On the Earth, climate fluctuations are expected to cause significant impacts on glaciers and the potential for natural hazards . The behaviour of ice masses is significantly influenced by geological, thermodynamic, and hydraulic processes occurring at the basal interface. Nevertheless, the hardly accessible nature of the ice–bedrock interface makes mapping of its heterogeneity a challenge. Ground-penetrating radar and active seismic techniques are commonly used for an investigation of physical properties of the subsurface glacier mass. These methods are not suited for repeated surveys within significant timescales capturing hydraulic changes over weeks to months. Moreover, the extent to which these methods retrieve spatio-temporal basal properties that affect ice flow is debated .

An alternative way to monitor glacial conditions with high spatio-temporal resolution and relatively low-cost acquisition is by analysing sustained ambient seismic vibrations . Studies have shown that the seismic power measured on glaciers can serve as a proxy for subglacial discharge and the hydraulic conditions in the subglacial conduits . Furthermore, the glaciohydraulic tremors can also be used to map the water pathways beneath glaciers in space and time . In addition to that, seismic interferometry can monitor subglacial properties such as ice anisotropy and bedrock material by probing subsurface seismic velocities and changes thereof . was able to extract transient velocity changes over 12 years related to the surging cycle of Bering Glacier (Alaska), which he attributes to the transition of an efficient channelized to an inefficient distributed drainage system (and vice versa).

In earthquake seismology, the horizontal-to-vertical spectral ratio (HVSR) analysis of ambient vibrations (i.e. seismic noise) is a widely applied technique that is used to determine a site's resonance frequency (f0), as well as its peak amplitude . The HVSR provides information on subsurface properties like shear-wave (S-wave) velocities, layer thickness, and site response to incident seismic waves (i.e. ). HVSR measurements are purely passive and thus non-invasive for the environment and only require a single station deployment. The HVSR is obtained by calculating the ratio between the Fourier amplitude spectra of the horizontal and vertical components of a seismic recording . HVSRs are typically calculated over a range of frequencies, giving rise to an “HVSR curve” with a characteristic peak–trough structure. The ambient vibration diffuse wavefield has a significant contribution of Rayleigh waves, which are dispersive seismic surface waves with elliptical particle motion that depends on the subsurface structure . Small contributions of Love and body waves may include the wavefield and contribute to the peaks in the HVSR curve by amplifying horizontal ground motion .

In cryoseismology, the HVSR curves have been used to invert for velocity profiles of the ice or firn , to obtain bedrock topography , and to identify the presence of basal sediments . These studies present HVSR curve computations for short time periods (1–12 h). However, seismic resonances within the soft ice layer and resulting HVSRs are expected to vary with changes in subglacial conditions on diurnal and seasonal timescales. Seismic wave velocities decrease in the presence of drained basal sediments , water, or air , making them dependent on the geological setting as well as spatial and temporal variations in hydraulic conditions. found that seasonality in HVSR is related to the variability in the active permafrost layer. At the same time, pitfalls in HVSR measurements exist in permafrost monitoring as they are influenced by changing noise conditions in addition to freeze–thaw variations within the soil. Consequently, given varying thermal and hydraulic conditions in cryospheric processes, short-period recordings of ambient seismic vibrations can lead to biases in HVSR curves.

Here we apply the HVSR method to seismic records of Glacier de la Plaine Morte, Europe's largest plateau glacier in Switzerland's Bernese Alps . Variations in the peak–trough structure of the HVSR curve reflect hydraulic changes beneath the ice surface, and we support this finding with additional noise-based seismic analysis. We interpret these changes in terms of temporary water storage as a response to the subglacial drainage of a nearby ice-marginal lake. Our results underline the value of passive seismic noise measurement and the HVSR method to monitor hydrological changes in the glacier in the subglacial environment. Here, we define the subglacial environment as the area near the ice–bed interface, which can encompass fractures and voids in the glacier sole as well as the top layer of the bedrock or sediments.

Glacier de la Plaine Morte (Fig. ) is the largest plateau glacier in the European Alps and is located along the border of Switzerland's cantons of Bern and Valais. Ice flow is limited, and minor crevasses are mostly observed on the outlet glacier Rezligletscher . From the 5 km wide plateau, the Rezligletscher tongue flows northwards feeding the Trüebbach stream, which produces several proglacial waterfalls towards the northwest (outside of Fig. ). A lake, named Lac des Faverges, formed during the melt season at the southeastern margin of Glacier de la Plaine Morte (Fig. b). Since 2011, outbursts of Lac des Faverges have caused floods in the Simme Valley . In 2012, a detailed monitoring of lake-level variations, as well as proglacial discharge level, was initiated for early-warning purposes by the municipality of Lenk and the engineering company Geopraevent (Fig. d and e). The relation of water level to lake volume was inferred from digital elevation models acquired after each lake drainage. High-resolution lake-level records during the drainage allow us to determine the lake discharge dynamics during the drainage events. In addition, there exist daily surface melt estimates based on long-term, seasonal, in situ mass balance measurements at a network of sites, extrapolated and temporally downscaled with a distributed accumulation and melt model .

In 2016, Lac des Faverges' drainage initiated through a moulin at the lake margin (green cross in Fig. ) feeding the subglacial drainage system towards the glacier tongue . The drainage began on 27 August 2016 (day of year 240) in the evening, lasted approximately 6 consecutive days, and amounted to a volume of 2×106m3 of water (Fig. d). In the first 6 h of the drainage, the water escaped rapidly with a discharge of 40 m3s-1 (Fig. e). After the discharge peak, the lake level dropped to the elevation of the moulin inlet, and the connection between the moulin and the lake was disrupted. Subsequently, the lake established a new link with the moulin through a supraglacial channel, but this slowed down the drainage process. The drainage of the lake finished in the night from day 246 to 247.

Multiple seismic arrays were deployed on Glacier de la Plaine Morte during the summer of 2016 (see , for deployment and instrument details). In this study, we use the Lennartz 1 Hz shallow borehole array (PM01–PM06), located 250 m north of Lac des Faverges, deployed from late April (day 120) to early September (day 250) 2016. At the end of July (day 212), a sixth borehole sensor was added to the array (PM06; Fig. ). We process the three-component seismic data within the frequency range of 0.5–10 Hz, with a focus on extracting the fundamental seismic resonance frequency of the ice mass using HVSR curves. Over the 4-month recording period, we distinguish a pre-drainage phase (day 120–240) and drainage phase (day 240–248), which is subsequently divided into smaller phases (Fig. ), depending on the power spectral characteristics and knowledge of the subglacial processes from . We observe glacial hydraulic tremors already from day 237 onwards until the start of the drainage (day 240), when pressure is building up and fractures and conduits are formed. These are pre-drainage precursor hydraulic tremors that formed subglacial features like fractures and voids that enable the drainage later on. According to and , seismic tremors in the frequency range of 1–10 Hz are linked to the turbulent water flow and sediment transport within subglacial conduits. In the spectrogram, anthropogenic seismic signals are present at approximately 3–4 Hz and are characterized by a diurnal pattern (power maxima from 06:00 to 18:00 LT) on weekdays (Fig. b).

We compute hourly-averaged power spectra (PSDs) for the vertical and horizontal components at all stations in the Glacier de la Plaine Morte array for days 120–248 following the methodology described in to derive the spectral ratios. Ambient noise records of 1 h long time windows with 75 % overlap are used to calculate PSDs for each component within each time window. The PSDs are then averaged over an hour, and the horizontal-to-vertical spectral ratio (HVSR) is computed using Eq. (2) from . We included all data in the analysis, without removing transients, as the aim of the study is to evaluate the sensitivity of HVSR to spatio-temporal variations in both noise sources and medium properties. As demonstrated by through polarization analysis, the seismic wavefield in Glacier de la Plaine Morte behaves as in a 1D medium with no detected 2D or 3D resonances. Hence, Glacier de la Plaine Morte serves as an ideal location for evaluating the potential of the HVSR method.

To characterize the ambient seismic wavefield contributing to the HVSR curves, we employ matched-field processing (MFP; Appendix ) on the Glacier de la Plaine Morte array. The MFP back azimuth within the 3–5 Hz range is selected for presentation in the subsequent sections. This frequency range is chosen because it encompasses frequencies where surface waves become sensitive to deeper velocity structures, making it suitable for probing the basal interface at a depth of approximately 130–160 m .

As additional means of characterizing subglacial changes, we employ seismic interferometry. We follow the standard approach to recover virtual seismic surface waves from station-pair cross-correlations of noise records and apply it to the phenomenon of glacial lake drainage . This may elucidate a varying fracture state and/or water saturation as seismic velocity changes . In temperate glacier applications, the measurement of small seismic velocity changes is challenging as meltwater-induced noise sources are typically non-stationary and the scattering of seismic waves is limited . Here, we make use of the noise source around a back azimuth of 315°, which is stable for several consecutive days and which we identify as a proglacial waterfall (Fig. b). As this source lies approximately on the axis connecting stations PM01 and PM03, it falls within their stationary-phase zone . The direct wave travelling between the two stations can thus be extracted by cross-correlating the recordings of the waterfall noise .

To this end, we calculate daily stacks of cross-correlations obtained from consecutive 900 s windows of days 230–235 (pre-drainage) and 245–246 (drainage), as these days show a stable waterfall noise (Fig. b). For day 246, we discard the last 3 h, since other noise sources become active during that time window. Prior to calculating the cross-correlations, the raw recordings are bandpass-filtered and subsequently clipped at 3 times the standard deviation as well as spectrally whitened.

The resulting cross-correlations reside in a narrow frequency band around 4 Hz (Fig. a and b). As expected, for all considered days, a clear direct wave propagating from PM01 to PM03 emerges, which carries maximum amplitudes near the estimated travel time t, obtained by dividing the inter-station distance by a Rayleigh wave velocity of 2800 ms-1 (see Sect. ). Due to the short inter-station distance, this direct wave converges towards the auto-correlation but is slightly shifted to positive lag times, whereas the response at negative lag times is absent because of the one-sided illumination. However, individual phases exhibit a different travel time between pre- and post-drainage cross-correlations. This is visible by slightly shifted waveforms (Fig. 6b), and we interpret this shift (or delay) as a change in seismic velocity.

We systematically investigate this observation by directly calculating travel time delays between the considered days and a reference cross-correlation formed by stacking the 6 pre-drainage days. For this purpose, we rely on the wavelet cross-spectrum technique , which yields dt values as a function of lag time and frequency. To obtain high-quality results, we keep only those dt values associated with a minimum cross-coherence of 0.95 and a minimum cross-spectrum amplitude of 0.9 of its maximum value in the frequency range of 3–5 Hz, which focuses on the region near the estimated travel time. From the remaining dt values, we determine the median and the standard deviation and transform these values to velocity changes dv/v using the relation dv/v=-dt/t. As we are considering the direct wave (and not scattered waves), we do not apply a linear regression to obtain velocity changes but instead rely on the statistical analysis as detailed above.

For the pre-drainage period, dv/v values scatter around zero with a maximum deviation of 0.9 % relative to the reference, as shown in Fig. c. By contrast, results for the 2 drainage days show velocity drops between 3 % and 4 % (albeit with a somewhat higher standard deviation compared to the pre-drainage days), indicative of a medium change. For a detailed depth investigation of the velocity drop, a frequency-dependent velocity change would be required, which cannot be obtained due to a less favourable source distribution at higher frequencies (Appendix ). However, compared to a Rayleigh wave travelling within ice (velocity of around 1800 ms-1; ), the significantly higher wave speed at above 4 Hz, for which the interferometry results are representative, indicates that the extracted direct wave samples the glacier bed.

Next, we use Rayleigh wave ellipticity together with velocity dispersion curves to determine differences in the glacier's S-wave velocity structure between day of year 230 representing pre-drainage conditions and day of year 245 representing drainage conditions. Dispersion curves (Fig. a) are obtained using high-resolution beamforming (Appendix ) of the vertical component signals. The dispersion curve reveals a saddle and reduced phase velocities for frequencies below 5 Hz during the drainage period. The uncertainties of the dispersion curve below 5 Hz for the drainage period are lower than the velocities for the pre-drainage (Fig. ); hence we believe these lower velocities are reliable. The ellipticity curves (Fig. b) are computed using the RayDec tool developed by . RayDec extracts Rayleigh wave ellipticity from the ambient noise measurements based on the random decrement technique. The shape of the ellipticity curves is similar to the HVSR curves, but the absolute ellipticity values are smaller than the HVSR measurements, which may include additional signal content from other seismic waves such as Love and/or body waves. During the drainage the ellipticity curve exhibits a pronounced trough at about 4.4 Hz, which is a feature not present in the pre-drainage ellipticity data.

Based on the observations from the seismic analyses for the pre-drainage and drainage periods, water is stored in fractures and other void spaces near the base of the ice and results in a reduction in the seismic velocity. In the next sections we discuss how such a transient seismic velocity decrease can be explained in relation to changes in the subglacial environment, building upon insights from .

In this study, we analysed 4 months of continuous seismic records on Glacier de la Plaine Morte with the HVSR technique to capture spatio-temporal variations at the basal interface. We aim to assess the reliability of the technique in such a dynamic environment. Subglacial processes change the medium properties for propagating seismic waves, but simultaneously, the source of the seismic ambient noise field varies. HVSR changes primarily originate from fluctuations in nearby noise conditions influenced by hydraulic tremors, drainage-related events, moulin resonances, and anthropogenic sources. Despite these source-related influences, a discernible spatio-temporal trend in HVSR curves reflects material changes within and/or beneath the ice. An HVSR trough emerges after the subglacial drainage of Lac des Faverges, an ice-marginal lake. Seismic velocity changes of 3 %–4 % inferred from interferometry indicate a velocity drop at the ice–bedrock interface. Inversion and forward modelling of Rayleigh wave ellipticity and dispersion curves further refine the dimensions of this low-velocity zone. A low-velocity-layer thickness of 10–30 m is estimated and a seismic velocity drop of up to 40 %. Based on the seismic analysis and discharge anomalies appearing after the drainage, we suggest that the basal low-velocity layer can be explained by subglacial water storage in newly formed fractures after drainage. This layer has a local extent, reflected in the spatial variations in the HVSR trough throughout the array, and covers an estimated 4.5 %–27 % of the glacier area. Our results thus demonstrate that the HVSR technique can be used as an indicator of a spatio-temporal medium change at the ice–bedrock interface.

We suggest that a deeper understanding of the seismic noise field and the response of HVSR to a dynamic and changing subsurface is needed to make a reliable characterization of the medium using the HVSR seismic method on a glacier. In addition, stacking or filtering multiple days- to weeks-long time series of hourly HVSR data is necessary to smooth transient events and changes in noise sources, ensuring a reliable fundamental resonance frequency. Relying solely on a few hours of measurements could result in a significantly biased HVSR curve. The single-station HVSR methodology has demonstrated its potential on glaciers. The next logical step could involve its application in remote and less noisy regions, such as the Antarctic or Arctic ice sheets. Subsequently, a study focusing on temporal variations in the HVSR over multiple seasons could be pursued.