Simulation of Long-Period Ground Motion near a Large Earthquake

Transcription

1 Bulletin f the Seismlgical Sciety f America, Vl. 87, N. 1, pp , February 1997 Simulatin f Lng-Perid Grund Mtin near a Large Earthquake by Minru Take and Hir Kanamri Abstract We estimated the pssible range f lng-perid grund mtin fr sites lcated n a sft sedimentary basin in the immediate vicinity f a large earthquake. Since many large cities in the wrld (e.g., Ls Angeles, San Francisc, and Tky) where many large structures have been recently cnstructed are lcated in this type f envirnment, a better understanding f lng-perid grund mtin is becming increasingly imprtant. Our bjective is t estimate the pssible range f lng-perid grund mtin, rather than grund mtin fr a specific fault mdel. We cmputed grund-mtin time series and pseud-velcity respnse spectra (PVS) fr mre than 5, mdels fr the 1923 Kant, Japan, earthquake (M w = 7.9) using 18 slip distributins, eight rupture gemetry, and rupture velcities ranging frm 1.5 t 3. krn/sec. Tw seismgrams recrded in Tky during the 1923 Kant earthquake are used fr cmparisn. The respnse spectra cmputed using seismlgically reasnable sets f surce parameters fr the 1923 Kant earthquake vary by mre than an rder f magnitude. At perids f 1 t 13 sec, they range frm 25 t 17 cm/sec in Tky. Fr sme cmbinatins f mdel parameters, the respnse spectra exhibit peaks in the range f 1 t 13 sec. Many f the cmputed respnse spectra have peaks at perids lnger than 1 sec, which is cnsiderably lnger than the dminant perid (6 t 8 sec) estimated frm studies f small earthquakes and micrtremr measurements. Thus, the dminant perid f the subsurface structure determined lcally may nt be representative f the dminant perid f grund mtin frm a nearby large earthquake, which is cntrlled by rupture directivity and surce depth. We perfrmed a similar simulatin fr a hypthetical M w = 7.5 earthquake lcated beneath the Ls Angeles basin. Fr a site just abve the center f the fault, the grund-mtin spectral amplitude at a perid f 1 sec can vary frm 5 t 35 cm/ sec. This range, thugh very large, is what is expected fr a seismlgically plausible range f surce parameters. ntrductin The ever-increasing cnstructin f large-scale structures such as high-rise buildings, il tanks, suspensin bridges, and ffshre drilling platfrms requires accurate estimatin f lng-perid (5 t 2 sec) grund mtins, especially thse that culd ccur in sft sediment-filled basins r landfills where significant amplificatin culd ccur. This prblem is especially imprtant because many majr urban centers in the wrld are lcated in such envirnments (e.g., Ls Angeles, San Francisc, and Tky). Sft subsurface sediments play a majr rle in gverning the excitatin and prpagatin f such grund mtins near the rupture zne f a large earthquake. With the advent f super cmputers and numerical techniques, significant advancements have been made recently in estimatin f path effects (e.g., Frankel and Vidale, 1992; Frankel, 1993; Olsen et al., 1995). Then, t estimate the actual grund mtin, we need t cnvlve these path effects and site respnse with the surce prcess. n this article, we address nly the questin f variability f near-surce grund mtin due t variatins f the surce parameters. Our results will eventually have t be cnvlved with the effects f 3D structures. Althugh it wuld be pssible t numerically simulate these mtins fr a given earthquake mdel, it is very difficult t verify the simulatin results because f the lack f near-surce grund-mtin data frm a very large earthquake (M = 8) recrded n such sft structures. Cnstructin regulatins t assure structural integrity against earthquakes are traditinally based n the standard engineering practices that include the use f spectral peaks determined by analysis f strng-mtin data frm earthquakes, cmputatin f 1D respnse, r ther related methds. n Japan, the design prcess fr high-rise buildings includes the standard regulatry guidelines requiring a 14

2 Simulatin f Lng-Perid Grund Mtin near a Large Earthquake 141 numerical analysis f its dynamic respnse t a grund-mtin recrd cnstructed frm sme typical bserved strngmtin seismgrams (e.g., the E1 Centr recrd f the 194 mperial Valley, Califrnia, earthquake and the Taft recrd f the 1952 Kern Cunty, Califrnia, earthquake) and ther lcal earthquakes. T use these recrds fr respnse studies, the maximum velcity amplitudes are nrmalized t 5 r 25 cm/sec. Unfrtunately, nne f these recrds measured the mtin n sft structures at a lcatin directly abve a very large, M , earthquake. t is clearly desirable t emply mre suitable seismgrams fr such vital design evaluatin purpses. n this regard, three lw-gain seismgrams recrded at Hng, Tky, during the 1923 Kant (Tky) earthquake in Japan (Ms = 7.9 t 8.2, Mw = 7.9) are f particular interest. These seismgrams were recrded with three different types f seismgraphs, i.e., Omri strng mtin, mamura strng mtin, and Ewing seismgraphs (Fig. 1). These seismgraphs were lcated clse t each ther n campus f the University f Tky. These recrds are unique because they measured strng grund mtins at a site n thick, sft sedimentary layers frming the Kant Plain, and the site is nly 5 km nrtheast f the hypcenter. n view f the engineering imprtance f near-surce lng-perid grund mtin, and f the almst cmplete lack f such recrds frm a large earthquake, we perfrm a series f numerical simulatins t place bunds n the amplitude and spectrum f near-surce grund mtin frm a very large earthquake expected fr sites n a sft sediment-filled basin. The scpe f this study is limited t very lng-perid (3 sec r lnger) grund mtin. Althugh tw specific lcatins, Tky and Ls Angeles, are cnsidered, ur bjective is t address a generic questin n the pssible range f lng-perid grund mtins. Since this study is an extensin f Take and Kanamri (1992) (hereafter abbreviated as TK92), there is inevitably sme verlap between this article and that f TK92. Seismgrams f the 1923 Kant Earthquake The mamura seismgram (E-W cmpnent) shwn in Figure 1 a was severely verdriven at abut 16 sec after the nset. Apparently, the seismgraph stylus hit the damper, which prevented the seismgraph frm recrding the principal part f grund mtin fr abut 3 sec. Since the extent f clipping is very excessive, we feel that it is difficult t estimate the actual grund mtin frm this recrd. Hwever, Ykta et al. (1989) made an extensive effrt t recnstruct the mtin f the stylus and estimated the grund mtin. Figures lb and lc shw the recnstructed seismgram and its respnse spectrum. The spectral amplitudes estimated frm this seismgram are mre r less in agreement with the cmmn sense view f strng grund mtins frm very large earthquakes. n cntrast, the N-E cmpnent f the Ewing seismgraph recrded the grund mtin almst n-scale. Hwever, the recrded grund mtin exhibits al- mst harmnic mtin with a perid f abut 13 sec. Since the natural perid f the pendulum is abut 6 sec, this recrd with 13-sec harmnic scillatin is ften cnsidered very peculiar. Take and Kanamri (1992) examined this recrd in detail and cncluded that the resnance f the instrument was prbably suppressed by increased slid frictin between the stylus and the recrding glass plate, and the verall grund mtin was crrectly recrded. The details are given in TK92. The trace shwn in Figure lb is taken frm Mrika (198), and its respnse spectrum is shwn in Figure lc. The pseud-velcity respnse spectrum (PVS) is used thrughut this article. The maximum peak-t-peak grundmtin displacement n the NE-SW cmpnent is abut 9 cm with a perid f 13 sec (Mrika, 1976, 198; Mrika and Yamada, 1986). The NW-SE cmpnent recrded the grund mtin with cnsiderably larger amplitudes and was clipped mre severely than the NE-SW cmpnent. t appears that because f this large amplitude and smewhat unusual character, this recrd has been discunted by many seismlgists and engineers. t ften has been thught that the instrument must have malfunctined and registered the peculiar harmnic mtin. Hwever, TK92 demnstrated that the large harmnic mtin is nt necessarily unrealistic, and a cmbinatin f a large earthquake, a sft sedimentfilled structure, and rupture directivity culd indeed prduce such grund mtin. t is surprising that tw seismgrams recrded at the same lcatin shw significantly different amplitudes and spectra. Althugh the later part f the Ewing recrd culd have been distrted because f pssible mechanical malfunctining, we believe that there must have been displacements large enugh t drive the Ewing seismgraph almst t its limit, at least in the beginning. The details f the spectrum cmputed frm the Ewing seismgram may nt be very reliable, but the maximum amplitude shuld be clse t what actually ccurred. On the ther hand, we feel that the amplitude restratin f the mamura seismgram is subject t large uncertainty because f the excessive clipping, and the spectrum may be clse t the lwer bund f the grundmtin spectrum. Cnsidering all the difficulties in the interpretatin f these seismgrams, we d nt attempt t mdel specifically ne f these recrds. Our apprach is, instead, t explre the pssible range f grund mtins expected fr sets f seismlgically reasnable fault parameters and t evaluate the results in the cntext f the bserved recrds with the abve uncertainties in mind. Simulatin f the 1923 Kant Earthquake Our bjective is t determine the range f grund-mtin spectral amplitudes fr a large number f fault mdels that are cnsidered realistic fr a given area. This apprach is desirable because it is nt pssible t make specific predictins f the magnitude, rupture pattern, and directivity f future earthquakes, yet these factrs, especially directivity, have a prfund influence n the strength and nature f

3 142 M. Take and H. Kanamri (a) 3cm September 1 * 1923 (Hng)... ~ ' 251 Tky cm S t v r r -91 -~, i, 6 12 sec (1) Ewing seismgram D, U (2) mamura seismgram 1 minute i (3) Omri seismgram (b) cm 9 MD -~'~ v%~'~"-xjn- cm/s 6 MV (C) 5 1 see 2...,...,... "~ 16 1) > , ,....,.....,....,'7~---i, Figure 1. (a) Three lw-gain seismgrams f the 1923 Kant earthquake recrded in Hng, Tky, by the Ewing (natural perid T = 6. sec; damping cnstant h =.45; magnificatin V = 1.), the mamura (T O = 1. sec, h =.17, V = 2.), and the Omri (T = 4. sec, n damper, V = 1.5) seismgraphs. The NE-SW cmpnent f the Ewing seismgram traced by Mrika (198) is shwn just beneath the riginal trace. The slightly clipped prtins were interplated by Mrika (198). (b) Grundmtin displacement and velcity estimated frm the SW- NE cmpnent f the Ewing seismgram by Mrika and Yamada (1986) (ED: displacement; EV: velcity), and thse frm the E-W cmpnent f the mamura seismgram by Ykta et al. (1989) (MD: displacement; MV: velcity) after recreating clipped prtins. (c) Crrespnding velcity respnse spectra (h =.5) are als shwn. The shrt-dtted and lng-dtted curves shw the respnse spectrum calculated frm the Ewing and mamura seismgrams, respectively. The slid curve is a reference spectrum btained by cmbining these tw spectra (TK92).

4 Simulatin f Lng-Perid Grund Mtin near a Large Earthquake 143 strng grund mtin t be experienced near the rupture zne (Wald et al., 1991; de et al., 1996; Wald, 1996). t is therefre imprtant t knw the pssible range f grund mtins, in additin t the grund mtin fr specific cases. The factrs that influence lng-perid grund mtin are slip distributin, directivity, rupture gemetry and velcity, and slip velcity r rise time f lcal dislcatin. We will vary these parameters fllwing the general scheme emplyed in TK92. Since the details are given in TK92, we will briefly explain the methd in the fllwing. Fault Mdel Figure 2 shws the tectnic features, the hrizntal prjectin f the fault plane, and the epicenter f the mainshck, as well as the majr aftershcks in the 24-hr perid after the mainshck (Kanamri, 1971). Several investigatrs have determined the fault mdel (e.g., Kanamri, 1971; And, 1971, 1974; Matsu'ura et al., 198; shibashi, 1985; Wald and Smerville, 1995). Kanamri (1971) examined the far-field bdy and surface waves and the initial prtin f the mamura seismgram (Kanamri, 1974) and btained the fllwing fault mdel: dip directin = N 2 ; dip angle = 34 ; fault area = 13 X 7 km2; right-lateral slip = 2 m; reverse dip slip =.65 m; rise time f dislcatin = 5 sec; and rupture velcity = 3 km/sec. Matsu'ura et al (198) subsequently analyzed the gedetic data and the mamura seismgram t determine the gemetry and size f the fault plane, rupture velcity, and rise time f dislcatin. They assumed tw fault planes with an east-west alignment fr which the ttal fault area is abut half that f Kanamri's. Hwever, as the slip n the west and east faults f the Matsu'ura et al. (198) mdel are, respectively, abut fur and tw times larger than the average slip f Kanamri's mdel, the ttal seismic mment f their mdel is abut the same as that f Kanamri's. Wald and Smerville (1995) analyzed gedetic and teleseismic data sets fr the 1923 Kant earthquake t determine bth tempral and spatial slip variatins. Their mdel suggests that the mst cncentrated slip is in the shallw central and western prtin f the fault and the maximum slip is apprximately 8 m. n this article, we use Kanamri's fault mdel as the basic mdel and investigate the effects f different surce parameters n simulated grund mtins by perturbing many f them frm their reference values. Althugh the hypcenter depth is prly cnstrained (Kanamri and Miyamura, 197; Matsu'ura et a., 198; Hamada, 1987), the epicenter is generally cnsidered t be near the western end f the fault plane (mamura, 1925; Kunitmi, 193; Kanamri and Miyamura, 197), which suggests that the verall rupture prpagatin initiated frm the suthwestern end f the fault plane and prpagated nrtheastward. Fault Gemetry and Slip Distributin The slip distributin n a fault plane is generally cmplex. T incrprate this cmplexity, we used the same methd as used in TK92. We divided the 7 13 km 2 fault plane (Fig. 2) int 3 3 km z subfaults. The amunt f slip n each subfault is varied s that the verall character f slip distributin is similar t that f the 1968 Tkachi- Oki earthquake (M w = 8.2) determined by Kikuchi and Fuka (1987). The slip n the subfaults is adjusted s that the average is 2.1 m, apprpriate fr the Kant earthquake. The Tkachi-Oki earthquake is f cmparable size and ccurred in a tectnic envirnment similar t that f the Kant earthquake. Since the spatial reslutin f slip distributin frm teleseismic analysis is abut 3 km, we assumed that the slip is unifrm ver a distance fl = 3 km. Since this distance, called the spatial reslutin parameter L, may als be an imprtant parameter, we will vary it ver a range frm 12 t 51 km. T test faults with different slip distributin, we perturbed the mdel described abve randmly and prduced a set f fault mdels with different slip distributins. Thus, this set f fault mdels, as a whle, exhibits a variety f slip patterns, ranging frm a peaked distributin t a mre unifrm ne. Slip Functin f Subfault The surce-time functin f each fault directly influences the verall grund mtin. Fr parameterizatin purpses, we use the surce-time functin, fit; t 1, t2), shwn in (a) 134*E 136"E 14'E (b),4, / 36 N 34"N 32'N 3"N 1km i i Figure 2. (a) Tectnic structure in suthwest Japan. An arrw indicates a slip directin f the Philippine Sea Plate. (b) Hrizntal prjectin f the fault plane f the 1923 Kant earthquake with the majr aftershcks immediately after the mainshck (Kanamri, 1971).

5 144 M. Take and H. Kanamri Figure 3. The time cnstants q and t2 crrespnd t the rupture time and rise time f each subfault, respectively. This surce-time functin crrespnds t the equivalent pintsurce-time functin fr a unilateral rupture within each subfault. The ith cmpnent f displacement prduced by all the subfanlts can be expressed as ui(t ) = ~ j=l N mj f gq(t -- ts2; r)f(z; tl, t2) dr, where N is the ttal number f subfaults, m 2 and t,2 are the seismic mment and nset time f the jth subfault, respectively, and gij(t; r) is the calculated Green's functin fr the ith cmpnent excited by the rupture n the jth subfault at t = r. The time cnstant t~j is given by (1) tsj = t~/12 r -Jr- trmd, (2) where vr is the rupture velcity, rj the distance frm the hypcenter t the nearest pint f jth subfault, and trma a randm value ranging frm -.1 r/vr t.2r~/v~. This term is included t add sme perturbatin t rupture prpagatin. Since the rupture velcity in the surce area is usually slwer than the lcal shear-wave velcity, we use a nnsymmetrical range fr t~d and perfrm many simulatins while randmly varying the slip and rupture patterns. This apprach is reasnable cnsidering the large variability f the slip distributin knwn t have ccurred fr many large earthquakes. T assess the effect f rupture prpagatin and directivity, we cnsidered eight different rupture prpagatin mdels (Fig. 4). '~ i( Surce-time functin tl t2 tl + t2 Figure 3. The surce-time functin used fr simulatin, t~ and t2 are the time fr the rupture frnt t prpagate thrugh a subfault and the rise time f dislcatin, respectively. This functin is quadratic in time fr the first part (between and fi) and the last part (between t2 and tl + t2), and linear in time fr the middle part (between t 1 and t2). ), Green's Functin We cmputed numerical Green' s functins fr a layered crustal structure using (1)reflectin-transmissin matrices (Kennett and Kerry, 1979) and (2) the discrete wavenumber methd (Buchn, 1981) in which an anelastic-layered crustal structure is used (Take, 1985). Table 1 summarizes the parameters describing the layered crustal structure fr the Kant Plain derived frm the fllwing surces: (1) an explsin study that determined the depth f bedrck beneath Tky (Research Grup n Undergrund Structure in Tky, 1989), (2) surface-wave grup velcity measurements fr the paths frm zu peninsula t Tky (Kud, 198), and (3) the velcity structure in the Sagami Bay (Yamanaka, 1991). 58. kin Tky. 13 km, ~; C1 Zq- u2 bi C2 u ] C5 C3 hypcenter C1-C5 are five circular rupture mdes which initiate frm different hypcenters. rupture starting lcatins fr bilateral and unilateral cases. statin / 39 kln fcal mechanism Figure 4. The hrizntal prjectin and the crss sectin f the fault plane f the 1923 Kant earthquake. Rupture prpagatin mdels used fr simulatin are als shwn, bi: bilateral rupture; ul and u2: unilateral ruputre; cl t c5: circular rupture. The hypcenter depths f the mdels el and c4, f the mdel c2, and f the mdels c3 and c5 are 38.3, 19.6, and.8 km, respectively. Small, pen circles indicate the hypcenters used fr the simulatins f circular rupture mdels. The fault parameters f the Kant earthquake btained by Kanamri (1971, 1974) are dip directin = N2 ; dip angle = 34, fault area = 13 7 km2; right-lateral slip = 2 m; reverse dip slip =.65 m; rise time f dislcatin = 5 sec; rupture velcity = 3 km/sec. The fcal mechanism used in this article is als shwn. The lcatin f Tky is indicated by a slid diamnd symbl. Table 1 Velcity Structure Used fr Simulatin f the Kant Earthquake v~ v~ p h G G

6 Simulatin f Lng-Perid Grund Mtin near a Large Earthquake ,... i... J... i... LD.58 Up,-, /] LD 4... i... i...,... ~ UD...' " " ' ' ~ ' ' ~.,, ~.. ~. 4,,,.,,,... i,, J... i ~ NS NS ,... ' " " "'~S'r~ " " " -~.25 lng-perid peak 4...,...,...,...,... - EW ,... j... i... r... ' EW ^i O... '... 1'... ' iiiiiii!!iiiiii!!!ii Figure 5. Representative Green's functins used fr the Kant earthquake and their pseud-velcity respnse spectra (h =.5). The hrizntal prjectin f the fault plane is shwn at the bttm f each clumn. The slid circle indicates the hypcenter, and the slid triangle indicates the lcatin f Tky. The time cnstants f the surcetime functin (Fig. 3) are t 1 = 1. sec and t2 = 2. sec. All wavefrms are grundmtin velcities in Tky calculated using the velcity structure listed in Table 1. The amplitude f the Green's functins in each clumn are nrmalized by a maximum amplitude f the three cmpnents, and the peak-t-peak amplitude f each recrd is listed abve each trace. 1,.., i... p... ilili!iiiiiiiiiii!!i] Representative Green's functins used fr the simulatins are shwn in Figure 5, where velcities f grund mtin in Tky are indicated alng with their velcity respnse spectra. These Green's functins give grund mtins excited by ne subfanlt whse size and slip are 3 3 km 2 and 2.1 m, respectively. Nte that when the pint surce is lcated in a shallw layer (depth < 1 km), shrt-perid surface waves with perids f several secnds are excited Lng-perid surface waves (1 t 13 sec) are excited when the surce lies frm 5 t 15 km deep, and spectral amplitudes at shrt perids are much smaller than that fr a shallw shrce. Sensitivity f Respnse Spectra t Fault Parameters Rupture Directivity and Slip Distributin We examined the effects f varying rupture directivity and slip distributin n the velcity respnse spectra (h =.5) in Tky. We varied the slip distributin n the fault plane as described in the previus sectin. Rupture directivity was varied using eight rupture prpagatin mdels (bi, ul, u2, cl, c2, c3, c4, and c5) shwn in Figure 4. We examined 18 different slip distributins fr each mdel. Figure 6 shws representative results fr velcity respnse spectra using fur rupture prpagatin mdels (bi, c2, c3, and c5). The rupture velcity (Vr) and the time cnstants tl and t2 are set at 3 km/sec, 1 sec, and 5 sec, respectively. Nte that a wide range f velcity respnse spectra are btained, even if the fault gemetry and seismic mment are fixed. A representative grund velcity fr the c5 rupture prpagatin mdel that gives the largest respnse spectrum is shwn in Figure 7. n general, a respnse spectrum having a sharp peak crrespnds t harmnic grund mtin, while a smth spectrum crrespnds t an impulsive wavefrm. Nte that the rupture mdel c5 has markedly different spectra, with a

7 146 M. Take and H. Kanamri (a) 1 6 ~ 18 ~12 ~"l. 8 > 6 4O 2O Pl.~! TO 3bi 1./5./3. UD h=.5 i i i TO 3bi 1./5./3. NS h=.5 /~'v%. / 'x /--,\ (b) TO 3C2 1./5./3. UO h=.5 2.,.. i i.... i ~ 14 ~ ~2, > TO 3c2 1./5./3. NS h=.5 2 ~.... i.... t.... i.... i ~14 ~12 ~ 1 4 2O ~-E TO 3hi 1./5./3. EW h=.5 i ! O 12 D. 'a TO 3c2 1./5./3. EW h= ) TO 3c3 1./5./3. UD h=.5 C i.... J.... i.... i ~ 14 ~ 12 8O TO 3c5 1./5./3. UD h=.5 (d) 2 ~.... i.... i.... i.... i ~14 12 d_ l ~ ~ 2O ~ '. ' TO 3c3 1./5./3. NS h=.5 J.... ~.... t ' '. [ ~ 14 6.,~, //" ~..~ 2, TO 3c5 1./5./3. NS h= i.... i.... i.... t ,, 16 /" --', ~1 ' _: 8 / > 6Q 4 /,~ / " ' ' ' ~ 12 1 ~ 8 > 6 4O 2 TO 3c3 1./5./3. EW 1=.5,t: "~C,." ~/'%"'.,,~/~ Q 18fl A 16 ~ 12 "~ 8Q 4O 2O TO 3c5 1./5./3. EW h: i.... i.... i.... i lo 15 2

8 Simulatin f Lng-Perid Grund Mtin near a Large Earthquake 147 cm/sec ~ O 4 Figure 6, Representative velcity respnse spectra (h =.5) fr the fur rupture prpagatin mdels (bi, c2, c3, and c5). The three cmpnents are shwn. Fr each rupture mdel, grund mtins are cmputed fr 18 different slip distributins. First tw characters in the label shwn abve each graph indicate the site: e.g., "TO" indicates Tky. Next tw characters shw the spatial reslutin parameter L: e.g., "3" means L = 3 km. The fifth and sixth characters dente the rupture prpagatin mdel, and the next three numbers are the tw time cnstants f the surce-time functin, t 1 and t2, and the rupture velcity, respectively. U p N Ea 1' 2' sec 2.1m W2N E2S N O Figure 7. A representative grund velcity fr the c5 rupture prpagatin mdel. The hrizntal prjectin f the fault plane with slip distributin is shwn at the bttm. The area f the circle indicates the amunt f slip at every 6 km n the fault plane. The scale fr slip is shwn abve the fault plane diagram. The slid circle indicates the hypcenter, and the slid triangle indicates the lcatin f Tky. The time cnstants f the surce-time functin (Fig. 3) are t 1 = 1. sec and t 2 = 5. sec. The rupture velcity is set at 3. km/sec. 1' dminant, relatively sharp peak at 1 t 13 sec, while the thers have brader peaks. Lng-perid (1 t 13 sec) surface waves are excited by a surce at a depth f abut 5 t 15 km, as suggested by the Green's functins shwn in Fig- ure 5. Hwever, the amplitude f this lng-perid wave is relatively small. Thus, we need subfanlts having large amunts f slip at a depth f 5 t 15 km t generate largeamplitude lng-perid grund mtin. T further investigate the excitatin mechanism f lng-perid (1 t 13 sec) waves, we perfrmed a test, as shwn in Figure 8. Figure 8a shws simulatins fr rupture prpagatin mdels c5 and c5' in which 8.4 m slip is assumed fr a cluster f subfanlts at the suthwestern crner n a shallw prtin f the fault plane. The slip n the ther part f the fault plane is assumed t be 1.4 m. The slip distributins are illustrated n the hrizntal prjectin f faults shwn in Figure 8a. Fr each rupture mdel, we cmputed grund mtins fr three slip distributins. The tp trace fr each cmpnent (slid curve) is fr the slip distributin shwn in the tp fault plane n the fight f the wavefrms. The middle trace (sparsely dtted curve) is fr the slip mdel that cnsists f the large-slip cluster nly. The bttm trace (heavy-dtted curve) is fr the slip distributin mdel withut the cluster. Figure 8a shws that, fr c5, the large-slip cluster is almst entirely respnsible fr the large-amplitude, lng-perid grund mtin. The remaining part f the fault cntributes very little t the grund mtin. n cntrast, fr c5', the large-slip cluster excites nly small-amplitude grund mtin. The difference between the c5 and c5' mdels shwn in Figure 8a is the lcatin f the hypcenter relative t the large-slip cluster. Fr c5, rupture prpagatin n the largeslip cluster is tward Tky, but fr c5', it is away frm Tky. These results clearly demnstrate the strng effect f rupture directivity n excitatin f grund mtin. Figure 8b shws the crrespnding velcity respnse spectra. Figures 8a and 8b clearly demnstrate that if rupture prpagates tward Tky and a large-slip cluster lies between the epicenter and Tky, then the amplitude f the lng-perid grund mtin wuld increase significantly. Rupture Velcity. Figure 9a cmpares simulatins fr different rupture velcities ranging frm vr = 1.5 t 3. kin/ sec. The rupture mdel c5 is used fr this simulatin. f the rupture velcity is smaller than 2 km/sec, the grund mtin is very small. The crrespnding velcity respnse spectra are shwn in Figure 9b. When Vr is increased frm 2 t 3 km/sec, the spectral amplitude at perids shrter than 5 sec increases significantly, but the amplitude changes very little at perids lnger than 1 sec. n cntrast, when vr is decreased frm 2 t 1.5 km/sec, the spectral amplitude at lng perids decreases significantly, and the peak at perids lnger than 1 sec disappears. Spatial Reslutin Parameter. The simulatins thus far have assumed that the spatial reslutin parameter L t be 3 kin, which is based n the rupture mdel f the 1968 Tkachi-Oki earthquake. We nw examine the effect f varying L n lng-perid grund mtin. We cmputed grund mtins using the c5 rupture mdel with L being varied frm 12 t 51 kin. As Figure 1

9 148 M. Take and H. Kanamri (a) rupture mde: c5 2.1m iiiiiiiiiiiii!i rupture mde: c5' Up------,_ m NiiiJ crrdsec Ea L\,".'... :._.L.LbL... {}, 5 1 see %1iiiii!iii T%iiiiii!!!il Ea ~... em/sec... "... " " " ' " i',, O l 5 1 see (b) mpture mde: c5 rupture mde: c5' ~12[ "~6~f~ 8... lid'... 1 ~12 "~'~ 2 t JD... ~ ~ ' ~21: p... NS''" ~... i~ "~ i~ ~ 12~" ~s~ n peak,l / t6 ~12 "~ 4~ ~ ~:;'::.:~-; shws, varying L has little effect n grund mtin. The dminant perid remains between 1 and 13 sec, thugh the amplitude f the spectral peak changes slightly. At L = 51 km, the rupture time fr distance L reaches abut 17 sec at v r = 3. km/sec, yet the dminant perid at 13 sec is unaffected. The results f the sensitivity tests shwn abve clearly demnstrates that directivity and the surce depth have a majr influence n lng-perid grund mtin. f the rupture velcity is faster than 2 km/sec, the amplitude f simulated lng-perid grund mtin varies little, and the spatial reslutin parameter L has relatively little effect. Summary f the Kant Earthquake Simulatins The respnse spectra cmputed using seismlgically reasnable sets f surce parameters fr the 1923 Kant earthquake vary by mre than an rder f magnitude. The range f variatin f the spectra fr Tky envelps the Figure 8. (a) Grund-mtin velcities fr the tw different rupture prpagatin mdels. Hrizntal prjectins f the fault plane are shwn t the right f the wavefrms. The slid circle indicates the hypcenter, and the slid triangle indicates the lcatin f Tky relative t the fault plane. The area f the circle indicates the amunt f slip at every 6 km n the fault plane. The scale fr slip is shwn abve the fault plane diagram. The line segment shwn at the lwer left side f each fault plane diagram indicates the line type used t shw the crrespnding wavefrm. (b) Crrespnding velcity respnse spectra (h =.5). The line type used fr respnse spectrum is the same as that used fr the wavefrms. respnse spectra estimated frm the mamura seismgram and the Ewing seismgram shwn in Figure lc. Fr sme cmbinatins, the respnse spectra exhibit peaks at abut 1 t 13 sec (Fig. 6d), suggesting harmnic grund mtin. Thus, even if we cannt prve that the harmnic grund mtin estimated frm the Ewing seismgram is real, we can cnclude that it is nt unrealistic. The grund mtin estimated frm the mamura seismgram is clse t the lwer bund f the simulated grund mtins. We believe that the recnstructin f the excessively verdriven mamura seismgram underestimates the real grund mtin. We nte that many respnse spectra shwn in Figure 6 have peaks at perids lnger than 1 sec, lnger than the dminant perid (6 t 8 sec) estimated frm studies f small earthquakes and micrtremr measurements (e.g., Tanaka et al., 1979). Thus, the dminant perid f the subsurface structure measured lcally may nt be representative f the dminant perid f grund mtin expected fr a nearby large

10 Simulatin f Lng-Perid Grund Mtin near a Large Earthquake 149 (a) Vr = 3. km/sec Vr = 2.5 km/sec (b) Vr = 3. km/s Vr = 2.5 km/s... _:.,?)~L:_:/_L :..:... Z 2:2i:.::.i.:i:J2;:ZZ:_L::,~i.2.1m ~" 16 ~12O 61 cn',jsec l. cm/sec 2... Ns' " ~2 2 f NS a... '""... O, -... :,2_,-'-L.~:..': Vr = 2. km/sec Up.....-,,.-, Vr = 1.5 km/sec -:;-7;;T 1 p~dd(see) 2 2}t... EW' v {=... Ew... 12O~ 8 " "". crrdsec pe~rid(see) Vr = 2. km/s UD... ~12O lo 2 pedd(see) Vr = 1.5 km/s 2[ ~12 ~ 4 8 ;,~ sec... -;-... ~id(see) 2, -., -..,..- % " ' i... ~ l~id(see) ~12O..,~ -., g 8 " ", 2 [ EW ,...,- -,.. Figure 9. (a) Grund-mtin velcities cmputed fr the c5 rupture mdel (see Fig. 4). Rupture velcities are varied frm 1.5 t 3. kmlsec. (b) Crrespnding velcity respnse spectra (h =.5). The line type used fr respnse spectrum is the same as that fr the wavefrrn. ~12 ~12 ~ 4 ' t 2 earthquake, which is cntrlled by rupture directivity and surce depth. Because f the relative lcatin f Tky with respect t the fault plane, the grund mtin in Tky is nt the largest expected f the 1923 Kant earthquake. The amplitude in the areas alng the suthern edge f the fault plane may have been significantly larger than in Tky. Sat et al. (1996) reached the same cnclusin. The areas in which the cllapsed huses reached mre than 3% f the ttal number in such areas extended alng the suthern edge f the fault plane, the Shunan area (nrthern side f the Sagami bay), the Miura peninsula, and the suthern part f the Bs peninsula (mamura, 1925). Design spectra fr high-rise buildings in the waterfrnt f Tky and Ykhama are cmpared with the velcity respnse spectra f the N-S cmpnents using the c5 rupture mdel (Fig. 11) (Tshiaki Sat, written cmm., 1996). Our simulatin is mainly cncerned with lng-perid waves with perids lnger than 5 sec. The simulated spectra at perids shrter than 5 sec are small because the smth surce-time functin (Fig. 3) was used in the simulatin. n the perid range lnger than 5 sec, almst all respnse spectra exhibit a peak at abut 1 t 13 sec, ranging frm 25 t t7 cm/ sec. n sme cases, the spectral amplitudes shwn in Figure 11 lk exceedingly large cmpared with the design spectra. We nte that the design spectra in Tky and Ykhama are abut a third f the largest velcity respnse spectra estimated fr a realistic range f fault parameters fr an M = 8 earthquake at sites lcated n a sft sedimentary basin. Hypthetical Earthquake in the Ls Angeles Basin Ls Angeles is anther majr urban city lcated n a thick sedimentary basin where a large earthquake (Ms > 7.5) culd ccur (Heatn et al., 1995; Dlan et al, 1995).

11 15 M. Take and H. Kanamri ~ L=51 km 16 LD!= 2~ L= 3kin 5 TO 3c5 1./5./ ~ plod d (see) 2 ~ 16 NS 8 C~ ' ~ 16 EW 12 t & 6, 2 cd > 1 c; pexid (se~) L=21 km L= 12km 1 1 ~' 16 UD ~16~ LD,2,2 8l ~ 1/i 2 p'e~i d (sec) ; ~... 1;tid'(;e'c; 2' ;: %... i...-i~ - 2[,6 Ns ] ~ 16 EW Figure 11. Design spectra fr high-rise buildings in the waterfrnt f Tky (shrt dashed line) and Ykhama (lng and shrt dashed line) with the velcity respnse spectra (h ---.5) f the N-S cmpnents fr the c5 rupture prpagatin mdel. LA basin fault mdel lo 2 Figure 1. Velcity respnse spectra (h =.5) fr varius L ranging frm 12 t 51 kin. The rupture mdel c5 is used. Fr each L, simulatins were made fr 18 different slip distributins. n view f the similarity between Tky and Ls Angeles in this cntext, and f the results we btained fr Tky, we investigated the pssible cnsequence f a large earthquake n grund mtin in the Ls Angeles basin. Since the methd is essentially the same as that used fr Tky, we just briefly explain the mdel used fr the Ls Angeles simulatin. Again, ur bjective here is t explre the pssible range f grund mtin, rather than t make very specific estimatins f grund mtin frm a scenari earthquake. We assume an M~ = 7.5 earthquake with a nrth-dipping reverse fault mechanism similar t that f the 1987 Whittier Narrws earthquake; i.e., dip angle = 3, and rake e; l ] C3 ~< 34.6 #2 ~ C5 C2 D kin n TM #1 O~ 1 kln C1 hypcenter C1-C6 are six circular rupture mdes which initiate frm different hypcenters. statin! fcal mechanism Figure 12. The hrizntal prjectin and crss sectin f a fault plane fr a hypthetical earthquake beneath the Ls Angeles Basin. Rupture prpagatin mdels used fr the simulatins are shwn. "c1" t "c5" are five circular rupture mdels. Small, pen circles indicate the hypcenters used fr the simulatins. The fcal mechanism used in this article is shwn. The lcatins f sites used fr simulatins are indicated by slid diamnds attaching the site numbers frm 1 t 4.

12 Simulatin f Lng-Perid Grund Mtin near a Large Earthquake 151 Table 2 Velcity Structure Used fr Simulatin f the Ls Angeles Earthquake V~ V, p h Qp Q, angle = 9 (Fig. 12). The fault is 12 km lng and 4 km wide, with an average slip f 2. m. Fr the velcity structure, we used the mdel determined by Scrivner (written cmm., 1992) (Table 2). Velcity respnse spectra are cmputed fr fur sites (1 t 4) lcated abve the assumed fault plane. Representative Green's functins cmputed fr site 2 are shwn in Figure 13 alng with their velcity respnse spectra. These Green's functins are cmputed fr a single 4 4 km ~ subfault with 2-m slip, tl = 1.8 sec, and t 2 = 4. sec (Fig. 3). T demnstrate the effect f sedimentary layers n excitatin f lng-perid grund mtin, the Green's functins and simulated velcity respnse spectra fr a hmgeneus half-space with P-wave velcity f 6.41 km/sec and S-wave velcity f 3.7 km/sec are included in Figure 13. These results clearly demnstrate that sedimentary layers play a ~....,....,....,.... Up.82,.22 UD 1 16_V%. v V v....,.... i.... t....,.... UD up. 1 7 ~.1~ ~ " '~ V " lo lo 2....,....,....,....,. A. 5 ~ - ~\/ v NS 1... N s '..21& 3. lng-perid peak. ~.. ' /. ~. 1...,...,...,...,... EW En v EW... 1 EW ~... ~smss...!lt ms~ss... '... ggg~8~... ~ZZZ ti ]] l mg,g... Figure 13. Representative Green's functins used fr simulatin f the Ls Angeles earthquake mdel and their velcity respnse spectra (h =.5) All wavefrms are grund-mtin velcities at site 2. The slid circle indicates the hypcenter, and the slid triangle indicates the lcatin f site 2. The upper traces in each panel are calculated using the velcity structure listed in Table 2, and their respnse spectra are shwn by slid curves The lwer traces are fr a hmgeneus half-space with P- and S-wave velcities f 6.4t and 3.7 km/sec, respectively Their respnse spectra are shwn by dtted curves. The amplitude f Green's functins in each clumn are nrmalized by a maximum amplitude f the three cmpnents, and the peak-t-peak amplitude f each recrd is shwn abve each trace

13 152 M. Take and H. Kanamri (a) #1 3c3 1.8/4./3. UD h=.5 (b) #1 3c4 1.8/4./3. UD h=.5 34O 32O,422 l..: 16 /~ ~ 14 ~. m > 12 i/ L~,~'~ /, ",, 24,422 2 _,16 a=14 > 12 4O 2O #1 3c3 1.8/4./3. NS h=.5 4Ol... ~... ~.... ~.... = ( ~'3 ii ii pedd (sec) #1 3c4 1.8/4./3. NS h=.5 _: 16 ~. ~, \ ' ~ #1 3c3 1.8/4./3. EW h=.5 32O ~" 2 - ~.-,.:~%', " -..~.~ 224." '~,-.-),.J > 12, j > O 6O 4O O '~':Z,4 22 m 2 ~ ~2 ~ 1 14 > 12 ~---'~" "~ r pedd (see) #1 3c4 1.8/4./3. EW h=.5 4O 2, ,,.. " ".... i, (c) #2 3c2 1.8/4./3. UD h=.5,4 22 ~ ~-~. 2 ~ ;-~.- 18,,~- ~"~\~ ~- "~ 14 ~" ~'~:=_~.'~.~"~,~.%,~ ~,"~, > 12 ~'~ %,l41iallbim ' 25 perid (eec) #2 3c2 1.8/4./3. NS h=.5 4 ~.... ~.... ~.... =.... ~ l / ~" " 32 Z ~ ~ " ~2 ~ ~ " 28 / ~ " ~,4 22 /.j 16 ~ ~ L ~ " > ~- i~b~,.'; r..'~, " O 38O #2 3c2 1,8/4./3. EW h=.5... i... t... i... i... (~) #2 3c5 1.8/4./3. UD h= i i... i O,4 22O l 2 ~ 18 ~ ~1~ " ~ ~ #2 3c5 1.8/4./3. NS h=.5 2~...,...,... ~... ~ ~'3 v24,422 ~--~ /",," ". (2O t," =" 18 / ~ ~" 16 i - ' 14 >12 /, 4O 2~ ' 25 #2 3c5 1.8/4./3. EW h=.5... i... =... t... J... 32O,4 22O m j 16, 14 > ~,., ~" 3,4 22O ~2 ~ 14 > 12,... T

14 Simulatin f Lng-Perid Grund Mtin near a Large Earthquake 153 (e) #3 3cl 1 8/4./3. UD h= 5 D. ). (f),= 38( 321 ~' 31 28( L~,, li 221 ) 21 E "~ 144 > 12( (;( #4 3c2 1.8/4./3. UD h=.5... L... i... i... i , = le.~ Q ~ ~'3 28 ~26 24 ~.22 2Q le ~ % #3 3cl 1,8/4./3. NS h= pedd (sec) #3 3cl 1.8/4./3, EW h=.5... J... i... J... i ( ( 34( 321 ~3e ~, 221 ) > 12 ;~ ' 25 #4 3c2 1.8/4 /3 NS h=.5... i... t... i... t..., 8O 6 4 2v ~ 2 E ~14 12 ~'~ 1 ' "- 8O 2 2 #4 3c2 1.8/4./3. EW h= Figure 14. Representative velcity respnse spectra (h =.5) fr the five rupture prpagatin mdels (cl, c2, c3, c4, and c5) (see Fig. 12). Three cmpnents f grund mtin are shwn. Fr each rupture mdel, grund mtins were cmputed fr 18 different slip distributins. The first tw characters in the header line f each panel indicate the site number shwn in Figure 12. majr rle in amplifying lng-perid grund mtin in the epicentral area f a large earthquake. Recently, Olsen et al. (1995) simulated lng-perid grund mtins frm a large earthquake (M = 7.75) alng the San Andreas fault in the Ls Angeles area. Their result als shws that the simulated spectral amplitudes fr sme regins in the Ls Angeles basin are up t 1 times larger than thse at sites withut sedimentary layers. The respnse spectra f the Green's functins cmputed fr deeper (5 t 15 kin) surces exhibit a peak at 1 t 13 sec, which is similar t that bserved fr the Kant earthquake simulatin. Figure 14 shws representative velcity respnse spectra fr varius rupture mdels (cl, c2, c3, c4, and c5) and slip distributins with Vr = 3. km/sec, t] = 1.8 sec, and t 2 = 4 sec. The spectral amplitude fr site 2 cmputed fr the c2 rupture mdel can reach 35 crrdsec at a perid f l sec; Figure 15a shws a representative grund velcity fr this case, which gives the largest amplitude. This large amplitude at lng perid is a result f cmbined effect f directivity and excitatin frm surces at a depth f abut 1 kin. A representative grund velcity fr the c2 rupture mdel at site 4 is als presented in Figure 15b, which gives a lngperid wave train. Using the same methd used fr the Kant earthquake, we investigated the effect f varying v r n velcity respnse spectra fr site 2, assuming the mdel c2 rupture mdel The result is similar t that btained fr the Kant earthquake. f vr < 2. km/sec, the amplitude at the dminant perid is reduced significantly. Als, as shwn in Figure 16, the amplitude f lng-perid grund mtin is relatively insensitive t a variatin f L ver a range 12 t 32 kin. The spectral amplitudes shwn in Figure 14 may lk exceedingly large cmpared with the bserved spectrum available t date. Hwever, as we have demnstrated, the surce parameters used fr cmputatins are all very plausible, s that we must cnclude that the range f respnse spectral amplitude shwn in Figure 14 represents a realistic range f grund mtin frm an M = 7.5 earthquake at sites lcated n a sft sedimentary basin.

15 154 M. Take and H. Kanamri (a) Up.,. N ~ cm/sec g E a ~ ~' ~ :~ ~ ~ e ~ sec a'o 9 l"oo 2.m (b) Up N cm/sec ~D Ea sec 2.m ,..... Q a~ Q Q~... r ~ ~ 1' Figure 15. (a) A representative grund velcity fr site 2 cmputed fr the c2 rupture mdel. The hrizntal prjectin f the fault plane with the slip distributin is shwn at the bttm. The area f the circle indicates the amunt f slip at every 4 km n the fault plane. The scale fr slip is shwn abve the fault plane diagram. The slid circle indicates the hypcenter, and the slid triangle indicates site 2. The time cnstants f the surce-time functin (Fig. 3) are tl = 1.8 sec and t2 = 4, sec. The rupture velcity is set at 3. km/sec, (b) A representative grund velcity fr site 4 cmputed fr the c2 rupture mdel.

16 Simulatin f Lng-Perid Grund Mtin near a Large Earthquake 155 L=32km 2...,...,......,... 2 ~'16 UD ~ 16 ~12 ~12 e, ff 8 ~ 8 L=2km...,....,....,....,.... UD 2 :...,...,..... bd... ~ 16 & 12 ~ 8 ~4 L= 12km... 1' ~,, ~ NS... ],-.~ 2()16 12,, ~ 4 $ ~ 16( 6 12 ~12 2 "5. "" ":'" 8(.~ 8 4 ~ 4 4, ;... 1'... :/-~ ' c O *... Ns'... ] 2... NS'... i ~" 16[",<.,,'~ ~ r 8.'~:,.-:-daim.~-..,,~,.~-..,~ ~' 8~.~,",,'.~~., EW'. 1...,...,... J... t... i r wmr. ":,... r...,, ~. Figure 16. Velcity respnse spectra (h =.5) at site 4 fr varius L ranging frm 12 t 32 km. The rupture mdel c2 is used, and grund mtins were cmputed fr 18 different slip distributins fr each rupture mdel. Cnclusins We have demnstrated with numerical simulatin that rupture directivity and surce depth have a prfund influence n the amplitude and spectrum f lng-perid grund mtin in the immediate vicinity f large earthquakes. Simulatins fr the Kant earthquake shw that if the directivity is tward Tky, the spectrum f grund mtin in Tky wuld have a peak at a perid f 1 t 13 sec, and the amplitude ranges frm 25 t 17 cm/sec. This large range is expected fr fault mdels with realistic ranges f surce parameters. This range is cnsistent with the bserved mamura and Ewing seismgrams. We nte that the dminant perid f grund mtin frm a large fault can be significantly different frm that estimated frm lcal measurements f micrtremrs. The same general cnclusin can be made fr an Mw = 7.5 earthquake mdel fr Ls Angeles. Fr a site just abve the center f the fault, the grund-mtin spectral amplitude at a perid f 1 sec can vary frm 5 t 35 cm/sec. This range, thugh very large, is what is expected fr the seismlgically plausible range f surce parameters. Acknwledgments We thank H. Ykta and S. Kataka, nstitute f Technlgy, Shimizu C., wh kindly prvided us with the digitized grund-mtin data reprduced frm the mamura seismgram, and M. Yamada, Waseda University, wh kindly prvided us with the digitized grund-mtin data reprduced frm the Ewing seismgram. This research was partially supprted by the CUREe-Kajima Research Prject. Cntributin N. 5786, Divisin f Gelgy and Planetary Sciences, Califrnia nstitute f Technlgy, Pasadena, Califrnia References And, M. (1971). A fault-rigin mdel f the great Kant earthquake f 1923 as deduced frm gedetic data, Bull Earthquake Res. nst. Univ. Tky 49, And, M. (1974). Seism-tectnics f the 1923 Kant earthquake, J. Phys. Earth 22, Buchn, M. (1981). A simple methd t calculate Green's functins fr elastic layered media, Bull. Seism. Sc. Am. 71, Dlan, J. F., K. Sieh, T. K. Rckwell, R. S. Yeats, J. Shaw, J. Suppe, G. J. Huftile, and E. M. Gath (1995). Prspects fr large r mre frequent earthquakes in the Ls Angeles metrplitan regin, Science 267, Frankel, A. (1993). Three-dimensinal simulatins f grund mtins in

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