Gutenberg-Richter Law & Seismic SOC
log N = a − bM · Omori aftershock decay · Burridge-Knopoff spring-block model
Gutenberg-Richter law: log₁₀N(≥M) = a − bM. The b-value ≈ 1 universally (tectonic = 1, volcanic ≈ 2). Each unit increase in M → 10× fewer earthquakes but ~32× more energy (E ∝ 10^(1.5M)).
Omori-Utsu law for aftershocks: n(t) = K/(t+c)^p, p ≈ 1. Stack aftershocks after a large event to see the power-law decay.
Self-organized criticality (Bak-Tang-Wiesenfeld 1987, Olami-Feder-Christensen 1992): spring-block model self-organizes to a critical state where avalanche sizes follow a power law — no tuning required.