Single-link cluster analysis, synthetic earthquake catalogues, and aftershock identification

SUMMARY This paper investigates several aspects of synthetic catalogue generation and aftershock identification schemes. First, we introduce a method for generating synthetic catalogues of earthquakes. This method produces a catalogue which has the geographic appearance of an actual catalogue when the hypocentres are plotted in map view, but allows us to vary the spatial and temporal relationships between pairs of close events. Second, we discuss six statistics to measure certain characteristics of synthetic and actual catalogues. These include four new statistics So, Bo, S1 and B1 which evaluate the distributions of link lengths between events in space and space-time as computed by single-link cluster analysis (SLC). Third, we develop a new scheme for identifying aftershocks in which a group of events forms an aftershock sequence if each event is within a space-time distance D of at least one other event in the group. We define the space-time separation of events by dst=√(d2+C2τ2), where d is the spatial separation of events, τ is the time separation, and C= 1km day-1. Our experience with several synthetic catalogues suggests that an appropriate trial value for D is 9.4 km1/2 (√S1) - 25.2 km. Here, S1, is the median link length using SLC with the metric dsT. Fourth, we generate synthetic catalogues resembling both teleseismic and local network catalogues to evaluate the validity and reliability of this aftershock identification scheme, as well as other schemes proposed by Gardner & Knopoff (1974), Shlien & Toksoz (1974), Knopoff, Kagan & Knopoff (1982), and Reasenberg (1985). Using a simple scoring method, we find that the SLC method compares favourably with other aftershock identification algorithms described in the literature.