The geometry of the conduit will determine the resonance characteristics of the system. Numerous conduit geometries have been proposed to accommodate water-flow beneath glaciers and ice-sheets, including channels cut into the ice [Röthlisberger, 1972], cut into the substrate [Nye, 1976], or a combination of the two [Walder and Fowler, 1994], a system of linked cavities [Kamb et al., 1985], and thin sheets and films [Weertman, 1972] (see Paterson  for a review). Notably, all of these possibilities, and others, can be represented by one of two major resonance models: a circular pipe, or a crack. The resonance frequency f of a perfectly cylindrical pipe of length L is f = a/4L, where a is the wave speed in the fluid modified by fluid-wall interaction (1100 m/s) [St. Lawrence and Qamar, 1979]. This holds for all pipe radii r, so long as L ≫ r. For our data, f = 3 Hz, and therefore L = 90 m. Alternatively, the resonant subglacial system can be represented as a crack of constant thickness d (in the direction normal to the bed) and length L (parallel to the bed). Values of L, d, and the ratio p = L/d consistent with the observed f = 3 Hz signal can be estimated from numerical results [Chouet et al., 1994] (see Métaxian et al.  for a detailed description applied to a glacial setting). Glaciologically viable solutions likely lie between p = 85, with L = 60 m, d = 70 cm, and p = 2000, with L = 20 m, d = 2 cm. Significantly lower values of p would suggest thicknesses d ≥ 1 m, which is unlikely under large ice sheets, and which might require so much uplift that it would fracture the ice and produce broadband sources that we do not detect. Higher values of p would require cracks so small that we consider them unlikely to serve as viable acoustic sources. With the channel model yielding a resonating cavity of L = 90 m, and the crack models indicating resonant cavities in the range of L = 20 to 60 m, the resonating cavity has one horizontal dimension of order tens of meters.
 Additional consideration of the subglacial environment and of our seismic data suggests that the observed resonance is from a crack tens of meters wide (measured transverse to ice and water flow) that originates from and remains connected to a lake upstream during propagation, possibly as a flood wave or sheet similar to those inferred for certain jökulhlaups in Iceland [e.g., Bjornsson, 2003; Flowers et al., 2004]. Following Engelhardt and Kamb , if the propagating water mass is unconnected to a lake upstream (a drop of water released from the source), the water overpressure required for downstream propagation would drive water flow in all directions (including the transverse and upstream directions), changing the “drop” size and thus changing the resonant frequency. Continued connection of the crack to a lake upstream would at least partially stabilize the overpressure driving crack-tip propagation, thus stabilizing crack-tip geometry and the resonant frequency, because of competing physical effects. The enhanced hydrologic conductivity along the crack compared to the preexisting drainage system would raise the overpressure at the crack tip as it propagated downstream, but the head drop from drainage of the lake would lower the crack-tip overpressure. If the resonance occurred along the flow direction, then our inference of a kilometers-or-longer connection to the upstream lake would require that the propagating crack maintained a notable change in thickness along flow to isolate the resonance in a propagating region a few tens of meters long just behind the crack tip. Resonance within the head of a comet or a tadpole connected to a thinner, non-resonant tail may be a useful analogy. However, the monochromatic nature of the events would then suggest a “comet head” either much wider or much narrower than tens of meters so as not to excite a second transverse resonance (or coincidentally almost exactly equant at all times), which we consider unlikely. Some uncertainty remains, however, our favored hypothesis, pending further data collection, is that the resonance most likely occurred transverse to water and ice flow, in a crack tens of meters wide that remained connected at the upstream end to a subglacial lake.