*3.1. Ground-Penetrating Radar*

Several GPR campaigns were carried out at the Belvedere Glacier between 2016 and 2018. In October 2016, 29 GPR profiles were acquired with an air-coupled 70-MHz GPR monostatic antenna (Subecho-70, Radarteam), for a total surveyed length of 2169 m (blue traces in Figure 2). The antenna was connected to an IDS K2 TR200 acquisition unit and manually transported above the ground surface. Traces were recorded for a total length of 1000 ns, with a sampling of 1024 samples/trace, and georeferenced by means of a GPS Ublox EVK-5T system.

In March 2018, 22 radar profiles were acquired with the same air-coupled 70-MHz antenna (green traces in Figure 2) transported on skis, for a total length of 2696 m of acquisitions (trace length = 2000 ns, 2048 samples/trace).

Finally, in December 2018 a lower frequency (40 MHz, Subecho-40, Radarteam) air-coupled antenna was manually moved along 15 profiles (red traces in Figure 2) focused on the terminal sector of the northern lobe of the glacier, for a total length of 2169 m of acquisitions (total recorded trace length = 1200 ns, 1024 samples/trace). The acquisition setup is shown in Figure 3a. The same acquisition unit and georeferencing instruments of October 2016 were adopted in all the later campaigns. In all surveys, the snow cover on site was limited (from absent to a few tens of centimeters on the debris cover). Unfortunately, due to the rough and rapidly evolving topography of the glacier along the years, the opening and/or relocation of crevasses and diffuse instabilities in the frontal sectors, it was not possible to follow the same profiles in each survey operating in safe conditions. In addition, due to the shape of both low-frequency antennas and the encountered topographic conditions, it was not possible to direct drag the instruments on the glacier surface to maximize the coupling. In each survey, the antenna was consequently maintained a few centimeters above the thin layer of snow partially hiding the cover of blocks and debris of the glacier (Figure 3a).

− **Figure 2.** Geophysical surveys carried out at the Belvedere Glacier. Green lines: 70-MHz ground-penetrating radar (GPR) profiles acquired on October 2016; blue lines: 70-MHz GPR profiles acquired on March 2018; red lines: 40-MHz GPR profiles acquired on December 2018. GPR profiles are labelled with a progressive number for each survey. Yellow dots (**A**–**D**): Single-station passive seismic measurements (HVSR method). Orange lines (**FF'** and **GG'**): Past cross-sections of the glacier interpreted from radar measurements, from VAW-ETH [36]. The background orthophoto was acquired during summer 2015 (AGEA 2015, RGB orthophoto, WMS service at www.geoportale.piemonte.it). The black dashed line highlights the approximate glacier perimeter in October 2016 (first GPR campaign).

Data processing was performed in ReflexW software. A basic processing procedure was adopted: (i) Start time of each trace was shifted to delete samples before the main bang and obtain exact zero time; (ii) low-frequency components were removed (dewow); (iii) high-pass horizontal filtering was applied to remove horizontally coherent components (background removal); (iv) geometrical spreading correction was applied, to gain signal amplitude with depth (divergence compensation).

Manual picking of the ice bottom reflections was finally performed on the processed time sections. Due to the reduced snow cover during the surveys, the picking of the reference glacier topography (corresponding to the top of the debris cover) was neglected. A uniform ice velocity of 0.17 m/ns was considered for a time to depth conversion, disregarding the top debris cover. The latter is expected to have significant lateral and vertical variations, from a few centimeters up to a metric thickness in correspondence of boulders and blocks.

**Figure 3.** On-site operations for GPR and passive seismic acquisitions. (**a**) GPR instrumentation and acquisition setup. Note that the GPR antenna is not ground-coupled, but maintained a few centimeters above the ground surface during acquisition. (**b**–**<sup>e</sup>**) Installation of the broadband triaxial seismometer and passive seismic instrumentation details.

#### *3.2. Single-Station Passive Seismic Measurements*

Four single-station passive seismic measurements were carried out on the N lobe of the Belvedere Glacier (A to D, in Figure 2). A 3-D 1-Hz broadband seismometer (L-4-3D, Sercel Inc.) connected to a 24-bit 3-channel digitizer was adopted for the acquisitions. To obtain the best coupling between sensor and ice, the surface layers of snow, ice, and debris were removed. The 3D seismometer was placed in direct contact with compact ice and then buried with the excavated materials to minimize external noise (Figure 3b–e). At each station, noise recording lasted from 30 to 45 min, with a sampling frequency of 100 Hz.

Details on the theoretical formulation and assumption underling the application of the HVSR methods in a glacial environment can be found in Picotti et al. [27]. If the width of the glacier is considerably larger than the ice thickness, the subsurface conditions can be approximated with a 1D model for which:

$$f\_0 = \frac{V\_S}{4H'} \tag{1}$$

where *f* 0 is the resonance frequency depicted from the HVSR curve, *VS* is the average S-wave velocity of ice and *H* is the ice thickness. If 2D effects are present at the station, *f* 0 value should be multiplied by correcting factors accounting for the shape of the basin [27,40]. Station locations along the axial position of the N lobe were chosen to minimize 2D lateral effects, due to the valley sides.

HVSR computation was carried out in Geopsy software. The original recordings (30–45 min) were divided into 120-s non-overlapping windows. An anti-triggering STA/LTA (short time average over long time average) algorithm was applied to each time window. This filtering procedure is based on the computation of the average signal amplitude over short (STA = 1 s) and long (LTA = 30 s) moving windows. If the STA/LTA ratio exceeds user-defined thresholds (STA/LTA < 0.2 or STA/LTA > 2.5, in this study), the window is filtered out from further computations. Otherwise, amplitude spectra of the horizontal components are combined using vector summation and the horizontal to vertical spectral ratio is computed. A smoothing function, with a 10% cosine taper and a bandwidth coefficient of 30 [32], was then applied to the resulting HVSR curve to ensure a constant number of points at low and high frequencies. This computation was repeated for all the 120-s windows passing the anti-triggering filter. The average curve and the standard deviation over the accepted HVSR curves were finally obtained. The spatial directivity of the HVSR peaks was computed using the same processing parameters, to check for the absence of 2D effects on the detected resonance frequencies.

The results were analyzed to search for HVSR peaks clearly indicating the presence of sharp subsurface contrasts in acoustic impedance and potentially estimate their embedment depth. Since no clear peaks were detected, further processing attempts, including inverse [41] or forward modeling [42,43] of the measured HVSR curves were not undertaken.
