Gutenberg-Richter-like relations in physical systems

TL;DR

This study investigates the energy distribution in earthquakes, revealing scale-invariant behavior with a specific exponent, and explores the physical mechanisms behind different regimes of seismic activity.

Contribution

It introduces a comprehensive analysis of earthquake energy distributions and identifies the physical mechanisms governing different scaling regimes.

Findings

Real earthquake energy distributions follow a power-law with exponent ~1.67.

Earthquake-like behavior occurs for exponents between 1.5 and 2.0.

Different regimes are governed by fault dynamics, external energy supply, or small event dominance.

Abstract

We analyze regional earthquake energy statistics from the Southern California and Japan seismic catalogs and find scale-invariant energy distributions characterized by an exponent $\tau \simeq 1.67$. To quantify how closely scale-invariant dynamics with different exponent values resemble real earthquakes, we generate synthetic energy distributions over a wide range of $\tau$ under conditions of constant activity. Earthquake-like behavior, in a broad sense, is obtained for $1.5 \leqslant \tau < 2.0$. When energy variations are further restricted to be within a factor of ten relative to real earthquakes, the admissible range narrows to $1.58 \leqslant \tau \leqslant 1.76$. We identify the physical mechanisms governing the dynamics in the different regimes: fault dynamics characterized by a balance between slow energy accumulation and release through scale-free events in the earthquake-like regime; externally supplied energy relative to a slowly driven fault for $\tau < 1.5$; and dominance of small events in the energy budget for $\tau > 2$