Abstract:S U M M A R YT h e problem of aftershock identification in earthquake catalogues is studied. Some empirical methods are considered and quantitavely analysed.Game theory approach is applied t o formulate the problem allowing a whole class of optimal methods of aftershock identification. Each method is optimal depending on the goals and gives the best trade-off between the number of missed aftershocks and the number of incorrectly identified ones. Some illustrations of the new approach to the aftershock identifi… Show more
“…Since there is no widely accepted criteria to define aftershocks [Gardner and Knopoff, 1974;Reasenberg, 1985;Molchan and Dmitrieva, 1992], we test different proposed criteria.…”
Section: Estimation Of α For Southern California Seismicitymentioning
confidence: 99%
“…A few studies measured directly α from aftershocks sequences, using a fit of the number of aftershocks as a function of the mainshock magnitude [Singh and Suarez, 1988;Yamanaka and Shimazaki, 1990;Molchan and Dmitrieva, 1992;Drakatos et al, 2001]. These studies yield α-value close to 1, but the limited range of the mainshock magnitude considered and the large scatter of the number of aftershocks per mainshock do not allow an accurate estimation of α.…”
Section: Introductionmentioning
confidence: 99%
“…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 .…”
Using a catalog of seismicity for Southern California, we measure how the number of triggered earthquakes increases with the earthquake magnitude. The trade-off between this scaling and the distribution of earthquake magnitudes controls the relative role of small compared to large earthquakes. We show that seismicity triggering is driven by the smallest earthquakes, which trigger fewer aftershocks than larger earthquakes, but which are much more numerous. We propose that the non-trivial scaling of the number of aftershocks emerges from the fractal spatial distribution of aftershocks.
“…Since there is no widely accepted criteria to define aftershocks [Gardner and Knopoff, 1974;Reasenberg, 1985;Molchan and Dmitrieva, 1992], we test different proposed criteria.…”
Section: Estimation Of α For Southern California Seismicitymentioning
confidence: 99%
“…A few studies measured directly α from aftershocks sequences, using a fit of the number of aftershocks as a function of the mainshock magnitude [Singh and Suarez, 1988;Yamanaka and Shimazaki, 1990;Molchan and Dmitrieva, 1992;Drakatos et al, 2001]. These studies yield α-value close to 1, but the limited range of the mainshock magnitude considered and the large scatter of the number of aftershocks per mainshock do not allow an accurate estimation of α.…”
Section: Introductionmentioning
confidence: 99%
“…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 .…”
Using a catalog of seismicity for Southern California, we measure how the number of triggered earthquakes increases with the earthquake magnitude. The trade-off between this scaling and the distribution of earthquake magnitudes controls the relative role of small compared to large earthquakes. We show that seismicity triggering is driven by the smallest earthquakes, which trigger fewer aftershocks than larger earthquakes, but which are much more numerous. We propose that the non-trivial scaling of the number of aftershocks emerges from the fractal spatial distribution of aftershocks.
“…In order to effectively measure this causal clustering, we first must isolate mainshock-aftershock pairs. This has traditionally been done using space-time window techniques, similar to declustering methods [Gardner and Knopoff, 1974;Molchan and Dmitrieva, 1992]. These methods, although very simple to implement, are known to depend on relatively arbitrary parameters.…”
[1] We investigate how aftershocks are spatially distributed relative to the mainshock. Compared to previous studies, ours focuses on earthquakes causally related to the mainshock rather than on aftershocks of previous aftershocks. We show that this distinction can be made objectively but becomes uncertain at long time scales and large distances. Analyzing a regional earthquake data set, it is found that, at time t following a mainshock of magnitude m, the probability of finding an aftershock at distance r relative to the mainshock fault decays as r −g , where g is typically between 1.7 and 2.1 for 3 ≤ m < 6 and is independent of m, for r less than 10 to 20 km and t less than 1 day. Uncertainties on this probability at larger r and t do not allow for a correct estimation of this spatial decay. We further show that a static stress model coupled with a rate-and-state friction model predicts a similar decay, with an exponent g = 2.2, in the same space and time intervals. This suggests that static stress changes could explain the repartition of aftershocks around the mainshock even at distances larger than 10 times the rupture length.Citation: Marsan, D., and O. Lengliné (2010), A new estimation of the decay of aftershock density with distance to the mainshock,
“…There is no standard definition of aftershocks, but several have been used for specific purposes. Molchan and Dmitrieva (1992) argue that aftershock identification depends on research goals. K2005 uses an aftershock definition in which any event within a time and space window of a previous larger event is labeled an "aftershock."…”
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