On entropy and clustering in earthquake hypocentre distributions

Abstract

The degree of clustering or disorder within earthquake distributions may be measured using the concept of entropy. A method for calculating the entropy of any 3-D point set (e.g. earthquake foci) is presented. This makes use of Voronoi cells (convex polyhedra representing nearest neighbour regions) to measure point density in three dimensions. An estimate of event density can be determined directly from the size of Voronoi cells. Normalizations are introduced to the denition of entropy that allow data sets containing dierent numbers of events and occupying dierent volumes to be compared quantitatively, for example, earthquake catalogues from dierent tectonic regimes. Our results show a clear correlation between earthquake entropy and tectonic regime. The most ordered are the mid-ocean ridges, followed by the subduction zones and nally intraplate seismicity.