Debris-flow velocity and volume estimations based on seismic data

The estimation of debris-flow velocity and volume is a fundamental task for the development of early warning systems, the design of control structures and other mitigation measures. Previous analysis of the seismic energy produced by debris flows showed that the peak amplitudes are representative of the kinetic energy of each surge and debris-flow discharge can be therefore estimated based on seismic signals. Also, the debris-flow velocity can be calculated using seismic data recorded at two spatial separated stations located along the channel by the use of cross-correlation. This work provide a first approach 5 for estimating the total volume of debris flows ::::: debris :::: flow ::::::: volume :::: and ::::::: velocity based on the seismic signal detected with simple, low-cost geophones installed along the debris-flow channel. The developed methods was :::: were : applied to seismic data collected on three different test sites in the Alps: Gadria (IT), Lattenbach (AT), and Cancia (IT) ::: and :::::: Cancia :::::: (Italy), :::: and ::::::::: Lattenbach :::::::: (Austria). An adaptable cross-correlation time window was used, which can offer a better estimation of the velocity compared to a constant window length. The analyses of the seismic data of 14 debris flows that occurred from 2014 to 2018 10 shows the strong control of the sampling rate and the sensor-distance on the velocity estimation. A simple approach based on a linear relation between square of the seismic amplitude and the event magnitude ::::::::: relationship ::::::: between :::: the :::::: squares ::: of :::::: seismic ::::::::: amplitudes :: (a :::::: proxy ::: for :::::: seismic ::::::: energy) ::: and ::::: event ::::::: volumes : is proposed for a first order estimation of the debris-flow magnitude. :: the ::::::: latters..

The Lattenbach Creek (district of Landeck, Tyrol) has a catchment area of 5.3 and is a monitoring site for debris flows operated by the Institute of Mountain Risk Engineering at the University of Natural Resources and Life Sciences, Vienna (Hübl and Moser, 2006). Three monitoring stations are installed along the channel (Figure 4), and these are equipped with flow 75 height (radar gauges), geophones, video cameras, 2D-Laser scanner. The station "Darwinalpe" is a meteorological monitoring station. At the middle monitoring station, a debris flow Pulse-Doppler Radar can be used for measuring the surface velocity.
Near this radar, two stations for testing the warning system MAMODIS are installed at a distance of 90 . The geophone data of these two stations (G1 and G2) are used to calculate the debris flow velocity and the lower one (G2) is used for the magnitude estimation in this study.

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(a) Overview of the test site Lattenbach (red line: catchment area); (b) Closer view of the monitoring station 1 and 2 and sensor setup (background images: ©Google Maps, 2020 (Maxar Technologies)).
Finally, the Cancia channel is located in the Dolomites within the Veneto Region ::::::: Province ::: of ::::::: Belluno(Italy)with , :::: and the catchment features an area of 2.5 km 2 on the southwestern slope of Mount Antelao (3264 m a.s.l.)It . :::: The ::::::::: catchment : ranges in elevation between the Salvella Fork at 2500 m a.s.l. down to a retaining basin at the village of Cancia at 1001 m a.s.l. (Gregoretti et al., 2019). The data used for the magnitude :::::: volume estimation and velocity calculation are recorded by the geophones installed at station 2 and 3 : 1 :::: and : 2 : belonging to the monitoring and warning system designed by the company CAE (CAE, 2014;Cavalli et al., 2020). Geophone G1 and G3 are used for the velocity estimation and geophone G2 is used for the magnitude :::::: volume estimation. Beside a monitoring system of the company CAE, three monitoring stations have been installed by UNIBZ and the Dipartimento di Scienze Biologiche, Geologiche e Ambientali, Universitá di Bologna :::::::::: Universities 90 ::
100 Table 1 gives an overview of the seismic sensors used at the different sites. The seismic amplitudes used for this study are calculated every second from the seismic data recorded at the reported sampling rates. At Cancia, an internal sample :::::::: sampling rate of 500 Hz is used, but the available seismic data are recorded as 0.1 Hz max. amplitude values. For the ::::::::: geophones :: of ::: the ::: type : SG-5 and SM-6 geophones amplitude values of 1 Hz are calculated from the raw signals sampled at 100 Hz and at Gadria the used data for this study are 0.5 Hz amplitude values.

Velocity estimation
Here ::: First : we present the results obtained about velocity estimation adopting the methods described above, applied to three 155 debris flows events recorded in different catchments. Figure 6 illustrates velocity estimations applied on :: to the Lattenbach event occurred on 30. July 2017, which featured a peak discharge of 88 m 3 s −1 , a total volume of 41,100 m 3 and an overall duration of around 3500 s.
This debris flow had a front about 1.3 m high, and the velocity (3.5 to 4.7 ms −1 ) calculated by using the time difference between maximum amplitude values results very similar to the velocity calculated by cross-correlation with 4 ms −1 . For the 160 peak discharge (flow height exceeding 3.5 m, the velocity calculated by means of maximum values turns out slightly higher (10 ms −1 ) than the one (9 ms −1 ) determined by cross-correlation. During the following part of the event (i.e., after 2500 s) no significant surges could be found to calculate flow velocities using maximum values, and the cross-correlation most likely leads to overestimating velocities.

Volumes estimation 175
To test the methodology described above for the estimation of debris flow volumes based on seismic signals, a total of 14 events (occurred from 2014 to 2018 ) are available from the three different catchments ( Table 2).
Our results suggest that :: the : cross-correlation method we used -based on a window length adaptable according to the signal waveform -provide solid estimates of debris-flow velocity, as temporal resolution is high during the most turbulent, faststage 195 ::: fast, :::::: initial ::::: stages : of the flow, while longer window length are applied for smoother flows, thus permitting to avoid wrong correlation results.
Importantly, our study benefited from three, quite different test sites. The influence of different distances between the geophones is evident. The longitudinal geophone distance in the Gadria (75 m) and Lattenbach (90 m) appear to be appropriate for fast debris flows, while the longer distance in Cancia (280 m) makes harder and more unreliable :::::: difficult :: or :::: even :::::::::: impossible 200 capturing the same surges at different sensors. However, a longer distance offers the possibility to use higher resolution for the velocity calculation. In any case, the transversal distance between the channel and the geophones should be much smaller :: (at :::: least ::: the :::: half) than the longitudinal distance between the two geophones . The distance has to be chosen to get :::::: provide : a significant difference in the signals in an appropriate time, so that the cross-correlation offers useful results for the calculation of the :::: valid :::::: results ::: for :::: flow velocity.

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The sampling rate also has an important effect on the reliability of velocity estimations. At Lattenbach and Gadria, one amplitude value every 1-2 s was available. This seems to be a proper sampling in combination with the sensor distances. At Cancia, only one sample per :::: every : 10 s is available, so that the signal shapes can be very different at the two geophones, which can determine ::::::::: determining : problems for the cross-correlation analysis. In fact, surges can be missed and such a low sampling rate coupled with the long distance lead to an exaggerated -i.e., not useful -averaging of flow velocity :: of ::::::: different :::::: surges.

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Studies of different events also showed a large dependency of the seismic amplitudes and their frequency spectrum on the velocity of the process :::: debris ::::: flow. For example, Lai et al. (2018) presents a model where the seismic amplitudes are most sensitive to the product of four physical parameters related to the debris flow: length and width of the boulder snout, grain size cubed, and average speed cubed. This model and also the model presented by Farin et al. (2019) shows that a method including the estimation of the process velocity and sediment concentration ::::: debris :::: flow ::::::: velocity ::: and ::::: grain :::: size ::::::::: distribution : can result in a 265 more accurate calculation of the magnitude ::::: debris :::: flow :::::: volume. The influence of the sediment concentration on the seismic data can therefore improve the results of the magnitude :::::: volume estimation, but there is still no method to automatically estimate the sediment concentration on seismic data, which could be implemented in the magnitude :::::: volume estimation. Currently it is only possible to differ between debris flow and debris floods based on the infrasound or seismic peak frequencies (e.g., Hübl et al., 2013), but this has still ::: still ::::: poses high uncertainties and is far off from an useful estimation of the :::: from :::::::: providing ::::::: reliable 270 :::::::: estimation :: of : sediment concentration.