Quality factor of seismic coda waves in garhwal

International Journal of Civil Engineering and OF CIVIL ENGINEERING AND
INTERNATIONAL JOURNAL Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME
TECHNOLOGY (IJCIET)
ISSN 0976 – 6308 (Print)
ISSN 0976 – 6316(Online)
Volume 3, Issue 2, July- December (2012), pp. 279-291
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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: priyam028@yahoo.com

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. Qc , using the single isotropic scattering model.
QC 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, QC fit the frequency dependent power-law QC = Q0 f n . The
frequency dependent power-law for 50 sec lapse time with 10 sec coda window length is
QC = 61.8 f 0.992 and for 50 sec lapse time with 40 sec coda window length is QC = 161.1 f 0.998 .
The Q0 ( QC 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 QC values increases both with respect to window length
and frequency. The low QC values or high attenuation at lower frequencies and high QC values

279

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

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 QC , 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)].

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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).

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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 t s , where t s 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
E S at frequency f can be expressed as

W ( f ) g 0 ( f ) 
ES ( f | r , t ) =  0
4πr 2
[ −1
 K (α ) exp − 2QC πft ] (1)
 

Where t is the lapse time measured from the origin time of the earthquake, t s is the S-wave
travel time, r is the hypocentral distance, W0 is the total energy radiated from the source, g 0 is
the total scattering coefficient, and

1  α +1
K (α ) = ln , (α > 1); and α = t / t s . (2)
α  α −1

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

 A ( f | r, t )   πf 
ln  obs  = ln C ( f ) −  Q
 t
 (3)
 k (r , α )   C 

where Aobs ( f | r , t ) represents the observed root mean square (rms) amplitude of the narrow band
pass filtered waveforms with central frequency f ; k(r , α ) = (1 / r )K (α ) 0.5 and C ( f ) is a constant.
Thus the QC can be easily obtained from the slope b of the least square fit straight line to the
measured ln[ Aobs ( f | r , t ) / k (r , α )] versus t for a given central frequency, using the relation
n
QC = πf / b . The frequency dependence law, QC = Q0 f is also fitted to the QC data for
different lapse time and window length, where Q0 is the value of QC 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

282


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 t ± 2s for the first frequency band and t ± 1s for the next nine
frequency bands. Then QC 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[ Aobs ( f | r , t ) / k (r , α )] . The QC 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 QC values
retained for further analysis which were having correlation coefficients greater than 0.5.

Stations Location
35.00

34.00

33.00
Latitute

32.00
Events
31.00
Stations
30.00

29.00
72.00 74.00 76.00 78.00 80.00 82.00
Longitude

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

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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 QC 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 Central frequency High cutoff
(HZ) (Hz) (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

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Table 3: The average numerical values of QC at different frequencies, lapse time (LT=50)
and coda window length (WL=10, 20, 30, and 40 s).

LT WL Values of QC at different frequencies
(s) (s) 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 QC value increases both with respect to frequency and
window length. It is observed that the QC increases with frequency. The average value of QC 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, QC is 179 at 1.5Hz and 2611 at 28Hz. Higher values of
QC are obtained at 30 and 40s window lengths. This observation of frequency dependence of
QC is due to the degree of heterogeneity of a medium and level of tectonic activity in an area
(Aki 1980). The low QC values or high attenuation at lower frequencies may indicate a high
degree of heterogeneity and decrease in rock strength at shallow parts. The high QC 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 QC = 126 f 0.95 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 QC . A total of 36 local
earthquake of magnitude range 2.4 - 4.8 have been used for QC 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 QC = 158 f 1.05 while the average QC 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 QC 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 QC = (92 ± 4.73) f (1.07 ± 0.23) analyzing the SH wave form
data of 1988 Nepal - India border earthquake.

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10000 10000
Qc= 61.75f0.992 Qc= 107.2f0.967
1000 1000
Qc

Qc
100 100

LT=50 LT=50
10 10
WT=10 WL=20

1 1
1 10 100 1 10 100

Frequency Frequency

10000 10000
Qc= 161.1f0.998
Qc= 113.5f1.016
1000 1000
Qc

100
Qc

100

LT=50 LT=50
10 10
WT=30 WL=40

1 1
1 10 100 1 10 100

Frequency Frequency

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 Q 0−1 is very high i.e. coda at 1Hz frequency attenuates very
fast. They also found that Q0 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.

286


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
QC 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 QC frequency
relations for 10, 20, 30, 40, and 50s window lengths are (33 ± 2) f (1.17 ± 0.03) , ( 55 ± 6) f (1.76± 0.05 ) ,
(78 ± 20) f ( 0.98± 0.08) , (93 ± 18) f (1.07 ± 0.08) , (122±20) f ( 0.98± 0.07 ) , 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 QC 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 QC = 30 f 1.21 ,
( 0.82 ± 0.04 ) ( 0.71± 0.03 )
Qα = (44 ± 1) f and Qα = (87 ± 3) f .

10000

1000 Present study

Northwestern Himalayas
Qc

100 Tripathi(2012)
Kumaun Himalayas
LT=50 Singh(2012)
WL=30
10 Garhwal Himalayas
Gupta(1995)
Western HimalayaS
Mukhopadhyay(2007)
1
0.1 1 10 100

Frequency

Figure 4: Comparison of estimated QC 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 Q0 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

287


20 to 50 s, Q0 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 Q c−1 values are frequency dependent in the
−n
considered frequency range, and they fit the frequency power-law Qc−1 ( f ) = Q 0−1 f . The Q0
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 QC = Q0 f n .

n
LT WL QC = Q0 f

50 10 61.8 f 0.992

50 20 107.2 f 0.967

50 30 113.5 f 1.016

50 40 161.1 f 0.998

For study region, increase in QC with the window length is attributed to increase in QC
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
Q0 as 126 and n as 0.9. Mukhopadhyay et al., (2010) estimated Q0 as 119 and n as 0.99. The

288


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 QC 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 QC 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 QC is a function of frequency in this region. The QC 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 Q0 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 QC 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 QC have been
carried out worldwide by using different methods and concentrate on seismically active zones
and densely populated area.

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