Boundary effects in a random neighbor model of earthquakes

TL;DR

This paper investigates how boundaries affect avalanche distributions in a modified earthquake model, revealing distinct boundary exponents and supporting a mean-field inhomogeneous branching process description.

Contribution

It introduces spatial boundaries into a random neighbor earthquake model and characterizes how boundary conditions influence avalanche size distributions.

Findings

Bulk avalanche exponent approximately 3/2

Boundary avalanche exponents approximately 3/2 and 7/4

Supports inhomogeneous critical branching process as a mean-field description

Abstract

We introduce spatial inhomogeneities (boundaries) in a random neighbor version of the Olami, Feder and Christensen model [Phys. Rev. Lett. 68, 1244 (1992)] and study the distributions of avalanches starting both from the bulk and from the boundaries of the system. Because of their clear geophysical interpretation, two different boundary conditions have been considered (named free and open, respectively). In both cases the bulk distribution is described by the exponent $\tau \simeq {3/2}$. Boundary distributions are instead characterized by two different exponents $\tau ' \simeq {3/2}$ and $\tau ' \simeq {7/4}$, for free and open boundary conditions, respectively. These exponents indicate that the mean-field behavior of this model is correctly described by a recently proposed inhomogeneous form of critical branching process.