Variation of intrinsic and scattering attenuation of seismic waves with depth in the Bam region, East-Central Iran

Soil Dynamics and Earthquake Engineering 31 (2011) 1338–1346

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Variation of intrinsic and scattering attenuation of seismic waves with depth in the Bam region, East-Central Iran M. Mahood, H. Hamzehloo n International Institute of Earthquake Engineering and Seismology (IIEES), Tehran, Islamic Republic of Iran

a r t i c l e i n f o

a b s t r a c t

Article history: Received 6 July 2008 Received in revised form 13 February 2011 Accepted 7 May 2011 Available online 8 June 2011

The attenuation properties of the lithosphere in the Bam region, East-Central Iran, have been investigated. For this purpose, 42 local earthquakes having focal depths less than 25 km have been used. The quality factor of coda waves (Qc) has been estimated using the single back-scattering model. The quality factors Qp, Qd (P and direct S-waves) have been estimated using the extended-coda normalization method. Qi and Qs (the intrinsic and scattering attenuation parameters) have been estimated for the region. The values of Qp, Qd, Qc, Qi and Qs show a dependence on frequency in the range of 1.5–24 Hz for the Bam region. The average frequencydependent relationships estimated for the region are Qp ¼ (3676)f (1.03 70.06), Qd ¼ (5978)f (1.00 70.03), Qc ¼ (7975)f (1.01 70.04), Qs ¼ (13174)f (1.01 70.04) and Qi ¼ (10476)f (1.01 70.05). A comparison between Qi and Qs shows that intrinsic absorption is predominant over scattering. The variation of Q has also been estimated at different lapse times to observe heterogeneities variation with depth. The variation of Q with frequency and lapse time shows that the lithosphere becomes more homogeneous with depth. The estimated Qo values at different stations suggest a low value of Q indicating a heterogeneous and attenuative crust beneath the entire region. & 2011 Elsevier Ltd. All rights reserved.

1. Introduction It is well known that some of the larger uncertainties in earthquake hazard analysis, simulation of strong ground motions and studying earthquake source parameters are caused by uncertainties in seismic wave attenuation and regional earth structure. Studying attenuation process helps to infer the physical laws related to the propagation of the elastic energy of an earthquake through the lithosphere. Attenuation of the medium is usually considered to be caused by two distinct physically processes; elastic and anelastic processes. Elastic processes conserve the energy in the propagating wave-field, but increase or decrease wave amplitudes by shifting around energy in the wave-field, such as geometrical spreading, multi-pathing and scattering. These effects depend on wave type, frequency, inhomogeneities and medium properties. Anelastic processes dissipate part of the seismic energy into heat and seismic wave amplitudes decrease due to this energy loss. Anelastic processes also depend on the medium anelasticity, material properties (wave velocities, density, temperature), and the wave-field under consideration (i.e. frequency) [1,2]. Seismic attenuation will be derived as a natural consequence of the application of energy conservation to the intrinsic absorption and

n

Corresponding author. E-mail address: [email protected] (H. Hamzehloo).

0267-7261/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.soildyn.2011.05.010

scattering model, due to distributed heterogeneities of varied scale inside the Earth’s interior. Scattering attenuates the direct wave amplitude and excites coda waves. Observations of coda waves that follow direct S-waves have shown that there are heterogeneities and contrasts of physical properties, scattered randomly throughout the Earth’s lithosphere. Analysis of coda waves can be employed to evaluate scattering strength using an appropriate model of coda wave excitation [1,3]. Tectonic processes such as folding, faulting and large scale crustal movements associated with plate tectonics contribute to making the lithosphere heterogeneous [2]. Scattering redistributes wave energy within the medium but does not remove energy from the overall wave-field. Conversely, intrinsic absorption refers to various mechanisms that convert vibration energy into heat through sliding along grain boundaries, friction, viscosity and thermal relaxation processes. However intrinsic absorption appears to dominate scattering attenuation. There has been considerable speculation about which process, intrinsic or scattering, dominates attenuation and several methods have been proposed to determine the amounts of both scattering and intrinsic attenuation [2–4]. Recent developed methods separately estimate the coefficient of intrinsic and scattering attenuation quantitatively. These methods have been widely applied to several tectonic areas, allowing a relative comparison of the attenuation properties of areas with different tectonic histories [2,6–9]. Attenuation of seismic waves is measured by Q (quality factor) which is directly related to the decay of elastic energy when its spreads through medium. Q is representation of physical properties of

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the material present in the medium and its state. Aki [4] develops a model for the rate of coda decay. The application of this model yields information both about the earthquake source and about the medium in which scattering and absorption occur. Aki and Chouet [5] show how to calculate Q from coda waves. Tsujiura [10] and Aki [11] argued that scattering attenuation plays a more significant role than intrinsic, while Frankel and Wennerberg [12] proposed the opposite view. Wu [13] proposed a method for an estimation of the relative contribution of Qs and Qi from the dependence of total S-wave energy on hypocentral distance. His method was based on the application of the radiative transfer theory to the seismic energy density. Wennerberg [15] provided the formulation to determine the contribution of Qs and Qi attenuation to the total attenuation. He described the possibility of reinterpreting the obtained single-station Qc values in terms of multiple scattering. He used the approximation given by Abubakirov and Gusev [16] to the model developed by Zeng [17] to describe the multiple-scattered wave-field in the case of a source colocated with the station. He has given the relations to estimate Qs and Qi from measurements of Qd and Qc (the direct S-wave Q and Q coda, respectively). Measurements of attenuation of direct seismic waves (Qd) give values for total attenuation. In the present article, we give an estimate of Qs and Qi to understand how much intrinsic and scattering attenuation affect seismic wave attenuation in the crust of the Bam region, in which both Qc and direct S-wave Qd, were measured at stations close to the source of the events, using the approach described by Wennerberg [15].

2. Study region The Iranian Plateau, characterized by active faulting, active folding, recent volcanic activities, mountainous terrain, and variable crustal thickness, has been frequently struck by earthquakes resulting in the massive loss of life. The active tectonics of Iran is dominated by the northward motion of Arabia with respect to Eurasia (Fig. 1). Several large earthquakes have occurred on the right-lateral strike-slip fault systems along the western margin of the Dasht-e-Lut, which accommodate right-lateral shear between central parts of Iran and Afghanistan. Destructive earthquakes of East-Central Iran, around the aseismic central Iran and Dasht-eLut, are shown in Fig. 1. Two recent major earthquakes in this region are: the Bam earthquake of 26 December 2003 (Mw 6.5) occurred around the city of Bam and the 2005 Zarand earthquake (Mw 6.4). The Bam fault, which was mapped before the event on the geological maps, has been reactivated during the earthquake. It seems that a length of about 10 km (at the surface) of this fault has been reactivated, where it passed exactly from the east of the city of Bam. The fault has a slope towards the west and the focus of the event was located close to the residential area (almost beneath the city of Bam). This caused a great damage in the macroseismic epicentral zone; however the strong motions have been attenuated very rapidly, especially towards the east and west (fault normal) direction. The comparison of observed and simulated ground motion indicates that rupture started at a depth of 8 km, south of Bam and propagated toward north ([18]). This region is also important from the engineering point of view, as many industrial projects are either in operation or under advanced stage of planning and construction.

Fig. 1. Destructive earthquakes of East-Central Iran are around the aseismic central Iran and Dasht-e-Lut. The focal mechanisms of earthquakes are from CMT (black) and Walker and Jackson (2002) (gray) [14].

operated by the International Institute of Earthquake Engineering and Seismology (IIEES) (Fig.2). The Bam local seismograph network consists of 17 stations which operated from 28 December 2003 until 27 January 2004, after the 2003 Bam earthquake. In this study, we used 42 earthquakes recorded by the Bam network. These earthquakes were recorded at least on four stations and the digital data used for the analysis are corrected with the instrumental responses. For filtered waveforms, noise level increases as central frequency, f, increases (Fig. 3). We have considered data with a good signal-to-noise ratio and waveforms with S/N ratio less than three were discarded. The S/N ratio for each filtered seismogram is calculated using the RMS amplitude of the last 5 s of data in the lapse time window and the noise data of the same window length prior to the P-wave arrival. We took only Q estimates greater than 0.85 as correlation coefficients of the linear regression. The focal depths of earthquakes are less than 25 km, with magnitude range 2.5–4.5, and were recorded at distances of less than 100 km from the hypocenter.

3. Data used 4. Methodology The local digital seismic network was operated in the Bam, East-Central Iran. All the instruments had three-component, ¨ broad-band, CMG-6TD Guralp seismometers and they were

Wennerberg [15] provided the formulation based on the Zeng et al. [17] model to estimate Qi and Qs. According to Zeng et al.

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where d(t) is 1/(4.44þ 0.738t) and t ¼ ot/Qs, o is the angular frequency, and t is the lapse time. Assuming Qd as the quality factor of the direct wave evaluated in the Earth volume equivalent to the volume sampled by coda waves, it can be written as [15]   1 1 1 1 ð3Þ ¼  Qs 2dðtÞ Qd Qc ðtÞ   1 1 1 2dðtÞ1 þ ¼ Qi 2dðtÞ Qc ðtÞ Qd

ð4Þ

If Qc is measured as a function of lapse time t, Qi and Qs can be estimated using Eqs. (2)–(4), where Qd is measured as a function of distance.

5. Qc estimation

Fig. 2. Local seismic network of Bam, seismic stations (triangles) and epicenter of recorded earthquakes (circles). O. Time

PS

Coda Window for Qc

Coda for Qp and Qd N-S Component

where S(f) is the source function at frequency f and is considered a constant as it is independent of time and radiation pattern, a is the geometrical spreading factor and considered as 1 for body waves and Qc represents the quality factor of coda waves. It has been observed that the coda spectrum of small earthquakes at local distances is independent of earthquake size, epicentral distance and the path between station and epicenter, but it depends on lapse time from the origin time of the earthquake [4–6]. This suggests that the coda part of the seismogram is due to an average scattering effect of the medium in the region near the source and station [18,19]. Eq. (5) can be written as

SH-Component

f = 1.5 Hz

f = 3.0 Hz

f = 6.0 Hz

f = 12.0 Hz

Counts

Analysis of coda waves can be employed to evaluate scattering strength using an appropriate model of coda wave excitation. The single back-scattering model proposed by Aki and Chouet [5] has been used for describing the behavior of the coda waves from local earthquakes. 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. The coda amplitudes, A(f,t), in a seismogram can be expressed for a central frequency f over a narrow band width signal, as a function of the lapse time t, measured from the origin time of the seismic event, as   pft Aðf ,tÞ ¼ Sðf Þa exp ð5Þ Qc ðf Þ

ln½Aðf ,tÞt ¼ c2bt

800 400 0 -400 -800

f = 24.0 Hz

0

20

40 Time (sec)

60

80

Fig. 3. An example of recorded and its band-pass filtered seismograms. An N–S component broad-band seismogram recorded at BAM station and SH-component obtained are shown in the top. The horizontal bars represent the time windows for the P, S and coda waves. Five band-pass filtered seismograms for central frequencies at 1.5, 3, 6, 12 and 24 Hz are displayed below.

[17], we can write the Qd in terms of Qi and Qs as follows: 1 1 1 ¼ þ Qd Qi Q s

ð1Þ

Wennerberg [15] showed that the observed Qc is related to the intrinsic and scattering Q as follows: 1 1 12dðtÞ ¼ þ Qc Qi Qs

ð2Þ

ð6Þ

where b and c are equal to –pf/Qc and ln(S(f)), respectively. Because the source factor can be treated as a constant for a single frequency, according to Eq. (6), the slope of the linear equation between ln[A(f,t)t] and t yields the Q value for a specific frequency and lapse time window. The coda wave amplitude measurement starts at twice the travel time of the S-waves (Fig. 3) [20]. The seismograms have been filtered at five different central frequencies of 1.5 (1–2 Hz), 3 (2–4 Hz), 6 (4–8 Hz), 12 (8–16 Hz) and 24 Hz (16–32 Hz) using a fourth-order Butterworth bandpass filter. Fig. 3 shows an example of recorded and its band-pass filtered seismograms. On the filtered seismograms, the root-mean square (rms) amplitudes of coda waves, A(f,t), in a time window of selected length with a sliding window along the coda and lapse time window length of 20, 30, 40, 50 and 60 s have been used to estimate Qc. Window lengths and increments used in this study, which work well for a variety of earthquakes, are listed in Table 1. Fig. 4 shows an example of unfiltered and filtered seismograms recorded at Bam station with local magnitude ML 4.3 on 2004/01/ 20. The slope of least-squares straight line, fitted between ln[A(f,t)t] and lapse time provides the Qc value for each central frequency using Eq. (6).

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The Q–f relation can be constructed by determining the Q values for different frequencies in the form of

Table 1 Control parameters for moving window FFT. Center frequency (Hz)

Window length(s)

Increment(s)

Q ðf Þ ¼ Qo f n

1.5 3 6–24

10.24 5.12 2.56

4 2 1

where Qo is the value of Q at 1 Hz and n a numerical constant [19]. For the Bam region, the average frequency-dependent relationship estimated is Qc ¼ (7975)f (1.01 7 0.04) (Tables 2 and 3) Fig. 5.

30000 Filtered at 1.5 HZ

ð7Þ

3.6

Qc = 88±7

2.4

0

1.2 -30000 20000

0 4 Qc = 169±21

Filtered at 3.0 HZ 0

3.2

-20000

2.4 4

20000 Filtered at 6.0 HZ

Qc = 390±32

3

0

2 1

-20000 20000

0 4

Filtered at 8.0 HZ

Qc = 660±56

3

0

2 1

-20000

0

20000

4

Filtered at 12.0 HZ

Qc = 885±74

3

0

2 -20000

1

4000

0

Ln (A (f, t)*t)

3 Filtered at 24.0 HZ

Qc = 1174±115 2 1 0

-4000

49:05

49:15 49:25 Time (Min:Sec)

49:35

40000 Amplitude (counts)

Origin Time

Unfiltered

20000 0 -20000 Coda Window -40000 03:48:20

03:49:00 03:49:40 Lapse Time (Hr:Min:Sec)

03:50:20

Fig. 4. Original (bottom) and band-pass-filtered coda waves observed for a local earthquake recorded at Bam region on 2004/01/20 at 03:48:19 with ML 4.3 (velocity seismogram). The coda window length used for the Qc estimation is indicated by arrows (left). Corrected and smoothed logarithmic coda amplitudes for the coda window are computed using the RMS technique. The straight line is fitted in a least-square sense. The estimated Qc value for each frequency component is also shown (right).

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6. Qp and Qd estimation In this study, Qp and Qd (P and S-waves) in the crust of the Bam, East-Central Iran, are estimated by applying the extended coda normalization method [21]. The coda normalization method is based on the empirical observation that the coda spectral amplitude at lapse times greater than roughly twice the S-wave travel time is proportional to the source spectral amplitude of the S-waves at distances of less than 100 km. This implies that the coda spectral amplitude is independent of the hypocentral distance and that site and source terms that are common in direct waves and coda can be removed by the coda normalization method [11]. Yoshimoto et al. [21] extended this method to P waves by assuming that the ratio of P- to S-wave source spectra is constant for a small magnitude range, from 2.5 to 4.5. Since our data are mainly distributed in the limited range from 2.5 to 4.5, we also used the extended coda normalization method in this study. In addition, the source radiation effect was assumed to be

Table 2 The estimated Qd, Qc, Qs and Qi values with standard deviations over frequency range 1.5–24 Hz for different lapse time windows. Center frequency (Hz)

Qd

N

Qc

N

Qs

Qi

20 s lapse time window 1.5 89 7 6 45 105 7 12 3 171 7 40 59 211 7 22 6 364 7 48 76 425 7 36 12 709 7 97 81 856 7 78 24 1450 7 74 69 1724 7 115

91 2947 14 127 725 95 4687 63 269 734 96 1267 7 94 510 762 88 21107 121 1067 7173 92 46107 212 2115 7153

30 s lapse time window 1.5 89 7 6 45 119 7 11 3 171 7 40 59 239 7 16 6 364 7 48 76 481 7 20 12 709 7 97 81 968 7 53 24 1450 7 74 69 1950 7 70

93 2057 79 156 770 92 3647 67 321 798 94 8617 106 630 7174 93 1569 7 130 1293 7134 94 3298 7 186 2587 7186

40 s lapse time window 1.5 89 7 6 45 131 7 15 102 1877 67 169 727 3 171 7 40 59 260 7 26 99 3507 98 334 7132 6 364 7 48 76 516 7 51 103 8077 135 662 7109 12 709 7 97 81 1025 7 89 98 1536 7 97 1316 7123 24 1450 7 74 69 2037 7 136 103 3268 7 248 2606 7278 50 s lapse time window 1.5 89 7 6 45 143 7 12 3 171 7 40 59 280 7 18 6 364 7 48 76 549 7 48 12 709 7 97 81 1076 7 98 24 1450 7 74 69 2108 7 115

98 1847 45 171 728 96 3547 144 330 740 99 7997 172 668 7135 96 1562 7 265 1297 7185 99 3345 7 277 25597253

60 s lapse time window 1.5 89 7 6 45 165 7 12 99 1807 31 175 711 3 171 7 40 59 317 7 27 98 3557 34 329 780 6 364 7 48 76 607 7 56 101 7857 135 678 795 12 709 7 97 81 1165 7 104 97 1567 7 149 1294 7153 24 1450 7 74 69 2235 7 139 100 3362 7 174 2549 7207

independent of direction because the events were distributed directionally in a wide range around stations (Fig. 2). From the aforementioned coda normalization method, Qp and Qd can be obtained from the seismogram of earthquakes observed at different hypocentral distances by using the following equations:   AP ðf ,rÞr pf ln ¼ r þconstðf Þ ð8Þ cðf ,tc Þ Qp ðf ÞVP ln

  AS ðf ,rÞr pf ¼ r þconstðf Þ cðf ,tc Þ Qd ðf ÞVS

ð9Þ

where f is frequency and tc is a fixed lapse time from the origin time, r is the hypocentral distance, VP is the P-wave velocity (VP ¼ 6.5 km/s) and VS is the S-wave velocity (VS ¼3.2 km/s); AP(f, r) and AS(f, r) are the direct P- and S-wave maximum amplitudes, which are measured from U-D and SH-wave components of seismograms, respectively. The seismograms have been rotated to radial and transverse components and the coda spectral amplitude is derived from the same component of SH-waves for the coda normalization. S-wave analysis was based on the SH-waves because these are not affected by other seismic phases. C(f, tc) is the coda spectral amplitude. On the filtered seismograms, we measured the maximum peak-to-peak amplitude of direct P and S waves in a 5-s time window respectively starting from the onset of P and S waves. Half values of the peak-to-peak amplitudes represent AP(f, r) and AS(f, r), respectively. The spectral amplitude of the coda wave was assumed to be the rms of the amplitude of the seismic wave within the 5-s time window after the 60-s lapse time (tc ¼60 s). The lapse-time window is taken as twice that of the S-wave traveltime [3,9,20]. Coda waves of lapse time up to 60 s sample a volume having a radius of about 100 km. An example of recorded and its band-pass filtered seismogram are shown in Fig. 3. An N–S component broad-band seismogram recorded at BAM station and SH-component obtained are shown at the top. The horizontal bars represent the time windows for the P, S and Coda waves. Five band-pass filtered seismograms for central frequencies at 1.5, 3, 6, 12 and 24 Hz are displayed below. Applying the least-squares method to the values of the left-hand side of Eqs. (8) and (9) against the hypocentral distance for many earthquakes, we can estimate Qp and Qd from linear regression lines. In Fig. 6, we have displayed plots of the left-hand side of Eqs. (8) and (9) against hypocentral distance for P (crosses) and S-waves (circles), respectively.

7. Results The values of Qc, Qp, Qd, Qi and Qs show a dependence on the frequency range of 1.5–24 Hz in the region. The average frequency relationship of Qc is Qc ¼(7975)f (1.01 7 0.04). The Qc estimates, vary from 119 711 at 1.5 Hz to 1950770 at 24 Hz (Tables 2 and 3).

Table 3 Empirical relationship of Qc, Qs and Qi at each lapse time window length. Lapse time window(s)

Empirical relationship Qs

20 30 40 50 60

Qi (1.01 7 0.06)

Qs ¼(181 78)f Qs ¼(131 74)f (1.01 7 0.04) Qs ¼(119 76)f (1.04 7 0.05) Qs ¼(117 75)f (1.05 7 0.09) Qs ¼(115 74)f (1.06 7 0.07)

Depth (km)

3300 7300 13,000 20,000 30,000

30 50 65 80 100

Qc (1.0 7 0.06)

Qi ¼(85 79)f Qi ¼(104 76)f (1.01 7 0.05) Qi ¼(113 76)f (0.98 7 0.05) Qi ¼(115 77)f (0.97 7 0.03) Qi ¼(117 72)f (0.96 7 0.04)

The area coverage is computed using the formulation given by Pulli [23].

Coverage of area (km2)

Qc ¼ (707 6)f (1.01 7 0.05) Qc ¼ (797 5)f (1.01 7 0.04) Qc ¼ (887 4)f (0.99 7 0.04) Qc ¼ (977 7)f (0.97 7 0.06) Qc ¼ (1137 6)f (0.94 7 0.08)

M. Mahood, H. Hamzehloo / Soil Dynamics and Earthquake Engineering 31 (2011) 1338–1346

120

1.4 Qo

1.2 1.1

80

n

Q0

1.3

n

100

1 0.9

60

0.8 40

0.7 20

0

40 Lapse Time (S)

60

20 s window 30 s window 40 s window 50 s window 60 s window

2000

Qc 1000

500

0 5

Qc ¼(7076)f (1.017 0.05) at 20 s to Qc ¼(11376)f (0.94 7 0.08) at 60 s lapse window time length, respectively (Table 3). The values of Qp and Qd increase with increasing frequency from about (5278) and (8976) at 1.5 Hz to (935787) and (1450774) at 24 Hz, respectively (Table 2). By fitting power-law frequency dependence to the estimated values, we obtained Qp ¼(3676)f (1.03 7 0.06) and Qd ¼(5978)f (1.00 7 0.03) in the crust of the Bam, East-Central Iran. The estimated values of Qi and Qs vary from 156770 and 205779 at 1.5 Hz to 2587 7186 and 32987186 at 24 Hz, respectively. The Q–f relation varies from Qi ¼(8579) f (1.0 7 0.06) and Qs ¼(18178) f (1.01 7 0.06) at 20 s to Qi ¼(11772) f (0.96 7 0.04) and Qs ¼ (11574) f (1.06 7 0.07) at 60 s lapse window time length, respectively (Table 3). The size of the errors (SD) for each Q estimate for a given frequency and lapse time is also shown in Tables 2 and 3, where SD is the standard deviation for average Q value obtained from individual Q estimate at a given frequency and lapse time for all events and stations combination.

8. Discussion

1500

0

10 15 Frequency (Hz)

20

25

Not only can scattering be a major cause of attenuation of direct waves, the relative importance of intrinsic absorption and scattering due to heterogeneity also determines a gross feature of a seismogram [3]. Various observations in different regions of the world have indicated a striking difference in the rate of amplitude decay between tectonically active and stable regions. The scale of heterogeneities that are due to irregular subsurface geometry, velocity perturbations caused by changes in rock type, cracks and faults, play an important role to control the attenuation of the medium. Pulli [23] has shown that the scatters responsible for the generation of coda waves are generally assumed to be distributed over the surface area of an ellipsoid which can be calculated using the following formula: x2

2000

2

1.5 Hz 3.0 Hz 6.0 Hz 8.0 Hz 12 Hz 16 Hz

ðvt=2Þ

Qc

1500

1000

500

0 20

1343

40 Lapse Time(s)

60

Fig. 5. (a) Comparison of average Q0 and n with lapse time. (b) A comparison of mean values of Qc as a function of frequency obtained at five lapse time windows. Power law fitted for each window is also shown in the figure. (c) Plot of average values of Qc with lapse time at different central frequencies.

Lapse time dependence of Qc has also been studied for the region, with the coda waves analyzed at five lapse time windows from 20 to 60 s duration. The estimated average Q–f relation of Qc varies from

þ

y2 ðvt=2Þ2 R2 =4

¼1

ð10Þ

where, R, n and t are the source receiver distance, average velocity of S-waves and average lapse time, respectively. In this study source and receiver are assumed to be coincident. In the coda Qc method of Aki and Chouet [5], R equals to zero and Eq. (10) represents circular area of radius vt/2. The coda window length should be large enough to get stable results. Havskov and Ottemoller [22] suggest a minimum value of 20 s. There is no limit on the maximum window length. However, for our data stable results and S/NZ3 could be obtained for very few records for coda window length 460 s, hence it was set to be the upper limit for window length. We find that five window lengths, that is, 20, 30, 40, 50 and 60 s are sufficient to show the variation of Qc values with lapse time window length. In this study, S-wave velocity of 3.2 km/s is used and the coda estimation suggests approximately circular area of 3300, 7300, 13,000, 20,000 and 30,000 km2 with radii of 30, 50, 65, 80 and 100 km for the coda wave generation, respectively (Table 3). For events located by Bam network, we obtained that Qo ¼7975 and n ¼1.0170.04 for the 30-s lapse time window. The n parameter represents the level of medium heterogeneity and tectonic activity of a region. Observations of the exponent n, describing the frequency dependence for Qc in several regions of the world, seem to indicate that higher values of n are consistent with frequency-dependent exponents found in tectonically active areas [11,19]. All studies have been applied to observe the seismic activity and polarize the active regions from the stable regions.

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1 - 2 Hz

2 - 4 Hz 10 ln [rUP, S-Direct/US-Coda]

ln [rUP, S-Direct/US-Coda]

10

8

6

4

8

6

4

2

2 20

40 60 80 100 Hypocentral Distance r (km)

20

120

40 80 60 100 Hypocentral Distance r (km)

8 - 16 Hz

4 - 8 Hz 10 ln [rUP, S-Direct/US-Coda]

10 ln [rUP, S-Direct/US-Coda]

120

8

6

4

2

8

6

4

2 20

100 40 60 80 Hypocentral Distance r (km)

120

20

80 100 40 60 Hypocentral Distance r (km)

120

16 - 32 Hz

ln [rUP, S-Direct/US-Coda]

10

8

6

4

2 40 80 Hypocentral Distance r (km)

120

Fig. 6. Plots of the left-hand side of Eqs. (8) and (9) against hypocentral distance for P (crosses) and S (circles) waves, respectively. The regression lines from the least-squares estimate are expressed by two solid lines; the upper and lower lines are for S- and P-wave amplitude, respectively.

Our n values falls within the range of values obtained for tectonically active regions. We find that although n values for tectonically active regions are close to 1, for stable regions the value varies widely [23,24]. Similarly, a correlation between Qo and n seems to be existing worldwide: n appears to decrease as Qo increases. This tendency was observed by Xie and Mitchell [25] for Lg coda-Q in continental Africa, whereas Nuttli [26] suggested that smaller values of n are associated with larger values of Qo, as is generally true throughout the world. The variation of Qo and n are shown with increasing lapse time from 20 to 60 s in Fig. 5a. It

is observed that the exponent n decrease and Qo increase as lapse time increases. As shown in Fig. 5b the trend of average Qo with lapse time shows that its value increases with frequency. Fig. 5c shows an increase in Qc with increasing lapse time window. Most studies show this tendency. This effect can be caused by several factors but likely indicates an increase in Qc with depth, as a greater volume of less complex upper mantle material is included in the sampling volume [23,27–29]. Any increase of Q with depth or with distance from the source to receiver would cause the increasing of coda-Q with lapse time, since at later lapse times,

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This Study Qc = 79 f 1.01 Parkfield Qc = 79 f 0.74 Zagros Qc = 99 f 0.84 Garhwal Himalaya Qc = 126 f 0.90 NW Hymalaya Qc = 158 f 1.05 Koyna Qc = 169 f 0.77 New England Qc = 460 f 0.4 S. India Qc = 460 f 0.83 N. Iberia Qc = 600 f 0.45 NE U.S. Qc = 900 f 0.35

Qc = (79±5) f (1.01±0.04) Qd = (59±8) f (1.00±0.03)

10000

Qp = (36±6) f (1.03±0.06) Qs = (131±4) f (1.01±0.04) Qi = (104±6) f (1.01±0.05)

Qc

Log Q

1000

1345

1000

100

1

10 Log f

Fig. 7. Average values of Qc, Qd, Qp, Qs and Qi at different frequencies for the Bam region along with the least-squares best-fitted lines.

100 1

10 Frequency (Hz)

Fig. 8. Comparison of coda-Qc of Bam region with reported coda-Q of other regions of the world.

the coda-Q is an estimate of the average Q over a larger volume [27,28,30]. To compute the variation of intrinsic and scattering attenuation parameters with depth from coda waves, we analyzed local earthquake waveforms at different lapse time windows. The Qc, Qd, Qs and Qi values increase with increasing frequency (Table 2 and Fig. 7). The estimated values of Qi and Qs vary from 156770 and 205779 at 1.5 Hz to 2587 7186 and 3298 7186 at 24 Hz, respectively. The Q–f relation varies from Qi ¼(8579)f (1.0 7 0.06) and Qs ¼(18178)f (1.01 7 0.06) at 20 s to Qi ¼(11772)f (0.96 7 0.04) and Qs ¼(115 74)f (1.06 7 0.07) at 60 s lapse window time length, respectively (Table 3). A comparison between Qi and Qs shows that intrinsic absorption is predominant over scattering. Fig. 7 shows that the Qc estimates lie closer to Qi. This is in agreement with the theoretical as well as laboratory measurements. A comparison of Q-values obtained using coda waves and using direct waves in the present study shows that Qc is higher than that of Qd (Fig. 7). This supports the Zeng et al. [31] model that predicts that the effects of Qi and Qs combine in a manner that Qc should be more than Qd. Tables 2 and 3 show that the Qc and Qi values at each frequency increase with increasing lapse time window duration. On the other hand Qs values at a given frequency decrease with increasing lapse time window duration. This trend is opposite of that for Qc and Qi. This means that both coda and intrinsic attenuation decrease with increasing lapse time. Roecker et al. [27], Kvamme and Havskov [32], Ibanez et al. [30], Woodgold [28], Akinci et al. [33] and Del Pezzo et al. [6], Mukhopadhyay and Tyagi [9] are of the opinion that larger lapse time windows show the characteristics of deeper zones. This would imply that attenuation due to dissipation would decrease with increasing depth. This may indicate that as depth increases the rocks becomes more compact initially due to increase in pressure. As a consequence relative motion, consequent intergrain friction decreases with increasing depth, causing decrease in intrinsic attenuation. It would be more pertinent a comparison with other tectonically active regions in order to appreciate whether peculiarities are present in the study area (Fig. 8). Our results are in the range of those estimated for Qp, Qd and Qc of the other seismically active

region. Several studies generally show low value of Q0 (less than 200) for tectonic and seismic active regions such as: Washington State (Qc ¼63f 0.97, [34]), Parkfield (Qc ¼79f 0.74, [35]), Zagros Iran (Qc ¼ 99f 0.84, [36]), S. Iberia (Qc ¼100f 0.7, [37]), Garhwal Himalaya (Qc ¼ 126f 0.9, [38]), NW Himalayan region (Qc ¼158f 1.05, [39]), Koyna (Qc ¼169f 0.77, [40]). The larger values of Qo of more than 200 have been observed for inactive or stable regions such as New England (Qc ¼460f 0.4, [41]), South India (Qc ¼460f 0.83, [42]), North Iberia (Qc ¼600f 0.45, [37]), NE U.S. (Qc ¼900f 0.35, [19]) and Central U.S. (Qc ¼1000f 0.2, [19]). However, use of a more realistic earth model, where crustal velocity structure as well as intrinsic and scattering attenuation varying with depth, could be more appropriate than a homogeneous earth model for modeling attenuation in the crust as suggested by Margerin et al. [39], Hoshiba et al. [38] and several other workers. The results from this work provide an attenuation function that can be used in a variety of scientific and engineering applications including local magnitude estimates and earthquake hazard assessment in populated areas, understanding the physical laws related to the propagation of the elastic energy of an earthquake through the lithosphere. Our results indicate that the crust in the study area is highly heterogeneous and tectonically active.

9. Conclusion The present study is an attempt to understand the attenuation mechanism in the Bam region, East-Central Iran. The values of Qc, Qp, Qd (coda, P and S-waves), Qi and Qs show a dependence on the frequency range of 1.5–24 Hz in the region. – Based on the analysis, the frequency-dependent relationships are estimated as: Qc ¼(7975)f (1.01 7 0.04), Qp ¼(3676)f (1.03 7 0.06), Qd ¼(5978) f (1.00 7 0.03), Qs ¼(13174)f (1.017 0.04) and Qi ¼(10476)f (1.017 0.05).

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– We observed that Qc for a given frequency increases with increasing lapse time. The increase in Qc with lapse time is interpreted as a manifestation of decrease in attenuation with depth. This means for the study area attenuation decreases with depth. – A comparison between Qi and Qs shows that intrinsic absorption is predominant over scattering. – Measurements of Q at several areas in the world show high Q values for seismically stable regions, while seismically active regions show low Q values. In the study region, the average Q values estimated and their frequency dependent relationships correlate well with highly heterogeneous and highly tectonically active regions.

Acknowledgment The authors would like to express their thanks to reviewers for carefully commenting on the manuscript. The authors are thankful to International Institute of Earthquake Engineering and seismology (IIEES) and Building and Housing Research Center (BHRC) for supporting this research work. We are also thankful to Dr. M. Tatar for providing local seismograms data used in this study. References [1] Hoshiba M. Separation of scattering attenuation and intrinsic absorption in Japan using the multiple lapse timewindow analysis of full seismogram envelope. J Geophys Res 1993;98:15809–24. [2] Sato H, Fehler M. Seismic wave propagation and scattering in the heterogeneous earth. New York: Springer; 1998 (pp 1–308). [3] Aki K. Attenuation of shear waves in the lithosphere for frequencies from 0.05 to 25 Hz. Phys Earth Planet Int 1980;21:50–60. [4] Aki K. Analysis of the seismic coda of local earthquakes as scattered waves. J Geophys Res 1969;74:615–31. [5] Aki K, Chouet B. Origin of coda wa6es: source, attenuation and scattering effects. J Geophys Res 1975;80:3322–42. [6] Del Pezzo E, Ibanez J, Morales J, Akinci A, Maresca R. Measurements of intrinsic and scattering seismic attenuation in the crust. Bull Seism Soc Am 1995;85:1373–80. [7] Bianco F, Del Pezzo L, Malagnini Di Luccio F, Kinci A. Separation of depthdependence intrinsic and scattering seismic attenuation in the northeastern sector of the Italian Peninsula. Geophys J Int 2005;150:10–22. [8] Sharma B, Gupta K, Kameswari D, Kumar D, Teotia S, Rastogi K. Attenuation of high-frequency seismic waves in Kachchh Region, Gujarat. India Bull Seismol Soc Am 2008;98:2325–40. [9] Mukhopadhyay S, Tyagi C. Variation of intrinsic and scattering attenuation with depth in NW Himalayas. Geophys J Int 2008;172:1055–65. [10] Tsujiura M. Spectral analysis of coda waves from local earthquake. Bull Earthquake Res Inst 1978;53:1–48. [11] Aki K. Attenuation of shear-waves in the lithosphere for frequencies from 0.05 to 25 Hz. Phys Earth Planet Int 1980;21:50–60. [12] Frankel A, Wennerberg L. Energy flux model of seismic coda: separation of scattering and intrinsic attenuation. Bull Seism Soc Am 1987;77:1223–51. [13] Wu RS. Multiple scattering and energy transfer of seismic waves, separation of scattering effect from intrinsic attenuation, I. theoretical modeling. Geophys J R Astron Soc 1985;82:57–80. [14] Walker R, Jackson J. Offset and evolution of the Gowk fault S.E. Iran: a major intra- continental strike-slip system. J Struct Geol 2002;24:1677–98.

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