Scaling relationship for Vulcanian explosions derived from broadband seismic signals

A proposed conceptual model of Vulcanian explosions describes the volcanic explosion process as consisting of two stages (the movement of the fragmented magma to the surface and a subsequent explosion) and is constrained by four source parameters inferred from broadband seismic records (the counter force of the eruption F acting in the conduit before an explosion and governing the fragmented magma movement to the surface, the time D1 of the movement of fragmented magma in the conduit before an explosion, the duration of the explosion in the conduit D2, and the energy E of the explosion). Our paper discusses, within the framework of the proposed conceptual model, the source scaling relationship inferred from the parameters of 135 Vulcanian explosions occurring at two Mexican andesitic volcanoes: Volcán de Colima and Popocatépetl during 1996–2006. Two groups of explosions are discriminated, small (E < 1011 J) and large (E ≥ 1011 J), characterized by a different type of scaling and origin. The scaling of the counter force F on the source duration τ of the single force is different for large and small explosions but is characterized by the same tendency of F ∼ τ2. According to the dependence E versus D1, large explosions are generated within the narrow depth zone in the conduit corresponding to D1 from 3.5 to 7.5 s while small explosions are generated within a wide depth zone corresponding to D1 from 0 to 13 s. The counter force of the eruption strongly governs the energy of explosions. The duration of the explosion at the explosion surface within the conduit, D2, has a tendency to negatively correlate with the energy of the explosion.