(2024) 11:16
Alif et al. Geoscience Letters
https://doi.org/10.1186/s40562-024-00330-0

Geoscience Letters

Open Access

RESEARCH LETTER

Determination of Euler pole parameters
for Sundaland plate based on updated GNSS
observations in Sumatra, Indonesia
Satrio Muhammad Alif1,3, Kuo‑En Ching1* , Takeshi Sagiya2 and Widya Nabila Wahyuni3

Abstract
To provide a precise Euler pole parameter of Sundaland plate for earthquake potential evaluation in Sumatra, Indo‑nesia after the 2004 M9.2 Aceh earthquake, we adopted 37 new Global Navigation Satellite System (GNSS) observa‑
tions in Sumatra and 30 transformed published velocities in Indochina and Malaysia under the International Terrestrial
Reference Frame 2014 (ITRF2014). The 37 GNSS data were processed using the software Bernese v.5.2. The GNSS
velocities were calculated by the coordinate time series analysis with the least squares method. The grid search algo‑rithm was used in Euler pole parameter estimation, which was validated using the bootstrap resampling. The opti‑
mized Euler pole parameters are the latitude of 45.63 ± 0.45°, the longitude of − 88.71 ± 0.38° and the angular velocityof 0.337 ± 0.002°/Myr in counterclockwise direction. Besides, the distinguishable and systematic pattern in space
is shown in the residual velocities, which may imply the possibility of minor postseismic deformation, Tibetan crustal
flows, or the hypothesis that the Sundaland Plate is composed of several microplates.
Keywords Euler pole, GNSS velocity field, Sundaland plate, Sumatra
Introduction
To evaluate the earthquake potentials at plate boundaries using the geodetic observations, the estimated slip
deficit rate on the fault through the elastic block modelis the key parameter, which usually relies on a reasonably calculated long-term slip rate (McCaffrey et al.
2002). Because a reliable estimation of the Euler vector
could highly improve the inference accuracy of longterm fault slip rates (Meade and Hager 2005), the accuracy improvement of Euler pole parameters is always
essential. After the 2004 M9.2 Aceh earthquake occurredon the Sunda subduction zone, the earthquake potential evaluation along the Sunda trench becomes more
*Correspondence:
Kuo‑En Chingjingkuen@mail.ncku.edu.tw
1
Present Address: National Cheng Kung University, Tainan, Taiwan
2
Nagoya University, Nagoya, Japan
3
Institut Teknologi Sumatera, South Lampung Regency, Indonesia

important to mitigate the next catastrophe. Therefore,
the precision improvement of Euler pole parameters of
Sundaland plate is necessary based on the updated GNSS
observations.
Sundaland plate, situated in southeast Asia, covers
Indonesia (Sumatra, Kalimantan, and Java), Malaysia, andother Indochina countries (Simons et al. 2007). The interior of the Sundaland plate has been proposed as relatively stable with very low seismicity and a low strain rateof ~ 7 nanostrain/year (Simons et al. 2007). The northernside of the Sundaland plate is the collision zone with the
Yangtze plate, while the southern side of the plate is the
Baribis-Kendeng fault in Java (Kuncoro et al. 2019). The
Philippine Sea plate is in the eastern side of the Sundaland plate, while the western side of the plate is the IndoAustralian plate along the Sundaland subduction zone
and the Sumatran Fault Zone (McCaffrey 2009). The
earthquake activity along the Sundaland subduction zone
is high, especially since 2004. Seven M > 7 earthquakes
occurred along the subduction zone from 2004 to 2010

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Alif et al. Geoscience Letters(2024) 11:16(Fig. 1): the 2004 M9.2 Aceh earthquake, the 2005 M8.6
Nias earthquake, the 2007 M8.5 Bengkulu earthquake,the 2008 M7.4 Simeulue earthquake, the 2009 M7.6
Padang earthquake, the 2010 M7.8 Mentawai earthquake,and the 2010 M7.8 Simeulue earthquake. However, noother M > 7 earthquakes occurred in the Sundalandsubduction zone after 2010, and no M > 7 earthquakes
occurred in Sumatra Fault Zone since the 1943 M7.3 Ketaun earthquake (Hurukawa et al. 2014).
The Euler pole parameters of the Sundaland plate
have been estimated using the GNSS data. Simons et al.
(2007) first estimated the Euler pole parameters before
the 2004 M9.2 Aceh earthquake, using more than 25
GNSS sites scattered in Java, Sumatra, Borneo, Singapore, Malaysia, and Thailand. Kuncoro et al. (2019) thenPage 2 of 16

updated the Simons model under the ITRF2008. Yonget al. (2017) next used GNSS sites mostly in Malaysia(one in Java, one in Sumatra, one in Thailand, one in thePhilippines) to estimate the Euler pole by eliminating
the GNSS sites in Peninsular Malaysia that experienced
the postseismic deformation of Sumatran earthquake
sequence. Besides, to evaluate the global plate model,
Sella et al. (2002), Prawirodirdjo et al. (2004), Argus
et al. (2011), and Altamimi et al. (2012) also estimatedthe parameter of the Sundaland plate, using less than 4
GNSS sites. Therefore, the previous Euler pole models
were not estimated using whole geodetic data covered
whole Sundaland plate, and the Euler pole model underthe ITRF2014 is still not evaluated so far in terms of the
updated GNSS data.

Fig. 1 Tectonic background of this study with the distribution of GNSS sites (new GNSS dataset and published GNSS velocities. The red line shows
the boundary of Sundaland plate while the yellow transparent polygon shows the undeformed region of Sundaland plate (Simons et al. 2007). The
shown relative velocities refer to Sundaland plate. Terrain model is obtained from the SRTM data with 1 arc second spatial resolution. Red beachballs show Mw > 7 earthquakes from 2000 to 2020

Alif et al. Geoscience Letters(2024) 11:16

In this study, we not only provided the Euler poleparameters of the Sundaland plate under the ITRF2014,
but also adopted more GNSS sites in Sumatra to improve
the reliability of its pole parameters. Those sites aremostly newly built by the Geospatial Information Agency
of Indonesia (BIG) in 2018 to understand the crustal
deformation characteristics and improve the precision of
mapping control points in Indonesia (Aditiya et al. 2014).
In addition, we further validated the previous models andgave an insight into how the Sundaland plate moves withthe constraint from GNSS sites in Sumatra.

GNSS data processing and velocity field estimation
To re-estimate the Euler pole parameters of the Sundaland plate, we analyze the new GNSS data in Sumatra,Indonesia, in addition to the published GNSS data in the
Sundaland plate in this study.
New GNSS dataset in Sumatra, Indonesia

GNSS data between January 2017 and June 2022 inthis study are obtained from the Sumatran GPS Array(SuGAr) and the Indonesia Continuously Operating Reference Stations (InaCORS). These GNSS sites are locatedto the east of the Sumatran Fault Zone in the Sundalandplate, covering Sumatra and other islands east of Sumatra (Fig. 1). To prevent the surface deformation contaminated by the coupling of the Sumatran Fault Zone, GNSS
sites with a distance over 100 km from the fault zone
are used. Five of the thirty-seven selected GNSS sites inthis research (Table 1) are SuGAr sites, operated by the
Earth Observatory of Singapore (EOS) (McLoughlin
et al. 2011). Two of them (BAKO, NTUS) are the International GNSS Service (IGS) sites, which are also used in
the published Euler pole study. Five of remaining 30 sites(CLGI, CLHT, CNAT, CSBK, PALE) are the InaCORS
sites, built by the National Geospatial Agency of Indonesia (BIG) prior to 2017. Observations from those sites
have been used for crustal deformation studies (Alif et al.
2016, 2021, 2023). The other 25 sites also belong to the
InaCORS, built after 2017, mostly in 2018, whose data
have been never utilized in the Euler pole parameter estimation. All GNSS data are continuously recorded with asampling interval of 30 s.
The GNSS data were processed using the Bernese v.5.2
software with the double-difference positioning approachto obtain daily coordinate solutions in ITRF2014 (Dachet al. 2015). In this study, the GNSS sites from the IGS(Johnston et al. 2017), containing ALIC, DARW, DGAR,
IISC, KARR, PIMO, and YAR2, were also used for thedata processing under the ITRF2014 (Altamimi et al.
2016), covering all azimuthal directions from the study
area. The IGS final ephemeris and Earth rotation parameters were also utilized in the GNSS processing. The

Page 3 of 16

International Earth Rotation and Reference Systems
Service (IERS) Conventions 2010 was used as the tidal
correction of station coordinates. The global mapping
function (GMF) (Boehm et al. 2006), an a priori tropospheric model was used due to the high annual rainfall
and exposure to intense sunlight in the study area. The
10° elevation cut-off angle was defined to eliminate
low-altitude tropospheric zenith delay in the GNSS
processing.
Because no nonlinear pattern is detected in SumatranIsland, only the GNSS velocity, permanent offset, andtheir standard deviations were calculated by the classical coordinate time series analysis using the least squares
method (Fig. 2). The Heaviside step function (Fenget al. 2015) is applied to fit the permanent offset in thetime series, which may be caused by coseismic displacements, antenna replacement, or other unknown factors.
The outlier is defined as the coordinate larger than the
95% confidence level of the coordinate time series. The
weighting is established by assigning the reciprocal of thesquare of the coordinate uncertainty. For the purpose of
estimating Euler pole parameters, only horizontal velocities are used. In the study area, the ITRF2014 velocities
are mainly toward the East-Southeast direction, ranging
from 22 to 30 mm/year in Sumatran Island (Additional
file 1: Fig S1), which corresponds to the general direction of the Sundaland plate motion in previous studies(Simons et al. 2007; Yong et al. 2017; Hanifa et al. 2014;
Ramadian et al. 2017).
Published GNSS velocities in Sundaland plate

To improve the spatial coverage of the Sundaland platemotion, the published GNSS velocities from Simons et al.
(2007) and Yong et al. (2017) were also used to estimate
the Euler pole parameters in this study. These GNSS sites
are spread out of Sumatra in the Sundaland plate (Fig. 1).
Twenty-eight ITRF2000 GNSS velocities from Simons
et al. (2007) are spread in Sundaland plate but mainly
located in Indochina and Malaysia. Ten ITRF2008 GNSS
velocities mostly in Malaysia were adopted by Yong et al.
(2017) to estimate the Euler pole parameters. To makethe velocities in a uniform and consistent reference
frame, we directly transformed these published velocities into ITRF2014 using the Helmert transformation to
ITRF2014 from ITRF2008 and ITRF2000, respectively(Altamimi et al. 2011, 2002).
To validate the reliability of transformed velocities, the transformed velocities of four common sites(BAKO, NTUS, GETI, BINT) were compared with
their ITRF velocities (Altamimi et al. 2012, 2003, 2017)(Fig. 1). The ITRF2014 velocities used from Altamimi
et al. (2017) are the velocities without postseismic
relaxation, which are approximately 2–4 mm/yr larger

Alif et al. Geoscience Letters(2024) 11:16

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Table 1 GNSS sites used in this study
No

Site NameLongitude (°)

Latitude (°)

Location

Data period

Reference

1

CALI

106.4627− 3.0061

Toboali

2019.0–2022.5

InaCORS2

CBJY

105.2158− 4.9505

Bandar Jaya

2018.5–2022.5

InaCORS

3

CBLG

99.06942.3317

Balige2018.6–2022.5

InaCORS4

CBLT

108.2679− 2.8729

Bangka Belitung

2018.7–2022.4

InaCORS

5

CBTM

103.9306

1.0711

Batam

2018.7–2022.5

InaCORS

6

CDRI

101.1923

1.2673Duri

2020.0–2022.5

InaCORS7

CDUM

101.4460

1.6783

Dumai Timur

2018.7–2022.4

InaCORS8

CJBI

103.5895− 1.6072

Jambi

2020.0–2022.5

InaCORS

9

CKAG

104.8305− 3.3927

Kayu Agung2020.0–2022.5

InaCORS10

CKCN

97.81123.4876

Kutacane2020.0–2022.5

InaCORS11

CKMN

104.5668− 4.8654

Bukit Kemuning

2020.0–2022.5

InaCORS12CKPI100.0931

1.8925

Kotapinang

2018.8–2022.5

InaCORS13

CKTK103.4658− 0.8131

Tungkal 2

2018.8–2022.5

InaCORS

14

CLGI

105.2974− 5.8116

Keirong2017.0–2021.7

InaCORS15

CLHT

103.5332− 3.7952

Lahat2017.0–2022.5

InaCORS

16

CMEN

105.2527− 4.4743

Menggala

2018.7–2022.2

InaCORS

17

CMOL

102.2938− 0.3607

Kembang Harum2018.7–2022.4

InaCORS18

CMRT

102.7109

1.0133Tebing Tinggi

2020.0–2022.5

InaCORS19

CMTB

102.4415− 1.4791

Tebo Tengah2018.7–2022.5

InaCORS20

CMTP

104.3477− 4.3157

Martaputa

2018.7–2022.4

InaCORS21

CNAT

108.3877

3.9411Natuna2017.0–2022.5

InaCORS

22

CPBM

104.2371− 3.4320

Prabumulih

2018.7–2022.5

InaCORS

23

CSAP

102.1560

1.1217Sungai Apit2018.7–2022.4

InaCORS24

CSBK

105.5051− 5.9019

Sebuku2017.0–2021.5

InaCORS25

CSDH

101.5062− 0.9661

Sungai Dareh

2018.7–2022.4

InaCORS26

CSEK

103.8388− 2.8886

Sekayu2018.7–2022.5

InaCORS27

CTBT

99.1704

3.3354

Padang Hilir

2020.0–2022.5

InaCORS28

CTJB

99.80612.9644

Tanjung Balai

2020.0–2022.5

InaCORS29

CWJP

105.7061− 5.1742

Way Jepara

2018.7–2022.5

InaCORS30

PALE

104.6995− 2.9023

Palembang2017.6–2022.5

InaCORS

31

BAKO

106.8489− 6.4911

Cibinong2017.0–2022.5

Regional IGS

32

NTUS

103.6800

1.3458Singapore2017.0–2022.5

Regional IGS

33

JMBI

103.5203− 1.6156

Jambi

2017.0–2022.5

SuGAr

34

MREK

98.53812.9699Merek

2017.0–2021.5

SuGAr

35

PKN2

101.4474

0.4593

Pekanbaru

2017.0–2022.5

SuGAr

36

SING

103.7731

1.3622Singapore2017.0–2022.3

SuGAr

37

TJKG

105.1746− 5.2395

Tanjung Karang

2017.0–2022.5

SuGAr

than our transformed velocities (Table 2). Because the
ITRF2000 and ITRF2008 velocities are almost consistent with our transformed velocities (Table 2) (Altamimi
et al. 2012, 2003), the approximately 2–4 mm/yr differences in ITRF2014 are treated as the uncertainties oftransformation. Fortunately, these velocity differences
are less than the uncertainty in the Euler pole parameter estimation in this study. The two common sites
between this study and published velocities (BAKO,
NTUS) were also compared with their ITRF velocities.

The adopted velocities for these common sites are fromthe published velocities.
In addition, to exclude the sites within the deformation
zone in the plate boundaries, the outliers were removed
from the compiled ITRF2014 velocity field. The outlier isdefined as the velocity residuals calculated by subtracting the Sundaland plate motion of Simons et al. (2007)
and Yong et al. (2017) from the compiled velocities. The
compiled velocities were first transformed into the original ITRF2000 and ITRF2008 that are used to estimate theAlif et al. Geoscience Letters(2024) 11:16

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Euler poles of Simons and Yong, respectively. The sites
with velocity residuals larger than 3 mm/yr calculated
from both the Simons model and the Yong model, areconsidered to be in the non-undeformed region of the
Sundaland plate. This 3 mm/yr threshold is determinedbased on the undeformed region criteria defined by
Simons et al. (Simons et al. 2007) in their previous studies
as a trade-off between (relative) accuracy, unbalance inthe network, data impact factors, and possible deformation noise. These residuals, as well as the velocity residuals from the Euler pole estimation, are discussed in the
Discussion. Seven of sixty-four GNSS velocities (BUTU,
CBLG, CKCN, CSBK, CTBT, CKCN, MREK) were not
adopted for the Euler pole estimation (Fig. 3), because
they were probably dominated by the local factors, suchas the unknown inland faults, landslides, and land subsidence (Yong et al. 2019).

Euler pole parameter estimation for Sundalandplate
The optimized location (latitude, longitude) and angular velocity of the Euler pole were searched simultaneously through the grid search based on the minimum
χ2 between the observed and modeled ITRF2014 GNSS
velocities. The search was conducted in two steps. The
first step is conducted by utilizing the GNSS sites selected
after excluding the sites within the deformation zone.
The second step is conducted by utilizing the GNSS sites
selected based on the velocity residuals obtained fromthe first step. The large and systematic velocity residuals were not used in the second step so that the result of
the second step is the optimized Euler pole parameters(Fig. 4). The search settings initially cover the Euler poleparameters from the previous studies (Simons et al. 2007;
Yong et al. 2017), and then, based on the result from thewider search settings, it is narrowed to a predefined latitude boundary of 44° to 46° with a latitude interval of
0.01°, and longitude boundary of -89° to -87° with a longitude interval of 0.01°, and an angular velocity intervalof 0.001°/Myr (Fig. 5). The Euler pole using the original
velocities of Simons and Yong was also reestimated to
examine the reliability of Euler pole estimation method
used in this study. The location and angular velocity of
the Euler pole are evaluated by Eqs. (1) to (7) (Stein andWysession 2009).

Fig. 2 Coordinate time series of 37 GNSS sites for (a) east–west
component and (b) north–south component. Black points areobservations while red lines are linear fitting lines. Green lines
within the black points are error bars, enlarged by a factor of ten

A = cos ϕP sin P sin ϕT ω − cos ϕT sin T sin ϕP ω
(1)
B = − cos ϕP cos P sin ϕT ω + cos ϕT cos T sin ϕP ω
(2)

Alif et al. Geoscience Letters(2024) 11:16

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Table 2 Velocities on common sites between Altamimi result and transformed velocities
Reference frame
ITRF2014

ITRF2008

ITRF2000

Site name

Altamimi (mm/yr)

Simons (mm/yr)

Yong (mm/yr)

This Study(mm/yr)

BAKO

25.6

24.4

24.2

25.0

NTUS

31.0

31.1

30.6

26.9

GETI

33.6

32.7

31.9

–

BINT

31.0

29.7

29.4

–

BAKO

27.6

24.4

24.1

25.0

NTUS

24.4

31.1

30.6

26.9

GETI

32.7

32.6

31.7

–

BINT

29.4

29.6

29.3

–

BAKO

24.7

24.3

24.0

25.1
26.9

NTUS

31.8

31.1

30.6

GETI

–

32.5

31.6

–

BINT

–

29.6

29.3

–

Original velocities of Simons, Yong, and this study is under ITRF2000, ITRF2008, and ITRF2014, respectively

Fig. 3 Velocity residuals using Sundaland plate model of Simons et al. (2007) and Yong et al. (2017). Terrain model is obtained from SRTM datawith 1 arc second spatial resolution

Alif et al. Geoscience Letters(2024) 11:16

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Fig. 4 The selection sites for the Euler pole estimation. Terrain model is obtained from SRTM data with 1 arc second spatial resolution

C = cos ϕP cos P cos ϕT sin T ω
− cos ϕT cos T cos ϕP sin P ω

(3)

P = A sin ϕT cos T + B sin ϕT + sin T + −C cos ϕT(4)
Q = −A

sinT
cosT
+B
cosϕT
cosϕT

(5)

Vplate =
A2 + B2 + C 2(6)

αplate = tan−1

P
Q(sin(90 − ϕ T ))(7)

where ϕP is Euler pole latitude; P is Euler pole longitude;ω is Euler pole angular velocity in radians/yr; ϕT is latitude of point on Earth surface; T is longitude of point
on Earth surface; Vplate is the plate motion in radians/yr;
αplate is the plate motion azimuth in radians.
The optimized Euler pole parameters in this study
are the latitude of 45.63 ± 0.45°, the longitude of− 88.71 ± 0.38° and the angular velocity of 0.337 ± 0.002°/
Myr in the counterclockwise (Fig. 6). The minimum χ2 ofthe best-fit model is 0.05 mm/yr. Eight GNSS velocities
used in the first step were not adopted in the second step
(Fig. 7). The bootstrap method (Hall and Martin 1988)
was adopted in this study to estimate the stability of Euler
pole parameters. The velocities from the corresponding GNSS velocities are resampled randomly for 10,000
times. The resultant Euler pole parameters are distributed normally, and the mean values for the parameters
are statistically similar (Fig. 8). The latitude of 45.194°,

Alif et al. Geoscience Letters(2024) 11:16

Fig. 5 (a) The χ2 distribution of grid search in the first step with angular velocity as 0.339 mm/year. (b) The χ2 distribution of grid searchin the second step with angular velocity as 0.337 mm/yr. White star represents the minimum χ2

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Alif et al. Geoscience Letters(2024) 11:16

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Fig. 6 Euler pole locations of the Sundaland plate estimated in this study and the previous study. The colored ellipse is the two times standard
deviation of the estimation. The smaller dots are Euler pole locations validation of bootstrap resampling. Terrain model is obtained from SRTM datawith 1 arc second spatial resolution

the longitude of − 88.349° and the angular velocity of
0.3399°/Myr for the first step, and the latitude of 45.635°,
the longitude of − 88.714° and the angular velocity of
0.3369°/Myr for the second step. The 9488 (95%), 9284
(93%), and 9,966 (100%) samples are within the boundaryof three times standard deviation from the mean value
for latitude, longitude, and angular velocity estimationof the first step, respectively. Meanwhile, the 9414 (94%),9041 (90%), and 9964 (100%) samples are within the similar boundary criteria of the second step. These results
indicate that our optimized Euler pole parameters arestable and reliable.

Discussion
To examine the reliability of method for the Euler poleparameter estimation in this study, we also estimatedthe Euler pole parameters from their respective dataset (Simons et al. (2007) and Yong et al. (2017)) in corresponding reference frames (ITRF2000 and ITRF2008)
using our method (Table 3). The results show that the
published Euler pole locations are within the error
ellipse of our re-estimated Euler pole locations (Fig. 6).
The evaluated Euler pole is located close to the proposed pole locations in Yong et al. (2017). The angularvelocity is close to the velocity of Simons et al. (2007).
These comparisons imply that the velocities in Malaysia
as delineated in Yong et al. (2017) could be indicative of
their predominant influence on the Euler pole’s location,
attributable primarily to the region’s subdued tectonic
dynamism. However, a critical consideration is the methodology of Simons et al. (2007), who employed a dataset
approximately double in size compared to that of Yonget al. (2017). Additionally, the spatial arrangement of
the GNSS stations in Simons et al. (2007) demonstrates
a more comprehensive coverage than that in Yong et al.
(2017). These factors collectively enhance the robustness
and reliability of the angular velocity calculations presented by Simons et al. (2007).
We noticed that the residual velocities in our best-fit
model show a distinguishable and systematic pattern inspace. The residual velocities in Indochina (the northernmost area) are southward, while velocities in Sumatra (the southernmost area) are northward (Fig. 7).
According to the pattern of significant residual velocities in the first step (6 sites in the Sumatra, 2 sites in
the Malaysia), we proposed that these large and systematic velocity residuals are probably affected by theremaining linear postseismic deformation effect due toAlif et al. Geoscience Letters(2024) 11:16

Fig. 7 (a) Velocity residuals in the first step; (b) Velocity residuals in the second step

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Alif et al. Geoscience Letters(2024) 11:16

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Fig. 8 The distribution of Euler pole parameters using the bootstrap. The bin width is 0.1° for latitude and longitude, and 0.001 mm/yr
for the angular velocity. Green dash line and red dash line are the parameters from the estimation and validation, respectively. The red solid lines are
the parameter boundary for three times standard deviation from the mean value. (a) Results of first step. (b) Results of second stepsimilar orientation (northward motion) to the proposed
postseismic deformation in Sumatra (Alif et al. 2016).
These postseismic deformation could not be detectedin our linear pattern of time series analysis. The resultsof second step in this study show the optimized Euler
pole parameters with a more-centered distribution(Fig. 9, Table 4), since the stations with residual velocities containing the significant systematic patterns havebeen removed in this step. However, the systematic
northward-southward pattern of residual velocities still
exists in this optimized solution (Fig. 7).
Some possibilities were proposed in this study to
explain the systematic residual velocity pattern. First,
the systematic residuals in the Sumatra are still probably affected by the postseismic deformation of Sumatran earthquake in the west side of Sumatra (Fenget al. 2015) based on their orientations. This systematic northward residual, which is the orientation ofminor postseismic deformation in Sumatra, may be

still remained in this area (Alif et al. 2016), despite thepostseismic deformation-dominated velocities were
removed before the parameter estimation. This possible remaining postseismic deformation occurred in thecentral and the southern Sumatra while the epicenterof the largest earthquake is in the northern Sumatra,thus the residual orientation is northward. Second,
the southward systematic residuals in the Indochina
are probably affected by the Tibetan crustal flow in
the north side of Indochina (Panda et al. 2020). This
crustal flow related to the collapse of Tibetan plateau
and causes major deformation along the Sagaing Fault,
Myanmar (Panda et al. 2018). In addition, this systematic residual pattern may imply that the Sundalandplate is composed of several microplates. As Sundaland
Plate, which was once part of Eurasian plate, rotates
independent of Eurasian plate rotation, it is considered as different plate (DeMets et al. 2010). This leads
to classification of the several microplates of EurasianAlif et al. Geoscience Letters(2024) 11:16

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Table 3 Comparison of Euler pole parameter estimated in this study and the previous study
Reference frame

DatasetSites usedχ2

Pole rotation parameter
Lat (°)Lon (°)

ω (°/Myr)ITRF2000

Simons et al. (2007) (Original)

28

49.00

− 94.20

0.336 ± 0.007

1.04

ITRF2000

Simons et al. (2007) (Re-estimated)

28

49.25

− 94.79

0.336 ± 0.003

0.07

ITRF2008

Yong et al. (2017) (Original)

10

44.16

− 87.220.349 ± 0.038

0.66

ITRF2008

Yong et al. (2017) (Re-estimated)

10

44.51

− 88.160.349 ± 0.009

0.18

ITRF2014

First Estimation

57

45.19

− 88.35

0.339 ± 0.002

0.07

ITRF2014

Second Estimation

49

45.63

− 88.710.337 ± 0.002

0.05

Fig. 9 Velocity residuals histogram using Sundaland plate model of Simons et al. (2007) and Yong et al. (2017), the first estimation and the second
estimation. The M value is the mean of the distribution. The bin width is 30° for azimuth, and 1 mm/year for the east–west residual and north–south
residualplate, such as the Sundaland plate, the Yangtze plate,
and the Amur plate. Therefore, independent rotationon the Indochina and Malaysia could lead to the possibility of microplates within the Sundaland plate. Thishypothesis is also consistent with the GNSS residualin Simons et al. (Yong et al. 2017) that slightly clusters Sumatra, Malaysia, Indochina, and Java. However,more data and studies are still required to examine thismicroplate hypothesis. Finally, the possible causes forother residuals are the crustal shortening caused by
the unknown inland faults (Rangin et al. 1999; Mustafar et al. 2017) or a gravity sliding thrust (Milsom et al.
1997; King et al. 2010), accommodated by west of theAlif et al. Geoscience Letters(2024) 11:16

Page 13 of 16

Table 4 The GNSS velocities in mm/yr used in this study
Reference

Site

Sundaland plate ofSimonsSundaland plate of Yong First Estimation

SecondEstimation

VE

VN

VE

VN

VE

VN

VE

VN

New dataset

JMBI

− 2.9

0.3

− 1.6

− 2.0

− 1.3

− 1.7

− 1.4

− 1.6

New dataset

CMEN

− 0.6

0.2

0.8

− 1.9

1.0

− 1.6

0.9

− 1.5

New dataset

CKAG

− 0.4

0.3

1.0

− 1.8

1.2

− 1.5

1.1

− 1.5

New dataset

CALI

− 2.5

0.8

− 1.1

− 1.2

− 0.9

− 1.0

− 1.0

− 0.9

New dataset

CBLT

− 1.4

1.1

0.0

− 0.8

0.2

− 0.6

0.2

− 0.5

New dataset

CLGI

− 4.0

1.3

− 2.5

− 0.8

− 2.3

− 0.6

− 2.4

− 0.5

New dataset

CBTM

− 2.7

1.3

− 1.6

− 0.9

− 1.3

− 0.6

− 1.3

− 0.5

New dataset

CKMN

1.4

1.4

2.8

− 0.8

3.0

− 0.5

2.9

− 0.4

New dataset

CBJY

− 1.2

1.7

0.3

− 0.4

0.5

− 0.2

0.4

− 0.1

New dataset

CMRT

0.2

1.9

1.3

− 0.4

1.6

− 0.1

1.6

0.0

New dataset

CWJP

− 0.1

1.8

1.4

− 0.3

1.5

0.0

1.5

0.0

New dataset

CMTB

− 1.6

2.1

− 0.3

− 0.2

− 0.1

0.1

− 0.1

0.2

New dataset

CNAT

− 2.8

1.9

− 2.0

0.0

− 1.6

0.2

− 1.6

0.2

New dataset

TJKG

− 2.2

2.1

− 0.7

0.0

− 0.6

0.2

− 0.6

0.3

New dataset

SING

− 2.2

2.5

− 1.2

0.3

− 0.8

0.5

− 0.9

0.6

New dataset

PALE

− 2.8

2.5

− 1.4

0.4

− 1.2

0.6

− 1.3

0.7

New dataset

CSEK

− 2.9

3.0

− 1.5

0.7

− 1.3

1.0

− 1.4

1.1

New dataset

CMTP

− 2.9

3.1

− 1.4

0.9

− 1.2

1.1

− 1.3

1.2

New dataset

CPBM

− 1.9

3.1

− 0.6

0.9

− 0.4

1.2

− 0.4

1.3

New dataset

CMOL

− 1.5

3.6

− 0.3

1.3

0.0

1.6

− 0.1

1.7

New dataset

PKN2

− 0.4

3.7

0.8

1.3

1.1

1.7

1.1

1.8

New dataset

CLHT

− 2.8

3.7

− 1.4

1.5

− 1.2

1.7

− 1.3

1.8

New dataset

CSDH

0.8

4.3

2.0

1.9

2.3

2.2

2.2

2.3

New dataset

CKTK

1.1

− 1.6

2.3

− 3.9

2.6

− 3.6

–

–

New dataset

CJBI

1.1

− 0.1

2.3

− 2.4

2.6

− 2.1

–

–

New dataset

CDUM

− 2.7

2.8

− 1.6

0.4

− 1.3

0.8

–

–

New dataset

CKPI

− 3.3

4.3

− 2.3

1.8

− 1.9

2.2

–

–

New dataset

CSAP

− 0.2

4.8

0.9

2.4

1.2

2.7

–

–

New dataset

CDRI

− 0.1

5.0

1.0

2.5

1.3

2.9

–

–

New dataset

CBLG

− 4.5

1.8

− 3.5

− 0.8

–

–

–

–

New dataset

CKCN

− 5.5

2.0

− 4.5

− 0.6

–

–

–

–

New dataset

CSBK

− 4.7

0.8

− 3.2

− 1.3

–

–

–

–

New dataset

CTBT

− 5.3

− 0.4

− 4.3

− 2.9

–

–

–

–

New dataset

CTJB

− 4.8

− 0.2

− 3.8

− 2.7

–

–

–

–

New dataset

MREK

− 5.3

− 0.7

− 4.3

− 3.3

–

–

–

–

Simons

NNKI

− 1.5

− 2.4

− 0.7

− 4.6

− 0.7

− 2.6

− 0.6

− 2.5

Simons

UBRT

− 0.5

− 1.6

0.2

− 3.7

0.0

− 1.7

0.0

− 1.6

Simons

SRIS

− 0.5

− 1.5

0.2

− 3.6

− 0.1

− 1.6

0.0

− 1.5

Simons

UTHA

0.2

− 1.3

1.0

− 3.6

0.7

− 1.6

0.8

− 1.4

Simons

RYNG

− 0.9

− 1.1

− 0.2

− 3.4

− 0.7

− 1.4

− 0.7

− 1.3

Simons

NONN

− 0.8

− 1.2

− 0.1

− 3.0

− 0.3

− 1.1

− 0.2

− 1.0

Simons

CHMI

− 2.5

− 0.8

− 1.7

− 3.2

− 1.6

− 1.1

− 1.5

− 0.9

Simons

TANJ

1.4

− 0.7

2.6

− 2.8

1.4

− 0.8

1.4

− 0.8

Simons

SISM

− 1.6

− 0.5

− 0.8

− 2.9

− 0.8

− 0.8

− 0.8

− 0.7

Simons

CHON

− 0.5

− 0.4

0.2

− 2.8

− 0.3

− 0.7

− 0.2

− 0.6

Simons

BNKK

0.7

− 0.2

1.4

− 2.6

1.0

− 0.5

1.1

− 0.4

Simons

OTRI

− 2.9

0.0

− 2.2

− 2.3

− 2.1

− 0.2

− 2.0

− 0.1

Alif et al. Geoscience Letters(2024) 11:16

Page 14 of 16

Table 4 (continued)
Reference

Site

Sundaland plate ofSimonsSundaland plate of Yong First Estimation

SecondEstimation

VE

VN

VE

VN

VE

VN

VE

VN

Simons

BLKP

− 1.9

− 0.5

− 0.7

− 1.8

− 1.9

− 0.1

− 1.9

− 0.1

Simons

PUER

0.6

− 0.6

1.2

− 1.7

0.5

− 0.1

0.5

− 0.1

Simons

NTUS*

1.5

0.2

2.6

− 2.1

1.4

− 0.1

1.4

0.0

Simons

GETI*

1.4

0.6

2.2

− 1.8

1.2

0.3

1.2

0.4

Simons

TABA

1.3

0.4

2.4

− 1.5

1.3

0.4

1.2

0.4

Simons

HPAA

− 2.3

0.9

− 1.6

− 1.6

− 1.7

0.6

− 1.6

0.7

Simons

BANH

1.5

1.0

2.3

− 1.5

1.6

0.7

1.6

0.8

Simons

BAKO*

− 2.4

0.9

− 0.7

− 1.1

− 2.0

0.9

− 2.0

0.9

Simons

KTPK

1.4

1.2

2.3

− 1.2

1.3

0.9

1.2

1.0

Simons

IPOH

1.4

1.8

2.3

− 0.7

1.3

1.4

1.3

1.5

Simons

BINT*

− 2.7

− 1.7

− 1.7

− 3.3

− 2.8

− 1.5

–

–

Simons

BUTU​

4.0

1.6

5.8

− 0.2

–

–

–

–

Yong

UTMJ

0.7

− 0.6

1.7

− 2.9

0.6

− 0.9

0.5

− 0.8

Yong

KUCH

− 1.7

− 0.7

− 0.6

− 2.5

− 1.8

− 0.7

− 1.8

− 0.6

Yong

KUAL

0.7

− 0.4

1.6

− 2.7

0.6

− 0.7

0.6

− 0.6

Yong

KUAN

1.0

1.6

1.9

− 0.7

0.9

1.4

0.8

1.5

Yong

MIRI

− 3.5

2.3

− 2.6

0.8

− 4.0

0.7

–

–

*

Common sites compared in Table 2

eastern boundary of Sundaland Plate from Palawan in
Philippines to the Java Sea (Rangin et al. 1999).

Conclusion
To evaluate the Euler pole parameters of Sundalandplate in ITRF2014, we first processed the GNSS datafrom 37 new sites in Sumatra between January 2017 andJune 2022. To improve the reliability of parameter estimation, another 30 transformed published GNSS velocities at the Sundaland plate were also adopted in thisstudy. Based on the grid search strategy, the optimized
Euler pole parameters are the latitude of 45.63 ± 0.45°,
the longitude of − 88.71 ± 0.38° and the angular velocity of 0.337 ± 0.002°/Myr in counterclockwise direction.
In addition, the residual velocities in our best-fit model
also shows a distinguishable and systematic pattern inspace. The postseismic deformation, the Tibetan crustal flow, and the microplates are the possible causes ofthese residual velocities. However, more data and studies are necessary to examine these hypotheses in thefurther study.
Supplementary Information
The online version contains supplementary material available at https://​doi.​
org/​10.​1186/​s40562-​024-​00330-0.
Additional file 1: Figure S1. The original GNSS velocities refer to ITRF2014
from new datasets, including unused sites for the estimation.

Acknowledgements
Figures were drawn using Generic Mapping Tools (GMT) software (Wessel
et al. 2013). Thanks are given to the Geospatial Information Agency of Indone‑sia (BIG) for continuous GNSS data.
Author contributions
SMA: Conceived and designed the analysis, Collected the data, contributed
data or analysis tools, Performed the analysis, Wrote the paper, Created tables
and figures. KEC: Conceived and designed the analysis, Performed the analysis,
Wrote the paper. TS: Conceived and designed the analysis, Wrote the paper.
WNW: Created tables and figures. All authors read and approved the final
manuscript.
Funding
The author(s) received no financial support for the research, authorship, and/or publication of this article.
Availability of data and materials
The data availability (raw GNSS data and velocities) could be accessed bysending email to the first author (email: satrio.muhammad@gt.itera.ac.id).

Declarations
Ethics approval and consent to participate
Not applicable.
Consent for publication
Not applicable.
Competing interests
The authors declare that they have no competing interests.
Received: 9 November 2023 Accepted: 3 March 2024

Alif et al. Geoscience Letters(2024) 11:16

References
Aditiya A, Efendi J, Syafii A (2014) InaCORS: Infrastructure of GNSS CORS in
Indonesia. In FIG Congress 2014.
Alif SM, Meilano I, Gunawan E, Efendi J (2016) Evidence of postseismic defor‑
mation signal of the 2007 M8.5 Bengkulu earthquake and the 2012 M8.6
Indian Ocean earthquake in Southern Sumatra, Indonesia, based on GPS
data. J Appl Geod 10(2):103–108. https://​doi.​org/​10.​1515/​jag-​2015-​0019
Alif SM, Fattah EI, Kholil M, Anggara O (2021) Source of the 2019 Mw6. 9
Banten Intraslab earthquake modelled with GPS data inversion. Geod
Geodyn 12(4):308–314. https://​doi.​org/​10.​1016/j.​geog.​2021.​06.​001
Alif SM, Siagian JM, Anggara O (2023) Present-day crustal deformation in west
Sumatra after series of Sumatran great earthquake from 2004–2010. J
Earth Marine Technol 3(2):59–68. https://​doi.​org/​10.​3128/j.​jemt.​2023
Altamimi Z, Sillard P, Boucher C (2002) ITRF2000: a new release of the interna‑
tional terrestrial reference frame for earth science applications. J Geophys
Res: Solid Earth. https://​doi.​org/​10.​1029/​2001J​B0005​61
Altamimi Z, Sillard P, Boucher C (2003) The impact of a no-net-rotation condi‑tion on ITRF2000. Geophys Res Lett 30(2):36–41. https://​doi.​org/​10.​1029/​
2002G​L0162​79
Altamimi Z, Collilieux X, Métivier L (2011) ITRF2008: an improved solutionof the international terrestrial reference frame. J Geod 85(8):457–473.
https://​doi.​org/​10.​1007/​s00190-​011-​0444-4
Altamimi Z, Métivier L, Collilieux X (2012) ITRF2008 plate motion model. J
Geophys Res: Solid Earth. https://​doi.​org/​10.​1029/​2011J​B0089​30
Altamimi Z, Rebischung P, Métivier L, Collilieux X (2016) ITRF2014: a newrelease of the international terrestrial reference frame modeling nonlinear
station motions. J Geophys Res: Solid Earth 121(8):6109–6131. https://​doi.​
org/​10.​1002/​2016J​B0130​98
Altamimi Z, Métivier L, Rebischung P, Rouby H, Collilieux X (2017) ITRF2014
plate motion model. Geophys J Int 209(3):1906–1912
Argus DF, Gordon RG, DeMets C (2011) Geologically current motion of 56
plates relative to the no-net-rotation reference frame. Geochem Geophys
Geosyst. https://​doi.​org/​10.​1029/​2011G​C0037​51
Boehm J, Niell A, Tregoning P, Schuh H (2006) Global mapping function (GMF):
a new empirical mapping function based on numerical weather model
data. Geophys Res Lett. https://​doi.​org/​10.​1029/​2005G​L0255​46
Dach R, Lutz S, Walser P, Fridez P (2015) Bernese GNSS software version 5.2.
DeMets C, Gordon RG, Argus DF (2010) Geologically current plate motions.
Geophys J Int 181(1):1–80. https://​doi.​org/​10.​1111/j.​1365-​246X.​2009.​
04491.x
Feng L, Hill EM, Banerjee P, Hermawan I, Tsang LL, Natawidjaja DH, Sieh
K (2015) A unified GPS-based earthquake catalog for the Sumatranplate boundary between 2002 and 2013. J Geophys Res: Solid Earth
120(5):3566–3598. https://​doi.​org/​10.​1002/​2014J​B0116​61
Hall P, Martin MA (1988) On bootstrap resampling and iteration. Biometrika
75(4):661–671. https://​doi.​org/​10.​1093/​biomet/​75.4.​661
Hanifa NR, Sagiya T, Kimata F, Efendi J, Abidin HZ, Meilano I (2014) Interplate
coupling model off the southwestern coast of Java, Indonesia, based oncontinuous GPS data in 2008–2010. Earth Planet Sci Lett 401:159–171.
https://​doi.​org/​10.​1016/j.​epsl.​2014.​06.​010
Hurukawa N, Wulandari BR, Kasahara M (2014) Earthquake history of theSumatran fault, Indonesia, since 1892, derived from relocation of large
earthquakes. Bull Seismol Soc Am 104(4):1750–1762. https://​doi.​org/​10.​
1785/​01201​30201
Johnston G, Riddell A, Hausler G (2017) The international GNSS service. In:
Teunissen PJG, Montenbruck O (eds) Springer handbook of global navi‑
gation satellite systems. Springer, Cham, pp 967–982
King RC, Backé G, Morley CK, Hillis RR, Tingay MR (2010) Balancing deformation
in NW Borneo: quantifying plate-scale vs. gravitational tectonics in a delta
and deepwater fold-thrust belt system. Marine Petrol Geol 27(1):238–246.
https://​doi.​org/​10.​1016/j.​marpe​tgeo.​2009.​07.​008
Kuncoro H, Meilano I, Susilo S (2019) Sunda and Sumatra block motion in
ITRF2008. E3S Web Conf 94:04006. https://​doi.​org/​10.​1051/​e3sco​nf/​
20199​404006
McCaffrey R (2009) The tectonic framework of the Sumatran subduction zone.
Annu Rev Earth Planet Sci 37:345–366. https://​doi.​org/​10.​1146/​annur​ev.​
earth.​031208.​100212
McCaffrey R, Stein S, Freymueller J (2002) Crustal block rotations and plate
coupling. Plate Boundary Zones. Geodyn Ser 30:101–122. https://​doi.​org/​
10.​1029/​GD030​p0101

Page 15 of 16

McLoughlin IV, Wong KJ, Tan SL (2011) Data collection, communications andprocessing in the Sumatran GPS array (SuGAr). In Proceedings of theWorld Congress on Engineering. 2: 6–8.
Meade BJ, Hager BH (2005) Block models of crustal motion in southern
California constrained by GPS measurements. J Geophys Res: Solid Earth.
https://​doi.​org/​10.​1029/​2004J​B0032​09
Milsom J, Holt R, Ayub DB, Smail R (1997) Gravity anomalies and deep struc‑tural controls at the Sabah-Palawan margin, South China Sea. Geol Soc
126(1):417–427. https://​doi.​org/​10.​1144/​GSL.​SP.​1997.​126.​01.2
Mustafar MA, Simons WJ, Tongkul F, Satirapod C, Omar KM, Visser PN(2017) Quantifying deformation in North Borneo with GPS. J Geodesy
91(10):1241–1259. https://​doi.​org/​10.​1007/​s00190-​017-​1024-z
Panda D, Kundu B, Gahalaut VK, Rangin C (2018) Crustal deformation, spatial
distribution of earthquakes and along strike segmentation of the Sagaing
Fault, Myanmar. J Asian Earth Sci 166:89–94. https://​doi.​org/​10.​1016/j.​jseaes.​2018.​07.​029
Panda D, Kundu B, Gahalaut VK, Rangin C (2020) India-sunda plate motion,
crustal deformation, and seismic hazard in the Indo-Burmese arc. Tecton‑
ics. https://​doi.​org/​10.​1029/​2019T​C0060​34
Prawirodirdjo L, Bock Y (2004) Instantaneous global plate motion model from
12 years of continuous GPS observations. J Geophys Res: Solid Earth.
https://​doi.​org/​10.​1029/​2003J​B0029​44
Ramadian RR, Meilano I, Gunawan E, Susilo, Efendi J (2017) Time series analysis
of continuous GPS data in Central Java 2010–2015. In AIP Conference
Proceedings (Vol. 1857, No. 1, p. 040013). AIP Publishing LLC. https://​doi.​
org/​10.​1063/1.​49870​77
Rangin C, Le Pichon X, Mazzotti S, Pubellier M, Chamot-Rooke N, Aurelio
M, Quebral R (1999) Plate convergence measured by GPS across the
Sundaland/Philippine Sea Plate deformed boundary: the Philippinesand eastern Indonesia. Geophys J Int 139(2):296–316. https://​doi.​org/​10.​1046/j.​1365-​246x.​1999.​00969.x
Sella GF, Dixon TH, Mao A (2002) REVEL: a model for recent plate velocities
from space geodesy. J Geophys Res: Solid Earth. https://​doi.​org/​10.​1029/​
2000J​B0000​33
Simons WJF, Socquet A, Vigny C, Ambrosius BAC, Haji Abu S, Promthong C,
Subarya C, Sarsito DA, Matheussen S, Morgan P, Spakman W (2007) A dec‑ade of GPS in Southeast Asia: resolving Sundaland motion and bounda‑
ries. J Geophys Res: Solid Earth. https://​doi.​org/​10.​1029/​2005J​B0038​68
Stein S, Wysession M (2009) An introduction to seismology, earthquakes, andearth structure. John Wiley & Sons, Hoboken
Wessel P, Smith WH, Scharroo R, Luis J, Wobbe F (2013) Generic mapping tools:
improved version released. EOS Trans Am Geophys Union 94(45):409–
410. https://​doi.​org/​10.​1002/​2013E​O4500​01
Yong CZ, Denys PH, Pearson CF (2017) Present-day kinematics of the
Sundaland plate. J Appl Geod 11(3):169–177. https://​doi.​org/​10.​1515/​
jag-​2016-​0024
Yong CZ, Denys PH, Pearson CF (2019) Groundwater extraction-induced land
subsidence: a geodetic strain rate study in Kelantan, Malaysia. J Spatial Sci
64(2):275–286. https://​doi.​org/​10.​1080/​14498​596.​2018.​14293​29

Publisher’s NoteSpringer Nature remains neutral with regard to jurisdictional claims in pub‑lished maps and institutional affiliations.

Satrio Muhammad Alif Obtains Bachelor degree and Master
degree from Geodesy and Geomatics Engineering, Institut Teknologi
Bandung, Indonesia. He is currently the PhD candidate at Depart‑
ment of Geomatics, National Cheng Kung University, Taiwan, andthe lecturer and researcher in Geomatics Engineering Study Pro‑
gram, Regional and Infrastructure Technology Department, Institut
Teknologi Sumatera, Indonesia teaching Geometric Geodesy, Com‑
putational Geodesy, and Geodynamics. His interests include tectonic
geodesy and earthquake geodesy. His international publications areabout postseismic mechanism, geodetic slip rate of fault, and coseis‑mic slip distribution.

Alif et al. Geoscience Letters(2024) 11:16

Kuo‑En Ching Works in the field of crustal deformation using
geodetic observations, with researches mainly focus on earthquakerelated deformation analysis, creeping fault, mud tectonics, seismic
hazard assessment, land subsidence, and construction of the semidynamic geodetic datum in Taiwan. His major study areas are Taiwan,
Leyte in Philippines, Indian Himalaya, and Java in Indonesia.
Takeshi Sagiya Has been studying crustal deformation based on
geodetic observation such as GNSS and leveling, data analysis, andnumerical modeling. His research objectives are to understand thecrustal deformation over various spatiotemporal scales in a compre‑
hensive manner with a special focus on various phenomena associ‑ated with large earthquakes at subduction zones as well as inland
active faults, and also volcanic processes. He also aims to make a bet‑
ter forecast of future large earthquakes.

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