Multi-Sensor Fusion for Land Subsidence Monitoring: Integrating MT-InSAR and GNSS with Kalman Filtering and Feature Importance to Northern Attica, Greece

Abstract

Land subsidence poses a significant risk in built-up environments, particularly in geologically complex and tectonically active regions. In this study, we integrated Multi-Temporal Interferometric Synthetic Aperture Radar (MT-InSAR) techniques—Persistent Scatterer Interferometry (PS-InSAR) and Small Baseline Subset (SBAS)—with Global Navigation Satellite System (GNSS) observations to assess ground deformation in the Metamorphosis (MET0) area of Attica, Greece. A Kalman filtering approach was applied to fuse displacement measurements from GNSS, PS-InSAR, and SBAS, reducing noise and improving temporal consistency. Additionally, the PS and SBAS vertical displacement data were fused using Kalman filtering to enhance spatial coverage and refine displacement estimates. The results reveal significant subsidence trends ranging between −10 mm and −24 mm in localized zones, particularly near hydrographic networks and active fault systems. Fault proximity, fluvial processes, and unconsolidated sediments were identified as key drivers of displacement. Random Forest regression analysis, coupled with Partial Dependence analysis, demonstrated that distance to faults, proximity to streams, and the presence of stream drops and debris zones were the most influential factors affecting displacement patterns. This study highlights the effectiveness of integrating multi-sensor remote sensing techniques with data-driven machine learning analysis (Kalman filtering) to improve land subsidence assessment. The findings highlight the necessity of continuous geospatial monitoring for infrastructure resilience and geohazard risk mitigation in the Attica region.

1. Introduction

Land subsidence (LS) affects many areas around the globe, causing ground deformation [1]. There are numerous consequences associated with (LS), including damage to infrastructure, power lines, and buildings; sinkholes; flooding in coastal areas; and soil erosion [2,3,4]. There are two types of traditional geodetic methods for observing subsidence: leveling and total station geometry. In addition, Global Navigation Satellite System (GNSS) technology has become a well-established method for monitoring ground deformation, including subsidence. GNSS is particularly valuable due to its ability to provide accurate, continuous, three-dimensional displacement measurements over extensive areas, thereby effectively overcoming spatial and temporal limitations associated with conventional leveling and total station surveys. GNSS methods are being successfully used in subsidence monitoring across various regions, demonstrating high accuracy in detecting and quantifying ground deformation linked to both anthropogenic activities and natural processes [5,6,7,8]. For deformation monitoring, a general process involves selecting appropriate observation sites, installing observation stations or benchmarks, and determining a suitable monitoring period for either discrete (periodic) or continuous observations. In leveling surveys, stable benchmarks are established, and precise height differences between these benchmarks are measured repeatedly, typically at monthly, seasonal, or annual intervals, depending on the expected deformation rates and study objectives [9]. In total station geometry, angles and distances from a fixed reference point to reflectors placed at monitoring points are measured repeatedly to detect both horizontal and vertical displacements [10,11]. Although these traditional geodetic methods are effective, they have two significant limitations: (a) They require setting up physical observation stations and markers, and (b) the process is time-consuming and labor-intensive for each measurement campaign. Consequently, the first characteristic leads to the insufficient spatial sampling of monitoring observations, which makes it difficult to effectively identify new deformations from the monitoring results. Nevertheless, it is important to emphasize that traditional geodetic methods, particularly leveling and total station measurements, provide very high measurement reliability and low uncertainty. Under favorable conditions, these techniques can achieve sub-millimeter to millimeter-level precision, making them extremely appropriate for the high-accuracy monitoring of localized ground movements. The latter restricts the temporal sampling rate of the station or observation marker results, especially when the monitoring scope is relatively extensive [12]. In contrast, GNSS methods involve installing receivers at selected locations either permanently or temporarily, which provide continuous three-dimensional displacement data [13,14,15]. This allows for significantly improved spatial coverage and higher temporal resolution, overcoming many of the limitations associated with traditional methods. Therefore, for the early identification and monitoring of deformation areas, there is a need for a method that conducts extensive observations and, in a short period, can produce reliable results that allow for the early identification and continuous monitoring of geological disaster sites. Interferometric Synthetic Aperture Radar (InSAR) has the advantage of working under all weather conditions with high temporal resolution, covering extensive monitoring areas [16,17,18,19]. This technique can be used to measure land surface displacements ranging from a few millimeters, such as those associated with slow subsidence or tectonic creep, to several meters, such as those resulting from rapid phenomena like co-seismic deformation or landslides, depending on the spatial extent and temporal evolution of the event [20,21]. Common time series InSAR techniques used for LS include persistent scatterer (PS-InSAR) [22,23] and small baseline subset (SBAS) methods [16,24]. It is important to note that SBAS in this context refers to the Small Baseline Subset (SBAS) InSAR technique, which is distinct from the Satellite-Based Augmentation System (SBAS) [25] used in GNSS positioning.

PS-InSAR analyzes point targets with consistently high coherence over time, known as Persistent Scatterers (PSs), typically found in urban environments or exposed rocky terrains. Interferograms in PS-InSAR are generated using a common master image and longer temporal baselines, making it suitable for stable targets but limited in vegetated areas [23,26,27]. In contrast, SBAS constructs multiple interferograms using image pairs with short spatial and temporal baselines, improving phase coherence over time and enabling the inclusion of Distributed Scatterer (DS) targets with moderate but consistent coherence, thus offering better coverage in non-urban or vegetated areas [16,26,28]. It is important to note that the density of coherent points is primarily controlled by the electromagnetic backscattering properties of the Earth’s surface, not by the algorithm itself. While PS-InSAR is limited to isolated high-coherence points, SBAS increases point density by including DSs, which are more common in vegetated or heterogeneous terrains. Regarding unwrapping, PS-InSAR typically relies on network-based phase difference estimation from a reference point, whilst SBAS uses a least-squares approach across a redundant network of interferograms, enhancing robustness in decorrelated areas [27]. Compared with PS-InSAR, SBAS has the ability to obtain non-linear deformation information, especially in regions with greater signal decorrelation [29]. The temporal and spatial baselines affect the stability of the differential interferograms in InSAR. SBAS is a time series D-InSAR technique that increases spatial coherence by selecting interferogram pairs with short spatial and temporal baselines, thereby improving the quality of surface deformation time series [30,31]. When the surface deformation inversion model is used with a small baseline differential interferogram, the deformation time series of the coherent target can be obtained, while the factors affecting interferometric quality can be estimated and removed [12].

Despite numerous studies worldwide comparing MT-InSAR and GNSS techniques for monitoring ground movements [12,32,33], research in the Attica region in Greece—an area characterized by significant tectonic vulnerability—remains limited, particularly regarding the integration and comparative analysis of multiple geodetic techniques. Moreover, the application of advanced InSAR methods such as SBAS, which do extremely well at identifying non-linear displacement patterns, is notably underrepresented in Attica. To address this critical gap, our study focuses on the area where a GNSS station (coded MET0) is installed (one of the stations owned by the Metrica company and operated by the National Observatory of Athens), in Metamorphosis area in northern Attica, a strategic location influenced by complex geological and seismic factors, including active faults (such as Aspropyrgos-1, Menidi, and Pendeli) unique lithological units (e.g., Kifissos Lagoon Formations and Tourkovounia Limestone) and complicated hydrological conditions. Additionally, earthquake records from the University of Athens Earthquake Catalogue show that even during our relatively short monitoring period in 2021, the area experienced several minor seismic events (magnitudes ranging from Ms 2.0 to 3.3). Although such moderate seismic activity may not induce extensive immediate subsidence, the cumulative effects of these events, combined with sedimentary conditions and anthropogenic factors, enhance the potential for measurable surface deformation. Considering the geological, seismic, and hydrological complexities of the region, the MET0 station and its surrounding area is an optimal site for evaluating the capabilities and complementary nature of GNSS, PS-InSAR, and SBAS techniques in capturing both linear and non-linear ground deformation processes. Kalman filtering is an advanced estimation technique used to predict and update system states by continuously refining measurements from noisy observations [34]. It is particularly effective in processing time series data, where measurement error and missing values can reduce accuracy. One of its key advantages is its ability to integrate multiple data sources while accounting for different levels of noise, making it highly suitable for remote sensing and geodetic applications. In this study, we integrate Kalman filtering [35,36,37] as a key methodological approach to improve displacement estimates and mitigate noise in multi-sensor data fusion. Specifically, we utilize Kalman filtering in two stages: firstly, to estimate a refined fused displacement time series by integrating all three sensors’ displacements, and secondly, to fuse the PS-InSAR and SBAS datasets into a unified displacement field. This fusion approach leverages the strengths of each technique—GNSS for high-temporal resolution, PS-InSAR for high-spatial resolution, and SBAS for capturing broader deformation trends—while filtering out inconsistencies arising from atmospheric noise, decorrelation, or sensor-specific biases. By incorporating Kalman filtering, we integrate GNSS and InSAR-derived measurements into a unified displacement time series that enhances temporal consistency and reduces noise, offering a more vigorous representation of ground deformation. The fused PS-SBAS displacement map provides a more comprehensive spatial representation of ground deformation, improving the reliability of deformation assessments by combining information from different data sources. While each individual technique (i.e., GNSS, PS-InSAR, and SBAS) has distinct spatial resolution, temporal coverage, and noise characteristics, Kalman filtering enables their optimal integration by dynamically weighting measurements according to their relative uncertainties. Rather than simply averaging observations, the Kalman filter produces a refined time series that mitigates short-term fluctuations (e.g., GNSS noise) and fills potential temporal or spatial gaps (e.g., InSAR decorrelation), resulting in a smoother and more physically consistent displacement evolution. Although direct comparison to a single sensor can yield modest statistical agreement due to intrinsic differences between techniques, the fused Kalman-filtered output better captures the common deformation trends shared across all sensors, reducing random errors and inconsistencies.

To further understand the causal factors of ground displacement, we apply Random Forest regression to rank the importance of geological and environmental factors, such as distance to faults, proximity to streams, lithology, and land cover [38]. This machine learning approach enables us to identify the most critical variables influencing subsidence while minimizing overfitting and handling non-linear relationships between ground movement and predictor variables. Partial Dependence analysis is also used to examine the nature of these relationships, providing a clearer interpretation of how geological and hydrological conditions contribute to deformation trends.

In this study, we address a critical gap in Attica’s geohazard monitoring by systematically comparing multi-temporal InSAR data (PS-InSAR and SBAS) with GNSS observations, evaluating their consistency in detecting ground deformation, and applying Kalman filtering to improve displacement estimates. This refined methodology allows for a more accurate, spatially definite characterization of LS, which is essential for infrastructure resilience and risk management in this seismically active and geologically complex region. For this purpose, Sentinel-1 SAR data were processed to extract land deformation patterns in Attica, Greece, covering one year from December 2020 to December 2021, while GNSS daily measurements were obtained from the permanent MET0 station and processed via GAMIT/GLOBK software (version 10.71) [39,40,41]. This integrated approach provides a better understanding of subsidence mechanisms in the study area and delivers practical insights for urban planning, infrastructure management, and reduction in geologically active environments.

2. Study Area

The permanent MET0 station is located at (38°03′55″ N, 23°45′44″ E) in the Metamorphosis municipality of northern Attica, the metropolitan area of Athens, Greece’s capital. The MET0 site, founded by the Metrica company and operated by the National Observatory of Athens, serves as a key observation point for continuous GNSS measurements and is surrounded by a diverse geological environment, including Quaternary sediments and metamorphic basement rocks. To ensure a comprehensive assessment of ground deformation patterns, we define a 6 × 6 km buffering Area of Interest (AOI) centered around the MET0 station for PS-InSAR and SBAS analyses. This AOI involves a mix of urban and natural landscapes, allowing for the evaluation of displacement across different surface types. To better understand the geodynamic and environmental factors contributing to ground deformation in this area, we first outline the broader geological and seismic context of northern Attica, followed by a more detailed discussion of the local lithological formations.

2.1. Geological and Seismic Context of Northern Attica

Northern Attica is situated in an active tectonic environment driven by the ongoing extensional deformation related to the Hellenic Arc. Geologically, the region includes Alpine basement rocks—both metamorphic and non-metamorphic units—and post-Alpine sediments [42,43]. Specifically, the high-pressure metamorphic rocks of the Cycladic and Almyropotamos units stretch from Penteli Mountain in eastern Attica toward the southern Gulf of Evia. In contrast, the non-metamorphic carbonate rocks belonging to the Sub-Pelagonian units are predominantly found in Parnitha Mountain and western Attica [43].

The post-Alpine formations in the region mainly consist of alternating marls, lacustrine limestone marls, and sandstones. These sediments date from the Upper Miocene to the Holocene and form substantial Quaternary deposits, including talus cones, scree, and unconsolidated clays, significantly influencing seismic wave propagation and amplification [42]. These soft sedimentary basin fills amplify seismic waves because of their lower seismic velocities and reduced rigidity, allowing seismic energy to slow down and intensify as waves propagate through them, thereby increasing the shaking intensity at the surface. Structurally, the region is dominated by active normal faults trending predominantly WNW–ESE or NW–SE, dipping northwards toward the metropolitan basin of Athens. Key faults include Fili, Afidnai, Pendeli, and Aspropyrgos-1, (Figure 1) characterized by clear geomorphic evidence, such as linear scarps and fresh fault surfaces indicating recent seismic activity [44,45,46]. Slip rates measured for these faults range from approximately 0.1 to 0.4 mm/year [44], implying that significant seismic energy can accumulate over centuries, leading to earthquakes of moderate magnitude (Ms ~5–6), capable of causing substantial infrastructure damage, as demonstrated by the 1999 Ms 5.9 Athens earthquake [47,48]. Seismic tomography studies reveal that the shallow subsurface (0–4 km depth) consists primarily of soft, low-velocity sediments, whereas deeper layers (5–8 km depth) are composed of rigid basement rocks like marble and schist [47]. This velocity contrast intensifies seismic shaking, especially near the boundaries of sediment-filled basins.

Due to the relatively short historical seismic record in northern Attica, some faults have no recent documented earthquakes, but morphological and geological evidence confirm their potential activity and highlight the area’s moderate-to-high seismic risk. Accordingly, recent seismic hazard assessments, incorporating detailed fault and site-specific geological data, suggest stronger and potentially more frequent shaking intensities (Modified Mercalli scale VII–VIII) compared to older hazard estimations [42]. Overall, the seismic and geological setting of northern Attica, including the Metamorphosis area, indicate a pronounced susceptibility to ground deformation associated with active tectonic structures and significant sedimentary basin effects. Thus, comprehensive and continuous geodetic monitoring and analysis are vital for effective hazard assessment and urban planning.

2.2. Lithological Context of Area of Interest

The lithology of the MET0 area, digitized and provided by the University of West Attica, comprises diverse geological formations influencing local ground deformation patterns (Figure 2). The MET0 station itself is situated on the lake formations of Kalogreza–Pikermi, primarily composed of lacustrine sediments, such as marls and clays. These lacustrine sediments typically exhibit low rigidity and high compressibility, making them particularly vulnerable to subsidence due to compaction or groundwater extraction. Similarly, the Kifissos Lagoon Formations in nearby areas contribute to local instability, owing to their high porosity and low mechanical strength, which increases their susceptibility to seismic shaking and deformation.

Other localized geological units include the Margaikos horizon, consisting of alternating beds of marls, clays, sandstones, and conglomerates. These sedimentary units can also amplify seismic waves and may experience considerable deformation under seismic loading. Small occurrences of old lateral debris and debris cones, as well as river and lake deposits at the outskirts of Parnitha, further introduce instability due to their unconsolidated nature, potentially triggering localized slope failures, particularly under seismic disturbance. Conversely, limited areas within the AOI are characterized by the presence of Tourkovounia Limestone, a lithological unit that exhibits higher mechanical strength and lower compressibility compared to adjacent sediments, thereby offering greater geological stability and resilience to ground deformation. The variation in lithological units significantly influences local geotechnical properties, directly affecting susceptibility to subsidence and differential ground deformation. Therefore, understanding these lithological characteristics is essential for accurately assessing the spatial variability and intensity of deformation phenomena in the Metamorphosis AOI.

3. Materials and Methods

The methodology consists of applying MT-InSAR (PS-InSAR and SBAS) and GNSS analysis for detecting ground deformation at three locations in Attica. This methodology aims to provide a comprehensive and complementary assessment of surface displacement, combining the strengths of MT-InSAR’s wide spatial coverage and high-precision GNSS measurements.

3.1. Dataset Used

For the detection of ground deformation with the help of the MT-InSAR technique, we collected Sentinel-1 (C-band) SAR images from the Alaska Satellite Facility Vertex (ASF). To achieve C-band data analysis, SBAS or PS-InSAR requires at least 20 SAR images [50]. Ground subsidence measured with the SBAS and PS-InSAR techniques considers environmental topographic factors and signal noise. This sensor works in multiple acquisition modes, such as interferometric wide, strip map, and extra wide modes. In this study, we used 32 images each from both the ascending and descending orbit directions from December 2020 to December 2021 to estimate the vertical displacements for the selected AOIs. The properties of the Sentinel-1 C-band data acquired for the study are detailed in

Table 1. Properties and parameters of the Sentinel-1 ascending and descending dataset.

Data Information	Descending	Ascending
No. of images	32	32
Period of acquisition	3 December 2020–22 December 2021	9 December 2020–16 December 2021
Track no.	09	102
Parameters	Description
Product type	Sentinel-1 IW SLC	Sentinel-1 IW SLC
Polarization	VV+VH	VV+VH
Band	C	C
Coverage (km2)	250	250
Return frequency (day)	12	12
Range (m)	5	5
Azimuth resolution (m)	20	20

.

For PS-InSAR and SBAS analysis, ENVI-SARscape software (version 5.6.2) was implemented. The data collection for GNSS processing was carried out for three locations in the Attica region, with data including GNSS measurements, IGS (International GNSS Service) binding point data, and supporting data. The GNSS data were collected for a complete year from December 2020 to December 2021, whereas IGS stations were used as tie points, including 18 station points (namely YEBE, MAS1, POL2, KIT3, NICO, BUCU, METS, TRO1, WROC, GRAZ, NOT1, WTZR, ONSA, WSRT, HERS, RABT, MATE, and PDEL), as shown in Figure A1 (Appendix A). The supporting data include broadcast navigational ephemerides, ionospheric data, and precise orbital information.

3.2. Methods

MT-InSAR is a space geodetic technique for all weather conditions. The InSAR technique uses space-based SAR sensors to obtain SAR images and then generates a displacement phase by performing a differential operation on the interferometric phase of the dataset [51]. This technology offers high spatial resolution, enabling the detection and mapping of ground deformation areas. Based on Sentinel-1 SAR data (~5 m × 20 m native resolution) and considering multi-looking during interferometric processing, the minimum recognizable deformation footprint is approximately 20 m × 20 m under ideal conditions. However, due to coherence limitations, the practical detection threshold is around 40 m × 40 m, meaning that deformation smaller than this may not be reliably detected [52]. Since the satellite revisit cycle is usually approximately 12 days, InSAR technology cannot provide high-temporal-resolution monitoring. In principle, SBAS inversion results differ from those of PS-InSAR since the PS-InSAR and SBAS methods use different types of targets for inversion [27]. PS-InSAR techniques focus on identifying Persistent Scatterers (PSs), which are discrete, highly coherent point targets such as buildings, roads, and exposed rocks that maintain phase stability over time. In contrast, SBAS can exploit both Persistent Scatterers (PSs) and Distributed Scatterers (DSs), where DSs represent groups of partially coherent pixels, often vegetation or natural terrain that exhibits average coherence when considered collectively [16,23]. In areas with extensive urbanization, more PS points are typically selected due to the abundance of manmade structures, whereas in vegetated or natural areas with lower PS density, SBAS techniques incorporate DS to improve spatial coverage and ensure deformation detection across different surface types.

PS-InSAR is based on the processing of several multi-temporal satellite SAR images (at least 20) within a target area. In this technique, long radar datasets are stacked, and the backscattered signals are analyzed for estimation and removal of atmospheric artifacts [53]. The electromagnetic returns of stable, highly reflective pointwise targets (so-called permanent scatterers, or PSs) are statistically processed and analyzed to determine how much displacement has occurred between different acquisitions [54]. PSs correspond to manmade structures (e.g., buildings, roads, bridges, monuments, and pylons), as well as natural reflectors, such as outcropping rocks. This multi-interferometric approach allows us to estimate the LOS (line of sight) velocity at each permanent scatterer with high precision. While individual displacement measurements typically exhibit uncertainties between 1 and 3 mm, the aggregation of long temporal datasets (over 20–40 acquisitions) significantly reduces random noise. Under optimal conditions, such as highly coherent targets, stable atmospheric corrections, and extensive temporal observations, the linear velocity estimates can reach accuracies better than 0.1 mm/yr, though typical values range in the millimeter scale [55,56]. The PS-InSAR and SBAS methods are used to process Sentinel-1 Single Look Complex (SLC) images to obtain LS information at the three study sites in the Attica region. The SBAS method is also an InSAR technique that can improve monitoring accuracy. SBAS relies on differential interferograms within the threshold of temporal and spatial baselines so that geometric decorrelation is reduced to a minimum [57]. Figure 3 shows the main workflow of the methodology implemented to monitor LS.

3.2.1. PS-InSAR Processing

The PS-InSAR analysis in this study was carried out using the ENVI-SARscape 5.6.2 software with Sentinel-1 SAR images. We utilized 32 Sentinel-1 SLC images acquired from December 2020 to December 2021, covering both ascending (Track 102) and descending (Track 09) orbits. The master (reference) image was carefully selected from the dataset (18 August 2021) based on optimal coherence conditions, minimizing spatial and temporal baseline decorrelation (Figure 4), thus maximizing overall interferometric coherence.

Following the selection of the master image, a stack of 31 interferograms was generated by pairing each secondary acquisition with the master. To ensure interferometric stability and coherence, interferogram selection was constrained by a maximum temporal baseline of approximately 242 days, corresponding to the longest time separation between the master and the earliest acquisition (December 2020).

Topographic phase contributions were initially removed using the Shuttle Radar Topography Mission (SRTM v3) Digital Elevation Model (DEM) with a 30 m resolution. Subsequent interferograms underwent multi-looking with a factor of 4 × 4 pixels (range and azimuth directions). This process averages neighboring pixels to reduce speckle noise and random phase fluctuations, thereby improving the overall signal-to-noise ratio of the interferometric phase. Goldstein filtering [58] was also applied to reduce noise and further enhance the signal-to-noise ratio of the interferograms. Phase unwrapping was performed through the Delaunay Minimum Cost Flow (MCF) algorithm [59,60], a robust method particularly suited for urban environments, to convert wrapped phase differences into absolute deformation measurements. The PS-InSAR analysis employed a two-step inversion process. The first inversion provided initial displacement rates and estimated residual topographic errors, generating intermediate datasets, including deformation velocities, elevation adjustments, and coherence coefficients. The second inversion refined these results by estimating and subtracting atmospheric artifacts. Atmospheric phase contributions were effectively mitigated using a combined temporal high-pass and spatial low-pass filtering strategy, significantly enhancing displacement measurement accuracy. Before the decomposition of LOS measurements into vertical components, spatial correspondence between ascending and descending Persistent Scatterers was established using the ‘Shape Combination’ tool in ENVI SARscape. After geocoding, this tool aligns scatterers based on their geographic proximity, ensuring that only spatially corresponding observations from both orbits are used for deformation decomposition. This approach minimizes spatial mismatches and improves the accuracy of vertical displacement estimation. Following this alignment, ascending and descending orbit results were converted into vertical displacement values following a geometric decomposition method detailed by Hu et al. [12]. This step is crucial to minimize geometric distortions and to project satellite LOS measurements into the vertical direction, enabling a direct and meaningful comparison with GNSS vertical displacement measurements by ensuring that both datasets are in the same reference frame.

Final PS-InSAR outputs included geocoded maps displaying average vertical displacement rates and displacement time series across the Area of Interest (AOI). These results provided a detailed characterization of deformation patterns critical for subsequent validation and modeling analyses.

3.2.2. SBAS Processing

The SBAS technique, complementary to PS-InSAR, was implemented to capture the non-linear deformation pattern within the AOI. For SBAS processing, we used the same dataset of Sentinel-1 C-band SLC images as for the PS-InSAR analysis, comparing 32 scenes from ascending and descending orbits spanning from December 2020 to December 2021.

The SBAS approach requires forming multiple differential interferograms between images having small temporal and spatial baselines. Interferometric pairs were generated by selecting image combinations that minimize decorrelation effects, ensuring optimal coherence throughout the dataset. A total of 129 interferometric pairs were generated for SBAS analysis (Figure 5). These interferometric pairs were carefully chosen by constraining temporal and spatial baselines to maximize coherence and stability.

Interferogram formation began by co-registering the Sentinel-1 SLC images to the reference image. Subsequently, interferograms were generated, followed by the removal of topographic phases using the SRTM v3 DEM. To enhance signal-to-noise ratio and phase clarity, adaptive filtering based on coherence was applied. Next, coherence maps were produced to identify stable scatterers within the interferograms, which guided subsequent processing. Phase unwrapping was performed using the Delaunay Minimum Cost Flow (MCF) algorithm, applying robust criteria to manage noise and minimizing phase ambiguity errors. To ensure accurate phase unwrapping, interferograms with coherence below a threshold of 0.3 were excluded from further processing.

To optimize interferograms and ensure robust displacement estimates, manual refinement was conducted using Ground Control Points (GCPs). The coherence maps served as reference layers underlying the unwrapped interferograms to select stable GCP locations systematically. In total, more than 16 stable points (GCPs) (Figure 6), predominantly located on coherent urban features, such as buildings and roads, were manually identified across the AOI.

The initial inversion step involved the estimation of preliminary displacement rates and residual topographic phases from the interferometric stack. This inversion step simultaneously resolved displacement velocities and residual elevation errors, producing preliminary deformation estimates used for further processing. Residual topographic effects were minimized using the SRTM v3 DEM. In the second inversion step, time series deformation estimates were further refined by removing atmospheric artifacts identified in the initial inversion. This step entailed iterative adjustments of threshold parameters for atmospheric filtering, determined empirically after multiple processing trials to achieve optimized deformation estimates. By applying a combination of temporal high-pass and spatial low-pass filtering, atmospheric phase delays and other noise were effectively isolated and removed.

Finally, the refined deformation rates and displacement time series were geocoded into the WGS84 coordinate reference system, which defines a global ellipsoidal model of the Earth. The coordinates were represented in geographic format (latitude and longitude), allowing for accurate spatial interpretation and visualization across the AOI. After completing both ascending and descending analyses, the resultant LOS deformation rates were converted into true vertical displacements through geometric decomposition. This step is critical, as it provides a meaningful comparison with GNSS data and reduces geometric distortion effects inherent to SAR imaging geometries.

3.2.3. GNSS Data Processing

GNSS data processing was performed via the GAMIT/GLOBK software (version 10.71). To estimate the station position, we used the double-difference technique to eliminate satellite and receiver clock errors from daily RINEX data. The geometry of the GNSS network was considered when the station distribution scheme was optimized. To reduce baseline lengths and improve phase ambiguity resolution, the GNSS stations in each subnetwork were chosen every day based on their availability. Some of the most common issues in geodetic network design include (a) defining the reference frame by estimating the position coordinates at the GNSS network fiducial sites, (b) ensuring network geometry optimal observation selection, and (c) forming a weight matrix and densifying the local GNSS network beginning with the fundamental control network, i.e., the permanent IGS network [61]. The first step was to create a working directory with the data structures used by GAMIT for 2021. This working directory contains the following folders: RINEX, BRDC, IONEX, IGS, and tables. More specifically, in the Rinex folder, the GNSS observation data and IGS binding point data in “.o” format are stored; in the BRDC folder, broadcast ephemerides data in “.n” format are stored; in the IGS folder, precise orbital information in “.sp3” format; and in the IONEX folder, ionospheric information data in “.i” format are stored. Additionally, editing tables are involved in adjusting the processing parameters of the GNSS observations, such as site.defaults for adjusting binding point information; station.info for entering station details, such as receiver type, device height, and measurement date; and process.default for configuring interval values, observations, sets of priors, epochs, and output formats.

During the data-processing phase with GAMIT, GNSS measurement coordinates were generated in three phases. The outcomes from GAMIT processing corresponded to the number of DOY folders processed, each containing “h” files that were then utilized to estimate FIX coordinates through the GLOBK software. Furthermore, GLOBK processing generated a time series of observation points and a baseline length (Figure 3).

To validate the movements of MT-InSAR techniques with GNSS, we selected the displacement dates of the GNSS that coincided exactly with the displacement dates of MT-InSAR over one year. The permanent MET0 GNSS station, located in Metamorphosis, is part of the SmartNet Greece network operated by Metrica S.A. and the National Observatory of Athens. This station is equipped with a Leica GR10 geodetic receiver, which provides horizontal accuracy of approximately 0.18 mm/year and vertical accuracy of approximately 0.33 mm/year under continuous operation. These precision levels strengthen the reliability of GNSS observations as a ground-truth reference for comparison with InSAR-derived displacements in this study. In the timeframe, the GNSS displacement exhibits significant fluctuations, possibly influenced by noise, which can arise from various sources, such as atmospheric disturbances and instrumental errors. To address these issues, we applied a discrete Kalman filtering approach, integrating GNSS displacements with PS-InSAR and SBAS results. This fusion provided a smoother, more accurate displacement time series, reducing noise and enabling reliable validation of MT-InSAR results.

Although classical geodetic methods, such as precise leveling and total station surveys, are widely recognized for their high accuracy in monitoring localized ground deformation [9,57,62,63], such data were not available for the study area during the monitoring period. Consequently, only GNSS observations were used as the primary validation dataset. Similar approaches where InSAR-derived displacements were validated against GNSS observations have been successfully demonstrated in previous studies [64,65], supporting the reliability of the adopted methodology.

3.2.4. GNSS Kalman Filtering Fusion of GNSS, Ps-InSAR, and SBAS Displacement

Our study developed a multi-sensor fusion framework for high-accuracy ground displacement analysis. We explored two complementary approaches. The first approach integrated high-temporal-resolution GNSS, PS-InSAR, and SBAS observations to mitigate high-frequency noise and stabilize short-term displacement variations within the time series, improving the physical consistency of the recorded ground motion over weekly to monthly timescales. Integrating GNSS, PS-InSAR, and SBAS observations through Kalman filtering mitigates measurement noise by dynamically weighting each sensor’s input according to its estimated uncertainty. Each sensor is assigned a specific measurement noise covariance, and the Kalman gain adjusts adaptively at each time step, favoring more reliable measurements while suppressing noisier ones. This dynamic fusion process effectively reduces high-frequency fluctuations and outlier effects that are present in the individual sensor time series. Additionally, the incorporation of a process noise model (random walk with optimized covariance Q) allows the filter to capture gradual displacement trends without overfitting to noise. A grid search over a range of noise parameters was performed to optimize the filter settings, ensuring that the resulting fused displacement series provided a smoother and more accurate representation of ground deformation while minimizing random errors.

The second approach focused on fusing PS-InSAR and SBAS complete results, particularly valuable in regions where PS-InSAR coverage is sparse, to produce high-accuracy displacement estimates. We used Kalman filtering for both approaches in python scripts, with the second method extended to a two-dimensional state (displacement and velocity) to capture dynamic changes.

A discrete-time Kalman filter was implemented to estimate the true ground displacement. The state variable $x_k$ represents the underlying displacement at the time step $k$. The discrete-time Kalman filtering formulations applied in this study, including the random walk model for displacement estimation, are based on standard techniques widely used in time series estimation and geodetic applications [66]. The evolution of the state is modeled as a constant displacement (random walk) process, given as:

$$x_k=x_{k-1}+w_{k-1}, w_{k-1}\sim \mathcal{N}\left(0,Q\right),$$

(1)

where $Q$ donates the process noise covariance. The measurement model is expressed as

$${\mathrm{z}}_k=H\hspace{0.17em}{x}_k+{\mathrm{v}}_k,$$

(2)

with

$$H=\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right] \mathrm{and} R=\left[\begin{array}{ccc}{R}_{\mathrm{gnss}}& 0& 0\\ 0& R_{\mathrm{ps}}& 0\\ 0& 0& R_{\mathrm{sbas}}\end{array}\right].$$

(3)

This framework allows the filter to weight each sensor’s measurement according to its noise level. A grid search over a range of potential noise parameters was performed to determine the optimal Kalman filter settings. The candidate values tested for each sensor’s measurement noise covariance ($R_{\mathrm{gnss}}$, $R_{\mathrm{ps}}$, $R_{\mathrm{sbas}}$) included {1.0, 0.5, 0.1}, and the process noise covariance Q was similarly varied within {1.0, 0.5, 0.1}. The error metric was defined as the sum of squared differences between the fused displacement time series and the average displacement from the individual GNSS, PS-InSAR, and SBAS measurements. The settings that minimized this error metric were selected as optimal. The final chosen parameters were $R_{\mathrm{gnss}}=R_{\mathrm{ps}}=R_{\mathrm{sbas}}=0.1$ and $Q=0.1$, resulting in a fused displacement series that exhibited smoother behavior and closely tracked the underlying deformation trend while effectively mitigating high-frequency noise. Cross-validation or independent datasets were not used due to the limited availability of ground truth data; instead, the internal consistency and physical plausibility of the fused time series were verified to ensure reliability.

3.2.5. Kalman Filtering Fusion of PS-InSAR and SBAS to Estimate High Accuracy Displacement

To further improve, we chose decomposed vertical displacement time series from PS-InSAR and SBAS. Because the original CRS was in WGS 1984 (degrees), we explicitly set and reprojected both datasets to UTM projection (WGS 1984 UTM Zone 34N, EPSG:32634). This guaranteed that our spatial operations, such as the nearest-neighbor join using a 50 m search radius, were performed accurately in meters. This helps to improve spatial coverage, especially in regions where PS-InSAR data are barely covered.

Recognizing the complementary spatial coverage—PS-InSAR points are typically concentrated in urban areas, while SBAS extends into rural regions—we conducted a two-step spatial join: (a) a nearest-neighbor join from the PS-InSAR layer to the SBAS layer (within 50 m) retained all PS-InSAR points; (b) a similar join from the SBAS layer to PS-InSAR identified SBAS-only points. These results were concatenated, ensuring that the merged dataset included all relevant points. Missing PS-InSAR fields for SBAS-only points were set to NaN and appropriately handled in the fusion process. This approach ensured spatial resolution consistency by matching points based on geographic proximity (within 50 m), thus preserving the physical correspondence of displacement measurements across both datasets.

Displacement time series are stored in wide format (e.g., “D_20201209_ps” and “D_20201209_sbas”). We extracted these series and derived common time stamps (and time intervals, $\Delta t$) from the PS-InSAR columns. A two-dimensional Kalman filter was then applied to fuse the displacement measurements while also estimating velocity. The state space formulation used here, modeling both displacement and velocity evolution via a constant velocity model, follows standard Kalman filtering practices in geodetic time series analysis and remote sensing applications [67]. The state vector is defined as:

$${\mathrm{x}}_{\mathrm{k}}=\left[\begin{array}{c}{\mathrm{d}}_{\mathrm{k}}\\ {\mathrm{v}}_{\mathrm{k}}\end{array}\right],$$

(4)

where $d_k$ is displacement and $v_k$ is velocity. The state transition follows a constant velocity model:

$${\mathrm{x}}_k=F {\mathrm{x}}_{k-1}+{\mathrm{w}}_{k-1}, F=\left[\begin{array}{cc}1& \Delta t\\ 0& 1\end{array}\right],$$

(5)

with process noise $Q=q I$ and measurement model:

$${\mathrm{z}}_k=H {\mathrm{x}}_k+{\mathrm{v}}_k, H=\left[\begin{array}{cc}1& 0\\ 1& 0\end{array}\right].$$

(6)

Even though the sensors provided only displacement, available velocity attributes were used to initialize the state. Missing displacement measurements were imputed with the predicted value from the filter. A grid search was conducted over candidate values for the measurement noise variances ($R_{\mathrm{ps}}$ and $R_{\mathrm{sbas}}$ from $\{1.0,0.5,0.1\}$) and the process noise scalar $q$ ($\{0.001,0.01,0.1\}$). The error metric, defined as the sum of squared differences between the fused displacement and the average of the two sensor measurements, was minimized. The optimal parameters were found to be $R_{\mathrm{ps}}=0.1$, $R_{\mathrm{sbas}}=0.1$, and $q=0.1$.

3.2.6. Feature Importance and Partial Dependence Analysis

Random Forest regression was used to identify and quantify the most critical environmental and geological factors influencing subsidence in the study area. The key predictors considered in the analysis included distance to faults, distance to streams, lithology, and land cover. To achieve this, values for these predictors were extracted at the Kalman-filtered fused displacement points, ensuring that the analysis was based on refined displacement measurements. The distance-based predictors were calculated using Euclidean distance, which determines the shortest distance from each pixel to the nearest mapped fault or stream. All raster predictors were resampled and aligned to a common spatial resolution and projected to the WGS 84 _UTM Zone 34N coordinate system (EPSG:32634), which is suitable for the Attica region. This ensured consistency in spatial referencing and accuracy during distance-based sampling. Categorical variables, such as lithology and land cover, were processed using one-hot encoding to ensure compatibility with the machine learning model. This transformation allowed the model to accurately incorporate geological units and land cover types without imposing random numerical values that could misrepresent their influence. The Random Forest regressor was then trained using displacement values as the target variable, and feature importance scores were derived based on each factor’s contribution to reducing model prediction error.

To further validate the analysis, a Partial Dependence Plot (PDP) was generated to examine the direct relationship between each predictor and the displacement trends. These plots provided insights into how variations in specific factors, such as proximity to faults or streams, influenced displacement magnitude. By analyzing these relationships, we confirmed the significance of the most influential factors identified in the feature importance ranking and the reliability of the findings. This methodology enabled a data-driven interpretation of the geological and hydrological controls on subsidence, offering critical insights into the primary factors contributing to ground deformation in the study area.

4. Results

An MT-InSAR technique was applied to a 6 × 6 km area in the Metamorphosis municipality (northern Attica), where the permanent MET0 station is located. The selected area is surrounded by active faults, such as Aspropyrgos-1, Menidi, and Penteli. Recent research conducted in 2021 on landslide susceptibility mapping for the Attica region via the rock engineering system method [43] identified landslide events in the MET0 study area. These events are caused by slope collapse due to river erosion and the instability of adjacent slopes due to the corrosive action of streams. The PS-InSAR analysis derived 247,978 scattered points with velocities ranging from −33.42 to +25.29 mm/yr, and the SBAS analysis derived 211,020 points with velocities ranging from −27.79 to +6.73 mm/yr. The differences in maximum velocities between the PS-InSAR and SBAS results are expected and can be attributed to the intrinsic characteristics of the two methodologies. PS-InSAR focuses on detecting highly coherent, isolated scatterers (such as buildings, rocks, and infrastructure), enabling it to capture localized extreme displacement rates with high precision. In contrast, SBAS relies on a network of Distributed Scatterers (DSs), which tend to represent spatially averaged deformation over larger areas, particularly in non-urban or vegetated regions. Consequently, SBAS results generally smooth out localized high-velocity events that PS-InSAR can detect, leading to slightly lower maximum and minimum velocity values. Therefore, the observed differences between the PS-InSAR and SBAS maximum velocities are consistent with the complementary nature of the two techniques. To assess ground movements in the MET0 study area, we selected two subareas, A and B (Figure 7). To accurately characterize temporal displacement patterns at the permanent MET0 station, displacement data obtained from GNSS, PS-InSAR, and SBAS techniques were integrated using a Kalman filtering Python-based fusion approach. This integration utilizes the complementary strengths of each method: GNSS provides precise temporal displacement measurement at discrete locations, while PS-InSAR and SBAS ensure extensive spatial coverage, capturing both linear and non-linear displacement signals across the AOI. By fusing these datasets, the approach mitigates the inherent noise and data gaps in individual measurements, particularly gaps or signal fluctuations common in GNSS time series, by yielding a refined and accurate estimation of ground displacement. Consequently, this fusion approach offers a wide representation of ground displacement, enhancing both spatial coverage and measurement reliability compared to single-method analyses Figure 7.

The horizontal (north and east offsets) and vertical velocities (up offsets) of the GNSS data processing at the MET0 station are shown in Figure A2 (Appendix A) for the entire observation period. The PS-InSAR data indicate that the selected scatterer point coinciding with the permanent MET0 GNSS station exhibits minor displacement fluctuations, with a velocity of +0.15 mm/yr. There is a slight increase in variability and a subsidence trend with a velocity of −1.81 mm per year in the SBAS data. The GNSS up offset indicates a mean velocity of 2.42 ± 1.17 mm/yr, as derived from the daily GNSS time series shown in Figure A2 (Appendix A). The temporal displacement trends observed at the permanent MET0 GNSS station using PS-InSAR, SBAS, and GNSS are shown in Figure 8. We observe noise in the displacement trend of GNSS, which leads to poor correlation when compared with MT-InSAR techniques. The GNSS displacement time series exhibits higher short-term variability compared to the MT-InSAR results. This is expected due to the daily temporal sampling of GNSS measurements, which are more sensitive to local atmospheric disturbances, multipaths, and instrumental noise. In contrast, MT-InSAR techniques, by averaging information across multiple acquisitions, produce smoother deformation trends, thereby reducing apparent short-term noise. Instead of directly validating the MT-InSAR results with GNSS measurements, a Kalman filtering fusion approach was applied to integrate the displacement data from all three techniques, enhancing the temporal consistency and reducing noise-induced fluctuations. The PS-InSAR results indicate overall ground stability, with minor fluctuations ranging between 2 mm and −3 mm over the study period. The SBAS technique exhibits a more pronounced subsidence trend, with displacement values ranging from −4.5 mm to 0.5 mm. In contrast, the raw GNSS time series shows significant short-term variations, likely attributed to instrumental noise, atmospheric effects, or localized environmental influences. By applying Kalman filtering, we produced a refined displacement trend that effectively mitigates the noise in the GNSS observations and aligns more closely with the gradual subsidence trends identified by PS-InSAR and SBAS. The Kalman-filtered displacement curve (red line in Figure 8) reveals a smoother temporal evolution of deformation, balancing the high-temporal precision of GNSS with the spatial strength of InSAR techniques.

During the summer months of June, July, and August 2021, the raw GNSS displacement data exhibit increased variability, with multiple abrupt fluctuations between positive and negative displacement values [68]. In contrast, both PS-InSAR and SBAS demonstrate a relatively smoother trend, with minor fluctuations. The Kalman-filtered fusion output follows a more stable trend, reducing extreme variations seen in GNSS data, while aligning with the broader displacement patterns of InSAR techniques. The observed seasonal variations may still be influenced by factors such as thermal expansion, atmospheric propagation delays, or local environmental effects on GNSS measurements, but the fusion approach mitigates their impact, providing a more stable representation of displacement trends. This refined interpretation highlights the importance of integrating GNSS with PS-InSAR and SBAS to obtain a more comprehensive and accurate depiction of ground deformation in the study area.

To quantitatively assess the accuracy and effectiveness of the Kalman filtering fusion approach, a comparison was performed between the fused displacement series and the average of three input sensors (PS-InSAR, SBAS, and GNSS time series). A linear regression analysis revealed a strong linear relationship between the Kalman-filtered series and the average sensor displacement, as shown in Figure 9. The high coefficient of determination (R² = 0.94) confirms a strong agreement between the fused time series and the multi-sensor trend. Furthermore, the Root Mean Squared Error (RMSE = 0.4 mm) and Mean Absolute Error (MAE = 0.4 mm) indicate low residuals between the fused and reference series, supporting the capability of the method to mitigate short-term noise and inconsistencies present in individual measurements.

The choice to compare the Kalman-filtered output with the average of all three input sensors, rather than with any one individual sensor, is methodologically appropriate. The filtered result is not meant to replicate a single data source; in contrast, it represents an optimally fused time series that combines the complementary strengths of all three sensors resulting in a fused series not meant to match any one input individually. Instead, it reflects a statistically optimized trajectory that minimizes uncertainty across all sources. As such, comparing it directly to a single input sensor can result in misleading conclusions due to inherent differences in spatial resolution, atmospheric effects, and measurement noise profiles. To overcome this, the Kalman-filtered series are evaluated against the average of the three input sensors, which serve as a balanced benchmark. The averaging process neutralizes biases associated with any individual sensor and better represents the shared trend captured by all sources. This provides a more meaningful and fair assessment of the fusion output. The Kalman filter does not simply average data; it dynamically adjusts based on sensor uncertainty, yielding a smooth, physically meaningful displacement trajectory that retains the strengths of all contributing techniques. This integrated time series provides a more reliable and noise-resilient representation of ground deformation than any single sensor in isolation.

The PS-InSAR and SBAS techniques revealed significant vertical movements in Area A of the MET0 study region. From December 2020 to December 2021, PS-InSAR movements indicated initial minor subsidence and uplift, followed by a consistent subsidence trend that peaked in June 2021 and continued until December 2021, with the highest subsidence value of approximately −5.2 mm occurring in August 2021. A steady increase in subsidence is also evident in SBAS movements, with notable peaks around April, July, and October 2021, reaching a maximum subsidence of approximately −9.1 mm in September 2021 (Figure 10a).

The PS-InSAR and SBAS techniques reveal similar long-term subsidence trends for coinciding points in Area B, with some variations in displacement behavior. Both methods consistently indicate an overall downward displacement trend, confirming subsidence at these locations. However, key differences in their temporal patterns emerge upon closer examination. From October to December 2021, PS-InSAR displays abrupt fluctuations in displacement values, whereas SBAS exhibits a smoother, more gradual subsidence trend. This contrast highlights the sensitivity of PS-InSAR to short-term variations, possibly capturing localized ground movements and seasonal environmental influences. In contrast, SBAS provides a more continuous, stable trend, reinforcing its capability to track long-term, non-linear deformation patterns without sharp variations. A crucial observation is that PS-InSAR detects localized, rapid fluctuations between 10 September 2021 and 12 September 2021, while SBAS follows a more linear, gradual displacement pattern (Figure 10b). Since both methods observed the same general locations, the differences in displacement trends can be explained by their distinct methodological characteristics. PS-InSAR focuses on highly coherent, isolated scatterers (such as buildings or rocks), which may be locally influenced by subtle environmental changes, including thermal expansion and moisture effects. This sensitivity enables PS-InSAR to capture short-term displacement variations but also makes it more susceptible to short-term noise artifacts. In contrast, SBAS relies on a network of Distributed Scatterers (DSs) and applies temporal and spatial averaging across multiple interferograms, inherently smoothing out localized fluctuations and emphasizing broader, long-term deformation patterns. These methodological differences explain the observed contrast in temporal behavior between the two datasets [26]. Despite these differences, both methods exhibit a comparable overall subsidence rate, indicating a high level of agreement in detecting ground movement at these locations. The findings reinforce the complementary nature of PS-InSAR and SBAS, demonstrating that PS-InSAR does well in detecting localized, rapid variations, while SBAS is more effective in capturing long-term, non-linear displacement trends.

To quantitatively assess the relationship between PS-InSAR and SBAS displacement measurements at coinciding points in Area B, a multivariate linear regression analysis was performed. The resulting scatter plot (Figure 11) demonstrates a strong positive correlation (R² = 0.845) between the two techniques, indicating a high degree of agreement in the detected displacement trends. The regression line closely follows the data distribution, confirming that, despite some variations in short-term fluctuations, PS-InSAR and SBAS consistently capture the same overall deformation patterns in this area.

According to both the PS-InSAR and SBAS vertical velocity maps, a subsidence pattern extends from the river stream to urban areas, as indicated by the red and orange colors (Figure 7). River erosion and slope instability caused by the corrosion of adjacent slopes are significant contributors to the subsidence observed in Areas A and B. Subsidence spreading from the river stream and the surrounding urban areas supports the hypothesis that river erosion is the primary cause. An uplift trend is observed on either side of the subsidence zones, represented by the blue color. The proximity of areas to active faults, such as Aspropyrgos-1, Menidi, and Penteli, further suggests that tectonic movements have contributed to the observed ground instability. The significant subsidence in Areas A and B is likely caused by a combination of factors, including river erosion, tectonic activity, and potentially geological factors.

5. Discussion

Integrating PS-InSAR and SBAS techniques through Kalman filtering, combined with Random Forest regression analysis, provided critical insights into the spatial–temporal characteristics of ground movement in the study area. The findings highlight the interplay between geological, hydrological, and anthropogenic factors influencing subsidence and uplift patterns.

5.1. Fusion of PS-InSAR and SBAS

The fused PS-SBAS displacement map reveals significant ground movement trends, with three primary zones (A, B, and C) showing high subsidence rates, exceeding −10 mm/year. These areas coincide with active urbanization and proximity to hydrological networks, indicating that both human-induced and natural processes contribute to the observed displacement. The spatial correlation between these high-subsidence zones and historical landslides suggests that past slope failures may be indicative of ongoing instability, reinforcing the need for continuous monitoring.

The role of hydrological features in driving subsidence is evident, particularly along Streams 1 and 2, highlighted in Figure 12, where substantial subsidence is detected. The displacement behavior in these regions suggests that riverbank erosion and sediment loading may be key contributing factors. This observation aligns with prior research highlighting the impact of streambank erosion in destabilizing slopes and triggering subsidence [43]. In contrast, the uplift observed both near Stream 3 and on the opposite side of the AOI, with displacement values ranging from 2 mm to 10 mm/year, suggests an entirely different geomechanical response, potentially linked to tectonic activity.

The proximity of active faults, particularly the Aspropyrgos-1, Menidi, and Penteli faults shown in Figure 7, adds another layer of complexity to the observed deformation trends. The ground movements in the study area may be experiencing effects from fault-related strain accumulation and differential settling, making them particularly vulnerable to structural damage. These findings highlight the importance of accounting for active fault systems in subsidence assessments, as their influence extends beyond direct fault displacement to broader deformation processes.

Recent advancements in SAR signal processing, such as range ambiguity suppression using blind source separation [69], have significantly improved phase stability and reduced noise in spaceborne SAR data. Additionally, multi-scale detection methods developed for arbitrary-direction SAR applications [70] offer promising strategies for enhancing fusion approaches in heterogeneous environments, particularly where spatial scatterer density varies widely.

5.2. Feature Importance Regression Analysis and Causal Factors

To further investigate the primary factors influencing subsidence, a Random Forest regression model was applied to quantify the contribution of geological and environmental variables. The feature importance ranking revealed that distance to faults, distance to streams, and stream drops/debris zones were the most significant drivers of ground deformation across the study area (Figure 13). These findings align with established subsidence mechanisms, where tectonic activity [71], fluvial processes, and sediment compaction [43] collectively influence surface displacement patterns. Among the analyzed variables, distance to faults emerged as the most influential factor, suggesting a strong correlation between tectonic activity and the observed displacement trends. This finding is consistent with the geological setting of the study area, which is traversed by multiple active faults, including Aspropyrgos-1, Menidi, and Penteli.

The Partial Dependence analysis further reinforced this relationship, demonstrating a non-linear response of displacement to fault proximity (Figure 14). Specifically, displacement was not uniformly distributed along fault lines but instead exhibited threshold-dependent behavior, where certain distances from faults experienced intensified subsidence due to localized stress accumulation and strain release. This behavior is consistent with existing studies on fault-related subsidence, reinforcing the need for the continuous monitoring of deformation near active fault zones.

The second most influential factor was distance to streams, highlighting the significant role of fluvial processes in driving ground deformation. The results indicate that areas closer to streams exhibit greater displacement magnitudes, supporting the hypothesis that streambank erosion, sediment transport, and soil compaction contribute to land instability. This was particularly evident along Streams 1 and 2, where subsidence trends were significantly more pronounced. The displacement patterns in these regions suggest that erosional processes near riverbanks, combined with sedimentary loading, enhance ground instability, reinforcing findings from previous geomorphological studies.

The third most influential factor, stream drops and debris zones, maintained a consistently strong association with subsidence. These unconsolidated deposits are highly susceptible to compaction, erosion, and water infiltration, making them particularly vulnerable to surface deformation. The Random Forest feature importance ranking and Partial Dependence analysis confirmed that areas with these loose, unconsolidated sediments experience greater displacement magnitudes compared to more stable lithological formations. These findings are consistent with geotechnical studies that have identified alluvial and debris deposits as key contributors to long-term land subsidence due to their low shear strength and high porosity.

The consistency between feature importance rankings and Partial Dependence trends highlights the validity of these findings. The results demonstrate that fault activity, hydrological influences, and sediment composition collectively drive displacement trends in the study area. By integrating multi-sensor InSAR techniques with quantitative feature importance analysis, this study provides a framework for understanding subsidence mechanisms, offering valuable insights for future assessment.

6. Conclusions

This study demonstrated the effectiveness of integrating multi-temporal InSAR and GNSS observations, enhanced through Kalman filtering, for capturing land subsidence (LS) patterns and identifying their key driving factors in the Attica region in Greece. The findings reveal complex interactions between tectonic, hydrological, and geological processes, emphasizing the necessity of integrating multi-sensor observations for accurate ground deformation monitoring. By applying Kalman filtering to GNSS, PS-InSAR, and SBAS displacement time series, we successfully mitigated noise and inconsistencies in the temporal evolution of displacement trends. The filtered GNSS time series exhibited improved agreement with InSAR-derived subsidence patterns, allowing for a more precise validation of displacement magnitudes and trends. The fused time series provided a more reliable representation of vertical land motion, highlighting both linear and non-linear subsidence signals that would otherwise be obscured by short-term fluctuations in individual datasets. Furthermore, Kalman filtering was also applied to integrate PS-InSAR- and SBAS-derived displacement estimates, ensuring a more spatially coherent representation of ground motion across the study area. This methodological enhancement is particularly valuable for monitoring geohazards in complex environments where single-technique analyses may be insufficient.

The fused displacement map highlights three primary zones (A, B, and C) experiencing significant subsidence (>10 mm/year), predominantly in regions of active urbanization and hydrological influence. The spatial correlation between high-subsidence zones and historical landslides reinforces the notion that past slope failures may serve as indicators of ongoing instability, necessitating continuous geohazard monitoring. Feature importance analysis using Random Forest regression identified distance to faults, proximity to streams, and lithology (stream drops and debris zones) as the dominant factors influencing subsidence trends. The Partial Dependence analysis confirmed that displacement exhibits a non-linear response to fault proximity, suggesting localized stress accumulation and threshold-dependent strain release, rather than uniform subsidence across fault zones. These findings underscore the necessity of monitoring fault-proximal regions, where persistent subsidence could compromise infrastructure stability over time.

Hydrological influences also play a critical role, as evidenced by pronounced subsidence trends near Streams 1 and 2, likely driven by streambank erosion and sediment transport processes. Conversely, uplift trends near Stream 3 and the opposite side of the AOI suggest distinct geomechanically responses, potentially influenced by differential compaction or tectonic adjustments in the subsurface. The identification of these contrasting behaviors highlights the importance of incorporating hydrological and geomorphological dynamics into subsidence assessments. Lithology further contributes to subsidence variability, with unconsolidated deposits (stream drops and debris zones) exhibiting higher displacement rates due to their susceptibility to compaction and erosion. The consistency between feature importance rankings and Partial Dependence analysis trends reinforces the reliability of these findings, confirming that tectonic, fluvial, and geological factors collectively drive displacement in the study area. By integrating multi-sensor InSAR techniques with GNSS, Kalman filtering, and machine learning-based feature importance analysis, this study provides a methodological framework for interpreting land subsidence mechanisms. The results demonstrate that a combined geodetic and statistical approach significantly enhances the accuracy of ground motion assessments, offering practical insights for ground movement risk management.

Ultimately, this study highlights the importance of advanced remote sensing techniques and interdisciplinary approaches for monitoring and understanding ground deformation. To mitigate subsidence hazards, continuous monitoring and adaptive management strategies are needed. The integration of geological, hydrological, and land cover analyses contributes to understanding the impacts of ground instability when addressing subsidence challenges in both urban and rural areas. Our research efforts in the future will focus on developing predictive models and monitoring frameworks for managing ground deformation.