Viscoelastic Effects in Avalanche Dynamics: A Key to Earthquake Statistics

Abstract

In many complex systems a continuous input of energy over time can be suddenly relaxed in the form of avalanches. Conventional avalanche models disregard the possibility of internal dynamical effects in the interavalanche periods, and thus miss basic features observed in some real systems. We address this issue by studying a model with viscoelastic relaxation, showing how coherent oscillations of the stress field can emerge spontaneously. Remarkably, these oscillations generate avalanche patterns that are similar to those observed in seismic phenomena.

Spatiotemporal Patterns in Ultraslow Domain Wall Creep Dynamics

“…For classic avalanche models (e.g., depinning, directed percolation, Abelian sandpiles), the maximal value for b is 3=4 (which corresponds to the mean field exponent τ ¼ 3=2). From the analysis of the seismic records, one gets [21,22] b ≃ 1 > 3=4. Thus, we observe that, due to the presence of time correlation in the sequence of events, both earthquakes and creep events display an effective exponent τ bigger than the one predicted by simple avalanche models.…”

“…We observe that creep events are organized in compact spatiotemporal patterns in contrast with depinning avalanches that appear randomly distributed along the interface, as well illustrated by the activity maps that supplement the sequence of metastable configurations. Remarkably, there is a similarity of such time correlations between events with the ones observed in real earthquakes, where a large main shock is followed by a cascade of aftershocks [21][22][23][24]. The statistics of the energy dissipated by earthquakes is characterized by the Gutenberg-Richter exponent b, which is equivalent to the …”

“…In this way, our results give a clear interpretation of the FRG predictions. Further, they link the creep motion with the complex earthquake dynamics [21], where a main shock triggers a cascade of aftershocks [21][22][23][24]. We foresee these correlated dynamics being experimentally accessible by events' detection in ferromagnetic films [4].…”

Linking scales in sea ice mechanics

“…(5) Viscous-like relaxation of elastic stresses should be considered [66]. This introduces a viscosity η, hence a relaxation time λ = η/E (where E is an elastic modulus) that sets the characteristic time scale of direct aftershock sequences.…”

Power-law rheology controls aftershock triggering and decay

“…Viscous dumping introduces characteristic time and length scales into the problem and allows to consider a continuum limit of the slider-block type models455153. Introduction of viscoelastic effects, in order to study the relaxation phenomenon, has been recently performed in the context of the viscoelastic interface moving in a depinning potential5455. The decay rates of aftershocks consistent with the Omori-Utsu law, Equation (1), was observed in one particular variant of the model55, although, with the exponent p higher than empirically observed ones.…”