k Mulli-Tamsa Vol. 11, No. 2, 2008, p. 137~147 (M=4.8, '07. 1. 20) dqw * w y Fault rupture directivity of Odaesan Earthquake (M=4.8, '07. 1. 20) Kwan-Hee Yun* Environmental & Structural Lab., Korea Electric Power Research Institute 2007 1 20 w (M =4.8) p d DGY(», =7 km)» PGA(ƒ) d (> 0.1 g). wr DGY d ew yw d(, 2007) qù sp, šq j w p dqw(rupture directivity) w w. Boatwright (2007) w dq(v) q(c) w (= v/c) qww ƒ(θ, deviation angle) w w w dqw(unilateral rupture directivity) w. w dqw sƒw» w d w r p (Boore, 2003) w d Á d w w z, d w d w. Á w rp dl d PGA j» wš w dq w sƒw, PGA d NWW-SEE w d šƒ d SE w w t w dq w w., dqw, rp, ww Abstract: Fault rupture directivity of the Odaesan earthquake, which was inferred to be the main cause of the high PGAvalue (> 0.1 g) unusually observed at the near-source region, was analyzed by using the data from the nearby (R < 100 km) dense seismic stations. The Boatwright's method (2007) was adopted for this purpose in which the azimuth and takeoff angle of the unilateral rupture directivity function could be estimated based on the relative peak ground-motions of seismic stations resulting from the nature of the rupture directivity. In this study, the approximate values of the relative peak ground-motions was derived from the difference between the log residuals of the point-source spectral model (Boore, 2003) for the main and secondary events based on the Random Vibration Theory. In this derivation, the spectral difference for a frequency range between the source corner frequencies of main and secondary events was considered to reflect only the effect of the fault directivity. The inversion result of the model parameters for the fault directivity function showed that the fault-plane of NWW-SEE direction dipping steeply to the North with high rupture velocity near upward in SE direction is responsible for the observed high level of ground-motion at the near-source region. Keywords: Odaesan earthquake, fault rupture directivity, point-source spectral model, directivity function ù w d» w Á y(moderate- to-low seismicity) ewš, w sƒ w w j ³ w 2008 4 2 ; 2008 5 16 k *Corresponding author E-mail: kyun@kepri.re.kr Address: Korea Electric Power Research Insitute, 103-16, Munji-Dong, Yuseong-Gu, Daejeon, 305-380 Korea sƒ, sƒ y š. Á y p w» w ³ d p w š, sƒ y yw» w ƒ û ³ w p sƒƒ w. wr w d 1999 2007 1 w ü ³ (w ) w(table 1 ). w, wz» 137
138 Table 1. Basic source parameters reported for Odaesan Earthquake. // (KST) ³ ¾ š 2007.01.20 20:56:53.6 4.8 128.5841 o E 37.6889 o N 13.1 km w t KST: Korea Standard Time Fig. 1. Comparison of the ground-motion attenuation relation developed for the Class A seismic stations (Yun and Suh, 2007) with the corrected PGA-records (Yun et al., 2008). The unusually high PGA-value (> 0.1 g) was obviously observed at the near-source station (DGY). ƒ ü d d, w w ƒ w. w p w w ³ x p ql ùkù (,, 2007). w d p sƒ w ƒ d w» w d (, 2008). d p ew d(» DGY)» d { zw ƒ (> 0.1 g)ƒ d. Fig. 1 d w z w z d ³ 4.7 w p d (A-class) w w (, 2008). dƒ d ew yw ù, DGY d ùký yw. d ùkü x wz š sƒ w ƒ. w d ü x wz w p w w, w p xš w,» p w vƒ». sƒ p ƒ¾(r <50 km) w sƒ d w. j ³ w vw k w, ü Á y w y w» š ü rp w w rp». wr,, p p w q. d p DGY ƒ yw d(, 2007), p w z d Fig. 1 ùkû». w» p w ùkú y. p p šq j w dqw(rupture directivity; Boore and Joyner, 1989) w, yw ³ w dqw w. dq w p j» q w e, w ql ql w ûw ƒ(azimuth angle) j»ƒ j ee ùkù(šx(,, 2007) Fig. 11, 12 ) dqw p z wš. ü w dq w w ƒ w ù y eáš š l d w ³ w dqw wš (Mcguire, 2004; Boatwright, 2007). w w p Boatwright (2007) w wš w. Boatwright (2007) d e w ³ (earthquake cluster) w d PGA w d qw w, dqw d ew. w œm p p š PGA d w dqw w PGA p w ü.
(M=4.8, '07. 1. 20) dqw 139 w dqw w d w d d w y. p t d yš ³ d y ³w vƒ. t d w ƒ y y w sƒ w d p ¾ sƒ w. w dqw sƒw» w ww ql dq (rupture velocity), ƒ(azimuth) ƒ(take-off angle) d l w. w dq w ùkü ww ql p m wš, ww ql w w» w vw e (ƒ(pga) y (PGV)) d j» d qw rp el yw wš d w š w. dq ww ql dxl d¼(l) w w(unilateral) dq ww (Ben-Menahem, 1961). 1 v D = 1 - cosθ rj (1) χ 2 v = logpga j + log 1 - cosθ rj c c» v q, c q, θ rj dqw d j w q ƒ (deviation angle). Fig. 2(a) ùkù rp ww p p gq šq rp w wwƒ j w. w gq [π L (1/v 1/c cosθ rj )] 1 g q w. Fig. 2(b) dq(v) q(c) w (v/c) ƒ q rp ù ùkü (Boore and Joyner, 1978). Fig. 2(b) dq ù, ddq (v) q(c) w v/c =0.7 w ƒ 10 ƒ ùkû. w wr dqƒ jš(v/c >0.7) dq Fig. 2. Effect of shear-wave velocity relative to rupture velocity ratio (v/β) and deviation angle (θ ) from the fault rupture direction on the ground-motion spectrum. Strait solid lines indicate envelope of the theoretical ground-motion spectrum (a). Effect of shear-wave velocity and deviation angle on the peak ground-motion (b) (Boore and Joyner, 1978). w w w wš w dq w w j»ƒ û p. (2) dqw w d j» logpga (1) ww ùkü. Boatwright (2007) w d d w w w» d w de s³ w d j»ƒ logpgaƒ w, (2) yw dqw ql w ww dqw d w yw. (2) σ j» tr, s logb w ww ³yj» w. j (1), (2) dqw w ƒ θ rj ƒ ƒ ƒƒ φ j ζ j d j q ƒ φ r wl d ƒ(w dq ƒ) ζ r dqlƒ ƒ (3) tx. θ rj cos = cos ( φ r φ j ) sin ζ r sin wr d ƒ ƒ φ j ζ j ƒw logpga w ƒw, (2) (3) l dqw w ql dqw ƒ ƒ sw (v/c, φ r, ζ r, logb) 4 ƒ. w w ƒ ƒ d w logpgaƒ m yw dqw ζ j + cosζ r logb cos ζ j 2 /σ j 2 (2) (3)
140 ƒw. wr Á w d l logpga w Boatwright (2007) dqw wš w w 1) w PGA w» w 2) ³ƒ j» û y w š d w logpga. w wš w d rp s ³ w rp l d w z Boatwright (2007) w. w š j» ùküù, rp y(s/ N)ƒ ƒ q w w w w. wr w ww w rp ww w dqw w ù, ww rp xkƒ w rp w. rp l dqw p w d j d» t rp OBS (4) (SRC), (ATT), (SITE) p w(err) w tx. SRC( f ) ƒ 1 km rp(apparent source spectrum). OBS j ( f ) = SRC j ( f ) + ATT j ( f ) + SITE j ( f ) + ERR j ( f ) (4) (4) p ATT j, (nonparametric method) w rp l -q w x»ww (= GEO emp (R j, f )) w û w 0.4 j ο» Q k w (5) txw(, 2007).»ww - x w q w y 2~3 (linear hinged model) tx. (5) d q Q j (= Q 0j f ηj ) q m ¼ R j ATT j ƒ š. (5) e. ATT j f ( ) πfr j ------------- = log ( e ) + GEO emp ( R j, f ) βq j (5) (5) d p SITE j sww ƒü d kv w ksp(a( f )) šq κ 0 ql w w tx ƒ (w 1~2 km) w k (Anderson and Hough, 1984) w (6). (6) 2 Q w d p A j ( f ) (2007) w. SITE j ( f ) = log ( A j ( f )) π f κ 0j log ( e ) d rpl p(att j ) p(site j ) w, (4) w rp w š, p w ü d w s³ rp SRC (7) w. N j = 1 SRC( f ) = SRC j ( f )/N (6) (N = d ) (7) (4) q rp ERR( f ) --p. ERR( f ) w š (8) p d j w q (ATT loc j ( f )), p(site loc j ( f )) šw p dqw w w ƒw. ERR j f = ( ) ATT j loc loc ( f ) + SITE j ( f ) + RAD j ( f ) + Dir j ( f ) + ε f ( ) (8) (8) RAD j ( f ) d j j» y ù kü ql ùkü, Dir j ( f ) ww((1)) q rp j» ùkü. ε( f ) ùkü. wr (8) w ERR( f )(= ERR Mj ( f )) Á w s³ ERR( f ) (= ERR j ( f ) ) w, w d j dqw(dir Mj ( f )) (9) p q w. w d» w q, p wš dqw Fig. 2 ùkù gq ùkù». w gq f 0M, Á w gq f 0s š w ERR j ( f ) w d j w p ùký q f 0s < f < f 0M ƒ. wr Á d w ew ù (9) w Á w s³ ERR( f )ƒ w p (RAD j ( f )) š ƒw. ERR j ( f )=( ERR Mj ( f ) ERR j ( f )) ó Dir Mj ( f ) (f 0M < f < f 0S ) (9)
(M=4.8, '07. 1. 20) dqw 141 Fig. 3. Schematic figures of source spectra of main and secondary events (a) and spectral features of fault rupture directivity shown in the difference between the normalized source spectra (b). ( j = d, M =, f 0M = gq, f 0s =Á gq) Fig. 3 Á rpl (9) w q dqw w w. Fig. 3(a) Á w d¼ w dqw ƒ(θ) šq rp p wš dqw rp w 45 zk o. Á ³ ( M w ) 2.8, d¼(l) w ƒƒ 1 km, 0.03 km ƒ w. Fig. 3(b) Fig. 3(a) rp Á w w p w (4) ERR( f ) Á w sƒw. w (equalization)w ww, Á gq rp Á w p Fig. 3(b) ùkù dqw p ùký. dqw rp l j» gqƒ f 0 Brune rp(brune, 1970, 1971) q f max ƒ, RVT (Random Vibration Theory; Boore, 2004) w (10), (11) ƒ RMS a rms s³»e PGAƒ (Hanks and McGuire, 1981).» f 0 ³ d w yw ql. a f max rms σ ---------- f 0 (10) Fig. 4. Change of the high-frequency spectral level of Brune's source model according to stress drops. 2f max f 0 PGA a rms 2 ----------- ln (11) wr šq( f f 0 ) rp a hf Brune rp 2 ql w( σ), p(m 0 ) (12) ƒ (Atkinson and Hanks, 1995). (12) w šq w gq šq (12) rp(a hf ) w w f» (Fig. 4 ). a hf σ 2/3 1/3 M 0 (12) 3 (10), (11) σ f 0 (Brune, 1970, 1971), š gq w 1<f 0 <2 Hz w e (13) w šqrp l PGA j» w (14). M 0 w šk š f max dl q 40 Hz w. 2f max f 0 2 ----------- 0.812 ln f 0 0.844 PGA σ 0.562 a hf σ 0.812 3 (13) (14) (14) w šqrp w ƒ σ ql šw š dqw w e j w d šq rp f ql w. w w dqw w ƒ gq šqrp j w ql
142 Table 2. Source parameters for the fore and aftershocks of Odaesan Earthquake. ƒ» (, 2007) (KIGAM, 2008) ( o ) ( o ) ( o ) ( o ) 07/01/19 09:06:23 128.57 37.69 128.6742 37.6904 2.0 2.4 19 07/01/20 21:08:53 128.60 37.69 1.3 2.2 318 07/01/20 21:20:56 128.60 37.69 1.2 2.1 39 07/01/20 21:28:53 128.61 37.69 1.6 2.3 422 07/01/21 07:36:02 128.56 37.69 1.1 1.9 11 0.562. (14) PGA σ Boore (1983) 0.80 ƒ w PGA σ, Boore (1983) ³ 5.0 w (13) w, ³ 5.0 w w». wr (14)l (15) w. loga hf dqw d ƒ šq rp (15) mw w. wr loga hf (9) ERR j ( f ) dqw ù kù q w w ƒs³ ((16)). ³ M w (est.) σ (est.) š logpga 0.844 loga hf (15) N f df l ERR j ( f l ) l loga = 1 hf = -------------------------------------------- N f i = 1 df l ( f 0M < f < f 0s, (9) ) (16) (9) N f = ƒq ü q w, df l = l q j». d, (Table 2 ) w ƒ d. Table 3 dq w d w, Fig. 5 d e ùkü. Table 3 d w q y y»w d dy yw d w, q w ³w s ewš dqw sƒw» w. Table 3 w d ƒ Herrmann (2008) w w, d ƒ w ü w. (4) rp» w w» Table 3 d Fig. 5. Epicenter ( ) and locations of seismic stations used for the analysis of fault rupture directivity for Odaesan Earthquake. w Sq trp w w. w, d w Sq w,» (instrumental correction), s rp lw w. Sq ó 5% cosine tapering w z rp wš, S/Nƒ 3~4 q rp w. s rp, û t rp lww, rp ¼ ùip q ü 1,024 q w. wr ü d 100 v š, w ùi p q 50 Hz, rp q 0.05 Hz (ó 50 Hz /1,024). wr ƒ q w 0.4 k rp syy w. dqw m Fig. 6 rp dqp (9) ERR j ( f ) w, Table 3 d w w ERR Mj (f ) ERR j ( f ) ùkü. ERR Mj (f )
(M=4.8, '07. 1. 20) dqw 143 Table 3. Station information used for the analysis of fault rupture directivity of Odaesan Earthquake. No Station Longitude ( o ) Latitude ( o ) φ i ( o ) ζ i ( o ) R epi (km)» 1 YOW 128.4558 37.1737-169.5 93.5 58.41 KMA 2 JEC 128.1912 37.1538-150.4 93.0 68.89 KMA 3 WJU 128.0526 37.4034-124.7 93.9 56.59 KMA 4 KSR 127.8844 37.4421-114.5 93.0 68.75 KIGAM 5 HOC 127.8804 37.6836-91.1 93.0 61.92 KMA 6 CHC 127.8145 37.7776-82.2 93.0 68.38 KMA 7 IJA 128.1111 37.9867-52.0 94.5 53.12 KMA 8 KSA 128.3538 38.5926-12.0 92.0 102.48 KIGAM 9 SKC 128.5219 38.2899-5.4 93.0 67.05 KMA 10 KAN 128.8893 37.7425 76.7 101.4 27.49 KMA 11 DGY 128.6742 37.6904 88.1 125.6 7.93 KMA 12 TOH 129.1226 37.5026 112.7 94.8 51.76 KMA 13 NTY 128.9612 37.2571 144.5 93.5 58.42 KEPRI 14 TBA 128.9523 37.1227 151.9 93.0 70.87 KMA 15 JES 128.6654 37.4303 165.3 100.6 29.64 KMA 16 JSB 128.6876 37.3146 166.9 97.0 42.62 KIGAM KMA:», KIGAM:, KEPRI: ERR j ( f ) w (4)l, d p(att j ( f )) šz(site j ( f )) w w. ATT j ( f ) SITE j ( f ) (2007) ƒ, ERR Mj ( f ) w SRC(, 2007)ƒ. Á w ERR j ( f ) p³ w tx Brune rp(table 2 ) SRC. w Brune rp w rp e w ³ y 2-corner q p w Brune rp q rw ùkü» (,, 2007). w Fig. 6 d w swƒ wš ERR j ( f ) ƒ q p rw ùkü š, w, y p»wš q. (9) ERR Mj ( f ) ERR j ( f ) ERR j ( f ) w w(dir Mj ( f )) w, w Fig. 6 ùkù d ùkû. p d DGY ERR Mj ( f )ƒ ERR j ( f ) w 2~10 Hz š q j ùkùš DGY dƒ dq w w ewš w. w w ƒ ew wd(toh)ù k (NTY)d rp j» ùk ü yw. dqw w w rp w el logpga w z (15() ) ww ùkü (2) y w ww ql (v/c, φ r, ζ r, logb) w. Numerical Recipe (Press et al., 1996) downhill simplex x. φ r ζ r»w logpga w DGY d w ƒ ƒ. w d qw ql w» w logpga t rƒ vw, w tr Fig. 6 ERR j ( f ) w rp tr q s³ l w. wr (16)l w w rp j» loga hf wš l w» w q w w. w Fig. 6 dw p šqƒ ƒ ùkù d DGY d rp j»l 2~5.2 Hz q k w. 2 Hz (9) gq( f 0M ), 5.2 Hz Á w 10 Hz gq( f 0s ) w. 5.2 Hz loga hf q yj (2) w ùkü q kw. Table 4 Á rpl d logpga tr ùk ü. Table 4 y Á w ERR j ( f ) rp tr q s³ l logpga trƒ x¾ e w e 0.18 (Atkinson, 2006) (tr s³ = 0.11 ± 0.04)., p Á ERR j ( f ) rp tr j w Á p w w, (9) ERR j (f ) ww p ùkü» w kš w
144 Fig. 6. Comparison of log residuals for Odaesan mainshock with mean and ±1σ of log residuals for the secondary events. The log residual is the observed log spectral level minus the prediced values by the point-source spectral model of Boore (2003).. Fig. 6 DGY d 10 Hz šq w w ùkù rp j»ƒ û ùkùš šq d qƒ qƒ ù, Á w w» q. wr S/N ƒ y w p q w loga hf ((16)) logpga w» logpga w Boatwright (2007) w ³ƒ dqw sƒ w w. Fig. 7 Table 4 w w w w ql w ww logpga d w ùkü. Fig. 8 Table 3, 4 w w d ƒ ƒ logpga w w stereonet n Boatwright
(M=4.8, '07. 1. 20) dqw 145 Table 4. Estimated values of relative peak ground-motion ( logpga) for each seismic stations and standard deviation of log residual (σ log10 ). logpga was estimated by ERR j ( f ) for the frequency range of 2 ~ 5.2 Hz. No Station logpga σ log10 No Station logpga σ log10 1 YOW 0.127 0.181 9 SKC 0.062 0.040 2 JEC 0.000 0.160 10 KAN 0.081 0.106 3 WJU 0.003 0.059 11 DGY 0.316 0.109 4 KSR 0.002 0.090 12 TOH 0.121 0.126 5 HOC 0.060 0.082 13 NTY 0.152 0.108 6 CHC 0.039 0.114 14 TBA 0.119 0.147 7 IJA 0.006 0.131 15 JES 0.138 0.148 8 KSA 0.161 0.093 16 JSB 0.101 0.098 Fig. 7. Estimated values of relative peak ground-motions derived from the relative spectral level of difference between the log residuals for the main and secondary events are compared with the predicted values of rupture directivity function (Eq. (1)) calculated by using the inverted model parameters. (2007) w dqw sƒ ƒ w d wì. Fig. 8 d stereonet n ƒ 90 o nw. w dq w w =146 o, ƒ =164 o, v/c =0.77. d q q w v/c =0.77 Boatwright (2007)ƒ w w dq 0.63 v/c 0.87 w. w dq k d(nty) w q ƒà w w ù kü w, ƒ j ew d d w. Fig. 8 mw Table 3 d w logpga œ ƒ ûw d ùkü, w ƒ d logpga ùküš dqw û(se)w w. w Fig. 8 ±2σ ƒ t. w Fig. 8. Analysis result of fault rupture directivity for Odaesan Earthquake by using modified Boatwright's method (2007). Great circles for the focal mechanism of Jo and Baag (2007) are drawn with numbers of strike/dip and deviation angle from the fault rupture vector written below in degree ( o ). 4 ql ±2σ ƒ wl χ 2 =9.7 ql w. Boatwright (2007) ƒ w dqw ƒ dw ùkü yw. x w d t yš d w NNE-SSW w d š (, 2007; ½, 2007). ³ td w y w(psha) w d ³ wš d ww w w» td» d yw w. d w d. Table 5
146 Table 5. Comparison of different study results of focal mechanisms with fault rupture directivity estimated in this study for Odaesan Earthquake. dev1 and dev2 represents the angle between two conjugate fault-planes in degree ( o ). NNE-SSW w EES-NWW w»d w Strike Dip dev1 Strike Dip dev2 Min (dev1, dev2) Abs (dev1- dev2) KIGAM (2008) 026 79 25 120 74 23 23 02 Herrmann (2008) 205 85 09 115 85 13 NNE 09 04 (2007) 020 85 18 110 85 14 EEW 14 04 Jo and Baag (2007) 020 70 33 284 76 03 EEW 03 30 Havard CMT (2008) 026 88 16 296 85 03 EEW 03 13 dw w, dw NNE-SSW w y NWW-SEE w d w ewù ww w d w. w dqw ƒ j d w» d qw. w w» w Table 5 ƒ w d dqw ƒ w. Double-couple (Aki Richard, 2002)» w d w l dw s, dw dqw ƒ ƒ, œ(conjugate) d ƒ ƒ j dw ƒ j. Table 5 w w Jo Baag (2007). Jo Baag d w NWW-SEE w d dqw ƒ 3 o NNE-SSW w d ƒ 33 o ùkû. dq w d w w Fig. 8 ƒ ƒw. w (KIGAM, 2008) w d d w j ƒ ùkü, Herrmann (2008) NNE-SSW w d dqw w w ùküù, Jo Baag (2007) w ƒ jš NWW-SEE w d ƒ j ùkü w. Jo Baag (2007) NWW-SEE w d dq w w d Havard CMT (2008), NWW-SEE w d Jo Baag (2007) d ƒ wù, œ d ƒ. d w dqw ƒ y» w, d w dqw mw NWW-SEE w w šƒ d d ƒ j q. ³ ü w w d šq d w dqw mw d ww. Boatwright w (2007) wù dq w j (v/c >0.7), q w w( ƒ 70 ü) ƒ sw o. œ s mw d w. wr» w Á w w (, 2007), NWW-SEE d dqw ww ùkü. wz yw Á ¾ w ƒ w q. w (, 2003) y NWW-SEE w x w NWW- SEE dw ww ùkû. 2007 1 20 w (M L = 4.8) d DGY(», =7 km)» PGA(ƒ) d (> 0.1 g) ww» w Á w (R < 100 km) d d w( w) dq w(unilateral rupture directivity) sƒ w. w d q qw j» l qw j» w šq rp j w ww q q w w ƒ ql w. q qw j» Á gq w rp ((9) ERR j ( f ))l, Brune w( σ) w RVT (Boore, 1983) qwj» logpga y. rp ERR j ( f ) mw DGY d sww
(M=4.8, '07. 1. 20) dqw 147 ƒ ûw ew d» d qw yw. dqw w d logpgal Boatwright (2007) w dq(v) q(c) w (= v/c) qww ƒ(θ, deviation angle) w w dqw sƒw, PGA d NWW-SEE w š d SE w w t w dq w w, t w NNE-SSW w d w q. p dqw» w d w Jo Baag (2007) NNE-SSW w d(w = 284 o, =76 o ) ƒ ww. wz ü w ³ w d, dqw d w ƒw q. sƒ ³ p dqw w w šƒ vw q. 2007 w w» w w w (2007-02084), š w. šx, x,,, 2007, 2007 1 20 (M=4.8), dw d, w wz, 28.2, 202-213. ½, 2007, (2007/01/20) p w, œwz, 17.4, 665-672., 2007, w( xy ), x y( ) http://rm.samsung fire.com/pub/pub_zine_2007spr. html., 2007, w û w 2 Q m v, œww, w.,, 2007, (M=4.8, '07. 1. 20) rp p, k, 10.4, 241-251.,, 2007, ql w d, kwz, 10.3, 183-190.,,, k, 2008, d w y sƒ, 2008 w œwz w tz, '08. 3. 21( ) šw er, 116-123., 2003, ( ) (1:250,000). Aki, K., and Richards, P. G., 2002, Quantitative seismology(2nd Edition), University Science Books. Anderson, J. G., and Hough, S. E., 1984, A model for the shape of the fourier amplitude spectrum of acceleration at high frequencies, Bulletin of Seismological Society of America, 74, 1969-1993. Atkinson, G. M., and Hanks, T. C., 1995, A High-Frequency Magnitude Scale, Bulletin of the Seismological Society of America, 85, 825-833. Atkinson, G. M., 2006, Single-Station Sigma, Bulletin of the Seismological Society of America, 96, 446-455. Ben-Menahem, A., 1961, Radiation of seismic surface waves from finite moving sources, Bulletin of the Seismological Society of America, 51, 401-435. Boatwright, J., 2007, The persistence of directivity in small earthquakes, Bulletin of the Seismological Society of America, 97.6, 1850-1861. Boore, D. M., 1983, Stochastic simulation of high frequency ground motions based on seismological models of the radiated spectra, Bulletin of Seismological Society of America, 73, 1865-1894. Boore, D. M., 2003, Simulation of ground motion using the stochastic method, Pure and applied geophysics, 160, 635-676. Boore, D. M., and Joyner, W. B., 1978, The influence of rupture incoherence on seismic directivity, Bulletin of the Seismological Society of America, 68, 283-300. Boore, D. M., and Joyner, W. B., 1989, The effect of directivity on the stress parameter determined from ground motion observations, Bulletin of the Seismological Society of America, 79, 1984-1988. Brune, J. N., 1970, Tectonic stress and the spectra of seismic shear waves from earthquakes, Journal of Geophysical Research, 75, 4997-5009. Brune, J. N., 1971, Correction, Journal of Geophysical Research, 76, 5002. Centroid Moment Tensor (CMT) Catalog, 2007, http://www. seismology. harvard.edu/cmtsearch. html (last accessed November 2007). Hanks, T. C., and McGuire, R. K., 1981, The character of highfrequency strong ground motion, Bulletin of the Seismological Society of America, 71.6, 2071-2095. Herrmann, R.B., 2008, http://mnw.eas.slu.edu/earthquake_ Center/MECH.KR/ (last updated on 2008/03/28), Saint Louis University in U.S.A. Jo, N., and Baag, C. H., 2007, The 20 January 2007, M w 4.5, Odaesan, Korea, earthquake. Geosciences Journal, 11, 51-58. KIGAM, 2008, http://quake.kigam.re.kr. McGuire, J. J., 2004, Estimating Finite Source Properties of Small Earthquake Ruptures, Bulletin of the Seismological Society of America, 94.2, 377-393. Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., 1996, Numerical recipes in Fortran 77: The art of scientific computing, Cambridge Univ. Press.