Estimation of Coda-Q for Mainland Gujarat region of

Estimation of Coda-Q for Mainland Gujarat regionof Western Deccan Volcanic Province, India

ARPAN SHASTRI1,2,* and SANTOSH KUMAR1

1Institute of Seismological Research (ISR), Raisan, Gandhinagar, Gujarat 382 009, India.

2Space Applications Centre, ISRO, Ahmedabad, Gujarat 380 015, India.*Corresponding author. e-mail: [email protected]

MS received 17 January 2020; revised 7 April 2021; accepted 2 August 2021

In the present study, we have estimated the quality factor Coda-Q (Qc) using the single backscatteringmodel for Mainland Gujarat region of Western Deccan Volcanic Province (DVP) India. The said regioncomes under seismic zone III as per seismic zonation map of India and is vulnerable for earthquakes ofmagnitude up to 6.0. Mainland Gujarat comprises of the eastern rocky highlands and western alluvialplains. The broadband waveforms of 80 local earthquakes (Mw 2.5–4.3) having depths in the range(2.0–34.0 km) recorded at eight stations of Mainland Gujarat have been used for the analysis. The averagevalues of Qc for the lapse time windows of 20–90 s with standard error varies respectively from 113 ± 12 to411 ± 37 at 2 Hz and 1008 ± 150 to 3600 ± 400 at 16 Hz, respectively. This suggests that the region ismore attenuative and heterogeneous than the Kachchh and Saurashtra of DVP. The increase in ‘Qc’values with lapse time displays the depth dependence of ‘Qc’ because of the fact that longer lapse timewindows will sample larger area. We have compared the frequency-dependent relations for ‘Qc’ derivedhere with those of other parts of India and the World. The study is inevitable for the estimation of sourceparameters, thereby, evaluation of seismic hazard of the region.

Keywords. Coda wave; attenuation; lapse time; Mainland Gujarat.

1. Introduction

Attenuation of seismic waves is a frequent domin-ion of the Earth, whose alteration is governed bythe nature of the propagation of medium. Thefeatures supplying to the total attenuation consistsof geometrical spreading, scattering due to inho-mogeneity and inelasticity. Study of attenuation ofseismic waves is very important for the betterassessment of seismic hazard by scrutinizing theground-motion attenuation (Anderson et al. 1996).The large ‘Q’ values represent small attenuationand vice versa (Rautian and Khalturin 1978).Tectonically active regions generally have a high

heat Cow and are more attenuating than colderregions that are tectonically less active or inactive(KnopoA 1964). In addition, we have observed thatvariations in ‘Q’ values correlate with travel timevariations. We have probed the attenuation char-acteristics based on coda waves utilizing the singlebackscattering model of Aki and Chouet (1975).Numerous studies have been done worldwide aswell as in Gujarat state to understand the physicsof attenuation of seismic waves using coda wave(e.g., Pulli 1984; Van Eck 1988; Ambeh and Fair-head 1989; Gupta et al. 1996; Kumar et al. 1997;Mandal and Rastogi 1998; Gupta and Ashwani2002; Paul et al. 2003; Sharma et al. 2008, 2011).

J. Earth Syst. Sci. (2021) 130:238 � Indian Academy of Scienceshttps://doi.org/10.1007/s12040-021-01731-x (0123456789().,-volV)(0123456789().,-volV)

Several researchers (e.g., Frankel et al. 1990;Mitchell 1995; Aleqabi and Wysession 2006) havealso estimated the quality factor using coda waves.The 426 velocity time histories of 80 events

recorded at four to eight seismic stations have beenused to estimate the Coda-Q (Qc) for the MainlandGujarat region of Deccan Volcanic Province,Western India in the present analysis. The region isvulnerable for earthquake of magnitude up to 6.0.We have also analyzed the dependency of Coda-Q(Qc) on lapse time windows.Gupta et al. (2012) at Bve sites with different

datasets have acquired the attenuation diagnosticbased on coda waves previously for the MainlandGujarat region of western India. Chopra et al.(2011) reported ‘Q’ for single station of the Main-land Gujarat. The frequency-dependent ‘Q’ rela-tions for the nearby Kachchh and Saurashtraregions have been obtained previously by manyinvestigators such as Mandal et al. (2004), Guptaet al. (2006), Sharma et al. (2011) and Chopra et al.(2011).

2. Geology and tectonic setup

The geology of Gujarat is unique in its diversity.The Kachchh, Saurashtra and Mainland Gujaratare three distinct zones of Gujarat. There are threemajor marginal rift basins namely Kachchh,Cambay and Narmada basins in the western mar-gin of the Indian craton. These basins were formedat different times during the Mesozoic and are thusconsidered as important Mesozoic marginal marinebasins (Biswas 1982, 1987). Biswas (1982) hasexplained the evolution of the three basins duringdifferent stages of India’s northward drift afterbreak up from Gondwanaland in the late Trias-sic–early Jurassic. The Kachchh rifting occurred inthe late Triassic–early Jurassic, Cambay rifting inthe early cretaceous and Narmada rifting in thelate cretaceous time. Mainland Gujarat is desig-nated into western Deccan volcanic province(DVP). Deccan volcanic province (DVP) is one ofthe remarkable geo-events in the geologic history ofthe Indian plate that holds a prominent position inglobal tectonic models. The Deccan volcanic pro-vince (DVP) was formed during India’s northwardmigration as it passed over the reunion hotspot(which is today the Reunion Island). DVP coversan area of 500,000 km2. Deccan volcanism pro-duced the longest lava mega-Cow on Earth span-ning over 1500 km from the main Deccan province

across India to Rajahmundry and out into Gulf ofBengal (Gerta Keller et al. 2014). StratigraphicallyMainland Gujarat exhibits presence of Precam-brian crystalline, sedimentary rocks of Cretaceous,Tertiary and Quaternary periods and the Deccanbasalt (Merh 1995). Gujarat extends fromUmbergaon (Maharashtra border) in the South toMt. Abu (Rajasthan) in the North and from hillranges with forests in the east to the Arabian Sea,Gulf of Cambay, Saurashtra and Rann in the West(Kulkarni 1985). The Cambay basin is the majortectonic feature in the central portion of MainlandGujarat (Bgure 1). The Cambay basin is a Grabenbetween the Kathiawar (Saurashtra) uplift and theAravalli ranges and is extending along the westcoast through the Gulf of Cambay in a roughlyNNW–SSE alignment parallel to the Dharwartrend (Biswas 1987). Raju (1968) has explained thetectonic framework and history of the Cambaybasin. Near the mouth of Gulf of Cambay, Nar-mada Graben (Biswas 1987) crosses the NarmadaBasin. Aravalli, Vindhyan, Satpura and Sahyadrihill ranges bound the Eastern border of the basin.

Figure 1. Stars show epicentral locations of earthquakes usedin this study and stations used in this study have been shownby triangles. The Cambay rift is a noteworthy tectonic featurein this area other major tectonic feature is Narmada rift.

238 Page 2 of 13 J. Earth Syst. Sci. (2021) 130:238

Mainland Gujarat falls under zone III according tothe seismic zonation map of India, which desig-nates moderate damage risk zone. This zone mayproduce an earthquake of intensity VII on the MSKscale. The Cambay fault of Mainland Gujarat hasproduced numerous moderate size earthquakes.

The largest earthquake that occurred in this zone isthe 1919 Bhavnagar earthquake with a magnitudeof six. Rao et al. (1991) have reported the swarmtype of seismic activity in the proximity of Valsad,South Gujarat in 1986. The two earthquakes ofmagnitude 3.2 and 4.3 have occurred near the

Figure 2. Plot of event recorded at SIP station on 12/12/2013 from 96 km epicentral distance. (a) UnBltered data-trace withcoda window, (b–f) bandpass Bltered displacement amplitudes of coda window at 1–3, 2–6, 4–12, 6–18 and 8–24 Hz, respectivelyand the RMS amplitude values multiplied with lapse time along with best square Bts of selected coda window at centralfrequencies of 2.0, 4.0, 8.0, 12.0 and 16.0 Hz, respectively. The Qc is determined from the slope of best square line. Abbrevationsare P: P-wave arrival time; S: S-wave arrival time.

J. Earth Syst. Sci. (2021) 130:238 Page 3 of 13 238

Table 1. List of the epicentral parameters used in the present study.

Year MN DD HR MIN Sec Latitude Longitude Depth Mag

2007 2 14 11 45 10.2 21.666 72.423 15 2.9

2007 2 11 13 11 45.9 20.773 73.267 15 2.5

2007 3 10 23 28 53.9 20.554 73.557 6.2 2.8

2007 3 25 21 37 30.1 23.63 72.511 15 2.8

2007 4 9 3 22 47.5 21.625 73.608 33.1 2.5

2007 5 20 15 54 49 22.537 73.261 23.2 2.6

2007 8 23 8 54 13.2 22.031 72.798 29.6 2.7

2007 10 5 12 4 3.6 21.247 73.486 15 2.6

2007 11 25 13 13 5.8 24.238 72.01 6.1 2.7

2007 12 15 9 48 50.9 24.352 71.894 3.1 3.1

2008 1 25 23 36 56.4 21.8 71.742 33.7 2.8

2008 1 22 16 55 33.8 21.505 72.155 17 2.6

2008 2 21 6 24 59.4 21.374 72.604 30 2.8

2008 2 29 22 18 9.1 21.582 73.522 12.2 2.6

2008 2 4 11 23 31.9 21.583 72.151 23.7 2.5

2008 3 25 2 26 10.9 21.505 73.03 10.4 2.7

2008 3 29 9 25 5.7 21.717 71.99 8 2.5

2008 5 2 21 53 51.7 21.11 72.491 25.1 3.3

2008 5 2 22 31 34.1 21.124 72.461 13.8 3.2

2008 5 20 8 57 27.2 21.171 73.043 6.1 3

2008 5 11 0 42 12.7 21.493 72.598 6.1 2.9

2008 5 2 22 39 54.8 21.127 72.488 10.7 2.7

2008 11 27 9 25 41.1 22.096 73.552 2.1 2.8

2009 6 29 9 4 31.9 24.229 72.009 7.1 2.8

2009 10 10 6 57 10.2 22.797 72.041 12.4 3.2

2010 2 5 8 6 16.5 23.754 72.646 18.3 2.9

2010 3 30 14 27 53.7 23.6 72.577 10.4 3.2

2010 5 24 8 53 17.6 21.307 71.928 19.3 2.6

2010 6 2 11 52 0.8 21.73 72.401 24 2.5

2010 9 2 3 9 6.4 23.838 71.874 6.1 4.3

2010 10 22 14 50 45 24.024 72.122 7.7 2.5

2010 11 18 14 28 42.9 23.324 72.842 22.9 2.5

2010 12 12 12 45 17 21.513 73.144 20.6 2.9

2011 2 10 3 38 43.2 22.093 72.923 22.9 2.6

2011 3 2 18 45 13.4 24.236 72.505 4 2.6

2011 7 3 0 26 28.3 21.143 73.159 26 3.2

2011 9 21 20 23 55.3 24.224 71.714 2.4 2.9

2011 9 28 12 48 3.4 21.459 73.1 22 2.7

2011 9 1 19 35 7 21.556 72.916 6.4 2.6

2011 11 7 3 5 49.6 24.378 72.658 13.7 2.9

2012 2 19 11 13 1.1 21.118 72.29 22.1 3.2

2012 2 8 10 51 23 21.221 72.283 11.8 2.7

2012 3 21 14 50 29.1 21.716 72.405 15 3

2012 3 16 5 37 0.3 21.605 72.074 9.9 2.8

2012 4 23 3 6 45.3 23.79 72.463 15 3

2012 4 11 13 23 36.8 21.684 72.05 7 2.6

2012 4 23 6 37 26.5 23.782 72.428 6.7 2.5

2012 5 23 13 51 45.1 22.827 73.036 23.3 2.9

2012 7 30 8 3 49.1 21.213 72.826 9.8 3.6

2012 9 12 17 36 50.6 24.32 71.708 6 3.1

2012 9 25 13 51 42.4 21.682 71.987 6.1 2.5


Surat (ISR annual report 2008, 2016) on May 20,2008 and July 17, 2016, respectively.

3. Methodology

Aki and Chouet (1975) model of single backscat-tering model has been used for estimating the coda

‘Qc’. In accordance with this model, coda waves areelucidated as backscattered body waves producedfrom numbers of heterogeneities in the Earth’scrust and upper mantle. This indicates that scat-tering is not a strong process and each wavelet isscattered only once before reaching the receiver.Under this assumption, we express the codaamplitudes Ac(f, t) in a seismogram as a function of

Table 1. (Continued.)

Year MN DD HR MIN Sec Latitude Longitude Depth Mag

2013 2 15 10 23 55.8 24.296 71.696 10.4 3.2

2013 3 1 11 46 25.1 22.457 71.628 3.1 2.5

2013 4 26 14 16 12.3 23.641 71.635 13.8 2.7

2013 5 1 12 29 54 22.487 71.645 16.3 2.7

2014 1 10 12 24 49.8 23.244 72.971 15 2.5

2014 2 9 19 4 35.9 21.434 71.726 10.9 2.9

2014 2 4 8 56 21.9 23.234 72.014 27.6 2.6

2014 3 12 7 58 47 23.006 73.389 17.1 2.5

2014 3 14 13 22 26.1 22.522 71.645 17.7 2.5

2014 4 22 11 23 48.4 22.043 72.439 8 2.8

2014 6 21 15 59 35.4 21.55 73.298 15 3.5

2014 7 26 2 1 37.4 23.078 71.979 6.4 3.7

2014 8 5 4 13 48.4 22.49 71.759 33.8 2.5

2015 2 27 2 35 28.7 21.874 73.701 10.5 2.9

2015 3 19 9 41 53.7 24.095 72.707 5 3.9

2015 4 20 16 24 30.2 21.35 72.18 11.5 3.1

2015 6 28 19 26 41 24.376 71.817 9.8 3.7

2015 6 30 2 19 10.4 24.36 71.777 10 2.9

2015 8 31 20 38 28.9 24.243 72.675 8.3 3.5

2015 11 19 15 55 1.9 21.594 72.328 8.6 3.5

2016 1 11 6 42 6.1 24.324 71.89 4.3 2.8

2016 4 10 9 34 13.1 21.203 73.208 2.9 3.3

2016 5 12 16 59 48 24.29 72.68 25.1 3.4

2016 5 25 20 1 51.7 24.296 72.482 9.8 3

2016 5 11 11 19 38.5 24.265 71.767 4.3 2.8

2016 7 17 3 55 3.4 21.601 72.519 6.2 4.2

2016 7 17 5 53 47.3 21.629 72.495 6.3 2.9

2016 10 21 19 6 50.5 20.598 73.439 5 2.5

2016 12 5 14 9 20.5 20.483 73.368 4.2 3

Table 2. Site characteristics and epicentral locations of the recording stations of the MainlandGujarat region.

Station (code) Lat. (deg. N) Lon. (deg. E) Lithographic foundation

Radhanpur (RAD) 23.819 71.617 Basalt

Sipu (SIP) 24.386 72.294 Granite

Vadodara (VAD) 22.304 73.134 Hard soil

Ukai (UKI) 21.220 73.584 Basalt

Valsad (VAL) 20.130 73.027 Basalt

Kadana (KAD) 23.287 73.853 Basalt

Dharoi (DHR) 24.007 72.847 Granite

Kavdej (KAV) 20.703 73.308 Basalt


the lapse time ‘t’ considered from the origin time ofthe seismic event as Aki (1980)

Ac f ; tð Þ ¼ S fð Þt�a expð�pft=QcÞ; ð1Þ

where S(f ) is the source function at frequency ‘f’.We considered this function as constant, since itdoes not depend on time and radiation pattern andhence remains unaffected by factors inCuencingenergy loss in the medium. The term ‘a’ denotesgeometrical spreading factor and is chosen as onefor body waves and ‘Qc’ is the apparent qualityfactor of coda waves representing the attenuationin a medium. Rautian and Khalturin (1978)proposed that the coda parameters S(f) and Qc

do not depend on source–site distance if we takecoda start-time as twice the travel time of S-waves.We can rewrite equation (1) as:

lnðAc f ; tð ÞtÞ ¼ lnS fð Þ� ðpf =QcÞt: ð2Þ

This being a linear equation with slope –pf =Qc

can be utilized for estimating Qc (Bgure 2).

4. Data used

The Institute of Seismological Research (ISR) isrunning the Gujarat State Seismic Network since2006 (Chopra et al. 2008). In the present study, wehave analyzed the data of eight BBS stations run-ning in the Mainland Gujarat region. All the BBSconsists of 120s broadband sensors (Nanometrics &Guralp make) and 24-bit digitizers. The BBS arerunning on continuous mode and are recording thecontinuous data at 50 samples/s and with GPStime synchronization. We have used the digitaldata that occurred during 2007–2016. We haveused nearly 426-velocity time histories of 80earthquakes of magnitude ranging from 2.5 to 4.3.These earthquakes have been shown by star

symbol in Bgure 1. We have used waveforms ofevents recorded at four or more stations to ensurelocation accuracies. We have located these eventsusing SEISAN program (Havskov and Ottemoller2000). We have used vertical components of all theevents to calculate Coda-Q (Qc). Events are con-sidered after detrending the seismograms and Bl-tering them using Bve different central frequenciesof 2 (1–3 Hz), 4 (2–6 Hz), 8 (4–12 Hz), 12 (6–18 Hz)and 16 (8–24 Hz) utilizing a Butterworth bandpassBlter. We have used only those waveforms whichare having signal-to-noise ratio C3. In a similarway, the pattern of correlation coefBcient C0.5 isimplemented to acquire better estimates of ‘Qc’.During the calculation of value of ‘Qc’, we mustneglect the contamination produced by directS-phases (Rautian and Khalturin 1978; Herraizand Espinosa 1987). Therefore, Rautian andKhalturin (1978) proposed that the origin of thecoda wave must be considered from the time of an‘earthquake’, while lapse time is deBned as 2ts,where ts is the travel time of S-waves from theorigin time. For acquiring reliable results, theperiod of coda window should be sufBciently large.Havskov and Ottemoller (2005) proposed a mini-mum value of 20 s. There is no obstruction on themaximum lapse time. In the present study, we haveused minimum lapse time as 20 s. However, SNR C

3 was obtained for very few records above 90 s;hence, 90 s was set as the upper limit. Eight lapsetime window lengths of duration 20–90 s have beenused in the present analysis. We Bx the windowlength at 20 s. Figure 2(a) shows an example ofcoda portion used for analysis (the boxed portion),when window length is 20 s and tstart = 2ts. Wehave calculated the value of ‘Qc’ through‘CODAQ’ subroutine of SEISAN (Havskov andOttemoller 2003). The top panels in Bgure 2(a)show the 20 s window length of coda waves

Table 3. Average quality factor at different frequencies and lapse times ±r indicates the standard error and intervals show thefrequency band.

Lapse

time (s)

2.0 Hz (1–3)

Qc ± r N

4.0 Hz (2–6)

Qc ± r N

8.0 Hz (4–12)

Qc ± r N

12.0 Hz (6–18)

Qc ± r N

16.0 Hz (8–24)

Qc ± r N

20 113 ± 12 28 238 ± 23 46 506 ± 60 76 660 ± 97 75 1008 ± 150 75

30 160 ± 15 30 334 ± 34 57 716 ± 75 60 1016 ± 131 77 1359 ± 178 64

40 187 ± 19 27 417 ± 41 36 1018 ± 98 67 1238 ± 192 65 1630 ± 235 52

50 243 ± 22 35 538 ± 53 40 1014 ± 136 66 1409 ± 198 52 1868 ± 242 50

60 271 ± 26 39 564 ± 50 41 1094 ± 114 64 1605 ± 200 53 2354 ± 264 54

70 302 ± 32 31 605 ± 59 42 1157 ± 110 71 1903 ± 270 57 2719 ± 220 59

80 354 ± 40 38 674 ± 67 45 1208 ± 124 65 2210 ± 230 56 3317 ± 350 58

90 411 ± 37 39 705 ± 70 47 1304 ± 130 67 2103 ± 210 60 3600 ± 400 57


Table

4.Q

0(qualityfactor

at1Hz)

andnvalues

forallthestationsan

dtheiraverages.

Lapse

time(s)

Sipu(SIP

)No.of

events

Radhanpur(R

AD)

No.of

events

Vadodara

(VAD)

No.of

events

Ukai(U

KI)

No.of

events

Q0

gQ

0g

Q0

gQ

0g

20

53±

40.99±

0.04

65

74±

80.96±

0.05

54

121±

28

0.80±

0.04

58

112±

16

0.74±

0.04

49

30

58±

61.08±

0.06

67

82±

11

1.00±

0.08

61

127±

30

0.85±

0.05

54

122±

22

0.98±

0.01

55

40

69±

81.14±

0.08

58

95±

18

0.92±

0.01

47

136±

34

0.83±

0.09

48

132±

30

0.96±

0.08

41

50

65±

71.14±

0.07

61

102±

25

1.04±

0.09

56

140±

36

0.81±

0.08

51

138±

36

0.85±

0.04

57

60

67±

60.97±

0.03

69

109±

10

0.91±

0.03

49

134±

17

0.87±

0.04

53

134±

11

0.84±

0.03

62

70

74±

71.04±

0.02

57

116±

12

0.92±

0.04

47

154±

15

0.94±

0.07

57

144±

10

0.91±

0.06

53

80

78±

71.05±

0.06

60

98±

10

0.94±

0.05

53

164±

15

0.97±

0.09

41

152±

12

1.11±

0.07

52

90

81±

70.94±

0.01

56

126±

12

0.96±

0.06

50

182±

18

0.92±

0.08

44

170±

14

1.04±

0.02

46

Avg.value

68±

61.04±

0.04

100±

13

0.95±

0.05

144±

24

0.87±

0.06

138±

18

0.92±

0.04

Lapse

time(s)

Valsad(V

AL)

No.of

events

Kadana(K

AD)

No.of

events

Dharoi(D

HR)

No.of

events

Kavdej

(KAV)

No.of

events

Q0

gQ

0g

Q0

gQ

0g

20

98±

60.98±

0.02

51

100±

10

0.97±

0.03

62

92±

08

0.97±

0.08

44

66±

05

1.03±

0.06

41

30

104±

15

0.99±

0.09

50

102±

15

0.85±

0.01

54

98±

06

1.03±

0.02

54

72±

07

0.97±

0.04

46

40

110±

18

0.96±

0.01

52

108±

19

1.04±

0.06

49

107±

12

0.99±

0.06

57

92±

11

0.99±

0.01

51

50

113±

22

0.96±

0.04

48

114±

21

0.99±

0.05

47

111±

20

0.97±

0.04

64

98±

10

0.97±

0.07

39

60

107±

15

0.94±

0.03

42

105±

11

0.96±

0.03

56

112±

14

0.86±

0.04

62

96±

20

0.87±

0.02

48

70

111±

34

0.95±

0.05

47

111±

10

0.94±

0.05

48

116±

20

0.89±

0.05

49

102±

10

0.83±

0.06

44

80

122±

39

0.97±

0.07

43

120±

21

0.97±

0.06

45

121±

23

0.94±

0.06

52

106±

10

1.02±

0.07

50

90

130±

19

0.98±

0.09

54

109±

16

0.98±

0.07

60

127±

24

1.05±

0.10

56

110±

10

1.01±

0.03

43

Avg.value

111±

21

0.96±

0.05

108±

15

0.96±

0.04

110±

15

0.96±

0.05

92±

10

0.96±

0.04


considered for the estimation of ‘Qc’ for tstart equalto 2ts. The origin time, P-wave and S-wave arrivaltime of the earthquake are shown in the seismo-gram. We use the Butterworth bandpass Blter(eight poles) at central frequencies of 2.0, 4.0, 8.0,12.0 and 16.0 Hz for Bltering the CODA of all theseismograms. The root mean square (RMS)amplitudes of Bltered seismograms are estimatedusing a moving time window of 2.56 sec width with1.28 sec interval. Figure 2(b–f) exhibits the Blteredseismograms and plots of ln[A(f, t)�t] vs. t for anevent recorded at seismic station SIPU (SIP) fordifferent central frequencies along with the leastsquare Btted lines. The slopes (m) of these lines areused to estimate Qc (= –pf/m) (table 3).

5. Results and discussion

We have Bltered the seismograms at Bve centralfrequencies, i.e., 2 (1–3 Hz), 4 (2–6 Hz), 8 (4–12Hz), 12 (6–18 Hz) and 16 (8–24 Hz) utilizing aButterworth bandpass Blter. We have found outthe RMS amplitude of Coda waves on the Blteredseismograms. We have used lapse time of 20–90 sfor the estimation of Qc. Table 1 demonstrates thelist of the epicentral parameters used in the presentstudy. Site characteristics and epicentral locationsof the recording stations used in the present studyhave been shown in table 2. Table 3 shows theaverage quality factor of the region at different

frequencies and lapse times. The standard error isdenoted by r and N shows the number of seismo-grams used for different central frequencies andlapse time. The number of earthquakes used foranalysis may be different for different frequencyranges for the same coda window depending uponthe selection criterion like spreading parameter,signal-to-noise ratio, minimum correlation coefB-cient, maximum counts and are deBned w.r.t. fre-quency range. In all the methods which are used tocalculate the quality factor, the amplitude mea-sured at a given station must be corrected for thegeometrical spreading parameter. This parametertakes into account the amplitude decay caused bythe spreading of the propagating wavefront. If it isassumed that waves propagate in uniform media,then the geometrical spreading parameter for bodywaves is given as R�1, where R is the hypocentraldistance, for distances \100 km (e.g., Aki 1980;Ib�anez et al. 1990; Canas et al. 1991). For distancesgreater than 200 km, this parameter is assumed tobe equal to R�0.5, the theoretical value for surfacewaves in a half-space medium (e.g., Haswgawa1985; Shin and Herrmann 1987). However, aspropagation media are far from being uniform,especially in the short-distance range (local earth-quakes), a rough approximation is to take a valueof R�1 for this parameter. The coda waves arebackscattered body waves, therefore, geometricalspreading =1 is taken (Khan et al. 2016). Table 3demonstrates that the corresponding Qc values are

Table 5. Power laws (Qc = Q0 fn) obtained at all the lapse time windows (20–90 s) for all the stations.

Lapse time (s) Sipu (SIP) Radhanpur (RAD) Vadodara (VAD) Ukai (UKI)

20 Qc = (53±4)f(0.99±0.04) Qc = (74±8)f(0.96±0.05) Qc = (112±16)f(0.74±0.04) Qc = (121±28)f(0.80±0.04)

30 Qc = (58±6)f(1.08±0.06) Qc = (82±11)f(1.00±0.08) Qc = (122±22)f(0.98±0.01) Qc = (127±30)f(0.85±0.05)

40 Qc = (69±8)f(1.14±0.08) Qc = (95±18)f(0.92±0.01) Qc = (132±30)f(0.96±0.08) Qc = (136±34)f(0.83±0.09)

50 Qc = (65±4)f(1.14±0.07) Qc = (102±25)f(1.04±0.09) Qc = (138±36)f(0.85±0.04) Qc = (140±36)f(0.81±0.08)

60 Qc = (67±6)f(0.97±0.03) Qc = (109±10)f(0.91±0.03) Qc = (134±11)f(0.84±0.03) Qc = (134±17)f(0.87±0.04)

70 Qc = (74±7)f(1.04±0.02) Qc = (116±12)f(0.92±0.04) Qc = (144±10)f(0.91±0.06) Qc = (154±15)f(0.94±0.07)

80 Qc = (78±7)f(1.05±0.06) Qc = (98±10)f(0.94±0.05) Qc = (152±12)f(1.11±0.07) Qc = (164±15)f(0.97±0.09)

90 Qc = (81±7)f(0.94±0.01) Qc = (126±12)f(0.96±0.06) Qc = (170±14)f(1.04±0.02) Qc = (182±18)f(0.92±0.08)

Lapse time (s) Valsad (VAL) Kadana (KAD) Dharoi (DHR) Kavdej (KAV)

20 Qc = (98±6)f(0.98±0.02) Qc = (100±10)f(0.97±0.03) Qc = (92±8)f(0.97±0.08) Qc = (66±5)f(1.03±0.06)

30 Qc = (104±15)f(0.99±0.09) Qc = (102±15)f(0.85±0.01) Qc = (98±6)f(1.03±0.02) Qc = (72±7)f(0.97±0.04)

40 Qc = (110±18)f(0.96±0.01) Qc = (108±19)f(1.04±0.06) Qc = (107±12)f(0.99±0.06) Qc = (92±11)f(0.99±0.01)

50 Qc = (113±22)f(0.96±0.04) Qc = (114±21)f(0.99±0.05) Qc = (111±20)f(0.97±0.04) Qc = (98±10)f(0.97±0.07)

60 Qc = (107±15)f(0.94±0.03) Qc = (105±11)f(0.96±0.03) Qc = (112±14)f(0.86±0.04) Qc = (96±20)f(0.87±0.02)

70 Qc = (111±34)f(0.95±0.05) Qc = (111±10)f(0.94±0.05) Qc = (116±20)f(0.89±0.05) Qc = (102±10)f(0.83±0.06)

80 Qc = (122±39)f(0.97±0.07) Qc = (120±21)f(0.97±0.06) Qc = (121±23)f(0.94±0.06) Qc = (106±10)f(1.02±0.07)

90 Qc = (130±19)f(0.98±0.09) Qc = (109±16)f(0.98±0.07) Qc = (127±24)f(1.05±0.10) Qc = (92±10)f(0.96±0.04)


increasing with an increase in frequency for all theeight lapse time windows considered here. Theaverage values of Qc for the lapse time windows of20–90 s with standard error ranges respectivelyfrom 113 ± 12 to 411 ± 37 at 2 Hz and 1008 ± 150to 3600 ± 400 at 16 Hz, respectively (table 3). Thisdemonstrates that our Qc estimates are frequencydependent in nature. We notice here that there isan increase in Qc values with lapse time whichproves the depth dependence of Qc as we sample alarger area with longer lapse time windows. Q0

(quality factor at 1 Hz) along with n (heterogeneityfactor) has been shown in table 4. Several other

investigators have also found this result for otherregions (e.g., Roecker et al. 1982; Gupta et al.1996). This increase of Qc with lapse time asdescribed byWoodgold (1994), be ascribed to otherparameters like considering non-zero distancebetween source and reciever governing non-isotropic scattering and assumption of single scat-tering model where multiple scattering is evitable.Gao et al. (1983) observed that the impacts ofmultiple scattering are not significant for localevents, which govern lapse time\100 s. The lapsewindow lengths of local events considered here areless than 100 s. Hence, we can conclude that the

Figure 3. Plots of quality factors and central frequencies for all the eight stations and average with linear regression frequencydependent relationship (f ), Qc = Q0f

n at different lapse time 20, 30, 40, 50, 60, 70, 80 and 90 s.


lapse time dependence of Coda-Q in our area isassociated with alteration of attenuation withdepth. Our Power laws Qc = Q0f

n obtained foreach station and for all the lapse times have beenshown in table 5 and we acquired the average fre-quency-dependent relationships as Qc = 109 ±

15f 0.95±0.04 for the Mainland region. Power laws

(Qc = Q0fn) obtained at all the lapse time windows

(20–90 s) for all the stations have been shown intable 5. The values of Q0 and n have been obtainedin accordance with equation (Qc =Q0f

n), i.e., plottingQc with frequencies (Bgure3). It is demonstratedfrom table 4 that SIPU (SIP) site located ingneissic granite shows a low value of Q0 in com-parison to that at other sites. This indicates themore attenuative features of the medium proper-ties around localized zones around the SIPU area.We have tried to compare our acquired Q0 esti-mations with other regions of the world (e.g.,Roecker et al. 1982; Rovelli 1982, 1984; Rodriguiezet al. 1983; Pulli 1984; Rhea 1984; Sherbaum andKisslinger 1985; Van Eck 1988; Ambeh and Fair-head 1989; Havskov et al. 1989; Kvamme andHavskov 1989; Ibanez et al. 1990, 1998; Pujadeset al. 1991; Akinci et al. 1994; Hellweg et al. 1995)by plotting them with our results (Bgure 4). Wehave also compared our results with other Indianregions (Bgure 5). It has been noticed that the rateof decay of attenuation (Q�1) with frequency forthe relations obtained in the present study can becompared with those of other regions of the worldas well as of India. Table 6 represents the world-wide comparative study of observed Q0 and g val-ues for various active and stable regions. Thedegree of frequency dependence g has beenobtained to be high for tectonically active regionsas compared to that of tectonically stable regions.The value of g shows a variation from 0.70 to 1.10for the active regions (Rovelli 1982; Gupta et al.1995; Hellweg et al. 1995).Northern part of the Mainland Gujarat is mostly

covered by Quaternary deposits (low density)varying in thickness between 100 and 400 m and insouthern parts, criss-crossed fractures and dykesare found (Merh 1995). These features indicatethat the Mainland region is highly attenuative. Thelow coda ‘Q’ value obtained in the present studyalso indicates that the region is highly attenuative,and correlates well with the geology. Chopra et al.(2011) reported Qs = (118 ± 34)f 0.65±0.14 for oneseismic station, i.e., Kevadia of Mainland Gujaratand Gupta et al. (2012) reported the average lapsetime-dependent coda-Q relations as: Qc = (87 ±

13)f 1.01±0.06, Qc = (112 ± 20)f 0.94±0.08 and Qc =(120 ± 22)f 0.76±0.07 for lapse times 30 s, 40 sand 50 s, respectively. Sharma et al. (2011) foundQc = (158 ± 5)f 0.99±0.04, Qc = (170 ± 4.4)f 0.97±0.02,Qc = (229 ± 6.6)f 0.94±0.03 for lapse times 20 s,30 s and 50 s respectively for Junagarh andQc = (178 ± 3)f 0.95±0.05, Qc = (224 ± 6)f 0.98±0.06,

Figure 4. Comparison of Qc values for Mainland Gujarat,India with the existing Q studies worldwide.

Figure 5. Comparison of Qc values for Mainland Gujarat,India with the existing Q studies in India.

Figure 6. Comparison between predicted and observed decayof PGA values.


Qc = (282 ± 7)f 0.91±0.03 for lapse times of 20 s, 30 sand 40 s, respectively for Jamnagar areas in theneighbouring Saurashtra region. Mandal et al.(2004) reported Qc = 102 ± 0.80f 0.98±0.02, foranother neighbouring Kachchh region. Qc = 82f 1.17

(lapse time 20–50 s), Qc = 106f 1.11 (lapse time30–60 s), Qc = 126f 1.03 (lapse time 40–70 s), Qc =122f 1.02 (lapse time 50–80 s) have been reported byGupta et al. (2006). Our relation is analogous withthat obtained previously for Mainland Gujarat andKachchh regions. It appears that the region is moreheterogeneous as compared to that of neighbouringSaurashtra region. The errors obtained for thevalue of Q0 and n are neither more nor expected tochange the seismic hazard scenario of the regionsignificantly. However, if the errors are high, theobtained Q values are not reliable, and subse-quently, the source parameters will not bedependable. An attempt has been made to comparethe attenuation of observed PGA values in theregion with that of predicted by the Q0 valuesestimated in the present study. We note that veryfew observed PGA values are available in the

region for this analysis. Figure 6 shows the com-parison between predicted and observed decay ofPGA values. For an earthquake of magnitude 3.5,the decay rate of observed PGA values appears tofollow the predicted one. There is scatter in theobserved PGA values as compared to the predictedin case of an earthquake of magnitude 4.4. Thisneeds further investigation as and when moreobserved PGA values become available in theregion. The frequency-dependent relations, devel-oped here, are useful in estimating source param-eters in this region and could be utilized forsimulating earthquake strong ground motions inthe Mainland Gujarat (table 6).

6. Conclusions

This study describes the attenuation characteristicsof the Mainland Gujarat region of Western DeccanVolcanic province. The frequency-dependent rela-tionships for Coda-Q have been developed for thisarea using eight lapse time windows of 20, 30, 40, 50,

Table 6. Worldwide comparative study of observed Q0 and n values for various active andstable regions.

Places Q0 n Source

Active regions

Kachchh, 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 0.98 Havskov et al. (1989)

Mt. Cameroon, West Africa 65 1 Ambeh and Fairhead (1989)

Dead Sea 65 1.05 Van Eck (1988)

ParkBeld 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 regions

Norway 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 Gupta et al. (2012)

Mainland Gujarat region 109 0.95 Present study


60, 70, 80 and 90 s. There is an increase in coda ‘Q’estimates with an increase in lapse time windowssignifying the depth dependence of attenuation. Therate of decay of attenuation is found to be compa-rable to other worldwide results. The values of ‘Q0’estimated in the present study obtained for theMainland Gujarat suggest that the region is moreattenuative than the neighbouring Saurashtraregion of Gujarat, and comparable to nearbyKachchh region. The high value of g demonstratesthat theMainland area is very heterogeneous. Thesefrequency-dependent relations are inevitable formodelling earthquake strong ground motion andestimating source parameters, for the earthquakesoccurring in this region.

Acknowledgements

The authors are thankful to Director General, ISR,and Director, ISR for giving the permission to carryout this work. The authors are also thankful to DrDinesh Kumar, Kurukshetra University, Kuruk-shetra for his guidance and suggestions and to theanonymous reviewers for their useful comments,which helped in improving the quality of the MSsignificantly. The authors are grateful to theDepartment of Science & Technology, Governmentof Gujarat for funding support. The authors alsoexpress their sincere gratitude to Dr K M Sreejith(Scientist), Space Applications Centre, ISRO,Ahmedabad for his encouragement. This work wasoriginally carried out at the Institute of Seismolog-ical Research, Gandhinagar.

Author statement

Arpan Shastri undertook Coda-Q analysis, dataprocessing and wrote the manuscript. SantoshKumar undertook interpretation and contributedto manuscript writing and data analysis.

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Corresponding editor: ANAND JOSHI


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Estimation of Coda-Q for Mainland Gujarat region of