Reexamining the source parameters of the 2010 ML 6.4 JiaSian (Taiwan) earthquake using the inversion of teleseismic P-waves

Journal of Asian Earth Sciences 48 (2012) 24–30

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Reexamining the source parameters of the 2010 ML 6.4 JiaSian (Taiwan) earthquake using the inversion of teleseismic P-waves Ruey-Der Hwang a,⇑, Tzu-Wei Lin b, Chia-Chang Wu c, Wen-Yen Chang d, Jo-Pan Chang a a

Department of Geology, Chinese Culture University, No. 55, Hwa-Kang Rd., Yang-Ming-Shan, Taipei 111, Taiwan, ROC Seismology Center, Central Weather Bureau, Taipei 100, Taiwan, ROC c Institute of Geophysics, National Central University, Chung-Li 320, Taiwan, ROC d Department of Natural Sciences, National Science Council, Taipei 106, Taiwan, ROC b

a r t i c l e

i n f o

Article history: Received 29 July 2011 Received in revised form 6 December 2011 Accepted 26 December 2011 Available online 13 January 2012 Keywords: JiaSian earthquake P-wave inversion Rupture directivity Unilateral faulting Rupture velocity

a b s t r a c t A moderate-sized earthquake (ML = 6.4), named the 2010 JiaSian earthquake, occurred in southern Taiwan on March 4, 2010. Reports from several institutes indicated that the JiaSian earthquake had focal depths of 18–28 km and ruptures with a thrust mechanism. However, modeling of teleseismic P-waves in previously reported source parameters revealed significant differences between the observed and synthetic P-waves. Therefore, this study reexamined the source parameters of the 2010 JiaSian earthquake using a teleseismic P-wave inversion method. The inversion showed that the earthquake had a depth of 22 km, a best double couple of 304°/28°/48° and 170°/70°/110° (strike/dip/rake), and a seismic moment of 2.31  1018 N m (MW = 6.2). Rupture directivity analysis also suggested that the earthquake was a unilateral faulting event on the fault plane of 304°/28°/48°. The average source duration and the rupture length were 5.2 s and 19.4 km, respectively. The optimal rupture direction, measured counterclockwise from the strike on the fault plane, was 347°, which was projected onto the surface to correspond to the northwestward rupture, consistent with the aftershock distribution. The analysis also suggested a high rupture velocity during faulting, probably approximate to the crustal S-wave velocity, which may have resulted in a low static stress drop and caused the differences in PGA distribution along the direction of earthquake rupture. The dip angles of the fault plane estimated from the initial and centroid depths showed the initial rupture at a lower dip-angle plane and the later rupture at a higher dipangle one. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction On 4 March 2010, a moderate-sized earthquake with ML = 6.4, named the 2010 JiaSian earthquake, struck southwestern Taiwan (Fig. 1). The earthquake occurred in a zone where low seismicity was observed by a regional seismic network (Huang et al., 2011). The focal depth was initially reported by the Central Weather Bureau (CWB) to be 5 km from the routine location; eventually the CWB modified the focal depth to 23 km. The Broadband Array in Taiwan for Seismology (BATS) provided a focal depth of 18 km from the centroid moment tensor (CMT) inversion using a regional broadband seismic network; the CWB CMT found identical results. From the teleseismic data, the US Geological Survey (USGS) and the Global CMT (GCMT) reported focal depths of 24 km and 28 km, respectively. However, the relocation of the 2010 JiaSian earthquake from a 3D velocity model using the regional seismic network showed a focal depth of 23 km and an epicenter of 22.962°N and ⇑ Corresponding author. E-mail address: [email protected] (R.-D. Hwang). 1367-9120/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.jseaes.2011.12.021

120.699°E (Huang et al., 2011). The focal depth from the routine report of the CWB and the relocation from Huang et al. (2011) is regarded as the initial depth, determined from the travel-times of the first P-waves. The focal depth from CMT inversion is the centroid depth, which is an average depth of energy releases for an earthquake. Despite differences in the focal depth, the fault plane solution for the JiaSian earthquake from previous reports all revealed a thrust mechanism (Fig. 2A). Nevertheless, the seismic moments determined from regional seismic data appeared 3–8 times smaller than those estimated from teleseismic data (Fig. 2A). Fig. 2B shows synthetic teleseismic P-waves modeled only at stations KBL and CTAO (see Fig. 3) from the CWB, BATS, USGS, and GCMT. At the modeling for stations KBL and CTAO, inconsistencies were evident in the seismic-phases and amplitudes between the observed and synthetic P-waves. In fact, most of used stations exhibited obvious differences between the observed and synthetic P-waves. Such differences resulted from the inappropriate focal mechanism. Tseng et al. (2011) also found such inconsistencies. Thus, reexamining the focal mechanism of the 2010 JiaSian earthquake is necessary.

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Fig. 1. (Left) Map showing the location of the 2010 JiaSian earthquake. The star represents the epicenter of the main shock and the solid circles denote the aftershocks, which occurred within 1 day. The contour lines represent the peak ground acceleration (PGA) only from the recordings of the vertical component and are plotted in intervals of 10 gal. The arrow indicates the rupture direction on the surface from the rupture directivity analysis. Line AA0 , normal to the rupture direction, is the location of cross section. The dashed lines denote main faults in the source area, including the ChaoChou fault (CCF), the ChiShan fault (CSF) and the ChiShan transfer fault zone (CTFZ). (Right) Cross section of aftershocks along line AA0 . The circles denote the aftershocks, of which the sizes are proportional to the magnitude (ML). The gray circles are the aftershocks with ML P 3.0.

Fig. 2. (A) Focal mechanisms for the 2010 JiaSian earthquake from the CWB, BATS, USGS, and GCMT. (B) The synthetic teleseismic P-waves (black lines) are modeled at the KBL and CTAO stations (see Fig. 3) from the CMT solutions of the CWB, BATS, USGS, and GCMT. The gray lines denote the observed P-waves.

To begin with, the location of the earthquake was mistaken as in the ChaoChou fault (CCF) (Fig. 1). The distribution of aftershocks suggested the strike of the earthquake is considerably associated with the ChiShan transfer fault zone (CTFZ), not the CCF (Ching et al., 2011; Huang et al., 2011). Additionally, the anomalous distribution of peak ground acceleration (PGA) around the source area exhibited relatively larger values, spreading northwestward from the epicenter (Fig. 1). The

phenomenon was probably related to the structure under the site or the rupture directivity of the source (Huang et al., 2011). A source model derived by Lee et al. (2011) demonstrated the complex ruptures of the 2010 JiaSian earthquake, including three main energy releases and rupturing upward from the hypocenter. Moreover, they addressed a relatively larger source duration, rupture length, and seismic moment (MW = 6.5). However, Ching et al. (2011) obtained a relatively lower seismic moment (MW = 6.2)

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straint on determining focal depth (Warren and Shearer, 2005; Chen et al., 2008a; Lin et al., 2008). Before the P-wave inversion, each seismogram was converted to displacement after removing the instrumental response, and then filtered between 0.01 and 0.5 Hz. Fig. 3 shows the 28 stations used in this study. 3. Method for the P-wave inversion A far-field synthetic seismogram, uP(t), at a shallow focal depth for a given receiver can be expressed below (for details, refer to Kanamori and Stewart, 1976; Okal, 1992; Lin et al., 2006; Hwang et al., 2010).

uP ðtÞ ¼

M0 gðDÞ  ½RP f ðt  tP Þ þ RpP V pP f ðt  tpP Þ þ RsP  r 4pqh a3h

ah cos ih

V sP f ðt  t sP Þ  C P ðio Þ  Q ðtÞ  IðtÞ bh cos jh 1 gðDÞ P   C ðio Þ  ½M 0 RP f ðt  t P Þ  Q ðtÞ  IðtÞ ¼ r 4pqh a3h 

þ M 0 RpP V pP f ðt  tpP Þ  Q ðtÞ  IðtÞ þ M0 RsP 

Fig. 3. Distribution of the 28 stations (triangles) used in this study. The star is the epicenter of the main shock. Six stations are marked to display the P-wave modeling of the inversion process, as shown in Fig. 6A.

ah cos ih bh cos jh

V sP f ðt  t sP Þ  QðtÞ  IðtÞ

M0 is the seismic moment; ah, bh, and qh, the P-wave velocity, S-wave velocity, and density of the source area; g(D), the geometrical spreading factor, related to the epicentral distance (D) and focal depth; r, the radius of the Earth (6371 km); RP, RpP, and RsP, the radiation patterns for the P-, pP- and sP-waves; VpP, VsP, the reflection coefficients of the P- to P-wave and the S- to P-wave on the free surface; ih, jh, the takeoff angles of P- and S-waves leaving the source; io the incident angle of P-wave regarding the free surface; CP(io), the free surface effect at the receiver function of io; f(t), the triangular source time function used in this study; tP, tpP, and tsP, the travel times for the P-, pP-, and sP-waves; Q(t), the attenuation filter; and I(t) is the instrumental response. If the source parameters of an earthquake are known, the synthetic P-waves can be modeled from Eq. (1) using a known velocity model. Fig. 4 shows a diagram of how to generate synthetic teleseismic P-waves. As far as inversion is concerned, in Eq. (1), in addition to the seismic moment (M0), the radiation patterns (RP, RpP, and RsP) and source duration (f(t)) are unknown. The rest of the parameters, related to the focal depth, can be calculated theoretically using a known velocity structure and an average attenuation parameter of P-wave propagation (Okal, 1992; Aki and Richards, 2002). This study adopted the iasp91 velocity model (Fig. 4) and the attenuation parameter t = 1.0 of the P-wave (Kennett and Engdahl, 1991; Okal, 1992). Lin et al. (2006) reconstructed Eq. (1) into matrix form for completing the P-wave inversion at a given focal depth, and then determined the pseudo radiation pattern (M0RP, M0RpP, and M0RsP) and source duration of each station, used sequentially to determine the source parameters. The pseudo radiation patterns are used to estimate the seismic moment and the fault plane solution; the derived source duration that varies with station azimuth is also used to perform the rupture directivity analysis (Lin et al., 2006; Hwang et al., 2010). The matrix form of the P-wave inversion with n data points is as follows:

and a low stress drop of 5 bars for the earthquake from GPS data using an elastic uniform stress drop inversion. Because of the inconsistency of the focal mechanism in previous reports, and the anomalous distribution of PGA for the 2010 JiaSian earthquake, we reexamines the source parameters of the earthquake, including the seismic moment, focal depth, and fault plane solution using the P-wave inversion method of Lin et al. (2006, 2008). This method also inverts the source duration varying with azimuth, used to investigate the rupture directivity of the earthquake. 2. Data The Incorporated Research Institutions for Seismology (IRIS) Data Management Center provided the teleseismic P-waves generated by the 2010 JiaSian earthquake. The teleseismic data provide a better estimation of source size because of the abounding longperiod contents. The depth phases (pP- and sP-waves) from the teleseismic data also give additional constraint on estimating the focal depth. Moreover, the teleseismic P-waves propagate mostly in the mantle, relatively homogeneous than in the crust. Hence, applying a simple velocity in the source estimation from the teleseismic P-waves is more convenient than that from regional or local seismic data. To eliminate the interference of core phases (such as the PcP-wave) and multipathing waves (such as the PP-wave), we only used seismograms at epicentral distances of 30–90°. The 35-s-long P-wave, including the first 5 s of the P-arrival and the 30 s after the P-arrival, was extracted from each vertical component seismogram. The P-waves group was composed of the direct P-wave and two depth phases (pP- and sP-waves), providing a greater con-

3 3 2 P V sP f ðt 1  tsP Þ  Q ðt1 Þ  Iðt 1 Þ 2 3 u ðt1 Þ 7 M 0 RP 6 7 7 6 P 6 a cos i 6 f ðt  tP Þ  Q ðt2 Þ  Iðt2 Þ; V pP f ðt2  t pP Þ  Qðt 2 Þ  Iðt2 Þ; bhh cos jhh V sP f ðt 2  tsP Þ  Q ðt2 Þ  Iðt 2 Þ 76 7 6 u ðt2 Þ 7 PARA  6 2 7 74 M 0 RpP 5 ¼ 6 7 4 ... 5 6 ... ... ... 5 M 0 RsP 4 cos ih uP ðt n Þ f ðt n  t P Þ  Q ðt n Þ  Iðt n Þ; V pP f ðt n  tpP Þ  Q ðtn Þ  Iðt n Þ; abh cos V sP f ðt n  t sP Þ  Qðt n Þ  Iðtn Þ j 2

f ðt 1  tP Þ  Q ðt1 Þ  Iðt1 Þ; V pP f ðt1  t pP Þ  Qðt 1 Þ  Iðt1 Þ;

ð1Þ

ah cos ih bh cos jh

h

h

ð2Þ

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Fig. 4. (A) The used iasp91 velocity structure up to 120-km depth. a, b, and q are the P-wave velocity, S-wave velocity, and the density. (B) A simple diagram represents the ray paths for the P-, pP- and sP-waves at a shallow source. (C) A diagram of how to generate a synthetic far-field seismogram, excluding the instrumental response. The symbol (H) represents the convolution operator.

where PARA ¼ 4pq1 a3  gðrDÞ  C P ðio Þ. h h

To determine the focal depth using Eq. (2), we adopted an improved method of Lin et al. (2008) to determine the focal depth during the inversion process; that is, providing the inversion with various depths (i.e. grid searching for depths), and identifying the optimal one by minimizing the misfits between the observed and synthetic seismograms. Meanwhile, the pseudo radiation patterns and source duration were inverted and used to estimate the source parameters and rupture directivity of an earthquake. The improved teleseismic P-wave inversion process is a two-step waveform fitting (Lin et al., 2008). First, the waveform must be fitted preferentially after the onset of the P-wave, primarily including the P-wave pulse width. Then the inversion is completed by fitting the entire waveform. Through this inversion process, the determined focal depth is treated as the initial depth of the source, not a centroid depth. On the other hand, the method can also be used to obtain a centroid depth when only fitting the entire waveform. 4. Results and discussion 4.1. Focal depth Fig. 5 shows the estimated focal depth for the 2010 JiaSian earthquake. Using the two-step inversion process, this study obtained a focal depth of 22 km (Fig. 5A), which is regarded as the initial depth and is consistent with a renewed report (23 km) from the CWB and the relocation by Huang et al. (2011) using a 3D velocity model and Taiwan’s seismic network. The estimated focal depth is appropriate for waveform modeling. Fig. 6A shows the comparisons of the observed and synthetic P-waves of several stations (also see Fig. 3) using the two-step inversion.

Fig. 5. (A) Focal depth is determined by the two-step waveform fitting, as shown in Fig. 6A. (B) Focal depth determined from only entire waveform fitting.

When only fitting the entire waveform, the focal depth is estimated to be 20 km, treated as the centroid depth (Fig. 5B), and in

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Fig. 6. (A) The waveform fitting for six selected stations (also see Fig. 3). The black and gray lines are the observed and synthetic P-waves, respectively. As displayed by the CTAO station, the short horizontal line denotes the first-step fitting and the long horizontal line denotes the second-step fitting. Also included is the inverted pseudo radiation patterns. (B) Compare the pseudo radiation pattern (PRP) with the calculated radiation pattern (TRP) for the P-, pP- and sP-waves to determine the focal mechanism by searching the fault status (strike, dip, and rake) at an interval of 1°. The best regression line represents the seismic moment divided by 3.05  1018 N m. (C) Following (B), the best focal mechanism for the 2010 JiaSian earthquake is derived.

agreement with the CMT solution by the CWB and BATS. The difference between the centroid and initial depths roughly indicates the faulting feature of the 2010 JiaSian earthquake, where the rupture propagates toward the shallow from the hypocenter; a source rupture model from Lee et al. (2011) also exhibits similar rupture propagation. Although the differences between the two depths are considerably small, this implies probably the main energy releases are around the depth of 20 km. From Fig. 1, the larger aftershocks (ML P 3.0) occurred at depths of less than 20 km. According to the asperity model or barrier model, aftershocks would occurred mainly around the region of the main rupture of the fault plane (e.g., Das and Aki, 1977; Ruff and Kanamori, 1983; Tajima and Kanamori, 1985; Das and Henry, 2003). Hence, the two depths derived from this study seem to express the feature of energy releases for the 2010 JiaSian earthquake. 4.2. Fault plane solution and seismic moment The black and gray lines in Fig. 6A are the observed and synthetic seismograms, respectively. As displayed in the CTAO station, the short horizontal line is the first-step fitting and the long horizontal line denotes the second-step fitting. Similar to Eq. (2), the best pseudo radiation patterns and the source duration of each station are inverted (Figs. 6A and 7). We determined the seismic moment and fault plane solution using the pseudo radiations patterns through the grid searching in status of fault. For obtaining the optimal fault plane solution and seismic moment, a linear regression as y = ax was used, where y and x are the pseudo and theoretical radiation patterns and a is the slope indicating the seismic moment. Following Lin et al. (2006), there are two constraints in the above-mentioned linear regression: one is that the fitting line has to go through the origin; the other is that a positive slope (a > 0) is required (Fig. 6B).

Fig. 7. Source duration plotted against cos d, where d is the angle between the rupture direction and a ray taking off from the source. The rupture direction is measured counterclockwise from the strike of the fault on the fault plane. The rupture directivity analysis is performed using a least-squares technique while constraining the rupture velocity lower than the crustal S-wave velocity. Numbers in the parentheses denote the derived source duration.

Through a series of fault status searches (strike, dip, and rake) at an interval of 1°, and by simultaneously comparing the pseudo radiation patterns (PRP) with the theoretical radiation patterns (TRP) for the P-, pP-, and sP-waves (Fig. 6B), the best focal mechanism is obtained when the misfit between the PRP and TRP is minimal, as shown in Fig. 6B. The slope of the best regression line in Fig. 6B indicates the seismic moment, divided by 3.05  1018 N m. Thus, the fault plane solutions for the best double couple are (304°, 28°, 48°) and (170°, 70°, 114°) in (strike, dip, rake), and the seismic moment is 2.31  1018 N m, which corresponds to MW = 6.2 (Fig. 6C). The fault plane solution shows that the 2010 JiaSian earthquake was a thrust-faulting event, consistent with the previous reports

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by several institutes, as shown in Fig. 2. The seismic moment derived in this study also corresponds to those reported by USGS, GCMT, and Ching et al. (2011), but is 2–5 times larger than the seismic moments of the CWB CMT and BATS. The seismic moments of earthquakes in Taiwan, routinely reported by the BATS and CWB CMT, are typically underdetermined using data from local seismic network compared to estimations using global data (Chen et al., 2008b). However, the ‘‘cut and paste’’ (CAP) method by Zhu and Helmberger (1996) is capable of improving the estimation of seismic moment when using the local seismic data. The source parameters, estimated using teleseismic and regional (or local) data, are somewhat different; nevertheless these results are still acceptable. In this study, the estimated seismic moment and fault plane solution are also appropriate for modeling P-waves. The estimated dip angle of the fault plane is 28°, in agreement with the dip angle of 26° estimated from geodetic data (Ching et al., 2011). Notwithstanding Ching et al. (2011) changed the dip angle to 40° based on the BATS for fitting the aftershock distribution, they also stressed the dip angles of 26–41° all fitting the geodetic data well. The fault plane solution, derived from the pseudo radiation patterns based on the 20-km depth, showed 287°/38°/ 30° (strike/dip/rake). The dip angle of 38° from the 20-km-depth is comparable with the aftershock distribution, and larger than that (28°) from the 22-km-depth. This indicates that the earthquake ruptured initially at a plane with a lower dip-angle and ruptured later at a higher dip-angle plane. Such feature also responds to the aftershock distribution as shown in Fig. 1. 4.3. Rupture directivity analysis Based on the rupture directivity analysis (Lin et al., 2006; Hwang et al., 2010), we tests two source models, the unilateral faulting and the bilateral faulting models (Table 1), to determine the suitable faulting model and fault plane when constraining the rupture velocity lower than the crustal S-wave velocity. According to source finiteness theory (Ben-Menahem, 1961), for earthquakes with unilateral faulting, the relationship between the observed source duration and several fault parameters can be expressed as T ¼ VLR  VLC cos d; for earthquakes with bilateral faulting, the relationship is T ¼ 2VL R þ 2VL C j cos dj, where T is the source duration observed at each station, L is the rupture length, VR is the rupture velocity, VC is the P-wave velocity in the source area, and d is the angle between the rupture direction and the ray taking off from the source. The rupture direction is measured counterclockwise from the strike of the fault on the fault plane. When searching a series of rupture directions, the best result is that the 2010 JiaSian earthquake is a unilateral faulting event on the fault plane with a strike of 304°, a dip of 28°, and a rake of 48° (Fig. 7 and Table 1). The optimal rupture direction is estimated at 347°, which is projected onto the surface for an azimuth of N315°E (Fig. 1); therefore, the earthquake ruptured northwestward. This characteristic agrees well with the aftershock distribution (Fig. 1). Taking the P-wave velocity in the source area as 6.5 km/s (Warren and Shearer, 2006; Hwang et al., 2010), the rupture length is estimated to be 19.4 km. The average source duration (when cos d ¼ 0 in Fig. 7) and rupture velocity are 5.2 s and 3.73 km/s, respectively.

A complex source model for the 2010 JiaSian earthquake derived by Lee et al. (2011) showed three main ruptures (rupture length exceeding 30 km) and the entire source duration of 16 s. Our results seem only comparable with the first rupture in the work of Lee et al. (2011). However, the rupture length of our estimation might be comparable with that of Ching et al. (2011) using the inversion of GPS. One possible cause is that Lee et al. (2011) introduced a low rupture velocity into the source rupture model to produce long source duration and rupture length. In addition, the source duration derived from this study is also in agreement with that estimated from the image of rupture by the back-projection of the P-waves (Chao et al., 2011). The estimated rupture velocity is high and approximate to the S-wave velocity of the crust. The rupture directivity analysis of this study also confirmed the fault plane in the strike of N55°E, rather different from the NS-striking CCF and related to the CTFZ. In this analysis, the earthquake showed a feature of unilateral faulting. This is probably related to the CCF, located to the east of the 2010 JiaSian earthquake and hindering it from faulting southeastward. Thus, most of earthquake energy release toward the NW-direction. However, it is also possible to have a supershear faulting during the earthquake. Bouchon et al. (2010) concluded that there is the lack of aftershocks in the segment of fault with supershear faulting, which is a relatively weak fault with homogeneous friction (Tan and Helmberger, 2010). From aftershock distribution in Fig. 1, there is relatively low seismicity between the hypocenter and the location of larger aftershocks. The portion of fault with less aftershock might be responsible for the high rupture velocity during the 2010 JiaSian earthquake. Tan and Helmberger (2010) observed a reciprocal relationship between the static stress drop and the rupture velocity of the 2003 Big Bear, California, earthquake sequence, as theoretically stated by Kanamori and Rivera (2004). Ching et al. (2011) derived a relatively low static stress drop of 5 bars for the 2010 JiaSian earthquake from an inversion of GPS data. In other words, the estimated high rupture velocity of the 2010 JiaSian earthquake seems to respond to the low static stress drop. This differs from the 1999 Chi-Chi, Taiwan, earthquake, which had a relatively low rupture velocity and a larger static stress drop (Hwang et al., 2001a, 2001b). The high rupture velocity estimated in this study probably produces the anomalous PGA distribution. The observed amplitude of seismic waves is inversely proportional to the observed source duration. According to the estimated source parameters and rupture directivity, at an equal epicentral distance, the amplitude ratio of a NW-station to a SE-station from the epicenter is approximately 4.0, roughly agreeing with the distribution of PGA. However, the regional velocity structure is also a possible cause of anomalous PGA. 4.4. Radiated seismic energy We used the method proposed by Vassiliou and Kanamori (1982) to calculate the radiated seismic energy (ES) based on the source duration as:

" ES ¼

Table 1 Testing of the source rupture model. Fault plane strike/dip

304°/28° 170°/70°

Misfit (s) Unilateral faulting

Bilateral faulting

0.6909 1.4237

1.4240 1.4207

1

15pqa

þ 5

#

1 5

10pqb

M 20

2 2

xð1  xÞ T 30

ð3Þ

where a, b, and q are the P-wave velocity, S-wave velocity, and density of the source area. M0 and T 0 are the seismic moment and source duration. Vassiliou and Kanamori (1982) gave x = 0.2 for a trapezoidal source time function, i.e., rise time = xT0 = 0.2T0. For a triangular source time function, x is 0.5. At x = 0.2, the factor xð1  xÞ2 in Eq. (3) is 0.128; at x = 0.5, the factor is 0.125. That is,

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the ES determined from x = 0.2 is equivalent to that from x = 0.5 using the same M0 and T0. Selecting a P-wave of 6.5 km/s, S-wave of 3.75 km/s, and density of 2.71 g/cm3 in the source area based on the iasp91 velocity model, the estimated ES of the 2010 JiaSian earthquake is 1.0  1013 Nm using M0 = 2.31  1018 N m and T0 = 5.2 s, without considering the finite frequency bandwidth limitation (Wang, 2004). The estimated ES is slightly lower than that of the USGS’s report (1.7  1013 N m). However, the ES/M0 is 4.3  106, leading to the apparent stress drop of 1.6 bars (Wyss and Brune, 1968) and corresponding to the value of the reverse fault addressed by Pérez-Campos and Beroza (2001). 5. Conclusions In this study, the waveform fitting of the estimated source parameters was better than that of previous reports (Figs. 2 and 6). The derived focal depth of 22 km, which indicates the initial depth of the earthquake, agreed well with the relocation using a 3D regional velocity model (Huang et al., 2011), and differed from the centriod depth. This roughly stated the rupture feature of the 2010 JiaSian earthquake, which ruptured toward the shallows (Lee et al., 2011). The dip angles of the fault plane estimated from 20-km and 22-km depths showed the initial rupture at a lower dip-angle plane and the later rupture at a higher dip-angle one. The rupture directivity analysis suggests that the 2010 JiaSian earthquake was a unilateral faulting event on the NW-striking fault plane with a high rupture velocity, related to the CCF and the CTFZ and probably causing the anomalous PGA distribution and a low static stress drop (Ching et al., 2011). Acknowledgments The authors would like to express their gratitude to the IRIS for providing us with the GSN data, and thank the CWB (Central Weather Bureau, Taiwan) for the use of the earthquake catalog. Additionally, we offer special thanks to the two anonymous reviewers for their critiques, which have enabled us to significantly improve the manuscript. We also thank Prof. Yih-Min Wu, Dr. Tai-Lin Tseng and Mr. Wei-An Chao for their constructive comments. The GMT software developed by Wessel and Smith (1998) was used to create some of figures. This study was financially supported by the Chinese Culture University, Taiwan. References Aki, K., Richards, P.G., 2002. Quantitative Seismology, second ed. University Science Books, Sausalito, CA. Ben-Menahem, A., 1961. Relation of seismic surface-waves from finite moving sources. Bull. Seismol. Soc. Am. 51, 401–435. Bouchon, M., Karabulut, H., Bouin, M., Schmittbuhl, J., Vallée, M., Archuleta, R., Das, S., Renard, F., Marsan, D., 2010. Faulting characteristics of supershear earthquakes. Tectonophysics 493, 244–253. doi:10.1016/j.tecto.2010.06.011. Chao, W.A.V., Zhao, L., Wu, Y.M., 2011. Imaging the rupture front and slip distribution by the back-projection of P-wave envelope from strong-motion records: a case study for the 2010 Jiasian, Taiwan, earthquake. In: 2011 Annu. Congress of Chinese Geophysical Society and Geological Society of Taiwan, Taipei, Taiwan, 4–5 May, 2011. Chen, Y.R., Lai, Y.C., Huang, Y.L., Huang, B.S., Wen, K.L., 2008a. Investigation of source depths of the 2006 Pingtung earthquake sequence using a dense array at

teleseismic distances. Terr. Atmos. Ocean. Sci. 19, 579–588. doi:10.3319/ TAO.2008.19.6.579(PT). Chen, K.C., Liang, W.T., Liu, Y.H., Huang, W.G., Wang, J.H., 2008b. Seismic moments of Taiwan’s earthquakes evaluated from a regional broadband array. Earth Planets Space 60, 559–564. Ching, K.E., Johnson, K.M., Rau, R.J., Chuang, R.Y., Kuo, L.C., Leu, P.L., 2011. Inferred fault geometry and slip distribution of the 2010 Jiashian, Taiwan, earthquake is consistent with a thick-skinned deformation model. Earth Planet. Sci. Lett. 301, 78–86. Das, S., Aki, K., 1977. Fault plane with barriers: a versatile earthquake model. J. Geophys. Res. 82, 5658–5670. Das, S., Henry, C., 2003. Spatial relation between main earthquake slip and its aftershock distribution. Rev. Geophys. 41, 1013. doi:10.1029/2002RG000119. Huang, H.H., Wu, Y.M., Lin, T.L., Chao, W.A., Shyu, J.B.H., Chan, C.H., Chang, C.H., 2011. The preliminary study of the 4 March 2010 Mw 6.3 Jiasian, Taiwan earthquake sequence. Terr. Atmos. Ocean. Sci. 22, 283–290. doi:10.3319/ TAO.2010.12.13.01(T). Hwang, R.D., Wang, J.H., Huang, B.S., Chen, K.C., Huang, W.G., Chang, T.M., Chiu, H.C., Tsai, C.C.P., 2001a. Estimates of stress drop of the Chi-Chi, Taiwan, earthquake of September 20 1999 from near-field seismograms. Bull. Seismol. Soc. Am. 91, 1158–1166. Hwang, R.D., Yu, G.K., Wang, J.H., 2001b. Rupture directivity and source-process time of the September 20, 1999 Chi-Chi, Taiwan, earthquake estimated from Rayleigh-wave phase velocity. Earth Planets Space 53, 1171–1176. Hwang, R.D., Lin, T.-W., Yu, G.K., Chang, J.P., Chang, W.Y., 2010. Source parameters of the 2005 Mw 7.2 Miyagi-Oki earthquake as inferred from teleseismic P-waves. Terr. Atmos. Ocean. Sci. 21, 645–654. doi:10.3319/TAO.2009.08.25.01(T). Kanamori, H., Rivera, L., 2004. Static and dynamic scaling relations for earthquakes and their implications for rupture speed and stress drop. Bull. Seismol. Soc. Am. 94, 314–319. Kanamori, H., Stewart, G., 1976. Mode of the strain release along the Gibbs fracture zone, Mid-Atlantic ridge. Phys. Earth Planet. Inter. 11, 312–332. Kennett, B.L.N., Engdahl, E.R., 1991. Traveltimes for global earthquake location and phase identification. Geophys. J. Int. 105, 429–465. Lee, S.J., Liang, W.T., Mozziconacci, L., Hsu, Y.J., Lu, C.Y., Huang, W.G., Huang, B.S., 2011. 2010/03/04 M6.4 Jiashian earthquake, Taiwan: Finite-Fault Source Rupture Process. Posted on . Lin, T.W., Hwang, R.D., Ma, K.F., Tsai, Y.B., 2006. Simultaneous determination of earthquake source parameters using far-field P waves: focal mechanism, seismic moment, rupture length and rupture velocity. Terr. Atmos. Ocean. Sci. 17, 463–487. Lin, T.W., Hwang, R.D., Chang, J.P., Yu, G.K., Chang, W.-Y., 2008. Determination of source depth from teleseismic P-wave inversion. In: 2008 Annu. Congress of Chinese Geophysical Society and Geological Society of Taiwan, Tainan, Taiwan, 7–8 May, 2008. Okal, E.A., 1992. A student’s guide to teleseismic body wave amplitude. Seism. Res. Lett. 63, 169–180. Pérez-Campos, X., Beroza, G.C., 2001. An apparent mechanism dependence of radiated seismic energy. J. Geophys. Res. 106, 11127–11136. Ruff, L., Kanamori, H., 1983. The rupture process and asperity distribution of three great earthquakes from long-period diffracted P-waves. Phys. Earth Planet. Inter. 31, 202–230. Tajima, F., Kanamori, H., 1985. Global survey of aftershock area expansion patterns. Phys. Earth Planet. Inter. 40, 77–134. Tan, Y., Helmberger, D., 2010. Rupture directivity characteristics of the 2003 big bear sequence. Bull. Seismol. Soc. Am. 100, 1089–1106. Tseng, T.L., Jian, P.R., Liang, W.T., 2011. Earthquakes near Jiashian area of southwestern Taiwan. In: 2011 Annu. Congress of Chinese Geophysical Society and Geological Society of Taiwan, Taipei, Taiwan, 4–5 May, 2011. Vassiliou, M.S., Kanamori, H., 1982. The energy release in earthquakes. Bull. Seismol. Soc. Am. 72, 371–387. Wang, J.H., 2004. The seismic efficiency of the 1999 Chi-Chi, Taiwan, earthquake. Geophys. Res. Lett. 31, L10613. doi:10.1029/2004GL019417. Warren, L.M., Shearer, P.M., 2005. Using the effects of depth phases on P-waves spectra to determine earthquake depths. Bull. Seismol. Soc. Am. 95, 173–184. Warren, L.M., Shearer, P.M., 2006. Systematic determination of earthquake rupture directivity and fault planes from analysis of long-period P-wave spectra. Geophys. J. Int. 164, 46–62. doi:10.1111/j.1365-246X.2005.02769.x. Wessel, P., Smith, W.H.F., 1998. New, improved version of generic mapping tools released. Eos, Trans., AGU 79, 579. doi:10.1029/98EO00426. Wyss, M., Brune, J.N., 1968. Seismic moment, stress, and source dimensions for earthquakes in the California-Nevada regions. J. Geophys. Res. 73, 4681–4694. Zhu, L., Helmberger, D.V., 1996. Advancement in source estimation techniques using broadband regional seismograms. Bull. Seismol. Soc. Am. 86, 1634–1641.