GJI Geomagnetism, rock magnetism and palaeomagnetism
Geophys. J. Int. (2009) 176, 420–430
doi: 10.1111/j.1365-246X.2008.04009.x
Coseismic and postseismic deformation associated with the 2003
Chengkung, Taiwan, earthquake
Ya-Ju Hsu, Shui-Beih Yu and Horng-Yue Chen
Institute of Earth Sciences, Academia Sinica, PO Box 1-55, Nankang, Taipei, Taiwan. E-mail: [email protected]
Accepted 2008 October 7. Received 2008 October 7; in original form 2008 July 3
SUMMARY
We use GPS-derived coseismic and postseismic displacements of the 2003 M w 6.8 Chengkung,
Taiwan, earthquake to examine seismogenic behaviour of the southern Longitudinal Valley.
We invert for fault slip on the Chihshang fault, a segment of the Longitudinal Valley fault,
based on a simplified layered earth model and a listric-shape fault geometry. Our model infers
that maximum coseismic slip of about 0.72 m occurred at a depth of 15 km. Conversely,
postseismic slip of about 0.1 m over a 157 d period mainly occurred at depths less than 10 km.
We find an anticorrelation between coseismic and postseismic slip distributions. However, the
depth profiles of seismicity before and after the main shock are very similar and both show
the peak seismicity at 15–25 km depth, consistent with the depth range of large coseismic
slip. The potency distribution at depth reveals a coseismic slip deficit at shallow depths, which
is compensated by postseismic and interseismic creep associated with the Lichi Mélange.
Aseismic slip is an important component of the slip budget on the Chihshang fault. According
to the historic earthquake records, interseismic slip rate and coseismic slip on the Chihshang
fault, the recurrence interval of this type of event is between 12 and 36 yr. We use a ratedependent friction model of afterslip to infer the frictional parameter, dτ ss /dlnV = 0.03–
0.5 MPa, at shallow depths on the Chihshang fault. Assuming effective normal stress of
, is about 3 × 10−4 –5 × 10−3 ,
100 MPa at 5 km depth, the rheological parameter, a = ∂ ∂μ
ln V
which is in good agreement with laboratory experiments.
Key words: Inverse theory; Space geodetic surveys; Seismic cycle; Earthquake source observations; Kinematics of crustal and mantle deformation; Rheology and friction of fault
zones.
1 I N T RO D U C T I O N
The 2003 December 10 Chengkung earthquake occurred in southeastern Taiwan with a local magnitude (M L ) of 6.5 and a focal depth
of 10 km recorded by the Central Weather Bureau Seismic Network
(CWBSN). The reported magnitude (M w ) from the Broadband Array in Taiwan for Seismology (BATS) and Harvard-CMT (teleseismic data) are 6.6 and 6.8, respectively. The focal depth obtained
from these catalogues is about 25 km. Hundreds of aftershocks
have occurred at 5–30 km depth after the main shock. The relocated
aftershocks show a listric-shape distribution of seismicity at depth
(Wu et al. 2006), which could be connected to the Chihshang fault
on the surface. Field surveys in the Chihshang fault area show some
folding structures associated with the main shock (Lee et al. 2006).
The coseismic rupture of the Chengkung earthquake is believed to
break the Chihshang fault, which is a segment of the Longitudinal
Valley fault (LVF). The NNE-striking LVF represents the present
plate boundary between the Philippine Sea Plate and Eurasian Plate
and accommodates about half of the convergence across the Taiwan mountain belt. Yu & Liu (1989) found the central segment of
the LVF, extending from Juisui to Chihshang is creeping with both
vertical and horizontal motions. The geodetic measurements, field
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outcrop data and creep meter data indicate the horizontal shortening
rate across the Chihshang fault is about 20–30 mm yr−1 (Yu & Liu
1989; Liu & Yu 1990; Angelier et al. 1997; Lee et al. 2001; Yu &
Kuo 2001; Lee et al. 2003, 2006).
Field observations of the coseismic deformation near the
Chihshang fault are characterized by anticlinal folding in the hangingwall and minor gentle synclinal folding in the footwall (Lee
et al. 2006). The surface displacements measured using the Global
Positioning System (GPS) show that coseismic movements are not
significant near the surface trace of the Chihshang fault, mostly less
than 20 mm (Fig. 1). The maximum coseismic GPS horizontal and
vertical displacements of about 0.13 and 0.26 m, respectively, occurred near the coast (Chen et al. 2006). These observations suggest
that the coseismic rupture does not reach the surface. On the other
hand, the GPS-derived postseismic displacements in a 157 d period
after the main shock are larger on the fault zone than that near the
coast (Figs 2 & 3). The data recorded in creep meters shows significant displacements of about 70–90 mm during a 4 month period
following the main shock. Savage & Yu (2007) demonstrate that
the postseismic relaxation and aftershocks of the Chengkung earthquake are driven by fault slip on the coseismic rupture. In addition
to postseismic creep, the Chihshang fault also exhibits substantial
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Figure 1. Coseismic displacements of the 2003 Chengkung earthquake. (a) GPS horizontal displacements are shown in black vectors with a 95 per cent
confidence ellipse. Major active faults are indicated as solid purple lines. The star shows the main shock epicentre. (b) Vertical displacements are shown by
circles with uplift and subsidence indicated by red and blue colours, respectively. The black circles are standard deviations. Blue stars denote the 1951 M L 6.1
and 7.3 earthquakes.
Figure 2. Examples of GPS time-series of postseismic displacements following the 2003 Chengkung earthquake. Text in the first panel indicates the station
name. The locations of CGPS stations are shown in Fig. 3(a). The grey curves are predicted postseismic time-series using a rate- and state-dependent friction
law in eq. (3).
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Y.-J. Hsu, S.-B. Yu and H.-Y. Chen
shallow creep before the main shock. However, the spatial extent of
interseismic creep at depth remains unclear.
Our study aims to provide a better understanding of spatial distribution of coseismic and postseismic slip, using GPS data from
a dense local network. The large postseismic displacements near
the surface fault trace suggest that postseismic slip occurred on
the shallow segment of the Chihshang fault. Afterslip seems to
be the primary contribution to the postseismic deformation of the
Chengkung earthquake (Savage & Yu 2007). We estimate the frictional properties of the fault zone by fitting postseismic GPS timeseries to the equation in Perfettini & Avouac (2004a). They suggest
that postseismic deformation is driven by fault creep on the brittle
creeping fault zone. By investigating GPS displacements as well as
the seismicity before and after the Chengkung earthquake, we aim
for a better assessment of the spatial and temporal distribution of
fault slip at depth and the seismogenic behaviour of the southern
Longitudinal Valley.
2 G P S D ATA C O L L E C T I O N A N D
P RO C E S S I N G
The Chengkung earthquake occurred in the Longitudinal Valley
of eastern Taiwan, where repeated precise trilateration, first-order
levelling and the GPS surveys were conducted over the past two
decades (Yu & Liu 1989; Liu & Yu 1990; Yu & Kuo 2001). The
Institute of Earth Sciences, Academia Sinica (IESAS) has installed
more densely deployed GPS monuments in the southern Longitudinal Valley since 1997. Annual geodetic surveys including levelling,
GPS (Chen et al. 2006), as well as daily creep meter measurements
(Lee et al. 2001; Lee et al. 2003) have been carried out since the later
1990s. Most continuous GPS (CGPS) sites have recorded data for
about 2 yr before the Chengkung earthquake. Forty-one campaignmode sites in the southern Longitudinal Valley were occupied in
2003 November, right before the Chengkung earthquake. The first
and second campaigns after the Chengkung earthquake were carried
out at 6 and 104 days after the main shock, respectively. Estimates
of coseismic displacements in campaign-mode sites are described
in Chen et al. (2006). In this study, we integrate all available data,
including 20 CGPS sites installed by IESAS, the Central Weather
Bureau (CWB) and the Ministry of the Interior (MOI), as well as
41 campaign-mode sites deployed by IESAS (Chen et al. 2006).
Each campaign was occupied at least 7 hr, using dual frequency
geodetic receivers with a 15-s sampling rate and a cut-off elevation
angle of 10◦ . The GPS data is processed using Bernese 4.2 software
(Hugentobler et al. 2001) with a fiducial free approach. The daily solutions are combined into a free network solution. Precise ephemeredes provided by the International GNSS Services (IGS) are employed and fixed in the post-processing. Residual tropospheric
zenith delays are estimated simultaneously with the station coordinates, by least-squares adjustments. The Paisha, Penghu continuous GPS station (S01R), situated on the stable Chinese continental
margin, is chosen to define the minimum constrained conditions
to its value in the International Terrestrial Reference Frame 2000
(ITRF00). Chen et al. (2006) gives a more detailed description of the
GPS data acquisition and processing. The coseismic displacements
of the Chengkung earthquake are shown in Fig. 1.
The procedures of postseismic GPS data processing are similar
to the coseismic data. However, we only choose data from 20 CGPS
sites to analyse the postseismic deformation. The site positions
from daily solutions at each CGPS site are used to create GPS timeseries (Fig. 2). A moderate M L 6 aftershock occurred near Lutao
on 2004 May 19 and produced significant coseismic displacements
at some CGPS sites. To exclude the deformation associated with
the Lutao earthquake, we only analyse GPS time-series in a 157 d
period before the Lutao earthquake. The cumulative postseismic
surface displacements indicate displacements near the surface trace
Figure 3. Postseismic displacements in a 157 d period. (a) GPS horizontal displacements are shown in black vectors with a 95 per cent confidence ellipse.
Major faults are indicated as solid purple lines. Black texts show the station names. The star is the main shock epicentre. (b) Vertical displacements are shown
by circles with uplift and subsidence indicated by red and blue, respectively. The black circles are standard deviations.
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of the fault zone are much larger than those in the far field (Chen
et al. 2006; Ching et al. 2007). Combining the evidence of significant postseismic creep across the Chihshang fault inferred from the
creep meter data (Lee et al. 2006), we suggest the source of postseismic deformation is shallow. A related study by Savage & Yu (2007)
suggests that the postseismic deformation of the Chengkung earthquake results from afterslip on a 55◦ east-dipping fault, extended
from the surface to 16 km at depth.
We model afterslip, using an analytical formula derived by a
1-D system of springs and sliders model, loaded by a constant
force (Perfettini & Avouac 2004a,b). Each portion of the fault is
modelled by one slider and connected by one spring. The behaviour
of the fault system is determined from the constitutive law and
the equation of force balance on each slider. The fault model is
composed of three portions, including the seismogenic zone, the
brittle creep zone (the zone of afterslip) and the ductile zone. The
seismogenic zone and the brittle creep zone are modelled using rateand state-dependent friction laws, whereas the ductile fault zone at
depth is modelled using Newtonian viscosity. The interseismic GPS
displacement results from the combined effect of fault slip on the
ductile zone and the brittle creep zone. The contributions from
these two zones are unknown ratios of the long-term slip velocity,
V 0 , at depth depending on the site position relative to each fault
portion. Assuming the fractions of the long-term slip velocity (V 0 )
on the ductile zone and the brittle fault zone to be α and β, the
interseismic GPS displacement time-series, U(t), can be written as
(eq. 49 in Perfettini & Avouac 2004a)
U (t) = αV0 t + βV0 t.
(1)
At steady state, the postseismic GPS displacement time-series
resulting from rate-strengthening afterslip can be written as (eq. 50
in Perfettini & Avouac 2004a)
U (t) = αV0 t + βV0 tr log{1 + d[exp(t/tr ) − 1]},
(2)
where V 0 is the long-term slip velocity at depth; t r is the relaxation
time; d is the velocity jump due to coseismic stress change. The
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value of αV 0 + βV 0 is equivalent to the interseismic GPS velocity
(eq. 1). However, eq. 2 is valid only if the sliding velocity of the
ductile zone does not significantly change after the main shock.
The acceleration of slip on the ductile zone is observed at one
CGPS site following the 2001 M w 8.4 Peru earthquake (Perfettini
et al. 2005). This implies that the viscous flow at depth needs to be
considered. To evaluate the influence of accelerated viscous flow
on the postseismic deformation of the Chengkung earthquake, we
modify the eq. (2) as
U (t) = V1 t + V2 tr log{1 + d[exp(t/tr ) − 1]},
(3)
where V 1 and V 2 are contributions from slip on ductile fault zone
and the brittle fault zone, respectively. The parameters of V 1 , V 2 ,
t r and d for each time-series are independently solved by leastsquare adjustments, and the values with two standard deviations are
listed in Table 1. The modelled postseismic time-series are shown in
Fig. 2. By comparing the interseismic GPS velocity, αV 0 + βV 0 ,
and the modelled velocity, V 1 + V 2 , at each site, we can evaluate the influence of viscous relaxation on the ductile zone. If the
acceleration of viscous flow due to coseismic stress change is negligible, these two values (αV 0 + βV 0 and V 1 + V 2 ) are similar.
We list the interseismic velocity components and the modelled values of V 1 + V 2 at each component in Table 2. The observed and
modelled velocity components in the north–south and east–west
directions at most sites are similar before and after the Chengkung
earthquake, except for vertical components. The discrepancies between observed and modelled vertical components remain unclear.
If we focus on horizontal components, our result indicates that the
contribution of viscous relaxation to the postseismic deformation is
not significant.
We then calculate the cumulative postseismic displacements in
157 d (Fig. 3), between the occurrence of the main shock and the
Lutao earthquake, using eq. (3). The secular motion of each site is
removed using the interseismic velocity field from Yu & Kuo (2001)
and Chen et al. (2006). Uncertainties in the corrections of secular
velocities are propagated into the data covariance matrices.
Table 1. The parameters with two standard deviations, used to predicted the postseismic displacement time-series using eq. (3).
Site
CHEN
DONA
ERPN
JPIN
KNKO
LONT
MESN
MINS
MOTN
PAOL
PING
S104
S105
SHAN
TAPE
TAPO
TMAM
TTUN
TUNH
YULI
tr
(yr)
d
V e1
(mm yr−1 )
V e2
(mm yr−1 )
V n1
(mm yr−1 )
V n2
(mm yr−1 )
V u1
(mm yr−1 )
V u2
(mm yr−1 )
0.11 ± 0.05
0.04 ± 0.07
0.17 ± 0.16
0.37 ± 0.11
0.42 ± 0.38
0.03 ± 0.03
0.08 ± 0.14
0.11 ± 0.13
0.23 ± 0.31
0.17 ± 0.40
1.00 ± 1.04
0.06 ± 0.30
0.23 ± 0.14
0.98 ± 0.40
0.35 ± 0.15
1.16 ± 0.86
0.02 ± 0.02
0.03 ± 0.30
1.13 ± 0.57
0.02 ± 0.06
110.0 ± 30.0
35.0 ± 20.0
15.0 ± 19.9
15.0 ± 0.0
4.9 ± 20.3
5.0 ± 20.0
25.0 ± 29.9
45.0 ± 24.0
30.0 ± 30.0
6.7 ± 15.0
14.9 ± 10.2
25.0 ± 15.0
15.0 ± 19.9
15.0 ± 9.7
90.0 ± 30.0
60.0 ± 30.0
55.0 ± 25.0
15.0 ± 20.1
160.0 ± 30.0
40.0 ± 30.0
−126 ± 24
−101 ± 16
−28 ± 21
−58 ± 15
−67 ± 22
−23 ± 21
−67 ± 24
−71 ± 23
−54 ± 17
−92 ± 23
−62 ± 18
2 ± 22
−66 ± 23
−58 ± 21
−48 ± 13
−64 ± 10
−45 ± 20
−7 ± 30
−69 ± 13
−54 ± 25
74 ± 19
47 ± 16
−36 ± 14
7±5
7 ± 17
7 ± 20
38 ± 15
30 ± 19
19 ± 14
49 ± 22
5±9
−57 ± 21
41 ± 20
21 ± 19
21 ± 9
2±2
6 ± 16
−31 ± 26
8±5
30 ± 30
15 ± 21
12 ± 23
38 ± 24
33 ± 11
24 ± 22
28 ± 14
30 ± 23
14 ± 22
17 ± 22
8 ± 19
13 ± 25
39 ± 18
16 ± 23
28 ± 17
19 ± 13
−7 ± 18
−19 ± 20
7 ± 31
12 ± 8
38 ± 22
43 ± 13
−7 ± 17
14 ± 12
13 ± 4
20 ± 16
−32 ± 14
−34 ± 16
−12 ± 11
−15 ± 15
−7 ± 10
14 ± 21
−10 ± 12
−15 ± 16
−9 ± 9
−17 ± 8
20 ± 14
22 ± 16
−14 ± 26
9±5
−9 ± 21
−54 ± 5
32 ± 4
−48 ± 8
−91 ± 3
−31 ± 6
−16 ± 5
8±3
−2 ± 6
−13 ± 4
−34 ± 8
−56 ± 7
−16 ± 9
−31 ± 4
−56 ± 3
−38 ± 1
−36 ± 11
51 ± 2
−47 ± 8
−59 ± 5
−33 ± 9
77 ± 12
−32 ± 6
64 ± 11
38 ± 8
3±5
−26 ± 5
−11 ± 7
−11 ± 5
3±5
13 ± 5
10 ± 11
33 ± 8
−5 ± 7
2±2
−15 ± 7
20 ± 14
−79 ± 3
1 ± 12
18 ± 11
2 ± 15
Note: t r is the relaxation time; d is the velocity jump due to coseismic stress change; V e1 and V e2 correspond to the east component of velocities resulting from
slip on the ductile fault zone and the brittle fault zone, respectively; V n1 , V n2 are similar to V e1 and V e2 , but for the north component; V u1 and V u2 for the vertical
component.
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Y.-J. Hsu, S.-B. Yu and H.-Y. Chen
Table 2. Modelled and observed interseismic velocity components with two standard deviations.
Site
CHEN
DONA
ERPN
JPIN
KNKO
LONT
MESN
MINS
MOTN
PAOL
PING
S104
S105
SHAN
TAPE
TAPO
TMAM
TTUN
TUNH
YULI
V e1 + V e2 (mm yr−1 )
V e (mm yr−1 )
V n1 + V n2 (mm yr−1 )
V n (mm yr−1 )
V u1 + V u2 (mm yr−1 )
V u (mm yr−1 )
−52.0 ± 30.6
−54.0 ± 22.6
−64.0 ± 25.2
−51.0 ± 15.8
−60.0 ± 27.8
−16.0 ± 29.0
−29.0 ± 28.3
−41.0 ± 29.8
−35.0 ± 22.0
−43.0 ± 31.8
−57.0 ± 20.1
−55.0 ± 30.4
−25.0 ± 30.5
−37.0 ± 28.3
−27.0 ± 15.8
−62.0 ± 10.2
−39.0 ± 25.6
−38.0 ± 39.7
−61.0 ± 13.9
−24.0 ± 39.1
−49.5 ± 0.3
−51.5 ± 0.2
−46.6 ± 0.2
−40.6 ± 0.2
−46.2 ± 0.2
−51.2 ± 0.3
−30.7 ± 0.2
−28.7 ± 0.2
−29.0 ± 0.3
−41.3 ± 0.2
−45.0 ± 0.2
−48.4 ± 0.2
−30.7 ± 0.4
−34.6 ± 0.3
−45.0 ± 0.2
−47.8 ± 0.2
−31.2 ± 0.2
−39.7 ± 0.3
−48.1 ± 0.2
−27.1 ± 0.3
58.0 ± 24.7
5.0 ± 28.6
52.0 ± 26.8
46.0 ± 11.7
44.0 ± 27.2
−4.0 ± 19.8
−4.0 ± 28.0
2.0 ± 24.6
2.0 ± 26.6
1.0 ± 21.5
27.0 ± 32.6
29.0 ± 21.6
1.0 ± 28.0
19.0 ± 19.2
2.0 ± 15.3
13.0 ± 22.8
3.0 ± 25.6
−7.0 ± 40.5
21.0 ± 9.4
29.0 ± 30.4
43.2 ± 0.2
−1.1 ± 0.1
39.0 ± 0.3
35.6 ± 0.2
46.8 ± 0.2
31.9 ± 0.3
2.7 ± 0.1
3.2 ± 0.1
6.0 ± 0.2
−2.3 ± 0.1
46.3 ± 0.2
39.1 ± 0.2
12.6 ± 0.3
21.6 ± 0.2
37.6 ± 0.2
41.4 ± 0.3
8.1 ± 0.2
6.9 ± 0.4
42.6 ± 0.2
16.8 ± 0.3
23.0 ± 13.0
0.0 ± 7.2
16.0 ± 13.6
−53.0 ± 8.5
−28.0 ± 7.8
−42.0 ± 7.1
−3.0 ± 7.6
−13.0 ± 7.8
−10.0 ± 6.4
−21.0 ± 9.4
−46.0 ± 13.0
17.0 ± 12.0
−36.0 ± 8.1
−54.0 ± 3.6
−53.0 ± 7.1
−16.0 ± 17.8
−28.0 ± 3.6
−46.0 ± 14.4
−41.0 ± 12.1
−31.0 ± 17.5
−4.5 ± 0.7
5.3 ± 0.4
−3.9 ± 0.6
1.8 ± 0.4
−13.5 ± 0.4
3.2 ± 0.7
7.4 ± 0.6
6.0 ± 0.4
6.0 ± 0.5
4.3 ± 0.5
−3.3 ± 0.4
1.1 ± 0.4
−3.9 ± 0.6
−7.8 ± 0.4
1.7 ± 0.4
4.1 ± 0.5
−1.8 ± 0.5
0.3 ± 0.5
−0.9 ± 0.6
−16.7 ± 0.9
V e , V n , and V u are the east, north and vertical components of interseismic velocities, respectively; V e1 + V e2 is the modelled east component of velocity
resulting from slip on the ductile fault zone and the brittle fault zone; V n1 + V n2 is similar to V e1 + V e2 , but for the north component; V u1 + V u2 for the vertical
component.
Figure 4. The coseismic model of the Chengkung earthquake (a) Coseismic slip distribution projected on the surface is shown in colour. Black and blue
vectors indicate observed and predicted GPS horizontal displacements, respectively. Major faults are indicated as solid purple lines. The white star is the main
shock epicentre. Green dots denote relocated aftershocks from Wu et al. (2006). (b) Vertical displacements (black) and model predictions (blue).
3 INVERSION OF COSEISMIC AND
POSTSEISMIC SLIP DISTRIBUTIONS
We approximate the fault geometry using aftershocks and the surface trace of the Chihshang fault. Results from relocated seismicity
show the Chihshang fault is an east-dipping fault with a listric-shape
(Chen & Rau 2002). Our modelled fault has a dimension of 46 km
in length and 53 km in width. The fault dip is 60◦ at shallow depth
(0–12 km) and is about 20◦ at 25 km depth. To allow for spatial heterogeneous fault slip and match the surface trace of the Chihshang
fault, we divide the modelled fault into 121 patches. In addition,
we constrain slip directions to be left-lateral and updip to be consistent with the moving directions of surface GPS displacements. A
weighted least-square inversion algorithm is employed to solve for
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Table 3. The crustal model in the southern Longitudinal Valley simplified
from Wu et al. (2007).
VP
(km s−1 )
VS
(km s−1 )
Density
(g cm−3 )
Rigidity
×1010 N m−2
Thickness
(km)
2.19
2.68
2.90
3.02
3.34
3.69
3.92
4.22
4.41
4.39
4.75
2.4
2.5
2.5
2.5
2.6
2.7
2.7
3.0
3.0
3.0
3.0
1.30
1.90
2.27
2.45
2.99
3.73
4.41
5.43
5.79
5.79
6.89
2
2
2
3
4
4
8
10
15
20
50
4.06
4.80
5.20
5.38
5.87
6.49
6.99
7.37
7.61
7.61
8.30
coseismic slip distribution by minimizing the following functional
−1/2
F(s, β, m) = [G(m)s − d]2 + β1−2 ∇ 2 s2 + β2−2 s2 ,
(4)
−1/2
is the inverse square root of the data covariance matrix;
where
G(m) are Green’s functions in a layered earth structure (Table 3)
simplified from Wu et al. (2007), which depend on the fault geometry parameters m, s is slip; d is the observed displacements and ∇ 2
is the finite difference approximation of the Laplacian smoothing
operator (Harris & Segall 1987). The last term in eq. (4) is used to
minimize the solution length, meaning minimize the moment, and
suppress fault slip in areas without data coverage. The parameters
of β 1 and β 2 serve as the weighting of the model roughness versus
data misfit and minimum solution length, respectively. The values
of these parameters are obtained by cross-validation (Matthews &
Segall 1993).
We use the same coseismic fault geometry for the inversion of
postseismic slip in a 157 d period. Because of insufficient CGPS
data in the near field after the main shock, we use a slightly different approach from eq. (4) to solve for postseismic slip. Numerous
studies have shown that the coseismic slip and postseismic slip are
spatial anticorrelated, for instance, the 2003 Tokachi-oki, Japan,
earthquake (Baba et al. 2006), the 2005 Nias-Simeulue, Sumatra,
earthquake (Hsu et al. 2006), and 1995 Chile earthquake (Pritchard
& Simons 2006). To better resolve afterslip, a damping vector, s cos ,
scaled with the value of coseismic slip is used to suppress postseismic slip in areas where coseismic slip is large. In other words, we
substitute for the last term of eq. (4) that minimizes the moment
T
2
for a new term, β −2
2 (I s cos ) s , where I is an identity matrix. The
remaining terms are identical to eq. (4). The modelling results are
discussed in the next section.
4 R E S U LT S A N D D I S C U S S I O N
4.1. Coseismic slip distribution
Inferred coseismic slip and fits of predicted to GPS observed surface
displacements are shown in Figs 4 and 5(a). The average residuals
of modelled coseismic displacements are 12, 9 and 21 mm in the
east, north and vertical components, respectively, in contrast to the
average standard deviations of 5, 5 and 7 mm in the east, north and
vertical components, respectively, of observed coseismic displacements. To evaluate the goodness of the model fit, we estimate the
reduced chi-square value (χ 2r ). A good fit corresponds to a value of
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χ 2r of about 1.0, so that the model fits the data within uncertainties.
The value of χ 2r is 11 in our coseismic model. This is possibly due
to the underestimation of observational uncertainty in the coseismic
displacement rather than a less than satisfactory fit of the coseismic
model. The maximum coseismic slip is about 0.72 m at 15 km depth,
near the coast. We find that the reverse slip with average of about
0.3 m is the primary component, in contrast to a smaller component
of 0.1 m left-lateral slip (Fig. 5a). The inferred coseismic geodetic
moment is 2.0×1019 N m, equivalent to a M w 6.8 earthquake, and
is consistent with Harvard-CMT solution. To evaluate the influence
of depth-variable elastic properties on coseismic slip distribution,
we conduct the inversion in a homogeneous elastic half-space and
a layered earth model (Table 3). We invert for coseismic slip using identical fault geometry in two earth models. The difference of
maximum slip between two models is only 10 per cent. Inferred
coseismic potency (product of slip and slip area) is about 5 per cent
more in an elastic half-space model comparing with that in a layered
earth model. The coseismic potency distributions at depth in the two
models are very similar in that both show a peak at 15 km depth
(Fig. 6a). The coseismic model with minimizing moment constraint
shows a less deep slip (the blue line in Fig. 6a) and the potency is
about 12 per cent less than that without constraint of minimizing
moment (the red line in Fig. 6a). Despite different earth structure
models and inversion schemes, we demonstrate that the pattern of
coseismic slip distribution remains similar.
Note that the coseismic slip in the hypocentral region is small
and the large slip is located to the south of the hypocentre. A recent
analysis of repeating earthquakes near the Chihshang fault indicates
a cluster of repeating earthquakes to the north of hypocentre at a
depth range of 7–23 km (Chen et al. 2007). Regions exhibiting repeating earthquakes with small magnitude are usually characterized
by aseismic slip. Because of high stress surrounding the creeping
zone, a large earthquake is likely to nucleate there and eventually
grow into areas those are more tightly coupled. This behaviour has
been seen in many subduction zone earthquakes, for instance, the
2004 Aceh-Andaman, 2005 Nias-Simeulue earthquake, as well as
the 1995 Antofagasta, Chile, earthquakes (Hsu et al. 2006; Pritchard
& Simons 2006; Subarya et al. 2006). The Chengkung earthquake
possibly shares the same characteristic as these subduction zone
earthquakes.
We compare our coseismic slip distribution with previous studies
of coseismic source models based on various data sets, including
seismic strong motion and GPS, and different earth models (Wu
et al. 2006; Ching et al. 2007; Hu et al. 2007). The average values
of coseismic slip inferred using only GPS data are 0.30 m (this
study), 0.44 m (Ching et al. 2007) and 0.48 m (Hu et al. 2007),
respectively. The average values of coseismic slip inferred using
only seismic strong motion data are 0.34 m in Hu et al. (2007) and
0.39 m in Wu et al. (2006). This study and Ching et al. (2007)
use different layered earth models derived by Wu et al. (2007) and
Chen & Rau (2002), respectively. In this study, the large coseismic
slip mainly concentrates at a depth of 15 km and is consistent with
the result posted by Ching et al. (2007). However, Ching et al.’s
model shows another asperity at a depth of 25 km, between the
coastline and the Lutao Island. This asperity at depth is likely a
result of significant coseismic displacement on the GPS site Lutao,
or alternately, a possibility due to the choice of damping parameter
(β 1 ) for the smoothing operator. The coseismic asperity centred at
a depth of 15 km separates into two asperities if we choose a rough
coseismic slip model (Fig. 6a). Hu et al. (2007) use Poly3D, based
on angular dislocations, to invert for coseismic slip. The average
slip and the maximum coseismic slip in their model are about 1.5–2
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Y.-J. Hsu, S.-B. Yu and H.-Y. Chen
Figure 5. (a) Coseismic and (b) postseismic slip distributions of the Chengkung earthquake. The fault dip is 60◦ at a shallow depth and 20◦ at a depth of
25 km. Coloured and blue vectors indicate fault slip. The white star is the hypocenter.
Figure 6. The sum of potency at a given depth. (a) The coseismic potency distribution at depth in various models. The inset shows the trade-off between
weighted root mean square and model roughness. The red and yellow dots indicate the values of β 1 for models shown in red and yellow lines, respectively.
(b) Black and red curves indicate potencies at a given depth during the coseismic and postseismic periods, respectively. The blue curve is the sum of coseismic
and postseismic potencies.
times bigger than those in our model. However, both studies use
the same coseismic GPS displacements (Chen et al. 2006) and a
similar fault geometry determined by aftershock distributions. The
only difference is that Hu et al. (2007) use an elastic half-space
model. However, the large discrepancy in the slip amplitude cannot be explained by geological material properties. We demonstrate
that differences in the average slip and the maximum slip between
uniform and layered earth models are about 10 per cent (Fig. 6a).
In addition, the large slip in Hu et al. (2007) cannot be explained
by choosing a rough coseismic slip model (Fig. 6a), which only
contributes to an increase of 25 per cent in the maximum coseismic slip. The average residuals in Hu et al. (2007) are 22, 7 and
27 mm in the east, north and vertical components, respectively, and
are larger than 12, 9 and 21 mm, respectively, in our model. The
residuals in both models are larger than the average standard deviations of 5, 4and 12 mm in the east, north, and vertical components
of coseismic displacements, respectively. Wu et al. (2006) estimate
the average coseismic slip of about 0.39 m, which is comparable
with the average slip of 0.36 m if an elastic half-space model is used
in this study. To summarize, the main advantages of our coseismic
model include (1) utilizing a realistic 3-D fault geometry; (2) inverting for coseismic slip in a layered earth model and (3) suppressing
coseismic slip in areas without data coverage by implementing the
minimized moment constraint.
4.2 Postseismic slip distribution
Modelling of postseismic deformation resulting from afterslip in a
157 d period is shown in Figs 5(b) and 7. The predicted and observed
postseismic displacements are shown in Fig. 7. The average residuals are 8, 8 and 12 mm in the east, north and vertical components,
respectively, compared with the average standard deviations of 4, 3
and 8 mm, respectively, in the east, north and vertical components
of postseismic displacements. Our optimal postseismic model indicates a reasonable fit corresponding to a value of reduced chi-square
of 6. The maximum afterslip of 0.12 m occurred at a shallow depth
of 0–10 km (Fig. 5b), consistent with the postseismic slip distribution in Ching et al. (2007), based on cumulative displacements of
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427
Figure 7. Afterslip following the Chengkung earthquake in a 157 d period. (a) Postseismic slip distribution projected on the surface is shown in colour. Black
and blue vectors indicate observed and predicted GPS horizontal displacements, respectively. Major faults are indicated as solid purple lines. The white star is
the main shock epicentre. Green dots denote relocated aftershocks from Wu et al. (2006). (b) Vertical displacements (black) and model predictions (blue).
eight CGPS sites in a 4 month period. We also test a model without
the constraint of spatial anticorrelation between coseismic slip and
postseismic slip and find that the inferred postseismic slip distribution is not much different from that in our optimal model. Afterslip
mainly occurs at shallow depths, and there is little overlap between
postseismic and coseismic slip (Fig. 5). Surface measurements including postseismic GPS observations and daily creep meter data
show significant postseismic displacements near the surface trace of
the Chihshang fault (Chen et al. 2006; Ching et al. 2007; Lee et al.
2006). It is possible that afterslip occurs at the downdip end of the
coseismic rupture as well. However, we are not able to resolve deep
slip due to poor data coverage. The inferred geodetic moment of the
afterslip model is 2.7 × 1018 N m, corresponds to M w 6.2 and is
about 13 per cent of coseismic geodetic moment. The depth profiles
of postseismic potency and coseismic potency indicate an obvious
slip deficit at shallow depths (Fig. 6b). The accumulated strain in
the shallow portion has to be released either through earthquake
ruptures or interseismic creep. We plot depth profiles of seismicity
and seismic moment in a depth range less than 50 km and magnitude larger than 2.5 before and after the Chengkung earthquake
Figure 8. The percentage of earthquake numbers (M L > 2.5, Depth < 50 km) and moment at a given depth in the rupture area of the 2003 Chengkung
earthquake (earthquake data from the Central Weather Bureau). Black and grey dashed lines indicate the percentage of seismic moment before and after the
main shock. Black and grey solid lines indicate the percentage of earthquake numbers before and after the main shock.
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Y.-J. Hsu, S.-B. Yu and H.-Y. Chen
(Fig. 8). The depth profiles of seismicity and moment before and
after the main shock are very similar so that shallow events are
rare, whereas events are abundant in the depth range of 15–25 km,
consistent with coseismic potency distribution at depth (Fig. 6b).
Because of insufficient seismic moment release for shallow events,
the postseismic creep and interseismic creep seem to be a preferable
scenario to release accumulated strain at shallow depths. Indeed, our
afterslip model requires significant amount of shallow postseismic
slip. On the other hand, previous studies have shown that continuous interseismic creep at a rate of about 20–30 mm yr−1 across
the Chihshang fault (Yu & Kuo 2001; Lee et al. 2003, 2006). Incorporating these results with seismicity and potency distributions
at depth, we suggest that the extent of the shallow aseismic zone at
depth is possibly less than 10 km.
distributions of creeping zones in the interseismic and postseismic
periods are similar.
To better understand seismogenic behaviours of the Chihshang
fault, we examine the seismicity distribution at depth. Earthquakes
before the Chengkung earthquake mainly occurred within a depth
range of 15–25 km (Fig. 8), consistent with the 2003 coseismic
rupture at depths. The accumulated strain at shallow depths appears
to be released by aseismic slip; therefore, focal depths of large
earthquakes are possibly greater than 10 km. According to historic
records in 1951, the focal depths of 1951 earthquakes in the southern
Longitudinal Valley are about 30 km (Cheng et al. 1996). The
consistency of seismicity and coseismic slip distributions at depth
supports the idea that the accumulated strain in the Chihshang fault
is released by aseismic slip and seismic ruptures at shallow and deep
depths, respectively.
4.3 Seismogenic behaviour of the Chihshang Fault
To illustrate the seismic hazard in this region, we can estimate the
recurrence interval of the earthquake with similar magnitude as the
Chengkung earthquake by dividing the sum of coseismic potency
and postseismic potency by the interseismic potency. We assume
that the shallow part of the fault (depth < 10 km) continuously
creep in the seismic cycle; therefore, this portion of the fault is not
seismogenic. We only account for the potency in the depth range
larger than 10 km. Given the interseismic slip rate of about 20–
30 mm yr−1 on the fault (Yu & Kuo 2001; Lee et al. 2003, 2006),
the interseismic potency is about 29–43 km2 m yr−1 . The total potency of the Chengkung earthquake in the depth range larger than
10 km is about 510 km2 m and implies that the recurrence interval of
a similar event is about 12–18 yr, if accumulated interseismic strain
is fully released in this type of event. However, the recurrence interval inferred from the potency of the Chengkung earthquake seems to
be short compared with the earthquake records with M > 6 over the
past few decades. Alternatively, we can use the peak slip to estimate
the recurrence time. Given the peak slip of 0.72 and 1.27 m in our
model and Ching et al. (2007), respectively, the earthquake recurrence interval is 24–36 and 42–64 yr, respectively. According to the
historic record, the penultimate large earthquake near the Chihshang
fault occurred in 1951 (Hsu 1962; Cheng et al. 1996). The 1951 M L
7.3 Hualien–Taitung earthquake sequences composed of sequential
ruptures along four fault segments in the LVF, including Hualien,
Chihshang, Yuli and Taitung. Two large earthquakes with M L 7.3
and 6.1 occurred in, respectively, the northern and central portions of
the rupture zone of the Chengkung earthquake(Fig. 1b). Significant
coseismic surface displacements of about 1.5 m were observed near
Yuli during the 1951 M L 7.3 earthquake (Hsu 1962; Cheng et al.
1996). The Chihshang fault was also affected by M L 7.3 and 6.1
earthquakes; however, details of coseismic surface displacements
are not well documented. The seismic energy released by the 1951
M L 7.3 earthquake is about 16 times of that of the 2003 M L 6.5
Chengkung earthquake. The coseismic surface displacements near
the Chihshang fault resulting from the 1951 earthquake are likely
larger than coseismic displacements during the 2003 earthquake.
Knowing the slip amount on the Chihshang fault during the past
earthquake can provide a better chance to constrain the time of the
next earthquake if the slip behaviour is time-predictable.
Our particular interest is to know whether the shallow portion of
the Chihshang fault creeps both before and after the 2003 earthquake. A 2-D dislocation model indicate that slip rate of about
30 mm yr−1 on a 45◦ east-dipping fault at shallow depth fits the
interseismic GPS site velocity between 1993 and 1999 near the
Chihshang fault (Hsu et al. 2003). This implies that the spatial
4.4 Fault zone frictional properties
Studies on subduction thrust faults have found that earthquakes generate over a limited depth range. The updip limit of the seismogenic
zone is controlled by the presence of unconsolidated sediments or
stable-sliding clays (Hyndman et al. 1997; Oleskevich et al. 1999;
Peacock & Hyndman 1999). Similarly, the shallow creep on the
inland Chihshang thrust fault is associated with unconsolidated geological material, the Lichi Mélange, a highly sheared mud unit with
occasional coherent turbidite beds and exotic blocks of ophiolite and
sedimentary rocks. The frictional behaviour of unconsolidated sediments exhibits stable sliding, that is, velocity-strengthening. These
weak materials are characterized by low P-wave velocity on the
hanging wall of the Chihshang fault in seismic tomography studies
(Kim et al. 2005; Wu et al. 2007).
To assess the frictional parameters of shallow fault zones, we
model afterslip using a rate- and state-dependent friction law (Perfettini & Avouac 2004a). For steady-state sliding, this law can be
written
τss = σn μ∗ + (a − b)σn ln(V /V ∗ ),
(5)
where τ ss is the driving shear stress, σ n is the normal stress, (a – b)
is a rheological parameter, V is the sliding velocity and μ∗ and V ∗
are the reference values. We only consider a rate dependence of
friction and set b = 0 to neglect the state dependence. In the singledegree-of-freedom system (Perfettini & Avouac 2004a), we have
tr = aσn /τ̇ ,
(6)
d = exp(C F S/aσn ),
(7)
where t r is the relaxation time; d is the velocity jump due to coseismic stress change; a is a rheological parameter; σ n is the normal
stress; τ̇ is the interseismic shear stress rate and CFS is the coseismic Coulomb stress change on the fault patch. The values of
t r and d are determined by grid search in eq. (3) and the optimal
values are about 0.8 yr and 55 in the near-field sites, respectively.
Given coseismic stress change (CFS) of the order of 2 MPa in our
coseismic model and the recurrence interval of ∼M6 earthquake
of about 50 yr since the penultimate event occurred in 1951, we
estimate τ̇ to be about 0.04 MPa yr−1 . Based on the value of t r
and d and eqs (6) and (7), aσ n is about 0.03 and 0.5 MPa, respectively. Assuming effective normal stress of 100 MPa at 5 km depth,
a is about 3 × 10−4 –5 × 10−3 . These values are consistent with
1 × 10−4 –1 × 10−3 inferred from rate- and state-dependent friction
model of afterslip following the 2004 Parkfield earthquake (Johnson
et al. 2006), 1 × 10−3 in Tokachi-oki earthquake (Miyazaki et al.
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2004) and 5 × 10−4 from Nias-Simeulue, Sumatra, earthquake (Hsu
et al. 2006). Our estimates are in good agreement with a value of
(a – b) of about 5 × 10−4 –2 × 10−3 from laboratory experiments
(Marone 1998),
The value of aσ n is important in evaluating earthquake probability using the rate- and state- stress transfer model (Toda et al.
1998; Chen et al. 2008). The choice of aσ n controls the magnitude
of transient effect and therefore perturbs earthquake productivity.
Chen et al. (2008) use the values of aσ n at a range of 0.01–0.75 MPa
to calculate earthquake probability of subsequent events after the
main shock of 1951 M L 7.3 Hualien–Taitung, Taiwan, earthquakes. The values they used are comparable to our estimates of
0.03–0.5 MPa.
5 C O N C LU S I O N S
Inferred coseismic and postseismic slip distributions on the
Chihshang fault, associated with the 2003 Chengkung earthquake,
provide a key to understanding the seismogenic behaviour of the
southern Longitudinal Valley. The large coseismic slip of about
0.7 m occurred at a depth of 10–20 km, corresponding with the
seismogenic zone inferred from seismicity distribution at depth before the main shock. Significant postseismic displacements near
the surface rupture suggest that afterslip at shallow depths is the
primary contribution to the postseismic deformation. Our model
infers that the maximum postseismic slip of 0.12 m in a 157 d
period mainly occurred at a depth range less than 10 km. The postseismic geodetic moment is about 13 per cent of the coseismic
moment. We show a spatial anticorrelation between coseismic slip
and postseismic slip. According to the historic earthquake records,
interseismic slip potency and coseismic slip, we infer the recurrence
interval of the 2003-type earthquake is 12–36 yr. The accumulated
strain in the Chihshang fault is released by aseismic slip and seismic
ruptures at shallow and deep depths, respectively. The shallow creep
in the Chihshang fault is associated with the unconsolidated mud of
the Lichi Mélange. We use a rate-dependent friction law to derive
the rheological parameter, aσ n , of about 0.03–0.5 MPa at shallow
depth, given the effective normal stress of 100 MPa at a depth
of 5 km.
AC K N OW L E D G M E N T S
We thank the editor Dr J. Beavan and two reviewers Dr J. C. Savage
and Dr K. M. Johnson, for their thoughtful reviews and valuable
comments that helped to improve the manuscript. We are grateful to
many colleagues at the Institute of Earth Sciences, Academia Sinica,
who have participated in collecting GPS data. The generous provision of continuous GPS data by the Central Weather Bureau, the
Ministry of the Interior, and IGS community is greatly appreciated.
We thank Y. L. Chiang for preparing figures in the manuscript. GMT
was used to create several figures (Wessel & Smith 1998). This is
the contribution of the Institute of Earth Sciences, Academia Sinica,
IESAS1283 and the National Science Council of the Republic of
China grant NSC 95-2119-M-001-064-MY3 and NSC 96-2119-M001-013. This research was supported by the Taiwan Earthquake
Research Center. The TEC contribution number for this article is
00036.
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