Seismo-acoustic energy partitioning of a powder snow avalanche

. While ﬂowing downhill, a snow avalanche radiates seismic waves in the ground and infrasonic waves in the atmosphere. Seismic energy is radiated by the dense basal layer ﬂowing above the ground, while infrasound energy is likely radiated by the powder front. However, the mutual energy partitioning is not fully understood. We present infrasonic and seismic array data of a powder snow avalanche, that released on 5 February 2016, in the Dischma valley above Davos, Switzerland. A ﬁve element infrasound array, sensitive above 0.1 Hz, and a seven element seismic array, sensitive above 4.5 Hz, were deployed at 5 short distance ( < 500 m) from each other, and close ( < 1500 m) to the avalanche path. The avalanche dynamics were modeled by using RAMMS, and characterized in terms of front velocity and ﬂow height. The use of arrays rather than single sensors, allowed us to increase the signal-to-noise ratio, and to identify the event in terms of back-azimuth and apparent velocity of the recorded wave-ﬁelds. Wave parameters, derived from array processing, were used to identify the avalanche path and highlight the areas, along the path, where seismic and infrasound energy radiation occurred. The analysis showed that seismic energy 10 is radiated all along the avalanche path, from the initiation to the deposition area, while infrasound is radiated only from a limited sector, where the ﬂow is accelerated and the powder cloud develops. Recorded seismic signal is characterized by scattered back-azimuth, suggesting that seismic energy is likely radiated by multiple sources acting at once. On the contrary, infrasound signal is characterized by a clear variation of back-azimuth and apparent velocity. This indicates that infrasound energy radiation is dominated by a moving point source, likely consistent with the powder cloud. Thanks


Reply to the review by Emma Surinach
Reviewer: It is a very interesting contribution, although the authors have not take into account the previous paper of Kogelnig et al., (2011) where seismic and infrasound time series are compared for four different types of avalanches at the VdLS experimental site, descending along different paths, unlike the one presented in the manuscript under review in which only one avalanche is studied.In this paper the infrasound and seismic time series obtained in collocated sensors with a common time are compared, and also with the time series obtained in two more seismometers placed along the avalanche path.Additionally, a comparison was made with other "in situ" direct measurements (flow depth and internal velocities).The frequencies involved in the study are in the range of  Hz for both type of measurements.Of interest is the content of "low" [1][2][3] Hz frequencies of the seismic when comparing with the infrasound.Because of the completeness of these data, with respect to that of the data of the manuscript under review, the authors must take into account in their discussion and conclusions the results obtained previously.In principle, part of the obtained results by the authors could confirm the previous ones or contradict them.
We are perfectly aware of the work performed by Kogelnig et al., 2011, and it was already referenced in the text.However, following the comment of the reviewer, we included a better discussion of our findings compared to what presented already by Kogelnig et al., 2011.Reviewer: The use of the combination of the two arrays in this study is very positive, but the authors must be aware of the limitations of their study.In addition, the results presented also depend on the specific topography.One of the difficulties of the comparison of the results of the two arrays is that the infrasound array has a direct view of the avalanche flow and the array of geophones does not.What would happen in the case of the existence of a shadow zone for the infrasound?Or if the seismic array had been collocated with the infrasound array?
Infrasound propagation is strongly affected by the local topography.Basically, moving sources that are not line-of-sight to the infrasound array, are recorded with a limited variation of back/azimuth and/or apparent velocity.This is not the case of seismic data, that propagate in the ground, even if, in this case, variable seismic phases can make the analysis more complicated.This aspect has been further discussion in the manuscript.In case of a collocated seismic and infrasound array, p-wave induced variation of back-azimuth would mimic the back-azimuth variation induced by infrasound.
Reviewer: As regards Section 5. Kogelnig et al. (2011) includes a section dedicated to the source of infrasound and seismic signals.There, a synthetic signal is obtained using the expression of Ffowcs Williams (1963) that describes the acoustic intensity generated by a turbulent source in motion.The modeling results are compared with the infrasound time series obtained from an avalanche.In addition, due to the existence of a suspension layer that can generate infrasound, an explanation is included for not considering a unic specific source of infrasound.This is a possibility and is discussed in the text.
Reviewer: -Line 227.With your results, there is not enough information to generalize to all the avalanches, in plural.
We are quite confident that snow avalanches are characterized by a predominant source of infrasound energy.Based on previous experimental studies this is likely the front.This is very different for example from other density currents such as lahars and debris flows, where array processing identifies a clear lack of coherence that is interpreted as muktiple sources acting at once.This aspect has been clarified in the text.
The study of Kogelnig is discussed in detail.They analyse infrasound in terms of the elastic energy radiated by the turbulent flow at the avalanche front.Results are very promising.In terms of array analysis however, it can be considerd as a point source moving downhill.Therefore we believe that additional comment here, once the point above has been addressed are redundant.Moreover, in Kogeling too a point source is assumed to estimate the size (D) that is eventually used to calculate infrasound energy radiation by the turbulent flow.

Corrected in the text
Reviewer: -Line 249.Note that the effect of filtering from 1 to 10 Hz and realistically, from 4.5 to 10 Hz, also presents problems in the quantification of the energy, since part of the signal is lost.
Following the suggestion of the reviewer, the frequency limitation of our study has been highlighted clearly in the text.
Reviewer: -Line 252.This was also mentioned in Kogelnig et al., (2011) The reference is added in the text.
Reference has been corrected in the text and reference list.
Reviewer: -Line 277.Are you sure that including Π in eq. 2 is correct?Are you considering radians?
Yes. Considering a regid sphere that starts moving into the atmosphere, the characteristic angular frequency is proportional to the ratio between the sound wave propagation velocity and the radius of the sphere, resulting into equation 2. This equation, proposed to investigate the frequency of infrasound radiated by a snow avalanche by Naugolnykh, K., and Bedard, A., was developed already by Landau and Liftshitz, (Fluid Mechanics, 1959, page 287).We prefer referencing to the work of Naugolnykh, K., and Bedard, A., that applied the physics to snow avalanches, rather than a basic book of Fluid Mechanics.
Reviewer: -Lines 288 -Specify in the Conclusions that the results correspond to the case of study, for a powder-snow avalanche recorded at 1000 m from the starting point.

Reviewer: -Line 303. Please indicate in % what it means strongly affected. In addition, you must consider the different frequency content of the two time series in your calculations.
This has been addressed in the text.

Reviewer: -Line 313. Energy radiation
This has been corrected in the text.
Reviewer: -References Please, Indicate correctly the spelling of the surnames.

Reference list has been doublechecked carefully.
Reviewer: -Figures -Figure 1.In Figure 1b) the s7 sensor is missed.
There was s1 twice.This was corrected in the figure.Reviewer: -Figure 6.In Figure 6b) convert counts to ground speed and include in the horizontal axis the title like Figure 5a.For the benefit of the comparison, change the vertical scale on a more detailed scale for the posterior azimuth 6d) and the apparent velocity 6f) of the seismic data, even if you lose some outliers.The figure caption has been corrected following the comment of the reviewer.
While flowing downhill, the interaction of the dense basal flow with the ground radiates seismic energy (Sabot et al., 1998).
Infrasound energy is radiated by the compression of the atmosphere produced mostly by the powder front (see e.g.Schaerer and Salway, 1980;Bedard, 1989).The ratio between the dense and powder part of a snow avalanche, and hence between the seismic and infrasound energy radiation, is not constant while it depends on the front evolution through time (Carrol et al., 2013).
Seismic measurements have been widely applied to investigate avalanche dynamics and characteristics.Sabot et al. (1998) showed that slope changes, and the presence of obstacles on the flow path strongly affect the radiation of seismic energy.
Moreover, characteristics of recorded seismic signals depend on snow density and avalanche type and size (Biescas et al., 2003;van Herwijnen and Schweizer, 2011b;Vilajosana et al., 2007b).Seismic monitoring techniques deploying multiple sensors along the avalanche path (Biescas et al., 2003;Vilajosana et al., 2007a) or arrays (van Herwijnen and Schweizer, 2011a;Lacroix et al., 2012;Heck et al., 2017), that allow to identify the avalanche occurrence within a source-to-receiver distance up to ⇡ 3 km.Hammer et al. (2017) recorded very large avalanches up to 30 km away.
After the pioneer study by Bedard (1989), the use of the infrasound in avalanche monitoring and research has increased significantly (Chritin et al., 1996;Adam et al., 1998;Comey and Mendenhall, 2004).Naugolnykh and Bedard (1990) suggested that infrasound is possibly induced by the non-stationary motion and/or by the turbulence of the flow.Moreover, they suggested that the amplitude and frequency of the recorded infrasound signals should scale with the avalanche size and velocity.
Since then, infrasound avalanche observations improved substantially, both in number and accuracy.The development and use of infrasound arrays instead of single sensors (Scott et al., 2007;Ulivieri et al., 2011;Havens et al., 2014;Marchetti et al., 2015), allowed to increase the signal-to-noise ratio and to improve the investigation of the avalanche infrasound signature.
Specific wave parameters (back-azimuth and apparent velocity) of recorded signals were used to define array processing pro-cedures, able to detect medium size snow avalanches at distances of a few kilometers (Ulivieri et al., 2011;Marchetti et al., 2015;Mayer et al., 2018).Moreover, infrasound array derived information were used to remotely evaluate the avalanche front position and velocity through time (Marchetti et al., 2015;Havens et al., 2014).
However, many open questions remain and using infrasound and seismic signals to infer avalanche size is still debated.It is well known that seismic and infrasound energy interact at the earth free surface and are transmitted between the atmosphere and solid earth (Ichihara et al., 2012).The transmission affects the amplitude of recorded signal and should be considered when signal characteristics are used to constrain the source process or to calculate the energy of the event.
In this work we present a combined seismic and infrasound array analysis for a snow slab avalanche that occurred on 5 February 2016, in the Dischma Valley, south of Davos, Switzerland.The event was recorded by a seismic and an infrasound array located nearby (less than 1500 m) the path.The data obtained from the seismic and the infrasound array are used to investigate the mutual energy radiation as a function of the front position along the avalanche path.To investigate the properties of recorded signals as a function of event characteristics, the avalanche was modeled using the avalanche simulation software RAMMS (Christen et al., 2010) .
The seismic array (Seismic Instruments Inc.) consisted of 7 elements deployed with a circular geometry and maximum aperture (maximum distance between 2 array elements) of 75 m (Figure 2c :: 1b).The array was equipped with vertical geophones with a corner frequency of 4.5 Hz and a sensitivity of 28.8 V/m/s.The geophones were attached with anchors to large rocks on the ground and subsequently buried by snow, which substantially reduced the effect of wind noise.Seismic data were sampled at each geophone at 500 Hz and 24 bits precision.Data were recorded locally at the central acquisition system.The entire system was powered with solar panels and batteries, and the total power requirement was approximately 7 W.
The study site was also equipped with automatic cameras collecting images every ten minutes, used to visually monitor the activity on the slopes surrounding the arrays.The camera system was colocated with the central element of the infrasound array.3 The dry-snow avalanche of 5 February 2016 In the morning of 5 February 2016, at 05:18 UT, a medium sized dry-snow avalanche released from Chlein Sattelhorn (Figure 2b), at an elevation of ⇡ 2600 m.The avalanche traveled a distance of 1200 meters and stopped at the bottom of the Dischma valley, at an elevation of ⇡ 2030 m at a short distance (<100 m) from the infrasound array (Figure 3).The event occurred during a snow storm.Nevertheless, based on the images from the automatic cameras we confirmed that the avalanche released between 4 February 2016 at 17:40 UT and 6 February 2016 at 07:40 UT.The avalanche deposit was first clearly visible on the morning of Feb. 6 (08:30 UT), when the weather weather cleared (Figure 3).
The flow characteristics and evolution (flow depth and velocity) were reconstructed using the RAMMS model (Figure 8) (Christen et al., 2010).We used RAMMS::Avalanche (version 1.7.20) for the simulations of Chlein Sattelhorn.The model requires a detailed digital elevation model as well as an estimate of the initial release volume, i.e. an initial release area and a fracture depth.The inital digital elevation model (DEM) is the swissAlti3D DEM (2 m grid resolution).For the simulation, we did a bilinear interpolation to 5 m.The release volume (with release depth of 80 cm) was 9.525 m 3 .We used calibrated friction values for small avalanches, with a return period of 10 years.The modeled flow depth evolution (Marchetti et al., 2020) , predicts a total flow duration of ⇡ 90 seconds, with ⇡ 60 seconds required by the avalanche to initiate, accelerate, and reach the valley bottom, followed by ⇡ 30 seconds of snow deposition.Since the path geometry is characterized by a sharp terrain break at an elevation of approximately 2300 m (Figure 8c), the modeled avalanche accelerated along the release area with slopes exceeding 35 degrees, rapidly decelerated and lost mass at the terrain break (Figure 8d).The modeled avalanche then accelerated again after entering a steep (slope > 30 degrees), narrow channel (< 50 m), within the lowest part of the path.Finally, the flow slowed down when it reached the valley bottom at an elevation of ⇡ 2030 m (Figures 2,8), where the snow mass was spread out horizontally on the runout area.The modeled snow avalanche qualitatively compared well to the information we obtained from the images from the automatic cameras (Figure 2b).The event from 5 February 2016 was clearly recorded by the seismic and infrasound arrays (Figure 4a, b) (Marchetti et al., 2020).Both signals consisted of two distinct phases, according with the flow evolution modeled by RAMMS (Figure 8).These two phases appear to be controlled by the path geometry forcing the avalanche to slow down and loose mass at the terrain break at an elevation of 2300 m.
The seismic signal has an emergent waveform and a duration of ⇡ 60 s.It is characterized by two phases of similar amplitude (1.5 10 6 m/s), peaking around 05:18:50 and 05:19:20 UT.The signal spectrum shows energy mostly confined between 3.5 and 12 Hz, with the peak frequency around 6 Hz.The frequency response of the geophones limits the spectral analysis to frequencies > 4.5 Hz (Figure 4c), therefore we cannot exclude lower frequency components.
The infrasound record of the event is shorter (⇡ 35 :: 45 : sec), has a similar emergent waveform, with two sparate phases reaching a maximum amplitude of ⇡ 0.5 Pa (Figure 4b).The spectral energy of the infrasound signal is wider, spanning between 0.5 and 8 Hz, with a clear peak at ⇡ 3.3 Hz (Figure 4c). 3 ::::::: Methods The infrasound and seismic data were processed by applying a multichannel correlation analysis, to identify signal from noise in terms of signal back-azimuth and apparent velocity.The procedure, described in detail by Ulivieri et al. (2011), identifies coherent data recorded within a given time window assuming planar wavefront propagation.Once a coherent signal is identified, based on signal correlation threhsold (> 70 %), the corresponding back-azimuth (Baz) is calculated.The backazimuth corresponds to the propagation angle from the array to the source, measured with respect to the geographic North in the horizontal plane of the array.Once the back-azimuth is identified, the apparent velocity (c a ) is calculated, as the ratio between the real propagation velocity (c) and the sin of the take off angle (c a = c/ sin ✓).The apparent velocity corresponds to the velocity the wave would have if it was traveling in the plane of the array, and increases for higher elevation sources.It would be infinite for a source located directly above the array, as all the elements of the array would record the signal simultaneously.
Unlike infrasound, that has a duration of 35 : ⇡ ::: 45 seconds and is marked by a clear variation of wave parameters (backazimuth and apparent velocity), the seismic signal radiated by the event is much longer in duration (⇡ 60 sec), and changes in wave parameters were less clear.The first seismic detections were recorded around 05:18:40, ⇡ 10 seconds before the first infrasound detection, with a back-azimuth values between 220 and 250 degrees, corresponding reasonably well with the release area of the snow avalanches (Figure 1).During the following 20 seconds we observe a general migration of the seismic backazimuth, up to ⇡ 270-300 degrees N at 05:19:00 UT, corresponding to the runout area.Afterwards, the seismic back-azimuth remains rather stable until the end of the event at 05:19:45 UT.
Considering the apparent velocity, the array processing highlights high values (> 650 m/s) at the beginning and at the end of the event.These values are in agreement with phase velocities (500-950 m/s) measured by Vilajosana et al. (2007a) for snow avalanches in Ryggfonn in Norway, as well as values used by Lacroix et al. (2012) for beamforming in the French Alps.
The central part of the signal, between 05:19:00 and 05:19:15 UT, is characterized by a lower propagation velocity (⇡ 330 m/s), suggesting that the seismic array is likely recording infrasound waves.This corresponds to the time when the infrasound amplitude was maximum (Figure 6a).We suggest that the central part of the signal is strongly affected by the infrasound radiated by the event, that converts to seismic waves at the earth free surface and is efficiently recorded by seismometers.This is an agreement with results obtained by Heck et al. (2017) for an avalanche that did occur from the same path in 2017, and applying the multiple signal classification (MUSIC) analysis to seismic array data.

Elastic energy radiation along the avalanche path
The results of infrasound and seismic array processing presented in Figure 6, allow us to describe the mutual infrasound and seismic energy radiation during the avalanche.Just considering the event duration, it is clear from Figure 6, that the avalanche initiation phase is radiating seismic energy in the ground, while no or minor infrasound is radiated into the atmosphere.This is likely related to the first stage of the event, whilst the powder front is not developed yet.Only 20-25 seconds after the avalanche onset, once the flow accelerates (see auxiliary material), infrasound is radiated from :::::::::::::::::: (Marchetti et al., 2020) : , ::::::::: infrasound ::::: starts :: to :: be ::::::: radiated ::: by : a source that is moving downhill along the avalanche path, as tracked by the infrasound wave parameters (back-azimuth and apparent velocity, Figure 6c, e).
Following the approach described by Marchetti et al. (2015), we use the back-azimuth and the apparent velocity of the seismic and the infrasound detections to investigate the position along the :: In :::: order ::: to ::::::: calculate ::: the ::::::: portion :: of ::: the : avalanche The back-azimuth provides an estimate of the source position in the horizontal plane defined by the array, while apparent velocity is reflecting the source elevation.As expected, the map shows that the back-azimuth varies between 0 :::::: seismic and 360 degrees around the seismic and infrasound arrays (Figure 5a, b), independently of the elevation and the distance from the array.
The infrasound apparent velocity changes, according to the local topography, from a minimum of 330 m/s up to a maximum value of 400 m/s (Figure 5c), solely affected by the distance from the array and the absolute elevation.Therefore, a proxy of the 3d source position requires combining back-azimuth and apparent velocity.We account simultaneously for back-azimuth and apparent velocity by calculating for each point of the DEM the product (BV = Baz i x c a ) of theoretical values (Figure 5d).The resulting parameter defines a new map, with values depending from both the planar position and source elevation.
Such an approach can be easily applied to infrasound wave parameters, while the use of the apparent velocity derived for the seismic wavefield appears complicated by variable phases and complex source-to-receiver travel paths.
Theoretical values of back-azimuth at the seismic array (Baz s , a), back-azimuth (Baz i , b) and apparent velocity (c a , c) at the infrasound array for any point source of seismic and infrasound energy located on the DEM.Product between back-azimuth and apparent velocity of infrasound wavefield (d).The position of the infrasound and seismic arrays are shown by red and blue circles respectively.
Once the theoretical values of the seismic (Baz s ) and the infrasound (Baz i ) back-azimuth, the infrasound apparent velocity (c a ) and their product (BV ) are evaluated (Figure 5), the source radiating areas for the seismic and infrasound signals can be evaluated from real detections (Figure 6.)We ::::::::: infrasound ::::::: energies ::: are :::::::: radiated, ::: we performed a blind search to minimize the difference between wave parameters (Baz s , Baz i , c a and BV ) calculated for the seismic and infrasound detections :::::: and the theoretical values calculated for the DEM :::::: (Figure :: 5). Figure ( 7) shows all the possible source points along the DEM based on the seismic back-azimuth (Figure 7a), the infrasound back-azimuth (Figure 7b), the infrasound apparent velocity (Figure 7c) and their product (Figure 7d).The dark-red areas highlighting all the points of the DEM satisfying a minimum difference threshold.Figure 7 shows that, considering only one parameter at once, only a limited information on the source radiation area can be deduced, unless a constraint of the avalanche path is applied.Such an approach, was applied successfully in previous studies that evaluated the avalanche velocity from infrasound detections (Havens et al., 2014;Marchetti et al., 2015), but limits the analysis to a single avalanche path.
Considering the seismic back-azimuth (Baz s , Figure 7a) only, for example, the detections do not provide any constraint on the source position, as they are consistent with many different directions around the array spanning between 200 and 325 degrees N.However, if we assume that the seismic source is confined within the avalanche path (Figure 2a), it appears that the seismic energy is radiated from the detachment point to the depositional area.Moreover, the scattered values of the backazimuth of the recorded seismic signals, suggest that multiple sources of seismic energy are active at the same time in different sectors of the avalanche path.
The relative position of the avalanche path and the infrasound array, almost in line, influences the efficiency of the infrasound back-azimuth to identify the source position along the path.Considering the infrasound back-azimuth alone (Baz i , Figure 7b), the back-projection of infrasound detections to the topography does no allow us to constrain the position of the source along the path.The infrasound apparent velocity constrains the source elevation (c a , Figure 7c).The maximum value of the apparent velocity of 364 m/s (Figure 6) limits the energy radiation to the lowest part of the avalanche path, clearly suggesting that no, or minor, infrasound is produced high up in the path during the initiation phase.This conclusion is confirmed by the blind search of the infrasound energy radiation area, based on the combination of back-azimuth and apparent velocity (BV , Figure 7d).Here, the minimization of residuals between theoretical and measured values, highlights a limited area on the entire DEM, from the base of the starting zone, where the avalanche accelerates and follows the channel down to the valley.
Any possible contribution from multiple sources along the path or by an elongated source were not considered.This could lead to an underestimation of the total seismic energy of the event.
seismic energy is radiated all along the avalanche path (Figure 7a).Moreover, it requires a-priori characterization of the quality factor of surface waves at the site (Vilajosana et al., 2007b), thus preventing a general application of the proposed procedure at various sites.
Similarly, infrasound amplitude is expected to change dramatically as a function of avalanche type (dry/wet) and path geometry, and our results suggest that estimating avalanche size from infrasound signals could be difficult.Signal duration is, for example, reflecting only the part of the path where the avalanche is accelerated, or where the powder cloud develops (Figure 7d).Considering the radiation of sound by a moving body assumed to be a solid sphere, Naugolnykh and Bedard (1990) suggested that the frequency of recorded infrasound must scale inversely with the body size as follow: where c is the velocity of sound in the atmosphere while D is the diameter of the sphere.

Conclusions
Results presented here, and obtained from seismic and infrasound array analysis :: for : a ::::::: powder :::: snow ::::::::: avalanches :: at ::::: short :: (< ::::: 1000 :: m), highlight two separate mechanisms of elastic energy radiation by a snow avalanche.The infrasound energy is radiated only when the powder part develops, and is not produced during the initiation or deposition phase.The duration of the infrasound signal is thus not representative of the entire volume of snow that was transported by the avalanche.Because of the clear migration of infrasound detections in terms of back-azimuth and apparent velocity, we suggest that the source mechanism :: of ::: the ::::::::: infrasound ::::: signal : can be interpreted as a moving point source.The clear wave parameters ::::::: variation :: of :::::::::::: back-azimuth ::: and :::::::: apparent ::::::: velocity obtained from the array analysis, suggest that infrasound can be used as an efficient monitoring for avalanche detection purposes :: in ::: case :: a :::::: powder ::::: cloud :::::::: develops.Back-projection of the infrasound detections on the avalanche path, suggested that the infrasound energy is radiated only when the flow is confined within a narrow path.According to the analytical formulation of Carrol et al. (2013), such a condition enhances the formation of the powder front.
Reviewer: Figure Caption 1. Replace "array" by (c)  arrays.Indicate the meaning of si and mi.

Figure
Figure caption has been corrected.Reviewer: -Figure Caption 3 Specify the array (infrasound?).The arrays are distant 500 m and the scale is not included.

Figure
Figure caption has been corrected.Reviewer: -Figure 4. Redraw figures c) and d) according to my previous comments Subplots c and d have been replaced.

Figure
Figure has been corrected.

Figure 6
Figure 6 has been modified following all the suggestions of the reviewer.Reviewer: -Figure 7. Indicate units, when necessary, in the Figure and in the Figure caption.• N is it correct in Figure 7c).

Figure 7
Figure 7 has been corrected according to the comment of the reviewer.Reviewer: -Figure Caption 8. Indicate the location of the arrays.C6

Figure 1 .
Figure 1.Map (a) showing the location of the Dischma valley, south of Davos, Switzerland.The location of the infrasound array (red triangle) and the seismic array (white square) are show, as well as the Chlein Sattelhorn avalanche path (black arrow).Positions are given in Swiss coordinates (CH1903).Reproduced by permission of swisstopo (JA100118).Details of the geometry of the seismic (b) and infrasound array :::: arrays : (c).

Figure 2 .
Figure 2. (a) Digital Elevation Model showing the installation site within the Dischma valley, south of Davos, Switzerland, with the position of the seismic array (blue dots), the infrasound array (red dots) and the Chlein Sattelhorn avalanche path (black arrow).(b) Photo of the field site with the position of the seismic array (blue dot), the infrasound array (red dot) and the approximate contour of the Chlein Sattelhorn avalanche from 5 February 2016 (orange).The approximate backazimuth angles to the start zone and :::::::: maximum runout zone of the avalanche relative to the seismic and infrasound array are also shown (colored arrows).

125
RAMMS predicted a maximum flow depth of almost 3.5 m, that was reached after a travel distance of ⇡ 200 m along the path.The maximum front velocity, of ⇡ 35 m/s, was reached at the end of the first, and highest, part of the path, before the deceleration at the terrain break (Figure8).Lower values of front velocity and flow depth result from the model below the terrain break.

Figure 3 .
Figure 3. Picture showing the slope west from the :::::::: infrasound array in the afternoon of February, 2nd (a, last clear image before the event) and in the morning of February, 6th, 2016 (b, first clear image after the event) that shows the avalanche accumulation area.

Figure
Figure showing the flow extent modeled by RAMMS and highlighting maximum flow depth (a) and flow velocity (b).

Figure 6 .
Figure 6.Amplitude, back-azimuth and apparent velocity of infrasound (a,c and e, respectively) and seismic (b,d and f, respectively) detections for the avalanche of 5 February 2016.The shaded area highlights the time window of sound propagation velocity recorded for the seismic signal.

Figure 7 .
Figure 7. Possible radiation areas (dark red) of seismic and infrasound energy, obtained from seismic back-azimuth (Bazs, a), infrasound back-azimuth (Bazi, b), apparent velocity (ca, c) and the combination of infrasound back-azimuth and apparent velocity (BV , d) .