## 3 Materials and Methods
### Processing Techniques
#### 3.3.1 Sentinel-1
Each time a new SAR image (S1 IW SLC product) is downloaded by MOUNTS, it goes through a DInSAR processing chain with the preceding acquisition (shortest temporal baseline, typically 6-12 days) from the same relative orbit. Processing of the image pair is performed with SNAP, freely distributed by ESA, and managed through a Python API. Back-geocoding and terrain correction are by default achieved with the SRTM-3 DEM. No multilooking is performed, so that the ground pixel resolution of the output products is \(14\times 14\) m. We refer the reader to the Supplementary Material S1 for more details on the processing chain. The outputs are typically an interferogram and a coherence map. The interferogram depicts the deformation of the ground along the sensor's line-of-sight (LOS) direction, and is displayed with values ranging between 0 and \(2\pi\) which appear as a series of fringes (i.e., \"wrapped\" interferogram). The coherence is a measure of the interferometric quality, as it is related to the level of noise affecting the phase difference between the two SAR images. It ranges between 0 and 1, and reflects the degree of surface change, where values towards 0 indicate a loss of InSAR coherence (i.e., decorrelation). The main contributions to decorrelation are phase noise due to (i) the temporal change of the scatterers (e.g., vegetation, water, sand-covered areas will appear highly incoherent as the scatterers change continuously), (ii) geometric decorrelation (i.e., images have slightly different look-angles), and (iii) variation in atmospheric water vapor content. Although decorrelation usually renders interferograms useless for measuring ground deformation, it can be used to detect changes in the ground properties (e.g., emplacement of lava flows and eruptive deposits, delineation of eruptive fissures, etc.). Both the interferogram and coherence image are successively analyzed to derive quantitative parameters, which are meant to be plotted as time series and consequently inform on the evolution of relevant volcanic processes through time. The interferogram analysis is intended to detect strong ground deformation occurring in short time intervals (i.e., between two successive S1 acquisitions, usually 6 to 12 days apart), which typically imprint as multiple narrow fringes (one fringes in Sentinel-1 interferograms represents 2.8 cm displacement in the radar line-of-sight). Processes such as magma intrusion (dykes), caldera collapse, or sudden flank movements are typically detected. The deformation detection is performed using artificial intelligence, which recovers filtered phase gradients in wrapped geocoded interferograms. Unwrapping of the phase gradients is successively performed to recover a deformation map, from which a deformation score (DEF) informing on the amount of ground displacement is computed. The approach is described in detail in Section 3.4 and in Supplementary Material S2. The coherence map, on the other hand, is analyzed to derive a decorrelation score (COH), which counts the number of pixels below a given coherence threshold. Although this parameter can fluctuate due to a number of non-volcanic processes (see phase noise sources described above), it can be useful to track eruptive deposits (e.g., fresh lava flows, pyroclastic deposits, etc.). Hence, for each new SAR acquisition, an interferogram and coherence map are generated (shortest temporal baseline possible, typically 6 or 12 days), and disseminated on the website. From these, a deformation and decorrelation score are respectively computed, which are plotted as time series on the website.