Self-similar aftershock rates

TL;DR

This paper proposes a self-similar model for aftershock rates that aligns with observed earthquake data, resolving a longstanding paradox and potentially improving seismic hazard assessment.

Contribution

It introduces a generalized, self-similar description of aftershock rates consistent with known self-similar features and validated with high-resolution earthquake data.

Findings

Excellent agreement between theory and Southern California earthquake data

Evidence for a unified description of aftershocks and foreshocks

Potential improvements in seismic hazard assessment

Abstract

In many important systems exhibiting crackling noise --- intermittent avalanche-like relaxation response with power-law and, thus, self-similar distributed event sizes --- the "laws" for the rate of activity after large events are not consistent with the overall self-similar behavior expected on theoretical grounds. This is in particular true for the case of seismicity and a satisfying solution to this paradox has remained outstanding. Here, we propose a generalized description of the aftershock rates which is both self-similar and consistent with all other known self-similar features. Comparing our theoretical predictions with high resolution earthquake data from Southern California we find excellent agreement, providing in particular clear evidence for a unified description of aftershocks and foreshocks. This may offer an improved way of time-dependent seismic hazard assessment and earthquake forecasting.