
Fig. 1. (a) Recurrence interval as a function of time, (b) relative moment variation (ratio of Mo and average Mo of the sequence) as a function of time, and (c) relative moment as a function of recurrence interval for group 2 repeating sequences. Black and open circles indicate post and pre Parkfield events, respectively. (d) Recurrence interval as a function of time, (e) relative moment variation as a function of time, and (f) relative moment as a function of recurrence interval for group 5 repeating sequences. (g) Recurrence interval as a function of time, (h) relative moment variation as a function of time, and (i) relative moment as a function of recurrence interval for SAFOD repeating sequences.
Fig. 2. Simulation results for RES response to postseismic effects of a large nearby event using different model parameters. (a) Fault model for 3D simulation. A vertical strikeslip fault is embedded into an elastic medium and governed by rate and state friction laws (Chen and Lapusta, 2009). (be) Computed relative seismic moment as a function of recurrence interval for varying patch radius r and nucleation size h*. Open and filled circles indicate the preseismic and postseismic events, respectively.
Project Summary 
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 19872009 at Parkfield to examine the variation of their recurrence properties in space and time. These observations are qualitatively consistent with earthquake simulations in 3D continuum fault models with rate and statedependent friction shown in Fig. 2. In the models, RES are produced on velocityweakening patches surrounded by velocitystrengthening fault areas (Fig. 2a). In the simulations, the sign of the slope for the MoTr relation is controlled by the ratio r/h*, where r is the radius of the velocityweakening patch and h* is the socalled 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(sigmap)(ba)^2] where mu is the shear modulus,(sigmap) 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 velocityweakening 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 MoTr slopes, whereas larger radii and hence larger moments lead to weak positive MoTr 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 microearthquakes 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 preearthquake 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 magnitudedependent postseismic behavior can be qualitatively explained by 3D 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 velocityweakening 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 timevarying loading rate on the velocityweakening patch play a significant role in a repeater's seismic properties. Such an inference, however, should be tested with proper laboratorybased friction experiments in the future.

Tools  *** 
Geographic Location  Parkfield, California 
Group Members Involved 
Kate Huihsuan Chen <Email> <Personal Web Site> Roland Bürgmann Robert Nadeau Ting Chen & Nadia Lapusta(Caltech) 
Project Duration  20092010 (in revision, EPSL) 
More Information  K. H. Chen, Burgmann, R., and Nadeau, R. M. (2010), Triggering effect of M 45 earthquakes on the earthquake cycle of repeating events at Parkfield, Bull. Seismol. Soc. Am.,100, 2, doi:10.1785/0120080369. K. H. Chen, Burgmann, R., Nadeau, R. M., T. Chen, N. Lapusta (2010), Postseismic variations in seismic moment and recurrence interval of small repeating events following the 2004 Parkfield earthquake, Earth Planet. Sci. Lett.,in revision. > 
