Aftershock production rate of driven viscoelastic interfaces

TL;DR

This paper investigates the statistical behavior of aftershocks in driven viscoelastic interface models, revealing exponential decay with single relaxation time and power-law decay with wave-vector dependent relaxation, aligning with the Omori law.

Contribution

It provides an analytical and numerical analysis of aftershock decay laws in viscoelastic interface models, highlighting the influence of relaxation mechanisms on decay behavior.

Findings

Exponential decay of aftershocks with single relaxation time.

Power-law decay of aftershocks with wave-vector dependent relaxation.

Decay exponents are influenced by relaxation factors.

Abstract

We study analytically and by numerical simulations the statistics of the aftershocks generated after large avalanches in models of interface depinning that include viscoelastic relaxation effects. We find in all the analyzed cases that the decay law of aftershocks with time can be understood by considering the typical roughness of the interface and its evolution due to relaxation. In models where there is a single viscoelastic relaxation time there is an exponential decay of the number of aftershocks with time. In models in which viscoelastic relaxation is wave-vector dependent we typically find a power law dependence of the decay rate, compatible with the Omori law. The factors that determine the value of the decay exponent are analyzed.