Theoretical constraints on tidal triggering of slow earthquakes

TL;DR

This study investigates how tiny tidal-like stress perturbations can trigger slip on velocity-weakening faults near the RSF critical stiffness. Using a quasi-dynamic spring-block model with aging-rate-and-state friction, the authors develop a nondimensional framework with control parameters $P_T$ and $P_ extsigma$ to map when resonance enhances slip, producing creeping, slow, or fast events and varying the radiation efficiency. They find a finite triggering window (roughly $P_ extsigma o 0.2$ and $2 extless P_T extless 70$) where tidal forcing can induce observable slip, with phase locking occurring at specific periods and phases; the mean phase shifts from tidal stress to stress rate as $P_T$ increases. The results constrain frictional properties (e.g., $a \sigma_0$ in the kPa range and micrometer-scale $d_c$) and offer a framework for interpreting tidally modulated tremor/LFE activity, including energy partitioning via $ar{ ext{eta}}_R$ and phase-dependent triggering signatures. Overall, the work provides a physically grounded mechanism for tidal triggering, robust to several model variants, and links laboratory-scale frictional properties to large-scale seismic observations through a scalable, parametric description.

Abstract

Tidal stress is a globally acting perturbation driven primarily by the gravitational forcing of the Moon and the Sun. Understanding how tidal stresses can trigger seismic events is essential for constraining tectonic environments that are sensitive to small stress perturbations. Here, employing a spring-block with rate-and-state friction, we investigate tidal triggering on velocity-weakening stable sliding faults with stiffness slightly exceeding the critical stiffness. We first apply idealized step-like and boxcar normal stress perturbations to demonstrate a resonance-like amplification of slip rate when the perturbation period approaches the intrinsic frictional timescale of state evolution. Next, we perform nondimensional analyses and numerical simulations with harmonic tidal-like perturbations to identify the key parameters controlling tidal triggering and their admissible ranges. Triggered slip events are further characterized using physically interpretable quantities, including radiation efficiency and tidal phase. Our results show that even small stress perturbations can trigger periodic as well as complex slip events on stable sliding faults. The triggering behavior is primarily controlled by the normalized perturbation period and the normalized perturbation amplitude. An increase in the normalized period shifts event timing from the peak of tidal stress toward the peak of stress rate, whereas increasing the normalized amplitude promotes a transition from slow to fast events. The parameter space permitting triggered events suggests that the parameter which characterizes the instantaneous frictional strength of an interface, should not exceed tens to hundreds of kilopascals, and that the characteristic slip distance for frictional weakening is likely on the order of micrometers.

Figures (11)

• Figure 1: Spring–block model under stress perturbations. The block slides with velocity $V$ under a constant normal stress $\sigma_0$, subject to an imposed normal stress perturbation $\sigma_{\mathrm{p}}(t)$ and an applied shear stress perturbation $\tau_{\mathrm{p}}(t)$. The elastic loading is provided by a spring of stiffness $k$, driven at a constant velocity $V_{\mathrm{ss}}$. The resisting frictional shear stress is denoted by $\tau_f$.
• Figure 2: Responses of slip velocity to step changes in normal stress. (a) Downward step change and (b) Upward step change. Red dashed and blue solid curves correspond to $|\Delta\sigma| = 1~\mathrm{kPa}$ and $2~\mathrm{kPa}$, respectively. The dark gray line with circles indicates the reference case without stress perturbation. The inset in panel (a) illustrates the decaying oscillatory behavior of slip velocity following the transient step change. The other model parameters are listed in Table \ref{['tab:parameters']}.
• Figure 3: Responses of slip velocity to a box-up change in normal stress with $|\Delta\sigma| = 1.0~\mathrm{kPa}$ (the other model parameters are listed in Table \ref{['tab:parameters']}). (a) Upper: imposed normal stress histories for $T_{\mathrm{box}}=22.8~\mathrm{hours}$ (blue) and $15.6~\mathrm{hours}$ (red), compared with a single upward step (dark gray line with circles). Lower: corresponding slip velocity responses. (b) Maximum slip velocity $V_{\max}$ as a function of $T_{\mathrm{box}}$. The shaded region highlights the range of $T_{\mathrm{box}}$ associated with amplified responses compared to the upward step change.
• Figure 4: Responses of slip velocity to a box-down change in normal stress with $|\Delta\sigma| = 1.0~\mathrm{kPa}$. (a) Upper: imposed normal stress histories for $T_{\mathrm{box}}=22.8~\mathrm{hours}$ (blue) and $13.9~\mathrm{hours}$ (red), compared with a single downward step (dark gray line with circles). Lower: corresponding slip velocity responses. (b) Maximum slip velocity $V_{\max}$ as a function of $T_{\mathrm{box}}$.
• Figure 5: Normalized slip velocity $V/V_{\mathrm{ss}}$ as a function of time under periodic normal stress perturbations. Panels (a)-(c) show cases with fixed perturbation amplitude $P_{\sigma}=0.892$ and increasing perturbation period $P_T=1.995$, $10.000$, and $94.496$, respectively, illustrating a transition from creeping to episodic slip and back to quasi-creeping behavior. Panels (d)-(f) show cases with fixed perturbation period $P_T=10.000$ and increasing perturbation amplitude $P_{\sigma}=0.208$, $0.406$, and $0.946$, demonstrating progressively stronger slip responses. Dashed horizontal lines indicate velocity thresholds for stable sliding ($V/V_{\mathrm{ss}}=1$), slow events ($10^{3}$), and fast events ($10^{6}$). Time is normalized by $t_*$ (bottom axis) and by the elastic timescale $t_a$ (top axis).