Time to seismic failure induced by repeating SSEs in a single-degree-of-freedom spring-slider model

SUMMARY Some large earthquakes may have been triggered by large slow slip events (SSEs). This paper studies the time it takes from the most recent SSE to seismic failure in a situation where earthquakes are influenced by periodic SSEs, unlike in earlier studies that investigated the impact of a single SSE imposed at an arbitrary timing during a seismic cycle. A single-degree-of-freedom (SDOF) spring-slider model obeying a rate- and state-dependent friction (RSF) law is used to study the time to failure. The results are compared with those in Ohtani et al., which simulates megathrust earthquakes triggered by large, spontaneous SSEs along the deeper extension of a seismogenic zone in a 2-D elastic medium. Suppose a model fault under steady-rate tectonic loading is also impacted by stress steps induced by periodic SSEs. In the absence of SSEs, there is only a unique value of the characteristic slip distance L of RSF for a given seismic return period T. In the presence of SSEs, by contrast, synchronization occurs, and there exists a finite range of L values that corresponds to the same T. The timing (phase difference) of earthquakes relative to the SSEs varies continuously with L within that range. This study focuses on the case where T is triple the SSE return period, TSSE, (T = 3TSSE) to allow comparison with Ohtani et al. For each value of L in that range, disturbance tests that assign random values to T0, the timing of the third SSE within the seismic cycle, are conducted to obtain a probability distribution for tf, the time from that SSE to seismic failure. The distribution is converted into P(t; L), the cumulative probability that seismic failure occurs within time t of the SSE. The P(t; L) is averaged over the different L values to produce $\bar{P}$(t), which takes account of variability in the strength excess on the seismic fault at the time of the SSE, a parameter that is generally unknown. These numerical disturbance tests are conducted for three different values of an SSE size parameter. It is found that the larger the SSEs, the more intensely seismic failure is concentrated within short time intervals following an SSE. For the largest SSE, whereby a single SSE accounts for 3/10 of the total stress accumulated during a seismic cycle, there is a 50 per cent probability that seismic failure occurs within 132 d. These results contrast with those of Ohtani et al., in which tf was found to be concentrated more intensely within even shorter time intervals following an SSE (80 per cent probability that seismic failure occurs within 2.78 d of the SSE). It is suggested the timing of SSE-triggered seismic failure is concentrated more strongly on a fault embedded in a continuum because of a factor that cannot be taken into account by an SDOF model—a spatial structure of stress concentration that is already there on the fault even before the triggering event, the SSE.