Fractal Properties of the Distribution of Earthquake Hypocenters

TL;DR

This paper analyzes earthquake hypocenter distributions to determine if their fractal structure resembles the backbone of critical percolation clusters, using spectral dimension calculations across multiple datasets.

Contribution

It provides evidence that earthquake hypocenter distributions have a fractal backbone structure similar to critical percolation clusters, based on spectral dimension analysis.

Findings

Spectral dimension $d_s$ matches that of the percolation backbone.

Hypocenter distributions exhibit fractal properties consistent with percolation theory.

Supports the hypothesis of a percolation-like structure in earthquake hypocenters.

Abstract

We investigate a recent suggestion that the spatial distribution of earthquake hypocenters makes a fractal set with a structure and fractal dimensionality close to those of the backbone of critical percolation clusters, by analyzing four different sets of data for the hypocenter distributions and calculating the dynamical properties of the geometrical distribution such as the spectral dimension $d_s$. We find that the value of $d_s$ is consistent with that of the backbone, thus supporting further the identification of the hypocenter distribution as having the structure of the percolation backbone.