During eruptions, diatremes are bodies of unconsolidated juvenile and lithic material and can be expected to have significant water storage capacity and potentially high permeability. Water from adjacent aquifers is likely to keep a diatreme at least locally water saturated. Much of the material in eruptive jets collapses back into the crater, recycling liquid water caught up in an explosion back into the upper diatreme (White and McClintock, 2001). As magma enters a diatreme it is likely that the intrusion will wander and take on an irregular shape in the unconsolidated fill, and, if it does not explode, cause local drying and redistribution of water. Thus, we argue the diatreme itself serves as a heterogeneous aquifer through which intrusions ascend.

Dikes play important roles in feeding most volcanoes, including diatremes and other small volcanoes in volcanic fields. Recognition of sills in the upper half-kilometer of volcanic fields complicates this picture (Valentine and Krogh, 2006; Muirhead et al., 2016). Diatremes can form from these sills, or where inclined sheets or small magma diapirs ascend from the sills (Diez et al., 2009) and undergo subsequent phreatomagmatic explosions. Another complication is evidence for magma withdrawal in dikes connected with diatremes (Lefebvre et al., 2012; Re et al., 2016), severing the link between dike ascent and initiation of explosions. Thus, while many or most diatremes are rooted by dikes, explosions do not necessarily initiate during dike ascent, and sills, inclined sheets, and small diapirs can also be diatreme feeders.

A key parameter for phreatomagmatic explosions is the range of mechanical energies involved and the efficiency with which magma's thermal energy is converted to mechanical energy. Data form a linear trend on a log-log plot of crater diameter (D) from single explosions vs. energy (E; Goto et al., 2001), but the log scale over 14 orders of magnitude obscures variability with factors of 10–100 in the data. Sonder et al. (2015) presented an empirical relation between scaled crater radius (r_sc = R · E^−1/3, where R is the measured radius) and scaled depth (d_sc = d · E^−1/3, where d is the physical depth of the explosion center), showing that scaled radius is maximum when d_sc = 0.004 m · J^−1/3 (see also Goto et al., 2001). Crater diameter does not uniquely equate to a value of energy for a given set of host-rock properties, i.e., the same crater size can be produced by different energies at different scaled depths, and a single energy produces different diameters depending upon its depth (Figure 1C). In the absence of independent data on the depth of an explosion it is not possible to uniquely constrain its energy based upon crater diameter. Compounding this is the fact that most maar-diatremes show evidence of having been produced by numerous explosions, presumably with a range of energies. Sonder et al. (2015) concluded that, in multi-explosion craters in which explosions migrate only in the vertical dimension, the diameter cannot be simply related to either the cumulative energy of explosions or the energy of the single largest explosion. These problems become even less tractable when explosions shift both vertically and laterally, as probably happens in most natural maar-diatremes. Thus, we conclude that crater sizes are not a useful proxy for explosion energy at maar-diatremes.

The field evidence for this includes: observations of the 1977 eruptions of Ukinrek maars, where two vents were observed erupting simultaneously within the East Maar (Self et al., 1980); clearly scalloped perimeters and multiple circular depressions on the floors of large maars (e.g., Begét et al., 1996); and reconstructed ballistic trajectories of tephra-ring blocks that point to multiple eruption sites (Jordan et al., 2013). Recent work provides further insight into the effects of multiple epicenters. The maximum diameter of a crater (D_ref) made by an explosion of energy E is D_ref = (0.014 m · J^−1/3) · E^1/3 (Goto et al., 2001), which we refer to as the reference footprint of an explosion (Valentine et al., 2015). Experiments suggest that, when explosions all have epicenters within each other's reference footprints, the result will be a circular crater. If two explosions have overlapping reference footprints but each epicenter is outside the other explosion's footprint, the surface expression will be a single compound crater with an irregular shape. Separate craters form when reference footprints do not overlap at all (Valentine et al., 2015). This information can be used to assess the combination of explosion energies and lateral distances between explosions. For example, a circular crater implies that the lateral distances between explosions were centered within circles defined by D_ref, for all of the individual explosion energies involved. Thus, crater morphology can provide semi-quantitative information on the combinations of explosion energies and lateral distances between explosion loci.

Most tephra rings are rich in lithic clasts derived from the rocks beneath a maar. Within Lorenz' (1986) framework for maar-diatremes, the appearance of deeper-seated lithic clasts in the upper tephra-ring deposits was taken as an indicator of the progressive deepening of explosion loci and of the diatreme bottom, with an implication that the bed containing a given deep-seated lithic clast was produced by an explosion at the depth of origin of that clast.

The effects of scaled depth on subsurface explosions pose a major roadblock for this interpretation. As scaled depth increases beyond the optimal cratering value of ~0.004 m · J^−1/3 the amount of material ejected and the crater size progressively decrease until d_sc = 0.008 m · J^−1/3; larger scaled depths produce fully contained explosions from which no material is ejected (Graettinger et al., 2014). Valentine et al. (2014) assessed the range of explosion energies that might be expected at maar-diatremes and concluded that realistic magma-water explosions will only erupt material when their depths are less than ~200 m. Furthermore, deposition of erupted material onto a tephra ring requires most explosions to occur at depths of ~100 m or less. Tephra-ring lithic clasts that originate at depths of a few hundred meters are not ejected directly from explosions at those depths. Rather, repeated subsurface explosions at a range of depths cause both upward and downward mixing via debris jets and subsidence (Ross et al., 2008a,b; Sweeney and Valentine, 2015; Andrews et al., 2016). This step-wise mixing takes time, explaining why deep-seated lithic clasts normally occur late in a tephra ring sequence; in some cases an eruptive episode might end before deep-seated clasts have mixed to shallow levels, thus leaving no eruptive record of that part of the diatreme. We conclude that deeper-seated lithic clasts in tephra rings are the result of gradual upward mixing of wall-rock clasts, and they represent, at best, the minimum vertical extent of an underlying diatreme.

Papers on tephra-ring deposits often equate the grain size of a given facies to the efficiency of fragmentation (e.g., Clarke et al., 2009; Jordan et al., 2013). This implies that the deposit grain size results only from the fragmentation process at the site of magma-water interaction. However, other factors play important roles in the grain size of deposits at a given location in a tephra ring, including the scaled depth of an explosion, which determines how far the jet is able to throw coarse material, and the presence or absence of a pre-existing crater for a given explosion (e.g., Graettinger et al., 2015b). Eruptive jets through the debris fill at the centers of existing craters, such as would occur after initial maar-diatreme development, tend to be vertically focused and collapse back into the crater rather than onto the tephra ring (Taddeucci et al., 2013). When the jet collapses and rapidly sediments onto the crater floor, it expels gas and fine ash which then feed laterally flowing, fine-grained density currents (base surges; Graettinger et al., 2015b), leaving coarser deposits in the diatreme (Lefebvre et al., 2013). Such processes would be expected at the natural scale to produce fine-grained pyroclastic surge deposits and ash fallout in a tephra ring; however, there is no implication at all about the efficiency of fragmentation during the explosion.

Additional factors in the grain size of tephra ring deposits include: (1) host materials and how they disintegrate during explosions (e.g., weakly- or non-consolidated fine-grained sediments, compared to competent granitic hosts; e.g., Blaikie et al., 2012); (2) the duration of activity and the number and energies of explosions that progressively break up country rocks and recycled juvenile material; and (3) the amount of recycled material that is fragmented, ejected, and then deposited back into the crater to undergo subsequent explosions and associated fragmentation (e.g., Houghton and Smith, 1993). The grain size characteristics of a tephra-ring bed can reflect a long and complicated history of subsurface explosions, even if that bed is the deposit of a single explosion. Some proportion of the clasts do not make it onto the tephra-ring, but rather return to the crater and diatreme, resulting in an exaggeration of fine-grained components in tephra rings (White and Valentine, 2016). Thus, we conclude that grain size of tephra ring deposits is not a good proxy for fragmentation efficiency.

Many tephra rings contain both products of phreatomagmatic explosions and of those potentially driven by magmatic volatiles, for example, agglomerates (but see White and Valentine, 2016), scoria fall layers, and terminal lava flows or scoria cones. This is often interpreted to be the result of groundwater depletion (e.g., Lorenz, 1986).

Other key factors enable magmatic-volatile driven activity during a maar-diatreme's eruptive episode. First, magma-water interaction depends not only upon water availability, but also on magma flux and other factors that are poorly understood and difficult to infer from nature, such as the geometry of an intrusion of a given batch of magma into a diatreme. Some dikes may not encounter wet parts of a diatreme, for example if a preceding intrusion(s) locally dried or sealed off water from the path of an incoming dike, and so make it to the surface with no phreatomagmatic interaction or interact in the subsurface without explosion, while other dikes intersect wet diatreme fill under the right conditions and do explode. It seems likely that, if magma flux temporarily increases during an eruption, it might overwhelm the effects of water and rise directly to the surface to feed Strombolian or Hawaiian styles of activity. Additionally, multiple vents can be active simultaneously within a maar. Ukinrek East Maar activity had simultaneous steam and ash emissions and Strombolian activity from two vents within the single crater (Self et al., 1980). Thus, we conclude that the presence of deposits from magmatic-volatile driven activity is not a simple indicator of the availability of groundwater from host aquifers.

The importance of pyroclastic density currents (PDCs), especially dilute ones (a.k.a. pyroclastic surges), in tephra-ring deposits has been recognized since the seminal work of Moore et al. (1966) and Fisher and Waters (1970), and some deposits indicate deposition from concentrated PDCs (e.g., White, 1991). Well sorted, topography-mantling fallout deposits are also widely recognized in tephra rings, as are individual blocks and bombs that were emplaced ballistically.

Another mechanism is ballistic curtains, which form when discrete eruptive jets simultaneously collapse and expand radially. Particles in the ballistic curtain follow ballistic paths, but proximally as dispersions rather than as isolated clasts. Deposition occurs both downward and outward at a given point (Figure 1D). Proximal deposits in field-scale experiments were massive and poorly sorted, and varied in thickness and coarseness in the circumferential direction; these graded laterally into sheet-like deposits that may resemble fallout and finally to individual scattered clasts distally (Graettinger et al., 2015a,b). Proximal, poorly sorted tuff breccias at some maars (e.g., Sohn and Chough, 1989) may have been emplaced by ballistic curtain mechanisms. Ballistic curtain deposits are expected to be favored early in the development of a maar because, as the crater deepens and grows, jets become increasingly vertically focused if they are centered in the crater, or inclined if they are off-center (e.g., Valentine et al., 2015); both factors decrease the effectiveness of the ballistic curtain mechanism. We conclude that there are likely four distinct mechanisms that contribute to tephra ring deposition: pyroclastic density currents, fallout, individual ballistic clasts, and ballistic curtains.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.