Snow avalanche energy estimation from seismic signal analysis

Abstract A method to determine the dissipated seismic energy into the ground by a down going avalanche is presented. Evaluation of the seismic energy is useful for avalanche size classification, model validation, and for characterization and better understanding of the avalanche evolution as it propagates downhill along the changing slope. The method was applied to two different type avalanches that were released artificially on 2004/02/28 and 2005/04/15 at Ryggfonn (Norway) avalanche experimental site, operated by the Norwegian Geotechnical Institute (NGI). The analysed seismic data were recorded by the University of Barcelona seismic instruments consisting of two three-component wide-range seismometers located respectively, in the middle and on the side of the avalanche path. The energy determination requires a priori seismic characterization of the site and the knowledge of the avalanche front speed. In this paper a seismic characterization (surface wave phase velocity and amplitude attenuation factor) of the Ryggfonn site is presented. This characterization will serve for subsequent studies. We attribute the main source of seismic signals for the studied events to basal friction and ploughing occurring at the avalanche front and related to the changing slope in the propagation path, which causes high seismic energy dissipation. A comparative study of the evolution of the dissipated seismic energy with the energy generated by a simple sliding block model of constant mass was performed. The observed differences highlight the importance of ploughing and basal friction and the specific characteristics of the avalanches, such as their length and type. The difference between the calculated total dissipated seismic energy for the two similar size avalanches reflects their different flow type. As expected, the dry/mixed event dissipates a smaller amount of energy (∼ 1.2 MJ) than the dry/dense event (∼ 2.8 MJ).


Introduction
Estimations of the seismic energy transmitted into the ground by snow avalanches could be useful for model validation and avalanche size classification. Moreover, evolution of the energy transmitted into the ground could give information on the source of the seismic signals generated by an avalanche and, in consequence, on the evolution of the avalanche. In addition, similar to earthquakes, the estimation of the radiated energy by snow avalanches can provide good estimates of their magnitude which could be used as a new tool to classify avalanches. Unlike other physical parameters (impact pressure, snow deposit density), there are few estimations on the energy dissipated by snow avalanches. In this paper a method to estimate the energy transmitted into the ground by snow avalanches using seismic observations is presented.
In general, it is known that stronger ground vibrations are observed with denser avalanches. However, the exact nature of energy conversion from potential to seismic energy during the avalanche propagation is not known. In this paper we also aim to clarify this point.
A significant amount of the potential energy of a snow avalanche propagating down the slope is spent in overcoming the resistance of the flow at the fluid/solid interface. This energy is transformed into a combination of heat, ground vibration and sound waves.
The energy transmitted into the ground by snow avalanches, besides the impacts produced by intrinsic elements travelling inside the flow, is mainly attributed to the friction produced by the bottom of the avalanche in contact with the ground. Earlier studies carried out by Suriñach et al. (2000 and2001) where video images and seismic signals from snow avalanches were compared, demonstrated that the most energetic peaks of the seismic signals coincided with the passing of the avalanche front through a change of slope. However, no quantification of the transmitted energy was given. Firstov et al., (1990) presented one of the firsts studies on energy transmitted into the ground by snow avalanches using seismic data, however, the method used was not presented in detail. For other natural phenomena, such us Tornados (Tatom and Vitton, 2001) and debris flows (Suwa et al., 2003), similar techniques have been presented to obtain the energy transmitted into the ground and proved to be useful for the event magnitude classification.
In this paper the evolution of the energy transmitted into the ground by two avalanches was calculated using the method presented. We took advantage of the availability of two seismic stations installed in an avalanche experimental site, and that their spatial location was suited for the developed methodology. Additionally, the energy evolution estimates were compared with simple sliding block models (Kanamori, H., and J. W. Given., 1982, Brodsky et al., 2003 to asses the reliability of the methods. The analysed data came from Ryggfonn (Norway) avalanche experimental site operated by the Norwegian Geotechnical Institute (NGI) (Lied et al., 2002) and recorded by the University of Barcelona seismic instruments during the artificially released avalanches of 2004/02/28 and 2005/04/15. In addition, these data were complemented with the speed evolution profiles for the analysed events, which were obtained from the analysis of video images recorded by NGI and PCM model numerical simulation (Perla et al., 1980). The avalanche group at the Universitat de Barcelona (UB) has been studying the seismic signals generated by avalanches at different sites in Europe since 1994 (Suriñach, 2004). The recent studies of the group have focused on: the identification of the main sources of the seismic signals produced by snow avalanches, the determination of avalanche front speeds and the characterization of avalanche seismic signals for detection purposes. (e.g. Biescas et al., 2003;Suriñach et al., 2005;Vilajosana et al., 2006). The method for the energy determination of avalanches presented here is a continuation of these previous studies.

Experimental Site and Data
The Ryggfonn full-scale avalanche site, situated 500 km north-west of Oslo, Norway, was set up to study snow avalanches by the NGI in 1980(Lied et al., 2002. Since then, approx. 2-3 avalanches per year have been released at this site. The avalanche path at Ryggfonn has a vertical drop of 900 m and a horizontal length of 2100 m (Figure 1).
The avalanches released at the site according to the Canadian snow avalanche size classification (McClung and Schaerer., 1993) range in size between 2 (mass of 100 T) and 4 (mass of 10.000 T), and occasionally may even reach class 5 (mass of 100.000 T). concrete structure containing three load cells is placed approx. 230 m up-slope from the dam also in the main avalanche path. Moreover, a 5.5 m high cylindrical steel tower equipped with two more load cells and one geophone (GF1) which triggers the recording system is placed 90 m above this structure (Figure 1). A shelter containing control and recording instruments is located in the valley 500 m east of the dam. The shelter is provided with power, telephone line and ISDN connection. The recording system consists of a data-logger REFTEK DAS 130-06, which is triggered by GF1 geophone when the avalanche front hits the steel tower. The data are recorded at a sampling rate of 200 sps. A GPS antenna installed on top of the shelter provided accurate base of time.
In this study we analyzed the seismic data recorded by University of Barcelona from the avalanches of 2004/02/28 and 2005/04/16. Henceforth referred as events A and B.
Event A was an artificially released dry/mixed medium sized (Size 4) avalanche. A subsequent field survey showed that although much of the debris was retained by the dam, the dust cloud went far beyond. The volume of the deposit in the run-out zone below the load cells on the concrete structure was estimated to be around 100,000 m 3 .
The speed estimates of the avalanche on the upper part of the path were provided by NGI from a numerical simulation of the flow using a PCM model (Perla et al., 1980). Event B was an artificially triggered medium sized (Size 4) dry/dense avalanche with a frontal aerosol part which disappeared 100 m upslope of the dam. In the lower part of the path wet snow was incorporated into the avalanche. In order to obtain speed estimates of the avalanche on the upper part of the path, video images from the event were recorded. Useful data in the interpretation of the results from the subsequent field survey of the event included cartography of the deposits, snow depth and density of the snow in the deposition area (Gauer and Kristensen, 2005).

Data Analysis and Methodology
Our previous studies on avalanche wave characterization showed that the seismic signals generated by snow avalanches are mainly composed of surface waves (Suriñach et al., 2001). For this reason, the seismic energy transmitted into the ground by the avalanche is obtained following the methodology proposed by Suwa et al., (2003) which is suitable for surface waves. If we assume that the near surface ground is homogeneous and isotropic (or that the local ground heterogeneities are smaller than the seismic signal wavelength considered, in our case from 70 m to 2777 m), the total amount of energy dissipated for surface waves over a cylindrical wave front ( Figure 3) can be calculated as: Where A is the amplitude of the ground motion recorded at the observation point in (m/s), c is the phase velocity of the seismic surface waves, ρ is the ground density, r is the distance avalanche front-seismometer, h corresponds to ¼ of the wave length (surface waves amplitude at depth h has been reduced by a factor 1/e and hence the contribution of deeper waves is not significant (Aki and Richards (1980)), f is the frequency in Hz and Q(f) is the amplitude attenuation factor for seismic waves at Ryggfonn. In this expression, the amplitude decay with time is produced by the geometric spreading of the waves and the anelastic attenuation of the amplitude with distance.
According to Eq. 1 the determination of the energy transmitted into ground should be a straightforward task. However, for snow avalanches this is not the case. The specific seismic characteristics of the site must be previously determined and a characterization of the seismic records produced by the avalanche must be performed. The process to obtain the seismic energy dissipated into the ground by the avalanche is summarized below: Site: 1) Phase velocity calculation for seismic waves at Ryggfonn site; 2) Amplitude attenuation factor determination at Ryggfonn site. Avalanche: 3) Determination of the distance avalanche front-seismometer per unit of time; 4) Avalanche seismic signal characterization; And Energy estimation: 5) Calculation of the seismic energy dissipated for each frequency and each component of the seismic signals; 6) Integration over all frequencies and; 7) Integration over horizontal components.

Phase velocity calculation for seismic waves at Ryggfonn site
Taking advantage of the availability of seismic data from the explosions that triggered the artificially released avalanches (A, B) the determination of the phase velocities of the P, S and surface waves at this site was performed. The velocity of the P waves was obtained through the difference in the arrival time, performed by picking of the P wave generated by the explosion, at the two distinct seismometers (UBtrack and UBhut in Figure 2). The difference in the distance explosion-UBtrack in front of the distance explosion-UBhut, which is 181.44 m permitted this calculation. According to Aki and Richards (1980), S wave velocities are, in general, Unluckily, only two explosions were available to perform this calculation; more data could have given more reliable results. However, the obtained values for the seismic wave propagation velocities seem to be reasonable estimates for the existing soil characteristics.

Amplitude attenuation factor determination at Ryggfonn site
To obtain an estimation of the amplitude attenuation factor Q for superficial waves at Ryggfonn, we adapted the methodology proposed by Jolly et al., (2002). We used the known locations of the explosions and the two seismic stations ( Figure 2).
Basically, the method consists of determining the Q value that minimizes the difference in the amplitudes recorded at the two different seismometers corresponding to a same source, once they have been corrected by geometrical spreading and anelastic attenuation of waves due to the different distance explosion-seismometer. This process is performed in the time-frequency domain for convenience and each of the explosions signals is treated independently. The attenuation factor Q was estimated given that the location of the explosions that triggered the avalanches was known. To this end, 1) we selected in the time series (UBtrack and UBhut) the signals generated by the explosion value minimizing the RMS residual amplitude (daRMS), was also selected. This value corresponds to the Q value that best fits in the two independent stations. The same procedure was repeated for each of the available explosions, finally, 6) a linear relationship between the Q values in function of the frequency was obtained (Figure 4).
The specific relationship for the Ryggfonn site can be given as: 3

Distance avalanche front-seismometer
The avalanche front-seismometer distance (r), which varies in time, is necessary to determine the decay due to distance observed in the recorded seismic amplitudes (Eq. 1)

Avalanche seismic signal characterization and processing
Before proceeding with the energy estimation, the time-frequency avalanche seismic signal characterization was necessary. The specific characteristics of the signals recorded during the events were determined in order to isolate the signals generated by the avalanche itself from the signals generated by other seismogenic sources. Each time series was filtered with a 1-40 Hz 8th order band pass Butterworth filter to obtain the band were the maximum seismic energy was concentrated in accordance with the information obtained in the total spectrum of the time signal. Moreover, a 17-21 Hz 4th order band reject filter was applied to remove the noise generated by the helicopter that was flying during the experiments (Biescas, 2003). Finally, for each component (N-S, E-W, Z), 17 "mono-frequency" time series were obtained by filtering the pre-filtered time series with overlapped windows 2 Hz wide, from the 1-3 Hz window to 37-39 Hz.
The central frequency value of each window was considered to be the frequency of the "mono-frequency" filtered time series.
Earlier studies of our group in other sites, showed that main parts of the seismic signals generated by snow avalanches were composed of surface waves (Suriñach et al., 2001).
In consequence, we assume the same behaviour for the signals obtained at Ryggfonn.
However, due to the importance of this assumption in the energy estimation, a ground particle motion analysis of the filtered signals obtained at Ryggfonn was performed to confirm this hypothesis (Figure 7).
In general, the vertical component, Z, of the seismic signal presents lower amplitude than the horizontal components (E-W, N-S). In addition, it is also observed that the ground particle motion for a number of wave packets is completely confined in the horizontal plane (this is specific for Love waves). The ground particle motion in other cases consists of elliptical motion in the vertical plane parallel to the direction of propagation of the avalanche (Figure 7). For these reasons we conclude that the main part of the seismic signals produced by the avalanches in Ryggfonn are superficial waves. In order to compare the energy estimations obtained using the seismic data recorded in UBtrack and UBhut, and to detect local site effects, the method of Nakamura (1989) was applied. The results showed that the energy estimations obtained in UBtrack and UBhut are of the same order.

Energy estimation
The energy dissipated by the surface waves was obtained following Eq. 1.

Results and Discussion
Using the method described in the previous section we estimated the energy dissipated  (Figs 8a and 8b) is also predicted by the sliding block model (Figures 8c and 8d). The evolutions of the seismic energy obtained for avalanches A and B seems to contradict the experience and also the sliding block model predictions. Owing to the incorporation of mass and the increase of the avalanche speed, as the avalanche evolves, we would expect the energy transmitted in the upper part to be smaller than that in the lower part. However, when considering the source of the seismic signals generated by the avalanches an explanation to this apparent contradiction comes out. In earlier studies where seismic signals were compared with FMCW-radar measurements it was concluded that the main source of the seismic energy are the snow ploughing at the avalanche front and the erosion produced by the basal friction of the dense body inside the flow in contact with the ground (or snow cover) (Biescas et al., 2002). It is known that ploughing can be a dominant mechanism at the avalanche front when there is a The total energy transmitted for avalanche B from the upper part of the path to UBtrack seismometer location is 4.2 10 6 J this value corresponds to a 0.03% of the potential energy of the avalanche if we consider that the mean mass of the avalanche was 18.900 T. This mass value was estimated as an average between the starting slab volume and the volume of the final deposits obtained in the corresponding subsequent field survey.
Similar value of the total energy dissipated was obtained using the speeds from the PCM simulation (4.1 10 6 J). The total energy transmitted for event A from the upper part of the path to the UBtrack seismometer location is 2.7 10 6 J. This value is slightly lower than that observed for event B. This result was expected due to the presence of lower density snow in the dry/mixed avalanche (A) compared to the dry/dense avalanche (B).

Conclusions
A method to determine the seismic energy dissipated by snow avalanches and its evolution was developed and applied to two events of different type (dry/dense and dry/mixed artificially released avalanches). The seismic signals obtained from the explosions that triggered the avalanches recorded at two seismic stations were used besides the corresponding avalanche seismic signals. The energy determination needs a prior seismic characterization of the site and the knowledge of the avalanche front speed. In this paper a seismic characterization (surface waves phase velocity and attenuation factor) of the Ryggfonn site is presented. This characterization will serve for subsequent studies. The energy estimations obtained suggest that it is possible to identify the source of the seismic signals produced by the avalanche. The main source of seismic signals for the studied events corresponds to basal friction and ploughing at the avalanche front in changes of slope; the latter causing high seismic energy dissipation. The energies obtained could be a useful input parameter for the avalanche model validation and the presented method can be used as a new tool for empirical avalanche size classification.
The total energy dissipated from the top cornice to the location of the sensor in the avalanche path was obtained for the two events. The different type of these events, although they had the same size (4, Canadian size classification, McClung and Schaerer, 1993) is reflected in the seismic energy dissipated. The dry/mixed event dissipates a smaller amount of energy (2.7 MJ) than the dry/dense event (4.2 MJ). This is supported by the comparison of the evolution of the seismic energy dissipated with the energy generated by a simple sliding block model of constant mass.
In the present study the speed of the avalanche front needed for the seismic energy estimation was obtained through video images and PCM model simulations owing to the data available. In this type of study, calibrated PCM model simulations proved to be useful in the case of lack of reliable avalanche front speeds. However, in cases of an adequate distribution of sensors, the seismic method presented in Vilajosana, et al, (2006) is a tool to precisely determine the speed of the avalanche front. This method and the method presented in this paper could be a good solution to estimate the seismic energy and became a good tool to determine the avalanche size from seismic measurements.

Simple sliding block model
Simple sliding block models have been employed to calculate dipole-like basal force histories from the acceleration-deceleration phases of historical slides and to compare with the force histories inferred from seismic records (Kanamori, H., andJ. W. Given., 1982, Brodsky et al., 2003). A theoretical estimation of the energy per unit of mass dissipated by the avalanche in a simple block model in the downslope direction is given by: Where ∆s is the displacement experienced by the block in the down slope direction and (Eq.A2) is the down-slope component of the acceleration experienced by the sliding block; And g is the acceleration of gravity, θ is the slope angle, v(t) is the speed of the avalanche front, ξ is drag friction coefficient and µ is the basal friction coefficient.