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Bulletin of the Seismological Society of America, Vol. 92, No. 2, pp. 555–569, March 2002

Ground Motion in Delhi from Future Large/Great Earthquakes in the Central Seismic Gap of the Himalayan Arc by S. K. Singh, W. K. Mohanty, B. K. Bansal, and G. S. Roonwal

Abstract We estimate ground motions in Delhi from possible future large/great earthquakes in the central seismic gap in the Himalayan arc. The closest distance from the rupture areas of such postulated earthquakes to Delhi may be about 200 km. We have used two methods to synthesize the expected ground motions. In the first, recordings in Delhi (three on soft sites and one on a hard site) of the 1999 Chamoli earthquake (Mw 6.5; epicentral distance, ⬃300 km), which was located in the gap, are used as empirical Green’s functions (EGFs). The ground motion during the target event is synthesized by random summation of the EGFs. In the second, the stochastic method, the motions have been estimated from the expected Fourier spectrum of the ground motion in Delhi through the application of Parseval’s theorem and results from random vibration theory. We apply two versions of the stochastic method: the first assumes a point source while the second considers the source to be finite. The predictions from the two methods are in reasonable agreement for Mw ⱕ 7.5. For Mw ⬎ 7.5 events, the finiteness of the source becomes important. Several rupture scenarios are considered in the application of the finite-source stochastic method. The largest ground motions are predicted in Delhi for rupture occurring between the main boundary thrust and main central thrust and the hypocenter located at the northeast edge of the fault. For this rupture scenario and a postulated Mw 8.0 earthquake, the maximum expected horizontal acceleration (Amax), and velocity (Vmax) at soft sites in Delhi range between 96 and 140 gal and 8 to 19 cm/sec, respectively. For Mw 8.5 event, the corresponding values range between 174 and 218 gal and 17 to 36 cm/sec. Amax at the hard sites are 3 to 4 times less than at the soft sites. The differences are somewhat smaller for Vmax, which are roughly 2 to 3 times at soft sites as compared to the hard site. The horizontal Amax and Vmax estimated by Khattri (1999) for Mw 8.5, using a composite source model, are remarkably similar to those estimated here. The seismic hazard in Delhi may be especially high to the east of Yamuna river because the area is underlain by recent fluvial deposits. More extensive earthquake recordings, microzonation studies, research on liquefaction potential of the fluvial deposits, and further work on the estimation of expected ground motions in Delhi area are urgently needed. Introduction The relative velocity of Indian plate with respect to the Eurasian plate near Delhi is about 5 cm/yr in the direction of N13⬚E (NUVEL-1A model of DeMets et al. [1994]). The collision of these continental plates results in crustal shortening along the northern edge of the Indian plate. This process has given rise to three major thrust planes (e.g., Gansser, 1964; Molnar and Chen, 1982): the Main Central Thrust (MCT), the Main Boundary Thrust (MBT), and the Main Frontal Thrust (MFT) (Fig. 1). The relative role of these thrust planes in the Himalayan seismicity remains a matter of debate (see, e.g., Rajendran et al. [2000] for a brief dis-

cussion). The region has experienced several great earthquakes in the past hundred years or so (1897 Assam; 1905 Kangra; 1934 Bihar-Nepal; 1950 Assam). The magnitudes of these earthquakes are listed in Table 1. The Himalayan geodynamics and the occurrence of great earthquakes are well summarized by Seeber and Armbruster (1981), Khatttri (1999), and Bilham and Gaur (2000). During the last episode of strain release, a 750-km-long segment, which lies between the eastern edge of the 1905 rupture zone and the western edge of the 1934 earthquake, remained unbroken (Fig. 1). This segment, called the central seismic gap, continues to be 555

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S. K. Singh, W. K. Mohanty, B. K. Bansal, and G. S. Roonwal

Figure 1. (Top) Tectonic map of the region (modified from Seeber and Armbruster, 1981). Hatched areas denote intensity greater than or equal to VIII. The segment between the rupture areas of the 1905 and 1934 earthquakes is known as the central seismic gap. MCT, main central thrust; MBT, main boundary thrust. Locations and focal mechanisms of 1991 Uttarkashi and 1999 Chamoli earthquakes are shown. (Bottom) A closer view of the area in the box shown in the top figure (modified from Yu et al., 1995). Triangles, sites where ground motions during the 1999 Chamoli were recorded; stars, epicenters of 1991 and 1999 earthquakes. Target rupture areas are either centered at the Chamoli hypocenter or confined within MBT and MCT with center at 30⬚ N, 79.2⬚ E. Rectangle, rupture area of a Mw 8.0 earthquake in the region of the Chamoli. Dashed rectangle, area used by Khattri (1999) to compute ground motions from a postulated Mw 8.5 earthquake. A, B, and C indicate three possible hypocenters.

Table 1 List of Great Earthquakes in the Himalayan Arc Date

12 June 1897 4 April 1905 15 January 1934 15 August 1950

Magnitude

m 8*; Ms⬎8.2† MGR 8‡; MD 8.6; Ms 8.1|; Ms 7.5# MGR 8.3‡; MD 8.4§; Ms 8.3**; Mw 8.1†† MGR 8.6‡; MD 8.7§; Ms 8.6**

*Gutenberg (1956). † Kanamori and Abe (1979) ‡ Gutenberg and Richter (1954) § Duda (1965) |; Abe and Noguchi (1983a) # Abe and Noguchi (1983b) **Geller and Kanamori (1977) †† Chen and Molnar (1977)

under high strain. In 1803 and 1833 large earthquakes occurred in this seismic gap but the magnitudes of these earthquakes were less than 8, and, hence, they were not gap-filling events (Khattri, 1999; Bilham, 1995). Based on these considerations and a shortening rate of 20 mm/yr across the Himalayas (Lyon-Caen and Molnar, 1985; Avouac and Tapponnier, 1993; Gahalaut and Chander, 1997; Bilham et al., 1998), Khattri (1999) has estimated the probability of occurrence of a great Mw 8.5 earthquake in the gap in the next 100 yr to be 0.59. A large/great earthquake in the central seismic gap is likely to cause great loss of life and severe damage to construction in and near the epicentral zone. This emphasizes the need for realistic estimation of ground motion from future earthquakes in the gap. Delhi, a city of more than 10 million inhabitants, lies approximately 200 km from MBT and 300 km from MCT (Fig. 1). The city now extends over swamps and recent fluvial deposits on the banks of Yamuna river (Fig. 2). For these reasons, there is an increasing con-

Ground Motion in Delhi from Future Large Earthquakes in the Central Seismic Gap of the Himalayan Arc

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We apply two methods to synthesize the expected ground motions. One method uses the recordings of Chamoli mainshock and an aftershock as empirical Green’s functions (EGFs). The second, called the stochastic method (Hanks and McGuire, 1981; Boore, 1983), is based on the spectrum of the ground motion that, in turn, is described by a physically reasonable seismological source spectrum, modified by path and site effects. One significant advantage of the EGF method comes from the fact that the wave propagation and the site effects are included in the recordings. We note, however, that the EGF method as applied here assumes that the rupture can be approximated by a point source, an assumption that may be valid for Mw ⱕ 7.5 earthquakes but may not be tenable for larger events. We apply two versions of the stochastic method. The first assumes a point source (henceforth called the point-source stochastic method), whereas the second considers the source to be finite (henceforth called the finite-source stochastic method). Recently, Khattri (1999) has synthesized expected strong ground motions at nine critical sites, including Delhi, from a postulated Mw 8.5 earthquake in the central seismic gap. The method assumes a composite source model (Zeng et al., 1993) and uses theoretical Green’s functions. It is not known whether the crustal structure used in computing the Green’s functions corresponds to a generic site in Delhi. For this reason, the estimated ground motions by Khattri need validation. Furthermore, Khattri limits his study to a target event of Mw 8.5. It is clearly important to estimate ground motions during postulated earthquakes of magnitude less than 8.5.

Data Figure 2.

Map of Delhi showing surface geology (modified from Bhatnagar and Firozuddin, 1979) and stations which recorded the mainshock (Ridge Observatory [RO]; CSIR; IHC; CPCB) and the aftershocks (University of Delhi, South Campus, UDSC).

cern about the seismic hazard in the capital, especially after the Bhuj earthquake of 26 January 2001 (Mw 7.6) that caused damage to the city of Ahmedabad located ⬃300 km from the epicentral zone. The sparse strong-motion data set presently available in Delhi region, however, makes the estimation of ground motion during future earthquakes quite a challenge. Two moderate earthquakes have recently occurred in the western part of the central seismic gap: the Uttarkashi earthquake of 19 October 1991 (Mw 6.8) and the Chamoli earthquake of 28 March 1999 (Mw 6.5). Fortunately, the Chamoli earthquake and some its aftershocks were recorded in Delhi. In this study, we take advantage of these recordings in the estimation of ground motions in Delhi from future large/great earthquakes in the western part of the central seismic gap.

The digital recordings of the mainshock, which were available to us for the analysis, are summarized in Table 2. The recordings consist of accelerograms from networks operated by the Department of Earthquake Engineering (DEQ), University of Roorkee; the Central Building Research Institute (CBRI), Roorkee; and seismograms from Ridge Observatory (RO), Delhi, a station operated by the India Meteorological Department (IMD). We have also used seismograms of the early aftershocks recorded at a station located in the University of Delhi, South Campus (UDSC). These aftershocks are listed Table 3. Tables 2 and 3 give characteristics of the recording system, the sampling rate, and the peak values of the recorded accelerations (Amax) and the velocities (Vmax). Since the recordings from Delhi are critical to our study, we briefly mention some relevant features of this data set. The accelerograms of the mainshock were recorded by digital accelerographs (Kinemetrics, model K2, sampling rate 200 Hz) at three sites in Delhi: CSIR, Rafi Marg; IHC, Lodhi Road; and CPCB, Arjun Nagar (Fig. 2). A description of the instrumentation and the site characteristics is given in a Central Building Research of India report, henceforth referred to as CBRI (1998). The stations are situated on the top of

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Table 2 Peak Accelerations and Velocities during the Chamoli Earthquake Amax (gal)

Distance (R, km)

22.6 29.8 37.7 76.9 91.0 96.9 96.9 101.8 107.9 125.6 160.0 265.0 268.0 291.8 286.8 293.3 287.5

Vmax (cm/sec)

H1§

H2§

Z

H1

H2

Z

Station

199.0 71.0 91.0 73.0 54.0 27.0 5.0 54.0 52.0 17.0 56.0 45.61 13.5 10.92 11.55 9.67 2.69

359.0 63.0 96.0 83.0 62.0 28.0 6.0 64.0 45.0 23.0 47.0 28.0 — 8.86 14.32 11.41 3.30

156.0 41.00 47.00 39.0 34.0 27.0 11.0 23.0 49.0 19.0 17.0 9.43 8.23 5.78 5.59 8.23 2.29

22.55 3.180 6.850 3.310 4.600 2.350 0.175 3.550 3.120 0.830 — — — 1.299 2.010 1.745 0.617

45.30 8.940 5.450 4.080 5.380 1.893 0.214 4.670 3.300 1.240 — — — 0.690 1.645 1.240 0.978

7.50 2.72 4.05 2.00 2.11 1.270 0.248 1.580 3.140 0.766 — — — 0.546 0.634 0.673 0.394

Gopeshwar* Joshimath* Ukhimath* Ghansiali* Tehri* Almora* Lansdowne* Uttarkashi* Chinyalisaur* Barkot* Roorkee* Panipat* Baghpat* CSIR, Delhi† CPCB, Delhi† IHC, Delhi† Ridge Obs., Delhi‡

*Accelerograph operated by Department of Earthquake Engineering (DEQ), University of Roorkee. Data available at 50 samples per sec. † Accelerograph (19 bit K2) operated by Central Building Research Institute, Roorkee. Data available at 200 samples per sec. ‡ Seismograph (RefTek 24 bit digitizer connected to 1-sec natural period L-4C-3D seismometer) operated by India Meteorological Department (IMD). Data available at 50 samples per sec. § Except for DEQ stations, H1 and H2 refer to north–south and east–west component, respectively.

Table 3 Peak East–West Ground Motions during Chamoli Aftershocks at University of Delhi, South Campus (UDSC)* M:D

Hr:Min

Mw

Amax (gal)

Vmax (cm/sec)

03:29 03:30 03:29 04:06 04:06 04:07

08:49 15:52 21:02† 19:37 20:47 15:47

3.78 3.71 4.63 4.63 4.27 4.38

0.106 0.067 0.331 0.265 0.107 0.155

0.0043 0.0027 0.0166 0.0111 0.0055 0.0073

*Recorded by a broadband seismograph (Quanterra 24-bit digitizer connected to a WRI seismometer) at 20 samples per sec. † Event used as empirical Green’s function.

sandy silt (Fig. 2). The bedrock lies at a depth of about 100 m. The CPCB site, which is located to the east of Yamuna river (Fig. 2), is also underlain by recent fluvial deposits. A summary and a brief and preliminary analysis of the strongmotion data recorded during the mainshock is given in an IMD monograph (2000). Ridge Observatory (RO) is located on top of quartzites of Alwar series (Fig. 2). The seismograph consisted of 24-bit RefTek digitizer connected to a three-component L-4C-3D seismometer with a natural period of 1 Hz. Figures 3a and 3b show plots of Amax and Vmax versus hypocentral distance R, respectively. The large dispersion seen in the observed peak values is most probably due to variable local site effects. We note that the Amax at soft sites

in Delhi (CSIR, IHC, and CPCB) are about 4 to 5 times greater than the value at the hard site of RO. The aftershocks were recorded at a hard site located at UDSC (Fig. 2), where a Quanterra 24-bit digitizer connected to WRI seismometer is operated. The response of the system is flat for velocity in the frequency range of 0.02–20 Hz. The mainshock recording at UDSC was clipped on the S-wave. Only east–west and Z components of the aftershocks were recorded, as the north–south component malfunctioned. The station is located on tightly folded quarzites of Alwar series (Fig. 2). We estimated the seismic moments of the aftershocks from the long-period spectral level of the S-wave displacement spectra (see subsequent section).

Synthesis of Ground Motion A brief description of the two methods used in groundmotion synthesis is given in a following section; here we note that the EGF method used by us requires the specification of the seismic moment, M0, and the stress drop, Dr, of both the EGF and the target event. The point-source stochastic method requires the specification of the stress drop of the target event and knowledge of the path and the site effects. In the following we take M0 of the Chamoli earthquake as 7.7 ⳯ 1025 dyne cm, which is the scalar seismic moment reported in the Harvard CMT catalog. In the next section we use the recordings of the Chamoli earthquake to infer the parameters required in the synthesis of the ground

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Figure 3. Observed peak ground motion (triangles) versus hypocentral distance R during the Chamoli earthquake. Continuous curves show estimated values at hard site for three values of stress drops (50, 100, and 200 bars), based on the point-source stochastic model (see text). (a) Amax; (b) Vmax.

Table 4 Focal Parameters of the 28 March 1999 Chamoli Earthquake Source

IMD Harvard CMT

Latitude (⬚N)

30.41 30.38

Longitude (⬚E)

Depth (km)

Mo (dyne cm)

Strike

Dip

Rake

21 15

2.8 ⳯ 10 7.7 ⳯ 1025

— 280⬚

— 7⬚

— 75⬚

79.42 79.21

motion. These same parameters, along with a few others, are needed in the application of the finite-source stochastic method.

25

C = Rθϕ FP(2π )2 /(4πρβ 3 ),

(2)

and S(f), the source acceleration spectrum, may be written as

Chamoli Earthquake and Delhi Data

S(f) = f 2 M0 ( f ),

The focal parameters of the earthquake are listed in Table 4. Our analysis is based on the location given by IMD and the seismic moment reported in Harvard CMT catalog.

where M0(f ) is the moment-rate spectrum. For an x2-source model, S(f) = f 2 fc2 M0 /( f 2 + fc2 ).

Source Spectrum, Q, and Dr To estimate the stress drop, Dr, of the Chamoli earthquake and the quality factor, Q, between the source region and Delhi, we analyze the spectra of the recordings at Delhi. This analysis is based on following considerations. The farfield Fourier acceleration spectral amplitude of the intense part of the ground motion at a distance R from the source, A(f, R), can be written as A(f,R) = C S(f) e −π fR / β Q / G(R), where

(1)

(3)

(4)

For Brune’s source model (Brune, 1970), f c, the corner frequency, is given by fc = 4.9 × 106 × β (∆σ / Mo)1 / 3 ,

(5)

where b is in km/sec, Mo is in dyne cm, and Dr, the stress drop, is in bars. In the previous equations, b is shear-wave velocity (3.6 km/sec), q is density (2.85 gm/cm3), Q(f) is the quality factor, Rh␾ is the average radiation pattern (0.55), F is the free surface amplification (2.0), P takes into account the partitioning of energy in the two horizontal components

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(1 / 2 ), and M0 is the seismic moment of the earthquake. G(R) in equation (1) is the geometrical spreading term, which may be taken as G(R) ⳱ R for R ⱕ Rx and G(R) ⳱ (RRx)1/2 for R ⬎ Rx. The form of G(R) implies dominance of body waves for R ⱕ Rx and of surface waves for R ⬎ Rx. Herrmann and Kijko (1983) showed that Rx is roughly twice the crustal thickness. In this study Rx has been taken as 100 km. Figure 4 (left) shows source displacement spectrum (continuous curve), M0(f ), and source acceleration spectrum (dashed curve), f 2M0(f ), determined from the RO data using equations (1)–(3). In correcting the spectrum we have taken Q(f) ⳱ 508f 0.48, a relationship found by Singh et al. (1999) for the Indian shield region. For an x2-source model, the source acceleration spectrum is flat at frequencies greater than the corner frequency, f c. As seen from Figure 4 (left), this is, indeed, the case for f ⬎ 1 Hz. This suggests that Q(f) for the Indian shield region may also provide a reasonable approximation to the Q value for the region of interest, at least within the framework of the x2-source model. Both the low- and the high-frequency levels of the spectrum are well fit by x2-source model with M0 ⳱ 7.7 ⳯ 1025 dyne cm and f c ⳱ 0.132 Hz (corresponding to a stress drop, Dr, of 60 bars, equation 5) (smooth curves in Fig. 4, left). The source displacement and acceleration spectra determined from the recordings at IHC, CSIR, and CPCB sites are shown in Figure 4 (right). The x2-source spectrum corresponding to M0 ⳱ 7.7 ⳯ 1025 dyne cm and Dr ⳱ 60 bars is also shown in

this figure. We note that the observed source spectrum now significantly deviates from the theoretical source spectrum. The misfit strongly suggests significant site effects at IHC, CSIR, and CPCB between 0.4 and 10 Hz. As mentioned previously, a strong site effect at these stations is expected from the subsoil profile and from the fact that horizontal Amax values at these stations are about 4 to 5 times greater than at the hard site of RO. Our further analysis is based on high-pass-filtered records. All CBRI accelerograms were decimated to 50 Hz and high-pass filtered at 0.2 Hz. The velocity traces were obtained by integration of the accelerograms. The recordings at the RO were first corrected for the instrumental response to obtain acceleration traces. These traces were then processed in a similar fashion as the CBRI accelerograms. Site Characteristics of Stations in Delhi Our predictions of future ground motions in Delhi rely heavily on the recordings of the Chamoli earthquake. Thus, it is useful to quantify the site effects at the stations where these recordings were obtained. Figure 4 (left) suggests that the RO station may be considered free from local site effects and may conveniently be taken as a reference site. The site effect is clearly visible in Figure 5 which shows that the high-frequency ground motions (e.g., accelerations) at “soft” sites (IHC, CSIR, CBCB) are about 3 to 4 times greater than that at the “hard” RO, while the difference is less for lowfrequency signals (e.g., velocity traces). The figure also

Figure 4. Source displacement (continuous curve) and acceleration spectra (dashed curve), M0(f ), and f 2M0(f ), of the Chamoli earthquake from data recorded in Delhi. Median and Ⳳ one standard deviation curves for each spectra are shown. (Left) Data from the hard Ridge Observatory site. Note that the spectra are well fit with M0 ⳱ 7.7 ⳯ 1025 dyne cm; an x2-source model, Q ⳱ 508f 0.48; and a stress drop, Dr, of 60 bars (continuous smooth curve). This is not the case for the spectra from CSIR, IHC, and CPCB (right), suggesting a strong local site effect at these sites.


shows the synthesized ground motions at the UDSC site, using an aftershock an EGF. We discuss this synthesis in a later section. Figure 6 shows spectral ratios of the horizontal components at the “soft” sites with respect to RO. The spectral ratios suggest that the amplification of seismic waves at “soft” sites of Delhi may reach a factor of up to about 20 at the dominant frequencies of the sites, which are roughly 1.4, 1.0, and 2.2 Hz at sites CPCB, IHC, and CSIR, respectively. Except for the IHC site, the estimations of the dominant frequencies obtained here agree with those given in CBRI (1998).

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Estimation of Ground Motion in Delhi from Large/ Great Earthquakes in the Central Seismic Gap Point-Source Approximation Random Summation of Empirical Green’s Functions. We use a technique for random summation of EGF to synthesize ground motions from future large earthquakes proposed by Ordaz et al. (1995). This scheme obeys the x2-source scaling law at all frequencies. The method requires specification of only the seismic moments and the stress drops of the EGF and the target event. The details of the method are given in Ordaz et al. (1995).

Figure 5.

East–west component of acceleration and velocity traces (high-pass filtered at 0.2 Hz) at sites in Delhi during the Chamoli earthquake. The simulated ground motion at UDSC, using an aftershock of the Chamoli earthquake as an EGF, is also shown (top traces).

Figure 6. Spectral ratios of soft sites to Ridge Observatory site during the Chamoli earthquake. Continuous curve, north–south component; dashed curve, east–west component. The traces were high-pass filtered 0.2 Hz before computing the spectral ratios.

562 We note that if only peak ground motion parameters are desired, then the computation of the time histories is not needed; the Fourier spectrum along with an estimation of duration (TR) of the intense part of the ground motion and application of results from random vibration theory (RVT) suffices (see Appendix B of Ordaz et al. [1995] for relevant formulas). In the synthesis, we have taken Dr ⳱ 60 bars for both the target and the EGF event. The duration TR in sec is given: TR ⳱ f cⳮ1 Ⳮ 0.05R, where f c is the corner frequency (equation 5) and R is the hypocentral distance in km (Herrmann, 1985). The expected values of Amax and Vmax as function of Mw at all Delhi sites and for all components are shown in Figure 7. For Mw 8.0, the expected Amax and Vmax on horizontal components at soft sites range between 40 to 60 gal and 5 to 13 cm/sec, respectively. The corresponding values for the Z component range between 18 to 40 gal, and 4 to 5 cm/sec, respectively. As expected, Amax at the hard site of RO is 3 to 4 times less than at the soft sites. The difference is smaller for Vmax, which is roughly half at the hard site as compared to the soft sites. Figure 8 summarizes observed and estimated horizontal Amax and Vmax as function of Mw at Delhi sites. In this figure, we have included the peak values from aftershocks recorded at UDSC (Table 3), which are shown by large plusses. The smaller plusses indicate estimated values using the aftershock of 29 March 1999 (Mw 4.63) as the EGF (Table 3) and the random summation technique described previously. In these simulations we have again used Dr ⳱ 60 bars. Examples of synthesized traces for a Mw 6.5 earthquake are shown in Figure 5. The estimated Amax and Vmax values at UDSC for Mw 6.5 earthquake are within a factor of 2 of the recorded value at RO during the Chamoli earthquake (Figs. 5 and 8). In Figure 8 the peak values corresponding to Mw⬎6.5 are taken from Figure 7, which were synthesized using the Chamoli recordings as the EGFs. Simulation of Ground Motion Using Point-Source Stochastic Method. This method was first proposed by Hanks and McGuire (1981) and later extended by Boore (1983). Hanks and McGuire (1981) related root mean square (rms) acceleration to x2-source spectrum modified by attenuation, through Parseval’s theorem. The expected peak amplitude is obtained from the rms amplitude using equations of the RVT (Cartwright and Longuet-Higgins, 1956). Boore (1983) extended these results to predict Vmax and response spectra by generating time series of filtered and windowed Gaussian noise whose amplitude spectrum approximated the acceleration spectrum. Here, we briefly outline some relevant aspects of the method. For an x2-source model, the source spectrum of an earthquake is completely specified by its seismic moment and the stress drop (equations 1–5). To simulate the observed spectra at a site, the right-hand side of equation (1) needs to be multiplied by a high-cut filter. Following Boore (1986),


we choose a butterworth filter given by [1 Ⳮ (f /f m)8]ⳮ1/2. In our calculations we have set f m to 15 Hz. Figure 8 shows expected Amax and Vmax for Q ⳱ 508f 0.48 and Dr ⳱ 60, 100, and 200 bars. The aftershock data at UDSC and the mainshock data at RO are well explained by Dr between 50 and 200 bars. In Figure 8 we notice that the estimated Amax value for Mw ⱖ7.0 using the EGF technique (crosses) lies above the predicted curve from the point-source stochastic method with Dr ⳱ 100 bars. However, the corresponding estimated Vmax values lie below the predicted curve for Dr ⳱ 100 bars. Our tests show that there are two reasons for this. First, the Chamoli EGF recordings have been high-pass filtered at 0.2 Hz. The contribution to Vmax from low-frequency waves become important for large earthquakes. Signals below 0.2 Hz are missing in simulations using the EGF technique but not in the synthesis using the point-source stochastic method. Second, Chamoli Amax and Vmax data cannot be simultaneously explained by a single Dr even when the EGF is not high-pass filtered. From Figure 8 we conclude that the predicted ground motions at hard sites in Delhi from the two techniques are within a factor of about 2 of each other. It is useful to compare the observed peak values during the Chamoli earthquake over the entire distance range with the predicted ones from the point-source stochastic method for a Mw 6.5 earthquake. The comparison shows that, at some sites, the observed horizontal Amax and Vmax values are much higher than those predicted even with Dr ⳱ 200 bars (Fig. 3a). For example, this is the case at Gopeshwar, Ghansiali, Tehri, Uttarkashi, Roorkee, Panipat, and at the three soft sites in Delhi. We attribute this difference to the effect of local surface geology. As we verified earlier, this is the case of the soft sites in Delhi. Simulation of Ground Motion Using Finite-Source Stochastic Method The estimation of ground motion above is based on the assumptions that the source follows x2 scaling in the far field irrespective of the size of the earthquake and that the pointsource approximation is valid (i.e., the source dimension and the wavelength of interest are smaller than the distance to the observation). Rupture area, A, of an earthquake may be estimated from the relation: log A ⳱ Mw ⳮ 4.0, where A is in km2 (Wyss, 1979; Singh et al., 1980). Assuming that the width, W, of the fault along the Himalayan arc does not exceed 80 km, the length, L, for Mw 8.0 and 8.5 earthquakes are 125 and 400 km, respectively. As the closest distance from the postulated earthquake to Delhi may be between 200 and 300 km, the point-source approximation for such earthquakes is grossly violated. To account for the finiteness of the source, we use a modification introduced by Beresnev and Atkinson (1997, 1998, 1999, 2001) to the point-source stochastic method. A description of the computer program is given in Beresnev and Atkinson (1998). The fault plane is divided in subfaults whose size, Dl, in km, is given by log


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Figure 7.

Predicted peak ground motions at sites in Delhi from postulated future large earthquakes. High-pass filtered (.02 Hz) Chamoli earthquake recordings have been used as empirical Green’s functions (EGFs). Stress drop is 60 bars for the both the EGF and the target event. Crosses, Ridge Observatory; triangles, IHC; open circle, CPCB; square, CSIR.

Dl ⳱ 0.4 Mw ⳮ 2.0. The subfaults are stochastic x2 sources. The subevent time history at a site is generated following the procedure of Boore (1983). The rupture propagates radially from a specified hypocenter. A standard technique sums the contribution from each subfault. Randomness is introduced in the subevent rupture times. A stress parameter, which relates subfault moment and its size, is fixed at 50 bars. A free parameter, called the strength factor, which controls the level of high-frequency radiation, needs to be specified (see Beresnev and Atkinson, 1997, 1998). In the present case, we assume a standard earthquake (strength factor ⳱ 1.0). All other required parameters are the same as in the case of point-source stochastic method. The program permits site effect to be included in the computation. We assume no site effect at RO. The logarithmic average of north–south and east–west spectral ratios (Fig. 6) between 0.4 Hz and 15 Hz is taken as the site effect at CBCP, IHC, and CSIR. We assume that below 0.4 Hz and above 15 Hz the spectral ratio has the same value as at 0.4 and 15 Hz, respectively.

In finite-source calculations we consider two locations of the rupture area (Fig.1b). In one, the rupture area is centered at the hypocenter of the Chamoli earthquake. In the other, this area lies between MCT and MBT, centered at 30.0⬚ N, 79.2⬚ E. In both cases, the center of the fault is at a depth of 16 km. The second location corresponds to the scenario considered by Khattri (1999). The strike and the dip of the fault have been taken as 300⬚ and 7⬚, respectively. These values are similar to those chosen by Khattri (1999). Simulations were performed for three hypocenter locations: the northeast edge of the fault, the center of the fault, and the center of the downdip edge of the fault (points A, B, and C in Fig. 1b). Assuming W ⱕ 80 km, the expected L ⳯ W for Mw 7.0, 7.5, 8.0, and 8.5 are 32 ⳯ 32 km, 56 ⳯ 56 km, 125 ⳯ 80 km, and 400 ⳯ 80 km, respectively. Khattri (1999) takes a rupture area of 240 ⳯ 80 km in his simulations of the target earthquake of Mw 8.5. We performed computations for both rupture areas for this earthquake. The results do not differ significantly.

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Figure 8. Observed and predicted horizontal Amax and Vmax as function of Mw at Delhi sites. Results from both the EGF technique and the point-source stochastic method are shown. EGF predictions are based on Dr ⳱ 60 bars; for Mw ⬎6.5 they are taken from Figure 7. The figure also includes the peak values from aftershocks recorded at UDSC shown by large plusses. The smaller plusses indicate predicted values using an aftershock as the EGF (see text). Continuous curves show predictions at hard sites in Delhi from the stochastic method with Q ⳱ 508f 0.48 and Dr values of 60,100, and 200 bars.

Table 5 summarizes Amax and Vmax values for different rupture scenarios. Each value corresponds to an average of 15 simulations. The results given in Table 5 for Mw 8.5 are based on a rupture area of 240 ⳯ 80 km. Figure 9 shows estimated peak ground motions from finite-source simulations (open and solid circles). The hypocenter is located at B, the center of the fault. The predicted values from EGF technique are also shown in the figure (crosses). These values should be compared with finitesource calculations for rupture area centered at the hypocenter of the Chamoli earthquake (open circles). The predictions from the finite-source stochastic model for Mw 6.5 earthquake are in rough agreement with the observed data at all four sites, giving us confidence that the parameters chosen in the simulations are reasonable. Figure 9 also suggests that the predictions from the point-source EGF summation technique may be acceptable for target events in the Chamoli region of magnitude less that about 7.5. For larger earthquakes, the finiteness of the source can not be ignored. Table 5 shows that the expected peak ground motions are larger for a postulated rupture area confined between MBT and MCT as compared to the rupture centered at the Chamoli hypocenter. This is expected since the former rupture area is closer to Delhi than the latter one (Fig. 1b). Generally, the largest ground motions in Delhi result from hypocenter A, located at the northeast edge of the fault. This is because of the directivity effect. For a rupture confined

between MBT and MCT and hypocenter at A, the predicted Amax and Vmax for Mw 8.0 at the hard site of RO are about 28 gal and 6 cm/sec, respectively. The corresponding values at soft sites range between 96 and 140 gal and 8 to 19 cm/ sec. For Mw 8.5, the values of Amax and Vmax at RO are about 52 gal and 13 cm/sec, respectively. The corresponding values at soft sites range between 174 and 218 gal and 17 to 36 cm/sec. It is interesting to note that horizontal Amax and Vmax estimated by Khattri (1999) for Mw 8.5 range between 160 to 210 gal and 28 to 32 cm/sec, respectively. These values are remarkably similar to those given in Table 5 at soft sites. Simulated Ground-Motion Time Series, and Response Spectra Samples of simulated horizontal accelerations, as well as velocities, for Mw 7.5, 8.0, and 8.5 at sites CPCB and RO are shown in Figure 10. These computations correspond to the rupture area lying between MBT and MCT and the hypocenter located at A (Fig. 1b). The figure also illustrates the east–west component of the Chamoli earthquake recording. The expected horizontal pseudoacceleration response spectra (5% damping), Sa, from these postulated earthquakes at CPCB and RO sites (average of 15 simulations) are shown in Figure 11. For comparison, the figure also includes Sa computed by Khattri (1999) for a Mw 8.5 earthquake. At CPCB, Sa presented by Khattri is nearly equal to

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Table 5 Predicted Horizontal Amax and Vmax in Delhi from Earthquakes in the Central Seismic Gap of the Himalayan Arc Using the Finite-Source Stochastic Method Ridge Obs. Rupture Location*

Centered at Chamoli hypocenter

IHC

CSIR

Amax (gal)

Vmax (cm/sec)

Amax (gal)

Vmax (cm/sec)

Amax (gal)

Vmax (cm/sec)

Hypocenter*

Mw†

A

7.5 8.0 8.5 7.5 8.0 8.5 7.5 8.0 8.5

11.9 23.1 35.6 11.8 19.6 32.9 11.9 20.7 36.0

2.4 5.6 11.9 2.3 5.2 11.9 2.3 5.1 13.0

59.6 110.2 165.4 48.7 88.1 151.3 52.4 99.8 171.6

7.2 15.2 26.4 6.0 13.4 27.8 5.9 13.5 26.2

55.8 103.1 162.1 50.4 91.5 144.2 56.2 90.2 137.7

8.9 16.8 27.0 8.0 13.5 24.4 8.1 14.2 24.4

43.8 76.4 114.8 39.5 66.8 112.4 54.9 95.8 173.9

3.8 6.7 12.7 3.4 6.5 13.7 4.1 8.0 17.1

7.5 8.0 8.5 7.5 8.0 8.5 7.5 8.0 8.5

17.3 28.3 51.9 15.4 27.7 47.6 18.5 26.9 50.1

2.9 6.2 12.9 2.4 6.2 14.3 2.8 6.2 16.8

81.1 139.6 218.0 72.5 120.7 202.5 72.5 125.6 189.2

9.4 16.7 32.9 8.4 14.5 30.8 8.2 16.1 33.0

70.2 121.4 208.6 69.8 116.7 198.6 70.0 120.2 219.3

10.9 19.4 36.2 10.6 17.6 37.0 10.8 19.3 40.7

54.9 95.8 173.9 51.8 89.0 159.9 55.8 94.4 158.1

4.1 8.0 17.1 3.7 8.1 18.9 4.1 8.1 17.2

B

C

Between MBT-MCT with center at 30.0⬚, 79.2⬚

CPCB

Vmax (cm/sec)

Amax (gal)

A

B

C

*See Figure 1b. † Rupture area computed from the relation log A ⳱ Mw ⳮ 4.0, where A is in km2. Width is not allowed to exceed 80 km. For Mw 8.5, length ⳱ 240 km, width ⳱ 80 km.

the Sa estimated here for Mw 8.5 at frequencies between 4 and 10 Hz. At lower frequencies the two spectra deviate: the Sa given by Khattri is smaller by a factor of 2 to 4 between 0.8 and 2 Hz as compared to our estimation. The Sa given by Khattri clearly overestimates the expected Sa predicted here for hard sites in Delhi, such as the RO site.

Discussion and Concluding Remarks Figures 7–9 summarize our predictions of peak ground motions in Delhi from future earthquakes in and near the Chamoli region of the central seismic gap. These predictions are for two groups of sites: hard sites that may be similar to the Ridge Observatory (RO) and University of Delhi, South campus (UDSC) sites, and soft ones whose characteristics may be similar to CSIR, IHC, and CPCB sites. There must be zones in Delhi that do not fall in either of the two groups. A microzonation of the region will be needed to identify them, to determine their transfer functions with respect to a reference hard site, such as the RO or UDSC, and to estimate ground motions in these areas. The predictions in Figure 7 and 8 are based on pointsource approximation using random summation of EGF and the stochastic method. The results from the EGF technique is, of course, valid for target events located in the Chamoli area only. The rupture areas of future earthquakes may lie closer to Delhi, delimited by the main boundary thrust (MBT) and main central thrust (MCT) (Fig. 1b). Figure 9 and Table 5 summarize expected peak ground motions com-

puted from finite-source stochastic method for several of rupture scenarios. A comparison of Figures 7–9 suggest that point-source approximation may be valid for Mw less than about 7.5. Thus, Figures 7 and 8 may be useful in estimating Amax and Vmax for Mw ⬍ 7.5 from target events located in the Chamoli region. The largest ground motion in Delhi result from rupture areas confined between MBT and MCT, with rupture initiating at the northeast edge of the fault. In this case, the calculations based on the finite-source stochastic method predict horizontal Amax and Vmax at soft sites in Delhi between 174 and 218 gal and 17 to 36 cm/sec, respectively for Mw 8.5 (Table 5). These values are remarkably similar to those reported by Khattri (1999). However, there are significant differences in the pseudoacceleration response spectra (5% damping) (Fig. 11), reflecting the effect of local surface geology that is included in our study but is missing from Khattri’s estimations. Our point-source predictions are based on a stress drop of 60 bars, and the finite-source estimations correspond to a standard earthquake (see Beresnev and Atkinson, 1998). The estimated peak ground motions are uncertain by a factor of at least 2 due to uncertainty in these assumptions and the deviation of the source spectrum from x2-source model. These are only the model-inherent uncertainties, the total uncertainty, of course, is likely to be larger. Perhaps the area of highest seismic hazard in Delhi is the one located to the east of Yamuna river, which is underlain by recent fluvial deposit (Fig. 2). The CPCB site is located in this area. For postulated Mw ⱖ 8.0 earthquakes,

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Figure 9. Predicted peak ground motions at sites in Delhi from postulated earthquakes using finite-source stochastic method. The hypocenter is taken at the center of fault (Fig. 1b). Open circles, rupture areas centered at the Chamoli hypocenter; solid circles, the rupture confined between MBT and MCT (Fig. 1b). Crosses at Mw 6.5 represent recorded peak motions during the Chamoli earthquakes; those corresponding to larger magnitudes represent predicted values using high-pass filtered (0.2 Hz) Chamoli earthquake recordings as empirical Green’s functions. (a) Ridge Observatory, (b) CPCB site, (c) IHC site, and (d) CSIR site.


567

Figure 10. Samples of simulated horizontal ground motions at CPCB and RO, using finite-source stochastic method. Chamoli recording (east–west component) is also shown.

the predicted Amax values exceed 100 gal at CPCB, as they do also at IHC and CSIR. At this level of ground motion significant liquefaction may be expected in areas underlain by the fluvial deposits (see, e.g., Kramer, 1996, chapter 9). Clearly, there is an urgent need to record earthquakes simultaneously at many representative sites in the Delhi area and to carry out a microzonation of the city. This study and the work of Khattri (1999) provide a preliminary and rough estimation of ground motions in Delhi from future large earthquakes in and near the Chamoli region. More work is

needed in the synthesis of ground motion during large/great earthquakes, using different techniques.

Acknowledgments We are grateful to Central Building Research Institute (CBRI), Roorkee; Department of Earthquake Engineering (DEQ), University of Roorkee; for providing us with the Chamoli earthquake recordings. The India Meteorological Department (IMD) kindly made the seismograms recorded at Ridge Observatory, Delhi, available to us. We thank I. Beresnev for providing us the finite-source program; K. N. Khattri, R. K. Midha, and H. K.

568


Figure 11.

Pseudoacceleration response spectra (5% damping), Sa, at CPCB and RO sites obtained from finite-source stochastic method for Mw 7.5, 8.0, and 8.5. For comparison, the Sa curves (N–S and E–W components) reported by Khattri (1999) for an Mw 8.5 earthquake are also shown.

Gupta for their interest and encouragement during the course of this research; Mario Ordaz for fruitful discussions; Joan Gomberg for a careful revision of the manuscript; and Javier Pacheco and Lars Ottemoeller for helping us in casting some of the data in a form that we could easily use. Comments by G. Atkinson and an anonymous reviewer forced us to consider some important issues that we had previously ignored. V. K. Gahalaut participated in the early stage of the research. Lourdes Godinez helped us in preparing some figures. The research was partially supported by DGAPA, UNAM Project IN109598.

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