Estimates of Source Parameters of Two Large Aftershocks of the 1999 Chi-Chi , Taiwan , Earthquake in the Chia

Two large aftershocks of the 1999 Chi-Chi earthquake (ML =6.4 and 6) occurred to the south of the Chelungpu fault and in the Chia-Yi in Taiwan. Near-field seismograms estimated some source parameters of the two events. The near-field displacement spectra can be described by Brune's co-square model. The estimated values of stress drop ( 8CJ ), apparent stress (CJ a), and scaled energy (E /M ), of these two events varied from station to station 5 0 with mean values of: 8cr=991 bars, O'a=402 bars, and E /M =1.3x10-3 for 5 0 the ML 6.4 event; and 8CJ =831 bars, O' a =337 bars, and E/M0=1.0x10-3 for the ML 6.0 one. This shows a high dynamic stress drop between these two events. The larger values calculated from the ML 6.4 event indicated a higher percentage transformation of strain energy into seismic-wave energy com­ paring to the ML 6.0 event. (


INTRODUCTION
Stress change on the fault plane is one of the significant indicators specifying dynamic behavior of earthquake ruptures (e.g., Brune 1970).The scaled energy (E /M ) defines the < 0 ratio of seismic-wave energy (E,), over seismic moment (M0), is related to the degree of fric- tion drop and can indicate the stress condition of an earthquake (Kikuchi and Fukao 1988;Kanamori and Heaton 2000).However, the values of E /M estimated from far-field seismo-account for the relationship of dynamic stress and final stress during earthquake rupturing processes (Kikuchi andFukao 1988;Smith et al. 1991;Ramon Zuniga 1993;Kanamori 1994;Hwang et al. 2001).A stress model specified with frictional overshoot, as the final stress level being lower than the dynamic one (see Kikuchi and Fukao 1988), further confirms Vassiliou and Kanamori's earlier observations (1982).In contrast, Ramon Zuniga (1993) considered another model of partial-stress-drop model to interpret the observations by Smith et al. (1991) and some others.The distinction of these two models might be due to the differences seismic wave energy estimation.Choy and Boatwright (1995) improved the estimates of seismic-wave energy from teleseismic data, and stated the frictional overshoot model is more appropriate than the partial-stress-drop model.Hwang et al. (2001) also obtained the same conclusion for the 1999 Chi-Chi earthquake.
On September 20th, 1999, rupturing along the Chelungpu fault initiated an M 7.6 earth- • quake beneath the town of Chi-Chi in central Taiwan (cf.Ma et al. 1999;Shin et al. 2000;Wang et al. 2000).Huang et al. (2001) and Hwang et al. (2001) estimated the stress drop, apparent stress, and E/M 0 of the earthquake from near-field seismograms through different ways.Their results showed that the stress drop is higher in the north segment of the fault than the south one.About one month after the mainshock, two large aftershocks of M L =6 . 4and M L =6 .0)are 5 km apart from each other, and located near the south end of the fault in the Chia Yi area.The epicenters of the two events are shown in Fig. 1.This paper estimates the stress drop of these two events their relationship with the mainshock.
Since 1991, the Central Weather Bureau (CWB) has constructed an island-wide network composed of more than 600 free-field strong-motion stations.This network recorded a huge number of high-quality data generated by the Chi-Chi earthquake and its aftershocks (cf.Shin et al. 2000).Several stations in the vicinity of epicenters recorded and generated seismograms of two aftershocks (Fig. 1).Such near-field seismograms can be used to estimate the stress drop, apparent stress, and E/M0 of these two aftershocks through a simple method proposed by Andrews (1986).

2.DATA
The accelerographs, operated by the CWB, are specified by a flat frequency response from DC to about 50 Hz with 16-bit resolution for full scale digital recordings up to 2g.The accelerogram is recording at a rate of 200 samples per second for A900 type, and 250 samples per second for IDS type (Liu et al. 1999).On October 22nd, 1999, two large aftershocks with local magnitudes of 6.4 and 6.0, respectively, were located near the southern end of the Chelungpu fault in the Chia-Yi area.Although the CWB routinely determine the hypocenters of these two aftershocks.In order to obtain more reliable hypocenters for the source parameter estimations, we relocated epicenters at 23.47 °N, 120.52 °E with a focal depth of 24.5 km for the M L 6.4 event, and at 23.51°N, 120.50 °E with a focal depth of 24.0 km for the M L 6.0 one.
The focal mechanisms of these two events show thrust faulting for the M L 6.4 event and strike slip faulting for the M L 6 one (Kao and Ange lier 2001; Fig. 1 ).The Harvard CMT earthquake catalogue shows M 0 ==6.9X1024dyne-cm with M,==5.6 for the M L 6.4 event and M0==2.5X1024dyne-cm with M,=5.3 for the ML 6.0 one.Many seismic stations recorded these two events, and generated several seismograms.In order to reduce the path effects, we only used the seismo grams recorded from five near-field stations CHY046, CHY038, CHY047, CHYOlO, and CHY034 (shown by solid circles in Fig. 1) with their distance to epicenter ranging from 2 km to 11 km.
Owing to the flat and wide frequency response of the instruments, the instrumental effect on the accelerograms can be ignored since only the transverse-component waveforms are used to estimate the values of C>a and i1.. e>.We rotated the waveforms from the original geographic coordinate system to a system defined based on the wave propagating direction.This new system contains 3 directional components of R, N and T. The radial (R) component defines the vibrating motion along the hypocenter-station while the N-component is on the slant plane and the T-component is normal to the slant plane.Both T and N components are normal to the R component.We further add the waveforms of T and N components to form a composite waveform.The velocity and displacement waveforms are integrated once and twice, respectively, from the accelerograms.Figure 2 shows the rotated accelerograms, velocity waveforms, and displacement waveforms for the ML 6.4 event with the left-handed-side dia grams for the T-component and the right-handed-side ones for the N-component.Figure 3 shows the similar waveforms for the M L 6.0 event.The two vertical dashed lines marked the existence boundaries of predominant signal in Figs. 2 and 3.These signal are used for the source parameters estimations below.Obviously, the waveform of the predominant signal is less complicated for the ML 6.4 event than for the M L 6.0 one, but with similar duration of 3 seconds at all stations for the two events.

3.METHOD
This study applied an objective method proposed by Andrews (1986) for estimating the values of stress drop and apparent stress of the two aftershocks.Based on this method, the integrals of squared velocities and squared displacements are first applied to measure seismic wave energy (E) and seismic moment (M ), respectively, of an earthquake by means of the    (2) s.=21tR2 is the surface area of a hemisphere with a radius R based on the assumption that the spherical spreading is confined to the lower hemi-sphere of the source area (Bolt 1986).R is the distance from the source to the station, and 00=2Iv-114I0314 (Andrews 1986), where Iv and 10 are, respectively, the squared-velocity and squared-displacement integrals in time domain at the low-frequency spectrum level according to Brune's ro-squared model (Brune 1970).Al though the corner frequency, f0, can be calculated from (Iyfl0)112/2 7t (Andrews, 1986), the f0 values are 0.8 Hz for M L 6.4 event and 1.2 Hz for the M L 6 event as mentioned above (Fig. 4).
The two qualities p and � denotes, respectively, the density and the S-wave velocity of the materials in the source area.In this study, we applied the same values of p (2.4g/cm3) and � (3.0cm/sec) as the CWB for the routine earthquake location.In order to include the free sur face amplification, the seismograms are corrected by a factor of 2. Due to uneven distribution of stations, an average radiation pattern 0.66 for the dip-slip mechanism and 0.55 for the strike slip mechanism for the S waves are adopted to adjust the amount of seismic energy caused by a non-uniform spatial distribution of seismic-wave radiation pattern (cf.Boore and Boatwright 1984).
According to Eqs. ( 1) and (2), Wyss and Brune (1968) defined the apparent stress ( cr a ), as the product of the seismic efficiency and the averaged stress (neither of them can be deter mined seismologically directly.), in terms of (3) where µ is the rigidity of the materials in the source area.A commonly-used value of µ for the crust materials is 3.0x10 1 1 dyne-cm•2• The apparent stress is usually regarded as the prod uct of seismic efficiency and averaged stress on the fault plane.From Brune's circular source model (1970), the static stress drop ( ilcr), is given in terms of the integrals of squared veloci ties and squared displacements as Of course, the attenuation effect of seismic waves propagating in between the hypocenter and the stations must be taken into account to adjust the recorded waveforms.Generally, a frequency-dependent parameter (Q.) represents the attenuation effect on the S waves, and the averaged value of Q, is about 250 in the study area (Rau et al. 1996).

4.RESULTS
In addition to the instrumental response and noise, the choice of frequency range or period range of a filter retrieving the filtrated waveforms from the original will also influence the source parameters estimations.Hence, we first examine the effects on of a band-pass filter for source parameter estimations with different period ranges.Figure 4 shows the displacement spectra of the Tand N-component waveforms at five stations by a solid line and short-dashed line respectively.In general, the spectral amplitudes of these two components are almost con stant when f is less than a certain frequency (f0; f0=0.8Hz for the ML 6.4 event and ( =1.2 Hz for the M L 6.0 one), and decrease with increasing frequency when f>f0 (These as (is named as corner frequency, cf.Aki 1967).The amplitudes of these two components are close to each other for all stations when f>f0, but different when f <f0• Moreover, the spectral amplitudes seem to decay with increasing frequency in a power-law function, with an exponent of about -2 when f>f 0 • This indicates that the high-frequency spectral amplitudes can be described by the m-square scaling model (Aki 1967;Brune 1970).Hence, it is appropriate to use Andrews's method to estimate the low-frequency spectral level, i.e., Q0, and related source parameters based on them-squared model.The value of Q0 for each station is the mean of two estimated values from the T-and N-component spectra.For the M L 6.4 event, Q0 is 2.1 cm-sec for CHYOIO, 4.5 cm-sec for CHY046, 4.1 cm-sec for CHY034, 2.6 cm-sec for CHY047, and 5.1 cm-sec for CHY038.As for the ML 6.0 event, Q0 is 0.9 cm-sec for CHYOlO, 1.8 cm-sec for CHY046, 1.0 cm-sec for CHY034, 1.6 cm-sec for CHY047, and 1.7 cm-sec for CHY038.Figure 4 show the distribution of Q0 and f0 values and the scaling law for each station deter mined from Q0 and f0 values as long-dashed lines.The theoretical spectra amplitudes, except for CHY046 station, are indicated by long-dashed line in Fig. 4.
Figure 5 shows the variation between frequency with cumulative value of the sum of squared velocities of the T-and N-component waveforms.The value defines kinematic energy by dividing seismic waves to the density of the material.The cumulative value increases rap idly within the range from f=O to 6 Hz, and turns flat when f>6 Hz.This means that seismic wave energy recorded at each station mainly distribute in the frequency range of 0 to 6 Hz.Hence, f=6 Hz is the upper bound frequency for waveform filtration.The variations for the five stations are different for these two events.
We retrieve the waveforms from rotated seismograms through a band-pass filter when different values of the upper bound period (T ) or the lower bound frequency (f 1 ) are taken.

upr ow
The lower bound period (T1 ; associated with the upper bound frequency f 1 of the filter is -� fixed at 0.17 sec (or fu p r=6 Hz) for the two events.Figure 6 shows the distribution of a a and 6-cr for each station with T between 2.5 and 17.5 sec.When the left-handed-side diagrams upr for the M L 6.4 event and the right-handed-side ones for the M L 6.0 event.The values of the two source parameters decreased rapidly with T , and then approach individual constants when upr T > 10 seconds.The distance varies from the two epicenters to five stations.Table 1 listed the upr averaged values of a a and 6-cr of T from 10 sec to 17 .5sec obtained at the five stations of upr the two aftershocks are listed in Table 1.The averaged values are: 6.cr=991 bars and O"a=402 bars for the M L 6.4 event, and 6.cr=831 bars and O"a=337 bars for the M L 6.0 one.In order to examine the possible effect of distance variations, we plot the values of cra and 6-cr against distance for the two events (a solid circle for the M L 6.4 event and an solid triangle for the M L 6. 0 one) in Fig. 7a along with the averaged values of these two events (a solid line for the M L 6. 4 event and a dashed line for the M L 6.0 one).
Unlike the values of 6-cr and O"a the E, and M0 values do not change too much from  station to station (Fig. 7b).The Harvard CMT earthquake catalogue shows M =6.9X1024dynea cm with M,=5.6 for the M L 6.4 event, and M0=2.5 X 1024 dyne-cm with M,=5.3 for the M L 6.0 one.The estimating method for E, values developed by Choy and Boatwright (1995) yield E,=6.3 X 1019 erg and 2.2x1019 erg, respectively, for the two events, thus leading to E /M =9.1X10-6 for the M L 6.4 event and E IM =8.8X10-6 for the M L 6.0 one.Figure 7b Hwang et al. (2001).Lines associated with four values of E/M 0 , i.e., 5 X 10-3, 5 x 10•4, 5 x 10•5, and 5 x 10-6, calculated from the relation be tween E and M calculated by Vassiliou and Kanamori (1982) and Kikuchi and Fukao (1988) s 0 for global observations.Included in Table 1 are the averaged values of E , M , and E IM of the s 0 s 0 five stations for the two events estimated from related data: M =l.2X 1025 dyne-cm, E =1. 0 s 6 X 1022 erg, and E /M =1.3x10-3 for the M L 6.4 event; and M =4.6X1024 dyne-cm, E =4.8X1021 •:: <\:::: :::::: (a) •2 •2 §' 1000 I-----"�-_.,,--____ ____ _.. Q 800 ---e: --5 --•4---------- ' 0 e., 5 x 10-6, 5 x 10-5, 5 x 10-4, and 5 x 10-3, as explained in the text.source model.Although the observed spectral amplitude does not fit the theory perfectly, it still shows that the observed spectral amplitudes do follow Brune's source model.We esti mated the M0 value by applying the value of 0.0 with infinite time period instead of a period of 17 .5seconds.Of course, the estimated M value could be less than M value obtained from the 0 0 long-period seismic waves recorded at remote stations since the amount of longer-period seis- stations, we assumed the spatial variation in seismic-wave radiation caused by a focal mecha nism must be the main reason to cause these observations.In addition, when f is larger than 6 Hz, the cumulative value of the M L 6.4 event is several times larger than that of the ML 6.0 one, because the former is larger than the latter.
From Fig. 7a, it is obvious that the L\.cr value for the ML 6.4 event is slightly dependent on the hypocentral distance, but not for the M L 6.0 one.The estimated L\.cr values for the two events vary in a large range from 500 bars to 1600 bars.The reason to cause this large variation is the same as that mentioned previously for Fig. 5.
From Fig. 7b, we can see that the E /M values of the two aftershocks estimated from s 0 seismograms from five stations do not vary much between stations.The averaged E IM vals 0 ues estimated from near-field data are 1.3x10•3 and 1.0X10-3, for the M L 6.4 and M L 6.0 events (Table 1). the line with 5x104 (cf.Fig. 7b).The values of the two aftershocks are slightly larger than that of the mainshock.This might mean that the percentage of strained energy transferred to seis mic-wave energy is slightly larger for the two aftershocks than for the mainshock.The values of E IM estimated from teleseismic data also showed the same conclusion.
s 0 Ramon Zuniga (1993) proposed a parameter of E denoted by E= L\.cr /( cra +0.5 L\.cr) to be an indication to classify stress drop model: E> 1 for a frictional overshoot mechanism and E<l for a partial-stress-drop mechanism.According to Table l, cra and L\.cr /2 values of th ese two events both lead to E:::: 1.104> 1 suggested rupture processes by frictional overshoot mecha nism for these two events.For the Chi-Chi mainshock, Hwang et al. (2001) also obtained the same conclusion.Smith et al. (1991) and Ramon Zuniga (1993) obtained different result and proposed.They described the displacement spectra beyond the corner frequency by a ro-1decay function.For such spectra, the seismic-wave energy shows a w•2 decay.In this study, the displacement spectra beyond the corner frequency show a ro•2 decay (Fig. 4).Hence, the seismic-wave energy estimated in this study, especially at high frequencies, is not as high as expected by Smith et al. (1991).
Based on the assumption that the dynamic stress level on the fault plane equals to the final one after an earthquake, Orowan (1960) stressed that the theoretical O'a/ L\.cr value is 0.5.The estimated O'af L\.cr value in this study is about 0.4, which is somewhat close to 0.5, this might indicate the dynamic stress levels of these two aftershocks are close to the final one.The cr a I �a ratio of the Chi-Chi mainshock is 0.4 (Hwang et al. 2001), which is the same as ours, indicated of mechanically uniform conditions in the whole seismogenic zone.

CONCLUSIONS
The averaged source parameters of stress drop (�a), apparent stress (CTa), and scaled energy (E/M) for the two large aftershocks (M L =6.4, M L =6) of the Chi-Chi Earthquake are : �a =991 bars, a a =402 bars, and E/M0=1.3X 10-3 for the M L 6.4 event; and �a =831 bars, O'a=331 bars, and E/M 0 =1.0X 10-3 for the M L 6.0 one.These results suggest high dynamic stress drop, which is also proportional to the magnitude of the aftershock.This suggested the larger aftershock transformed a higher percentage of strain energy into the seismic-wave energy.Both local and teleseismic data yielded slightly larger E/M0 values for the two aftershocks than the mainshock, and suggested frictional overshooting stress model as the rupturing pro cesses based on Ramon Zuniga's parameter (1993).The dynamic stress levels of these two events are close to the final one according to Orown' s assumption (1960).

Fig. 1 .
Fig. 1.The distribution of epicen ters (denoted by a solid star) with focal mechanisms of the two aftershocks and the locations (shown by a solid circle) of five stations in use.

Fig. 2 .
Fig. 2. The diagrams showing T-and N-component velocity and displacement seismograms of the ML6.4 after shock from five stations integrated once and twice from the original accelerograms after a band-pass filter with frequencies ranging from 0.06 to 6 Hz.The dashed lines specify the part of seismogram used for the source parameter estimations.

Fig. 3 .
Fig. 3.The diagrams showing T-and N-component velocity and displacement seismograms of the ML 6.0 after shock from five stations integrated once and twice from the original accelerograms used after a band-pass filter with frequencies ranging from 0.06 to 6 Hz.The dashed lines specify the part of seismogram used for source parameter estimations.

Fig. 4 .
Fig. 4. Diagrams show the displacement spectra ofT-component (in a dark solid line) and ofN-component (in a short-dashed solid line) and the theoreti cal spectrum (in a long-dashed line) calculated based on Brune's m-2 model (Brune 1970).

Fig. 5 .
Fig. 5. Distribution of cumulative energy of the two components in use with frequency for the two aftershocks (solid lines for the M L 6.4 aftershock and dashed lines for the M L 6.0 one) recorded from the five stations (1 for CHY046, 2 for CHY047, 3 for CHYOIO, 4 for CHY034, and 5 for CHY038). 307 and M0 values as open circles for the M L 6.4 event, open triangles for the M L 6.0 one, and solid squares from near-field data by Figure4shows the displacement spectra for the five stations ( solid line for the T-compo nent and short-dashed one for the N-component).It is obvious that all spectral amplitudes

Fig. 6 .
Fig. 6.Distribution of apparent stress and stress drop within upper-bound period, T , as defined in the text The left-handed-side diagrams belong to the upr M L 6.4 aftershock and the right-handed-side ones belong to the ML 6.0 aftershock.

Fig. 7 .
Fig. 7. (a) The distributions of stress drop with hypocentral distance: circles for the M L 6.4 aftershock and triangles for the M L 6.0 aftershock.(b) Loga rithmic diagram of E versus M (solid symbols for the values estimated ' 0 from local data and open symbols for those estimated from related data listed in the Harvard CMT earthquake catalogue; circles for the M L 6.4 aftershock and triangles for the M L 6.0 aftershock) and the relative values of the Chi-Chi mainshock obtained by Hwang et al. (2001): The solid squares for the values estimated from near-field data and the open square from the USGS catalogue.Lines associated with four values of E fM , i.
mic waves are weak in local seismograms.As shown in Fig.5, the variations of cumulative energy for the two events at five stations varied from each other.This might be mainly due to three reasons: the first one is that the stations are situated at positions with different values of seismic radiation, the second one is the path effect, and the third is the site effect.Since the five stations are all close to the epicen ters of these two events, they all situated in almost similar geological structures, thus eliminat ing the path effects.In the Taiwan region,Lee et al. (2001) stated large site effects exist mainly in the higher-frequency range.With similar pattern of the variations of cumulative values at all (Smith et al. 1991;the near-field E,IM0 vHwang et al. 2001)o orders larger in magni tude than the teleseismic one, this is the same conclusion obtained by other authors(Smith et al. 1991; Singh and Ordas 1994;Hwang et al. 2001)that the E/M value estimated from s 0near-field seismograms is usually larger than that from far-field ones.Based on near-field data, the values of E /M for the Chi-Chi mainshock and the two aftershocks distribute around s 0