Dynamic Weakening by Acoustic Fluidization during Stick-Slip Motion

The unexpected weakness of some faults has been attributed to the emergence of acoustic waves that promote failure by reducing the confining pressure through a mechanism known as acoustic fluidization, also proposed to explain earthquake remote triggering. Here we validate this mechanism via the numerical investigation of a granular fault model system. We find that the stick-slip dynamics is affected only by perturbations applied at a characteristic frequency corresponding to oscillations normal to the fault, leading to gradual dynamical weakening as failure is approaching. Acoustic waves at the same frequency spontaneously emerge at the onset of failure in the absence of perturbations, supporting the relevance of acoustic fluidization in earthquake triggering.

Figure 1

Time evolution of the top plate position. The inset shows the evolution in a large time interval, while the main panel focuses on a shorter time interval following time $t_{s_0}=0$. In this shorter interval, we observe three small slips, at time $t_{s_0}$, $t_{s_1}=321$, and $t_{s_2}=576$, and a large one at time $t_{s_3}=890$.

Figure 2

(a) Time dependence of the system’s response ${\mathrm{\Pi }}_{+}(t,W-1)$ to perturbations increasing the confining pressure, at different frequencies. (b) The response ${\mathrm{\Pi }}_{+}(t,z)$ for grains belonging to different vertical positions $z$. (c) Frequency dependence of the advance time $\mathrm{\Delta }{t}_a$ of the slips occurring at times $t_{s_1}$, $t_{s_2}$, and $t_{s_3}$, induced by perturbation $P_{+}(t)$. (d) As in (c), for single pulse perturbations increasing the pressure (full symbols) or decreasing the shear stress (open symbols). (e) and (f) show that the characteristic triggering frequency scales as ${\omega }^{\mathrm{tr}}\propto k_n^{1/2}/W$, with $k_n$ grain stiffness and $W$ fault width.

Figure 3

The left column illustrates the response of the top plate to perturbations decreasing the confining pressure (a), increasing the shear stress (b), or decreasing the shear stress (c). The right column illustrates the frequency dependence of the advance time, which is peaked around the acoustic fluidization frequency ${\omega }^{\text{af}}\simeq 1.5\pi$. Symbols are as in Fig. 2.

Figure 4

(a) The map of the logarithm of the power spectral density, $|\widehat{C}(t,\omega )|$, as a function of $t$ and $\omega$. (b) Time dependence of the power spectral density at three different frequencies: $\omega \simeq \pi$ (squares), $\omega ={\omega }^{\text{af}}\simeq 1.5\pi$ (circles), and $\omega \simeq 2\pi$ (triangles). The dashed vertical lines indicate the slip occurrence time $t_{s_1}$ and $t_{s_2}$.

Figure 5

(a) Time dependence of the power spectral density at the characteristic frequency $|\widehat{C}(t,{\omega }^{\text{af}})|$, in a temporal interval centered at the slip occurrence time $t_{s_1}$. The bottom panels illustrate the temporal evolution of $C(t,t^{\prime })$ evaluated at different times $t$ indicated in (a) as open blue squares for $t_{s_1}-t>2$ (b), filled red circles $t_{s_1}-t<2$ (c), and filled green squares $t-t_{s_1}>2$ (d).