Exponential Distributions in a Mechanical Model for Earthquakes

TL;DR

This paper analyzes a mechanical earthquake fault model and finds that exponential distributions describe event sizes, durations, and block involvement under specific parameter conditions, aligning with recent experimental observations.

Contribution

It demonstrates that exponential distributions naturally arise in a classical earthquake model when elastic constants are similar, providing insight into earthquake statistics.

Findings

Exponential distributions occur in the model within certain parameter ranges.

Similar exponential behavior observed in experimental earthquake-like systems.

The model links elastic constants to statistical distribution types.

Abstract

We study statistical distributions in a mechanical model for an earthquake fault introduced by Burridge and Knopoff [R. Burridge and L. Knopoff, {\sl Bull. Seismol. Soc. Am.} {\bf 57}, 341 (1967)]. Our investigations on the size (moment), time duration and number of blocks involved in an event show that exponential distributions are found in a given range of the paramenter space. This occurs when the two kinds of springs present in the model have the same, or approximately the same, value for the elastic constants. Exponential distributions have also been seen recently in an experimental system to model earthquake-like dynamics [M. A. Rubio and J. Galeano, {\sl Phys. Rev. E} {\bf 50}, 1000 (1994)].