Viscoelastic Interfaces Driven in Disordered Media

Abstract

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The influence of the brittle-ductile transition zone on aftershock and foreshock occurrence

“…Realistic b values of the GR law have already been found by Jagla et al 58,59 in models of only one layer, but including viscoelastic couplings or aging effect in the static friction coefficients 36,[54][55][56][57][58][59][60][61][62] , which in both cases results in an effective additional degree of freedom per lattice site (all these models are spatially extended).…”

“…For this reason, we assume that the viscoelastic interactions 34 in U are implemented assuming that neighboring degrees of freedom are connected by means of a dashpot and a spring placed in series ( Fig. 1) 35,36 . The constitutive equations for the layer U reads:…”

“…Major examples of class I models are those implementing a viscous relaxation [48][49][50][51] or a reductions in fault friction by means of RSF laws 50 . Concerning class II, the relevance of frictional heterogeneities in earthquake triggering has been deeply investigated 52 and, in particular, the OFC model with a random fth corresponds to the quenched Edwards-Wilkinson (qEW) model 35,36,53 . This is a typical model for driven elastic interfaces in a random media and, in this case, it is well established that the seismic moment is power-law distributed with b independently of the value of ϵ 2 .…”

“…Nevertheless, statistical patterns of seismic occurrence are better reproduced by class III models as shown in refs. 36,50,[54][55][56][57][58][59][60][61][62] .…”

“…Indeed under this short-range approximation, aftershocks can be triggered only within or at the boundary of the rupture zone, as was shown in refs. 35,36 . Finally, we note that this spatial clustering law can be related to the m-logA scaling of Fig.…”