# IJEGE-11_BS-Fang-et-alii

*Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza*

*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**

**INTRODUCTION**

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.

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**

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*

*Y.-M. FANG, Y.-M. HUANG, B.-J. LEE, T.-Y. CHOU & H.-Y. YIN*

*5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011*

*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

factor and the frequency recorded ranged mostly be-

tween 20-80 Hz, particularly 40-60 Hz. R

frequency of a debris flow ranges between 10-300 Hz,

with evident frequency of 30-80 Hz.

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

*et alii*(2008) ana-

geophone was in a relatively lower range of 5-60 Hz.

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

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.

Co. were used and the measurable frequency ranges

between 8 to1500 Hz.

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.

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*

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

*et alii*(1990), who obtained

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.

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*

**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*

*TRANSFORM*

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.

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.

square waves with amplitude of ±1 in certain inter-

vals and 0 in others:

Let

*Φ*a scaling function and can be defined as

*Φ*

*0*

*0*

*(t)*=

*Φ(t)*implies the special case. The

low.

*sp*denotes the linear space,

*j*is related

tion shift. The normalization constant

will change.

Definition 2 (The Haar Scaling Function)

*ψ*the mother wavelet function and can be de-

*ACCUMULATED ENERGY*

tion of geophones for debris flows. l

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.

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.

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*

*Y.-M. FANG, Y.-M. HUANG, B.-J. LEE, T.-Y. CHOU & H.-Y. YIN*

*5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011*

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.

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.

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.

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

form can be expressed as

*Φ*

*0*

*0*

*(t)*=

*Φ(t)*implies the special case. The general

*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

*f*, with 8 samples. The pro-

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

following expression.

*f,Φ*

*i*

*j*

*>*and <

*f,ψ*

*i*

*j*

*>*are the inner products of

*Φ*

*i*

*j*

*ψ*

*i*

*j*

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*

**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*

utze River, and the triggered debris flow had seriously

damaged the Aiyutze Bridge.

ure 6 shows the time history of rainfall and the timing

of wire rupture.

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

TOR

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.

plication of three times of wavelet transform had been

conducted as standard procedure in this study.

**CASE STUDIES OF GEOPHONE SIGNAL**

**ANALYSIS**

*TYPHOON MINDULLE*

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.

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*

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*

*Y.-M. FANG, Y.-M. HUANG, B.-J. LEE, T.-Y. CHOU & H.-Y. YIN*

*5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011*

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.

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-

station and served as a factor to determine the scale

and occurrence of debris flows.

**CONCLUSIONS**

cate directly the characteristic lower frequency range

of debris flow, as well as filtering out the higher fre-

quency range.

obtain the original signal sequence. The Haar trans-

form is the original and simplest transform function.

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.

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*

**ANALYSIS OF DEBRIS FLOW UNDERGROUND SOUND BY WAVELET TRANSFORM - A CASE STUDY OF EVENTS IN AIYUZIH RIVER**

flow database.

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**

*Monitoring the presence of the debris-flow front and its velocity through ground vibration detectors.*The

*Real time estimation of discharge of debris flow by an acoustic sensor.*

**XA**: 127-131.

*Detecting Debris Flow Using Ground Vibration.*USGS Fact Sheet: 236-296.

*Analysis of Debris Flow*

*Underground Sound by wavelet Transform - A Case Study of Events in Aiyuzih River.*Journal of Chinese Soil and Water

Conservation,

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**:**27-44. (Taiwan)