Rise time and source duration of the 2008 MW 7.9 Wenchuan (China) earthquake as revealed by Rayleigh waves
The fault parameters of the 2008 Wenchuan earthquake were studied in a rupture directivity analysis by simultaneously inverting the period of the first Fourier spectral-node and the 100-s phase-delay time of the Rayleigh wave. The results show that the earthquake is a unilateral event with an optimal rupture azimuth of N59°E, consistent with the distribution of aftershocks. They also indicate that the fault plane strike is in the NE-SW direction, corresponding to the fault plane strike of 238° and NW-dipping (reported by the USGS). The inversion shows the source duration (including the rise time and rupture time) and rise time are 70±0.8 s and 9.3±0.6 s, respectively. The rupture velocity estimated only from the rupture time exhibits relatively higher value, 3.45±0.10 km/s, close to or larger than the S-wave velocity in the crust. One possible cause is that the rupture mechanism transferred from the thrust faulting in the southwestern portion of the fault to the strike-slip faulting in the northeastern one. The rise time offers an estimate of the dynamic stress drop (37.8±2.3 bars), from which through a macroscopic view the radiated seismic energy of (5.93±0.4) × 1016 N m is calculated. Although the estimated rupture length (∼210 km) and source duration are shorter than several source rupture models, the current analyses show the first-order rupture feature of the 2008 Wenchuan earthquake rupturing the Longmenshan fault zone.
Key wordsRise time source duration Rayleigh waves phase velocity rupture directivity
A large earthquake due to long faulting and extension typically causes variations in seismic-wave duration and amplitude with the station azimuth; this is referred to as rupture directivity. Ben-Menahem (1961) first proposed the finite moving source theory to account for the effect of rupture propagation (i.e., source finiteness) on far-field seismo-grams, such as the Doppler effect. Source finiteness results in a time delay in surface-wave propagation and a number of nodes in the Fourier spectra (Ben-Menahem, 1961; Hwang et al., 2001; Aki and Richards, 2002; Chang et al., 2010). In the study reported here, we have estimated the azimuth-dependent phase-delay time of Rayleigh waves (i.e., source duration variation with azimuth) due to source rupture directivity during the 2008 Wenchuan earthquake (cf. Chang, 2009). Subsequently, this work combines the phase-delay time and spectral-node periods of Rayleigh waves to determine the fault parameters of the 2008 Wenchuan earthquake based on the finite moving source theory and to reveal its first-order rupture feature.
2. Data and Phase-Velocity Measurements
Long-period Rayleigh waves generated by the 2008 Wenchuan earthquake were extracted from vertical-component seismograms provided by the IRIS Data Management Center. Only seismic data with good Rayleigh-wave energy excitation and epicentral distances ranging from 30° to 90° were used in this study to measure the phase-velocity along the great-circle path. Prior to performing the phase-velocity measurements, we removed the instrumental response from each seismogram.
3. Rupture Directivity Analysis
Because the phase-velocity (C) in Eq. (3) is also a function of period, it is difficult to perform the joint inversion with Eq. (4) only using a 100-s phase-velocity of the Rayleigh wave. It is known that the rise time is azimuth independent and not a function of period. Under the same C, the apparent source duration estimated from travel-time is larger than that estimated from the period of spectral-node; the difference in time between the two apparent source duration is then the rise time (see Eqs. (2) and (3)). The distribution of aftershocks and fault plane solution (from the USGS and GCMT) showed possible rupture azimuth, ∼60°. In order to make the observed source duration independent of azimuth and period (i.e., average source duration), we first selected the stations located at the azimuth around ∼150° or ∼330°, perpendicular to the rupture direction, in order to remove cos Θ from Eqs. (2) and (3). The apparent source duration observed at the azimuth around ∼150° or ∼330° is approximately 60–70 s, which can be regarded as the average source duration. Following Geller (1976), the rise time is about 10–20% of the average source duration. That is, the rise time is probably 6–14 s. In fact, in this study, spectral-nodes observed at stations with an azimuth around ∼150° are absent, so only those observed at a station azimuth of around ∼330° are used. For stations with an azimuth around ∼330°, we picked out the period of the first spectral-node that was less than the apparent source duration estimated from the travel-time by 7–14 s, averaging ∼10 s, adhering to Geller’s suggestions. In other words, the difference in time between the two apparent source durations (estimated from travel-time and spectral-node period, respectively) for the rest of stations should also be around ∼10 s since the rise time is independent of both azimuth and period. This gives us information for assessing the spectral-node period. Hence, in order to make Eq. (4) available only using the 100-s phase-velocity of Rayleigh-wave, we have to apply the following criteria in choosing the applicable spectral-node period for a given station: (1) the apparent source duration estimated from spectral-node period (Open image in new window) is less than that estimated from Rayleigh-wave travel-time (TSPT), i.e., Open image in new window; (2) (TSPT - nTn) is around ∼10 s.
Fault parameters estimated in this study.
Static stress drop
Dynamic stress drop
Radiated seismic energy
(5.93 ± 0.4) × 1016 Nm
Following Mai and Beroza (2000), the efficient width (w) of the fault is about 0.77-fold as large as the width of the source rupture model. Hence, from the source model of Ji and Hayes (2008), the efficient width of the fault for the 2008 Wenchuan earthquake is about 30.8 km. Using Open image in new window and taking Open image in new window N m (seismic moment from the USGS), Open image in new window (the rigidity in the source area using Open image in new window with Open image in new window and Open image in new window) and A = 209.6 × 30.8 km2 (the area of the fault), the average dislocation (D) is then about 4.27 m. Since this study estimates the rise time to be 9.3 s, the average particle velocity (D) is about 46±2.8 cm/s. For this reason, we determine the average dynamic stress drop to be about 37.8±2.3 bars following Brune (1970), using Open image in new window (the average S-wave velocity β = 3.36 km/s in the source area within a 20-km depth of the crust following Pei et al. (2010)). Given that the 2008 Wenchuan earthquake did break the surface (cf. Nishimura and Yagi, 2008; Sladen, 2008; Wang et al., 2008; Shen et al., 2009; Zhao et al., 2010), we estimate the static stress drop to be 32.5 bars using Open image in new window when taking λ = μ and w = 30.8 km. An estimate of the radiated seismic energy (ES), according to Open image in new window (Kanamori and Heaton, 2000), is (5.93 ± 0.4) x 1016 N m; moreover, the ES/M() ratio is (7.8 ±0.5) × 10−5. Table 1 lists these estimated fault parameters of the 2008 Wenchuan earthquake.
5. Discussion and Conclusions
A steep variation in travel-time was observed at stations RER and XMIS, particularly for RER (Fig. 2). Because these stations are approximately located at the opposite direction of faulting, the rupture directivity reduces significantly the observed amplitude of Rayleigh wave to make it difficult to measure phase-velocity due to the problem of phase-skip, especially for the short-period surface waves. We also derived the fault parameters from the 60-s Rayleigh wave; these show high consistencies with those derived from the 100-s Rayleigh wave, but appear to underestimate slightly the fault parameters when using short-period surface waves. Furthermore, Chang (2009) found that it is better to use the 100-s period surface wave in analyzing the fault parameters for large earthquakes with Mw 7.5–8.5.
Several groups have reported the fault plane solution for the 2008 Wenchuan earthquake using as the best double couple either 238°/59°/128° and 2°/47°/45° (strike/dip/rake) from the UGGS or 231°/35°/138° and 357°/68°/63° from the Global CMT. Our study measures the optimal rupture azimuth at 59° in the clockwise direction from the north, and the results indicate that the earthquake ruptured northeastward and that its fault plane is 238°/59°/128° (from the USGS) or231°/35°/138° (from the Global CMT), with a NW-dipping plane. This feature is consistent with the geological survey (cf. Xu et al., 2009a) and the aftershock distribution (see Fig. 1).
The estimated source duration and rupture length are 70.0 s and ∼210 km (see Table 1), which are relatively shorter than those reported from source rupture models (e.g., Hikima, 2008; Ji and Hayes, 2008; Nishimura and Yagi, 2008; Hao et al, 2009; Nakamura et al, 2010). However, our estimates also agree with a source rupture model reported initially in the article of Chen et al (2008) and the multiple event analysis of Hwang et al. (2010). Following Mai and Beroza (2000), the efficient rupture length of the fault for the 2008 Wenchuan earthquake is ∼240 km from the source model of Ji and Hayes (2008), and ∼190 km from that of Sladen (2008). Spatial distribution of the b-value (Zhao and Wu, 2008) also showed relatively low b-values (∼0.5–0.7) in most northeast segments of the fault, implying relatively small slips there (e.g., Wiemer and Katsumata, 1999). This probably indicates that the rupture length is shorter from the b-value map (∼250 km) than that from the aftershock distribution. In addition to those characteristics mentioned above, slip distribution estimated from GPS and InSAR data revealed three maxima in slip near the towns of Yingxiu, Beichuan, and Nanba (Shen et al., 2009; also see Fig. 1). Wang et al. (2008) and Xu et al. (2009b) obtained similar results, and indicated a relatively low energy release (<30% of total energy releases) to the Qingchuan town (see Fig. 1). Since the surface waves mainly detect large energy releases, the rupture length from the epicenter to the Nanba town, according to the source models of Shen et al. (2009), Xu et al. (2009b), and Wang et al. (2008), is approximately 220–230 km. Furthermore, an empirical formula of seismic moment versus source duration (Furumoto and Nakanishi, 1983) suggested a source duration of 67 s for M0 = 7.6 × 1020 N m (from the USGS) or a source duration of 71 s for M0 = 8.97 × 1020 Nm (from the Global CMT), with which our estimated source duration is in good agreement. Concerning the relationship between seismic moment and the fault area (cf. Kanamori and Anderson, 1975), the fault’s area is ∼7254 km2 for M0 = 7.6 × 1020 N m, leading to the rupture length of ∼235 km when the fault’s width is taken to be ∼30.8 km. As addressed above, our estimates account for 70% of the energy released during the 2008 Wenchuan earthquake from surface-wave analyses (cf. Xu et al., 2009b). In other words, our estimations are probably the lower bound of the rupture process, revealing the first-order rupture features for the 2008 Wenchuan earthquake, namely, the main energy release process.
The rise time for earthquakes is an important parameter related to the dynamic stress drop during earthquake faulting. The entire source duration includes the rise time and the rupture time. Because the rise time is shorter relative to the entire source duration, it is not easily separated from the entire source duration. Generally, the rise time is about 10–20% of the entire source duration (cf. Geller, 1976). However, simultaneous use of the phase-delay time and the Fourier spectral node period of surface waves are capable of solving the rise time from the entire source duration. Hwang et al. (2001) and Chang et al. (2010) have done such work. Equation (4) shows that by sorting a series of rupture azimuths, the rise time for the 2008 Wenchuan earthquake can be determined to be 9.3 s, which is ∼0.13-fold the value of the entire source duration. This leads to a particle velocity of 46 cm/s and a dynamic stress drop of 37.8 bars, corresponding to the observations for large earthquakes (Kanamori, 1994).
The rupture velocity estimated from the entire source duration is ∼3.0 km/s, which agrees well with the average one from Nishimura and Yagi (2008) and Zhang et al. (2009). However, the rupture velocity determined only from the rupture time is ∼3.45 km/s, probably exceeding the S-wave velocity in the crust. This is in accordance with the estimation (∼3.4 km/s) of Du et al. (2009) from tele-seismic array analysis. Of course, variable s-wave velocities lead to various rupture features during earthquake faulting, i.e., subsonic, sonic, and supersonic faulting. A three-dimensional velocity structure derived by Pei et al. (2010) indicates that the velocity of the s-wave velocity across the source area within the crust ranges from 3.25 to 3.5 km/s. In other words, the estimated rupture velocity might exceed or be close to the s-wave velocity. This is quite different from other thrust-type earthquakes, for instance the 1999 Chi-Chi earthquake and the 2004 great Sumatra earthquake (cf. Hwang et al., 2001; Chang et al., 2010). Nevertheless, previous studies have reported strike-slip earthquakes with a relatively larger rupture velocity, such as the 2001 Kunlun (China) earthquake and the 2002 Denali fault (Alaska) earthquake (cf. Walker and Shearer, 2009; Wen et al., 2009). Multiple event analysis and the source rupture model for the 2008 Wenchuan earthquake suggest that ruptures in the former segment of the fault exhibit a thrust-type mechanism while those in the later one show a strike-slip mechanism (cf. Ji and Hayes, 2008; Nishimura and Yagi, 2008; Sladen, 2008; Zhang et al., 2009; Hashimoto et al., 2010; Hwang et al., 2010; Nakamura et al., 2010; Zhao et al. , 2010). The rupture process of the 2008 Wenchuan earthquake with a strike-slip-type in the later portion of the fault might result in higher average rupture velocity.
Since rupture velocity is high; once fracture energy is ignored (cf. Kanamori and Heaton, 2000), the radiated seismic energy can be estimated to be (5.93 ± 0.4) × 1016 N m based on the static and dynamic stresses according to Kanamori and Heaton (2000). Although this value is larger than that from the routine report of the USGS (1 . 4 × 1016 N m), both sets of results have the same order of magnitude. Our estimate also agrees with that from multiple event analysis of Hwang et al. (2010). Moreover, the ES/M0 ratio, approximately (7.8±0.5) × 10−5 is quite close to global observations (approx. 5.0 × 10−5) (cf. Kanamori and Heaton, 2000). From the rupture directivity analysis based on the Rayleigh-wave phase-velocity and its Fourier spectrum, we were able to efficiently estimate the fault parameters for the 2008 Wenchuan earthquake, showing a unilateral faulting event.
The authors would like to express their gratitude to the IRIS (Incorporated Research Institutes for Seismology) for providing us with the GSN data. We offer a special thanks to Dr. Kazunori Yoshizawa and an anonymous reviewer, who have helped us significantly improve the manuscript. The National Science Council, ROC, financially supported this study under Grant Nos. NSC98-2119-M-034-001, NSC98-2811-M-034-002, and NSC99-2116-M-034-003.
- Aki, K. and P. G. Richards, Quantitative Seismology, 700 pp., University Science Books, Sausalito, CA, 2002.Google Scholar
- Ben-Menahem, A., Radiation of seismic surface-waves from finite moving sources, Bull. Seismol. Soc. Am, 51, 401–435, 1961.Google Scholar
- Chang, J.-P., Rupture Directivity Analysis for Large Earthquakes, 102 pp., ph.D. Dissertation, National Central University, Chung-Li, Taiwan, 2009.Google Scholar
- Chang, J.-P., R.-D. Hwang, C.-Y. Wang, G.-K. Yu, W.-Y. Chang, and T.-W. Lin, Analysis of rupture directivity for the 2004 Sumatra earthquake from the Rayleigh-wave phase velocity, Terr. Atmos. Ocean. Sci., 21, 243–251, doi:10.3319/TAO.2009.03.27.01(T), 2010. 10.3319/TAO.2009.03.27.01(T)CrossRefGoogle Scholar
- Chen, Y.-T., L.-S. Xu, Y. Zhang, H.-L. Du, W.-P. Feng, C. Liu, and C.-L. Li, Preliminary result (1): A report of source characteristic for the 12 May 2008 Wenchuan earthquake, posted on http://www.csi.ac.cn/sichuan/chenyuntai.pdf, 2008 (in Chinese).
- Du, H.-L., L.-S. Xu, and Y.-T. Chen, Rupture process of the 2008 great Wenchuan earthquake from the analysis of the Alaska-array data, Chinese J. Geophys., 52, 372–378, 2009 (in Chinese with English abstract).Google Scholar
- Ewing, C. E. and M. M. Mitchell, Introduction to Geodesy, 304 pp., Elsevier Science Ltd, 1970.Google Scholar
- Geller, R. J., Scaling relations for earthquake source parameters and magnitudes, Bull. Seismol. Soc. Am, 66, 1501–1523, 1976.Google Scholar
- Hikima, K., The 2008 Sichuan Earthquake (preliminary finite fault model), posted on http://www.eri.u-tokyo.ac.jp/topics/china2008/source_eng.html 2008.
- Hwang, R.-D., C.-C. Wu, and J.-P. Chang, Multiple event analyses of the 2008 Wenchuan (China) earthquake, Tectonophysics, 2010 (submitted).Google Scholar
- Ji, C. and G. Hayes, Preliminary result of the May 12, 2008 Mw 7.9 Eastern Sichuan, China Earthquake, posted on http://earthquake.usgs.gov/eqcenter/eqinthenews/2008/us2008ryan/fimte_fault.php, 2008.
- Kanamori, H. and D. L. Anderson, Theoretical basis of some empirical relations in seismology, Bull Seismol Soc Am, 65, 1073–1095, 1975.Google Scholar
- Kanamori, H. and T. H. Heaton, Microscopic and macroscopic physics of earthquakes, in Geocomplexity and the Physics of Earthquakes, edited by L. B. Rundle, D. L. Turcotte, and W. Klein, 284 pp., AGU Geophys. Mono. 120, AGU, Washington, D.C., 2000.Google Scholar
- Li, C.-Y., Z.-Y. Wei, J.-Q. Ye, Y.-B. Han, and W.-J. Zheng, Amounts and styles of coseismic deformation along the northern segment of surface rupture, of the 2008 Wenchuan Mw 7.9 earthquake, China, Tectonophysics, 491, 35–58, doi:10.1016/j.tecto.2009.09.023, 2010. 10.1016/j.tecto.2009.09.023CrossRefGoogle Scholar
- Liu-Zeng, J., Z. Zhang, L. Wena, P. Tapponnier, J. Sun, X. Xing, G. Hu, Q. Xu, L. Zeng, L. Ding, C. Ji, K. W. Hudnut, and J. van der Woerd, Co-seismic ruptures of the 12 May 2008, Ms 8.0 Wenchuan earthquake, Sichuan: East-west crustal shortening on oblique, parallel thrusts along the eastern edge of Tibet, Earth Planet. Sci. Lett, 286, 355–370, 2009. 10.1016/j.epsl.2009.07.017CrossRefGoogle Scholar
- Nakamura, T., S. Tsuboi, Y. Kaneda, and Y. Yamanaka, Rupture process of the 2008 Wenchuan, China earthquake inferred from teleseismic waveform inversion and forward modeling of broadband seismic waves, Tectonophysics, 491, 72–84, doi:10.1016/j.tecto.2009.09.020, 2010. 10.1016/j.tecto.2009.09.020CrossRefGoogle Scholar
- Nishimura, N. and Y. Yagi, Rupture process for May 12, 2008 Sichuan Earthquake, posted on http://www.geol.tsukuba.ac.jp/∼nisimura/20080512, 2008.
- Pei, S., J. Su, H. Zhang, Y. Sun, M. N. Toksoz, Z. Wang, X. Gao, J. Liu-Zeng, and J. He, Three-dimensional seismic velocity structure across the 2008 Wenchuan Ms 8.0 earthquake, Sichuan, China, Tectonophysics, 491, 211–217, doi:10.1016/j.tecto.2009.08.039, 2010. 10.1016/j.tecto.2009.08.039CrossRefGoogle Scholar
- Sladen, A., Preliminary result: 05/12/2008 (Mw 7.9), East Sichuan, posted on http://www.tectonics.caltecri.edu/slip_history/2008_e_sichuan/e_sichuan.html, 2008.
- Wang, W.-M., L.-F. Zhao, J. Li, and Z.-X. Yao, Rupture process of the Ms 8.0 Wenchuan earthquake of Sichuan, China, Chinese J. Geophys., 51, 1403–1410, 2008 (in Chinese with English abstract).Google Scholar