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Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
545
DOI: 10.4408/IJEGE.2011-03.B-060
ANALYSIS OF DEBRIS FLOW UNDERGROUND SOUND BY WAVELET
TRANSFORM - A CASE STUDY OF EVENTS IN AIYUZIH RIVER
y
ao
-m
in
FANG
(*)
, t
i
-m
in
HUANG
(**)
, b
inG
-J
ean
LEE
(***)
, t
ien
-y
in
CHOU
(****)
& H
siao
-y
uan
YIN
(*****)
(*)
Research Associate Professor, Geographic Information System Research Center, Feng Chia University, Taichung 40724
(**)
Postdoctoral Fellow, Geographic Information System Research Center, Feng Chia University, Taichung 40724
(***)
Professor, Department of Civil Engineering, Feng Chia University, Taichung 40724
(****)
Distinguished Professor, Department of Land Management, Feng Chia University, Taichung 40724
(*****)
Chief Department Officer, Slopeland Monitoring Section, Monitoring and Management Division, Soil and water conser-
vation Bureau, Council of Agriculture, Executive Yuan
INTRODUCTION
Taiwan locates in the circum-Pacific seismic zone
and frequent seismicity results in loose topsoil in the
mountainous areas. When rainy season comes, ty-
phoons accompanied by heavy rain usually cause se-
vere disaster in Taiwan. Because of common existence
of steep slopes, intensive precipitation, and piled-up
sediment in the area, debris flow is not uncommon to
occur. Debris flows have occurred more often after
the Chi-Chi Earthquake in 1999 and Typhoon Toraji
in 2001. The increase of debris flow has struck Tai-
wan badly in terms of economic and environmental
loss. Debris flow has become a pronoun of landslide-
related hazards in Taiwan. Because of the concerns
of serious impacts, a debris flow monitoring system
has been developed to capture debris flows before
and after their occurrence. The monitoring system has
not only provided data for debris flow researches, but
also helped local agencies on disaster response with
a real-time warning system. The Soil and Water Con-
servation Bureau (SWCB) of Council of Agriculture
has established 17 permanent debris flow monitoring
stations which has effectively enhanced government’s
capability of emergency response.
In order to obtain ground vibrations during a de-
bris flow, two sets of geophones were installed in a
serial manner at Aiyutze River. The downstream geo-
phone was set at the right bank of river, close to Aiy-
utze Bridge. The midstream geophone was installed
about 178 m away from the bridge. The two sets were
ABSTRACT
Since 2002, the Soil and Water Conservation Bu-
reau, which is responsible for the conservation and
administrative management of hillside in Taiwan,
has been cooperating with Feng Chia University. To-
gether, they have successively carried out the estab-
lishment and maintenance of 17 debris flow monitor-
ing stations over the Taiwan and 3 mobile debris flow
monitoring stations. Geophone is one of the most im-
portant sensor to detect whether debris flow occur or
not. The wavelet transform is employed in this study
to analyze the underground sound of debris flows
obtained from the geophones. Three debris flow
events observed at Shenmu monitoring station (Nan-
tou County) on July 2, 2004 and on August 8, 2009
are selected as examples. It is found that the wavelet
transform not only can separate ambient noise effec-
tively but also can be used to determine the begin-
ning time of debris flow event. In order to estimate
the magnitude of debris flow event, a so-called wave-
let accumulated energy indicator is proposed. When
debris flow occurs, the wavelet accumulated energy
will increase. So the wavelet accumulated energy’s
threshold value is double of normal value. It can be
used to determine the occurrence of debris flow and
to estimate its magnitude.
K
ey
word
: geophone, debris flow underground sound, wavelet
transform, wavelet energy accumulated indicator
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Y.-M. FANG, Y.-M. HUANG, B.-J. LEE, T.-Y. CHOU & H.-Y. YIN
546
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
measuring geophones with known distance. i
takuRa
et
alii (1997) measured the signals of debris flows at Nojiri
River and found that the predominant frequency of de-
bris flow ranged in 20-60 Hz. l
iu
(1999) revealed that,
from lab and field experiments, particle size was not a
factor and the frequency recorded ranged mostly be-
tween 20-80 Hz, particularly 40-60 Hz. R
iCHaRd
(1996)
at U.S. Geological Survey (USGS) also found that the
frequency of a debris flow ranges between 10-300 Hz,
with evident frequency of 30-80 Hz.
SWCB successfully collected the first repre-
sentative data of debris flow, since the establishment
of monitoring stations, at Shenmu Village in Nantou
County during Typhoon Mindulle in 2004. The geo-
phone signals obtained from Aiyutze River were ana-
lyzed by FFT, as shown in Fig. 1. The figure shows that
the predominant frequency is between 10-60 Hz with
peak of amplitude at 20 Hz. f
anG
et alii (2008) ana-
lyzed same debris flow and found that the frequency of
geophone was in a relatively lower range of 5-60 Hz.
Most of the documents mentioned above utilized
FFT to transform signals from time domain into fre-
quency domain, and determined the occurrence of
debris flow by evaluating characteristics of low fre-
quency range. However, using FFT to analyze non-
stationary, instantaneous signals may cause frequency
distortion as a result. The vibration signals of a debris
flow are transient, non-periodical, and non-stationary.
To improve frequency distortion, H
uanG
(2005) and
H
sieH
(2004) used the Gabor Transform to perform
signal analysis. Gabor Transform has capability of de-
scribing the characteristics of instantaneous signals in
terms of frequency and time domains. Yet both FFT
and Gabor Transform require more computation time
that makes the system unable to evaluate debris flow
signals in a real-time manner. At current, most sig-
nal analyses are conducted after debris flow events.
Therefore, it is necessary to develop an analysis pro-
cedure for geophone signals which could allow real-
time indication of debris flow for decision makers.
173 m apart. Triaxial geophones made by Geospace
Co. were used and the measurable frequency ranges
between 8 to1500 Hz.
The characteristic of frequency generated by col-
lision and friction between sand and cobbles inside a
debris flow should be at a low frequency range, which
is distinctive from signals of water flowing, rain, wind,
and voltage noises. However, high sampling rate
should still be applied in measurement, because high
frequency signals cannot be excluded. Accordingly,
this study used sampling rate of 500 Hz, with maxi-
mum effective frequency of half 500 Hz, i.e., 250 Hz.
In this paper, current signal analysis methods for
geophones have been explored to find an approach
which can identify a debris flow quickly and effectively.
The proposed approach can allow engineers to discover
the variation of signals when a debris flow is about to
happen, and determine the scale of hazard during an
event. The signal analysis of geophones, as a result, can
improve the public’s response to debris flow disasters.
GEOPHONE SIGNAL ANALYSIS
FAST FOURIER TRANSFORM (FFT) ANALYSIS
Geophone measures the signals of ground vi-
bration caused by large cobbles rolling on, friction
against and colliding with channel bed in a debris flow.
Such signal of vibration, also known as underground
sound of debris flow, propagates through soil or on
the ground surface. w
u
et alii (1990), who obtained
data from 18 debris flows using piezo-electric ceramic
geophones, indicated that the soil composition and
particle size can affect the characteristics of frequency
of debris flow. After FFT, their analyses show that the
frequency ranges mostly between 25 to 80 Hz.
a
Rattano
(2003) analyzed the signals of four debris
flows at Moscardo, Eastern Italian Alps. He found that
the amplitude reached a maximum when the debris flow
surged over the geophone, showing a peak on the graph.
Also found in his study was that the average velocity of
debris flow can be estimated when using two adjacent
Fig.1 - The FFT analysis of x axis lo-
cated at downstream from 16:41
to 16:42 on July 2, 2004
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ANALYSIS OF DEBRIS FLOW UNDERGROUND SOUND BY WAVELET TRANSFORM - A CASE STUDY OF EVENTS IN AIYUZIH RIVER
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
547
TRANSFORM
In order to effectively capture the vibration signals,
wavelet analysis is employed to separate signals into
various bands of frequency, from which the character-
istic frequency range can be selected to further signal
process. The wavelet transform shows the advantage
of processing non-stationary signals and the capability
of indicating signals of unbalanced vibration.
y
anG
(2006) mentioned that one feature of wave-
let analysis is that the resulting transform differs with
the selection of mother wavelet. Thus, a mother wave-
let with specific characteristics can be chosen accord-
ing to different requirements. Wavelet transform can
reach better screening results when using short-time
and long-time windows for higher and lower frequen-
cies, respectively. Hence, wavelet analysis is suitable
for non-stationary and instantaneous signals of geo-
phones. The method of Haar mother wavelet was ap-
plied and studied in this paper.
k
Ristian
(2000) study shows that the orthogo-
nal set of Haar wavelets is composed of a group of
square waves with amplitude of ±1 in certain inter-
vals and 0 in others:
Definition 1 (The Haar Scaling Function)
Let Φ a scaling function and can be defined as
Eq. (1) is a lowpass function as shown in Fig.
3(a). The general form can be expressed as
where Φ
0
0
(t)=Φ(t) implies the special case. The
general expression forms a vector space, Wj, as fol-
low.
where sp denotes the linear space, j is related
with function expansion, and i is related with func-
tion shift. The normalization constant
is chosen
such that
If one considers the wavelet function on other
intervals rather than [0,1], the normalization constant
will change.
Definition 2 (The Haar Scaling Function)
Let ψ the mother wavelet function and can be de-
fined by
ACCUMULATED ENERGY
Conventional FFT analyses take large amount of
computations and cannot perform real-time evalua-
tion of geophones for debris flows. l
in
& l
iu
(2005)
used the method of energy integration to analyze
characteristics of debris flow and found that there ex-
ists a notable spike in accumulated energy of known
debris flow incidents. An accumulated energy, thus,
is defined as the integration of 500 records per sec-
ond over the time history of velocity. The accumu-
lated energy represents the work (in Joule), product
of force and displacement, from a debris flow. The
estimated accumulated energy will be immediately
transmitted back to the monitoring center and used
for debris flow prediction. Figure 2 shows the ac-
cumulated energy per second from the downstream
geophone of Aiyutze River during the debris flow on
July 2, 2004.
As monitoring equipments have to continuously
monitor potential debris flow torrents 24 hours a
day, noises can occur in geophone recordings when-
ever the spot light is turned on at night or a genera-
tor starts in case of power failure. These noises are
analyzed, by FFT, to be multiples of 60 Hz, which is
at higher frequency range. Because the accumulated
energy per second uses time history of geophone
data, the power generator and spotlight switch can
affect the energy estimated, influencing the determi-
nation of debris flow incident.
Therefore, a new method utilizing wavelet trans-
form proposed by the authors provides a solution to
resolve the drawbacks of FFT and energy estimation
for geophone signal analysis.
METHOD OF ANALYSIS wITH wAVELET
Fig.2 - The accumulated energy of geophone located at
downstream from 16:00 to 17:00 on Aug 8, 2008
(1)
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Y.-M. FANG, Y.-M. HUANG, B.-J. LEE, T.-Y. CHOU & H.-Y. YIN
548
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
the averaging procedure tends to smooth the data. For
Harr wavelets, the lowpass filter can be expressed as
the average of two consecutive signals. The differenc-
ing values correspond to highpass filter, which can fil-
ter out low frequency signals. Since the noises usually
occur at high frequency ranges, the Harr wavelets can
detect the noises and reflect the signals.
Let f(Hz) represent the effective frequency of sig-
nal, f, and the frequency range can be divided into the
portions of Low and High frequencies, after n times
of wavelet transform. The low frequency is represent-
ed by L1 and H1~Hn, represent the high frequency
range. Equations are expressed as follows.
where
As the equations define, in the interval [0,1), every
Haar wavelet comprises exactly one wavelet at certain
intervals and 0 at others. Therefore, the Haar set forms
a partial base, and the zeros of an interval make Haar
wavelet transform easier and faster than any other
transform methods. Because wavelet transform divides
signals into low and high frequencies, it is similar to
Fourier transform. Since the characteristics of different
signals (background noise) correspond to different fre-
quencies, the signal process using wavelet transform is
an important method for geophone data analysis.
The Haar wavelet transform can divide the geo-
phone signals into two portions of high and low fre-
quency zones. This study used sampling rate of 500
Hz with effective frequency of 250 Hz. The authors
found that in analyzing the geophone signals at Aiy-
utze River, the characteristic frequency of spike was
at about 20 Hz. After three times of wavelet transform,
the low frequency range of 0-31.25 Hz was consider-
ably suitable to represent the signals of debris flow
in Aiyutze River. In comparison to this finding, four
times of wavelet transform which resulted in fre-
quency range of 0-15.63 Hz, implying overlook of the
spike, and two times transform which had frequency of
0-62.5 Hz, including the equipment voltage frequency
Eq. (2) is a
highpass function as shown in Fig. 3(b). The general
form can be expressed as
where Φ
0
0
(t)=Φ(t) implies the special case. The general
expression forms a vector space, W
j
, as follow.
where sp denotes the linear space, j is related with
function expansion, and i is related with function
shift. The normalization constant √2 is chosen such
that
We consider a signal, f, with 8 samples. The pro-
cedure to be described can be applied to any finite
signals. The analysis can be simplified if the length
(dimension) of the signal is 2k, where k is positive
integer. Let f expand to space of
w h e r e
denotes addition of spatial vectors.
Then, according to Definition 1 and 2, we can get the
following expression.
where<f,Φ
i
j
> and <f,ψ
i
j
>are the inner products of
spatial vectors,Φ
i
j
and ψ
i
j
represents averaging and
differencing values. The number of computations
should be 2 to the power of n. The expressions above
can also be used as filter for signals. The averaging
value corresponds to a lowpass filter and it can filter
out high frequency signals. Since the partial signals of
significant change correspond to high frequency parts,
Fig. 3 - The define function of Haar wavelet transform; 3a
Lowpass function, 3b Highpass function
(2)
(3)
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ANALYSIS OF DEBRIS FLOW UNDERGROUND SOUND BY WAVELET TRANSFORM - A CASE STUDY OF EVENTS IN AIYUZIH RIVER
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
549
had caused massive collapse in the upstream of Aiy-
utze River, and the triggered debris flow had seriously
damaged the Aiyutze Bridge.
The first event of debris flow on August 8 caused
the wire broken in the upstream of Aiyutze River. Fig-
ure 6 shows the time history of rainfall and the timing
of wire rupture.
The signal analysis of geophones for the debris
flows at 4:38 and 16:57 on August 8 reveals obvious
signal vibration in either time history or wavelet trans-
form, as shown in Fig. 6and 7. The evidences from wire
ruptures, character frequencies in the wavelet transform,
and CCD images confirm that a debris flow did occur at
Aiyutze River during Typhoon Morakot. Based on the
records of geophones in the midstream and downstream
of Aiyutze River, the flowing velocity of debris flow
events is 17 m/sec, respectively, as shown in Fig. 8.
wAVELET ACCUMULATED ENERGY INDICA-
TOR
We compared the total precipitation of two typhoons
on July 2, 2004 and Aug. 08, 2009 and found that on July
2, 2004, the accumulated 3-day precipitation was 1,254
mm (418 mm/day in average), and 1,596.5 mm over four
days (399 mm/day in average) on Aug. 08, 2009. The
maximum 10-minute rainfall intensities were of 70 and
80 mm, respectively. The two incidents were thus similar
in both accumulated rainfall and rainfall intensity. From
the analysis results in previous sections, the debris flow
of Aug. 08 was greater in scale than that of July 2.
As the wavelet transform has been verified that it
is possible to filter out the high frequency portion from
of 60 Hz, were both not appropriate. Therefore, the ap-
plication of three times of wavelet transform had been
conducted as standard procedure in this study.
CASE STUDIES OF GEOPHONE SIGNAL
ANALYSIS
TYPHOON MINDULLE
In 2004, Taiwan was stricken by Typhoon Mindulle
during June 28 to July 3. The monitoring station at Aiy-
utze River captured the debris flow first time after the
establishment of monitoring system. The accumulated
precipitation was high up to 1,254 mm in three days
(July 2 to 4), and the heavy rain had triggered land-
slides in the upstream area, resulting in debris flows and
caused serious damage to downstream facilities.
The debris flow incident, occurred at 4:41 p.m. on
July 2, was observed by two sets of geophones deployed
along the Aiyutze River. The signal of downstream geo-
phone (in Fig. 4) was analyzed by wavelet transform and
separated into low and high frequency parts, as shown
in Fig. 5. It is clear from the figure to view the spike
indicating the occurrence of debris flow when in the fre-
quency range of 0-31 Hz. Similar result can be found for
frequency of 31-62 Hz. These results show the success
of wavelet transform and support the low-frequency.
TYPHOON MORAkOT
During Typhoon Morakot in August, 2009, the
monitoring station at Aiyutze River captured two in-
cidents of debris flow. The accumulated precipitation
was measured as high as 1,596.5 mm during the five-
day period (Aug. 6 to 10) of heavy rain. The rainfall
Fig. 4 - The original data located at down-
stream from 16:00 to 17:00 on July
2, 2004
Fig. 5 - The wavelet transform result of
lower frequency located at down-
stream from 16:00 to 17:00 on July
2, 2004
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Y.-M. FANG, Y.-M. HUANG, B.-J. LEE, T.-Y. CHOU & H.-Y. YIN
550
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
the original ground vibration time history, only the
low frequency portions were considered from events
of 2004/07/02 and 2009/08/08, and the resulting accu-
mulated energy are shown in Fig. 9 and 10. It can be
seen from the figures that when debris flow arrives, the
wavelet energy accumulation increases significantly.
Compared to accumulated energy per second, as pre-
viously mentioned, the energy after wavelet transform
accumulates only over the low frequency portion of the
ground vibration history and the results are not affected
by interference of environmental signals and can bet-
ter serve in the determination of debris flow trigger-
ing. Therefore, the energy accumulation after wavelet
transform can be used as an indicator, Wavelet Energy
Indicator, for debris flow evaluation.
The Wavelet Energy Indicator was applied to de-
bris flows of July 02, 2004, and Aug. 08, 2009, in the
Aiyutze River area. After applying wavelet transform
and estimating accumulated energy, energy indicators
of background and three scales were set for reference,
as shown in Table 1. A debris flow is determined to
occur when the estimated wavelet energy is twice or
greater than the background value. This energy indica-
tor will be sent with other data back to the monitoring
station and served as a factor to determine the scale
and occurrence of debris flows.
CONCLUSIONS
1. Wavelet transform can isolate different ranges
of frequency from a whole time domain, and can indi-
cate directly the characteristic lower frequency range
of debris flow, as well as filtering out the higher fre-
quency range.
2. Superposing a number of sequences of wavelet-
transformed lower and higher frequency ranges can
obtain the original signal sequence. The Haar trans-
form is the original and simplest transform function.
3. It is useful to obtain high and low frequency
ranges by applying wavelet transform three times to
the original geophone data. The energy indicator es-
timated over the low frequency range can be used to
determine the occurrence and scale of a debris flow.
4. The energy indicators for downstream area of
Aiyutze River was estimated and determined based
on the incidents of July 02, 2004, and Aug. 08, 2009.
More debris flow data will be gathered in the near fu-
Fig. 6 - The original data located at down-
stream from 16:00 to 17:00 on Au-
gust 8, 2009
Fig. 7 - The wavelet transform result of
lower frequency located at down-
stream from 16:00 to 17:00 on Au-
gust 8, 2009
Fig.8 - The wavelet transform result at up-
stream and downstream from 16:56
to 17:00 on August 8, 2009
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ANALYSIS OF DEBRIS FLOW UNDERGROUND SOUND BY WAVELET TRANSFORM - A CASE STUDY OF EVENTS IN AIYUZIH RIVER
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
551
ture to update the indicators and to establish the debris
flow database.
5. Featuring fast and effective analysis for geophone
signals, the method proposed in this study can be in-
stalled directly on the computers at a monitoring station.
When a debris flow is about to occur, the on-site com-
puter can conduct wavelet transform and send back the
results for further analysis.
Fig. 9 -
The accumulated energy of
geophone using wavelet tran-
sform located at downstream
from on July 2, 2004
Fig. 10 - The accumulated energy of geo-
phone using wavelet transform
located at downstream from on
July 2, 2004
Tab. 2 - The Indicator value of geophone located at down-
stream (unit: Joule)
REFERENCES
a
Rattano
m. (2003) - Monitoring the presence of the debris-flow front and its velocity through ground vibration detectors. The
Third Int. conf. on Debris-Flow Hazards Mitigation: Mechanics, Prediction, and Assessment, Davos, Switzerland: 719-730.
I
takuRa
, y., n. k
amei
, J. i. t
akaHama
& y. n
owa
(1997) - Real time estimation of discharge of debris flow by an acoustic sensor.
14th IMEKO World Congress, New Measurements- Challenges and Visions, Tampere, Finland, XA: 127-131.
l
aHusen
R.G. (1996) - Detecting Debris Flow Using Ground Vibration. USGS Fact Sheet: 236-296.
f
anG
y.-m., l
ee
b.-J., C
Hou
t.-y., C
HanG
k.-f., l
ien
H.-P., l
in
y.-i, l
ien
J.-C. & y
in
H.-y. (2008) - Analysis of Debris Flow
Underground Sound by wavelet Transform - A Case Study of Events in Aiyuzih River. Journal of Chinese Soil and Water
Conservation, 39 (1): 27-44. (Taiwan)
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