Anal y sis of Tai pei Ba sin Re sponse for Earth quakes of Var i ous Depths and Locations Using Empirical Data

Transcription

1 Terr. Atmos. Ocean. Sci., Vol. 20, No. 5, , October 2009 doi: / (T) Anal y sis of Tai pei Ba sin Re sponse for Earth quakes of Var i ous Depths and Locations Using Empirical Data Vladi mir Sokolov 1, *, Kuo-Liang Wen 2, Joachim Miksat 1, Friedemann Wenzel 1, and Chun-Te Chen 2 1 Geo phys i cal In sti tute, Karlsruhe Uni ver sity, Karlsruhe 76187, Ger many 2 In sti tute of Geo phys ics, Na tional Cen tral Uni ver sity, Jhongli, Tai wan, ROC Re ceived 26 May 2008, ac cepted 15 October 2008 AB STRACT The re sponse of Tai pei ba sin upon earth quake ex ci ta tion was stud ied us ing re cords of re cent earth quakes. The strong-mo tion da ta base in cludes re cords ob tained at 32 sta tions of the Tai pei TSMIP net work from 83 deep and 142 shal low earth quakes (M > 4.0) that oc curred in The char ac ter is tics of fre quency-de pend ent site re sponse were ob tained as spec tral ra tios be tween the ac tual earth quake re cords (hor i zon tal com po nents) and those mod elled for a hy po thet i cal Very Hard Rock (VHR) con di tion. The mod els for VHR spec tra of Tai wan earth quakes had been re cently pro posed by Sokolov et al. (2005b, 2006). Anal y sis of site re sponse char ac ter is tics and com par i son with sim ple 1D mod els of the soil col umn re sulted in the fol low ing con clu sions: (1) The spec tral ra tios through out the ba sin ob tained from deep earth quakes (depth > 35 km) ex hibit good agree ment with the the o ret i cal ra tios cal cu lated us ing the 1D mod els con structed us ing avail able geo log i cal and geotechnical data. (2) The spec tral ra tios ob tained from shal low earth quakes show in flu ence of: (a) sur face waves gen er ated when trav el ling from dis tant sources to the ba sin and (b) rel a tively low-fre quency (< 1-2 Hz) waves gen er ated within the ba sin. (3) Some shal low earth quakes pro duce ex tremely high am pli fi ca tion at fre quen cies Hz within the ba sin that may be dan ger ous for high-rise build ings and high way bridges. (4) The ob tained re sults may be used in proba bil is tic seis mic microzonation of the ba sin when many pos si ble earth quakes lo cated at various distances are considered. 2D and 3D simulation is necessary to model the seismic influence from particularly large earthquakes. Key words: Site ef fect, Tai pei ba sin, Deep and shal low earth quakes Ci ta tion: Sokolov, V., K. L. Wen, J. Miksat, F. Wenzel, and C. T. Chen, 2009: Anal y sis of Tai pei ba sin re sponse for earth quakes of var i ous depths and locations us ing em pir i cal data. Terr. Atmos. Ocean. Sci., 20, , doi: / (T) 1. INTRODUCTION Seis mic ity in the Tai wan area is very high, and many large earth quakes (M > 6.5) have oc curred in the re gion in his tor i cal and mod ern times. Some of these earth quakes, e.g., the re cent Chi-Chi earth quake of 21 Sep tem ber 1999, caused se vere dam age. Tai pei City is the cap i tal of Tai wan and is lo cated on a sed i ment-filled ba sin in the north ern part of the is land. The area has ex pe ri enced sev eral dam ag ing earth quakes, the most re cent of which oc curred on 31 March The re sults of pre vi ous re search on earth quake ground mo tion pe cu liar i ties in the Tai pei ba sin (e.g., Kuo et al. 1995; Wen et al. 1995; Loh et al. 1998; Wen and Peng 1998a, b; Sokolov and Jean 2002; Wang and Lee 2002; Chen 2003; * Cor re spond ing au thor Vladi mir.sokolov@gpi.uni-karlsruhe.de Fletcher and Wen 2005) showed that large lat eral vari a tions in ground-mo tion char ac ter is tics (peak ground ac cel er a - tion, re sponse spec tra, dom i nant fre quen cies, etc.) are ap - par ent. Re cent needs of earth quake en gi neer ing re quire con - sideration of site ef fect in seis mic haz ard anal y sis. When ap plying the proba bil is tic ap proach for seis mic haz ard es ti - ma tion in ur ban ter ri to ries, it is nec es sary to take into ac - count the fol low ing: 1. Ex tended ar eas cov ered by large cit ies are char ac ter ized by va ri ety of lo cal geo log i cal and geotechnical con di - tions. 2. Dif fer ent en gi neer ing struc tures (build ings, bridges, life - lines, etc.) re quire con sid er ation of dif fer ent pa ram e ters

2 688 Sokolov et al. of ground mo tion within a rel a tively broad fre quency range of mo tion. 3. Op ti mi za tion of en gi neer ing de ci sions de mands es ti ma - tion of ground mo tion pa ram e ters for dif fer ent re turn periods (prob a bil i ties of be ing ex ceeded) con cern ing structures of different importance factors. 4. Con sid er ation of var i ous re cur rence in ter vals and a broad fre quency range of ground mo tion cause the ne ces sity to cover the in flu ence of dif fer ent earth quakes that may oc - cur in dif fer ent seismogenic zones. In this study we an a lyzed re cords of re cent earth quakes to ex plore fre quency-de pend ent re sponse of the Tai pei basin. The strong-mo tion da ta base in cludes re cords ob - tained at 32 sta tions of the Tai pei net work from 83 deep and 142 shal low earth quakes (M L > 4.0) that oc curred in the pe - riod, (Fig. 1). Most of the se lected sta tions cover evenly the ter ri tory of the ba sin. In ad di tion, we also con - sider two sta tions lo cated out side the ba sin (TAP053 and TAP071). Ta ble 1 sum ma rize the in for ma tion about the strong-mo tion da ta base. the ap pli ca tion of the H/V tech nique, how ever, are af fected by lo cal and subsurface fac tors in flu enc ing the ver ti cal com - po nent of ground mo tion. Among the fac tors we can men - tion, for ex am ple, the fol low ing: (a) con tri bu tion of com - pressional de for ma tion (P-wave) to ver ti cal com po nent at fre quen cies more than 8-10 Hz (Beresnev et al. 2002); P-wave con ver sion from the SV-waves at the bound aries of the lay ers above the base rock (e.g., Takahashi et al. 1992); in crease of am pli tudes at ver ti cal com po nent due to nonlinear ef fects in gran u lar ma te ri als (Loukachev et al. 2002). Such ef fects may be min i mized by us ing data only from rock sta tions (e.g., Chen and Atkinson 2002; Sokolov et al. 2005a, 2007). It was pro posed re cently (Sokolov 1998; Sokolov et al. 2000) to use so-called very hard rock (VHR) spec tral model to es ti mate site re sponse char ac ter is tics in terms of fre quency-de pend ent am pli fi ca tion (spec tral ra tios). The approach con sists of cal cu la tion spec tral ra tios be tween the actual earth quake re cords (hor i zon tal com po nents) and the spec tra mod elled for a hy po thet i cal VHR con di tion. On the one hand, be sides lo cal site re sponse, the spec tral ra tios 2. THE TECH NIQUE For es ti ma tion of the site re sponse from earth quake re - cords it is nec es sary to re move the source and prop a ga tion path effects. Various techniques for site-response estimation, which use the S-wave win dow, have al ready been de - vel oped and stud ied (e.g., Bard 1995). The most com mon pro ce dure (Borcherdt 1970) for the es ti ma tion of the site re - sponse from earth quake data is to de ter mine the sed i mentto-bed rock ra tio by di vid ing the Fou rier spec trum of a site by that of a nearby ref er ence (rock) site us ing earth quake re - cords. How ever, in many cases, in clud ing the Tai pei ba sin, it is dif fi cult to find a sta tion that can be de fined, un doubt edly, as a hard-rock ref er ence sta tion. There are a few strongmo tion bore-hole ar ray sites within the Tai pei Ba sin (Wang 2008). Bot tom sta tions from some of these ar rays may be con sid ered as ref er ence hard rock sites. How ever, the array due to tech ni cal rea sons does not ac cu mu late enough records. Al ter na tive meth ods not re quir ing a ref er ence site have been de vel oped re cently. One of them in volves di vid ing the hor i zon tal-com po nent shear-wave spec tra at each site by the ver ti cal com po nent spec tra ob served si mul ta neously at that site (Lermo and Chavez-Gar cia 1993). The H/V tech nique, as has been shown re cently by many au thors (e.g., Field and Ja cob 1995; Theodulidis and Bard 1995; Theodulidis et al. 1996; Bonilla et al. 1997; Cas tro et al. 1997; Chen and Atkinson 2002; Huang et al. 2002; Siddiqqi and Atkinson 2002; Mucciarelli et al. 2003; Sokolov et al. 2005a, 2007), pro vides re sults that are con sis tent with the gen eral geo - logical con di tions of the re cord ing sites, i.e., show ing the fundamental frequency of site amplification. The re sults of Fig. 1. Dis tri bu tion of epi centres of earth quakes used in this study (open cir cles - shal low events, grey cir cles - deep events) and lo ca tion of the con sid ered sta tions (tri an gles) within the Tai pei ba sin. The depth of Qua ter nary sed i ments is also shown in gra da tions of grey.

3 Analysis of Taipei Basin Response Using Empirical Data 689

4 690 Sokolov et al. include ef fects of source rup ture pe cu liar i ties and in ho - mogeneous prop a ga tion path. On the other hand, when us ing a large enough num ber of events var ied by mag ni tude, source depth and az i muth, the ef fects of fo cal mech a nism and directivity are ex pected to be av er aged out. The ap - proach was ap plied to eval u ate the char ac ter is tics of spec tral am pli fi ca tion for (1) par tic u lar sites in Tai pei ba sin (Sokolov et al. 2000, 2001; Sokolov and Jean 2002; ) and (2) gen er al - ised site con di tions (classes) in Tai wan (Sokolov et al. 2003, 2004, 2007). The spec i fi ca tion of the very hard rock spec trum is of par tic u lar sig nif i cance in the ap proach. The ground mo tion da ta base col lected in Tai wan pro vides an op por tu nity to study both re gional source scal ing (e.g., Tsai 1997) and at - ten u a tion mod els (e.g., Wang 1988, 1993), as well as lo cal site re sponse upon earth quake ground mo tion. The mod els of Fou rier am pli tude spec trum (FAS) for typ i cal site con di - tions were an a lyzed by Sokolov et al. (2000, 2003, 2004). Re cently, Sokolov et al. (2005b, 2006) re-eval u ated the FAS mod els for var i ous source zones in Tai wan us ing a large num ber of ac cel er a tion re cords ob tained from earth quakes that oc curred dur ing The an a lyzed earth quake source zones are the fol low ing. The zone ST con tains shal - low (hypocentral depth less than km) earth quakes that oc curred within Tai wan Is land. The zone SO rep re sents shal low earth quakes that oc curred to the east of the is land un der the ocean. The zone DT con tains re cords from deep (hypocentral depth more than km) earth quakes. The pa ram e ters of the re gional FAS model are sum ma rized in Table 2 (see also Sokolov et al. 2006). The value of seis mic mo ment is es ti mated from re gional re la tion ships be tween seis mic mo ment and lo cal mag ni tude. 3. IN PUT DATA AND PRO CESS ING The data were re corded by the Tai wan Strong Mo tion seis mic net work im ple mented by the Seis mo log i cal Ob ser - va tion Cen ter of the Cen tral Weather Bu reau (CWB), Tai - wan, ROC. More than 650 dig i tal free field strong-mo tion in stru ments are in stalled in this net work. Each sta tion is equipped with one strong-mo tion in stru ment a forcebalanced three-component accelerometer. Most instruments (Geotech and Terra Tech in stru ments) have 16-bit and some in stru ments (Kinemetrics) have 24-bit res o lu tion. These in -

5 Anal y sis of Tai pei Basin Response Using Empirical Data 691 stru ments are ca pa ble of re cord ing high-res o lu tion ground motion within 2 g and with a pre-event and a post-event mem ory. All sta tions have AC power and when the power sys tem is shut down by an earth quake or other prob lem, the re cord ing sys tem can still op er ate by the in ter nal DC power for about 4 days. Fourier amplitude spectra were calculated, using 10% co sine win dow ta pered on both sides, for se lected parts (the stron gest shak ing) of the ac cel er a tion re cords (Fig. 2). The stron gest part of the shak ing con tains the S-wave por tion and, in some cases, sur face waves from large dis tant earth - quakes and ad di tional waves gen er ated within the ba sin. For se lec tion of the part of the re cord to be pro cessed we used a win dow con tain ing 90% of to tal en ergy us ing the in te gral t 2 I( t ) a ( t ) dt, where t s is the time of S wave ar rival. In t ts some case, where the length of the re cord is not long enough, ex pert de ci sion was ap plied. The cal cu lated Fou rier spec tra were smoothed twice within 0.2 Hz run ning win dow. For the low-fre quency range, be sides the noise level, it is nec es sary to con sider the ef fect of trun ca tion in the time do main (Bath 1974). The trun ca tion leads in cor rectly to a flat spec trum for long pe ri ods. It is rec om mended to use a time-do main-win dow length at least equal to twice the lowest an a lyzed wave pe riod. Thus, the com bined ef fect of noise and trun ca tion lead to dif fer ent lower fre quency val ues for var i ous re cords. As a re sult, the num ber of an a lyzed spec tral am pli tudes in the low-fre quency range was smaller than that at the higher fre quen cies. The trun ca tion ef fect is significant especially for spectral analysis of records from small earth quakes, for which the sig nal du ra tion does not exceed 2-3 sec onds. For the whole data set, the low est frequencies var ied from 0.25 to 1.0 Hz de pend ing on the station and mag ni tude range. Fig. 2. Cal cu la tion of the VHR spec tral ra tio (mag ni tude M, fo cal depth H, hypocentral dis tance R).

6 692 Sokolov et al. Ref er ence VHR spec tra were cal cu lated us ing the mo d - els de scribed above (Ta ble 2). Es ti ma tions of seis mic mo - ment (M 0 ) and stress pa ram e ter ( ) are not avail able for al - most all of the se lected earth quakes. When us ing the em pir i - cal relationship between seismic moment and local magni - tude, it is nec es sary to bear in mind the pos si ble scat ter of the M 0 values. Ideally, the observed and theoretical spectra should fit each other at low fre quen cies where the in flu ence of lo cal ge ol ogy is be lieved to be neg li gi ble. The in flu ence may be very small for the case of rock sites or sites with a thin layer of sed i ments over rigid bed rock. Such a case may be con sid ered as a ref er ence site when the proper val ues of earth quake source pa ram e ters are se lected to be used in the FAS model. It has been found in our pre vi ous study (Sokolov et al. 2000) that sta tion TAP053 sat is fies the cri - teria to be con sid ered as a ref er ence site. The site re sponse at the station is characterized by narrow-band amplification at fre quen cies around 4 Hz. Fig ure 3 shows ex am ples of the ob served and mod elled spec tra for sta tion TAP053. Sim i - larly, sta tion TAP071 with small-am pli tude site am pli fi ca - tion is lo cated out side the ba sin that min i mizes pos si ble in - flu ence of rel a tively long-pe riod waves trapped within the ba sin. 4. RE SULTS AND DIS CUS SION Ide ally, for the case of lin ear soil re sponse upon earth - quake mo tion, site am pli fi ca tion func tions or the ra tios be - tween the ob served and the mod elled spec tra should not de - pend on earth quake mag ni tude. On the other hand, site ef fect should be in de pend ent on the ap plied source mod els. There - fore, if the proper spec tral mod els are used for var i ous mag - nitudes, the characteristics (averaged amplitudes and shape) of the ra tios be tween the ob served and the mod elled spec tra should be ap prox i mately the same for dif fer ent earth quakes, at least for those of sim i lar dis tance and az i muth. The cha - racteristics of the VHR ra tio eval u ated for sta tions TAP073 and TAP071 are shown in Fig. 4. In gen eral, the ra tios ob - tained us ing re cords from the deep (DVHR) and shal low (SVHR) earth quakes ex hibit a sim i lar na ture. The SVHR ra - tios are char ac ter ized by slightly higher am pli tudes at fre - quen cies less than 2-3 Hz than the DVHR ra tios, which may be ex plained by the pres ence of sur face waves gen er ated by shal low and dis tant earth quakes. Let us ana lyse the VHR ra tios cal cu lated for sta tions lo cated within the ba sin. The sta tions near the ba sin edge (Fig. 4) with rel a tively shal low de pos its (e.g., TAP002, Fig. 3. Sta tion TAP053, com par i son of the spec tra of real re cords from par tic u lar earth quakes (mag ni tude M, depth H, hypocentral dis tance R) and the mod elled spec tra (VHR model).

7 Analysis of Taipei Basin Response Using Empirical Data 693 Fig. 4. Characteristics of the VHR spectral ratios (mean amplitude values and 1 standard deviation limits) evaluated for stations located outside the Taipei basin and near the basin edge. The depth of Quaternary sediments is shown in gradations of grey colour. TAP009, TAP022, TAP027, and TAP093) reveal the same character in terms of the ratios, as the stations located outside the basin, namely: the SVHR and the DVHR ratios show approximately the same amplitudes in the whole considered frequency range. For the central part of the basin (Fig. 5), the difference between the SVHR and DVHR ratios at low frequencies becomes much larger than that for the basin edge. Figure 6 shows the frequency-dependent averaged ratio between the SVHR and DVHR amplitudes calculated for the considered sets of stations located (a) near the basin edge and outside the basin and (b) in the central part of the basin. We assume that the difference between the SVHR and DVHR ratios at low frequencies most likely reflects the influence of additional waves generated within the basin. However, to check the suggestion we have to answer the following question: in what extent could the VHR curves reflect real site response? We used a simple 1-D technique to calculate theoretical spectral amplification of a multilayered soil column overlying a rigid half-space for SH-

8 694 Sokolov et al. and SV-waves approaching the bottom of the soil with arbitrary angles of incidence. The subsurface geology of the Taipei basin has been established by boring, and electrical and seismic prospecting (Lee et al. 1978; Fei and Lai 1994; Wang et al. 1994, 1996, 2004; Wang and Lee 2002). The geological structure inside the basin consists of Quaternary layers above tertiary base rock. The stratigraphic formations of the Quaternary layers are, in descending order, surface soil, the Sungshan For- mation, the Chingmei Formation, and the Hsinchuang Formation. The Sungshan Formation is composed mainly of alternating beds of silty clay and silty sand, and covers almost the whole Taipei basin. The Chingmei Formation is a fanshaped body of conglomerate deposits. The Hsinchuang Formation, recently renamed into the Wuku and Panchiao Formations, consists of bluish gray and clayey sand with some conglomerate beds. The available data, which include the digital models of thickness of the whole Quartenary de- Fig. 5 Characteristics of the VHR spectral ratios (mean amplitude values and 1 standard deviation limits) evaluated for stations located within the Taipei basin and near the basin edge. The depth of Quaternary sediments is shown in gradations of grey.

9 Anal y sis of Tai pei Basin Response Using Empirical Data 695 Fig. 6. Ra tios be tween the VHR data for shal low and deep earth quakes (SVHR/DVHR) av er aged for the con sid ered sta tions lo cated near the ba sin edge (curve 2) and within the ba sin (curve 1). pos its and of the Sungshan For ma tion, al low con struct ing nu mer i cal mod els of soil col umn for sev eral sites and cal cu - lating the o ret i cal am pli fi ca tion (Wen and Peng 1998a, b; Sokolov et al. 2000; Fletcher and Wen 2005). The qual ity fac tor Q( f ) that rep re sents the damp ing in the soil was eval u ated by Wen and Peng (1998b). De pend ing on the depth in ter val, the Q-model may be de scribed as fol - lows: 0-30 m, Q( f ) = 3.6 f 0.96 ; m, Q( f ) = 7.2 f 0.99 ; m, Q( f ) = 10 f 1.17 ; m, Q( f ) = 40 f When con struct ing the nu mer i cal mod els of soil col umns, we assigned every Q-model to particular stratigraphic formation as fol lows: the Sungshan For ma tion, up per part - Q( f ) = 3.6 f 0.96, lower part - Q( f ) = 10 f 1.17 ; the Chingmei For ma tion - Q( f ) = 40 f A low-damp ing Q-model [Q( f ) = 200 f 1.0 ] was as - signed to the the Wuku and Panchiao For ma tions. We have to note that the geotechnical prop er ties of the Qua ter nary de pos its in the Tai pei ba sin have still not been stud ied in de tail. A rel a tively low Q value, as com pared with the av er aged data, is ex pected for high crack den sity and fluid-sat u rated soil in the Tai wan re gion (Shieh 1992). Am - pli tudes of ground mo tion am pli fi ca tion are very sen si tive to the de gree of damp ing (qual ity fac tor). There fore, for com - par i son we used two vari ants of the Q-model. In the first one (Q1-model), the qual ity fac tors were taken as those pro vided by Wen and Peng (1998b). The higher, grad u ally in creas ing with depth, val ues of the qual ity fac tor were ac cepted in the sec ond model (Q2-model). Ta ble 3 lists pa ram e ters of the soil models for particular sites. We calculated the theoretical spectral amplification for S-wave as sum ing the bot tom of the ba sin as a rigid halfspace. The ter tiary base ment could not be con sid ered as very hard rock as used in our spec tral model. There fore, when com par ing the VHR ra tios and re sults of the the ore - tical mod el ing, the gen er al ized hard-rock am pli fi ca tion (see Sokolov et al. 2007) was added to the 1D mod el ing. Of course, the theoretical models of layered deposits in many cases can pro vide only a rough ap prox i ma tion to re al - ity. For ex am ple, the soil lay ers can be char ac ter ized, as a rule, by a grad ual change of shear-wave ve loc ity with depth. This phe nom e non causes a broad band am pli fi ca tion. The theoretical model describes the layers by uniform velocities, which re sults in sep a rate res o nance peaks. We do not know ex actly the geotechnical prop er ties and thick ness of the con - sid ered strati graphic for ma tions in ev ery con sid ered point. This may cause dis crep an cies in the am pli tude and the lo - cation of par tic u lar am pli fi ca tion peaks be tween the em pir - i cal and the mod eled spec tral ra tios. De spite the ap prox i mate char ac ter of the 1D model, the re sults of the mod el ing show that in al most all con sid ered cases (30 points or Tai pei net work sta tions, ex cept sta tions TAP003 and TAP016) the the o ret i cal spec tral ra tios show a good agree ment with the VHR data ob tained from re cords of deep earth quakes (Fig. 7). In gen eral, the site am pli fi ca tion char ac ter is tics for the ar eas lo cated near the ba sin edge (e.g., TAP002, TAP009, TAP022, TAP027, TAP028, TAP030, TAP033, TAP043, TAP048, TAP053, and TAP093) re veal one or two sep a rate peaks within rel a tively nar row fre qu - ency bands, reflecting influence of particular layers. The areas with thick sed i ments are char ac ter ized by broad band amplification. The com par i son of em pir i cal and the o ret i cal data may also al low a proper se lec tion of geotechnical pro - perties for fur ther, more de tailed, mod el ing. To analyse site amplification characteristics obtained from re cords of shal low earth quakes we ap plied the fol low - ing scheme. The FAS am pli tudes for the re cords ob tained out - side the ba sin from deep [A OUTD ( f )] or shal low [A OUTS ( f )] earth quakes may be ex pressed as fol lows: A OUTD ( f ) = A VHR ( f ) AMPL D ( f ), or A OUTS ( f ) = A VHR ( f ) AMPL S ( f ) (1a) AMPL D ( f ) = SG ( f ), AMPL S ( f ) = SP ( f ) SG ( f ) (1b) where f is the fre quency, Hz; A VHR ( f ) is the spec trum at rock base ment; AMPL( f ) is the over all spec tral am pli fi ca tion; SP( f ) reflects influence of propagation path (surface waves); and SG ( f ) is the am pli fi ca tion caused by site ge ol ogy. The FAS am pli tudes for the re cords from shal low earth quakes ob tained in side the ba sin A INBS ( f ) (be sides the in flu ence of prop a ga tion path and lo cal ge ol ogy) may re flect in flu ence of the ad di tional waves gen er ated within the ba sin (ba sin fac - tor) SB( f ) and the ex pres sion may be writ ten as: A INBS ( f ) = A VHR ( f ) SP( f ) SG ( f ) SB( f ) (2) Let us, for ex am ple, con sider a pair of sta tions that are lo cated out side (e.g., TAP053) and within (e.g., TAP020) the ba sin (see Figs. 4, 5), which re corded a large num bers of earth quakes (Ta ble 1). The VHR ra tio av er aged from the avail able set of deep earth quakes (VHR D ) can be in ter preted as the in flu ence of lo cal ge ol ogy, or the SG( f ) term, for both stations, i.e., VHR D ( f ) = AMPL D ( f ) = SG( f ). The ra tio

10 696 Sokolov et al. SDR( f ) between the averaged VHR ratio for shallow earthquakes (VHRS) and the averaged VHR ratio for deep earthquakes (VHRD) for station TAP053 (reference station located outside the basin) may be considered as describing the influence of propagation path, or the SP( f ) term, i.e.,: (3) = SP( f ) SBTAP020 ( f ). Of course, in this case the function SDRTAP020 ( f ) reflects only the generalized characteristics obtained from many earthquakes occurring at different locations. However, when comparing the data at both stations from the same set of shallow earthquakes, we can assume that generalized characteristics of the additional waves generated within the basin, or the SBTAP020 ( f ) term, may be evaluated as: SBTAP 020 ( f ) = SDRTAP 020 ( f ) SDRTAP 053 ( f ) The ratio for stations that are located inside the basin, e.g., TAP020, may be considered as a description of the joint influence of propagation path and the basin, or SDRTAP020 ( f ) (4) However, station TAP053 is characterized by a highamplitude amplification at frequencies between 2-5 Hz

11 Anal y sis of Tai pei Basin Response Using Empirical Data 697 Fig. 7. Com par i son of the VHR spec tral ra tios (av er age val ues) cal cu lated us ing the data from deep and shal low earth quakes and the re sults of 1D mod el ing (the Q1- and Q2-mod els). (Fig. 4). The high vari abil ity of the VHR ra tios within this fre quency range could cause un sta ble val ues of the SDRfactor evaluated form different sets of earthquakes. There - fore, for anal y sis of the in flu ence of prop a ga tion path (SPterm) and the ba sin ef fect (SB-term), we also used the data from sta tion TAP071 with a low-am pli tude broad band am - plification (Fig. 4). Fig ure 8a shows an ex am ple of the gen er al ized char ac - teristics of the SP ( f ) term (in flu ence of prop a ga tion path) for sta tions TAP053 and TAP071 av er ag ing dif fer ent sets of the data in clud ing: (a) all shal low earth quakes; (b) the large mag ni tude (M > 6.0) earth quakes (see also Fig. 1). The in -

12 698 Sokolov et al. flu ence of prop a ga tion path, in es sence, is a fre quency-de - pend ent pa ram e ter and it also de pends on mag ni tude of earth - quakes. The com bined ef fect of the prop a ga tion path [SP ( f ) term] and the ba sin [SB ( f ) term] is shown at Fig. 8b for two sta tions lo cated in side the ba sin, namely: TAP017 and TAP020. Fig ure 8c shows char ac ter is tics of the ba sin ef fect, or the SB( f ) term. Again, the ba sin ef fect is a fre quencydepen dent pa ram e ter that de pends clearly on sta tion lo ca - tion in side the ba sin. Sta tion TAP017, which is lo cated in the west ern part of the ba sin where the sed i ments thick ness is the great est (Fig. 5), re veals a much higher ba sin-fac tor am - pli fi ca tion at low fre quen cies (less than Hz) than the sta tion TAP020, which is lo cated in the east ern part of the ba sin where thin sed i ments ex ist. The av er age-am pli tude fre quency-de pend ent ba sin ef - fect [SB( f ) term], which is eval u ated for a few par tic u lar sta tions within the ba sin, is shown in Fig. 9. It seems that it is pos si ble to di vide the ba sin into at least three zones show ing: (a) (b) (c) Fig. 8. Frequency-dependent characteristics of site am pli fi ca tion (path and ba sin ef fects, see text) av er aged for var i ous sta tions and earth - quakes. Fig. 9. Char ac ter is tics of the ba sin ef fect for par tic u lar sta tions av er aged us ing the data from all earth quakes re corded at ev ery sta tion.

13 Anal y sis of Tai pei Basin Response Using Empirical Data 699 (a) almost negligible amplification due to the basin effect (near the ba sin edge); (b) a rel a tively high-am pli tude lowfre quency am pli fi ca tion (deep est part of the basin); and (c) a transition zone. The char ac ter is tics of the site re sponse may be eval u - ated for var i ous sets of shal low earth quakes (e.g., large and small, nearby and dis tant, etc.). They may be used jointly with re gional source scal ing and at ten u a tion mod els, char ac - ter is tics of prop a ga tion path ef fect and site am pli fi ca tion due to local geology (1D effect) for probabilistic seismic micro - zonation of the ba sin when many pos si ble earth quakes lo - cated at dif fer ent dis tances and az i muths are con sid ered. Particular events, however, may reveal some peculiarities in fre quency con tent of ground mo tions (Figs. 10, 11). For exam ple, the data from the shal low event of 31 March 2002 (M 6.8, depth 14 km, also known as the Hualien 331 earth - quake) show rel a tively high am pli tudes of am pli fi ca tion as com pared with the av er age val ues at low fre quency range. The data from an other large, dis tant, and shal low event, 1 No vem ber 1999 (M 6.9, depth 30 km) are char ac ter ized by relatively low amplitudes of amplification as compared with the av er age val ues at low fre quen cies. Even deep earth - Fig. 10. Com par i son of VHR ra tios cal cu lated for par tic u lar earth quakes of var i ous mag ni tudes M and depths H (km) (red lines) with the gen er al ized charac ter is tic of the ra tios (mean am pli tude val ues and 1 stan dard deviation limits).

14 700 Sokolov et al. 1D-mod els based on the avail able geo log i cal and geo - technical data. (2) The data from shal low earth quakes show in flu ence of: (a) sur face waves gen er ated by dis tant sources to the ba - sin; and (b) rel a tively low-fre quency (< 1-2 Hz) waves gen er ated within the ba sin. (3) Some shal low earth quakes pro duce ex tremely high am - pli fi ca tion at fre quen cies Hz within the ba sin that may be dan ger ous for high-rise build ings and high way bridges. Fig. 11. Lo ca tion of large earth quakes (see leg end in Fig. 1) that re - vealed pe cu liar i ties of the Tai pei ba sin re sponse in low-fre quency range. 1 - the earth quake did not re veal un usual low-fre quency am - plificat ion; 2 - events caused high-am pli tude am pli fi ca tion at low frequencies. quakes, for ex am ple the event of 24 March 1995 (M 5.6, depth 76 km), may show sig nif i cant low-fre quency ba sin effect. It has been shown re cently (Lee et al. 2009), that deep earth quakes lo cated south east of the Tai pei ba sin, such as the event of 24 March 1995, may pro duce high-am pli tude low-fre quency am pli fi ca tion in the north west ern part of the ba sin. Be sides the lo ca tion of the events men tioned above, Fig. 11 shows the lo ca tions of a few large shal low earth - quakes (sym bols N 2) that oc curred south east of the ba sin that caused high-am pli tude low-fre quency am pli fi ca tion within Tai pei ba sin. It seems that 2D and 3D sim u la tion is nec es sary to model seis mic shak ing in the Tai pei ba sin when par tic u larly large events are con sid ered (e.g., so-called worst-case or dominant earthquakes). 5. CONCLUSION We stud ied site am pli fi ca tion of the Tai pei ba sin us ing the avail able ground-mo tion da ta base and re cently deve - loped re gional spec tral mod els (Sokolov et al. 2006). The fol low ing con clu sions may be drawn from the anal y sis. (1) The characteristics of frequency-dependent site response for par tic u lar lo ca tions or sites (sta tions of the TSMIP net work) in the Tai pei ba sin, which were ob tained us ing re cords of deep earth quakes (depth > 35 km), show good agreement with the theoretical ratios calculated using the The re sults may be used in proba bil is tic seis mic micro - zonation of the Tai pei ba sin many earth quakes lo cated at var i ous dis tances are con sid ered (Sokolov and Chernov 2001; Sokolov et al. 2001). We have to note that fre quencyde pend ent am pli fi ca tion func tions were ob tained in this study within a lim ited fre quency range from 0.3 to 12 Hz. The lower-fre quency ground-mo tion char ac ter is tics may be stud ied us ing nu mer i cal 2D and 3D mod el ing. For the pre - diction of seismic influence from particularly large earth - quakes, a spe cial pro ce dure com bin ing long-pe riod wave - form mod el ing and sto chas tic sim u la tion of high-fre quency wave forms should be used. Ac knowl edge ments The au thors would like to thank Jer-Ming Chiu for his thought ful com ments and sug ges - tions. The com ments from an anon y mous re viewer are also grate fully ac knowl edged. This work was spon sored by National Sci ence Coun cil, ROC (grant NSC M ) and Deut sche Forschungsgemeinschaft (DFG), Ger many, (pro ject WE 1394/13-1). REFERENCES An der son, J. and S. Hough, 1984: A model for the shape of the Fou rier am pli tude spec trum of ac cel er a tion at high fre - quen cies. Bull. Seismol. Soc. Am., 74, Bard, P. Y., 1995: Ef fects of sur face ge ol ogy on ground mo tion: Re cent re sults and re main ing is sues. Proc. of 10th Eu ro - pean Con fer ence on Earth quake En gi neer ing, Balkema, Rot ter dam, Bath, M., 1974: Spec tral Anal y sis in Geo phys ics, Elsevier Sci - en tific Pub lish ing Com pany, Am ster dam, 563 pp. Beresnev, I. A., A. M. Nightengale, and W. J. Silva, 2002: Properties of ver ti cal ground mo tions. Bull. Seismol. Soc. Am., 92, , doi: / [Link] Bonilla, L. F., J. H. Steidl, G. T. Lindley, A. G. Tumarkin, and R. J. Archuleta, 1997: Site am pli fi ca tion in the San Fernando val ley, Cal i for nia: Vari abil ity of site-ef fect es ti ma tion us - ing the S-wave, coda and H/V meth ods. Bull. Seismol. Soc. Am., 87, Borcherdt, R., 1970: Ef fect of lo cal ge ol ogy on ground mo tion near San Fran cisco Bay. Bull. Seismol. Soc. Am., 60, Cas tro, R. R., M. Mucciarelli, F. Pacor, and C. Petrungaro,

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