## 2 Data and Methods  
### SAR Data and Methods  
We analyzed a catalog of SAR amplitude images acquired by the Italian Space Agency (ASI) COSMO-SkyMed satellite constellation (CSK). The two values that characterize a SAR image are the azimuth and the range [36]. The SAR amplitude signal represents the intensity of the energy backscattered by all ground scatterers within a resolution cell (pixel) [37]. The signal backscatter is determined by the local incidence angle of the electromagnetic radiation, the surface roughness, the surface chemical characteristics, as well as the water content of the soil [20]. This difference in intensities makes recognizing the surface features and volcano eruption deposits possible [20]. As a result, rough surfaces facing the sensor (i.e., whose slope has a value close to the incidence angle) have a strong backscatter, which results in brighter pixels in the SAR image; conversely, surfaces with an opposite slope (backslope) are characterized by lower scattering values, resulting in darker pixels [20]. Data are displayed in greyscale maps, and white represents the highest amplitude and black the lowest. The images used in this study were acquired in both ascending and descending strip map (HIMAGE) mode with a spatial resolution of about 3 m and in HH polarization. Geometric distortions such as layover [38], foreshortening, and shadowing effects [22] (Figure 2) characterize the SAR images. With the help of an available digital elevation model (DEM), the geometric distortions from the layover and foreshortening areas can be corrected by means of geolocation procedures [22; 37]; the images can be converted into  
Figure 1: Study area. (**a**) The Canary Islands, highlighting La Palma Island inside the white box. (**b**) Close-up view of La Palma Island, highlighting the location of Cumbre Vieja Volcano inside the yellow box. (**c**) Close up of the 2021 eruptive cone showing a Skysat Image acquired on 31 December 2021 and indicating the location of the newly formed cone in 2021 in the red box. Here, it is possible to visualize the craters’ final surface structure and alignment. The white dots represent the location of three cameras, with their respective view angles, used to record the time-lapse images. a geographic (latitude, longitude) or cartographic (easting, northing) map projection for integration into GIS systems, thus allowing for easy comparison with other data [38]. In the case of rapidly and significantly changing topography, as in the La Palma example, the DEM would need to be updated before each acquisition for the terrain correction procedures to be effective. As theses DEMs were not available, some residual geometric distortions remain visible in our data. This however does not hamper their interpretation. Figure 2: SAR amplitude analysis. (**a**) SAR amplitude image taken on 29 September 2021. The white dots represent the location of the center of each of the craters. (**b**) Schematic perspective view of the geometric distortion caused by aligned craters. The dashed lines radiating from the satellite indicate the direction of the satellite’s line of sight (LOS). The oval black part represents the shadowed and elongated area of the crater, while the white shows the brightened and foreshortened opposite flanks in LOS. The dots represent the location of the crater’s centers located close to the transition area between dark and white to compensate for the elongation and foreshortening. (**c**) Amplitude profile analysis. The gray line represents the amplitude values extracted along the profile of the image from 29 September 2021. The profile was horizontally elongated for demonstration purposes. The peaks of the profile align with the brighter parts of the craters, meaning a higher amplitude signal. In the case of the fourth crater on the right side, only one flank was brightened, and the opposite flank was shadowed. Thus, the presence of this crater was corroborated in the intensity profile and the optical Unmanned Aircraft System (UAS) orthophoto.