Near mean-field behavior in the generalized Burridge-Knopoff earthquake model with variable range stress transfer

TL;DR

This paper investigates how extending the Burridge-Knopoff earthquake model to include variable-range stress transfer reveals mean-field critical behavior, with implications for understanding earthquake dynamics and other driven systems.

Contribution

It introduces a generalized Burridge-Knopoff model with variable-range stress transfer, highlighting qualitative differences from traditional models and identifying mean-field critical phenomena.

Findings

Long-range stress transfer leads to different behavior than nearest-neighbor models.

The model exhibits quasiperiodic events and mode-switching phenomena.

Results support the existence of a mean-field critical point.

Abstract

Simple models of earthquake faults are important for understanding the mechanisms for their observed behavior in nature, such as Gutenberg-Richter scaling. Because of the importance of long-range interactions in an elastic medium, we generalize the Burridge-Knopoff slider-block model to include variable range stress transfer. We find that the Burridge-Knopoff model with long-range stress transfer exhibits qualitatively different behavior than the corresponding long-range cellular automata models and the usual Burridge-Knopoff model with nearest-neighbor stress transfer, depending on how quickly the friction force weakens with increasing velocity. Extensive simulations of quasiperiodic characteristic events, mode-switching phenomena, ergodicity, and waiting-time distributions are also discussed. Our results are consistent with the existence of a mean-field critical point and have important implications for our understanding of earthquakes and other driven dissipative systems.