Engineering Geology 121 (2011) Contents lists available at ScienceDirect. Engineering Geology

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1 Engineering Geology 121 (2011) Contents lists ville t ScienceDirect Engineering Geology journl homepge: Response spectrl ttenution reltions for shllow crustl erthqukes in Tiwn Po-Shen Lin, Chyi-Tyi Lee,, Chin-Tung Cheng c, Chih-Hsun Sung d Institute of Geophysics, Ntionl Centrl University, No.300, Jungd Rod, Jungli City, Toyun County, 32001, Tiwn Institute of Applied Geology, Ntionl Centrl University, No.300, Jungd Rod, Jungli City, Toyun County, 32001, Tiwn c Geotechnicl Engineering Reserch Center, Sinotech Engineering Consultnts, Inc., Bsement No.7 Lne No.26, Yt-sen Rod, Tipei, 11071, Tiwn d Institute of Applied Geology, Ntionl Centrl University, Tiwn rticle info strct Article history: Received 14 My 2009 Received in revised form 21 April 2011 Accepted 28 April 2011 Aville online 10 My 2011 Keywords: Attenution reltionship Crustl erthqukes Strong ground motion Pek ground ccelertion Spectrl ccelertion Hnging-wll effect In this study, locl set of response spectrl ttenution equtions, developed for seismic hzrd nlysis in Tiwn, re introduced s n exmple for determining the locl strong motion ttenution reltionship for region. Strong ground-motion dt for shllow crustl erthqukes re otined from the Tiwn Strongmotion Instrumenttion Progrm (TSMIP). These dt re used to estlish pek ground ccelertion () nd response spectrl ccelertion (SA) ttenution equtions tking into considertion oth hnging-wll effects nd site conditions. The otined results show tht the locl set of ttenution equtions gives significntly lower vlues of nd SA for structurl periods shorter thn 0.3 s s compred to set of glol reltions otined from interntionl dt. The SAs otined for structurl periods longer thn 0.3 s re similr to those otined for glol sets. This indictes tht developing locl set of ground-motion ttenution equtions is necessry for more ccurte prediction of ground motion vlues Elsevier B.V. All rights reserved. 1. Introduction Corresponding uthor. Tel.: ; fx: E-mil ddresses: person@gis.geo.ncu.edu.tw (P.-S. Lin), ct@ncu.edu.tw (C.-T. Lee), ctcheng@sinotech.org.tw (C.-T. Cheng), kren@gis.geo.ncu.edu.tw (C.-H. Sung). A set of locl response spectrl ttenution equtions is essentil for proilistic seismic hzrd nlysis (PSHA) in specific region. The nlysis should include the ground-motion for different response spectrl periods, nd should dequtely reflect the fct tht the mplitude of the ground-motion increses with erthquke mgnitude nd decreses s propgtion distnce increses. Utmost cre should e tken when developing set of ttenution equtions for prcticl use in PSHA. In prticulr, the stndrd devition of the ground-motion vlues should not e too ig, since PSHA is very sensitive to the stndrd devition, whose vlues, if excessively lrge, cn led to overly-conservtive ground-motion predictions (Anderson nd Brune, 1999; Bommer nd Arhmson, 2006). The development of locl set of response spectrl ttenution equtions is required for ny plce where erthquke resistnt design or sfety evlution of existing structures is needed. This is definitely true of Tiwn, ecuse high seismicity nd disstrous erthqukes hve lredy een experienced. However, there is lck of response spectrl ttenution equtions for shllow crustl erthqukes in Tiwn, with the exception of those used for suduction zone erthqukes in northestern Tiwn (Lin nd Lee, 2008) nd for descriing the ground motion chrcteristics of the Chi-Chi erthquke (Loh et l., 2000). The redy-mde locl ttenution equtions utilized in most previous studies hve only investigted, nd do not report stndrd devition (Hwng, 1995; Liu et l., 1999; Chng et l., 2001; Wu et l., 2001). In the lst twenty yers, five different forms of ttenution equtions (four clculted y Tsi et l., 1987 nd one y Loh et l., 2000) do provide stndrd devition nd re still widely used y engineering consultnts in Tiwn. The present prolem in Tiwn is not only the lck of spectrl ttenution, ut lso the inherent wekness of using just locl mgnitude scle for erthqukes nd the lck of considertion of site clssifiction. For exmple, right fter the 1999 Chi-Chi erthquke (M et l., 1999; Ko nd Chen, 2000) it ws found tht, due to the mgnitude sturtion phenomenon, the Richter mgnitude scle ws not pproprite for developing the ground-motion ttenution equtions for PSHA nd the use of the seismic moment mgnitude M W ws recommended. We lso need to develop ttenution equtions using the closest distnce from the rupture surfce insted of hypocentrl distnce, s in the reltions used until now. Furthermore, for the Chi-Chi erthquke, significnt differences were found in ground-motion vlues etween the hnging-wll nd the footwll side of the fult nd this is yet nother point tht should e reflected in the ttenution equtions. Lin nd Lee (2008) estlished set of response spectrl ttenution equtions for suduction zone erthqukes in northestern Tiwn, using M W nd hypocentrl distnce. This pper introduces set of response spectrl ttenution equtions for shllow crustl erthqukes in Tiwn using M W nd the closest distnce from the rupture surfce. This locl set of ttenution equtions covers /$ see front mtter 2011 Elsevier B.V. All rights reserved. doi: /j.enggeo

2 P.-S. Lin et l. / Engineering Geology 121 (2011) spectrl periods from 0 to 5 s, nd emphsizes differences in site clsses nd the hnging-wll effect. 2. Seismotectonics of Tiwn The islnd of Tiwn is locted t the oundry etween the Philippine Se plte nd the Eursin plte. The Philippine Se plte is moving towrds northwest t rte of out 7 8 cm/yr (Seno, 1977; Seno et l., 1993; Yu et l., 1997), while the Luzon rc, t the leding edge of the Philippine Se plte, is colliding with the Eursin plte in estern Tiwn. In northestern Tiwn, the Philippine Se plte is suducting eneth the Eursi plte. In southwestern Tiwn, the Philippine Se plte is oducting over the ocenic lithosphere of the South Chin Se which is ttched to the Eursin plte (Fig. 1). The rc continent collision strted in the Lte Miocene (Chi, 1972; Bowin et l., 1978; Letouzey nd Kimur, 1986), nd hs produced the highly deformed terrin of Tiwn, mrked with intensely folding nd thrusting. The islnd is experiencing ctive crustl deformtion (Bonill, 1975, 1977; Yu et l., 1997) nd frequent erthqukes (Hsu, 1971; Tsi et l., 1977; Wu, 1978). Also, the region is ffected y numerous typhoons nd chrcterized y high erosion rte (Ddson et l., 2003) ll of which re rpid erth ltering processes leding to chnging lndforms in the Tiwn region. Over the lst four hundred yers or so, more thn 130 disstrous erthqukes hve occurred in nd round Tiwn (Lee et l., 1976; Hsu, 1983; Tsi, 1986). Some hve produced lrge mounts of dmge, such s the 1999 Chi-Chi Tiwn erthquke of M W 7.6 (M et l., 1999; Ko nd Chen, 2000). The erthqukes in this seismotectonic environment my e grouped into two seismogenic ctegories: shllow crustl erthqukes nd suduction zone erthqukes. The former re the focus of this rticle. 3. Dt description Beginning in 1991, the Seismology Center of the Centrl Wether Bureu, Tiwn (CWB), emrked on progrm known s the Tiwn Strong Motion Instrumenttion Progrm (TSMIP) (Liu et l., 1999). The min gol of this progrm is to collect high qulity instrumentl recordings of strong erthquke shking. These dt re crucil for understnding erthquke source mechnisms, seismic wve propgtion nd locl site effects. At the present time, there re more thn 700 sttions, nd more thn one hundred thousnd high-qulity 3-component digitl ccelerogrms hve een collected. These new recordings provide n excellent dtse for ground-motion ttenution studies (Liu, 1999; Chng et l., 2001; Wu et l., 2001; Lin nd Lee, 2008). The loctions of the TSMIP sttions re shown in Fig. 1. Except in the mountinous res, these free-field sttions re densely spced pproximtely 5 km prt on verge nd only out 3 km prt in urn res. The deployment of instruments strted in 1991, with most ecoming opertionl y Decemer Ech operting freefield sttion includes trixil ccelerometers, digitl recording suunit, power supply, nd timing system. The CWB releses informtion out the mgnitude of ech erthquke in locl mgnitude (M L ). However, when lrge mgnitude erthqukes (M L N6.5) re considered, sturtion prolem rises (Heton et l., 1986). To void this prolem, the moment mgnitude, M W (Hnks nd Knmori, 1979), which is directly relted to the fult rupture re nd erthquke energy, is used s the mgnitude prmeter in the ttenution model discussed in the present study. We use M W M L reltion developed y Tsi nd Wen (1999) to convert M L to M W. The eqution is s follows: M L =0: :993M W : ð1þ Fig. 1. Mp showing the distriution of erthquke epicenters (str) used in this study nd the distriution of TSMIP strong-motion sttions (gry tringles). Becuse the dt used in developing this eqution is from M L 4.8 to M L 7.1, this conversion is used only for erthquke mgnitude less thn or equl to M L 6.8. For the moment mgnitude of the Chi-Chi minshock, the USGS estimte ws dopted. For strong-motion dt, screening is performed on the erthquke records prior to processing. Originl erthquke records re put through se line correction, nd then plotted s time history. Erthquke records re selected mnully, nd dmged or questionle records re excluded. Records with squre wves due to the ground-motion vlues eing too smll re lso disposed of. After screening, 4383 sets of 3-component dt remin. Erthquke epicentres for this dt set re shown lso in Fig. 1, nd detils of erthquke prmeters re listed in Tle 1. For the purpose of estlishing set of spectrl ttenution equtions, we clculte the 5% criticl-dmping rtio response spectrum for ech strong-motion record, with periods rnging from 0.01 to 5 s, t smpling intervls of 0.01 s. Prior to the regression nlysis, the geometric men of the two horizontl components ws used s the horizontl ground-motion vlue. We use the site clssifiction results otined y Lee et l. (2001) to distinguish etween rock (ctegories B nd C in Lee et l., 2001) nd soil sites (ctegories D nd E in Lee et l., 2001). Considering the hnging-wll effect, the records from the Chi-Chi erthquke re divided into three groups: hnging-wll sites, footwll sites nd others, s shown in Fig. 2. Hnging-wll of dip-slip fult is defined s the overlying side of fult: we ssumed tht it extends within 30 km of the fult line nd eyond the ends of the fult line within 30 from the norml to the fult strike. Footwll of dip-slip fult is defined s the underlying side of fult: we ssume tht it extends within 40 km of the fult line

3 152 P.-S. Lin et l. / Engineering Geology 121 (2011) Tle 1 Prmeters of the Tiwn erthqukes used in this study. No. Dte Time Lon. Lt. Depth M L M W Fult type Rec._no /12/13 09:23: RO /12/15 21:49: R /12/20 03:32: SS /12/21 03:14: R /12/22 16:22: SS /03/28 08:11: RO /04/06 01:12: SS /05/31 15:00: NO /06/05 01:09: NO /01/19 11:39: RO /02/26 08:08: RO /03/22 03:30: R /04/11 17:47: R /04/23 02:47: RO /04/23 02:57: SS /04/23 03:01: SS /05/01 14:50: RO /05/27 18:11: R /07/07 03:04: R /07/14 16:52: SS /07/14 17:40: SS /09/28 17:58: SS /10/31 22:27: R /11/14 07:26: SS /04/07 16:55: R /05/28 21:53: /10/19 19:16: R /11/16 00:22: RO /04/02 22:36: N /06/24 16:37: SS /09/05 12:41: SS /10/29 23:18: RO /11/14 04:29: /01/18 19:56: SS /01/20 23:29: RO /07/17 04:51: R /09/20 17:47: R /09/20 18:03: N /09/20 18:11: /09/20 18:16: /09/20 21:46: R /09/22 00:14: RO /09/25 23:52: R /10/22 02:18: RO 67 Note: Fult type dt dopted from Wu et l. (2008), clssified into Strike-slip (SS), Norml fult (N), Norml-olique fult (NO), Reverse fult (R), Reverse-olique fult (RO), sed on the rke ngle. Depth is in km. nd lso eyond the ends of the fult line within 30 from the norml to the fult strike. (see Fig. 2). Since there is lck of ground-motion dt for erthquke mgnitudes from 6.5 to 7.6 nd distnce in the ner field, some dt reltive to lrge erthqukes, hnging-wll, nd ner field conditions re derived from similr geotectonic environment outside Tiwn to develop relile ttenution reltionships for PSHA. The dt selected from interntionl sources re listed in Tle 2. In the end, we re left with four groups of dt, i.e. for hnging-wll rock sites, hnging-wll soil sites, footwll rock sites, nd footwll soil sites. There re totl of 52 erthqukes nd 5,268 records; only 87 records (1.7%) re tken from glol dt set so tht the developed ttenution equtions still siclly represent locl reltions. The mgnitude nd distnce distriution re shown in Fig. 3; the vlue rnges for the moment mgnitude re nd for distnce re km. The distnce prmeter used in this study is the closest distnce from the rupture surfce, while hypocentrl distnce is used for erthqukes without finite fult model (Beresnev nd Atkinson, 1999). Most of the dt re reltive to erthqukes with reverse nd reverse-olique fult mechnisms nd only few of them re of other Fig. 2. Mp showing the distriution of strong-motion sttions round the Chelungpu fult, where full circles indicte sttions on the hnging-wll side nd full tringles indicte sttions on the footwll side. Blck circles nd lck tringles men tht strongmotion records from the Chi-Chi erthquke minshock re ville, wheres gry circles nd gry tringles men tht records of the Chi-Chi minshock re missing. types (some strike-slip fult, two norml-olique fult nd two norml fult mechnisms). Thus, differences in fult types were not considered in developing our ttenution model. With regrd to hnging-wll effect, it cn e generlly oserved only in cse of dip-slip fults which rupture or deform ground surfce. Among ll the 44 locl erthqukes, only the Chi-Chi minshock deformed nd ruptured the ground surfce, therefore, only its records re used in developing the hnging-wll/footwll ttenution equtions. Additionlly, dt reltive to erthqukes outside Tiwn were used deriving hnging-wll/footwll ctegory from relted wesites nd/or reports. 4. Attenution model nd regression method An ttenution reltionship descries the ground-motion vlue expected t site, given source chrcteristics, wve pth, nd site effects, prmeterized in simplified wy. The most common Tle 2 Prmeters of erthqukes of res outside Tiwn used in this study. No. Dte Time Lon. Lt. Depth M W Rec. no. Eq. nme /09/ Ts, Irn /05/02 23: Coling /12/ Nhnni, Cnd /07/08 09: N. Plm Springs /10/01 14: Whittier Nrrows /10/18 00: Lom Priet /04/25 18: Cpe Mendocino /06/28 11: Lnders Note: The record numers represent the numer of records used in this study not the records for tht erthquke. Depth is in km.

4 P.-S. Lin et l. / Engineering Geology 121 (2011) Mgnitude (Mw) Mgnitude (Mw) Distnce (km) Distnce (km) Fig. 3. Mgnitude nd distnce distriution of the ground-motion dt set used in this study: () rock sites; () soil sites. The full lck circles represent dt used in the hnging-wll model nd full gry tringles represent dt used in the footwll model. Open tringles mens others (or not differentited etween hnging-wll nd footwll). Tle 3 Regression coefficients of ttenutions for the hnging-wll nd rock sites. Tle 5 Regression coefficients of ttenutions for the footwll nd rock sites. c 1 c 2 c 3 c 4 c 5 σ lny Note: Regression eqution ln(y)=c 1 +c 2 M+c 3 ln(r+c 4 e C5M )±σ ln y. c 1 c 2 c 3 c 4 c 5 σ lny Note: Regression eqution ln(y)=c 1 +c 2 M+c 3 ln(r +c 4 e C5M )±σ ln y. pproch is to use oserved ground-motion dt to develop set of empiricl ttenution equtions sed on semi-theoreticl ttenution model. Although synthetic modeling of erthquke ground-motion (e.g., Kme et l., 1998) nd hyrid methods (e.g., Field, 2000) were lso used in ground-motion predictions, the empiricl method is dopted in the present study. Tle 4 Regression coefficients of ttenutions for the hnging-wll nd soil sites. Tle 6 Regression coefficients of ttenutions for the footwll nd soil sites. c 1 c 2 c 3 c 4 c 5 σ lny Note: Regression eqution ln(y)=c 1 +c 2 M+c 3 ln(r+c 4 e C5M )±σ ln y. c 1 c 2 c 3 c 4 c 5 σ lny Note: Regression eqution ln(y)=c 1 +c 2 M+c 3 ln(r +c 4 e C5M )±σ ln y.

5 154 P.-S. Lin et l. / Engineering Geology 121 (2011) Commonly used ttenution models re comprised of source chrcteristics, geometry spreding nd inelstic ttenution. When the site effect is considered, the generl form ecomes: y = 1 f 1 ðmþf 2 ðrþf 3 ðm; RÞf 4 ðp i Þε; ð2þ in which y is the ground-motion prmeter; 1 is constnt; f 1 (M) is function relevnt to mgnitudes; f 2 (R) is function relevnt to distnce; f 3 (M, R) is function relevnt to mgnitude nd distnce; f 4 (P i )isfunctionrelevnttositeeffect;ε represents rndom error. In the pst, y in Eq. (2) hs een minly, ut for the purpose of estlishing uniform hzrd response spectrum in seismic hzrd nlysis, y cn refer lso to the mplitude of the response spectrum for the structure period T. In such cse Eq. (2) cn e rewritten s yt ð Þ = 1 f 1 ðm; T Þf 2 ðr; T Þf 3 ðm; R; T Þf 4 ðp i ; TÞεðTÞ: ð3þ To otin this eqution, dt for regression nlysis re otined y clculting 5% criticl-dmping rtio response spectrum from ech ville erthquke record. In this study periods rnging from 0.01 s to 5 s were selected nd in prticulr 0, 0.01, 0.06, 0.09, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.75, 1.0, 1.5, 2.0, 3.0 nd 5.0 s. As ttenution model for the regression nlysis, given the physicl properties of the ttenution model, we dopted the functionl form proposed y Cmpell (1981) for nlyzing the horizontl, which hve proved its dequcy in previous studies, i.e.: ln ij = c 1 + c 2 M i + c 3 ln R ij + c 4 e c 5 M i + lnε; ð4þ where i denotes the ith erthquke; j denotes the jth sttion tht recorded the ith erthquke; (g) is the geometric men of the horizontl vlues; M is the moment mgnitude; R is the closest distnce (in km) to the rupture surfce; ε is rndom error. (g) Rock (g) 01 1 Soil 0.01 Hnging-wll Mw=5 Hnging-wll Mw=6 Hnging-wll Mw=7 Hnging-wll Mw=8 Footwll Mw=5 Footwll Mw=6 Footwll Mw=7 Footwll Mw= Hnging-wll Mw=5 Hnging-wll Mw=6 Hnging-wll Mw=7 Hnging-wll Mw=8 Footwll Mw=5 Footwll Mw=6 Footwll Mw=7 Footwll Mw=8 Rupture Distnce (km) Rupture Distnce (km) c d 1 T = 1 sec, Rock 1 T = 1 sec, Soil Hnging-wll Mw=5 Hnging-wll Mw=6 Hnging-wll Mw=7 Hnging-wll Mw=8 Footwll Mw=5 Footwll Mw=6 Footwll Mw=7 Footwll Mw= Hnging-wll Mw=5 Hnging-wll Mw=6 Hnging-wll Mw=7 Hnging-wll Mw=8 Footwll Mw=5 Footwll Mw=6 Footwll Mw=7 Footwll Mw=8 Rupture Distnce (km) Rupture Distnce (km) Fig. 4. Comprison of hnging-wll nd footwll ttenution for different erthquke mgnitudes: (), rock sites; (), soil sites, (c) SA t 1 s, rock sites; (d) SA t 1 s, soil sites. The difference etween the hnging-wll nd footwll ground-motion ws in the short distnce rnge (10 30 km).

6 P.-S. Lin et l. / Engineering Geology 121 (2011) Cmpell (1981) proposed two versions of his model sed on the functionl form, one unconstrined, for which ll the coefficients in Eq. (4) re derived from regression, nd nother constrined, for which c 3 ws fixed ( fr field constrint ) ndc 5 ws ssumed equl to c 2 /c 3. The ltter constrint implies tht ssumes equl vlues for ny mgnitude s distnce from rupture surfce goes to zero ( totl mgnitude sturtion ).Sincewehve lrge dt set (52 erthqukes nd 5268 records), in our study we did not dopt the fr field constrint nd let the regression to determine the reltive coefficient. On the contrry the totl mgnitude sturtion ws incorported in our model. Our considertion is tht erthquke mgnitude is proportionl to fult re nd fult displcement, nd ground motion is lso proportionl to fult re nd fult displcement, nd inversely proportionl to squre distnce. Therefore, when distnce is closing to zero, only smll re my influence the pek motion, no mtter how ig is the fult plne. With regrd to the response spectrum ttenution form for different periods, the functionl form dopted ws the sme s for, i.e.: ln SA ij = c 1 + c 2 M i + c 3 ln R ij + c 4 e c 5 M i + lnε: ð5þ Here SA, in g units, is the mplitude of response spectrum for ech period; M, R, nd ε re defined the sme s for the horizontl ttenution form. In this cse, the unconstrined functionl form of Cmpell (1981) is dopted, nd ll the coefficients in Eq. (4) re derived from regression. The lest squres sis for the non-liner regression model (Eqs. (4) nd (5)) cn e formulted s n S = i =1 m j =1 h i 2; lny ij f M i ; R ij ; C ð6þ ~0.1sec 0.2~5sec SA 0.01 SA 0.06 SA 0.09 SA 0.1 Hnging-wll Distnce (km) SA 0.2 SA 0.3 SA 0.4 SA 0.5 SA 0.6 SA 0.75 SA 1.0 SA 1.5 SA 2.0 SA 3.0 SA 5.0 Hnging-wll Distnce (km) c d ~0.1sec 0.2~5sec SA 0.01 SA 0.06 SA 0.09 SA 0.1 Footwll Distnce (km) SA 0.2 SA 0.3 SA 0.4 SA 0.5 SA 0.6 SA 0.75 SA 1.0 SA 1.5 SA 2.0 SA 3.0 SA 5.0 Footwll Distnce (km) Fig. 5. Attenution curves for rock sites t mgnitude of 6.0: () for nd SA with periods from 0.01 to 0.1 s for hnging-wll; () for SA with periods from 0.2 to 5.0 s for hnging-wll; (c) for nd SA with periods from 0.01 to 0.1 s for footwll; (d) for SA with periods from 0.2 to 5.0 s for footwll.

7 156 P.-S. Lin et l. / Engineering Geology 121 (2011) in which Y ij is the oserved ground-motion vlue, nd f M i ; R ij ; C is the men vlue of the logrithm of the response of the ijth cse following the non-liner function of Eqs. (4) nd (5). ThesymolC is vector representing coefficients c 1, c 2,, c n. In the present study, the c 1, c 2,, c n vlues tht minimize the function S were found through numericl serch method, i.e. the "lock hill-climing serch" pproch descried in Lin nd Lee (2008). C 1 C 2 C 3 Coefficient C 1 Coefficient C Coefficient C C 4 C 5 Coefficient C Coefficient C Hning-wll Coefficient C Coefficient C Coefficient C C 1 C 2 C 3 Coefficient C C 4 C 5 Coefficient C Footwll Fig. 6. Vrition of coefficients (c 1 c 5 ) with period in the SA ttenution equtions: () hnging-wll model; () footwll model.

8 P.-S. Lin et l. / Engineering Geology 121 (2011) Stndrd devition Hnging-wll Stndrd devition Footwll (sec) (sec) Fig. 7. Vrition of the stndrd devition in the SA equtions for periods from 0.01 to 5.0 s for: () hnging-wll; () footwll. 5. Results Four distinct groups of equtions were otined from regression nlysis results for hnging-wll or footwll, nd rock site or soil site. The otined horizontl ttenution equtions re s follows: Hnging-wll rock site: lnðþ = 3: :035 M 1:651ln R +0:152e 0:623M ; ð7þ Hnging-wll soil site: lnðþ = 3: :943 M 1:471ln R +0:100e 0:648M ; ð8þ Footwll rock site: lnðþ = 3: :047 M 1:662ln R +0:192e 0:630M ; ð9þ Footwll soil site: lnðþ = 3: :935 M 1:464ln R +0:125e 0:650M : ð10þ R rup =50km, Hnging-wll, In these equtions, the is the geometricl men of the horizontl in g, M is the moment mgnitude nd R is the closest distnce from the rupture surfce. The coefficients of the response spectrum ttenution equtions for ech period re tulted in Tles 3 6; the stndrd devitions of the regression errors σ lnε (sigm) re lso listed therein. The differences etween the four ttenution reltions developed in this study cn e seen in Fig. 4. It is cler tht higher prediction of vlues (y out 50%) re otined for the hnging-wll ttenution reltionship for rock sites t distnces less thn 10 km from the source (Fig. 4). A similr difference (y out 40%) is lso oserved for soil sites (Fig. 4). A comprison of the footwll ttenutions etween rock sites nd soil sites shows generlly higher ground-motion vlues in the ltter. However, since our dt set is very limited for distnces less thn 10 km, we cnnot conclusively demonstrte tht t such distnces soil mplifiction still ctully exists. We lso compre the differences of SA ttenution reltions t structurl period of 1 s. Hnging-wll ttenution reltion predict lso higher vlues (y out 40% for oth site ctegories), nd soil-site reltion shows higher ground-motion vlues (Fig. 4c, d). The R rup =150km, Hnging-wll, M W =3.5 M W =4.5 M W =5.5 M W =6.5 M W = M W =3.5 M W =4.5 MW=5.5 MW=6.5 MW= (sec) (sec) Fig. 8. Vritions of normlized spectrl shpes with different mgnitudes for the hnging-wll nd rock site model t fixed source-to-site distnce of 50 km () nd of 150 km ().

9 158 P.-S. Lin et l. / Engineering Geology 121 (2011) ttenution reltions clerly show the totl mgnitude sturtion imposed y the model (Fig. 4, ), wheres the unconstrined SA ttenution reltions do not show similr sturtion (Fig. 4c, d). Fig. 5 presents the nd SA ttenution curves for rock site t M W 6.0 for vrious periods. s of 0.1 to 0.2 s give the highest predicted vlues, oth in the hnging-wll nd footwll ttenution models. A comprison of the coefficients of the four ttenution models otined with the vrious period response spectrum ttenution equtions is shown in Fig. 6. For incresing periods, coefficient c 1 increses until period of 0.1 s nd then decreses; this implies tht the ccelertion response spectrum vlues grdully decrese for longer periods. Coefficient c 2, which is relted to mgnitude, hs the minimum t period of 0.1 s nd the mximum t period of 5 s for soil sites nd 2 s for rock sites. Coefficient c 3, which is relted to the rte of ttenution with distnce, shows the lrgest slope of out 0.1 s nd lower slope t longer periods. Coefficient c 4 hs the highest vlue t period close to 0.1 s, wheres coefficient c 5 t the sme period hs the lowest vlue. The sigms listed in Tles 3 6 re plotted ginst periods in Fig. 7. Their vlues show generl scending trend with incresing periods. The lrgest vlue of sigm is found t the lrgest period on soil sites, EQ1998_0717_0451_14,M=6.05 (rock site) EQ1998_0717_0451_14,M=6.05 (soil site) (g) (g) c Hnging-wll rock Footwll rock Averge Averge+SD Averge-SD EQ1999_0920_1747_15,M=7.6 (rock site) Hnging-wll rock Footwll rock Averge Averge+SD Averge-SD (g) (g) Hnging-wll soil Footwll soil Averge Averge+SD Averge-SD d EQ1999_0920_1747_15,M=7.6 (soil site) Hnging-wll soil Footwll soil Averge Averge+SD Averge-SD Fig. 9. Comprison of the dt with the medin vlue predicted y the hnging-wll model (solid thick line), y the footwll model (dotted line) nd y n verge model (solid thin line)±σ (dshed lines) for: () M W 6.05 nd rock sites; () M W 6.05 nd soil sites; (c) M W 7.6 nd rock sites; (d) M W 7.6 nd soil sites. Oserved vlues re represented y symols similr to those in Fig. 3, i.e. full lck circles: hnging-wll; full gry tringles: footwll; open tringles: others.

10 P.-S. Lin et l. / Engineering Geology 121 (2011) ut not for the rock site cses, where the mximum is found t 0.1 s. The sigm rnges from to At periods lrger thn 2 s the soil site model gives lrger sigms thn the rock site model for oth the hnging-wll nd the footwll conditions. For more detiled comprison of ttenution models with different mgnitudes nd distnces, we plot normlized ccelertion response spectrum for distnces of 50 km nd 150 km for hngingwll nd rock site conditions (Fig. 8). The normliztion ws done y dividing SAs y the. The results show tht the spectrl ccelertion increses with mgnitude t periods greter thn 0.2 s, ut decreses for incresing mgnitudes t periods smller thn 0.2 s. According to our results, the phenomen nd trends for the soil sites re similr. A similr trend ws lso found for the suduction zone cse discussed y Lin nd Lee (2008). We exmine the goodness of fit of the models y plotting the oserved vlues s function of rupture distnce together with the otined ttenution curves. Fig. 9 shows the dt for two typicl erthqukes together with the ttenution curves for the hnging-wll site model, the footwll model, the verge of oth models, the verge plus one sigm, nd the verge minus one sigm. EQ1998_0717_0451_14, M=6.05 () EQ1998_0717_0451_14, M=6.05 (soil site) c Hnging-wll rock Footwll rock Averge Averge+SD Averge-SD T = 1 sec EQ1999_0920_1747_15, M=7.6 (rock site) T = 1 sec d Hnging-wll soil Footwll soil Averge Averge+SD Averge-SD T = 1 sec EQ1999_0920_1747_15, M=7.6 (soil site) T = 1 sec Hnging-wll rock Footwll rock Averge Averge+SD Averge-SD 0.01 Hnging-wll soil Footwll soil Averge Averge+SD Averge-SD Fig. 10. Comprison of the SA vlues t period of 1 s with the medin vlue predicted y the hnging-wll model (solid thick line), y the footwll model (dotted line) nd y n verge model (solid thin line)±σ (dshed lines) for: () M W 6.05 nd rock sites; () M W 6.05 nd soil sites; (c) M W 7.6 nd rock sites; (d) M W 7.6 nd soil sites. Symols re similr to those in Fig. 9.

11 160 P.-S. Lin et l. / Engineering Geology 121 (2011) log residuls Hnging-wll, log residuls Hnging-wll, c d log residuls Footwll, log residuls Footwll, e f log residuls Hnging-wll, log residuls Hnging-wll, g h log residuls Footwll, log residuls Footwll, Fig. 11. Residuls for different nd SA ttenution equtions versus distnce: (), hnging-wll, rock sites; (), hnging-wll, soil sites; (c), footwll, rock sites; (d), footwll, soil sites; (e) SA, hnging-wll, rock sites; (f) SA, hnging-wll, soil sites; (g) SA, footwll, rock sites; (h) SA, footwll, soil sites.

12 P.-S. Lin et l. / Engineering Geology 121 (2011) Hnging-wll Hnging-wll c Residul Footwll d Residul Footwll e g Residul Hnging-wll Residul Footwll f h Residul Hnging-wll Residul Footwll Residul Residul Fig. 12. Histogrm of residuls of different nd SA ttenution equtions for: (), hnging-wll, rock sites; (), hnging-wll, soil sites; (c), footwll, rock sites; (d), footwll, soil sites; (e) SA, hnging-wll, rock sites; (f) SA, hnging-wll, soil sites; (g) SA, footwll, rock sites; (h) SA, footwll, soil sites.

13 162 P.-S. Lin et l. / Engineering Geology 121 (2011) Fig. 9 nd shows the vlues oserved for n erthquke of mgnitude 6.05 occurred in 1998, without the specifiction of site loction on hnging-wll or footwll side; Fig. 9c nd d show the dt from the Chi-Chi erthquke for which the distinction etween hnging-wll nd footwll dt ws ville. Fig. 10 shows, for the sme two erthqukes, the fitting of the oserved dt to the SA ttenution curves t 1 s. Fig. 10 nd shows the SA vlues oserved for the 1998 erthquke; Fig. 10c nd d shows the dt from the Chi- Chi erthquke. All the figures show tht our model fits well the dt. To exmine if there is ny trend in the regression results, we plot the residul vlues etween oserved nd predicted ground-motions ginst distnce for the ttenution model. As shown in Fig. 11, residuls do not exhiit ny is. A histogrm plot of the residuls is shown in Fig. 12, nd indictes tht the residuls closely follow lognorml distriution. These figures demonstrte the good qulity of our regression results. 6. Discussion Is it necessry to develop locl set of ground-motion ttenution equtions for ground-motion predictions nd PSHA ppliction? This question my e clrified through the comprison of the results from the present study with some glol sets of ttenution equtions (Fig. 13) nd spectrl ttenution equtions (Fig. 14) resulted from the Next Genertion Attenution (NGA) project. Equtions otined y different uthors within the frmework of this project (Arhmson nd Silv, 2008; Boore nd Atkinson, 2008; Cmpell nd Bozorgni, 2008; Chiou nd Youngs, 2008; Idriss, 2008) were compred with the Tiwn rock-site reltions, dopting Vs30 vlue of 760 m/s to chrcterize rock-sites in the NGA models. In the Tiwn cse, site clsses B nd C re tken s rock site with Vs30 rnging from 360 m/s to more thn 760 m/s. Therefore, the comprison is on the sme sis or the Tiwn cse is rther conservtive (predicting higher ground motion vlues). An exmintion of Fig. 13 shows tht the Tiwn set is similr to tht of the NGA ttenution equtions for distnces less thn out 20 km. However, it is significntly lower thn tht of the NGA ttenution equtions for distnces greter thn 20 km. The steeper slope of the Tiwn ttenution curves could e due to the fct tht Tiwn is very young orogen, so tht the crust is wek nd Q vlues re low (Wng et l., 2003). This implies reltively high ttenution, especilly for high-frequency wves. This is confirmed y the oservtion tht, for structurl periods shorter thn 0.3 s, the spectrl ccelertions otined in this study re significntly lower thn those of NGA's equtions. On the contrry, for periods longer thn 0.3 s, they re more similr to (Fig. 14) or little it lower (Fig. 14) thn in NGA models. This indictes tht locl set of ground-motion ttenution equtions could e needed for deriving more ccurte ground-motion prediction. This is prticulrly importnt for correct definition of design spectr of smll uilding with limited numer of stores (i.e. with resonnce frequency higher thn 3 Hz). Lin nd Lee (2008) lso otined lower ground-motion prediction in their suduction zone erthquke results thn tht of glol sets. They otined significntly lower vlue for periods of less thn 0.3 s, nd not so different vlues for periods greter thn 0.3 s (Lin nd Lee, 2008, Figure 17). This suggests tht oth shllow crustl erthquke sources nd suduction zone erthquke sources hve similr ttenution ptterns for wve propgtion through low-q young orogen. Ten yers go, Cliforni consulting compny predicted 475- yer return time level of 0.47 g for downtown Tipei (Chiou et l., 2001). This cused ig shock to seismologists nd erthquke engineers in Tiwn, ecuse this vlue is twice s lrge s the uilding code vlue in Tipei. We exmined the report nd the pper of Chiou et l. (2001), nd relized tht 4 set of Cliforni crustl ttenution equtions (Arhmson nd Silv, 1997; Boore et l., 1997; Cmpell, 1997; Sdigh et l., 1997) nd glol set of suduction zone ttenution equtions (Youngs et l., 1997) hd een used in the PSHA. We thought tht the key to explin their results might e the use of ttenution equtions not proper for the Tipei cse, nd we strted to develop locl ttenution equtions. A recent study (Cheng et l., 2010) revising those results predicted 475-yer level of 0.30 g for downtown Tipei, using the sme source dt ut different ttenution equtions, i.e. the shllow crustl ttenution equtions presented in this study nd the suduction zone ttenution equtions of Lin nd Lee (2008). In other words, using locl set of ttenution equtions for the PSHA reduced the level y 42% in the Tipei cse. (g) TW_HW TW_FW AS08 BA08 CB08 CY08 IS08, M W =6 (g) TW_HW TW_FW AS08 BA08 CB08 CY08 IS08, M W =7 Fig. 13. Comprison of the ttenution curves from results otined in this study nd some glol sets for: () M W 6; () M W 7. Solid red nd lck lines indicte hnging-wll nd footwll models of present study, respectively. The other curves re reltive to the following reltions: AS08, Arhmson nd Silv (2008); BA08, Boore nd Atkinson (2008); CB08, Cmpell nd Bozorgni (2008); CY08, Chiou nd Youngs (2008); IS08, Idriss (2008).

14 P.-S. Lin et l. / Engineering Geology 121 (2011) , M W =7, R=50 km 0.1, M W =7, R=150 km TW_HW TW_FW AS08 BA08 CB08 CY08 IS08 (sec) (sec) TW_HW TW_FW AS08 BA08 CB08 CY08 IS08 Fig. 14. Comprison of spectrl ccelertion predicted y this study nd some glol sets for: () M W 7 nd distnce 50 km, () M W 7 nd distnce 150 km. Definition for line styles nd colors is the sme s in the previous figure. It is now generlly ccepted tht ground-motion scles nonlinerly with mgnitude. We hve plotted dt vs. mgnitude to exmine the model we used. Results revel tht the present model lso scle non-linerly with mgnitude nd the oserved dt fit good with the model within the dt rnge etween M W 3.5 nd M W 7.6 (Fig. 15) Plotting SA vs. distnce for long-period spectr of 3 typicl erthqukes (Fig. 16), results revel tht most dt fit the medin ttenution curve. However, in our dtse, only the Chi-Chi minshock hs plenty of ner field dt nd shows distnce sturtion. Other erthqukes re still lcking for ner field dt so tht the occurrence of mgnitude sturtion phenomenon cnnot e evluted from the ville dt. We elieve there re still rooms for discussion of mgnitude sturtion t long periods nd this topic needs more studies in the future. Although severl studies hve shown tht soil motion tends to e de-mplified under lrge strin, the otined equtions predict significnt soil mplifiction lso under such conditions. However, in Fig. 9d, it is cler tht our equtions over-predict the soil from Chi-Chi erthquke for rupture distnce less thn 20 km. Nevertheless, this over-prediction feture is not seen in SA t 1 s s shown in Fig. 10d. Soil de-mplified under lrge strin nd for short periods my e considered in the future studies. 7. Conclusions nd recommendtions A set of response spectrl ttenution equtions, including nd SAs with structurl periods of up to 5.0 s, for oth hnging-wll (g) Dt HW FW Dis. 1km 5km 20km 50km 100km Hnging-wll EQ.Dte Mw 1999_09_ _07_ _10_ T = 1 sec Moment Mgnitude, M w Fig. 15. Plot of dt vs. mgnitude oserved t different distnces (represented with different colors), showing nonliner mgnitude scling (uffer zone for distnce is 2 km). Solid nd dshed lines represent the vlues predicted y the otined ttenution reltions for hnging-wll nd footwll sites, respectively. Fig. 16. SA dt vs. distnce plot for 3 typicl erthqukes (represented with different colors), showing distnce sturtion nd possile mgnitude sturtion t long period. The legend reports dte nd moment mgnitude (M w ) of the three erthqukes.

15 164 P.-S. Lin et l. / Engineering Geology 121 (2011) nd footwll models nd rock nd soil sites, for Tiwn shllow crustl erthqukes, hs een completed. The otined ttenution equtions give higher ground-motion estimtes for the hnging-wll thn for the footwll side, nd higher ground-motion estimtes for soil sites thn for rock site. These ttenution equtions should provide etter ground-motion estimtes for Tiwn, nd mke it possile to construct uniform hzrd response spectrum from PSHA. The results confirm tht the locl set of ttenution equtions gives lower predicted vlues thn glol sets for distnces greter thn 20 km. The steeper slope of the Tiwn ttenution curves could e due to the fct tht, Tiwn eing very young orogen, the crust is wek nd hs low Q vlues. The spectrl ccelertions otined in this study re lso lower thn those otined with the glol sets for structurl periods shorter thn 0.3 s, ut re similr to those of glol sets for longer periods. The development of locl set of groundmotion ttenution equtions is necessry for more ccurte prediction of ground-motion vlues. This would e of gret ssistnce in engineering plnning, design, nd sfety evlution of existing structures in the Tiwn region. In the use of this locl set of ground-motion ttenution equtions, the hnging-wll sets nd the footwll sets my e comined nd n verge vlue my e used in cse of strike-slip erthquke or if n erthquke is not expected to rupture or to deform the ground surfce. Acknowledgments We extend our deepest thnks to the Seismology Center of the Centrl Wether Bureu of Tiwn for providing the strong-motion dt. The mnuscript ws gretly improved sed on the comments nd suggestions mde y the nonymous reviewers. This reserch ws supported y the Tiwn Erthquke Reserch Center (TEC) funded through the Ntionl Science Council (NSC) under Grnt Numer NSC M References Arhmson, N.A., Silv, W.J., Empiricl response spectr ttenution reltions for shllow crustl erthqukes. 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