HR: 13:55h
AN: S32D-02    [PDF]
TI: Importance of direct and indirect triggered seismicity and derivation of Bath's law for the largest aftershock
AU: * Sornette, D
EM: sornette@moho.ess.ucla.edu
AF: Department of Earth and Space Sciences and Institute of Geophysics and Planetary Physics, University of California Los Angeles, 3845 Slichter Hall, Los Angeles, CA 90095-1567 United States
AU: * Sornette, D
EM: sornette@moho.ess.ucla.edu
AF: Laboratoire de Physique de la Matiere Condensee, Universite de Nice-Sophia Antipolis, Parc Valrose, Nice, 06106 France
AU: Helmstetter, A
EM: helmstet@moho.ess.ucla.edu
AF: Department of Earth and Space Sciences and Institute of Geophysics and Planetary Physics, University of California Los Angeles, 3845 Slichter Hall, Los Angeles, CA 90095-1567 United States
AB: Using the simple ETAS branching model of seismicity, which assumes that each earthquake can trigger other earthquakes, we quantify the role played by the cascade of triggered seismicity in controlling the rate of aftershock decay as well as the overall level of seismicity in the presence of a constant external seismicity source. We show that, in this model, the fraction of earthquakes in the population that are aftershocks is equal to the fraction of aftershocks that are indirectly triggered and is given by the average number of triggered events per earthquake. Previous observations that a significant fraction of earthquakes are triggered earthquakes therefore imply that most aftershocks are indirectly triggered by the mainshock. For some values of the parameters, the ETAS model also reproduces Bath's law, which states that the average magnitude difference $\langle \Delta m \rangle$ between a mainshock and its largest aftershock is $1.2$, regardless of the mainshock magnitude. We first point out that the standard interpretation of Bath's law [Vere-Jones, 1969] in terms of the two largest events of a self-similar set of independent events is incorrect, because it neglects the selection procedure entering the definition of aftershocks. We reconcile Bath's law with (i) the existence of a universal Gutenberg-Richter (GR) law for all earthquakes and (ii) with the empirical observation (productivity law) that each earthquake of magnitude $m$ triggers other earthquakes at a rate $\sim 10^{\alpha m}$ with $\alpha \approx 0.8$.
DE: 7209 Earthquake dynamics and mechanics
DE: 7223 Seismic hazard assessment and prediction
DE: 7260 Theory and modeling
SC: Seismology [S]
MN: 2003 Fall Meeting