Earthquakes big and small: same physics, different boundary conditions

Self-similarity indicates that large and small earthquakes share the same physics, where all variables scale with rupture length $L$. Here I show that rupture tip acceleration during the start of dynamic rupture (break-out phase) is also self-similar, scaling with $L_c$ in space and $L_c\mathrm{/}{C}_{lim}$ in time (where $L_c$ is the breakout patch length and $C_{lim}$ the limiting rupture velocity in the subsonic regime). Rupture acceleration in the breakout phase is slower for larger initial breakout patches $L_c$. Because small faults cannot host large breakout patches, a large and slower initial breakout may be indicative of a potentially large final earthquake magnitude. Initial moment rate ${\dot{M}}_o$ also grows slower for larger $L_c$, therefore it may reflect fault dimensions and carry a probabilistic forecast of magnitude as suggested in some Early Warning studies. This result does not violate causality and is fully compatible with the shared fundamental, self-similar physics across all the magnitude spectrum.