Single-Link Cluster Analysis, Synthetic Earthquake Catalogues, and Aftershock Identification

Abstract

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 S, , , B,,, S, and B , 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 = d(d2 + C 2 t 2 ) , where d is the spatial separation of events, t is the time separation, and C = 1 km day-'. Our experience with several synthetic catalogues suggests that an appropriate trial value for D is 9.4 kmln (G) -25.2 km. Here, S, 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.

Spatial variation of seismicity parameters across India and adjoining areas

“…Therefore, the catalog in use must exhibit random space time characteristics. Aftershocks and foreshocks show a major deviation from a Poisson process and several methods have been suggested for the separation of aftershocks from the raw earthquake data (Savage 1972;Gardner and Knopoff 1974;Reasenberg 1985;Davis and Frohlich 1991;Molchan and Dmitrieva 1992). Deleting aftershocks and other dependent events leads approximately to a Poisson, or random data set for a better estimation of return periods of randomly occurring events which is an important goal of seismic hazard studies.…”

Is Earthquake Triggering Driven by Small Earthquakes?

“…The number of aftershocks n M triggered by a mainshock of magnitude M has been proposed to scale with M as [Utsu, 1969;Kagan and Knopoff, 1987;Kagan, 1991;Reasenberg, 1985;1999;Singh and Suarez, 1988;Ogata, 1988;Reasenberg and Jones, 1989;Yamanaka and Shimazaki, 1990;Davis and Frohlich, 1991;Molchan and Dmitrieva, 1992;Hainzl et al, 2000;Drakatos et al, 2001;Felzer et al, 2002] n M ∼ 10 αM .…”

“…While there is a significant amount of literature on the b-value, very few studies have measured accurately the α exponent in real seismicity data. Many studies use α = b without justification [Kagan and Knopoff, 1987;Reasenberg and Jones, 1989;Davis and Frohlich, 1991;Console and Murru, 2001;Felzer et al, 2002]. In this case, small earthquakes are just as important as large earthquakes for the triggering process.…”

K-Means Cluster for Seismicity Partitioning and Geological Structure Interpretation, with Application to the Yongshaba Mine (China)

“…Hierarchical cluster has been applied for seismicity partitioning since the 1990s, and Davis and Frohlich [11], Frohlich and Davis [12], Wardlaw et al [13], Hudyma [14], Hudyma and Potvin [15], Hashemi and Mehdizadeh [16], and Hashemi and Karimi [17] selected the hierarchical clustering technique using single-link analysis/Ward's method to evaluate spatial and temporal properties of earthquake catalogues. However, the hierarchical cluster has a tendency to form seismic events into linear groups [12].…”