Structure of Motifs in Seismic Networks

We report detailed statistical results on the structure of motifs in seismic networks covering four distinct terrain regions. Our main finding is that all seismic networks under investigation display motifs which have a distinct scale-free-like structure. 

The seismic networks were constructed from public seismic data using a standard procedure which relies on splitting the seismic region into equally sized cubes, which are the nodes of the seismic network. Then, placing each earthquake, in chronological order, into the cube corresponding to its epicenter, we define a link between two nodes as a series of two subsequent earthquakes with epicenters in different cubes. Using these seismic networks we study the occurrence of 3-node and 4-node motifs, which are triangles and tetrahedrons of the network, and report a scale-free-like behavior of the area or volume of these motifs weighted by the total energy released by the earthquakes contained in the nodes of the motif.

The statistical properties of motifs, in particular the scaling exponents of the aforementioned scale-free-like distributions, can be used to assess the differences and similarities between different seismic regions, without taking into account the inner workings of the plate tectonics. Our approach is fully customizable as all relevant parameters of the network (e.g., size of the cubes, magnitude of earthquakes, considered timeframe, coordinates of epicenters) can be changed to accommodate virtually all seismic regions.