Conference Agenda

Synthetic Aperture Radar Interferometry (InSAR) has become a cornerstone technique for the precise measurement of Earth’s surface deformation, enabling millimetric monitoring of phenomena such as urban subsidence, volcanic activity, and landslides. By exploiting the phase differences between radar acquisitions performed at different times, InSAR provides highly sensitive deformation measurements over wide areas and under nearly all weather conditions. The advent of systematic satellite missions such as Sentinel-1 has dramatically increased data availability, with free and frequent acquisitions every 6 to 12 days, leading to the generation of dense and high-dimensional SAR time series. While this abundance of data offers unprecedented opportunities for detailed temporal analysis of ground deformation, it also raises major challenges in terms of computational cost, memory requirements, and processing flexibility.

Traditional Multi-Temporal InSAR (MT-InSAR) approaches rely predominantly on so-called offline processing strategies, in which all SAR images in a time series are processed jointly. Although these methods are known for their statistical robustness and estimation accuracy, they suffer from several limitations. First, they exhibit high algorithmic complexity, often scaling cubically with the number of acquisitions. Second, they require significant memory resources to store and manipulate large covariance matrices. Third, they lack flexibility when new acquisitions become available, since integrating additional images typically requires reprocessing the entire time series. These constraints limit their applicability in operational contexts where near-real-time monitoring of continuously evolving deformation phenomena is required.

This work addresses these limitations by introducing a coherent methodological framework for the sequential estimation of interferometric phases in MT-InSAR. The central objective is to design algorithms capable of progressively integrating new SAR acquisitions while preserving the robustness and accuracy of state-of-the-art offline methods, and simultaneously reducing computational complexity and storage requirements. The proposed framework relies on a rigorous statistical modeling of SAR data, temporal correlations, and possible non-Gaussian behavior. In particular, the covariance matrix of the SAR time series is modeled in a factorized form that explicitly separates phase contributions from coherence structure, thereby enabling efficient parameter estimation strategies.

Three complementary sequential approaches are proposed.
- The first contribution, termed Sequential Maximum Likelihood Phase Linking (S-MLE-PL), extends classical Phase Linking methods into a sequential setting. Unlike conventional approaches that assume Gaussian-distributed SAR data, S-MLE-PL adopts a more general Scaled Gaussian model, which is better suited to heterogeneous environments and high-resolution imagery, especially in urban areas where heavy-tailed statistics are frequently observed. In this framework, when a new acquisition becomes available, the covariance matrix is updated in a structured block form, allowing the negative log-likelihood (NLL) function to be incrementally updated rather than recomputed from scratch. The joint estimation of the new phase, correlation parameters, variance terms, and scale factors is formulated as a constrained optimization problem. A Block Coordinate Descent (BCD) algorithm is derived, providing closed-form updates for each parameter block. This structured optimization significantly reduces computational complexity, from cubic dependence on the full time series length to quadratic dependence on the number of previously processed images, while maintaining estimation accuracy comparable to that of offline maximum likelihood methods.

- The second contribution, Sequential Covariance Fitting Phase Linking (S-COFI-PL), shifts the perspective from likelihood maximization to covariance matrix fitting. Instead of directly optimizing a statistical likelihood, this approach seeks to minimize a dissimilarity measure between the empirical extended covariance matrix (including new acquisitions) and a theoretical covariance model parameterized by the interferometric phase vector. This formulation naturally accommodates the integration of multiple new acquisitions simultaneously, making it particularly suitable for block-wise updates. The optimization is performed on the complex torus defined by unit-modulus phase vectors, under geometric constraints ensuring physical consistency. Depending on the structure of the chosen matrix distance, such as the Kullback–Leibler divergence or the Frobenius norm, the optimization is carried out using Majorization–Minimization algorithm. An important strength of this method lies in its flexibility: it can incorporate robust covariance estimators, including phase-only or regularized covariance matrices, thereby enhancing resilience to non-Gaussian disturbances and model mismatches.

- While the two previous methods still require storing historical acquisitions to update the covariance structure, the third contribution introduces a more memory-efficient strategy tailored to very long SAR time series. The proposed Sliding Interferometric Phase Linking (Sl-IPL) method relies on a sliding temporal window of fixed size, moving along the time axis with a specified overlap. Within each window, phase estimation is formulated as a covariance fitting problem under a circular complex Gaussian assumption. To ensure temporal consistency between consecutive windows, a penalization term enforces coherence between overlapping phase estimates. The optimization remains constrained to the unit-modulus torus, and the Frobenius norm is favored for its numerical stability and computational efficiency. By limiting the size of the processed covariance matrices, Sl-IPL achieves substantial reductions in both computational load and memory usage, while preserving performance close to full sequential methods.

The proposed approaches were validated on both simulated datasets and real SAR time series processed through a complete multi-temporal InSAR chain, including co-registration, interferogram formation, topographic phase correction, phase unwrapping, and line-of-sight displacement estimation. Two contrasted case studies were considered: an urban area affected by significant land subsidence in Mexico City, and a volcanic environment in Hawaii Island. The results demonstrate that the sequential methods achieve mean squared errors and deformation time series estimates comparable to those obtained with reference offline approaches. Furthermore, comparisons with independent GPS measurements, when available, confirm the geophysical consistency of the estimated displacements. From a computational standpoint, the benefits of the proposed sequential framework are substantial. Processing times and memory consumption are significantly reduced, enabling incremental updates of deformation time series as soon as new SAR acquisitions become available.

In summary, this work provides a comprehensive and coherent set of sequential methodologies for interferometric phase estimation in multi-temporal SAR analysis. By combining statistical robustness, optimization on complex manifolds, and efficient incremental updates, the proposed approaches address the growing challenges posed by dense and long SAR time series. They bridge the gap between high-accuracy offline processing and the practical requirements of scalable, near-real-time Earth deformation monitoring.

Synthetic aperture radar interferometry (InSAR) enables precise monitoring of surface and infrastructure stability. The increasing availability of InSAR data provides valuable opportunities for near real-time stability monitoring. To facilitate the systematic ingestion of newly acquired observations and the subsequent estimation of relevant parameters, Instantaneous State (IS) InSAR has been proposed as a novel framework for parameterizing the motion of InSAR scatterers. The method implements sequential estimation of the instantaneous kinematic state, e.g., position, velocity, and optionally acceleration, explicitly accounting for dynamic evolution between acquisitions by imposing smoothness constraints.

To enable near real-time displacement anomaly detection, we propose a strategy that preforms synchronously with data acquisition and state estimation within the IS-InSAR framework. The method is implemented on individual arcs between pairs of scatterers, without requiring full InSAR network construction, thereby allowing anomalous behavior to be detected promptly. A Chi-squared test is employed to assess the temporal stability for each updated observation. At each epoch, predicted phase residuals are evaluated for multiple subsequent epochs, and observations from these epochs are incrementally integrated into the detection framework, thereby enhancing redundancy and reducing the likelihood of missed detections. To evaluate the risk associated with detected anomalies, we introduce the risk depth, defined as the number of the most recent observations used to assess the risk of the current epoch. The risk at each epoch is categorized into different levels based on multiple preceding observations, e.g., a high-risk level is assigned when continuous anomalies are detected. By integrating multiple preceding observations, the risk depth enables a more robust assessment of the risk of anomalies and reduces the likelihood of false alarms compared to relying on a single observation.

The proposed approach is applied and evaluated using both Sentinel-1 and TerraSAR-X data. The results demonstrate that IS-InSAR effectively captures this dynamic behavior without relying on hindsight information. In addition, the reliability of anomaly detection is improved through the use of single- and multiple-update epochs, thereby reducing the likelihood of false alarms and missed detections. The method identifies anomalies associated with behavioral changes, including both deviations from the original motion pattern and transitions back to regular behavior, which is particularly important from a monitoring perspective. Furthermore, the method effectively detects anomalies simultaneously with the state estimation without re-evaluation of past observations, enabling near real-time monitoring.

Multi-track InSAR line-of-sight (LoS) displacements can be decomposed into full three-dimensional East–North–Up (ENU) motion given that the underlying deformation field is spatially smooth and exhibits coherent iso-displacement contours. Under these conditions, the strapdown decomposition method treats each Point Scatterer (PS) as an independent sample of the continuous displacement field. Thus, for every PS, a local Transversal–Longitudinal–Normal (TLN) coordinate system is defined, with the longitudinal axis aligned along iso-displacement contours (i.e., the zero-velocity direction), enabling a PS-specific ENU-to-TLN coordinate transformation.

However, this requires the multiple InSAR LoS datasets to be referenced to a common datum. Each LoS velocity field is defined relative to a track-specific datum, typically realized by, e.g., the mean displacement or by a Point Scatterer with minimum normalized amplitude dispersion (NAD). Even millimetric offsets between these datums will propagate into the 3D reconstruction, biasing both the magnitude and direction (sign flip) of the estimated ENU components. To overcome this issue, we incorporate datum alignment directly into the strapdown-based 3D decomposition framework, specifically adapted here to bowl-shaped subsidence.

We propose a modification to the original strapdown approach for subsidence regimes with smooth, radially inward deformation orthogonal to iso-deformation lines, with a sign convention that is positive toward bowl centers, consistent with gravity-driven motion. The method searches the TLN solution space to homogenize the overall displacement field. A bounded grid search aligns two Sentinel-1 LoS velocity datasets up to sub-millimeter per year precision and retrieves a physically consistent 3D displacement velocity field, including its full variance–covariance information.

Applied to Jakarta—one of the fastest subsiding megacities worldwide—we identify six subsidence bowls with vertical velocities reaching −7.9 cm/yr and significant northward horizontal motion up to 1.7 cm/yr. Beyond these localized bowls, the entire metropolitan area experiences slow regional subsidence, with a mean vertical velocity of −11.2 mm/yr across Jakarta. Nevertheless, the strongest subsidence occurs in northern and western neighborhoods, where access to municipal piped water is limited.

Relying solely on InSAR data, the modified strapdown decomposition exploits the spatial coherence of smooth iso-deformation contours and strong radial gradients of bowl-shaped deformation to jointly address two key limitations in InSAR-based displacement analysis: (i) reduced sensitivity to north–south motion and (ii) multi-track datum inconsistencies in the absence of GNSS constraints.

Multi‑temporal InSAR is widely used for infrastructure monitoring as it provides dense spatial sampling and regular temporal coverage. In many applications, empirical parameterizations or simple kinematic descriptions, such as combining a linear trend with a seasonal term, are sufficient to characterize the observed signals. However, in more complex settings the surface displacement field reflects multiple processes that are superposed in space and time and that depend on local geological and operational conditions. Reliable interpretation and prediction then requires a physics‑based model that causally links the measured displacements to some source mechanism. Such models usually depend on unknown local parameters, that often can not be robustly inferred from the either temporally or spatially sparse geodetic measurements that are available from levelling and GNSS. Long time series of InSAR data, however can provide the spatial and temporal density needed to identify and constrain these local parameters and to separate the signals of interest from confounding processes.

The storage cavern site Epe (North Rhine-Westphalia, Germany) displays spatiotemporally complex surface displacements. These displacements are primarily caused by 114 gas‑ and liquid‑filled caverns in a salt rock layer of different sizes and depths that are operated by different provider companies with distinct filling schedules. As the pressure inside a cavern is kept lower than the surrounding lithostatic pressure, the cavern converges over time due to viscoelastic creep. This convergence causes the surface above to subside. The magnitude and shape of these displacements vary spatially and temporally with cavern geometry, depth, local geological conditions, and operational practices. Each cavern produces an individual spatiotemporal displacement pattern, and these patterns superpose at the surface. In addition to cavern‑related deep‑source displacements, Epe also exhibits a strong shallow surface response to groundwater‑level variations in some areas of the cavern field, resulting in isolation of the cavern induced signals to be challenging.

We present an integrated monitoring and modeling approach for Epe that combines multi‑temporal InSAR, GNSS, and levelling to derive a geophysical source model that explicitly links cavern filling levels to convergence and surface displacements, while accounting for local geological conditions. We process ten years (2015–2025) of Sentinel‑1 acquisitions from four tracks in both ascending and descending orbits. Persistent and Distributed scatterers are used jointly to maximize spatial coverage in predominantly rural terrain. To separate the signals, we apply Independent Component Analysis to the InSAR time series to identify cavern‑induced displacements and to separate them from other correlated displacements, in particular those associated with groundwater dynamics.

The source model describes cavern convergence by accounting for transient (primary) and steady‑state (secondary) viscoelastic creep of rock salt. We combine a Kelvin–Voigt representation (similar to Even et al., 2022) with a cavern‑pressure‑dependent Norton creep law (as in Ślizowski et al., 2010). We then propagate cavern volume loss to the surface using a multi‑cavern variant of the Sroka–Schober model (Sroka et al., 2017), which relates the volume loss of each cavern at depth to their associated surface displacements. Model parameters that represent local geological conditions and salt‑rock rheology are determined through a global optimization of rheological and site parameters under a multi‑dataset misfit, using the InSAR time series as the primary constraint and GNSS and levelling as supporting datasets.

In our model, the lithostatic pressure is estimated from available depth and lithological information and is used to determine the stress state, defined as the pressure difference between the internal gas pressure and the estimated lithostatic pressure. Because temperature variations inside the caverns are relatively small, this stress difference predominantly controls the convergence rate. Since direct pressure measurements are usually not released by the provider companies, we substitute cavern pressure with the publicly available mean filling level curves per provider and impose assumed minimum and maximum pressures to bound plausible operating conditions. To address uncertainties in cavern depth and lithology, we include a per‑cavern lithostatic‑stress adjustment parameter that permits limited variation in the estimated lithostatic pressure and, consequently, in the inferred stress difference.

The final model enables daily 3D surface displacement predictions across the entire storage field. The modeled displacements show good agreement with the InSAR observations and with independent GNSS and levelling measurements. The estimated convergence is consistent with annual measurements of cavern convergence supplied by one of the provider companies. Remaining residuals are plausibly linked to the use of provider‑mean filling level curves instead of per‑cavern filling levels or exact pressure histories, and further reduction would be expected if individual cavern operational data was available.

Our work shows that the combined use of InSAR time series analysis and geophysical source modeling enables high resolution and accurate monitoring of cavern convergence induced surface deformation through local parameter derivation at underground energy storage sites such as Epe.