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
(*V*_{f}) 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/*V*_{f}. 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 *V*_{f} are the recurrence
interval and geodetically derived long-term average fault slip rate
for the different areas, and *V*_{parkfield} = 2.3 cm/yr
is the reference loading rate assumed for the fault segment where
SAF repeaters are located. We use a *V*_{f} for the
Chihshang fault of 3.7 cm/yr and a *V*_{f} 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.