A rate-state model for aftershocks triggered by dislocation on a rectangular fault: a review and new insights

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R. Console
F. Catalli


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 perturbated 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 10M. 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.

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How to Cite
Console, R. and Catalli, F. (2006) “A rate-state model for aftershocks triggered by dislocation on a rectangular fault: a review and new insights”, Annals of Geophysics, 49(6), pp. 1259–1273. doi: 10.4401/ag-3095.

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