Single-Link Cluster Analysis As A Method to Evaluate Spatial and Temporal Properties of Earthquake Catalogues

Abstract

SUMMARY Single-link cluster analysis is a straightforward method to quantitatively measure the degree of clustering or isolation of groups of elements in a set, such as a catalogue of earthquakes. to apply single-link cluster analysis to a set of N earthquakes, individual earthquakes are first linked to their nearest neighbours to form event sub-groups. the process is then repeated and each sub-group linked to its nearest neighbour, recursively, until N-1 links are found to join all the earthquakes. This paper shows how knowledge of these links can be used to divide a group of earthquakes into any number of spatial clusters. With various modifications this analysis can identify earthquake nests, isolated events, aftershock sequences, and zones of seismic quiescence. to illustrate this method we apply it to; (i) a global data set of 2178 earthquakes having mb of 5.8 or greater reported by the International Seismological Centre (ISC) between 1964 and February 1986, and (ii) sets of earthquakes having mb of 4.9 and greater as reported by the ISC, occurring in Central America and in the Aleutians. to facilitate comparison with real data, this study also investigates the distribution of link lengths for synthetic events placed randomly on 1-D (circular line), 2-D (circular area) and 3-D (spherical volume) geometries. If we remove links between nuclear explosions from the ISC data, the resulting link distribution is quite similar to that for synthetic events placed along a 1-D fault. For the shortest links, the similarity improves markedly if the synthetic fault has a finite width, or if relative location errors cause events to be located away from the fault trace, with a standard deviation of about 15 km.