Nonlinear Soil Response in the Vicinity of the Van Norman Complex Following the 1994 Northridge, California, Earthquake

Transcription

1 Bulletin f the Seismlgical Sciety f America, 89, 5, pp , ctber 1999 Nnlinear Sil Respnse in the Vicinity f the Van Nrman Cmplex Fllwing the 1994 Nrthridge, Califrnia, Earthquake by Givanna Cultrera, David M. Bre, William B. Jyner, and Christpher M. Dietel Abstract Grund-mtin recrdings btained at the Van Nrman Cmplex frm the 1994 Nrthridge, Califrnia, mainshck and its aftershcks cnstitute an excellent data set fr the analysis f sil respnse as a functin f grund-mtin amplitude. We searched fr nnlinear respnse by cmparing the Furier spectral ratis f tw pairs f sites fr grund mtins f different levels, using data frm permanent strng-mtin recrders and frm specially deplyed prtable instruments. We als cmpared the amplitude dependence f the bserved ratis with the amplitude dependence f the theretical ratis btained frm 1-D linear and 1-D equivalent-linear transfer functins, using recently published brehle velcity prfiles at the sites t prvide the lw-strain material prperties. ne pair f sites was at the Jensen Filtratin Plant (JFP); the ther pair was the Rinaldi Receiving Statin (R/N) and the Ls Angeles Dam (LAD). Mst f the analysis was cncentrated n the mtins at the Jensen sites. Prtable seismmeters were installed at the JFP t see if the mtins inside the structures husing the strng-mtin recrders differed frm nearby fleefield mtins. We recrded seven small earthquakes and fund that the high-frequency, lw-amplitude mtins in the administratin building were abut.3 f thse utside the building. This means that the lack f high frequencies n the strngmtin recrdings in the administratin building relative t the generatr building is nt due slely t nnlinear sil effects. After taking int accunt the effects f the buildings, hwever, analysis f the suite f strng- and weak-mtin recrdings indicates that nnlinearity ccurred at the JFP. As predicted by equivalent-linear analysis, the largest events (the mainshck and the 2 March 1994 aftershck) shw a significant deamplificatin f the high-frequency mtin relative t the weak mtins frm aftershcks ccurring many mnths after the mainshck. The weak-mtin aftershcks recrded within 12 hurs f the mainshck, hwever, shw a relative deamplificatin similar t that in the mainshck. The sil behavir may be a cnsequence f a pre pressure buildup during large-amplitude mtin that was nt dissipated until smetime later. The mtins at (R/N) and (LAD) are frm free-field sites. The cmparisn amng spectral ratis f the mainshck, weak-mtin cda waves f the mainshck, and an aftershck within ten minutes f the mainshck indicate that sme nnlinearity ccurred, presumably at (RIN) because it is the sfter site. The spectral rati fr the mainshck is between that calculated fr pure linear respnse and that calculated frm the equivalent-linear methd, using cmmnly used mdulus reductin and damping rati curves. In cntrast t the Jensen sites, the rati f mtins sn after the high-amplitude prtin f the mainshck differs frm the rati f the mainshck mtins, indicating the mechanical prperties f the sil returned t the lw-strain values as the high-amplitude mtin ended. This may indicate a type f nnlinear sil respnse different frm that affecting mtin at the Jensen administratin building. Intrductin The seismic respnse f near surface sils has usually been mdeled by seismlgists n the assumptin that the stress-strain relatinship f such materials is linear. Getechnical labratry measurements, hwever, indicate that 1214

2 Nnlinear Sil Respnse in the Vicinity f the Van Nrman Cmplex Fllwing the 1994 Nrthridge, Califrnia, Earthquake 1215 sils behave in a nnlinear fashin at the strain levels crrespnding t damaging grund mtins. The labratry measurements shw a reductin f shear mdulus and an increase in damping as the strain level increases. The effect n seismic waves wuld be an increase in damping and a decrease in prpagatin velcity, with cnsequent reductin in high-frequency amplitudes and shifts t lwer frequencies f the spectral resnant peaks f the sil depsit. There are reasns, hwever, fr cncern abut the degree t which the labratry measurements are representative f the behavir f the sil in situ (EPRI, 1993, Appendix 7A). It is imprtant, therefre, t verify the labratry-based predictins with actual strng-mtin data. It is necessary t evaluate nt nly whether nnlinear behavir ccurs, but als mre specifically, the degree f nnlinearity, the frequency range and amplitude levels at which it ccurs, and the materials in which it ccurs. In ur subsequent discussin f nnlinear sil respnse, it will be useful t distinguish between tw frms f nnlinear sil respnse. In ne frm, the mdulus decreases and the damping increases as the amplitude increases, returning t their lw-strain values as sn as the high-amplitude mtin ends. In the ther frm, particularly cmmn in lse sands, the pre pressure may build up gradually as a cnsequence f repeated cycles f shear defrmatin. As the pre pressure builds up, the mdulus decreases, the damping increases, and the changes may persist fr hurs after the mtin ceases. These tw frms f nnlinear sil behavir may ccur in cmbinatin with each ther. Until recently, nly very limited strng-mtin data were available fr evaluating sil nnlinearity at high strains. Many recrdings f strng mtin, hwever, have been cllected frm recent large earthquakes (1985 Michacan, 1989 Lma Prieta, 1994 Nrthridge, 1995 Hyg-ken Nanbu), creating new pprtunities t evaluate the issue f sil nnlinearity. In particular, fr the Nrthridge earthquake, a systematic nnlinear respnse at sil sites has been fund by several grups f researchers. The cnclusin that sil nnlinearity was present was arrived at in a number f ways, but in all cases the basic evidence was that the mtins at sil sites subjected t strng shaking was smaller than expected. Trifunac and Tdrvska (1996) fund that nnparametric attenuatin functins fit t mainshck peak acceleratins at sil sites resembled thse frm rck sites at distances beynd abut 2 km but, unlike rck sites, leveled ff at clser distances. Field et al (1997, 1998) and Hartzell (1998) derived spectral amplificatin factrs fr sil sites relative t a selected set f rck sites after remving distance dependence; the amplificatins frm recrdings f the mainshck in the San Fernand Valley were significantly less than fund fr much weaker-mtin aftershcks recrded n a set f prtable recrders. Beresnev et al. (1998a) and Su et al. (1998) als used weak-mtin amplificatin functins but applied them t theretical rck-mtin simulatins t predict sil mtins; their simulatins fit the rck mtins but verpredict the sil mtins (as did studies by Field et al., 1997, 1998). Beresnev et al. (1998b) studied spectral ratis fr sil and rck statins separated by 3.2 and 4.8 km; 34 24, 2 - AS7 4.~ 34"18' _J 34 12' 3 AS6 IN -118"42' 3 km 8 AS5-118"36' MS Y~ JFP LA AS1 AS *3' Lngitude , Figure 1. Map shwing the epicenters f the events used in ur study. The event numbers are keyed t event infrmatin in Table 3 (event 9 is lcated utside f the area shwn in the figure). Events recrded n permanent accelergraphs and GES prtable instruments are indicated by filled and empty circles, respectively. The triangles indicate the psitins f the SMA-1 recrding statins: LAD, RIN, and the tw sites (JAB and JGB) at the Jensen Filtratin Plant (JFP). The numbers in curly brackets are the rute numbers f majr highways. The area within the shaded rectangle is shwn in Figure 2.

3 1216 G. Cultrera, D. M. Bre, W. B. Jyner, and C. M. Dietel ur statin pairs are much clser tgether (.3 and 1.5 km) than in the ther studies. Shear-velcity and lw-strain damping values are available frm brehle lgging at each site that we used in ur analysis. Spectral ratis fr a very wide range f grund-mtin amplitudes were used in ur study. We deplyed digital seismic recrders t define the effect f the buildings n the strng-mtin recrdings btained frm the permanent statins lcated within the buildings. We cmpared the bserved amplitude dependence f the spectral ratis with that predicted frm cnventinal engineering practice (using SHAKE91). In the predicted respnse we used lw-strain damping btained frm the brehle data, and we included the respnse f the reference site (smething that is rarely dne in site respnse analysis) by decnvlving the bserved reference-site mtin t a depth at which we judged the material prperties underlying the sites t be the same. In the subsequent sectins, we describe the statins and the data recrded, discuss the methds f data analysis, and finally shw the recrded and theretically predicted relative site respnse at the tw pairs f statins fr different events. Data Figure 2. Tpgraphic map (San Fernand Quadrangle) with the psitin f the fur SMA-1 statins in the Van Nrman Cmplex (this is the regin indicated by the shaded rectangle in Figure 1). they fund a shift in the frequency f spectral peaks fr the mainshck, aftershcks, and the 1987 Whittier Narrws earthquake that are cnsistent with nnlinear sil respnse. As in many f the studies just mentined, we als used spectral ratis t lk fr nnlinear sil respnse. We feel that using spectral ratis is the simplest and mst direct way t demnstrate sil nnlinearity. ur study, hwever, differs in a number f essential ways frm ther studies f nnlinear sil respnse during the 1994 Nrthridge, Califrnia, earthquake: We used tw pairs f statins in the Van Nrman Cmplex (VNC), which were situated in an area subjected t sme f the strngest shaking prduced by the earthquake. The VNC includes imprtant engineering facilities wned and perated by the Ls Angeles Department f Water and Pwer (LADWP) and the Metrplitan Water District f Suthern Califrnia (MWD). It is lcated in the nrthern San Fernand valley (Figs. 1, 2) and supplies a large amunt f water and pwer t the city f Ls Angeles. Because f its imprtance and psitin clse t active faults, the VNC has been instrumented with strng-mtin accelergraphs since the 1971 San Fernand earthquake. Figure 1 shws the lcatin f the VNC and the epicentral lcatins f the 17 January 1994 Nrthridge mainshck and the aftershcks used in this study. The mainshck ccurred 11-km suthwest and ruptured updip tward the VNC, such that the VNC is abve a prtin f the rupture surface (Trifunac et al., 1994; Scientists, 1994; Wald et al., 1996). Field bservatins revealed sand bils, bth at the nrth end f the VNC (Bardet and Davis, 1996c) and clse t the Jensen Filtratin Plant (JFP) (Stewart et al., 1996), and evidence f liquefactin at the Lwer San Fernand Dam, lcated between the Ls Angeles Dam (LAD) and the Rinaldi Receiving Statin (RIN) (Bardet and Davis, 1996b). Sme f the strngest shaking recrded during the mainshck ccurred in this regin (e.g., Bardet and Davis, 1996a). The large grund mtins make this regin an ideal ne fr lking fr nnlinear sil respnse. The psitin f the fur sites we analyzed in this study are shwn in Figure 2, with statin infrmatin cntained in Table 1. Tw f the statins are in the JFP, and the ther pair are the statins at the west abutment f LAD and RIN.

4 Nnlinear Sil Respnse in the Vicinity f the Van Nrman Cmplex Fllwing the 1994 Nrthridge, Califrnia, Earthquake 1217 Table 1 Lcatin f Recrding Statins Statin Cde Instrument wner/agency Lat.* (deg) Lng.* (deg) Admin. building JAB SMA-1/GES MWD-USGS Admin. free-field JABF GES USGS Generatr building JGB SMA-1/GES MWD-USGS Generatr free-field JGBF GES USGS LA Dam west abutment LAD SMA-1 LADWP Rinaldi receiving statin RIN SMA- 1 LADWP *Crdinates at Jensen Filtratin Plant using a handheld precisin GPS unit with accuracy better than 4m. Brehle measurements clse t these sites (Figure 4 and Table 2) prvided shear-wave velcity prfiles t depths f abut 9 m and sil damping factrs fr lw strain (Gibbs et al., 1996; J. Gibbs, persnal cmm., 1997). Details abut the earthquake lcatins and magnitudes, as well as infrmatin abut the recrded mtins, are given in Table 3. Recrds f the mainshck and sme aftershcks are als available at several ther sites in the vicinity (in particular, the Sylmar Cnvener Statin abut.7 km east f the Jensen administratin building). We did nt use recrds frm these ther sites in this article because it was nt clear with which recrdings they shuld be cmpared. The tw statins at the JFP and the statins RIN and LAD prvided a mre clsely spaced pair f recrdings n different materials than if we had cmpared recrdings at the Sylmar Cnverter Statin with ne f the Jensen statins r with the LAD statin. Jensen Filtratin Plant: Statins and Recrdings ur main fcus in this study is n recrdings btained frm tw triggered, analg strng-mtin accelergraphs (SMA-1) at the JFP [the statins are wned by the MWD but are maintained by the U.S. Gelgical Survey (USGS)]. These accelergraphs are lcated in the administratin building (JAB) and the generatr building (JGB) at JFP (Figure 3). The accelergraph at JAB is lcated abut 3-4 m belw grund level in a crner f the basement f a 28 X 6 meter tw-stry building, and the instrument at JGB is in the grund flr f a 1 X 1 x 3.6 m cncrete blck structure, with a cncrete slab fundatin ver fill (D. Dean, persnal cmm., 1998). The JAB and JGB sites are 26 m apart but situated n very different sils. Brehle measurements clse t JAB and JGB (within 57 and 31 meters, respectively) indicate that JAB and JGB are sited n abut 14 m f engineered fill and alluvium and 3 m f engineered fill, respectively (Gibbs et al., 1996; J. Tinsley, persnal cmm., 1998). At bth sites, the Hlcene fill and alluvium are underlain by the upper member f the Pli-Pleistcene Saugus Frmatin. The material under JAB has a significantly lwer shear-wave velcity than under the JGB fr depths less than abut 6 m (Figure 4 and Table 2). Hwever, the average lw-strain shear-wave damping rati D (related t quality factr Qs by D = 1/(2Qs ), with D in percent) under each site is similar (D = 3.6% and D = 3.% fr JAB and JGB, respectively; see Table 2). Table 2 Brehle Infrmatin Latitude Lngitude depth range V3t Brehle (deg) (deg) D* (%) (m) (m/see) JAB JGB LAD RIN *D (damping rati in percent = 1/[2 Qs]) determined by J. Gibbs frm analysis f dwnhle recrdings (written cmmun., 1997) tshear velcity averaged ver the upper 3 m Althugh the brehles are displaced sme distance frm the strng-mtin accelergraph sites (Figure 3), cnsideratin f the lcal gelgy, alng with brings made fllwing the 1971 San Fernand earthquake ('Rurke et al., 1992), suggests that the brehle velcities are representative f the velcities beneath the recrding sites (J. Tinsley, persnal cmm., 1998). The lw-velcity zne shwn under the brehle near JAB (Figure 4) crrespnds t fluvial terrace depsits. Liquefactin fllwing the 1971 San Fernand earthquake (and pssibly fllwing the 1994 Nrthridge earthquake) ccurred within these terrace depsits. Furthermre, as we discuss later, nnlinear calculatins shw that these terrace depsits are f fundamental imprtance in the nnlinear respnse f the site. The accelergraphs at JAB and JGB that were triggered by the mainshck cntinued perating fr abut 146 sec and recrded a number f aftershcks n the same film. The same accelergraphs als recrded a number f aftershcks hurs t years after the mainshck. The mainshck time series were btained frm the USGS web site ( we digitized the aftershcks AS 1, AS2, AS3, AS4, 1, 2, 3, and 4 (Table 3) frm the riginal film recrds with standard USGS prcedures (a 6 dpi flatbed scanner and trace-fllwing sftware frm Kinemetrics). The time series fr aftershcks AS6 and AS7 were btained frm independent digitizing f the film recrds by the University f Suthern Califrnia (USC; data prvided by M. Tdrvska). Immediately after the mainshck, digital aftershck recrders were deplyed at JGB by the USGS (G. Glassmyer,

5 1218 G. Cultrera, D. M. Bre, W. B. Jyner, and C. M. Dietel Table 3 Events Used in this Study (SCEC data base) and PGV and PGA f Recrdings at the Statins Event Date rigin Time Lat. Lng. Depth PGV (cm/s)# PGA (g)** (yy/mm/dd) (hh:mm:ss) MII (deg) ((leg) (Km) JAB JGB JAB cda JGB cda MS* 94/1/17 12:3: ASI? 94/1/17 12:31: AS2 94/1/17 12:32: AS3 94/1/17 12:32: ,69.16 AS4 94/1/17 12:33: AS5:~ 94/1/17 12:4: AS6 94/1/17 23:33: AS7 94/1/18 :43: /3/2 21:2: /6/26 8:4: /4/26 1:37: /4/27 11:9: /11/27 1:43: /11/29 :12: /12/4 9:16: /1/4 9:11: /1/5 18:14: /1/12 6:36: /1/15 22:54: Event LAD R1N LAD cda RIN cda MS AS *Nrthridge mainshck.?events AS1, 2, 3, 4 are the aftershcks within 2 minutes after the mainshck: AS1 and AS3 lcatins frm CNSS (Cuncil f the Natinal Seismic System) catalg; AS2 and AS4 were nt lcated by the suthern Califrnia seismic netwrk. Cda waves fr events AS2 and AS4 were nt used. SEvents AS5, 6, 7 were prcessed by University f Suthern Califrnia; lcatins frm CNSS catalg. Numbers are used t identify events in Figure 1. HMagnitudes are M L, except fr the mainshck (Mw) and AS3 (cda magnitude). #Gemetric mean f hrizntal peak grund velcities determined frm uncrrected time series fr events 5 t 11 (GES recrdings) and frm cn'ected time series fr events AS5, 6, 7. Velcities f all ther events btained by integratin f filtered grund acceleratins. **Gemetric mean f hrizntal peak grund acceleratins; GES recrdings nt prcessed t yield PGA. persnal cmm., 1998) and near JAB by the University f Califrnia at Santa Barbara (J. Steidl, persnal cmm., 1997). These recrders were in the field fr several weeks t several mnths. Unfrtunately, the instrument at JAB was nt clcated at the strng-mtin accelergraph; it was lcated at least 3 m utside the sutheast crner f the building. As discussed belw, we have gd evidence that the mtins frm the accelergraph at JAB are nt equivalent t a free-field site utside f the building, and because we wish t cmpare strng and weak mtins at JAB, the aftershck deplyments immediately fllwing the mainshck did nt help us. Frtunately, we culd btain recrds fr a wide range f amplitudes frm the accelergraphs themselves. As a result f ur initial analysis f the accelergraph data, we suspected that the recrding f the mainshck at JAB was significantly affected by the respnse f the structure in which the recrder is lcated. We cnfirmed that this was the case by using a special deplyment f prtable recrders in t btain grund mtin inside and utside the buildings in which the permanent accelergraphs are lcated. We used fur General Earthquake bservatin System (GES) velcity digital recrders (see Brcherdt et al., 1985), which we placed at sites next t the SMA-1 accelergraphs in the tw buildings and at free-field sites clse t the buildings. The lcatins are shwn in Figure 3. Rinaldi Receiving Statin and Ls Angeles Dam: Statins and Recrdings The ther pair f statins studied in this article are RIN and LAD; the tw sites are 1.5 km apart. These are free-field sites; the instruments are hused in small shelters and are attached t islated cncrete slabs that are firmly anchred t the grund, away frm the influence f any building structures (Bardet and Davis, 1996a). The instruments are perated by LADWP and the recrdings f the mainshck were digitized by Lindvall-Richter-Benuska Assciates (1994). We als used time series fr an aftershck (AS5 in Table 3) prvided by M. Tdrvska at USC. Statin RIN is lcated at the suthern tip f the VNC, n relatively fine-textured surficial alluvium depsits (the average velcity t 3 m, V3, is 336 m/sec, and the damping D = 1.1%). The mainshck accelergram at this statin prvided the largest velcity ever instrumentally recrded (Heatn et al., 1995; Wang et al., 1996).

6 Nnlinear Sil Respnse in the Vicinity f the Van Nrman Cmplex Fllwing the 1994 Nrthridge, Califrnia, Earthquake 1219 L Q 5.e- C E~ ~..,. i i I i I I I I I I w I I I I I I brehle Generatr JGBF~G B 1 m Building Administratin Building JAB~ brehle JABF ' _1182g'55 '' '5 " '45 " Figure 3. Map f the Jensen Filtratin Plant, shwing an apprximatin f the building utlines and the lcatins f the accelergraphs (JAB and JGB), the brehles, and the prtable GES units (JABF, JGBF). Statin LAD is lcated n the grund surface at the west abutment f the dam. Peak grund acceleratins recrded at the dam are lwer than elsewhere in the VNC. The brehle investigatin at 35 m frm the accelergraph shwed that the site is a rck site (V3 = 647 m/sec) within the lwer (Sunshine Ranch) member f the Saugus Frmatin; the measured shear-wave velcities are higher than thse measured in the yunger Sangus Frmatin sites. Using the methds f Gibbs et al. (1994), Gibbs (persnal cmm., 1997) used the brehle data t derive a lw-strain damping f D = % (Q = 6.4), averaged ver a depth f 1 t 89 m (Table 2). This may seem like an unusually large amunt f damping fr a rck site, but the large value is supprted by the spectral decay parameter tc that we determined by fitting a straight line t a lg-linear plt f the Furier spectrum f the mainshck recrd at each statin (see Andersn and Hugh, 1984). We fund K =.63 sec at the rck site (LAD), which is clse t that at the sil site (RIN, (k =.59 sec). The value f K is determined ver a greater depth range than is penetrated by the brehles, s we d nt expect a ne-t-ne crrelatin with the damping values determined frm the brehle measurements. The values f bth tc and D, hwever, are greater fr the rck site (LAD) than fr the sil site (RIN). As discussed by Lindvall-Richter-Benuska Assciates (1994), the digital acceleratin time series we used fr RIN was crrected t accunt fr an apparently shrt-duratin stall f the film transprt mechanism. Recently, Trifunac et al. (1998) crrected the acceleratin time series fr many ther but shrter stalls. The acceleratin, velcity, and displacement wavefrms, as well as the undamped respnse spectra, fr the newly crrected acceleratin time series are very similar t thse frm the time series we used in this article, and therefre we did nt red the analysis using the newly crrected time series. Methd f Data Analysis The heart f ur analysis is a cmparisn f spectral ratis f the mtins at nearby sites fr different amplitudes f the shaking at the reference site, the site that prvides mtins fr the denminatr f the spectral ratis. The spectral rati methd is based n the assumptin that a seismic signal is represented by the cnvlutin f functins describing surce, path, site effect, and instrumental respnse. If the distance between the statins is much smaller than their hypcentral distances, the surce and path effects n the recrds are nearly identical. In ur case, the instruments are essentially identical, and therefre any differences in the recrds can largely be attributed t site effects, with minr variatins due t differing incidence angles and the hetergeneity f the medium. The distance between JAB and JGB (.3 km) is small enugh that the spectral rati mst likely eliminates all but the differences in grund mtin due t variatins in the lcal gelgic materials; this is less true fr RIN and LAD, which are separated by 1.5 km. Fr bth pairs f sites, we chse the site underlain by the higher velcity materials as the reference site. These are JGB and LAD. We cmputed the spectral ratis as fllws. We first cnditined the time series by remving a linear trend frm the uncrrected SMA-1 data (this was nt required fr the GES data), windwing the time series t extract the S-wave mtin (r in sme cases, a specified prtin f the signal cda), and padding with zers in rder t ensure the same frequency spacing (.1 Hz) fr all analyses. We tried several windw lengths t make sure that the results were nt sensitive t the chice f windw length. After windwing, we cmputed spectral amplitudes f the hrizntal mtins frm the Furier transfrms f the tw hrizntal cmpnents by summing the squared amplitude spectra, smthing the value f the sum with an peratr that returns the median f the amplitude in.5 Hz bins (using the MATLAB functin medfiltl), and taking the square rts f the smthed spectra. The ratis were cmputed frm the smthed spectra, and t facilitate the cmparisn fr the varius events, emphasizing the verall trend and eliminating large fluctuatins, the ratis were smthed using a 1 Hz median peratr. We did tests t insure that the results are nt sensitive t the chice f smthing peratrs. The decisin t cmbine the hrizntal cmpnents instead f rtating them int lngitudinal and transverse directins was mtivated by the difficulty f determining a single pint surce frm which the mtins riginated; the near-fault recrdings f the Nrthridge 1994 mainshck are cmprised f three successive S-wave arrivals cming frm

7 122 G. Cultrera, D. M. Bre, W. B. Jyner, and C. M. Dietel shear-wave velcity (m/sec) Gelgic lgs I I I I I I I I U. Fill _ 2 i1 11 n E t," E v t-- c~ (D 4 6 m m ~ B A JD E L. t~ t-i UJ C Z I.U "~ m C I'- U. ffl n E 1} Q,. :D U. t,.- t~ tt. 8 I. C tl " IP C ltl I.t. U E C rr a) r- C U) U C "m N m "~ e- g. C 8 " -J I :;D '-! 9 8 Jensen admin, building - - Jensen generatr building mlm me : I - : _ - - Rinaldi Ls Angeles Dam JAB JGB Figure 4. Shear-wave velcity prfiles cmputed at fur sites clse t the recrding statins (JAB, JGB, RIN, and LAD). Simplified gelgic lgs are shwn fr crrelatin with velcities, giving the prbable gelgic age and the crrelatin with reginally mapped gelgic units (frm Gibbs et al. 1996). RIN LAD different psitins n the fault (Wald et al., 1996). In additin, the lcatins f sme f the aftershcks ccurring within a few minutes f the mainshck have nt been determined. We restricted ur study t frequencies between 1 and 1 Hz, a frequency range f imprtance t civil engineering. We perfrmed a signal-t-nise analysis t shw that the windwed recrds are reliable at least frm 1 t 1 Hz, and we simulated the analg-t-digital prcess t verify that dig- itizing the lw-amplitude film recrds did nt alter the spectral estimates abve 1 Hz. We did the latter by simulating the time series f a small earthquake, cnverting the amplitudes t pixel units, truncating t the nearest integer values, and then cmparing the Furier amplitude spectrum f the "digitized" recrd with the spectrum f the riginal recrd. The differences were nt significant in the 1-1 Hz frequency range. We als prcessed ne f the fixed traces adjacent t the smallest aftershck (AS4) as if it were a data

8 Nnlinear Sil Respnse in the Vicinity f the Van Nrman Cmplex Fllwing the 1994 Nrthridge, Califrnia, Earthquake I E.m >.3.3 JGBF.3 I I I I I I q I I I I I I I time (s) time (s) Figure 5. Nrth cmpnent velcity f the 29 Nvember 1997 event recrded by the fur GES velcity digital recrders inside and utside the Jensen administratin and generatr buildings (JAB, JABF and JGB, JGBF). I I I trace and fund that the Furier spectrum frm this fixed trace was at least a factr f 8 times smaller than the Furier spectrum frm the aftershck ver the 1-1 Hz frequency range. We cnclude that digitizing and prcessing nise is much smaller than the signal between 1 t 1 Hz, even fr the smallest mtins studied in this article. JGB), and at free-field sites, clse t the brehle lcatins (JABF, JGBF). The relative lcatins f the building sites and free-field sites are shwn in Figure 3. The instruments recrded several events whse peak grund velcity (PGV) at JGB ranged frm.5 t.15 cm/sec (Table 3). Figure Analysis f Data frm the Jensen Filtratin Plant The tw permanent accelergraph statins at the JFP cnstitute an ideal site-respnse experiment: they are situated n very different sils and yet are clse t ne anther (thereby making it likely that they have the same surce and path effects), and they prvided many recrds f differentsize earthquakes. Unfrtunately, bth f the SMA-1 accelergraphs are hused in buildings, and as we will shw, there is a significant effect f the buildings n the recrds. We first discuss the results f ur experiment fr assessing the imprtance f the structures n the recrdings. We then cmpare the spectral ratis f data btained frm the permanent accelergraphs, after crrecting the ratis fr the effects f the structures. The data include recrdings f the mainshck, aftershcks that ccurred minutes t years after the mainshck, cda waves f the mainshck, and a few cda waves f the aftershcks. The aftershcks have been divided int tw grups: thse that ccurred mnths t years after the mainshck, and aftershcks that ccurred within a half day f the mainshck. Effect f the Buildings n the Recrdings (GES Data) In rder t investigate the influence f the structures n the seismic mtin, we set up GES recrding statins in the buildings, clse t the SMA-1 accelergraphs (JAB, z LL J [3_ BLDG / FREE_FIELD JGB/JGBF ~ Weak Mtin Average (PGV.15 cm/s) I T m ~ FREQUENCY (HZ) Figure 6. Gemetric mean f the spectral rati f mtin recrded inside and utside the administratin building (JAB/JABF) and the generatr building (JGB/ JGBF). The errr bars represent plus and minus ne standard deviatin f the mean fr seven weak-mtin events (PGV at JGB less than.15 crrgsec) recrded n the prtable GES instruments.

9 1222 G. Cultrera, D. M. Bre, W. B. Jyner, and C. M. Dietel 5 shws the velcity time series f a weak-mtin event recrded inside and utside the tw buildings. The mtin recrded at JAB is lacking high-frequency grund mtin cmpared with the free-field site (JABF). The JGB instrument, n the ther hand, recrded a signal very similar t that f JGBF, thugh there is a slight difference in amplitude. These time-dmain differences shw up clearly in the gemetric average f the spectral ratis inside and utside the structure (Figure 6). The differences in the building/freefield respnse between the tw sites is dramatic: the average spectral rati between the basement f the administratin building and the free-field site (JAB/JABF) decreases strngly with frequency beginning at 2.5 Hz, but the data frm the generatr building statin shws a relatively cnstant, small amplificatin relative t the free-field site (JGB/ JGBF). T unravel the varius effects f embedment depth, sil-structure interactin, and the averaging f mtins ver the hrizntal dimensins f the structures, plans are currently underway by C.B. Cruse (persnal cmm., 1998) t vibrate the structures and analyze the respnse using cmputer mdeling (as Cruse and Hushmand, 1989, did in studying the effect f the structure husing an accelermeter in the Imperial Valley, Califrnia). Spectral Ratis f the Accelergraph Data The main purpse f ur study is t evaluate the dependence f the spectral amplitudes at the sfter site n the level f the grund shaking at the reference site. Unfrtunately, the larger-amplitude data were recrded inside the buildings nly; free-field recrdings are available fr seven f the 1 MAINSHCK (Jan 17,1994).5 AFTERSHCK (June 26, 1995)._,,i.a JAB.5 t~ 1 "g.m t~ i i i i i t i i i i 1 2 a JGB / N68W ] 2 a time (s) JGB i i i i i i i i i J time (s) "13 1 Q. E 11 L.. ~ 1 2 ii d 13 frequency (Hz) JAB frequency (Hz) Figure 7. Hrizntal acceleratins (N22E and N68W directins) recrded at JAB and JGB SMA-1 statins during the 1994 Nrthridge mainshck and fr a weak-mtin aftershck ccurring n 26 June The figure shws the average f the Furier amplitude spectra fr the tw hrizntal cmpnents in [g sec] units; thin line, JAB; thick line, JGB. JGB JAE i 1

10 Nnlinear Sil Respnse in the Vicinity f the Van Nrman Cmplex Fllwing the 1994 Nrthridge, Califrnia, Earthquake 1223 events, but the mtins fr these recrdings are very small (see the peak velcities in Table 3). We shwed in the previus sectin that the recrdings in the structures can be very different frm the nearby free-field recrdings, particularly at JAB. In rder t remve the imprint f the structures n the data, we decided t crrect the Furier spectra f the SMA-1 acceleratins frm within the buildings by using the average building/free-field spectral ratis btained with the GES data. Several cnsideratins allwed us t use thse ratis as crrectin factrs fr the bserved spectra at the tw buildings, particularly (1) the sensr-mass release test n the GES instruments shws that their calibratin respnses are very similar, and (2) we cllected enugh event recrdings t have a stable average. In applying these crrectin functins, which were cmputed frm weak-mtin data, t the strng-mtin accelergrams, we implicitly assume that the effect f the buildings n the grund mtin is nt strngly dependent n the amplitude f the mtin. Sme justificatin fr this assumptin is that even fr very weak mtins, the administratin building shws a large structure effect. In the fllwing analysis, we apprximated the free-field spectral rati that wuld have been btained frm sites utside the buildings by multiplying the bserved spectral ratis JAB/JGB frm SMA-1 recrds by the frequency-dependent curve (JGB/JGBF)/(JAB/JABF), where (JGB/JGBF) and (JAB/JABF) are gemetric averages f the ratis frm the seven events recrded n the GES units. Mainshck and Later Afiershcks Figure 7 shws the hrizntal time series and average Furier amplitude spectra recrded at bth statins fr the 1994 Nrthridge mainshck and fr a small event in The mst evident characteristic n the recrds is the deficiency f high frequencies at JAB, particularly fr the mainshck. In Figure 8, we cmpare the crrected spectral ratis f the tw largest events (the 1994 Nrthridge mainshck, M = 6.7 and the 1994 March 2 aftershck, M = 5.3) with the crrected gemetric average f spectral ratis f weak-mtin events 2 thrugh 11 (Table 3) recrded frm 1995 t 1998 at SMA-1 and GES statins. The gemetric average f the peak grund acceleratin n the tw hrizntal cmpnents at JGB is.75 g fr the mainshck,.22 g fr the 1994 aftershck, and less than.32 g fr the small aftershcks. The relative site respnse is strngly dependent n the amplitude f the mtin. The amplificatins f the mainshck and the 2 March 1994 event are similar and significantly smaller than thse fr the weak-mtin events fr frequencies greater than abut 2.5 Hz. Even withut crrectin fr the building/ free-field respnse factr, the relative differences in the JAB/ JGB ratis between strng and weak mtin wuld be the same, indicating the sil respnse is a functin f the strength f grund shaking. Immediate Aftershcks We refer t aftershcks AS1 thrugh AS4 (Table 3) as "immediate" aftershcks because they ccurred within tw minutes f the mainshck. We als Z D u.l t JAB/JG B independ~_eve~ _~ _ m MAINSHCK (PGA=.75 g; PGV=69 em/s) - MARCH 2, 1994 (PGA=.22 g; PGV=16.9 cm/s) WEAK MTIN (PGA.32 g; PGVI.8 cm/s) I I I I I I I I FREQUENCY (HZ) Figure 8. Spectral ratis (JAB/JGB) crrected fr the effect f the structure in which the recrdings were made, f the malnshck, March 2 aftershck, and gemetric average f the independent weak-mtin recrdings. We cmputed the PGA and PGV values as the gemetric mean f the maximum peaks in the tw hrizntal directins at JGB. The small amplitude signals (ten events) have been recrded frm 1995 t 1998 at SMA-1 (three events) and GES statins (seven events) inside the tw Jensen buildings (JAB, JGB) and the errr bars were derived by cmbining the standard deviatin f the bservatins abut the mean spectral rati f the weak-mtin events (events 2-11 in Table 3) and the uncertainty in the free-field/building effect. include AS6 and AS7 in this gruping, althugh they ccurred eleven t twelve hurs after the mainshck (AS5 was nt recrded at JAB and JGB). The peak grund-mtin values at JGB fr these aftershcks range frm.13 g (fr AS1) t.16 g (fr AS4). Figure 9 shws the crrected spectral ratis cmputed fr the immediate aftershcks and, fr cmparisn, the average spectral rati f the weak-mtin aftershcks ccurring several years after the mainshck (this rati is referred t as the weak-mtin average in the figures). Als shwn is the rati f the mainshck mtins. (The spectra f the immediate aftershcks will be influenced by the cda f the mainshck, particularly at lw frequencies; what is imprtant is that we are extracting lw-amplitude mtins fr cmparisn with the strnger mtins.) Fr frequencies between abut 2 and 4 Hz, the ratis f the smaller immediate aftershcks (AS2, AS4, and AS6) are similar t thse fr the later weak mtins and differ frm the larger immediate aftershcks (AS1, AS3, and AS7). Whether this difference is meaningful is uncertain. Mre imprtantly, the high-frequency ratis (abve abut 4 Hz) fr

11 1224 G. Cuitrera, D. M. Bre, W. B. Jyner, and C. M. Dietel 4 3 Z 2 m -- 1._ ~,&~4,~~ Mainshck (PGA=.75 g; PGV=69 cm/s) AS2 (PGA=.37 g; PGV=1. cm/s)... AS4 (PGA=.16 g; PGV=.4 cm/s)... AS6 (PGA=.27 g) WEAK MTIN AVERAGE ~4~# Mainshck (PGA=.75 g; PGV=69 cm/s) AS1 (PGA=.13 g; PGV=6.4 cm/s)... AS3 (PGA=.7 g; PGV=2.7 cm/s)... AS7 (PGA=.65 g) WEAK MTIN AVERAGE (a! (b! ] FREQUENCY (HZ) FREQUENCY (HZ) Figure 9. Cmparisn between the crrected spectral ratis f six immediate aftershcks (mst within three minutes f the mainshck) and the crrected average f the independent weak-mtin recrdings at the Jensen statins (the errr bars shw the standard deviatin f the bservatins abut the average spectral rati and include the uncertainty f the free-field/building crrectin). The ratis have been crrected fr the effect f the structure in which the recrdings were made. T facilitate the cmparisn, the smaller and larger immediate aftershcks are shwn separately in parts (a) and (b). All peak mtins are fr JGB; see Figure 8 captin. all f the immediate aftershcks are very different frm the ratis f the later aftershcks and are similar t the mainshck rati despite the relatively small-amplitude mtins f the immediate aftershcks. As we discuss later, the apparent difference f the ratis f small-amplitude mtins accrding t whether the mtins were btained immediately after the mainshck r at a later time may be explained by an increase in pre pressure during the mainshck strng shaking that did nt dissipate fr hurs. Cda Waves T augment the mtins frm individual events, we cmputed spectral ratis f the hrizntal mtin frm cda waves f the larger events. We defined the cda as the prtin f the S-wave starting after the shaking drpped t less than abut 2% f the peak acceleratin. Figure 1a shws the ratis fr the mainshck cda, the cda f the tw larger immediate aftershcks, and fr cmparisn, the rati f the S-wave prtin f the mainshck. In spite f the large difference in amplitudes (peak acceleratins ranging frm.16 t.75 g), the spectral ratis f the mtins within the first tw minutes f the mainshck are all similar (ratis f the S-wave prtins f the immediate aftershcks are shwn in Figure 9 and t avid clutter have nt been included in Figure 1a). In cntrast, Figure 1b shws that the ratis f cda amplitudes fr the 2 March 1994 and 26 June 1995 aftershcks are similar t the ratis f the S-wave prtins f the ten weak-mtin events that we use as a reference, even thugh the amplitudes f the cdas are similar t thse f the cdas f the immediate aftershcks. The rati f the cda fr the March 2 event differs significantly frm the rati f S-wave prtin f the March 2 earthquake (Figure 8). Discussin T summarize, the spectral ratis frm the mainshck and their cda, the immediate aftershcks and their cda, and the large aftershck n 2 March 1994 all shw a deficiency f high-frequency mtin at JAB relative t JGB that is nt seen in the spectral ratis f the weakmtin aftershcks ccurring several years later. We cnsider the differences in the ratis f strng shaking and the weak-mtin average t be direct evidence fr nnlinear respnse f the sils. In a later sectin, predictins based n cnventinal engineering practice indicate that the nnlinearity is ccurring at shallw depths, primarily between 9 and 15 m. A questin is whether the nnlinearity wuld be the same in the absence f the structure, r whether sme prperty f the structure r its respnse mdified the nnlinear sil respnse. We have n way answering this questin, but

12 Nnlinear Sil Respnse in the Vicinity f the Van Nrman Cmplex Fllwing the 1994 Nrthridge, Califrnia, Earthquake 1225 JAB/JGB: cda f MS and early AS 4 JAB/JGB: cda f later AS~: z2 u- 1.J n FREQUENCY (HZ) S-wave: WEAK MTIN AVERAGE.3 cda: MARCH 2, 1994 (PGA=.2 g)... cda: JUNE 26, 1992 {PGA=13 ) (b).2 I I I I I I I I FREQUENCY (HZ) Figure 1. Cda-wave spectral ratis: (a) fr the larger events n 17 January 1994; (b) fr independent events. Fr cmparisn, (a) cntains the rati f the S-wave prtin f the mainshck, and (b) cntains the weak-mtin average (the errr bars shw plus and minus ne standard deviatin f the bservatins abut the average spectral rati and include the uncertainty f the free-field/building crrectin). The ratis have been crrected fr the effect f the structure in which the recrdings were made. All peak mtins are fr JGB; see Figure 8 captin. we will maintain the prtable instruments in the field as lng as pssible, hping that they will recrd a mtin large enugh t assess whether the nnlinear respnse is identical at the free-field sites and the building sites. Analysis f Data frm Rinaldi and Ls Angeles Dam The secnd pair f sites we analyzed (RIN and LAD) are installed suth f the JFP in free-field lcatins; unlike the case fr the Jensen plant recrdings, we d nt have t make crrectins fr the effect f structure in which the recrder is hused. The distance between the tw statins is 1.5 km (Figure 2), and the difference in the S-wave velcity mdel at the tw sites is greater than fr the Jensen statins (Figure 4). Because f the greater distance between the statins, the assumptin that the spectral rati is a direct estimate f the relative site respnse between the tw statins is less certain than it is fr the Jensen statins. The deepest parts f the brehles penetrated different gelgic units, althugh the ages and velcities f these units are similar (Figure 4). In the calculatin f spectral ratis, we chse LAD as a reference site because it wuld be classified as a rck site based n the gelgic descriptin f the brehle cuttings (see Gibbs et al., 1996). This descriptin is cnsistent with the shear-wave velcities beneath the site (V3 = 647 m/sec, cmpared with 62 m/sec fr an average rck site, accrding t Bre and Jyner, 1997). It shuld be nted, hwever, that the measurement f D = 8% indicates strng attenuatin in the upper 9 m. As we will see, this large attenuatin will influence the level f the spectral ratis (with the spectra frm LAD in the denminatr). The nly data we have recrded at bth RIN and LAD are the recrds f the mainshck and ne aftershck ccurring abut ten minutes after the mainshck (AS5); we als used the cda waves f the mainshck mtin as a surrgate fr small amplitude earthquake recrdings. Time series and spectra fr the mainshck recrded at RIN and LAD are shwn in Figure 11. The largest grund-mtin velcity ever recrded frm an earthquake (ver 17 cm/sec n ne hrizntal cmpnent) was derived frm the accelergraph recrding at RIN (the gemetric average f the tw hrizntal cmpnents is 114 cm/sec). The spectrum fr tile mtin at RIN suggests the presence f three peaks at 1, 3, and near 5 Hz, which is clse t the sequence f frequencies expected fr resnance in a layer ver a halfspace. If the peaks are due t resnances in site respnse, it might be expected that the frequencies f these peaks wuld be a functin f amplitude f shaking because f changes in shear-wave velcity resulting frm nnlinear sil respnse. We fund n cnsistent patterns in the peaks f the mtins. Anticipating the

13 1226 G. Cultrera, D. M. Bre, W. B. Jyner, and C. M. Dietel I1) E MAINSHCK (Jan 17,1994) 1~,q~ NS 1 ' RIN 1 I I [ I I I I I f I LAD EW I I I I I [ I I I I ] time (s) 1 ~ 11 d 1 e RIN I I i I I I I I 1 1 frequency (Hz) Figure l 1. Hrizntal acceleratins (N-S and E- W directins) recrded at RIN and LAD SMA-1 statins during the 1994 Nrthridge mainshck. The figure shws the hrizntal average amplitude Furier spectra f these recrds in [g sec] units, with thin line fr RIN and thick line fr LAD. result, we d nt think that a cnvincing case fr nnlinear sil respnse can be made frm the peaks in the spectral ratis; n the ther hand, differences in the verall levels f the RIN/LAD spectral rati fr the mainshck, the mainshck cda, and AS5 are prbably an indicatin f sil nnlinearity. Mainshck and Weak-Mtin Spectral Ratis The spectral ratis fr the mainshck S-wave, a prtin f the cda fllwing the S-wave, and AS5 are shwn in Figure 12. The mainshck mtin at RIN relative t the grund shaking recrded at LAD is amplified by factrs ranging frm 1.1 t 3 fr frequencies higher than 1 Hz, with three peaks in the frequency range f 1 t 6 Hz. The spectral Z _ ii._1 13_ RIN/LAD Jan 17, 1994 MAINSHCK (PGA=.37 g; PGV=58.8 cm/s)... CDA RATI (PGA=.68 g) AS5 (PGA=.54 g) I I I I I FREQUENCY (HZ) I I I 7891 Figure 12. Hrizntal spectral ratis f mtins recrded at RIN and LAD, including the mainshck, cda waves f the mainshck, and an aftershck ccurring abut 1 min after the mainshck. The PGA values are the gemetric means f the tw hrizntal cmpnents at LAD. ratis fr the cda waves and AS5 are generally larger than thse fr the mainshck, unlike the case fr the Jensen recrdings, fr which the mainshck ratis, aftershck ratis, and cda ratis were similar (e.g., Figures 9 and 1a). The cda and AS5 ratis have spectral peaks, but they ccur at different frequencies frm each ther and frm the peaks in the mainshck rati. We think it is difficult t relate these peaks t thse in the mainshck spectral rati, and mrever, as shwn later they d nt agree in lcatin with predictins using the shear-wave velcities frm the brehles. The imprtant bservatin is the verall difference in spectral rati between the mainshck and the weaker amplitude cda and AS5 mtins. We cnsider this t be an indicatin f sil nnlinearity. In the next main sectin we will cmpare the bservatins with predictins using cnventinal engineering practice fr accunting fr sil nnlinearity. Hrizntal t Vertical Spectral Rati Sme authrs have fund that the rati f hrizntal t vertical mtin (H/V) can be used t identify site resnances, at least fr the resnant peak f the fundamental mde (e.g., Lerm and Chavez-Garcia, 1993; Field and Jacb, 1995; Bnilla et al., 1997). Shifts in the frequencies f the resnance mdes as a functin f amplitude f shaking might be an indicatin f sil nnlinearity. We shw the H/V spectral ratis at RIN and LAD fr the mainshck, cda, and AS5 in Figure 13. The H/V fr the mainshck has peaks near 1, 2.8, and 5.5 Hz, which are grssly similar t thse in the RIN/

14 Nnlinear Sil Respnse in the Vicinity f the Van Nrman Cmplex Fllwing the 1994 Nrthridge, Califrnia, Earthquake RIN Jan 17, 1994 (a) 1 LAD Jan 17, 1994 (b) ~2 "1- I 2- L i I I II ml I 1 I I i # MAINSHCK... CDA RATI - - AS5 I I I I I I I I I MAINSHCK... CDA RATI AS5 I I I I I I I I FREQUENCY (HZ) FREQUENCY (HZ) Figure 13. Ratis f hrizntal-cmpnent t vertical-cmpnent Furier amplitude spectra at PIN and LAD fr the mainshck, the cda f the mainshck, and an aftershck ccurring abut 1 rain after the mainshck. A limited frequency range is shwn fr LAD because the AS5 data were filtered at 1.8 Hz n the vertical cmpnent. LAD rati fr the mainshck. The cmparisn, hwever, is nt very certain. The mre bvius feature in Figure 13 is the large difference in H/V between the mainshck and the weaker mtins at statin RIN (similar differences are nt seen at LAD). We d nt knw if the difference is related t sil nnlinearity r t sme ther factrs that are nt amplitude-dependent (such as radiatin pattern r surce finiteness). We shw H/V mre fr cmpleteness f the analysis than because we can use it in an argument fr r against nnlinearity f sil respnse; the dependence f the RIN/LAD rati is a mre direct indicatin f sil nnlinearity. Cmparisn f the Spectral Ratis with Predictins f Sil Respnse using Cnventinal Engineering Practice The data analysis in the previus sectins shwed that the spectral ratis depend n the amplitude f the grund shaking. The mst bvius explanatin fr this behavir is nnlinear sil respnse. In this sectin, we fllw cnventinal engineering practice t simulate the effects f sil nnlinearity n the spectral ratis; we cmpare the simulated ratis t the bserved ratis. The Cmputatin f Nnlinear Respnse Cnventinal engineering practice fr the simulatin f nnlinear sil respnse uses the equivalent linear methd, as implemented by the prgram SHAKE91 (Schnabel et al., 1972, Idriss and Sun, 1992). We fllw that practice in ur simulatins. The equivalent linear methd is based n the assumptin that the sil respnse can be apprximated by a linear viscelastic mdel, whse prperties (shear mdulus and damping) are chsen in accrd with the average strain ccurring at the middle f each sil layer. Given the time series at the base f the stack f sil layers, the respnse f the system t vertically prpagating shear waves is calculated. The cmputer prgram requires a time series as input mtin and curves describing the strain-dependence f shear mdulus and damping at varius depths. We used tw different sets f shear mdulus and damping rati curves. ne is included in the sample input fr the SHAKE91 prgram (Idriss and Sun, 1992, Table 1), and the ther was recmmended t us by W. Silva as being apprpriate fr ur applicatin (W. Silva, persnal cmm., 1997). We mdified the lw-strain damping using the measured values frm Table 2, and we used the brehle velcity prfiles in Figure 4 t define the lw-strain values f the shear mdulus. The theretical spectral ratis (JAB/JGB) btained with the tw sets f mdulus reductin and damping curves were very similar and, fr simplicity, fr cmparisn with data we decided t use nly the curves included in the sample input fr the SHAKE91 prgram. The SHAKE91 prgram requires the specificatin f a time series as input at the base f the sil layers. This is

15 1228 G. Cultrera, D. M. Bre, W. B. Jyner, and C. M. Dietel ften taken as the surface mtin at the reference site. As pinted ut by a number f authrs (e.g., Steidl et al., 1996, and Bre and Jyner, 1997), hwever, this prcedure is incrrect: it is imprtant t remve the respnse f the reference site, even if the site is underlain by rck. We did this by using an ptin in SHAKE91 t decnvlve the bserved surface mtins t btain the mtins at the bttms f the reference site brehles (JGB and LAD). This gave mtins at the bttm that are cnsistent with any nnlinear respnse included in the SHAKE91 calculatins. We used these decnvlved reference-site mtins as input t the sil clumns under the ther pair f statins (i.e., decnvlved JGB and LAD as input t JAB and RIN, respectively). Surface mtins were calculated fr each f the tw hrizntal cmpnents f input mtin. We treated these in the same way as we did the bserved time series, cmputing spectral ratis (JAB/JGB and RIN/LAD) f the averaged hrizntal cmpnents. In these ratis, the actual surface mtins at the reference sites, rather than the decnvlved mtins, were used in the denminatrs; the decnvlved mtins were nly used as input at the base f the numeratr sites (we verified that cnvlving the decnvlved recrds returned the surface mtins). All f ur calculatins assume hrizntally stratified layers and vertical incidence; runs with a purely linear mdel fr angles f incidence up t 4 degrees gave results similar t vertical incidence. T emphasize the dependence f the sil respnse n the amplitude f the input mtin, we present ratis f the relative site respnse (e.g., JAB/JGB) cmputed fr strng shaking and fr weak shaking. The advantage f using ratis f ratis is that it islates the relative changes due t nnlinearity; even if the cmputed relative-site respnses are nt cmputed exactly because f differences between reality and ur mdels (due, fr example, t lateral hetergeneities in sil prperties), we expect that relative changes in the ratis as a functin f sil amplitude will nt be sensitive t these inadequacies in the sil mdel. Cmparisn f Simulated and bserved Amplitude -Dependence In Figure 14 we cmpare the rati f spectral ratis (that is, JAB/JGB fr strng mtin divided by the average JAB/ JGB rati fr weak mtins) fr the simulatins and fr the tw largest earthquakes recrded at the Jensen sites. The bserved and simulated ratis fr the mainshck are smewhat similar in shape. Perhaps mst significant is the agreement f the reductins in amplitude (by factrs f.2-.6) fr frequencies abve abut 4 Hz. The cmparisn between bservatins and simulatins fr the March 2 event is nt nearly s gd, with the bservatins indicatingmre nnlinearity than predicted by the thery. Bth the bservatins and the simulatins, hwever, shw reductins in amplitude fr frequencies greater than abut 4 Hz. The cmparisns shwn in Figure 14 suggest that a significant prtin f the relative sil respnse f the tw sites can be explained by standard equivalent-linear mdels. t~ m (.9 v 133 (.9 v JAB/JGB bservatins & thery: large/weak 4 MAIN/WEAK: bserved 3 MAINANEAK: equivalent linear... MAR2/WEAK: bserved... MAR2D/VEAK: equivalent linear 2 Qs_JAB = 14., Qs_JGB = \ "\ I' I \ "'.U If 1, KJ' I I I I I I I I FREQUENCY (Hz) Figure 14. Ratis f relative site respnse at JAB/ JGB fr large events (mainshck and March 2 aftershck) and weak-amplitude mtins. Cmparisn between the bserved data and the theretical cmputatins frm the equivalent linear methd (SHAKE91 cde). Recall that the JAB/JGB spectral ratis fr the weakamplitude mtins immediately fllwing the mainshck are similar t the rati f mainshck spectra (Figures 9 and 1a). In cntrast, the predicted rati f spectral ratis fr the small aftershcks are essentially equal t unity (we did the cmputatins fr the 26 June 1995 aftershck with PGA =.32 g, but fr clarity did nt plt the results in Figure 14). An explanatin fr this difference in bserved and predicted dependence f the spectral ratis n amplitude f shaking might be that pre pressure increased as a result f the strng shaking, causing changes in the prperties f the sil that persisted fr at least the fllwing twelve hurs. The persistence f excess pre pressure during the mainshck culd explain the differences in site respnse fr the immediate aftershcks and fr the cda waves. A recent study f liquefactin, bserved with a vertical array during the 1995 Kbe earthquake (Aguirre and Irikura, 1997), shws that the change f sil rigidity gradually recvers with time and the liquefied state remains at least 3 hr after the mainshck but n mre than 24 hr. Similar behavir was bserved during the 1987 Superstitin Hills earthquake (Hlzer et al, 1989). The existence f elevated pre pressure at the Jensen Filtratin Plant is suggested by lateral displacements bserved near JAB, althugh we cannt be sure that liquefactin ccurred because n sand bils were bserved at the surface f the site (Stewart et al., 1996). The cmparisn f the simulated and bserved re-

16 Nnlinear Sil Respnse in the Vicinity f the Van Nrman Cmplex Fllwing the 1994 Nrthridge, Califrnia, Earthquake 1229 spnses fr RIN/LAD are shwn in Figure 15. Because we d nt have a well determined estimate f the lw-amplitude ratis, we cannt cmpute a rati f spectral ratis, as we did fr the Jensen recrdings. In this case, the figure shws the spectral ratis themselves. The spectral ratis fr bth the linear and equivalent-linear mdels and the bservatins are greater than unity. (The linear calculatins were dne using C. Mueller's prgram RATTLE and are based n the Thmsn-Haskell methd.) The theretical ratis are cntrlled bth by amplificatins at RIN and by a reductin f the high-frequency amplificatin at the reference site (LAD) caused by the large lw-strain damping at that site (D = 8%). (The high-frequency amplificatin fr the linear mdel is abut 1.5 times higher than it wuld be if n attenuatin were included.) Bth the purely linear and the equivalent-linear calculatins match the verall bserved level f the spectral rati fr frequencies less than abut 4 Hz. Fr higher frequencies, hwever, the bserved respnse lies between the purely linear and the equivalent-linear respnses. Based n this cmparisn, we cnclude that the sil respnse was nt quite as nnlinear at RIN as predicted by standard engineering practice. f interest in the understanding the results are the layers in which mst f the nnlinearity ccurs. This infrmatin is part f the utput f prgram SHAKE91. At JAB, mst f the nnlinearity ccurred at depths between 9 t 15 m. The lw shear mdulus in this depth range (see Figure 4) pr- 2 1 RIN/LAD bservatins & thery Qs_RIN=45.3 Qs LAD=6.4,, 3 e ~ t~, # ~ n MAINSHCK: bserved... MAINSHCK: linear.-..-,-,- MAINSHCK:equivalent linear I I I t I I I I FREQUENCY (HZ) Figure 15. Cmparisn between the bserved and theretical spectral ratis (RIN~AD) fr the 1994 Nrthridge earthquake. We cmputed the transfer functins at the tw sites using purely linear calculatins (prgram RATTLE) and equivalent linear calculatins (prgram SHAKE91). duced a very large cncentratin f strain cmpared with the ther layers (mre than 1 times higher). Even thugh the shear-wave velcities beneath RIN are generally lwer than thse at JAB, the strain cncentratin beneath RIN was nt as great as at JAB, being abut 3 times higher than in ther layers fr depths between 6 t 13 meters. Therefre, the nnlinearity f the respnse was nt as great. The difference in strain is understandable in terms f the details f the velcity prfiles (Figure 4): the velcity is smaller at RIN near the surface, but shear strain must g t. near the surface, s the lw near-surface velcity at RIN des nt lead t a strain cncentratin. In cntrast, the lw velcity fluvial terrace depsits at JAB are sandwiched between the higher velcity engineered fill abve and the Saugus frmatin belw at a sufficient depth that significant strain cncentratins can ccur. ur gal in this sectin was simply t cmpare the bserved sil respnse with that cmputed using cnventinal engineering practice. We have made n attempt t prvide a quantitative assessment f the discrepancies between the simulated and bserved respnses. This wuld require estimates f the uncertainty in the equivalent linear calculatins due t variatins in the sil prperties, the input mtin, and the mdel f nnlinear respnse (plane layers, vertical prpagatin, equivalent linear analysis). Cnclusins We have shwn that the spectral ratis f mtins at tw pairs f sites in the VNC n the edge f the San Fernand Valley in Califrnia are dependent n the amplitude f the shaking. At the JFP, the spectral rati fr site JAB relative t JGB fr the mainshck was as much as a factr f.3 smaller than the rati fr lw-strain mtins, indicating substantial nnlinear respnse f the sils. The amplitude dependence f the ratis is in general agreement with equivalent linear calculatins using cnventinal engineering practice and lw-strain prperties measured at the sites. ne exceptin t the amplitude dependence f the ratis were the ratis fr small mtins within the first twelve hurs after the mainshck; at high frequencies these mtins have similar spectral ratis t that f the mainshck. The difference in behavir f these lw-strain mtins immediately after the mainshck and mtins recrded mnths t years after the mainshck may be due t the persistence f increases in pre pressure at JAB that riginated during the mainshck. Using recrdings f small earthquakes n prtable seismgraphs installed almst fur years after the mainshck, we cnclude that the mtins f the permanently-installed accelermeters that recrded the mainshck and a number f aftershcks are influenced by the buildings in which the instruments are hused. The effect is particularly nticeable at statin JAB, fr which the high-frequency mtins are reduced t less than.4 f thse at a nearby free-field site. This strng building effect des nt impact ur cnclusins abut sil nnlinearity, fr we use the relative change in

17 123 G. Cultrera, D. M. Bre, W. B. Jyner, and C. M. Dietel ratis as a functin f amplitude f grund mtin fr a suite f recrdings made n the same instruments. It des impact t sme extent many f the studies that used the JAB mainshck recrd and the weak-mtin aftershck recrding frm the U.C. Santa Barbara statin lcated utside f (nt clcated with) JAB in their search fr sil nnlinearity during the 1994 Nrthridge earthquake; this includes Trifunac and Tdrvska (1996), Field et al. (1997, 1998), Beresnev et al (1998a), and Suet al. (1998). Frtunately, these studies used data frm many sil sites, s the impact f including JAB wuld be strngly diluted. At the Rinaldi Receiving Statin, ur data are nt as cmplete as at the Jensen plant, but we again find evidence fr nnlinear sil respnse during the mainshck. The spectral amplitudes at the sil site (RIN) are elevated relative t thse at the rck site (LAD) fr all frequencies studied in this paper (1-1 Hz). This is prbably due t a cmbinatin f site amplificatin at RIN and the large amunt f shearwave damping at the reference site (LAD). The bserved rati fr the mainshck falls between the predictins frm the linear and equivalent linear mdels, suggesting that the degree f nnlinearity is smewhat smaller than predicted by standard practice. Acknwledgments We we thanks t many peple wh helped us in this research: Craig Davis and Rn Tgnazzini f the LADWP fr data, discussins, and a tur f the sites; Gerge Barker, Duglas Cx, and David Dean f the MWD fr assistance in the deplyment f the prtable GEtS recrders at the Jensen Filtratin Plant; Jack Batwright and Walt Silva fr prviding a number f useful suggestins; Walt Silva fr a set f mdulus reductin and damping rati curves; Jhn Tinsley fr sharing his knwledge f the gelgy f the area; Jim Gibbs fr prviding his measurements f attenuatin in advance f publicatin; C. B. Cruse fr giving us advice regarding the influence f the buildings n the recrded mtins and prdding us int munting the field experiment with the prtable recrders; Rn Prcella fr infrmatin abut the strng-mtin recrdings at the Jensen plant; Chris Stephens fr help in digitizing the film recrds; and Fabian Bnilla, Ken Campbell, Rb Kayen, Paul Spudich, Maria Tdrvska, and an annymus reviewer fr thughtful cmments n the manuscript. We als thank Mafia Tdrvska fr aftershck data. This prject was initiated by G. Cultrera while she was visiting the USGS n an verseas fellwship frm the University f Palerm, Italy. References Aguirre, J., and K. Irikura (1997). Nnlinearity, liquefactin, and velcity variatin f sft sil layers in Prt Island, Kbe, during the Hygken Nanbu earthquake, Bull. Seism. Sc. Am. 87, Andersn, J. G., and S. E. Hugh (1984). A mdel fr the shape f the Furier amplitude spectrum f acceleratin at high frequencies, Bull. Seism. Sc. Am. 74, Bardet, J. P., and C. Davis (1996a). Engineering bservatins n grund mtin at the Van Nrman Cmplex after the 1994 Nrthridge Earthquake, Bull. Seism. Sc. Am. 86, $333-$349. Bardet, J. P., and C. Davis (1996b). Perfrmance f the San Fernand Dams during the 1994 Nrthridge earthquake, J. Getech. Eng. Div., ASCE, 122, 7. Bardet, J. P., and C. Davis (1996c). Perfrmance f the tw reservirs during the 1994 Nrthridge earthquake, J. Getech. Eng. Div., ASCE, 122, 8. Beresnev, I. A., G. M. Atldnsn, P. A. Jhnsn, and E. H. Field (1998a). Stchastic finite-fault mdeling f grund mtins frm the 1994 Nrthridge, Califrnia earthquake. II. Widespread nnlinear respnse at sil sites, Bull. Seism. Sc. Am. 88, Beresnev, I. A., E. H. Field, K. Van Den Abeele, and P. A. Jhnsn (1998b). Magnitude f nnlinear sediment respnse in Ls Angeles basin during the 1994 Nrthridge, Califrnia, earthquake, Bull Seism. Sc. Am. 88, Bnilla, L. F., J. H. Steidl, G. T. Lindley, A. G. Tumarkin, and R. J. Archuleta (1997). Site amplificatin in the San Femand Valley, Califrnia: variability f site-effect estimatin using the S-wave, cda, and H/V methds, Bull. Seism. Sc. Am. 87, Bre, D. M., and W. B. Jyner (1997). Site-amplificatins fr generic rck sites, Bull. Seism. Sc. Am. 87, Brcherdt, R. D., J. B. Fletcher, E. G. Jensen, G. L. Maxwell, J. R. Van Schaak, R. E. Warrick, E. Cranswick, M. J. S. Jhnstn, and R. McCleam (1985). A general earthquake-bservatin system, Bull. Seism. Sc. Am. 75, Cruse, C. B., and B. Hushmand (1989). Sil-structure interactin at CDMG and USGS accelergraph statins, Bull. Seism. Sc. Am. 79, Electric Pwer Research Institute (EPRI) (1993). Guidelines fr determining design basis grund mtins, Electric Pwer Research Institute, Pal" Alt, Califrnia, Rept. N. EPRI TR Field, E. H., and K. H. Jacb (1995). A cmparisn and test f varius siterespnse estimatin techniques, including three that are nt referencesite dependent, Bull. Seism. Sc. Am. 85, Field, E. H., P. A. Jhnsn, I. A. Beresnev, and Y. Zeng (1997). Nnlinear grund-mtin amplificatin by sediments during the 1994 Nrthridge earthquake, Nature 39, Field, E. H., Y. Zeng, P. A. Jhnsn, and I. A. Beresnev (1998). Nnlinear sediment respnse during the 1994 Nrthridge earthquake: bservatins and finite-surce simulatins, J. Gephys. Res. 13, 26,869-26,883. Gibbs, J. F., D. M. Bre, W. B. Jyner, and T. E. Fumal (1994). The attenuatin f seismic shear waves in Quaternary alluvium in Santa Clara Valley, Califrnia, Bull. Seism. Sc. Am. 84, Gibbs, J. F., J. C. Tinsley, and W. B. Jyner (1996). Seismic velcities and gelgic cnditins at twelve sites subjected t strng grund mtin in the 1994 Nrthridge, Califrnia earthquake, U. S. GeL Surv. pen-file Rept , 13 pp. Hartzell, S. (1998). Variability in nnlinear sediment respnse during the 1994 Nrthridge, Califrnia, earthquake, Bull Seism. Sc. Am. 88, Heatn, T. H., J. F. Hall, E. H. Field, and M. W. Halling (1995). Respnse f high-rise and base-islated buildings t a hypthetical M W 7. blind thrust earthquake, Science 267, Hlzer, T. L., T. L. Yud, and T. C. Hanks (1989). Dynamics f liquefactin during the 1987 Superstitin Hills, Califrnia, earthquake, Science 244, Idriss, I. M., and J. I. Sun (1992). User's Manual fr SHAKE91. Center fr Getechnical Mdeling, Dept. f Civil and Envirnmental Engineering, U. f Califrnia, Davis. Lerm, J., and F. J. Chavez-Garcia (1993). Site-effect evaluatin using spectral ratis with nly ne statin, Bull. Seism. Sc. Am. 83, Lindvall-Richter-Benuska Assciates (1994). Prcessed LADWP pwer system strng-mtin recrds frm the Nrthridge, Califrnia earthquake f January 17, 1994a, reprt prepared fr Ls Angeles Department f Water and Pwer, LRB N. 7-27, 165 pp. 'Rurke, T. D., B. L. Rth, and M. Hamada (1992). Large grund defrmatins and their effects n lifeline facilities: 1971 San Fernand earthquake, in Case Studies f Liquefactin and Lifeline Perfrmance During Past Earthquakes, T. D. 'Rurke and M. Hamada (Editrs) Natinal Center fr Earthquake Engineering Research, Buffal, New Yrk, Reprt NCEER-92-2, 3-iii-3-85.

18 Nnlinear Sil Respnse in the Vicinity f the Van Nrman Cmplex Fllwing the 1994 Nrthridge, Califrnia, Earthquake 1231 Schnabel, P., H. B. Seed, and J. Lysmer (1972). Mdificatin f seismgraph recrds fr effects f lcal sil cnditins, Bull. Seism. Sc. Am. 62, Scientists f the U.S. Gelgical Survey and the Suthern Califrnia Earthquake Center (1994). The magnitude 6.7 Nrthridge, Califrnia, earthquake f January 17, 1994, Science 266, Steidl, J. H., A. G. Tumarkin, and R. J. Archuleta (1996). What is a reference site? Bull. Seism. Sc. Am. 86, Stewart, J. P., R. B. Seed, and J. D. Bray (1996). Incidents f grund failure frm the 1994 Nrthridge earthquake, Bull, Seism. Sc. Am. 86, $3- $318. Su, F., J. G. Andersn, and Y. Zeng (1998). Study f weak and strng grund mtin including nnlinearity frm the Nrthridge, Califrnia, earthquake sequence, Bull. Seism. Sc. Am. 88, Trifunac, M. D., M. I. Tdrvska, and S. S. Ivanvic (1994). A nte n distributin f uncrrected peak grund acceleratins during the Nrthridge, Califrnia, earthquake f 17 January 1994, Sil Dyn Earthquake Eng. 13, Trifunac, M. D., and M. I. Tdrvska (1996). Nnlinear sil respnse Nrthridge, Califrnia, earthquake, J. f Getechnical Engineering 122, Trifunac, M. D., M. I. Tdrvska, and V. W. Lee (1998). The Rinaldi strng mtin accelergram f the Nrthridge, Califrnia earthquake f 17 January 1994, Earthquake Spectra 14, U. S. Gelgical Survey Hme Page (1999). Wald, D. J., T. H. Heatn, and K. W. Hudnut (1996). The slip histry f the 1994 Nrthridge, Califrnia, ear,quake determined frm strngmtin, teleseismic, GPS, and leveling data, Bull. Seism. Sc. Am. 86, Wang, L.-J., Q. Gu, and W. D. Iwan (1996). A cllectin f prcessed near field earthquake aceelergrams with respnse and drift spectra, a reprt by Earthquake Engineering Research Labratry, Calif. Institute f Technlgy, Pasadena, Califrnia, Reprt N. EERL 96-5, 141 pp. Istitut Nazinale di Gefisica Via di Vigna Murata Rma, Italy cultrera@ing75.ingrrn.it (G.C.) U.S. Gelgical Survey, MS Middlefield Rad Menl Park, CA usgs.gv jyner@usgs.gv usgs.gv (D.M.B., W.B.J., C.M.D.) Manuscript received 28 July 1998.