TRAVELLING WAVES IN THE OCCURRENCE OF EARTHQUAKE IN TAIWAN

Fu-Tai Wang*, Jenny Chih-Yu Lee**, Shun-Hsyung Chang**,Jhih-Jhen Chen*, Chiu-Hung Su*, Chen-Chain Hwu* and Haw-Jyi Lin*

*Department of Electrical Engineering, Hwa Hsia Institute of Technology111 Gong Jhuan Rd., 23568 Chung Ho, Taipei, Taiwan, Republic of China

phone: + (886) 2-8941-5137 ext 25, fax: + (886) 2-8941-5161, email: wft@cc.hwh.edu.twweb: www.hwh.edu.tw

**Department of Microelectronic Engineering, National Kaohsiung Marine University142 Haichuan Rd., 81143 Nantzu, Kaohsiung, Taiwan, Republic of China

ABSTRACTPredictions based on the past history of seismicity can be

useful for reducing the earthquake loss. It can help peopleto prepare for shorter term forecasting. There is not a simplematter to predict the spatial-temporal pattern of earthquakeover time and geography because of the presence of nonsta-tionarity and nonlinearity in fault movement data. An un-derstanding of the spatial-temporal pattern of past seismicevents would aid the preparedness to moderate earthquakedamage. In this paper, a method of empirical mode decom-position (EMD) to show a spatial-temporal travelling wavein the past history of seismicity is proposed.

1. INTRODUCTION

For earthquake forecast, one has to specify three ele-ments,that is where, when and how large the earthquake mag-nitude scales will be. With regard to “when”, it customarilygroups prediction techniques into three categories, namelythe long-term (decades), medium (few years), and short-timeintervals (less than one year) before a seismic event [1]. For-mer two classes of predictions are based on seismicity andthe past history of fault movement. Short term predictiontechnique tends to measure earth properties that change be-fore fracture. These wide variety of precursor include seis-mological, geochemical, electromagnetic, hydrological andbiological phenomena. A dilatancy model seems to give rea-sons for some of the observed precursor. The volume of mi-crofractures increase in the rocks as crustal stresses evolve[1, 2, 3, 4]. From the plot of precursor time against to theRichter magnitude “M” [5] of the main shock associated withthose precursor, the precursor time “T” in days can be de-scribed by log10T=0.60M-1.01.

Animals forecast earthquakes ranging from about oneminute up to three months. It seems that small animals, rats,squirrels, moles are associated with precursor times fromseveral hours up to 100 days, and have a mode at severaldays. Medium-sized animals, dogs, cats, monkeys exhibitthe ability to sense something from a few days down to aminute. Pigs, cows, deer have a strong mode at a few hours.These numbers have some bias involved for reasons of hu-man reporting unreliability [1]. These seismic anomalousanimal behaviors (SAABs) prior to an earthquake are oftenobserved [6]. The author of [6] proposes that ionization inthe lower atmosphere is responsible and akin to the piezo-electric effect that involves a pressure-induced charging of acrystal surface [1]. A model for the appearance of electriccharges in order to illustrate seismoatmospheric phenomena

is proposed. Based on this model, electric field effects thatmight elicit SAAB-like behaviors are demonstrated [4, 7, 8].

Seismological and geological field data help to under-stand the associated creation and development of a faultzone and determine the seismic fracture energy during anearthquake [5, 9]. Seismic forecasting involves probabil-ity and current behavior of secsmicity. An understandingof the spatial-temporal pattern of past seismic events wouldaid the preparedness to moderate earthquake damage. Dueto the presence of nonstationarity and nonlinearity in faultmovement data it is difficult to predict the spatial-temporalpattern of earthquake over time and geography. Empiricalmode decomposition (EMD) is a new method pioneered byHuang et al. for non-linear and non-stationary signal anal-ysis [10]. Another available analysis for processing nonsta-tionary signals is the wavelet method [11]. Unlike waveletanalysis, EMD uses an adaptive basis derived from data setto decompose the variance of that set into a finite numberof intrinsic mode function (IMFs) [10]. Some of its appli-cations have been made in signal detection underwater andsome have also been made to the analysis of epidemiologicaldata [12, 13, 14]. In this paper, a method of empirical modedecomposition (EMD) to show a spatial-temporal travellingwave in the past history of seismicity is proposed.

2. EMPIRICAL MODE DECOMPOSITION

In most of the input data X(t), more than one oscillatorymode is involved, and X(t) are not IMFs. The process to re-duce the data into IMF components is designated as the em-pirical mode decomposition (EMD) of the HHT [10]. ThisEMD is illustrated in Fig. 1. All the local minima are linkedby a cubic spline as the lower envelope. For the local max-ima, the upper envelope is produced. m1 is denoted as themean of these two envelopes. Two purposes of the siftingprocess are: (1) to eliminate riding waves; and (2) to makethe wave-profiles more symmetrical [10].

As shown in Fig. 1, the wave h1 is still asymmetric andit needs to be treated as the data and then take the the siftingprocess until h1k is IMF. This IMF h1k is then designated asthe first IMF component of the data. The stopping criteriaare provided in [15], [16]. The shortest period content of thedata should be contained in c1. Separating c1 from the restof the data, we have the residue r1. By repeating the siftingprocess on r1 and all the following r js, the EMD of the HHTget

X(t) =n

∑i=1

ci + rn. (1)

©2007 EURASIP 1926

15th European Signal Processing Conference (EUSIPCO 2007), Poznan, Poland, September 3-7, 2007, copyright by EURASIP

1500 2000 2500 3000 3500

−2

0

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4 Solid line : The data X(t).

Illustration of the sifting processes.

Am

plitu

de

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4 Dash line : The upper and lower envelops.

Thick solid line : The mean m1

Am

plitu

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4Solid line : The first component h

1.

Am

plitu

de

Time (sec)

Figure 1: Illustration of the sifting process.

0 1000 2000 3000 4000 5000 6000

−2

0

2

4

x

The EMD result showing three IMFs and a residue for analytical signal x.

0 1000 2000 3000 4000 5000 6000

−1

0

1

c1

0 1000 2000 3000 4000 5000 6000

−1

0

1

c2

0 1000 2000 3000 4000 5000 6000−2

0

2

c3

0 1000 2000 3000 4000 5000 6000

−2

0

2

r3

Time (sec)

Figure 2: The EMD result showing three IMFs and a residuefor analytical signal x.

Then a decomposition of the input data into n IMFs and oneresidue is achieved. The detail of the decomposition processis presented in [10]. Let us examine the linear sum of threecosine waves

x(t) = cos2

10πt + cos

220

πt + cos2

200πt. (2)

The EMD of HHT has to be used for the asymmetric waveform. The three IMF components after applying the EMDare shown in Fig. 2.

3. TRAVELLING WAVES

Empirical mode decomposition (EMD) is a new method fornon-linear and non-stationary signal analysis [10]. An ap-plications have been made to the analysis of epidemiologicaldata [14]. The spatial-temporal dynamics of dengue haem-orrhagic fever (DHF) incidence are examined in a data set

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Figure 3: Example of the EMD sifting process. a. Timeseries of the weekly occurrence of Earthquake in Pingtung,Taiwan, 1998-2003. b. Time series of the highest frequencyIMF. c. The second IMF component obtained by the EMD.d. The third IMF component.

describing 850,000 infections occurring in 72 provinces ofThailand during the period 1983 to 1997.

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Figure 4: Example of occurrence of Earthquake in Taitung,Taiwan, 1998-2003.

EMD isolates a 3-yr periodic mode of variance which isthought to reflect hostpathogen population dynamics. Thenonparametric covariance function is used to characterizethe spatial synchrony of incidence fluctuations. Spatial syn-chrony reflects both the amplitude and relative timing of in-cidence across provinces. Time series decomposition revealsa phenomenon that is not apparent in the raw incidence dataand can aid the formation of hypotheses [14]. Motivated bythis application, a method of EMD to show a spatial-temporaltravelling wave in the past history of seismicity is proposed.Data of occurrence of Earthquakes in Taiwan are available onthe Central Weather Bureau for Earthquakes Report website

http://www.cwb.gov.tw/V5e/index.htm

©2007 EURASIP 1927

15th European Signal Processing Conference (EUSIPCO 2007), Poznan, Poland, September 3-7, 2007, copyright by EURASIP

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Figure 5: Example of occurrence of Earthquake in Kaohsi-ung, Taiwan, 1998-2003.

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Figure 6: Example of occurrence of Earthquake in Chyayi,Taiwan, 1998-2003.

Example of the EMD sifting process of the weekly oc-currence of Earthquake in Pingtung, Taiwan 1998-2003, isshown in Fig. 3. Fig. 4 shows the IMF components ob-tained by the EMD for raw data of occurrence of Earthquakein Taitung, Taiwan 1998-2003. And Fig. 5 indicates timeseries of the weekly occurrence of Earthquake in Kaohsiung,Taiwan, 1998-2003 and the highest frequency IMF, the sec-ond IMF component, and the third IMF component obtainedby the EMD. Examples of the EMD sifting process of oc-currence of Earthquake in two middle provinces, Chyayi andNantou, are shown in Fig. 6 and Fig. 7, respectively . Fig.8 shows the weekly epicenter of earthquake for each Taiwanprovince. Data are presented for provinces from the mostsoutherly to the most northerly from top to bottom. Fig. 9shows the IMFs of the first periodic mode for these provincesof Taiwan. The IMFs of the second periodic mode for theseprovinces is illustrated in Fig. 10. The IMFs of the thirdperiodic mode is shown in Fig. 11.

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Figure 7: Example of occurrence of Earthquake in Nantou,Taiwan, 1998-2003.

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Figure 8: Weekly epicenter in each of the 12 provinces ofTaiwan. Data are presented for provinces from the mostsoutherly to the most northerly from top to bottom. Thereare 3756 individual data points.

4. CONCLUSION

Empirical mode decomposition (EMD) is a method pio-neered by Huang et al. for non-linear and non-stationarysignal analysis. In this paper, the EMD to show a spatial-temporal travelling wave in the past history of seismicity isproposed. In the seismological sense, analysis of frequency,magnitude and location of past seismic events can help peo-ple to prepare for shorter term forecasting. An understandingof the spatial-temporal pattern of past seismic events wouldaid the preparedness to moderate earthquake damage.

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©2007 EURASIP 1928

15th European Signal Processing Conference (EUSIPCO 2007), Poznan, Poland, September 3-7, 2007, copyright by EURASIP

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aiw

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at th

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15th European Signal Processing Conference (EUSIPCO 2007), Poznan, Poland, September 3-7, 2007, copyright by EURASIP