Source model of an earthquake doublet that occurred in a pull

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Source model of an earthquake doublet that occurred in a pull
Geophys. J. Int. (2010) 181, 141–153
doi: 10.1111/j.1365-246X.2010.04511.x
Source model of an earthquake doublet that occurred in a pull-apart
basin along the Sumatran fault, Indonesia
1 National
Research Institute for Earth Science and Disaster Prevention, Tsukuba, Ibaraki 305-0006, Japan. E-mail: [email protected]
Fault and Earthquake Research Center, National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8567, Japan
3 Meteorological and Geophysical Agency, Jakarta Pusat 10720, Indonesia
2 Active
Accepted 2010 January 7. Received 2010 January 5; in original form 2009 January 6
SUMMARY
On 2007 March 6, an earthquake doublet occurred along the Sumatran fault, Indonesia. The
epicentres were located near Padang Panjang, central Sumatra, Indonesia. The first earthquake,
with a moment magnitude (M w ) of 6.4, occurred at 03:49 UTC and was followed two hours later
(05:49 UTC) by an earthquake of similar size (M w = 6.3). We studied the earthquake doublet by
a waveform inversion analysis using data from a broadband seismograph network in Indonesia
(JISNET). The focal mechanisms of the two earthquakes indicate almost identical rightlateral strike-slip faults, consistent with the geometry of the Sumatran fault. Both earthquakes
nucleated below the northern end of Lake Singkarak, which is in a pull-apart basin between
the Sumani and Sianok segments of the Sumatran fault system, but the earthquakes ruptured
different fault segments. The first earthquake occurred along the southern Sumani segment
and its rupture propagated southeastward, whereas the second one ruptured the northern
Sianok segment northwestward. Along these fault segments, earthquake doublets, in which
the two adjacent fault segments rupture one after the other, have occurred repeatedly. We
investigated the state of stress at a segment boundary of a fault system based on the Coulomb
stress changes. The stress on faults increases during interseismic periods and is released by
faulting. At a segment boundary, on the other hand, the stress increases both interseismically
and coseismically, and may not be released unless new fractures are created. Accordingly,
ruptures may tend to initiate at a pull-apart basin. When an earthquake occurs on one of
the fault segments, the stress increases coseismically around the basin. The stress changes
caused by that earthquake may trigger a rupture on the other segment after a short time
interval. We also examined the mechanism of the delayed rupture based on a theory of a fluidsaturated poroelastic medium and dynamic rupture simulations incorporating a rheological
velocity hardening effect. These models of the delayed rupture can qualitatively explain the
observations, but further studies, especially based on the rheological effect, are required for
quantitative studies.
Key words: Earthquake source observations; Earthquake interaction, forecasting, and prediction; Continental tectonics: strike-slip and transform; Dynamics and mechanics of faulting;
Dynamics: seismotectonics; Rheology and friction of fault zones.
1 I N T RO D U C T I O N
The Sumatran fault is a trench-parallel strike-slip fault system that
accommodates the oblique convergence of the Indo-Australian Plate
subducting beneath Sumatra, Indonesia (Fig. 1). Over its entire
length of 1900 km, the fault is divided into 19 major fault segments,
ranging in length from 35 to 200 km (Sieh & Natawidjaja 2000).
∗ Now at: Disaster Prevention Research Institute, Kyoto University, Uji,
Kyoto 611-0011, Japan
C
2010 The Authors
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Journal compilation The convergence rate between the Indo-Australian Plate and the
Eurasian Plate at Sumatra ranges from 60 mm yr−1 in the south
to 52 mm yr−1 in the north (Prawirodirdjo et al. 2000). The slip
rate on the Sumatran fault also varies from north to south. Recent
Global Positioning System (GPS) observations show that the rightlateral slip rate is about 20 mm yr−1 in central Sumatra (Genrich
et al. 2000). More than 20 destructive earthquakes with magnitudes
larger than six have occurred along this fault system in the past
100 yr (e.g. Pacheco & Sykes 1992; Bellier et al. 1997).
On 2007 March 6, an earthquake doublet occurred along the
Sumatran fault near Padang Panjang, central Sumatra (Fig. 2).
141
GJI Geodynamics and tectonics
M. Nakano,1 H. Kumagai,1 S. Toda,2 ∗ R. Ando,2 T. Yamashina,1 H. Inoue1 and Sunarjo3
142
M. Nakano et al.
Figure 1. Map of Sumatra showing tectonic features. Open triangles with
station codes indicate locations of the JISNET broad-band seismic stations.
The Sumatran fault trace, represented by the solid black lines on Sumatra,
is based on data collected by Sieh & Natawidjaja (2000). The trace of the
Sunda trench is based on data collected by Muller et al. (1997). The rectangle
outlined by dotted lines is the area shown in Fig. 2(a).
The first earthquake of the doublet, with a moment magnitude (M w ) of 6.4, occurred at 03:49 (UTC). Two hours later
(05:49 UTC), the second earthquake of similar size (M w =
6.3) occurred close to the source location of the first earthquake. The rapid hypocentre determinations by the National Earthquake Information Center (NEIC) of the U.S. Geological Survey
(USGS, Sipkin 1994) and the GEOFON global seismic monitor system of the GeoForschungsZentrum Potsdam, Germany
(GFZ, http://www.gfz-potsdam.de/geofon/seismon/globmon.html)
indicated that the hypocentres of the two earthquakes were north
of Lake Singkarak at a depth of about 10 km and within a horizontal distance of 10 km (Fig. 2b). The centroid moment tensor
(CMT) solutions estimated by the Global CMT (GCMT) Project
(http://www.globalcmt.org), on the other hand, placed the source
centroid locations of these earthquakes about 20 km apart. The
source centroid of the first earthquake was below the southwestern
shore of Lake Singkarak, whereas that of the second earthquake
was below a point north of the lake (Fig. 2b). The centroid depths
of both earthquakes were estimated as about 20 km.
A week after the earthquakes, Natawidjaja et al. (2007) conducted field investigations of the surface fault ruptures caused by
the earthquakes. They also interviewed local people affected by
the earthquakes, and found that people who lived south of Lake
Singkarak felt a stronger shock during the first earthquake and those
who lived north of the lake experienced the second earthquake as
stronger. Natawidjaja et al. (2007) found two separated fault rupture zones, one southeast and one northwest of the lake (red dots in
Fig. 2a), which may correspond to the first and second earthquakes,
respectively. Surface fault ruptures of the first earthquake were observed along the Sumani segment of the Sumatran fault, southeast
of Lake Singkarak. The surface ruptures run from the middle of the
southwestern shore of the lake to southeast of the lake, for a total
distance of about 15 km. The fault ruptures represent a right-lateral
movement with the strike oriented NW–SE. The maximum offset
Figure 2. (a) Tectonic features around Lake Singkarak, central Sumatra.
Three segments of the Sumatran fault are labeled. Years of major historical
earthquake doublets are also shown. The labels ‘A’ and ‘B’ attached to
the years denote the first and second earthquakes, respectively, for each
earthquake doublet. Red solid circles show the locations of the surface
rupture traces of the 2007 earthquake doublet observed by Natawidjaja
et al. (2007). Open squares show populated areas. (b) Enlarged map of the
area around Lake Singkarak. Circles and squares indicate the epicentres
of the 2007 earthquake doublet estimated by NEIC and GFZ, respectively.
Diamonds indicate the horizontal source centroid locations estimated by the
GCMT Project. The source models of the 2007 earthquakes estimated by
this study are also shown. The thick lines denote the source faults, the stars
indicate the rupture initiation points, and the focal mechanisms are plotted at
the most probable horizontal source centroid locations. Red and blue colours
denote the first and second earthquakes, respectively. The Sumatran fault
trace is based on data collected by Sieh & Natawidjaja (2000).
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2010 The Authors, GJI, 181, 141–153
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Journal compilation Source model of an earthquake doublet
of the surface ruptures is about 20 cm. The ruptures also show clear
vertical movement with the western side moving down. Natawidjaja
et al. (2007) found fault traces of the second earthquake north
of the lake along the southern half of the Sianok segment, which
extend 22 km from the northern tip of Lake Singkarak towards the
northwest. The surface fault ruptures show a right-lateral movement
with a maximum offset of about 10 cm. These observations indicate
that the first and second earthquakes ruptured the southern Sumani
segment and the northern Sianok segment, respectively.
Lake Singkarak is in the middle of the Sumatran fault system in a
pull-apart basin (Burchfiel & Stewart 1966) formed at the boundary
between the Sumani and Sianok fault segments (Sieh & Natawidjaja
2000). The discontinuity between these faults consists of a 4.5-kmwide right step and is a dilatational step over. The basin may have
formed by repeated earthquakes with right-lateral strike-slip motion
along the fault segments, resulting in opening of the crust between
the fault segments at the jog (Sieh & Natawidjaja 2000). At Lake
Singkarak, the total estimated geomorphic offset of the misaligned
fault segments is ∼23 km. The dextral rate of slip estimated from
offsets of stream channels is ∼11 mm yr−1 , while the rate obtained
from recent GPS measurements is 23 mm yr−1 (Prawirodirdjo et al.
2000). The slip rate estimated from GPS observations represent
recent crustal motions, while the one estimated from geomorphological observations may represent the motion of long-term average.
Therefore, these estimations do not always give the same value if
tectonic features have changed after the geomorphological features
were created. Geological features indicate that the lake is no more
than a few million years old, which is consistent with the offset and
slip rate.
Around Lake Singkarak, earthquake doublets have occurred repeatedly (Fig. 2a) (Untung et al. 1985; Pacheco & Sykes 1992). In
1926, the first earthquake of a doublet occurred along the Sumani
segment and, a few hours later, the second earthquake of similar
size ruptured the northern Sianok segment. The magnitudes of both
earthquakes have been estimated as M w ∼ 7 by data inversion of
historical triangulation data and recent GPS survey measurements
(Prawirodirdjo et al. 2000). The estimated surface displacement
associated with these earthquakes is 1.7 ± 1.0 m. In 1943, another earthquake doublet occurred: The first earthquake ruptured the
Suliti segment, and the second earthquake ruptured the Sumani segment several hours later. Their estimated magnitudes (Ms ) were 7.1
and 7.4 for the first and second earthquakes, respectively (Pacheco
& Sykes 1992). The observed surface offsets associated with these
earthquakes were 1–2 m (Untung et al. 1985; Sieh & Natawidjaja
2000).
The tectonic settings of the source regions of the 1926 and 1943
doublets are very similar. The discontinuity of the Suliti and Sumani
segments at the jog is a 4.5-km-wide right step and represents a
dilatational step over. Lakes Diatas and Dibawah are at the segment
boundary, suggesting that a pull-apart basin is also evolving there.
Therefore, the occurrence of earthquake doublets may be controlled
by the tectonic settings at the segment boundary. The fault models
of the doublets constructed by Prawirodirdjo et al. (2000) show
that the two fault segments associated with the individual doublets
adjoin each other at the segment boundary.
In this paper, we extensively studied the earthquake doublet of
2007 using various approaches to better understand the source processes. We used data obtained from a broadband seismograph network in Indonesia (JISNET) to estimate the source locations, focal
mechanisms, and rupture propagations of the earthquake doublet.
Our analysis indicates that the two earthquakes initiated at the segment boundary and ruptured the Sumani and Sianok segments in
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2010 The Authors, GJI, 181, 141–153
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Journal compilation 143
dividually and in opposite directions. We proposed a source model
to explain the observed feature of the earthquake doublet based on
interseismic and coseismic Coulomb stress changes. We further investigated the mechanism of the delayed rupture in the doublet based
on a theory of a fluid-saturated poroelastic medium and dynamic
rupture simulations incorporating a rheological velocity hardening
effect.
2 D ATA A N D WAV E F O R M I N V E R S I O N
METHOD
We used waveform data obtained from a broad-band seismograph
network in Indonesia (JISNET) to analyse the earthquake doublet
that occurred on 2007 March 6. JISNET is operated by the National Research Institute for Earth Science and Disaster Prevention
(NIED) and the Meteorological and Geophysical Agency of Indonesia (BMKG) (Nakano et al. 2006). The distribution of JISNET
stations around Sumatra is shown in Fig. 1. Each JISNET station is
equipped with a CMG-3T EBB three-component broad-band seismograph (0.02–360 s). Data from the seismographs are sampled at
20 Hz for each channel and transmitted to BMKG and NIED in
nearly real time.
We used the waveform inversion method of Nakano et al. (2008)
to estimate the source centroid locations and focal mechanisms of
the two earthquakes. In this method, the inverse problem is solved
in the frequency domain for efficient computation, as follows. The
displacement field excited by a point seismic source may be written
in the frequency domain as (e.g. Stump & Johnson 1977)
u n (ωk ) =
Nm
ni (ωk )
m i (ωk ), k = 1, . . . , N f ,
G
(1)
i=1
ni (ωk ) are
where ωk is the angular frequency; u n (ωk ), m
i (ωk ) and G
the Fourier transforms of the nth trace of a displacement seismogram, the ith base of the moment function tensor, and the spatial
derivative of Green’s function, respectively; Nm is the number of
independent bases of moment tensor components; and Nf is the
number of frequency components used for the waveform inversion.
Eq. (1) is written as Nf sets of matrix equations
k )
d(ωk ) = G(ω
m(ωk ), k = 1, . . . , N f ,
(2)
k ) is the data
where d(ωk ) is the data vector consisting of
u n (ωk ), G(ω
ni (ωk ), and m
(ωk ) is the model
kernel matrix with its elements G
parameter vector consisting of m
i (ωk ). In this approach, the matrix
equations for all frequencies are independent of each other and can
be solved separately (Stump & Johnson 1977), and the computation
is much more efficient than that for solving the inverse problem in
the time domain. A double-couple focal mechanism is assumed in
our inversion in order to stabilize the solution by using data from
a small number of seismic stations. The source centroid location
is estimated by a spatial grid search, in which we minimize the
normalized residual R defined by
2
N f mest (ωk )
k=1 d(ωk ) − G(ωk )
,
(3)
R=
N f
2
k=1 |d(ωk )|
(ωk )
est (ωk ) is the estimated model parameter vector m
where m
and |·| represents the length of a vector. The moment function
est (ωk ) corresponds
obtained by the inverse Fourier transform of m
to a bandpassed form, as we need to apply a bandpass filter to the
observed waveforms before the inversion. The seismic moment and
rupture duration are estimated from the deconvolved form of the
moment function (see Nakano et al. 2008, for details).
M. Nakano et al.
(a)
100˚E
101˚E
0˚
0˚
3
0.
0.
0.
1
2
0.
2
A’
0.
3
Three-component seismograms obtained from stations BSI, KSI,
TPI and LEM were used for the inversion of both earthquakes.
Data from station PPI, which is closest to the sources, were not
used, since the waveforms were clipped during the two earthquakes.
The observed velocity seismograms were corrected for instrument
response and then integrated in time to obtain the displacement
seismograms. These waveforms were bandpass filtered between 50
and 100 s and decimated to a sampling frequency of 0.5 Hz. We
used the total data length of 512 s (256 data points in each channel)
for the inversion. Green’s functions were synthesized by using the
discrete wavenumber method (e.g. Bouchon 1979). We assumed the
standard earth model ak135 (Kennet et al. 1995) for calculation of
Green’s functions. We used the hypocentre locations estimated by
the automatic GEOFON global seismic monitor system as the initial
locations. For the spatial grid search, we used adaptive grid spacings,
starting from a horizontal grid spacing of 0.5◦ and a vertical grid
spacing of 10 km. In the next step, the grid spacing was reduced
to 0.2◦ horizontally and 5 km vertically. Finally, the horizontal grid
spacing was reduced to 0.1◦ . At each source location of the spatial
grid search, the fault parameters (the dip, slip, and rake angles)
were searched in 5◦ steps. For each combination of source location
and fault and slip orientation angles, the waveform inversion was
carried out to estimate the best-fitting source parameters.
1˚S
1˚S
km
A
0
20
100˚E
40
101˚E
(b)
Depth (km)
144
0
10
20
30
A
A’
0.2
0.1
-60
-40
-20
0
20
40
60
Distance (km)
3 R E S U LT S
We first estimated the source centroid location and focal mechanism
of the first earthquake. Figs 3(a) and (b) show the horizontal and
vertical residual distributions, respectively, around the best-fitting
source location obtained from our waveform inversion. The bestfitting source is about 10 km southwest of Lake Singkarak at a
depth of 15 km. The focal mechanism obtained at the best-fitting
source location shows strike-slip motion on a vertical fault: Two
nodal planes correspond to the fault parameters (strike, dip, rake) =
(147, 80, 165)/(240, 75, 10). The strike of one nodal plane (147◦ ) is
similar to that of the Sumatran fault (Fig. 2). The seismic moment
of this earthquake was estimated as M 0 = 5.38 × 1018 N m, and the
corresponding moment magnitude was M w = 6.4. The estimated
moment function shows a step-like function with a rupture duration
of 4 s. Waveform fits between observed and synthetic seismograms
calculated for the best-fitting source parameters are shown in Fig. 4.
We obtained good fits with a normalized residual of 0.10.
Although the fits were good at the best-fitting location, the contour plot of the horizontal residual distribution shows elongation in
the NE–SW direction (Fig. 3a). This indicates a weak resolution for
the estimated source location in this direction. The weak resolution
may be because the stations used for our inversion and the earthquake source are aligned almost linearly in the NW–SE direction
(Fig. 1). The field investigations of Natawidjaja et al. (2007) show
that the first earthquake ruptured the Sumani segment. The focal
mechanism estimated from the waveform inversion is also consistent with the rupture of this segment. The slight deviation of the
estimated source centroid location from the Sumani segment may
be caused by the weak resolution in the NW–SE direction. The actual source should be on this segment, and is most probably under
the middle of Lake Singkarak (Fig. 3c), where the residual of the
waveform inversion is the minimum along the segment (Fig. 3a).
This location is close to the one estimated by the GCMT Project
(Fig. 2b).
The rupture initiation point of this earthquake was investigated from the particle motion at the event onset in the original
(c)
100.25˚E
100.5˚E
100.75˚E
0.25˚S
0.25˚S
PPI
0.5˚S
0.5˚S
Lake
Singkarak
km
0.75˚S
0
100.25˚E
10
20
0.75˚S
100.5˚E
100.75˚E
Figure 3. (a) Contour plot of the horizontal residual distribution around
the best-fitting source of the first earthquake. The open star indicates the
best-fitting source centroid location obtained by the waveform inversion.
The grey star indicates the source centroid location under the assumption
that this earthquake ruptured the Sumani segment of the Sumatran fault
as discussed in the text. Crosses denote the node points for the spatial grid
search. (b) Vertical cross-section of the residual distribution along the profile
A–A’ shown in Fig. 3(a). (c) Source model of the first earthquake of the
doublet. The solid black line indicates the horizontal particle motion of the
event onset at station PPI. The black dashed line indicates an extrapolation
of the particle motion to the direction of the P-wave arrival. The black and
grey stars indicate the estimated rupture initiation point and source centroid
location, respectively. The thick grey line denotes the source fault, and the
open arrow indicates the direction of the rupture propagation. See text for
details.
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2010 The Authors, GJI, 181, 141–153
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Journal compilation Source model of an earthquake doublet
BSI EW
BSI NS
BSI UD
KSI EW
KSI NS
KSI UD
TPI EW
TPI NS
TPI UD
LEM EW
LEM NS
LEM UD
0
100
200
300
400
500
0.5 mm
Time/s
145
Obs.
Syn.
Residual = 0.10
Figure 4. Waveform matches obtained from the waveform inversion of the first earthquake. Black and grey traces represent the observed and synthesized
seismograms, respectively. The station code and component of motion are indicated at the upper left-hand side of each seismogram.
seismograms observed at station PPI (Fig. 3c), which is about 20 km
northwest of Lake Singkarak. Although the seismograms at this station were clipped during the arrival of the S wave, the onset portion
of the P wave was clearly recorded in the three-component seismograms. The initial horizontal motion was towards the northwest.
Since the initial vertical motion was upward, the P wave arrived
from the southeast. The extrapolation of the horizontal particle motion towards the southeast intersects the surface trace of the Sumani
segment at the northern end of Lake Singkarak (see Fig. 2b). Therefore, we concluded that the first earthquake initiated at the northern
end of the Sumani segment and ruptured this segment towards the
southeast.
We also analysed the second earthquake using the same methodology. The horizontal and vertical residual distributions obtained
from the waveform inversion around the best-fitting source location
are shown in Figs 5(a) and (b), respectively. The estimated focal
mechanism shows a strike-slip of a vertical fault: Two nodal planes
correspond to (strike, dip and rake) = (145, 80, 165)/(238, 75, 10),
which are almost identical to those obtained for the first earthquake.
The strike of one nodal plane (145◦ ) is also similar to that of the
Sumatran fault (see Fig. 2). The seismic moment of this earthquake
was estimated as M 0 = 3.25 × 1018 Nm corresponding to a moment
magnitude of M w = 6.3, which is slightly smaller than that of the
first earthquake. The estimated moment function shows a step-like
function with a rupture duration of 4 s. The fits between observed
and synthesized seismograms are shown in Fig. 6. We obtained
good waveform fits for this earthquake with a normalized residual
of 0.08.
The best-fitting source of the second earthquake is located off the
Sumatran fault, about 20 km west of Lake Singkarak. The horizontal
residual distribution shows elongation in the NE–SW direction,
and therefore the resolution is weak in this direction (Fig. 5a). It
is also evident from the field investigations of Natawidjaja et al.
(2007) that the second earthquake ruptured the Sianok segment,
and thus the source centroid is most probably northwest of Lake
Singkarak (Fig. 5c), where the residual of the waveform inversion
is the minimum along the Sianok segment (Fig. 5a). We note that
the estimated centroid depth of 20 km may be too deep because the
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2010 The Authors, GJI, 181, 141–153
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Journal compilation locking depth of the Sumatran fault in this region is about 20 km
(Genrich et al. 2000). This discrepancy may also originate from the
weak resolution of the source depth (Fig. 5b).
We also investigated the rupture initiation point of the second
earthquake. Fig. 5(c) shows the horizontal particle motion at the
event onset, which was towards the northwest. Since the vertical
initial motion was upward, the P wave arrived from the southeast.
The direction is slightly different from that of the first earthquake
(see Fig. 3c). The extrapolation of the particle motion to the southeast intersects with the surface trace of the Sianok segment at the
northern end of Lake Singkarak. We therefore concluded that the
second earthquake initiated at the northern end of Lake Singkarak
and ruptured the Sianok segment towards the northwest.
We estimated the relative hypocentre location between the two
earthquakes using the differences in the arrival times at stations
KSI and BSI. The distance L between the hypocentres of the two
earthquakes along the fault can be approximated by
L =
v
{(t K 2 − t B2 ) − (t K 1 − t B1 )} ,
2
(4)
where t K1 and t K2 are the P-wave onset times of the first and second
earthquakes, respectively, measured at station KSI; t B1 and t B2 are
the onset times of the two earthquakes measured at station BSI; and
v is the P-wave velocity. A positive L means that the hypocentre
of the first earthquake was closer to station KSI. We picked the onset
times at stations KSI and BSI from the original seismograms, and
obtained t K1 − t B1 = −56.05 s for the first event and t K2 − t B2 =
−55.60 s for the second event. Assuming the P-wave velocity of
the shallow crust to be v = 5.8 km s−1 , which we adopted from the
velocity structure shallower than 20 km in the ak135 earth model,
we obtained L = 1.3 km. Therefore, the hypocentres of these
earthquakes were very close to each other, supporting the results of
our particle motion analysis.
We also found the effect of the rupture directivity in the original seismograms of the two earthquakes. We plotted the vertical
components of the original velocity seismograms of the first and
second earthquakes (Fig. 7). Since the earthquakes share similar
focal mechanisms, we may use the observed amplitudes to evaluate
146
M. Nakano et al.
(a)
100˚E
101˚E
0˚
0˚
B’
1
0.
0.
3
2
0.
2
0.
3
0.
0.1
1˚S
1˚S
B
km
0
20
100˚E
40
101˚E
4 S O U RC E M O D E L O F T H E
E A RT H Q UA K E D O U B L E T
Depth (km)
(b)
0
10
20
30
B
B’
0.2
4.1 Coseismic stress changes
0.1
0.1
-60
-40
-20
0
20
40
The proximity of the two earthquakes in time and space suggests that
the second earthquake was triggered by the stress changes caused
by the first one. Triggering of seismic activity by large earthquakes
is generally evaluated by the Coulomb failure criterion (e.g. King
et al. 1994). The change in the static Coulomb failure function
CFF caused by an earthquake is given by
60
Distance (km)
(c)
100.25˚E
100.5˚E
100.75˚E
0.25˚S
0.25˚S
PPI
0.5˚S
0.5˚S
Lake
Singkarak
km
0.75˚S
0
100.25˚E
10
tion of rupture propagation, whereas the rupture of the second one
propagated northwestward and short-period waves were amplified
in that direction. Similar features were also observed in the horizontal components, although they are not shown here. The effect of
the rupture directivity becomes smaller as the periods of waves get
longer than the rupture duration. In our inversion we used the seismograms filtered between 50 and 100 s, which are much longer than
the rupture duration (4 s); thus, the effect of the rupture directivity
is negligible in the inversion results.
We summarize the results of our waveform analyses of the doublet
earthquakes as follows: The first earthquake initiated below the
northern end of Lake Singkarak and ruptured the Sumani segment
southeastward (Fig. 3c). Two hours later, the second earthquake
initiated at a location close to the hypocentre of the first one, and
the rupture propagated along the Sianok segment northwestward, in
the opposite direction to that of the first earthquake (Fig. 5c).
20
100.5˚E
0.75˚S
100.75˚E
Figure 5. (a) Contour plot of the horizontal residual distribution around
the best-fitting source of the second earthquake of the doublet. (b) Vertical
cross-section of the residual distribution along the profile B–B’ shown in
Fig. 5(a). (c) Source model of the second earthquake. Symbols here are the
same as those in Fig. 3.
the effect of the rupture directivity. Because the difference in the
hypocentres of the two earthquakes is very small compared with the
distances to the sources from the stations, the effect of the difference
in the hypocentre locations is negligible except at station PPI. At
the stations located southeast of the source (KSI, TPI and LEM),
the maximum amplitudes of the first earthquake at the individual
stations were larger than those of the second one. At the station to
the northwest (BSI), on the other hand, the maximum amplitude
of the second earthquake was larger, even though its magnitude
was smaller than that of the first one. This may be attributed to the
rupture directivity. The rupture of the first earthquake propagated
southeastward and short-period waves were amplified in the direc-
CFF = σs + μ (p − σn ),
(5)
where σ s is the shear stress change on a given fault plane (positive
in the direction of fault slip), σ n is the fault-normal stress change
(positive when the fault is clamped), p is the pore pressure change,
and μ is the effective coefficient of friction. When CFF is positive,
a failure on the given fault plane tends to occur, whereas a negative
value of CFF indicates that failure is suppressed. It has now been
widely recognized that static stress transfer plays a governing role
in interactions of earthquakes, including aftershock activity (Harris
1998; Stein 1999).
We calculated CFF around Lake Singkarak associated with the
first earthquake using the Coulomb 3.1 program (Lin & Stein 2004;
Toda et al. 2005). For simplicity, we assumed a rectangular vertical
fault as the geometry of the input fault. The length of the fault
along strike was assumed to be 26 km, which we estimated from the
distance between the epicentre location of our waveform analysis
and the southern end of the surface fault ruptures (Natawidjaja
et al. 2007). The fault extended vertically from the surface to 20
km depth. The seismic moment was set at 5.38 × 1018 N m, from
the result of our waveform inversion. A linear taper with width of
10 km in the horizontal direction was applied to the slip distribution
on the fault, in which the seismic moment was kept as the input
value. Poisson’s ratio, Young’s modulus, and the effective coefficient
of friction were assumed to be 0.25, 80 GPa, and 0.6, respectively.
The fault and slip orientation angles of the receiver fault were set at
those of the second earthquake. We did not consider pore pressure
change here. The calculated spatial Coulomb stress changes at a
depth of 15 km caused by the first earthquake (Fig. 8a) and the
stress profile along the fault plane of the second earthquake (Fig. 8b;
thick solid line) indicate that Coulomb stress increased along the
Sianok segment at the time of rupture on the Sumani segment. This
modelling of the Coulomb stress field was relatively consistent for
different combinations of effective coefficient of friction, dip angle,
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BSI EW
BSI NS
BSI UD
KSI EW
KSI NS
KSI UD
TPI EW
TPI NS
TPI UD
LEM EW
LEM NS
LEM UD
0
100
200
300
400
500
0.25 mm
Time/s
147
Obs.
Syn.
Residual = 0.08
Figure 6. Waveform matches obtained from the waveform inversion of the second earthquake. Black and grey traces represent the observed and synthesized
seismograms, respectively. The station code and component of motion are indicated at the upper left-hand side of each seismogram.
1st event (03:49)
2nd event (05:49)
BSI V
0.2 mm/s
PPI V
14 mm/s
KSI V
4 mm/s
TPI V
0.5 mm/s
LEM V
0.5 mm/s
0
250
Time/s
500 0
250
500
Time/s
Figure 7. Comparison of the original vertical velocity seismograms of the first earthquake (left-hand column) with those of the second one (right-hand
column). The rows are ordered from top to bottom according to the alignment of the stations from northwest to southeast. The station code is indicated at the
left-hand side of each row. The vertical scale of the seismograms is the same for both events. Note that the waveforms at station PPI were clipped during the
two earthquakes.
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M. Nakano et al.
(a)
y
x
-l/2
l/2
(b)
Stress change / Δσ
0.2
0.0
ΔCFF
-0.2
-0.4
Pore pressure
-0.6
10-4
10-3
10-2
10-1
100
Nondimensional time (t/tr)
101
Figure 9. (a) Schematic representation of the fault system used in our
calculation of stress changes in a poroelastic medium. The thick solid line
indicates the source fault. The filled star indicates the location where the pore
pressure and the Coulomb stress changes are calculated. (b) Black and grey
lines indicate the pore pressure and CFF. The values of pore pressure and
CFF are normalized by the stress drop σ of the main rupture. The time
is normalized by the characteristic relaxation time tr . See text for details.
4.2 Delayed rupture
Figure 8. (a) The Coulomb stress changes (CFF) at 15 km depth on the
fault of the second earthquake caused by the first earthquake. The yellow
and white stars indicate the epicentres of the first and second earthquakes,
respectively. The white solid and black dotted lines indicate the fault models
of the first and second earthquakes, respectively. The green lines indicate
the surface fault traces of the Sumatran fault, after Sieh & Natawidjaja
(2000). (b) CFF along the source fault of the second earthquake. Thick
grey, thick black, and thin grey solid lines indicate CFF assuming effective
coefficients of friction of 0.4, 0.6 and 0.8, respectively, with the fault dipping
at 90◦ . Black and grey dotted lines indicate CFF assuming the fault dips
of 80◦ and 70◦ , respectively, with an effective coefficient of friction of 0.6.
The dash–dotted line indicates CFF assuming an effective coefficient of
friction of 0.6 and a fault dip of 90◦ obtained at a depth of 10 km.
and the depth at which Coulomb stress was estimated (Fig. 8b).
These results suggest that the second earthquake was triggered by
the stress changes caused by the first one.
We also estimated the effect of the Coulomb stress changes on
the faults of the earthquake doublet due to the 2005 Nias-Simeulue
earthquake (M w = 8.6). For this estimation we used the source centroid location and fault parameters obtained for the Nias-Simeulue
earthquake by the GCMT project and its fault dimension of 300 ×
200 km2 (Konca et al. 2007). We obtained that the Coulomb stress
changes on the faults of the doublet were decreases of less than
5 KPa. These changes are one order of magnitude smaller than that
of the first event of the doublet, and thus may be negligible.
The deformation of a fluid-infiltrated poroelastic medium is a mechanism that may explain the delayed triggering of an earthquake
(e.g. Nur & Booker 1972). Because the pore fluid in a poroelastic
medium diffuses down the pressure gradient, the pore pressure, and
accordingly the Coulomb stress, changes with time after an earthquake (e.g. Piombo et al. 2005). Hudnut et al. (1989) and Horikawa
(2001) explained delayed triggering of earthquakes based on a linear, quasi-static, elasticity theory of a 2-D fluid-saturated porous
medium developed by Rice & Cleary (1976). We calculated changes
in the pore pressure and CFF due to the first earthquake of the
2007 doublet by following the method of Rice & Cleary (1976) and
Li et al. (1987). Fig. 9(a) shows schematically the fault system we
used in our calculation. We assumed ν = 0.25, ν u = 0.34 and B =
0.85 for the poroelastic medium, where ν and ν u are Poisson’s ratios
when the medium is deformed under drained and undrained conditions, respectively, and B is Skempton’s coefficient, which is defined
as the ratio of the induced pore pressure to the change in applied
stress for the undrained condition (Wang 2000). These values were
obtained from Westerly granite samples (table 1 of Rice & Cleary
(1976). We also assumed μ = 0.6 for the effective coefficient of
friction.
Fig. 9(b) shows the temporal changes of pore pressure and CFF
at the source location of the second earthquake, which is located
4 km away from the fault of the first one. In this figure the stress
changes are shown in non-dimensional units normalized by the
stress drop σ of the main rupture of the first earthquake. The time
is also normalized by the characteristic relaxation time tr = l 2 /16c,
where l is the fault length and c is the fluid diffusivity of the medium.
Since the hypocentre of the second earthquake is within the region of
dilatation, the pore pressure initially decreases from its static value.
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It then gradually recovers to its static value because of diffusion of
pore fluids from the surrounding region. Because of the decrease
in the pore pressure, CFF is initially less than zero. As the pore
pressure recovers, CFF increases, which may cause the delayed
triggering of a second earthquake. The relaxation becomes evident
after t/tr ∼ 0.01 and CFF becomes positive after t/tr ∼ 0.06
(Fig. 9b). Assuming c = 0.22 × 10−4 m2 s−1 estimated for Westerly
granite samples (Rice & Cleary 1976) and a fault length l = 26 km,
we obtain tr ∼ 1012 s and the time when CFF becomes positive
td = tr × 0.06 ∼ 3 × 1011 s, which are much longer than the observed
delay of 2 hr. As the hypocentre region may be heavily fractured
because of repeated earthquakes, the fluid diffusivity may be much
higher there. If we assume c = 5 m2 s−1 , which is comparable to
that of sandstone (Hudnut et al. 1989), we have tr ∼ 107 s and td ∼
141 hr, which are still longer than the observed delay.
We investigated the effect of dynamic stress changes on the
delayed triggering by solving the temporal evolution of dynamic
fault ruptures. We employed an elastodynamic boundary integral
equation method (BIEM) for the simulation of dynamic mode II
fault rupture in a 2-D infinite, homogeneous, and isotropic elastic medium. We used the method developed by Tada & Madariaga
(2001) and Ando et al. (2004). Two strike-slip faults were aligned
with an offset representing a dilatational step over (Fig. 10a). The
initial rupture is nucleated on Fault 1, at the step over, and the rup-
(a)
y
ture propagates along Fault 1. When the dynamic stress change on
Fault 2 caused by the rupture on Fault 1 is large enough, rupture on
Fault 2 may be triggered. The fault length, strike, and slip direction
were fixed during our calculations.
In previous studies of dynamic fault rupture propagations
(e.g. Harris et al. 1991; Harris & Day 1993, 1999; Duan & Oglesby
2006) the rupture of the second event is triggered immediately after the passage of seismic waves of the first event. These studies
assume the linear slip weakening friction law (e.g. Ida 1972; Ando
& Yamashita 2007). In addition to the slip weakening friction, we
introduced a rheological velocity hardening effect commonly observed in rock frictions (e.g. Dieterich 1979), using the power-law
form of creep behaviour in frictional properties. The shear traction
τ on the fault surface is given by
τ = f (d)σn + ηv p ,
Fault 1
w
0
-l
l
lt
6
u
Fa
lt
u
Fa
4
2
2
1
25
20
0
Slip velocity (m/s)
8
(b)
x
10
-2
15
10
e
Tim
(s)
5
20
is
D
ta
e
nc
0
(k
m
)
-
10
0
Slip velocity (m/s)
(c)
4
x=-11.4 km
p=0.5
η=0
η=0.5
η=1.0
2
η=1.13
η=1.12
0
0
10
20
Time (s)
30
40
Figure 10. (a) Schematic diagram showing the fault system used in our
calculation of dynamic fault ruptures. Thick lines indicate the alignment
of the faults of the first (‘Fault 1’) and second (‘Fault 2’) earthquakes,
respectively. (b) Spatio-temporal distribution of slip velocity on the fault
planes, in which Tp = 1.1 and η = 0 were assumed. (c) The slip velocity
functions on Fault 2 for the effective viscosities η = 0, 0.5, 1.0, 1.12 and
1.13. The functions were obtained at x = −11.4 assuming p = 0.5 and
Tp = 1.1.
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where d and v are the slip and slip velocity, respectively; f (d) is
the coefficient for the slip weakening friction; σ n is the effective
normal stress; η is the pre-exponent factor and p is the exponent.
We first assumed only the slip weakening friction (i.e. ignoring
rheological effect) in our simulations. The friction coefficients at
the static and dynamic states were assumed to be 0.6 and 0.2, respectively. The length of critical slip displacement Dc was assumed
to be 0.5 m. The shear strength of the faults relative to the level of
initial shear stress applied to the faults is specified by a parameter
Tp , which is defined as
Tp =
Fault 2
149
τ p − τr
,
τ0 − τr
(7)
where τ p , τ r and τ 0 are, respectively, the shear strength of the static
state, the shear strength when fault slip is larger than Dc , and the
initial shear stress. See Ando & Yamashita (2007) for the definitions
of τ p , τ r and τ 0 . Note that the stress drop due to fault slip is given by
τ 0 − τ r . Ando & Yamashita (2007) used Tp = 2 for the simulations
of rupture propagation along a branched fault. Using this value in
our study, the rupture on Fault 2 was not triggered by the dynamic
stress changes caused by the rupture on Fault 1. Smaller values
of Tp , namely a higher level of the initial stress, may be required.
Therefore, we searched the range of Tp within which the rupture on
Fault 2 was triggered by the rupture on Fault 1. We assumed P-wave
velocity, rigidity, and Poisson’s ratio of 6 km s−1 , 30 GPa and 0.25,
respectively. The stress drop was assumed to be constant at 10 MPa
along the two faults. The fault length l and step-over width w were
assumed to be 26 and 4 km, respectively. The rupture initiation point
on Fault 1 was set at the jog (x = 0 in Fig. 10a). We simulated the
ruptures on the faults using a time window of 40 s. Fig. 10(b) shows
the slip velocity on the fault planes as a function of the location and
time and assumes Tp = 1.1. When we assumed Tp = 1.1 and 1.2,
the rupture on Fault 2 was triggered immediately after the arrival of
rupture-stopping phase from Fault 1. If we assumed Tp larger than
1.2, namely a higher peak strength compared to the initial stress,
the rupture on Fault 2 was not triggered.
Next, we added the rheological effect to our simulations. In the
following calculations, we assumed Tp = 1.1. Accordingly, the behaviour of fault ruptures depends on the parameters η and p. We
investigated the fault-slip behaviour assuming p = 0.3, 0.5, 0.8 and
1. The slip-velocity functions for various values of η at the centre
of Fault 2 assuming p = 0.5 are shown in Fig. 10(c). As the value of
η increases, the rupture initiation delays on Fault 2. A delay longer
than 20 s was observed for η = 1.12. Assuming η = 1.13, the rupture
on Fault 2 was not observed within the calculated time window. The
delayed rupture was clearly observed in the calculations assuming
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p = 0.3 and 0.5. The delay became shorter for p = 0.8, and was
hardly observed for p = 1.
Our calculations indicated that the delay in the rupture on the
second event occurred when we used both the slip-weakening friction and the power-law creep. Therefore, the rheological velocity
hardening effect may also be a mechanism of the delayed rupture
of the second earthquake. However, we obtained a delay of up to
20 s, which is much shorter than the observed delay of 2 hr. A
longer delay may occur if we set the parameters properly. However, we were not able to carry out such calculations, which require
a longer time window and thus extensive computer memory and
time.
4.3 Model of an earthquake doublet at a segment
boundary
As described above, earthquake doublets have occurred repeatedly
around Lake Singkarak, which suggests that there is a common
mechanism that generates the doublets during sequential earthquake
cycles. We modelled the interseismic and coseismic static Coulomb
stress changes at a segment boundary of a fault system as follows.
Two vertical fault segments representing a right-lateral strike-slip
motion are aligned in a half-space, as shown in Fig. 11. The discontinuity of the faults at the segment boundary is a right step and thus
represents a dilatational step over. During an interseismic period, the
crust is loaded by the motion of the oceanic plate. In this period, the
faults are locked, that is, the slip shallower than the locking depth is
zero. At extensions of the faults below the locking depth, slip may
occur aseismically at a steady rate (Savage & Burford 1973; Scholz
2002). Genrich et al. (2000) showed that the interseismic crustal
movement around the Sumatran fault, as estimated from GPS measurements, was well explained by the model of Savage & Burford
(1973). This indicates that the Sumatran fault is locked above a
depth of about 20 km and aseismic slip occurs below that level during interseismic periods. We therefore estimated the interseismic
Coulomb stress changes by assigning secular slip during an interseismic period on the deep extensions of the faults below the locking
depth. The coseismic stress changes due to faulting were computed
by assigning slip on the faults above the locking depth, while zero
slip was assumed on the deeper extensions. The Coulomb stress
changes were evaluated for right-lateral strike-slip faulting with the
same strike as the fault segments depicted in Fig. 11.
Figs 11(a) and (b) show schematic views of the interseismic and
coseismic Coulomb stress changes. During an interseismic period,
the Coulomb stress increases both along the faults and at the segment
boundary as a result of crustal loading (Fig. 11a). After earthquakes
occur along the faults, the Coulomb stress decreases on and around
the faults because the causative stress is released by the faulting
(Fig. 11b). At the segment boundary, on the other hand, the Coulomb
stress increases again. This occurs because the lobes of the increase
of Coulomb stress due to faulting are distributed asymmetrically
with respect to the fault plane (see Fig. 8a). Because the faults are
aligned with only a small offset, the areas of stress increase due to the
slip of the two faults interfere positively with each other, resulting
in a coseismic stress increase at the segment boundary. Thus, the
stress there increases both interseismically and coseismically, and
remains at a high level unless new fractures are created. Accordingly,
ruptures may tend to initiate at a segment boundary representing a
dilatational step over.
When an earthquake occurs along one fault segment, a rupture
of the other segment may be triggered after a short time interval
by stress changes caused by the first event. The earthquakes may
constitute a doublet, in which the ruptures propagate in opposite
directions.
Figure 11. Schematic diagrams of the Coulomb stress changes around a segment boundary of a fault system representing a dilatational step over. (a) Continuous
Coulomb stress accumulations during an interseismic period. (b) Coseismic Coulomb stress changes associated with faulting on the fault segments. The lefthand panels show spatial distributions of the Coulomb stress changes. The black lines indicate strike-slip fault segments. The right-hand figures display the
Coulomb stress changes as a function of time. The purple and green lines indicate the Coulomb stress on the fault (annotated as ‘1’ in the left-hand panel) and
at the segment boundary between the faults (annotated as ‘2’ in the left-hand panel), respectively.
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5 DISCUSSION
Our waveform analyses of the earthquake doublet along the Sumatran fault indicate that the earthquakes nucleated below the segment
boundary and ruptured the two adjacent fault segments. We presented a model to explain this feature based on the interseismic and
coseismic Coulomb stress changes. We can find a similar example
of an earthquake rupture that initiated at a fault segment boundary of a dilatational step over. The İzmit earthquake (M w = 7.4)
on 1999 August 17 in Turkey. This earthquake occurred along the
North Anatolian Fault Zone (NAFZ). The tectonic setting of the
fault system is similar to that of the Sumatran fault. The NAFZ is
a 1500-km-long fault system with right-lateral, strike-slip motion
(Barka & Kadinsky-Cade 1988). GPS observations show that the
slip rate on the fault is 20–30 mm yr−1 (e.g. McClusky et al. 2000).
This fault system can be separated into a number of fault segments,
and pull-apart basins are found at the segment boundaries. The rupture of the İzmit earthquake initiated at the boundary between the
Sapanca and Gölcük segments of the NAFZ. It then propagated
bilaterally along both fault segments and along other segments beyond the eastern Sapanca segment, resulting in a single large event
(e.g. Yagi & Kikuchi 2000; Delouis et al. 2002; Sekiguchi & Iwata
2002).
Barka & Kadinsky-Cade (1988) thoroughly investigated the historical activity of each fault segment along the NAFZ. Sixteen
earthquakes of M > 6 occurred along the NAFZ between 1939 and
1967. After 1967, there was little seismic activity along the NAFZ
until the İzmit earthquake of 1999. Dewey (1976) recalculated the
epicentres of earthquakes that occurred in northern Anatolia between 1930 and 1972. Poor seismic data quality during this period
limited the accuracy of these epicentre locations to a few tens of
kilometres at best. Accordingly, if a recalculated epicentre was at
a segment boundary, within that range of the accuracy, we considered it to be an earthquake that initiated at a segment boundary.
We found five such earthquakes at segment boundaries of dilatational step overs along the NAFZ. In particular, earthquakes on 1943
November 26 and 1944 February 1 initiated at a segment boundary
representing a dilatational step over near Bayramuren, and these
earthquakes ruptured the segments east and west of the boundary,
respectively. These observations support our proposal that ruptures
tend to initiate at segment boundaries.
Initiation of earthquake ruptures at segment boundaries is also
supported by numerical simulations. Duan & Oglesby (2006) simulated dynamic ruptures on two parallel, strike-slip faults representing a dilatational step over. In their computations, the rupture
initiation point is not fixed: its location depends on the state of
stress immediately before an earthquake, which is determined by the
stress changes due to previous earthquakes and interseismic loading. Their simulations showed that the coseismic stress changes,
which are non-uniform along the two faults, accumulate after repeated ruptures and the ruptures of the two fault segments initiate at
the jog after the system approaches a steady state. Segall & Pollard
(1980) also showed that ruptures tend to initiate at jogs representing
dilatational step overs because the normal stress decreases around
such jogs.
The conditions that govern rupture propagation along adjacent fault segments were investigated by Lettis et al. (2002) and
Wesnousky (2006). They showed from field observations that ruptures can propagate beyond segment boundaries where step overs
are less than 1–2 km, whereas step overs wider than 4–5 km arrest ruptures. Numerical studies (e.g. Harris et al. 1991; Harris
& Day 1993, 1999) agree with these observations. During the
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1999 İzmit earthquake on the NAFZ, the rupture propagated beyond the segment boundaries because step-over widths were small
(1–2 km), as shown by Lettis et al. (2002). The step-over widths
between the Sumani and Sianok segments and between the Suliti
and Sumani segments of the Sumatran fault are about 4.5 km
(Sieh & Natawidjaja 2000), which may be large enough to arrest
ruptures.
We examined the mechanism of delayed ruptures based on pore
pressure changes in a poroelastic medium and the dynamic stress
changes. Assuming a porous medium corresponding to sandstone,
the time scale of the pore pressure change is two orders of magnitude
larger than the observed delay. Our dynamic rupture simulations
showed that a delayed rupture occurred if we employed the rheological velocity hardening effect using the power-law form of creep
behaviour in frictional properties. A similar rheological effect, in
the form of the logarithm of the slip velocity, is used in the rate and
state friction law (e.g. Dieterich 1994). Belardinelli et al. (1999)
pointed out that the rate and state friction law can explain a delayed
rupture of a subevent (nearly 20 s after the first rupture) during the
1980 Irpinia earthquake in Italy. We believe that our study is the
first that has simulated a delayed rupture by using a fully dynamic
rupture model. However, we obtained a delay of up to 20 s, which
is two orders of magnitude smaller than the observed delay. Limitations of available computer power prevented us from performing
extensive dynamic simulations using time windows long enough to
reproduce the observed delay. Clearly, further studies are required
to investigate the mechanism that governs delayed triggering of
earthquakes.
6 C O N C LU S I O N S
On 2007 March 6, an earthquake doublet occurred near Lake
Singkarak, which is in a pull-apart basin between the Sumani and
Sianok segments of the Sumatran fault system, in Indonesia. Our
study showed that the first earthquake initiated at the northern end
of the Sumani segment, and the rupture propagated along this fault
southeastward. The second earthquake initiated at a location close
to that of the first one, and its rupture propagated along the Sianok
segment northwestward. Earthquake doublets for which two adjacent fault segments have ruptured sequentially have occurred repeatedly near Lake Singkarak. Our study of the Coulomb stress
changes in the region of the fault segment boundary showed that
stress increases both interseismically and coseismically at the segment boundary. Accordingly, the stress below a pull-apart basin that
has formed at a segment boundary remains high until new fractures
form, and earthquakes tend to initiate there. When an earthquake
occurs along one such fault segment, after a short time interval the
stress changes caused by that earthquake trigger rupture on the other
segment. This pair of earthquakes may constitute a doublet in which
the first and second ruptures propagate in opposite directions. We
also investigated the mechanism of the delayed rupture based on
pore pressure changes in a poroelastic medium and the dynamic
stress changes. Although these models can qualitatively explain
the delayed rupture, we were not able to reproduce the observed
delay, and further studies especially based on the dynamic stress
changes are required. Our detailed waveform analysis of the earthquake doublet, the model of interseismic and coseismic Coulomb
stress changes, and the examination of the delayed rupture provide
new clues to understand source processes of earthquake doublets at
segment boundaries.
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AC K N OW L E D G M E N T S
All the figures presented here were drawn using Generic Mapping
Tools (GMT, Wessel & Smith 1995). We greatly appreciate valuable
comments from M. Cocco and four anonymous reviewers.
REFERENCES
Ando, R. & Yamashita, T., 2007. Effects of mesoscopic-scale fault structure on dynamic earthquake ruptures: dynamic formation of geometrical complexity of earthquake faults, J. geophys. Res., 112, B09303,
doi:10.1029/2006JB004612.
Ando, R., Tada, T. & Yamashita, T., 2004. Dynamic evolution of a fault
system through interactions between fault segments, J. geophys. Res.,
109, B05303, doi:10.1029/2003JB002665.
Barka, A.A. & Kadinsky-Cade, K., 1988. Strike-slip fault geometry in
Turkey and its influence on earthquake activity, Tectonics, 7, 663–
684.
Belardinelli, M.E., Cocco, M., Cooutant, O. & Cotton, F., 1999. Redistribution of dynamic stress during coseismic ruptures: evidence for fault
interaction and earthquake triggering, J. geophys. Res., 104, 14 925–
14 945.
Bellier, O., Sebrier, M., Pramumijoyo, S., Beaudouin, T., Harjono, H., Bahar,
I. & Forni, O., 1997. Paleoseismicity and seismic hazard along the great
Sumatran fault (Indonesia), J. Geodyn., 24, 169–183.
Bouchon, M., 1979. Discrete wave number representation of elastic wave
fields in three-space dimensions, J. geophys. Res., 84, 3609–3614.
Burchfiel, B.C. & Stewart, J.H., 1966. “Pull-apart” origin of the central
segment of Death Valley, California, Geol. soc. Am. Bull., 77, 439–442.
Delouis, B., Giardini, D., Lundgren, P. & Salichon, J., 2002. Joint inversion
of InSAR, GPS, teleseismic, and strong-motion data for the spatial and
temporal distribution of earthquake slip: application to the 1999 İzmit
mainshock, Bull. seism. Soc. Am., 92, 278–299.
Dewey, J.W., 1976. Seismicity of northern Anatolia, Bull. seism. Soc. Am.,
66, 843–868.
Dieterich, J., 1979. Modeling of rock friction 1. Experimental results and
constitutive equations, J. geophys. Res., 84, 2161–2168.
Dieterich, J., 1994. A constitutive law for rate of earthquake production and
its application to earthquake clustering, J. geophys. Res., 99, 2601–2618.
Duan, B. & Oglesby, D.D., 2006. Heterogeneous fault stresses from previous earthquakes and the effect on dynamics of parallel strike-slip faults,
J. geophys. Res., 111, B05309, doi:10.1029/2005JB004138.
Genrich, J.F., Bock, Y., McCaffrey, R., Prawirodirdjo, L., Stevens, C.W.,
Puntedewo, S.S.O., Subarya, C. & Wdowinski, S., 2000. Distribution
of slip at the northern Sumatran fault system, J. geophys. Res., 105,
28 327–28 341.
Harris, R.A., 1998. Introduction to special section: stress triggers, stress
shadows, and implications for seismic hazard, J. geophys. Res., 103,
24 347–24 358.
Harris, R.A. & Day, S.M., 1993. Dynamics of fault interaction: parallel
strike-slip faults, J. geophys. Res., 98, 4461–4472.
Harris, R.A. & Day, S.M., 1999. Dynamic 3D simulations of earthquakes
on en echelon faults, Geophys. Res. Lett., 26, 2089–2092.
Harris, R.A., Archuleta, R.J. & Day, S.M., 1991. Fault steps and the dynamic
rupture process: 2D numerical simulations of a spontaneously propagating
shear fracture, Geophys. Res. Lett., 18, 893–896.
Horikawa, H., 2001. Earthquake doublet in Kagoshima, Japan: rupture of
asperities in a stress shadow, Bull. seism. Soc. Am., 91, 112–127.
Hudnut, K.W., Seeber, L. & Pacheco, J., 1989. Cross-fault triggering in
the November 1987 Superstition Hills earthquake sequence, southern
California, Geophys. Res. Lett., 16, 199–202.
Ida, Y., 1972. Cohesive force across the tip of a longitudinal-shear crack and
Griffith’s specific surface energy, J. geophys. Res., 77, 3796–3805.
Kennet, B.L.N, Engdahl, E.R. & Buland, R., 1995. Constraints on seismic
velocities in the Earth from traveltimes, Geophys. J. Int., 122, 108–124.
King, G.C.P., Stein, R.S. & Lin, J., 1994. Static stress changes and the
triggering of earthquakes, Bull. seism. Soc. Am., 84, 935–953.
Konca, A.O. et al., 2007. Rupture kinematics of the 2005 M w 8.6 NiasSimeulue earthquake from the joint inversion of seismic and geodetic
data, Bull. seism. Soc. Am., 97, S307–S322.
Lettis, W., Bachhuber, J., Witter, R., Brankman, C., Randolph, C.E., Barka,
A., Page, W.D. & Kaya, A., 2002. Influence of releasing step-overs on
surface fault rupture and fault segmentation: examples from the 17 August
1999 İzmit earthquake on the north Anatolian fault, Turkey, Bull. seism.
Soc. Am., 92, 19–42.
Li, V.C., Seale, S.H. & Cao, T., 1987. Postseismic stress and pore pressure
readjustment and aftershock distributions, Tectonophysics, 144, 37–54.
Lin, J. & Stein, R.S., 2004. Stress triggering in thrust and subduction
earthquakes and stress interaction between the southern San Andreas
and nearby thrust and strike-slip faults, J. geophys. Res., 109, B02303,
doi:10.1029/2003JB002607.
McClusky, S. et al., 2000. Global Positioning System constraints on plate
kinematics and dynamics in the eastern Mediterranean and Caucasus,
J. geophys. Res., 105, 5695–5719.
Muller, R.D., Roest, W.R., Royer, J., Gahagan, L.M. & Sclater, J.G., 1997.
Digital isochrons of the world’s ocean floor, J. geophys. Res., 102,
3211–3214.
Nakano, M. et al., 2006. Source estimates of the May 2006 Java earthquake,
EOS, Trans. Am. geophys. Un., 87, 493–494.
Nakano, M., Kumagai, H. & Inoue, H., 2008. Waveform inversion in the frequency domain for the simultaneous determination of earthquake source
mechanism and moment function, Geophys. J. Int., 173, 1000–1011,
doi:10.1111/j.1365-246X.2008.03783.x.
Natawidjaja, D.H., Tohari, A., Subowo, E. & Daryono, M.R., 2007. Western
Sumatra earthquakes of March 6, 2007, The West Sumatra Earthquakes
of March 6, 2007, EERI Special Earthquake Report, May 2007, 1–5.
Nur, A. & Booker, J.R., 1972. Aftershocks caused by pore fluid flow?,
Science, 175, 885–887.
Pacheco, J.F. & Sykes, L.R., 1992. Seismic moment catalog of large shallow
earthquakes, 1900 to 1989, Bull. seism. Soc. Am., 82, 1306–1349.
Piombo, A., Martinelli, G. & Dragoni, M., 2005. Post-seismic fluid flow and
Coulomb stress changes in a poroelastic medium, Geophys. J. Int., 162,
507–515.
Prawirodirdjo, Y., Bock, Y., Genrich, J.F., Puntodewo, S.S.O., Rais, J.,
Subarya, C. & Sutisna, S., 2000. One century of tectonic deformation
along the Sumatran fault from triangulation and Global Positioning System surveys, J. geophys. Res., 105, 28 343–28 361.
Rice, J.R. & Cleary, M.P., 1976. Some basic stress diffusion solutions for
fluid-saturated elastic porous media with compressible constituents, Rev.
Geophys., 14, 227–241.
Savage, J.C. & Burford, R.O., 1973, Geodetic determination of relative plate
motion in central California, J. geophys. Res., 78, 832–845.
Scholz, C.H., 2002. The Mechanics of Earthquakes and Faulting, 2nd edn,
Cambridge University Press, Cambridge.
Segall, P. & Pollard, D.D., 1980. Mechanics of discontinuous faults, J. geophys. Res., 85, 4337–4350.
Sekiguchi, H. & Iwata, T., 2002. Rupture process of the 1999 Kocaeli,
Turkey, earthquake estimated from strong-motion waveforms, Bull. seism.
Soc. Am., 92, 300–311.
Sieh, K. & Natawidjaja, D., 2000. Neotectonics of the Sumatran fault, Indonesia, J. geophys. Res., 105, 28 295–28 326.
Sipkin, S.A., 1994. Rapid determination of global moment-tensor solutions,
Geophys. Res. Lett., 21, 1667–1670.
Stein, R.S., 1999. The role of stress transfer in earthquake occurrence,
Nature, 402, 605–609.
Stump, B.W. & Johnson, L.R., 1977. The determination of source properties by the linear inversion of seismograms, Bull. seism. Soc. Am., 67,
1489–1502.
Tada, T. & Madariaga, R., 2001. Dynamic modelling of the flat 2-D crack
by a semi-analytic BIEM scheme, Int. J. Numer. Methods Eng., 50, 227–
251.
Toda, S., Stein, R.S., Richards-Dinger, K. & Bozkurt, S.B., 2005. Forecasting the evolution of seismicity in southern California: animations
built on earthquake stress transfer, J. geophys. Res, 110, B05S16,
doi:10.1029/2004JB003415.
C
2010 The Authors, GJI, 181, 141–153
C 2010 RAS
Journal compilation Source model of an earthquake doublet
Untung, M., Buyung, N., Kertapati, E., Undang, & Allen, C.R.,
1985. Rupture along the great Sumatran fault, Indonesia, during the
earthquakes of 1926 and 1943, Bull. seism. Soc. Am., 75, 313–
317.
Wang, H.F., 2000. Theory of Linear Poroelasticity with Applications to
Geomechanics and Hydrogeology, Princeton University Press, Princeton,
New Jersey.
C
2010 The Authors, GJI, 181, 141–153
C 2010 RAS
Journal compilation 153
Wesnousky, S.G., 2006. Predicting the endpoints of earthquake ruptures,
Nature, 444, 358–360, doi:10.1038/nature05275.
Wessel, P. & Smith, W.H.F., 1995. New version of the generic mapping tools
released, EOS, Trans. Am. geophys. Un., 76, 329.
Yagi, Y. & Kikuchi, M., 2000. Source rupture process of the Kocaeli, Turkey,
earthquake of August 17, 1999, obtained by joint inversion of near-field
data and teleseismic data, Geophys. Res. Lett., 27, 1969–1972.

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