Multi-Source SAR-Based Surface Deformation Analysis of Edgecumbe Volcano, Alaska, and Its Relationship with Earthquakes

Abstract

Edgecumbe, a dormant volcano located on Kruzof Island in the southeastern part of Alaska, USA, west of the Sitka Strait, has exhibited increased volcanic activity since 2018. To assess the historical and current intensity of this activity and explore its relationship with seismic events in the surrounding region, this study utilized data from the ERS-1/2, ALOS-1, and Sentinel-1 satellites. The Permanent Scatterer Interferometric Synthetic Aperture Radar (PS-InSAR) and Small Baseline Subset InSAR (SBAS-InSAR) techniques were employed to obtain surface deformation data spanning nearly 30 years. Based on the acquired deformation field, the point-source Mogi model was applied to invert the position and temporal volume changes in the volcanic source. Then, by integrating seismic activity data from the surrounding area, the correlation between volcanic activity and earthquake occurrences was analyzed. The results indicate the following: (1) the coherence of interferograms is influenced by seasonal variations, with snow accumulation during the winter months negatively impacting interferometric coherence. (2) Between 1992 and 2000, the surface of the volcano remained relatively stable. From 2007 to 2010, the frequency of seismic events increased, leading to significant surface deformation, with the maximum Line-of-Sight (LOS) deformation rate during this period reaching −26 mm/yr. Between 2015 and 2023, the volcano entered a phase of accelerated uplift, with surface deformation rates increasing to 68 mm/yr after August 2018. (3) The inversion results for the period from 2015 to 2023 show that the volcanic source, located at a depth of 5.4 km, experienced expansion in its magma chamber, with a volumetric increase of 57.8 × 10⁶ m³. These inversion results are consistent with surface deformation fields obtained from both ascending and descending orbits, with cumulative LOS displacement reaching approximately 210 mm and 250 mm in the ascending and descending tracks, respectively. (4) Long-term volcanic surface deformation, changes in magma source volume, and seismic activity suggest that the earthquakes occurring after 2018 have facilitated the expansion of the volcanic magma source and intensified surface deformation. The uplift rate around the volcano has significantly increased.

1. Introduction

Volcanoes are unique geological phenomena that significantly influence surface morphology and have profound impacts on human societies [1]. In recent years, volcanic activity worldwide has increased noticeably, triggering various disasters that cause significant casualties and property damage. Volcanic eruptions release vast amounts of toxic gases and may cause secondary hazards such as ash falls, lava flows, and volcanic earthquakes, all of which can severely affect surrounding regions [2]. Therefore, the long-term monitoring of volcanic activity, along with detailed investigations into surface deformation and its influencing factors, is critical. These studies are essential for understanding volcanic mechanisms, predicting volcanic hazards, and developing effective mitigation strategies.

Edgecumbe Volcano, a dormant stratovolcano located on Kruzof Island in southeastern Alaska, USA, west of the Sitka Strait, is part of the Mt. Edgecumbe volcanic field. At an elevation of 976 m, the volcano has been dormant for nearly 800 years, though recent seismic activity since 2018 has raised concerns about potential volcanic reactivation. Notable for its symmetrical conical shape, Edgecumbe is situated along the Fairweather–Queen Charlotte Fault system, a major transform fault accommodating most of the relative motion between the Pacific and North American plates. The tectonic forces along this fault contribute to both seismic and volcanic activity in the region. Recently, the frequency of seismic events near Edgecumbe has increased, indicating a potential resurgence in volcanic activity. This rise in seismicity, coupled with observed surface deformation from remote sensing, underscores the need for the continuous monitoring of the volcano. Identifying and understanding surface deformation patterns is crucial for gaining insights into the underlying volcanic processes, especially magma dynamics, beneath the surface.

Traditionally, monitoring volcanic activity in remote environments has been challenging, particularly for volcanoes with infrequent eruptions. Ground-based measurements and field surveys are often limited by accessibility issues and cannot provide continuous, real-time data. This limitation has driven the need for more advanced monitoring techniques. Satellite-based radar technologies, particularly Interferometric Synthetic Aperture Radar (InSAR) [3,4,5,6,7,8,9,10], have revolutionized volcano monitoring. InSAR allows precise measurements of surface deformation over large areas and extended time periods, providing valuable data for early-warning systems and enhancing our understanding of volcanic hazards.

Monitoring the surface deformation of Edgecumbe Volcano is particularly critical given its proximity to populated areas in southeastern Alaska. The early detection of changes in the volcanic magma source could help mitigate potential impacts from future eruptions, such as pyroclastic flows, lava flows, and volcanic earthquakes. To address this need, the present study employed InSAR-based techniques to obtain time series surface deformation data for Edgecumbe. Using advanced inversion models, including the Mogi model, this research aimed to estimate the volume changes of the volcanic magma source and track its temporal evolution from 1992 to 2023. By investigating the relationship between surface deformation and seismic activity, the study sought to improve predictions of future volcanic behavior and assess the associated hazards.

The advantages of modern technologies, especially InSAR, address many of the challenges faced by traditional monitoring methods. Traditional monitoring methods face various challenges, but modern technologies, especially InSAR, offer new possibilities. InSAR provides high temporal and spatial resolution, non-contact monitoring, and all-weather, day-and-night capability, making it an indispensable tool for tracking volcanic activity [11]. Emerging time series InSAR techniques such as Differential InSAR (D-InSAR) [12], PS-InSAR [13], and SBAS-InSAR [14] further enhance these capabilities. These advanced methods allow for a more accurate study of surface deformation associated with volcanic activity, aiding in early warning and threat mitigation.

To evaluate the historical and current volcanic activity and investigate its correlation with seismic events in the surrounding area, this study applied nearly 30 years of multi-source SAR data with time series InSAR techniques. The Mogi model was combined with the Markov Chain Monte Carlo [15,16] (MCMC) algorithm to invert the location and volume changes of the volcanic magma source. The Mogi model simulates the deformation caused by magma movement beneath the surface while the MCMC algorithm optimizes the inversion process by iteratively adjusting parameters such as the depth, location, and volume of the magma source to best fit the observed surface deformation data. Finally, the relationship between volcanic activity and seismic events was analyzed. This research is crucial for predicting future deformation trends at Edgecumbe Volcano and reducing potential losses from volcanic hazards.

2. Study Area and Datasets

2.1. Study Area

Edgecumbe Volcano is located on Kruzof Island in the southeastern part of Alaska, USA, to the west of the Sitka Strait. It is part of the Mt. Edgecumbe volcanic field (Figure 1), with an elevation of 976 m. The volcano is snow-covered during the long winter months [17]. Mt. Edgecumbe has a rich history of volcanic activity, although it has been dormant for nearly 800 years [18,19]. In April 2022, a series of seismic events occurred around the volcano, prompting local geologists to recognize that Edgecumbe Volcano had resumed activity, which led to an intensified monitoring effort.

Geologically, approximately 15 km west of Kruzof Island lies the Fairweather–Queen Charlotte Fault, a major transform fault that accommodates most of the relative motion between the Pacific and North American plates [20,21,22]. The collision of these plates generates frequent earthquakes, which can cause both transient ground deformation (TGD) and permanent ground deformation (PGD), both of which can significantly impact surface infrastructure and subsurface structures [23].

On 9 February 2024, the United States Geological Survey (USGS) released the latest update from the Alaska Volcano Observatory [24] (AVO), which includes the most recent monitoring data for Edgecumbe Volcano. According to the report, from August 2023 to late January 2024, approximately one small earthquake per day was detected beneath the Mt. Edgecumbe volcanic field, with most occurring at depths between 4 and 10 km below sea level. The AVO announcement further noted that the continuous analysis of InSAR data and Global Positioning System (GPS) monitoring stations on the island indicates that surface deformation at Edgecumbe Volcano is ongoing, though at a lower rate than observed in previous years. As of early February, the surface uplift rate was reported to be between 20 and 30 mm/yr.

2.2. Datasets

This study utilized multi-source SAR image data from ERS-1/2, ALOS-1, and Sentinel-1A/B to monitor the long-term surface deformation of Edgecumbe Volcano from 1992 to 2023. The coverage of the multi-source imagery is shown in Figure 1b, with detailed image parameters listed in

Table 1. Multi-source SAR image parameters.

Sensor	Path	Frame	Direction	Flight Angle	Start Date	End Date	Total/Scene
ERS-1/2	192	1143	Ascend	−24.5°	24 July 1992	26 June 2000	10
ALOS-1	238	1130/1140	Ascend	−10°	6 January 2007	17 January 2011	12
Sentinel-1A	50	182	Ascend	−17°	8 April 2017	22 October 2023	99
Sentinel-1B	174	402	Descend	−163°	3 April 2015	22 October 2021	98

. The data processing was performed using software packages and algorithms such as GAMMA2013, StaMPS4.1, and MintPy1.5.3. Additionally, AW3D-DEM data with a 30 m resolution, provided by the Japan Aerospace Exploration Agency (JAXA), were used to assist in the processing. In addition, to analyze the relationship between earthquake and volcanic activity, we selected the seismic data of the area near Kruzof Island from 1992 to 2023. Various factors, including the earthquake magnitude, source depth, and duration of shaking [25,26,27,28,29,30,31,32], were considered in order to assess the extent of seismic-induced surface deformation and associated hazards. A total of 1652 seismic events, including earthquakes and icequakes within 120 km of Edgecumbe Volcano from 1992 to 2023, were selected from the USGS and Alaska Earthquake Center databases, filtered by moment magnitude ≥ 1.0, focal depths ≤ 50 km, and exclusion of aftershocks and served as the research data for this study. The location of Edgecumbe Volcano and the corresponding seismic information are shown in Figure 1c. Sentinel-1 ascending orbit satellites captured data from early 2017 onwards, but they did not capture the entire island individually. However, these data are essential for assessing recent activity as the power system of Sentinel-1B encountered a malfunction, and since December 2021, no descending orbit imagery of Edgecumbe Volcano has been available.

3. Method

This study utilized multi-source data obtained from ERS-1/2, ALOS-1, and Sentinel-1A/B. Initially, PS-InSAR and SBAS-InSAR techniques were employed to process the data and acquire surface deformation fields for Edgecumbe Volcano over the past 30 years. The deformation characteristics of the volcano were then analyzed over this extended period. Subsequently, the Mogi model was applied, and the MCMC algorithm was used to invert the location and volumetric time series changes of the volcanic source. Finally, by integrating the volcanic source volume changes, surface deformation data, and seismic activity in the surrounding area, the relationship between volcanic activity intensity and seismic events was analyzed. The technical workflow for this study is illustrated in Figure 2.

3.1. Temporal InSAR Technique

3.1.1. SBAS-InSAR

In this study, we applied the Small Baseline Subset InSAR [33,34] (SBAS-InSAR) technique to monitor surface deformation at Edgecumbe Volcano, utilizing interferometric data from Sentinel-1. The processing was conducted using the NASA Alaska Satellite Facility’s (ASF) Hybrid Pluggable Processing Pipeline [35] (HyP3), with subsequent data analysis performed through the MintPy1.5.3 software package. SBAS-InSAR allows for the generation of a dense time series of surface deformation by using interferograms with small baselines, thereby minimizing atmospheric noise and temporal decorrelation. The key steps involved in the SBAS-InSAR approach are (1) the selection of images and interferometric pairs and (2) time series deformation processing.

(1)

Selection of Images and Interferometric Pairs

For this study, a total of 138 and 166 Sentinel-1 SAR scenes from the ascending and descending orbits, respectively, were processed, generating 435 and 585 interferograms along paths 50 and 174. Interferogram pairs were selected within a 48-day temporal window to ensure high temporal coherence. Data from the winter season (1 November to 31 March) were excluded to mitigate decorrelation caused by snow accumulation, which can significantly degrade interferometric coherence. The coherence analysis revealed that the volcanic summit typically experiences decorrelation from November to March each year due to snow cover; the volcanic interferogram coherence analysis is discussed in Section 4.1. As a result, interferograms from this period were excluded from the analysis, with only those obtained outside the winter period being considered for deformation monitoring.

In addition, 11 scenes from ERS-1/2 and 23 scenes from ALOS-1 were selected and analyzed. For both ERS-1/2 and ALOS-1, images and interferometric pairs were selected in a similar manner to maintain high coherence and reduce noise caused by seasonal variations and atmospheric interference. As a result, 10 scenes from ERS-1/2 and 12 scenes from ALOS-1 were retained for further processing and analysis. A total of 99 scenes from Sentinel-1A (producing 299 interferogram pairs) and 98 scenes from Sentinel-1B (producing 316 interferograms) were used. For ALOS-1, the interferometric pairs were selected based on the temporal baseline and the coherence threshold, ensuring that only reliable interferograms with minimal seasonal decorrelation were included. The spatiotemporal baseline connectivity diagrams for both Sentinel-1A/B and ALOS-1 are shown in Figure 3 and Figure 4, respectively.

To preserve the integrity of the time series analysis, interferogram pairs that crossed the winter period were combined, ensuring that at least three interferograms were retained for each winter season. This approach minimized seasonal interference and improved the accuracy of deformation estimates.

(2)

Time Series Deformation Processing

The time series deformation analysis was conducted using SBAS-InSAR, focusing on removing pixels with temporal coherence below 0.7 and interferograms with spatial coherence below 0.7. Coherence, defined as the correlation between interferometric phase values across multiple acquisitions, is a crucial metric for ensuring the reliability of phase measurements and the accuracy of deformation estimates.

Atmospheric corrections were performed using the ERA-5 reanalysis dataset, which combines satellite and ground-based observations with numerical weather prediction models to provide high-resolution atmospheric data. Topographic phase residuals, influenced by DEM errors, were corrected using the method proposed by Fattahi and Amelung, which estimates residual terrain errors by combining phase information with the DEM to adjust for topographic effects.

Phase unwrapping was carried out using the minimum-cost flow method, chosen for its robustness in handling large datasets and complex phase patterns. To further reduce unwrapping errors, a bridging technique was applied, ensuring that the most coherent pairs with the shortest baselines were connected, promoting continuous and smooth phase transitions.

To isolate volcanic deformation signals, a stable reference point on Kruzof Island, located away from the volcanic deformation area, was used. This method ensured that only local deformation associated with Edgecumbe Volcano was captured. Distant field observations were excluded to focus on the region of interest.

Subsequent to these corrections, tropospheric delays were mitigated using the ERA-5 dataset, and terrain phase residuals were corrected by analyzing their correlation with vertical baseline time series. Any residual noise that could not be eliminated or modeled was evaluated using the root mean square (RMS) method. The final RMS values for the ascending and descending tracks were determined as 9.56 mm and 7.73 mm, respectively, confirming the reliability of the derived deformation solutions. The deformation rate was then estimated, and the results were averaged to generate time series deformation data and mean deformation rate maps.

SBAS-InSAR and PS-InSAR were complementary techniques in this study, each addressing the limitations of different SAR datasets and environmental conditions. SBAS-InSAR was selected for Sentinel-1 data processing due to its ability to generate continuous deformation time series with high spatial density, benefiting from short revisit intervals and improved coherence. However, for early SAR missions (ERS-1/2 and ALOS-1), where long temporal baselines and lower data acquisition frequency resulted in reduced interferometric coherence, PS-InSAR was adopted. The PS-InSAR approach, with its robustness in low-coherence and decorrelation-prone environments, allowed us to reliably extract deformation signals from historical datasets. This integrated strategy ensured that both long-term historical and recent surface deformation characteristics of Edgecumbe Volcano were accurately captured.

3.1.2. PS-InSAR

To complement the SBAS-InSAR analysis, the Permanent Scatterer InSAR (PS-InSAR) technique was employed for processing historical SAR datasets (ERS-1/2 and ALOS PALSAR), which are characterized by longer temporal baselines and lower acquisition frequency. PS-InSAR leverages the phase stability of Permanent Scatterers (PS), making it particularly suitable for low-coherence scenarios and regions affected by significant decorrelation, such as in snow-covered volcanic summits. This robustness enables the reliable extraction of deformation signals from sparse or noisy datasets, providing essential long-term deformation information that complements the continuous and dense time series derived from SBAS-InSAR. Since its first application at Mount Etna in Italy in 1995, PS-InSAR has been widely adopted for monitoring volcanic deformation [36,37]. The persistent snow cover on volcanic summits, which often leads to decorrelation, can complicate traditional InSAR processing [38,39]. To address this, multi-temporal InSAR (MT-InSAR) methods [40,41], including PS-InSAR, were introduced, with significant success in volcanic monitoring.

The PS-InSAR algorithm models the SAR signal as a sum of spatially correlated and uncorrelated components [13]. The spatially uncorrelated component is isolated by subtracting a spatially filtered interferogram from the original interferogram, a process known as interferogram filtering. After extracting Digital Elevation Model (DEM) errors through a least-squares solution, the noise level of the spatially uncorrelated component is estimated using a defined estimator. This method helps remove atmospheric and topographic errors, enabling the accurate extraction of surface deformation.

In practice, PS-InSAR works by organizing multiple SAR images (N + 1) taken over time [37,42]. One image is chosen as the “super-master” image, with the remaining N images serving as auxiliary images. These auxiliary images are co-registered and resampled to match the coordinate system of the super-master image, creating a series of interferograms. Once processed, N interferometric phase maps are obtained. Point optimization algorithms are then applied to extract PS points from the time series radar images, separating atmospheric and topographic errors to obtain surface deformation data for each point [43,44,45,46].

The key to successful PS-InSAR analysis is the accurate selection of PS points [47]. Traditional methods may struggle in areas with dense vegetation or complex surface conditions, such as volcanic regions, where surface clutter hinders the identification of stable PS points. To overcome these challenges, this study employed an enhanced version of the Stanford Method for Persistent Scatterers [48,49] (StaMPS). This method uses statistical filtering to select PS points, improving PS point density and reliability in areas with heterogeneous or complex surfaces.

The StaMPS algorithm utilizes a combination of interferometric phase spatial correlation and amplitude dispersion to select PS points. By applying these statistical filters, it ensures that only stable points with consistent scattering properties are selected. This approach significantly improves PS point density and reliability in non-urban areas, such as volcanoes, where traditional methods may struggle.

For this study, PS candidate points were initially selected using an amplitude dispersion threshold of 0.4 [48,50]. Stable points with gentle slopes were chosen as reference points for further analysis. The StaMPS method was applied to SAR data from ERS-1/2 (1992–2000) and ALOS PALSAR (2007–2010). Two master images acquired on 6 August 1995 and 29 August 2009 were selected for the interferometric time-series analysis, and the spatiotemporal baseline generated from SAR images (after excluding winter-season imagery) is shown in Figure 4. This allowed for the generation of detailed surface deformation fields for Edgecumbe Volcano, enabling the precise monitoring of volcanic activity and its relationship with seismic events.

This methodology offers a novel approach for monitoring surface deformation in volcanic regions, particularly those with significant vegetation cover or complex terrain. By accurately capturing time series deformation data, it provides valuable insights into the underlying mechanisms of volcanic activity and advances the application of InSAR technology in volcanic monitoring.

3.2. Mogi Model for Volcano Inversion

Based on the surface deformation characteristics of Edgecumbe Volcano obtained from the InSAR data and historical records, we performed further inversion using the point pressure source model [51]. The Mogi model describes the surface deformation caused by a point pressure or expansion source embedded in an elastic half-space, which is particularly suited for inverting symmetric surface deformation fields [52,53].

To begin, we downsampled the accumulated LOS deformation data using a variance-based algorithm. This process appropriately weights the near-field and far-field pixels to account for the differing information they carry while also balancing the two orbital tracks. The downsampled displacement fields, consisting of 170 and 116 pixels from paths 174 and 50, respectively, were then applied to the MCMC Bayesian inversion method. This method, implemented using quadtree sampling in the GBIS algorithm, generates 100,000 sample solutions after the burn-in period of the samples. The Poisson’s ratio is typically set to 0.25 in this inversion process.

The main advantage of using the point-source model is its computational simplicity and high reliability when simulating symmetric surface deformations such as radial deformation caused by magma intrusion. The model effectively simulates the radial symmetry of volcanic deformation due to magma movement beneath the surface, making it an ideal tool for understanding volcanic activity and its relationship with the surface displacement observed in the InSAR data.

For the volcanic magma source inversion in this study, we used the open-source Geodetic Bayesian Inversion Software (GBIS1.1). The specific inversion steps were as follows. (1) Deformation data downsampling: the deformation results were downsampled using the quadtree method. (2) Multi-source inversion with Mogi model: the Mogi model was applied to jointly invert for the volcanic source using multi-source data. (3) Convergence curve and posterior distribution: the inversion outputs included the convergence curve of the model parameters, as well as the posterior distribution probability of the model. (4) Model results: the final inversion results included the surface deformation field, residuals, and the optimal solution for the parameters of the volcanic source. This methodology allowed for the inversion of the volcanic magma source’s location and volume changes, providing valuable insights into the ongoing volcanic activity at Edgecumbe Volcano. The specific inversion steps were as follows (Figure 5).

4. Results

4.1. Coherence Analysis

4.1.1. Winter Snow Cover

In this study, SBAS-InSAR technology was first applied to process the data, using 23 scenes of ALOS-1 data to generate 79 interferograms, 138 scenes of Sentinel-1A data to generate 435 interferograms, and 166 scenes of Sentinel-1B data to generate 585 interferograms. This section presents a coherence analysis using ALOS-1 as an example.

Figure 6 shows the coherence maps generated from ALOS-1 imagery. The coherence coefficient ranged from 0 to 1, with the yellow areas representing the highest coherence and the blue areas showing the lowest coherence. In Figure 6a,b, significant decorrelation is observed in the region marked by red circles, which was caused by the snow cover on the summit of Edgecumbe Volcano during February, as the snow had not yet melted. In contrast, Figure 6c shows good coherence in the same region, as the snow had melted by August and the following April, revealing an exposed surface.

By analyzing the interferometric pairs of ALOS-1 and Sentinel-1 images [54], it was found that the decorrelation period at the volcanic summit typically occurs between November and March each year, during the winter season. To avoid the impact of decorrelation, this study excluded image data acquired from November 1 to March 31 each year. As a result, 11 scenes from ERS-1/2, 12 scenes from ALOS-1, 99 scenes from Sentinel-1A (generating 299 interferometric pairs) and 98 scenes from Sentinel-1B (generating 316 interferograms) were retained.

4.1.2. Summer Vegetation

Figure 7 presents the coherence map generated from ALOS-1 imagery. The regions highlighted in purple or blue in the image represent areas with low coherence. Notably, high coherence was observed at the summit of Edgecumbe Volcano from July to October while a significant area of decoherence was present on the island during the summer months. This decorrelation was primarily due to the surface vegetation, which caused changes in the radar backscatter over time. As the vegetation grew and varied seasonally, the radar pulses were unable to consistently capture the surface phase, leading to a loss of coherence in the interferometric pairs.

A statistical analysis of the ALOS-1 and Sentinel-1 interferometric pairs reveals that the lower-elevation regions on the island, where vegetation is denser, exhibited reduced coherence while high-coherence periods at the summit aligned with the dry summer season. This indicates that vegetation-induced decorrelation is more prominent in lower-lying, vegetated areas while the summit remains stable during the summer.

Therefore, non-winter imagery (excluding the period from November to March) was selected for the long-term monitoring of surface deformation at the volcano as these images provided better temporal coherence and more reliable data for deformation analysis.

4.2. LOS Deformation Field Analysis

4.2.1. ERS-1/2 LOS Deformation Analysis

By analyzing the average deformation rate for ERS-1/2 data from 1992 to 2000 (Figure 8a), it was found that the overall average rate of deformation for the island where Edgecumbe Volcano is located was approximately ±10 mm/yr. During this period, seismic activity was minimal, and the volcano was almost in a stable state. Therefore, the ERS-1/2 deformation results were not included in the subsequent inversion analysis to avoid any potential impact on the inversion outcomes. We also extracted co-located points from 1992 to 2010 for analysis and performed a time series analysis of the early volcanic surface deformation, described in the next subsection.

4.2.2. ALOS-1 LOS Deformation Analysis

We first extracted the surface deformation field from the ALOS-1 sensor data for the non-winter period between 2007 and 2010, which showed an initial uplift followed by subsidence, with the most noticeable deformation occurring at the volcanic summit. The surrounding area exhibited a stable trend, as shown in Figure 9.

By observing the average deformation rate map for ALOS-1 data from 2007 to 2010 (Figure 8b), it was found that the overall average deformation rate of the island where Edgecumbe Volcano is located increased compared to the 1992–2000 period. The LOS deformation rate at the volcano’s summit showed an overall decreasing trend, with the maximum subsidence rate reaching −26 mm/yr. These results indicate that the volcano and surrounding areas experienced a slow subsidence process from 2007 to 2010. Further analysis incorporating seismic data and other geological information is needed to gain a deeper understanding of the volcanic activity during this period.

The time series results of four homologous points extracted from the ERS and ALOS-1 deformation fields are shown in Figure 10. It can be observed that during the period from 1992 to 2001, the volcanic surface remained generally stable, with a maximum Line-of-Sight (LOS) deformation rate of 2 mm/yr. Between 2007 and 2011, points A1 and A3, which were stable surface feature points located away from the volcanic crater, showed no significant deformation. In contrast, points A2 and A4, which were surface feature points selected at two volcanic craters, exhibited a subsidence trend, with LOS deformation rates of −5.7 mm/yr and −4.6 mm/yr, respectively. This indicates that Edgecumbe Volcano began to show slight activity as early as 2007.

4.2.3. Sentinel-1 LOS Deformation Analysis

This section presents the analysis of the surface deformation from the Sentinel-1A/B time series deformation maps (Figure 11). From 2015 to 2018, the surface remained largely stable, but, after 2019, the volcano began to experience rapid uplift, with the cumulative LOS deformation in both ascending and descending orbits exceeding 200 mm. Further analysis of the volcano’s surface deformation activity is provided, based on recent deformation rate maps, cumulative deformation maps, and co-located points.

The deformation rates for Sentinel-1 descending orbit from 2015 to 2021 and ascending orbit from 2017 to 2023 are shown in Figure 12, with the corresponding cumulative deformation maps presented in Figure 13. From 2015 to 2021, the maximum deformation rate in the descending orbit was 36 mm/yr, with a maximum cumulative deformation of 210 mm. For the period from 2017 to 2023, the maximum deformation rate in the ascending orbit was 45 mm/yr, with the maximum cumulative deformation reaching 250 mm. Due to the absence of Sentinel-1 descending orbit data after the end of 2021 and the recent intensification of volcanic deformation, the surface deformation in the ascending orbit has become significantly larger than that in the descending orbit. As a result, the deformation rate in the ascending orbit is also higher.

To further analyze the temporal variation of volcanic deformation, three co-located points from both ascending and descending orbits were selected, with their locations shown in Figure 13. The time series for these points are presented in Figure 14. Points A1, A2, and A3 were selected from the ascending orbit, and their corresponding time series are shown in Figure 14b. Points D1, D2, and D3 were selected from the descending orbit, and their time series are shown in Figure 14a. The results indicate that the time series for the co-located points from both orbits show an overall uplift trend during the monitoring period of Edgecumbe Volcano, especially after August 2018.

Further linear fitting was applied to the time series with the highest deformation rates after August 2018. The fitting period for the ascending orbit was from August 2018 to October 2022, and for the descending orbit, it was from August 2018 to October 2021. The results show that the maximum average annual deformation rate for the ascending orbit reached 68 mm/yr while that for descending orbit reached 67 mm/yr, indicating very active volcanic activity at Edgecumbe Volcano between 2018 and 2022.

Additionally, from the deformation data at the end of 2023 for the ascending orbit (shown in Figure 14b), it is evident that the rate of uplift had significantly decreased, suggesting a reduction in volcanic activity and a gradual return to stability. This was consistent with the deformation trend reported in the official Edgecumbe Volcano Advisory from the USGS.

4.3. Sentinel-1 Deformation Field Inversion Results

By establishing the relationship between surface deformation and model parameters, and using surface geometric deformation as a constraint, it is possible to infer information about the Earth’s internal structure and the location of deformation sources [55,56]. This study focused on the surface deformation of Edgecumbe Volcano and used the Mogi volcanic model inversion method to establish the relationship between surface deformation and the volcanic magma source. This approach allows the long-term volumetric change of the magma source to be determined. The relationship between magma source volume changes and seismic activity in the surrounding area was then analyzed to investigate the connection between volcanic and seismic activities.

First, a variance-based quadtree sampling algorithm was applied to downsample the Sentinel-1 ascending and descending LOS deformation fields. The number of quadtree sampling points was 116 for the descending orbit and 170 for the ascending orbit. The downsampled pixel points were then input into the Bayesian inversion method using the MCMC approach. This method utilizes the Metropolis–Hastings algorithm for sampling, which is implemented in the pymc library. It was assumed that the input parameter space had a uniform prior distribution, and after the burn-in period, 100,000 sample solutions were generated. The final inversion results for the Sentinel-1 ascending and descending orbit models are shown below.

The model inversion results indicate that the Mogi model effectively reproduces the Sentinel-1 ascending and descending LOS surface deformation fields. The Mogi inversion results for Edgecumbe Volcano from 3 April 2015 to 22 October 2023 show that the magma chamber at a depth of 5.4 km was undergoing expansion, with a cumulative volume increase of 57.8 × 10⁶ m³. The optimal inversion parameters for the Mogi model are listed in

Table 2. Optimal Mogi model inversion parameters for the period from April 2015 to October 2023.

Model Parameter	Parameter Value
Reference point position (°)	(−135.7464W, 57.0533N)
X (m)	864
Y (m)	771
Depth (m)	5438
DV (m3)	57.8 × 106

. The Mogi model inversion deformation fields and residuals for the Sentinel-1 descending and ascending orbits are shown in Figure 15 and Figure 16, respectively.

5. Discussion

The results of the InSAR inversion provide an idealized representation of the volcanic activity characteristics. Based on the time series surface deformation data of Edgecumbe Volcano, the Mogi model was employed to invert the geometric parameters of the volcanic source and its temporal volume changes [53,57]. These findings were further analyzed in conjunction with nearby seismic activity to examine the correlation between volcanic and seismic events.

The seismic data for Edgecumbe Volcano and the surrounding region were retrieved from the specified search range, as shown in Figure 1. Efforts were made to include all seismic events that could potentially influence volcanic activity. A total of 1652 seismic events of magnitude 1 or higher, including ice-induced earthquakes, were recorded between 1992 and January 2023. The following sections provide a detailed analysis of the relationship between the volcanic source volume changes, surface deformation, and nearby seismic activity, exploring their interconnections.

5.1. Relationship Between Volcanic Source Volume Change and Seismic Activity

To obtain the time series volume changes of the volcanic source, a total of 124 single-track and multi-track joint inversions were conducted using Sentinel-1A/B data for Edgecumbe Volcano. The joint inversion results of Sentinel-1 ascending and descending tracks from 2015 to 2023 show that the magma reservoir at a depth of 5.4 km beneath Edgecumbe Volcano had been continuously expanding, with a cumulative volume increase of 57.8 × 10⁶ m³. The time series variation in volcanic magma source volume and the monthly seismic event statistics are shown in Figure 17. From the figure, it is evident that between 2015 and August 2018, seismic activity was minimal, and the volcanic magma source remained stable, with little to no change. However, in August 2018, seismic events occurred near the volcano, triggering the rapid expansion of the magma source and subsequent intensification of surface deformation. In April 2022, a series of seismic events further destabilized the magma source. By the end of 2023, seismic activity in the region had decreased, and the rate of magma source expansion slightly reduced. The time series inversion results indicate that seismic activity had accelerated the expansion of the volcanic magma source, with the most pronounced effect occurring in August 2018, which also correlated with the intensification of surface deformation.

5.2. Relationship Between Volcanic Deformation and Seismic Activity

The seismic data analysis revealed that seismic activity in the region around Edgecumbe Volcano has significantly increased in recent years. This section compares the cumulative deformation data from three different sensors—ERS-1/2, ALOS-1, and Sentinel-1A—using corresponding points to examine the relationship with seismic activity. The cumulative deformation from the three sensors and the location of corresponding points are shown in Figure 18. The cumulative deformation data from 1992 to 2023, along with the monthly seismic event statistics, are presented in Figure 19.

The results show that, from 1992 to 2000, seismic activity was minimal and the volcanic surface remained relatively stable. From 2007 to 2010, seismic activity slightly increased, with the volcano experiencing a period of minor instability. During this period, surface deformation increased, and a localized subsidence trend was observed at the volcano summit. From 2015 to August 2018, seismic activity gradually increased, and the volcanic surface exhibited a slow uplift. However, from August 2018 to 2023, the volcano entered a period of disturbance, characterized by a significant surge in seismic activity. The rapid expansion of the magma source during this period was accompanied by enhanced surface deformation.

Based on the above analyses, it is clear that long-term volcanic surface deformation and changes in magma source volume indicate that seismic activity exacerbates volcanic deformation. The seismic events and seismic swarms after August 2018 played a key role in promoting the expansion of the magma source and the intensification of surface deformation. This resulted in a more pronounced surface uplift around the volcano.

5.3. Uncertainty Analysis

Early SAR datasets (e.g., ERS-1/2 and ALOS PALSAR) were constrained by the absence of precise orbit corrections and external validation sources (e.g., GNSS networks), which likely amplified the impacts of residual atmospheric delays and orbital errors on the derived deformation fields. To mitigate these uncertainties, we implemented a four-fold strategy: (1) selecting only non-winter acquisitions to eliminate snow cover interference, (2) addressing the decorrelation issues caused by excessively long temporal baselines in early SAR datasets (given the robustness of PS-InSAR under low-coherence conditions, we applied a complementary PS-InSAR processing strategy to analyze historical deformation trends from 1992 to 2010), (3) performing cross-platform consistency checks between ERS and ALOS time series, and (4) incorporating Sentinel-1A/B results to enhance temporal continuity and improve deformation tracking accuracy. While these efforts improved signal stability, the limited spatiotemporal resolution of early SAR data precluded definitive conclusions about pre-2010 deformation trends. Future work should prioritize integrating advanced tropospheric correction methods and multi-sensor fusion to enhance the robustness of long-term volcanic deformation monitoring.

The Sentinel-1 descending orbit inversion results (Figure 15) reveal a mirror-symmetric uplift pattern centered on the volcanic edifice. The observed deformation field (Figure 15a) exhibited a maximum LOS displacement of 200 mm, demonstrating close agreement with the modeled displacements (Figure 15b). Residual signals (Figure 15c) showed localized discrepancies concentrated northwest and southeast of the caldera, likely reflecting unmodeled magma conduit geometries or residual atmospheric artifacts. In contrast, the Sentinel-1 ascending orbit results (Figure 16) maintained comparable symmetry despite pronounced decorrelation noise in vegetated peri-volcanic regions (Figure 16c), attributable to seasonal vegetation dynamics and incomplete tropospheric delay correction.

Notably, both viewing geometries confirm the first-order validity of the Mogi model while highlighting its limitations in resolving shallow hydrothermal interactions or anisotropic medium properties. In this study, initial inversions using Yang’s inflationary source and Okada’s dislocation model failed to adequately reproduce the observed surface deformation or exhibited non-convergent behavior for key parameters. Comparative analyses incorporating prior volcanic studies, geological constraints, and the axisymmetric deformation characteristics confirmed the appropriateness of the Mogi model, which assumed an isotropic point source in an elastic half-space. While this approach provided geodetically consistent solutions, it inherently neglected fault interactions. The residual spatial patterns and model uncertainties underscore the necessity of integrating viscoelastic rheological constraints and fault geometry models in future studies to better characterize depth-dependent mechanical stratification and complex subsurface dynamics.

Additionally, we analyzed seismic events (M1+) within 20 km and 50 km of Edgecumbe Volcano, as illustrated in Figure 20. The temporal distribution of seismicity follows a three-stage evolution: a Stable phase, Disturbance phase, and Acceleration phase, aligning with broader regional seismic activity trends. However, the correlation between near-field seismicity and surface deformation or volcanic activity appears to weaken. This observation suggests that tectonic processes, such as fault zone activity, seismic events, and magmatic dynamics, may interact in a complex manner, inducing surface deformation even when spatially decoupled [16]. For instance, regional stress perturbations or energy release from distal earthquakes could modulate magma migration or fault network activity, thereby amplifying volcanic signals. In this study, the influence zone affecting Edgecumbe Volcano may have extended up to 120 km or beyond. Therefore, we selected seismic data within a 120 km radius for analysis and extended the range near fault zones accordingly.

6. Conclusions

In this study, multi-source SAR imagery from 1992 to 2023 was used to obtain nearly 30 years of historical surface deformation data for Edgecumbe Volcano. By analyzing and discussing the relationship between volcanic activity and seismic events, the following conclusions were drawn:

(1)

Seasonal factors, particularly winter snow cover and summer vegetation, significantly degrade interferometric coherence at Edgecumbe Volcano. To mitigate these effects, we implemented a winter data exclusion strategy, enhancing deformation measurement accuracy and reliability.

(2)

The surface deformation at Edgecumbe Volcano exhibited distinct periods of activity. From 1992 to 2000, the volcanic surface remained stable with minimal deformation. From 2007 to 2010, there was a slight increase in surface deformation, with an LOS deformation rate of −26 mm/yr. From 2015 to August 2018, the deformation rate slowly increased, with a gradual uplift observed. Between August 2018 and 2022, surface deformation intensified, with a maximum LOS deformation rate reaching 68 mm/yr. In 2023, the surface uplift rate slowed down, with values ranging between 20 and 50 mm/yr.

(3)

The joint inversion results from Sentinel-1 ascending and descending tracks, covering the period from 2015 to 2023, indicate the continuous expansion of the magma reservoir at a depth of 5.4 km beneath Edgecumbe Volcano. The cumulative increase in magma volume during this period was 57.8 × 10⁶ m³, contributing to the observed surface deformation. From 2015 to August 2018, the magma source remained stable, but after seismic events in August 2018, rapid expansion occurred, significantly accelerating surface deformation. In April 2022, a series of seismic events led to instability in the magma source, which slowed down in 2023 as seismic activity decreased.

(4)

The long-term volcanic surface deformation and changes in magma source volume indicate that seismic activity has a significant impact on the intensification of volcanic surface deformation. The earthquakes and seismic swarms after August 2018 played a key role in promoting the expansion of the magma source and exacerbating surface deformation, resulting in a more pronounced uplift around the volcano.