1. Magnitude change before and after the Tohoku-oki earthquake
To check whether the difference in magnitude fluctuation between before and after the
Tohoku-oki earthquake is significant, we examined the frequency distributions of the
relative magnitudes of repeaters shown in Fig. 5 using F-test. The distributions are
shown in Fig. S1 and the result of the F-test indicates the variances of the two
distributions are significantly different.
We also checked the change in the magnitudes of repeaters in different magnitude
threshold (lower limit of the magnitude). This is because sometimes completion
magnitude of the earthquake catalogue changes after a large earthquake and it may
produce apparent change in the averages magnitude of repeaters. Here, we limited
repeater sequences whose averaged magnitudes are larger than 3.0. Note that the
original catalogue includes earthquakes with magnitude 2.5 or larger. Using the
threshold, 64% of earthquakes were selected in this subset of earthquakes and the
change between before and after the Tohoku-oki earthquake is significant too as shown
in Fig. S2.
The temporal variation of relative magnitude is plotted in Fig. S3 together with the
ground velocity at a GPS station 0170 (square in Fig.1) located close to the Kamaishi
sequence and the main postseismic slip area. We used daily location of the GPS station
processed by routine procedure of the Tohoku university and estimated an averaged
ground velocity using a moving time widow of 30 days. The upper limit of repeater
magnitude and GPS velocity gradually decrease in the latter half of 2011. Many events
with relatively large magnitudes occurred in the period of about three months just after
the Tohoku-oki earthquake, but the maximum relative magnitudes seem to be saturated
at about 0.7 in this period. We do not know the reason of the saturation but one possible
explanation is that the waveforms may become dissimilar and not be registered as
members of a repeating sequence when the magnitude change is too large; in such a
case detailed investigation of slip distributions is needed in identifying the ‘repeaters’ as
we did for the Kamaishi earthquake sequence. If we consider the time history of the
GPS velocity after the Tohoku-oki earthquake as a proxy of the temporal change of
postseismic slip, the faster ground velocity corresponds to faster postseismic slip on the
plate boundary. Thus we consider the fast postseismic slip is related to the change in the
repeater magnitudes.
Fig S1. Frequency distribution of relative magnitude before (a) and after (b) the
Tohoku-oki earthquake. The relative magnitude for 126 earthquakes shown in Fig. 5
are shown here. The 126 earthquakes are from 42 sequences with three or more
earthquakes both before and after the Tohoku-oki earthquake.
Fig S2. The same as Fig. 5 but for sequences with averaged magnitude are larger than 3
(Evolution of the magnitudes of repeaters before and after the 2011 Tohoku-oki
earthquake). We plotted 27 sequences with three or more earthquakes both before and
after the Tohoku-oki earthquake.
Fig S3. Evolution of the magnitudes of repeaters from 2009 to 2012 together with
on-land GPS ground velocity (red line). Black dots show the difference in magnitude
(relative magnitude) between each event and average of its sequence. Red line shows
eastward ground velocity observed at a GPS station 0170 to International Terrestrial
Reference Frame 2008 (Fig. 1). The GPS data was provided from the Geospatial
Information Authority of Japan (GSI). The ground velocity is plotted at the end of
30-day moving window. Vertical line denotes the timing of the Tohoku-oki earthquake.
2. Inversion results for the seven Kamaishi earthquakes from 2008 to 2011
The analyses described in the main text were conducted for the January 11, 2008, March
30, 2011, April 13, 2011, April 29, 2011, May 31, 2011, July 11, 2011 and September
23, 2011 Kamaishi earthquakes independently. Here we describe the result for each
earthquake. The 2008 event (M4.7) has rupture area with a diameter of about 1.2 km
and the maximum slip occurred west of the hypocenter (Fig. S4). The rupture duration
is about 0.3 second. The March 20, 2011 event (the first after the Tohoku-oki
earthquake) showed a slip area of about 8 km in diameter, with the maximum slip
located east of the hypocenter. A sharp moment rate peak is seen around 0.4-0.8 second
after the initial break (Fig. S5c). The first part of this moment release (Fig S5c, 0.3-0.45
second) occurred west of the hypocenter (Fig. S5a), which is the direction of the 2008
earthquake’s hypocenter. The rupture duration is about 2 seconds. The April 13, 2011
event (M5.5) has ruptured a ~7 km length area (Fig S6). Main slip areas are located ~2
km northeast of the hypocenter. The rupture duration is about 2 second. The April 29,
2011 event had a slip area of 1.6 km in diameter with maximum slip located west of the
hypocenter (Fig. S7). Its rupture duration is about 0.3 seconds (Fig. S7c). The May 31,
2011 event (M5.3) has rupture area with a length of about 4.4 km (Fig S8). Main slip
areas are located ~2 km northeast of the hypocenter. The rupture duration is about 2
second. July 11, 2011 event (M5.1) has a ~2.2 km diameter rupture area and its main
slip area occurred near the hypocenter (Fig. S9). The source time function shows a
relatively long duration but the main slip of the ~3 km diameter finished within 1
second. The September 23, 2011 event (M5.0) ruptured a ~3.6 km length area (Fig S10).
The main slip occurred ~2 km northeast of the hypocenter. The rupture duration is about
2 second. The maximum slip and rupture dimensions are summarized in the Table 2. All
these slip distributions are superimposed in Fig. 10 and discussed in the main text.
Fig S4. The waveform modeling results for the January 11, 2008 Kamaishi earthquake.
(a) Snap shots of the slip distributions. Each window spans 0.05s except for the last
window, in which moment releases in plural 0.05s time spans are plotted together.
Circle size shows the moment relative to the EGF. The hypocenter is located at the
origin of the coordinate. (b) Spatial distribution of total moment release. (c) Source
time function.
Fig S5. The waveform modeling results for the March 20, 2011 Kamaishi earthquake.
(a) Snap shots of the slip distributions. Each window spans 0.15s except for the last
window, in which moment releases in plural 0.15s time spans are plotted together.
Circle size shows the moment relative to the EGF. The hypocenter is located at the
origin of the coordinate. (b) Spatial distribution of total moment release. (c) Source time
function.
Fig S6. The waveform modeling results for the April 13, 2011 Kamaishi earthquake. (a)
Snap shots of the slip distributions. Each window spans 0.15s except for the last
window, in which moment releases in plural 0.15s time spans are plotted together.
Circle size shows the moment rate relative to the EGF. The hypocenter is located at the
origin of the coordinate. (b) Spatial distribution of total moment release. (c) Source time
function.
Fig S7. The waveform modeling results for the April 29, 2011 Kamaishi earthquake. (a)
Snap shots of the slip distributions. Each window spans 0.05s except for the last
window, in which moment releases in plural 0.05s time spans are plotted together.
Circle size shows the moment rate relative to the EGF. The hypocenter is located at
the origin of the coordinate. (b) Spatial distribution of total moment release. (c)
Source time function.
Fig S8. The waveform modeling results for the May 31, 2011 Kamaishi earthquake. (a)
Snap shots of the slip distributions. Each window spans 0.15s except for the last
window, in which moment releases in plural 0.15s time spans are plotted together.
Circle size shows the moment rate relative to the EGF. The hypocenter is located at
the origin of the coordinate. (b) Spatial distribution of total moment release. (c)
Source time function.
Fig S9. The waveform modeling results for the July 11, 2011 Kamaishi earthquake. (a)
Snap shots of the slip distributions. Each window spans 0.15s except for the last
window, in which moment releases in plural 0.15s time spans are plotted together.
Circle size shows the moment rate relative to the EGF. The hypocenter is located at
the origin of the coordinate. (b) Spatial distribution of total moment release. (c)
Source time function.
Fig S10. The waveform modeling results for the September 23, 2011 Kamaishi
earthquake. (a) Snap shots of the slip distributions. Each window spans 0.15s except
for the last window, in which moment releases in plural 0.15s time spans are plotted
together. Circle size shows the moment rate relative to the EGF. The hypocenter is
located at the origin of the coordinate. (b) Spatial distribution of total moment release.
(c) Source time function.
3. Comparison between observed and synthetic (modeled) waveforms
In figures S11-17, we show waveform comparisons between observed and synthetic
(modeled) data for all the seven earthquakes analyzed in this study. All the events have
good waveform similarity between observed and synthetic ones for most of the stations.
Fig S11. Observed (black) and calculated (red) waveforms for the January 11, 2008
Kamaishi earthquake. (a) P-waves and (b) S-waves. Numerals above and left of each
waveform pair show observed waveform amplitude and amplitude ratio
(observation/calculation), respectively.
Fig S12. Observed (black) and calculated (red) waveforms for the March 20, 2011
Kamaishi earthquake. (a) P-waves. (b) S-waves. Numerals above and left of each
waveform pair show observed waveform amplitude and amplitude ratio
(observation/calculation), respectively.
Fig S13. Observed (black) and calculated (red) waveforms for the April 13, 2011
Kamaishi earthquake. (a) P-waves. (b) S-waves. Numerals above and left of each
waveform pair show observed waveform amplitude and amplitude ratio
(observation/calculation), respectively.
Fig S14. Observed (black) and calculated (red) waveforms for the April 29, 2011
Kamaishi earthquake. (a) P-waves. (b) S-waves. Numerals above and left of each
waveform pair show observed waveform amplitude and amplitude ratio
(observation/calculation), respectively.
Fig S15. Observed (black) and calculated (red) waveforms for the May 31, 2011
Kamaishi earthquake. (a) P-waves. (b) S-waves. Numerals above and left of each
waveform pair show observed waveform amplitude and amplitude ratio
(observation/calculation), respectively.
Fig S16. Observed (black) and calculated (red) waveforms for the July 11, 2011
Kamaishi earthquake. (a) P-waves. (b) S-waves. Numerals above and left of each
waveform pair show observed waveform amplitude and amplitude ratio
(observation/calculation), respectively.
Fig S17. Observed (black) and calculated (red) waveforms for the September 23, 2011
Kamaishi earthquake. (a) P-waves. (b) S-waves. Numerals above and left of each
waveform pair show observed waveform amplitude and amplitude ratio
(observation/calculation), respectively.
4. Determination of maximum rupture speed and other parameters for the
waveform inversion
The parameters used in the inversion are listed in Table 1 of the main text. Even if the
slip is very heterogeneous both in space and time domains, the true slip distribution
seems to be obtained if we adopt faster maximum rupture speed and many basis
functions. Such inversion, however, become very unstable. Therefore we need to limit
the maximum rupture speed and the number of basis functions. We evaluated variance
of residuals (amplitude differences between observed and synthesized waveforms; Mori
and Hartzell, 1990, Shimamura et al., 2011) obtained from the inversions using various
maximum rupture speed as shown in Fig. S18.
Fig. S18a shows the results for the events whose slip distributions were estimated
using the January 11, 2008 M4.7 event. The events on March 20, 2011 and April 13,
2011 show minima of variances around 3 km/sec. Although other events show no
minima, we decided that the maximum rupture speed of 3.0 km/s was appropriate for
the inversion using the 2008 M4.7 event as the EGF. On the other hand, the variances
for 2008 event and April 29, 2011 events whose slip distributions were estimated using
the February 27, 2011 event as the EGF decrease as the maximum rupture speed
increases. This pattern was also seen in the result of previous studies (Okada et al.,
2003; Shimamura et al., 2011), and indicating the poor resolution of the maximum
rupture speed for events smaller than M5.0. Shimamura et al. (2011) adopted 3.8km/s as
the maximum rupture speed from the local minimum of the variance and the result of
Okada et al. (2003). According to their result, we also used 3.8km/s as the maximum
rupture speed of these two events.
For other parameters, the frequency ranges for the analyses were determined from
dominant frequency of waveforms. We set the grid spacing for each inversion as the
similar size with the EGF event and the number of basis functions to be 4. The intervals
of the basis functions were set to be half of the EGF rise time or smaller.
Fig. S18 Relationship between the maximum rupture speed and variance of the residuals.
Results for the slip distribution inversions using the January 11, 2008 M4.7 event (a)
and the February 27, 2011 M3.4 event (b) as the EGFs.
5. Estimation of stress drops
For the rough estimate of stress drops from the slip distribution, we assumed circular
crack model. In that model, the displacement at location
on the crack is expressed as
follows (Aki and Richards, 2002),
S1
Here
is the crack radius,
is the shear modulus and
By using the maximum slip at the center of the crack (
is the stress drop.
, the stress drop can be
written as,
 
7G
u (0) .
24r0
S2
Therefore, we can estimate the stress drop from the maximum slip (
and
crack radius ( ). The values used for the maximum slip and crack radius are listed in
the Table 2 of the main text.
References:
Aki, K. and P.G. Richards (2002), Quantitative Seismology: Theory and methods.,
University Science Books, Sausalito, CA.
Mori , J., and S. Hartzell, Source inversion of the 1998 Upland, California, earthquake:
Determination of a fault plane for a small event, Bull. Seism. Soc. Am., 80, 507-518,
1990.
Shimamura, K., T. Matsuzawa, T. Okada, N. Uchida, T. Kono, and A. Hasegawa,
Similarities and Differences in the Rupture Process of the M~4.8 Repeating-Earthquake
Sequence off Kamaishi, Northeast Japan: Comparison between the 2001 and 2008
Events, Bull. Seism. Soc. Am., 101, 10.1785/0120100295, 2011.
Okada, T., T. Matsuzawa, and A. Hasegawa, Comparison of source area of M4.8±0.1
repeating earthquakes off Kamaishi, NE Japan: are asperities persistent features?, Earth
Planet. Sci. Lett., 213, 10.1016/S0012-821X(03)00299-1, 2003.