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

**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

3of16

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

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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 Green’s 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,

Bayes’theorem 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

pmðjdÞ∝pdðjmÞpmðÞ: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 Green’s tensor with respect to x.Surface dis-

placement, d

i

, describe to figure out the integration with

respect to x, and the convolution with Green’s 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 Matsu’ura [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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