ETAS model: branching aftershock sequence following n(t) = K/(t+c)^p
The Omori-Utsu law n(t) = K/(t+c)^p describes how aftershock rate decays after a mainshock.
The ETAS (Epidemic Type Aftershock Sequence) model adds branching: each aftershock can itself
trigger further aftershocks with productivity ∝ 10^(α·m). Magnitude distribution follows
Gutenberg-Richter: log₁₀N(≥m) = a − bm with b≈1. The log-log rate plot reveals the
Omori power law slope −p.