Characteristics of Seismic Source Spectra from the Chia-Yi and Tai-Nan area of Taiwan

Source spectra of S waves were determined using records of eighteen earthquakes occurring in the Chia-Yi and Tai-Nan area with local magni­ tudes of 2.8 � ML �5.8 as obtained from a rock-site station. In addition to the correction of geometrical spreading, elimination of the anelastic attenua­ tion effect from the observed spectra was carefully examined to measure the high-frequency spectral levels of seismic sources. As to the source spectra, two types of spectral shapes may be observed. For earthquakes of ML< 5.4, the spectra obey the m-squared model with a single corner frequency. However, this observation cannot provide an ad­ equate representation for earthquakes of ML �5.4, since they clearly dem­ onstrate the existence of two corner frequencies on the spectrum. The dif­ ference in spectral shapes may reveal that the rupture of larger earthquakes proceeded as a series of multiple events while a single fault patch results in smaller earthquakes. This explanation is supported by both spectral shapes and waveform characteristics, and may disclose the complexity of earth­ quake sources of larger magnitude. The seismic moment of M0 measured from spectral level at low fre­ quency range satisfies a relation with lower corner frequency of lo in M0 oo /0-3• For the set of earthquakes, the average stress drop is 125 bars. Nonetheless, this model is a poor fit to the shapes of source spectra for events of ML� 5.4. The source spectra obtained by the two greater events, the 1991 Chiali (ML= 5. 7) and 1993 Tapu (ML= 5.8) earthquakes, were discussed in this subject. In describing these spectra, a stress drop of about 60 bars was estimated from the spectral level in a lower frequency range, while 600 bars was required to interpret the high-frequency amplitudes. By applying the Sato and Hirasawa (1973) source model, the average scale length of the fault heterogeneities inferred from the higher corner frequency of /0 is about 300 meters, and this is almost identical to the source radius of the Brune (1970, 1971) model for small events with a magnitude of around 3. Based on the seismic moments taken from the Harvard centroid-mo11nstitute of Earth Sciences, Academia Sinica, P.O. Box 1-55, Nankang, Taipei, Taiwan, ROG 21nstitute of Geophysics, National Central University, Chungli, Taoyuan, Taiwan, ROG 415 416 TAO, Vol. 10, No. 2, June 1999 ment tensor (CMT) solution and this study, for the Tapu earthquake the estimated values of local stress drop obtained using the specific barrier model (Papageorgiou and Aki, 1983) are about 700 and 516 bars. The high stress drop of 600 bars for our result, as observed from high-frequency source spectra, lies in between, and its validity is also confirmed by the agreement of total seismic energy between the results obtained from specific barrier model and those from the Gutenberg-Richter relation (1956). (


INTRODUCTION
The Chia-Yi and Tai-Nan (hereafter referred to as CN) plain is one of the most seismically active areas on Taiwan island. According to historical records, several disastrous earthquakes occurred in this area since 1700 (Cheng and Yeh, 1989). As discussed by Cheng and Yeh (1985), the average rate of damaging earthquakes with M L > 6 occurring in the region is approximately in every 25 years. No major event has occurred in this area since the 1964 Paiho earthquake (M L = 6.4). Although future large and catastrophic earthquakes are antici pated in this region, predictions of strong-ground motion in this area are hindered by a lack of data for large events. For this reason, a number of film-recording accelerographs have been operated by the Institute of Earth Sciences (!ES) in the CN area since 1972. Unfortunately, most of the stations are placed in the basement of civil structures and in buildings. In order to obtain the free-field ground motions generated by earthquakes, National Chung-Cheng Uni versity (NCCU) installed a local digital accelerographic network with fourteen stations in the CN area and this began operating in 1990. Even with these improvements, there are still too few to attain a high probability of recording strong motion information for earthquakes. Thus, if we want to extract the source parameters from them, extensive sets of near-source ground motion recordings are desirable. Later, in 1993, a new digital dense array of strong-motion seismographs, consisting of more than one-hundred stations, was widely deployed in this area by the Central Weather Bureau (CWB). Since then, the ground motion database for southwest ern Taiwan has improved greatly.
During the past few years, many earthquakes of small-to-moderate magnitude have been located in the CN area. Because the strong motion stations are densely distributed, these earth quakes produced many near-source ground-motion records. At near-source distances, these recordings are dominated by primary S waves. These phases are important both for their direct association with the strongest ground motions of engineering interest, as well as for their frequency content which is of direct relevance to the distribution of heterogeneities of the fault plane. Results from previous ground-motion predictions in a close-in sites (e.g., Brune, 1970;Hanks and McGuire, 1981;Aki, 1979;Pagageorgiou and Aki 1983;Boatwright, 1988) led one to believe that the interaction of the rupture front with the heterogeneities over the fault plane is responsible for the radiation of high-frequency waves. Traditionally, such a description can be in terms of the S-wave source spectrum (accounting properly for attenuation and site ampli fication) and its associated high-frequency spectral content of the radiated waves. The high frequency excitation of earthquake sources has attracted the attenuation not only because it might be used to improve our understanding of the character of quasi-static and dynamic stress differences during the faulting, but also because it can be used to account for the heterogene ities of slip distribution on a fault plane.
Only a few studies have been done on information concerning earthquake source spectra in the CN area. Based on the theoretical model from Brune (1970Brune ( , 1971, Ou and Tsai (1993) and Tsai ( 1997) constructed the scaling of the earthquake sources from the relation of seismic moments and comer frequencies of source S-wave spectra. Using the dataset from locally recorded earthquakes from 1976 to 1992, Ou and Tsai (1993) showed that the seismic mo ments are proportional to the comer frequencies in a power law with an exponent value of -3. They concluded that Brune's model, with an average stress drop of about 150 bars, can ad equately represent the source spectra for earthquakes 3.6 ::;; M L ::;; 6.3. In a substantial analysis using data from 1990 to 1993, Tsai (1997) did not support the above conclusion as a general feature of CN earthquakes with M L � 4. He reported that the seismic moment does not scale with comer frequency in a commonly used power law with an exponent value of -3. This suggests a breakdown in constant stress drop scaling. Tsai (1997) stressed that this contro versy may be due to insufficient strong-motion data to adequately judge the relation from his study. The apparent discrepancy of the scaling behavior of earthquake source from the above two studies may arise from different instruments and from different recordings. The data used by Ou and Tsai (1993) included some of the events from old instruments (pre-1990), and there has been concern about uncertain instrument calibration . Furthermore, the car-· rection for attenuation and geometrical spreading possibly biased both studies because the recordings are from a variety of sites. Also, in consideration of the different seismic circum stances, the earthquakes used by Ou and Tsai (1993) were located in a region confined by 23°-240N and 120°-121°E;however, Tsai (1997) considered the events within an area bound by 21°-23.5°N and 119°-121°E. Thus, source parameters obtained by Tsai (1997) might only be the average values for the whole of southwestern Taiwan and cannot be reasonably represen tative of a particular area, e. g., the CN area. Consequently, one question that may be posed but not yet answered is: what is the scaling law of small to moderate earthquakes which is appli cable in the CN area?
The work of this article is to estimate source parameters based on modeling source spectra of S-waves. First, we inspect the anelastic attenuation (Q) model currently used in the CN area to remove its effects from the observed spectra. Next, source parameters, i.e. , source dimen sion, stress drop and seismic moment of the earthquakes are estimated through the spectrum fitting technique developed by Brune (1970). Our goal is to understand the source characteris tics for small to moderate earthquakes. In this paper, we report the results of our study on source spectra.

A NEW DATA-SET OF STRONG-GROUND MOTIONS
The CN strong-motion network is operated jointly by the CWB and NCCU. Figure 1 shows the layout of the free-field stations and the mapped fault traces. near the network. Each  The data presented in this paper are from seismic events recorded by station CHY087

120-00
which had a Teledyne Geotech A900 digital accelerograph. There are two reasons for select ing this station. The first is that it is installed at a rock site (Yeh et al., 1992), and hence not only could the site effects be minimized, but also the seismograms are able to contain high frequency signals. The second is that this station was triggered by various small-to moderate sized earthquakes. The earthquakes include the seismic events occurring when station CHY087 was part of the NCCU seismic network in 19 91 and 1992. During that time, this station was called USH, but was renamed CHY087 in 199 3. The location of this station is indicated by a solid square in Figure 1.
To obtain high-frequency motion data, near-source observations from earthquakes are required. For a site near the source, we expected the waves to suffer less from complication over their paths from the heterogeneous velocity structure under the site as well as guarantee ing the enrichment of high-frequency motion to the data used. As distance from the earthquake increases, the attenuation of high-frequency energy makes it difficult to identify events in detail. To this end, a total number of eighteen earthquakes recorded by station CHY087 from 1991to 199 6 were selected for their small hypocentral distances (all within 67 km, 15 within 30 km) and shallow focal depths ( < 15 km). All events range in magnitude from M L 2. 8 to 5. 8 and are distributed within an area bound by 23°-23.6°N and 120°-120.7 5°E. This area covers the main geological features in the CN area -the Chukou fault system and the Meishan fault system. The numbered solid circles in Figure 1 represent the epicenters of the earthquakes.
Information about the events is listed in Table 1. The configuration of the station relative to the various events covers a wide range of azimuthal directions. As can be seen in Table 1, there are two major events. One of them is the Chiali earthquake (12 March 1991, M L = 5. 7), which is a strike-slip fault (Shin et al., 1994). The other is the Tapu earthquake ( 1 5 December 19 93 , M L = 5. 8) , which has a thrust fault mechanism (Shin, 1995 ;Huang et al., 1996;Huang and Yeh, 1998). The two events, which are of comparable magnitude, are the most significant to occur in the study area in the last 30 years. Shown in Figure 2 is an example of the representative velocity records along the east-west direction at station CHY087. They are produced through integration of accelerograms for three events: 5, 9 and 11 (see Table 1) . Bars indicated the parts of S-waves used for the spectral analysis. In Figure 2, it is found that the S-wave form is considerably more complicated for event 5 ( M L = 5. 8) than that for event 9 (M L = 5.0 ) in different source azimuths. We can also find that the complexity of S-wave form occurs only for event 5, but not for event 11 (M L = 4.3). The locations of these two earthquakes are almost the same (see Figure 1). At such a short source-spacing, the effects of anelastic attenuation along the ray path could be identical for the two earthquakes. Hence, the complex nature of S-wave form for event 5 is mainly due to source effect.

3.METHOD
The computational method of the Fourier amplitude spectrum of ground motion U o b s ( f) for S waves at frequency /from an earthquake is described with reference to the Atkinson and Boore (1995) model, using the following general form:  where Qs(f) is the earthquake source spectrum for a specified seismic moment, R is the source to station distance, Q is a dimensionless average quality factor for S waves that de scribes the anelastic attenuation, and P(f) is the high-cut filter that accounts for the observed spectral amplitudes rapidly decay at high frequencies. The high-cut filtering process is impor tant because it controls the ground motion at high frequencies, even at very short distances for a hard-rock site (Hanks, 1982;Anderson and Hough, 1984).
The input parameter of the earthquake source spectrum Qs (f) for the method was modi fied slightly from that of Atkinson and Boore (1995). Seismic wave theory predicts that the spectral amplitude of source S-wave spectra, for displacement, plateaus at low frequencies and decays in inverse proportion to some power of frequency beyond the comer frequency (e.g., Aki, 1967;Brune, 1970;Sato and Hirasawa, 1973;Molnar et al., 1973). The source In equa ti o n (2 ), fo is th e so urce co mer fre quen cy, p and ,B ar e de nsi ty and shear wa ve ve loc ity of the so urce vo lume. The co nsta nt of 0.781 acco unts for the av er ag e va lu e of shear exci tat ion 0.5 5 (Atkinson, 1993; At kin son and Boore, 1995), togethe r wi th th e free-surface eff ec ts of 2.0 and th e pa rti tion of a ve ct or int o horizont al comp on ents 1 / �. For ev ent s in the CN ar ea , we use d va lue s of p= 2.6grn/cm 3 and /3= 3.4 km/ sec fo r th e de nsity an d shea r wa ve ve lo city, ba se d on the av er ag e foc al de pth ( ""' 8 km) fo r the ea rth qua ke s an d th e cru stal mode l by Ye h an d Tsai (1981). Fr om equa ti on (2), the hi gh -f reque nc y de ca y ra te is re la ted to the dyna mi c prop ertie s of th e se ismi c source , wh ich is gi ve n by y=pq. He re , p and q ar e positive constant s. Th e ra ti o of p to q re la tes th e be havior of the sp ec trum at th e intercept of the high an d low fre que nc y nea r to th e come r . For a sma ll ra ti o of p/q , gr adua l deca y be gi n s at fre que nc y some what lowe r th an th at of th e come r freq uency and th e rate in cr ea ses un ti l th e fina l va lue is atta i ne d at hi gher fre quenc y.
In ma ppi ng th e observe d sp ect ru m back to the source sp ect rum, equa tion (1 ) inc orp orates all th e effec ts antic ip ate d for Uobs(f). Howe ve r, there is a que st i on co nce rnin g th is me th od, an d tha t is si te effec t. Hump hre y and An de rson (1994) and An de rson et al.
(1 996) po inte d ou t th at si te effects ca n cause va ria bi l i ty in th e sp ect ru m due to se ismi c st ruct ure nea r the re cord in g si te, ev en th ough th e stati on is locate d on roc k. Th e work of Ou and Tsai (1995) quan ti fie d an av er age site re sp on se at sev er al CN stat ions by a linea r inve rsi on me th od. Th eir re sults in dica te d tha t the si te re sp onse at stat ion CHY087 is re la tiv ely flat from 0. 4 to 30 Hz; thi s im pl ie s th at nea r-s ite effec ts due to impe dance co nt rast s ar e ne gligi ble in th e pr es en t st udy. Procee ding to es ti mate the source sp ec tra , we fi rst ca lcula te th e S-wa ve di sp la ce men t am pl itude sp ec tra for tw o ho ri zont al comp one nts for each ev en t. A da ta se que nc e wa s win dowe d from th e on set of the S pha se to a po int at wh ich 95% of th e shea r wa ve ene rgy wa s cont aine d in the wi ndow. The sp ect ra es tima te d from the trunca ted ti me se rie s are de ter mine d usin g a Fa st Fourie r Tran sform (FFr). To re duc e le aka ge in FFT esti ma tion, a re ct an gula r cosi ne ta pe r wa s use d over 10% of each en d of the da ta . Eac h S-wa ve sp ect rum on th e log (a mpl itude) ve rsus log (fre quency) disp la y in thi s pape r is ca lcula te d from th e squa re root of th e sum of tw o hori zontal comp on en ts. Our ne xt st ep is to exa mine the inf luence of curren tly used Q models in the re gi on to re move its eff ec ts from the sp ec tra. In the thi rd step , a prop er choice of p and q wa s in ve stig ate d to de sc ri be th e high -fr equenc y de ca y ra te of the spectrum. Fi na lly, tria l va lue s of the se ismic moment an d stre ss drop ar e se lec ted for eac h ea rth qua ke by fi tti ng a mode l sp ect rum of e qua ti on (2 ) with th e envel op e s for th e obser ved sp ec tra.

The Observed Spectra
Fi gure 3 dep ic ts an exa mpl e of obse rve d di sp lace ment -am pl it ude sp ec tra of S-wa ve s for se ven ev en ts of M L = 3. 0 to 5. 8 wit h inc rem ents of app rox imately 0. 4 ma gnitu de un its (e xc ep tion of M L =3.4). The eff ect due to ge omet rica l sp rea ding ha s be en co nside re d by multip lyin g the sp ec tral am p li tude by h yp oc ent ral distan ce R. A re ma rka ble feat ure in Figu re 3 is th e si mi la r de ca y rate of sp ectral am p li tude s for ev ent s in de pen dent of the epice ntral di sta nc e and azimut h, alth ough the re is some va riat ion in th e ir de ta il s. Gene rally , th e sp ec tral am plit ud es de cr ea se as 1-2 at hi gh fre que nc ie s ( � 10 Hz). It is al so foun d that th e sp ect rum wit hout attenuation correction for earthquakes of M L < 5.4 (thin line) has one comer frequency. How ever, this feature seems to begin to change as magnitude nears 5.4. As magnitude increases to 5.8, the spectral shape has two comer frequencies (heavy lines), where the spectral envelope changes its general trend.
Another feature shown in Figure 3 is that for frequencies greater than a certain frequency (denoted as f max), spectral amplitudes de _ cay more rapidly than f-2 as frequency increases. This decay is often modeled by a high-cut filter of P(f) as in equation (1 ). Descriptions of P(f) may be suggested by either the fmax model (Hanks, 1982) or the kappa (denoted K') model (Anderson and Hough, 1984). Both the f max and K' representations act to filter out high-frequency motions; their behaviors can be proposed as corresponding respectively to (Boore, 1986) and P ( f) = e-mif (Anderson and Hough, 1984). The physical origin of fmax or TC is still unsolved. There is some debate among many authors as to whether f m ax is due to source properties (e.g., Papageorgiou and Aki, 1983;Singh et al., 1987;Aki, 1987;Papageorgiou, 1988) or the effects of local site conditions (e.g., Hanks, 1982;Anderson and Hough, 1984). Atkinson (1996) noted that T< might possibly have both source and site effects. It has previously been mentioned that station CHY087 has a relatively flat site response up to frequency of 30 Hz (Ou and Tsai, 1995). This suggests that the apparent high-frequency decay of displacement spectra (Figure 3) for several CN events may possibly arise from the source effect. More evidence is needed to understand the factors that influence the observed high-frequency spectral shapes. Examining the origin of fmax (or r<) using seis mographic data is not the main purpose of this article. For the present calculation, we therefore chose to use the f max filter from Boore (1986) for the high-cut filter process. For the displace ment-amplitude spectra, beyond fmax the spectral levels begin to drop even faster; for the acceleration-amplitude spectra, the spectral levels diminish abruptly when f > fmax. Figure 4 shows a typical observed horizontal acceleration spectrum for the 15 December 1993 Tapu earthquake. In this case, the estimated value of f max is 12 Hz. For the eighteen earthquakes in this study, fmax ranged from 8 to 18 Hz.

The Effect of Attenuation
The source spectrum is usually distorted due to anelastic attenuation, which is in an expo nential function as described in equation (1). The anelastic attenuation also influences the high-frequency decay rate of spectral amplitudes. However, the Q value representing anelastic attenuation cannot be determined exactly. Uncertainty in the measurement of the Q value makes it difficult to estimate the comer frequency accurately. This can lead to inaccuracy in estimates of seismic source parameters. Hence, the use of a proper Q value is important. Since our data sets for earthquakes are all for shallow events (<15 km) and are located in a confined region, the effects of anelastic attenuation may be considered identical for all earthquakes.
There have been numerous reports on the determination of the value of Q for the Taiwan region (Shin et al., 1987;Wang et al., 1989;Chen, et al., 1989;Wang and Liu, 1990). An important review of the subject was made by Wang in 1993. Together with the results from the above studies, Wang (1993) revised the Q values currently in use into six provinces based on geological and geophysical considerations. One of the provinces is west ern Taiwan including the Western Foothill and the Coastal Plain. According to the part of seismograms used for the present study, three values of Q were chosen from Table 1 in Wang (1993): Qc = 260 � 300, for all frequencies (Shin et al., 1987) and Qp=IlO, for2Hz </ <6Hz  for western Taiwan, and Qc (f) = 117 fo.77 , for lHz < f < lOHz (Chen, et al., 1989) (3c) 425 for the whole Ta iw an region. Although Qc in eq ua tion (3c) ma y be co n si de red as an av er age va lu e over a wi de regio n, it ca n be eva lua ted in the lo ca l regio n (CN ). He re Qc is th e Q va lue for co da wa ve s and Q /1 is the Q va lu e for shea r wa ve s.
Typi ca l so urce sp ectra for two ea rthqua ke s, ev en t 5 (M L = 5.8) and ev ent 6 (M L = 4.4), ar e sho wn in Fi gure s 5( a) an d 5(b), re sp ect ive ly. The foc al de pt h is 12 .5 km for th e fir st ev ent an d 3. 5 km for the se co nd. The sp ec tr a in Figu re 5 ar e co rre cted for th e effe ct of an el asti c at ten uatio n us in g th e three Q va lue s me ntione d abo ve . The straig ht li ne wi th a slope of -2 atte nding the hi gh-fr equency en vel ope for sp e ctra co rre cted by Qc fro m Chen et al. (19 89) is used as a referen ce to co mp are wi th the re su lt s ev al uate d fro m th e ot her two Q va lue s. Fro m the se sp ec t ra , we ca n se e the shape of th e spe ctra is not ve ry sens iti ve to Qc. Ho we ve r, the sp ec tra in Fi gu re 5(a) are pa rticu la r ly la rge when Q /1 is ta ke n into acco unt at fre que ncies hi gh er than 7 Hz. Thi s is be ca use th e hi gh-fr eq uen cy le ve l of the sp ectrum is re sulted fro m the ba nd -l im it e d (2 to 6 Hz ) av aia la ble fo r the Q va lue in Wa ng' s (19 88) re su lts. Co mp ar is on of the se cu rve s indica tes tha t the fre quen cy-depen de n t fun ction of the Q va lue de scri be d by Chen et al . ( 19 89 ) is pr efer red . This is due to the f-2 slope fo r the hig h-fre qu en cy end of the cur ve sho wn� Fu rther ev id ence is th at this Q functio n is su ita ble for exp lai ni ng the so ur ce spe ctra for   and Qc=300 (Shin et al., 1987).
both shallow ("" 3.5 km) and deep events ("" 12.5 km) in this case, even though such a function is an average over the whole Taiwan region. As shown in Figure 5(a), two corner frequencies are still found on the source spectrum for the event of M L = 5.8, while the event of M L = 4.4 only has one comer frequency, suggesting that the attenuation correction does not strongly affect the spectral behaviors, as displayed in Figure 3. This result is consistent with the notion that the existence of two comer frequencies on the displacement-amplitude spectra for the earthquake M L= 5.8 is due to the complex faulting process rather than path effect.

Spectral Characteristics and Source Parameters
Having a better understanding of attenuation, we can correct the observed spectrum back to the source. Figure 6 displays the source spectra for each event, and these have been cor rected for overall attenuation as the product of the geometric and whole-path anelastic attenu ation of Qc (Chen et al., 1989). In Figure 6, all events of ML< 5.4 have spectra with two asymptotic lines (one horizontal and the other inclined with a slope of -2) that intersect at a corner frequency fo (i.e., the shape of the Brune model). However, these properties for spec-:. tral shape are disrupted for events of M L approaching 5.4. As the magnitude increases to 5.4, the spectra depart from the shape of Brune model. This feature will be dominant as the magni tude approaches 5.8 (events 1 and 5). Notice that the shape of these spectra is ge11erally ch<l! acterized by three basic trends which intersect at two comer frequencies fo and l o , where l o denotes the higher one. At low frequencies the spectrum remains at a relatively constant levej. Between the corner frequencies and the spectra decay as an intermediate trend, and beyond fo the slope of the inclined asymptote behaves as 1-2 • On the basis of theoretical work on source models, several studies (e.g., Haskell, 1964;Brune, 1970Brune, , 1971Savage, 1972;Sato and Hiwasara, i973) have used the (lower) comer frequency fa to determine the source size. Because all the events in this study are shallow earthquakes, we assumed these earthquakes have ruptured from circular faults. Based on this assumption, the most simple and widely adopted model for general quantification of earth quake sources is the m-squared model of Brune ( 1970Brune ( , 1971. Brune (1970) proposed a circu lar crack model with an instantaneous stress pulse to produce a displacement spectrum with a 1-2 falloff. The high-frequency level of the source spectrum is controlled by stress drop, whereas the low-frequency is proportional to the seismic moment. From Burne (1970) model and later later revised (Brune, 1971), the fo for shear wave spectra is related to the source radius r as: Another parameter which describes the spectrum of earthquake source is the stress drop, Aa. Brune related this stress drop to the static (global) stress drop from the standard circular static crack solution by Keilis-Borok (1959) and it can be expressed in terms of the well-known relation between seismic moment and corner frequency by: For a constant stress drop, log M0 is proportional to log j0 with slope -3. As stress drop in creases for an earthquake of a given moment, so does fo, and the high-frequency level of the source spectrum (see Eq. 2).
So far, the only parameters that take values appropriate to each earthquake source spec trum are seismic moment and stress drop. To estimate both parameters, the theoretical func tion form of Eqs.
(2) and (5) were fit to the source spectra of S waves for an assumed seismic moment with a constant stress drop. At present, there is some ambiguity regarding the identi fication of the location of fo. This uncertainty is because stress drop is proportional to the cube of comer frequency. We know that the parameters of p and q in equation (2) are related to the behavior of the spectral shape at intermediate frequencies near the comer frequency and their product is related to the high-frequency decay rate of the spectrum. To clearly demon strate the comer frequency, tests were carried out for various sets of p and q until the theoreti cal spectra were best fit to the observed spectra. In the tests, the choice of values of p and q was somewhat arbitrary� however, they can be interpreted in two ways. One of these is that both parameters were dictated by Sato and Hirasawa (1973), Madariaga (1976) and Masuda et al. (1977). They demonstrated the ranging of p from 4 to 10 and of q from 0.2 to 0.5. The second one is that the S-wave spectrum inclined with slope 2 at high-frequency, as shown in Figure 6, appears reasonably fixed at pq=2. Figure 7 shows an example of the fit of the theoretical spectrum to the source spectrum of event 3. To illustrate this comparison, we consider three sets of values of p and q: (i) p=2, q=l; (ii) p=4, q=0.5; and (iii) p=lO, q=0.2. For the first set with p=2 and q=l, equation (2) repre sents the idealized Brune displacement spectrum. At this point, it should be noted that the pq=2 of each set would produce a source spectrum exhibiting a f-2 shape at high-frequency as it as in Figure 6. For these cases, the ratio of p!q increases from 2 to 20. As seen in Figure 7, the difference in spectral shape due to the p/q ratio is apparent only around the comer fre quency. Comparing the theoretical spectra with the observed spectra, we found that the con structed shape of the source spectrum using p=4 and q=0.5 (curve b) seems to fit the data at the locus of f0 better than the other curves. For a lower p/q ratio of 2 (curve a), the transition from the low frequency plateau to the high frequency plateau is expected to be smoother. Nonethe less, the spectrum for intermediate frequencies is enhanced. As increasing the p/q ratio to 20 (curve c) results in the transition around the comer of the spectrum being sharper, this would produce an increase in amplitudes at intermediate frequencies.
As mentioned in section 4.1, the similarity in spectral shape for high-frequency decay rate in Figure 3 implies that dynamic processes are common for this group of earthquakes. The parameters p and q are related to the dynamic properties of the seismic source, and thus may be fixed at common values for all earthquakes. In the succeeding analysis, the theoretical predictions of the spectral shape are representative for a set of values of p=4 and q=0.5 for each individual earthquake.
Since we have assumed the co-squared model for the source, the spectral parameter, M0, can be simultaneously obtained from the source spectral amplitude at low frequency while searching to obtain 6.a at high frequencies. From the estimated moment and stress drop, we determine the corner frequency for each event. In Figure 6, the smooth line represents the best fit of theoretical spectra to the envelope of observed spectra. The results obtained by the method for this group of earthquakes yield seismic moments in the range of 1.2 Xl0 21 to 1.1 xl0 24 dyne-cm and stress drops from 30 to 350 bars. The comer frequencies f0 may then be esti mated and these vary from 0.63 to 4.87 Hz. Based on equation (4), the source radius of the equivalent circular fault plane is between 260 and 2005 meters. Estimated values of source parameters for the events in this study are summarized in the last three columns in Table 1. Seismic moment is plotted as a function of corner frequency in log-log scale, and these results are presented in Figure 8 (a). It can be seen that both M0 and fo align with a very small scatter. Using the least-square method, the straight line shows the trends of M0 and fo can be fitted by the following_ equation: (6) This linearity can be explained in term of constant stress drop irrespective of seismic moment. On average, the observations agree with this proportionality with slope -3. The relation be tween seismic moment and radius is shown in Figure 8 From the function form of Brune (1970Brune ( , 1971) and a non-linear, least-square simplex algorithm, Ou and Tsai (1993) also obtained the relation of M0 -fo in the CN area: log!OMO =-3.091og\O fo+23.86 ,fo r3.6 �M L �6. 3 .

( 7 )
This relation is in agreement with equation (6), and also supports the constant stress drop scaling, including even the data from separate seismic catalogs. They concluded that these earthquakes have an average stress drop of about 150 bars, which is close to our result.

Spectra with Two Corner Frequencies
Except for the three large events (M L � 5.4), as demonstrated in Figure 6, the spectral shapes of the other fifteen re latively small ones ( 2.8 �ML � 5.0) are in agreement with the ©-squared model. Two of the larger earthquakes are the most important ones in the recent years. One of them is the 12 March 1991 earthquake near Chiali and the other is the 15 Decem ber 1993 earthquake near Tapu. The spectra of these events not only exhibit two well-sepa rated comer frequencies, but also clearly demonstrate that their high-frequency content is much more abundant than that predicted by the ©-squared model. The fitted low-frequency levels (below f0 ) corresponding to seismic moment M0 of these two events are 0.75 xl0 24 and 1.1 xl0 24 dyne-cm, respectively. Considering the CMT solutions, the seismic moments of both shocks are about the same with M0 of 1.5 Xl0 24 dyne-cm. Although seismic moment in this study is evaluated from the record at one station, it is consistent within a factor of two with the CMT value. In additiqn, the second comer frequency fo of these two events was also measured. The values of fo for both events are almost equal, being about 3.26 Hz.
The existence of more than one comer frequency on source spectra is supported by evi dence observed for most other earthquakes (Papageorgiou, 1988;Boore and Akintson, 1992;Boatwright and Choy, 1992;Atkinson, 1993;Takemura et al ., 1993;Boatwright, 1994). They are also demonstrated by the theoretical work on source model in the literature (Savage, 1972;Brune, 1970Brune, , 1971Hartzell and Brune, 1979;Papageorgiou and Aki, 1983;Boatwright, 1988). On the basis of the Savage (1972) and Brune (1970) models, both theories provide for a spec trum in which the average trends are in the middle frequencies. In Savage's model, the two comer fre quencies exist for a rectangular fault of length Land width W, as W<< L. Conversely, Brune believes that the introduction of an intermediate trend is due to only a fraction of the effective stress released. In actual fault zones, except where geometrical irregularities are dis tributed, the faults are not simple homogeneous surfaces that permit idealized rupture propa gation. The inhomogeneous faulting processes were recognized by an irregular slip motion over a heterogeneous plane, and they also produce more than one corner frequency on the spectra (e.g., Hartzell and Brune, 1979;Papageorgiou and Aki, 1983;Boatwright, 1988). These heterogeneities are significant to earthquake ground motion because they represent locations of concentrated stress (local stress drop) release of the fault, and rupture proceeds as a series of multiple shocks. Despite the various differences between the models, the re sults of these stud ies are consistent with the conclusion that the lower corner frequency of the spectrum is re lated to the rupture duration of the whole fault, whereas the higher corner frequency may reflect the average scale length of the heterogeneities on the fault plane.   Figure 9 construct the spectrum for a given moment with stress drops of 60, 150, 300 and 600 bars. It should be noted that two stress drops are required to explain the source spectrum with its general trend. By close inspection of Figure 9, the behav ior of the spectrum can be more readily identified. The level at low to intermediate frequencies is matched by a stress drop of 60 bars for both events, and is deficient in amplitude at higher frequencies. In contrast, a high stress drop on the order of 600 bars, much higher than 60 bars, was required to describe the high-frequency level of the spectrum, but the spectral amplitudes in the frequency range 0.63 to 3.26 Hz are considerably higher than the predictions of the OJ squared model. Analyses of data from the other recordings from the Tapu earthquake were also examined to confirm two comer frequencies on source spectra for this event. Similar trends were identi fied to data from CHY087 (Appendix).

DISCUSSION
We have described local Q values and estimated of source parameters from the observed displacement-amplitude spectra for several CN' s earthquakes. To remove the effects of anelastic attenuation as the wave travels along the ray path, the associated Q value of Qc =l 17 j0· 77 estimated from the early-arriving coda waves by Chen et al. (1989) was used. The source spectra computation from time windows containing S-wave motion is a crucial question of fundamental relevance to the Q model. As noted by Aki ( 1981 ), the attenuation of S waves also has a similar frequency dependence to that of coda waves. Synthesizing these results, Aki (1981) concluded that the coda waves are S-to-S back-scattered waves for locally earthquakes . We adopt this assumption and maintain that Qc in the CN area is likely to be the Q {J to determine the source spectra. Current uses of the Q function may be considered as an average over the whole Taiwan region. However, this Q function seems suitable to explain the S-wave spectra that are expected to provide some source parameters for the earthquakes in this study. This is likely because not only the /-2 slope for high-frequency end of the curve shown in Figure 5, and it is also sufficiently suitable to explain the source spectra for both the deeper ("" 12.5 km) and shallower ( ""3.5 km) events.
The relation of M0 -/0 in both this study and that of Ou and Tsai (1993) supports a cubic relation between source radius and seismic moment, and indicates that the stress drops of crustal earthquakes in the CN area are independent of source dimension compilation of mag nitudes in the range of 2.8 to 6.3. Although the values vary for different events, an average stress drop of 125-150 bars appears well-established in this area. It should be noted that the scaling of source spectra in present study was determined by the lower frequency of fo and the level of horizontal asymptote. We know that stress drop estimated in this sense is referred to as a global one, which is inferred by assuming the entire rupture area to be uniform over a smooth fault without discontinuities. Although this stress drop estimate provides useful insight re garding the general quantification of earthquakes, locally, however, the stress drop can be much higher than average, and for moderate and larger earthquakes.
This distinction can be seen in Figure 6 because the spectral behavior has a major change talcing place near magnitude 5.4. At magnitudes less than 5.4, the spectra have a readily iden tifiable corner frequency, followed by a plateau, after which the spectral amplitude has a /-2 falloff. This implies that the fault plane is somewhat simpler in character for these small events.
It seems clear that for small earthquake s, the fault plane can be considered as a circular crack (a single patch) with smooth-rupture faulting. The obvious evidence for this explanation is that the seismograms with simple S-waves generally can be seen for small events (Figure 2) .
On the other hand, for spectra of the two main shocks of the 1991 Chiali and 1993 Tapu earthquakes, the source spectrum departs greatly from the assumed Brune's spectral shape.
These two earthquakes are characterized by the high-frequency source spectra shown in Fig   ures 9(a) and 9(b). An interesting observation concerning the spectra is that the data are asso ciated with two-comer-frequency in place of the single one of the Brune's model. It was sug gested that for events with two comer frequencies may have come acro ss some obstacles during the faulting. This explanation is supported by the fact that the time domain records of earthquakes show that the S-wave waveforms are relatively complex, at least on the time scale of 1t o5 sec (Huang and Yeh, 1988). In order to fit the high-frequency spectral amplitudes with the commonly used co-squared model, we further found that a high stress drop of about 600 bars (or perhaps somewhat greater) deduced from the earthquakes is about 10 times as high as the average stress drop (ca., 60 bars). As pointed out by Wald et al. (1993), variations in tectonic stress can be large over a scale length to a few kilometers , but regions of high and low stress drops are averaged out resulting in stress drops of several tens of bars. This strongly suggests that faulting was initiated with localized but massive faulting with associated stress differences not at all representative of those inferred for the entire faulting process.
Important direct observational evidence, indicating maj or differences of source spectra between small and moderate earthquakes, has been obtained from the discussion above. The high-stress events accompanied by an anomalous spectral shape may exist for events as large as M L 5 .8. This implies that an CO-squared model with a constant stress drop cannot cover the entire range of seismic spectra in the magnitude range of 2.8 to 5.8. Such a phenomenon would contradict the results obtained by Ou and Tsai (1993), as they indicated that the spectral scal ing as a function of magnitude. Consequently, the issue of stress drop for moderate earth quakes has become an acute one for seismic hazards in the CN area. For this reas on, .the Tapu earthquake on 15 December 1 993 is of exceptional interest. This is because the results of previous investigations (Chang and Shin, 1994;Chung and Yeh, 1997;Shin, 1995;Huang et al., 1996;Huang and Yeh, 1998) can be used to examine our analysis.
An attempt to obtain source parameters of the Tapu earthquake utilizing synthetic seismo grams to model actual data at near-source distances was first made by Shin ( 1995) and later by Huang et al. ( 1996) and Huang and Yeh (1998) using different approaches. The first two studies represented the source as a point. However, in the most recent study, a kinematic complexity in modeling the source time function for a circular fault model with a radius of 2 km was assumed. For this waveform modeling, the seismic moment is determined from the observed amplitude of S waves and its frequency content depends on the pulse width of a source-time function. For a simple circular fau lt model, the pulse width of the source-time function ( T) is given in terms of the source rad ius (r) and the S-wave speed ( /3) by T = 2. 62r I f3 (Cohn et al ., 1982). The stress drop is then estimated to be proportional to the moment divided by the cube of the source dimension from the circular crack solution as f).. a = (7 /1 6)(M0/r 3 ) (Keilis-Borok, 1959). Following the procedure outlined above, Huang et al . (1996) estimated that the stress drop of the earthquake was about 320 bars based on 't' of 1.0 sec, which is about twice as large as the value obtained by Huang and Yeh (1998). With further work, Huang et al., (1996) and Huang and Yeh (1998) found that an exceedingly high stress drop of 2.5 Kbars was predicted using r of 0.3 sec (Shin, 1995). As discussed by Haung and Yeh (1998), the essential differences among these stress drops may be attributed to the pulse width of the source-time function used. A shorter source-time function produces a de crease in source radius and an increase in stress drop, thus raising questions concerning the validity of the source model for this event.
As a point, we would like to comment on the source area of the Tapu earthquake. Based on the aftershock distribution following this earthquake, Chang and Shin (1994) proposed that this earthquake could have a fault length of 4.0 km and a width of 7 .0 km. Following this fault model, Chung and Yeh (1997) assumed a propagation process to simulate the ground motion of short-period surface waves at an epicentral distance greater than 24 km. We disagree with their assumption of a rupture surface because it was determined by the aftershocks occurring with the following 45 days. This definition is somewhat questionable. Most frequently, the aftershock area is defined about one day after the main shock (Magi, 1967). Thus, the overall distribution of the aftershocks may give an overestimate of the main shock area. In subsequent analysis of the earthquake, Huang and Yeh (1998) demonstrated that the assumption of the rectangular fault model was invalid for appropriately describing the ground motions at shorter distances. Instead of the rectangular fault model, they established that a circular model with 2km radius could be properly used to explain the observed waveforms and the computed seis mograms.
Determinations of the area of the rupture surface (A) have been correlated with seismic moment (M0) by various researchers (e.g., Kanamori andAnderson, 1975� Prucaru andBerekhemer, 1982). Specifically, the last two authors used a dataset of 240 events ( M ;;::: 5) to obtain the relationship log1 0M0 = l.5log10A + 22.5 for 10 2 4 :::; M0 :::; 10 30 , where A is in km2 and M0 is in dyne-cm. We assume that A as function of M0 as expressed in this equation is valid on average. Also, we accept the teleseismic estimate of the moment ( 1.5 x10 2 4 dynecm) for the Tapu earthquake. Under these considerations, the fault area for the earthquake is about 13 km2• If we take a circular fault model as the fault plane, the earthquake has a source radius of about 2 km. This can agree perfectly with the source radius obtained by Huang and Yeh (1988), who picked the comer frequency as the intercept of the high and low-frequency asymptotes of the spectra from widely distribute<l: seismic stations. If fo :::. 0.63 Hz, this yields a source radius of about 2 km for /3 = 3.4km/sec and also supports the validity of a source radius of 2 km. From the above results, the event did not show evidence for such a source as described by Chang and Shin (1994), or by Shin (1995) and Huang et al. (1996). We strongly believe that the source area of the Tapu earthquake is about 13 km2 with rupture length and width roughly comparable (i.e., a circular crack).
Apart from the source area analysis, a trade-off exists in estimation of stress drop for this event to be significantly too large as shown by Shin (1995) and Huang et al. (1996). Stress drop in the associated derived source spectral amplitude in this article is 60 bars, which is smaller by a factor of 2 than our 1998 results (Huang and Yeh, 1998). Indeed, neglecting the Q correction in our waveform modeling could cause this overestimate.
Finally, we would lik� to comment on the subevent size based on o�servations from the characteristic frequency f0 for the Chiali and Tapu earthquakes.,. The fo is about 3.26 Hz. Using a stoch�tic fault model, Koyama (1983) deduced that the fo is related t9 the averag_e scale length ( d) and the rupture velocity ( v , ) of the fault heterogeneities as fo = v, /2'Trd .
For an assumed rupture velocity of vr = 0.7 fJ (Kanamori, 1994), the estimated average scale length of both events which corresponds to the second comer frequency is about 116 meters. Papageorgiou and Aki (1983) used a specific barrier model to interpret strong motion data. In this model, they used Sato and Hirasawa's (1973) circular crack model with radius P o to represe,. n t the localized subFvents. The Po is related to the expected values of corner fre qu ency (fo) as Po =Csf3/2'1if 0 (where Cs is an implicit function of rupture velocity). Assuming a ratio of vJ{J = 0.7, Cs is 1.81 (Sato and Hirasawa, 1973), and p0=300 meters. Inter preting the diameter 2 Po as the barrier interval, the inferred barrier interval for these events is about 600 meters, which is about a factor of 5 higher than Koyama' s model. Considering the four smaller events of ML around 3.0 in this study (see final entry in Table 1), the averaged value of diameter 2r ""564 meters nearly coincides with the barrier interval of Papageorgiou and Aki's model. If true, this would have important implications for attempts to simulate ground motion from large earthquakes by using small earthquakes as Green 's functions (Hartzell, 1978).
For the Tapu earthquake, the scale length enters into the description of the spectra as in the previous section and its . associated local stress drop is discussed below. Based on the spe cific barrier model developed by Papageorgiou and Aki (1983 ), the local stress drop ( Aa) can be obtained by : where Au= is the maximum relative slip of the faces of an individual crack, which can be represented by /)..u ==M0!(n!6 X µ X A) [from equation (57) of their paper] based on their specific barrier model. Here, A is the area of the entire fault plane and µ is the shear modulus. We considered A=l2.6 km2 as described above and assumed µ = 3X1011 dyne/cm2• Two estimates of Au= are "" 76 cm and 56 cm corresponding respectively to M0 =1.5 Xl024 (taken from the CMT solution) and 1.1 xl024 dyne-cm (this study). Substituting the values into equation (8), we obtain (i) Aa ,,,, 700 bars, for Aumax 76 cm and (ii) Aa ""516 bars, for Aumax ""56 cm. It is noteworthy that the local stress drop of 600 bars , that was constructed based on the level of high frequency obtained for the Tapu earthquakes, falls in this range.
If we considered Po "" 300 meters as an average scale length on the fault plane for the Tapu earthquake, the total number of cracks which are distributed on the fau lt plane can be inferred as 1 2. 6km2 /( n · 0 . 3km2 ) ""45 cracks . The total energy Es radiated by the fault should be equal to the sum of the seismic energies Es1 radiated from each individual crack. An estimate of Esi can be obtained from Sato and Hirasawa's model (1973). Following Sato and Hirasawa' s ( 1973) formula, Papageorgiou and Aki ( 1983) presented their specific barri er model with al {3 =1.73 and v, I f3 =0.75 to calculate the total seismic energy radiated from the entire faul t which is given by: 1 Ll.cr E =0.46·-·M ·s 2 0 µ (9) Here, Acr represents the local stress drop. From Huang and Yeh's (1998) analysis of this event we know that a/f3 ""1.74 and vrl/3 z 0.7. Both estimates do not vary much fr om Papageorgiou and Aki's assumption. Assuming that µ= 3x10 11 dyne/cm2 and substituting the estimate of M0 =1.1x1024 dyne-cm and Ll.<J = 600 bars from this study in equation (9), we calculate the total seismic energy is Es "" 5 X 1020 erg. An estimate of the same quantity also obtained using the Gutenberg-Richter relation (logEs = 1. SM + 11. 8) is Es = 3. 2 X 102 0 erg.

CONCLUSION
We analyzed S-wave source spectra for eighteen events with 2.8 :::; M L :::; 5.8 recorded by the CN network from 1991 to 1996. Within a limited range of epicentral distances and a wide range of source-receiver azimuth, the results provide some information on CN earthquakes which is summarized as follows: (1) The frequency-dependent attenuation of O.: = 117 j 0 ·7 proposed by Chen et al. (1989) was found to be in good agreement with those found in the observed spectra for CN earthquakes, whether their depths were deep ( ::= 12.5 km) or shallow ("" 3.5km) focus.
(2) The source scaling between corner frequency ( fo) and seismic moment ( M0 ), as shown in Figure 8, is considered to be linear with a slope of -3. This dependence is generally ex plained in term of a constant stress drop. The overall trend appears to indicate that the stress drops are averaged out resulting in an estimate of 125 bars. Similar results were also ob tained by Ou and Tsai (1993). However, the relation in a previous investigation by Ou and Tsai (1993) and in the present work must be justified on the basis of inferences from two moderated-size earthquakes which occurred near Chiali in 1991 (event 1) and near Tapu in 1993 (event 5). The complicated source spectral shape and the enhanced high-frequency of the two main shocks were not reflected in a simple CO-squared model with a stress drop of 125 bars. (3) The spectral shapes of events 1 and 5 appear to be similar, but distinctly not 1-2 , which is in clear contrast to the spectra obtained from the M L < 5.4 earthquakes. Apparently two corner frequencies always exist. The intermediate spectral behavior extends from 0.63 to 3 .26 Hz. The spectral amplitude below the low frequency of fo and this intermediate trend is well described by a stress drop of 60 bars. In contrast, the high-frequency level at the source surprisingly required a stress drop of 600 bars to match it. This observational result implies that the shape of the source as described by the co-squared model ceases to be valid as magnitude increases up to 5.8 in the CN area.
(4) According to Sato and Hirasawa' s (1973) circular rupture model, the scale length (barrier A interval) inferred for the events from higher comer frequency ( / 0 ) is about 300 meters. This is comparable to the source dimension for small earthquakes of M L "" 3 selected for this study . The high-frequency decay beyond the second comer frequency associated with a high stress value of 600 bars was verified by the specific barrier model from Pagageorgiou and Aki (1983) and by the energy-magnitude relation from Gutenberg and Richter (1956).