Pure and Applied Geophysics

, Volume 169, Issue 1, pp 89–100

Attenuation of Coda Waves in the Saurashtra Region, Gujarat (India)

  • Babita Sharma
  • Dinesh Kumar
  • S. S. Teotia
  • B. K. Rastogi
  • Arun K. Gupta
  • Srichand Prajapati
Article

DOI: 10.1007/s00024-011-0295-1

Cite this article as:
Sharma, B., Kumar, D., Teotia, S.S. et al. Pure Appl. Geophys. (2012) 169: 89. doi:10.1007/s00024-011-0295-1

Abstract

The attenuation characteristics based on coda waves of two areas—Jamnagar and Junagarh of Saurashtra, Gujarat (India)—have been investigated in the present study. The frequency dependent relationships have been developed for both the areas using single back scattering model. The broadband waveforms of the vertical components of 33 earthquakes (Mw 1.5–3.5) recorded at six stations of the Jamnagar area, and broadband waveforms of 68 earthquakes (Mw 1.6–5) recorded at five stations of the Junagarh area have been used for the analysis. The estimated relations for the Junagarh area are: Qc = (158 ± 5)f(0.99±0.04) (lapse time : 20 s), Qc = (170 ± 4.4)f(0.97±0.02) (lapse time : 30 s) and Qc = (229 ± 6.6)f(0.94±0.03) (lapse time : 40 s) and for the Jamnagar area are: Qc = (178 ± 3)f(0.95±0.05) (lapse time : 20 s), Qc = (224 ± 6)f(0.98±0.06) (lapse time : 30 s) and Qc = (282 ± 7)f(0.91±0.03) (lapse time : 40 s). These are the first estimates for the areas under consideration. The Junagarh area appears to be more attenuative as compared to the Jamnagar area. The increase in Qc values with lapse time found here for both the areas show the depth dependence of Qc as longer lapse time windows will sample larger area. The rate of decay of attenuation (Q−1) with frequency for the relations obtained here is found to be comparable with those of other regions of the world though the absolute values differ. A comparison of the coda-Q estimated for the Saurashtra region with those of the nearby Kachchh region shows that the Saurashtra region is less heterogeneous. The obtained relations are expected to be useful for the estimation of source parameters of the earthquakes in the Saurashtra region of Gujarat where no such relations were available earlier. These relations are also important for the simulation of earthquake strong ground motions in the region.

Keywords

Saurashtra Coda-Q attenuation frequency lapse time 

1 Introduction

The Saurashtra region of the Gujarat state (India) is covered by the Gulf of Kachchh in the north and the Arabian Sea to its south and west. This region is a horst bounded by North Kathiwar Fault in the north and the Narmada Geo-fracture in the south (Biswas, 1987). The seismic activity is mainly concentrated in two areas—Jamnagar and Junagarh—lying north and south, respectively, of the Saurashtra region (Chopraet al., 2008 and Rastogiet al. 2008). This study is reporting, for the first time, the attenuation characteristics of the Saurashtra region based on coda waves.

The continuous slowly dying wave trains observed at the tail of the seismograms following the passage of primary waves are termed coda waves. These waves are the results of the scattering of seismic waves by random heterogeneities in the crust of the Earth (Aki, 1969, 1980). Coda waves are widely used to estimate the attenuation of seismic waves in the crust of a region (Pulli, 1984; Catherine, 1990; Guptaet al., 1996; Kumaret al., 1997; Mandal and Rastogi, 1998; Gupta and Ashwani, 2002; Paulet al., 2003). These are also used to investigate the tectonic properties of the seismically active regions as the attenuation of the seismic waves is affected by the tectonic pattern of the crust.

The study of attenuation of seismic waves is also important for estimating the seismic hazard of a region as the relations developed for attenuation are used to determine the earthquake source parameters and to predict the strong ground motions. The attenuation properties of the media are inherent elements governing the amplitude of seismic waves at various distances from an earthquake source. This attenuation of seismic waves is attributed to several factors like geometrical spreading, scattering due to inhomogeneities in media, inelasticity and multipathing. The attenuation of seismic waves when they traverse through an imperfectly elastic medium is characterized by the dimensionless quantity known as quality factor (Q) which expresses the decay of wave amplitude during its propagation in the medium. The frequency dependent relations for Q (=Q0fn) have been developed for different regions of the world. The Q0 values are found to be varied according to the tectonic activity and geological age of the regions. Aki, (1980) found that the frequency dependency (n) of Q increases with intensity of tectonic activity.

The attenuation characteristics based on coda waves of two areas—Jamnagar and Junagarh of Saurashtra—have been investigated in the present study. The single back scattering model of Aki and Chouet, (1975) has been used for this purpose. The broadband seismograms of 33 and 68 events that occurred in the Jamnagar and Junagarh areas, respectively, have been used in this analysis. The frequency dependent relationships for coda-Q (Qc) have been developed for the two areas. The dependency of coda-Q on lapse time windows has been investigated. These are the first estimates for the Saurashtra region. However, the frequency dependent Q relations for the nearby Kachchh region (north of Saurashtra) are available (Mandalet al., 2004, and Babitaet al., 2008). The frequency dependent relationships for Qc obtained here have been compared with those of other regions of the world.

2 Geology and Seismotectonics of Saurashtra

The state of Gujarat is situated in the highly tectonised zone along the western border of the Indian continental plate. Since the breakup of Indian continental plate from the African plate, at least three major tectonic episodes—Jurassic-Early Cretaceous rifting, Late Cretaceous-Early Eocene drifting and Late Miocene—to ongoing inversion have affected this region (Biswas, 1987). There are four distinct tectonic regimens within the boundaries of the Gujarat State: (1) Narmada rift zone, (2) Saurashtra Horst, (3) Cambay rift zone, and (4) Kachchh rift Zone (Biswas, 1987).

The Saurashtra is a rhombic block bounded by major faults on all sides. It fragmented from the main craton by rifting during the break up of the Indo-African plate and evolution of the passive margin. A number of fault zones are recognized within Saurashtra. Most of the Saurashtra region falls under zone III of the seismic zoning map of India. This zone indicates the moderate damage risk zone which may experience an intensity of VII on the MSK scale. A zone factor of 0.16 has been assigned to this zone which indicates the effective peak horizontal ground acceleration of 0.16g that may be generated during a maximum credible earthquake considered in the zone. The Cambay fault on the eastern boundary of Saurashtra has produced a number of moderate size earthquakes, the largest being magnitude 6 near Bhavnagar in 1919. The Saurashtra region is critically stressed as evidenced by frequent small shocks in the region (Rastogi, 2003).

The Jamnagar area of Saurashtra has witnessed a swarm type of seismic activity near Lalpur (in 2003 and 2007) and Kalawad (in 2006 and 2007) (Chopraet al., 2008). Historically this region has experienced earthquakes of magnitude 4.4 in 1886 and 5.0 in 1940 (Chandra, 1977). The Junagarh area of Saurashtra has also experienced localized swarm activity near Haripur in 2001 and 2004–05. This region has witnessed earthquakes of magnitude 4.6 on August 3, 2000 near Una and magnitude 5.0 on November 6, 2007 near Talala (Rastogiet al. 2008). This region is about 35 and 70 km away from the two major fault systems, namely the extension of the west coast fault (NW trend), which defines the western boundary, and the extension of the Son-Narmada fault (NE trend), which defines the southern boundary. Figure 1 shows the tectonics of the Saurashtra region along with the major faults. The epicenters of the earthquakes and locations of recording stations in the Jamnagar and Junagarh areas are also shown in Fig. 1.
Fig. 1

Region of study along with epicentral locations of events and stations

3 Method

Qc has been estimated using the single backscattering model proposed by Aki and Chouet, (1975). According to this model, the coda waves are interpreted as backscattered body waves generated by numerous heterogeneities present in the Earth’s crust and upper mantle. It implies that scattering is a weak process and outgoing waves are scattered only once before reaching the receiver. Under this assumption the coda amplitudes, Ac(f,t), in a seismogram can be expressed for a central frequency f over a narrow bandwidth signal, as a function of the lapse time t, measured from the origin time of the seismic event, as (Aki, 1980):
$$ {\text{A}}_{\text{c}} \left( {{\text{f}},{\text{t}}} \right) = {\text{S}}\left( {\text{f}} \right){\text{t}}^{\text{ - a}} { \exp }\left( { - \pi {\text{ft}}/Q_{\text{c}} } \right) $$
(1)
where S(f) represents the source function at frequency f, and is considered a constant as it is independent of time and radiation pattern, and, therefore, not a function of factors influencing energy loss in the medium; a is the geometrical spreading factor, and taken as 1 for body waves, and Qc is the apparent quality factor of coda waves representing the attenuation in a medium. Equation (1) strictly holds when station and source are coincident. It has been shown by Rautian and Khalturin, (1978) that the coda parameters S and Qc are independent of source-site distance if coda start time is taken as twice the travel time of S-waves. Equation (1) can be rewritten as:
$$ { \ln }\left( {{\text{A}}_{\text{c}} \left( {{\text{f}},{\text{t}}} \right){\text{t}}} \right) = {\text{lnS}}\left( {\text{f}} \right) - \left( {\pi {\text{f}}/Q_{\text{c}} } \right){\text{t}} $$
(2)

This equation can be used to least square fit the data and Qc can be estimated from the slope given by −πf/Qc.

4 Data and Analysis

The earthquakes occurred in two areas—Jamnagar and Junagarh of Saurashtra—and recorded by the broadband network of the Institute of Seismological Research (ISR) have been used in the present analysis. ISR, Gandhinagar has installed seven permanent broadband CMG-3T sensors having CMG-DCM recorders and GPS timing system instruments at Lalpur (LAL), Rajkot (RAJ), Surendranagar (SUR), Morvi (MOR), Junagarh (JUN), Amreli (AMR) and Una (UNA), with continuous data recording at a sampling rate of 50 samples/sec. Further, four temporary broadband CMG-3T sensors having REFTEK 24-bit recorders and GPS timing system instruments have also been installed at Maliya (MLA), Talala (TAL), Dudhai (DUD) and Naliya (NAL), with continuous data recording at a sampling rate of 100 samples/sec. The waveforms of the vertical components of 33 earthquakes (Mw 1.5–3.5) recorded at six stations—NAL, DUD, LAL, RAJ, SUR and MOR—have been used for analysis of the Jamnagar area. For the Junagarh area waveforms of 68 earthquakes (Mw 1.6–5) recorded at five stations—JUN, AMR, UNA, MLA and TAL—have been used for the analysis. The magnitudes of the events have been estimated by fitting the Brunes, (1970) model to the source displacement spectra of observed seismograms. In order to take into account the attenuation factor a relation Q(f) = 169f0.77 (Mandal and Rastogi, 1998) developed for the Koyna region has been used as most of the Saurashtra region and Koyna region are based on Deccan rocks. As has been discussed later, the Q0 values estimated here for 20 s lapse time window are comparable with the relation used while estimated value of n is higher than that of the relation used. Tables 1 and 2 give the list of earthquakes of these two regions. The earthquakes have been selected on the basis of quality the waveforms available at the time of present analysis. Table 3 gives the characteristics and locations of the recorded stations. Figure 1 shows the locations of the earthquakes and recording stations. The maximum epicentral distances for the earthquakes in the Jamnagar and Junagarh areas are 113 and 74 km, respectively. The focal depths are up to 25 km. The root mean square error in time is 0.1–0.4 s and ±2–5 km error in hypocentral location.
Table 1

Events used for the Jamnagar area

Year

Month

Date

Hour

Minute

Second

Latitude (ºN)

Longitude (ºE)

Depth (km)

Ml

Mw

2007

6

12

20

37

34.1

22.015

71.357

24

2.1

2

2007

6

17

3

30

16.6

22.102

72.033

15

1.5

1.8

2007

7

16

21

21

21.9

22.444

71.288

10

1.5

1.6

2007

8

11

3

3

46.3

22.396

70.222

10

2.4

2.2

2007

8

11

3

29

29.4

22.303

69.995

10

2.3

2.4

2007

8

11

6

44

22

22.423

70.085

15

2.5

2.2

2007

8

11

19

18

29.1

22.318

70.246

10

3.3

3.5

2007

8

12

4

43

57.4

22.545

70.134

20

1.7

2.2

2007

8

12

5

2

17.1

22.454

70.103

10

2

2.2

2007

8

13

11

14

20.7

22.339

70.255

24

2.4

3

2007

8

13

13

11

15.4

22.295

70.218

10

2.4

2.7

2007

8

13

13

41

44.4

22.308

70.262

10

1.6

1.5

2007

8

18

12

7

12.8

22.103

70.195

20

2.7

3

2007

8

18

14

31

54.1

22.398

70.17

21

2.3

2.8

2007

8

19

6

56

56.5

22.434

70.187

5

2.4

2.5

2007

8

19

16

55

41.5

22.444

70.04

25

2.8

2.9

2007

8

21

19

36

3.2

22.326

70.087

22

2

2.4

2007

8

22

15

54

45.9

22.287

71.221

19

2.1

3

2007

8

24

4

9

46.6

22.427

70.155

25

2.2

2.3

2007

8

24

9

53

46.5

22.282

70.285

14

2.9

2.8

2007

8

24

20

55

25.1

21.961

69.842

20

2.1

2.2

2007

8

24

23

55

34.6

21.994

69.855

10

2.1

1.9

2007

8

25

6

40

30.2

22.312

70.243

10

1.8

2.1

2007

8

25

7

27

11.5

22.314

70.242

10

1.7

2

2007

8

25

7

39

26.4

22.303

70.231

16

2.1

2.3

2007

8

25

14

52

7

22.402

69.956

10

2.2

2.1

2007

8

26

11

17

59.1

22.495

71.482

15

1.7

2.3

2007

8

26

15

25

6.8

22.416

70.155

10

1.8

2.2

2007

8

26

19

14

27.5

21.965

72.37

15

1.5

1.6

2007

8

26

22

58

9.9

22.353

70.203

15

2.4

2.3

2007

8

28

15

10

56.9

22.345

70.234

11

2.4

2.9

2007

8

31

21

41

28.4

22.422

69.983

25

2.5

2.6

Table 2

Events used for the Junagarh area

Year

Month

Date

Hour

Minute

Second

Latitude

Longitude

Depth

Ml

Mw

(ºN)

(ºE)

(km)

2007

11

6

0

27

29

21.12

70.521

10

4.5

4.4

2007

11

6

1

0

50.6

21.159

70.608

3

2.6

2.7

2007

11

6

1

31

11.5

21.167

70.558

12

1.5

1.6

2007

11

6

1

43

9

21.165

70.568

17

2.3

2.4

2007

11

6

1

51

41.1

21.175

70.582

20

2.3

2.1

2007

11

6

2

50

12.1

21.17

70.584

19

1.5

1.7

2007

11

6

3

18

11.7

21.163

70.524

11

1.8

1.7

2007

11

6

3

24

53.7

21.175

70.562

18

2.9

3.1

2007

11

6

3

59

0.5

21.159

70.548

10

2

2

2007

11

6

4

35

0.6

21.147

70.544

15

2.7

2.6

2007

11

6

4

37

0.4

21.169

70.544

11

2.8

3

2007

11

6

8

34

18.5

21.118

70.596

15

2.2

2.3

2007

11

6

9

38

4.7

21.152

70.569

3

4.9

5

2007

11

6

9

51

52.2

21.544

70.629

15

2

2.1

2007

11

6

10

37

33.2

21.158

70.628

15

1.9

2.2

2007

11

6

10

41

17.6

21.307

70.663

15

1.7

2

2007

11

6

11

52

6.5

21.21

70.557

15

1.9

2.2

2007

11

6

12

31

36.7

21.406

70.552

4

2.8

3

2007

11

6

12

45

2.6

21.173

70.627

3

3.1

3.3

2007

11

6

13

13

23.3

21.151

70.557

12

2.6

2.8

2007

11

6

14

17

15.7

21.123

70.609

15

2.3

2.4

2007

11

6

15

40

19

21.202

70.485

6

2.9

3.4

2007

11

6

15

41

38.4

21.176

70.543

9

2.8

3.1

2007

11

6

15

53

22

21.158

70.631

7

3.7

3.9

2007

11

6

16

27

3.8

21.164

70.578

3

2.1

2.2

2007

11

6

17

24

48.9

21.153

70.565

3

2.2

2.4

2007

11

6

18

39

56.7

21.185

70.618

18

2.5

2.7

2007

11

6

19

11

0.9

21.13

70.553

3

3.3

3.5

2007

11

6

19

15

53

21.324

70.994

3

2.7

2.8

2007

11

6

20

0

8.6

21.341

71.001

3

2.5

2.7

2007

11

7

2

52

22.5

21.128

70.516

10

2.6

2.7

2007

11

7

4

41

18.3

21.131

70.494

11

2.3

2.9

2007

11

7

9

45

25.9

21.163

70.582

10

1.8

1.7

2007

11

7

10

11

3.8

21.172

70.577

10

1.9

1.8

2007

11

7

10

15

56.7

21.168

70.585

10

1.9

1.8

2007

11

7

10

33

0.9

21.188

70.636

12

2.6

2.7

2007

11

7

11

20

9.6

21.168

70.623

3

1.8

2

2007

11

7

17

5

27.2

21.192

70.635

21

3.1

3.3

2007

11

7

17

15

58.3

21.331

70.994

3

2.1

2

2007

11

8

23

43

52.9

21.15

70.528

9

1.8

2

2007

11

9

3

29

47.4

21.182

70.526

5

2.5

2.6

2007

11

9

4

18

43.7

21.149

70.532

3

2.6

2.6

2007

11

9

4

59

47.3

21.159

70.55

3

2

2.1

2007

11

9

5

4

1.5

21.162

70.55

3

2.2

2.2

2007

11

9

7

48

1.9

21.208

70.519

15

1.8

1.7

2007

11

9

8

47

32.8

21.145

70.531

6

2.1

2.3

2007

11

9

14

33

30.2

21.118

70.556

15

1.7

1.8

2007

11

10

23

9

47.5

21.095

70.499

15

1.8

2.1

2007

11

11

0

42

18.1

21.151

70.539

10

1.7

1.8

2007

11

11

2

38

30.9

21.123

70.517

3

2.1

2.3

2007

11

12

9

57

20.1

21.116

70.522

15

2.4

2.6

2007

11

12

12

11

40.7

21.156

70.541

6

2.1

2.2

2007

11

12

17

10

13.2

21.125

70.532

15

2.1

2.1

2007

11

12

21

17

48.9

21.146

70.525

10

2.1

2

2007

11

12

22

11

4

21.142

70.53

10

1.8

2

2007

11

12

23

51

37.9

21.14

70.547

10

2.2

2.3

2007

11

13

0

7

11.1

21.107

70.492

10

1.7

1.8

2007

11

13

0

11

53.6

21.124

70.538

15

2.2

2.3

2007

11

13

0

27

45.5

21.237

72.096

15

2

2.2

2007

11

13

0

55

14.9

21.152

70.544

10

3.2

3.1

2007

11

14

14

10

11.7

21.141

70.536

10

3

3

2007

11

15

9

56

23.6

21.166

70.523

6

3

2.8

2007

11

16

15

27

10.9

21.131

70.492

6

2

2.2

2007

11

17

19

51

60

21.058

70.524

15

1.5

2.1

Table 3

Site characteristics and locations of the recording stations

Station

Station code

Latitude (°N)

Longitude (°E)

Foundation geology

Morbi

MOR

22.48

70.89

Basalt

Lalpur

LAL

22.35

69.96

Basalt

Rajkot

RAJ

22.36

70.76

Basalt

Surendranagar

SUR

22.73

71.58

Sandstone

Junagarh

JUN

21.35

70.72

Basalt

Amreli

AMR

21.31

71.24

Basalt

Una

UNA

20.98

70.93

Basalt

Maliya

MLA

21.16

70.29

Basalt

Talala

TAL

21.03

70.31

Basalt

Dudhai

DUD

23.32

70.13

Sandstone

Naliya

NAL

23.33

68.83

Limestone

The broadband seismograms are filtered using a band pass Butterworth filter at central frequencies of 1.5, 3, 6, 12 and 18 Hz. The coda part of the seismograms is taken to be twice the arrival time of S-waves. The root mean square (RMS) amplitudes of filtered seismograms are estimated using a moving time window of 2.56 s wide with 1.28 s interval. In order to investigate the lapse time window dependency of the Q estimation, the RMS amplitudes are obtained for lapse time windows of 20, 30 and 40 s. Figure 2 displays the filtered seismograms and plots of ln[A(f,t).t] versus t for an event recorded at RAJ for different central frequencies along with the least square fitted lines. The slopes (m) of these lines are used to estimate Qc (=−πf/m).
Fig. 2

Qc estimates for an event recorded at RAJ on 19 June 2007 (using 30 s lapse time window)

5 Results and Discussions

The mean values of Qc estimated at different recording sites of the Junagarh and Jamnagar areas at different central frequencies for lapse time window length of 20 s are given in Tables 4, 5. The Qc values obtained for lapse time window lengths of 30 and 40 s are given in Tables 6, 7, 8, and 9 respectively. The variation in Qc values at different sites may be attributed to the heterogeneities present in the regions and/or difference in the distances of the events from the recording stations. We note from these tables that Qc values increase with increase in frequency for both the regions and for all the three lengths of lapse time window considered here. The average values of Qc for the lapse time windows of 20, 30 and 40 s at the Junagarh area varies, respectively, from 231, 246 and 379 at 1.5, to 2,442, 3,073 and 3,556 at 18 Hz. The corresponding Qc estimates for the Jamnagar area varies from 241, 311 and 399 at 1.5 Hz, to 2,873, 3,958 and 4,372 at 18 Hz. This shows the frequency dependent nature of Q estimates for the two areas. The plots of average Qc values versus frequency are shown in Fig. 3a, b for the Junagarh and Jamnagar areas, respectively. The fitting of the power law Qc = Q0fn gives the frequency dependent relationships for Junagarh area as: Qc = (158 ± 5)f(0.99±0.04) (lapse time: 20 s), Qc = (170 ± 4.4)f(0.97±0.02) (lapse time: 30 s) and Qc = (229 ± 6.6)f(0.94±0.03) (lapse time: 40 s). Similar relationships estimated for the Jamnagar area are (Fig. 3b): Qc = (178 ± 3)f(0.95±0.05) (lapse time: 20 s), Qc = (224 ± 6)f(0.98±0.06) (lapse time: 30 s) and Qc = (282 ± 7)f(0.91±0.03) (lapse time: 40 s). The estimated error in calculating the frequency dependent relationships in mean and standard deviation ranges from 2.9 to 3.15 and 0.35 to 0.52, respectively. We note that the estimated coda-Q values are more in the Jamnagar area than those of the Junagarh area for all three lapse time windows studied here. This shows the more attenuative characteristics of the medium properties of the Junagarh area. These relations represent the average attenuation characteristics of the medium properties of the localized zones around the Junagarh and Jamnagar areas. The value of n varies from 0.94 to 0.99 for the Junagarh region and 0.91 to 0.98 for the Jamnagar region, which is not significant taking into account the standard deviations in the values on n.
Table 4

Coda-Q estimates at the five stations of Junagarh area for 20 s lapse time window

C.F.

No. of events

JUN

No. of events

AMR

No. of events

UNA

No. of events

MLA

No. of events

TAL

Average Qc

1.5

36

201 ± 42

34

290 ± 65

37

219 ± 30

21

198 ± 34

20

245 ± 53

231

3

33

398 ± 52

35

499 ± 54

46

389 ± 35

14

234 ± 54

18

305 ± 44

365

6

37

567 ± 51

39

987 ± 55

44

1,076 ± 39

13

467 ± 56

16

888 ± 57

797

12

51

1,488 ± 66

40

1,589 ± 76

52

1,577 ± 45

09

1,098 ± 65

21

1,056 ± 66

1,362

18

37

2,032 ± 78

32

2,566 ± 59

25

2,775 ± 86

12

2,890 ± 93

10

1,945 ± 75

2,442

Table 5

Coda-Q estimates at the six stations of Jamnagar area for 20 s lapse time window

C.F.

No. of events

NAL

No. of events

DUD

No. of events

LAL

No. of events

RAJ

No. of events

SUR

No. of events

MOR

Average Qc

1.5

22

155 ± 45

21

289 ± 34

25

250 ± 56

24

202 ± 55

19

345 ± 45

27

203 ± 54

241

3

25

456 ± 67

15

706 ± 56

30

765 ± 65

25

465 ± 66

31

677 ± 56

25

435 ± 55

584

6

29

890 ± 89

29

1,198 ± 78

26

1,006 ± 75

19

1,065 ± 80

28

1,156 ± 77

28

876 ± 76

1,032

12

26

1,877 ± 67

19

1,569 ± 89

15

2,455 ± 98

30

2,133 ± 92

21

1,588 ± 98

21

1,475 ± 87

1,850

18

19

3,098 ± 98

27

2,566 ± 137

27

3,045 ± 69

25

2,998 ± 111

20

3,074 ± 85

19

2,457 ± 78

2,873

Table 6

Coda-Q estimates at the five stations of Junagarh area for 30 s lapse time window

C.F.

No. of events

JUN

No. of events

AMR

No. of events

UNA

No. of events

MLA

No. of events

TAL

Average Qc

1.5

32

264 ± 23

29

311 ± 18

23

163 ± 24

15

215 ± 11

18

275 ± 22

246

3

44

442 ± 27

37

562 ± 43

38

481 ± 33

19

272 ± 25

12

395 ± 32

431

6

41

682 ± 36

46

1,134 ± 39

52

1,595 ± 56

17

509 ± 34

14

1,091 ± 45

1,002

12

39

2,165 ± 50

35

1,713 ± 41

49

1,824 ± 51

22

1,149 ± 56

16

1,194 ± 54

1,609

18

40

2,533 ± 54

25

3,432 ± 68

29

3,414 ± 72

11

3,288 ± 78

10

2,697 ± 66

3,073

Table 7

Coda-Q estimates at the six stations of Jamnagar area for 30 s lapse time window

C.F.

No. of events

NAL

No. of events

DUD

No. of events

LAL

No. of events

RAJ

No. of events

SUR

No. of events

MOR

Average Qc

1.5

29

196 ± 33

19

340 ± 29

22

340 ± 34

18

262 ± 31

22

422 ± 42

24

307 ± 34

311

3

21

608 ± 25

23

829 ± 32

25

908 ± 47

16

581 ± 29

25

949 ± 38

21

643 ± 39

753

6

26

1,160 ± 36

32

1,336 ± 28

28

1,182 ± 28

29

1,278 ± 37

31

1,301 ± 55

30

1,178 ± 45

1,239

12

22

2,418 ± 47

21

1,870 ± 56

17

2,976 ± 36

32

2,689 ± 66

29

1,987 ± 39

22

2,075 ± 56

2,336

18

30

4,334 ± 59

18

3,993 ± 45

26

3,777 ± 60

30

4,912 ± 57

23

3,514 ± 65

28

3,215 ± 68

3,958

Table 8

Coda-Q estimates at the five stations of Junagarh area for 40 s lapse time window

C.F.

No. of events

JUN

No. of events

AMR

No. of events

UNA

No. of events

MLA

No. of events

TAL

Average Qc

1.5

43

305 ± 45

36

450 ± 34

32

344 ± 37

11

405 ± 49

08

389 ± 56

379

3

35

509 ± 34

33

666 ± 45

34

598 ± 67

09

650 ± 45

12

599 ± 65

604

6

45

1,215 ± 37

47

1,455 ± 33

43

1,986 ± 78

13

1,867 ± 76

11

1,356 ± 47

1,576

12

30

2,076 ± 78

30

2,198 ± 35

24

2,569 ± 56

12

1,569 ± 65

08

2,298 ± 76

2,142

18

29

3,098 ± 59

25

3,245 ± 76

26

4,087 ± 37

07

3,675 ± 39

05

3,677 ± 33

3,556

Table 9

Coda-Q estimates at the five stations of Jamnagar area for 40 s lapse time window

C.F.

No. of events

NAL

No. of events

DUD

No. of events

LAL

No. of events

RAJ

No. of events

SUR

No. of events

MOR

Average Qc

1.5

22

301 ± 54

21

398 ± 34

30

402 ± 56

16

344 ± 33

22

503 ± 23

30

443 ± 29

399

3

15

852 ± 34

22

908 ± 38

24

876 ± 67

19

655 ± 45

21

888 ± 36

22

706 ± 33

814

6

18

1,567 ± 35

24

1,678 ± 29

28

1,456 ± 46

22

1,345 ± 65

19

1,543 ± 54

19

1,322 ± 57

1,485

12

20

3,098 ± 48

26

2,685 ± 76

16

3,203 ± 37

29

2,987 ± 62

21

2,223 ± 39

22

2,345 ± 69

2,386

18

19

4,567 ± 76

14

4,432 ± 39

22

4,233 ± 54

17

4,482 ± 45

18

4,007 ± 57

26

4,508 ± 71

4,372

Fig. 3

a Estimation of frequency dependent relationship for Junagarh area in Saurashtra. b Estimation of frequency dependent relationship for Jamnagar area in Saurashtra

The estimated relations show the increase in Q0 values with increase in lapse time window while n does not change much. The degree of frequency dependence n has been found to be high for tectonically active regions as compared to that of tectonically stable regions. The value of n varies from 0.70 to 1.10 for the active regions (Hellweget al., 1995; Rovelli, 1982; Guptaet al., 1995). The high values of n estimated here indicate that both the areas—Junagarh and Jamnagar—are tectonically active. No significant variation in n with lapse time window lengths has been found for smaller lapse time window lengths (e.g. Ibáñezet al., 1990; Akinciet al., 1994). The value of n obtained here for different lapse time window lengths can be considered as stationary.

The increase in Qc values with lapse time found in this study show the depth dependence of Qc as a larger area will be sampled with longer lapse time windows. The increase of Qc with lapse time has been found by other investigators also for other regions (e.g. Rockeret al. 1982; Guptaet al., 1996). The increase in Qc with lapse time can also, as pointed out by Woodgold, (1994), be attributed to other factors like consideration of non-zero source receiver distance with nonisotropic scattering and assumption of single scattering model where multiple scattering is important. The coda start time has been taken as twice of the S-wave travel time for all the three lapse time windows considered here and therefore only back scattered waves arrive at this time (Aki and Chouet, 1975). Gaoet al. (1983) has reported that the effects of multiple scattering are not important for local events with lapse time less than 100 s. The lapse time window lengths of local events analyzed here are less than 100 s. Therefore the lapse time dependence of coda-Q in the two areas studied here can be attributed to the variation of attenuation with depth.

A comparison of Qc values estimated here with those of found for other regions of the world is shown in Fig. 4. We note that rate of decay of attenuation (Q−1) with frequency for the relations obtained in the present study are comparable with those of other regions of the world though the absolute values differ. Also, the decay curve of attenuation for the two areas studied here fall below the theoretically predicted curve (Sato, 1984). This shows that the regions under consideration are less attenuative as compared to the model considered by Sato, (1984) for the predictive curve.
Fig. 4

Comparison of Qc values for the Junagarh and Jamnagar areas of Saurashtra, Gujarat, India with the existing Q studies worldwide. Satos, (1984) theoretically predicted curve is also shown

The coda-Q estimates of the nearby Kachchh region in the north of the Saurashtra region are available (Mandalet al., 2004; Guptaet al., 2006 and Babitaet al., 2008). The Q estimates obtained in the present analysis for the Saurashtra region (Qc = 170f0.97 for Junagarh; Qc = 224f0.98 for Jamnagar; lapse time: 30 s) are found to be higher as compared to that of estimated for the Kachchh region (Qc = 102f 0.98 by Mandalet al., 2004; Qc = 106f 1.11 by Guptaet al., 2006 and Qc = 148f1.01 by Babitaet al., 2008). This shows that there is a low level of heterogeneity for the Saurashtra region as compared to that of the adjacent Kachchh region.

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

6 Conclusions

This study reports for the first time the attenuation characteristics of two local areas—Junagarh and Jamnagar of the Saurashtra region in Gujarat, India. The frequency dependent relationships for coda-Q have been developed for the two areas using three lapse time window lengths. The coda-Q estimates increase with increase in lapse time window indicating the depth dependence of attenuation. The rate of decay of attenuation is found to be comparable with those of other regions. Based on Q relations, the Saurashtra region is found to be less heterogeneous as compared to the nearby Kachchh region. The frequency dependent relations estimated here are very useful for the modeling of earthquake strong ground motions as well as estimation of earthquake source parameters in the Saurashtra region.

Acknowledgments

The authors are grateful to the Science and Technology Department of Gujarat and Ministry of Earth Science, New Delhi for the financial support of this study. The authors are thankful to the anonymous reviewers for their valuable comments.

Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  • Babita Sharma
    • 1
    • 2
  • Dinesh Kumar
    • 3
  • S. S. Teotia
    • 3
  • B. K. Rastogi
    • 2
  • Arun K. Gupta
    • 1
    • 2
  • Srichand Prajapati
    • 2
  1. 1.Ministry of Earth SciencesNew DelhiIndia
  2. 2.Institute of Seismological ResearchGandhinagarIndia
  3. 3.Department of GeophysicsKurukshetra UniversityKurukshetraIndia

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