Delayed State Evolution in Rate-and-State Earthquake Nucleation: Amplification, Localization, and Scaling

Abstract. Rate-and-state friction assumes instantaneous adaptation of state to slip velocity, but the consequences of this temporal assumption for earthquake nucleation remain poorly constrained. We introduce a constitutive response time t_c into ageing-law feedback and isolate its effect in a spatially distributed fault model. Eight simulations use the same Master configuration and differ only in t_c = 0–0.12 s. Peak velocity increases by approximately 87 %, from 7.38 × 10⁻³ to 1.38 × 10⁻² m s⁻¹, while finite delays permit local crossing of 10⁻² m s⁻¹. The response separates into a moderate-velocity footprint that remains approximately 0.918 km wide and a delay-sensitive high-velocity core that expands to approximately 0.449 km. The response remains localized, separating constitutive amplification from subsequent large-scale propagation. To our knowledge, this is the first spatially distributed demonstration that explicit finite response time in ageing-law feedback can create a high-velocity inner core within a localized nucleation region. The diagnostic Π_d = t_c V_max/D_c relates delay to state-evolution time. The results establish temporal state adaptation as an independent constitutive dimension and provide benchmarks for laboratory calibration and fully dynamic modelling.