1 Introduction

Today, Global Navigation Satellite Systems (GNSS) and interferometric synthetic aperture radar methods are generally used for geodetic monitoring of surface movements at cm and below. Considering the cost of GNSS method receivers, measurement cost, and cost of facility and operator for each point, it is an expensive method. In InSAR technology, on the other hand, surface movements can be monitored faster and at lower costs. In addition, the InSAR method can obtain velocities of too many measurement points in large areas. However, the biggest problem here is that the velocities obtained by the multi-temporal InSAR (MT InSAR) method are generally estimated by the regression analysis method, which generally uses the linear model. Ignoring periodic effects on InSAR data leads to misleading results. While these subsidence and uplift are determined by the MT InSAR method, velocities are calculated by generally considering the trend component on the time series. However, the periodic effects in these time series are generally ignored. Therefore, while estimating the velocities of PS points, it is necessary to distinguish the periodic and trend components and then estimate the velocity values free from periodic effects. There are a limited number of studies using different deformation models with different methods in monitoring deformations with the PSInSAR method (Li et al. 2015; Morishita and Hanssen 2015; Wang et al. 2017; Ilieva et al. 2019; Bao et al. 2021; Hu et al. 2021). However, these studies did not use the FFT time series analysis method. Yang et al. (2019), the ratio of the deformations in the dry and rainy seasons to the total deformation was calculated using the Sentinel-1A SAR with the SBAS method, and the seasonal effect was tried to be revealed proportionally. Dalaison and Jolivet (2020), deformations were monitored using the time-dependent Kalman filter method created on the phase differences, and it was determined that the results were compatible with the classical time series analysis results used in the least squares method. Lei et al. (2021), the relationship between the 3D deformations obtained by combining InSAR and GPS technologies and the change in groundwater level was evaluated graphically by observing the trend changes. Khoshlahjeh Azar et al. (2021), SAR deformation and piezometric data were interpolated using a linear model. By calculating the trend of each model, the piezometric relationship with the SAR results was revealed. Zhu et al. (2022), the correlation between surface deformations and groundwater level changes determined by the independent component analysis (ICA) method from Sentinel-1A SAR data of Los Angeles, USA, Santa Ana Basin was determined. For the first time in our study, the FFT analysis method was used to determine the periodic effect on the MT InSAR results, and the success of the method was analyzed. In this study, a post-process FFT-based method has been developed to reveal the seasonal effects and their causes by analyzing the displacement time series obtained from the MT InSAR process.

InSAR is a technique that calculates the phase difference between two different radar images obtained with very close imaging geometries (Massonnet & Feigl 1998; Hanssen 2001; Burgmann et al. 2002; Rosen et al. 2000; Gens & van Genderen 1996). Permanent Scatterers-based PSInSAR is one of the InSAR analysis techniques performed with the help of time series analysis of SAR data taken at different times (Ferretti et al. 2001). The aim is to detect the points (permanent scatterer) showing continuous high reflectivity in each time period from which satellite data is received, monitor them with sub-cm precision, and estimate the relative topographic heights/deformations. Although each PS measurement is given its position relative to a reference point with high precision, the actual measurement uncertainty is low due to uncertainties in the satellite orbit, instrumental problems, delays in the radar signal path, and center uncertainty of the scattering point (Sousa et al. 2010). Basically, PSInSAR is a powerful method for detecting and monitoring surface deformations (in environments where vertical movement occurs, such as landslides, collapses, and normal faulting.) over time. Each PS can reflect stability problems in buildings, the reflection of changes in groundwater level to the surface (subsidence/ uplift), and deformations caused by the effects of landslides (Cakir et al. 2005). The plane defined by the two angles of incidence of the ascending and descending configurations is called the "co-plane" (Ozawa and Ueda 2011). The LOS changes detected on the interferograms are located in this co-plane. Two components can express the movements detected in the LOS direction in this co-plane. This co-plane is close to being an east–west oriented vertical plane. Therefore, the displacement values are determined with reasonable accuracy for the vertical and eastern components, while for the northern component, they can be determined only to a small extent and are generally unsuccessful. (Fujiwara et al. 2000; Ozawa and Ueda 2011). Monitoring of deformations with the InSAR method is used in different fields, such as monitoring of tectonic movements in the Western Anatolian Menderes region (Arikan et al. 2009), monitoring active volcanoes (Hooper et al. 2004, 2007), earthquake-induced surface movements (Yen et al. 2011; Poyraz et al. 2016), landslides (Peyret et al. 2008; Hastaoglu et al. 2018), monitoring urban areas (Meisina et al. 2006), mine sites (Abdikan et al. 2013; Poyraz et al. 2020), aseismic movements (Poyraz and Hastaoğlu 2020). In recent years, surface deformations obtained from InSAR results have been tried to be associated with external forces that cause these deformations. (Hu et al. 2018; Zheng et al. 2018; Yang et al. 2019; Imamoglu et al. 2019; Shi et al. 2020; Shahzad et al. 2020; Darvishi et al. 2021; Lei et al. 2021; Bui et al. 2021; Khoshlahjeh Azar et al. 2021; Zhu et al. 2022). In many of these studies, the relationship between InSAR surface movements and external force is presented only graphically, and the results are interpreted on these graphs (Zheng et al. 2018; Shi et al. 2020; Shahzad et al. 2020; Lei et al. 2021; Bui et al. 2021). Alternatively, interpretations are made by calculating the correlation values between InSAR surface movements and the external force (Hu et al. 2018; Imamoglu et al. 2019; Darvishi et al. 2021; Zhu et al. 2022; Gezgin 2022). In all these studies, the LOS displacement values obtained using different software are presented graphically, or then the trend is determined by them using the regression method according to the linear model. In all these studies, displacements in the LOS direction were analyzed through a linear regression model, which only includes intercept and trend terms. A linear harmonic regression model, including periodic signals, was not considered. It is well known that trends could be biased when periodic signals are not considered in GPS time series analysis (Blewitt and Lavallée 2002). Even though InSAR and GPS are different techniques, deterministic parameters would be similar if these are indeed not related to hardware. Our study determined the periodic effect using the FFT analysis method.

A geodetic time series such as InSAR time series generically consists of deterministic, e.g., trend, seasonal signals, and stochastic parts. For instance, if an InSAR time series of a selected PS point is analyzed by introducing seasonal signals in addition to the trend parameter, the trend estimates would be unbiased. The consequence of unbiased trend estimates makes interpretations more explicit. Many PSI approaches estimate trend parameters through a linear regression model. The linear model is a necessity to unwrap interferometric phases. However, it might have a drawback on trend estimation if geophysical phenomena are characterized by non-linear deformations (Crosetto et al. 2016). Today, with the evaluation of PSInSAR data, velocity values in the line of sight (LOS) direction of surface movements are calculated by generally determining the trend component, and periodic effects are generally ignored. In this study, the periodic components of the surface movements obtained from the SAR data and the physical causes of these periodic movements were determined using the FFT time series analysis method. For this purpose, studies have been carried out in the Gediz Graben, which is possible in aseismic seasonal periodic movements and tectonic surface movements in previous studies. Within the scope of the study, tectonic and aseismic movements on the Gediz graben were successfully determined from SAR data by the FFT time series analysis method.

2 Material and methodology

2.1 Study area

This study aims to obtain periodic component and velocity values by subjecting the temporal surface movements of PS points produced as a result of PSInSAR evaluation to time series analysis. For this purpose, Tıraz, Yesilyurt, and Sarigol regions were chosen as the study area (Fig. 1). These areas are located in the eastern part of Gediz Graben in Turkey and are thought to have aseismic deformations apart from the tectonic effect (Koca et al. 2011; Poyraz et al. 2016; Poyraz and Hastaoğlu 2020). Today, the Western Anatolian Expansion Zone (WAEZ) is under the influence of approximately North–South continental expansion at a rate of 30–40 mm/year (Le Pichon et al. 1995; Oral et al. 1995; Bozkurt 2001) and is an area which is effective during Plio-Quaternary. It is typical with NE-SW and EW trending basins that developed under the influence of NS extensional tectonics. The Gediz Graben, in which the study area is located, is one of the most important EW trending neotectonic structures in Western Anatolia (Paton 1992; Seyitoğlu & Scott 1996; Hakyemez et al. 1999; Koçyiğit et al. 1999; Bozkurt & Sözbilir 2004). The graben, which has a northward arcing arc geometry, is approximately 140 km long and 10–15 km wide. According to the active fault map of Turkey updated in 2012 (Emre et al. 2011), the eastern part of the graben, where the study area is located, is represented by three NW–SE trending fault branches between Ahmetli and Sarıgöl. Among the faults mapped in this area, the Alaşehir segment is 45 km long, and the Salihli segment is 30 km long, and they control the southern edge of the graben. The Killik fault, located in the eastern part of the graben, is 50 km long and controls the northern edge of the graben. These faults have the potential to produce earthquakes with magnitudes between 6.8 and 7.1 (Duman et al. 2018; Emre et al. 2018). The GPS-based opening velocity in this part of the graben was calculated as 6.4 mm/year (Reilinger et al. 2006; Aktug et al. 2009; Aktuğ et al. 2013). In this section, the southern margin faults of the graben are more active than the northern ones, and morphologically, the southern margin is represented by distinct mountain fronts with a steeper slope. The destructive earthquake (Ms:6.5) that occurred on the Gediz Graben in 1969 and created a surface rupture of approximately 30 km between Sarıgöl in the east and Salihli in the west is the most destructive earthquake known to have occurred in the eastern region of the graben (Arpat & Bingöl 1969; Allen 1974). This earthquake occurred on the Alaşehir segment dipping north from the southern boundary faults of the Gediz Graben.

Fig. 1
figure 1

Study area

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The velocities obtained by Poyraz et al. (2019) for the GNSS points in the eastern part of the Gediz graben vary horizontally between 12 mm/year and 27 mm/year. When the vertical movements are examined, it is seen that high subsidence values are obtained at the points within the graben. The annual vertical velocity at TRAZ (at Tırazlar locality) was approximately -90 mm/year. BGCL and AKCL points were -33 and -13 mm/year, respectively. It is seen that there are uplifts at the points outside the graben. McClusky et al. (1999), Reilinger et al. (2006), where the velocity area of the Aegean region is calculated as approximately 33 mm/year, and Poyraz et al. (2019) results are similar. In Poyraz et al. (2019), the TRAZ point showed a different movement from the Aegean region's velocity field and the general movement character of the Gediz Graben. It is thought that there are local effects in addition to tectonic effects at and around the TRAZ point. The vertical displacements along the fault were recorded because of areal consolidation settlements (depression), microseismic activity, tectonic cripple, and excessive groundwater withdrawal between 2000 and 2010 in the vicinity of Sarıgöl District (Koca et al. 2011; Demirtaş et al. 2008).

2.2 Data acquisition and evaluation

Sentinel-1A/B images in IW mode used in this study are open-access and obtained from the European Space Agency (ESA). We used 114 radar imageries in descending direction between 2020-05-01 and 2021-12-01 and 116 in ascending direction between 2020–01-04 and 2021–12-06. The temporal resolution of these was 6 days. The track numbers for ascending and descending are 131 and 138, respectively. All of these data were analyzed by adopting the StaMPS PSI method. SeNtinel Application Platform (SNAP) and StaMPS software were used in the analysis. The interferograms were generated through the SNAP software. Here, the master image for both ascending and descending, 2020-12-17 sensed by S1A and 2020-12-12 sensed by S1B (Fig. 2), respectively, was determined through the SNAP. The StaMPS software was used for estimating the LOS velocities.

Fig. 2
figure 2

Baselines

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In the first stage, the steps, splitting the images, correcting the orbits of the satellites, matching the master and slave images, merging, obtaining the interferograms from each pair of images, and topographic phase removal from the interferograms through the SNAP software were performed. Then, the results were exported in a format suitable for the StaMPS software.

In the second stage, StaMPS software, developed by Hooper et al. (2007), was used to obtain the velocities of the PS points in the LOS direction. StaMPS is a software that implements the InSAR permanent scattering method (PS) developed to process in areas subject to deformation in natural or unnatural (buildings, dams, etc.) objects on the earth. In addition, the pixel amplitude values in each image form the time series. Pixels that are affected by geometric and temporal correlation disorder and have a fixed amplitude value array are selected as PS points. In the PS selection, StaMPS uses amplitude dispersion (DA) to select PS candidates (PSCs). StaMPS filters the PSC phase separately into small patches in spatial and temporal dimensions to divide the correlated interferogram phase into the incidence angle error, deformation trends, and noisy parts. The thresholds for selecting a pixel as PS are determined by calculating the PS probability of each PSC, considering both temporal consistency and amplitude distribution. In the selected PS candidates, the processing approach returned to the wrapped differential interferometric phase of these PSs and accepted the noise standard deviation of each interferogram as the weighting to calculate the phase due to the spatial uncorrelated look angle error from the wrapped phase (Yao et al. 2020). After that, the deformation series are unwrapped by a three-dimensional unwrapping algorithm (Sousa et al. 2010). In this study, we adopted the amplitude distribution threshold for PS candidates as 0.42 (Sousa et al. 2010). In general, the threshold value range is between 0.40–0.42. Atmospheric correction was introduced using the linear tropospheric correction model of TRAIN software (Bekaert et al. 2015). GACOS data was used for tropospheric delay estimates. (Yu et al. 2018a, 2018b). As a result, a total of 700 days of Sentinel-1A/B data covering the years 2020–2021 were evaluated, and two-year time series were obtained. The LOS velocities obtained as a result of this evaluation are presented in Figs. 3 and 4. LOS velocities values are calculated relative to the mean velocity value in the process area by StaMPS (Serco Italia SPA 2020). Negative values in the LOS direction indicate that the movements move away from the satellite, while positive movements indicate that they approach the satellite. When Figs. 3 and 4 are examined, both descending and ascending satellite data show subsidence in the Graben.

Fig. 3
figure 3

a Velocity values in the LOS direction of the ascending orbit with trace number 131 (January2020-January2022), b Standard deviation values of the ascending orbit with trace number 131

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Fig. 4
figure 4

a Velocity values in the LOS direction of the descending orbit with trace number 138 (January2020-January2022), a, b Standard deviation values of the descending orbit with trace number 138

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2.3 FFT analysis with the software developed

The behavior of PS point velocities obtained as a result of InSAR evaluations under different effects (linear, periodic, etc.), and size can be explained by the time series analysis. If we denote the displacement of the PS points in the LOS direction with X(ti), the time series can be written as follows depending on the time.

$$X\left( {t_{i} } \right) = \underbrace {{at_{i} }}_{Trend ~Comp.} + \underbrace {{\mathop \sum \limits_{s = 1}^{r} \left[ {b_{s} \cos \left( {2\pi f_{s} t_{i} } \right) + c_{s} \sin \left( {2\pi f_{s} t_{i} } \right)} \right] + v\left( {t_{i} } \right)}}_{Periodic~ Comp.}$$
(1)

where a trend component parameters, bs, cs periodic component parameters, fs (s = 1,2,….r) frequencies, v(ti) mean zero, variance σ2 random are errors. The magnitude of linear or non-linear change in PS points is significantly affected by periodic movements. Periodic behaviors created by some unmodeled periodic effects at PS points are also determined by time series analysis. In particular, the main source of annual and semiannual periodic changes are external forces such as seasonal weather changes (rain, snow, extreme temperatures, etc.) and groundwater movements. For this reason, the periodic component must be determined by analyzing the time series of PS points. However, frequencies for any significant periodic oscillations must be known to model in Eq. (1). To achieve this, velocities statistically significant should be estimated and removed from the time series. Time series analysis distinguishes the trend, periodic and irregular movements that define the characteristics of the time series system and is frequently applied especially in non-parametric situations. This study aims to determine the periodic movements in the time series by using the FFT method. Therefore, firstly, the trend component in the time series was removed, and then FFT analysis was performed on the remaining series, including periodic and irregular movements. For the separation of the trend component from the series, it is obtained with the least squares method and a time-dependent equation (Yt = a + b.t). The coefficients of the obtained equation are calculated by regression analysis. According to the least squares method, with a and b unknown parameters, and standard deviations of the parameter (sa, sb) are calculated. To test whether the calculated parameters are significant, the test value (parameter /standard deviation of the parameter) was compared with the student(t)-distribution value for 95% level of confidence. Otherwise, the linear trend component in the series affects the spectral analysis results and gives a peak at zero frequency. For the separation of the trend component from the series, it is obtained with the least squares method and a time-dependent equation (Yt = a + b.t). The coefficients of the obtained equation are calculated by regression analysis.

The trend component removed series from the time domain to the frequency domain is transformed with the fast Fourier transform (FFT) given by Eq. 2. FFT is a highly optimized implementation of the discrete Fourier transform (DFT), which converts discrete signals from the time domain to the frequency domain. FFT computations provide information about the signal's frequency content, phase, and other properties (Frigo & Johnson 1998).

$$X(f) = \sum\limits_{{t_{i} = 0}}^{N - 1} {P(t_{i} ) \cdot e^{{ - jf\frac{2\pi }{N}t_{i} }} }$$
(2)

In Eq. 2, the value of X(f) and e2πjt represent the complex and exponential function. Since the values obtained from the FFT are complex numbers, they are still insufficient to determine the series' frequencies. Therefore, the square of the modulus of X(f) is calculated, and so called as Fourier spectrum Pxx(f).

$$P_{xx} (f) = \left| {X(f)} \right|^{2}$$
(3)

Thus, by detecting at which frequencies the energy of a signal is concentrated, the frequencies of the periodic movements existing in the series are determined. These frequencies are replaced in the periodic component in Eq. (1), and the frequency parameters bs, cs are tested (Fig. 6). Insignificant parameter frequencies are removed from the function, and this process is continued until significant parameter frequencies are only left. At last, the parameters of the time series are composed of trend and periodic signals statistically significant through FFT in Eq. (1). Additionally, the amplitude values of the periodic signals are determined.

In light of the method described above, software was developed that automatically performs FFT time series analysis of PS data using the MATLAB programming language. The software algorithm is presented in Fig. 5. The developed software computes the discrete Fourier transform (DFT) using an FFT algorithm. FFT analysis is generally applied to equally spaced data. Since the Sentinel 1A/B data are published in equally 6-day periods, it is thought that the FFT method will be successfully applied to the equally 6-day displacement data produced from the Sentinel 1A/B data. Sometimes, interruptions occur in Sentinel 1A/B data due to hardware problems. The DFT method works successfully in the analysis of time series with such temporal discontinuities. Munteanu et al. (2016) stated that FFT produces better results than other tested methods for reliably estimating the spectral slope of a signal recorded in a turbulent environment when the time series data contains gaps. Considering that the gaps in the InSAR results will not cover large time intervals, it was thought that there would be no problem in using the DFT method in the InSAR time series analysis.

Fig. 5
figure 5

Software FFT process flow chart

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3 Analysis and results

In the LOS velocity, values obtained from the descending and ascending satellite data, 10 points that will provide the general distribution on the graben, especially where the settlement areas are located, were determined, and FFT time series analyzes were performed at these points. Thus, the characteristics of the movement at these points were examined. Figure 6 shows the locations of the selected points on the ascending satellite LOS velocities and the underground water level monitoring well in the region.

Fig. 6
figure 6

a Selected points for FFT analysis, ILGIN water well and faults on horizontal velocities obtained from decomposing ascending and descending satellite radar images, b Selected points for FFT analysis, ILGIN water well and faults on vertical velocities obtained from decomposing ascending and descending satellite radar images

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For the selected points, using the software developed within the scope of the study, FFT time series analyzes were performed on the ascending and descending satellite data, respectively. Figures 7 and 8 present graphs of the software output FFT analysis results obtained from the ascending and descending satellite data of the fifth point with the highest deformation.

Fig. 7
figure 7

FFT analysis graphs and report of point 5 from LOS velocities obtained from ascending satellite images with trace number 131

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Fig. 8
figure 8

FFT analysis graphs and report of point 5 from LOS velocities obtained from descending satellite images with trace number 138

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FFT analysis results for PS point 5 are presented in Figs. 7 and 8. The graph, expressed as "Point id 5 Time Series" in Figs. 7 and 8, shows the 700-day displacement values for point 5 descending and ascending satellites. In the graph expressed by "Point id 5 Trend Estimation", the trend component (for m = 2 in Eq. 1) and velocity values calculated according to the Y = a1 + a2*t linear function with least squares method (LSM) from displacement data are presented. The a1 and a2 parameters and standard deviations of the linear function were calculated according to LSM, and the significance of the calculated parameters was tested according to the t-distribution for the degree of freedom (f1 = 114 and f2 = 112) and 95% (α = 0.05) confidence level. These results are presented under the title of "Trend Estimation" of the report presented in Figs. 7 and 8. The important thing here is whether the a2 parameter depending on t (time: taken as days) is significant or not. Because the parameter that will be used to determine the change, that is, the magnitude and the direction of the velocity, is a2. The annual velocity value at a point is calculated as velocity = a2*365.

Figures 7 and 8 show the spectrum values for the frequencies obtained as a result of the FFT analysis in the "Point id 5 Fourier Spectrum" graph. For example, here the frequency value with the maximum spectrum value is determined as 0.00260. Thus, the period duration was determined as 1/0.00260 = 384 days. The trigonometric functions of the determined frequencies, that is, the harmonic parameters and the standard deviations of these parameters are determined according to the LSM. Then, these parameters are tested to determine whether they are significant, similar to testing the parameters in a linear function. These results are presented in Figs. 7 and 8 under the report section "Estimation of Periodic Effect". In Figs. 7 and 8, "Point id 5 Trend Free Data" graph, the graph of the displacement data free from the trend component and the periodic component determined as a result of the FFT analysis are presented. In the graph presented under the title of "Point id 5 Trend + Periodic Effect" in Figs. 7 and 8, the curve of the model, which includes liner and periodic movements estimated according to displacement values, is presented. Under the title of "Point id 5 Periodic Effect Free Data", displacement values free from periodic effect are presented. Then, new trend component and velocity values are calculated from the displacement values free from periodic effects, and these values are presented in the "Point id 5 Trend Estimation from Periodic Effect Free" graphic and under the "Trend Estimation from Periodic Effect-free Data" heading of the report in Fig. 7 and 8. Thus, using FFT analysis for PS point 5, new velocity values free from periodic effects were calculated. Finally, the estimated new trend and periodic model for the data are presented in the "Point id 5 New Trend + Periodic Effect" graph.

Periodic effects are clearly observed for both ascending and descending satellite data in Figs. 7 and 8. In both data, effects are observed in a period of approximately one year. When Fig. 7 is examined, a cosinesoidal effect with an amplitude of 20.5 mm and a period of 384 days was determined at point 5 for the ascending satellite. When this periodic effect is removed from the data set, the annual velocity value decreases from approximately -49 mm to -44 mm. When Fig. 8 is examined, a cosinesoidal effect with an amplitude of 18.8 mm and a period of 384 days was determined at point 5 for the descending satellite. When this periodic effect is removed from the data set, the annual velocity value decreases from approximately -53 mm to -49 mm. There is a 10% change in the velocity value due to the periodic effect in both satellite data. FFT analysis was performed in all other 10 points. FFT analysis results for all points are presented in Table 1.

Table 1 LOS direction FFT analysis results for all points
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Periodic effects with amplitudes ranging from 14 to 25 mm and a period of 384 days were modeled at all points. An average of 23.5% change was observed for the ascending satellites, and 8.5% for the descending satellites in the velocity values estimated from the displacement values cleaned from periodic effect. Periodic effects with an average amplitude of 19 mm were observed for descending and ascending satellites. In the results of the FFT analysis, a movement pattern with a nearly one-year period, which is stable in winter, subsidence in spring and summer, and slightly uplift in autumn, has been determined.

The data of descending and ascending satellites were converted into up and east components from the LOS direction by using the formulas presented in Eq. 4 (Hanssen 2001).

$$\left( {\begin{array}{*{20}c} { - \cos \left( {\alpha_{ASC} } \right)} & {\sin \left( {\alpha_{ASC} } \right)X\cos \left( {\delta_{ASC} } \right)} \\ { - \cos \left( {\alpha_{DSC} } \right)} & {\sin \left( {\alpha_{DSC} } \right)X\cos \left( {\delta_{DSC} } \right)} \\ \end{array} } \right)\left( {\begin{array}{*{20}c} {V_{UP} } \\ {V_{EW} } \\ \end{array} } \right) = \left( {\begin{array}{*{20}c} {V_{LOS,ASC} } \\ {V_{LOS,DSC} } \\ \end{array} } \right)$$
(4)

In Eq. 4, for ascending and descending satellites,\({\alpha }_{ASC}\), \({\alpha }_{DSC}\) show the heading angles, and\({\delta }_{ASC}\), \({\delta }_{DSC}\) show the incidence angles.\({V}_{UP}\): velocity for the up component, \({V}_{EW}\): velocity for the east component, \({V}_{LOS,ASC} :\) velocity in the LOS direction of the ascending satellite, \({V}_{LOS,DES}:\) velocity in the LOS direction of the descending satellite. The surface movements in the North–South direction can only be determined between 10–15% of the actual deformation amount with the SAR method due to the North–South orientation of the SAR satellites' orbits and the side-looking radars of the SAR satellites. Therefore, in many SAR studies, the deformations in the north direction are assumed to be zero, and the two-dimensional transformation matrix in Eq. 4 is used (Pawluszek-Filipiak and Borkowski 2020). As can be seen in the equation in Eq. 4, since two ascending and descending LOS values of a pixel are measured, only the unknown in two directions can be solved. In addition, using Sentinel1A and Sentinel 1B descending and ascending LOS values of the same pixel, four equations can be obtained, and the unknowns in three directions can be solved. However, in this case, the matrix performance deteriorates due to the very small coefficient values in the North–South direction, and realistic results cannot be obtained. The condition number of a matrix (cond) is a measure of the sensitivity of the solution of a system of linear equations to errors in the data. It indicates the accuracy of the results from matrix inversion and linear equation solutions. For a correct solution, this value should not exceed 1. However, this value is around 10 in the A coefficients matrix used for the transformation from LOS to three dimensions with the least square estimation method, causing the results to be erroneous (Fuhrmann & Garthwaite 2019). Therefore, unfortunately, only the two-dimensional transformation in Eq. 4 can be performed using existing satellite configurations. Using the developed software, the displacement values in the up and east directions were calculated using the displacement values in the descending and ascending LOS directions of 10 points in the study area. Then, trend and periodic components were determined by performing FFT analysis for the up and east directions. Figure 9 presents the FFT analysis outputs for the up and east components of point 5. When Fig. 9 is examined, the velocity value for the up component changed from -70 mm/year before the analysis to -62 mm/year after the analysis, and the seasonal effect was determined in a 384-day period. For the east component, the velocity value was determined as 0 mm/year. In Table 2, the results of the up and east components FFT analysis for all 10 points are presented.

Fig. 9
figure 9

After decomposing, Up and East FFT analysis outputs of point 5

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Table 2 Up and east component FFT analysis results for all points
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When Table 2 is examined, in accordance with the general deformation character of the Gediz Graben, subsidence with velocities of approximately 10 to 60 mm/year were detected at points 1–7 falling into the graben, while values close to zero were obtained at points 8, 9, and 10, which are partially on the graben boundary. In addition, small movements in the small EW direction were detected. Especially at points 6 and 7, besides vertical movement, significant horizontal movements were determined. Especially at point 6, a westward movement was determined at a velocity of approximately 43 mm/year. A periodic effect with an amplitude varying between 19–30 mm in a period of 384 days was determined at all points in the vertical direction. In addition to this, 384-day periodic effects with amplitudes varying between 3–7 mm were determined, except for points 6 and 7 in the horizontal direction. At points 6 and 7, different from the general movement, 256-day periodic effects were determined. Already at points 6 and 7, unlike other points, dominant movements were observed in the west direction. At points 6 and 7, movements seem to be different from the graben behavior. By examining these and their neighboring points visually, it is suspected there could be a possible buried normal fault. Any outcrops were not observed in the field study not because an alluvial formation covers the graben but because physical conditions of surface cover is changing wherefore intensive agricultural activities.

As can be seen from Table 2, the general dominant movement character of the graben is subsidence, and a periodic effect of 384 days has been determined for the up component of all points. In order to examine the reasons for this periodic effect, the underground level change values of the Ilgın water well in the region between 2013 and 2018 were obtained from İzmir Regional Directorate for State Hydraulic Works (DSI in Turkish). Since DSI could not measure water wells during the COVID-19 pandemic, groundwater levels are available until 2018. Then, these values were subjected to FFT and periodic component analysis in order to determine the groundwater level change model. Although it is known that the amplitude of the periodic effect decreases as a result of applying the FFT analysis to the data with large gaps, the FFT analysis method was used because the main purpose here is to reveal the general characteristics of the groundwater level change. In Fig. 10, monthly groundwater level changes and FFT and periodic component analysis results of the ILGIN water well in the Graben are given between January 2013 and November 2018.

Fig. 10
figure 10

ILGIN water well groundwater level changes

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As a result of the analysis of the groundwater level values of the Ilgın water well, a model with an amplitude of 4.16 m and a period of 393 days was determined. This periodic groundwater level change and the 384-day periodic displacement movement obtained from the PS results are in harmony. This suggests that the main reason for the seasonal effects in the region is the change in groundwater level. Therefore, the relationship between groundwater level and InSAR displacement values has been studied in more detail.

Figure 11 shows the average monthly precipitation amounts between 1962 and 1995 at Alaşehir District Meteorology Observation Station (Dikmen et al. 2019), and the average monthly water levels of the Ilgın water well between 2013 and 2018 are presented. A correlation coefficient of 0.78 was calculated between groundwater levels and precipitation amounts. As it can be understood from here, the main source of groundwater in the region is seasonal precipitation.

Fig. 11
figure 11

Average amount of precipitation (1962–1995) and water level (2013–2018)

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In Fig. 12, vertical displacement and groundwater level models obtained as a result of FFT analysis are presented. As stated in Eser Mühendislik Müsavirlik (2014), the groundwater recharge is 142 × 106 m3/year in the Salihli-Alaşehir-Sarıgöl region, which also includes the study area, while the draft and discharge are 165 × 106 m3/year. In summary, groundwater reserve change in the region is 23 × 106 m3/year. As it can be understood from here, unplanned and excessive underground water withdrawal and discharge take place in the region. When Fig. 12 is examined, a decrease is observed in the groundwater level between January and August. The main reason for this decrease is the decreasing amount of precipitation in the region since January (Fig. 11) and the agricultural activities that started in March. Groundwater is mostly used in agricultural activities in the region. Depending on both the increase in the use of groundwater for agricultural purposes and the decrease in precipitation amounts, decreases in water levels are observed in the spring and summer months. In the autumn, there is an increase in groundwater levels again due to the increasing rainfall in the region and the decrease in agricultural irrigation. In general, the groundwater level in the region has a decreasing trend, and the decrease accelerates in the spring and summer months, and the water level rises in the autumn. When the vertical displacement motion patterns in the region, presented in Fig. 12, are examined in detail, a subsidence trend is observed at all points depending on the general tectonic structure of the graben. However, in addition to this trend, especially between August and December, the rate of subsidence approaches zero and even tends to uplift. In summary, while the general subsidence trend increases in January-August, this movement slows down between August and January and even shows a slight uplift trend. This movement pattern clearly shows the existence of the seasonal effect. It is clearly observed from Fig. 12 that the groundwater level change is the main reason for this seasonal effect. In order to reveal this relationship more clearly, seasonal groundwater level change values were calculated from the periodic component model, which is free from the trend component for the groundwater level values. Likewise, seasonal vertical displacement values at the points were calculated according to the trend-free periodic component model (Fig. 13). Then, the correlation coefficient values between the seasonal changes in the groundwater level and the seasonal displacement values at the points were calculated (Table 3).

Fig. 12
figure 12

InSAR vertical displacement model and groundwater level models determined by FFT analysis

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Fig. 13
figure 13

Groundwater level and vertical displacement seasonal movement patterns

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Table 3 Correlation coefficient (R) values between the underground level seasonal motion model value and the seasonal vertical displacement model values of the points
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When Table 3 and Fig. 13 are examined, it is observed that there is a very high correlation between the seasonal behavior of the groundwater level and the seasonal behavior of vertical displacement values. The effect of groundwater level on vertical displacement values is clearly observed in Table 3 and Fig. 13. While the rate of subsidence in the graben increases during the periods when the groundwater level decreases in January-August, the rate of subsidence slows down and even shows a slight uplift trend during the periods when the groundwater level increases in August-January. As a result, the seasonal surface deformation model in the Gediz graben and the relationship of these seasonal movements with the groundwater level have been successfully determined.

4 Conclusions

According to the data obtained, vertical displacements (subsidence) with a velocity of approximately 10 to 62 mm/year have been detected at the base of the graben (at points 1–7) within a two-year period (between 2020 and 2022). Considering that the long-term average vertical slip rates calculated on some normal faults in Western Anatolia vary between 0.1 and 0.5 mm/year (Özkaymak et al. 2011, 2015, 2019; Kürçer et al. 2021). It is clear that these values obtained along the Alaşehir segment are largely not of tectonic origin. However, it can be said that the areas where subsidence is detected are bordered by faults, and lithology control is also effective. For instance, the points (e.g., 8 and 9) located in the northern part of the graben depict 0–4 mm/year LOS velocities. This part geologically accompanies the normal faults showing minimum activity and unconsolidated alluvial lithology. Additionally, the area (e.g., the points 2, 3, 4, 5, and 7), bounded by Alaşehir in the west, Bağlıca in the east, Delemenler in the south, and Killik in the North, reaches maximum LOS velocities. Conversely, both in the east of this area (e.g., point 6) and in the west of this area (e.g., point 10), they show relatively lower LOS velocities. Hence, these inhomogeneities of LOS velocities along with the direction of graben clearly demonstrate that subsidence behavior varies spatially. This shows that there might be deep basins within the graben, which are controlled by structural lines extending approximately perpendicular or obliquely to the graben.

By using the developed software, the periodic movements at the PS points have been successfully determined. Thanks to this analysis, the characteristics of the deformations at the PS points were examined and modeled in detail. It has been demonstrated that the developed method can be used successfully, especially in modeling dynamic deformations due to external forces. Periodic effects on deformations can be determined in regions where deformations occur due to external effects (groundwater level change, precipitation change, temperature change, etc.), and external forces causing these effects can be examined in detail from InSAR data with the developed method. Moreover, the velocity values estimated according to the linear model from the displacement values that contain large amplitude periodic effects may cause false interpretations. By removing this periodic effect from the time series, more accurate velocity values can be obtained, the results can be interpreted more accurately, and region-specific solutions can be realized. By using the developed method and software, it is possible to estimate generally time-dependent linear velocity values by eliminating periodic effects due to external forces from InSAR data. Thus, dynamic deformations due to external forces can be successfully monitored from InSAR data, thanks to the developed method and software.