Simulated Strong Ground Motion in Southern China based on Regional Seismographic Data and Stochastic Finite-Fault Model Yuk Lung WONG and Sihua ZHENG ABSTRACT The acceleration time histories of the horizontal components at bedrock of possible strong earthquakes in southern China are simulated by a stochastic finite-fault method using an equivalent point-source model and the attenuation parameters calibrated from the digital seismic data of 44 small/medium earthquakes recorded in the region. The simulations are performed for the moment magnitudes of 5.5, 6.5, 7.5, and 8.5 at the epicentral distances ranging from 1.0 to 1000 km, from which the velocities and displacement time histories, and the subsequent PGA, PGV, and PGD can be established/measured. The simulated peak ground accelerations are then compared with those determined from the Huo s empirical ground motion attenuations that were deduced from intensity records. It is found that the simulated results are generally consistent with the Huo s empirical equations. This encouraging verification provides confidence in applying our proposed ground motion relations in the probabilistic and deterministic seismic-hazard studies of southern China. Yuk Lung WONG, Research Center for Urban Hazards Mitigation, The Hong Kong Polytechnic University, Hong Kong. Tel no: (852)-27666009, E-mail: ceylwong@inet.polyu.edu.hk. (contact person and presenter) Sihua ZHENG, Center for Analysis and Prediction, China Seismological Bureau, Beijing, 100036, China.
1. INTRODUCTION Although the seismic levels of many parts of southern China are considered to be low to moderate, the recently tremendous economic growth and traditionally dense population of the region urge an increasing concern on the seismic risks, and the consequences of damage to structures/society in the region. The needs to rationally quantify the seismic hazard and to establish an acceptable level of protection against major earthquakes are becoming apparent. Publications (Wong et al., 1998) show that there were several large earthquakes occurred in southern China during the historic and modern times but no strong ground motion data was ever recorded by instrument. The lack of observed strong motion data imposes difficulties in assessing the seismic hazard with confidence. In order to resolve this deficiency, the estimated ground motion relations were traditionally converted from the observed intensity attenuation using a deductive method suggested by Hu and Zhang (1984), and Huo et al. (1992). This paper presents an alternative approach to determine the strong ground motion characteristics in southern China using an established finite-fault simulation model with seismological parameters that were derived from the seismographic data of small and medium earthquakes measured in this region. The simulated peak ground acceleration data so obtained are then compared with those deduced from intensity records proposed by Huo et al (1992). 2. STOCHASTIC SIMULATION METHOD The method starts with the generation of a windowed time series of band limited random white Gaussian noise with zero mean amplitude. A shaping window (Saragoni and Hart, 1974) is applied into the time series to produce a windowed time series. The length of the shaping window is controlled by the source duration, which depends on the size of an earthquake and the epicentral distance. The spectrum of the windowed time series is then normalized by the root of the mean square amplitude spectrum. The normalized spectrum is firstly multiplied by the desired Fourier amplitude spectrum, which will be described in the following section, and then transformed back to the time domain to yield a simulated ground motion time history. Thus by repeating this process many times, and changing just the seed of the pseudo-random number generator, a suite of representative time series is obtained, from which the peak values can be measured. 2.1 Desired Acceleration Amplitude Spectrum The horizontal component of a desired acceleration amplitude spectrum a ( M, R, f ), defined by a source model and a propagation model, is a function of moment magnitude ( M ) and distance ( R ). It is expressed as: a( M, R, f ) = C S( M, f ) D( R, f ) P( f ) A( f ) (1) where C is a scaling factor; S ( M, f ) is a source function; D ( R, f ) is a seismic attenuation function, P ( f ) is a high-frequency truncation filter, and A ( f ) is a site amplification (Atkinson and Boore, 1995).
The scaling factor C is given by < Rϑϕ > F V C = (2) 3 4π ρ β where < R ϑϕ > is the radiation pattern averaged over an appropriate range of azimuth and take-off angle, F accounts for free surface effects, V represents the partition of a vector into horizontal 2 components. These constants are taken as follows: < R ϑϕ >= 0. 55, F = 2. 0, V = = 0. 71, ρ = 2 2.7 gm/cm 3, and β = 3.5 km/sec (Fan et al., 1986). It is assumed that the energy is equally partitioned into two horizontal components. The seismic attenuation function is represented by π f R D ( R, f ) = G( R) exp[ ] (3) Q( f ) β where G(R) is a geometric attenuation function, and Q( f ) is a frequency-dependent anelastic attenuation. The P( f ) filter is used to model the observation that an acceleration spectral density appears to fall off rapidly beyond maximum frequency (Hanks, 1982; Silva and Darragh, 1995). In the stochastic simulation method, the band limits are the source corner frequency at a low frequency and the high-frequency truncation filter at a high frequency. We adopt P ( f ) (Anderson and Hough, 1984) as: P( f ) = exp( π κ f ) (4) The parameter Kappa ( κ ) represents the effect of an intrinsic attenuation upon the wavefield as it propagates through the crust from the source to the receiver. However, for southern China, the coefficient κ of the high-frequency truncation filter is still unsolved. Nevertheless, as only the ground motion at bedrock is considered in this study, we assume the coefficient κ to be 0.002 sec (Atkinson and Boore, 1995; Atkinson and Beresnev, 2002), and the site amplification A ( f ) = 1. 2.1.1 Equivalent Point-source Model Atkinson and Silva (2000) postulated also that a point-source with a two-corner source spectrum was equivalent to a finite-fault model comprised of a number of Brune point-sources. It means that the two-corner point-source and the finite-fault stochastic models will generate similar ground motions, when averaged over all azimuths. The point source model with two-corner frequencies is called the equivalent point-source model. The equivalent point-source spectrum is characterized by a high-frequency level that corresponds to a Brune point-source model. However, the spectrum sags at intermediate frequencies, relative to the Brune model. The acceleration spectrum of the equivalent point-source can be described by the functional form suggested by Atkinson (1993) and Atkinson and Boore (1998): 2 (1 ε) ε S( M, f ) = (2πf ) M[ + ] (5) f 2 f 2 1+ ( ) 1+ ( ) f a f b
where f a is the lower corner frequency, f b the higher corner frequency, and ε is a relative weighting parameter whose value lies between 0 and 1 (when ε = 1, the two-corner model is identical to a single-corner Brune model). The lower corner frequency, f a, is determined by the source duration ( T 0 ) as. T = 1 0 2 f a (Boarwrite and Choy, 1992). From the empirical data of source durations, it is suggested (Atkinson, 1993) that: log f a = 2.181 0. 496M (6) The higher corner frequency, f b, is the frequency at which the spectrum attains half of the high-frequency amplitude level. By determining f b for the simulated events of moment magnitudes M of 4.0 to 8.0, and fitting these values as a function of M, Atkinson and Silva (2000) obtained: log f b = 2.41 0. 408M (7) The value of ε was also determined by fitting the average finite-fault spectra defined at R = 1km to Equation (5). The best fit (Atkinson and Silva, 2000) was derived as: logε = 0.605 0.255M (8) In this case, the stochastic-based ground-motion relations, expressing median expected levels of peak-ground acceleration as a function of magnitude and distance, can be developed directly from the equivalent point-source model using Equation (5) as S ( M, f ) in Equation (1). This approach has the advantages of simplicity and stability. Figure. 1 illustrates the resultant simulated spectrum created by multiplying the normalized spectrum of windowed time series with the desired acceleration amplitude spectrum with two corner frequencies f a and f b. The desired acceleration amplitude spectrum in the Figure 1 has incorporated the seismic attenuation function and the high-frequency truncation filter, details of which will be reported in the next section. The resultant simulated spectrum is transformed back to the time domain to yield a final acceleration waveform through integration. Figure 1 Formulation of desired simulated spectrum
2.1.2 Attenuation model Based on the study of the intensity data, Hanks and Johnston (1992) firstly suggested that near-source damage levels were similar in the different regions, for example, eastern North America (ENA) and California. Beresnev and Atkinson (1999, 2002) performed detailed finite-fault stochastic modeling of all well-recorded moderate-to-large earthquakes in ENA and California, and found no systematic regional differences in source properties. The observed differences between ENA and California motions could be mainly attributable to the regional differences in crustal properties and seismic attenuation. We determine the seismic attenuation function for the Guangdong region (the largest province in southern China) by empirical analysis of the regional seismographic data. The dataset consists of 249 selected horizontal-component digital seismograms from 44 earthquake events (M L = 2.5 to 5.1) between September 1999 to October 2000, recorded by the Guangdong Telemetered Network. Figure 2 shows the locations of the stations and the events. Straight lines indicate the propagation paths of the available data. The distances between the earthquake sources and the observation stations vary from 10 km to 500 km. Figure 2 Distribution of stations and events (open triangles indicate location of stations and solid circles indicate locations of events) A lag-window spectra technique similar to the analytical technique reported by Atkinson and Mereu (1992) is adopted to obtain the stable Fourier spectra of these seismic signals, and to perform the inversion regression using Genetic Algorithm technique. It is found that the geometrical spreading function of the region can be best represented by a 1 tri-linear piecewise continuous function. The amplitude of the seismic wave is a function of R for a distance less than 45 km. It remains constant within a distance from 45 to 100 km, and takes the 0.5 form of R at a distance beyond 100 km (see Figure 3). The anelastic attenuation associated with
this spreading model is represented by a frequency-dependent regional quality factor 0.31 Q ( f ) = 481.5 f. Figure 3 Observed decay of normalized amplitude (for f = 8.91Hz). Here we assume that the propagation property in southern China is more or less the same as that in the Guangdong region. 3. RESULTS AND DISCUSSIONS 3.1 Desired Acceleration Spectrum Based on the above-mentioned equivalent point-source model and the selected parametric values, the desired acceleration amplitude spectrum a ( M, R, f ) can be calculated. As an example, the desired acceleration amplitude spectra of southern China earthquakes with moment magnitudes M of 8.5, 7.5, 6.5 and 5.5, at a distance of R = 10 km, are shown in Figure 4. The spectra fall off at high frequencies due to the effect of the seismic anelastic attenuation and the high-frequency truncation filter. Figure 5 compares the desired acceleration amplitude spectrum at different distances. It is also evident that the spectrum at longer distances decays rapidly at a high frequency because of the effect of the frequency-dependent anelastic attenuation.
Figure 4 Desired acceleration amplitude spectrum at R = 10 km Figure 5 Desired acceleration amplitude spectrum at different distances
3.2 Simulated Peak Ground Motions Simulations for the moment magnitudes M of 8.5, 7.5, 6.5, and 5.5 are performed for 38 distances ranging from 1 to 1000 km. A total of 200 simulations are calculated for each pair of M and R values, and a family of representative horizontal components of acceleration time histories are determined. From the acceleration time histories, we can estimate ground velocities and ground displacements by integration as shown in Figure 6, which is for the waveforms from an earthquake with M of 8.5 at distance of 10 km. The peak parameters of the ground motions, PGA (Peak Ground Acceleration), PGV (Peak Ground Velocity) and PGD (Peak Ground Displacement) are measured from the respective time histories. The simulated results for PGA, PGV, and PGD on the bedrock in southern China for M of 8.5, 7.5, 6.5 and 5.5 at different source distances are also plotted in Figures 7, 8, and 9 respectively. Figure 6 Simulated acceleration, velocity and displacement time histories of earthquake with moment magnitude of 8.5 at distance of 10 km Figure 7 Simulated PGA at bedrock in southern China
Figure 8 Simulated PGV at bedrock in southern China Figure 9 Simulated PGD at bedrock in southern China 3.3 Comparison with Empirical Ground Motion Models for Southern China In China, there are ample intensity data of historical earthquakes but very limited measured strong ground motion data. Consequently, the ground motion relations at bedrock were traditionally determined using a deductive method suggested by Hu and Zhang (1984). By converting the intensity attenuation relation, Huo et al. (1992) suggested the following attenuation relation of PGA for southern China using an elliptical attenuation model:
For the major axis: log( ) = 1.2629 + 1.4956M a L 0.0513M 2 2.2252 log( D + 0.3618 exp(0.6989m )) (9) For the minor axis: 2 log( a S ) = 2.0301+ 1.4573M 0.0501M 1.9731 log( D + 0.1201 exp(0.7654m )) (10) where D is epicentral distance, M is magnitude Although the definition of the magnitude scale was not mentioned in that paper, the same authors in another paper adopted M = M for a magnitude equals to or greater than 6; and M = M for a magnitude smaller than 6. L S Figure 10 shows the simulated PGA obtained in this study and the logarithm-average of the major and minor axes of the elliptical attenuation model of Huo et al. (1992). For easy comparison purposes, M s is chosen as a common magnitude scale. The conversion relations are assumed to be M W = M S for the moment magnitude M w between of 5 and 7.5; and M W > M S for the moment magnitude greater than 7.5 (Hu, et al., 1996). When M L is smaller than 6, M S = 1.13M L 1. 08. We also define the residual as the difference between the nature-logarithms of the PGA derived from the Hu s attenuation model and that obtained in this study. It is found that although the residual value increases with the epicentral distance (see Figure 11), the absolute values of the residual are considered to be small (less than 0.2 and 0.6 for the epicentral distances of 20 km and 200 km respectively). Thus the simulated ground motions from our stochastic simulation are comparable to those proposed by the Huo s empirical attenuation relations established from the intensity data of earthquakes. Figure 9 Comparison between simulated PGA in this study and that proposed by Huo et al. (1992)
Figure 10 Residuals between simulated PGA in this study and that proposed by Huo et al. (1992) 4. CONCLUSIONS The acceleration time histories of the horizontal components at bedrock of possible strong earthquakes in southern China are simulated by a stochastic finite-fault method using an equivalent point-source model and the attenuation parameters calibrated from the digital seismic data of 44 small/medium earthquakes recorded in the region. The simulations are performed for the moment magnitudes of 5.5, 6.5, 7.5, and 8.5 at the epicentral distances ranging from 1.0 to 1000 km, from which the velocities and displacement time histories, and the subsequent PGA, PGV, and PGD can be established/measured. The simulated peak ground accelerations are then compared with those determined from the Huo s empirical ground motion attenuations that were deduced from intensity records. It is found that the simulated results are generally consistent with the Huo s empirical equations. This encouraging verification provides confidence in applying our proposed ground motion relations in the probabilistic and deterministic seismic-hazard studies of southern China. 5. ACKNOWLEDGEMENTS This study is part of the ASD Project on ground motions and response spectra for seismic design in Hong Kong funded by The Hong Kong Polytechnic University. Simulations are performed using SMSIM code (Boore, 2000). Some figures in this paper have been produced using the free software GMT (Wessel and Smith, 1998).
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