Volume 5 Issue 9 - September 26, 2008
Towards a universal rule on the recurrence interval scaling of repeating earthquakes?
Kate Huihsuan Chen1, Robert M. Nadeau2, and Ruey-Juin Rau1*

1: Department of Earth Sciences, National Cheng Kung University, Tainan, Taiwan
2: Berkeley Seismological Laboratory, University of California, Berkeley, California, USA
*Email: raurj@mail.ncku.edu.tw

Geophysical Research Letters, 34, L16308, doi:10.1029/2007GL030554, 2007

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Chosen as an AGU 2007 Journal Highlight

In some tectonic settings, groups of earthquakes rupture at the same patch of fault repeatedly with nearly identical waveform (Fig. 1). These repeating sequences are suggestive of a renewal process taking place on the fault patches. Determining what controls the recurrence time of these ruptures is important to understanding dynamic failure processes fundamental to earthquakes. The repeating earthquakes recently found in a creeping oblique thrust fault zone, the Chihshang fault in eastern Taiwan, provide an excellent opportunity for investigating the recurrence properties of repeating sequences from the perspective of different tectonic settings and different earthquake sizes.
Fig. 1. Waveforms example for a RES in the Chihshang area. Filtered 2-18 Hz waveforms recorded at station CHK, TWF1, and TWG from a repeating sequence. Each trace is normalized by its maximum amplitude.

With creeping behavior and high surface slip rate of 2-3 cm/yr, the Chihshang fault is the most active segment along the Longitudinal Valley fault in eastern Taiwan (LVF in Fig. 2a). Application of repeating earthquake search approach to ~3400 M1.9-5.4 earthquakes reveals the existence of 30 repeating sequences on this fault. The earthquakes were recorded by the short-period Central Weather Bureau Seismic Network during the period 1991-2003. The 30 repeating sequences are composed of 110 repeating events with magnitudes ranging from 1.9 to 3.7 and recurrence interval of 39 minutes to 6 years. The number of repeating events in each sequence ranges from 3 to 7. The repeating sequences appear to concentrate on the northern portion of the Chihshang segment (Fig. 2b), with depth range between 7 to 23 km.
Fig. 2. (a) Geodynamic framework of Taiwan. Open arrow indicates relative motion between Philippine Sea plate and Eurasian plate in Taiwan Region. Box indicates the study area. (b) Spatial distribution of the repeating earthquake sequences in map-view. Red circles represent the locations of RESs. Yellow stars indicate major events occurred during the study time period from 1991-2003 December. Background seismicity are shown as open gray circles. Aftershock sequences from the 1992 and 1995 M 5+ events are shown as blue and green circles, respectively. Open star indicates the event that occurred on December 10, 2003 just after the study period. Aftershocks of the 2003 M6 event are shown by open black circles.

For the 30 repeating sequences on the Chihshang fault, the logarithm of their average recurrence interval (Tr) is plotted against the logarithm of their average seismic moment (Mo) and compared with that for repeating data from California and Japan (Fig. 3). We find that the ratio of recurrence interval to seismic energy released in each location varied widely. The repeating sequences in Taiwan and Japan are generally characterized by 2 and 4 times shorter recurrence intervals (respectively) than those observed along the central SAF.
Fig. 3. (a) Comparison of Tr-Mo relations between the 62 SAF repeating sequences (solid symbols), the 30 Taiwan repeating sequences (open triangles), and the 5 Japan repeating sequence (open circles). The moments and recurrence intervals are taken to be the average values for the members of that sequence. The straight line is a least-squares fit to SAF repeating data, which leads to Tr∝(Mo)1/6. (b) Legend shows the number of repeating sequences, magnitude range, and coefficient of variation (COV) in recurrence intervals for different regions.

Tr differences is probably a result of varying long-term tectonic loading rates between regions. Another possible explanation is that the strength of the repeatable fault patches is different for each region. Or, a combination of the above effects may be responsible for the regional Tr differences. We investigate how much of regional Tr difference can be explained by differences in long-term tectonic loading rate. First we use the assumption that the average loading rate on the fault plane (Vf) during the period of repeats for a sequence is equal to the cumulative seismic displacements (minus the displacement of the first sequence event) divided by the sum of the sequence recurrence intervals (Vd). This assumption leads to the average recurrence interval scaling with the average tectonic loading rate as Tr∝1/Vf. We therefore, can compare recurrence properties between regions with different loading rates by normalizing the recurrence intervals by the ratio of the loading rate to that used for the SAF data:
,
(1)

where is the normalized recurrence interval, Tr and Vf are the recurrence interval and geodetically derived long-term average fault slip rate for the different areas, and Vparkfield = 2.3 cm/yr is the reference loading rate assumed for the fault segment where SAF repeaters are located. We use a Vf  for the Chihshang fault of 3.7 cm/yr and a Vf for Japan subduction zone of 8 cm/yr. After normalizing for the different loading rates, the Chihshang and Japan repeating sequences recurrence intervals are in much better agreement with the trend of the SAF repeating data (Fig. 4). The normalized recurrence for Chihshang and Japan data together with Parkfield data yield a scaling relation Tr∝(Mo)0.160, which is similar to the scaling relation derived from Parkfield’s repeating data, Tr∝(Mo)0.161. The consistency of these data after accounting for differences in the long-term average loading rate among the different regions suggests that tectonic loading rates are likely the most important factors that control earthquake repeat times, and that a universal rule governing recurrence intervals of repeating earthquakes may possibly exist despite differences in tectonic settings.
Fig. 4. Comparison of Tr-Mo relations using normalized recurrence intervals. Normalized data for Taiwan and Japan are determined by Eq. (2). Red line is the scaling line for the SAF repeating data with a slope of 0.161, and black regression line is determined by the overall normalized repeating data with a slope of 0.157. Legend is shown in Fig. 3.

Conclusions
The scaling of recurrence intervals among repeating earthquake sequences in different tectonic environments are consistent when differences in long-term tectonic loading rate are taken into account. The scaling also reveals a dependence of recurrence interval on seismic moment that is weaker than expected when constant stress-drop is assumed. The consistency in scaling among the different regions, California, Japan, and Taiwan, indicates that the mechanical processes responsible for the recurrence of the repeating events is similar despite the diverse environments of the repeating events considered and that differences in recurrence intervals among the regions can be largely accounted for by differences in the regional tectonic loading rates. It also suggests that the tectonic loading rate is likely the most important factor that controls the repeat time. There seems to exist a universal rule on recurrence interval scaling of repeating earthquakes in diverse tectonic settings. These findings offer useful constraints for further studies on the controls of earthquake renewal process, the physics of earthquakes and faulting and associated applications to earthquake forecasting and hazard estimation.
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