Spatiotemporal correlations of earthquakes in the continuum limit of the one-dimensional Burridge-Knopoff model

TL;DR

This study investigates the spatiotemporal correlations in the one-dimensional Burridge-Knopoff earthquake model, examining how these properties change as the model approaches the continuum limit with and without viscosity, revealing the potential disappearance of doughnut-like quiescence.

Contribution

It provides a systematic analysis of the continuum limit of the 1D Burridge-Knopoff model, highlighting the effects of viscosity and the conditions under which certain seismic phenomena vanish.

Findings

Many properties of the discrete model are preserved in the continuum limit with viscosity.

The size of the minimum earthquake decreases as block size shrinks.

Doughnut-like quiescence may disappear in the continuum limit, indicating it's related to the model's short-length scale.

Abstract

Spatiotemporal correlations of the one-dimensional spring-block (Burridge-Knopoff) model of earthquakes, either with or without the viscosity term, are studied by means of numerical computer simulations. The continuum limit of the model is examined by systematically investigating the model properties with varying the block-size parameter a toward a\to 0. The Kelvin viscosity term is introduced so that the model dynamics possesses a sensible continuum limit. In the presence of the viscosity term, many of the properties of the original discrete BK model are kept qualitatively unchanged even in the continuum limit, although the size of minimum earthquake gets smaller as a gets smaller. One notable exception is the existence/non-existence of the doughnut-like quiescence prior to the mainshock. Although large events of the original discrete BK model accompany seismic acceleration together with a doughnut-like quiescence just before the mainshock, the spatial range of the doughnut-like quiescence becomes narrower as a gets smaller, and in the continuum limit, the doughnut-like quiescence might vanish altogether. The doughnut-like quiescence observed in the discrete BK model is then a phenomenon closely related to the short-length cut-off scale of the model.