Slow slip generated by dehydration reaction coupled with slip-induced dilatancy and thermal pressurization

Abstract

Sustained slow slip, which is a distinctive feature of slow slip events (SSEs), is investigated theoretically, assuming a fault embedded within a fluid-saturated 1D thermo-poro-elastic medium. The object of study is specifically SSEs occurring at the down-dip edge of seismogenic zone in hot subduction zones, where mineral dehydrations (antigorite, lawsonite, chlorite, and glaucophane) are expected to occur near locations where deep slow slip events are observed. In the modeling, we introduce dehydration reactions, coupled with slip-induced dilatancy and thermal pressurization, and slip evolution is assumed to interact with fluid pressure change through Coulomb’s frictional stress. Our calculations show that sustained slow slip events occur when the dehydration reaction is coupled with slip-induced dilatancy. Specifically, slow slip is favored by a low initial stress drop, an initial temperature of the medium close to that of the dehydration reaction equilibrium temperature, a low permeability, and overall negative volume change associated with the reaction (i.e., void space created by the reaction larger than the space occupied by the fluid released). Importantly, if we do not assume slip-induced dilatancy, slip is accelerated with time soon after the slip onset even if the dehydration reaction is assumed. This suggests that slow slip is sustained for a long time at hot subduction zones because dehydration reaction is coupled with slip-induced dilatancy. Such slip-induced dilatancy may occur at the down-dip edge of seismogenic zone at hot subduction zones because of repetitive occurrence of dehydration reaction there.

Appendix A—effects of assumed values of time increment and smoothing of calculated slip velocity

Even if the stability conditions for the fluid and heat diffusion equations are satisfied, our calculation shows that numerically calculated slip velocity contains numerical noise and depends on assumed values of time increment ΔT in a range ${S}_u>{\overline{P}}_0$. Figure 10 illustrates the dependence of temporal change of slip velocity on three assumed values of ΔT; values of S _u , S ^' _u , and χ ' are fixed at 1.4, 1.47 × 10⁻⁷, and −0.05, respectively, which are assumed in many numerical examples in the present paper. Assumption of ΔT much smaller than assumed here is impractical, considering the capacity of our computer. We find in Fig. 11 that the noise amplitude, which does not much depend on ΔT, is largest in a time period just before the slip-induced porosity attains the upper limit. This suggests that the origin of numerical noise principally lies in strong coupling between the slip-induced dilatancy and dehydration reaction.

Fig. 10

Dependence of slip velocity on the assumed values of time increment ΔT; we assume three values for ΔT here, that is, 0.01, 0.025, and 0.05. The values of S _u and χ ' are fixed at 1.4 and −0.05, respectively. The white curve denotes the slip velocity obtained by the smoothing procedure. The other parameter values are the same as assumed in Fig. 3. The solid arrows denote times when the evolution of slip-induced dilatancy is complete for three values of ΔT

Fig. 11

Dependence of slip duration on the assumed values of time increment ΔT and χ '; the value of S _u is fixed at 1.4. The other parameter values are the same as assumed in Fig. 3

We now suppress the numerical noise by employing a smoothing procedure. We first obtain the temporal change of slip by numerically integrating the slip velocity with respect to time T. Smoothed slip velocity is then obtained by numerically differentiating the thus-obtained slip plotted every 100,000 time step. Smoothed slip velocities are illustrated with the white curves in Fig. 10. All slip velocities illustrated in the present paper for ${S}_u>{\overline{P}}_0$ are obtained using the above smoothing procedure. No smoothing procedure is employed for ${S}_u<{\overline{P}}_0$ and the time increment is fixed at ΔT = 0.5 × 10^− 4. Figure 10 shows that the smoothed slip velocity is slightly lower for smaller values of ΔT only in a time range just before the slip-induced porosity attains the upper limit. Specifically, it is worthy of attention that the smoothed slip velocity is hardly dependent on ΔT after the slip-induced porosity attains the upper limit. Hence, smoothed slip velocity does not seem to depend much on ΔT, as a whole, during its evolution. Figure 10 also shows that the slip duration is shorter for smaller values of ΔT. However, the change rate of slip duration with respect to the change of parameter values does not much depend on ΔT as exemplified in Fig. 11.