Tectonophysics 530–531 (2012) 264–271

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Tectonophysics

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Attenuation characteristics of coda waves in Mainland Gujarat (India)

Arun K. Gupta a,⁎, Anup K. Sutar a, Sumer Chopra a, Santosh Kumar b, B.K. Rastogi b

a Ministry of Earth Sciences, New Delhi-110 003, Indiab Institute of Seismological Research, Gandhinagar-382 009, Gujarat, India

⁎ Corresponding author.E-mail address: akg_mgs@yahoo.com (A.K. Gupta).

0040-1951/$ – see front matter © 2012 Elsevier B.V. Alldoi:10.1016/j.tecto.2012.01.002

a b s t r a c t

a r t i c l e i n f o

Article history:Received 3 August 2011Received in revised form 2 January 2012Accepted 2 January 2012Available online 10 January 2012

Keywords:Coda waveAttenuationLapse timeMainland Gujarat

The attenuation characteristics based on coda waves of Mainland Gujarat (India) have been investigatedin the present study. The broadband waveforms of 53 local earthquakes (Mw 1.1–3.3) having focal depthsin the 6.0–33.6 km range recorded at five stations of Mainland Gujarat region has been used for the analysis.The frequency-dependent relationships (Q=Q0f

n) for coda-Q (Qc) and dependency of coda-Q on lapse timewindows have been determined for the said region. The average lapse time dependent coda-Q relations es-timated for the region are: Qc=(87±13)f(1.01±0.06) (lapse time: 30 s), Qc=(112±20)f(0.94±0.08) (lapsetime: 40 s) and Qc=(120±22)f(0.76±0.07) (lapse time: 50 s). The increase in Qc values with lapse timeshows the depth dependence of Qc as longer lapse time windows will sample larger area. The observed qual-ity factor is strongly dependent on frequency and lapse time, which indicates that the upper lithosphere, ismore heterogeneous and seismotectonically active, while the lower lithosphere is homogeneous and rela-tively less active. A comparison of the coda-Q estimated for Mainland Gujarat region with those of nearbyKachchh and Saurashtra regions shows that Mainland Gujarat region is more heterogeneous. The rate ofdecay of attenuation (Q−1) with frequency for the relations obtained here is found to be comparable withthose of other regions of the world though the absolute values differ. The obtained relations are expectedto be useful for the estimation of source parameters of the earthquakes in the Mainland Gujarat regionwhere no such relations were available earlier. These relations are also important for the simulation of earth-quake strong ground motions in the region.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

Seismic wave attenuation, expressed by the dimensionless quantityknown as quality factor (Q), represents the decay of wave amplitude orenergy caused by heterogeneity or anelasticity or both in the earthcrust. It is one of the most important basic physical parameters whichis directly related to the seismicity and tectonic activity of the study re-gion. The attenuation characteristics of seismic waves have beenwidelyestimated using coda waves in the crust of a region (Ambeh andFairhead, 1989; Catherine, 1990; Gupta and Kumar, 2002; Gupta et al.,1996; Kumar et al., 1997; Mandal and Rastogi, 1998; Paul et al., 2003;Pulli, 1984; Sharma et al., 2008, 2011; Van Eck, 1988; Parvez et al.,2008). Several researchers (Aleqabi and Wysession, 2006; Frankel etal., 1990; Mitchell, 1995) have used coda waves for structure and tec-tonic interpretation to investigate the tectonic properties of the seismi-cally active regions as the attenuation of the seismicwaves is affected bythe tectonic pattern of the crust. The study of attenuation of seismicwaves is also important for seismic hazard assessment by studyingthe ground-motion attenuation (Anderson et al., 1996) and for moni-toring nuclear explosions (Mayeda et al., 2003). The attenuation

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(Q−1), for local or regional earthquakes is determined from the rate oftime decay of coda wave amplitude or analysis of direct waves (P andS waves) and Lg wave amplitude (Aki, 1969; Aki, 1980; Aki andChouet, 1975; Chung and Sato, 2001; Davis and Clayton, 2007; Frankelet al., 1990; Sato, 1977; Yoshimoto et al., 1993). The relations estimatedfor attenuation may be used to determine the earthquake source pa-rameters for understanding source processes (Abercrombie, 1997),and to predict the strong ground motions (Chopra et al., 2010).

The attenuation of seismic waves is affected by several factors likegeometrical spreading, scattering due to inhomogeneities in themedia, inelasticity and multipathing. The attenuation properties of themedia are governed by the amplitude of seismic waves at variousdistances from an earthquake source. The frequency dependent rela-tions for Q (=Q0fn) have been developed bymanyworkers for differentregions of the world. The Q0 values are found to be varied according tothe tectonic conditions and geological history of the regions. Aki (1980)found that the frequency dependency (n) of Q increases with intensityof tectonic activity.

The attenuation characteristics based on coda waves have been in-vestigated in the present study using the single back scattering modelof Aki and Chouet (1975). The broadband seismograms of 53 eventsthat occurred in Narmada and its adjoining area of Mainland Gujarathas been used in this analysis. The frequency-dependent relationshipsfor coda-Q (Qc) have been estimated atfive stations inMainlandGujarat

265A.K. Gupta et al. / Tectonophysics 530–531 (2012) 264–271

region. The dependency of coda-Q on lapse timewindows has also beeninvestigated. These attenuation characteristics based on codawaves arethe first estimates for Mainland Gujarat region. However the frequencydependent Q relations for the nearby Kachchh region (Gupta et al.,2006; Mandal et al., 2004; Sharma et al., 2008), Saurashtra region(Sharma et al., 2011) and three distinct zones (Kachchh, Saurashtraand Mainland Gujarat) of Gujarat region (Chopra et al., 2010) areavailable. Chopra et al. (2010) have studied the attenuation ofhigh frequency P and S waves in Kachchh (9 stations), and Saurashtra(5 stations) and used only one station in Mainland Gujarat. The fre-quency dependent relationships for Qc obtained here have been com-pared with those of other active and stable regions of the world. Thepresent study of coda wave attenuation in Mainland Gujarat regionwill enhance our knowledge about the medium properties of thestudied region.

2. Geology and seismotectonics of Mainland Gujarat

Gujarat state is situated in a highly tectonized zone along the west-ern border of the Indian continental plate. The breakup of the Indianplate started from Gujarat region as the rifting process migrated fromnorth to south. Since the breakup of Indian continental plate from theAfrican plate at least three major tectonic episodes — Jurassic–EarlyCretaceous rifting, Late Cretaceous–Early Eocene drifting and LateMiocene to ongoing inversion affected this region (Biswas, 1987).There are four distinct tectonic regimes within the boundaries of theGujarat state: 1) Narmada rift zone, 2) Saurashtra horst, 3) Cambayrift zone, and 4) Kachchh rift zone (Biswas, 1987).

Physiographically, Gujarat state comprises of three distinct zones:Kachchh, Saurashtra and Mainland Gujarat (Fig. 1). Stratigraphically,

Fig. 1. The rectangular region on the map is expanded. Epicentral locations of 53 events usshown by open circles, and stations used in this study are shown by triangles. The tectonBelt Fault, GF: Gedi Fault, KMF: Kachchh Mainland Fault, KHF: Katrol Hill Fault, NSF: Narma

Mainland Gujarat comprises Precambrian crystallines, sedimentaryrocks of Cretaceous, Tertiary and Quaternary periods and the Deccanbasalt (Merh, 1995). Mainland Gujarat is largely occupied by a flat allu-vial plain. Cambay basin is a major tectonic feature in the central por-tion. It is surrounded by Deccan traps in the east and west andAravalli system of Precambrian age in the north-east. In the southernpart, the EW trending Narmada fault system is a zone of weakness fol-lowing Narmada–Son Geofracture (NSG) comprising of Narmada–Sonfault (NSF) in the north and Satpura fault (SF) in the South. The Cambaybasin occupies a long narrow rift extending from south of Narmada tothe Jaisalmer-Mari arch of Rajasthan to the north in NNW–SSE direc-tion. Northward the rift becomes narrower and ends up as Barmerbasin in Rajasthan. It extends to the south across the Narmada rift,along the west coast fault in the offshore shelf. It is a sub-surface struc-ture below the alluvial plains of Gujarat (Biswas, 1987).

The Cambay and Narmada are conjugate rifts displacing each otherwhile crossing in the region of Gulf of Cambay, which is supposedlythe tri-junction point over the plume head along the west coast faultin the offshore shelf. Significantly, this is the zone of maximum subsi-dence in the present tectonic framework where Surat deep depressionis located. The NSG has been the site of resurgent tectonics since Neo-Archaean times including neotectonic rejuvenation and recent seismic-ity (Biswas, 1987). In the present neo-tectonic cycle, the NSF is the ac-tive strike-slip fault, undergoing right lateral movement andresponsible for frequent earthquake (Biswas, 1987).

Historical and instrumental records indicate that the compressivestresses still continue to accumulate along the NSF due to continuednorthward movement of the Indian plate. This is evidenced by thefault plane solution studies of the earthquakes at Broach M5.4 (23March 1970) and Jabalpur M5.8 (22 May 1997), which suggest a

ed in present study are shown by dark circles, epicenters of historical earthquakes areic features are as follows: NPF: Nagar Parker Fault, ABF: Allah Bund Fault, IBF: Islandda Son Fault and BSF: Barwani Sukta Fault.

Table 1Site characteristics and epicentral locations of the recording stations.

Station Station code Latitude (N) Longitude (E) Foundation geology

Sipu SIP 24.39 72.29 GraniteKadana KAD 23.29 73.85 BasaltKevdia KEV 21.88 73.71 BasaltVadodara VAD 22.31 73.13 Hard soilUkai UKE 21.22 73.58 Basalt

Table 2Velocity model for locating earthquakes in Mainland Gujarat (Kaila et al., 1981).

Depth to the top of layer (km) Velocity of P-wave (km/s)

0.0 4.901.0 5.332.0 5.764.0 5.896.0 6.028.0 6.1510.0 6.3813.0 6.4716.0 6.5619.0 6.6025.0 6.8028.0 6.8931.0 6.9834.0 7.1038.0 8.10

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thrustingmechanism (Acharya et al., 1998; Chandra, 1977; Gupta et al.,1972, 1997). However, the underlying cause of the seismicity in the NSFzone is not yet understood (Quittmeyer and Jacob, 1979).

Mainland Gujarat region falls under zone III of the seismic zoningmap of India which indicates the moderate damage risk zone. Thiszone may experience an intensity of VII on the MSK scale. A zone factorof 0.16 has been assigned to this zonewhich indicates the effective peakhorizontal ground acceleration of 0.16 g thatmay be generated during amaximum credible earthquake considered in the zone. Historically thisregion has experienced several earthquakes of magnitude between 4and 5.7 (Fig. 1). The Cambay fault of Mainland Gujarat has produced anumber of moderate size earthquakes in the eastern boundary ofSaurashtra, largest being magnitude 6 near Bhavnagar in 1919. Valsadarea of south Gujarat has witnessed swarm type of seismic activity in1986 (Rao et al., 1991). The region has also witnessed earthquake ofmagnitude 3.2 on May 20, 2008 near Surat (ISR Annual report, 2008).Fig. 1 shows the tectonics of the Mainland Gujarat region along withthe major rift zones. The epicenters of the earthquakes and locationsof recording stations in the Mainland Gujarat are also shown in Fig. 1.

3. Methodology

Aki and Chouet (1975) proposed amethod to estimate the Qc usingthe single backscattering model. Single backscattering model assumesthat the coda waves are backscattered body waves generated bynumerous heterogeneities present in the Earth's crust and upper man-tle. Under this assumption the coda amplitudes, Ac(f,t) in a seismogramcan be expressed for a central frequency ‘f’ over a narrow band widthsignal, as a function of the lapse time t, measured from the origin timeof the seismic event, as (Aki, 1980):

Ac f ;tð Þ ¼ S fð Þt−aexp −pft=Qcð Þ ð1Þ

where S(f) represents the source function at frequency f, and is consid-ered a constant as it is independent of time and radiation pattern, andtherefore, not a function of factors influencing energy loss in the medi-um; a is the geometrical spreading factor, and taken as 1 for bodywaves, and Qc is the apparent quality factor of codawaves representingthe attenuation in a medium. Rautian and Khalturin (1978) suggestedthat the coda parameters S(f) andQc are independent of source-site dis-tance if coda start time is taken as twice the travel time of S-waves. TheEq. (1) can be rewritten as:

ln Ac f ;tð Þtð Þ ¼ lnS fð Þ− pf=Qcð Þt: ð2Þ

The linear Eq. (2) with slope −πf/Qc can be used to estimate Qc.

4. Data and analysis

Digital data of earthquakes that occurred during 2007–2010 inMainland Gujarat region and recorded by the broadband seismograph(BBS) network of Institute of Seismological Research (ISR), Gandhina-gar are analyzed for the estimation of Qc in the present analysis. ISR,Gandhinagar has installed five permanent 120 s broadband (CMG-3T,Guralp) sensors having 24 bit CMG-DCM recorders with an externalhard disk (4 GB) and GPS synchronized timing system instruments atKadana (KAD), Sipu (SIP), Vadodara (VAD), Kevdia (KEV) and Ukai(UKE) stations. All the five recording stations are connected throughVSAT and continuous data is being recorded at all these stations at thesampling rate of 50 samples/s (Chopra et al., 2008). Table 1 gives thelocations and site conditions of the recording stations. The eventswere located in SEISAN (Havskov and Ottemoller, 2000) program. TheKoynamodel (Kaila et al., 1981) constrained by Deep Seismic Soundingis used for locating earthquakes in Mainland Gujarat. The velocitymodel of Koyna is given in Table 2. The error in an epicenter is 5 km,and the error in origin time is 1 s. The magnitudes of the events have

been estimated by fitting the Brune's (1970) model to the source dis-placement spectra of observed seismograms. Out of 100 local earth-quakes, seismograms of 53 events having Mw (1.1–3.3) were selectedbased on signal-to-noise ratio and correlation criteria for estimation ofQc. Fig. 1 shows the locations of the earthquakes and recording stations.The maximum and minimum epicentral distances for the earthquakesare 113 km and 20 km respectively.

Only waveforms with good signal-to-noise ratio (S/N≥2) are usedfor the analysis. S/N ratios are calculated for each central frequency foreach record separately. We have also checked how the Qc estimatesare affected when S/N is increased (≥5). It is observed that the estimat-ed Qc values for both cases are almost the same or lie within the errorrange. As for S/N≥2, the number of data available is higher, andas this does not significantly affect the result, we have decided to useS/N≥2. In the same manner the criteria of correlation coefficient≥0.50 is applied to obtain reliable Qc values.

In order to estimate Qc, it is necessary to eliminate contaminationcaused by the direct S-phases (Herraiz and Espinosa, 1987; Rautianand Khalturin, 1978). In order to do so, Rautian and Khalturin (1978)suggested that the beginning of the coda window should be placed ata time measured from the origin time of an earthquake that is abouttwice the S-wave travel time (ts). This time is called lapse time. Wecall it start time tstart following Havskov et al. (1989). Spudich andBostwick (1987) have shown that for ts≤ tstart≤2ts, near-site rever-berations can be the dominant component of the coda, at least for fre-quencies less than about 10 Hz. In the present study, we haveanalyzed the data set by selecting the start times tstart at 2ts.

The coda window length should be large enough to get stableresults. Havskov and Ottemoller (2005) suggest a minimum value of20 s. There is no limit on the maximum lapse time. However, it is as-sumed that S/N≥2 could be obtained for very few records for lapsetime >50 s; hence, it was set as the upper limit. Three lapse time win-dow lengths of duration 30 s, 40 s and 50 s are selected and we fix thewindow length as 20 s. Fig. 2 shows an example of coda portion usedfor analysis (the boxed portion) when window length is 20 s andtstart=2ts. The Q values are calculated through the CODAQ subroutineof SEISAN (Havskov and Ottemoller, 2003). The S-wave time is calculat-ed through the Pwave time usingVp/Vs=1.74. The top panels in Fig. 2a

420400380360340320300208

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f=1.5Hz. Qc(1.5Hz)=150

f=3Hz.Qc(3Hz.)=317

f=6Hz. Qc(6Hz.)=441

f=12.0Hz. Qc(12Hz)=923

Qc(18Hz.)=1832.zH81=f

a

b

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d

e

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h

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Fig. 2. Plot of event recorded at UKE station on 12/12/2010 from 66 km epicentral distance. (a) Unfiltered data trace with coda window, (b) to (f) bandpass filtered displacement ampli-tudes of codawindowat 1–2 Hz, 2–4 Hz, 4–8 Hz, 9–15 Hz and 16–20 Hz respectively, (g) to (k) theRMS amplitude valuesmultipliedwith lapse time alongwith best squarefits of selectedcoda window at central frequencies of 1.5, 3.0, 6.0, 12.0 and 18.0 Hz respectively. The Qc is determined from the slope of best square line. Abbreviations are: P: P-wave arrival time;S: S-wave arrival time.

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show the 20-s window length of codawaves considered for the estima-tion of Qc for tstart equal to 2ts. The origin time, P wave and S wave ar-rival time of the earthquake is shown in the seismogram. Coda of all theseismograms is filtered using the Butterworth band pass filter (eightpoles) at central frequencies of 1.5, 3.0, 6.0, 12.0 and 18.0 Hz. The root

mean square (RMS) amplitudes of filtered seismograms are estimatedusing a moving time window of 2.56 s width with 1.28 s interval.Fig. 2 displays the filtered seismograms and plots of ln[A(f,t).t] versust for an event recorded at UKE for different central frequencies alongwith the least square fitted lines. The slopes (m) of these lines are

Table 3Average quality factor at different frequencies and lapse time. ±σ indicates the standard error and intervals show the frequency band.

Lapse time (s) 1.5 Hz (1–2) Qc±σ N 3.0 Hz (2–4) Qc±σ N 6.0 Hz (4–8) Qc±σ N 12 Hz (9–15) Qc±σ N 18 Hz (16–20) Qc±σ N

30 133±66 28 246±102 48 586±242 77 991±252 74 1633±386 7540 173±88 39 323±99 58 617±197 89 1081±328 76 1634±448 6450 175±60 27 286±77 38 664±169 68 1152±303 64 1686±265 52

268 A.K. Gupta et al. / Tectonophysics 530–531 (2012) 264–271

used to estimate Qc (=−πf/m). Table 3 shows average value of Qc forthe region at different lapse times and central frequencies. An increas-ing frequency band is used for increasing central frequency to avoidringing and to take constant relative bandwidths as suggested byHavskov and Ottemoller (2005). The comparison of the number of seis-mograms selected for each frequency and lapse time to observe theaverage Qc is described by the factor N in Table 3. Table 4 shows the pa-rameters of frequency dependent Q for different lapse times at differentstations whereas Table 5 shows the worldwide comparison of Q value.

In the single scattering model the estimated attenuation of codawave is the average decay of amplitude of back-scattered waves onthe surface of ellipsoid volume having earthquake source and stationas foci (Pulli, 1984). On this basis the approximate ellipsoidal volumefor five seismic stations is estimated, which shows average attenuationproperties of the area around station. The observed Qc reflects the aver-age attenuation properties of the volume of ellipsoid at an averagedepth, h=hav+a2, where hav is the average focal depth of the events

and a2 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia12−Δ2

� �ris the small semi axis of the ellipsoid for Δ as

average epicentral distance (Canas et al., 1995; Havskov et al., 1989;Pulli, 1984). The large semi-axis of the ellipsoidal volume is a1=ct/2for lapse time t and velocity c of the S wave (c=3.5 km/s). The averagelapse time is taken as t= tstart+W/2where tstart is the starting time ofthe coda window and W is the coda window length. The depths calcu-lated for the ellipsoidal volume for different stations of data are givenin Table 6.

Table 5Worldwide comparative study of observed Q0 and n values for various active and sta-ble regions.

Places Q0 n Source

Active regionsKachchh, India 102 0.98 Mandal et al. (2004)Guerrero, Mexico 47 0.87 Rodriguiez et al. (1983)Yugoslavia 50 1 Rovelli (1984)Hindukush 60 1 Roecker et al. (1982)Washington State 63 0.97 Havskov et al. (1989)Mt. Cameroon, West Africa 65 1 Ambeh and Fairhead (1989)Dead Sea 65 1.05 Van Eck (1988)

5. Results and discussions

The seismograms have beenfiltered atfive different central frequen-cies of 1.5 (1–2 Hz), 3 (2–4 Hz), 6 (4–8 Hz), 12 (9–15 Hz), and 18 Hz(16–20 Hz) using a Butterworth band-pass filter. On the filtered seis-mograms, RMS amplitudes of coda waves in a window length of 256samples and lapse time of 30, 40 and 50 s have been used to estimateQc. The frequency dependent average Qc values of the region at differentlapse times is given in Table 3 and Q0 (quality factor at 1 Hz) alongwithn, the degree of frequency dependence are given in Table 4. We notefrom Table 3 that Qc values increase with increase in frequency andfor all the three lengths of lapse time window considered here. The av-erage values of Qc for the lapse time windows of 30, 40 and 50 s withstandard error varies, respectively, from 133±66, 173±88 and175±60 at 1.5 Hz to 1633±386, 1634±448 and 1686±265 at 18 Hz(Table 3). This shows the frequency dependent nature of Q estimates.

Table 4Q0 (quality factor at 1 Hz) and n values for all the stations and their averages.

Lapsetimes (s)

Q0 n Q0 n Q0 n

UKE SIP KEV

30 70±6 1.06±0.04 109±20 0.94±0.08 89±6 1.02±0.0340 104±21 0.97±0.09 122±32 0.85±0.11 108±14 0.92±0.0650 134±37 0.88±0.11 90±16 1.00±0.08 108±16 0.95±0.07

KAD VAD AVG

30 67±8 1.10±0.05 101±27 0.97±0.11 87±13 1.01±0.0640 66±11 1.11±0.08 160±20 0.85±0.06 112±20 0.94±0.0850 90±4 1.03±0.02 178±39 0.74±0.10 120±22 0.76±0.07

Fig. 3 shows the fitting of the power law Qc=Q0fn for each stationand gives the average frequency dependent relationships as: Qc=(87±13)f(1.01±0.06) (lapse time: 30 s), Qc=(112±20)f(0.94±0.08)

(lapse time: 40 s) and Qc=(120±22)f(0.76±0.07) (lapse time: 50 s)forMainlandGujarat. It is clear from Fig. 3 and Table 4 that SIP site locat-ed in granitic basement shows Q0 decreasingwith increasing lapse timeas compared to other sites and average Q values. This seems to be basi-cally due to the relatively large standard error in Q estimation.We triedto compare the results of Q0 estimation in Mainland Gujarat with otherregions of the World (Akinci et al., 1994; Ambeh and Fairhead, 1989;Havskov et al., 1989; Hellweg et al., 1995; Ibanez et al., 1990;Kvamme and Havskov, 1989; Pujades et al., 1991; Pulli, 1984; Rhea,1984; Rodriguiez et al., 1983; Roecker et al., 1982; Rovelli, 1982;Rovelli, 1984; Sherbaum and Kisslinger, 1985; Van Eck, 1988). A plotwas made to compare the results with some of the other systems ofthe world (Fig. 4). We note that rate of decay of attenuation (Q−1)with frequency for the relations obtained in the present study are com-parable with those of other regions of the world. It has been observedthat the average Q0 variation ofMainland Gujarat is very close to the ac-tive region of Dead Sea (Table 5) which is a part of Jordan rift structure.This may be due to similarity of geological and tectonic setup ofMainlandGujarat andDead Sea regions. Cambay rift is themain tectonicstructure in the center of Mainland Gujaratwhich is largely occupied bya flat alluvial plain and comprises Precambrian crystallines, sedimenta-ry rocks of Cretaceous, Tertiary and Quaternary periods and the Deccanbasalt (Merh, 1995). Dead Sea region is characterized by a large fill ofsediments up to 6 to 8 km on top of the more consolidated Cretaceoussediments of 2 km and its subsequent crystalline Precambrian base-ment rock and evaporates including diapirs (Van Eck, 1988). Thevariation in Qc values at different sites may be attributed to the

Parkfield 79 0.74 Hellweg et al. (1995)Friuli, Italy 80 1.1 Rovelli (1982)South Iberia 100 0.7 Pujades et al. (1991)NW Himalayas 158 1.05 Naresh et al.(2005)Garhwal, Himalayas 126 0.9 Gupta et al. (1995)South Spain 155 0.89 Ibanez et al. (1990)Koyna, India 169 0.77 Mandal and Rastogi (1998)West Anatolia, Turkey 183 0.76 Akinci et al. (1994)Aleutian 200 1.05 Sherbaum and Kisslinger (1985)

Stable regionsNorway 120 1.09 Kvamme and Havskov (1989)South Carolina 190 0.94 Rhea (1984)South India 460 0.83 Mandal and Rastogi (1998)New England 460 0.4 Pulli (1984)North Iberia 600 0.45 Pujades et al. (1991)Mainland Gujarat 87 1.01 Present study

Table 6Maximum depth of the ellipsoidal volume.

Stations Average distance Δð Þ Average depth havð Þ Average lapse time (t) a1=ct/2 c=3.5 km/s a2 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia12−Δ2

pDepth (km) h= havð Þ+a2

SIP 100.8 20.9 67.4 118.0 61.2 82.1KAD 95.3 15.6 78.8 137.9 99.6 115.2VAD 123.5 9.5 95.0 166.3 111.4 120.9KEV 86.7 18.7 54.4 95.2 39.3 58.0UKE 130.9 17.6 79.1 138.5 45.4 63.0

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heterogeneities present in the regions and/or difference in the distancesof the events from the recording stations.

It has been observed from Table 4 that Q0 values increase with theincrease in lapse-time along with n for all the stations and their aver-ages. The degree of frequency dependence, n, has been found to behigh for tectonically active region as compared to that of tectonicallystable regions (Table 5). The value of n varies from 0.70 to 1.10 for theactive regions (Gupta et al., 1995; Hellweg et al., 1995; Rovelli, 1982).The high values of n estimated here indicate that Mainland Gujarat is

frequency(Hz.)

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1500

2000

2500

30sec. c=(109±20)f(0.94±0.08)

40Sec. c=(122±32)f(0.85±0.11)

50Sec. c=(90±16)f(1.00±0.08)

30sec. c=(101±27)f(0.97±0.11)

40Sec. c=(160±20)f(0.85±0.06)

50Sec. c=(178±39)f(0.74±0.10)

30sec. c=(70±06)f(1.06±0.04)

40Sec. c=(104±21)f(0.97±0.09)

50Sec. c=(134±37)f(0.88±0.11)

0

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2000

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1000

1500

2000

2500

0 4 8 12 16 20

frequency(Hz.)0 4 8 12 16 20

frequency(Hz.)0 4 8 12 16 20

SIPU

DAV

UKE

a

c

e

Fig. 3. Plots of quality factors and central frequencies for all the five stations (a) to (e) and avlapse times of 30, 40 and 50 s.

seismotectonically active. No significant variation in n with lapse timewindow lengths has been found for smaller lapse timewindow lengths(e.g. Akinci et al., 1994; Ibanez et al., 1990). The value of n obtained herefor different lapse timewindow lengths can be considered as stationaryas it has not changed much for different lapse times. The increase in Qc

values with lapse time found in this study show the depth dependenceof Qc as larger area will be sampled with longer lapse time windows.The increase of Qc with lapse time has been observed by other re-searchers for other regions (e.g. Akinci et al., 1994; Gupta et al., 1996;

30sec. c=(87±13)f(1.01±0.06)

40Sec. c=(112±20)f(0.94±0.08)

50Sec. c=(120±22)f(0.76±0.07)

30sec. c=(67±08)f(1.10±0.05)

40Sec. c=(66±11)f(1.11±0.08)

50Sec. c=(90±04)f(1.03±0.02)

30sec. c=(89±6)f(1.02±0.03)

40Sec. c=(108±14)f(0.92±0.06)

50Sec. c=(90±04)f(1.03±0.02)

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

frequency(Hz.)0 4 8 12 16 20

frequency(Hz.)0 4 8 12 16 20

frequency(Hz.)0 4 8 12 16 20

KAD

VEK

AVG

b

d

f

erage with linear regression frequency dependent relationship (f), Qc=Q0fn at different

Fig. 4. Comparison of Qc values for Mainland Gujarat, India with the existing Q studiesworldwide.

270 A.K. Gupta et al. / Tectonophysics 530–531 (2012) 264–271

Havskov et al., 1989; Roecker et al., 1982; Sharma et al., 2011). Theestimated maximum depth of ellipsoidal volume varying from 58.1 to120.9 km (Table 6) indicates that the region is seismically active andthe upper lithosphere is quite heterogeneous (Naresh et al., 2005).

The increase in Qc with lapse time can also, as pointed out byWoodgold (1994), be attributed to other factors like consideration ofnon-zero source receiver distance with anisotropic scattering andassumption of single scattering model where multiple scattering is im-portant. The coda start timehas been taken as twice of the S-wave traveltime for all the three lapse times considered here and therefore onlyback scattered waves arrive at this time (Aki and Chouet, 1975). Gao

Fig. 5. Comparison of Qc values for Mainland Gujarat, India with the existing Q studiesin India.

et al. (1983) has reported that the effects of multiple scattering arenot important for local events with lapse time less than 100 s. Thelapse time window lengths of local events analyzed here are less than100 s. In view of this, the lapse time dependence of coda-Q in the stud-ied region can be attributed to the variation of attenuation with depth.

The coda-Q estimates of nearby Kachchh region are available (Guptaet al., 2006; Mandal et al., 2004; Sharma et al., 2008). Sharma et al.(2011) have studied the Q estimates for Saurashtra and Chopra et al.(2010) have studied Q for P and S waves for three distinct zones(Kachchh, Saurashtra and Mainland Gujarat) of Gujarat region. Chopraet al. (2010) have reported Q of S-wave, Qs=118f0.65 for Kevadia(KEV) station ofMainlandGujaratwhich is comparable to the estimatedQc=(89±6)f(1.02±0.03) (lapse time: 30 s), Qc=(108±14)f(0.92±0.06)

(lapse time: 40 s) and Qc=(108±16)f(0.95±0.07) (lapse time: 50 s) inthe present study for the same station. The estimated averageQc=(87±13)f(1.01±0.06) at 30 s lapse time is low as compared to thatof Saurashtra region (Qc=170f0.97 for Junagarh and Qc=224f0.98 forJamnagar areas at a lapse time of 30 s by Sharma et al., 2011) and com-parable to the Kachchh region (Qc=102f0.98 by Mandal et al., 2004;Qc=106f1.11 by Gupta et al., 2006 and Qc=148f1.01 by Sharma et al.,2008) (Fig. 5). This shows that the region is more heterogeneous ascompared to that of adjacent Saurashtra and Kachchh regions. The re-gion is infested with many of criss-crossed fracture and dykes, whichmay be the reason of getting low coda Q values.

The frequency dependent relations developed here are useful forthe estimation of source parameters of the earthquakes in the Main-land Gujarat region where no such relations were available earlier.These relations can also be used for the simulation of earthquakestrong ground motions in the region.

6. Conclusions

This study reports the attenuation characteristics of MainlandGujarat (India) region. The frequency dependent relationships forcoda-Q have been estimated using three lapse times 30 s, 40 s and50 s with fixed 20 s coda window length. The coda-Q estimate increasewith increase in lapse time window indicates the depth dependence ofattenuation. The rate of decay of attenuation is found to be comparablewith those of otherworldwide results. The variation of Qcwith frequen-cy and lapse time shows that the upper crustal layers are seismicallymore active compared to the lower lithosphere. The decreasing valueof the frequency parameter with increasing lapse time shows that thelithosphere acquires homogeneity with depth. Based on Q relations,the Mainland region is found to be more heterogeneous as comparedto the nearby Kachchh and Saurashtra regions. The frequency depen-dent relations estimated here are very useful for themodeling of earth-quake strong ground motions as well as estimation of earthquakesource parameters in the Mainland Gujarat region.

Acknowledgments

The authors are grateful to Gujarat State Disaster ManagementAuthority and Department of Science and Technology, Government ofGujarat for financial support in establishment of seismological network.The authors are very thankful to Dr. Anna Dobrynina for her critical re-view and useful comments for enhancing the quality of the paper.

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