Testing Automatic Detection Algorithms of Volcanic Unrest in SAR time series using Synthetic data

The increasing availability of free and global satellite Interferometric Synthetic Aperture Radar (InSAR) data, combined with the development of automatic InSAR processing chains operating at regional to global scales makes it possible to obtain dense and regularly updated spatio-temporal measurements of ground deformation over hundreds of active volcanoes worldwide. This growing volume of InSAR time series offers new opportunities for operational monitoring, but raises significant challenges for automated analysis and interpretation. Surface deformation reflects magmatic and hydrothermal processes associated with magma storage, pressurization, migration and withdrawal within volcanic plumbing systems and may constitute a precursory signal during the early stages of volcanic unrest. From an operational perspective, automatic detection of the onset of deformation in SAR time series is required to support early warning strategies, but it remains a major methodological challenge. Early-stage deformation signals are low-amplitude, spatially heterogeneous, and temporally non-stationary, while InSAR observations are affected by atmospheric delays, temporal decorrelation, and topography-related noise. These effects significantly reduce the detectability of deformation, particularly at active volcanoes characterized by low signal-to-noise ratios, raising the question of how early deformation can be detected with statistical confidence. Machine learning approaches based on convolutional neural networks (CNNs) rely on spatial pattern recognition to detect deformation signals on individual interferograms. CNNs require the use of extensive training datasets across many volcanoes, and often do not consider temporal information. As a result, the approach is more suitable fo scenarios with large signal-to-noise ratios. Additionally, independent component analysis (ICA) exploits both spatial and temporal information. However, it requires long-duration and complete time series to separate persistent deformation signals from noise and relies on the assumption of statistical independence between deformation and noise components. Here, we propose an operational detection framework that jointly exploits the spatial and temporal structure of InSAR data, enabling the identification of coherent deformation signals while explicitly accounting for their spatio temporal evolution. This study investigates detection strategies for the automatic identification of volcanic deformation in synthetic SAR time series coupling deformation signals and noise sources. Synthetic deformation scenarios representative of different volcanic processes, including linear, exponential, and transient inflation or deflation driven by analytical models (Mogi, Okada), are generated and embedded within spatially and temporally correlated atmospheric noise fields, providing a ground-truth framework to evaluate detection performance under varying deformation regimes and noise conditions. Recursive filtering techniques, such as Kalman filters, are considered to improve signal-to-noise ratio and enable continuous tracking of deformation in the presence of irregular acquisitions. Probabilistic change-point detection methods are investigated to identify transitions in deformation regimes and assess the likelihood of deformation onset, particularly at early stages. In parallel, cumulative detection statistics are examined, based on persistent exceedances relative to background noise variance, including the spatio-temporal CUSUM method, in order to exploit both the temporal persistence and spatial consistency of deformation signals. By comparing and combining these methods, the framework aims to identify which detection strategies are most appropriate for different unrest scenarios and noise environments.