Arrhenius behavior of aftershock sequences

Abstract

Arrhenius expression of static fatigue is used to model aftershock sequences. Assuming that the initial stress condition σ0 at the mainshock origin time t0 is the superposition of the stress before the mainshock and of a stress step σod produced by the dynamic rupture of the mainshock, we may express a general Arrhenius aftershock model as Δ∑(τi) = σod + (RT/γ)Δti where Δ∑(τi) is the cumulative stress drop of mainshock and aftershocks at time τi = ti ‐ t0 ti is the origin time of ith aftershock and Δti = ln ti ‐ ln t0. The fit of the model to the aftershock sequences of May 6, 1976, ML = 6.3 Friuli earthquake (northeastern Italy) and of November 23, 1980, ML = 6.6 Campania‐Basilicata earthquake (southern Italy) is rather good: the coefficient of variation obtained by regression analysis is around 3% and indicates that, at least for the time window length considered (around 780 hours since the mainshock), the cumulative stress drop is entirely coseismic. The present aftershock model is derived from the empirical model t = s exp ((U ‐ γσ)/RT), considering the aftershock origin time to be equivalent to time to fracture t. Results show the validity of this approach. As an example, the derivatives of stress with respect to time to fracture obtained by the analysis of the two sequences are in good agreement with those obtained on laboratory samples; in particular, when the laboratory conditions (confining pressure, characteristics of the specimen) are similar to field conditions, the scatter is between 5 and 50%. The model appears also to be consistent with experimental evidences of direct correlation of p (exponent of Omori law) on surface heat flow.