Abstract
We compute the static displacement, stress, strain and the Coulomb failure stress produced in an elastic medium by a finite size rectangular fault after its dislocation with uniform stress-drop but a non uniform dislocation on the source. The time-dependent rate of triggered earthquakes is estimated by a rate-state model applied to a uniformly distributed population of faults whose equilibrium is perturbed by a stress change caused only by the first dislocation. The rate of triggered events in our simulations is exponentially proportional to the shear stress change, but the time at which the maximum rate begins to decrease is variable from fractions of hour for positive stress changes of the order of some MPa, up to more than a year for smaller stress changes. As a consequence, the final number of triggered events is proportional to the shear stress change. The model predicts that the total number of events triggered on a plane containing the fault is proportional to the 2/3 power of the seismic moment. Indeed, the total number of aftershocks produced on the fault plane scales in magnitude, M, as 10 M . Including the negative contribution of the stress-drop inside the source, we observe that the number of events inhibited on the fault is, at long term, nearly identical to the number of those induced outside, representing a sort of conservative natural rule. Considering its behavior in time, our model does not completely match the popular Omori Law; in fact it has been shown that the seismicity induced closely to the fault edges is intense but of short duration, while that expected at large distances (up to some tens times the fault dimensions) exhibits a much slower decay.
Highlights
Studying the space-time interaction of earthquakes is important for the comprehension of earthquakes, and for its possible application to the assessment of seismic hazard.In this paper we revisit the physical modeling of the interaction between seismic events, seeking a relationship between the source parameters of an earthquake and the rate of all other earthquakes that follow it
We assume that the time-dependent behavior of the seismicity triggered by a shear stress change in a population of faults is described by the rate-state model introduced by Dieterich (1992, 1994) where the constitutive model proposed by Ruina (1983) and Dieterich
This is a simple consequence of the proportionality between the stress drop, ∆σ, and the shear stress change, ∆τ, at any point of the space around the source; it is an example of the proportionality expressed in equation 7 between ∆τ and the total number of triggered events, integrated on the whole space
Summary
Studying the space-time interaction of earthquakes is important for the comprehension of earthquakes, and for its possible application to the assessment of seismic hazard. The seismicity rate increases in general where the stress change (called Coulomb Stress Change) is positive, according to the Coulomb model (Mendoza and Hartzell , 1988; Boatwright and Cocco, 1996; Stein et al, 1997; Gomberg et al, 1998, 2000; Harris, 1998; King and Cocco, 2001; Stein, 1999; Toda and Stein, 2000; Kilb et al, 2002; Belardinelli et al, 2003; Nostro et al, 2005) These studies were able to give a physical interpretation for earthquake interaction observed in specific real cases, but were not suitable for the general application of the model in predictive way that can be tested for example using the information contained in a seismic catalog. The results of simulations are analyzed to find out the scaling relationships existing between the free parameters of the model and the expected seismicity in a way that will allow the validation of the model by real observations
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