Similarity in seismic source scaling relations for tectonic and volcanic processes

It is well known that many brittle failure processes follow self-similar scaling relationships. Both tectonic earthquakes and fractures created during laboratory experiments have source dimensions that follow power law distributions. Here, using seismic observations from the 1998 to 2011 eruption of Volcan de Colima, an andesite volcano in Mexico, we observe analogous scaling relationships for seismicity produced by pyroclastic flows, rockfalls and volcanic explosions. Using duration as a measure of event size, we find that the seismic signals generated by pyroclastic flows and rockfalls during periods of lava extrusion have frequency–size relationships that follow power-law distributions over the full range of observed event sizes. Such observations are typical of fractal sets and may suggest self-similarity in the dimensions of fractures produced by the gravitational collapse of lava structures. When using a counter force of eruption as the measure of event size, volcanic explosion earthquakes also follow power-law distributions. However, as demonstrated by the Kolmogorov–Smirnov tests, differences in scaling relationships are observed for explosion earthquakes with the counter force of eruption smaller and larger than 4 × 109 N. This breakdown in self-similarity between small and large events is similar to that observed for tectonic earthquakes.