Introduction

The 2023 February 6 Mw 7.8 Pazarcik Türkiye earthquake caused severe damage to a large area, followed by the Mw 7.5 Elbistan earthquake within 10 hours and with a distance of less than 100 km. The interferometric synthetic aperture radar measurements provide rupture distribution of the earthquake sequence (Reitman et al. 2023). However, the spatiotemporal closeness makes it difficult to distinguish the coseismic deformation caused by each event. Daily GPS observations with a sampling interval of 30 seconds provide effective constraints for velocity, deformation, slip distribution and other kinematic information of crustal movements (Abdrakhmatov et al. 1996; Li et al. 2012; Jiang et al. 2014; Goudarzi et al. 2016; Zhan 2021; Li et al. 2022, Wu et al. 2022), but they are limited in rapid coseismic displacement estimations due to temporal resolution. High-rate GPS measurements show a prominent advantage in temporal resolution for earthquake sequences with short intervals (Ge et al. 2000; Larson et al. 2003; Elósegui et al. 2006; Larson 2009; Avallone et al. 2012; Clotaire Michel et al. 2017; Guo et al. 2021; Li et al. 2023). High-rate GPS data are used for rapid determination of earthquake magnitude, centroid moment tensor determination and rupture evolution to provide earthquake or tsunami early warning and disaster prevention (Blewitt et al. 2006; Melgar et al. 2012; Goldberg et al. 2018). In this article, preliminary coseismic displacement estimates for the Mw 7.8 and Mw 7.5 events are obtained using high-rate (1 Hz) GPS data provided by Türkiye Ulusal Sabit GNSS Ağı (tusaga-aktif.gov.tr) and the international GNSS service (IGS) through the Crustal Dynamics Data Information System (CDDIS) (Noll 2010). Further inversion of the rupture process and source mechanism can be made based on the displacement estimates (Yokota et al 2009; Yue et al. 2011; Xu et al. 2021; Zhijie Jia et al. 2022). Sub-daily process of slow slip events can also be inverted from high-rate GPS observations (Itoh Yuji et al. 2022). The GPS time series with complete records are used to estimate the propagation speed of the surface wave radiated by the earthquake. For stations closest to the epicenters of the two events which stopped recording data shortly after the events and reactivated later, observations before and after each event are used to estimate coseismic displacements. Together with continuous coseismic observations, the results provide preliminary constraints for ground deformation field and rupture process inversion. The GPS stations used in this article are shown in Figure 1. Also shown are the active faults in the vicinity (Seyitoğlu et al. 2022), the focal mechanism from the Global Centroid-Moment-Tensor (CMT) Project (Ekström et al. 2012) and the tectonic setting in the inset map.

Fig. 1
figure 1

Distribution of GPS stations (stations annotated in the inset map are IGS stations) and sketch of tectonic setting in the area (inset map). Yellow squares denote GPS stations. The focal mechanism of the Mw 7.8 earthquake is denoted with the red beachball. Three other earthquakes include Mw 6.7, Mw 7.5, and Mw 6.0 on February 6, 2023 are denoted with red asterisks. White rectangles denote profiles for surface wave speed analysis. NAF is the abbreviation for North Anatolian Fault and EAF is for East Anatolian Fault. Plate boundary is plotted with grey solid lines. Block boundary is plotted with grey dashed lines. The relative motions of major tectonic structures are qualitatively denoted with blue arrows in the inset map

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The African and Arabian plates move northward and converge with the Eurasian plate, which causes the westward motion of the Anatolian block (Dan McKenzie 1972; Barka 1997). The Anatolian block rotates counter-clockwise while escaping from the collision between the Eurasian plate and the Arabian plate and the motion occurs mainly on the North Anatolian Fault and East Anatolian Fault (Barka 1997; Bulut et al. 2012). Along the North Anatolian Fault, the right-lateral strike-slip accommodates most of the westward motion of the Anatolian block, while the left-lateral strike-slip motion mainly occurs along the East Anatolian Fault. Seismicity in this area is usually related to the tectonic movements of the three first-order plates (the Eurasian plate, the African plate and the Arabian plate) and the smaller tectonic block (the Anatolian block).

The earthquake sequence including 4 Mw≥6.0 earthquakes (Fig. 1) occurred on the boundary between the Arabian plate and the Anatolian block. The Anatolian block moves southwestward relative to the Arabian plate with left-lateral strike-slip motion mainly occurring along the East Anatolian fault (denoted as EAF in Fig. 1) (Emre 2018). In this article, we describe the method used to process high-rate GPS data in the region. Position time series of near-field sites are plotted with indications of coseismic movements to verify the results. Then, the time series of all sites recording distinguishable coseismic movements are used to estimate the propagation speed of the surface waves. To preliminarily estimate coseismic displacements at each site, linear fitting is then used to analyze the position time series of the sites. An eastward component displacement of 31cm at site ante and a southward component displacement of 39cm at site mly1 are estimated to be the largest displacements caused by the Mw 7.8 event. The displacements show left-lateral movement along the nodal plane, which is consistent with the focal mechanism. A westward component displacement of 450cm and a northward component displacement of 97cm at the site ekz1 are the largest displacements caused by the Mw 7.5 event. Using high-rate GPS position time series, the surface wave propagation speed caused by the Mw 7.8 Elbistan earthquake is preliminarily estimated at an overall speed of approximately 2.9 km/s.

Data processing

The TRACK module of GAMIT/GLOBK software is used to process the high-rate GPS data (Herring et al. 2003). Data from 46 local GPS stations and 6 IGS stations are processed (Fig. 1 and Appendix Tab. 1). The high-rate GPS data are concatenated to one-hour sessions of GPS time 00, 01, 02, 03, and 10, 11, 12, 13, and 14 on February 6. List of observations of the first 4 sessions is shown in appendix Table 1, IGS stations are labeled with asterisks. Firstly, the IGS sites sofi and ista are used to estimate the far field effects of the Mw 7.8 earthquake. To analyze the long-term movements of those IGS stations, we reference to results provided by Nevada Geodetic Laboratory. Daily GPS data are routinely processed at Nevada Geodetic Laboratory (Blewitt G. et al. 2018). According to their analysis, those IGS stations are moving at a long-term speed of less than 50 mm/yr, which makes it appropriate to assume the stations are relatively static in a few hours if they are not affected by seismic waves. We processed data from the station sofi with station ista as reference station and vice versa, through which we confirmed sofi with minor effects of the events and chose it as the reference station. The GPS data of other stations before seismic wave propagated to the station sofi is used in kinematic mode processing. Secondly, we use IGS final precise ephemeris of GPS constellation. Linear combinations of observations are used to eliminate first-order ionospheric delay. The ionex files from Center for Orbit Determination in Europe (CODE) are used to estimate second order ionospheric delay. GPT3 model and VMF mapping functions are used for atmospheric delay estimation (re3data.org - Registry of Research Data Repositories. http://doi.org/10.17616/R3RD2H). Local coordinates of stations with continuous observations covering the Mw 7.8 event are obtained. The time series of 4 stations are shown in Fig. 2.

Fig. 2
figure 2

Time series of the stations adn2(upper left), ante(upper right), mly1(lower left), nico(lower right) at GPS time 01on February 6,2023. In each panel, the positions of east (top) and north (bottom) components are shown with black dots for each second with grey error bars. X axis denotes GPS time, while Y axis denotes station position in centimeters. The X axis starts at the GPS time of the Mw 7.8 earthquake origin. Horizontal red dashed lines are least square fitting of time series before and after the event. Vertical red dashed lines denote the fitting time

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The accuracy of horizontal components of local coordinates of the stations is better than 2cm, which is appropriate to estimate displacements larger than several centimeters. The vertical components are less distinguishable for coseismic estimates, so only horizontal components are analyzed in this article.

Using least squares linear fitting, coseismic displacements are estimated as the difference between interceptions of fitting lines after and before the event. The estimated largest displacements occurred are at station ante with an eastward component displacement of 31 cm and at station mly1 with a southward component displacement of 39cm.

High-rate GPS time series analysis

As shown in Fig. 1, the focal mechanism for the Mw 7.8 event from GCMT gives one rupture nodal plane with a strike azimuth of 54° and a dip of 70° and the other with a strike azimuth of 320° and a dip of 80°. The focal mechanism for the Mw 7.5 event gives one rupture nodal plane with a strike azimuth of 261° and a dip of 42° and the other with a strike azimuth of 358° and a dip of 84°. To estimate the propagation speed of the surface wave radiated by the Mw 7.8 earthquake, three profiles are made along two nodal planes and eastward of the hypocenter as shown in Fig. 1. To simplify the processing, the middle time between the largest and smallest positions is defined as the average arrival time. Then each arrival time of the surface wave to the stations is obtained. The X axis is defined as the time measured in seconds after the event and the Y axis as the epicentral distance in kilometers, the time series are plotted in Fig. 3.

Fig. 3
figure 3

Time series after the Mw 7.8 event. Upper-left panel for all stations. Upper-right panel is for profile 1 in Fig. 1. Lower-left panel is for profile 2. Lower-right panel is for profile 3. Red lines denote north component of time series while green lines denote east component. Blue dots denote average arrival times of stations. Yellow dashed lines are linear fitting to blue dots. X axis denotes seconds after the event. Y axis on the left denotes epicentral distances of the stations in kilometers, while Y axis on the right denotes position change with minimum tick interval indicating 10 centimeters

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The overall estimation of surface wave propagation caused by the Mw 7.8 earthquake is at a speed of 2.983 km/s, while a speed of 3.135 Km/s at profile 1 in the NE direction, a speed of 3.101 km/s at profile 2 in the NW direction, and a speed of 3.055 km/s at profile 3 in the east direction.

Coseismic displacement estimates

Coseismic displacements at stations with continuous observations are estimated using time series that covers the Mw 7.8 event. However, 4 sites (kls1, ekz1, akle, and vir2) near the epicenter stopped recording data shortly after the event, possibly because of the severe shaking from the earthquake. The sites kls1 and vir2 stopped observation tens of seconds after the origin time and resumed observation at the nest hour, while the sites ekz1 and akle stopped and resumed observation at one hour later. Data of one whole hour at GPS time 00 and 03 are processed and linearly fitted to the origin time of the Mw 7.8 event. Differences of the intercepts of the fitting lines at the origin time of the event are the displacement estimates accordingly.

To get consistent reference frames for the 4 stations, the Cartesian coordinates for the stations in ITRF 2014 are obtained for the two separated one-hour sessions. In order to use least squares linear fitting for the two sessions in the same reference frame, we concatenate the Cartesian coordinates of these two sessions of each station. Then the formulas 1, 2, and 3 are used to obtain local coordinates for each station, which leads to the north, east, and up component coordinates relative to the first epoch local position at 0 o’clock of each station (Gerdan 1999). Thus the displacements of these stations in the consistent local coordinate system can be estimated using linear least squares estimation. To attest to the method, two stations (ante and mly1) with continuous observations through the Mw 7.8 earthquake are also processed. The estimations are shown in Fig. 4.

$$\left[ \begin{gathered} {\text{E}} \hfill \\ {\text{N}} \hfill \\ {\text{U}} \hfill \\ \end{gathered} \right] = \left[ {\begin{array}{*{20}c} { - \sin B\cos L} & { - \sin B\sin L} & {\cos B} \\ { - \sin L} & {\cos L} & 0 \\ {\cos B\cos L} & {\cos B\sin L} & {\sin B} \\ \end{array} }\quad \right]\left[ {\begin{array}{*{20}c} {X - X_{0} } \\ {Y - Y_{0} } \\ {Z - Z_{0} } \\ \end{array} } \right],$$
(1)
$$L = \arctan \frac{Y}{X},$$
(2)
$$B = \arctan \frac{Z}{{(1 - f)\sqrt {X^{2} + Y^{2} } }},$$
(3)
Fig. 4
figure 4

Horizontal coseismic displacement estimates of ante, ekz1, mly1, and vir2. Horizontal red dashed lines are least squares fitting of time series before and after the event. Vertical red dashed lines denote the fitting time. Vertical yellow lines denote the origin time of the Mw 7.8 earthquake

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X0, Y0 and Z0 are initial reference positions of local coordinates in the Cartesian coordinate system. B and L are geodetic latitude and longitude, and \(f\) is flattening of the ellipsoid.

The horizontal displacements of the two stations (ante and mly1) with continuous observations through the event are also estimated using this method and compared with linear fitting of continuous observations. Then the coseismic displacement distribution of all relevant stations is shown in Fig. 5.

Fig. 5
figure 5

Coseismic displacements of the stations caused by the Mw 7.8 event. Red arrows denote direct estimates of displacements from continuous high-rate GPS observation cover the Mw 7.8 event, blue ones denote estimates from 2 separate one-hour observations before and after the event

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The inferred displacements of these two stations (ante and mly1) show good consistency with direct estimates considering the centimeter level accuracy of the kinematic positioning. The north and east component differences at station ante are − 3.8cm and 2.4cm, which is close to the positioning accuracy and less than 15% of total displacements. Furthermore, it should be noted that the method doesn’t take other earthquakes into consideration, especially the Mw 6.7 earthquake (Fig. 1) which occurred close to the station ante and at the time shortly after the Mw 7.8 earthquake.

It can be seen from Fig. 5 that the stations in the northwest of the rupture moved southwest while the stations in the southeast moved northeast. The displacements decrease while the epicentral distances increase. The displacements caused by the event show left-lateral movement along the nodal plane, which is consistent with the GCMT focal mechanism. The estimated largest displacements occurred are at station ante with an eastward displacement of 31 cm and at station mly1 with a southward displacement of 39 cm.

Using the same method, coseismic displacements of the stations caused by the Mw 7.5 earthquake are shown in Fig. 6. The largest component displacements caused by the Mw 7.5 event are a westward displacement of 450 cm and a northward component displacement of 97 cm at the station ekz1 which is only 6km from the epicenter of the event. The coseismic displacements to the east of the epicenter are mostly southward, while displacements to the west of the epicenter are mostly northward. The distribution of coseismic displacements is consistent with GCMT focal mechanism.

Fig. 6
figure 6

Coseismic displacements of the stations caused by the Mw 7.5 event. Red arrows denote direct estimates of displacements from continuous high-rate GPS observations cover the Mw 7.5 event, the blue one at the station ekz1 denote estimates from 2 separate one-hour observations before and after the event. The displacement of station ekz1 is plotted with the blue scale which is different from the red ones. The displacement at station ekz1 is over 4 meters

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Discussions

The kinematic mode processing of high-rate GPS data provides an efficient method for coseismic displacement estimation, because only a short time of observations (several hours) is needed and it has a high temporal resolution to distinguish displacements caused by different earthquakes which occurred sequentially with a short interval. For the stations nearest to the epicenter which are severely affected by the earthquake, coseismic displacements could still be estimated with timely redeployed observations. It is critical that the reference station is static during the observation.

The background movement of the reference station is at a rather low speed to affect the position estimates during a few hours. Our method makes it possible to estimate coseismic displacements shortly after an event with a prominent advantage of distinguishing seismic effects caused by each earthquake in one sequence which happened with short time intervals.

The linear fitting of time series could be made more plausible to estimate the start time of seismic waves of each station. With higher accuracy and higher sampling rate, it would effectively improve the estimation of surface wave propagation speed. The distribution of GPS stations at different epicentral distances would also contribute to better estimation. It should also be noted that post-seismic effects are ignored in this article because of short duration.

Using high-rate GPS observations, preliminary estimates of coseismic displacements and corresponding surface wave forms could be recorded with only a few hours of observations. The estimated largest displacements caused by the Mw 7.8 Pazarcik earthquake are observed at station ante with an eastward component displacement of 31 cm and at station mly1 with a southward component displacement of 39 cm. The Mw 7.8 Pazarcik earthquake shows left-lateral movement along the nodal plane, which is consistent with the focal mechanism. The largest displacements caused by the Mw 7.5 Elbistan earthquake are a westward component displacement of 450 cm and a northward component displacement of 97 cm at the station ekz1 which is about 6 km from the epicenter of the event. Based on high-rate GPS time series, the surface wave propagation of the Mw 7.8 Elbistan earthquake is preliminarily estimated at an overall speed of approximately 2.9 km/s. High-rate GPS observations show prominent advantage of temporal resolution for earthquake sequences with short intervals. The displacement estimation provides constraints for inversion of the rupture process and seismic source mechanism. Daily observations provide another way of estimation of coseismic displacements. Comparisons between these two methods are relevant to observation time and models, which is beyond the scope of this article. As a prominent advantage of high-rate GPS observations for coseismic displacements are the rapid estimations and further applications for geophysical purposes.

With shorter observation time, the coseismic displacement estimations of different earthquakes could be available for higher temporal resolution, while other geodetic observations with longer interval could only provide the comprehensive displacements of earthquakes. The linear fitting of position time series of high-rate GPS observations is meaningful only for sites with displacements large enough to be distinguished from noise, so more accurate observations will prompt coseismic displacement estimations. And other earthquakes such as the Mw 6.7 event would be distinguished from position time series with closest sites within tens of kilometers. Additionally, spatially uniform distributed sites will provide more information on surface wave propagation speed, especially sites at different epicentral distances will provide constraints for different locations.