ISET Journal of Earthquake Technology, Paper No. 468, Vol. 43, No. 1-2, March-June 2006, pp Anand Joshi

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ISET Journal of Earthquake Technology, Paper No. 468, Vol. 43, No. 1-2, March-June 26, pp ANALYSIS OF STRONG MOTION DATA OF THE UTTARKASHI EARTHQUAKE OF 2TH OCTOBER 1991 AND THE CHAMOLI EARTHQUAKE
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ISET Journal of Earthquake Technology, Paper No. 468, Vol. 43, No. 1-2, March-June 26, pp ANALYSIS OF STRONG MOTION DATA OF THE UTTARKASHI EARTHQUAKE OF 2TH OCTOBER 1991 AND THE CHAMOLI EARTHQUAKE OF 28TH MARCH 1999 FOR DETERMINING THE Q VALUE AND SOURCE PARAMETERS Anand Joshi Department of Geophysics Kurukshetra University, Kurukshetra ABSTRACT Analysis is presented in this paper to fit the theoretical S-wave acceleration spectra conditioned by frequency-independent Q with the observed acceleration spectra. The estimate of error is given in the root-mean-square sense over all the frequencies. The data of two major earthquakes in the Garhwal Himalayas, namely the 1991 Uttarkashi Earthquake and the 1999 Chamoli Earthquake, has been used in the present study to obtain source parameters of these earthquakes and Q value in the source region. Independent estimates of Q at various stations give its average value as 267±87. The stress drop for the Uttarkashi and the Chamoli earthquakes is computed as 77 and 29 bars, respectively, from the near-field acceleration spectra of BHAT and GOPE stations. This agrees with the other observed values of stress drop in the Himalayas. KEYWORDS: Source Spectrum, Inversion, Q, Attenuation INTRODUCTION Acceleration spectrum is one of the most direct and common functions used to describe the frequency content of strong ground earthquake shaking (Hudson, 1962). An acceleration spectrum contains valuable information regarding the source and medium characteristics. The source spectrum of an earthquake can 2 be approximated by the omega-square model (Brune, 197), which has ω decay of high frequencies above the corner frequency. The source acceleration spectrum can be estimated from an acceleration record after correcting it with diminution function, which accounts for the geometrical spreading and anelastic attenuation. The anelastic attenuation of seismic waves is characterized by a dimensionless quantity called quality factor Q (Knopoff, 1964). Until today very few studies have been carried out to understand the attenuation characteristics of the Himalayan crust. Examples include the work by Gupta et al. (1995) and Mandal et al. (21). Their work is based on the microtremor and aftershock data and thus contains information on the shallow crust. An analysis scheme for obtaining source parameters and quality factor Q using the least-square inversion technique has been presented in this paper. The work presented here is based on the technique of Fletcher (1995) that uses nonlinear least-square algorithm and Newton s method. In this paper the Brune s source model (Brune, 197) is used together with the propagation filter. This study uses the strong motion data of the Uttarkashi ( M s = 7.) and the Chamoli ( M s = 6.6) earthquakes recorded by strong motion array maintained by the Department of Earthquake Engineering, Indian Institute of Technology Roorkee, India. The epicenters of these two earthquakes were close to each other and were in the same tectonic environment. The main objectives of this paper are: (i) to compute the source parameters of these two Himalayan earthquakes by using the strong motion data, and (ii) to compute the mid-crustal Q value in the Garhwal Himalayas. INVERSION PROCEDURE The acceleration spectrum of shear waves at distance R due to an earthquake of seismic moment M can be described by (e.g., Boore, 1983; Atkinson and Boore, 1998): o 12 Analysis of Strong Motion Data of the Uttarkashi Earthquake of 2th October 1991 and the Chamoli Earthquake of 28th March 1999 for Determining the Q Value and Source Parameters A( f ) = CM o S( f ) D( f ) Rs ( f ) (1) where C is a constant for a particular station; filter S ( f ) represents the source acceleration spectrum; R s ( f ) denotes the site amplification factor; and D ( f ) denotes the frequency-dependent diminution function (e.g., Boore and Atkinson, 1987): π fr / Qβ e P( f, f ) D( f) = m (2) R π fr / Qβ In the above equation, P ( f, f m ) is a high-cut filter, and e R is a propagation filter. The term f m in the high-cut filter may be interpreted as attenuation near the recording site (Hanks, 1982), but for most recorded accelerograms, selection of f m is governed by the signal-to-noise ratio at high frequencies and is usually set as 25 Hz (Trifunac and Lee, 1973). In the present work, f m is kept as 25 Hz. The parameter t = R Qβ is defined as attenuation time. If Q is independent of frequency, the form of attenuation function will be as in the κ model (Trifunac, 1994; Anderson and Hough, 1984). By introducing t, Equation (1) is rewritten as πt f CS( f ) e Rs ( f ) A( f) = (3) R This expression serves as the basis for our analysis. In this expression, C is constant for any site for a given earthquake and for a double couple embedded in an elastic medium, while considering only S waves. It is given as (Boore, 1983) M orθφ FS PRTITN C = (4) 3 4πρβ where R θφ is the radiation pattern; M o is the seismic moment; FS is the amplification due to the free surface; PRTITN is the reduction factor that accounts for partitioning of energy into two horizontal components; and ρ and β are density, and the shear wave velocity, respectively. The filter S ( f ) defines the source spectrum of the earthquake under consideration. In the present work, we follow the spectrum defined by Brune (197) and therefore consider 2 (2πf ) S( f ) = (5) 2 1+ ( f / f c ) where f c is the corner frequency, and fc = 2.34β / 2πro with r o denoting the radius of the equivalent earthquake source. The exponential term in Equation (1) explains the decay of acceleration spectrum with distance due to the anelastic attenuation and scattering. As the data used in the present analysis scheme is from the short distances, and because both earthquakes are shallow earthquakes with most of the energy confined to the uppermost layer of the crust, the quality factor will be assumed to be constant and independent of frequency (Sriram and Khattri, 1997). Fletcher (1995) has also used a frequencyindependent Q value as it fitted well with his dataset (see also Boatwright et al., 1991; Atkinson and Mereu, 1992). There are some independent evidences in conjunction with the seismic exploration technique that indicate that Q can be approximated by a constant value in the shallow crust (Knopoff, 1964; Tullos and Reid, 1969; Trifunac, 1994; Hamilton, 1972, 1976; Ganley and Kanasewich, 198; Hauge, 1981; McDonal et al., 1958). As the Himalayan earthquakes have been occurring in the shallow crust, the assumption of frequency-independent Q will be made here. Equation (1) serves as the basic equation for our analysis. We linearize it by taking its natural logarithm: ln A( f) = ln C+ ln S( f) πt f ln R+ ln R ( f) + ε (6) where t and ε are unknown parameters. The parameter ε is introduced to account for the error in the computations. The term representing the source filter S ( f ) can be replaced with its expression in Equation (5). For a known value of f c, the two unknowns, Q and ε, can be obtained from inversion by s ISET Journal of Earthquake Technology, March-June minimizing in the least-square sense, whereas the value of f c is chosen in an iterative manner. The leastsquare inversion minimizes [ ( f ) S( f )] 2 χ = A s (7) where S ( f ) is the source acceleration spectrum as proposed by Brune (197). For the purpose of analysis, we rearrange Equation (6) in the following form: ln Mo π ft = ln A( f) ln C ln S( f) + ln R ln Rs( f) + ε (8) This leads to the following set of equations for frequencies f 1, f 2, f 3,..., f n, where n denotes the total number of samples in the acceleration record: ε π f t = DA( f ) ε π f t = DA f2 3 DA f3 ε π f t = ( ) (9)... ε π fnt = DA( fn) with DA( fi) = ln A( fi) ln C ln S( fi) + ln R (1) In matrix form Equations (9) can be written as 1 π f1 DA( f1) 1 π f 2 DA( f2) ε 1 π f 3 DA( f 3) t = (11) 1 π f n DA( fn) The above expression provides a basic statement of the following problem in which the model parameters and the data are in some way related to each other (Menke, 1984): Gm = d (12) Here, G represents the rectangular matrix, m the model matrix, and d the data matrix. Inversion of G gives the following model matrix: T 1 T m = ( G G) G d (13) This inversion is prone to problems if G T G is close to being singular, and for such a case, singular value decomposition (SVD) is used to solve for m (Press et al., 1993). Our formulation of SVD follows Lancose (1961). In this formulation the G matrix is decomposed into U p, V p and A p matrices as (Fletcher, 1995) where V p, U p and 1 G = V p A U p T p ( ) 2 A p have nonzero eigenvectors and eigenvalues. Our technique differs from that of Fletcher (1995) as acceleration spectrum has been used to obtain t from the independent estimates of f c and M o. The entire scheme of analysis for obtaining t is shown in Figure 1 in the form of a flow-chart. DATA-SET Under a project funded by the Department of Science and Technology, Government of India, the Department of Earthquake Engineering, Indian Institute of Technology Roorkee maintains a network of strong motion stations in the Uttaranchal region of the Himalayas. This network is equipped with three (14) 14 Analysis of Strong Motion Data of the Uttarkashi Earthquake of 2th October 1991 and the Chamoli Earthquake of 28th March 1999 for Determining the Q Value and Source Parameters component SMA-1 accelerographs. These are triggered accelerographs with recording on 7 mm film. The analogue records have been converted into digital records as described in Chandrasekaran and Das (1992). This array has recorded two recent earthquakes in this region, namely the Uttarkashi Earthquake of 2th October, 1991 and the Chamoli Earthquake of 28th March, The parameters of these two earthquakes are listed in Table 1. Fig. 1 Flow-chart of the entire process of inversion; the source model is that given by Brune (197) ISET Journal of Earthquake Technology, March-June Table 1: Parameters of the Uttarkashi Earthquake of 2th October, 1991 and the Chamoli Earthquake of 28th March, 1999 Hypocenter Size Source Fault Plane Solution Reference Uttarkashi Earthquake 21:23:14.3 (GMT) 3.78 N, E 1 km 21:23:21.6 (GMT) 3.22 N, E 15 km m b = 6.5, M s = 7. M = dyne-cm O M = 6.8 w M w = 6.8 M = dyne-cm Chamoli Earthquake m 19:5:11. (GMT) b = 6.4 M 3.51 N, 79.4 s = 6.6 E M O = dyne-cm 15 km O NP1: ϕ = 296, δ = 5, λ = 9 NP2: ϕ = 116, δ = 85, λ = 9 NP1: ϕ = 317, δ = 14, λ = 115 NP2: ϕ = 112, δ = 78, λ = 84 NP1: ϕ = 282, δ = 9, λ = 95 NP2: ϕ = 97, δ = 81, λ = 89 PDE, Monthly CMT (Harvard) USGS 19:5:18.1 (GMT) 3.38 N, E 15 km m b = 6.4, M s = 6.6 M w = 6.5 M = dyne-cm O NP1: ϕ = 28, δ = 7, λ = 75 NP2: ϕ = 115, δ = 83, λ = 92 CMT (Harvard) In the present work digital acceleration records processed from the analogue records have been used. The correction and filtering procedures used for processing (Lee and Trifunac, 1979) are described in Chandrasekaran and Das (1992). The data-sampling rate is.2 sec, and the data has been band-pass filtered by using Ormsby filter. The specifications of the Ormsby filter used for processing of the records of the Chamoli Earthquake are given in Table 2. The filter settings for the records of the Uttarkashi Earthquake are same for all stations, with the low- and high-filter settings as and Hz, respectively. Due to these filters, used in the processing of the acceleration data, it became difficult to determine the corner frequency. Further, as the triggered recording mode is used in the instruments, at many stations their records with unclear starting phase were seen. This made it difficult to clearly identify the S-phase of those records. Clear identification of the S-phase was possible at five stations for the Uttarkashi Earthquake and five for the Chamoli Earthquake. Stations lying within 6 km distance range are usually dominated by the direct shear waves. Beyond this distance, the post-critical reflection from Moho and a layer within the crust, and the L g phases contribute significantly to the strong ground motion (Sriram and Khattri, 1997). Due to this reason only four stations have been retained for the analysis. The other stations lie at distances greater than 6 km. The selected stations are located mostly along the trend of Main Central Thrust (MCT), and lie in the Lesser Himalayan sequence except BHAT that lies in the Higher Himalayan sequence (Figures 2 and 3). Table 2: Filtering Specifications of the Processed Accelerograms Recorded during the Chamoli Earthquake Station Epicentral Filtering Parameters of Distance (km) L-Component (Hz) T-Component (Hz) GOPE JOSH GHAN TEHR Both of the earthquakes considered in this study had shallow focus, occurring in the basement thrust (Jain and Chander, 1995; Joshi, 2, 21; Joshi et al., 21). The Uttarkashi Earthquake was recorded at thirteen stations while the Chamoli Earthquake was recorded at nine. Locations of all stations that had 16 Analysis of Strong Motion Data of the Uttarkashi Earthquake of 2th October 1991 and the Chamoli Earthquake of 28th March 1999 for Determining the Q Value and Source Parameters recorded these two earthquakes are shown in Figure 2. Locations of the stations used in the analysis in this paper are shown in Figure 3, together with the geology and tectonics of the area. Site conditions seen from the geological map show that most of the sites are in a high Himalayan mountain terrain and in the meta-sedimentary Lesser Himalayan province, which is expected to be devoid of thick sedimentary cover. However, they could be on sediments in the river valley or on severely fractured and weathered rock. Among these stations, only Bhatwari is located on the central crystalline province of the Higher Himalayas. It can be seen from Figure 3 that most of the selected stations are located in the Lesser Himalayan region. The Lesser Himalayas consist of the sediments of the Precambrian-Palaeozoic age, and locally of the Mesozoic age, metamorphosed and subdivided by thrusts with progressively older rocks toward the north (Sharma and Wason, 1994). The Lesser Himalayas have been thrust southwards over the Siwaliks of the Sub-Himalayas along the Main Boundary Thrust (MBT). The northern boundary of the Lesser Himalayas is defined by the MCT. This separates it from the Higher Himalayas. Historically earthquakes have been recorded in the region between the MBT and the MCT (Seeber and Armbruster, 1984). The fault mechanism of the 195 Kangra Earthquake and the fault plane solutions of the 1979 Dharchula Earthquake, 1991 Uttarkashi Earthquake, and 1999 Chamoli Earthquake showed that the dominant deformation model for the region is low-angle northeasterly dipping thrust faulting (Thakur and Kumar, 22). Khattri et al. (1989) indicated that moderate earthquakes occur in this region due to the reactivation of the low-angle thrust faults in the upper crust parallel to the detachment surface. These earthquakes have been discussed in terms of reactivation of upper crustal faults, which are possibly slip surfaces of crustal shear zones facilitating the uplifting of Lesser as well as Higher Himalayas, and are a consequence of the same underthrusting Himalayan orogenic process prevalent in the entire region (Mandal et al., 21). Fig. 2 Locations of all stations that had recorded the Uttarkashi and Chamoli earthquakes (the black triangles denote the locations of those stations that had recorded the Uttarkashi Earthquake, the empty triangles denote the locations of those stations that had recorded the Chamoli Earthquake, and the half-filled triangles denote the locations of those stations that had recorded both Uttarkashi and Chamoli earthquakes; the stars denote the epicenters of the Uttarkashi and Chamoli earthquakes) ISET Journal of Earthquake Technology, March-June Uttarkashi earthquake (M s = 7.1) Alaknanda River BHAT UTTAR Vaikrita Thrust 3.5 Munsiari Thrust JOSH TEHR GHAN KOTE GOPE Chamoli earthquake (M s = 6.6) LEGEND Vaikrita Group Munsiari Group Ramgarh Group Garwhal Group Higher Himalayan crystallines Lesser Himalayan sequence Fig. 3 Tectonics of the region surrounding the epicenters of the Chamoli and Uttarkashi earthquakes (after Metcalfe (1993)); locations of the stations that are used in the inversion process are shown by the triangles; stars denote the epicenters of the Uttarkashi and Chamoli earthquakes An upward increase in the metamorphic grade across the Himalayas has been noticed by various geologists (Mallet, 1874; Medlicott, 1864; Oldham, 1883; Hodges et al., 1996; Pêcher, 1975; Stephenson et al., 2). The inverted gradient is most obvious within and close to the MCT zone (Bollinger et al., 24), which marks the contrast between the High Himalayan Crystalline (HHC) unit and the Lesser Himalayas. This observation has been interpreted due to the thermal structure with recumbent isotherms (Le Fort, 1975). The metamorphic and exhumation history of Lesser Himalayas remains poorly documented due to the poor mineralogy of these rocks and supposedly low metamorphic grade (Bollinger et al., 24). Based on the data of Lesser Himalayas it is estimated that peak metamorphic temperatures decrease gradually from C below MCT zone down to less than 33 C. These temperatures describe structurally a 2-5 C/km inverted exhumation history of Lesser Himalayas, thus supporting the view that since the Miocene, the Himalayan orogen has essentially grown by underplating rather than by frontal accretion (Bollinger et al., 24). The thermal structure of the Himalayan orogen is consistent with the metamorphic rock exhumed from the Himalayas, and has temperature of C at the earth surface and a constant mantle heat flow of 15 mw/m 2 at the base of the model. The upper crust heat production is taken to be 25 W/µm 3 (Cattin et al., 21). The computed thermal structure of the Indian plate away from the Himalayas implies a surface heat flow of about 6 mw/m 2, which is consistent with the measurement made in the cratonic areas of northern India (Pandey and Agrawal, 1999). This model suggests that density of the Himalayan crust might not be uniform due to the thermal structure and possible petrological changes related to the underthrusting of the Indian crust (Le Pichnon et al., 1997; Henry et al., 1997). 18 Analysis of Strong Motion Data of the Uttarkashi Earthquake of 2th October 1991 and the Chamoli Earthquake of 28th March 1999 for Determining the Q Value and Source Parameters RESULTS OF INVERSION The first step in the analysis is the identification of S-phase from the available strong motion data. Because of the threshold level of g as the triggering level of the strong motion recordings it is difficult to say whether a record actually started after arrival of the P-phase or from the S-phase, especially in the case of less energetic motions. We have taken those stations at which we can identify S- phase visually after zooming onto the portion before the onset of S-phase. Four stations in the case of the Chamoli earthquake and four in the case of the Uttarkashi earthquake have been selected for the analysis. Our procedure gives t for the case of the Brune s source model. The obtained t value is used to compute the source spectrum at each station from the digitized accelerogram. In the present work analysis has been made for Rs ( f ) = 1., i.e., without considering the site effects. Sriram and Khattri (1997) and Singh et al. (22) have estimated the corner frequency for the Uttarkashi and the Chamoli earthquakes as.8 Hz and.13 Hz, respectively. The seismic moment has been assumed as and dyne-cm for the Uttarkashi and Chamoli earthquakes, respectively, as given by USGS. By using these values of corner frequency and seismic moment, inversion is performed to obtain t. Tables 3 and 4 give the values of Q obtained after the inversion at different stations. The source spectrum and the corresponding Brune s model
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