Self-Arresting and Runaway Earthquakes:Nucleation, Propagation, Gutenberg-Richter law and Dragon-King Events

TL;DR

This paper introduces a dissipation-based framework for understanding earthquake nucleation, arrest, and propagation, linking physical rupture processes to seismicity statistics and extreme events like dragon-kings.

Contribution

It distinguishes between nucleation and propagation scales, derives the Gutenberg-Richter law from fault fractal geometry, and interprets run-away ruptures as dragon-king events.

Findings

Identifies two characteristic fault sizes: nucleation and propagation radii.

Derives Gutenberg-Richter law from fault fractal geometry.

Interprets run-away ruptures as extreme, amplifying events.

Abstract

We develop a dissipation-based framework for earthquake rupture on homogeneous faults that explicitly separates the onset of unstable slip from the conditions required for self-sustained rupture propagation. This distinction explains the coexistence of self-arresting earthquakes and run-away ruptures (subshear and supershear events) observed in numerical simulations and empirical studies. We identify two distinct characteristic fault sizes: a nucleation radius controlling the instability of slip, and in general a larger propagation radius controlling whether an unstable rupture can be energetically sustained. Ruptures initiated above the nucleation scale but below the propagation scale spontaneously arrest. We further derive the Gutenberg-Richter law for self-arresting earthquakes by linking rupture physics to the fractal geometry of faulting. Finally, we interpret run-away ruptures as extreme events generated by an amplifying mechanism, consistent with the dragon-king concept. These results provide a unified physical basis for earthquake initiation, arrest, and seismicity statistics.