Determination of Euler pole parameters for Sundaland plate based on updated GNSS observations in Sumatra, Indonesia

Abstract

To provide a precise Euler pole parameter of Sundaland plate for earthquake potential evaluation in Sumatra, Indonesia after the 2004 M9.2 Aceh earthquake, we adopted 37 new Global Navigation Satellite System (GNSS) observations 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 algorithm was used in Euler pole parameter estimation, which was validated using the bootstrap resampling. 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. 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.

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 model is 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 long-term fault slip rates (Meade and Hager 2005), the accuracy improvement of Euler pole parameters is always essential. After the 2004 M9.2 Aceh earthquake occurred on the Sunda subduction zone, the earthquake potential evaluation along the Sunda trench becomes more 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, and other 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 rate of ~ 7 nanostrain/year (Simons et al. 2007). The northern side 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 Indo-Australian 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 (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, no other M > 7 earthquakes occurred in the Sundaland subduction zone after 2010, and no M > 7 earthquakes occurred in Sumatra Fault Zone since the 1943 M7.3 Ketaun earthquake (Hurukawa et al. 2014).

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 beach balls show M_w > 7 earthquakes from 2000 to 2020

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) then updated the Simons model under the ITRF2008. Yong et al. (2017) next used GNSS sites mostly in Malaysia (one in Java, one in Sumatra, one in Thailand, one in the Philippines) 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 estimated the 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 under the ITRF2014 is still not evaluated so far in terms of the updated GNSS data.

In this study, we not only provided the Euler pole parameters 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 are mostly 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 and gave an insight into how the Sundaland plate moves with the 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 in this study are obtained from the Sumatran GPS Array (SuGAr) and the Indonesia Continuously Operating Reference Stations (InaCORS). These GNSS sites are located to the east of the Sumatran Fault Zone in the Sundaland plate, 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 in this 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 a sampling interval of 30 s.

Table 1 GNSS sites used in this study

The GNSS data were processed using the Bernese v.5.2 software with the double-difference positioning approach to obtain daily coordinate solutions in ITRF2014 (Dach et 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 the data 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 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 Sumatran Island, only the GNSS velocity, permanent offset, and their standard deviations were calculated by the classical coordinate time series analysis using the least squares method (Fig. 2). The Heaviside step function (Feng et al. 2015) is applied to fit the permanent offset in the time 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 the square 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).

Fig. 2

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

Published GNSS velocities in Sundaland plate

To improve the spatial coverage of the Sundaland plate motion, 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 make the 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 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 of transformation. 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 from the published velocities.

Table 2 Velocities on common sites between Altamimi result and transformed 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 is defined 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 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, are considered to be in the non-undeformed region of the Sundaland plate. This 3 mm/yr threshold is determined based 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 in the 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, such as the unknown inland faults, landslides, and land subsidence (Yong et al. 2019).

Fig. 3

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

Euler pole parameter estimation for Sundaland plate

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 from the 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 pole parameters from the previous studies (Simons et al. 2007; Yong et al. 2017), and then, based on the result from the wider 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 interval of 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 and Wysession 2009).

Fig. 4

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

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 search in the second step with angular velocity as 0.337 mm/yr. White star represents the minimum χ²

$$A = \cos \varphi _{P} \,\sin \lambda _{P} \,\sin \varphi _{T} \omega - \cos \varphi _{T} \,\sin \lambda _{T} \,\sin \varphi _{P}\, \omega$$

(1)

$$B = - \cos \varphi _{P} \,\cos \lambda _{P} \,\sin \varphi _{T} \omega + \cos \varphi _{T} \,\cos \lambda _{T} \,\sin \varphi _{P}\, \omega$$

(2)

$$C = \cos \varphi _{P} \,\cos \lambda _{P} \,\cos \varphi _{T} \,\sin \lambda _{T} \omega - \cos \varphi _{T} \,\cos \lambda _{T} \,\cos \varphi _{P} \,\sin \lambda _{P}\, \omega$$

(3)

$$P = A\sin \varphi _{T} \,{\text{~}}\cos \lambda _{T} \, + B\sin \varphi _{T} \, + {\text{~}}\sin \lambda _{T} \, + - C\cos \varphi _{T}$$

(4)

$$Q=-A\frac{\mathit{sin}{\lambda }_{T}}{{\text{cos}}{\varphi }_{T}}+B\frac{\mathit{cos}{\lambda }_{T}}{{\text{cos}}{\varphi }_{T}}$$

(5)

$${V}_{plate}= \sqrt{{A}^{2}+{B}^{2}+{C}^{2}}$$

(6)

$${\alpha }_{plate}= {{\text{tan}}}^{-1}\frac{P}{Q({\text{sin}}{( 90 - \varphi }_{T}))}$$

(7)

where ${\varphi }_{P}$ is Euler pole latitude; ${\lambda }_{P}$ is Euler pole longitude; $\omega$ is Euler pole angular velocity in radians/yr; ${\varphi }_{T}$ is latitude of point on Earth surface; ${\lambda }_{T}$ is longitude of point on Earth surface; ${V}_{plate}$ is the plate motion in radians/yr; ${\alpha }_{plate}$ 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 of the 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°, 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 boundary of three times standard deviation from the mean value for latitude, longitude, and angular velocity estimation of 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 are stable and reliable.

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 data with 1 arc second spatial resolution

Fig. 7

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

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 step

Discussion

To examine the reliability of method for the Euler pole parameter estimation in this study, we also estimated the 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 angular velocity 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 Yong et 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).

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

We noticed that the residual velocities in our best-fit model show a distinguishable and systematic pattern in space. 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 the remaining linear postseismic deformation effect due to similar orientation (northward motion) to the proposed postseismic deformation in Sumatra (Alif et al. 2016). These postseismic deformation could not be detected in our linear pattern of time series analysis. The results of 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 have been removed in this step. However, the systematic northward-southward pattern of residual velocities still exists in this optimized solution (Fig. 7).

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 residual

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

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 (Feng et al. 2015) based on their orientations. This systematic northward residual, which is the orientation of minor postseismic deformation in Sumatra, may be still remained in this area (Alif et al. 2016), despite the postseismic deformation-dominated velocities were removed before the parameter estimation. This possible remaining postseismic deformation occurred in the central and the southern Sumatra while the epicenter of 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 Sundaland plate 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 plate, such as the Sundaland plate, the Yangtze plate, and the Amur plate. Therefore, independent rotation on the Indochina and Malaysia could lead to the possibility of microplates within the Sundaland plate. This hypothesis is also consistent with the GNSS residual in 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 this microplate hypothesis. Finally, the possible causes for other 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 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 Sundaland plate in ITRF2014, we first processed the GNSS data from 37 new sites in Sumatra between January 2017 and June 2022. To improve the reliability of parameter estimation, another 30 transformed published GNSS velocities at the Sundaland plate were also adopted in this study. 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 in space. The postseismic deformation, the Tibetan crustal flow, and the microplates are the possible causes of these residual velocities. However, more data and studies are necessary to examine these hypotheses in the further study.