Fault Mechanics: From Elastic Rebound to Earthquake

Elastic rebound: the earthquake cycle

After studying ground deformation across the 1906 San Francisco earthquake, Harry Fielding Reid proposed elastic rebound theory, still the foundation of earthquake physics. The crust on either side of a locked fault deforms elastically, like a bent spring, as plates move, storing strain energy. When accumulated stress exceeds the fault's frictional strength, it slips, the rock springs back, and the stored energy radiates away as seismic waves. A fault accumulating strain for 150 years can release it all in under a minute — a power amplification of roughly eight orders of magnitude.

Mohr-Coulomb failure and stick-slip

The Mohr-Coulomb failure criterion says a fault slides when shear stress exceeds frictional resistance, which depends on the normal stress clamping the fault shut minus the pore fluid pressure pushing it apart.

τ ≥ C + μ_f·(σ_n − P)
τ = shear stress   C = cohesion (~0 on old faults)
μ_f = friction coefficient (~0.6-0.85, Byerlee's law)
σ_n = normal stress   P = pore fluid pressure

Injecting fluid underground — wastewater disposal, geothermal stimulation, reservoir filling — can trigger induced seismicity precisely because it unclamps faults already close to failure. Faults exhibit stick-slip behaviour: they stick under friction, load up stress, then slip suddenly. Burridge and Knopoff's 1967 spring-block model reproduces this, with each block sticking until spring force overcomes static friction, then slipping and loading its neighbours in turn. The decisive ingredient is velocity-weakening friction, which makes the slip unstable rather than a smooth creep, and the model spontaneously produces a power-law spectrum of slip sizes without any tuning — a textbook case of self-organised criticality.

Seismic moment and magnitude

The most physically meaningful measure of earthquake size is the seismic moment M₀, which captures the actual work done by the rupture.

M₀ = μ·A·D            (μ ≈ 30 GPa, A = rupture area, D = mean slip)
M_w = (2/3)·log₁₀(M₀) − 6.07
+1 magnitude unit  → ~31.6× more energy
+2 magnitude units → ~1000× more energy

Older local-magnitude scales like Richter saturate for great earthquakes; moment magnitude does not, which is why it is the standard scale used by seismological agencies today. Because M₀ scales with rupture area times slip, the largest events — the 2011 Tohoku (M9.0) and 2004 Sumatra-Andaman (M9.1) earthquakes — required subduction megathrusts hundreds to over a thousand kilometres long.

The Gutenberg-Richter law and early warning

Plot the log of earthquake frequency against magnitude and you get a straight line spanning many orders of magnitude: log₁₀N = a − bM, with b ≈ 1.0 typical of tectonic regions, meaning each unit drop in magnitude brings roughly ten times more earthquakes. This power-law scaling — no characteristic earthquake size, just a smooth spectrum from microquakes to megathrusts — is the statistical fingerprint of self-organised criticality, and it underpins modern probabilistic seismic hazard assessment. Because P-waves (~6 km/s) always outrun the slower, damaging S-waves (~3.5 km/s), and electromagnetic alerts travel at light speed, earthquake early warning systems like Japan's network or California's ShakeAlert can detect the harmless P-wave near the epicentre and broadcast a warning seconds to tens of seconds before the destructive shaking arrives.

Frequently asked questions

Try it live

Everything above runs in your browser — open Earthquake Fault and tune loading rate and friction to watch stress accumulate, trigger stick-slip rupture, and see the Gutenberg-Richter b-value emerge from the resulting event catalogue. Nothing is installed, nothing is uploaded.