E3S Web of Conferences 415, 03033 (2023)
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Detection of debris-flow events from seismic signals using
Benford's law
Qi Zhou1, 2*, Hui Tang1, Jens M. Turowski1, Jean Braun1, 2, Ci-Jian Yang1, Michael Dietze1, 3, Sophie Lagarde1, 2,
Ahmed Abdelwahab1, 2, and Fabian Walter4
1Helmholtz Centre Potsdam, GFZ German Research Centre for Geosciences, 14473 Potsdam, Germany
Institute of Geosciences, University of Potsdam, 14473 Potsdam, Germany
3
Faculty of Geoscience and Geography, Georg-August-Universität Göttingen, 37077 Göttingen, Germany
4
Swiss Federal Institute for Forest, Snow and Landscape Research, 8903 Zürich, Switzerland
2Abstract. The first step in building an early warning system using seismic signals is to automatically identify
events of interest. Here, the first digit distribution of seismic signals generated by debris flows and othersurface processes was calculated to validate compliance with Benford's law (BL). A detector model fordebris flow events was introduced based on amplitude range and goodness of fit of BL. We show that seismic
signals generated by debris flows, landslides, and bedload transport follow the BL. These events release
more energy and last longer than rockfalls, which do not follow BL. In the test dataset with 1224 samples,
the accuracy of the detector model in identifying debris flow events was 0.75.

1 Introduction
Debris flows are hazards that occur in channels (e.g.,gullies, ravines, and valleys) with massive destructive
power [1, 2]. Despite significant efforts to mitigate
debris flow hazards through warning systems, risk
assessment, and structural measures [3-5], extensive
damage and casualties still cannot be prevented due tothe complex geological conditions and dynamic
processes governing debris flows [6]. Early warning is apromising approach to reducing debris flow hazards,
which is becoming more precise and reliable as dataacquisition and transmission improve.
Debris flow warning systems could employ two
types of sensors to collect data: measuring the indicating
parameters and monitoring the flow dynamics [7].
Traditional rainfall data-driven systems belong to theformer class and require locally tailored thresholds totrigger alarms [8]. However, obtaining rainfall data andmaintaining monitoring devices is not straightforward
for catchments with large elevation differences andmultiple sediment supply areas [9]. In the case of
Illgraben (Switzerland), where we conducted the present
study, the locally convective short-duration storms are
difficult to monitor but are sufficient to trigger debris
flows [10]. Continuous seismic signals belong to thesecond sensor type offering a relatively new opportunity
to monitor debris flows with high temporal resolution.
Coviello et al. [11] proposed an early warning system
based on an automatic debris flow detector using
seismic waveforms and a short-term average to longterm average ratio (STA/LTA) trigger algorithm.
Chmiel et al. [12] combined the random forest algorithm* Corresponding author:and seismic waveform features to detect debris flow
fronts and identify when they pass over check dams. Inaddition, seismic networks can contribute to detecting
and locating large mass movements on a regional scale[13]. However, a seismic station senses all groundshaking within its bandwidth and records the signals,
blending events of interest with ambient noise. Only asmall amount of seismic data corresponds togeomorphic processes, which makes labelling events atime-consuming work requiring expert knowledge. The
present seismic-driven early warning methods requirelabelled data to train a detection model. Transferabilityof these models to other study sites where little or notraining data exist is not guaranteed.
Benford's law (BL) is a statistical phenomenon of theprobability distribution of the first digit in a dataset. It
originated from the observation that the first few pagesof the logarithm tables were more worn out than others.
Newcomb [14] declared that the probability of the firstdigit is such that the mantissae of their logarithms areequally probable. BL was rediscovered and tested with
20 different data domains by physicist Frank Benford[15] and named after him. BL gives the probability of
the first digit:
PD = log10 (1+1/D)(1)where PD is the theoretical probability of the first nonzero digit. D ranges from 1 to 9. For example, 0.01,
100, -1 share the same first digit one with a probabilityof 0.301.
A classical mathematical theory to explain why thefirst digit of a dataset appear in BL is that after asufficiently long computation in floating-point
arithmetic, the occurring mantissas have a nearlyqi.zhou@gfz-potsdam.de© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0(https://creativecommons.org/licenses/by/4.0/).

E3S Web of Conferences 415, 03033 (2023)
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logarithmic distribution [16]. For more information, werefer to [17-18]. Even if BL is base and scale-invariant[19], not all collected datasets follow it. Durtschi et al.
[20] summarized the guidelines on when data may
conform to BL: (1) unrestricted (data from human height
and weight is, e.g., restricted) and assigned data (e.g.,check numbers and invoice numbers), and (2) large setsof data across several orders of magnitude (e.g. arrayfrom 1 to 107 with a sample size of 1.2×105). BL has
been typically applied to examine data anomalies [21],and some researchers have adopted it to finance andsociology [22-23]. Recent work has applied BL togeoscience data, such as investigating natural hazard
dataset homogeneity and anomalies [24-25]. It has been
demonstrated that earthquakes and marsquakes aredetectable with BL using seismic waveforms [26-27].
In this work, we calculate the first digit distributionof seismic signals (generated by debris flows, floods,
and other surface processes [28-29]) and validate thecompliance with BL. Then, an event detector model
based on seismic signals and BL is introduced with theexample of debris flow.

respectively. Considering seismogenesis is concentrated
at the debris flow front [33], the greater the distance
between the flow front and the seismic station, the moresignificant the proportion of noise in the recorded signal.
Here, only station IGB02, which is closest to the channel
and far from the nearby residential area of Leuk, wasselected as the data provider.
2.2 Event catalog
From 2013 to 2014, 24 debris flow events (true positiveevent, TPE) were collected, and one may be a flood. Tenof these events were observed by the Swiss Federal
Institute for Forest, Snow and Landscape Researchwarning systems (henceforth referred to as “WSL”). A
debris flow example with a WSL label is shown in Fig.
2. Based on amplitude durations in the waveform andspectral features between 1 and 50 Hz, the remaining 14
debris flow events were manually labelled by us(henceforth referred to as “GFZ”). Unfortunately, noother data for these 14 events were available for crossvalidation. The statistics of the time accounted for by
TPE (about 160 hours in total) and non-TPE has a ratioof 1:58. To create a true negative event (TNE) catalog(all non-debris flow events), we selected 1200 TNE (50times of TPE) events at random start times and random
duration (from 20 minutes to 6 hours) outside the TPEperiod. Finally, a test dataset containing 1224 events wascreated. Besides, one rockfall event (rockfall1) werecollected in Illgraben, outside the Illgraben catchment,
one landslide in Iceland [28], one rockfall (rockfall2) inGermany [29], and one bedload transport in Taiwan(ROC) were collected to test for compliance with BL.

2 Study site and event catalog
2.1 Study site
The Illgraben catchment, located near the village ofLeuk, in southwestern Switzerland (Fig 1), covers an
area of about 9.5 km2 and ranges in elevation from theRhône River at 610 m to Illhorn mountain at 2716 m[30]. In the upstream channel trunk, the limestones(north side) and quartzites (south side) are susceptible toerosion and weathering, which provides debris flow
material [31]. The Illgraben covers less than 0.2% of theRhone Valley, but it contributes more than 5% of theannual sediment to the Rhône basin [32]. The local
annual rainfall is concentrated from May to October,and debris flows are mainly triggered by short-duration
storms [10]. Three to five debris flows and several
floods are observed at the Illgraben catchment each year.

Fig. 2. Waveforms and spectrograms of a debris flow with
WSL label (12th July, 2014). The vertical black lines aremanually labelled start and end times (14:40, 18:00).

3 Methods
3.1 Validate natural hazard's conformity to BL
The vertical component of raw waveform data, without
instrument response deconvolution, demeaning,detrending, filtering, or tapering, is utilized to validate
the event conformity to BL. To this end, the first digits
are counted with a 60s sliding window. The raw
amplitude equal to zero for each moving window will bediscarded. To compare the observed first digit
distribution with the theoretical BL distribution(Equations in 2-3), we refer to the goodness of fit (Ф)

Fig. 1. Network of seismometers (red dot) in the Illgraben
catchment.

For monitoring the surface processes, such as
rockfall, landslide, and debris flow, ten three component(N-S, W-E, vertical) seismic stations were installedaround the Illgraben (IGB01-10) during the period 2012
to 2014. The signal bandwidth and sampling frequencyof these seismic stations are 1-100 Hz and 200 Hz,
2

E3S Web of Conferences 415, 03033 (2023)
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https://doi.org/10.1051/e3sconf/202341503033[26] and introduce the Shannon entropy (H) [34] toassist the assessment and detection:é æ 9 ( p - P )2 ö ùf = ê1- ç å d d ÷ ú ´100%Pdêë è d =1ø úû

respectively. We combine the ar and Ф orthogonally,
then feed them into the model for testing.
We use a confusion matrix to assess our detector
performance. The detector outputs were divided into
four categories (Fig. 4). We employed positive ratio
TPR and false positive ratio FPR to evaluate the detector
model performance.

1/2

(2)

H( D) = -å dÎD p(d )logb p(d )(3)where Pd and pd are the theoretical and observed
probabilities of first digits; H(D) is the Shannon entropy
H, D={1, 2, …, 8, 9}. When b=2, the unit of H(D) is bitsor shannons. Parameter H describes the relationshipbetween information and uncertainty. The higher theoccurrence probability, the less information an event
carries. In our case, noise dominates most of the year, so
H is expected to increase from a true negative event to atrue positive event. The theoretical maximum of H is
3.17 when the first digit (1-9) is a uniform distribution
with a probability of 1/9.

Fig. 4. The confusion matrix for evaluating detector modelperformance. TP, FP is True positive and False positive number.
P, N is the Positive and Negative number.

3.2 Detector with BL method

4 Preliminary results and concluding
remarks

There are two indicators to design a debris flow detector
with BL, the amplitude range ar and goodness of fit Фof BL (Fig. 3a). The ar is more concentrated during theTNE (noise) (Fig. 3b), ranging only by 1-2 orders ofmagnitude, while the amplitude could cross several
orders during the TPE (event). ar is defined as:
ar = Q1 - Q100
(4)where Q is the amplitude value from smallest to largest
value within the sliding window, Q1 and Q100 are theaverage within largest and smallest one percentage.

Our preliminary results show that the first digit
distribution of seismic signals generated by debris flows,landslides, and bedload transport follow BL, while ourtwo rockfall cases do not conform to BL (Fig 5).
Moreover, one flood case does not allow for rigorous
conclusions to be drawn. When Ф is less than 0, and SH
is close to 0, the event cannot be considered a highenergy mass movements like debris flows and landslides.
The detector model has an optimal TPR of 0.75 and FPRof 0.01, and it could be improved by more parameter
sensitivity analysis in the future.

Fig. 5. The first digit distribution of different events. The
bedload event is recorded by an acoustic sensor.

The seismic signals from long-duration and high-energy
mass movements (e.g., debris flow and landslide)conform to BL (e.g., when the event starts in Fig. 2).
This phenomenon provides a new potential approach for
rapid and relatively accurate filtering events fromseismic signals. In future work, we will explore why BL
appears in seismic signals generated by some processes
but not in others. Understanding conformity with BL
will provide important insights into the performance ofseismic mass movement monitoring. Furthermore, thedebris flow detector is not yet efficient and reliable
enough. It will be necessary to boost and compare ourdetector model to other approaches, such as the shortterm average to long-term average ratio (STA/LTA) andrandom forest model in the future.

Fig. 3. Amplitude range ar over time (a) and amplitude
probability distribution (b) of the 12th July, 2014 debris flow.

A sliding window (Fig. 3a) will scan ar and Ф at 60s
intervals. If ar at the time i is greater than the thresholdstart (5000 bits), a potential event will be recorded until
ar at time j is less than the threshold off (1500 bits).
When the potential event duration (tj-ti) is greater than
20 and Ф is greater than a given threshold g, thepotential event will be marked as predicted positive. If
the above conditions are not met within the entire event,the test event will be marked as predicted negative. The
1224 events in the test dataset will be extracted one by
one for model testing. The range of ar, Ф is set as[3×103, 1×105], [0, 80], and the interval is 104 and 20,3

E3S Web of Conferences 415, 03033 (2023)
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