Linking off-fault strain to rate-and-state friction nucleation: Implications for monitoring precursory velocity changes

Precursory signals preceding large earthquakes are commonly attributed to the acceleration of localized slip during rupture nucleation, yet their spatial expression in the surrounding medium remains poorly constrained. Here, we model the evolution of off-fault strain during earthquake nucleation governed by rate-and-state friction. Our results show that strain accumulates gradually during the early nucleation phase and then accelerates sharply, exceeding a threshold of ε ~ 10^-7—comparable to natural strain levels and detectable by modern strainmeters and geodetic instruments—tens to hundreds of days before instability, depending on the uncertainty in the characteristic slip distance D_c and effective normal stress σ_eff. Approximately 0.7 times the nucleation duration prior to failure, the strained region (ε > 10^-7) extends to distances exceeding one nucleation length away from the fault and spans most of its entire length. We further show that σ_eff  controls both the magnitude and spatial distribution of strain, whereas D_c primarily influences the spatial extent of the strained region. Assuming a representative value for the sensitivity of seismic velocity changes to strain (η ≈ 10⁴), the predicted strain amplitudes correspond to ~0.1%-100% changes in seismic velocity, well above the detection limits of ambient-noise monitoring. A comparison between strain footprints and seismic wavelengths further suggests that analysis of short-period noise (T = 0.1 - 1 s) would be most favorable for identifying these precursory signals. Together, these findings directly link nucleation theory to observable field-scale precursors and provide a physics-based framework for precursor identification in natural fault systems.