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Baruah, Santanu; Baruah, Saurabh; Kalita, Aditya; Biswas, Rajib; Gogoi, N.; Gautam, J. L.; Sanoujam, M.; Kayal, J. R.

"Geomatics, Natural Hazards and Risk"
, Volume 3 (4): 11 – Nov 1, 2012

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- Taylor & Francis
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- 1947-5705
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- 10.1080/19475705.2011.596577
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Geomatics, Natural Hazards and Risk Vol. 3, No. 4, November 2012, 365–375 Moment magnitude – local magnitude relationship for the earthquakes of the Shillong-Mikir plateau, Northeastern India Region: a new perspective SANTANU BARUAH{, SAURABH BARUAH*{, ADITYA KALITA{, RAJIB BISWAS{, N. GOGOI{, J. L. GAUTAMx, M. SANOUJAM{ and J.R. KAYAL# {Geoscience Division, North East Institute of Science & Technology (CSIR), Jorhat 785006, Assam, India {National Geophysical Research Institute, Hyderabad 500007, India xSeismology Division, India Meteorological Department (IMD), Lodi Road, New Delhi 110003, India {Manipur University, Department of Earth Sciences, Imphal, Manipur 795003, India #School of Oceanographic Studies, Jadavpur University, Kolkata 700032, India (Received 04 February 2011; in ﬁnal form 09 June 2011) An attempt has been made to examine the empirical relationship between moment magnitude (M ) and local magnitude (M ) of earthquakes recorded in the W L Shillong-Mikir Plateau of Northeastern India. Moment tensor solutions of 106 earthquakes recorded during the period 1976–2009 are used. The focal mechanism solutions of these earthquakes include 1 Harvard-CMT solution (M 4.0), 54 solutions from diﬀerent publications and 51 solutions obtained for the local earthquakes (2.0 M 5.0) recorded by a 20-station permanent broadband network during 2001–2009 in the region. The moment tensor solutions of these local earthquakes are obtained by the discrete wave number method. The M –M relationship in the region is determined by generalized W L orthogonal regression analysis, which is found to be M ¼ M (1.00+ 0.02) þ W L (0.02+70.05). It is observed that, on average, M is equivalent to M with an W L uncertainty of about (0.02+70.05) magnitude units for earthquakes of the Shillong-Mikir Plateau. Conversion of M to M is recommended for seismic L W hazard analysis and tectonic studies in the region. 1. Introduction The Richter local magnitude M scale (Richter 1935) for an earthquake is still widely used in diﬀerent parts of the world, though it is observed that for higher magnitude events (M 6) the scale gets saturated (Hutton and Boore 1987). The moment magnitude scale (M ), as deﬁned by Kanamori (1977), has an advantage of not getting saturated for larger earthquakes, unlike the Richter amplitude based scales (e.g. Hanks and Kanamori 1979, Howell 1981, Ottemo¨ ller and Havskov 2003). Thus, *Corresponding author. Email: saurabhb_23@yahoo.com Geomatics, Natural Hazards and Risk ISSN 1947-5705 Print/ISSN 1947-5713 Online ª 2012 Taylor & Francis http://www.tandf.co.uk/journals http://dx.doi.org/10.1080/19475705.2011.596577 366 S. Baruah et al. M is widely accepted as a stable scale, particularly for larger magnitude events (Lay and Wallace 1995). Several studies have been made to examine the region speciﬁc relation between M and M (e.g. Ristau et al. 2003, 2005). Although the size of the events occurring W L in the Shillong-Mikir plateau of Northeastern (hereafter NER) India is designated by M in the IMD (India Meteorological Department), Shillong catalog, but its consistency with moment magnitude (M ) has not been examined yet. In a recent study, an empirical relation between M and M (duration magnitude) is reported L D by Sitaram and Bora (2007), and they observed that M starts to saturate above magnitude 6.5. Ristau (2009) suggested that the relationship between M and M L W could be related to the physical source properties such as low stress drop or high stress drop. The study region is not represented by any proper relationship between M and M based on the digital seismic database. In view of the above, an attempt L W is made here to understand the relationship between M and M , which could be L W useful for seismic hazard and tectonic studies in the region. In this present study the moment tensor solutions of the local earthquakes 2.0 M 5.0 have been estimated by the ASPO method (Amplitude Spectra and POlarities) (Zahradnik et al. 2001). A sum of 106 moment tensor solutions is used to examine M – M relations; the results are highlighted here. W L 2. Tectonic setting The Shillong-Mikir Plateau is considered to be one of the deformed zones of the NER, India; the plateau area is seismically very active (ﬁgures 1 and 2). The Shillong Plateau in the NER, India is a part of the Indian shield that is separated out from the peninsular shield and moved to the east by about 300 km along the Dauki fault (Evans 1964). The east–west trending Dauki fault separates the plateau to the north and the Bengal basin to the south. The Brahmaputra River/Valley, on the other hand, separates the plateau from the Himalaya to the North. The east–west segment of the river at the Northern boundary of the plateau is named the Brahmaputra fault (Nandy 2001). The Mikir massif, a part of the Shillong massif, moved to the northeast; the nearly 300 km long northwest–southeast trending Kopili fault separates them (ﬁgures 1 and 2). A graben formation exists between the Shillong and Mikir Massifs. The major geotectonic structures associated with this region are: the Brahmaputra fault to the north, the east–west Dauki fault to the south and the northeast–southwest Naga thrust to the east. Further, two major faults are geologically mapped in the Shillong Plateau; the Dapsi thrust and the Barapani shear zone. The Dapsi thrust separates the Archaean to the north and the Tertiary to the south, whereas the Barapani shear zone separates the Archaean to the west and the Proterozoic Shillong Group to the east (Nandy 2001, Baruah et al. 2009). Kayal and De (1991) identiﬁed that the Dapsi thrust is seismogenic and north dipping. The western boundary of the plateau is characterized by a north–south trending Dhubri fault. Recently, Bilham and England (2001) suggested a south dipping hidden fault at the northern boundary of the plateau; they named it Oldham fault. Geologically the entire area has evolved during the Mesozoic to Tertiary time. The Shillong Plateau and Mikir Hills consist of crystalline rocks, which are partly covered by gently dipping Tertiary and younger sediments (Evans 1964). The complex geodynamics of Shillong Plateau resulted in the 1897 great earthquake (M ¼ 8.7) (Oldham 1899). Moment magnitude 367 Figure 1. Tectonic map of NER, India and surrounding areas (modiﬁed from Nandy 2001), showing broadband seismic stations (green triangles). The major tectonic features are Main Central Thrust; Main Boundary Thrust; DF: Dauki Fault; Da T: Dapsi Thrust; Dh F: Dhubri Fault; Du F: Dudhnoi Fault; OF: Oldham Fault; BF: Brahmaputra Fault; CF: Chedrang Fault; BS: Barapani Shear Zone; KF: Kopili Fault; NT: Naga Thrust; DT: Disang Thrust; EBT: Eastern Boundary Thrust; Mishmi Thrust; Lohit Thrust; Brahmaputra River; Ganga; Podma; Nagaland Hills; Manipur Hills; TFB: Tripura Fold Belt. Inset: Location map. 3. Magnitude scales Richter (1935, 1958) deﬁned local magnitude M as: M ¼ log A log A þ S ð1Þ L 0 where A is the maximum amplitude (in mm) of the horizontal ground displacement of a particular earthquake at a given station measured by a Wood–Anderson torsion seismograph, A is the corresponding amplitude of a reference event at a chosen epicentral distance and S is a station correction term. The distance correction term7log A is given by log A ¼ a logðR=100Þþ bðR 100Þþ 3:0 ð2Þ 0 368 S. Baruah et al. Figure 2. Map shows 106 earthquake solutions with major tectonic features of the study area. The major tectonic features are: DF: Dauki fault; DT: Dapsi thrust; DF: Dhubri fault; DhF: Dudhnoi fault; OF: Oldham fault; BS: Barapani shear zone; KF: Kopili fault; SP: Shillong plateau; MP: Mikir plateau; TF: Tista fault; NT: Naga thrust. The red beach ball represents the CMT solution, the black beach balls represent the focal mechanism solution obtained from the published literature and the blue beach balls represent the solutions obtained through waveform inversion under the present study. Inset: Map of India. where, a and b are coeﬃcients for geometrical spreading and anelastic attenuation, respectively, and R is the hypocentral distance (km). Richter’s original method used the largest zero-to-peak amplitude regardless of the phase (Richter 1935, Hutton and Boore 1987). However, in practice, M is normally based on the maximum trace amplitude of the regional distance S waves (Lay and Wallace 1995). Local magnitude M may vary considerably from station to station depending on the radiation pattern and travel path. Thus M is normally estimated at several stations at diﬀerent azimuths and the values are averaged (Lay and Wallace 1995). The IMD routinely estimates M for the NER, India using the Shillong observatory data. Moment magnitude M , derived from the seismic moment M , is a reliable W 0 estimate of the magnitude since it is calculated using much longer periods; the attenuation is not greatly aﬀected by near-surface structure. Further, full waveform modelling eliminates the variability of the radiation pattern. Kanamori (1977) derived a relationship for calculating M from M as: W 0 log M M ¼ 10:7 ð3Þ 1:5 We have used this relation in order to estimate M for the smaller events (2.0 M 5.0) in this region. The CMT solutions for the events M 4.0 are used L W from the Harvard catalog. Moment magnitude 369 4. Database In this study we have used moment tensor solutions of 106 earthquakes that were recorded during the period 1950–2009 (ﬁgure 2). Out of these 106 solutions, 1 moment tensor solution is obtained from the Harvard-CMT catalog and 54 solutions from the published literature (e.g. Chandra 1975, Chen and Molnar 1990, Radha Krishna and Sanu 2000, Singh 2000, Nandy 2001, Mitra et al. 2005 and Kayal et al. 2006). The remaining 51 solutions are obtained by a waveform modelling technique by Zahradnik et al. (2001). Some of these focal mechanism solutions have been used by Angelier and Baruah (2009) in order to observe the stress pattern of the Shillong-Mikir plateau of NER, India and their results are in agreement with the observed geodetic data obtained from GPS studies. No ambiguities among the moment magnitudes obtained from diﬀerent sources are observed. We estimated M by modelling the low frequency band of the waveforms (0.01–0.04 Hz). These 51 selected events are recorded by the 20-station local permanent broadband network, which are shown as green triangles in ﬁgure 1. The broadband seismic data are recorded in the frequency bands of 0.005–50 Hz, and are suitable for moment tensor analysis. The epicentres of the earthquakes are determined using the HYPOCENTER program of Lienert et al. (1986) using the crustal velocity model of Bhattacharya et al. (2005). Uncertainties involved in the estimates of epicentres are 0–2 km in depth and epicentre, and the error in origin times is of the order of 0–0.5 s. These broadband digital data, along with improved methods and increased computing power, made it possible to compute regional moment tensor solutions for the smaller earthquakes of magnitude M 5.0 in the region. The magnitude of the events ranges from 2.0 to 5.5 (M ). The frequency distribution of the number of events versus the moment magnitude (M ) range for the study region is illustrated in ﬁgure 3(a). Figure 3. (a) Histogram showing the number and magnitude distribution of the events for the study area; (b) M –M relationship is illustrated; the red line represents the 1:1 relationship, W L the solid black line represents the best-ﬁt line obtained from the standard least-squares method, the dashed line from the orthogonal least-squares method, and the dashed-dotted line from the inverted least-squares method. It is found that the standard least-squares line is parallel and overlapping to the orthogonal least squares line. 370 S. Baruah et al. The local magnitude M estimates are provided by the IMD catalog. Till date IMD-Shillong observatory, use a torsion seismometer, which is a modiﬁed version of the original Wood–Anderson seismometer to standardize the magnitudes of local earthquakes and to record stronger shocks when the other instruments are either saturated or go oﬀ the scale. The instrument designed at the IMD has a free period of T ¼ 0.8 s, a damping co-eﬃcient of h ¼ 0.8 and a static magniﬁcation of V ¼ 1000. Damping is provided by a permanent horseshoe magnet, the details of which have been described by Srivastava (1989) and Bhattacharya and Dattatrayam (2000). For estimation of M , the IMD implemented the procedure of Hutton and Boore (1987), in which equation (2) can be written as: log A a logðR=R þ bðR R Þþ KðRÞð4Þ 0 ref ref ref Where K(R ) is a constant and found to be 2 by IMD for R ¼ 17 km, as suggested ref ref by Hutton and Boore (1987). Taking into account geometrical spreading, anelastic attenuation and station corrections, IMD utilizes the following equation for calculating M M ¼ log A þ 0:91 log R þ 0:00087R 1:31 þ S ð5Þ where, A (mm) is the instrument corrected maximum ground amplitude, R is the hypocentral distance (km) and S is the station correction term. During estimation of M and M , radiation pattern aﬀects both the measure- W L ments in a similar manner (Deichmann 2006). Richter (1958, p. 344) emphasized that ‘an acceptable assignment of magnitude calls for data from a number of stations surrounding the epicenter’ in order to average out the aﬀect of radiation pattern. We believe that wide coverage of the IMD network in NER India helps to eliminate the inﬂuence of radiation pattern by averaging the magnitude from all the stations surrounding the epicentre. 5. Local moment tensor analysis The local moment tensor solutions presented here are determined using the code of Zahradnik et al. (2001). In this method, the prime approach is to calculate Green’s function for a trial depth by the discrete wave (DW) number of Bouchon (1981). For the trial values of the scalar moment, strike, dip and rake, the moment tensor is calculated with a step time function. The inversion is carried out with the waveform ﬁltered in a frequency band (0.03–0.05 Hz) that is free of noise or with higher signal to noise ratio, and falls below the corner frequency. The moment tensor and the Green’s tensor are multiplied in a complex spectral domain, and the modulus is taken. A correction is applied, compensating the artiﬁcial attenuation employed in the DW method as a regularization and anti-alias operation. A ﬁne grid search of the strike, dip and rake is performed for the best depth and moment. A fault plane solution is considered when all the observed polarities are satisﬁed at a given scalar moment. However, we have inverted for full moment tensors of the displacement records from 3 to 5 nearest stations. The inverted records were pre-processed by a low pass ﬁltering range of 0.01 Hz to 0.04 Hz. Subsequently, the records were re- sampled from a frequency of 100 Hz to 33 Hz and corrected for the transfer function Moment magnitude 371 of the seismometer. The seismograms are checked to have a suﬃciently high signal- to-noise ratio. The seismic moment is obtained by averaging the seismic moments from all inverting stations and was ﬁnally used to scale the amplitudes. Comparing the observed and synthetic amplitude waveforms and spectra, ﬁnal validation of the best ﬁtting solution is accomplished. A minimum of four station data with good azimuthal coverage have been used for the determination of focal mechanism solutions by the Moment Tensor Inversion Technique. 6. Moment magnitude–local magnitude relationship This study ascertains a systematic comparison of M with M for the earthquakes W L of Shillong and the Mikir plateau earthquakes of NER, India. The M versus M W L relation is established for the study region. Figure 3(a) shows the distribution of events as a function of magnitude (M ). The estimated moment magnitude (M ) W W ranges from 2.0 to 5.5. The most common method of comparing diﬀerent magnitude estimates is by a least-squares regression (Ristau 2009). Detailed studies on diﬀerent least-squares linear regression techniques viz. standard least-squares (minimizing the square of the vertical oﬀsets to the best ﬁt line), inverted standard least-squares (minimizing the square of the horizontal oﬀsets to the best ﬁt line), and orthogonal regression (minimizing the square of the perpendicular oﬀsets to the best ﬁt line) for comparing diﬀerent magnitude estimates are carried out by Castellaro et al. (2006) and Castellaro and Bormann (2007). However, orthogonal regression (OR) rather than the conventionally followed standard linear least square method has been demonstrated to be more appropriate for magnitude scale regressions (Castellaro et al. 2006). Accordingly, generalized orthogonal regression (GOR) is performed in the present analysis. GOR employs an error variance ratio, denoted by Z, between the error variances of the linearly related variables on the vertical and horizontal axes, respectively. The results of these regressions are summarized in table 1. Figure 3(b) illustrates the M 7 M relation for the Shillong-Mikir plateau. The W L red line, which has a slope of 1, represents a 1:1 relationship between M and M . W L The solid black line represents the best-ﬁt line obtained from the standard least- squares method, the dashed line from the orthogonal least-squares method, and the dashed dot line from the inverted least-squares method. It is found that the standard least-squares line is parallel and overlapping to the orthogonal least squares line. It is observed that the standard least squares method indicates less error estimates of slope and intercept as compared to other techniques, hence in our study we accept the standard least-squares line as the best ﬁt line for the regression analysis. The oﬀset of the best ﬁt line is estimated by taking the average of the residuals between M and the 1:1 line. Basically the standard deviation of the residual determines an Table 1. Regression parameters for M /M . W L Orthogonal least-squares Standard least-squares Inverted least-squares Slope 1.00+ 0.02 1.00+ 0.02 0.98+ 0.05 y-intercept 0.02+ 0.05 0.04+ 0.10 70.008+70.02 372 S. Baruah et al. estimate of the error. For our study region the best ﬁt line is parallel to the 1:1 line; the M is on average 0.02+70.05 magnitude units larger than M . W L 7. Results and discussion In the present study an attempt has been made to scale Richter’s local magnitude M with moment magnitude M for the Shillong-Mikir Plateau, which is one of the most seismically active zones of northeast India. Both M and M are, in principle, L W measures of dimension of the earthquake sources. The source processes of all the studied events are varying. These varying processes pertain to the diﬀerent magnitude levels. At certain threshold values, the sizes of all the source processes of earthquakes are the same. It is considered that the factors inﬂuencing the amplitude of the observed waves, such as the radiation pattern, paths and site eﬀects, are properly accounted for and then the local magnitude M should be equal to the moment magnitude M . In this study, we have observed that, on an average, M is W W equivalent to M with an uncertainty of about (0.02+70.05) magnitude units for the Shillong-Mikir Plateau, which is represented by the relation M ¼ M W L (1.00+ 0.02) þ (0.02+70.05). Sitaram and Bora (2007) did a comparative study between M and M for the L D earthquakes of NER, India which is given as: M ¼ð1:05 0:01Þ M þð0:17 0:05Þð6Þ D L The above relation is in conformity with the derived relation between M and M L W for the Shillong-Mikir Plateau. The M and M relation shows that M is D L D underestimated to M values whereas M values are always overestimated to M L W L values. The discrepancy between M and M estimates is also examined in relation to W L the seismotectonics of the study region. As we know, the travel path depends mainly on the crustal heterogeneities, the intrinsic and extrinsic attenuation etc. The longer the wave interacts with a signiﬁcant amount of heterogeneity in the crust the more the discrepancy between M and M estimates may result. For W L events occurring in this region, the travel path is through the Precambrian Indian Shield and from the relation we can aﬃrm the fact that for the shield region M is nearly equal to M i.e. the relation should indicate less diﬀerence between M W L and M . According to theory, both the local magnitude M and the moment W L magnitude M are measures of basic properties of the earthquake source. Any observed diﬀerences between M and M are telling us something either about L W the physics of the earthquake source or about the inadequacies in our wave- propagation model and in our ways of measuring M (Heaton et al. 1986, Deichmann 2006). In our case M is 0.02 magnitude units higher than that of M . The main aim of our study is to perceive how M varies with M for the L L W Shillong-Mikir Plateau of Northeastern India, which is proclaimed now. For ideal source scaling, the various magnitude scales should be compatible with the size of the source, no matter where the measurement is taken and what frequency band is used. We mention the stress issue that the relationship between M and M W L could be related to physical source properties such as low stress drop and high stress drop, which remains a scope for further study. Thus local tectonic stress patterns prevailing in the region in the earthquake catalog need to be converted Moment magnitude 373 to M for eﬀective seismic hazard analysis and tectonic studies for the region. Hanks and Boore (1984) showed that the scaling relation between M and log (M ) (and hence M ) are frequency dependent. In this study M is estimated at 0 W W a frequency lower than the corner frequency of the earthquake measured by a broad band seismometer, and the local magnitude from a 1-Hz Wood–Anderson seismometer. Further, the magnitudes describe the energies in diﬀerent frequency ranges and their diﬀerence may reﬂect properties of the source (e.g. stress drop) and of the path (attenuation), which remain as scope for further study. Acknowledgments We thank Dr P.G. Rao, Director, North East Institute of Science and Technology (NEIST), Council of Scientiﬁc and Industrial Research (CSIR), Jorhat for his support and encouragement for carrying out this research. 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