of loose pyroclasts accumulated as fallback from previous eruptions and talus from crater walls. The thickness of this clastic infill is highly variable, from a few meters for weak Strombolian explosions, up to 2 km in the case of maar-diatreme volcanoes [White and Ross, 2011]. Explosions occurring at any depth will have to penetrate infill material if they are to erupt [Valentine and White, 2012]. Both topographic confinement and initiation within infill are likely to strongly affect the key parameters of the eruptive gas-particle jet (e.g., exit velocity and geometry), the consequent emplacement process and dispersal area of pyroclasts, and, ultimately, the associated volcanic hazards.
 Several lab- and field-scale experiments have investigated the effect of charge energy and burial depth on the resulting explosion, with respect to military [e.g., Nordyke, 1961], quarrying [e.g., Tu-qiang, 2008], and volcanological [e.g., Goto et al., 2001] applications. As a result, scaling relationships between craters formed by individual explosions and charge energy and depth have been produced and compared with natural cases [e.g., Yokoo et al., 2002]. However, to our knowledge, only Valentine et al.  performed field-scale explosion experiments that involved multiple explosions occurring within the same crater. The crater shapes and sizes were documented after each explosion [Valentine et al., 2012], while the sub-crater deposits (partly analogous to natural diatremes) are investigated by Ross et al. [submitted]. This paper focuses on high-speed video observations of the initial phase of the explosion and formation of the ejecta jets, and on how these are controlled by the presence of a crater at the explosion sites.
 Explosive charges (a mixture of trinitrotoluene – TNT – and pentaerythritol tetranitrate – PETN –, with an explosive energy density of ~6 × 106 Jkg−1) were buried in prepared pads of loose, layered granular material [gravel to sand, see Valentine et al., 2012 for experimental details]. Three experiments were performed: Pad 1 hosted only one explosion from a charge (Run 1) of energy ~3 × 106 J buried at the optimal crater excavation depth of 0.5 m [Goto et al., 2001]. Pad 2 included three explosions from charges of energy ~1 × 106 J (i.e., each 1/3 of the Run 1 charge) buried initially at 0.5 m (Run 2a) and later within the previously formed craters at decreasing depths (Run 2b at 0.32 m and Run 2c at 0.03 m) below crater floor. The first explosion at Pad 3 (Run 3a) was the same as for Pad 2 (Run 2a). For Runs 3b and 3c the charges (again ~1 × 106 J each) were buried at the same depth (0.45 m ca.) below the previously formed crater floor. Each explosion ejected material and produced or modified a crater.
 All explosions were filmed using a CASIO Exilim™ camera operated at 600 frames per second with a resolution of 432 × 192 pixels. The camera field of view (FOV) covered an area of about 4.2 × 1.8 m centered on the pad, capturing the details of the initial doming and ejecta jet rise, but not the maximum vertical extent of the “eruptive” phenomena. Manual video analysis provided the following information: (1) morphology and evolution of the ejecta jet, obtained from tracing and stacking the outline of the jet every ten frames; (2) vertical speed of the jet front, obtained by tracking ejecta jet front throughout the FOV; and (3) ejecta jet spread angle, defined as the angle between the sides of the jet (positive if diverging upward and vice versa) after its initial development. Particle Image Velocimetry (PIV) performed through the PIVlab Matlab® program was then used to produce two-dimensional “maps” of the projected vertical and horizontal velocity components associated with the motion of the jet. In addition, each explosion generated an air pressure wave that displaced the high-speed camera, causing it to oscillate. These oscillations are unequivocally attributable to the explosion because: (1) no motion of the camera is visible before their onset, ruling out external factors (e.g., windshake, ground vibrations); and (2) the delay time between the explosion and oscillations onset matches, within measurement error, the expected travel time of acoustic waves from ground zero to the camera. Therefore, we use the amplitude of the displacement (in pixels), measured from a stable reference point in the images, as a proxy for pressure wave amplitude.
 Each explosion started with the pad surface doming upward at ground zero as ejection began. Simultaneously, the surface of the pad around ground zero was uplifted slightly as the compression wave traveled away from the shot point. Within 10–20 frames (0.016–0.032 s), a “deflation wave” moved back inward from the periphery of the pad towards its center and returned the pad surface to its original position; this is the surface manifestation of a rarefaction wave. In each case, the pad surface area affected by the visible passage of these waves was larger than the area finally occupied by the post-shot crater. We focus the remainder of the paper on the ejecta jet that began its formation while the compression and rarefaction waves propagated in the surrounding pad media.
 Within the FOV, jets evolved through initial rapid upward growth and slower lateral spreading which slowed until a jet with almost stable (with respect to initial expansion) width and variably inclined sides was attained (Figure 1). This general evolution varies as a function of the initial conditions. For instance, progressively shallower explosions (Runs 2a, b, and c) produced progressively faster-growing jets with more shallowly-inclined sides (larger spread angle), up to the extreme case of Run 2c, for which a very shallow explosion produced an extremely fast, radially expanding jet (Figure 1). Conversely, deeper explosions (Runs 2a, 3a, and 3b) produced slower jets with steeply-inclined sides (smaller spread angle). These latter three cases were also marked by more-complex jets, featuring a central, narrower, faster portion that, having the highest vertical velocity component and a small horizontal component, pierced upward through a larger, slower annulus that had a stronger component of lateral expansion (Figure 1). The result is a break in slope, or kink, in the jet outline, which moved upward and outward during jet evolution defining an inner core within the jet envelope (Figure 1) which is somewhat similar to that observed in jets from underwater explosions [Ichihara et al., 2009]. Run 3c, the deepest of the crater-confined explosions, produced a narrower jet with an inner core strikingly similar to the inner cores of the previous runs, but with a negligible radially expanding annulus.
 There is a clear effect of the presence of a crater on jet width. The first explosion in each pad experiment (Runs 1, 2a, and 3a) occurred in undisturbed pad material and produced jets that expanded laterally beyond the resulting crater. The second explosions in Pads 2 and 3 (Runs 2b and 3b) occurred within existing craters, enlarging the craters and producing jets only slightly larger than the resulting crater. Finally, in Runs 2c and 3c, which only marginally enlarged the craters where they occurred, the base of the jets was entirely confined within the crater (Figure 1). Also the pattern of expansion of the jets seems to be largely controlled by the initial presence of a crater, as shown by the very different PIV-derived velocity patterns of, e.g., Runs 3a and 3c (Figure 1).
 After a very short acceleration phase (one frame), the vertical velocities of jet fronts slowly decrease within the field of view. Averaged ejection velocities range between 7.7 and 273.2 ms−1 for the different runs, while jet spread angle ranges from −17 to +98° (Table 1). Both parameters are strongly controlled by the scaled depth of the explosion (Figure 2), defined as the burial depth divided by the cube-root of the energy of the explosive charge (Table 1). In particular, jet-front velocity decreases exponentially with increasing scaled depth, while jet spread angle decreases linearly [as per Ohba et al., 2002], although with a large scatter due to crater effects. The amplitude of camera oscillations, proxy for the amplitude of the air pressure wave, shows a direct, linear correlation with jet-front velocity, hence a reverse, exponential correlation with scaled depth (Figure 2), in broad agreement with Goto et al. . None of the above recognized trends holds true if explosion energy is scaled to burial depth with respect to the original surface of the pads, rather than to the burial depth with respect to the crater bottom.
Table 1. Initial run conditions and measured jet parameters
 Despite differences in the types of explosive used, burial material, and recording setup, our results confirm those of previous field experiments [Goto et al., 2001; Ohba et al., 2002] concerning the relationships between jet spread angle, amplitude of pressure waves, and scaled depth, thus strengthening the applicability of this last parameter in predicting the characteristics of buried explosions. To this picture, we add the information on jet velocity, which decreases exponentially with increasing scaled depth, likely because a larger part of the explosion energy is consumed to accelerate the overlying material.
 Similarity of our results with previous ones suggests that the laws governing the parameters related to scaled depth act independently of the presence of a pre-existing crater infill. In fact, all the above mentioned trends hold irrespective of whether a charge was detonated in undeformed pad material or in the backfill of a crater, possibly because of the loose nature of the material used to prepare the experimental pads. The only exception is spread angle, showing, overprinted on the major control exerted by scaled depth, the effect of the presence of a crater.
 Indeed, the presence of a crater around the explosion site does exert a strong control on the expansion pattern of the jet. For instance, the presence of a crater can confine the jet base (Runs 2c and 3c) within the crater itself, or it can produce different jet expansion patterns and morphologies even in explosions with comparable scaled depths (and resulting jet velocities and spread angles), as seen comparing Runs 1 and 2b and, even better, Runs 3a to 3c. Runs 3a–c occurred at similar scaled depths but first in undisturbed material and then within increasingly developed crater infills. The morphology of the resulting jets varies significantly, but, as an effect of the presence of a crater, the whole of the variation resides in the evolution of the external, lateral-expanding annulus of the jet, while the inner, vertically-expanding core rises at very similar rate and angle in all cases.
 High-speed and high-definition imaging of explosive volcanic activity is becoming increasingly relevant in eruption studies and monitoring [Taddeucci et al., 2012]. The observation that scaled depth holds robust relationships with jet parameters, especially ejection velocity, even for intra-crater explosions has important implications. For instance, jet evolution detected by monitoring camera systems could be combined with independent estimates of explosion depth by, for example, seismic array location of eruption-related earthquakes, to provide key information about the energy released by individual eruptive pulses, even for multiple pulses within the same crater.
 Since measurable quantities like jet velocity and pressure wave amplitude are insensitive to the presence or absence of a crater confining the explosion, other means must be used to understand the effects of craters on eruptions involving numerous explosions [e.g., phreatic or phreatomagmatic eruptions, Yokoo et al., 2002, Valentine and White, 2012]. Our preliminary experiments provide a first reference frame against which to compare recordings of volcanic explosions. The complex development of explosions with both a vertically-expanding central core and a peripheral, lateral expanding annulus seems promising for characterizing the intra-crater evolution of an eruption. Moreover, this distinction has implications for both hazard assessments and for investigations of eruptive products. The vertical core and radial annulus can be tentatively associated with the formation of a buoyant jet with attendant ballistic showers, and the formation of dilute pyroclastic density currents (surges), respectively. Results from Pad 3 illustrate how these two portions of the jet seem to originate and evolve differently, independently of scaled depth but depending on crater evolution. In particular, it appears that the formation of the radial annulus tends to be inhibited when explosions occur within a relatively deep crater. This could promote a decrease in the occurrence of coarse-grained pyroclastic surges (and their deposits, which might take the form of relatively massive tuff breccias or coarse lapilli tuffs) extending beyond a crater as an eruption and the respective crater evolve over time. However, as discussed in Valentine et al. , the fallback of a vertically-focused jet back onto a crater floor can, through multiphase effects, trigger a fine-grained pyroclastic surge that overtops the crater rim, potentially leaving deposits in the form of fine-grained, bedded tuffs and lapilli tuffs.
 We thank R. Andrews, G. Babonis, J. Ball, M. Bursik, P. Johnson, S. Ogburn, S. Pansino, D. Ruth, and D. Schonwalder for assistance in preparing the site and during the experiments. D. Goralski provided invaluable logistics support. The experiments were funded by the University at Buffalo through the Center for Geohazards Studies. We also acknowledge support from INGV (to J.T. and P.S.), Hazards Platform funding from the New Zealand Ministry of Business, Innovation and Employment (to J.D.L.W.), and NSERC (Discovery grant to P.S.R.).