After a mainshock, aftershock rate decays as K/(t+c)^p. The modified Omori law governs this power-law decay. ETAS model shows self-similar cascade structure.
Omori (1894) law: n(t) = K/(t+c)^p
Modified (Utsu 1961): p ≈ 0.9–1.5, c ≈ 0.05–0.5 day
Gutenberg-Richter: log₁₀N = a - bM, b≈1
Båth's law: Largest aftershock ≈ M₀ - 1.2
ETAS model (Epidemic Type Aftershock Sequence): each quake triggers children via Poisson process. Self-similar branching process → subcritical if K·10^(α-b)M < 1.
Log-log plot (right) shows power-law Omori decay.