Vertical Deformation Extraction Using Joint Track SBAS-InSAR Along Coastal California, USA

Abstract

Ground deformation poses a major threat to socioeconomic development, especially in coastal regions where compounding effects of anthropogenic activities and natural processes exacerbate its destructive consequences. This urgency calls for comprehensive, spatially extensive, and temporally continuous deformation monitoring. In this study, we propose a joint track small baseline subset synthetic aperture radar interferometry (SBAS-InSAR) methodology that enhances conventional SBAS-InSAR workflows through integration of ascending and descending orbit data processing, enabling accurate extraction of vertical surface deformation. By analyzing 2348 Sentinel-1 acquisitions, we derived vertical ground deformation across coastal California. The proposed method demonstrates superior measurement accuracy (4.81 mm/year) compared to individual ascending track (7.19 mm/year) or descending track (7.07 mm/year) results. Our analysis identifies substantial deformation signals in coastal urban centers, reveals deformation-fault distribution correlations, and documents characteristic subsidence patterns induced by subsurface resource extraction. These comprehensive data and insights provide invaluable support for the prevention and mitigation of ground deformation in coastal California, and serve as a scientific basis for formulating effective prevention and control strategies, ensuring the safety and sustainable development of these vulnerable coastal regions.

1. Introduction

As a natural phenomenon, surface deformation poses a grave threat to human societal stability and economic prosperity [1]. Especially in coastal areas, projections indicate that by 2050, the sea level along the U.S. coastline is expected to rise by 0.25 to 0.3 m, amplifying the erosion and flood risks in low-lying coastal zones [2,3,4]. Compounding these challenges, anthropogenic activities such as excessive groundwater extraction contribute to land subsidence [5,6]. Furthermore, coastal pollution severely compromises ecological integrity and freshwater resources, exacerbating ecological pressures [7]. The intricate geological landscapes, including coastal erosion and estuary siltation, further escalate deformation risks [8]. In coastal areas, these compounded hazards manifest far-reaching consequences [9,10,11].

In recent years, the issue of surface deformation in the western coastal region of California has garnered widespread concern. This area experiences dual pressure from human-induced factors (e.g., urban development and groundwater pumping) and natural processes including tectonic activity and rising sea levels. These deformations not only disrupt community livelihoods but also endanger infrastructure and ecological stability. Alarmingly, estimates indicate that 4.3–8.7 million coastal residents in California are vulnerable to subsidence [12]. As such, the accurate and timely monitoring and early warning of surface deformation in this region are paramount in safeguarding human lives, property, and the sustainable socio-economic development of the region.

Traditional monitoring methods, such as leveling surveys, while precise, prove impractical for large-scale monitoring due to labor-intensive operations and high costs [13,14]. Similarly, the Global Positioning System (GPS), despite its global coverage and precision, has limitations in such applications due to sparse station distribution and limited point density [15,16]. Alternately, Interferometric Synthetic Aperture Radar (InSAR) technology has emerged as a promising solution, exhibiting remarkable potential in regional-scale deformation monitoring [17,18,19,20,21]. Its high resolution, wide coverage, and timely responses enable it to rapidly acquire surface deformation information and continuously monitor deformation processes, providing crucial technical support for disaster warning and risk assessment [22,23,24,25,26,27].

The high-risk status of coastal areas has driven extensive InSAR applications. Blackwell’s application of InSAR technology in 2020 provided unprecedentedly detailed estimates of vertical land motion rates for the entire California coast, achieving sub-millimeter precision [12]. This advancement significantly enhances the analysis of natural and anthropogenic changes in relative sea levels and related hazards. Similarly, in 2024, Ohenhen integrated high-resolution vertical land motion data (indicating land uplift or subsidence) with sea level rise predictions to quantify potential inundation areas in 32 major coastal cities in the United States, aiming to raise awareness of this critical issue [28]. These studies not only deepen our understanding of the mechanisms behind coastal surface deformation, but also offer invaluable insights and references for future monitoring and early warning systems.

Given the current dearth of InSAR monitoring data along the California coast and the limited resolution of existing findings, we have made full use of a wealth of Sentinel-1 data spanning from early 2017 to August 2023 to undertake an extensive and in-depth joint inversion study encompassing both ascending and descending track Sentinel-1 data in the California coastal region. Through this approach, we have achieved a resolution of up to 20 m in capturing surface deformation data, enabling us to conduct a comprehensive analysis of the typical de-formation signals in this area. These comprehensive data and analytical insights offer invaluable support for the prevention and mitigation of deformation in the California coastal region, deepening our understanding of the deformation dynamics and providing a scientific basis for the development of effective deformation prevention and control strategies.

2. Materials and Methods

2.1. Study Area and Data

The study area encompasses the Pacific coastline of California, situated in the western United States along a critical tectonic boundary between the North American and Pacific Plates, as depicted in Figure 1. The area exists within one of Earth’s most seismically active regimes, characterized by complex plate boundary interactions that drive sustained crustal deformation. At the heart of this dynamic system lies the San Andreas Fault Zone (SAFZ), a dextral transform boundary accommodating approximately 70–80% of the relative Pacific–North American plate motion through right-lateral strike-slip displacement [29]. This powerful tectonic framework generates multi-scale deformation patterns: localized fault-related displacements superimposed upon regional inter-seismic strain accumulation across the plate boundary. The complex interplay of these geodynamic processes creates spatially variable vertical motions measurable at millimeter-to-centimeter scales, making the region an ideal natural laboratory for studying tectonic geomorphology and crustal deformation mechanisms.

For the experimental data, we have selected Sentinel-1 satellite SAR data covering both ascending and descending tracks, spanning from January 2017 to August 2023. The coverage of these data aligns with the study area, as illustrated in Figure 1. Both tracks feature a single-look complex (SLC) type, utilizing the IW mode with VV polarization.

Table 1. Detailed SAR data information.

Tile Identifier	Acquisition Dates 1	Direction	Total Acquisitions	Tile Identifier	Acquisition Dates 1	Direction	Total Acquisitions
P35F117	201701–202308	Ascending	163	P42F467	201701–202308	Descending	188
P35F122			163	P42F472			188
P35F127			163	P71F480			189
P64F103			176	P115F462			190
P64F108			177	P144F476			199
P137F108			182	P173F480			188
P137F113			182

¹ Acquisition dates are represented in yyyymm format.

provides detailed information on the data, totaling 13 frames and 2348 acquisitions.

2.2. Methods

For spaceborne repeat-pass InSAR technology, satellites scan the Earth’s surface by emitting radar waves and collecting the reflected echoes. This process generates SAR image data acquired over varying time intervals for specific regions. By subjecting these images to differential interferometric processing, we are able to analyze phase differences, thereby extracting precise information regarding ground deformation. Notably, surface deformation induces additional path variations in radar waves, resulting in alterations in the phase of the received signals. Through quantitative measurement of these phase variations, researchers can determine the magnitude and pattern of ground deformation.

It is important to note that InSAR measurements from a single direction (ascending or descending) only capture line-of-sight deformation [30,31]. To obtain the three-dimensional deformation of the ground surface, especially the most useful vertical deformation, it often requires the assistance of LOS observations from multiple geometries [32,33]. Therefore, we propose a joint track SBAS-InSAR processing workflow, as illustrated in Figure 2. The specific steps are as follows:

First, we collect Sentinel-1 data, SRTM DEM, and the corresponding orbit state vector. Upon data collection, precise co-registration of the Sentinel-1 datasets is performed with an accuracy threshold set to 0.001 pixels. Following successful registration, subsequent processing steps are executed on the co-registered single-look complex (SLC) data stacks. To uphold temporal and geometric coherence, we establish thresholds for the temporal baseline at 365 days and the spatial baseline at 50 m during the interferometric pair screening [34,35]. After identifying optimal interferometric pair combinations, differential interferometric processing is conducted to generate interferograms. Prior to the initial phase unwrapping, we utilize the Goldstein method for phase filtering. This approach significantly diminishes residual phase components, thereby reducing the influence of phase noise and enhancing the stability of phase unwrapping. Subsequently, the MCF method is employed for phase unwrapping, with a rigorous threshold set at 0.4. This ensures that only pixels exhibiting a coherence value exceeding 0.4 contribute to the unwrapping process, thereby minimizing the effects of decorrelation on the precision of deformation measurements [36,37].

Subsequently, baseline refinement is implemented through uniform phase sampling across interferograms. Leveraging elevation data, nonlinear least squares analysis is performed to accurately estimate baseline parameters, including the perpendicular baseline length and baseline inclination angle, which are then used to refine the phase data as follows:

$$\left\{\begin{array}{c}{\displaystyle \frac{\partial h}{\partial B_{\perp }}}=-{\displaystyle \frac{R\cdot \mathit{sin}\theta \cdot \mathit{tan}\left(\theta -\alpha \right)}{B_{\perp }}}\hfill \\ {\displaystyle \frac{\partial h}{\partial \alpha }}=R\cdot \mathit{sin}\theta \hfill \end{array}\right.$$

(1)

where $h$ represents the elevation value, $B_{\perp }$ denotes the perpendicular baseline, $\theta$ is the radar incidence angle, $\alpha$ is the baseline inclination angle, and $R$ is the radar slant range distance.

Following this, the Singular Value Decomposition (SVD) method is applied to compute the least squares solution for the initial deformation rate. Subsequently, an iteration processing is carried out to obtain the iterated unwrapped interferograms. Following that, an error correction procedure systematically removed topographic residual phases, terrain-related atmospheric errors, and residual linear trends, yielding final line-of-sight deformation rate maps.

The relationship between radar line-of-sight deformation and three-dimensional surface deformation is

$$D_{los}=r_V·cos\theta +r_N·sin\mu ·sin\theta -r_E·cos\mu ·sin\theta$$

(2)

where $D_{los}$ refers to the radar line of sight deformation rate, and $r_V$, $r_N$, and $r_E$ are the vertical, north-south, and east-west components of the deformation velocity, respectively. $\mu$ is the radar heading angle.

As evident from the aforementioned equation, the line-of-sight deformation derived through InSAR technology aggregates three-dimensional surface deformation. Consequently, relying solely on the line-of-sight deformation data from a single orbit is insufficient to determine the full three-dimensional surface deformation. To resolve this limitation, integration of multi-platform and multi-orbit line-of-sight datasets becomes essential. Given that InSAR technology exhibits limited sensitivity to north-south deformation, we disregard the deformation along the north-south axis within the study area. Instead, we simultaneously invert the ascending and descending orbit interferometric data to retrieve the temporal deformation sequences in the vertical and east-west directions within the study area. With this approach, the aforementioned equation is rephrased as

$$\left\{\begin{array}{c}{D}_{asc}=r_V·cos{\theta }_{asc}-r_E·cos{\mu }_{asc}·sin{\theta }_{asc}\\ D_{des}=r_V·cos{\theta }_{des}-r_E·cos{\mu }_{des}·sin{\theta }_{des}\end{array}\right.$$

(3)

where $D_{asc}$ and $D_{des}$ are the radar line-of-sight deformation rates obtained from the ascending and descending track, respectively. ${\theta }_{asc}$ and ${\theta }_{des}$ represent the radar incidence angles for the ascending and descending orbits, while ${\mu }_{asc}$ and ${\mu }_{des}$ are the radar heading angles for the ascending and descending orbits.

Based on the aforementioned mathematical relationships, we can combine ascending and descending SAR data to establish corresponding observation equations for all target points within the study area, enabling overall solution computation. This allows us to obtain the most preferred and intuitive vertical deformation results. Meanwhile, as we observe in Figure 1, some regions only have data coverage from a single orbit direction. For these areas lacking redundant observations, we directly convert the line-of-sight deformation $D_{LOS}$ into pseudo-vertical deformation $r_V$ using their incidence angle $\theta$ as the final result.

$$r_V=D_{LOS}·cos\theta$$

(4)

To address massive data volumes and computational demands, a cloud computing framework was deployed. All data were uploaded to cloud servers, where a data processing environment was established. Computational tasks were formulated on a scene-by-scene basis and uploaded to the cloud computing center. These tasks were then distributed to different computing nodes for parallel processing. Finally, the resultant data were downloaded locally for subsequent processing.

3. Results

The separate radar line-of-sight deformation results acquired via InSAR technology for ascending and descending tracks are shown in Figure 3a and Figure 3b, respectively. In these figures, red signifies subsidence, indicating a negative deformation rate, while blue represents uplift, denoting a positive deformation rate. Both maps reveal distinct surface deformation patterns across the region. Subsequently, employing the methodology proposed in this study, ascending and descending track data were combined through data fusion to generate the final vertical ground deformation rate map for the study area, as illustrated in Figure 4.

To quantify the advantages of the joint track SBAS-InSAR approach, we performed a systematic statistical analysis (

Table 2. Comparative deformation statistics across processing methods.

Parameter		Ascending Track	Descending Track	Joint Track
Total Detected Points		229,198,008	186,641,213	277,808,906
Point Density (points/km2)		879	716	1066
Velocity (mm/year)	Minimum	−24.79	−27.71	−25.49
	Maximum	24.53	28.16	28.43
	Average	−0.10	−0.11	−0.11
	Std	0.93	0.89	0.82
Cumulative Displacement (mm)	Minimum	−140.31	155.17	142.74
	Maximum	137.36	157.69	159.20

). The joint track method significantly improved spatial sampling, achieving a point density of 1066 points/km²—a 21% increase over ascending (879 points/km²) and 49% over descending (716 points/km²) tracks. Vertical deformation velocities exhibited comparable magnitudes across modes, with maximum uplift rates of +28.43 mm/year (joint track) and subsidence minima of −25.49 mm/year. Notably, the joint track results demonstrated reduced variability (standard deviation: 0.82 mm/year vs. 0.89–0.93 mm/year for single-track modes), reflecting enhanced measurement stability. Over the six-year observation period (2017–2023), cumulative displacements ranged from −140.31 mm (subsidence) to +159.20 mm (uplift).

4. Discussion

To evaluate the effectiveness of the joint track method, we benchmarked it against single-track results from ascending and descending orbit measurements. To accomplish this, we projected the single orbit results onto the vertical direction using Equation (4) and compiled histograms of the deformation rate distributions for all three cases, presented in Figure 5. Given the large-scale study area encompassing multiple Sentinel-1 frames and merged sampling points, the deformation distributions of all three methods exhibit a clear normal distribution pattern. Notably, joint track results demonstrated smoother distribution curves. It is noteworthy that the peaks of the ascending and descending track histograms occur on opposite sides of the zero line. Specifically, the ascending track peak is negative, while the descending track peak is positive. This discrepancy is attributed to the distinct flight directions and observation angles adopted by the radar satellites during ascending and descending flights. However, as our analysis relies primarily on pseudo-deformations calculated directly from the formula, we primarily focus on the joint track results. According to the joint track results, 52.4% of the study area experiences positive deformation, while 47.6% undergoes negative deformation. A closer examination reveals that most areas maintain relatively stable ground conditions, with minor deformations concentrated between ±4 mm/year, accounting for 55.8% of the total area. However, it is crucial to highlight that 9.7% of the regions exhibit absolute deformation rates exceeding 8 mm/year. These areas merit particular attention and require continuous monitoring to mitigate the risk of potential disasters.

For quantitative accuracy assessment, we performed validation using 105 GPS stations, as depicted in Figure 6a, determining vertical ground deformation through linear fitting to establish the ground truth. We then subjected the results of our joint track method (depicted in Figure 6b) to a comparative analysis with those of the single ascending track (Figure 6c) and descending track (Figure 6d) approaches. The analysis showed that the error distribution of the joint track method is more concentrated, indicating improved precision. Conversely, the error distributions of the single-track methods were more dispersed. To quantify the precision, we calculated the root mean square error (RMSE) for each approach. Our findings indicate that the ascending track results achieved a precision of 7.19 mm/year, while the descending track results attained 7.07 mm/year. However, the joint track method proposed in this study outperformed both, achieving a precision of 4.81 mm/year, representing a 31.97% improvement over the best single-track result. This enhancement in precision underscores the reliability of our method and the credibility of the conclusions derived from its application.

Through a comprehensive analysis of deformation rate data, distinct patterns of surface deformation emerge in several Californian cities. As shown in Figure 7, these urban centers exhibit pronounced deformation features. Firstly, Figure 7a reveals the surface deformation in San Jose. Significant subsidence has occurred in the central area of the city, where the cumulative subsidence, based on the deformation curves at points 1 and 2, exceeded −40 mm during the monitoring period. Bakersfield, too, exhibits significant subsidence in its northern and southern areas, reaching a maximum cumulative subsidence of over 60 mm, as depicted by the cumulative deformation curve at point 3. Meanwhile, a slight uplift is observed in the city’s western and eastern sections, as shown in Figure 7b. Furthermore, the surface deformation in San Bernardino is also evident, as shown in Figure 7c. The central part of the city exhibits slight subsidence, with a magnitude slightly higher than 30 mm, while a wide-area uplift has occurred in the eastern part of the city, with a total uplift of over 45 mm, as evidenced by the cumulative deformation curve at point 6. The surface deformation in Los Angeles is equally striking (Figure 7d). Significant subsidence has occurred in the central part of the city and the Beverly Hills area in the northwest. The subsidence in the central part of the city is approximately 40 mm, while the subsidence in Beverly Hills to the north exceeds 50 mm. Finally, the wide-area subsidence in the central area of Ontario is particularly significant, as shown in Figure 7d. During the monitoring period, the cumulative subsidence in this area exceeded 80 mm, which can be clearly seen from the cumulative deformation curve at point 10.

The frequent tectonic activities in California are renowned for their impact on geological structures, which are further reflected in the complicated surface deformation patterns captured by InSAR. To comprehensively understand these impacts, we have systematically integrated fault distributions of the study area and integrated them into the surface deformation rate map, depicted in Figure 8. For enhanced visual clarity, we adopted a distinct red-blue color scheme to represent the surface deformation rate. The red signifies negative deformation rates, indicating areas of surface subsidence, while the blue depicts positive deformation rates, representing surface uplift. This vibrant color contrast effectively highlights even the most subtle surface deformation contrast. Upon closer inspection, it becomes apparent that certain faults are associated with notable surface deformations. More interestingly, we observe stark contrasts in surface deformation rates across the fault boundaries. For instance, in Figure 8b, the Santa Yenz fault is flanked by a red zone indicating subsidence to the north and a blue zone representing uplift to the south. Similarly, this dichotomy is evident on both sides of the Wildcat fault and Chabot fault in Figure 8c, as well as near the San Jacinto fault in Figure 8d. A particularly striking pattern emerges in the northern region of Cathedral City in Figure 8e, where the San Andreas fault zone creates a profound depression zone of subsidence sandwiched between two uplifted regions. The opposing vertical movements observed across the Santa Ynez and San Andreas fault zones align with their strike-slip nature, where localized compression or extension near bends in the fault trace can generate differential subsidence/uplift. These intricate surface deformation patterns not only underscore the complexity of fault activities in the region but also offer critical insights into geological processes and seismic risks. They serve as invaluable tools for our assessment and understanding of the dynamic nature of the Californian geological landscape.

In addition to the fault activities, the InSAR deformation results revealed distinct deformation anomalies resulting from underground resource extraction. As depicted in Figure 9b, two prominent subsidence funnels stand out, clearly indicating mining-induced deformations. These deformations are located within the Elk Hills Naval Petroleum Reserve, an area comprising Naval Petroleum Reserve No.1 (NPR-1) and Naval Petroleum Reserve No.2 (NPR-2), whose optical imagery is shown in Figure 9c. Thick, unconsolidated sedimentary basins exhibit pronounced subsidence from fluid extraction due to their high compressibility. To gain a deeper understanding of the temporal surface deformation in these oil reserves, we selected specific section lines within the subsidence funnels. Section Line 1 traverses NPR-1, spanning 25 km, while Section Line 2 cuts through NPR-2, covering 15 km. By collecting cumulative deformation data at a bi-monthly interval and analyzing these data, we have plotted temporal cumulative deformation curves that comprehensively capture the deformation patterns from January 2017 to August 2023. Each profile location features 40 curves, comprehensively outlining the temporal evolution of cumulative deformation, as illustrated in Figure 9d,e. During the monitoring period, NPR-1 experienced a cumulative subsidence of over 40 mm, while NPR-2 recorded an even more significant cumulative subsidence of more than 65 mm. Despite NPR-1’s visually larger subsidence funnel, NPR-2 exhibited a more pronounced subsidence rate. Intriguingly, we also observed signs of surface uplift in the peripheral regions of the subsidence funnels. These distinct deformation patterns align with the expected geo-mechanical responses to oil extraction, providing valuable insights into the geological implications of such resource extraction activities.

5. Conclusions

Coastal regions hold immense significance for human communities, particularly along the west coast of California. In this region, the interplay of human activities, climate change, sea-level rise, and tectonic plate movements has significantly increased the ground surface’s susceptibility to deformations. These deformations pose dire threats to the lives of local residents, infrastructure, and ecological security, necessitating urgent, targeted, wide-area, and routine monitoring efforts. To meet this need, this study introduces a joint track SBAS-InSAR methodology for wide-area ground deformation monitoring, integrating both ascending and descending track data. By applying this approach to the coastal areas of California, we have successfully obtained high-resolution vertical ground deformation information from 2348 Sentinel-1 SAR acquisitions. Notably, this methodology demonstrated a precision enhancement of 31.97% compared with results from single-track datasets. A detailed analysis of specific deformation patterns in this region reveals significant deformation signals in several coastal cities, including San Jose and Los Angeles. Furthermore, some of the deformations are closely correlated with fault distributions, with some areas exhibiting opposing deformation trends on either side of a fault line. Additionally, we have identified typical ground deformations triggered by underground resource extraction activities, particularly in the Elk Hills Naval Petroleum Reserve area.

The methodology and results of this study offer valuable scientific data to inform the development of effective strategies for coastal ground deformation prevention and mitigation. While the analysis highlights deformation patterns linked to resource extraction and tectonic activity, it also underscores the potential contributions of other anthropogenic factors, such as urban construction practices and groundwater management, which warrant further investigation through comprehensive attribution analyses integrating urban infrastructure records, hydrological data, and geotechnical surveys. To advance coastal resilience, future work will focus on enhancing InSAR technology, including the integration of InSAR and GPS measurements, and incorporating machine learning or physics-based models to predict deformation trends under scenarios of groundwater extraction, tectonic activity, and sea-level rise. Although applied here to California’s coast as a high-risk exemplar, the joint track SBAS-InSAR and vertical deformation inversion framework is generalizable and can be extended to other coastal or tectonically active regions worldwide, including subsidence-prone deltas and urbanized coastlines, to support adaptive and sustainable management strategies.