Control of Strong Motion by the Upper 30 Meters

Transcription

1 Bulletin f the Seismlgical Sciety f America, Vl. 86, N. 6, pp , December 1996 Cntrl f Strng Mtin by the Upper 3 Meters by Jhn G. Andersn, Yajie Lee, Yuehua Zeng, and Steven Day Abstract Lcal site effects have an enrmus influence n the character f grund mtins. Currently, sil categries and site factrs used in building cdes fr seismic design are generally based n, r at least crrelated with, the seismic velcity f the surface layer. We nte, hwever, that the upper 3 m (a typical depth f investigatin) wuld almst never represent mre than 1% f the distance frm the surce;.1% t.% wuld be mre typical f situatins where mtin is damaging. We investigate the influence f this thin skin n the high-frequency prperties f seismgrams. We examine prperties f seismgrams cnsisting f vertically prpagating S waves thrugh an arbitrarily cmplex stack f flat, slid, elastic layers, where the prperties f the lwermst layer (taken at 5 km depth) and a surface layer (thickness 3 m) are cnstrained. nput at the bttm f the stack is an impulse. We find that the character f the seismgrams, and the peak spectral frequencies, are strngly influenced by the prperties f the intervening layers. Hwever, fr infinite Q, the integral f amplitude squared at the surface (which determines energy if the input and utput are regarded as velcity, r Arias intensity if the input and utput are regarded as acceleratin) is independent f the intervening layers. Als, the peak amplitude f the seismgram at the surface is relatively independent f the intervening prperties. Fr finite, frequency-independent Q, the integral f amplitude squared and peak amplitude decrease as t* increases. There is sme scatter that depends n the intervening layers, but it is surprisingly small. These calculatins suggest that the surficial gelgy has a greater influence n grund mtins than might be expected based n its thickness alne. They suggest that variable influences f Q alng the entire path have a cmparable imprtance fr predictins f grund mtins. Finally, they suggest that detailed characterizatin f deeper velcity structure in regins where a 1D mdel is apprpriate gives nly a limited amunt f added infrmatin. Based n ur 1D numerical results, we prpse a new methd t characterize these prperties as site factrs that culd be used in building cdes. Full three-dimensinal synthetics are tested and give a similar cnclusin. ntrductin n engineering site investigatin, 3 m is a typical depth f brings and detailed site characterizatins. Therefre, mst f the site-effect studies in earthquake grund mtins are based n the prperties in the upper 3 m. Fr instance, Bre et al. (1993, 1994) based their regressins fr grund mtins n average shear velcity in the upper 3 m. Brcherdt (199, 1994) and Martin and Dbry (1994) recmmended that design f structures be based n these prperties. Frm the seismlgical perspective, the upper 3 m is an extremely thin skin. Fr an earthquake at a depth f 1 t 15 kin, it represents, at mst,.3% f the path. ven at 1 Hz, it is less than the wavelength f a shear wave unless the velcity is quite lw, less than.3 km/sec. Frm this perspective, even thugh it is the sectin clsest t the structure, it is nt bvius that it shuld play a critical rle. Surprisingly, we have fund few systematic studies, either theretical r empirical, cmparing the cntributins f the upper 3 m with the rest f the path. Tw strng-mtin recrds frm the 1989 Lma Prieta earthquake prvide a gd example. Figure 1 shws the lcatins f tw strng-mtin statins, ASH (Agnews State Hspital) and HAL (Halls Valley), and the vertical prjectin f the rupture zne in the 1989 Lma Prieta earthquake. Bth statins are abut the same distance frm the rupture zne: Frm Figure 1, ASH is 4 km frm the epicenter and 4 km frm the fault, while HAL is 37 krn frm the epicenter and 3 km frm the fault. The shear velcities f the upper

2 175 J.G. Andersn, Y. Lee, Y. Zeng, and S. Day Lrn Priet arthquke Oct 17, 1989 A ASH We examine numerical results fr bth simple and very irregular 1D velcity mdels. Als, we change the prperties in the upper 3 m t examine their influence n the grund mtins. We als shw preliminary 3D simulatins using the cmpsite surce mdel apprach (Zeng et al, 1994; Yu, 1994) that indicate that the results frm the 1D vertical prpagatin mdel are similar t thse fr mre realistic situatins. Theretical Results \ 15km Figure 1. Map shwing lcatins f statins ASH and HAL, relative t the surface prjectin f the rupture f the 1989 Lma Prieta earthquake, after Zeng et al. (1993). m under these tw statins are 64 and 65 m/sec (Thiel and Schneider, 1993), respectively. Hwever, the grund mtins shwn in Figure at these tw statins have significant differences. The accelergrams at statin ASH have mre high-frequency energy than thse at statin HAL. Between abut.8 and Hz, hwever, they are cmparable. Differences at lwer frequencies culd result frm the radiatin pattern and surce directivity. Fllwing the methd f Andersn and Hugh (1984) t quantify the high-frequency spectral fallff, in the frequency range frm 1. t 1. Hz, we fund ~c =.64 sec at ASH, and K =.95 sec at HAL. The similar cnditins in the upper 3 m undubtedly influence the general amplitudes and characteristics f their accelergrams, but ther parts f the path then wuld be a likely cause f the significant differences. This article addresses the relative imprtance f effects f the upper 3 m, cmpared t the velcity structure belw, n vertically prpagating S waves in a hrizntally layered earth mdel. We take the perspective that we can draw upn seismlgical infrmatin fr reasnably gd cntrl f the velcity structure and Q value at 5 km depth but that the structure is cmpletely unknwn, and any reasnable structure is pssible between 5 km and 3 m belw the surface. The 5-km depth is arbitrarily chsen, and the results are independent f exactly where this lwer interface is lcated. Figure 3 illustrates the mdel that is examined in this article. The arth is mdeled as a series f N hrizntal layers verlying a unifrm half-space. The ith layer is hmgeneus and istpic, with thickness hi, density Pi, shear velcity fli, and frequency-independent spatial attenuatin quality factr Qi. The mdel is excited by a planar S wave, prpagating vertically frm within the half-space. Thus the wave is purely SH in plarizatin. By intrducing discntinuities in material prperties and cnsequent reflectin and transmissin cefficients, this mdel is mre general than the ne cnsidered by Jyner et al. (1981). They fund that the nnresnant amplificatin prduced by waves prpagating thrugh nnattenuating materials f gradually changing velcity is, in ur ntatin, ~PN + lfln + l/plfla " This amplificatin, f curse, wuld be dubled when the effect f the free surface is included. Day (1996) used the general layered mdel t examine the respnse f a perfectly elastic halfspace t an incident SH wave. He fund that certain spectral averages f the site amplificatin functin, taken ver bandwidth Af, depended nly n the elastic structure dwn t a tw-way travel-time depth f 1/Af Bth f these results are nly valid when Q is infinite. Still, they suggest a surprisingly strng influence f the shallwest part f the path, and the mtivated this numerical study. Transfer functins, and synthetic seismgrams at the surface f the layered half-space, are cmputed using prpagatr matrices based n the methd f Luc and Apsel (1983). We cmpare the surface seismgram with the input in tw ways. First, we find the rati f peak amplitude at the surface t peak amplitude f the input. This rati might generally be expected t be greater than, since the free-surface effect cntributes. Hwever, when attenuatin is included, it des nt need t be this large. Secnd, we examine the integral f amplitude squared: A = f ~ sz(t)dt in which s(t) is the seismgram at the surface. The rati asurface/ainpu t is the quantity examined by Day (1996). When the impulse and, cnsequently, s(t), is regarded as velcity, A is prprtinal t the energy in the wave field. When the seismgram is an accelergram, A is prprtinal t the Arias intensity (Arias, 197), which is (n/g) A, where g is

3 Cntrl f Strng Mtin by the Upper 3 Meters 1751 Cq ASH ( DG) : ~,, i,,, ~ i, s,,,~ LO HAL ( DG) c" ~ (1) -6 LO.84g -.57g ASH ( UP ) HAL( UP ) O O) 13. &9-6 O D AS H ~ ~'~ _ HAL ',V~ ASH (9 DG) HAL (9 DG) i i i 3O v~. L F f ~ i,,ll,,, i,,, t l frequency(hz) time(sec) Figure. Accelergrams and crrespnding Furier spectra frm statins ASH and HAL in the 1989 Lma Pfieta earthquake. Peak mtins are indicated. Furier spectra are the average f the tw hrizntal cmpnents and smthed s that the RMS amplitude is nt affected. 4,,B1 Q1 /)1 h 1 3m T-- # Q /) h #.3 Q3 /).3 h3 fin Qn #n #n+1 Qn+1 Pn+1 (Haft Space) Figure 3. t SH-wave hn The mdel used in ur calculatins. 5kin the acceleratin f gravity. Regarding the input as acceleratin, A is als clsely related t the RMS acceleratin: a~ns = RMS{s(t)} = ]A/T, where Tis the duratin f the recrd (e.g., Hanks, 1979; Hanks and McGuire, 1981). Since peak acceleratin is generally prprtinal t RMS acceleratin (e.g., Hanks and McGuire, 1981), the peak amplitudes and the squared integral A are expected t shw similar trends. The rati f peak amplitudes r the integrals f amplitude squared at the surface t the input are the same regardless f whether this input is cnsidered t be acceleratin, velcity, r displacement. Hwever, the spectrum f the input is mre like the typical spectrum f strng-mtin acceleratin (e.g., Brune, 197; Hanks, 1979) than the spectrum f strng-mtin velcity r displacement. Thus, fr applicatins t strng-mtin seismlgy, it is mst apprpriate t think f the input as an impulse in acceleratin. This article defines the "stratified medium index" (SM) as SM = (Asurface/4Ainput), fr ntatin t describe changes in A as a functin f differences in the velcity mdel. With the factr f 4 in the denminatr, SM equals unity at the surface f a unifrm, nnattenuating half-space. Thus, it culd simulate an experiment that finds the rati f Arias intensity at an arbitrary site t the Arias intensity n "rck." xcept fr the factr f 4 in the denminatr, it is the square f the RMS amplificatin, as defined by Day (1996). The terminlgy is analgus t terminlgy used by Sanchez- Sesma et al. (1986), wh defined the tpgraphical effects index (Tl) as the rati f the Arias intensity at a site affected by tpgraphy t a site in the free field. Bth f these indexes culd be special cases f a "site effects index (S)," which gives the Arias intensity rati t a reference rck site. t is cnvenient t define t* in the traditinal seismlgical sense as an average prperty f the attenuatin in the layered stack. Specifically, hi t* = ~ i= 1 ~ifli"

4 175 J.G. Andersn, Y. Lee, Y. Zeng, and S. Day n the frequency dmain, the ttal effect f attenuatin n a ray that passes directly thrugh the stack is t reduce the amplitude by e-'~*. This amplitude reductin des nt accunt fr frequency-independent transmissin cefficients at the layer bundaries. Further, waves that take a less direct path, due t multiple reflectins alng the way, will have their spectra mdified by a different factr, accunting fr multiple passages thrugh varius layers. Still, we examine this parameter t evaluate if it is a useful parameter t describe the average effects f attenuatin. Numerical Results Results based n vertical SH-wave prpagatin thrugh the mdel in Figure 3 are shwn in Figures 4 thrugh 1. Our input fr these runs is an impulsive pulse--in ther wrds, a time series with ne pint nly that is different frm zer. The pulse is input as a signal traveling vertically in layer n + 1 frm belw the interface; the respnse f the interface at a 5-km depth depends n the cntrast with the layer abve. nitially, the prperties f the surface layer are fixed as fllws: h 1 = 3 m, Pl = 1.7 g/cm 3, fix = 4 m/sec, and Q~ = 3. n additin, the prperties f the basement are fixed as ZN+ 1 = 5 m, PN+ i =.8 g/cm 3, flu+ 1 = 364 m/sec, and QN+ ~ = 1. ntervening layers are varied in a number f ways. The tw-way travel time thrugh the upper 3 m is.15 sec in this mdel, s Day (1996) indicates that spectral averages ver a bandwidth f 6.7 Hz wuld be independent f the deeper layers if Q were infinite. Q values used in ur numerical mdels are chsen t be similar t real situatins. Several studies have investigated the attenuatin effects f the near surface n shear waves. Fr instance, Haukssn et al. (1987) estimated that Q fr shear waves averages 5 between 4 m and the surface in Plicene-Pleistcene sediments in the Ls Angeles basin. At Vinyard Canyn, near Parkfield, Gibbs and Rth (1989) btained Q = 4 in the 57- t 1-m depth interval f a 195- m brehle. Fletcher et al. (199) studied tw granitic sites near Anza, Califrnia~ n the upper 5 m, they fund Q = 8 at ne and 11 at the ther. Gibbs et a. (1994) btained a mean value f Q clse t 1 ver the depth range 1 t 115 m in Santa Clara Valley, Califrnia. All these studies indicate very lw Q values near the surface. n ur numerical calculatins, we assign a Q value t the surface layer that is reasnably cnsistent with these studies and assume that it generally increases as velcity increases. The Q values assigned t intermediate layers are between thse f the surficial layer and the basement. The simplest case is fr tw layers ver the half-space (N = ). Figure 4 shws an example seismgram and spectrum fr this case, in which r = 15 m/sec Q = 15, and P =. g/cm ~. On the left, the slid line gives the cmplete seismgram at the base f the stack, at z = 5 km, and the dashed line shws the seismgram at the surface. The input S wave is an impulse arriving at the interface at t = 1. sec. The pulse arrives at the surface abut 3.5 sec later and causes the surface layer t resnate. Sme f the energy is transmitted back int layer, first arriving at the lwer interface anther 3.5 sec later. The high-frequency reverberatin at the lwer interface is caused by a series f pulses sequentially leaving layer 1 after a series f surface a- f1 = 15. Q = 15. t*=.47 (1) time(s).1 t i t i,,, i i i i i i [ frequency(hz) Figure 4. Sample calculatins fr tw layers. Seismgrams frm the base (slid) and surface (dashed) are shwn at the left. The seismgram at the base shws the vertically prpagating impulse used fr all calculatins arriving at t = 1. sec, fllwed by reflectins frm the surface. Prperties f the mdel are given in the figure. The Furier spectrum f the seismgram at the surface is given at the right.

5 Cntrl f Strng Mtin by the Upper 3 Meters 1753 reflectins. Sme f this energy is, in turn, reflected back, causing the secnd packet f energy t arrive at the surface starting at abut 11 sec. The Furier amplitude spectrum n the fight cnsists primarily f the superpsitin f tw features. Mst cnspicuus are strng peaks at 3.3, 1, and 16.7 Hz caused by the reverberatins in the thin shallw layer. This causes the "ringy" character f the signal. The clsely spaced peaks and trughs superimpsed n this majr trend are caused by the "resnance" f the thick middle layer, with a fundamental frequency f abut.8 Hz (perid f abut 13 sec). This resnance is nt seen in the seismgrams in Figure 4, since the spectral cntent f the surce emphasizes much higher frequencies. Figure 5 shws sme generalized results fr tw layers ver a half-space. The right side shws the peak amplitude rati f the seismgram n the surface t the amplitude f the input fr a series f cmputatins in which/7 and Q are taken t be variables. On the left, it shws SM fr the same cmbinatins f/7 and Q. The dashed line represents the case with very high Q] (= 1) in the surface layer. Fr the highest values f Q1 and Q, SM becmes nearly independent f flz, as predicted by Day (1996). Peak amplitude ratis are nt cmpletely independent ffl. n the limits f the intermediate layer being the same as the half-space r the upper 3 m, there is effectively nly ne layer ver the half-space, and because it is much weaker, the transmissin cefficient appraches.. With very high Q, the amplitudes are dubled again at the free surface, resulting in amplifi- catin f the peak amplitude by abut a factr f 4.. Where layer has an intermediate velcity, there are tw transmissin cefficients, and their prduct is greater than., causing the peak in the amplificatin functin when Q is high. As btained frm the equatin frm Jyner et al. (1981) that was cited earlier, the limiting amplificatin fr this case, which wuld be apprximated by a large number f layers each with a small velcity cntrast, is 7.7. As Q decreases, bth the SM and the peak amplitudes decrease. These simple calculatins indicate that the attenuatin prperties alng the entire path f wave prpagatin play a significant rle n grund-mtin predictins. n fact, they indicate that the attenuatin prperties may be mre imprtant than the velcity in the intermediate layer in affecting peak amplitude and RMS amplitudes at the surface. We nw mve t mre cmplicated cases. Figure 6 plts three f a class f mdels with bth velcity and Q values mntnically increasing with increasing depth. Figure 7 shws a very irregular mdel in which velcities in intermediate layers are chsen at randm within limits. Lwvelcity layers are included in these irregular mdels, and there is n definite relatin between the velcity and the Q values. We first examine the crrelatin between t* and the character f the seismgram in terms f SM and peak amplitudes. Figure 8 shws the results btained frm these mdels. The dashed line is fr mdels whse velcity and Q values increase mntnically with depth, and the stars 1 =- O,O(Q~ =1) / ~ " / / / 4 / 'L' " " P(m/s) P(m/s) Figure 5. Peak amplitude ratis and the stratified medium index (SM) fr mdels cnsisting f tw layers ver a half-space, as a functin f velcity in the intermediate layer. ach curve crrespnds t a different value f Q in the intermediate layer, with values as given. All curves except fr the dashed nes use ]71, = 4 rn/sec and Q = 3; the dashed curves increase Q1 t 1. SM is the rati f the integral f amplitude squared at the surface t the input at 5 km in depth. Ratis are divided by 4. t cmpensate fr amplitude dubling at the free surface and give SM = 1. n a unifrm, nnattenuating half-space.

6 1754 J.G. Andersn, Y. Lee, Y. Zeng, and S. Day (~/~) v-;, ' ' ' ' ' l i:... : Q L~ i : ' ' L:....., looo [_ :... C~ - 1._, :: r- Q) "1... i _!::... 4 J L ~'... L - - [ : -] 1 ld f~ c r~ ll CO O_ 15 1 O 5 i i....:v-,.;~,..;,-:..:.';... 1~ 1 O 69 "5 1 i ~,%,.,.,,,,,,,~ q'...,'.,,. :..:, ,;.,:....,...,.,..,,.,,,;;..; i i i,, h i, ~,,, i,,, ,,, i t, ~, 1, ~, J time(s) frequency(hz) Figure 6. Velcity (tp left) and Q (tp right) mdels with mntnic increases between the surface and 5 km in depth, and crrespnding seismgrams (bttm left) and spectra (bttm right). Tw f the seismgrams are ffset frm zer fr clarity f presentatin. T generate a velcity mdel, we fund a cntinuus functin f the frm fl(z) = cl + cz n that matched the velcity at the base f the layer 1 and the tp f the half-space. The velcity f each layer is the value f this functin at the midpint f the layer. Q mdels are fund the same way, and use the same value f n as the shear velcity mdel. Different members f this class are btained using different values f n in the range.5 N n =<.. represent the results btained frm the irregular mdels. The SM decays apprximately expnentially n t* with sme scatter, depending n the intervening layers, reaching an upper limit when velcity and Q values increase mntnically with depth (the dash line). A similar result ccurs fr the peak amplitudes. Frm these calculatins, we cnclude that fr a specific surficial site cnditin, bth SM and peak amplitude f grund mtins are reasnably well crrelated with t*, which is able t describe the attenuatin prperties f the underlying structures. Anther imprtant feature f Figure 8 is the ttal amunt f scatter in the mdels with irregular velcity prfiles. n generating the randm velcity prfiles, we allwed the velcities t deviate frm the mean by up t 3% f the mean. This is a very large range cmpared t what we believe t be mst realistic, which is a deviatin f 5% t 1%. Still, the scatter in bth SM and the peak value rati is generally less than abut 5%. Since the amunt f scatter increases with an increased amplitude f randmness in the velcity prfile, these plts suggest that the ttal influence f the details f the velcity prfile is quite small cmpared t the influence f t*. This extends the cnclusins fund by Day (1996), indicating that t* and the elastic structure at the tp f the stack, t surprisingly gd precisin, cntrl the SM and the peak mtin. As in Day (1996), these are largely independent f the deeper elastic structure. We next investigate the influence f the near-surface prperties simultaneusly with thse f underlying layers. We fix the shear velcity f the upper 3 m t the bundary values fr site classificatin prpsed by Martin and Dbry (1994) and change the prperties belw it. There are minr differences in the cutff velcities between Martin and Dbry (1994) and ther articles using this apprach (Bre et al., 1993; Brcherdt, 199, 1994). We then repeat the same calculatins as befre but use nly thse mdels with velcity and Q increasing mntnically with depth because f the upper-limit prperties mentined abve. Results btained are shwn in Figure 9. Znes A, A, B, C, and D are

7 Cntrl f Strng Mtin by the Upper 3 Meters fl(m/s) 3 OO Q v c" "13 4 t v - X3 h t 1 C 5O O -~ Q_ t*=.4 1} ~ "S time(s) O frequency(hz) Figure 7. An example f a velcity and Q mdel with randmized prperties and lw-velcity layers, tgether with the seismgram and Furier spectrum, presented with the same frmat as Figure 6. The velcity and Q mdels begin with a 1-layer representatin, fr the depth range between 3 m and 5 km, f ne f the smth mdels in the class f mdels described in the captin t Figure 6. Velcity and Q were chsen at randm frm a unifrm distributin ver a range f _+ 3% relative t the velcity and Q in the smth mdel at the center f each layer. There is n crrelatin between the deviatin f velcity and Q frm the smth mdel. site classes fr hard rck, firm rck, gravel sils t sft rck, stiff clays and sandy sils, and sft sils, respectively. The SM and the peak amplitude increase as the velcity f the surface layer decreases. This is cnsistent with regressins, such as Bre et al. (1993, 1994), that predict larger mtins n sfter materials. What is als cnspicuus is that, ver the range f t* cvered in this figure, the influence f attenuatin in the underlying layers is just as strng a factr. Sites that are in different site classes based n their shallw velcity structures can have the same RMS and peak amplitudes if the deeper attenuatin prperties cmpensate. Since we believe the range f t* cvered n this figure is representative f the range fund in the field, we cnclude that the influence f the surface layer n grund mtins is n the same rder as that f attenuatin in the underlying layers. There is n reasn that either ne can be neglected. These results suggest that an imprtant cntributin t the scatter in the predictin f grund mtins, in regressins that use a site classificatin based n surficial velcity, culd cme frm the attenuatin prperties in underlying layers. Still, these regressins d find a crrelatin between nearsurface velcity and amplitude, which culd result frm a crrelatin between t* and the near-surface velcity. Figure 9 suggests that a site classificatin that uses t* culd allw predictin f peak and RMS acceleratins with greater accuracy than site classificatins that d nt use t*. T apply this, we need a way t measure t*, and we need t assciate typical values f t* with each site categry. The first questin is if there is a practical way t evaluate t*. Andersn and Hugh (1984) bserved that at high frequencies, f, the spectrum f S-wave acceleratins is characterized by a trend f expnential decay, e ~f The spectral decay parameter, ~c, is an empirical parameter that can be easily measured frm the spectra f seismgrams f large r small earthquakes. Several subsequent articles (e.g., Andersn, 1986; Hugh et al., 1988; Hugh and Andersn, 1988) suggest that phenmena assciated with attenuatin give the mst reasnable physical explanatin fr the magnitude and behavir f K. Under certain assumptins, Tc is identical t t*: (1) when the earthquake surce spectrum is flat t accel-

8 J.G. Andersn, Y. Lee, Y. Zeng, and S. Day k ts3 C~ cq O, ~-~ ~** ~) 1k * '** ~'~ ** O,l k,, ~ ~,,,, Figure 8. SM and peak amplitude ratis, as a functin f t*, fr a series f mdels such as thse in Figures 6 and 7. The pen circles, cnnected by the dashed lines, result frm the mntnic mdels in the class described in Figure 6. Output f mdels f the type shwn in Figure 7 are pltted with asterisks. Fr these, several members f the class are used as starting mdels t achieve a full range f t* shwn here. Mdels with mntnic increases f velcity with depth are an upper bund n the scatter in the data. ' ' ' 13 ~3 u~ [] [] x [] [] [] [] 9,1 > U 3- x *, * * x [] ~ ~ k C', *..4.6 i.8 t* t* Figure 9. SM and peak amplitude ratis fr mdels with mntnic increases f velcity with depth, as a functin f t*. Curves crrespnd t different velcities in the upper 3 m. Site classificatin schemes that use nly velcity can have verlapping SM and peak amplitude ranges. eratin at high frequencies, () when Q is independent f frequency, (3) when site resnances d nt severely distrt the shape f the spectrum ver the frequency band where tc is measured, and (4) where the spectral fallff is predminantly that f the direct wave. The first tw assumptins are matched by ur numerical experiments. We test assumptins 3 and 4 by examining the relatin between K and t* fr all f ur numerical mdels. The parameter K is fund by a linear regressin n the spectrum. The results are shwn in Figure 1, which shws that t* is nearly equal t K. Since the first tw assumptins are at least rather widely used, Figure 1 suggests that K can substitute fr t* in practical use. This wuld be cnsistent with the results in Figure, where the statin with the lwer value f ~c (ASH) has a larger peak acceleratin (by abut 35%). The range f t* shwn in Figure 9 matches the bserved range f K in Califrnia (Andersn and Hugh, 1984; Hugh et al., 1988; Andersn, 1991). Hwever, we need t ass-

9 Cntrl f Strng Mtin by the Upper 3 Meters 1757 O qo t*=1.3~c-6.3-5, ~,/ Table 1 Preliminary values f t* assciated with transitin velcities between site categries, and preliminary estimates f increase in SM! ver that n a very hard rck utcrp, assuming linear sil behavir Bundary fl (m/sec) t* (sec) SM A-A A-B B-C C-D eq r O i i J J Figure 1. Relatinship between t* and K. K ~ u ciate a typical value f t* t each site class bundary in rder t develp an imprved site classificatin system. Based n bserved values f tc in Califrnia and additinal preliminary results fr the Nrthridge earthquake (Lee and Andersn, 1996), we used the preliminary values given in Table 1. Given these, we can define site classes A, B, C, and D by cmmn levels f SM, as given in Table 1. Figure 11 shws cnturs f SM as a functin f t* and fl fr the numerical experiments in this study. We test this site classificatin cncept using 3D simulatins t include the additinal effects f P waves, cnversin f phases, nnvertical incidence, and presence f surface waves. We utilize the cmpsite surce mdel (Zeng et al., 1994) t generate the seismgrams. The test earthquake has a mment magnitude 6., with hypcenter 13. km in depth. The epicentral distance is 5 km. Similar t 1D calculatins, we fix the prperties f the upper 3 m t the bundaries fr site classificatin and vary the prperties belw t 5 km in depth. Fr each mdel, we calculate the Green's functin and cnvlve it with a surce functin t generate the synthetic seismgrams. Since the hrizntal cmpnents are f greatest cncern, we present the average Arias intensity and peak value (neither nrmalized in this case) frm the tw hrizntal cmpnents as a functin f tc in Figure 1. The range f Arias intensity in Figure 1 is cnsistent with a regressin and the range f bservatins given by Wilsn (1993). The frequency band we use t calculate ~c is frm. t. Hz. The results shw the same trends as thse btained frm 1D numerical mdels. Discussin and Cnclusin We have examined the influences f bth the surficial prperties and the underlying gelgy n tw characteristics 4 O O ~ ~ F q r ~ t* (s) Figure 11. Cnturs f SM as a functin f t* and average velcity in the upper 3 m. Based n the mdel in this article, this culd be used t refine site classificatins based n near-surface velcity alng. Bundaries between different site categries are based n a preliminary assciatin between velcity and average value f tc (Table 1). f grund mtins: peak amplitudes and SM. SM is simply the term used in this article fr the integrated squared amplitude f the seismgram, nrmalized t equal unity at the surface f a unifrm half-space representing a rck utcrp. Our numerical results suggest that, while the surficial gelgy has a greater influence n grund mtins than might be expected based n its thickness alne, criteria fr site classificatin based n near-surface prperties alne are incmplete. Resnant frequencies depend n the depth f the depsit, f curse, but the SM and peak amplitudes depend n a bandwidth that is brader than these resnances. xtending the cnclusins f Day (1996), the SM and peak amplitudes depend nly weakly n the velcity structure f the intermediate layers even in an attenuating medium. The attenuatin structure in the deeper depsits is, hwever, a critical factr that seems t have an influence cmparable in strength t the velcity in the upper 3 m but has been ver-

10 1758 J.G. Andersn, Y. Lee, Y. Zeng, and S. Day 1",3 4 ~ - c"._ 'c- \,~,,, ~ ~ ',~ q] > -Y- g 11. \ ~ ~ ~ LO i i i i K" K" Figure 1. Mdified Arias intensity (integral f acceleratin squared) and peak acceleratins (frm hrizntal cmpnents) fr a series f synthetic seismgrams generated with a three-dimensinal simulatin methd (see text). All seismgrams are frm a surce with a mment magnitude f 6. at a distance f 5 km. Lines cnnect calculatins with cmmn velcity in the upper 3 m. Differences in t result frm differing velcity and Q mdels between 3 m and 5 km in depth. lked in the past t sme extent. We find that the SM and peak amplitudes at the surface shuld depend expnentially n t*, which depends primarily n Q in intermediate layers. We suggest that ~c is a useful parameter t characterize attenuatin prperties f the underlying structures, since it can be measured empirically and, under the assumptins used in this article, is crrelated t t*. These results thus predict that the velcity in the upper 3 m, the bserved value f t, and bserved resnant frequencies might be sufficient t characterize a site in regins where 1D mdels are apprpriate. Our results are based n a quite idealized, ne-dimensinal fiat mdel. Nnlinear site respnse t the incident grund mtin als is nt included in ur mdels. Hwever, ur preliminary calculatins indicate that the results will generalize t three-dimensinal situatins, and thus the resuits shuld have general significance. Acknwledgments We thank Leif Wennerberg fr helpful infrmatin n the examples shwn in Figure. We appreciate helpful reviews f the manuscript by W. Jyner and M. Chapman. This research was supprted by the Suthern Califrnia arthquake Center (SCC Cntributin Number 4). References Andersn, J. G. (1986). mplicatin f attenuatin fr studies f the earthquake surce, arthquake Surce Mechanics, Gephysical Mngraph 37, (Maurice wing Series 6), American Gephysical Unin, Washingtn, D.C W. Andersn, J. G. (1991). A preliminary descriptive mdel fr the distance dependence f the spectral decay parameter in suthern Califrnia, Bull Seism. Sc. Am. 81, Andersn, J. G. and S. Hugh (1984). A mdel fr the shape f the Furier amplitude spectrum f acceleratin at high frequencies, Bull. Seism. Sc. Am. 74, Arias, A. (197). A measure f earthquake intensity, in Seismic Design f Nuclear Pwer Plants, R. J. Hansen (ditr), M.. T. Press, Cambridge, Massachusetts, pp Bre, D. M., W. B. Jyner, and T.. Fumal (1993). stimatin f respnse spectra and peak acceleratins frm western United States earthquakes: an interim reprt, U.S. GeL Surv. Open-File Rep , 7 pp. Bre, D. M., W. B. Jyner, and T.. Fumal (1994). stimatin f respnse spectra and peak acceleratins frm western United States earthquakes: an interim reprt, Part, U.S. Gel. Surv. Open-File Rep , 4 pp. Brcherdt, R. D. (199). Simplified site classes and empirical amplificatin factrs fr site-dependent cde prvisins, in Prc. NCR, SAOC, BSSC Wrkshp n Site Respnse during arthquakes and Seismic Cde Prvisins, Nvember 18-, University f Suthern Califrnia, Ls Angeles, Califrnia. Brcherdt, R. D. (1994). stimates f site-dependent respnse spectra fr design (methdlgy and justificatin), arthquake Spectra 1, Brune, J. N. (197). Tectnic stress and spectra f seismic shear waves frm earthquakes, J. Gephys. Res. 75, Day, S. M. (1996). RMS respnse f a ne-dimensinal half-space t SH, Bull. Seism. Sc. Am. 86, Fletcher, J. B., T. Fumal, H.-P. Lin, and L. C. Haar (199). Near-surface velcities and attenuatin at tw brehles near Anza, Califrnia, frm lgging data, Bull. Seism. Sc. Am. 8, Gibbs, J. F. and. F. Rth (1989). Seismic velcities and attenuatin frm brehle measurements near the Parkfield predictin zne, central Califrnia, arthquake Spectra 5, Gibbs, J. F., D. M. Bre, W. B. Jyner, and T.. Fumal (1994). The

11 Cntrl f Strng Mtin by the Upper 3 Meters 1759 attenuatin f seismic shear waves in Quaternary alluvium in Santa Clara Valley, Califrnia, Bull Seism. Sc. Am. 84, Hanks, T. C. (1979). b values and ) -r seismic surce mdels: implicatins fr tectnic stress variatins alng active crustal fault znes and the estimatin f high-frequency strng grund mtin, J. Gephys. Res. 84, Hanks, T. C. and R. K. McGuire (1981). The character f high-frequency strng grund mtin, Bull. Seism. Sc. Am. 71, Haukssn,., T. Teng, and T. L. Henyey (1987). Results frm a 15 m deep, three-level dwnhle seismmeter array: site respnse, lw Q values, and fmax, Bull Seism. Sc. Am. 77, Hugh, S.. and J. G. Andersn (1988). High-frequency spectra bserved at Anza, Califrnia: implicatins fr Q structure, Bull. Seism. Sc. Am. 78, Hugh, S.., J. G. Andersn, J. Brune, F. Vernn, J. Berger, J. Fletcher, L. Haar, T. Hanks, and L. Baker (1988). Attenuatin near Anza, Califruia, Bull Seism. Sc. Am. 78, Jyner, W. B., R.. Warrick, and T.. Fumal (1981). The effect f Quaternary alluvium n strng grund mtin in the Cyte Lake, Califrnia earthquake f 1979, Bull Seism. Sc. Am. 71, Lee, Y. and J. G. Andersn (1996). Typical values f the spectral decay parameter, 'kappa' (in preparatin). Luc, J.. and R. J. Apsel (1983). On the Green's functin fr a layered half space, Part, Bull. Seism. Sc. Am. 73, Martin, G. R. and R. Dbry (1994). arthquake site respnse and seismic cde prvisins, NCR Bull. 8, 1-6. Richards, P. G. and W. Menke (1983). The apparent attenuatin f a scattering medium, Bull Seism. Sc. Am. 73, Sanchez-Sesma, F. J.,. Faccili, and R. Fregnese (1986). An index fr measuring the effects f tpgraphy n seismic grund mtin intensity, arthquake ng. Struct. Dyn 14, Thiel Jr., C. C. and J. F. Schneider (1993). nvestigatins f thirty-three Lma Pl-ieta earthquake strng mtin recrding sites, Final Reprt f Prject Spnsred by the Building Cntractrs Sciety f Japan and the lectric Pwer Research nstitute, Califrnia Universities fr Research in arthquake ngineering (CURe), Dept. f Civil ngineering, Stanfrd Univ., Stanfrd, Califrnia. Wilsn, R. C. (1993). Relatin f Arias intensity t magnitude and distance in Califrnia, U.S. GeL Surv. Open-File Rept , Menl Park, Califrnia. Yu, G. (1994). Sme aspects f earthquake seismlgy: slip partitining alng majr cnvergent plate bundaries; cmpsite surce mdel fr estimatin f strng mtin; and nnlinear sil respnse mdeling, Ph.D. Thesis, University f Nevada, Ren, 144 pp. Zeng, Y., K. Aki, and T.-L. Teng (1993). Mapping f the high-frequency surce radiatin fr the Lma Prieta earthquake, Califrnia, J. Gephys. Res. 98, Zeng, Y., J. G. Andersn, and G. Yu (1994). A cmpsite surce mdel fr cmputing realistic synthetic strng grund mtins, Gephys. Res. Lett. 1, Seismlgical Labratry and Department f Gelgical Sciences Mackay Schl f Mines University f Nevada Ren, Nevada (J.G.A., Y.L.) Seismlgical Labratry Mackay Schl f Mines University f Nevada Ren, Nevada (Y.Z.) Department f Gelgical Sciences San Dieg State University San Dieg, Califrnia 918 (S.D.) Manuscript received 9 August 1995.