Evaluation of a snow avalanche possibly triggered by a local earthquake at Vallée de la Sionne, Switzerland

Snow avalanches are moving sources of infrasonic and seismic energy. They can be triggered by many different mechanisms that include the shaking produced by earthquakes. The forces induced by an earthquake can cause an increase in the load down the slope and can also decrease the shear strength and both effects can cause the release of an avalanche. This phenomenon represents an important hazard associated with earthquakes in snow-covered mountain areas with high seismicity. On 6 December 2010 a snow avalanche was released at the experimental site of Vallée de la Sionne (VDLS) in Switzerland seconds after a local earthquake of magnitude M L 3.1 with the hypocenter in France, approximately 43 km from the avalanche starting zone. The seismic and infrasound signals generated by the earthquake and the snow avalanche were recorded by an array of sensors installed at VDLS. This paper analyses these data and shows that the avalanche was possibly triggered by the earthquake. This analysis also allows us to determine the characteristics of the avalanche (type and path). The infrasound data shows that the time of the avalanche release coincided with the arrival of the seismic waves of the earthquake. We calculate the values of the ground vibration parameters (PGD, PGV, PGA, PSA, I a and TD) measured at the release area of the avalanche and compare them with those of two other earthquakes that did not trigger an avalanche. To evaluate the influence of the snowpack stratigraphy with the effectiveness of the earthquakes to trigger an avalanche, we simulate the snow cover using the one-dimensional snow cover model SNOWPACK. The weather and snow cover conditions of the days on which these events occurred are compared and used to evaluate the snowpack stability and the consequent likelihood of avalanche activity. The snowpack stability is the primary factor that determines whether an avalanche may be triggered by minor earthquakes. We conclude that when the snowpack is only marginally stable then the displacement caused by even a small earthquake could be enough to trigger an avalanche. Furthermore, the analysis of the other two, even stronger, earthquakes shows that in stable conditions no avalanche was triggered.


Introduction
In mountain areas snow avalanches cause significant economic losses and numerous fatalities. The snowpack develops over the winter and consists of different layers with widely varying physical properties which evolve according to the heat, water vapour A C C E P T E D M A N U S C R I P T 4 out with artificial snowpacks containing a weak layer over a shaking table have revealed that vibration reduces the effective shear strength by increasing the peak shear loading (Chernouss et al., 2006;Podolskiy et al., 2008;Podolskiy et al., 2010b). In cases of natural seismicity, a slab avalanche can be released by the loading due to accelerations produced by an earthquake. This loading produces an amplification of the stress that can cause a fracture between the snow layers (Higashiura et al., 1979). The shear stress amplification is larger at higher accelerations which depend on the earthquake magnitude, the hypocentral distance and local conditions (site effect).
We present a case study of an avalanche possibly triggered by a local earthquake at the Vallée de la Sionne (VDLS, Switzerland) test site operated by the WSL Institute for Snow and Avalanche Research SLF (SLF/WSL). VDLS is situated in Valais, in the western Swiss Alps, where the seismic hazard is moderate and higher than in the rest of Switzerland (Giardini et al., 2004). One historical example of a mass flow event triggered by an earthquake in the proximity of the VDLS site is the rock avalanche caused by the second M w 6 earthquake of the 1946 earthquake sequence (Moore et al., 2012). In the present study, data from two local earthquakes that did not trigger any snow avalanches were used for comparison. The intensity of shaking of these earthquakes is compared using six quantification parameters. In addition, we present an evaluation of the snowpack stability conditions comparing the nivo-meteorological situation and the snow cover simulations of the days in which they occurred. Finally the maximum cumulative displacement of the earthquake that possibly triggered the avalanche is calculated and compared with load-controlled experiments with layered snow samples (Reiweger et al., 2010a).

Experimental site and data
A C C E P T E D M A N U S C R I P T 5 The experimental site of Vallée de la Sionne ( Fig. 1) was built in 1998 by the SLF/WSL to study the dynamics of snow avalanches (Amman, 1999;Issler, 1999). At the site, snow avalanches of different types and sizes are released, naturally or artificially. Most of the snow avalanches are released from two main starting zones oriented in an East / South-East direction: Crêta Besse 1 with slope angles between 35º-40º and heights of 2300-2500 m a.s.l. and Crêta Besse 2 with slope angles between 30º-40º and heights of 2500-2700 m a.s.l. The starting zones are channelled between 1800-2050 m a.s.l. in two different channels: the main channel, termed as channel 1 and a secondary one, known as channel 2 ( Fig. 1). Both channels merge in the runout zone which has slope angles between 5º-20º between 1800 and 1450 m a.s.l.
Many different instrumentation systems are installed along the main avalanche path, channel 1. These include a seismic station (Table 1, (Table 1). All the measurements are recorded at a sampling rate of 100 Hz in two streams, continuous and trigger mode. One of the UB seismic stations is installed at cavern B, in the channel 1, at 1900 m a.s.l. A second UB seismic station is located at cavern C, close to an instrumented pylon at 1650 m a.s.l. (Sovilla et al., 2008;Sovilla et al., 2010) at the beginning of the runout zone. The third seismic station is situated at cavern D, in the opposite slope of the avalanche track, close to a shelter that operates as an instrumented A C C E P T E D M A N U S C R I P T 6 control centre (Fig. 2). In addition to the seismic stations, one infrasound sensor has been installed since the 2008 winter season near cavern D (Kogelnig et al., 2011). The infrasound sensor is a Chaparral, Model 24. This sensor is connected to the same data acquisition system of the seismic sensor of cavern D with a common timebase.
Furthermore, a Frequency Modulated Continuous Wave Phased Array radar (henceforth referred to as the GEODAR radar) is located at the shelter (Vriend et al., 2013;Ash et al., 2014). It can track the avalanche over the whole slope with a downslope spatial resolution of 0.75 m, and gives information on avalanche position, velocity and size.
The technical specifications were described in Ash et al. (2010). The system emits up and down chirps, with a bandwidth of 200 MHz centred at 5.3 GHz, of different lengths from a single transmitter. Eight receivers arranged in a linear array of ≈ 6m base width collect the reflected signal. Each channel is mixed with the outgoing chirp before being filtered and digitally sampled. The reflected signals carry both position information, because the frequency predictably varies in time, and velocity information through the Doppler effect. The wavelength of the radar is 57 mm and penetrates any suspension of snow particles smaller than this. Therefore, the acquired velocities represent the front of the underlying dense layer, which also generates the seismic signal.
The data of the seismic and infrasound sensors were processed and converted to A C C E P T E D M A N U S C R I P T 8 2011). Fig. 3 shows two differentiated packets of energy in the seismic time series, corresponding to the earthquake and subsequent avalanche. This is not the case of the infrasound time series that displays a spindle shape and will be discussed below. Fig. 4 displays the corresponding spectrograms.
The arrival of the earthquake is observed at all the seismic stations at approximate 16.5 s (arrival of P-wave in Fig. 3. The origin of time is arbitrary). Note the clear and sudden appearance of energy at all frequencies in the seismic spectrograms (Fig. 4). This is a characteristic of earthquakes. The arrival time of the S-wave is approx. at 22 s (Fig. 3).
The maximum amplitudes in the earthquake seismic time series were recorded at approximately 23 s. The seismic spectrograms show that the signals of the earthquake and the avalanche overlapped (Fig. 4). The coda of the earthquake (last part of the signal where the amplitudes decrease) overlaps the beginning of the seismic signal of the snow avalanche (approx. 40 s). After the coda of the earthquake (approx. at 50 s) the increase in amplitude of the seismic signal produced by the snow avalanche is observed at different times in the different seismic records. This is a consequence of the evolution of the relative position of the avalanche and the sensors. Information on the evolution of snow avalanches can be obtained from the analysis of the avalanche generated signals recorded at the different locations as shown in e.g. Vilajosana et al. (2007) and Kogelnig et al. (2011). The gradual appearance of the energy at the different frequencies in the seismic spectrogram is a characteristic of mass movements (Suriñach et al., 2005). The evolution of the frequency content in time allows to estimate the relative position of the snow avalanche with respect to the seismic stations. The approach of the snow avalanche to a sensor results in an increase of the energy content of the higher frequencies. Maximum amplitudes in the highest frequencies are recorded when the snow avalanche flows near or over the seismic sensor. The maximum seismic  to a maximum in the amplitudes of the highest frequencies in the spectrogram (t 1 and t 2 Fig. 3 and 4). The arrival of front 2 at the range of cavern C corresponds to t 3 ( Fig. 3 and 4). The latter, third front (3) travels slowly at 1-3 m/s and expands far into the runout zone. This front appears in the radar record at a range of 1020 m and still moves when the recording finishes after 3 minutes. Note that the maximum runout distance has been reached by the last slow moving front (Fig. 3). The seismic and infrasound energy generated by this front is not detected because their amplitudes were very low with an order of magnitude similar to that of the background noise.
The infrasound time series displays a spindle shape with a maximum value in the time series amplitude of 1.1 Pa in the [65-110] s interval (Fig.3), which also corresponds to the maximum in the spectrograms (Fig. 4). This shape was also observed in other avalanche infrasound signals (Kogelnig et al., 2011). The infrasound energy interval coincides with that of the seismic signals although the frequency content is lower, up to A C C E P T E D M A N U S C R I P T 11 amplitudes are observed in the earthquake interval (up to 50 s), whereas the highest amplitudes are present in the snow avalanche interval. The maximum amplitudes of the infrasound signal were recorded seconds after (infrasound time travel at sound speed) when the avalanche moved along the channelled path, reaching the maximum velocity.
We can consider that the infrasound signal attenuation is negligible at local distances (d < 5 km; Kogelnig et al., 2011). Note that the maximum energies in the infrasound (recorded at D) coincide when the avalanche is in between the range of B and C, in the channelled path before reaching C. The amplitudes and shape of the infrasound indicate that the avalanche developed a dilute faster part in this part of the path according to the analysis of other avalanches at the site (Kogelnig et al., 2011).
The analysis of the evolution of the seismic signals allows us to determine first, that it was an avalanche and second, the approximate path that it followed. The velocities of the first fronts and the characteristics of the infrasound signal indicate that it was a dry avalanche. According to the length of the avalanche path (around 1500 m), we can classify it as a medium size avalanche (or size 3 following Canadian Classification described in McClung and Scharer, 2006).

Determination of the approximate start time of the avalanche
Snow avalanches are extended moving sources of seismic and infrasound waves. Recent studies have shown that the suspended powder cloud and the dilute layer are the main sources of infrasound, whereas the interaction between the dense core of an avalanche and the basal friction is the main source of the seismic signal (Kogelnig et al., 2011).
Earthquakes also generate infrasound waves by different mechanisms. Near the epicenter, the vertical displacement of the seismic waves generates ground-coupled air waves (Le Pichon et al., 2003). At greater distances, infrasound is generated by the interaction of the surface waves with topographic features such as mountains. Finally, the vertical oscillations in the ground caused by an earthquake also induce infrasound signals (Che et al., 2007).
In order to determine whether the snow avalanche was triggered by the earthquake or not, first it is necessary to determine the arrival time of the earthquake at the site and the time when the snow avalanche was released. The determination of the arrival time of the earthquake does not present problems. The sudden appearance of the P-wave arrival in all the seismic stations is visible in the time series and spectrograms at 16.5 s ( Fig. 3 and 4). In addition, the snow avalanche had to be released after the arrival of the earthquake because no seismic energy of the avalanche is observed before the earthquake. However, the starting of the avalanche is not easy to detect due to the presence of the energy of the earthquake ( Fig. 3 and 4). The comparison of the seismic and infrasound signals of the 6 December 2010 event with that obtained for two regional earthquakes recorded at the experimental site which did not trigger a snow avalanche are helpful.
On 11 February 2012 one regional earthquake occurred 132 km from VDLS (M L 4.2; 22:45:26 UTC; earthquake 2 in Fig. 2 and Table 2) with the hypocenter in Switzerland  Table 2. A comparison of these values shows that earthquake 3 generated higher infrasound amplitudes (A max = 0.76 Pa) than the other two earthquakes which had a lower PGV and longer epicentral distances. However, earthquake 1 with lower PGV, but closer to the station, yields higher infrasound amplitudes (A max = 0.11 Pa) than earthquake 2 (A max = 0.07 Pa).
In order to compare the different shapes of the seismic and infrasound signals of the three earthquakes, the envelopes of the complete seismic signals and those of the infrasound of these earthquakes recorded at cavern D were calculated. The envelope of the entire seismic signal was calculated using the norm of the three seismic components smoothed each 50 points (0.5 s). Fig. 8 shows the envelopes normalized for comparison of the three earthquakes. In earthquakes 2 and 3, the infrasound amplitudes correlate well with the seismic signals although the distances from the epicentre were different and hence the shape of the seismograms, i.e. a) a sudden increase in the infrasound amplitude that corresponds to the P-wave arrival of the earthquake at the sensor, b) maximum infrasound amplitudes that correspond to the maximum seismic amplitudes and c) a decrease in the infrasound amplitude for the coda of the earthquake (Fig. 8).
A different relative behaviour between the envelopes of the seismic and the infrasound signals is observed in the case of the event in which the avalanche was triggered ( Fig. 5 and bottom Fig. 8). The sudden increase in the infrasound signal at the moment of the arrival of the P-wave is not observed in the envelopes and in the time series. This is due to two factors: a low signal-to-noise ratio and the low seismic energy of the earthquake.
The infrasound background noise of the given day had mean amplitude of 0.008 Pa (calculated 10 s before the earthquake). This value is similar to that of the day of earthquake 3 (0.007 Pa) and higher than that of earthquake 2 (0.003 Pa). The low signal-to-noise ratio of the amplitude of the infrasound generated by the P-wave and the immediate phases that follow is not sufficient to distinguish the increase in the infrasound signal (Fig. 8). The low energy of the seismic signal of these phases (maximum value below of 10 -5 m/s) did not generate enough infrasound energy to be distinguished at the beginning of the earthquake. However, at t = 23 s, a local maximum of the infrasound is observed on the arrival of the maximum energy of the earthquake.
Note that the delay observed is due to the travel time difference between the seismic and infrasound waves (Ichihara et al., 2012). The similar decrease in amplitudes of the coda section of the infrasound and seismic envelopes observed for earthquakes 2 and 3 (without avalanche) is not observed in the event. The fall in the seismic envelope amplitude does not correspond to a decrease in the infrasound envelope amplitudes. By contrast, the amplitude of the infrasound envelope increases, reaching a maximum at 28.01 s that exceeds the local maximum at 23 s ( Fig. 8). A possible explanation for this increase that surpasses the local maximum is that the sensor was receiving the infrasound generated by the avalanche. We therefore infer that the avalanche was released a few seconds before this time and after the arrival of the earthquake. This assumes that the only sources of infrasound were the avalanche and the earthquake.
In our seismic recordings of the 6 December 2010 event the most energetic waves are the S-waves around 22 s ( Fig. 3 and 4). Therefore the inertial forces induced by the acceleration of these waves will be stronger and might cause more effects in the snow cover. Our data indicate that the avalanche was released shortly after the arrival of the waves of the earthquake, which strongly suggests that the avalanche was triggered by the earthquake. A quantification of the signals generated by the earthquakes could yield more information.

Earthquakes ground motion quantification
Six indices are usually employed in earthquake engineering to measure the effect of ground motion or shaking on a structure. We considered the snow slab using the same approach.
In order to evaluate the ground shaking produced by the earthquake on 6 December 2010, we compared the seismic signals of this earthquake with those of the two earthquakes aforementioned (earthquakes 2 and 3). The seismograms obtained at cavern A were used because this cavern is situated at the release area (Fig. 1). We assume that the earthquake shaking is similar over the entire release area.
These indices take into account the amplitude, duration and frequency content of the punctual maximum values of the whole time series (Newmark, 1965). The TD and the I a values are more related to the power of the shaking over the entire time series. The PSA, conversely, gives the maximum acceleration response of a structure (in this case the snow slab) for each period (T) (Newmark and Hall, 1982). Resonance effects in the structure can appear owing to the frequency content of the ground motion causing amplification of the vibration. The values of the PSA for T= 0 s corresponds to the PGA values. In the field of earthquake engineering the incorporation of a damping (viscous) reduction factor in the design of the structures is considered (Newmark and Hall, 1982).
This factor depends on the structure characteristics, in our case on the characteristics of the snow slab, but the exact characteristics are unknown. Therefore we calculate the PSA using three different damping ratios in an appropriate range. The loss factor (two times the damping ratio) calculated in snow tests showed a dependence of the density and temperature of the snow in a range between [0.005 -0.16] (Mellor, 1975). Hence, to evaluate the different possibilities three variable damping ratios (1%, 5% or 8%) were considered in this study.
The Arias intensity, I a , is a quantitative measure of the shaking intensity produced by the earthquake. It is calculated by means of the integral over time of the square of the acceleration, expressed as (Arias, 1970): ( 1) where has units of velocity, a (t) is the ground acceleration time series and g is acceleration due to gravity. It has been observed a good correlation of this measure of the total shaking with the distribution of earthquake-induced landslides (Jibson, 1993).

The Trifunac duration (TD) is the time interval in which the normalized Arias intensity
of the ground motion is between 5% and 95 %. i.e. where t satisfies 0.05 (Trifunac and Brady, 1975).
The parameters were calculated for all three seismic components. The ground accelerations were obtained from the derivative of the ground velocity time signals recorded at the station at cavern A, the cavern situated in the release area (Fig. 1) The corresponding PGD, PGV, PGA, TD and I a values are shown in Table 3 However, the explosions usually have a TD much lower than the earthquakes.
The maximum PGD and PGV are obtained for the slope parallel plane components (X and Y) of the earthquake 3 (Table 3). However the PGD and PGV values of earthquakes 1 and 2 are of the same order of magnitude, slightly higher for earthquake 2. Also in these earthquakes the values of the horizontal components are higher than the vertical components. The effects of the PGV and PGD of the ground are even more important

A C C E P T E D M A N U S C R I P T
18 than PGA values because they lead to fissures in the ground surface (Newmark, 1965).
The highest values are obtained for the earthquake 3 and the effect of this earthquake might produce more damage leading to a failure.
The maximum PSA values and the associated periods (or frequencies) are important factors to consider in the analysis of the shaking. Earthquake 1 and 3 present higher frequency content (lower period) of PSA than earthquake 2 because they were closer to the VDLS site: The periods for earthquakes 1 and 3 are in the range of [0.04 -0.15] s and earthquake 2 in [0.08-0.17] s (Fig. 9, 10 and 11). This is a consequence of the geometrical and anelastic attenuation of the seismic waves that produce, for the same magnitude earthquake, lower amplitude and frequency content for longer epicentral distances. The relationship between the frequency content of the seismic source and the slab failure has not been studied yet. All the documented cases of earthquakes-induced avalanches (Podolskiy et al., 2010a) were for earthquakes located at a distance relatively close to the source (in a range of 0.2-640 km). Teleseismic earthquakes do not usually trigger snow avalanches, although the peak ground acceleration recorded at the site could be higher than that of the studied local earthquakes. This suggests that the most effective accelerations that induced the slab failure are those of high frequencies (shorter epicentral distances). Note that snow avalanches are often triggered by explosions which are very high frequency seismic sources, though the analogy is only approximate.
The PSA values in the downwards direction to the slope (X) of earthquakes 1 and 2 are of the same order of magnitude, and earthquake 3 has the largest value, 0.25 m/s² for a period of 0.07 s (f ≈ 14.3 Hz) for a damping ratio of 1% (Fig. 9, 10 and 11

A C C E P T E D M A N U S C R I P T
19 earthquake 3 is one order of magnitude higher than those of earthquake 1 (0.029 m/s²; f ≈ 16.7 Hz; 1%) and earthquake 2 (0.059 m/s²; f ≈ 8.3 Hz; 1%). In summary, earthquake 1, which was followed by the avalanche, presents the minimum values of PGA and I a , and the highest frequencies involved in the maximum PSA, although they are not the maxima. Nonetheless, only small differences between these values have been detected.
The maximum values of the PSA represent the maximum acceleration loading to the slab when the slab had this frequency of resonance. Although the resonance frequency of a snow slab is unknown it must be related to the type of snow grain and the geometry of the slab as well as its stiffness.
The values at cavern A presented here can be considered as an upper boundary of the accelerations obtained. The earthquake accelerations at cavern A, at the top of the mountain, are higher than those at caverns B, C and D. Table 4 displays the PGA values of the three components for earthquake 1 at the different caverns as an example. This amplification could be due to site effects produced by the topography (Geli et al., 1988;Pedersen et al., 1994) and to geological effects. Recent papers claim that high amplifications on mountain slopes observations cannot be explained purely by topographic effects (Del Claudio and Wasowski, 2011). Moreover, numerical simulations have found that topographic amplification factors hardly exceed 2 (Assimaki and Kausel, 2007). In particular, pure topographic effects have been found to be considerably smaller than the complex interaction of combined topographic and geological effects (Bourdeau and Havenith, 2008). The values obtained for earthquake 1 at cavern A, where the topography is more abrupt, are the highest (Table 3). By contrast, at cavern B (Table 4) where the slope inclination is larger than at C and D, the amplitude of the seismic signal is lower than at those sites. This is an example that shows that the topographic amplification is not the only factor to be considered.

A C C E P T E D M A N U S C R I P T 20
We can compare the magnitude and epicentral distance of the event with previous reported cases of earthquake induced avalanches. Podolskiy et al. (2010a) suggested a limit for earthquake induced snow avalanches of M w 1.9 earthquakes at zero source to site distance, that implies a PGA around 0.03 g approx. This threshold is based on reported cases of avalanches triggered by underground explosions in the Khibiny Mountains in Russia (Chernouss et al., 2006). However, data derived from statistical analysis (Podolskiy et al., 2010c) showed an important reduction of that threshold. In particular, statistically identified earthquakes of magnitudes in the range M w 3-3.9 induced snow avalanches at distances 100-199 km. The corresponding PGA is between 10 -6 g and 10 -4 g. Our case study fits inside the limit of the reported statistical cases, although the reliability of these cases is questionable because most of them could be incorrectly identified or they correspond with an extremely unstable snowpack.
Therefore it is difficult to estimate a threshold shaking intensity without knowledge of In summary, we have shown that the characteristics of earthquake 1, which could trigger an avalanche, are similar to those of earthquakes 2 and 3, which did not trigger avalanches. The most likely explanation for the different effects of the earthquakes with respect to the avalanche release is the differences in the snowpack stability. The snowpack stability has a clear influence in the evaluation of the possibility that these earthquakes of minor magnitude can act as triggering mechanism for snow avalanches.

6. Nivo-Meteorological Conditions and Snow Cover Simulations
Avalanche release mechanisms can be more or less effective depending on the snowpack conditions. The snow cover stratigraphy is the key contributing factor for dry slab avalanche formation (Schweizer et al., 2003). The triggering of this type of avalanches can occur because of three factors (Schweizer et al., 2003): To obtain detailed information of the snow stratigraphy at the days of the earthquakes, we conducted simulations with the one-dimensional snow cover model SNOWPACK (Lehning and Fierz, 2008). The simulations are computed using data from the nearest automatic weather station Donin Du Jour (VDLS2 at 2390 m a.s.l. and 2 km from the VDLS release area) that provide all the required data to run SNOWPACK. The result of simulations of the snow cover conditions of the three investigated days showed a significantly different stratigraphy and stability (Fig. 12). Additionally, data from the automatic weather station close to the release area (VDLS1 station, 2696 m a.s.l.) and avalanche bulletins of the region have been used to complete the analysis. Below, the detailed snow cover characteristics with the complementary meteorological information for each day are presented. Other different arrangements of seismic sensors (Lacroix et al, 2012;Van Herwijnen and Schweizer, 2011)) or infrasound sensors (Ulivieri et al., 2011) allow the location of avalanches in nearby regions.

February 2012:
On 11 February 2012 the temperature of the air was -17 ºC (VDLS 1 station) and there was no precipitation on the previous days. The VDLS2 station recorded a snow depth of 3.07 m. The resulting snow cover simulation of the day consisted (Fig. 12) of a very homogeneous snow cover of a 3.00 m thick layer of rounded grains with a layer of faceted crystals between 2.80-3.00 m. The snow cover consisted of well bonded crystals which were not very favorable for the formation of avalanches.
The weekly report of the SLF indicated a moderate avalanche danger (level 2) at Valais because of the stable snowpack and only low winds from the northeast in this part of the

A C C E P T E D M A N U S C R I P T 24
Alps. According to SLF data, there were no natural snow avalanches on the days before and after the earthquake because the snowpack was fairly stable.

March 2012:
On 21 March 2012 the temperature of the air was -3 ºC and there was 0.1-0.2 m of snow precipitation during the night of 20 March 2012. There was a snow cover of 2.73 m at the VDLS2 weather station. The SNOWPACK simulation of this day (Fig. 12) showed a snow cover that consisted of 0.7 m of rounded grains below 1.8 m of melt forms. At the top a 0.2 m thick layer of decomposed forms was observed. The only possible weak layer was situated at the interface of the rounded grains and the decomposed forms at 2.5 m above the ground. The snow cover was mainly well bonded.
Moreover, this day, the regional avalanche bulletin indicated a moderate avalanche danger (level 2) for the area of VDLS. It was a spring situation with the possibility for spontaneous wet avalanche formation.
Comparing the snow cover conditions of the three days we can conclude that at the day of the earthquake followed by the avalanche, the conditions for an avalanche release were more favourable than for the days of the two other earthquakes. The snow profile this day showed a new snow layer on a very unfavourable old snow cover that consisted of a weak layer of faceted crystals over a crust. Therefore, the existence of this weak, non-cohesive layer in the snow cover, the loading produced by the snow precipitation during the previous hours and the rapid increase in the air temperature together with the rapid loading produced by the shaking of the earthquake were the factors that contributed to the avalanche release on 6 December 2010.

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25 Another possible factor in the relationship between the snow cover conditions and the effectiveness of the shaking of the earthquakes should be taken into account. This is the position of the weak layer in the snow cover that could be fractured due to the shaking of the earthquake. Since the seismic waves propagate through the ground before reaching the snow cover and therefore could be attenuated inside the different snow layers before reaching the weak layer. The amplitude of the shaking on the weak layer will depend on the distance travelled inside the snow cover. Field experiments carried out with explosives to release avalanches have shown that the effective range of an explosive depends on the position of the charge relative to the snow surface, the charge mass, the snow profile and the characteristics of the ground (Gubler, 1977). The snow cover simulations of the different days ( Fig. 12) showed that snow cover depths and position of the possible weak layers are much higher up in the snow cover of days of the earthquakes 2 and 3 than in the event, which can also contribute to the attenuation of the seismic waves travelling through the snow cover.

Stability Factor and Newmark's analysis
The shaking of the earthquake produces inertial forces in the layered snow cover and in consequence a change in the elastic stress field within the snow. This loading of the snow induced a stress with shear, tensile and compressive components (Podolskiy et al., 2010b).
Taking into account the snow conditions analyzed in the previous section, we calculate the stability factor of the slope in the presence of ground vibration and the maximum cumulative deformation produced by the earthquake.

A C C E P T E D M A N U S C R I P T 26
The relationship between the retaining forces and shearing forces yields the stability factor of the slope S. For each layer boundary, the resulting stability index S is calculated as (Schweizer et al., 2003): ( 2) where is the shear strength, is the shear stress due to weight of the overlaying slab layers and is the additional shear stress due to the earthquake in this case. The shear stress (denominator of Eq. 2) of the snowpack in down slope direction is described as the sum of the weight of the different layers and the loading produced by the acceleration of the earthquake in this direction: ( 3) where is the shear stress, and are the density and height of each layer, and the acceleration due to the earthquake in downslope direction. In the presence of the earthquake, this shear stress is a function of time. In consequence, the maximum shear stress applied to the weak layer, during the time interval of the earthquake, is obtained at the instant when the earthquake reached the maximum acceleration (PGA): (4) Jamieson and Johnston (1998) obtained the following expressions for the shear strength of layers composed of decomposing forms (Eq. 5) or faceted crystals (Eq. 6): (5) or (6) where is the density of the layer and is the density of ice. In our study is 917 kg/m 3 (McClung and Schweizer, 2006  The stability index (Eq. 2) in this case is: The values obtained for S are in the range of [1.5-3.5] which correspond to stable conditions (S > 1). Finally, to evaluate the whole effect of the earthquake, we apply Newmark's method (Newmark, 1965) that has also been applied to landslides (Wilson and Keefer, 1983;Jibson, 1993;Jibson, 2011) and snow avalanches triggered by artificial seismicity Chernouss et al., 2006). This analysis calculates the cumulative displacement (D) of one block, the Newmark displacement, owing to the effects of the earthquake acceleration time-history:

2-
where a(t) is the acceleration of the earthquake and a c is the critical acceleration. In this approach, displacement depends on the critical acceleration (Eq. 10) which depends on the values of the shear strength and shear stress of the slab. The critical acceleration is (Jibson, 1993): where α is the slope inclination (40º) and S is the stability factor calculated using Eq. 2 without considering the earthquake.
The values of the critical acceleration calculated in the evaluation 2 give a range of values of critical acceleration that oscillates from negative values (the snow slab is unstable before the shaking of the earthquake) to values up to 1.2 m/s 2 (over the PGA of the earthquake). We assume that our snowpack is at or very close to the static equilibrium (the stability factor is 1) in the evaluation 2 and then we calculate the maximum cumulative displacement. In a situation very close to the static equilibrium the block experiences a very low critical acceleration (theoretically, a c =0) and thus should undergo higher inertial displacements (Jibson, 1993). Therefore, the maximum cumulative displacement (zero critical acceleration) produced by the earthquake in the downslope direction from Eq. 9 is 0.084 mm. In addition, the maximum cumulative displacement in the direction normal to the shear plane (the vertical component of the acceleration is used in Eq. 10) is 0.068 mm. Both shear and normal to the shear plane displacements are calculated because the initial failure could be in compression or in shear (Reiweger et al., 2010b).
Ductile materials can accommodate more displacement without failure, while brittle materials can accommodate less (Jibson, 1993). Snow is one of the most rate dependent materials known (Kirchner et al., 2000). Laboratory experiments (Schweizer, 1998) showed that at high deformation rates snow behaves as a brittle material, but at at low deformation rates as a ductile material. What displacement causes a failure varies according to the material and the conditions. The strain necessary to reach the residual strength can be estimated from laboratory shear-strength tests (Jibson, 1993). Reiweger et al. (2010a) performed loading experiments to study the material behavior of snow samples containing a weak layer before fracture. They observed that in layered snow samples the global deformation is concentrated in the weak layer. They used layered snow samples consisting of small grains at the top and bottom and a weak layer of faceted crystals and some depth hoar in between. Comparing two photographs before fracture, they measured displacements between 0.06-0.08 mm within the weak layer.
These values are of the same order of magnitude as the maximum cumulative displacement produced by the earthquake on 6 December 2010. Therefore, the effects of a minor earthquake on a snow cover with a faceted weak layer, close to static equilibrium can produce enough displacement to cause failure.

Conclusions
We analysed a small earthquake that occurred on 6 December 2010, 43 km from the VDLS test site and showed that it possibly triggered an avalanche. The study was carried out using seismic and infrasound data generated by three earthquakes and one avalanche obtained by instruments at different locations at the test site. The joint analysis of the infrasound and seismic data shows that the avalanche occurred after the arrival time of the earthquake, in agreement with the GEODAR radar data, suggesting that the earthquake was the triggering factor. The comparison of the radar with the seismic and infrasound data allows us to characterise the avalanche size and path. The avalanche was a dry medium size avalanche flowing down the secondary channel. The A C C E P T E D M A N U S C R I P T 31 maximum infrasound signal was recorded when the avalanche descended in the channelled zone at a high velocity. The avalanche runout below cavern C was determined by analyzing data from the GEODAR and seismic sensors.
The quantification of the ground motion of the earthquakes shows that the PGD, PGV, PGA, I a , TD and PSA values of the 6 December 2010 earthquake are not particularly high with the result that we cannot be absolutely sure that the avalanche was triggered by the earthquake. Two other earthquakes with higher quantification parameters did not trigger any avalanches at the same site, because they occurred when the snowpack was much more stable. However, this small earthquake can be significant due to the instability conditions of the snowpack on 6 December 2010.
Despite the fact that possible resonance effects of a snow slab under vibration are unknown, the PSA values calculated for the earthquake of the event indicate that the snow slab could suffer amplifications of the acceleration being up to one order of magnitude higher (PSA maximum values are one order of magnitude higher than the PGA). Therefore in the case of resonance, higher increases of the stresses are produced due the acceleration of the earthquake. On the other hand, the accelerations used in our calculations recorded at the top of the mountain at the avalanche release area are higher than the values obtained at the stations situated at lower heights. The maximum acceleration values, PGA, at the top can be doubled (Table 3). For a better evaluation and quantification of the earthquake-induced avalanches, it is necessary to know the acceleration time-history of the ground motion in the areas where the avalanches can be released. These data are not easy to obtain because only few seismic stations are situated in these areas where access and installation are complicated.
The main contribution of this paper is the evaluation of the shaking produced by the earthquake to trigger an avalanche using for the first time acceleration data measured in A C C E P T E D M A N U S C R I P T 32 the release area of an avalanche. The low magnitude of the earthquake and the existence of an unstable snowpack hinder the determination of the exact triggering mechanism.
However, the evidence of a temporal coincidence of the two seismic sources, the earthquake and the avalanche, reinforces the idea that the earthquake could contribute to the triggering of the snow avalanche.
Owing to the uncertainty in the parameters involved in avalanche release, it is not easy to establish an area affected by snow avalanches triggered by an earthquake taking into account only the earthquake magnitude and distance without considering the snowpack conditions on a given day. These conditions vary widely in mountain areas and are the key factors in limit cases. The SNOWPACK simulation computed for 6 December 2010 revealed an unstable snow cover with the presence of a weak layer of faceted crystals over a hard crust which was buried by the subsequent snowfall. In these unstable conditions, the maximum cumulative displacement that the earthquake can produce is in the order of magnitude of displacements measured before fracture in laboratory experiments for snow samples with faceted weak layers. This small displacement could be enough to produce failure when the snow is loaded at high loading rates, like in the case of an earthquake.
Further studies are warranted to evaluate the relationship between the seismic source (amplitude, duration and frequency content) and its effect on the snow, which is one of the most brittle and rate-depended materials that exist.         arbitrary. The infrasound generated by the snow avalanche is received at t i and at t r the radar started to record the movement of the snow avalanche. Highlights:

Site Station Data Acquisition
A snow avalanche was released shortly after a minor magnitude earthquake Snow cover stability is a determining factor for avalanche release due to earthquakes Minor magnitude earthquakes can trigger avalanches in unstable snow cover conditions