Postseismic Variations in Seismic Moment and Recurrence Interval of Repeating Earthquakes at Parkfield

Kate Huihsuan Chen (National Taiwan Normal Univ.), Roland Bürgmann, Robert M. Nadeau, Ting Chen (Caltech), and Nadia Lapusta (Caltech)

Observations of postseismic recurrence behavior

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$\sim$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 (Figure 2.44a). 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 times the 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 ($M_{o}$), where most sequences experienced an immediate increase in $M_{o}$ and subsequent decay as $T_r$ approached pre-quake durations. Figure 2.44 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 $T_r$ and $M_{o}$ (Figure 2.44a-b), whereas deeper RES show smaller variation (Figure 2.44d-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 $T_r$ but small variation in $M_{o}$ (Figure 2.44g-h).

To further explore the variability in seismic moment $M_{o}$ and recurrence interval $T_r$, and to investigate their potential relation, we plot $M_{o}$ vs. $T_r$, with $M_{o}$ normalized by the average $M_{o}$ ($M_{ave}$) of the whole sequence in Figure 2.44c, f, and i. To quantify the relation between $M_{o}$ and $T_r$, we fit the postseismic data with $M_{o}$/$M_{ave}$ $\sim$ $qlog(T_r)$ 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 Figure 2.44c, f, and i. Positive/negative slopes $q$ of the $M_{o}$-$T_r$ relation correspond to an increase/decrease in moment with increasing recurrence time. We find that 19 out of 26 RES have decreasing $M_{o}$ as $T_r$ increases.

Rate and state models of repeating sequences

These observations are qualitatively consistent with earthquake simulations in 3D continuum fault models with rate- and state-dependent friction shown in Figure 2.45. In the models, RES are produced on velocity-weakening patches surrounded by velocity-strengthening fault areas (Figure 2.45a). In the simulations, the sign of the slope for the $M_{o}$-$T_r$ relation is controlled by the ratio $r/h \star$, where r is the radius of the velocity-weakening patch and $h\star$ is the so-called nucleation size dependent on the friction properties of the patch (Chen and Lapusta, 2009):

\begin{displaymath}h \star = (\pi^2/4) \cdot \mu b L /(\pi \sigma(b-a)^2) \end{displaymath}

where $\mu$ is the shear modulus, $\sigma$ is the effective normal stres, and $a$, $b$ and $L$ are friction parameters. Given the same nucleation size $h \star$ (i.e., the same frictional properties and effective normal stress), smaller radii, and hence smaller seismic moments, result in negative $M_{o}$-$T_r$ slopes, whereas larger radii, and hence larger moments, lead to weak positive $M_{o}$-$T_r$ slopes, consistent with observations. Conversely, with only a small percentage of its slip accumulated seismically, a small asperity appears to grow in $M_{o}$ under high loading rate, which is contrary to the view that $M_{o}$ should decrease due to a reduced strength recovery time. Our simulations show that the recurrence intervals $T_r$ are systematically reduced for larger loading velocity, as intuitively expected and confirmed by our observations.

Figure 2.44: (a) Recurrence interval, (b) relative moment variation (ratio of $M_{o}$ and average $M_{o}$ 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-f) For group 5 repeating sequences. (g-i) For SAFOD repeating sequences.
\begin{figure*}\centering\epsfig{file=katechen10_1_1.eps, width=11.2cm, bb=10 23...

Figure 2.45: Simulation results for RES response to postseismic effects of a large nearby event using different model parameters. (a) Fault model for 3-D simulation. A vertical strike-slip fault is embedded into an elastic medium and governed by rate and state friction laws (Chen and Lapusta, 2009). (b-e) Computed relative seismic moment as a function of recurrence interval for varying patch radius r and nucleation size $h \star$. Open and filled circles indicate the preseismic and postseismic events, respectively.
\begin{figure}\centering\epsfig{file=katechen10_1_2.eps, width=8.5cm, bb=47 170 ...


Most shallower RES ($<$7 km) experienced a strong reduction in $T_r$ accompanied by an increase in $M_{o}$ 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 in and time-variability of the loading rate on the velocity-weakening patch plays 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.


Chen, T., and N. Lapusta, Scaling of small repeating earthquakes explained by interaction of seismic and aseismic slip in a rate and state fault model, J. Geophys. Res., 114, B01311, doi:10.1029/2008JB005749, 2009.

Johnson, K. M., R. Bürgmann, and K. Larson, Frictional properties on the San Andreas Fault near Parkfield, California, inferred from models of afterslip following the 2004 earthquake, Bull. Seism. Soc. Am., 96(4B), S321-S338, doi: 10.1785/0120050808, 2006a.

Johanson, I. A., E. J. Fielding, F. Rolandone, and R. Bürgmann, Coseismic and postseismic slip of the 2004 Parkfield earthquake from space-geodetic data, Bull. Seismol. Soc. Am., 96(4B), S269-S282, doi: 10.1785/0120050818, 2006b.

Murray, J., and J. Langbein, Slip on the San Andreas fault at Parkfield, California over two earthquake cycles and the implications for seismic hazard, Bull. Seismol. Soc. Am., 96(4B), S283-S303, doi: 10.1785/0120050820, 2006.

Peng Z., J. E. Vidale, C. Marone, and A. Rubin, Systematic variations in recurrence interval and moment of repeating aftershocks, J. Geophys. Res., 32 doi:10.1029/2005GL022626, 2005.

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