Continuous Time Random Walks and South Spain Seismic Series

TL;DR

This paper investigates whether Continuous Time Random Walks, modeled by Levy distributions, can explain seismic activity patterns in South Spain, analyzing three earthquake series to validate this approach.

Contribution

It provides empirical validation of CTRW models for seismic data, highlighting their applicability to earthquake waiting times and hypocenter distributions in South Spain.

Findings

Seismic series exhibit scale-invariant behavior consistent with Levy flights.

Qualitative similarity observed across different seismic regions.

Quantitative differences suggest regional variations in seismic dynamics.

Abstract

Levy flights were introduced through the mathematical research of the algebra or random variables with infinite moments. Mandelbrot recognized that the Levy flight prescription had a deep connection to scale-invariant fractal random walk trajectories. The theory of Continuous Time Random Walks (CTRW) can be described in terms of Levy distribution functions and it can be used to explain some earthquake characteristics like the distribution of waiting times and hypocenter locations in a seismic region. This paper checks the validity of this assumption analyzing three seismic series localized in South Spain. The three seismic series (Alboran, Antequera and Loja) show qualitatively the same behavior, although there are quantitative differences between them.