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Isolating along-strike variations in the depth extent of shallow creep and fault locking on the northern Great Sumatran Fault

Article (PDF Available) inJournal of Geophysical Research Atmospheres 117(B6):6409- · June 2012
DOI: 10.1029/2011JB008940
Takeo Ito at Nagoya University
  • 25.08
  • Nagoya University
Endra Gunawan at Bandung Institute of Technology
  • 18.17
  • Bandung Institute of Technology
Fumiaki Kimata at Tono Research Institute of Earthquake Science
  • 29.37
  • Tono Research Institute of Earthquake Science
Didik Sugiyanto at Syiah Kuala University
  • 10.39
  • Syiah Kuala University
Abstract
The Great Sumatran Fault system in Indonesia is a major right-lateral trench-parallel system that can be divided into several segments, most of which have ruptured within the last century. This study focuses on the northern portion of the fault system which contains a 200-km-long segment that has not experienced a major earthquake in at least 170 years. In 2005, we established the Aceh GPS Network for the Sumatran Fault System (AGNeSS) across this segment. AGNeSS observes large displacements which include significant postseismic deformation from recent large megathrust earthquakes as well as interseismic deformation due to continued elastic loading of both the megathrust and the strike slip system. We parameterize the displacements due to afterslip on the megathrust using a model based on a rate- and state-dependent friction formalism. Using this approach, we are able to separate afterslip from other contributions. We remove predicted deformation due to afterslip from the observations, and use these corrected time series to infer the depth of shallow aseismic creep and deeper locked segments for the Great Sumatran Fault. In the northern portion of this fault segment, we infer aseismic creep down to 7.3 ± 4.8 km depth at a rate of 2.0 ± 0.6 cm/year. In the southwestern portion of the segment, we estimate a locking depth of 14.8 ± 3.4 km with a downdip slip rate of 1.6 ± 0.6 cm/year. This portion of the fault is capable of producing a magnitude 7.0 earthquake.
Figures
Isolating along-strike variations in the depth extent of shallow
creep and fault locking on the northern Great Sumatran Fault
Takeo Ito,
1
Endra Gunawan,
1
Fumiaki Kimata,
1
Takao Tabei,
2
Mark Simons,
3
Irwan Meilano,
4
Agustan,
5
Yusaku Ohta,
6
Irwandi Nurdin,
7
and Didik Sugiyanto
7
Received 18 October 2011; revised 9 May 2012; accepted 14 May 2012; published 28 June 2012.
[1]The Great Sumatran Fault system in Indonesia is a major right-lateral trench-parallel
system that can be divided into several segments, most of which have ruptured within
the last century. This study focuses on the northern portion of the fault system which
contains a 200-km-long segment that has not experienced a major earthquake in at least
170 years. In 2005, we established the Aceh GPS Network for the Sumatran Fault
System (AGNeSS) across this segment. AGNeSS observes large displacements which
include significant postseismic deformation from recent large megathrust earthquakes as
well as interseismic deformation due to continued elastic loading of both the megathrust
and the strike slip system. We parameterize the displacements due to afterslip on the
megathrust using a model based on a rate- and state-dependent friction formalism. Using
this approach, we are able to separate afterslip from other contributions. We remove
predicted deformation due to afterslip from the observations, and use these corrected
time series to infer the depth of shallow aseismic creep and deeper locked segments for
the Great Sumatran Fault. In the northern portion of this fault segment, we infer aseismic
creep down to 7.3 4.8 km depth at a rate of 2.0 0.6 cm/year. In the southwestern
portion of the segment, we estimate a locking depth of 14.8 3.4 km with a downdip
slip rate of 1.6 0.6 cm/year. This portion of the fault is capable of producing a
magnitude 7.0 earthquake.
Citation: Ito, T., E. Gunawan, F. Kimata, T. Tabei, M. Simons, I. Meilano, Agustan, Y. Ohta, I. Nurdin, and D. Sugiyanto
(2012), Isolating along-strike variations in the depth extent of shallow creep and fault locking on the northern Great Sumatran
Fault, J. Geophys. Res.,117, B06409, doi:10.1029/2011JB008940.
1. Introduction
[2] The Great Sumatran Fault (GSF) system in Indonesia
is a major right lateral trench-parallel fault systems that
accommodates a significant fraction of the strike-slip com-
ponent of the oblique convergence between the Australian/
Indian and Eurasian plates [Genrich et al., 2000; Sieh and
Natawidjaja, 2000]. The 1900-km-long fault system can be
divided into several segments, most of which have broken
within the last century in earthquakes with magnitudes
between 6.0 and 7.7 (see Figure 1a). However, two segments
are devoid of any record of recent earthquakes. One of these
segments traverses the northwestern part of the Sumatra
Island passing through the suburb of Banda Aceh city, the
local capital of the Aceh Province with a population of
over 260,000. The lack of major earthquakes in at least in
170 years along this 200-km-long segment suggest the
potential for high seismic hazard for this region [Bellier et al.,
1997; Sieh and Natawidjaja, 2000]. Here, we focus on GPS
observations of crustal deformation on this northern portion of
the GSF to constrain estimates of regional seismic potential.
1.1. Previous Studies
[3] Deformation along the GSF system has been studied
based on variety of geodetic and geological observations
[Bennett et al., 1981; Natawidjaja and Sieh, 1994; Sieh et al.,
1994; Bellier and Sebrier, 1995; Sieh and Natawidjaja,
2000]. Geologic estimates of slip rates on the GSF increase
from southeast to northwest, with maximum rates estimated to
reach about 3.8 cm/year in the northwestern part of the
Sumatra Island (see Figure 1a) [Bennett et al., 1981;
Natawidjaja and Sieh,1994;Sieh et al., 1994; Bellier and
Sebrier,1995;Sieh and Natawidjaja, 2000].
1
Graduate School of Environmental Studies, Nagoya University,
Nagoya, Japan.
2
Department of Applied Science, Kochi University, Akebono-cho,
Japan.
3
Seismological Laboratory, California Institute of Technology,
Pasadena, California, USA.
4
Geodesy Research Division, Bandung Institute of Technology,
Bandung, Indonesia.
5
Center of Technology for Natural Resources Inventory, BPPT, Jakarta,
Indonesia.
6
Graduate School of Science, Tohoku University, Sendai, Japan.
7
Physics Department, Syiah Kuala University, Aceh, Indonesia.
Corresponding author: T. Ito, Graduate School of Environmental
Studies, Nagoya University, D2-2 (510), Furo-cho, Chikusa-ku, Nagoya,
Aichi, 464-8602, Japan. (takeo)_ito@nagoya-u.jp)
©2012. American Geophysical Union. All Rights Reserved.
0148-0227/12/2011JB008940
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117, B06409, doi:10.1029/2011JB008940, 2012
B06409 1of16
[4] Using GPS observations, Genrich et al. [2000] reports
estimated slip deficit rates of 2.3 2.6 cm/year on the GSF
between 0.8S to 2.7
N. Estimated locking depths for the
GSF between 0.8S to 1.3
N are about 21 24 km. How-
ever, around 0.6
N, the estimated locking depth was esti-
mated to be 56 35 km [Genrich et al., 2000]. This region
experienced a M
w
= 7.8 in 1892, the largest documented
event of this class on the GSF(see Figure 1a). Further north,
on the GSF, between 2.2
N to 2.7
N, the locking depth is
estimated to be about 9 km, significantly shallower than to
the south. Moreover, for the Banda Aceh transect, the
locking depth is shallower than 15 km, with an estimated
slip deficit rate 0.5 0.2 cm/year [Genrich et al., 2000].
This estimated slip deficit rate is significantly slower than
estimated geological slip rate. This discrepancy may be
partially due to the complexity associated with the branching
fault system in the Banda Aceh segment (see Figure 1b).
2. GPS Observations
[5] The 2004 Sumatra-Andaman earthquake (M
w
9.2)
occurred at the subducting zone in the northern part of Sunda
trench. GPS observations observed about 3 m of coseismic
displacements in a southwesterly direction in Aceh region
[Subarya et al., 2006]. After the 2004 Sumatra-Andaman
earthquake, we began to install a mixed continuous and
campaign GPS network in northern Sumatra called the Aceh
GPS Network for the Sumatran fault System (AGNeSS).
AGNeSS is constructed across the northwestern segment of
the GSF in Aceh province, located between 4.0N to 5.5
N.
We installed a permanent continuous GPS site on March
Figure 1. (a) Overview of the GSF system. Source regions of large earthquake from historical records are
shown in bold red lines. Also shows are the long-term offset rates along the GSF system. Long-term offset
rates are based on Bennett et al. [1981], Sieh et al. [1994], Natawidjaja and Sieh [1994], and Bellier and
Sebrier [1995]. Yellow circles are GPS site belonging to Sumatran GPS Array (SuGAr) network. The gray
rectangle is our study area. (b) Zoom into grayish rectangle of Figure 1a. Observation map of AGNeSS.
Red, blue, and yellow squares are campaign, continuous, and SuGAr GPS sites, respectively. Red lines
indicate the Sumatran and Batee faults, respectively. Rectangles with grayish broken line show profiles
of GPS site.
ITO ET AL.: ALONG-STRIKE VARIATIONS ON THE GSF B06409B06409
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2005 in Banda Aceh city, which we have continued to
operate since then. AGNeSS started with 1 continuous
and 8 campaign GPS sites in November 2005, we added
4 campaign GPS sites to AGNeSS in November 2006, 5
continuous and 4 campaign GPS sites in November 2007,
and 1 continuous and 3 campaign GPS sites in June 2008.
AGNeSS currently consists of 7 continuous and 17 cam-
paign GPS sites. We conducted separate campaigns in
November 2005, November 2006, November 2007, June
2008, October 2008, June 2009, and November 2009.
[6] Our goal is to evaluate the seismic hazard on the
northwestern part of the GSF. Therefore, we designed
AGNeSS to monitor earthquake activity and to detect strain
accumulation in the vicinity of the GSF (see Figure 1b).
AGNeSS consists of two approximately linear profiles
across the GSF, which we refer to as PA (Profile A [the
northwestern profile]) and PB (Profile B [the southeastern
profile]). The PA consists of 4 continuous and 7 campaign
GPS sites, and the PB consists of 2 continuous and
10 campaign GPS sites. The mean fault normal distance
between each GPS site in PA is less than 5 km near the
fault, although GPS sites are more sparsely located on the
southwestern side of the fault due to the challenge of deal-
ing with the jungle. In general, PB is sparser than PA due to
both jungle and rough terrain. See Appendix A for a
description of monumentation and data reduction.
[7] Figures 2, 3, and 4 show observed displacement time
series. These time series clearly show postseismic deforma-
tion due to 2004 and 2005 megathrust earthquakes. There is
additional anomalous behavior in the east-west component
of site TNDP. The observation period of TNDP site is only
two years, the shortest in AGNeSS. Further complicating
things, TNDP is located near a stream which may induce
local hydrological effects. Thus, from here on out, we do not
use observations from TNDP.
3. Postseismic Deformation
[8] Immediately after the 2004 Sumatra-Andaman earth-
quake, we established one continuous and 8 campaign GPS
sites on the northern part of Sumatra Island. These sites
include some of the sites that were earlier installed and
occupied by BAKOSURTANAL before the earthquake.
After the earthquake, large postseismic displacements toward
Figure 2. Time series of postseismic displacement at stations, ACEH, UMLH, LEWK, and BSIM.
Locations of GPS station are shown in Figure 1b. (right) North-south and (left) east-west components.
Each thin line are fitted lines using equation (1). These time series are respect to ITRF2005.
ITO ET AL.: ALONG-STRIKE VARIATIONS ON THE GSF B06409B06409
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southwest were detected [e.g., Hashimoto et al., 2006]. For
example, south-westward displacements of 80 cm have
been observed at the continuous site, ACEH, in Banda
Aceh, over a five year period from February 2005 until
November 2009 (see Figure 2).
[9] Postseismic deformation is generally attributed to
three classes of phenomena: (1) bulk viscoelastic (VE)
relaxation [e.g., Pollitz et al., 2006, 2008], (2) poroelastic
(PE) processes [e.g., Hughes et al., 2010], and (3) afterslip
on the primary fault in and/or around the region of coseismic
slip [e.g., Hashimoto et al., 2006; Hsu et al., 2006]. In case
of the 2004 Sumatra-Andaman earthquake, a VE model can
fit postseismic deformation for regions exceeding 500 km
from source [Pollitz et al., 2006]. However, we find that
the VE model does not explain postseismic observations
closer to the source. Figures 3 and 4 show predicted time
series of crustal deformation due to VE responses as dashed
lines. The VE responses are calculated using VISCO1D
version 3, which calculates quasi-static deformation on a
layered spherical Earth from a specified input fault move-
ment [Pollitz, 1997]. In this study, we use a spherically
symmetric viscoelastic structure consisting of an elastic
plate of thickness 62 km depth underlain by a Burgers body
asthenosphere from 62 to 220 km depth and a homogeneous
Maxwell viscoelastic upper mantle bellow 220 km depth
[Pollitz et al., 2006]. Postseismic deformation due to VE
relaxation can be expressed by exponential functions with
very long decay times. Thus, time series of VE response has
linear trend in our observation period (see Figures 3 and 4).
Predicted crustal deformation rate due to VE relaxation in
our observation period is about 3 cm/year along lines PA
and PB. Spatial variation due to the VE response is smaller
than 3 mm/year along lines PA and PB. Thus, we assume
the VE effect is linear in time. Hughes et al. [2010] suggests
that we should expect PE effects of several centimeters in
the region of Sumatra. However, PE deformation is expec-
ted to decay rapidly (1 month) in the overriding plate
[Hughes et al., 2010]. The PE model does not explain the
observed large postseismic deformation. In contrast to the
VE and PE models, an afterslip model can fit both near-
field and far-field observations [Hashimoto et al., 2006;
Hsu et al., 2006]. Thus, in this study, we rely only on an
afterslip model to estimate the post-seismic effects associ-
ated with the 2004 and 2005 megathrust events.
3.1. Afterslip Model
[10] We show GPS time series in Figures 2, 3, and 4, with
the locations of each GPS station shown in Figure 1. The
Figure 3. Time series of postseismic displacement at GPS site in PA. Each dashed line is predicted VE
response due to the 2004 event. Same description as Figure 2.
ITO ET AL.: ALONG-STRIKE VARIATIONS ON THE GSF B06409B06409
4of16
time series clearly show post-seismic transients associated
with the 2004 Sumatra-Andaman and other earthquakes. In
the early period of postseismic deformation, we assume that
deformation is predominantly driven by frictional afterslip
and follows a logarithmic function. Afterslip can be modeled
using a rate- and state-dependent friction law. Following
Perfettini and Avouac [2004], the postseismic displacement
resulting from rate-strength brittle creep can be written as
UtðÞ¼aV0tþX
3
eq¼1
Fstep tteq

þbeqV0tr
log 1 þdeq exp tteq
tr

1

ð1Þ
where U(t) is the surface displacement, V
0
=5 cm/year is the
interseismic slip rate on the plate interface, F
step
is the step
function due to the coseismic displacement, aand b
eq
are
geometric factors, t
r
is the relaxation time, d
eq
is the velocity
jump due to coseismic stress change, and tis time since
December 26, 2004. In this study, we consider the Sumatra-
Andaman earthquake (M
w
=9.2) on December 26, 2004, the
Nias earthquake (M
w
=8.7) on March 28, 2005, and the
Simeulue earthquake (M
w
=7.5) on February 20, 2008. t
eq
are
dates of the modeled earthquakes. In a single-degree-of-
freedom system, t
r
and d
eq
in equation (1) can be written as
tr¼Asn=_t
deq ¼exp DCFSeq=Asn

ð2Þ
where Ais a rheological parameter, s
n
is the normal stress, _t
is the interseismic shear stress rate, and DCFS
eq
is the
coseismic coulomb stress change on the creeping patch
[Perfettini and Avouac, 2004]. In order to determine a rough
estimate of rheological parameters, we assume that As
n
and
_tare regional parameters, and that t
r
and d
eq
are the same for
each component of displacement. Thus, t
r
has one value for
the region, and d
eq
is fixed for each earthquake. These
assumptions are consistent with previous studies [Hsu et al.,
2006]. The values of t
r
and d
eq
are determined by least
squares adjustments using ACEH and some sites LEWK,
UMLH and BSIM. We obtain t
r
equal to about 8.76 years,
and values of d
eq
for the 2004, 2005, and 2008 earthquakes
of 46, 1060, and 2650, respectively. These value are con-
sistent with previous studies[e.g., Hsu et al., 2006; Gahalaut
et al., 2008]. Figure 2 shows time series of displacement and
the associated model fits. The characteristic relaxation time
Figure 4. Time series of postseismic displacement at GPS site in PB. Same description as Figure 3.
ITO ET AL.: ALONG-STRIKE VARIATIONS ON THE GSF B06409B06409
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(t
r
=8.76 years) has also been shown to match the decay of
aftershocks in the northern part of the Sumatra Island region
[Hsu et al., 2006]. Global analyses of aftershocks obtain an
average value of t
r
of about 10.2 years [Dieterich, 1994],
similar to our analysis of postseismic deformation in the
northern part of the Sumatra island. For comparison,
Parsons [2002] reports that triggered events globally obey
an Omori law with characteristic decay time typically
between 7 and 11 years after the main shock. Of course,
t
r
will depend on local tectonic setting.
[11] When t<t
r
, equation (1) results in a logarithmic
decay of displacement [e.g., Hsu et al., 2006]. While our
estimates of t
r
is several years, postseismic deformation
drops below the accuracy of GPS measurements on shorter
timescales. After one year, displacement rates have dropped
significantly and are 0.162, 0.009, and 0.004 times that
estimated just after the 2004, 2005 and 2008 earthquakes,
respectively. The source regions of the 2005 and 2008
earthquakes are located over 100 km from AGNeSS.
Although, site TANG, which is located at center of AGNeSS,
experienced coseismic displacements of 8 mm southwards
and 5 mm eastward due to the 2008 earthquake, postseismic
displacement due to this event are below our current mea-
surement capabilities (see Figure 3). Henceforth, we ignore
postseismic deformation due to afterslip of the 2005 and
2008 earthquakes.
3.2. Corrected Deformation Rate From Observed
Postseismic Deformation
[12] We interpret the velocity at each site as being the sum
of the interseismic velocity as well as transient afterslip.
Following the 1D model of Perfettini and Avouac [2004]
there are two terms in equation (1). One is due to ductile
flow at depth, which is assumed to be a constant unknown
fraction, a, of the velocity, V
0
. The second term is the con-
tribution of the creeping brittle fault zone, which is assumed
to control postseismic relaxation. The steady state creep rate
on the transition zone is a fraction for each earthquake, b
eq
,
of the long-term slip rate, V
0
. The interseismic velocity, V
int
,
at GPS site relative to the footwall is described as
(a+b
eq
)V
0
[Perfettini and Avouac, 2004; Hsu et al.,
2006]. However, the estimated interseismic velocity, V
int
,
will include VE relaxation due to the 2004 event, which we
expect to be nearly a constant rate through our observation
period. It is difficult to decompose estimated linear velocity
into VE relaxation and interseismic velocities. The spatial
variation of the predicted VE relaxation velocity in our study
area is smaller than 3 mm/year, which is equivalent to our
observation error. Figures 3 and 4 show the observed and
expected displacement time series at each GPS site. Table 1
shows corrected velocity at each GPS site. However, because
of the assumption of a simple 1-D system of springs and
sliders, the model provides only a rough estimate of the
rheological parameters and does not provide much insight
into possible spatial variations of friction parameters. Black
arrows in Figure 5 indicate the deformation rate after
removing inferred effects due to afterslip. The corrected
velocity consists of the linear term, (a+Sb
eq
)V
0
,in
equation (1). The corrected deformation fields include the
effects of elastic coupling on the megathrust and the
Sumatran faults as well as any uncertainly in the reference
frame, all of which we will consider in the modeling
described below. As mentioned above, we assume that the
VE response is linear rate in the study area. At the scales of
Table 1. Estimated Parameters From Postseismic Displacement
Site
Location North(cm/year) East(cm/year)
Latitude Longitude V
int
aV
0
Sb
eq
V
0
V
int
aV
0
Sb
eq
V
0
ACEH 5.569 95.368 3.35 1.48 1.89 2.57 0.52 2.03
umlh 5.053 95.338 3.46 1.20 2.30 2.72 0.68 2.04
lewk 2.923 95.804 1.91 3.40 1.47 0.38 1.48 1.14
bsim 2.409 96.326 0.75 1.92 1.15 1.20 2.12 1.00
CALA 4.539 95.718 3.56 1.92 1.64 2.73 2.00 0.73
PIDI 5.366 95.933 2.98 1.44 1.58 0.71 1.12 1.85
KEMA 5.234 95.889 2.96 1.36 1.60 1.09 0.52 1.59
UGDN 5.223 95.872 2.95 1.52 1.37 1.28 0.40 1.68
MALO 5.100 95.894 2.96 1.36 1.60 1.07 0.92 2.01
BEUN 5.140 95.883 2.74 1.27 1.47 1.38 0.53 1.83
TANG 5.017 95.917 2.96 1.64 1.32 1.67 0.32 1.37
MANE 4.881 96.067 3.00 1.84 1.16 1.68 0.36 1.32
GEUM 4.844 96.125 3.09 1.96 1.19 1.68 0.72 0.96
MNYK 4.628 96.083 3.96 2.90 1.06 2.44 1.60 0.84
SARP 4.519 96.123 3.75 2.96 0.79 2.84 2.24 0.60
KAWA 4.368 96.186 3.70 3.06 0.64 2.81 2.28 0.51
BIRN 5.208 96.822 3.19 3.12 0.09 0.80 0.76 0.12
SKTN 4.986 96.694 3.26 3.16 0.06 1.58 1.52 0.10
UJNG 4.709 96.816 3.17 2.88 0.27 1.70 1.56 0.18
CELA 4.584 96.683 3.30 2.96 0.30 1.62 1.48 0.10
TNDP 4.519 96.628 3.12 2.79 0.02 0.44 0.52 0.08
BTAT 4.458 96.519 3.70 3.62 0.08 2.09 2.04 0.11
SGMT 4.375 96.513 3.78 3.66 0.12 2.88 2.64 0.24
KLMJ 4.256 96.424 3.66 3.64 0.02 2.73 2.68 0.03
PTRA 4.279 96.449 3.70 3.68 0.02 2.83 2.64 0.21
BTBW 4.247 96.448 3.41 3.00 0.39 2.69 2.32 0.35
JERM 4.214 96.306 3.33 2.92 0.47 2.54 2.16 0.34
MBMG 4.048 96.247 3.69 3.32 0.43 2.84 2.64 0.28
ITO ET AL.: ALONG-STRIKE VARIATIONS ON THE GSF B06409B06409
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this study, the VE response can be lumped into the refer-
ence frame uncertainly.
4. Inversion Method
[13] We assume that corrected deformation includes
effects of interplate coupling on the subducting plate inter-
face, coupling on the GSF and reference frame motion. We
model these effects as
d¼GmðÞ
¼GSPmSP þGGSF mGSF
ðÞþGREF mREF ð3Þ
where Gand mare Greens function and model parameters,
respectively. G
SP
represents the effect of interplate coupling
on the curved subducting plate interface and m
SP
is the
associated backslip vector on the curved subducting plate
interface. We introduce a parametric expansion of the fault
slip distribution using a finite number of B-splines functions.
The estimated interplate coupling ratio is typically less than
0.4. Details of implementation of the plate interface effect
are described in Appendix B. The characteristic length scale
of crustal deformation due to interplate coupling is
longer than 100 km. The typical magnitude of crustal defor-
mation due to coupling of the subducting plate is of order
10
7
strain/year. The aperture of AGNeSS is about 100-km-
wide normal to trench. Thus, the difference in velocity from
one edge to another of AGNeSS is about 1 cm/year. There-
fore, in order to remove long wavelength crustal deformation
due to a megathrust, we simultaneously estimate the inter-
plate coupling effect.
[14] The second term of equation (3) employs a backslip
function for elastic coupling on the GSF system. Assuming
pure strike slip motion, G
GSF
(m
GSF
) can be written as
GGSF mGSF
ðÞ¼
Vslip
ptan1XGPS þXshift
Zlock

þtan1Zcreep
XGPS þXshift

ð4Þ
where V
slip
,Z
lock
and Z
creep
are the slip deficit rate, locking
depth and creeping depth on the GSF, respectively
[Chinnery, 1961; Segall, 2010]. Thus, the GSF is locked
Figure 5. Black arrows mean corrected deformation from postseismic deformation. White arrows are
calculated velocity using the no-shallow-creep model. Red, blue, and yellow squares are campaign,
continuous, and SuGAr GPS sites, respectively. Green arrows are the fault normal directions. Intersections
of green lines are the reference point of surface fault locations for Figures 9, 10, and 11.
ITO ET AL.: ALONG-STRIKE VARIATIONS ON THE GSF B06409B06409
7of16
from Z
creep
to Z
lock
. This term includes an apparent block
motion, across the GSF. To account for mislocation of the
fault trace, we introduce X
GPS
and X
shift
in equation (4),
representing the perpendicular distance between the surface
trace of the GSF and each GPS site and differences distance
between X
GPS
and actual locking fault trace, respectively.
Thus, X
GPS
is a known constant value for each GPS site, and
X
shift
is an unknown parameter for each observation profile.
We estimate V
slip
,Z
lock
,Z
creep
, and X
shift
, for each profile.
The third term of equation (3) allows us to correct the ref-
erence flame for the entire GPS network.
[15] We estimate all the unknown parameters in equation(3)
using a fully Bayesian approach [e.g., Tarantola, 2005]. In a
Bayesian formulation, prior information on a vector of
unknowns, m, is expressed by a prior probability density
function (PDF), p(m). The posterior PDF, p(m|d) denotes the
probability density of unknowns, m,given,d. Specifically,
Bayestheorem is
pmðjdÞ¼ pdðjmÞpmðÞ
Rþ
pdðjmÞpmðÞdmð5Þ
where p(d|m) is the PDF of dgiven m,andR
+
p(d|m)p(m)
dmnormalizes the posterior PDF, which is independent of m.
Therefore,we can restate equation (5) as
pmðjdÞpdðjmÞpmðÞ:ð6Þ
[16] We assume that the PDF, p(d|m), follows a Gaussian
distribution of mean, G(m), and covariance matrix, s
d
, such
that
pdðjmÞ¼ 2pðÞ
N
2jsdj1
2exp 1
2dGmðÞðÞ
Ts1
ddGmðÞðÞ

ð7Þ
where Nis number of observation. Given a prior PDF, p(m),
the posterior PDF, p(m|d), is estimated using equation (6).
[17] We assume a homogeneous prior PDF, p(m), which
in this case is a uniform value. We make two modifications
to the prior, first is the physically sensible constraint on the
locking and creeping depths such that m
lock
is deeper than
m
creep
. We also assume that the magnitude of interplate
coupling velocity is less than 5 cm/year, corresponding to
the velocity of the subducting India/Australia plate relative
to the Sunda plate, which is about 47 mm/year in this region
[e.g., Socquet et al., 2006; Delescluse and Chamotrooke,
2007].
[18] The posterior PDF, p(m|d), is a non-Gaussian distri-
bution. Because closed-form analytical expressions are not
available, we construct a discrete representation of the pos-
terior PDF by sampling with a Markov Chain Monte Carlo
(MCMC) method. Specifically, we employ a Metropolis-
Hastings (M-H) algorithm. For a detailed explanation of
MCMC method and M-H algorithm, we refer the reader to
other texts on the topic [e.g., Metropolis et al., 1953;
Figure 6. Marginal posterior PDF of locking depths, Z
lock
, and slip deficit rates, V
slip
, for each profile
region in the no-shallow-creep model. (a, b) The marginal posterior PDF of locking under limit depths
in the each region. (c, d) Marginal posterior PDF of slip deficit rate in the each profile. Positive value is
right lateral slip. Dotted lines of all figures mean maximum likelihood estimation value.
ITO ET AL.: ALONG-STRIKE VARIATIONS ON THE GSF B06409B06409
8of16
Hastings, 1970; Gamerman, 1997]. In the M-H algorithm,
we discard the first 1.0 10
8
samples as having memory
of the initial parameters and regard the subsequent 3.0
10
8
samples as samples drawn from the posterior PDF.
Note that we do not introduce any smoothing or damping.
5. Results and Discussion
[19] We investigate two classes of models of elastic cou-
pling on the GSF. One is a no-shallow-creep model, which
assumes locking between surface and locking depth, Z
lock
,
and the another class allows for shallow creep. Figure 6
shows the posterior PDF for the no-shallow-creep model.
The estimated locking depth, Z
lock
, for PA and PB are
1.9 1.2 km and 14.8 3.4 km depth, respectively. We
suspect that creep occurs on the segment of the GSF
sampled by PA. We discuss this creep later. The estimated
slip deficit rates, V
slip
, of for PA and PB are 2.0 0.6 and
1.6 0.6 cm/year, respectively. Estimated slip deficit rates
are smaller than inferred from geological studies [e.g., Bennett
et al.,1981;Sieh and Natawidjaja, 2000]. For example,
Bennett et al. [1981] suggests that long-term slip rate in
this region is 3.8 0.4 cm/year from geological studies.
Our results are not consistent with previous geological
studies. A discrepancy between geodetic and geologic rates
may be reconcilable if fault behavior is non-stationary
whereby a given fault experiences clustered earthquakes
with a number of large earthquakes on the same fault
occurring in a short period of time followed by an extended
quiescent period. In the later stages between a cluster or
even within the period between two individual earthquakes,
the apparent geodetic slip rate may appear to be substan-
tially slower than the long-term average [i.e., Savage and
Prescott, 1978; Meade and Hager, 2005; DiCaprio et al.,
2008]. On the other hand, the estimated slip deficit rate
from a previous geodetic study is 0.5 0.2 cm/year, based
on earlier GPS data in the Banda Aceh transect about 50 km
northwest of our study area [Genrich et al., 2000]. We also
show predicted deformation and spatial residual in Figures 5
and 7. These residuals would be spatially random if they
were mainly due to GPS observation error.
[20] Fault length, L, and width, W, are empirically found
to be approximately related in strike slip earthquakes with
the length of the slipping area being approximately twice the
down dip extent [Geller, 1976]. In the case of PB, if the fault
width is equal to the estimated locking depth (14.8 km),
we can infer an estimated rupture length of about 29.6
6.8 km, corresponded to a magnitude 7 class earthquake.
Figure 7. Spatial distribution of the residual velocities using the no-shallow-creep model.
ITO ET AL.: ALONG-STRIKE VARIATIONS ON THE GSF B06409B06409
9of16
Such events are not rare on the GSF system (see Figure 1), for
example, a M
w
7.8 earthquake occurred in 1892.
[21] In order to evaluate seismic potential, the integral of
the product slip deficit rate (1.6 cm/year) times the estimated
locking depth is about 236.8 122 m
2
/year, which is
equivalent to an accumulation rate of seismic moment of
about 7.1 3.7 10
12
Nm/year per meter of fault length,
using a rigidity for the crust of 30 GPa. The accumulated
seismic moment on a 30-km-long segment since the last
earthquake, which probably occurred about 170 years ago
[Bellier et al., 1997; Sieh and Natawidjaja, 2000], is
M
o
=3.6 1.9 10
19
Nm. Thus, the GSF on the region of
PB appears capable of producing earthquake of magnitude 7.
5.1. Estimated Creep Fault
[22] In the region of PA, the no-shallow-creep model finds
a slip deficit rate and locking depth of 2.0 0.6 cm/year and
1.9 1.2 km, respectively. In effect, the shallow locking
depth of PA implies that entire fault is creeping, and that
only small earthquakes are likely.
[23] On the other hand, we can explore a model that
allows for shallow creep. Figure 8 shows posterior PDF of
the locking and creeping depths for each profile. Estimated
shallow creep depths for PA and PB are 7.3 4.8 and
0.7 1.8 km depth, respectively. We show the fault-parallel
component of velocity profile across the GSF as predicted
by the two models (see Figure 9). Discriminating between
the creep and no-creep models is not possible with the cur-
rent geodetic network. We also find no significant fault
normal component deformation (see Figure 10). For com-
parison, Figure 11 shows the fault-parallel component of
uncorrected velocity profile across the GSF. The deforma-
tions are similar to corrected deformation (see Figure 9).
Because, the characteristic length scale of crustal deforma-
tion due to afterslip is longer than 100 km. The GSF-parallel
direction is normal to direction of dominant postseismic
deformation. Both the afterslip component and the linear
viscous/reference frame component are small influence on
the GSF-parallel direction component.
Figure 8. Marginal posterior PDF of locking depth, Z
lock
, creeping depths, Z
creep
, and slip deficit rates,
V
slip
, in the shallow-creep model. (a, b) Marginal posterior PDF of the upper (blue) and lower (red) limits
of the locked portion for each profile. (c) Marginal posterior PDF of the width of the locked zone. Dashed
lines of all figure indicates the maximum likelihood value.
ITO ET AL.: ALONG-STRIKE VARIATIONS ON THE GSF B06409B06409
10 of 16
Figure 9. Fault-parallel component of corrected velocity across the GSF. Positive values of fault-parallel
velocity in the south-eastern direction. (a) PA and (b) PB. Blue, red, and green circles denote continuous,
campaign observation with benchmark type, and campaign observation with pillar type, respectively.
Error bars are one standard deviation. The Sumatran fault is approximately located at x = 0. (c, d) Marginal
posterior PDFs of fault locations, X
shift
, at PA and PB, respectively. The fault location PDFs are based on
the shallow-creep model.
ITO ET AL.: ALONG-STRIKE VARIATIONS ON THE GSF B06409B06409
11 of 16
[24] The fault in the region of PB probably does not
experience shallow creep. Although, the distance between
PA and PB is only 50 km, the GSF appears to experience
spatially heterogeneous coupling. Indeed, this segment of
the fault is geologically quite complex [e.g., Bellier and
Sebrier, 1995; Sieh and Natawidjaja, 2000]. Especially,
there is large intrusive rock at center of PA [Bennett et al.,
1981].
[25] Figure 8c shows the posterior PDF of the width of
fault locking. The estimated width of the locked zone for the
region of PA and PB are 9.4 6.4 and 10.6 7.2 km,
respectively. Thus, despite the possibility of shallow creep in
the upper 7 km depth, the fault segment near PA appears
capable of producing significant earthquakes.
[26] Finally, the Batee fault is a major right-lateral
strike-slip fault that diverges from the GSF (see Figure 7
and 9). Sieh and Natawidjaja [2000] suggests the Batee
fault does not appear to be active. The lack of clear small
offsets suggests either no activity in the past few tens of
thousands of years or activity at a rate much lower than along
the GSF. However, Bellier and Sebrier [1995] estimate
1.2 0.5 cm/year as long-term offset rate from geomorphic
evidence. Our result does not require any significant slip
deficit rate on the Batee fault (see Figure 9).
6. Conclusion
[27] Beginning in 2005, we established AGNeSS in the
northwestern part of the Sumatra Island. AGNeSS consist of
7 continuous and 17 campaign GPS sites spanning the
northwestern segment of the GSF system. AGNeSS observes
postseismic deformation exceeding 80 cm in five years fol-
lowing the 2004 Sumatra-Andaman earthquake. We remove
postseismic deformation due to afterslip from observed
postseismic deformation using a parameterized afterslip
model. The afterslip model fits the observed postseismic
deformation well. The characteristic relaxation time, t
r
,
is 8.76 years from time series of postseismic deformation.
[28] We evaluate a seismic potential on the northwestern
part of the GSF using the corrected deformation field. The
GSF near PA may be creeping in the upper 7.3 4.8 km
Figure 10. Fault-normal component of corrected velocity profile across the GSF. The positive value of
fault-normal velocity is the south-western direction. Other descriptions are same as Figure 9.
ITO ET AL.: ALONG-STRIKE VARIATIONS ON THE GSF B06409B06409
12 of 16
with an estimated slip deficit rate of 2.0 0.6 cm/year.
Despite the shallow creep, the estimated width of the locked
zone is 9.4 6.4 km. Thus, this fault segment appears to be
capable of producing significant earthquakes. Further to the
south near PB, the estimated locking depth and slip deficit
rate are 14.8 3.4 km depth and 1.6 0.6 cm/year,
respectively. This result suggests that the accumulated seis-
mic moment in 170 years corresponds to an earthquake of
magnitude 7.
Appendix A: Monumentation and Data Reduction
[29] All GPS sites are either located on hard rock or on a
deeply buried cement pillar reinforced with iron rods with
proper benchmarks. For continuous GPS sites, an approxi-
mately 1.5-m-high concrete pillar supports the GPS antenna
as well as the GPS receiver, download device, solar con-
troller, and backup battery are stored in a steel box embed-
ded in the foundation. Due to the risk of theft, we use older
Trimble 4000SSI receivers set to sample every second. The
data are automatically downloaded and converted to 30-sec
samples. 1-sec data are stored on site using a three month
ring buffer. For campaign GPS sites, we use two styles of
monuments, one using a 1.5-m-high steel pipe pillar
imbedded in a 1.0 m deep foundation, with the antennae
directly attached to the pipe. The another monument type
simply uses a 1.5 m deep foundation with a embedded
benchmark. We measure the benchmarks using a tripod
installation. For all campaign GPS measurement, we used
Trimble 5700 receivers and occupied each site for between
24 and 48 hours.
[30] To estimate the daily positions, we used the Bernese
software version 5.0. We include the permanent IGS sites
(KUNM, PIMO, HYDE, and COCO), the IGS final ephem-
eris, earth rotation parameters, ionosphere model parameters,
and differential code biases for satellites and receiver. We use
the coefficients of ocean tidal loading model based on
FES2004 [Lyard et al., 2006] from the Onsala Space
Figure 11. Fault-parallel component of uncorrected velocity across the GSF. Using period is from 2008
to 2009. Other descriptions are same as Figure 9.
ITO ET AL.: ALONG-STRIKE VARIATIONS ON THE GSF B06409B06409
13 of 16
Observatory [Penna et al., 2007]. The GPS velocities, dis-
placements and their uncertainties are calculated with respect
to ITRF2005 [Altamimi et al., 2007]. Typical errors of the
daily positions in the north, east, and vertical components are
0.43, 0.62 and 0.81 cm, respectively. For campaign sites,
there is an additional error due to resetting of the tripod.
Typical resetting error is less than 0.2 cm.
Appendix B: Implementation of Estimating Plate
Interface Effect
[31] In order to infer the spatial interplate coupling distri-
bution, we introduce a curved plate interface geometry based
on the Slab Models for Subduction Zones [Hayes et al.,
2009; Hayes and Wald, 2009]. To estimate coefficients of
interplate coupling on the curved plate interface, we intro-
duce a parametric expansion of the fault slip distribution
using a finite number of known basis functions. We repre-
sent the spatial distribution of each slip component, Du
j
,by
linear combination of a finite number (kand l) of basis
function, F
kl
, defined on the plane, x,as
Dujx1;x2
ðÞ¼
X
K
k¼1X
L
l¼1
ajklFkl x1;x2
ðÞ ðB1Þ
where ais coefficient of B-spline function, F
kl
(x
1
,x
2
). Let d
i
be the observed displacement at surface, G
ij
(x) is the
derivative of Greens tensor with respect to x.Surface dis-
placement, d
i
, describe to figure out the integration with
respect to x, and the convolution with Greens function and
Figure B1. Model outline of the curved plate interface on
the Sunda subduction zone. The modeled plate interface is
700 km 500 km. Red squares are GPS sites used. Letters
at the corners of the model area indicate the positions on the
map of the equivalent points shown in Figure 13.
Figure B2. Marginal posterior PDF of slip deficit on the plate interface. Each subsection corresponds to
each sub fault, respectively. Each posterior PDF of each subsection denote slip vector. Interval of each
contour is 0.5 %. Letters correspond to locations shown in Figure 12.
ITO ET AL.: ALONG-STRIKE VARIATIONS ON THE GSF B06409B06409
14 of 16
fault slip. Then, using (equation B1), we may write obser-
vation equations as
di¼X
2
j¼1Zx
Gij x1;x2
ðÞDujx1;x2
ðÞdx
¼X
2
j¼1X
K
k¼1X
L
l¼1
ajklZx
Gij x1;x2
ðÞFkl x1;x2
ðÞdx
¼X
2
j¼1X
K
k¼1X
L
l¼1
Hijklajkl ðB2Þ
Substituting this expression into equation (3), then we can
evaluate the posterior PDF straightforwardly. For more
detail of implimention of the B-spline formulations, please
see Yabuki and Matsuura [1992].
[32] We set a curved plate interface on the Sunda sub-
duction zone (see Figure B1). We distribute 10 7 bicubic
B-splines so that they cover homogeneously the whole
model fault region. The distribution of each slip component
on the rectangular fault plane is represented by the super-
position of the 10 7 bicubic B-splines with various
amplitudes. We divide the rectangular model fault into 7 4
subsections. Figure B2 shows the posterior PDF distribution
at each subsection. The posterior PDF on the offshore region
is low and wider than near land. Estimated interplate cou-
pling ratio is typically less than 0.4. The velocity of sub-
ducting plate India/Australia relative to Sunda is about
47 mm/year in this region [e.g., Socquet et al., 2006;
Delescluse and Chamotrooke, 2007]. Although our method
dose not introduce smoothing hyper-parameters, the esti-
mated coupling ratio are reasonable value. Because, a pur-
pose of this implication in interplate coupling estimation is
to remove long wavelength crustal deformation due to the
plate interface effect, we do not discuss a pattern and
amplitude of interplate coupling distribution.
[33]Acknowledgments. We thank the Editor, Tom Parsons, and two
reviewers, Danny Hilman Natawidjaja and an anonymous reviewer, for
their thoughtful reviews and valuable comments that helped to improve the
manuscript. This is Caltech Seismological Laboratory contribution number
10076 and Caltech Tectonics Observatory contribution number 197. This
material is supported by the grants-in-aid for scientific research (19253003
and 23740337) of MEXT of Japan.
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