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Quality factor of seismic coda waves in garhwal
1. International Journal of Civil Engineering and OF CIVIL ENGINEERING AND INTERNATIONAL JOURNAL Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME TECHNOLOGY (IJCIET)ISSN 0976 – 6308 (Print)ISSN 0976 – 6316(Online)Volume 3, Issue 2, July- December (2012), pp. 279-291 IJCIET© IAEME: www.iaeme.com/ijciet.aspJournal Impact Factor (2012): 3.1861 (Calculated by GISI) IAEMEwww.jifactor.com QUALITY FACTOR OF SEISMIC CODA WAVES IN GARHWAL HIMALAYAS Priyamvada Singh, J.N. Tripathi Department of Earth and Planetary Sciences, University of Allahabad, India Email: firstname.lastname@example.org ABSTRACT Seismic wave propagating through the earth experiences some reduction in the energy content. This decay in the wave energy is known as the seismic wave attenuation. The study of attenuation characteristics of these waves shed light on the heterogeneous nature of the Earth. Usually, seismic wave attenuation for local earthquakes is determined from the analysis of coda waves. Digital seismogram data of 75 earthquakes that occurred in Garhwal Himalaya region during 2004 to 2006 and recorded at different stations have been analyzed to study the seismic coda wave attenuation characteristic in this region. In the present study, 90 seismic observations from local earthquake events with hypocentral distance less than 250 km and magnitude range between 1.0 and 5.0 is used to study coda Q , i.e. Qc , using the single isotropic scattering model. QC Values are estimated at 10 central frequencies 1.5, 3, 5, 7, 9, 12, 16, 20, 24 and 28 Hz using a starting lapse-time LT=50 s and four coda window-lengths , WL= 10, 20, 30, 40 s . In the considered frequency range, QC fit the frequency dependent power-law QC = Q0 f n . The frequency dependent power-law for 50 sec lapse time with 10 sec coda window length is QC = 61.8 f 0.992 and for 50 sec lapse time with 40 sec coda window length is QC = 161.1 f 0.998 . The Q0 ( QC at 1 Hz) estimates vary from about 61.8 for a 50 sec lapse time and 10 sec window length, to about 161.1 for a 50 sec lapse time and 40 sec window length combination. The exponent of the frequency dependence law n ranges from 1.016 to 0.967, which correlates well with the values obtained in other seismically and tectonically active and heterogeneous regions of the world. It is observed for the study region that QC values increases both with respect to window length and frequency. The low QC values or high attenuation at lower frequencies and high QC values 279
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEMEor low attenuation at higher frequency may indicate that the heterogeneity decreases withincreasing depth, in the study region.Keywords: Attenuation, Coda Q, Single backscattering model, Lapse time window, GarhwalHimalayaI. INTRODUCTIONThe attenuation of seismic wave is one of the basic physical parameter which is closely related tothe seismicity and regional tectonic activity of a particular area. This is also important forseismic hazard measurement. In this work, the seismic attenuation in the Garhwal Himalayas isstudied using local earthquakes. The amplitude of seismic waves decreases with increasingdistance from the earthquake. This reduction of the energy content cannot be explained bygeometrical spreading of the wave only. This decay in the wave energy is known as the seismicwave attenuation. Seismic wave attenuate because the earth is not a perfect elastic andhomogeneous. Usually, seismic wave attenuation for local earthquakes is determined from theanalysis of direct body waves, surface waves or coda waves. The dimensionless parameter, Q , isstudied in the present work which is defined as a measure of the rate of decay of the coda waveswithin a specified frequency band. Aki (1969) referred Coda as the tail part of seismograms oflocal earthquakes. Aki and Chouet (1975) suggested that the S Coda of local earthquakes issuperposition of incoherent backscattered S-wave and surface waves generated from numerousheterogeneity distributed randomly in the Earth’s crust and upper mantle. The great variety ofpaths traveled by these waves provides information concerning the average attenuationproperties of the medium instead of just the characteristics of a particular path (Aki and Chouet1975).The QC , quality factor of Coda wave has been estimated for different parts of the world (Aki andChouet 1975; Sato 1977; Ugalde et al., 2002; Tripathi and Ugalde, 2004, Ugalde et al., 2007,Pezzo et al., 2011,). Coda wave characteristics have also been estimated for different parts of theHimalayas (Gupta et al., 1995; Kumar et al., 2005; Hazarika et al., 2009; Sharma et al., 2009;Mukhopadhyaya et al., 2010; Padhy et al., 2010; Tripathi et al., 2012).In the present work the coda attenuation properties have been estimated in the Garhwal region ofHimalayas using local earthquakes. The frequency dependence of coda wave is also estimated.II. STUDY AREAThe Himalayas is the consequence of the collision of the Indian plate with the plates of centralAsia during mid to late Eocene. The Outer Himalayas, Lower Himalayas and the HigherHimalayas are the three major terrains identified in the Garhwal Himalayas [Valdiya, (1980)]. 280
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEMEThe major thrust fault striking parallel to the Himalayan arc, from north to south are the MainCentral Thrust (MCT), the Main Boundary Thrust (MBT) and the Himalayan Frontal Thrust(HFT) (Figure 1).The high grade metamorphic units of Higher Himalayas, situated north ofMCT, are considered to be inactive generally, due to no signs of break of Quaternary deposits(Ni and Barazangi, 1984; Brunel 1986). The outer Himalayas comprises of Tertiary rocks that isunderlain by the marine water to brackish origin subathu formation. This is followed upward bysiwalik group. The siwalik group is overlain by Quaternary gravel and sand. The LowerHimalayas are mainly made up of Precambrian sedimentary rocks with some outcrops ofCambrian Tal formation. The Higher Himalayas are made up of high grade metamorphic rockslike amphibolites to granulites grade metasedimentary rocks, auger gneisses and intrusiveleucogranite. In the Garhwal-Kumaon Himalayas region these groups of rocks are known as thevaikrita group (Srivastav and Mitra 1994)Figure 1: (a) Simplified map of the Himalya. (b) Map of the study area modified after Valdiya(1980). 281
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEMEIII. METHOD AND DATAThe single backscattering model of coda wave envelopes of Aki and Chouet (1975) considers thecoincidence of source and receiver. So, for the practical application of the model, we have toconsider lapse time t >2 t s , where t s is the S wave travel time (Rautian and Khalturin, 1978).Sato (1977) proposed the single isotropic scattering model for non coincident source andreceiver. Thus, we can analyse the coda window just after the S wave arrival. In this model, it isassumed that the elastic energy is radiated spherically, scatterers are distributed homogeneouslyand randomly, and the single scattering is isotropic in the media. Thus, the coda energy density E S at frequency f can be expressed as W ( f ) g 0 ( f ) ES ( f | r , t ) = 0 4πr 2 [ −1 K (α ) exp − 2QC πft ] (1) Where t is the lapse time measured from the origin time of the earthquake, t s is the S-wavetravel time, r is the hypocentral distance, W0 is the total energy radiated from the source, g 0 isthe total scattering coefficient, and 1 α +1K (α ) = ln , (α > 1); and α = t / t s . (2) α α −1The energy density is considered to be proportional to the mean square amplitudes of coda wavesand taking natural logarithms of Eq.1 and reshuffling the terms, we get A ( f | r, t ) πf ln obs = ln C ( f ) − Q t (3) k (r , α ) C where Aobs ( f | r , t ) represents the observed root mean square (rms) amplitude of the narrow bandpass filtered waveforms with central frequency f ; k(r , α ) = (1 / r )K (α ) 0.5 and C ( f ) is a constant.Thus the QC can be easily obtained from the slope b of the least square fit straight line to themeasured ln[ Aobs ( f | r , t ) / k (r , α )] versus t for a given central frequency, using the relation nQC = πf / b . The frequency dependence law, QC = Q0 f is also fitted to the QC data fordifferent lapse time and window length, where Q0 is the value of QC at 1 Hz and n is frequencydependent parameter (Table 3).The digital waveform seismograms of 75 events used for coda attenuation in the present studywere recorded at 20 stations of Garhwal Himalayas during 2004 to 2006 (Figure 2, Table 1). TheCMG 40T1 triaxial broadband seismometers were used for the digital data collection. The data is 282
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEMEacquired in continuous mode at 100 samples per second for three components at the stations.SEISAN (version 8.1) software package (Havskov and ottemoller, 2005) was used to pick P andS wave arrival times of each earthquake recorded at the different seismic stations. Thehypocentral parameters, viz, origin time, latitude, longitude and focal depth of these events werealso computed using the SEISAN software. Most of the events are within the crust and localmagnitude ranges from 1.0 to 5.0. First of all we preformed a visual inspection of more than 450seismograms, 90 waveforms with hypocentral distances less than 250 km have been finallyprocessed for the present work.IV. DATA ANALYSIS AND RESULTSFirst of all the seismograms were band pass filtered for ten frequency bands, 1.5 ± 0.5 Hz, 3 ± 1Hz, 5 ± 1 Hz, 7 ± 1 Hz, 9 ± 1 Hz, 12 ± 1 Hz, 16 ± 1 Hz, 20 ± 2 Hz, 24 ± 2 Hz, and 28 ± 2 Hz(Table 2), using eight-pole Butterworth filters. As the sampling rate was 100 samples per second,the maximum frequency for which reliable result could be obtained was 50 Hz. Then, the rootmean squared amplitudes of the filtered seismograms were computed at an interval of 0.5 s withmoving time windows of length t ± 2s for the first frequency band and t ± 1s for the next ninefrequency bands. Then QC was estimated applying a least square regression technique to Eq.3for one starting lapse time window length LT = 50 s from the S-wave onset, having WindowLength WL=10, 20, 30 and 40s for ln[ Aobs ( f | r , t ) / k (r , α )] . The QC estimates were computedonly for the amplitudes greater than signal to noise ratios. The coda wave is analyzed only thevertical component, because it has been shown that the coda analysis is independent of thecomponent of the particle ground motion analyzed (Hoshiba, 1993). The estimated QC valuesretained for further analysis which were having correlation coefficients greater than 0.5. Stations Location 35.00 34.00 33.00 Latitute 32.00 Events 31.00 Stations 30.00 29.00 72.00 74.00 76.00 78.00 80.00 82.00 Longitude Figure 2: Station Locations (open circles) with events used in the Study. 283
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME Table 1: Station code and their location Station Longitude Latitude DEO 76.67 32.09 TZG 76.79 32.59 UDA 76.67 32.72 CHT 76.37 32.45 TSA 76.14 32.82 UNA 76.32 31.52 LGR 75.91 32.29 BNK 75.94 32.55 RJA 76.24 32.00 BRM 76.54 32.44 PAL 78.62 30.81 GRG 79.44 30.46 JKH 78.43 30.4 PRT 78.48 30.46 YOL 76.4 32.17 AMB 76.04 31.67 BEED 75.94 32.58 NEL 78.52 30.4 GYL 78.51 30.36 NAD 76.31 32.24The frequency dependent Coda Q relationship provides average attenuation characteristics ofthe medium. The average values of QC at different frequencies, one lapse time and four windowlengths obtained from the mean values for the whole study area are given in Table.3.Table.2: Central frequencies and frequency range as low and high cutoff. Low cutoff Central frequency High cutoff (HZ) (Hz) (Hz) 1 1.5 2 2 3 4 4 5 6 6 7 8 8 9 10 10 12 14 14 16 18 18 20 22 22 24 26 26 28 30 284
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEMETable 3: The average numerical values of QC at different frequencies, lapse time (LT=50)and coda window length (WL=10, 20, 30, and 40 s).LT WL Values of QC at different frequencies(s) (s) 1.5 Hz 3 Hz 5 Hz 7 Hz 9 Hz 12 Hz 16 Hz 20 Hz 24 Hz 28 Hz50 10 121.00 171.96 287.8 386.55 553.72 856.37 1249.76 1596.24 1700.58 1790.0450 20 179.10 294.54 511.71 732.39 1002.40 1553.47 1825.29 2091.45 2382.79 2611.6750 30 201.03 333.08 587.83 806.85 1059.86 1707.75 2228.78 2702.07 3153.7 3202.7950 40 279.23 500.61 863.62 1166.27 1487.98 2212.82 2718.69 3384.61 4523.86 5200.77For the study area it is observed that QC value increases both with respect to frequency andwindow length. It is observed that the QC increases with frequency. The average value of QC forthe study region varies from 121 at 1.5 Hz to 1790 at 28 Hz for lapse time 50s and windowlength 10s. When window length is 20, QC is 179 at 1.5Hz and 2611 at 28Hz. Higher values ofQC are obtained at 30 and 40s window lengths. This observation of frequency dependence ofQC is due to the degree of heterogeneity of a medium and level of tectonic activity in an area(Aki 1980). The low QC values or high attenuation at lower frequencies may indicate a highdegree of heterogeneity and decrease in rock strength at shallow parts. The high QC values orlow attenuation at higher frequencies may be related to the comparatively less hetrogeneousdeeper zones (Aki and Chouet, 1975).Gupta et al. (1995) obtained a frequency relation QC = 126 f 0.95 using records of seven microearthquake in the adjoining southwestern part of Garhwali Himalayas for 30s coda windowlength.Kumar et al., (2005) employed the time domain coda - decay method of a single - back –scattering model to calculate frequency dependent values of coda QC . A total of 36 localearthquake of magnitude range 2.4 - 4.8 have been used for QC estimation at central frequencies1.5, 3.6, 6.9, 9.0, 12.0 and 18.0 Hz through eight lapse time windows from 25 to 60s starting atdouble the time of the primary S-wave from the origin time. The estimated average frequencydependence quality factor gives the relation QC = 158 f 1.05 while the average QC values vary fromthe relation 210 at 1.5Hz to 2861 at 18Hz central frequencies. The observed coda quality factor isstrongly dependent on frequency, which indicate that the region is Seismic and tectonicallyactive with high heterogeneity.Paul et.al., (2003) estimated QC for Kumaun Himalayas using data from eight micro earthquakerecord by a five station array with epicentral distance range varying between 10 km to 80 km for30 sec window length and obtained a QC = (92 ± 4.73) f (1.07 ± 0.23) analyzing the SH wave formdata of 1988 Nepal - India border earthquake. 285
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME 10000 10000 Qc= 61.75f0.992 Qc= 107.2f0.967 1000 1000 Qc Qc 100 100 LT=50 LT=50 10 10 WT=10 WL=20 1 1 1 10 100 1 10 100 Frequency Frequency 10000 10000 Qc= 161.1f0.998 Qc= 113.5f1.016 1000 1000 Qc 100 Qc 100 LT=50 LT=50 10 10 WT=30 WL=40 1 1 1 10 100 1 10 100 Frequency FrequencyFigure 3: Frequency dependency power law for lapse time 50s and coda window length 10, 20, 30, 40,50 s.Hazarika et al., (2008) found that Q 0−1 is very high i.e. coda at 1Hz frequency attenuates veryfast. They also found that Q0 and n values are different at Arunachal Himalayas, Shilong massifand Indo- Burma ranges with the former two being characterized by lower attenuation comparedto the last one. 286
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEMEFor NW Himalayas Mukhopadhyay and Tyagi (2008) found that coda and intrinsic attenuationdecreases with depth, whereas scattering attenuation increases with depth. The mean values ofQC reveals a dependence on frequency varying from 292.9 at 1.5 Hz to 4880.1 at 18 Hz.In the Chamoli region of the Himalayas Mukhopadhayay et al., (2008) found that QC frequencyrelations for 10, 20, 30, 40, and 50s window lengths are (33 ± 2) f (1.17 ± 0.03) , ( 55 ± 6) f (1.76± 0.05 ) ,(78 ± 20) f ( 0.98± 0.08) , (93 ± 18) f (1.07 ± 0.08) , (122±20) f ( 0.98± 0.07 ) , respectively.Mukhopadhayay and Sharma (2010) analyzed the coda of local earthquakes to study theattenuation characteristics of the Garhwal - Kumaon Himalayas. It is observed that QC increaseswith frequency and also varies.Sharma et al., (2009) estimated quality factor for P-wave, S-wave and Coda- waves in Chamoliregion, and estimated frequency dependent relations for quality factors are QC = 30 f 1.21 , ( 0.82 ± 0.04 ) ( 0.71± 0.03 )Qα = (44 ± 1) f and Qα = (87 ± 3) f . 10000 1000 Present study Northwestern Himalayas Qc 100 Tripathi(2012) Kumaun Himalayas LT=50 Singh(2012) WL=30 10 Garhwal Himalayas Gupta(1995) Western HimalayaS Mukhopadhyay(2007) 1 0.1 1 10 100 Frequency Figure 4: Comparison of estimated QC with other studies of Himalayas. Makhopdhyaya and Tyagi (2007), analyzing the events from Northwestern Himalayashave shown that the region is highly heterogeneous and tectonically very active andheterogeneity decreases with depth in this area Q0 increases from 113 ± 7 to 243 ± 10 and ndecreases from 1.01 ± 0.05 to 0.86 ± 0.03 when lapse time increases from 30 sec to 70 sec.Singh et al., (2012) analyzed the local earthquakes in Kumaon Himalayas region to estimatelapse time dependence of coda waves and obtained that by increasing lapse time window from 287
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME20 to 50 s, Q0 increases from 64 to 230 while dependent parameter n decreases from 1.08 to0.81.Tripathi et al., (2012) estimated coda wave attenuation using the single isotropic scatteringmethod for frequency range 1-30 Hz for the Garhwal region for other data set. They used severalstarting lapse times and coda window lengths for the analysis to study the variation ofattenuation characteristics. Results show that the Q c−1 values are frequency dependent in the −nconsidered frequency range, and they fit the frequency power-law Qc−1 ( f ) = Q 0−1 f . The Q0estimates vary from about 50 for a 10 s lapse time and 10 s window lengths, to about 350 for a60 s lapse time and 60 s window length combinations. The exponent of the frequencydependence law n ranges from 1.2 to 0.7; however, it is greater than 0.8, in general, whichcorrelates well with the values of others in Himalaya region.The estimated coda attenuation values in the present study are comparable with that obtainedfrom other regions of the Himalayas, as shown in Figure 4.Table 4: Frequency dependent power law QC = Q0 f n . n LT WL QC = Q0 f 50 10 61.8 f 0.992 50 20 107.2 f 0.967 50 30 113.5 f 1.016 50 40 161.1 f 0.998 For study region, increase in QC with the window length is attributed to increase in QCwith depth, as longer the time window the larger will be the sampled area of the earth’s crustand mantle. This observation seems to indicate that there is a decrease in the level ofheterogeneities with depth in the Garhwal Himalayas. This would imply that attenuationdecreases with increasing depth.A strong correlation between the degree of frequency dependence , n value, and the level oftectonic activity was claimed (Aki 1980). This is also observed by others, in Himalayan region,that n value is higher for tectonically active regions compared to the tectonically stable regions(Kumar et al., 2005; Mukhopadhyaya et al., 2010; Hazarika et al., 2009; Sharma et al., 2009;Tripathi et al., 2012; Padhy et al., 2010;). For Garhwal Himalaya Gupta et al., (1995) estimatedQ0 as 126 and n as 0.9. Mukhopadhyay et al., (2010) estimated Q0 as 119 and n as 0.99. The 288
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEMEobtained values of n is close to 1 in the present study which indicate that the region is highlyhertogeneous and tectonically very active.V. CONCLUSIONIn the present study, the QC values have been estimated for Garhwal Himalayas region, using 90seismograms from 75 local earthquakes recorded digitally at 20 different stations and analyzedfor one lapse time (e.g. 50 s), four window lengths ( e. g. 10, 20, 30, and 40 s) and at 10frequency bands with the central frequency in the range of 1.5 Hz to 28 Hz.The estimated QC values for the lapse time 50 s vary from 121 to 279 at 1.5 Hz and from 1790to 5200 for 28 Hz where the coda window varies from 10 to 40 s. It is clear from the results(Table 3) that QC is a function of frequency in this region. The QC value increases as frequencyincreases. A frequency dependent relationship has also been obtained for the region (Table 4),which shows that there is a significant increase in Q0 values with increasing window length,while there is a nominal decrease in the degree of frequency dependence, n. This can also beinterpreted that the scattering effect in the region exhibits a decreasing trend with increasingdepth (Aki 1980). This may be due to decrease in the heterogeneities level of the medium. Thegeneral trend of the present coda attenuation study is similar to seismically and tectonicallyactive region (Figure 4).Attenuation parameter QC is an important factor for understanding the physical mechanism ofseismic wave attenuation in relation to the composition and physical condition of the Earth’sinterior and it is also an essential parameter for the quantitative prediction of strong groundmotion for the viewpoint of engineering seismology. Hence numerous studies of QC have beencarried out worldwide by using different methods and concentrate on seismically active zonesand densely populated area.REFERENCES Aki, K (1969), “Analysis of the seismic coda of local earthquakes as scattered waves”, J. Geophys. Res., Vol.74, pp. 615-631. Aki, K (1980), “Scattering and attenuation of shear waves in the lithosphere”, J. Geophys. Res., Vol. 85, pp. 6496-6504. Aki, K, and Chouet, B (1975) , “Origin of the coda waves: source, attenuation and scattering effects “, J. Geophys. Res., Vol. 80, pp. 3322-3342. Brunel, M., (1986) , “Ductile thrusting in the Himalayas: Shear sense criteria and stretching lineation”, Tectonics, Vol. 5, pp. 247-265. Chandrasekhar, A. R. and Das J. D.(1992) , “Analysis of strong motion accelerograms of Uttarkashi earthquake of October 20, 1991”, Bull. Indian Society of Earthquake Technology, Vol. 29, pp. 35-55 Fehler M., Sato H., (2003),” Coda “, Pure and Applied Geophysics, Vol. 130, pp. 349–364. 289
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