Seismic detection and tracking of avalanches and slush flows on Mt. Fuji, Japan

Avalanches are often released at the dormant stratovolcano Mt. Fuji, which is the highest mountain of Japan (3776 m a.s.l.). These avalanches exhibit different flow types, from typical dry-snow avalanches in winter to slush flows triggered by heavy rainfall in late winter to early spring. Avalanches from different flanks represent a major natural hazard as they can reach large dimensions with run-out distances up to four kilometres, regularly destroy parts of the forest and sometimes damage infrastructure. For monitoring the volcanic activity of Mt. Fuji, a permanent and dense seismic network is installed around 5 the volcano. The small distance between the seismic sensors and the volcano flank (< 10 km) allowed us to detect numerous avalanche events from the seismic recordings and locate them in time and space. We present the detailed analysis of three avalanche/slush flow periods in the winters of 2014, 2016 and 2018. The largest events (size class 4–5) are detected by the seismic network at maximum distances of about 15 km, medium-size events (size class 3–4) within a radius of 9 km. For localizing the seismic events, we used the automated approach of amplitude source location (ASL) based on the decay of the 10 seismic amplitudes with distance from the moving flow. The recorded amplitudes at each station have to be corrected by the site amplification factors, which are estimated by the coda method using data from local earthquakes. Our results show the feasibility of tracking the flow path of avalanches and slush flows with considerable precision and thus, estimating information such as the approximate run-out distance and the average front speed of the flows, which are usually poorly known. To estimate the precision of the seismic tracking, we analyzed aerial photos of the release area and determined the flow path and run-out 15 distance, estimated the release volume from the meteorological records and conducted numerical simulations with Titan2D to reconstruct the dynamics of the flow. The precision as a function of time is deduced from the comparison with the numerical simulations showing mean location errors in the range between 85 m and 271 m. The average front speeds estimated seismically, which ranged from 27.1 m s−1to 50.6 m s−1, are consistent with the numerically predicted speeds. In addition, we deduced two scaling-relationships based on seismic parameters to quantify the size of the mass flow events. Our results are indispensable 20 for assessing avalanche risk in the Mt. Fuji region as seismic records are often the only available dataset for this natural hazard.


Introduction
Rapid gravity-driven flows such as snow avalanches and slush flows are major natural hazards in mountain areas worldwide.
The fast socio-economic development of these regions demands reliable early-detection systems of these flows. Remote seismic 5 monitoring has proven to be a successful non-invasive technique for detecting avalanches (e.g. Suriñach et al., 2001) and other types of mass movements (e.g. Suriñach et al., 2005). These systems, being relatively inexpensive, enable monitoring mass movements in an extended area regardless of weather and visibility conditions. Avalanche monitoring systems based on seismic sensors were developed in the past decades (e.g. Leprettre et al., 1996;Nishimura and Izumi, 1997;Suriñach et al., 2001) and are at present installed in different sites (e.g. Pérez-Guillén et al., 2016;Heck et al., 2018a). However, these monitoring systems 10 are not deployed as operational, real-time avalanche detection systems yet due to the challenges of both rapid detection and precise localization of events.
In recent years, seismic monitoring has been employed in different branches of avalanche research as an indirect method to 20 study or detect them. Automatic detection of avalanches in the continuous seismic data has been a focus of study for several decades (e.g. Leprettre et al., 1996;Bessason et al., 2007;Hammer et al., 2017;Heck et al., 2018a, c). One goal has been to create a catalog of avalanche activity to validate forecasting models, another to develop warning systems. In addition, seismic methods have been used to infer the front speed (Nishimura and Izumi, 1997;Vilajosana et al., 2007a;Lacroix et al., 2012), the energy dissipation into the ground (Vilajosana et al., 2007b), and the avalanche flow regimes and runout distances (Pérez-25 Guillén et al., 2016), which are indispensable for assessing avalanche risk.
Apart from detecting and characterizing the source, seismic monitoring systems are a powerful tool for locating different types of natural hazards. So far, these systems have not been widely used to locate avalanches because of methodical limitations.
Unlike earthquakes, avalanches are extended moving sources of seismic energy that generate a complex wave field. Different wave types and phases may arrive simultaneously, complicating their identification (Biescas et al., 2003;Vilajosana et al., 30 2007a). Consequently, traditional earthquake localization procedures based on phase-picking methods are not suitable for localizing this type of sources. The usual method for locating moving seismic sources is based on beam-forming techniques that exploit the inter-trace correlation of signals from several seismic sensors deployed as a seismic array (Almendros et al., 1999).  Using this methodology, Lacroix et al. (2012) successfully localized eighty snow avalanches in the French Alps. Recently, Heck et al. (2018b) compared two different array processing techniques to locate avalanches, the common beam-forming approach and the multiple signal classification (MUSIC) method; they were able to map eleven avalanches in Switzerland.
Both techniques allow computing the back-azimuth angles and the apparent velocities of the incident wave field. Avalanche paths can thus be reconstructed by intersecting these back-azimuths. However, ambiguities in the path assignment may arise in 5 some directions (Lacroix et al., 2012).
An alternative approach for the location of moving sources is the amplitude source location (ASL) method that has been used previously to locate different types of mass movements such as rockfalls (Battaglia and Aki, 2003), lahars (Kumagai et al., 2009(Kumagai et al., , 2010 and debris flows (Ogiso and Yomogida, 2015;Walter et al., 2017). ASL is based on the decay of the seismic amplitudes with distance from the moving flow. While array techniques require setting the sensors in a specific configuration 10 (i.e. array geometry), where the inter-sensor distance is usually small (< 100 m), ASL is able to locate seismic sources with an open distribution of sensors commonly configured as a seismic network. ASL provides the spatial location of the source automatically by fitting the site-corrected amplitudes at several sensors with the expected amplitudes derived from fundamental properties of wave propagation. Previous studies showed that the estimated flow paths using the ASL approach were consistent with the observed deposits (Kumagai et al., 2009;Ogiso and Yomogida, 2015;Walter et al., 2017), but the precision of the 15 seismic localization as a function of time still remains unknown.
Besides providing the source location, ASL is also capable of estimating additional flow properties. For instance, Ogiso and Yomogida (2015) applied this technique to locate five debris flows released at Miharayama volcano, Izu Oshima island (Japan), obtaining estimates of the average speeds of the flows. They also compared the source amplitudes of the debris flows, which may be used to quantify the size of the events (Kumagai et al., 2013). Kumagai et al. (2015) proposed two parameters, the 20 source amplitude and the cumulative source amplitude, deduced from ASL to quantify the sources of the tremors generated by lahars. However, a scaling relationship between them and the size of the mass movement has not been inferred yet. In this study, we applied the ASL method for the first time to locate snow avalanches and slush flows. Our study area is the stratovolcano Mt. Fuji (Japan), where a dense local seismic network is deployed for the study of the volcanic activity and the seismicity of the region (Fig. 1). Avalanches and slush flows, which release frequently on all flanks of the volcano, are the dominant natural hazard in Mt. Fuji's present period since its last eruption in 1707. Large-size avalanches on the western and northern slopes have been reported since 1980 by the Yamanashi Road Corporation, whereas historical events have been 5 determined by dendrochronology (Tanaka et al., 2008). Slush flows are often triggered by heavy rainfall events that destabilize the snowpack. They attain run-out distances up to four kilometres and regularly destroy parts of the forest (Anma, 2007).
The next section characterizes the Mt. Fuji region and describes the instrumentation deployed around the volcano and the analysis of the avalanche/slushflow events by traditional methods. The ASL method for locating flows, the correction of the observed amplitudes by site amplification factors and the seismic tracking of seven flow events are presented in Sec. 3. In

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Sec. 4, we use numerical simulations to reconstruct the avalanche trajectories and thus to assess the precision of the ASL method. We also estimate the average speeds of the flows from the seismic tracking and compare them with the numerically predicted speeds, and determine the limits of seismic detection with the local network (Sec. 5). We also examine possible correlations between source amplitude and seismic energy with the approximate run-out distance. Finally, a discussion of the main results and conclusions are presented in Sec. 6 and Sec. 7. 2 Observed avalanche and slush flow events at Mount Fuji

Study area
The stratovolcano Mt. Fuji is the highest mountain of Japan (3776 m a.s.l.) and located 100 km SW from the Tokyo metropolitan area (Fig. 1). The summit of the volcano towers almost 2000 m above all mountains within a range of 50 km. The mean annual temperature at the summit is −7°C, ranging from −20°C in February to +5°C in August (Anma et al., 1988). The annual 5 precipitation at Mt. Fuji is about 2500 mm, with frequent heavy-precipitation episodes that may exceed 200 mm in a few hours.
As a typical stratovolcano, Mt. Fuji has gradual slopes that range from ∼10°at low elevations (< 1700 m a.s.l.) to ∼25°at mid elevations and ∼35°at high elevations (> 2900 m a.s.l.). From winter to early spring, the slopes are usually covered by snow at elevations above 2000 m a.s.l. (Anma et al., 1988).

Instrumentation
A dense permanent seismic network is installed around Mt. Fuji for monitoring its volcanic activity ( This station was operative during the winters 2016 and 2017, recording data continuously with a sampling rate of 100 Hz. For this study, the raw seismic data from the different stations were first transformed to ground velocity (m s −1 ), and all signals 10 were filtered with a 4th-order Butterworth band-pass filter between 1 and 45 Hz.
Meteorological data are acquired by three automatic weather stations (WS1, WS2 and WS3 of Fig. 1

Avalanche events
The small distance between the seismic sensors and the volcano flank (< 10 km) allowed us to detect numerous avalanches and slush flows that released spontaneously in three episodes in 2014, 2016 and 2018, respectively (Table 1). We used information about observed avalanche deposits, aerial photos and weather data to constrain the time window within which to search manually for avalanche signals in the seismic data from the local network. Other seismic sources could be discarded by comparing the candidate events with a regional seismic catalog provided by NIED.

The event of 13 March 2014
A spontaneously released avalanche descended the Namesawa path, which is located at the west-northwest (WNW) flank of 5 Mt. Fuji (avalanche #1 of Table 1), on 2014-03-13. An aerial photograph taken after the event shows the deposits of a large avalanche that impacted the road and destroyed part of the nearby forest ( Fig. 2.a and b). A run-out distance of 2.9 ± 0.2 km (size 4-5 according to McClung and Schaerer (2006)) was estimated from aerial photos, the observed deposits and damage.
This avalanche was first seismically detected at 18:14:43 by the V.FUJ2 station ( Fig. 3.a), which is located at the summit of the volcano. At this time, the temperature recorded by WS2 at the summit of Mt. Fuji was −4°C. WS1 reported a temperature 10 of +5°C and a cumulative precipitation of 140 mm in the 12 hours before the avalanche; the wind speed ranged from 4 to 16 m s −1 during the previous 24 hours, blowing mainly from SE and S (Fig. 4).
The normalized vertical seismograms recorded at each location are shown in Fig. 3.a, ordered according to increasing distance from the avalanche. V.FUJD was closest (∼1 km from the run-out area) and EV.FJO1 farthest at a distance of ∼20 km.
In general, maximum amplitudes decrease as a function of distance to the source. However, some stations (V.* and EV.*) show 15 great amplifications due to local site effects. This avalanche was detected by 11 seismic stations at a maximum distance of 15 km. The envelope of the signal from V.FJUD exceeded a signal-to-noise ratio of 2 during 505 s ( Table 1) that is slowly moving downwards, following a gully that approaches the location of V.FUJD (path #2 of Fig. 2.a).
Three other candidate snow avalanches, #2, #3 and #4 of Table 1, were seismically detected in a time window of two hours after the large avalanche. For these avalanches, no field observations or photos are available. The seismograms generated by these avalanches are shown in Sp. 1 of the supplementary material.
The event of 14 February 2016 10 Two wet avalanches descended almost simultaneously in the Yoshidaosawa path (north-eastern flank; avalanche #5) and the Namesawa path (west-north-western flank; avalanche #6) on 2016-02-14 (Table 1). Aerial photographs taken two days later show that the flow #5 split into two branches (#1 and #2 of Fig. 2.c) and impacted the road on the NE flank. The fracture of a large slab was identified at elevations of 3200-3400 m a.s.l., and the estimated maximum run-out distance was 3.0 ± 0.4 km (size 5). This avalanche was seismically detected at 05:27:18 ( Fig. 3.b). The avalanche #6 impacted the deflecting dam on the 15 WNW path (#1 of Fig. 2.d) and destroyed several instruments installed just beneath it so that the release time was known. A large seismic signal was first identified at 05:34:03 ( Fig. 3.b). The aerial photograph shows a fracture line at ∼3400 m a.s.l.
( Fig. 2.d). The observed deposits were a mixture of snow, ice and rocks, the latter entrained at lower elevations where there was no snow. The estimated run-out distance is 2.5 ± 0.2 km (size 4-5). An average temperature of +7.4°C and a cumulative precipitation of 134 mm were recorded by WS1 over the 12 hours before the two releases ( Fig. 4.a). The wind speed ranged 20 from 2 to 10 m s −1 in the preceding 24 hours, blowing from SSE and S ( Fig. 4.b). The temperature recorded by WS2 at the summit of Mt. Fuji was −1.8°C.
The normalized vertical seismograms generated by these flows are shown in Fig. 3.b. The avalanche #5 was detected by 11 seismic stations at a maximum source-receiver distance of 12 km, whereas the avalanche #6 was detected by 8 stations at a maximum distance of 10 km. The seismograms of the avalanche #5 show the usual spindle-shape pattern of avalanche 25 signals. However, the triangular shape of the spectrogram is not so well developed, with all the seismic energy concentrated below 10 Hz ( Fig. 3.b) due to the relatively large distance between V.FJUD and the moving flow (∼4-7 km). Despite the large dimension of avalanche #5, the duration of its signals (70 s at V.FJUD; Table 1) is shorter than for avalanche #6 (173 s at V.FJUD), mainly due to signal attenuation with distance. The longest signal duration for avalanche #5 (101 s) is recorded at N.FJ5V, the station that is closest to the flow path. The spectrogram of avalanche #6 shows an increase of the higher-frequency The ASL method exploits the progressive attenuation of seismic amplitudes with increasing distance. The method compares the recorded amplitudes at several sensor locations x j with the expected amplitudes that are derived from fundamental properties of wave propagation, namely (i) attenuation due to geometrical spreading, (ii) attenuation due to absorption during propagation, and (iii) local site effects. The decay relationship of the seismic amplitude, u j , at the jth station and instant t due to the attenuation of body waves with distance is expressed by (Kumagai et al., 2010): where r j (t) ≡ x(t) − x j is the distance between the source and the jth station at time t, β is the seismic wave velocity, A 0 (t) the source amplitude. The factor 1/r j (t) accounts for purely geometric attenuation, while exp(−Br j (t)) represents absorption with mean attenuation coefficient B = πf /(Qβ). B depends on the quality factor Q, the seismic velocity β in the medium and the frequency f of the waves. The source amplitude is estimated from: where N is the total number of stations and u o j are the observed amplitudes. In order to use ASL to locate seismic events, the observed amplitudes should be corrected for local site effects that are caused by the variability of the terrain characteristics (e.g. different rock types, consolidated or unconsolidated sediments) at the locations of the seismic station. Therefore, we first estimated the site amplification factors using the coda method (Sec. 3.2) and then used these factors to correct the raw amplitudes at each station. Finally, the avalanche location x(t) is estimated by minimizing the residual as a function of t. Equation (3) is minimized by sampling x at the nodes of a regular grid with a mesh spacing of 10 m. The source-sensor distances r j were calculated using a digital elevation model (DEM) with 10 m resolution. The dimension of the 5 grid was about 14 km (East) by 12.5 km (North), which includes all the potential avalanche paths of Mt. Fuji.
The ASL method uses the high-frequency seismograms generated by the recorded flows under the assumption of isotropic S-wave radiation. This assumption is valid in highly heterogeneous media, such as volcanoes, where multiple scattering of high-frequency S-waves results in an isotropic radiation pattern (Kumagai et al., 2010;Morioka et al., 2017). Dominance of body waves over surface waves is highly plausible because surface waves are usually trapped in a shallow layer at the volcano 10 surface (Yamamoto and Sato, 2010) and S-waves are the dominant body waves in volcanic areas (Kumagai et al., 2010).
The observed vertical components were filtered using a band-pass filter between 4 and 8 Hz, which is the highest frequency band with sufficient signal-to-noise ratio in the stations selected for source location. We estimated the mean amplitudes of the envelope using a 5 s wide sliding window, shifting it at 1 s increments. At each location, the amplitudes are corrected by the site amplification factors, and the emission-time window is shifted according to the S-wave travel times. We used a mean S-wave 15 velocity of β = 1400 m s −1 , typical of volcanic surface material (Ogiso and Yomogida, 2015;Kumagai et al., 2010). A quality factor Q = 125 was adopted after testing a range of Q values. Ogiso and Yomogida (2015) used Q = 100 to locate debris flows at Miharayama volcano on Izu-Oshima island (Japan), which is located near Mt. Fuji, and they obtained the best flow locations for Q ≥ 100.

Site amplification factors 20
In the present study, the recorded seismic amplitudes at each station were corrected by site amplification factors that account for local site effects on seismic waves due to the topography and soil stratification. These factors are estimated by the coda method using earthquake records. Coda waves from local earthquakes are interpreted as backscattered waves generated by numerous heterogeneities in the crust. The ratio of coda-wave amplitudes from an earthquake is free of source and path effects and depends only on the local site amplifications for lapse times greater than twice the S-wave travel time (Aki and Chouet,25 1975; Phillips and Aki, 1986). We selected 13 earthquakes with epicentral distances between 30 and 154 km (Table 2) from a seismic catalog provided by NIED. We determined the site factor of each station of the Mt. Fuji network relative to the reference station N.FJYV (Fig. 1) because the latter is located in a deep borehole and has low background noise.
We calculated the envelopes of the vertical, band-passed filtered signals in the four frequency bands 1-2, 2-4, 4-8 and 8-16 Hz. We selected five time windows of 10 s in length and 5 s of overlapping, starting at twice the travel time of the direct

Seismic tracking
For locating the recorded events, we use all stations that have a sufficient signal-to-noise ratio over a time interval from t 1 to t 2 (Table 3). We discard the initial and final parts of the signals generated by the flows because these are detected by too few sensors. The spatial distribution of the residuals is calculated for sliding time windows of 5 s length, shifted at 1 s increments. Figure 6 displays the residual distributions estimated for the observed events detected in two different time and slush flow #7 at 2430 m a.s.l. on the W side ( Fig. 6.d, upper panel). The second set of residual distributions show avalanche #1 at 2110 m a.s.l., which is 230 m from the NW road where it impacted ( Fig. 6.a, lower panel); avalanche #5 is estimated at 2270 m a.s.l., which is 140 m from the NE road where it impacted ( Fig. 6.b, lower panel); avalanche #6 is estimated to be at 2540 m a.s.l., which is in the middle of the flow path ( Fig. 6.c, lower panel); finally, slush flow #7 is estimated to be at 1500 m 15 a.s.l., which is 90 m from the video camera that recorded the flow (Fig. 6.d, lower panel).
A map of the locations of the minimum residuals estimated at each time interval for all the detected events (Table 1)  The seismic locations extend over a range of distances from 1.5 km (avalanche #4) up to 3.0 km (slush flow #7 of Table 3).
Since only a part of the seismic signal is used to locate the flows, these distances (D s of Table 3) are shorter than the maximum run-out distances estimated from field observations (Table 1).

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The source amplitudes, A 0 (t), computed according to Eq.
(2), can be used as a quantitative measure of the size of the mass movement (Kumagai et al., 2013). We also estimated the radiated seismic energy, assuming energy radiated from a point source over a spherical surface in an isotropic homogeneous medium, by the mass flows in the frequency band of 4-8 Hz (Vilajosana   where E s (t) is the radiated energy and ρ = 2300 kg/m 3 is the ground density (Kumagai et al., 2009). This energy represents a small fraction of the total radiated energy as it only considers a narrow frequency band of the vertical seismograms. Earlier studies showed that the main sources of the seismic waves generated by avalanches are i) basal friction, ii) the impacts of the flow on the snow cover, the terrain and the obstacles in the avalanche path, and iii) erosion and dissipation processes (Biescas et al., 2003;Vilajosana et al., 2007b;Pérez-Guillén et al., 2016).  Table 3. Source functions are characterized by increasing amplitudes at the beginning of the motion, multiple local maxima, and decreasing seismic energy generation at the end of the motion. Accordingly, the seismic energy functions increase monotonously throughout the whole time interval, with larger rates during intervals of more intense generation of seismic energy (Fig. 8). The largest source amplitudes and seismic energies are generated by slush flow #7, which is the flow 10 of largest size (size class 5). The source amplitude function of this flow displays three main local maxima at lapse times of 3.0 6.9 · 10 −3 6.9 · 10 4 34 s, 61 s and 95 s, respectively. At t = 95 s, the location of the flow is estimated at 1500 m a.s.l., i.e., near the video camera ( Fig. 6.d, lower panel). There three different gullies converge and the slope decreases to ∼10°. This topographic obstacle and the change in the slope are most likely responsible for this high seismic energy generation rate.
The second largest flow is avalanche #5, which shows a maximum seismic energy of 2.4 · 10 4 J, which is slightly larger than the seismic energy generated by the consecutive flow #6 of smaller size (Table 3). For lapse times between 33 s and 63 s,  (Table 3).
The correlation between the flow size and the parameters presented here is investigated in Sec. 5.3.   as h ij (t 0 ) = h 0 if the grid point x ij is inside a user-defined elliptically-shaped domain on the surface, and 0 otherwise. The avalanche starts from rest, i.e., u ij (t 0 ) = v ij (t 0 ) = 0 for the slope-parallel velocity components u, v.
For adjusting the simulations of the visually identified flows, we determined the most likely bounds of the run-out distance from the aerial photos and the recorded damage (Fig. 2). A range of flow scenarios were simulated to find the best-fit model parameters and initial conditions for each avalanche/slushflow (Table 4). The flow depths simulated for events #1, #5, #6 and 5 #7 are shown in Fig. 9. The release area of avalanche #1 is centred at 3250 m a.s.l. in the Namesawa path of the WNW flank ( Fig. 9.a). The simulation reproduces the deposition pattern satisfactorily if the bed friction angle is set to 20°above 2500 m a.s.l. and to 25°below 2500 m a.s.l. We increased the basal friction angle for the remainder of the avalanche path to account for the effect of the forest (Takeuchi et al., 2018) in addition to higher snow temperature. The maximum flow depth predicted for this avalanche is 5.25 m. The simulation recreates the impact of the flow on the road in the run-out area (Fig. 2.a), where station E.NAG is located, in accord with field observations (path #1 of Fig. 2.a). Part of the simulated flow continues moving downhill through gully #2 (Fig. 2.a) towards V.FUJD ( Fig. 9.a).
The release area of the simulation of avalanche #5 is centred at 3300 m a.s.l. in the Yoshidaosawa path of the NE flank 5 ( Fig. 9.b). The bed friction angle is set to 25° (Table 4). The simulation recreates the flow path adequately, showing that the flow splits into two branches and impacts the NE road in the run-out area at 2220 m a.s.l. (Fig. 9.b), which is consistent with the observed deposits (Fig. 2.c). The predicted maximum flow depth of this flow is 5.2 m. Avalanche #6 is simulated using the same release area and volume as avalanche #1 since both flows were triggered at the same site and followed similar paths. However, the run-out areas are different, with avalanche #6 impacting the deflection dam and depositing its mass above the road. With 10 a variable bed friction angle ranging from 25°above 2500 m a.s.l. to 28°below 2500 m a.s.l., the simulation reconstructs the run-out area in agreement with these field observations ( Fig. 9.c). Owing to the lack of snow cover at mid-elevations on the western flank (Fig. 2.d), we assigned a larger bed friction as the basal surface was directly the ground. The simulated maximum flow depth is 6.5 m. Slush flow #7 is simulated with an initial volume centred at 3050 m a.s.l. in the Osawa valley on the W flank ( Fig. 9.d). We used a bed friction coefficient of µ b1 = tan 20 • to fit the simulated slush flow with the observed run-out 15 area ( Fig. 2.e). The simulated maximum flow depth is 7 m.

Precision of seismic localization
The numerical simulations provide a reference for assessing the precision of the ASL method. We compared the seismic location at each time interval with the evolution of the simulated avalanche flow. Seismic locations could first be determined several seconds after the avalanche signal first emerges from the noise at station V.FUJ2 at the summit of the volcano (Fig. 1), 20 which is closest to the avalanche/slushflow release areas (Fig. 9). We also assumed an additional delay of a few seconds because the first movements of the avalanche are unlikely to generate enough seismic energy to be detected at a distance of > 1 km.
This second time delay was estimated by minimizing the mean error in the locations.
We defined the location error as the minimum distance between the avalanche flow and the seismic location. We set this value to zero if the seismic location is within the avalanche flow. Figure 10 shows the location errors and the residuals as a  (Fig. 9).
An interval of erroneous migrations of the seismic locations in north-western direction is observed in the two flow events 30 that descended the Namesawa path ( Fig. 9.a and c). The spurious migrations of avalanche #1 occur at 28-36 s ( Fig. 9.a) with location errors over 400 m (Fig. 10.a); avalanche #6 shows wrong migrations at 38-42 s (Fig. 9.c) with location errors over 300 m (Fig. 10.c). Ogiso and Yomogida (2015) also observed migrations of the locations in a wrong direction, probably caused by an inadequate distribution of stations in that phase. The lack of stations close to the release area may explain the observed We also examined whether there is a correlation between the location errors and the residuals. Avalanche #1 shows a moderate correlation with a Pearson correlation coefficient of r = 0.64. However, events #5, #6 and #7 show very weak correlation with coefficients below r = 0.2. The average speed of the flow can be deduced from the seismic tracking conducted in Sec. 3.3. We selected a reference site placed in the run-out area of each flow to compute the distance as a function of time between the seismic location and this site, which is E.NAG for avalanche #1, a location on the NE road for avalanche #5, the dam for avalanche #6, and a location 5 on Osawa river close to the video that recorded the slush flow #7. To estimate an average speed of each flow, we selected two seismic locations in the release area and the run-out area that are near the avalanche front and we computed the ratio of the distance travelled versus time. We discarded estimating the average speed from the linear regression of distance versus time because they also count times when the observed locations are far behind the front. We estimated the average speed of avalanche #1 at 50.6 m s −1 (Fig. 11.a), avalanche #5 at 27.1 m s −1 (Fig. 11.b), avalanche #6 at 35.7 m s −1 (Fig. 11.c) and slush 10 flow #7 at 30.1 m s −1 (Fig. 11.d). Since the slush flow #5 is split into two well-separated branches before reaching the NE road ( Fig. 9.b), we estimated the mean speed in the time interval over which the flow is approaching the NE road. Figure 11.e shows the speed functions of each flow simulated with Titan2D. The maximum flow speeds predicted by the numerical simulations are (Fig. 11.c): 46.9 m s −1 , for avalanche #1, 29.8 m s −1 , for avalanche #5, 35.5 m s −1 , for avalanche #6 and 44.6 m s −1 , for slush flow #7. In addition, we compared the mean speeds estimated seismically with the ones predicted numerically. During

Detection range
The detection range of the seismic network of Mt. Fuji is different for each recorded event. Fig. 12 shows the source-receiver distances versus the run-out distances. For each event, the source-receiver distance varies during the flow motion and therefore we plot the maximum source-receiver distance for the seismic stations that detected the event and the minimum source-receiver distance for the seismic stations that non-detected the event. We estimated the detection range using the vertical component of 25 the seismic signal and assuming for a detected event a minimum duration of the recorded signal of 10 s at each seismic location.
The same assumption was adopted in previous studies of avalanches detected seismically (Lacroix et al., 2012;Hammer et al., 2017). The maximum detection distance is 15 km for the avalanche #1. For the events #5, #6 and #7 the maximum detection radius is between 10 and 12 km, lower than the avalanche event due to a higher background noise recorded on these days (Fig. 3). The detection radius of the three non-visually identified avalanches released on 2014-03-13 is between 9 and 9.5 km 30 according to their paths estimated seismically (avalanches #2, #3 and #4 of Fig. 7).

Flow size
We classified the size of each avalanche/slush flow event according to their maximum run-out distances. The events #5 and #7 are classified as extremely large events of size 5 according to the Canadian classification system for avalanche size (McClung and Schaerer, 2006), whereas avalanches #1 and #6 count as size 4-5. The non-visually identified events, avalanches #2, #3 and #4 are classified as size 3-4 according the length of their paths estimated by the ASL localizations. These extents 5 of the seismic locations, here referred to as D s (Table 3), are several hundreds of metres less than the run-out distances, that is, between 75% (avalanche #5) and 90% (avalanche #6) of the maximum run-out distance. In order to correlate the size of each event and the seismic parameters of maximum source amplitude and energy, we used the known parameter D s for all the events as a representative measure of the flow size. Figure 13 shows the fitting models between the maximum  source amplitude (A 0 of Table 3) and energy (E s of Table 3) versus the path length estimated seismically. The fits are i) y 1 = (0.004 ± 0.001) · x − (0.006 ± 0.002) for the maximum source amplitude and ii) y 2 = (343.2 ± 785.9) · x (4.8±2.2) for the energy. There is a high linear correlation (R 2 = 0.95 in Fig. 13) between the source amplitude and the length of the avalanche path estimated by ASL, which is proportional to the maximum run-out distance. The best fit model between the energy and the avalanche path is a power function (R 2 = 0.92). like seismogram and a characteristic triangular shape of the spectrogram (Fig. 3.c), which is mainly due to the variation of the source-receiver distance during the flow motion (Vilajosana et al., 2007a;Pérez-Guillén et al., 2016).
The knowledge of an accurate release time of the flows allowed correlating with the weather patterns that triggered them.
In the first period of 2014-03-13, four snow avalanches have been seismically identified in a time window of two hours during 15 a storm. The combination of heavy precipitations, strong winds which accumulated drifted snow at higher elevations of Mt.
Fuji and a rising air temperature of several degrees (Fig. 4) were the main meteorological factors that led to the release of  2.9 km (Fig. 12), yielding a source-receiver distance of about five times the avalanche run-out distance. The likely reason for the avalanche detection limit in this study being lower than in Switzerland is the strong scattering and attenuation beneath volcanoes (Kumagai et al., 2018), which are one of the most heterogeneous media of the Earth's crust (Yamamoto and Sato, 2010). The range of detection of wet flows is somewhat lower, with maximum source-receiver distances up to four times their run-out distances (events #5 and #6 of (Fig. 12). The higher background noise caused by the severe weather conditions during the wet flow events is likely to be the principal reason for the reduced detection limit of these flows, considering that their source amplitudes are similar or even higher than for dry avalanches ( Fig. 8 and Table 3). In addition, the higher water content 5 in the interface between the flow and the terrain (particularly in slush flow #7) reduces the effective bed friction, which is one of the main sources of the seismic waves (Vilajosana et al., 2007b).

Mass flows localized by seismic methods
The localization of mass movements through their seismic signals is a challenging task because avalanche signals have no clear phase arrival, thus conventional methods for hypocentre determination are not applicable. Given the nature of these sources 10 and the large inter-sensor distances of more than 1 km in Mt. Fuji's seismic network (Fig. 1), ASL method is the most suitable method for locating the sources of the signals generated by these flows. ASL is based on the spatial distribution of the seismic amplitudes under the assumption of isotropic radiation of S-waves (Kumagai et al., 2010). To obtain the spatial distribution of the amplitudes, it is imperative to correct for site amplification because this stronly affects the accuracy of the source locations (Kumagai et al., 2013). These amplification factors are frequency-dependent and are much more larger at stations located at 15 the volcano surface due to unconsolidated deposits in the upper layers of the volcano. In the seismic network of Mt. Fuji, site amplification at the station V.FJUD is 6.3 times stronger than at the station N.FJYV (Fig. 5) in the frequency band of 4-8 Hz that is used for localizing the seismic sources. After correcting for the local amplification effects, we applied ASL for the first time to locate the snow avalanches and slush flows and demonstrated that the estimated locations (Fig. 7) are in good agreement with the observed flow paths (Fig. 2). 20 The precision of ASL is an important question in view of practical applications of the method to avalanches. Earlier applications of ASL to locate lahars (Kumagai et al., 2009) and debris flows (Ogiso and Yomogida, 2015;Walter et al., 2017) demonstrated that the flow paths were correctly identified by this method and the estimated locations were well constrained in the area of the observed deposits (Ogiso and Yomogida, 2015). Walter et al. (2017) measured the distance between the confined channel where a debris flow descended and the seismic locations estimated by ASL, giving an order of magnitude of 25 the accuracy of the ASL locations between 100 m to 900 m, but these accuracies were not estimated with regard to the temporal evolution of the flow. Kumagai et al. (2009) performed numerical tests using synthetic waveforms generated by a vertical single source at a given location of the volcano and then applied ASL to determine its location, finding that both locations differed slightly. They also tested the method with two simultaneous and spatially well-separated sources at the volcano. The minimum residual was located between the two sources, with a broad area of small residuals between them. This result may explain 30 why some of the ASL locations of the avalanche #5 are between its two branches for lapse times of t > 60 ( Fig. 9.b) and why the region of small residuals then is fairly large (Fig. 6.b lower panel). How to analyse situations with multiple simultaneous sources with ASL is an important issue to address because avalanches and slush flows are extended sources of seismic energy on the scale of the source-receiver distance.
Ideally, the precision of ASL should be studied at an avalanche test site, where video recordings and radar measurements provide comprehensive information about the location and extent of the avalanche through time. However, no suitable seismic network is available at any of the presently operating test sites. At Mt. Fuji, only limited information about the location of the fracture line and the run-out area is available for four events (Fig. 2). Numerical flow simulations can fill this gap to some degree: The initial conditions-location and extent of the release area, fracture depth-as well as one to several model 5 parameters can be varied independently until the deposit location and any other available constraints (e.g., extent and degree of forest damage) are satisfactorily reproduced. The time evolution of the best-fit Titan2D simulation can then be compared to the time series of seismic localizations. Using this approach, the mean location errors are between 85 m (avalanche #6) and 271 m (slush flow #7) with point-wise maximum location errors up to ∼1 km (Fig. 10). This precision is similar to that of previous applications of ASL (Walter et al., 2017). 10 The only two previous studies studies of avalanches localized by seismic methods were based on array techniques (Lacroix et al., 2012;Heck et al., 2018b), which are not applicable with Mt. Fuji's network due to the configuration of the seismic stations. Array techniques allow computing the back-azimuth of the incoming wave field, which is then compared to known avalanche paths. Lacroix et al. (2012) tracked the location of eighty snow avalanches in the French Alps, estimating the precision of azimuth determination to about 15°based on a correlation criterion. The corresponding location errors amount to 15 several hundred metres-similar to the ASL location errors estimated in this study (Fig. 10).
6.3 Inferring flow properties from seismic data Kumagai et al. (2013) found a scaling relationship between the magnitude and the source amplitudes of different seismic signals from volcanos (explosions, volcano-tectonic earthquakes and long-period events), showing the feasibility of using them to quantify their size. In addition, Kumagai et al. (2015) showed that the source amplitudes of lahars increase linearly 20 with the cumulative source amplitudes, but a scaling relationship between them and the size of the lahar was not deduced.
They estimated the source amplitudes of the lahars in the order of 10 −2 m 2 /s, which is one order of magnitude higher than the source amplitudes estimated in this study (Fig. 13). Ogiso and Yomogida (2015) also estimated the source amplitudes generated by five large-size debris flows using ASL. The maximum source amplitudes of these flows in the frequency band of 5-10 Hz were in the range of (1-4) · 10 −3 m 2 /s. Even though our amplitudes are estimated in a slightly different frequency 25 band of 4-8 Hz, these values are in the same order of magnitude than the source amplitudes estimated for our events (Fig. 8), suggesting that those debris flows have similar flow size than the avalanches and the slush flow released at Mt. Fuji.
The two parameters deduced by the ASL method, D s and A 0 (Table 3), can be used as quantitative measures of the event size as D s is proportional to the maximum run-out distance and A 0 is linearly correlated with D s (Fig. 13). In addition, another size-scaling relationship between D s and the radiated energy was found. We estimated the radiated seismic energy of 30 the flow following the simplified approach used by Vilajosana et al. (2007b); Hibert et al. (2011). At volcanic areas, however, the diffusion model is more appropriate for modelling seismic energy transport as it reflects multiple scattering of the seismic energy due to the heterogeneities of the volcano (Yamamoto and Sato, 2010). The maximum energy values estimated are in the order of 10 4 J (Table 3). These values are low compared to the estimated energies (∼ 10 6 J) of two avalanches of size 4 in Norway (Vilajosana et al., 2007b), but here we consider only a narrow frequency band of the spectra so that our values represent only a small fraction of the total generated seismic energy.
Using ASL localizations at different times, we can estimate the average front speed of a flow (Sec. 5.1). We obtained a maximum speed of 50.6 m s −1 for the dry-snow avalanche #1. The typical speeds measured in large dry-snow avalanches of size 4-5 range widely from 40 m s −1 up to 70 m s −1 (Gauer et al., 2007a, b;Köhler et al., 2016). The estimated speeds of wet 5 flows detected in this study (Fig. 8) are in the order of ∼30 m s −1 , similar to the front speeds measured for large wet-snow avalanches (Gauer et al., 2007a).

Conclusions
Large avalanches and slush flows are often released at different flanks of Mt. Fuji and can be detected by the local seismic network at distances up to 10-15 km. Using the analysis from several sensors of this local network, we successfully applied 10 the ASL method to localize the seismic signals generated by the avalanches and slush flows at Mt. Fuji. The ASL method has proven a useful technique for locating the position of these flows in an extended area where a seismic network with a large inter-sensor distance of more than 1 km is available. Our results show that it is feasible to determine in which path an avalanche descended, to track the avalanche flow with reasonable precision and to infer additional flow properties such as the approximate run-out distance and the average speed of the flow. This is the first time dynamical properties characterizing avalanches and 15 slush flows at Mt. Fuji have been measured. These parameters are necessary for calibrating dynamical models for applications at Mt. Fuji, such as for the design of structural protection measures against these hazardous mass movements. In addition, the size-scaling relationships obtained here will be useful when establishing an empirical seismic method for quantifying the size of the detected mass flows, independently of the type of flow (avalanches and slush flows), path location and orientation. All this information is of great value for assessing avalanche hazard on Mt. Fuji, given that in most cases seismic records are the 20 only available information on snow avalanche and slush flow events.
An important task in the near future will be to develop highly effective methods for automatically detecting and tracking avalanche events in the seismic data in near-real-time. A first challenge to achieve this aim will be developing reliable algorithms to discriminate between avalanches and other seismic sources or in training a system based on machine learning. Once the avalanche has been successfully identified in the seismic records, the ASL method can be easily automated in several data 25 processing steps, providing the path location and tracking of the mass flow event. Such a tool can be applied in avalancheprone areas of many regions and will be an economical tool supporting the authorities in the management of avalanche risk.
Specifically, many volcanic areas are equipped with dense seismic networks and could benefit from this inexpensive method for locating mass movements and inferring their dynamical properties.
Competing interests. The authors declare that they have no conflict of interest.
and Disaster Resilience, and the Japan Meteorological Agency for providing the seismic data and related information. We thank the Mt. Fuji Toll Road Administrative Office, Yamanashi Prefecture for providing the meteorological data. We are also grateful to Dr. Ryo Honda and Dr.
Mitsuhiro Yoshimoto from Mount Fuji Research Institute, and Dr. Shinichiro Horikawa from Nagoya University for their support. We are also grateful to Prof. Hiroyuki Kumagai from Nagoya University and Prof. Hiroshi Aoyama from Hokkaido University for the discussion of the results. Tanaka, A., Yamamura, Y., and Nakano, T.: Effects of forest-floor avalanche disturbance on the structure and dynamics of a subalpine forest