Bulletin of the Seismological Society of America

Transcription

1 Bulletin f the Seismlgical Sciety f America Vl. 81 December 1991 N. 6 ESTIMATION OF GROUND MOTION AT DEEP-SOIL SITES IN EASTERN NORTH AMERICA BY DAVID M. BOORE AND WILLIAM B. JOYNER ABSTRACT The stchastic mdel used previusly t estimate mtins at hard-rck sites in eastern Nrth America has been mdified t include the effect f deep sils. We simulated mtins fr a number f distances and magnitudes fr a representarive sil clumn and used these mtins t derive equatins giving grund mtin as a simple functin f magnitude and distance. These new equatins are intended fr use in building cdes and thse engineering applicatins that d nt require detailed site evaluatins. The grund mtins fr which we derived equatins include 5%-damped respnse spectra at 13 perids ranging frm 0.05 t 4 sec, peak acceleratin and the maximum pseudvelcity and maximum pseudacceleratin respnses. The latter tw quantities are intrduced here fr the first time. They represent the maxima ver the perid range 0.1 t 4 sec fr a given magnitude and distance, and they may be useful as a basis fr determining the seismic cefficient in building cdes. INTRODUCTION Equatins giving grund mtin as a functin f magnitude and distance were published by Bre and Atkinsn (1987) fr hard-rck sites in eastern Nrth America. These equatins were btained by fitting a parametric mdel t synthetic grund mtins cmputed frm the stchastic mdel intrduced by Hanks and McGuire (1981; see Jyner and Bre, 1988, fr a recent summary f the methd). The equatins are fr distances less than 100 km and are relatively cmplex. Recgnizing the need fr estimatin f mtins at greater distances and the desirability f a simpler functinal frm, particularly in prbabilistic hazard analyses, Atkinsn and Bre (1990) published new equatins valid fr distances up t 400 km. With a minr exceptin (resulting frm different chices f the gemetrical spreading and Q functins fr distances beynd abut 100 km), the synthetic data t which the new equatins were fit were the same as thse used in Bre and Atkinsn (1987). In this paper, we cntinue the evlutinary sequence by presenting equatins fr grund mtins n generic deep-sil sites ("$2" sil cnditins in the terminlgy f recent editins f the Unifrm Building Cde r the Building Seismic Safety Cuncil Prvisins). The equatins give peak acceleratin, respnse spectral values, and tw newly defined quantities prpsed as an alternative basis fr building cdes. These new equatins are intended fr use in building cdes and thse engineering applicatins that d nt require detailed site evaluatins. They are applicable ver brad areas and are nt intended fr site-specific evaluatins f grund mtin. 2167

2 2168 D.M. BOORE AND W. B. JOYNER METHOD The essential difference between this paper and the papers f Bre and Atkinsn (1987) and Atkinsn and Bre (1990) is that the effect f a sil clumn is included here. A frequency-dmain filter is derived that apprximates the amplificatin and attenuatin f the sil clumn. This filter is used alng with a specified surce-scaling relatin in the simulatin f grund mtins fr a set f distances and magnitudes. Because the magnitude and distance dependence f the grund mtins is a cmplicated functin f a number f parameters and equatins, it is nt practical t derive an expressin fr this dependence directly frm the underlying equatins. Instead, the simulated mtins are treated as if they were an bserved data set; an attenuatin equatin is fit t the simulated grund mtins, in the same way that empirical attenuatin equatins are derived frm bserved data. The cefficients in the attenuatin equatin are determined using the tw-stage regressin intrduced by Jyner and Bre (1981). The effect f the sil clumn is apprximated by the methd suggested by Jyner et al. (1981). The prcedure is based n the nnresnant amplificatin prduced as a result f energy cnservatin f waves prpagating thrugh materials f gradually changing velcity. Fr high frequencies, this amplificatin is given by A = v/p~/pst~s, (1) where p and/3 are the density and shear velcity and the subscripts indicate the prperties at the earthquake surce (subscript 0) and at the site (subscript s). In general, there is much less variatin in density than in shear velcity, and variatin in density will be ignred in this study. Jyner et al. (1981) intrduced frequency dependence fr the amplificatin given in equatin (1)by substituting a frequency-dependent effective velcity fr #s. They defined the effective velcity at a particular frequency as the average velcity frm the surface t a depth f a quarter wavelength. Specifically, the depth is fund frm which the accumulated travel time t the surface is ne quarter f a given perid, and that depth is divided by the accumulated travel time t yield an average velcity fr the perid. Substituting this effective velcity int equatin (1) prduces a frequency-dependent amplificatin. The sils will als prduce attenuatin, particularly at high frequencies, and these are accunted fr by the equatin P(f) = exp(-~kf), (2) where c is btained by integrating z/(f3q) ver the thickness f the sil clumn (where z is depth and f~ and Q are the shear velcity and a frequencyindependent measure f damping, respectively, at that depth). In Appendix A, we test the apprximatins embdied in equatins (1) and (2) by cmparing the results with thse frm a calculatin that accunts fr the wave prpagatin in a sil clumn. THE SOIL COLUMN AND ITS EFFECTS Our apprach is t derive the grund mtins fr a single sil prfile whse prperties represent an average f the prperties f many individual prfiles. This differs frm Bernreuter et al. (1985), wh use a Mnte Carl scheme in

3 GROUND MOTION AT DEEP-SOIL SITES IN E. NORTH AMERICA 2169 which mtins are cmputed fr a series f sil clumns btained frm perturbatins f an average prfile. Unlike ur methd, their scheme can prvide estimates f the uncertainty in the predicted mtin, estimates whse validity depend n the accuracy f the distributin functin f the material prperties. Our apprach, hwever, is much less cmputer intensive and shuld prvide a reasnable apprximatin t the median grund mtins. In this study, we restrict ur attentin t sites underlain by deep sils (the $2 categry in the 1988 Building Seismic Safety Cuncil (BSSC) Prvisins r the 1988 Unifrm Building Cde (UBC), defined in the UBC as "a sil prfile with dense r stiff sil cnditins, where the sil depth exceeds 200 feet [60 m]"). The grund-mtin equatins must be applicable in a brad sense t ttal sil depths frm the 60-m minimum that defines $2 t many hundreds f meters. The cunteracting effects f attenuatin and amplificatin will prduce depth-dependent sil respnse: shrt-perid respnse will be higher fr shallw depsits because the attenuatin represented by d 0 is less; lnger-perid respnse will be higher fr deep depsits because the lw-frequency ~8 is smaller (this is illustrated later in Fig. 3). We d nt want the equatins t underestimate the respnse t a significant degree fr any cmmn site cnditins that fit the definitin f $2. T accmplish that purpse, we were frced t use a sil clumn that des nt represent any real site r even the average f a number f real sites: the attenuatin was cmputed ver a smaller-than-average depth range, and the thickness is greater than usual. In additin, the density is cnstant. The shear velcities in the upper part f the sil clumn were based n Bernreuter et al.'s (1985) cmpilatins frm a number f deep sil sites (Fig. 1). We used the average shwn by the dark line in the figure t a depth f 150 m. Belw this, we included a thick prtin f cnstant velcity in the lwer prtin Shear Wave Velcity (m/s) r ~ L E:] L FIG. 1. Shear velcity as a functin f depth fr an average deep-sil site (heavy line), based n a cmpilatin f velcities frm PSAR and FSAR reprts fr nuclear pwer-plant sites thrughut the United States (light lines). The shrt hrizntal bars indicate bedrck. (Adapted frm a figure in Bernreuter et al., 1985.)

4 2170 D. M. BOORE AND W. B. JOYNER f the sil clumn, befre terminating the clumn with a hard-rck half-space. The ttal thickness f the clumn was taken as 650 m, cnsistent with the depth f the sediments in the Mississippi embayment (Andrews and Mney, 1985). This is prbably thicker than mst deep-sil sectins in eastern Nrth America, but the greater-than-average depth leads t cnservative estimates f the sil respnse at lw frequencies. Fr the attenuatin we assigned Q values t the layers that are reasnably cnsistent with thse inferred by Andrews in the Mississippi embayment (M. Andrews, written cmm., 1990). The K used in the grund-mtin simulatins (0.02) was based n the value crrespnding t the upper 100 m f the sil sectin, with a small allwance fr attenuatin in the rck belw (this additinal K crrespnds t an fmax f abut 40). This has the effect f prducing less attenuatin than wuld prbably ccur fr a sil clumn as thick as 650 m. The parameters f the generic deep-sil clumn that we used t derive the amplificatin and attenuatin are tabulated in Table 1 and pltted in Figure 2. Als included in the table are clumns giving fur times the cumulative travel time and the cumulative K frm the surface dwn. These clumns are useful in assessing the relative cntributins f varius parts f the sil sectin t the amplificatin and attenuatin f the waves. TABLE 1 MATERIAL PROPERTIES FOR A DEEP-SIL SITE Layer Depth t Tp Thickness Shear Velcity Q Density 4,Cure. Time Cum. K (m) (m) (m/sec) (gm/cm 3) (sec) (sec) , , , , , Half-space

5 GROUND MOTION AT DEEP-SOIL SITES IN E. NORTH AMERICA 2171 The amplificatin was cmputed fr a number f frequencies, using the effective velcity and equatin (1). Fr use in cmputer prgrams, it is cnvenient t give the amplificatin as a cntinuus functin f frequency. We apprximated the respnse by a sequence f line segments; the equatin fr segment i is given by lg A(f) = lg A i + S/lg f, (3) where the cefficients lg A i and S i and the frequency range defining each segment are given in Table 2. The amplificatin and the cmbined effect f the amplificatin and the attenuatin fr the adpted mdel are shwn in Figure 3. As frequency increases, there is little effect until a frequency f abut 0.2 Hz is reached, at which pint there is a rapid rise in the amplificatin t a factr greater than 2. (Frm Table 1 it can be seen that the sharp rise in amplificatin ccurs fr a perid clse t fur times the cumulative travel time thrugh the whle sil sectin--3.3 sec.) Withut attenuatin (plus signs in Fig. 3), the site respnse rises slwly with frequency; with attenuatin, hwever, the respnse is almst cnstant up t a frequency f abut 4 Hz. The attenuatin factr reduces the cmbined effect t unity near 20 Hz, with a diminutin at higher frequencies. Als shwn in Figure 3 are the sil-respnse filters fr the generic mdel using the whle sil clumn (650 m) and the upper 60 m f the sil clumn. We assume that these tw mdels are representative f the range f depths fr $2 cnditins. Unlike the adpted mdel used in the calculatin f mtins frm 2O0 Shear Velcity (m/s) \ Q tq ' ' ~Z 400 D 600 FIG. 2. Shear velcity and attenuatin (Q) used in this paper fr deep-sil sites. TABLE 2 COEFFICIENTS FOR SHEAR-WAvE AMPLIFICATION FILTER Frequency Segment lg A i S i Range (ttz) 1 f< < f < f < =< f< ~ f< =< f

6 2172 D.M. BOORE AND W. B. JOYNER c 3 O3 C 0 CL Adpted Mdel - - Generic Mdel, 650 m Sectin -- Generic Mdel, 60 rn Sectin Adpted Mdel, Amplificatin Only \ CO 1 \ \ Freq (Hz) FIG. 3. The site-respnse filter fr the adpted mdel (heavy line). Fr cmparisn, the site respnses fr mdels with thick and thin sil sectins verlying bedrck are als shwn (light lines), as is the respnse fr the adpted mdel with n attenuatin (this is the same amplificatin that wuld ccur fr the mdel with a 650-m sil sectin). The filter shwn by the heavy line is used in the stchastic mdel t accunt fr the respnse f deep-sil sites. which the new attenuatin equatins were derived, the K fr these mdels crrespnds t the attenuatin ver the indicated depth (60 and 650 m), again with a small allwance fr near-surface attenuatin in the rcks belw the sediments. The curves in Figure 3 illustrate the pints made earlier abut the hybrid nature f the adpted mdel: the mdel cmbines the amplificatin at lw frequencies f the thick mdel and the attenuatin at high frequencies f the thin mdel. (The sil-respnse filter fr the adpted mdel des nt envelpe the ther tw respnses because we used a smewhat larger K (0.02) than the value calculated fr the thin mdel (0.015); K is nt well determined, and ur chice was guided but nt cnstrained by the value fr the thin mdel.) SYNTHETIC GROUND MOTIONS The next step in the analysis is t generate simulated grund mtins fr a set f magnitudes and distances. We did this using the stchastic mdel described elsewhere (e.g., Jyner and Bre, 1988), clsely fllwing Bre and Atkinsn (1987) with Atkinsn and Bre's (1990) chice f gemetrical spreading and attenuatin. The primary new feature in ur analysis is t include the sil respnse given by equatins (2) and (3). We als used a slight mdificatin f Jyner's (1984) spectral mdel rather than the simple 0-2 surce mdel used in the Bre and Atkinsn papers. We did this because f the pssible applicatin f ur results t the estimatin f grund mtins fr very large earthquakes. We cnsider it likely that the surce scaling changes fr earthquakes larger than a critical size (such an earthquake, fr example, might crrespnd t rupture thrugh the brittle layer f the lithsphere), and it is awkward t accunt fr this using the usual -u mdel, which has nly ne crner frequency. Jyner's (1984) mdel, n the ther hand, has tw surce crners, and he argues that the effect f the change in scaling can be included by fixing the higher-frequency crner at the value fr the critical-sized earthquake. The slight mdificatin that we made t Jyner's mdel eliminates a kink in the spectral shape at the lw-frequency crner. The surce displacement spectrum is given by S( W) : MZaSb, (4)

7 GROUND MOTION AT DEEP-SOIL SITES IN E. NORTH AMERICA 2173 where M is the seismic mment and S a 1.0/(1.0 --~ (f/fa)2) 0"75 (5) and S b = 1.0/(1.0 + (f/fb)) (6) The tw crner frequencies, fa and fb, are given by equatin (24) in Jyner and Bre (1988). The parameters cntrlling the values f the crner frequencies are G (shear velcity near the surce), X (the rati f fa t fb), Mc (the mment magnitude f the critical earthquake), and A a (the stress parameter). The values we chse fr these and the ther parameters in ur mdel are given in Table 3. Fr ~ we used Jyner's (1984) suggested value f 4. Jyner (1984) argued that the critical earthquake shuld be a mment magnitude 6.5 alng the San Andreas fault system. In view f the pssible cler lithsphere and cnsequently greater seismgenic thickness in intraplate regins, we assigned the critical magnitude as M c = 7.5, realizing that this number is very uncertain. The ther parameters are thse used by Bre and Atkinsn (1987) and Atkinsn and Bre (1990). Of these parameters, A a is the mst imprtant. Based n scanty data, Bre and Atkinsn (1987) chse 100 bars. Subsequent determinatins f spectral amplitudes fr intraplate earthquakes thrughut the wrld by Batwright and Chy (1987; J. Batwright, written cmm., 1990) suggest values averaging arund 20 t 30 bars. (On accunt f directivity, values f Aa determined by Batwright and Chy frm teleseismic data may need t be increased by as much as a factr f 2 fr use in the grund-mtin simulatins by pint-surce mdels (Bre and Jyner, 1989).) The recent Saguenay, Quebec, earthquake, n the ther hand, had a stress parameter in excess f 200 bars (Fig. 12 in Bre and Atkinsn, 1989). Furthermre, a study f seismic intensities by Hanks and Jhnstn (1992) suggests that stress parameters fr earthquakes in eastern Nrth America are larger than fr western Nrth America. Results in Bre (1986) and in a recently cmpleted study by TABLE 3 PARAMETERS OF THE STOCHASTIC MODEL Surce Prperties p = 2.70 gm/cm 3 M c = 7.5 Aa = 100 bars G = 3.50 km/sec )x=4 Q = 1100f -17 1/r gemetrical spreading Duratin = 1/f a r Path Prperties Site Prperties Partitin factr = 0.71 Radiatin cefficient = 0.55 ~ = 0.02 sec Free surface factr = 2.0 Amplificatin factr: equatin (3), Table 2

8 2174 D. M. BOORE AND W. B. JOYNER Bre and Jyner (1992) suggest that a stress parameter near 70 bars with a K clse t 0.02 explains the strng-mtin data frm western Nrth America. If Hanks and Jhnstn are crrect, then the results f the western Nrth America studies imply that, n the average, A~ shuld be larger than 70 bars fr earthquakes in eastern Nrth America. In view f these tenuus arguments, and lacking cmpelling evidence t the cntrary, we decided t keep the stress parameter at 100 bars. ATTENUATION EQUATIONS We simulated grund mtins fr 17 distances ranging in equal lgarithmic steps frm 10 t 400 km and fr mment magnitudes frm 5.0 t 8.5, in steps f 0.25 magnitude units. The grund mtins included peak acceleratin (amax) and 5%-damped, pseudrelative velcity respnse spectra (Sv) fr 13 perids (12 f which were used by Jyner and Bre (1982, 1988). Fr each grund-mtin parameter, the 255 simulated mtins were fit t a simple functin f magnitude and distance. T prvide fr a cnvenient frm fr use in generating seismic-hazard maps, the functinal frms were kept as simple as pssible. As we will subsequently see, this entailed sme cmprmises in fitting the simulated data. Fllwing Jyner and Bre (1981), a tw-step regressin was used t fit the equatins t the simulated data. The first step was t find the distance attenuatin, given by the fllwing equatin: lg y = E i - lg r + kr, (7) where y is the grund-mtin parameter, E i is an ffset factr fr each earthquake, k is an attenuatin factr (always negative), and r is the hypcentral distance in km (the calculatins assume a pint surce). This equatin assumes that the shape f the attenuatin is the same fr all magnitudes. The simulated data shw this t be a pr assumptin fr higher-frequency mtins fr the brad range f distances represented by the simulated data (this is shwn in a later figure). Rather than cmplicate the functinal frm t accunt fr this (as Bre and Atkinsn, 1987, did), we used an iterative, subjective prcedure, guided by the ntin that mismatches culd be tlerated at large distances fr small earthquakes but nt fr large earthquakes (the grund mtins frm small earthquakes at large distances are t small t cause any significant damage). The first step in each iteratin was t chse a value fr k (guided by an initial regressin determinatin with k in equatin (7) as a free variable) and use regressin t find the ffset factrs E i. The secnd step used the ffset factrs t determine the magnitude scaling. Because we wanted predictin equatins in terms f mment magnitude (M) and Nuttli magnitude (my, als knwn as mlg r mblg), we perfrmed tw separate regressins.fin the first we fit a plynmial in M t E i, and in the secnd we first cnverted M t m N by inverting the equatin f Atkinsn and Bre (1987) M = m N m 2 (8) befre ding the secnd regressin. In ur initial analyses, we used a single quadratic equatin fr the secnd regressin. Because f the change in scaling at the critical-sized earthquake, hwever, we fund that the fit t the ffset

9 GROUND MOTION AT DEEP-SOIL SITES IN E. NORTH AMERICA a) [ Ld- [] [] [] [] C~ 0.0 E:C O LJ 4 3 b) E~ [] 0.05 Kn 0.0 CE (7) 4 C) 0.05 h~- 3 2 [] 1:3 0.0 CE E b ~0.05 M FI. 4. Offset factrs (filled squares, left rdinate) and difference between the simulated and cmputed ffset factrs (squares, right rdinate) as a functin f mment magnitude. The factrs are fr 5%-damped respnse spectra at a perid f 4 sec. The regressin fit t the ffset factrs is given by the slid line. The ffset factrs were fit with (a) a single quadratic in magnitude, (b) tw quadratics, n either side f M = 7.5, and (c) a single cubic equatin. factrs E i was relatively pr. A sample f the fit t the E i and the residuals f the fit fr ne f the wrst cases is shwn in Figure 4a. A much better fit was btained by using tw quadratic equatins, ne fr earthquakes less than r equal t the critical earthquake (M = 7.5) and ne fr larger earthquakes. Figure 4b shws the residuals fr this fit. Twice as many cefficients are needed t describe this fit t the simulated data, hwever, and therefre we finally settled n a single cubic equatin. The residuals, shwn in Figure 4c, are tlerable. The cubic equatin fr the magnitude scaling is E i= a+ b(m- 6) + c(m- 6) 2+d(rn-6) 3, (9) where m is either M r my. The fit f this equatin t the Ei factrs are shwn in Figure 5 fr scillatr perids spanning the range cnsidered in this paper. The residuals are generally less than 0.03 lg units. Nte als the change f magnitude scaling with scillatr perid: shrt-perid scillatrs are much less sensitive t mment magnitude than are lng-perid scillatrs. This cnclusin is a straightfrward and rbust cnsequence f all surce-spectral mdels and has been cnfirmed in a number f bservatinal studies, including Jyner and Bre's (1982) analysis f strng-mtin data frm western Nrth America. After the tw regressins were perfrmed, the residuals between the simulated mtins and thse predicted frm equatins (7) and (9) were pltted. Plts f the residuals were prduced fr a series f attenuatin cefficients k, and the

10 2176 D.M. BOORE AND W. B. JOYNER 4 a) 0.ts [] 0.05 w] 9 U 0.0 r J b) 1.0s y ~ D ~ D DD I I I I 0.05 O3 0.0 r'r U c) 4.0 s [] [] [] [] yj. [] [] 0.05 u] Q) [:D (l) 0.0 [E E ~h i t I I M FIG. 5. As in Figure 4, but the three parts shw the ffset factrs fr the cubic equatin and respnse spectra at perids f 0.1, 1.0, and 4.0 sec. final value f k was chsen subjectively t reduce the residuals fr large earthquakes at large distances, at the expense f the small-earthquake residuals (which are unimprtant at large distances). As a final step, we smetimes fund that adding a small scalar quantity a' t a in equatin (9) als imprved the verall fit. Weighted regressin wuld have accmplished the same thing. The final predictin equatin is given by cmbining equatins (7) and (9): lg y = a" + b(m - 6) + c(m - 6) 2 + d(m - 6) 3 - lg r + kr, (10) where a" = a + a'. The cefficients fr this equatin are given in Tables 4 and 5. These tables are the primary cntributin f this paper. Nte that a cnsequence f the cubic scaling with magnitude is that the predicted mtin can actually decrease fr large magnitudes. Such a decrease is, f curse, nt realistic and is an artifact f the particular functinal frm we chse fr the magnitude scaling. The last clumn in Tables 4 and 5 gives the magnitudes beynd which the mtins decrease. These magnitudes are large, and fr practical purpses the equatins can be used withut regard t the pssibility f decreases in mtin. If fr sme reasn mtins are needed fr magnitudes mre than several tenths larger than the magnitudes in the last clumn, we recmmend that the mtins be equated t thse fr the magnitudes in the last clumn f the tables. T see hw well equatin (10) matches the simulated data, we shw in Figure 6 the difference between the simulated mtins and thse predicted frm equatin (10) as a functin f distance. With the exceptin f magnitudes near

11 GROUND MOTION AT DEEP-SOIL SITES IN E. NORTH AMERICA 2177 TABLE 4 COEFFICIENTS FOR GROUND-MTION ESTIMATION AT DEEP-SOIL SITES IN EASTERN NORTH AMERICA IN TERMS OF M* T (sec) a I a" b c d k M at max ~ Sv area x Symax SA,~a x * The distance used in equatin (10) is generally the hypcentral distance; we suggest {based n unpublished wrk in prgress) that, clse t lng faults, the distance shuld be the nearest distance t seismgenic rupture. The respnse spectra are fr randm hrizntal cmpnents and 5% damping. The units f a,~a~ and S A are cm/sec2; the units f S y are cm/sec. The cefficients in this table shuld nt be used utside the ranges 10 < r _< 400 km and 5.0 < M < 8.5. * "M at max" is the magnitude at which the cubic equatin attains its maximum value; fr larger magnitudes, we recmmend that the mtins be equated t thse fr "M at max." 5, the residuals are very small fr the lnger-perid scillatrs. Fr the shrterperid scillatrs, hwever, the residuals are larger and shw systematic variatins with distance. The variatins are the result f trying t accunt fr magnitude-dependent attenuatin with the simple functinal relatin in equatin (7). As mentined earlier, we sught t keep the residuals fr the small and large earthquakes within reasnable limits at small and large distances, respectively, by chsing k and a" apprpriately. As is clear frm Figure 6c, this results in sme cmprmises. As a cnvenient summary f ur predicted mtins, Figure 7 shws ur predicted pseudacceleratin spectra at perids f 0.3 and 1.0 sec as a functin f distance fr a suite f magnitudes, and in Figure 8 we cmpare ur predictins fr a generic deep sil site with the rck-site predictins f Atkinsn and Bre (1990) as a functin f scillatr perid fr several distances and magnitudes. Over mst f the perid range shwn, the sil mtins are unifrmly abve the rck mtins by factrs f 1.4 t 2.0. This is larger than the difference between cde site cefficients fr sil and rck. The differences between sil and rck shwn in Figure 8, hwever, are similar t thse indicated by data in the western United States fr perids greater than abut 0.5 sec (Jyner and Bre, 198S). CONSTRUCTION OF RESPONSE SPECTRA FOR BUILDING CODES: A PROPOSAL The mdern apprach t develping seismic design requirements fr buildings dates back t ATC-3 (Applied Technlgy Cuncil, 1978), whse prvisins are

12 2178 D. M. BOORE AND W. B. JOYNER TABLE 5 COEFFICIENTS FOR GROUND-MTION ESTIMATION AT DEEP-SIL SITES IN EASTERN NORTH AMERICA IN TERMS OF mn* T (sec) a" a" b c d k ra N at max ~ Sv ama ~ Sv,~a x SAmax * The distance used in equatin (10) is generally the hypcentral distance; we suggest (based n unpublished wrk in prgress) that, clse t lng faults, the distance shuld be the nearest distance t seismgenic rupture. The respnse spectra are fr randm hrizntal cmpnents and 5% damping. The units f area x and S A are cm/sec2; the units f S y are cm/sec. The cefficients in this table shuld nt be used utside the ranges 10 _< r < 400 km and 5.4 < m N <= 7.8. "m~v at max" is the magnitude at which the cubic equatin attains its maximum value; fr larger magnitudes we recmmend that the mtins be equated t thse fr "m N at max." based n apprximate respnse spectra. These apprximate spectra are prprtinal t "effective peak acceleratin" at shrt perids and t "effective peak velcity" at lng perids. ATC-3 prvides maps intended t shw effective peak acceleratin and effective peak velcity crrespnding t a 10% prbability f exceedence in a 50-yr perid. The use f tw parameters fr scaling the design respnse spectrum (as prpsed by Newmark and Hall, 1982) is preferable t scaling by peak acceleratin alne, because use f tw parameters permits partial accmmdatin fr the significant variatin in shape f respnse spectra with changing earthquake magnitude and site cnditins. The ATC apprach was incrprated in the NEHRP Recmmended Prvisins fr the Develpment f Seismic Regulatins fr New Buildings (Building Seismic Safety Cuncil, 1985, 1988). Mre recently, the cncept has been intrduced f using respnse values themselves at tw r mre perids as scaling parameters in develping apprximate spectra fr use in seismic design requirements. The Building Seismic Safety Cuncil's Technical Subcmmittee N. 1 (Algermissen et al., 1991) has prpsed the use f the 5%-damped pseudacceleratin respnse at 0.3 sec (SA(0.3)) and 5%-damped pseudvelcity respnse at 1.0 sec (Sv(1.0)). The cncept is based n the assumptins, true in western Nrth America, that the pseudacceleratin respnse tends t be apprximately cnstant fr perids arund 0.3 sec, and the pseudvelcity respnse tends t be apprximately cnstant fr perids arund 1.0 sec. Since the pseudacceleratin respnse is

13 i i i i I GROUND MOTION AT DEEP-SOIL SITES IN E. NORTH AMERICA , M= M--6 ~--~ M=7 u--: M=8 0.1 D] El:: t 0.0 (h ~ -0.~ a) 0.1s O] E (~ Ch 0.~ b) s D] 0.1 c)._._ 4.0 s 8 (/) c2h I I I I Lg R(km) FIG. 6. The difference between the simulated data and the estimatins frm equatin (10) fr respnse spectra at perids f 0.1, 1.0, and 4.0 sec, as a functin f distance fr a suite f mment magnitudes. 10 s a) 102 E < 101 (/) s b) 102 E < 101 b R(krn) 10 s FIG. 7. Attenuatin curves predicted frm the results in this paper fr pseudacceleratin spectra at perids f 0.3 and 1.0 sec.

14 2180 D. M. BOORE AND W. B. JOYNER 104 M=7.5, R=20 km 10 s M:7.5, R:100 km E <~ (/) 10 s ~ i n mr ~i n 102 ii ". Deep Sils [, Rck 10 ~ 101 4~ 10s E (D < 102 L8 10 ~ M=6.5, R=20 km ~mni Deep Sils Rck in ar... i... i nt T (s) M=6.5, R= 100 km,,,r,rl,,... I I T (s) FIG. 8. Cmparisn f pseudacceleratin spectra in central and eastern Nrth America at hard-rck and deep-sil sites, bth based n the same methdlgy. The cmparisn is fr mment magnitudes f 6.5 and 7.5 and hypcentral distances f 20 and 100 km. The sil mtins are frm this paper, and the rck mtins are frm Atkinsn and Bre (1990). equal t 27r/T times the pseudvelcity respnse, the pseudacceleratin spectrum can be apprximated in terms f S A and S V as SA(0.3), fr T <= 27rSv(1.O)/SA(0.3 ) SA= 27rSv(1.0)/T, fr T>27rSv(1.0)/SA(0.3 )" (11) When this cncept was tried ut at selected sites in the western United States with prbabilistic calculatins by E. V. Leyendecker using the attenuatin equatins f Jyner and Bre (1982, 1988), the apprximate spectra cmputed using the tw parameters SA(0.3) and Sv(1.0) agreed well enugh with spectra cmputed fr the 12 perids used by Jyner and Bre. In eastern Nrth America, hwever, the S A fr perids less than 0.3 sec are greater than SA(0.3) fr mst f the relevant magnitudes and distances if the equatins given in this paper are used. The larger spectral values fr perids less than 0.3 sec are a cnsequence f the lwer values f K adpted fr eastern Nrth America (r equivalently, a higher fmax), crrespnding t less attenuatin at the site. Hw the large values at shrt perids affect the seismic design requirements is a questin that we, as seismlgists, will nt and shuld nt address. We are mved, hwever, t suggest a simple alternative that will ensure that the apprximate spectrum will envelpe the spectrum calculated at all perids f engineering interest. We define SAmax and Svmax as the largest values f pseudacceleratin and pseudvelcity respnse, respectively, fr 5% damping in the perid range f engineering interest, taken here as 0.1 t 4 sec. The perid range is an essential part f the definitin. In eastern Nrth America, higher values f pseudacceleratin may ccur fr perids less than 0.1 sec. We chse 0.1 t 4 sec t illustrate the cncept; the final chice is a matter fr

15 GROUND MOTION AT DEEP-SOIL SITES IN E. NORTH AMERICA 2181 engineering judgement. SArna x and Syrup, x are functins f magnitude and distance. Using these new quantities, the equatins SA... fr T ~_ 27TSvmax/SArna x SA = 2~rSvmax/T, fr T~ > 27(Svmax/ZAmax (12) will define the desired apprximate spectrum. An illustratin f the tw ways (equatins 11 and 12) fr estimating respnse spectra is given in Figure 9. The left panel shws the simulated spectrum at 32 km frm a magnitude 7 earthquake, using the deep-sil mdel f this paper. The dashed lines shw the apprximate spectrum frm equatin (11), using S A at 0.3 sec. The largest value f S A ccurs at a perid f 0.1 sec, hwever, and therefre equatin (11) leads t an underestimate f the spectrum fr this magnitude and distance. The prpsed methd fr apprximating the spectrum (equatin 12) prduces an envelpe f the simulated spectrum. The right panel f Figure 9 shws the cmparisn f the simulated and apprximate spectra fr a distance f 320 km. In this case, the largest value f S A ccurs at a perid f 0.3 sec, and bth apprximate spectra are the same fr shrt perids. The largest S y f the simulated spectrum, hwever, ccurs at 2.0 sec, and therefre the apprximate spectrum based n fixed perids (equatin 11) underestimates the simulated spectrum at lng perids. Tables 4 and 5 cntain cefficients fr Symax and SAmax. These quantities were determined by searching ver the perid range 0.1 t 4.0 sec fr the maximum f the pseudvelcity and pseudacceleratin respnse spectrum fr each pair f magnitudes and distances in the simulated data, and then fitting equatin (10) t these derived data using the tw-stage regressin methd. Fr cmpleteness we include Table 6, based n the attenuatin equatins f Jyner and Bre (1982, 1988), which can be used with equatin (10) fr cmputing SAmax and Svrna x at sil sites in western Nrth America. We shuld emphasize that determinatins f SAmax and Symax shuld nt be made using peak values f pseudacceleratin and pseudvelcity frm individual bserved recrds, fr they will be biased tward high values and thereby nt be usable fr apprximating prbabilistic spectra. The apprpriate prcedure is first t derive equatins giving the median values f pseudacceleratin as a 800 ~" 60 E 400 2OO - R=32 km ~~ M=7 -- ; - O~ O~ R=320 km M=7 1 1 T (s) T (s) FIG. 9. Cmparisn f simulated pseudacceleratin spectra (circles) and apprximatins based n S A and S v at fixed perids f 0.3 and 1.0 sec (dashed line: equatin 11) and n the largest values f S A and S y ver the perid range 0.1 t 4 sec (slid line: equatin 12).

16 2182 D.M. BOOREANDW. B. JOYNER TABLE 6 COEFFICIENTS FOR Svmax AND Snmax AT SOIL SITES IN WESTERN NORTH AMERICA IN TERMS OF M* a" b c d k h t Svma~ SAmax *The respnse spectra are fr randm hrizntal cmpnents and 5% damping. The units f Svmax and SAmax are cm/sec and cm/sec 2, respectively. The cefficients in this table can be used fr r < 100 km and 5.0 < M < t The distance r used in equatin (10) is btained frm r = ~22 + h 2, where r is the hrizntal distance, in kilmeters, t the nearest part f the vertical prjectin f the rupture surface t the earth's surface. functin f distance and magnitude fr a suite f perids, and then use these t determine SAmax and Svmax. SUMMARY AND CONCLUSIONS A generic mdel f shear velcity and attenuatin fr deep sil sites has been cnstructed frm cmpilatins by Bernreuter et al. (1985) and wrk by Andrews and Mney (1985) and by Andrews (written cmm., 1990), amng thers. We derived a filter accunting fr the sil clumn by using the apprximate methd fr cmputing the amplificatin and attenuatin prpsed by Jyner et al. (1981). This filter was cmbined with the stchastic mdel f Bre and Atkinsn (1987) t generate equatins fr the estimatin f respnse spectra, peak acceleratin, and the maximum pseudvelcity and pseudacceleratin respnses as a functin f distance and magnitude. The equatins are intended t give estimates f the median value f the mtins fr deep sil sites (class $2 in the Unifrm Building Cde) and are t be used in central and eastern Nrth America, fr mment magnitudes ranging frm 5 t 8.5 and distances frm 10 t 400 km. Equatins are given bth fr mment magnitude (M) and fr the shrt-perid Nuttli magnitude (mn). Direct cmparisn shws that the apprximate methd fr cmputing the sil respnse is in gd agreement with the respnse cmputed frm exact calculatins, even when a large step in seismic impedance exists at the bttm f the sil clumn. The maximum pseudvelcity and pseudacceleratin respnses are intrduced fr the first time here, and a discussin is included f their pssible use in determining the seismic cefficient in building cdes. ACKNOWLEDGMENTS We thank J. C. Chert fr prviding the data used t cnstruct Figure 1, Walt Silva fr prviding a cnvenient frm f the average curve in Figure 1, Charles Mueller fr his prgram that cmputes the exact SH respnse f sil clumns, and E. V. Leyendecker and Ted Algermissen fr discussin related t the use f the results in this paper. We thank Ken Campbell, C. B. Cruse, E. V. Leyendecker, and Erdal ~afak fr their thughtful reviews f the paper. This wrk was partially funded by a grant frm the U.S. Nuclear Regulatry Cmmissin. REFERENCES Algermissen, S. T., E. V. Leyendecker, G. A. Bllinger, N. C. Dnvan, J. E. Ebel, W. B. Jyner, R. W. Luft, and J. P. Singh (1991). Prbabilistic grund-mtin hazard maps f respnse spectral rdinates fr the United States, in Prc. 4th Int. Cnf. Seismic Znatin, Stanfrd, Califrnia II,

17 GROUND MOTION AT DEEP-SOIL SITES IN E. NORTH AMERICA 2183 Andrews, M. and W. Mney (1985). The relcatin f micrearthquakes in the nrthern Mississippi embayment, J. Gephys. Res. 90, 10,223-10,236. Applied Technlgy Cuncil (1978). Tentative Prvisins fr the Develpment f Seismic Regulatins fr Buildings, Applied Technlgy Cuncil Publicatin ATC 3-06, 505 pp. Atkinsn, G. M. and D. M. Bre (1987). On the mn, M relatin fr eastern Nrth America, Seism. Res. Lett. 58, Atkinsn, G. M. and D. M. Bre (1990). Recent trends in grund mtin and spectral respnse relatins fr Nrth America, Earthquake Spectra 6, Bernreuter, D. L., J. B. Savy, R. W. Mensing, and J. C. Chen (1985). Seismic hazard characterizatin f 69 nuclear plant sites east f the Rcky Muntains, U.S. Nuclear Regulatry Cmmissin NUREG/CR-5250, UCID-21517, Vl. 7. Batwright, J. and G. L. Chy (1987). Acceleratin surce spectra fr large earthquakes in nrtheastern Nrth America (abstract), EOS 68, Bre, D. M. (1986). Shrt-perid P- and S-wave radiatin frm large earthquakes: implicatins fr spectral scaling relatins, Bull. Seism. Sc. Am. 76, Bre, D. M. and G. M. Atkinsn (1987). Stchastic predictin f grund mtin and spectral respnse parameters at hard-rck sites in eastern Nrth America, Bull. Seism. Sc. Am. 77, Bre, D. M. and G. M. Atkinsn (1989). Spectral scaling f the 1985 t 1988 Nahanni, Nrthwest Territries, earthquakes, Bull. Seism. Sc. Am. 79, Bre, D. M. and W. B. Jyner (1989). The effect f directivity n the stress parameter determined frm grund mtin bservatins, Bull. Seism. Sc. Am. 79, Bre, D. M., W. B. Jyner, and L. Wennerberg (1992). Fitting the stchastic -2 surce mdel t bserved respnse spectra in western Nrth America: Tradeffs between Aa and K, Bull. Seism. Sc. Am. (submitted). Building Seismic Safety Cuncil (1985). NEHRP Recmmended Prvisins fr the Develpment f Seismic Regulatins fr New Buildings, Building Seismic Safety Cuncil, 3 parts, 471 pp. Building Seismic Safety Cuncil (1988). NEHRP Recmmended Prvisins fr the Develpment f Seismic Regulatins fr New Buildings, Building Seismic Safety Cuncil, 2 parts, 440 pp. Hanks, T. C. and A. C. Jhnstn (1992). Sme cmmn features in the excitatin and prpagatin f strng grund mtin fr Nrth American earthquakes, Bull. Seism. Sc. Am. 82, (in press). Hanks, T. C. and R. K. McGuire (1981). The character f high-frequency strng grund mtin, Bull. Seism. Sc. Am. 71, Haskell, N. (1960). Crustal reflectin f plane SH waves, J. Gephys. Res. 65, Jyner, W. B. (1984). A scaling law fr the spectra f large earthquakes, Bull. Seism. Sc. Am. 74, Jyner, W. B. and D. M. Bre (1981). Peak hrizntal acceleratin and velcity frm strng-mtin recrds including recrds frm the 1979 Imperial Valley, Califrnia, earthquake, Bull. Seism. Sc. Am. 71, Jyner, W. B. and D. M. Bere (1982). Predictin f earthquake respnse spectra, U.S. Gel. Surv. Open-File Rept , 16 pp. Jyner, W. B. and D. M. Bre (1988). Measurement, characterizatin, and predictin f strng grund mtin, in Prec. Earthquake Eng. Sil Dyn. H, GT Div/ASCE, Park City, Utah, June, 1988, Jyner, W. B., R. E. Warrick, and T. E. Fumal (1981). The effect f Quaternary alluvium n strng grund mtin in the Cyte Lake, Califrnia, earthquake f 1979, Bull. Seism. Sc. Am. 71, Newmark, N. M. and W. J. Hall (1982). Earthquake Spectra and Design, Earthquake Engineering Research Institute, E1 Cerrit, CA, 103 pp. Unifrm Building Cde (1988). Unifrm Building Cde, Internatinal Cnference f Building Officials, Whittier, CA, 926 pp. APPENDIX: CHECKING THE VALIDITY OF THE METHOD FOR ESTIMATING SOIL RESPONSE Several studies have cmpared the sil respnse cmputed frm the simplified methd prpsed by Jyner et al. (1981) with the respnse frm a cmplete slutin that accunts fr the reverberatins and the leakage f energy int the half-space beneath the sil clumn. J. Batwright (persnal cmm., 1987) and W. Silva and R. Darragh (persnal cmm., 1987) have made such tests, and

18 2184 D. M. BOORE AND W. B. JOYNER they find reasnable agreement between the estimates f the site respnse frm the tw methds. These earlier tests have demnstrated the general reliability f the simplified methd. We reprt n sme similar studies in this appendix. It is nt ur aim t d a cmprehensive analysis. Rather, we were curius abut the cmparisn f the simplified and exact site respnses fr the sil mdel used in ur study (Table 1 and Fig. 2). The velcity prfile in the sil mdel has a large cntrast in shear velcity at the base f the sediments, and this cntrast will prduce reverberatins nt accunted fr in simplified analyses f site respnse. As in the earlier studies, we cmpared the site respnse cmputed using bth the simplified methd described earlier and the wave-thery calculatin due t Haskell (1960). We cnsider nly vertically prpagating SH waves, using the prgram RATTLE frm C. Mueller. The K factr t be used in the diminutin factr (equatin 2) was cmputed by summing z/(~q) ver the entire thickness f sediments; the result was K = The velcity, density, and Q distributins used in the wave-thery calculatins are thse tabulated in Table 1. The impulse respnse at the surface (Fig. A1) shws that the direct wave dminates the mtin. Because the simplified methd des nt accunt fr reverberatins, we thught it wuld be instructive t cmpute spectra fr a series f windws f increasing length. Accrdingly, we cmputed the spectra frm the time series in Figure A1 fr windws that include the direct wave and zer, ne, tw, and mre than 10 reverberatins. The results are shwn in Figure A2 as a series f curves. The spectra were nrmalized t the value that wuld be btained at the surface f a half-space made up f the rck under the sediments. In spite f the apparent dminance f the direct arrival in the time dmain (Fig. A1), the transfer functin is highly dependent n the reverberatins. Althugh interesting, this bservatin is a side issue. The pint f this appendix is t cmpare the exact respnse (lines in Fig. A2) with that cmputed frm the simplified methd (slid circles in Fig. A2). At higher frequencies, the simple methd verestimates the respnse f the direct wave but gives a smthed apprximatin f the cmplete respnse, including all reverberatins. The differences in respnse-spectral values cmputed using the simple and exact sil-effect calculatins wuld be less than the differences in Furier spectra Impulse Respnse I.... I I Time (sec) FIG. A1. The impulse respnse fr vertically prpagating SH waves in the sil clumn f Figure 2. The arrws indicate the direct arrival (d) and the arrivals that have made an additinal ne and tw rund trips thrugh the entire sil clumn (lb and 2b, respectively).

19 GROUND MOTION AT DEEP-SOIL SITES IN E. NORTH AMERICA >10 ~ With Velcity Step O9 c- 3 1 ck (/3 2 0 \ 0 i i r ~ Freq (Hz) FIG. A2. The sil respnse, relative t a half-space withut the sil clumn. The slid circles are the respnse predicted by the apprximate methd f Jyner et al. (1981); the curves are the respnse frm the exact calculatins. Different numbers f reverberatins, indicated by the labels, are included in the exact respnse. (b 9 c- c 8.1 =8 N Velcity Step -- Exact Apprximate Freq (Hz) I 10 2 FIG. A3. As in Figure A2, but fr a mdel withut a step at the bttm f the sil clumn. In this case there are n reverberatins, and the spectrum frm nly ne exact calculatin is shwn. Nte the scale change n the rdinate between this and the previus figure. shwn in Figure A2. In the wrst case, the errrs prduced in the respnse spectral estimatins by using the simple crrectin fr the sil respnse wuld be cmparable t the errrs in grund-mtin predictin based n the empirical analysis f data. We als cmputed the respnse f the sils withut a step increase at the bttm (in ther wrds, we let layer 29 in the mdel shwn in Table 1 be the half-space). As expected, the amplificatin is smaller than when the sil clumn is terminated by a high-velcity halfspace (Fig. A3). In this case, the respnse frm the simple methd underestimates the exact respnse, but nly by abut 25%. We cnclude that the sil respnse cmputed frm the simple methd prpsed by Jyner et al. (1981) gives an adequate apprximatin f the site respnse, even fr cases invlving large step changes in impedance (fr which reverberatins in the sil clumn are imprtant). U.S. GEOLOGICAL SURVEY MAIL STOP MIDDLEFIELD ROAD MENLO PARK, CALIFORNIA Manuscript received 25 January 1991