In laboratory experiments, longer stationary contact time leads to larger seismic moment during repeated ruptures. However, not all observations in natural fault systems agree with the prediction. We analyze a subset of 34 M 0.4 ~ 2.1 repeating earthquake sequences (RES) from 1987-2009 at Parkfield to examine the variation of their recurrence properties in space and time.
Following the 29 September 2004, M 6.0 Parkfield earthquake, a strongly accelerated rate of postseismic repeats is observed for 22 of the 34 event sequences. These repeating events have greatly reduced recurrence intervals that increase systematically with time (Fig. 1a). The rapid event recurrences reflect increased loading of the RES asperities by coseismic stress changes and accelerated fault creep surrounding the 2004 rupture [Johanson et al., 2006; Johnson et al., 2006; Murray and Langbein, 2006]. 36 % of the 773 recurrence intervals are shorter than 0.1 of average interval, and 100% of these short intervals follow the 2004 Parkfield event.
In addition to this recurrence acceleration, we also find systematic changes in seismic moment (Mo), where most sequences experienced an immediate increase in Mo and subsequent decay as Tr approached pre-quake durations. Fig. 1 shows the temporal evolution of recurrence intervals and seismic moment for three example groups. The RES at shallower depth tend to have a larger range in both Tr and Mo (Fig. 1a~b), whereas deeper RES show smaller variation (Fig. 1d~e). The shallowest RES with the greatest magnitude (the M1.8-2.1 SAFOD target events) among the events we studied reveal large variation in Tr but small variation in Mo (Fig. 1g~h).
To further explore the variability in seismic moment Mo and recurrence interval Tr, and to investigate their potential relation, we plot Mo vs. Tr, with Mo normalized by the average Mo (Mave) of the whole sequence in Fig. 1c, f, and i. To quantify the relation between Mo and Tr, we fit the postseismic data with Mo/Mave ~ q logTr using the least squares method, for the 26 Parkfield RES with more than four postseismic events (following Peng et al., 2005). The fits are shown by dashed lines in Fig. 1c, f, and i. Positive/negative slopes q of the Mo-Tr relation correspond to an increase/decrease in moment with increasing recurrence time. We find that 19 out of 26 RES have decreasing Mo as Tr increases. Magnitude ranges for the postseismic RES characterized by negative and positive Mo-Tr slopes are M 0.36~1.82 and M 0.64~2.12, respectively.

These observations are qualitatively consistent with earthquake simulations in 3D continuum fault models with rate- and state-dependent friction shown in Fig. 2. In the models, RES are produced on velocity-weakening patches surrounded by velocity-strengthening fault areas (Fig. 2a). In the simulations, the sign of the slope for the Mo-Tr relation is controlled by the ratio r/h*, where r is the radius of the velocity-weakening patch and h* is the so-called nucleation size dependent on the friction properties of the patch (Chen and Lapusta, 2009 and references therein):h*=(pi^2/4)mu b L/[pi(sigma-p)(b-a)^2] where mu is the shear modulus,(sigma-p) is the effective normal stress, p is the pore fluid pressure, and a, b and L are friction parameters. Dynamic instability is able to develop (i.e., an earthquake could occur) only if the size of the velocity-weakening patch is comparable to or exceeds the nucleation size h*, corresponding to ratios r/h* comparable to or larger than 1. Given the same nucleation size h* (i.e., the same frictional properties and effective normal stress), smaller radii and hence smaller seismic moments result in negative Mo-Tr slopes, whereas larger radii and hence larger moments lead to weak positive Mo-Tr slopes, consistent with observations. Conversely, with only a small percentage of its slip accumulated seismically, a small asperity appears to grow in Mo under high loading rate, which is contrary to the view that Mo should decrease due to a reduced strength recovery time. Our simulations show that the recurrence intervals Tr are systematically reduced for larger VL, as intuitively expected and confirmed by our observations.

The large population of repeating micro-earthquakes at Parkfield provides a unique opportunity to examine, model and test the extent to which fault interaction in the form of static stress changes and transient postseismic fault creep produces changes in frequency and magnitude of the events. Most shallower RES (< 7 km) experienced a strong reduction in Tr accompanied by an increase in Mo immediately following the 2004 Parkfield mainshock, evolving towards pre-earthquake values in subsequent years. Among the shallow RES, larger events show less variability in seismic moment than small events, even though their transient recurrence acceleration is strong. This magnitude-dependent postseismic behavior can be qualitatively explained by 3-D models using rate and state friction laws. Small asperities tend to accumulate most of their slip aseismically, with earthquakes occupying a small fraction of their area. When experiencing higher loading rates, these small events are found to rupture a larger area of the velocity-weakening asperity, producing the observed behavior of increasing moment with increasing loading rate and decreasing recurrence intervals. For the postseismic period, the good correlation between the observation and model predictions implies that the sudden increase and time-varying loading rate on the velocity-weakening patch play a significant role in a repeater's seismic properties. Such an inference, however, should be tested with proper laboratory-based friction experiments in the future.