Scale free networks of earthquakes and aftershocks

TL;DR

This paper introduces a new correlation metric for earthquakes that automatically classifies events and reveals a scale-free network structure, reproducing known seismic laws and challenging fixed window methods.

Contribution

It proposes a novel correlation metric that constructs earthquake networks without predefined windows, uncovering scale-free properties and consistent seismic laws.

Findings

Aftershock networks are scale free with exponent 2.0.

The Omori law with p=1 is robust over years.

Distance distribution suggests fixed window methods are inadequate.

Abstract

We propose a new metric to quantify the correlation between any two earthquakes. The metric consists of a product involving the time interval and spatial distance between two events, as well as the magnitude of the first one. According to this metric, events typically are strongly correlated to only one or a few preceding ones. Thus a classification of events as foreshocks, main shocks or aftershocks emerges automatically without imposing predefined space-time windows. To construct a network, each earthquake receives an incoming link from its most correlated predecessor. The number of aftershocks for any event, identified by its outgoing links, is found to be scale free with exponent $\gamma = 2.0(1)$. The original Omori law with $p=1$ emerges as a robust feature of seismicity, holding up to years even for aftershock sequences initiated by intermediate magnitude events. The measured fat-tailed distribution of distances between earthquakes and their aftershocks suggests that aftershock collection with fixed space windows is not appropriate.