Multiple Event Analysis of the 2008 Mw 7.9 Wenchuan Earthquake: Implications for Variations in Radiated Seismic Energy During Faulting

A forward modeling of P-waves for the 2008 Wenchuan earthquake revealed at least seven sub-events that occurred during faulting with the largest event (i.e., the third sub-event) located at a position ~50 km northeast of the epicenter. Simulations of P-waves showed that it would be more appropriate to model the P-waves using thrust faulting for the first three sub-events and using strike-slip faulting for the last four. In other words, the faulting for the 2008 Wenchuan earthquake was composed substantially of two mechanisms; the former was a thrust faulting and the latter was a strike-slip rupture. The mechanical transition was near the town of Beichuan, ~100 km northeast of the epicenter. Variations in radiated seismic energy (ES) showed the largest ES released from the fourth sub-event. Results also indicated remarkable distinctions between ES and ES0 (called the available energy). On the whole, the total ES, which was higher than ES0 estimated from static stress drop, suggested that the earthquake should be interrupted by a stress model of abrupt-locking. Further, the former thrust faulting released a relatively lower amount of ES than the latter strike-slip event. Orowan’s stress model, i.e., ES ≈ ES0, can specify former thrust ruptures implying a high rupture velocity. Because ES > ES0 for latter strike-slip ruptures, a stress model of abrupt-locking, implying higher dynamic stress drop and lower friction during an earthquake, can account for the feature of the latter ruptures. This might suggest that the 2008 Wenchuan earthquake should have a high rupture velocity, perhaps approaching the crustal Swave velocity or even higher.


INTRODUCTION
The M w 7.9 Wenchuan earthquake of May 12, 2008 occurred along the Longmenshan fault zone located on the border between the eastern Tibetan plateau and the Sichuan basin (Fig. 1).The earthquake caused extreme destruction in the eastern Sichuan region, China.Aftershocks spread northeastward up to ~300-km occurring to the left of the fault zone to indicate a northwest-dipping fault plane (Fig. 1).Analysis of rupture directivity from surface waves also showed a northeastward rupture with an azimuth of N59°E (Hwang et al. 2011).Field surveys identified an obvious surface rupture terminating near the town of Shikan (also see Fig. 1) (Liu-Zeng et al. 2009;Xu et al. 2009a).Ji and Hayes (2008) and Nishimura and Yagi (2008) first reported source rupture models for the 2008 Wenchuan earthquake from body-wave inversions and was comparable with others (e.g., Hashimoto et al. 2010;Nakamura et al. 2010).Variations in rupture velocity with an average of 2.6 -2.9 km s -1 were also documented in Wen et al. (2012).These source models not only exhibited the complexity of the earthquake, but also indicated that the rupture mechanism varied from thrust faulting to strike-slip faulting along the fault.Nakamura et al. (2010) further stated that the transformation of faulting mechanisms occurred ~110 km northeast of the epicenter.Additionally, slip distributions estimated from GPS and InSAR data revealed larger slips near the towns of Yingxiu, Beichuan, and Nanba (Hao et al. 2009;Shen et al. 2009;Xu et al. 2009b).
Investigation of the 2008 Wenchuan earthquake from seismic and GPS data focus primarily on understanding  (GJF).Source time function is also included: numbers 1 -3 for the sub-events with thrust faulting and numbers 4 -7 for the sub-events with strike-slip faulting as in Table 1.
Table 1.Source parameters derived in this study.

No.
Focal mechanism (strike/dip/rake) Source duration (sec) source rupture features.However, macroscopic source parameters (as radiated seismic energy) are also useful to grasp the rupture features of earthquakes (Kikuchi and Fukao 1988;Kanamori 1994;Kanamori and Heaton 2000).In general, radiated seismic energy can either be determined from the integration of seismic waves (e.g., Choy and Boatwright 1995;Hwang et al. 2001;Pérez-Campos and Beroza 2001) or source time function (e.g., Vassiliou and Kanamori 1982;Kikuchi and Fukao 1988;Hwang et al. 2010Hwang et al. , 2012;;Hwang 2012).Scaled energy, the ratio (E S /M 0 ) of radiated seismic energy (E S ) to seismic moment (M 0 ), is related to the dynamics of earthquake faulting.A rapid drop in friction during earthquake faulting results in a large E S /M 0 , whereas a slower drop in friction leads to a relatively low E S /M 0 (Kanamori and Heaton 2000).However, uncertainty in the estimated radiated seismic energy would cause high divergence in the ratio of E S /M 0 (Kanamori 1994;Kanamori and Heaton 2000).Furthermore, the usage of a finite frequency bandwidth in seismic waves would also give rise to an underestimation of E S , due to a lack of high-frequency content (e.g., Wang 2004).The estimation of E S from the source time functions of multiple events (Kikuchi and Fukao 1988;Hwang et al. 2008;Hwang 2012) and finite-fault source model (Kanamori 2006) appears to detect a certain amount of high-frequency energy.In spite of the difficulties in estimating radiated seismic energy, the E S /M 0 of strike-slip earthquakes is significantly different from that of reverse or normal earthquakes (e.g., Choy and Boatwright 1995;Pérez-Campos and Beroza 2001).Hence, to gain a deeper understanding in the rupture behavior of the 2008 Wenchuan earthquake, the purpose of this study is to investigate the multiple shocks through forward P-waves modeling and subsequently estimate the E S of each sub-event to state the dynamic rupture process during the earthquake from the viewpoint of macroscopic source parameters.

DATA
During the 2008 Wenchuan earthquake, the Incorporated Research Institutions for Seismology Data Management Center (IRIS DMC) collected hundreds of seismograms, recorded by global seismic networks.This provided a wealth of high-quality seismic data from which it is of great use to analyze the rupture feature of the 2008 Wenchuan earthquake.To avoid interference from core phases (such as PcPwaves) or multipath waves (such as PP-waves) on the direct P-waves, this study only used P-waves from the verticalcomponent seismograms recorded at epicentral distances of 30° -90°.From an empirical relationship between seismic moment and source duration (Furumoto and Nakanishi 1983), the 2008 Wenchuan earthquake had a source duration of ~70 sec estimated from the seismic moment of 7.6 × 10 20 Nm as reported by the US Geological Survey (USGS).Taking account of the effects of rupture directivity to the 2008 Wenchuan earthquake, we extracted a 145-sec-long seismogram, including the first 5 sec of the P-arrival and continuing for 140 sec after the P-arrival.Figure 2a shows the available stations around the epicenter.

FOCAL DEPTHS FOR SUB-EVENTS
In Fig. 2b, the seismograms generated by the 2008 Wenchuan earthquake showed obvious multiple sources as observed at station ESK, particularly for the first 50 sec of recordings.The first P-arrival was the first sub-event, and the maximum sub-event appeared ~16-sec after the first Parrival.We inverted the focal depths of the two sub-events from the extracted waveforms as shown in Fig. 2b by a teleseismic P-wave inversion method of Lin et al. (2008) (also refer to Hwang et al. 2012).The 2008 Wenchuan earthquake was a shallow source such that the synthetic P-waves must include two depth phases (pP-and sP-waves), excluding the direct P-wave (cf.Lin et al. 2006;Hwang et al. 2010Hwang et al. , 2012)).The P-waves were created synthetically following the iasp91 velocity model (Kennett and Engdahl 1991) (also see Appendix A).In the analysis, the PP-wave would probably influence the P-waves.For a shallow source depth, the PP-wave arrived at ~68 sec after the onset for an epicentral distance of 30° and at ~212 sec after the onset for an epicentral distance of 90°.Since the two sub-events were within the first 50 sec of recordings, the PP-wave would not interfere with the two sub-events.Figure 2c shows the  misfit between observed and synthetic P-waves for the two sub-events and indicates an ideal focal depth of 12 km.

MULTIPLE EVENT ANALYSIS AND RADIATED SEISMIC ENERGY
As mentioned above, the two sub-events (Fig. 2) had a focal depth of 12 km.Aftershocks occurred mainly within depths of 20 km and were distributed from southwest to northeast (Fig. 1).An analysis of surface waves indicated the optimal rupture direction of N59°E which agrees with the distribution of aftershocks (Hwang et al. 2011).Here we assumed that all sub-events occurred at a focal depth of 12 km and successively ruptured the Longmenshan fault zone from the epicenter toward N59°E.For simplification in the forward P-wave modeling only stations located at the azimuth normal to the rupture direction of the 2008 Wenchuan earthquake were used to perform the multiple-event analysis.Therefore, from the geometry of the ray-path to the direction of rupture, several stations, KONO, ESK, CAN, TOO and TAU as in Fig. 2a, were considered to be independent of rupture directivity and appropriate for the multiple-event analysis.The epicentral distances of the stations employed for the multiple event analysis were 65° -85°; hence, the PP-wave arrived at ~140 -195 sec after the first P-arrival.That is, the PP-wave would not interfere with the P-wave modeling in this study.Furthermore, these stations used for the multiple event analysis had take-off angles of 15 -20 degrees; thus, all located on the compression quadrant from which the P-waves have an upward first-motion (i.e., positive polarization).In addition, the phases (PmPP, pPmp, and PPmp etc.) from the Moho reflection near the source and receiver are also discounted in waveform modeling because of their small amplitudes compared with the initial P-waves through the calculations of reflection coefficients.
In this study, the synthetic P-wave train (i.e., direct Pwave, pP-and sP-waves) for forward modeling was calculated according to a point source with a triangular source time function and the iasp91 model (cf.Lin et al. 2006;Hwang et al. 2010Hwang et al. , 2012; also see Appendix A).Before the multiple-event analysis using the forward modeling of Pwaves, we used an empirical Green's function (EGF) deconvolution technique to investigate roughly the multiple sources of the 2008 Wenchuan earthquake.First, the synthetic P-waves (Fig. 3), as the EGFs (Ammon et al. 2006), were produced at stations CAN and ESK using a delta source time function, a source depth of 12 km, and a thrust fault plane of 231°/35°/138° (strike/dip/rake).In Fig. 3, the retrieved relative source time function (RSTF) showed several obvious sub-events.The largest sub-event with source duration of ~17 sec was about 16 sec later after the onset (i.e., the first sub-event with source duration of ~5 -8 sec).The initial feature was in agreement with the work of Wen et al. (2012).In addition, the largest sub-event was followed by two sub-events, ~35 and ~45 sec later after the onset, respectively.From Fig. 3, roughly speaking, five obvious sub-events occurred during the earthquake.However, from waveform readings, it seemed to have two extra sub-events occurring after ~45 sec.With regard to waveforms appear- ing after ~70 sec, it cannot be confirmed if the signals were released from the earthquake rupture.For this reason, the purpose of this study was only to analyze seven sub-events during the 2008 Wenchuan earthquake up to ~70 sec, and to calculate the radiated seismic energy for each sub-event.Subsequently, we modulated the time lag relative to the first sub-event, source duration and seismic moment for each sub-event to ensure that the synthetic P-waves corresponded with the observed P-waves.This analysis was a process of trial and error.Recordings in stations CAN and ESK were taken as examples to interpret the procedure of multipleevent analysis as displayed in Fig. 4.
In this study, we modeled the P-waves for each subevent under fixing the strike of fault plane (231°).In Fig. 4a, it was necessary to add a sub-event between the first and the largest sub-events for a better waveform fitting.Then again, the first three sub-events can be modeled well using a thrust mechanism wherein the status is from the GCMT's report (see Table 1).To put the fourth sub-event (~35-sec later to the onset) using a thrust (231°/35°/138°) or a strike-slip (231°/35°/181°) mechanism to model the P-waves showed that the synthetic waveforms seemed to match the observed waveforms in Figs.4b and c.However, using a thrust faulting to the fourth sub-event would underestimate the seismic moment of this sub-event.When using thrust mechanisms (231°/35°/138°) to model all sub-events, the synthetic waveforms were out of phase compared with the observations (shown in Fig. 4d).Such waveform modeling resulted in a lower seismic moment for the earthquake.That is, the mechanisms of sub-events after the largest sub-event must be different from the first three sub-events.Figure 4e shows that the rest of the sub-events after the largest sub-event were modeled using a strike-slip mechanism of 231°/35°/181°, but the fitting between the observed and synthetic P-waves was not perfect and the seismic moment was overestimated.As a result, a change in the status of the strike-slip faulting is necessary for the last three sub-events.During testing, the dip and rake in the last three sub-events had to be changed slightly to obtain a better fit between the observed and synthetic P-waves as shown in Table 1 and Fig. 4f.To model P-wave for the fourth sub-event using a mechanism of 231°/55°/195°, similar to the last three sub-events, would  also lead to an underestimation of seismic moment.Because we could not confirm whether the later phases after 70 sec from the first P-arrival were generated by the source rupture, we conservatively estimated the source duration to be 71 sec (Table 1).
As mentioned above, results by the forward test based upon trial and error showed that the 2008 Wenchuan earthquake consisted of at least seven sub-events during the rupture (Table 1 and Fig. 5).We deemed it better to fit observed P-waves using thrust faulting for the first three sub-events and strike-slip faulting for the last four sub-events (Fig. 4).Additionally, the fault status used to compute the synthetic P-waves for the last four sub-events in the northern segment of the fault had a greater dip angle (55°) relative to the first three sub-events (35°) in the southern segment.With this analysis, the total source duration and seismic moment were 71 sec and 7.448 × 10 20 Nm (M w = 7.85), respectively.Table 1 lists the preferred multiple-source parameters for each sub-event, including seismic moment, source duration, and time of occurrence to the first sub-event.
Vassiliou and Kanamori (1982) proposed a method to calculate the E S using source duration (also see Appendix A).By taking the P-wave of 5.8 km s -1 , S-wave of 3.36 km s -1 and density of 2.45 g cm -3 in the source area, the estimated E S for the seven sub-events varied along the fault from 0.014 × 10 16 Nm to 5.420 × 10 16 Nm with the maximum intensity measured at the fourth sub-event; the total E S was 9.081 × 10 16 Nm.Table 1 also lists the E S for each sub-event.

DISCUSSION
The multiple event analysis indicates that at least seven sub-events occurred during the 2008 Wenchuan earthquake rupturing the Longmenshen fault zone (Figs. 1, 4, and 5).The third sub-event has the largest seismic moment (corresponding to M w = 7.5) located at a position ~50 km NE from the epicenter (Fig. 1).The largest sub-event dominates the entire rupture mechanism as thrust faulting, as reported by the USGS and GCMT (Global CMT).From Table 1, the largest sub-event started at 15.7 sec and stopped at 30.7 sec with the peak energy at 23.2 sec and source duration of 15 sec.Hence, the maximum energy release occurs around 20 -30 sec from this study, also consistent with those from previous studies (e.g., Wang et al. 2008;Nakamura et al. 2010;Wen et al. 2012).Application of the thrust mechanism to all sub-events during analysis leads to a failure in waveform fitting between the observed and synthetic P-waves, whereas using the thrust mechanism for the first three sub-events and the strike-slip mechanism for the last four sub-events provides a better waveform fitting (Table 1 and Figs  2009; Shen et al. 2009;Hashimoto et al. 2010;Nakamura et al. 2010;Wen et al. 2012).In addition, the last three subevents with strike-slip faulting required a larger dip angle (~55°), compared with those with the thrust faulting (cf.Shen et al. 2009;Xu et al. 2009a).Table 1 shows the latter strike-slip ruptures with slightly normal faulting, which are different from the previous source rupture models (e.g., Wang et al. 2008;Shen et al. 2009;Nakamura et al. 2010).However, such results from this study seem comparable with those from Zhang et al. (2009).
In Table 1, the time difference, ~18 sec, between the third and fourth sub-events appears to show that the ruptures are obstructed in a region, where the fault status is variable (Shen et al. 2009).The transition in mechanism from thrust to strike-slip faulting occurs ~34.0 sec later after the onset and is ~100 km NE of the epicenter using an average rupture velocity of 3.0 km s -1 (Hwang et al. 2011;Hartzell et al. 2013).The location of mechanism transformation is near the town of Beichuan (Fig. 1), where field surveys also denoted the change in fault status (Liu-Zeng et al. 2009;Xu et al. 2009a).The multiple-event analysis from this study is also comparable with the work of Wen et al. (2012), using the EGF deconvolution to reveal the time in change of faulting mechanism is ~35 sec.
By adopting an average rupture velocity ~3.0 km s -1 derived from the rupture directivity analysis of surface waves (Hwang et al. 2011) or the source rupture model used by Hartzell et al. (2013), we derived a rupture length of approximately 210 km for the 2008 Wenchuan earthquake.The rupture length derived from this study is the so-called effective length which was created by the main energy release during earthquake rupture.Generally speaking, the effective rupture length is shorter than the surface rupture length (cf.Yen and Ma 2011).According to Mai and Beroza (2000), the effective rupture length for the 2008 Wenchuan earthquake is ~240-km-long from the source model of Ji and Hayes (2008), and ~190-km-long from that of Sladen (2008).From field investigation, the surface rupture length is ~240 km from Xu et al. (2009a), ~240 km from Zhou et al. (2010), ~230 km from Liu-Zeng et al. (2009), and ~285 km from Lin et al. (2009).Xu et al. (2009b) using a P-wave back-projection also indicated that there is a relatively low energy release (< 30% of total energy releases) to the town of Qingchuan (see Fig. 1) implying the effective rupture length to be shorter than 250 km.Because we were unable to confirm whether or not the waves arriving at 70 sec after the first P-arrival as those in Fig. 2b were signals released from the main shock, this study only estimates the source duration to be 71 sec.Although the estimated rupture length and source duration are shorter than those derived from several source rupture models (e.g., Ji and Hayes 2008;Nishimura and Yagi 2008;Hao et al. 2009;Shen et al. 2009;Hashimoto et al. 2010;Nakamura et al. 2010;Wen et al. 2012) and field surveys of surface ruptures (Lin et al. 2009;Liu-Zeng et al. 2009;Xu et al. 2009a;Zhou et al. 2010), this study is comparable to those from rupture directivity analysis of surface waves (Hwang et al. 2011) and a source rupture model of Sladen (2008).An empirical relationship between the seismic moment and source duration (Furumoto and Nakanishi 1983) suggests that the 2008 Wenchuan earthquake should have a source duration of ~67 sec from M 0 = 7.448 × 10 20 Nm (this study), ~71 sec from M 0 = 8.97 × 10 20 Nm (GCMT), and ~73 -76 sec from M 0 = 1.0 -1.1 × 10 21 Nm (Wen et al. 2012;Harztell et al. 2013).In terms of the effective rupture length and source duration, the results from this study seem acceptable.
Following Vassiliou and Kanamori (1982), the total E S is 9.081 × 10 16 Nm and the fourth sub-event has the maximum E S ~5.420 × 10 16 Nm (Table 1).The estimated E S is greater than that derived from the USGS (1.4 × 10 16 Nm) and surface-wave analysis (5.93 × 10 16 Nm) (Hwang et al. 2011), but these results still have the same order of magnitude.The lower E S from the surface-wave analysis is because the surface-wave analysis used a single source model to result in an underestimation in E S .The multiple-event analysis reveals more E S during earthquake rupture than from the surface-wave analysis.Such multiple event analysis (Kikuchi and Fukao 1988;Hwang et al. 2008, Hwang 2012) seems to decrease the effect of finite-frequency bandwidth on the estimate of E S (Wang 2004).Overall, the E S /M 0 ratio ~1.22 × 10 -4 for the Wenchuan earthquake is larger than those (5 × 10 -5 ) for ordinary earthquakes, and then a rapid drop in friction may occur during earthquake faulting which implies a high rupture velocity (e.g., Kanamori and Heaton 2000).
Since the rupture process includes two faulting mechanisms from the forward multiple event analysis, here we divide the ruptures into two parts.The first part is a thrust rupture (i.e., the first three sub-events) with the radiated seismic energy (E ST ) of 1.007 × 10 16 Nm; the other (i.e., the last four sub-events) is a strike-slip rupture with the radiated seismic energy (E SS ) of 8.074 × 10 16 Nm.In the Orowan model, in which the dynamic stress equals the final stress during faulting (cf.Kanamori 1994), the radiated seismic energy can be expressed as 2 where Δσ is the static stress drop, M 0 is the seismic moment and μ is rigidity.The E S0 is referred to as available energy estimated from Δσ and M 0 (cf.Kanamori and Rivera 2006).Kanamori (1994) summarized the stress models to account for the dynamic ruptures during the earthquakes.For an Orowan fault model, then E S equals E S0 ; for a stress model of frictional overshoot, then E S is smaller than E S0 ; for an abrupt-locking stress model, then E S is larger than E S0 .Broadly speaking, the 2008 Wenchuan earthquake exhibits slips coinciding with an abrupt-locking stress model, because the total E S (9.081 × 10 16 Nm) estimated in this study was larger than E S0 (4.475 × 10 16 Nm) calculated from the static stress drop of ~32.5 bars following Hwang et al. (2011).
The effective rupture length for the thrust faulting is ~102 and ~111 km for the strike-slip faulting using an average rupture velocity of 3.0 km s -1 (Table 1).The efficient width of the fault for the Wenchuan earthquake is about 30.8 km estimated from the source model provided by Ji and Hayes (2008).According to a rectangular finite-fault model with surface rupture (Kanamori and Anderson 1975), for the ruptures with thrust faulting Δσ is ~24 bars estimated from the fault length ~102 km and fault width ~30.8 km; for the ruptures with strike-slip faulting Δσ is ~28.5 bars calculated from the fault length ~111 km and fault width ~30.8 km.For the thrust faulting, the available energy (E ST0 ) is 1.190 × 10 16 Nm, calculated from Δσ = 24 bars and M 0 = 2.736 × 10 20 Nm, and approximates to E ST of 1.007 × 10 16 Nm; for the strike-slip faulting, the available energy (E SS0 ) is 2.433 × 10 16 Nm, derived from Δσ = 28.5 bars and M 0 = 4.712 × 10 20 Nm, and lower than E SS of 8.074 × 10 16 Nm.As a result, the Orowan model is likely to describe the rupture behavior of the former thrust faulting due to E ST ≈ E ST0 , in which high rupture velocity occurs.The rupture feature of the last strike-slip faulting corresponds to an abrupt-locking stress model because of E SS > E SS0 , indicating a higher dynamic stress drop and low friction during faulting (Kanamori 1994;Kanamori and Heaton 2000).The E S /M 0 ratio (3.68 × 10 -5 ) for the former thrust rupture is also significantly lower than that (1.71 × 10 -4 ) for the last strike-slip rupture.The feature also agrees with global observations, from which the strike-slip earthquakes have relatively larger E S /M 0 (e.g., Choy and Boatwright 1995;Pérez-Campos and Beroza 2001).

CONCLUSIONS
Multiple event analysis from the forward P-wave modeling exhibited the complexity of ruptures during the 2008 Wenchuan earthquake.The rupture process demonstrated two main faulting mechanisms: first, there was a thrust mechanism for the first three sub-events and the other was a strike-slip mechanism for the last four sub-events.The transition position of the faulting mechanism seemed to be near Beichuan town, ~100-km northeast of the epicenter (Fig. 1).The mechanism transformation might be related to changes in fault status, particularly for variations in the dip-angle of the fault as it increased along the fault from southwest to northeast (Shen et al. 2009;Xu et al. 2009a).From a view of a single source, the Wenchuan earthquake can be interrupted by a stress model of abrupt-locking due to E S > E S0 .In terms of the variations in E S and E S0 for the multiple sources, the dynamic ruptures varied from Orowan's stress model to abrupt-locking stress processes during the Wenchuan earthquake.Such results also implied a high rupture velocity for the 2008 Wenchuan earthquake.Through multiple event analysis, this study not only revealed the complexity of the rupture, but also provided a deeper understanding of dynamic process involved in the ruptures during the 2008 Wenchuan earthquake.

APPENDIX A (1) Calculation of the Far-Field P-Waves
For a shallow earthquake, a synthetic far-field P-wave at a given receiver can be expressed in the following form (cf. Kanamori and Stewart 1976;Okal 1992): where u P (t) is the synthetic far-field seismogram; M 0 is the seismic moment; α h , β h , and h t are the P-wave velocity, Swave velocity and density in the source area, respectively; g(Δ) denotes the geometrical spreading factor as a function of epicentral distance (Δ) and focal depth; r is the radius of the Earth (about 6371 km); R P , R pP , and R sP are the radiation patterns for the P-, pP-and sP-waves (cf.Kanamori and Stewart 1976); V pP and V sP denote the reflection coefficients of the P-to P-waves and the S-to P-waves at the free surface (cf.Aki and Richards 2002); i h and j h are the take-off angles of the P-and S-waves just leaving the source and i o is the incident angle of the P-waves to the free surface; C P (i o ) is the free surface effect at the receiver (cf.Aki and Richards 2002); f(t) stands for a triangular source time function and its duration representing the source-process time; t p , t pP , and t sP are the travel times for the P-, pP-and sP-waves, which are calculated according to a given Earth velocity model; Q(t) is the attenuation filter of the earth based on Azimi's law (e.g., Yoshida 1988); I(t) is the instrumental response.
After taking into account some corrections to the seismogram, we can rewrite Eq. (A1) in the following form (Lin et al. 2006).
where u t c P ^h is the corrected seismogram, not inclusive of the instrumental effect, geometrical spreading, or free surface effect.The iasp91 velocity model (Kennett and Engdahl 1991) is used to calculate the travel time of seismicwaves as well as several parameters.The attenuation filter Q(t) is calculated by Azimi's law using t* = 1.0 (travel time over quality factor) for the P-waves (cf.Okal 1992).
The unknown parameters in Eq. (A2) are M 0 , R P , R pP , and R sP .Following Lin et al. (2006) and Hwang et al. (2010Hwang et al. ( , 2012)), Eq. (A2) can be expressed in matrix form with n data points and 3 unknown parameters (M 0 R P , M 0 R pP , M 0 R sP ) as follows.The parameters to be solved in Eq. (A3) are M 0 R P , M 0 R pP , and M 0 R sP , which are called the pseudo radiation patterns by Lin et al. (2006).Equation (A3) can be resolved by the standard least-squares technique.We solve the corresponding pseudo radiation pattern when giving a source duration at a fixed focal depth.Thus, by searching for a succession of source duration and focal depths, the appropriate source duration, focal depth and pseudo radiation patterns are obtained for each station by minimizing misfits between the observed and synthetic seismograms (cf.Lin et al. 2006Lin et al. , 2008;;Hwang et al. 2010Hwang et al. , 2012)).

A t A t A t A t A t
(2) Estimation of Radiated Seismic Energy Following Vassiliou and Kanamori (1982), the estimated radiated seismic energy (E S ) can be written as: where α, β, and t are the P-wave velocity, S-wave velocity and density, respectively, at the source area.M 0 and T 0 are the seismic moment and source duration.Vassiliou and Kanamori (1982) used the trapezoid-type source time function with total source duration T 0 and x = 0.2, i.e., rise time = xT 0 = 0.2 T 0 , to calculate the radiated seismic energy.At x = 0.2, the factor x x 1 1 2 -^h 6 @ in Eq. ( A4) is . 1 0 128 .However, a triangular source time function used in this study has x = 0.5, making the factor x x 1 1 2 -^h 6 @ calculated as . 1 0 125 .The two values of radiated seismic energy determined from x = 0.2 and x = 0.5 are mutually consistent.

Fig. 1 .
Fig. 1.Maps showing the topography (data from NGDC, National Geophysical Data Center) around the source area of the 2008 Wenchuan earthquake.The star and circles denote the main shock and aftershocks (mb ≥ 5.0).The beach ball stands for the focal mechanism reported by the USGS.The closed squares indicate several cities around the source area.Three faults displayed by red lines in the Longmenshan fault zone are Wenchuan-Maowen fault (WMF), Beichuan-Yingxiu fault (BYF) and Guanxian-Jiangyou fault (GJF).Source time function is also included: numbers 1 -3 for the sub-events with thrust faulting and numbers 4 -7 for the sub-events with strike-slip faulting as in Table1.

Fig. 2 .
Fig. 2. (a) Stations (open triangles) used to determine the focal depth of two sub-events.The closed triangles are the stations, ESK, KONO, CAN, TAU and TOO, independent of the source rupture directivity and used to investigate the multiple sources.(b) Seismogram (P-waves) at station ESK shows two obvious sub-events.The gray lines denote the synthetic P-waves and the black lines are the observed P-waves.(c) Misfit between the observed and synthetic P-waves indicates the best focal depth ~12 km for the two sub-events in (b).

Fig. 3 .
Fig. 3. Using an empirical Green's function (EGF) deconvolution technique to retrieve the relative source time function (RSTF), revealing roughly the feature of multiple sources for the 2008 Wenchuan earthquake.The EGFs were created synthetically at stations CAN and E S K using a delta source time function, a source depth of 12 km, and a thrust fault plane of 231°/35°/138° (strike/dip/rake).

Fig. 4 .
Fig.4.P-waves observed at stations CAN and ESK are taken as examples to account for the procedure of multiple-event analysis.The thick lines denote the observed P-waves and the thin lines stand for the synthetic ones.(a) The first three sub-events modeled using a thrust mechanism as in Table1.(b) and (c) The fourth sub-event modeled by a thrust and a strike-slip faulting, respectively.(d) The P-waves modeled using a thrust mechanism to all sub-events.The synthetic P-waves show out of phase relative to the observed P-waves after ~35 sec.(e) The first three sub-events modeled using a thrust mechanism and the last four sub-events modeled using a strike-slip mechanism.(f) The synthetic P-waves modeled using a slight change in the mechanisms for the last three sub-events show a better fitting as compared with the observed P-waves.For details in the multiple event analysis based on trial and error, refer to the text.
. 4 -5).That is, the source rupture for the 2008 Wenchuan earthquake can be divided into two faulting mechanisms; the former is a thrust faulting and the latter is a strike-slip one (cf.Ji and Hayes 2008;Nishimura and Yagi 2008;Hao et al.

Fig. 5 .
Fig.5.Comparisons of the observed (thick lines) and synthetic (thin lines) P-waves at several stations, located at azimuths normal to the rupture direction.The source time function for the seven sub-events from the forward P-waves modeling is also shown.