Distribution of Earthquake Cluster Sizes in the Western United States and in Japan

Earthquakes occur in clusters, which classically are described as foreshock-mainshock-aftershock sequences or swarms. In this paper, every earthquake in a seismicity catalog is assigned to a cluster if it is separated from at least one other event in the cluster by less than Delta t in time and less than Delta r in space. The minimum cluster size is one earthquake. For catalogs that are complete to small magnitudes, this approach is successful in capturing the full spatial extent of an extensive cluster even for Delta r much smaller than the actual cluster dimension. The declustered catalogs are much closer to Poissonian distribution than the originals. This was applied to seismicity catalogs for Japan, Southern California, and Nevada. Cluster sizes measured by the number of earthquakes in the cluster exhibit an approximate power-law frequency distribution. An upper bound to cluster durations is proportional to K-0.5, where K is the number of earthquakes in the cluster. This paper demonstrates an analytical approach suitable for selecting values of Delta t and Delta r that are appropriate for the earthquake catalog.