Earthquake aftershock networks generated on Euclidean spaces of different fractal geometry

TL;DR

This paper models earthquake aftershock epicenters as networks on fractal spaces, analyzing their statistical features and showing these features are consistent across different fractal geometries.

Contribution

It introduces a model for earthquake aftershock networks on various fractal geometries and compares their statistical properties to observed data.

Findings

Network features are independent of fractal dimension.

Degree and link length distributions match observed earthquake data.

Statistical properties are robust across different fractal geometries.

Abstract

According to some recent analysis (M. Baiesi and M. Paczuski, Phys. Rev. E {\bf 69}, 066106, 2004 \cite{maya1}) of earthquake data, aftershock epicenters can be considered to represent the nodes of a network where the linking scheme depends on several factors. In the present paper a model network of earthquake aftershock epicenters is proposed based on this scheme and studied on fractals of different dimensions. The various statistical features of this network, like degree, link length, frequency and correlation distributions are evaluated and compared to the observed data. The results are also found to be independent of the fractal geometry.