Omori (1894) discovered that aftershock rate decays as an approximate power law in time. The modified Omori-Utsu law adds the exponent p (typically 0.9–1.5, averaging ~1.1). K is proportional to the mainshock magnitude; c prevents the singularity at t=0 (typically hours to days).
The Gutenberg-Richter relation (log N = a − bM) governs magnitude distribution — each unit increase in magnitude is roughly 10× rarer. Bath's law states the largest aftershock is typically 1.2 magnitude units below the mainshock.
Aftershocks cluster spatially near the mainshock rupture plane, with density falling off as ~1/r². The ETAS model (Epidemic Type Aftershock Sequence) treats each event as potentially triggering its own sequence — a branching process that explains earthquake swarms and aftershock-of-aftershock cascades.