Anomalous diffusion in volcanic seismicity

Volcanic seismicity is of extreme interest in view of complexity science. It
exhibits complex dynamics on complex geometry. Here, the diffusion property
of volcanic earthquakes is discussed based on the data from Mt. Etna. It is
discovered that the jump probability distribution well obeys a standard exponential
law, whereas the waiting-time distribution follows a power law. The consequent
diffusion property is found to be subdiffusive. To understand these results, four
major approaches to anomalous diffusion are examined. In the end, it turns out that
no theories are conclusive, and therefore volcanic seismicity is highly challenging
for complexity science.