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International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),

ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME

279

QUALITY FACTOR OF SEISMIC CODA WAVES IN GARHWAL

HIMALAYAS

Priyamvada Singh, J.N. Tripathi

Department of Earth and Planetary Sciences, University of Allahabad, India

Email: [email protected]

ABSTRACT

Seismic wave propagating through the earth experiences some reduction in the energy

content. This decay in the wave energy is known as the seismic wave attenuation. The study of

attenuation characteristics of these waves shed light on the heterogeneous nature of the Earth.

Usually, seismic wave attenuation for local earthquakes is determined from the analysis of coda

waves.

Digital seismogram data of 75 earthquakes that occurred in Garhwal Himalaya region

during 2004 to 2006 and recorded at different stations have been analyzed to study the seismic

coda wave attenuation characteristic in this region. In the present study, 90 seismic observations

from local earthquake events with hypocentral distance less than 250 km and magnitude range

between 1.0 and 5.0 is used to study coda Q , i.e. cQ , using the single isotropic scattering model.

CQ Values are estimated at 10 central frequencies 1.5, 3, 5, 7, 9, 12, 16, 20, 24 and 28 Hz

using a starting lapse-time LT=50 s and four coda window-lengths , WL= 10, 20, 30, 40 s . In

the considered frequency range, CQ fit the frequency dependent power-law n

C fQQ 0= . The

frequency dependent power-law for 50 sec lapse time with 10 sec coda window length is 992.08.61 fQC = and for 50 sec lapse time with 40 sec coda window length is 998.01.161 fQC = .

The 0Q ( CQ at 1 Hz) estimates vary from about 61.8 for a 50 sec lapse time and 10 sec window

length, to about 161.1 for a 50 sec lapse time and 40 sec window length combination. The

exponent of the frequency dependence law n ranges from 1.016 to 0.967, which correlates well

with the values obtained in other seismically and tectonically active and heterogeneous regions

of the world.

It is observed for the study region that CQ values increases both with respect to window length

and frequency. The low CQ values or high attenuation at lower frequencies and high CQ values

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ISSN 0976 – 6308 (Print)

ISSN 0976 – 6316(Online)

Volume 3, Issue 2, July- December (2012), pp. 279-291

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or low attenuation at higher frequency may indicate that the heterogeneity decreases with

increasing depth, in the study region.

Keywords: Attenuation, Coda Q, Single backscattering model, Lapse time window, Garhwal

Himalaya

I. INTRODUCTION

The attenuation of seismic wave is one of the basic physical parameter which is closely related to

the seismicity and regional tectonic activity of a particular area. This is also important for

seismic hazard measurement. In this work, the seismic attenuation in the Garhwal Himalayas is

studied using local earthquakes. The amplitude of seismic waves decreases with increasing

distance from the earthquake. This reduction of the energy content cannot be explained by

geometrical spreading of the wave only. This decay in the wave energy is known as the seismic

wave attenuation. Seismic wave attenuate because the earth is not a perfect elastic and

homogeneous. Usually, seismic wave attenuation for local earthquakes is determined from the

analysis of direct body waves, surface waves or coda waves. The dimensionless parameter, Q , is

studied in the present work which is defined as a measure of the rate of decay of the coda waves

within a specified frequency band. Aki (1969) referred Coda as the tail part of seismograms of

local earthquakes. Aki and Chouet (1975) suggested that the S Coda of local earthquakes is

superposition of incoherent backscattered S-wave and surface waves generated from numerous

heterogeneity distributed randomly in the Earth’s crust and upper mantle. The great variety of

paths traveled by these waves provides information concerning the average attenuation

properties of the medium instead of just the characteristics of a particular path (Aki and Chouet

1975).

The CQ , quality factor of Coda wave has been estimated for different parts of the world (Aki and

Chouet 1975; Sato 1977; Ugalde et al., 2002; Tripathi and Ugalde, 2004, Ugalde et al., 2007,

Pezzo et al., 2011,). Coda wave characteristics have also been estimated for different parts of the

Himalayas (Gupta et al., 1995; Kumar et al., 2005; Hazarika et al., 2009; Sharma et al., 2009;

Mukhopadhyaya et al., 2010; Padhy et al., 2010; Tripathi et al., 2012).

In the present work the coda attenuation properties have been estimated in the Garhwal region of

Himalayas using local earthquakes. The frequency dependence of coda wave is also estimated.

II. STUDY AREA

The Himalayas is the consequence of the collision of the Indian plate with the plates of central

Asia during mid to late Eocene. The Outer Himalayas, Lower Himalayas and the Higher

Himalayas are the three major terrains identified in the Garhwal Himalayas [Valdiya, (1980)].



281

The major thrust fault striking parallel to the Himalayan arc, from north to south are the Main

Central Thrust (MCT), the Main Boundary Thrust (MBT) and the Himalayan Frontal Thrust

(HFT) (Figure 1).The high grade metamorphic units of Higher Himalayas, situated north of

MCT, are considered to be inactive generally, due to no signs of break of Quaternary deposits

(Ni and Barazangi, 1984; Brunel 1986). The outer Himalayas comprises of Tertiary rocks that is

underlain by the marine water to brackish origin subathu formation. This is followed upward by

siwalik group. The siwalik group is overlain by Quaternary gravel and sand. The Lower

Himalayas are mainly made up of Precambrian sedimentary rocks with some outcrops of

Cambrian Tal formation. The Higher Himalayas are made up of high grade metamorphic rocks

like amphibolites to granulites grade metasedimentary rocks, auger gneisses and intrusive

leucogranite. In the Garhwal-Kumaon Himalayas region these groups of rocks are known as the

vaikrita group (Srivastav and Mitra 1994)

Figure 1: (a) Simplified map of the Himalya. (b) Map of the study area modified after Valdiya

(1980).



282

III. METHOD AND DATA

The single backscattering model of coda wave envelopes of Aki and Chouet (1975) considers the

coincidence of source and receiver. So, for the practical application of the model, we have to

consider lapse time t >2 st , where st is the S wave travel time (Rautian and Khalturin, 1978).

Sato (1977) proposed the single isotropic scattering model for non coincident source and

receiver. Thus, we can analyse the coda window just after the S wave arrival. In this model, it is

assumed that the elastic energy is radiated spherically, scatterers are distributed homogeneously

and randomly, and the single scattering is isotropic in the media. Thus, the coda energy density

SE at frequency f can be expressed as

[ ]ftQKr

fgfWtrfE CS πα

π

1

2

00 2exp)(4

)()(),|( −

−

= (1)

Where t is the lapse time measured from the origin time of the earthquake, st is the S-wave

travel time, r is the hypocentral distance, 0W is the total energy radiated from the source, 0g is

the total scattering coefficient, and

);1(,1

1ln

1)( >

−

+= α

α

α

ααK and ./ stt=α (2)

The energy density is considered to be proportional to the mean square amplitudes of coda waves

and taking natural logarithms of Eq.1 and reshuffling the terms, we get

tQ

ffC

rk

trfA

C

obs

−=

π

α)(ln

),(

),|(ln (3)

where ),|( trfAobs represents the observed root mean square (rms) amplitude of the narrow band

pass filtered waveforms with central frequency ( ) 5.0)(/1),(; αα Krrkf = and )( fC is a constant.

Thus the CQ can be easily obtained from the slope b of the least square fit straight line to the

measured )],(/),|(ln[ αrktrfAobs versus t for a given central frequency, using the relation

bfQC /π= . The frequency dependence law, n

C fQQ 0= is also fitted to the CQ data for

different lapse time and window length, where 0Q is the value of CQ at 1 Hz and n is frequency

dependent parameter (Table 3).

The digital waveform seismograms of 75 events used for coda attenuation in the present study

were recorded at 20 stations of Garhwal Himalayas during 2004 to 2006 (Figure 2, Table 1). The

CMG 40T1 triaxial broadband seismometers were used for the digital data collection. The data is



283

acquired in continuous mode at 100 samples per second for three components at the stations.

SEISAN (version 8.1) software package (Havskov and ottemoller, 2005) was used to pick P and

S wave arrival times of each earthquake recorded at the different seismic stations. The

hypocentral parameters, viz, origin time, latitude, longitude and focal depth of these events were

also computed using the SEISAN software. Most of the events are within the crust and local

magnitude ranges from 1.0 to 5.0. First of all we preformed a visual inspection of more than 450

seismograms, 90 waveforms with hypocentral distances less than 250 km have been finally

processed for the present work.

IV. DATA ANALYSIS AND RESULTS

First of all the seismograms were band pass filtered for ten frequency bands, 1.5 ± 0.5 Hz, 3 ± 1

Hz, 5 ± 1 Hz, 7 ± 1 Hz, 9 ± 1 Hz, 12 ± 1 Hz, 16 ± 1 Hz, 20 ± 2 Hz, 24 ± 2 Hz, and 28 ± 2 Hz

(Table 2), using eight-pole Butterworth filters. As the sampling rate was 100 samples per second,

the maximum frequency for which reliable result could be obtained was 50 Hz. Then, the root

mean squared amplitudes of the filtered seismograms were computed at an interval of 0.5 s with

moving time windows of length st 2± for the first frequency band and st 1± for the next nine

frequency bands. Then CQ was estimated applying a least square regression technique to Eq.3

for one starting lapse time window length LT = 50 s from the S-wave onset, having Window

Length WL=10, 20, 30 and 40s for )],(/),|(ln[ αrktrfAobs . The CQ estimates were computed

only for the amplitudes greater than signal to noise ratios. The coda wave is analyzed only the

vertical component, because it has been shown that the coda analysis is independent of the

component of the particle ground motion analyzed (Hoshiba, 1993). The estimated CQ values

retained for further analysis which were having correlation coefficients greater than 0.5.

Figure 2: Station Locations (open circles) with events used in the Study.

29.00

30.00

31.00

32.00

33.00

34.00

35.00

72.00 74.00 76.00 78.00 80.00 82.00

Lati

tute

Longitude

Stations Location

Events

Stations



284

Table 1: Station code and their location

Station Longitude Latitude

DEO 76.67 32.09

TZG 76.79 32.59

UDA 76.67 32.72

CHT 76.37 32.45

TSA 76.14 32.82

UNA 76.32 31.52

LGR 75.91 32.29

BNK 75.94 32.55

RJA 76.24 32.00

BRM 76.54 32.44

PAL 78.62 30.81

GRG 79.44 30.46

JKH 78.43 30.4

PRT 78.48 30.46

YOL 76.4 32.17

AMB 76.04 31.67

BEED 75.94 32.58

NEL 78.52 30.4

GYL 78.51 30.36

NAD 76.31 32.24

The frequency dependent Coda Q relationship provides average attenuation characteristics of

the medium. The average values of CQ at different frequencies, one lapse time and four window

lengths obtained from the mean values for the whole study area are given in Table.3.

Table.2: Central frequencies and frequency range as low and high cutoff.

Low cutoff

(HZ)

Central frequency

(Hz)

High cutoff

(Hz)

1 1.5 2

2 3 4

4 5 6

6 7 8

8 9 10

10 12 14

14 16 18

18 20 22

22 24 26

26 28 30



285

Table 3: The average numerical values of CQ at different frequencies, lapse time (LT=50)

and coda window length (WL=10, 20, 30, and 40 s).

LT

(s)

WL

(s)

Values of CQ at different frequencies

1.5 Hz 3 Hz 5 Hz 7 Hz 9 Hz 12 Hz 16 Hz 20 Hz 24 Hz 28 Hz

50 10 121.00 171.96 287.8 386.55 553.72 856.37 1249.76 1596.24 1700.58 1790.04

50 20 179.10 294.54 511.71 732.39 1002.40 1553.47 1825.29 2091.45 2382.79 2611.67

50 30 201.03 333.08 587.83 806.85 1059.86 1707.75 2228.78 2702.07 3153.7 3202.79

50 40 279.23 500.61 863.62 1166.27 1487.98 2212.82 2718.69 3384.61 4523.86 5200.77

For the study area it is observed that CQ value increases both with respect to frequency and

window length. It is observed that the CQ increases with frequency. The average value of CQ for

the study region varies from 121 at 1.5 Hz to 1790 at 28 Hz for lapse time 50s and window

length 10s. When window length is 20, CQ is 179 at 1.5Hz and 2611 at 28Hz. Higher values of

CQ are obtained at 30 and 40s window lengths. This observation of frequency dependence of

CQ is due to the degree of heterogeneity of a medium and level of tectonic activity in an area

(Aki 1980). The low CQ values or high attenuation at lower frequencies may indicate a high

degree of heterogeneity and decrease in rock strength at shallow parts. The high CQ values or

low attenuation at higher frequencies may be related to the comparatively less hetrogeneous

deeper zones (Aki and Chouet, 1975).

Gupta et al. (1995) obtained a frequency relation 95.0126 fQC = using records of seven micro

earthquake in the adjoining southwestern part of Garhwali Himalayas for 30s coda window

length.

Kumar et al., (2005) employed the time domain coda - decay method of a single - back –

scattering model to calculate frequency dependent values of coda CQ . A total of 36 local

earthquake of magnitude range 2.4 - 4.8 have been used for CQ estimation at central frequencies

1.5, 3.6, 6.9, 9.0, 12.0 and 18.0 Hz through eight lapse time windows from 25 to 60s starting at

double the time of the primary S-wave from the origin time. The estimated average frequency

dependence quality factor gives the relation 05.1158 fQC = while the average CQ values vary from

the relation 210 at 1.5Hz to 2861 at 18Hz central frequencies. The observed coda quality factor is

strongly dependent on frequency, which indicate that the region is Seismic and tectonically

active with high heterogeneity.

Paul et.al., (2003) estimated CQ for Kumaun Himalayas using data from eight micro earthquake

record by a five station array with epicentral distance range varying between 10 km to 80 km for

30 sec window length and obtained a )23.007.1()73.492( ±±= fQC analyzing the SH wave form

data of 1988 Nepal - India border earthquake.



286

Figure 3: Frequency dependency power law for lapse time 50s and coda window length 10, 20, 30, 40,

50 s.

Hazarika et al., (2008) found that 1

0

−Q is very high i.e. coda at 1Hz frequency attenuates very

fast. They also found that 0Q and n values are different at Arunachal Himalayas, Shilong massif

and Indo- Burma ranges with the former two being characterized by lower attenuation compared

to the last one.

Qc= 61.75f0.992

1

10

100

1000

10000

1 10 100

Qc

Frequency

LT=50

WT=10

Qc= 107.2f0.967

1

10

100

1000

10000

1 10 100

Qc

Frequency

LT=50

WL=20

Qc= 113.5f1.016

1

10

100

1000

10000

1 10 100

Qc

Frequency

LT=50

WT=30

Qc= 161.1f0.998

1

10

100

1000

10000

1 10 100

Qc

Frequency

LT=50

WL=40



287

For NW Himalayas Mukhopadhyay and Tyagi (2008) found that coda and intrinsic attenuation

decreases with depth, whereas scattering attenuation increases with depth. The mean values of

CQ reveals a dependence on frequency varying from 292.9 at 1.5 Hz to 4880.1 at 18 Hz.

In the Chamoli region of the Himalayas Mukhopadhayay et al., (2008) found that CQ frequency

relations for 10, 20, 30, 40, and 50s window lengths are (33 ± 2) )03.017.1( ±f , ( 55 ± 6) )05.076.1( ±f ,

(78 ± 20) )08.098.0( ±f , (93 ± 18) )08.007.1( ±f , (122±20) )07.098.0( ±f , respectively.

Mukhopadhayay and Sharma (2010) analyzed the coda of local earthquakes to study the

attenuation characteristics of the Garhwal - Kumaon Himalayas. It is observed that CQ increases

with frequency and also varies.

Sharma et al., (2009) estimated quality factor for P-wave, S-wave and Coda- waves in Chamoli

region, and estimated frequency dependent relations for quality factors are 21.130 fQC = , )04.082.0()144( ±

±= fQα and )03.071.0()387( ±±= fQα .

Figure 4: Comparison of estimated CQ with other studies of Himalayas.

Makhopdhyaya and Tyagi (2007), analyzing the events from Northwestern Himalayas

have shown that the region is highly heterogeneous and tectonically very active and

heterogeneity decreases with depth in this area 0Q increases from 113 ± 7 to 243 ± 10 and n

decreases from 1.01 ± 0.05 to 0.86 ± 0.03 when lapse time increases from 30 sec to 70 sec.

Singh et al., (2012) analyzed the local earthquakes in Kumaon Himalayas region to estimate

lapse time dependence of coda waves and obtained that by increasing lapse time window from

1

10

100

1000

10000

0.1 1 10 100

Qc

Frequency

Present study

Northwestern Himalayas

Tripathi(2012)

Kumaun Himalayas

Singh(2012)

Garhwal Himalayas

Gupta(1995)

Western HimalayaS

Mukhopadhyay(2007)

LT=50

WL=30



288

20 to 50 s, 0Q increases from 64 to 230 while dependent parameter n decreases from 1.08 to

0.81.

Tripathi et al., (2012) estimated coda wave attenuation using the single isotropic scattering

method for frequency range 1-30 Hz for the Garhwal region for other data set. They used several

starting lapse times and coda window lengths for the analysis to study the variation of

attenuation characteristics. Results show that the 1−

cQ values are frequency dependent in the

considered frequency range, and they fit the frequency power-law =− )(1

fQc

1

0

−Q

nf − . The 0Q

estimates vary from about 50 for a 10 s lapse time and 10 s window lengths, to about 350 for a

60 s lapse time and 60 s window length combinations. The exponent of the frequency

dependence law n ranges from 1.2 to 0.7; however, it is greater than 0.8, in general, which

correlates well with the values of others in Himalaya region.

The estimated coda attenuation values in the present study are comparable with that obtained

from other regions of the Himalayas, as shown in Figure 4.

Table 4: Frequency dependent power law n

C fQQ 0= .

For study region, increase in CQ with the window length is attributed to increase in CQ

with depth, as longer the time window the larger will be the sampled area of the earth’s crust

and mantle. This observation seems to indicate that there is a decrease in the level of

heterogeneities with depth in the Garhwal Himalayas. This would imply that attenuation

decreases with increasing depth.

A strong correlation between the degree of frequency dependence , n value, and the level of

tectonic activity was claimed (Aki 1980). This is also observed by others, in Himalayan region,

that n value is higher for tectonically active regions compared to the tectonically stable regions

(Kumar et al., 2005; Mukhopadhyaya et al., 2010; Hazarika et al., 2009; Sharma et al., 2009;

Tripathi et al., 2012; Padhy et al., 2010;). For Garhwal Himalaya Gupta et al., (1995) estimated

0Q as 126 and n as 0.9. Mukhopadhyay et al., (2010) estimated 0Q as 119 and n as 0.99. The

LT WL n

C fQQ 0=

50 10 992.08.61 f

50 20 967.02.107 f

50 30 016.15.113 f

50 40 998.01.161 f



289

obtained values of n is close to 1 in the present study which indicate that the region is highly

hertogeneous and tectonically very active.

V. CONCLUSION

In the present study, the CQ values have been estimated for Garhwal Himalayas region, using 90

seismograms from 75 local earthquakes recorded digitally at 20 different stations and analyzed

for one lapse time (e.g. 50 s), four window lengths ( e. g. 10, 20, 30, and 40 s) and at 10

frequency bands with the central frequency in the range of 1.5 Hz to 28 Hz.

The estimated CQ values for the lapse time 50 s vary from 121 to 279 at 1.5 Hz and from 1790

to 5200 for 28 Hz where the coda window varies from 10 to 40 s. It is clear from the results

(Table 3) that CQ is a function of frequency in this region. The CQ value increases as frequency

increases. A frequency dependent relationship has also been obtained for the region (Table 4),

which shows that there is a significant increase in 0Q values with increasing window length,

while there is a nominal decrease in the degree of frequency dependence, n. This can also be

interpreted that the scattering effect in the region exhibits a decreasing trend with increasing

depth (Aki 1980). This may be due to decrease in the heterogeneities level of the medium. The

general trend of the present coda attenuation study is similar to seismically and tectonically

active region (Figure 4).

Attenuation parameter CQ is an important factor for understanding the physical mechanism of

seismic wave attenuation in relation to the composition and physical condition of the Earth’s

interior and it is also an essential parameter for the quantitative prediction of strong ground

motion for the viewpoint of engineering seismology. Hence numerous studies of CQ have been

carried out worldwide by using different methods and concentrate on seismically active zones

and densely populated area.

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