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

TL;DR

The paper introduces a dissipation-based framework that separates earthquake initiation from propagation on homogeneous faults by identifying two key length scales: the nucleation radius $R_{ ext{nuc}}$ and the propagation radius $R_{ ext{prop}}$. Instability occurs when $R_0 > R_{ ext{nuc}}$, but self-sustained propagation requires $R_0 > R_{ ext{prop}}$, with $R_{ ext{nuc}}$ and $R_{ ext{prop}}$ derived from elastic unloading, frictional weakening, and dissipation via a slip-weakening law. It derives a Gutenberg-Richter distribution for self-arresting earthquakes by linking the fractal fault geometry, via the fractal dimension $D_f$, to the distribution of propagation thresholds, yielding $p(M_0) \propto M_0^{-igl(1+(D_f-1/2)/3\bigr)}$, which reproduces GR with $b \approx 2/3$ for $D_f \approx 2.5$. The authors reinterpret run-away ruptures as dragon-kings—extreme events driven by amplification beyond local dissipation—providing a coherent physical basis for initiation, arrest, and seismicity statistics, and connecting nucleation physics to the statistics of large earthquakes.

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.

Figures (1)

• Figure 1: Phase diagram in the plane $[ {\hat{D}}_c ; {\hat{T}}_e]$, defined by expressions (\ref{['eq:ar1']}), taken from WeiSAR2021 on which the curve ${\hat{T}}_e = 0.5 \sqrt{{\hat{D}}_c}$ is superimposed (dashed red line) as obtained from the derivation leading to equation (\ref{['eq:pwyyf8f89']}) with $\eta=2$. The vertical blue dashed line corresponds to $\hat{D}_c = 1/C_k$ (equation (\ref{['eq:pwyyf8f89']})) with $C_k \approx 1.15$, which separates the slow and fast self-arresting earthquakes.