This is a quasi-dynamic slip-weakening fault model (Rice, 1993): a 1-D chain of fault patches loaded by steady tectonic stressing and coupled elastically to their neighbours. Each patch's frictional strength drops linearly with slip over a critical distance Dc (Ida 1972 / Palmer & Rice 1973):
τ_strength(δ) = τ_d + (τ_s − τ_d) · max(0, 1 − δ/Dc)
τ_local(x,t) = τ_bg(t) + k·(s_{x−1} − 2s_x + s_{x+1})
slip rate v = max(0, τ_local − τ_strength) / η, η = μ / (2·Vs)
η is the radiation-damping coefficient that stands in for full elastodynamics: it caps how fast a patch can release its excess stress, so the rupture front can't outrun the physics — but it also lets the front's speed emerge on its own from μ, the stress drop, and Dc, rather than being set by hand.
- Stress Drop Δτ — the static-minus-dynamic strength; more stored energy per patch drives a faster, larger rupture.
- Crustal Rigidity μ — sets both the elastic coupling between patches and the shear-wave speed reference; stiffer rock lets stress transfer ahead of the front more efficiently.
- Slip-Weakening Dc — the breakdown-zone size; a larger Dc spreads the fracture energy Gc = ½Δτ·Dc over more slip, slowing nucleation.
- Loading Rate — how fast background tectonic stress rebuilds after an event (compressed to seconds here so a full seismic cycle is watchable).
When the front's measured speed passes the shear-wave speed Vs (dashed threshold — the real onset is the Rayleigh speed, ≈0.92·Vs), the rupture goes supershear: a regime confirmed seismically in a handful of real strike-slip earthquakes (1999 İzmit and Denali, 2001 Kunlun) where the front briefly outruns its own shear waves and a Mach cone of ground motion forms ahead of it. Magnitude is estimated from M₀ = μ·(rupture length)·(15 km seismogenic width)·(mean slip), Mw = ⅔log₁₀M₀ − 6.07 (Hanks & Kanamori, 1979).