abrahamsonand litehiser 1989 equation

5/24/2018 Abrahamsonand Litehiser 1989 Equation

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Bu l l e t i n o f t h eS e i sm ol og i c a l S oc i e t y o f m e r ic a

V o l . 7 9 J u n e 1 9 8 9 N o . 3A T T E N U A T I O N O F V E R T I C A L P E A K A C C E L E R A T I O N

BY N . A. ABRAHA MSON AND J . J . LITEHISERABSTRACT

P e a k v e r t i c a l a c c e l e r a t i o n s f r o m a s u i t e o f 5 8 5 s t r o n g g r o u n d m o t i o n r e c o r d sf r o m 7 6 w o r l d w i d e e a r t h q u a k e s a r e f it t o a n a t t e n u a t i o n m o d e l t h a t h a s am a g n i t u d e d e p e n d e n t s h a p e . T h e r e g r e s s i o n u s e s a t w o - s t e p p r o c e d u r e t h a t i sa h y b r id o f t h e J o y n e r a n d B o o r e ( 1 9 8 1 ) a n d C a m p b e l l ( 1 9 8 1 ) r e g r e s s i o n m e t h o d s .T h e r e s u l t i n g v e r t i c a l a t t e n u a t i o n r e l a t io n i s

I o g l o a v ( g ) - - - 1 . 1 5 + 0 . 2 4 5 M - 1 . 0 9 6 I o g lo ( r + e 2s 6 M ) + 0 . 0 9 6 F - 0 . 0 0 1 1 E r ,w h e r e M i s m a g n i t u d e , r is th e d i s t a n c e i n k i l o m e t e r s t o t h e c l o s e s t a p p r o a c h o ft h e z o n e o f e n e r g y r e l e a s e , F is a d u m m y v a r i a b l e t h a t i s 1 f o r r e v e r s e o r r e v e r s eo b l i q u e e v e n t s a n d 0 o t h e r w i s e , a n d E i s a d u m m y v a r i a b l e t h a t i s 1 f o r i n t e r p l a t ee v e n t s a n d 0 f o r in t r a p l a t e e v e n t s . T h e s t a n d a r d e r r o r o f Io glo av i s 0 . 2 9 6 .

B e c a u s e t h e v e r t i c a l to h o r i z o n t a l a c c e l e r a t i o n r a ti o is a ls o s o u g h t , t h e a t te n -u a t i o n o f th e h o r i z o n t a l p e a k s f ro m t h e s a m e s u i t e o f r e c o r d s i s a l s o o b t a i n e du s i n g t h e s a m e r e g r e s s i o n p r o c e d u r e . T h e r e s u l t in g h o r iz o n t a l a t t e n u a t i o n r e l a -t io n is

I o g ~ o a H ( g ) = - 0 . 6 2 + 0 . 1 7 7 M - 0 . 9 8 2 Io g ~ o( r + e 2 84 M ) + 0 . 1 3 2 F 0 . 0 0 0 8 E r ,w h e r e a H i s t h e p e a k a c c e l e r a t i o n o f t h e l a r g e r o f t h e t w o h o r i z o n t a l c o m p o n e n t s .T h e s t a n d a r d e r r o r o f Io g lo a H i s 0 . 2 7 7 .

T h e e x p e c t e d r a t io o f p e a k v e r t i c a l t o p e a k h o r i z o n t a l s t r o n g g r o u n d m o t i o np r e d i c t e d b y t h e s e e q u a t i o n s i s e n v e l o p e d b y th e w i d e l y u s e d r u l e -o f - th u m bv a l u e o f tw o - t h i rd s f o r e a r t h q u a k e s w i th m a g n i t u d e s l e s s th a n 7 . 0 a n d d i s t a n c e sg r e a t e r t h a n 2 0 k m . T h e e x p e c t e d r a ti o e x c e e d s 1 .0 fo r e a r t h q u a k e s w i t h m a g -n i t u d e s g r e a t e r t h a n 8 . 0 a t v e r y s h o r t d i s t a n c e s . T h e s t a n d a r d e r r o r o f Iog~o V/H)i s 0 . 2 0 , w h i c h i s le s s t h a n t h e s t a n d a r d e r r o r o f e i t h e r t h e v e r t ic a l o r h o r iz o n t a la c c e l e r a t i o n . T h e r e f o r e , t h e p e a k v e r t i c a l a n d h o r i z o n t a l a c c e l e r a t i o n s f o r a g i v e nr e c o r d a r e s t r o n g ly c o rr e l a te d a n d w e c a n h a v e m o r e c o n f i d e n c e i n t h e p r e d i c t e dr a t io t h a n i n e i t h e r th e p r e d i c t e d v e r t i c a l o r h o r iz o n t a l p e a k s .

INTRODUCTIONT h e e m p i r ic a l c h a r a c t e r i z a t i o n o f s t r o n g g r o u n d m o t i o n a t t e n u a t i o n h a s a lw a y s

e m p h a s i z e d h o r i z o n t a l s h a k i n g . T h i s f o l lo w s f r o m t h e p r i n c i p a l u s e o f s t r o n g -m o t i o n a m p l i t u d e d a t a: t h e e a r t h q u a k e r e s i s t a n t e n g i n e e r in g o f s t r u c tu r e s . T h et r a n s i e n t v e r t ic a l e a r t h q u a k e l o a d s h a v e b e e n v ie w e d a s r e l a ti v e l y u n i m p o r t a n tp e r t u r b a t i o n s o f t h e l o a d s i m p o s e d b y t h e e a r t h s g r a v i t a ti o n a l f ie ld . H o r i z o n t a l( t h a t i s , l a t e r a l ) e a r t h q u a k e l o a d s , a l t h o u g h j u s t a s t r a n s i e n t , a r e o f t e n v i e w e d a st h e l a r g e s t h o r i z o n t a l l o a d s t h a t a s t r u c t u r e w i ll e v e r h a v e t o b ea r . W i d e l y u s e db u i l d i n g c o d e s , s u c h a s t h e U n i f o r m B u i l d i n g C o d e ( I n t e r n a t i o n a l C o n f e r e n c e o f

549


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5 5 0 N A A B R A H A M S O N A N D J J L I T E H I S E R

Building Officials, 1985 or earlier editions), as well as recent recommendations oflocal jurisdictions developing their own building codes (Building Seismic SafetyCouncil, 1985), do not consider vertical seismic loads at all. Even for the dynamicdesign of critical facilities such as nuclear power plants, it is generally assumed tha tthe peak vertical acceleration is simply some fraction of the peak horizontalacceleration. A value of two-thirds is most often used as the maximum effectiveratio between vertical and horizontal accelerations (Newmark and Hall, 1982).

There is no doubt that, on average, vertical accelerations are smaller thanhorizontal accelerations for strong-motion data from earthquakes of all sizes re-corded at all distances. In fact, when averaging over all strong ground motionsrecords, the two-thirds ratio is conservative. Yet for larger earthquakes recorded at

2shorter distances. The V/H ratio seems to increase to values greater than ~. Aglimpse of this behavior was provided by the very first useful records of damagingearthquake motion. The magnitude 6.2 Long Beach earthquake of 1933 was recordedat several sites, one at a source distance of just over 6 km. Th elV/H ratio for thisrecord was just over 1.0. Data from other earthquakes, mos t notab ly the 1979Imperial Valley earthquake, seem to indicate that this behavior may be represent-ative. Bureau (1981) analyzed 75 strong-motion accelerograms recorded at distancesof 10 km or le ss and found that the V/H ratio was 1.0 or larger for magnitudesgreater than 6. Campbell (1982) developed an expression for peak vertical acceler-ation attenuation using the same near-source data (recorded within 50 km of therupture zone) compiled previously to study the near-source characteristics of peakhorizontal acceleration (Campbell, 1981). His expression implied that the V/H ratioexceeded 1.0 for earthquakes of magnitude 7 or greater at distances less than 5 km.

It is precisely the large earthquakes at near distances that often contribute mostsignificantly to earthquake design load estimates. This suggests tha t separateattenuation relations may be required for the peak vertical and peak horizontalground motions. The data to develop peak vertical relations exist and are as readilyavailable as horizontal data.

The curr ent s tudy has two purposes. Its primary purpose is to develop an empiricalalgebraic description of peak vertical ground accelerations as a function of earth-quake size and distance. Although work on atten uatio n of vertical acceleration hasbeen limited, attenuat ion of horizontal acceleration has been the subject of intensivestudy since the ear ly 1970 s. Campbel l (1985), for example, presents a summarytable of strong-motion attenuation relations published between 1974 and 1984 inwhich 16 citations appear for the attenuat ion of horizontal acceleration. Additionalpapers (for example, Luco, 1985; Boore and Atkinson, 1987; Sabet ta and Pugliese,1987; Toro and McGuire, 1987; Campbell, 1988; Fuk ushima e t a l . 1988) on this orclosely related topics have been published since. We have tried to adopt as muchdata and as many insights as possible from these earlier studies to our currentstudy.The second purpose of this paper is to develop estimates for the V /H ratio. Twoobvious choices are available: regression on the horizontal data, then forming theratio of the vertical and horizontal attenuation expressions, or regression directlyon the V/H data. Although the second approach is more direct, we choose the firstapproach because interest in horizontal attenuati on relations remains high.All studies of strong motion attenuation must consider and discuss basic topicssuch as data selection, the attenuation model used for regression, and the methodof regression. Although we too mus t discuss these topics as they apply to the currentstudy, we at tempt to make our discussion as brief as possible by referring to previousstudies whenever possible. In particular, the papers of Joyner and Boore (1981) and


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ATTENUATION OF VERTICAL PEAK ACCELERATION 551C a m p b e l l 1 9 8 1 ) p r o v id e th e s t a r t i n g p o i n t fo r o u r a n a l y s i s. T h e s e s a m e a u t h o r sh a v e w r i t te n t w o v e r y u s e f u l r ev i ew s o f t h e a n a l y s is o f s tr o n g - m o t i o n a t t e n u a t i o nC a m p b e l l , 1 9 8 5 ; J o y n e r a n d B o o r e , 1 9 8 8 ) .

I n a d d i t i o n t o t r e a t i n g a n a u g m e n t e d d a t a s e t a n d e m p h a s i z i n g v e r t i c a l d a t a , o n ea s p e c t o f t h i s s t u d y r e p r e s e n t s a n e x t e n s i o n , r a t h e r t h a n a s i m p l e a d a p t a t i o n , o fp r e v i o u s w o r k: w e u s e a r e g r e ss io n m e t h o d t h a t i s a h y b ri d o f t h e J o y n e r a n d B o o r e

1 9 8 1 ) a n d C a m p b e l l 1 9 8 1 ) m e t h o d s .STRONG-MOTION D ATA BASE

Th e fu ndam enta l da ta used for th i s s tu dy are the vert i ca l peak acce l era t ions f romrecords wh ose hor izonta l peaks were ana lyzed by Joyner and Boore 1981) and

TABLE 1LIST OF EARTHQUAKES

Focal TectonicNumber EarVhquake Date Magnitude " Mechanism* Envlronment

1 Long Beach 3/11/33 6.2 1 12 Helena, Mo ntana 10/31/35 5.5 2 03 Imperi al Valley 5/19/40 7.1 14 San ta Barb ara 7/01/41 5.9 4 15 K e r n o u n t y 7/21/52 7.7 5 16 Daly City 3/22/57 5.3 1 17 Hebge n Lake, Mo ntana 8/18/59 7.1 2 08 Parkf ield 6/28/66 6.0 1 19 Fairbanks , Alaska 6/21/67 5.7 1 1

10 Kovna, India 12/10/67 6.5 1 111 Borrego Mtn. 4/09/68 6.7 1 112 Sa nta Rosa (1) 10/02/69, 04:56 5.6 1 113 San ta Rosa (2) 10/02/69 06:19 5.7 1 114 Lytl e Creek 9/12 /70 5.4 1 115 San Fer nan do 2/09/7 6.6 4 116 Bea r Valley 2/24/72 5.1 1 117 Sitka , Alas ka 7/30/72 7.6 1 118 Managua, Nicaragua 12/23/72 6.2 1 119 Poi nt Mugu 2/21/73 5.9 4 120 Lima, Per u 10/03/74 7.6 4 121 Lima, Per u 11/09/74 7.2 4 122 H o l l i s t e r 11/28/74 5.1 1 123 Oroville 8/01 /75 5.7 2 124 Kalap ana, Hawaii 11/29/75 7.1 2 025 Gazli, US SR 5/17 /76 7.0 4 026 San ta Bara bara 8/13/78 5.1 4 127 Tabas, Ira n 9/16/78 7.7 4 028 Bishop 10/04/78 5.7 1 129 St. Elias, Alaska 2/28/79 7.2 4 130 Coyote Lake 8/06 /79 5.9 1 131 hnper ia l Valley 10/15/79, 23:16 6.9 1 132 hnp er ia l Valley (AS) 10/15/79, 23:19 5.0 1 133 Livermore (1) 1/24/80 5.5 1 134 Liv ermore (2) 1/27/80 5.6 1 135 Horse Canyon 2/25/80 5.3 1 136 Mam mo th Lake s 1 5/25/80, 16:33 6.1 3 137 Ma mm oth Lakes (AS) 5/25/80, 16:35 5.0 3 138 Mamm oth Lakes 2 5/25/80, 16:49 6.0 3 139 Mamm oth Lakes 3 5/25/80, 19:44 6.1 3 140 Ma mm oth Lakes (AS) 5/25/80, 20:35 5.7 3 141 Mam mo th Lakes 4 5/27/80, 14:50 6.0 3 142 Mexicali Valley, Mexico 6/09/80 6.1 1 1


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552 N. A. ABRAHAMSON AND J. J. LITEHISERTABLE 1 C o n t in u e dList of Earthquakes

Number Earthquake Date Magnitude Focal TectonicMechanism* Envlronmentt43 Eur eka 11/08/80 7.2 1 144 SMA RT 1 Eve nt 5 1/29/81 5.7 4 145 Wes tmor lan d 4/26/81 5.6 1 146 Coalinga 10/25/82 5.4 4 147 Lon g Valley 1/07/83 5.4 3 148 Coal inga MS) 5/02/83, 23:42 6.5 4 149 Coalinga AS) 5/09/83, 02:49 5.1 4 150 SMA RT 1 Eve nt 22 5/10/83 5.6 2 151 Coalinga AS) 6/11/83, 03:09 5.1 4 152 SMA RT 1 Eve nt 23 6/21/83 6.4 5 153 SMA RT 1 Eve nt 24 6/24/83 6.7 5 154 Long Valley 7/03/83 5.2 3 155 Coalinga AS) 7/09/83, 07:40 5.3 4 156 Coal inga AS) 7/22/83, 03:43 5.0 4 157 Coal inga AS) 7/25/83, 22:31 5.1 4 158 Coal inga AS) 9/09/83, 09:16 5.3 5 159 SMART 1 Eve nt 25 9/21/83 6.5 5 160 Borah Peak, Idaho 10/28/83 6.9 3 061 Wes te rn Idaho 10/29/83 5.8 2 062 Morg an Hill 4/24/84 6.1 1 163 Wes te rn Idaho 8/22/84 5.8 3 064 Bishop 11/23/84 5.9 3 165 SMA RT 1 Eve nt 33 6/12/85 5.2 3 166 Mexico MS) 9/19 /85 8.1 4 167 Mexico AS) 9/21 /85 7.5 4 168 Naha nni, Canad a 12/23/85 6.9 4 069 SMA RT 1 Eve nt 39 1/16/86 5.5 2 170 Ohio 1/31/86 5.0 1 071 SMA RT 1 Eve nt 40 5/20/86 6.4 5 172 SMART 1 Eve nt 41 5/20/86 5.5 5 173 Pal m Sprin gs 7/08/86 5.9 5 174 Chal fant Valley 7/21/86 6.0 1 175 E1 Salvado r 10/10/86 5.4 1 176 SMA RT 1 Eve nt 45 11/14/86 7.8 4 1

* 1 = Strike-slip, 2 = Normal, 3 = Normal oblique, 4 = reverse, 5 = reverse oblique.t Tectonic Environment: 0 = intraplate, 1 = interplate.

Campbell (1981), supplemented by more curren t strong-motion data for earthquakesoccurring through 1986. The earthquakes used in this study are listed in Table 1and the peak accelerations are listed in Appendix A. There are 585 recordings from76 worldwide earthquakes. All earthquakes used in this study have focal depths ofless than 25 kin. Just over three-fourths of the records are from 45 earthquakes inCalifornia where the frequency of events and the density of strong-motion instru-ments are both high. All station recordings listed contain a measurement of peakvertical acceleration, and all but 13 contain measurements of both horizontalcomponent peaks. In those few cases where only one horizontal acceleration valueis given, it is generally the larger horizontal component.We adopt Campbell s definitions of earthquakes magnitude and distance whichdiffer slightly from the Joyner and Boore definitions of these two importantindependent parameters. Thus, the distance from earthquake to recording stationused in this st udy is defined as the closest distance from the station to the zone ofenergy release. Whenever a distance value for a particular recording is listed in


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A T T E N U A T I O N O F V E R T I C A L P E A K A C C E L E R A T I O N 5 5

Campbell, it is used directly. For other records, distances are taken from otherstudies or are computed from our own best es timate of the closest surface expressionof the associated earthquake faulting or the inferred source extent based on thedistribution of aftershocks. Similarly, magnitudes are adopted directly from Camp-bell when available and, otherwise, are taken as either M s (surface-wave magnitude)or M L (local magnitude), following Campbell, where M s is used if it is greater thanor equal to 6.

A special subset of the data base is provided by recordings from the SMART 1accelerograph array in T~aiwan. A recent review of the data from this array appearsin Abrahamson et al (1987). The main SMART I array consists of 37 strong motionseismometers within a 2 km radius. Peak accelerations for this array are defined inAppendix A as the array average for each event. Therefore, these peak accelerationsare more stable estimates t han the single station accelerations. The variation of theaccelerations across the array are discussed in Abrahamson (1988). The location ofthe central stat ion is used for all earthquake-to-s tation distance determinations. Inall, 10 earthquakes in our data base were recorded by the SMART 1 array. Of these10 events, five have rnb and Ms < 6 as determined by the Internatio nal SeismologicalCentre or the U.S. Geological Survey. The mb values are used to define the sizes ofthese five events rather t han M L because ML for Taiwan appears t be systemat icallyhigh for moderate size events (Abrahamson, 1988).

Figure 1 is a plot of the distribution with magnitude and distance of the 585recordings. The data base includes accelerations for distance from 0.08 km (plotted,for convenience, at 0.1 kin) to 400 km, although the bulk of the data is for distancesof less than 100 km. Earthquake magnitudes range from 5.0 to 8.1. As is typicalwith most strong-motion data sets, there is a significant correlation betweenmagnitude and distance: the correlation coefficient is 0.52.

The data used in this study were recorded on instruments located generally eitherin the free-field, on an abutment of a dam or bridge, or in the basement or on theground floor of a building. Following Joyner and Boore (1981), the geologic foun-dation conditions of the recordings are classified as either rock or soil inAppendix A. In terms of the Campbell (1981) geological classification scheme,classifications C, D, and E are considered rock and A, B, and F are considered soil.Of the 585 recordings in Appendix A, 159 are classified as rock sites, 324 areclassified as soil sites, and 102 are unclassified. Since site condition in forma tion isnot readily available for many of the stations listed in Appendix A, we do notattempt to use site geology as part of the regression analysis, but rather examine apossible site geology dependence in the residuals.

Each event is classified by gross tectonic environment and fault type. Two tectonicenvironments are used: interplate and intraplate. The faulting is classified as strike-slip, normal, normal olbique, reverse, or reverse oblique. These five fault types arecombined into two groups: normal-strike-slip events and reverse events.

The four independent parameter s used in the regression analysis are magnitude,distance, fault type, and tectonic environment. The correlation matrix for thesefour independent parameters is given in Table 2.

The dependent parameters are peak vertical acceleration and peak horizontalacceleration. We define peak horizontal acceleration in this study as the larger ofthe two peaks from both horizontal components for a given record. This is done tobe in accord with our understanding of general engineering practice and with thedefinition of peak acceleration for the single vertical component.

Although the purpose of this paper is to determine the distance and magnitude


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5 5 4 N. A. ABRAHAMSON AND J. J. LITEHISERB . 5 . . . . . . . . I L ' ' '1 . . . . .

B 0

7 . 0b~::::H 6 . 5 ~ 3 5 m ~z.

6 . 0 ~ ~ ~> ~ ~> ,C

5 . 5 ~~>~> 3 > ~ ~>

C~5 . 0 l l l ~

4 . 5 w I I [ I . . |O . 1 1 0 1 0 0 1 0 0 0

CLOSEST DISTANCE kin)FIG. 1. Distribution in magnitude and distance of the strong-motion data used in this study. Thevertical lines indicate the distance bins used for the weighting scheme.

dependence of the peak vertical acceleration and the vertical-to-horizontal acceler-ation ratio, a few global statistics of the data base are usefully acknowledged here.The average vertical-to-horizontal peak acceleration ratio for the entire data set is0.61. The larger hor izonta l peak for a given record is, on average, 1.13 times themean of the two horizontal peaks for that record. The average vertical to horizontalpeak ratio, when the mean horizontal peak is considered, is 0.68.

REGRESSION MODELS AND METHODSFollowing previous studies on the a ttenuati on of horizontal acceleration forexample, Campbell, 1985), we consider an attenuation relation of the general form

log~oa~ g) = f~ M) + f2 r, E) + f3 r, M, E) +/4 /~) , 1)


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ATTENUATION OF VERTICAL PEA K ACCELERATION 55 5TABLE 2

C O R R E L A T I O N M A T R I X F O R T H E I N D E P E N D E N T P A R A M E T E R SM r F E

M 1 . 0 0r 0 . 5 2 1 . 0 0F 0 . 2 3 0 . 1 8 1 . 0 0E 0 . 2 6 0 . 1 7 0 . 0 3 1 . 0 0

w h e r e a u i s t h e p e a k v e r t i c a l a t t e n u a t i o n ; f l M ) is a f u n c t i o n o f e a r t h q u a k em a g n i t u d e ; f2 r , E) i s a fu n c t i o n o f e a r t h q u a k e - t o - r e c o r d i n g - s i t e d i s t a n c e a n d t h et e c t o n i c e n v i r o n m e n t ; f3 (r, M , E ) i s a n o n s e p a r a b l e f u n c t i o n o f m a g n i t u d e , d i s ta n c e ,a n d t e c t o n i c e n v i r o n m e n t ; a n d f 4 ( F ) i s a f u n c t i o n o f f a u l t t y p e . U s u a l l y , e i t h e r f2 (r ,E ) o r f3 r , M , E) is u s e d i n a n a t t e n u a t i o n e x p r e s s i o n b u t n o t b o t h . I f t h e d i s t a n c ed e p e n d e n c e o f p e a k a c c e l e r a t io n i s s e p a r a b l e f r o m t he m a g n i t u d e d e p e n d e n c e , t h e nf2 r , E) i s u s e d ; i f n o t , t h e n f3 r , M , E) i s u s e d . T h e a d o p t i o n o f e q u a t i o n (1 ) a l o n gw i t h t h e s p e c i f i c a t i o n o f t h e f u n c t i o n a l f o r m s o f f l , f2 o r f3 , a n d f4 d e f i n e s t h er e g r e s s io n m o d e l . T h e w a y i n w h i c h t h e m o d e l is f i t t o t h e d a t a d e f i n e s t h e r e g r e s si o nm e t h o d .

T h e s e l e c ti o n o f a n f2 o r a n f3 t y p e m o d e l is a n i m p o r t a n t i ss u e . T h e f l , / 2 m o d e la s s u m e s t h a t t h e d i s t a n c e a n d m a g n i t u d e h a v e s e p a r a b l e in f l u e n c e s o n p e a k a c c e l-e r a t io n , s o t h a t a t b o t h n e a r a n d f a r d i s t a n c e s t h e d i f f e re n c e b e t w e e n a c c e l e r a t io np e a k s f r o m t w o d i f f e r e n t e v e n t s i s u n i q u e l y d e t e r m i n e d b y t h e i r s p e c if ic m a g n i t u d e s .T h e s h a p e o f t h e a t t e n u a t i o n c u r v e d o e s n o t d e p e n d o n e a r t h q u a k e m a g n i t ud e . I nc o n t r a s t , t h e f l ,/ 3 m o d e l a s s u m e s t h a t t h e i n f l u e n c e s o f d i s t a n c e a n d m a g n i t u d e a r en o n s e p a r a b l e . T h e d i s t a n c e m u s t b e s p e c i fi e d t o d e t e r m i n e t h e d i f f e re n c e i n a tt e n -u a t i o n p e a k s f o r a n y s p e c if ic p a i r o f m a g n i t u d e s . T h e s h a p e o f t h e a t t e n u a t i o n c u r v eis a l lo w e d to b e m a g n i t u d e - d e p e n d e n t . B o t h m o d e l s al lo w f o r s a t u r a t i o n o f p e a ka c c e l e r a t io n f o r la r g e m a g n i t u d e e a r t h q u a k e s , b u t t h e f l, [3 m o d e l a ll o w s th es a t u r a t i o n e f f e c t t o b e d i s t a n c e - d e p e n d e n t .

I n t h i s i n v e s t ig a t i o n , w e u s e a r e g r e s s io n m o d e l a n d m e t h o d t h a t i s a h y b r i d o ft h e m o d e l s a n d m e t h o d s u s e d b y C a m p b e l l ( 1 9 81 ) a n d J o y n e r a n d B o o r e ( 1 9 8 1) . I nt e r m s o f e q u a t i o n ( 1) , C a m p b e l l c o n s i d e r s a n / 1 , [3 t y p e m o d e l . ( C a m p b e l l i n c lu d e sa f a u l t t y p e t e r m i n h i s la t e r a n a l y s e s : C a m p b e l l , 1 9 8 2, 1 9 8 8 .) T h e f o r m o f t h e s ef u n c t i o n s r e s u l t s i n a n o n l i n e a r p r o b l e m t h a t i s s o l v e d u s i n g n o n l i n e a r l e a s t - s q u a r e sr e g r es s io n . E x p l i c i t w e i g h t i n g o f t h e d a t a b y d i s t a n c e is u s e d i n t h e a n a l y si s . I nc o n t r a s t , J o y n e r a n d B o o r e c o n s i d e r a n f l , /2 t y p e m o d e l. T h e i r m o d e l is a ls on o n l i n e a r b u t i t c a n b e l i n e a r iz e d b y e m p l o y i n g a n i t e ra t i v e s c h e m e t o s o l v e f o r o n eo f t h e p a r a m e t e r s . I m p l i c i t e q u a l w e i g h t in g o f e a c h e v e n t i s u s e d i n d e t e r m i n i n g t h ec o n s t a n t s o f f l. B o t h t h e C a m p b e l l a n d J o y n e r a n d B o o r e r e g re s si o n m e t h o d o l o g ie sa r e e a s i l y m o d i f i e d t o i n c l u d e a t e r m f o r fa u l t t y p e : f4 ( F ) . T h e d e t a i l s o f t h e s e t w or e g r e s s i o n m e t h o d o l o g i e s a r e g i v e n i n t h e o r i g i n a l p a p e r s . A n o u t l i n e o f a s im p l em o d i f i c a ti o n o f t h e t w o m e t h o d o l o g i e s i s g i v e n i m m e d i a t e l y b e l o w a n d a h y b r i dm e t h o d o l o g y i s t h e n d e v e l o p e d .Jo yn er and Boore Typ e Regress ion

T h e J o y n e r a n d B o o r e ( 1 9 81 ) r e g r e s s io n m e t h o d o l o g y is f i rs t m o d i f i ed to i n c l u d ea f a u l t t y p e t e r m a n d t o d i f f e r e n t i a te b e t w e e n i n t e r p l a t e a n d i n t r a p l a t e a n e l a s ti ca t t e n u a t i o n . T h i s r e g r e s s io n m o d e l u s e s a n e q u a t i o n o f t h e f o r m

~BlOgloa , (g ) = l aB M ) + f ~ r , E ) + f 4 F ) , (2)


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556 N A ABRAHAMSON AND J J LIT EHIS ER

whereJBf2 (r, E) = -logl0(r 2 + h 2 ) 1 /2 + E b r 2 + h 2 ) ~ /2 , (3)

and/4(F) - F(b, (4)

where E is a dummy variable tha t is i for interplate earthquakes and 0 for intraplateearthquakes and F is a dummy variable that is 1 for reverse or reverse obliqueevents and 0 otherwise. In equation (3), the coefficient of loglo(r 2 + h 2 ) ~ /2 term isconstrained to be - 1, which restricts its physical interpreta tion to the effect of far-field geometrical spreading from a point source. The b coefficient, for values lessthan zero, represents anelastic att enuati on. Significant distance, r , is defined as theclosest distance to the surface projection of fault rupture. It does not, therefore,include a depth term. The constant, h, compensates fo r this and looks, in fact, verymuch like depth. It is not depth, however, but rather a term that is globallydetermined for the whole data set. That is, it is independent of the event or themagnitude. Its inclusion in equation (3) allows modeling of the characteristicflatten ing of peak acceleration at small distances and keeps acceleration estimatesfrom increasing without bound as the distance approaches zero.

The Joyner and Boore regression method employs a two-step approach. The firststep is summarized as follows. Let (a,)ik be the kth vertical peak accelerationrecording from the j th earthquake. Set h to a reasonable arb itra ry value andminimize the sum of the squares of the residuals defined by

residjk = I lo g l o [ a v ) j~ r ~ k + h2)~/2]} - f ~i= ~ i S i j + E j b r ~ k + h 2 ) ~ / 2 } , (5)where N is the to tal number of earthquakes, a j is a parameter for th ej th earthquake,and 5it is the Kronecker delta function. Compute the variance of the residuals.Select a new h and repeat the procedure. The value of h for which the variance ofthe residuals is minimized yields preferred values for h, b, and the aj s.

The second step in the Joyner and Boore regression methodology is to solve forfl (M) and f4 (F) in terms of the a (M, F) s. A plot of a versus M t (the magnitude ofth ej th earthquake) indicates tha t this parameter generally increases with increasingM (see, for example, Fig. 3 of Joyner and Boore, 1981). Both linear and quadraticparameterizations of f l M ) were analyzed by Joyner and Boore in their study ofpeak horizontal attenuation.A major computational advantage of the Joyn er and Boore regression methodol-ogy is that it can be linearized by using the iterative procedure described above tosolve for h. In addition, the first step in the regression involves inversion of a sparsematrix that can be easily inverted analytically. This leads to very fast programexecution.In trial application of this model and methodology to our da ta set, we found tha tb was very small and positive. This coefficient has no physical interpretation witha positive value. A similar finding has been reported by Sabetta and Pugliese (1987)for a data base of Italian strong-motion records. For this reason, we do not use the

JBf2 (r, E) model in thi s study.


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TTENU TION OF VERTIC L PE K CCELER TION 7C a mp b e l l T y p e R e g r e s si o n

The Campbell 1981) regression methodology is also modified to include a faulttype term. This modified model uses an equation of the form

logloa, g) = f C M ) + fC r , M , E ) + f4 F), 6)where

fC r , M, E) = -c loglo r + H M ) ) + E b r, 7a)and

H M ) = h le x p h 2 M ) . 7b)In this form, the attenuation curves are allowed to show different dependence onearthquake magnitude for differen t distances. Signi ficant distance, r, is now definedas the closest approach to the recording site of the zone of energy release. Thefl M) term is modeled as a linear func tion of M:

d e M ) = ~ + ti M . 8)A nonlinear least-squares regression analysis is performed simultaneously on all sixparameters: a, ~, ~, c, hi, and h2.Hy b r i d R e g r e ss i o n

The Joyner and Boore and Campbell models both have some drawbacks. TheJoyner and Boore method requires an f2 type model and therefore cannot accom-modate a dist ance-dependent saturat ion of peak acceleration at large magnitudes.The Campbell method, on the other hand, does not address the correlation betweendistance and magnitude. This problem is described below.

Fukushima et al. 1988) demonstrated that the correlation between magnitudeand distance can lead to poor estimation of the distance decay parameter c inequation 7a) if a single simultaneous regression is performed. They found that thedistance decay estimated from the entire data set does not agree with the averagedecay estimated for individual events see thei r Fig. 3). Since our data set alsoexhibits a correlation between distance and magnitude see Table 2) we mustconsider this problem. Note that Campbell 1981) avoided this problem by selectinga data set that had a small correlation between distance and magnitude: 0.06).Fukushima et al. found that using the Joyner and Boore two-step regression methoddecouples the distance and magnitude determination and yields a distance decayterm that agrees with the average distance decay term found for individual events.

Our hybrid regression is a two-step procedure that owes elements to both thepublished Campbell 1981) and Joyner and Boore 1981) procedures described above.The goal of our hybrid model is to combine the two-step approach of Joyner andBoore with an f3 type model such as used by Campbell. The first step uses theJoyner and Boore method with an f2 model to determine the distance decayparameter c. Then, with c held constant, the second step uses the Campbell methodwith an f3 model to determine the remaining parameters.

As mentioned earlier, use of the f2 form given in equation 3) results in a


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558 N. A. ABRAHAMSON AND J. J. LITEHISERnonphysical value for b. As a result, we drop the b term from the f2 model. Inaddition, we feel that constraining the coefficient of the log term to - 1 is toorestrictive. Since we use Campbell s definition of distance, we use r + h rather than(r 2 + he ) 1/2.Therefore , in step 1, we use an /2 model given by

f2 r ) = c logl0(r + h). (9)With this form, the first step of the Joyner and Boore regression method can berepeated with equation (5) rewritten as

resid;k = loglo[(av)jk]- { ~i=1 a i S i j + c l o g i o r j k + h ) } . (10)As before, a range of reasonable values for h is searched to find the minimumvariance solution. The c term corresponding to the minimum variance solution isdenoted 5. Using 5 from step 1, the second step of the hybrid regression uses an f~model given by equation (8), an f4 model given by equation (4), and an fa modelgiven by

f3 r , M, E) = -6 loglo(r + H M ) ) + E b r. (11)An impor tant issue concerns the form of H M ) . This term determines the characterof peak acceleration saturation at short distances. The Joyner and Boore methoduses a constant for H (M) while the Campbell method uses an exponential functionof magnitude (equation 7b). The form of H(M) is important in controlling thepredicted accelerations at short distances. This term is discussed in detail in theresults section.W e i g h t i n g

In an ideal data set, there would be a uniform sampling of peak acceleration overall magnitudes and distances; however, we have a limited data set. Some eventshave only one recording while other events have multiple recordings. The well-recorded events are important, but it is not desirable to have them completelycontrol the regression. For this reason, weights are introduced into the regression.The methodology used by Joyn er and Boore (1981) does not explicitly weight thedata, but it does implicitly give equal weight to each event in determining themagnitude dependence ([1 (M)). Campbell (1981), on the other hand, uses explicitweights. The weights are determined by dividing the data into a number of subsetsbased on distance. In each distance interval, each earthquake is given equal weightby assigning a relative weight of 1/njz to the record where n~z is the total number ofrecordings for the j th ea rthquake within t h e / t h distance bin. The weights are thennormalized so that they sum to the t otal number of recordings.

Campbell uses nine distance intervals for data in the range of 0 to 50 km. Thefirst four bins are 2.5 km wide. At distances greater than 10 km, the bins are ofequal width on the logar ithm of distance. For our study, the data extends out to 400kin, so we need more distance bins t han are given by Campbell. We simply continuethe equal bin width on the logarithm of distance out to 400 km. The only exceptionis that the last two bins are combined because there are so few data at largedistances. The distance bins used in this study are shown in Figure 1.


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ATTENUATION OF VERTICAL PEAK ACCELERATION 559RESULTS

Vertical ccelerationA number of trial solutions for the attenuat ion of peak vertical acceleration were

performed for the data of Appendix A. The effects of various data winnowingschemes such as removal of acceleration peaks from single-recording earthquake(after Joyner and Boore, 1981) and removal of records from shallow or soft soilsites (after Campbell, 1981) were also considered.The effects of data winnowing are small (less than, and generally much less than,10 per cent) in the magni tude range 5 to 8 and distance range 0 to 100 km consideredin detail. Effects on the unce rtain ty of the estimate, as measured by the variance ofthe regression solutuion, are also small for all of the winnowing schemes considered.The Appendix A data base is large enough so that removal of any small subset ofthe data has little effect on the results. The results discussed below are deri~edusing the extended Campbell weighting scheme and all of the data listed in AppendixA.Using the two-step hybrid regression method, we first compute the distance decayparameter, c. For vertical acceleration, we find 5 = -1.096. The second step followsa Campbell type regression with ~ held fixed.

An important question concerns the H(M) function: is this function magnitudedependent or not? To address this question, we use a nonparame tric form of H(M)given by

H( M) = F~ hjGj, (12)j l

where Gj is a dummy variable that partitions the earthquakes into half magnitudebins. The resulting nonparametric fit is shown in Figure 2. There is an indicationthat H(M) increases with increasing magnitude and an exponential form seemsappropriate; however, this conclusion depends critically on the two upper magnitudebins. It is important to note that the largest magnitude bin (8.0 to 8.4) containsonly one event: 1985 Mexico. Since this event produced low peak accelerations, theresulting h2 value is large. Therefore, this event may have a strong effect on theresulting H (M) function.

For reference, we first fit the data using a constant for H(M). Next, we fit thedata using Campbell s exponential form for H(M) (equation 7b). The H(M) func-tions are plotted in Figure 2. The exponential form produces a lower total variancecompared to the constant form, but the fit at short distances is controlled by the1985 Mexico earthquake. Since this earthquake may be anomalous, it is not desirableto have it control the regression. In addition, the hi term is not well-determined bythe regression: its value is 0.0088 with an asymptotic standard error of 0.073 and itis highly correlated with h2 (0.99). As an alternat ive, we use a simplified exponent ialmodel in which hi is restricted to unity. This model is much more stable in that the1985 Mexico earthquake does not completely control the fit at short distances. Thi smodel also has the advantage that all of the parameters are well-determined.Therefore, we adopt the form

H(M) = exp(h2M). (13)


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560 N. A. ABRAHAMSON AND J. J. LITEHIS ERT h e r e s u l t i n g v e r t i c a l a t t e n u a t i o n r e l a t io n i s g i v e n b y

lo g l0 a v g ) = - 1 .1 5 + 0 .2 4 5 M - 1 .0 9 6 lO g lo r + e 25~M )+ 0 . 0 9 6 F - 0 . 00 1 1 E r, 1 4)

w i t h a s t a n d a r d e r r o r o f 0 .2 96 . T h e a s y m p t o t i c s t a n d a r d e r r o r s o f t h e r e g r e s s i o np a r a m e t e r s a r e li s te d in T a b l e 3 . T h e v e r t i c a l a t t e n u a t i o n c u r v e s f o r n o r m a l / s t r i k e -

6 ~ I I I I I

5 5

4 5

~ _ ~ * j ~ ~ ~ ' H ( M ) = h 1

5 I I I I I I5 0 5 5 6 0 6 5 7 0 7 5 8 0 B 5

M G N I T U D EFIG. 2. Nonpar ametr ic magnitude dependence of the H M) function for vertical peak acceleration.The vertical bars indicate -+1 S.E. The regression results of three different forms of H M) are also shown.

TABLE 3PARAMETERS ESTIMATES AND ASYMPTOTIC STANDARD ERRORS

Vertical HorizontalParameter Est. Asym. s e. Est. Asym. s.e.

6 1.096 0.072 -0 .982 0.068-1.146 0.095 -0.624 0.089

0.245 0.017 0.177 0.015h2 0.256 0.025 0.284 0.025

0.096 0.028 0.132 0.026b 0 . 0 0 1 1 0 . 0 0 0 3 0 . 0 0 0 8 0 . 0 0 0 3


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ATTENUATION OF VERTICAL PEA K ACCELERATION 561s li p e v e n t s a r e p l o t t e d i n F i g u r e 3 . T h e s o li d c u r v e s a r e f o r t h e i n t e r p l a t e t e c t o n i ce n v i r o n m e n t a n d t h e d a s h e d c u r v e s ar e f o r t h e i n t r a p l a t e t e c t o n i c e n v i r o n m e n t .

C o m p a r i s o n s o f t h e p r e d i c t e d w i t h t h e o b s e r v e d a c c e l e r a t io n s a r e m a d e i n F i g u r e4. T h e d a t a a r e g r o u p e d i n t o h a l f -m a g n i t u d e i n t e r v a l s a n d a r e r e d u c e d t o a c o m m o nf a u l t t y p e b y s c a l i n g t h e r e v e r s e a n d o b l i q u e r e v e r s e p e a k a c c e l e r a t i o n b y 1 0 -9 6.A g a i n , t h e s o l i d c u r v e s a re f o r t h e i n t e r p l a t e t e c t o n i c e n v i r o n m e n t a n d t h e d a s h e dc u r v e s a r e f o r t h e i n t r a p l a t e t e c t o n i c e n v i r o n m e n t . F o r e a c h m a g n i t u d e i n t e rv a l ,t h e c e n t r a l c u r v e is t h e m e d i a n a c c e l e r a t io n f o r t h e m e a n m a g n i t u d e a n d t h eb o u n d i n g c u r v e s a r e t h e 8 4 t h a n d 1 6 t h p e r c e n t i l e l e v e ls f o r t h e u p p e r a n d l o w e rb o u n d m a g n i t u d e s , r e s p e c ti v e l y . T h e s e f i gu r e s s h o w t h a t c u r v e s p r o v i d e a g o o d f itt o t h e d a t a o v e r al l m a g n i t u d e i n t e r v a l s e x c e p t f o r t h e u p p e r m o s t m a g n i t u d e r a n g e.T h e o n l y e v e n t i n t h e 8 .0 to 8 .4 m a g n i t u d e r a n g e i s t h e 1 98 5 M e x i c o e a r t h q u a k e .T h e a c c e l e r a t i o n s r e c o r d e d a lo n g t h e c o a s t , d i re c t l y a b o v e t h e r u p t u r e z o n e , w e r elo w . S o m e r e s e a r c h e r s h a v e s u g g e s t e d t h a t t h e r u p t u r e o f t h i s e v e n t w a s a n o m a l o u s l ys m o o t h A k i e t a l . 1 9 87 ; S t e a c y e t a l . 1 9 8 7 ). A s m o o t h r u p t u r e w o u l d p r o d u c e l o w e ra c c e l er a t io n s t h a n a n u n e v e n r u p t u r e . W h a t e v e r t h e c a u se , o n l y re c o r di n g s f r o ma d d i t i o n a l g r e a t e a r t h q u a k e s a r e l ik e l y t o r e s o lv e th i s a p p a r e n t d i s c r e p a n c y .

T h e w e i g h t e d r e s id u a l s f o r d a t a w i t h i n 1 0 k m a r e s h o w n i n F i g u r e 5 . T h e r e is as m a l l p o s i t i v e s l o p e t o t h e w e i g h t e d r e s i d u a l s , b u t i t i s n o t s i g n i f i c a n t l y d i f f e r e n tf r o m z e r o a t t h e 9 0 p e r c e n t c o n f i d e n c e l e v e l s u g g e s t in g t h a t a m o r e c o m p l e x H M )f u n c t i o n is n o t r e q u i r ed .

1 I I . . . . . . . .M 8

M 7

M 6

M 5

0 . 1, , , x k

o

\

~ > 0 . 0 1X

O . 0 0 1 . . . . . . . . I . . . . . . . . i . . . . . . . . I . . . .o . 1 l O l O O l O O O

C L O S E S T D I S T A N C E k i n )FIG. 3. Vertical peak acceleration attenuation curves equation 14) for magnitudes 5 through 8. Thesolid curves are for interplate earthquakes and the dashed curves are for intraplate earthquakes.


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56 N . A. A B R A H A M S O N A N D J . J. L I T E H I S E R~ ~ 1 0 L L L I I I [ ] U I H H L I I l L l l l l I l I I L E I I l l l l L i l L l l l I I t l l l L l l ] n f i l i a l I I I t L I L U I L I I ~ I L l L I H l a l I I l l l n l l l I I Z l n l l

MAGNITUDE 5.0 5. 4 MAGNITUDE 5. 5 - 5. 9- MAGNITUDE B.O - B+4c:,

~ . \ \< . . . . . . . ,, . . . . . .~ 0 . 0 0 1

1 1 1 0 1 0 0 1 0 0 0 O . 1 1 1 0 1 0 0 1 0 0 0 O . 1 1 0 l O 0 1 0 0 0C L O S E S T D I S T A N C E ( k in ) C L O S E S T D I S T A N C E ( k m ) C L O S E S T D I S T A N C E ~ k m )

~ 1 0 ' m l ' ' ' ' l * L L L ] , ,E r a _ + L ' m L ~ ' ' 1 * L L m i ; I t L t m : + _ . .. . ~ l l n , [ ; l l m , t I I L H m l ~ ' I L m l .M A G N I T U D E 8 . 5 - 6 . 9 - i M A G N I T U D E 7 . 0 - 7 . 4 = M A G N I T U D E 7 . 5 - 7 . 9zo (9 -+

~ GMc ~ 0 . 1

0 . 0 1

~o . O O l . . . . . . . ~ . . . . . . . . I . . . . . . . . I _ . . .. . .. I . . . . . . . . I . . . . . . . . I , , \ ;

1 1 1 0 1 0 0 1 ) 0 0 O . 1 1 0 1 0 0 1 0 0 0 O . 1 1 0 1 0 0 1 0 0 0C L O S E S T D I S T A N C E ( k m ) C L O S E S T D ' r S T A N C E ( k i n ) C L O S E S T D I S T A N C E ( k m )

=

~ 0 1

o o l i

0 . 0 0 1 O . 1 1 0 1 0 0 1 0 0 0C L O S E S T D I S T A N C E ( k i n )

F IG . 4 . C o m p a r i s o n o f t h e p r e d i c t e d a n d o b s e r v e d p e a k v e r t i c a l a c c e l e ra t i o n s T h e c o m p a r i s o n i sm a d e b y h a l f - m a g n i t u d e r a n g e s f r o m 5 . 0 t o 5 .4 ( p a n e l a ) t o 8. 0 t o 8 .4 ( p a n e l g ) a n d t h e d a t a h a v e b e e nr e d u c e d to a c o m m o n f a u l t t y p e ( S t r i k e - sl i p / n o r m a l ) . T h e s o li d cu r v e s a re f o r in t e r p l a te e a r t h q u a k e s( c ir c le s ) a n d t h e d a s h e d c u r v e s a r e f o r i n t r a p l a t e e a r t h q u a k e s ( t r ia n g l e s ) . F o r e a c h s e t o f c u r v e s , t h ec e n t r a l c u rv e i s t h e m e d i a n a c c e l e r a t i o n f or t h e m e a n m a g n i t u d e i n t h e m a g n i t u d e r a n g e a n d t h eb o u n d i n g c u r v e s a re t h e 8 4 a n d 1 6 p e r c e n ti l e l e v e ls f or t h e u p p e r a n d l o w e r b o u n d m a g n i t u d e s ,r e s p e c t i v e l y .


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ATTENUATION OF VERTICAL PEAK ACCELERATION 56I I I I I

[ ]

]

2]

< []r~ 1 []b 4W

r~ [] [] []

i i ~ [] [][]]

I B]]

]2 I I I I l I

5 0 5 5 6 0 6 5 7 0 7 5 8 0 B 5M A G N I T U D E

FIG. 5. Near-source r < 10 kin) weighted residuals for the vertical attenuation relation equation14).We consider the effect of site geology soil versus rock) by examining the residuals

from equat ion 14). The mean weighted residual of logl0av is -0 .008 __ 0..029 forrock stat ions and 0.002 ___0.015 for soil stations. Therefore, for the simple geologicclassification scheme used in this study, the site geology effect on vertical acceler-ation is not significantly different from zero.Ratio of Vertical to Horizontal Peak cceleration

The second objective of this study is to estimate the ratio of peak-vertical topeak-horizontal acceleration. This ratio, coupled with the vertical accelerationattenuation relation given above, implies a horizontal attenuation relation. Becauseinterest in horizontal attenu ation relations remains high although not a particularobjective of this study), and because our regression models are already configuredto handle peak acceleration values, we repeat the hybrid regression procedure usingthe larger componen t of peak horizontal data of Appendix A and then take the ratioof the solution rat her than directly regressing on the ratio data.Repeat ing the first step of the hybrid regression on the weighted peak hor izontalacceleration data, we find that 5 = -0.982. Again, we consider a nonparametric fitfor H M). The horizontal data shows a stronger magnitude dependence of H M)than does the vertical data. Repeating the fitting procedure used for the vertical


16/32

564 N . A . A B R A H A M S O N A N D J . J . L I T E H I S E Rdata, we find that the Campbell exponential form for H M) is again controlled bythe 1985 Mexico earthquake for our data set. As a result, the horizonta l peakaccelerations are modeled by the same simplified exponential form given in equation13). The resulting horizontal attenuat ion relation is given by

lOgloaH g) --0.62 + 0.177M - 0.982 loglo r + e 2 s 4 M )+ 0 .132F- 0.0008Er, 15)with a standard error of 0.277. Again, the asymptotic standard errors of theregression parameters are listed in Table 3.The ratios of vertical to horizontal peak acceleration predicted by equation 14)and 15) are plotted in Figure 6. For comparison, the ratios predicted by Campbell1982) are also shown. The Campbell 1982) horizontal acceleration has been scaledby 1.13 to account for his use of the average of the two peak horizontal accelerationsrather than the larger peak horizontal acceleration. The expected ratio from thisstudy shows a much smaller magnitude dependence than the expected ratios fromCampbell 1982).Analysis of the logl0 V/H) residuals indicates that the V/H ratio data is approx-imate ly log normally distributed with a st andard error of 0.20; however, the residualsdeviate from a log normal dist ribution above the 2a level. This standard error ismuch smaller than the standard error of either the vertical or the horizontal dataand indicates tha t the vertical and horizontal accelerations are highly correlated.The predicted and observed ratios are compared in Figure 7. The data are againgrouped into half-magnitude intervals and have been reduced to a common fault

2 . 5 . . . . . . . . , . . . . . . . . , . . . . . . . . i . . . . . . . : j/

2 0 ~,

i1 . 5>

i- t M ff - _ _ ~ _ ,< 1 0 : ,

M6 ', ~ - . , _

0 . 5 ~ ~ '& , .- .- ' ~

O . O f . I i i I . . I . . l l l l e i . . IO . 1 1 1 0 1 0 0 1 0 0 0

C L O S E S T D I S T A N C E ( k i n )F I G . 6. P r e d i c t e d V / H c u r v e s f o r s t r i k e - s l ip / n o r m a l e v e n t s f o r m a g n i t u d e s 5 t h r o u g h 8 . T h e h e a v ys o l id c u r v e s a r e fo r i n t e r p l a t e e a r t h q u a k e s a n d t h e h e a v y d a s h e d c u r v e s a r e f o r i n t r a p l a t e e a r t h q u a k e s .T h e l i g h t d a s h e d c u r v e s a re b a s e d o n t h e C a m p b e l l 1 9 8 2 ) h o r i z o n t a l a n d v e r t i c a l a t t e n u a t i o n r e l a t io n s .


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A T T E N U A T I O N O F V E R T I C A L P E A K A C C E L E R A T I O N 5 6 5

10 ~ ]Hml ~Hmt I LtL.m , , . .~ ~ = =t.mj , , , . m I i , . , m I , L.. m I~ I I t , . . l t I,HLn ILII]IL] I LIIIL~M A G N I T U D E 5 . 0 - 5 . 4 - ~ I M A G N I T U D E 5 . 5 - 5 . 9 ~ M A G N I T U D E 6 ~ D - 6 . 4 -

21 -~ : 0 . 1 = - - -

A B C0 . 0 1 f rHr l l l i I rHrml r r r lZm[ r rHr r i r . l r r + r ,r r rl ; r , r l r . l . , ; r . r t f i r r t l l i r f r m l . r ; , l ; l f l , r r ru,

O . 1 l O l O 0 1 D O 0 0 . 1 1 1 0 1 0 0 l O 0 0 O . 1 1 0 1 0 0 O OOC L O S E S T D I S T A N C E ( km ) C L O S E S T D I S T A N C E ( km ) C L O S E S T D I S T A N C E ( k m

1 0 ~ ' ' " ' " ' I ' ~ ' " " ' I ' ' " " I E , . m , L . u . , I L , , . m . 1 , L . ,L J ,, , I L . l ~ ' ' " " " I ' ' ' '' " 'I ' ' " ' " ' I ' ' QI M A G N I T U D E 6 , 5 - 6 . 9 A A G N I T U D E 7 . 0 - 7 . 4 -- M A G N I T U D E ' 7 . 5 - 7 . 9

oH 0o ~ 0 . 1 0 - = - =

D E FO 0 1 I r H r m I r r r r r . ~ , ; + . . r l t r r . , , , . . I , r ; . . r l , r r r lt r , l t t , , , r r r J rr , , l . 1 , r . ,, l . , r t r ,, , i r , , , ,

O 1 1 0 1 0 0 0 0 0 O . 1 1 0 1 0 0 0 0 0 O 1 1 0 1 0 0 0 0 0C L O S E S T D I S T A N C E ( k in ) C L O S E S T D I S T A N C E ( k rn ) C L O S E S T D I S T A N C E ( k in )

- ~ I A g N I T U D E B . O - B. 4~.

>o e


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5 6 6 N . A . A B R A H A M S O N A N D J . J . L I T E H I S E Rtype. Again, the solid curves are for the interplate tectonic environment and thedashed curves are for the intraplate tectonic environment. For each magnitudeinterval, the central curve is the median acceleration for the mean magnitude andthe bounding curves are the 84th and 16th percentile levels for the upper and lowerbound magnitudes, respectively. The predic ted ratios show good agreement with theobserved ratios.

We consider the effect of site geology on the V/H ratio by examining the V/Hresiduals using equations 14) and 15). The mean weighted residual of lOglo V/H)is 0.034 + 0.016 for rock sites and 0.005 + 0.010 for soil sites. The soil site bias isnot significantly different from zero, but the rock site bias is significantly differentfrom zero at the 90 per cent confidence level. On average, the V/H ratio for rockstations is about 8 per cent larger than predic ted by equations 14) and 15).

C O N C L U S I O N SThis study supports several conclusions. First, the vertical peak acceleration dataare best fit by a model whose shape is magnitude dependent. The amount of data

from very small distances for large earthquakes is limited, but the magnitude-dependent shape is statistically significant at the 90 per cent confidence level.Second, we recognize that the standard errors of our solutions are larger than havebeen reported by previous studies notably Campbell, 1981 and Joyne r and Boore,1981). This is due to the expanded data set of Appendix A that includes someoutliers that were excluded from previous studies for example, the Pacoima Damrecord from the 1971 San Fe rnando earthquake) or were not yet available forexample, the high accelerations from the 1985 Naha nni earthquake). The data seemto require the standard errors derived. Third, although some vertical accelerationsexceed the horizontal acceleration for the same record, these cases are exceptions.The expected ratio of vertical to horizontal peak acceleration remains below 1.0 forearthquakes with magnitude less than 8.0 at distances greater tha n 1.0 kin. Fourth,the standard error of the ratio is less than the standa rd error of either the horizontalor vertical att enua tion relations. Therefore, the peak vertical and horizontal accel-erations for a given record are strongly correlated and we can have more confidencein the predicted ratio than in either the predicted vertical or horizontal peakacceleration. Fina lly, using a gross site geology classification scheme of soil or rock,the site effect on vertical acceleration is not significant. However, the site effect onthe V /H ratio is significant with rock sites yielding larger V/H ratios than soil sites.

A C K N O W L E D G M E N T SJ i m M a r r o n e p r o v i d e d m u c h a s s i s t a n c e i n t h e p r e p a r a t i o n o f t h e f i gu r es a n d A p p e n d i x A . t~ e n

C a m p b e l l a n d D a v e B o o r e p r o v i d e d u s e fu l c o m m e n t s o n t h e m a n u s c r i p t . T h i s s t u d y w a s f u n d e d e n t ir e lyb y B e c h t e l T e c h n i c a l G r a n t 9 7 2 7 5 - 0 0 9 .

R E F E R E N C E SA b r a h a m s o n , N . A . 1 9 8 8) . S t a t i s t i c a l p r o p e r t i e s o f p e a k g r o u n d a c c e l e r a t i o n s r e c o r d e d b y t h e S M A R T

1 a r r a y , B u l l S e i s m S o c A m 7 8 , 2 6 - 4 1 .A b r a h a m s o n , N . A ., B . A . B o l t , R . B . D a r r a g h , J . P e n z i e n , a n d Y . B . T s a i 1 9 8 7) . T h e S M A R T 1

a c c e l e r o g r a p h a r r a y 1 9 8 0 - 1 9 8 7 ) : a r e v i ew , E a r t h q u a k e S p e c t r a 3 , 2 6 3 - 2 8 7 .A k i , K . , S. S t e a c y , M . C a m p i l l o , H . K a w a s e , a n d F . S ~ n c h e z - S e s m a 1 9 8 7 ) . S o u r c e , p a t h a n d s i t e e f f e c t s

o n s t r o n g g r o u n d m o t i o n d u r i n g t h e M i c h o a c a n e a r t h q u a k e o f 19 85 a b s t ra c t ), E O S 68 , 1354 .B o o r e , D . M . a n d G . M . A t k i n s o n 1 9 8 7 ). S t o c h a s t i c p r e d i c t i o n o f g r o u n d m o t i o n a n d s p e c t r a l r e s p o n s e

p a r a m e t e r s a t h a r d - r o c k s i t e s in e a s t e r n N o r t h A m e r i ca , B u l l S e i s m S o c A m 7 3 , 4 4 0 - 4 6 7 .B u i l d i n g S e i sm i c S a f e ty C o u n c i l 1 9 85 ). N E H R P R e c o m m e n d e d P r o v i s io n s fo r t h e D e v e l o p m e n t o f

S e i s m i c R e g u l a t i o n s f o r N e w B u i l d i n g s , r e p o r t p r e p a r a e d f o r t h e F e d e r a l E m e r g e n c y M a n a g e m e n t


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ATTENUATION OF VERTICAL PEAK ACCELERATION 67Agency, Washington, D.C.Bureau, D. J. 1981). Near-source peak ground accelerations abstract), E a r t h q u a ke N o t e s 52, 81.

Campbell, K. W. 1981). Near-source attenuation of peak horizontal acceleration, Bul l . Se i sm . Soc . Am.71, 2039-2070.Campbell, K. W. 1982). A study of the near-source behavior of peak vertical acceleration abstract),L O S 63, 1037.Campbell, K. W. 1985). Strong motion attenuation relations: a ten-year perspective, E a r t h q u a ke S p ec t r a1,759-804.Campbell, K. W. 1988). Predicting strong ground motion in Utah, in Evalua t ion o f Reg iona l and UrbanE a r t h q u a ke H a z a r d s a n d R i s k i n U t a h Hays and Gori, Editors, U.S. Geol . Surv . Profess . P ap er inpress).Fukushima, Y., T. Tanaka, and S. Kataoka 1988). A new attenuation relationship for peak groundacceleration derived from strong-motion accelerograms, Proc. o f the 9 th Wor ld Con f . on Ear thquakeEngineer ing Tokyo, Japan in press).International Conference of Building Officials 1984). Uni form Bui ld ing Code Whittier, California.Joyner, W. B. and D. M. Boore 1981). Peak horizontal acceleration and velocity from strong-motionrecords including records from the 1979 Imperial Valley, California earthquake, Bull . Seism. Soc.A m . 71, 2001-2038.Joyner, W. B. and D. M. Boore 1988). Measurement, characterization, and prediction of strong groundmotion, P r o c . E a r t h . E n g i n . S o i l D yn . I I - - R e cen t A d va n ces i n G ro u nd Mo t i o n E va lu a t i o n ASCE,Park City, Utah, 43-102.Luco, J. E. 1985). On strong ground motion estimates based on models of the radiated spectrum, Bull .Se i sm . Soc . Am. 75, 641-649.

Newmark, N. M. and W. J. Hall 1982). Earthquake Spectra and Design, Monograph prepared forEarthquake Engineering Research Institute, Berkeley, California.Sabetta, F. and A. Pugliese 1987). Attenuat ion of peak horizontal acceleration and velocity from Ital ianstrong-motion records, Bul l . Se i sm . Soc . Am. 77, 1491-1513.Steacy, S., K. Aki, and M. Campillo 1987). The Michoacan earthquake of 1985: dislocation or crackgrowth abstract), L O S 68, 1354.Toro, G. R. and R. K. McGuire 1987). An investigat ion into earthquake ground motion characteristicsin eastern North America, Bul l . Se i sm . Soc . Am. 77, 468-489.BECHTEL CIVIL, INC.P.O. BOX 3965SAN FRANCISCO,CALIFORNIA94119

Manuscript received 9 February 1988


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568 N. A. ABRAHAMSON AND J. J. LITEHIS ERAPPENDIX. PEAK ACCELERATION DATASta Dist3 Peak Acc. g)Eqk Station Name No. 1 G 2 km) Ref4 H1 H2 V Source~5

1 Long Beach Pub Utl Bld 131 S 6.4 C 0,216 0.183 0.223 7,81 Vernon CMD Terminal 288 S 22.0 C 0,163 0.135 0.150 7,81 LA Subway Terminal 136 R 28.0 C 0.100 0.064 0.049 7,82 Helena Fed Bldg 2229 R 8.0 C 0.156 0. 14 1 0.099 7,83 E1Centro Sta 9 117 S 10.0 C 0.359 0.224 0.278 7,8,154 Santa Barbara Courthous 283 S 10.0 C 0.239 0.190 0.080 7,85 Taft Lincoln School 1095 S 42.0 C 0.196 0.177 0.123 7,8,155 Santa Barbara Courthouse 283 S 85.0 J 0.135 0.090 0.051 7,155 LA Hollywd Storage Lot 135 S 10 7. 0 J 0.062 0.044 0.022 7,155 PasadenaAthenaeam 475 S 10 9. 0 J 0.053 0.048 0.033 7,155 San Luis Obispo Rec Bldg 1083 R 14 8.0 J 0.059 0.042 0.029 7,155 Colton 113 S 156.0 J 0.0t4 0. 01 1 0.012 5,15,505 Bishop, LA Water Dept 1008 S 224.0 J 0.018 0.014 0.006 5,15,505 Hollister City Hall 1028 S 293.0 J 0.010 0.007 0.005 55 E1 Centro Sta 9 117 S 370.0 J 0.004 0.0 03 5,15,506 SF Golden Gate Park 1117 R 8.0 C 0.127 0. 10 5 0. 05 1 7,8 ,156 SFState Bldg 1080 S 12.0 C 0.103 0.067 0.050 7,86 SF Alexander Bldg 1065 S 14.0 C 0.055 0.050 0.036 7,86 SF So Pacific Bldg 1078 S 14.0 C 0.048 0.048 0.034 7,86 Oakland City Hall 1049 S 24.0 C 0.047 0.029 0.023 7,87 Bozeman, Mont. 2205 S 95.0 B 0.055 0.033 0.026 5,507 Butte, Mont. 2201 R 175.0 B 0.043 0.034 0.021 5,507 Helena, Mont. 2202 R 208.0 B 0.013 0. 01 1 0.008 5,508 Cholame sta 2 1013 S 0.08 C 0.73 0.509 0.349 7,8,158 Cholame sta 5 1014 S 5.5 C 0.467 0. 40 3 0. 181 7,8,158 Cholame sta 8 1015 S 9.6 C 0.279 0.276 0.138 7,8,158 Temblor 1438 R 10.6 C 0 . 4 1 1 0.282 0.165 7,8,1 58 Cholame sta 12 1016 S 14.9 C 0.072 0.066 0. 061 7,8,1 58 San Luis Obispo Rec Bldg 1083 R 63.6 J 0.018 0.016 0.007 7,158 Taft Lincoln School 1095 S 1 05 .0 J 0.012 0.008 0.007 7,159 Fairbanks Duck Hall 2721 R 15.0 C 0.056 0.056 0.053 5,8,5010 KoynaDam Gallery 1A) R 3.2 C 0.63 0,49 0.34 8,1711 E1Cent roS ta9 117 S 45.0 C 0.142 0, 06 1 0.036 7,8, 1511 Perr isRe serv oir 270 R 105 .0 J 0.018 0.012 0.006 5,15,5011 SanOnofreNPP 280 R 122.0 J 0.048 0.042 0.064 7,1511 Colton 113 S 130.0 J 0 .0 3 1 0.024 0.022 7,1511 SanBernadino, DevilsCan 116 R 141 .0 J 0 .0 1 1 0.009 0.009 5,7 ,1511 Cedar Springs, CWD 112 S 14 7.0 J 0.006 0.006 0.003 5,15 ,5011 Long Beach Terminal ls. 130 S 18 7. 0 J 0.010 0.010 0.006 7,1511 Pasadena, Anthenaeum 475 S 1 97 .0 J 0.010 0.007 0.004 7,1511 Pasadena, SeismoLab 266 R 200.0 J 0.007 0.006 0.002 5,15 ,5011 Pear Blossom Pump Plant 269 S 203.0 J 0.006 0.005 0.006 5,15,5011 LAHoUy wdStorageLot 135 S 211.0 J 0.013 0.012 0.005 7,1512 San Pablo, CC JC 1093 S 62.0 J 0.005 0.002 0 .001 15 ,5 012 Pleasant Hill, DVC 1057 R 77.0 B 0.007 0.005 0.002 512 S.F. 390 Main 1074 R 79.0 B 0 .0 1 1 0.007 0.004 512 S.F. Alexander Bldg 1065 S 79.0 B 0.008 0.008 0.003 512 S.F. Bethlehem Bldg 1071 S 79.0 B 0.015 0.014 0.007 512 S.F. So. Pac. Bldg 1078 S 79.0 B 0.016 0.013 0.007 512 Oakland City Hall 1049 S 82.0 B 0.006 0.005 0.002 512 APEEL Array Sta 1 1001 S 10 9. 0 B 0.018 0. 01 1 0.002 512 APEEL Array Sta 2 1002 S 11 0.0 B 0.017 0.012 0.002 513 San Pablo, CC JC 1093 S 62.0 J 0 . 0 0 3 0. 00 3 0.003 15,5013 Pleasant Hill DVC 1057 R 77.0 B 0.009 0.008 0.002 513 S.F. 390 Main 1074 R 79.0 B 0.012 0.009 0.004 513 S.F. Alexander Bldg 1065 S 79.0 B 0.012 0.008 0.003 513 S.F. Bethlehem Bldg 1071 S 79.0 B 0.027 0.014 0.007 513 S.F. So. Pac. Bldg 1078 S 79.0 B 0.020 0.016 0.008 5

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ATTENUATION OF VERTICAL PEAK ACCELERATION 569

APPENDIX. PEAK ACCELERATION DATASta Dist3 Peak Acc. g)Eqk Station Name No. 1 G 2 km) Ref4 H1 H2 V Sources5

13 Oakland City Hall 1049 S 82.0 B 0 . 0 1 3 0.006 0.004 513 APEEL Array sta 1 1001 S 10 9. 0 B 0.029 0. 02 7 0.002 513 APEELA rraySt a2 1002 S 110.0 B 0. 02 1 0.0 21 0.009 514 Wrightwood 290 R 15.0 C 0.205 0.146 0.076 7,8,1514 Cedar Spring Miller Cn 111 R 18.0 C 0.086 0. 05 7 0.093 7,8 ,1514 Cedar Springs CWD 112 R 18.0 C 0.073 0.062 0. 04 4 7,8,1 514 Devils Canyon Filter P1 116 R 19.0 C 0.179 0.164 0.094 7,8,1514 San Bern., Hall of Rcrds 274 S 28.0 C 0.119 0.065 0.055 7,814 Colton SCE Substation 113 S 29.0 C 0 . 0 4 5 0. 03 9 0.042 7,8,1514 PuddingstoneReservoir 278 R 32.0 C 0.022 0.019 0.018 7,815 Pacoima Dam Abutment 279 R 3.2 C 1 .25 1 1. 24 2 0.718 7,815 LA Orion Blvd 241 S 7.5 C 0.258 0.140 0.178 7,815 LA Van Owen St. 458 S 9.7 C 0.118 0. 11 1 0.111 7,815 LA 15910 Ventura Blvd 461 S 14.3 C 0.148 0.135 0.120 7,815 PasadenaJPL 267 S 14.8 C 0.215 0.160 0.146 7,815 LA 15250 Ventura Blvd 466 S 15.4 C 0.225 0.152 0.108 7,815 LaLankersh imBlvd 220 R 15.4 C 0 .1 8 1 0.154 0.085 7,815 LA 14724 Ventura Blvd 253 S 15.4 C 0 .2 6 3 0. 20 7 0.101 7,815 LA Griffith Park 141 R 16.9 C 0.188 0.180 0.138 7,8,1515 Pasadena Seismo Lab 266 R 18.4 C 0.204 0.096 0. 093 7,8 ,1515 Lake Hughes Sta 12 128 R 18.7 C 0.374 0.288 0.164 7,8,1515 LA Hollywd PE lot 135 S 20.5 C 0.217 0.187 0.119 7,8 ,1515 LA Hollywd storage 133 S 21.3 C 0.153 0.115 0.058 7,815 Pasadena Millikan Lib 264 S 21.8 C 0.206 0.189 0.108 7,815 Pasadena Athenaeum 475 S 22.5 C 0.114 0. 10 3 0.106 7,8 ,1515 Lake Hughes Sta 9 127 R 22.6 C 0.147 0. 13 1 0.089 7,8,1515 Cas ta icOldRdgR t 110 R 22.8 C 0.335 0.289 0.180 7,8,1515 LA Water + Power 137 R 24.1 C 0.188 0.137 0.078 7,815 Alhambra, Fremont Ave 482 S 24.8 C 0 . 1 2 1 0.117 0.084 7,815 Lake Hughes Sta 4 126 R 24.9 C 0.200 0.159 0.170 7,8,1515 LA 1640Marengo 181 S 25.2 C 0.147 0.139 0.086 7,815 LAZon al Ave 190 R 25.5 C 0.083 0. 07 1 0.060 7,815 Palmdale Fire Sta 262 S 27.6 C 0.150 0.118 0.10 5 7,8 ,1515 Santa AnitaDam 104 R 27.9 C 0.223 0.172 0.070 7,815 Lake Hughes Sta 1 125 S 29.6 C 0.152 0. 11 5 0.102 7,8 ,1515 Vernon CMD Terminal 288 S 30.7 C 0 .1 11 0. 08 5 0.047 7,815 FairmontReservoir 121 R 32.1 C 0.103 0.068 0.043 7,815 Pearblossom Pump Plant 269 R 35.5 C 0.148 0.1 03 0.056 7,8,1515 LA Century Blvd 229 S 36.1 C 0.069 0.0 58 0.028 7,815 LA Lincoln Blvd 244 S 36.1 C 0.035 0.0 34 0.047 7,815 LAAirportBlvd 247 S 36.1 C 0 . 0 4 5 0.041 0.025 7,815 Gormon Oso Pump Plant 1052 S 46.7 J 0.112 0.087 0.041 7,1515 Palos Verdes Estates 411 S 56.9 J 0 .0 4 3 0. 025 0.020 7,1515 Wrightwood 290 S 60.7 J 0.057 0.047 0.037 7,1515 Long Beach Terminal Is 130 S 61.4 J 0.030 0.029 0.016 7,1515 Port Hueneme Navy Lab 272 S 62.0 J 0.027 0.026 0.011 7,1515 Fort Tejon 1096 S 64.0 J 0.028 0. 02 3 0.018 7,1515 Edmonston Pump Plant 1027 R 66.0 J 0.057 0.026 0.047 7,1515 Wheeler Ridge 1102 82.0 J 0.034 0.028 0.015 7,1515 Cedar Springs CWR 111 R 87.0 J 0 . 02 1 0.016 0.010 7,1515 Cedar Springs CWD 112 88.0 J 0 . 03 1 0. 025 0.012 7,1515 Colton 113 91.0 J 0.039 0.034 0.026 7,1516 Hollister City Hall 1028 S 31.0 C 0.03 0.02 0 . 0 1 5,8, 1517 Sitka Mag Obs 2714 S 45.0 C 0.11 0.09 0.05 5, 8,1518 ManaguaEssoRefinery 3501 S 5.0 C 0.39 0.34 0.33 8,15,1619 Port Hueneme Naval Lab 272 S 24.0 C 0.13 0.08 0.04 5, 8,1519 Jensen Filter Plant 655 R 53.0 A 0.03 1 0.014 5,1519 LA, 16633 Ventura 497 S 50.0 A 0.06 0.03 0.01 44

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570 N. A. ABRAHAMSON AND J. J. LITEHISERAPPENDIX. PEAK ACCELERATION DATASta Dist3 Peak Acc. (g)Eqk Station Name No. 1 G2 (km) Ref4 HI H2 V Sources5

19 LA, 18321 Ventura 610 S 51.0 A 0.043 0.016 519 Santa Monica, 201 Ocean 657 51.0 A 0.036 0.012 519 LA, 16661 Ventura 118 S 53.0 A 0.042 0.016 519 LA, 16255 Ventura 512 S 54.0 A 0.036 0.016 519 LA, 415 Washington 560 S 54.0 A 0.09 0.07 0.02 4419 LA, 16055 Ventura 259 S 55.0 A 0.032 0.013 519 LA, 15910 Ventura 461 S 55.0 A 0.040 0.023 519 Culver City 990 61.0 A 0.05 0.04 0.03 4419 LA, 9841, Airport 247 S 61.0 A 0.05 0.05 0.02 4419 LA, 9750 Airport 586 S 62.0 A 0.04 0.03 0.02 4419 LA, 5249 Century 589 S 63.0 A 0.05 0.04 0.02 4419 LA, 5260 Century S 63.0 A 0.05 0.05 0.01 4419 LA, 4411 Eleventh 524 S 66.0 A 0.06 0.05 0.04 4419 LA, 4827 Central 645 S 72.0 A 0.06 0.05 0.02 4420 Lima Geophys Inst 4302 S 38.0 C 0.24 0.21 0.13 8,4520 Lima Huaca Residence 4304 S 40.0 C 0.18 0.17 0.13 8,4521 Lima, La Molina 4305 103.0 H 0.14 0.11 0.05 4521 Lima, Geophys Inst 4302 S 95.0 H 0.08 0.05 0.03 8,4522 San Juan Baufista 1377 S 8.9 C 0.12 0.05 0 . 0 5 5, 8,1522 Hollister City Hall 1028 S 10.8 C 0.17 0.10 0.07 5,8,1522 Gilroy Gavilian Col. 1250 S 10.8 C 0.14 0.10 0.03 5,8, 1522 SAGO Central 1032 R 20.0 H 0. 01 1 0.013 5,1522 Stone Canyon East 1202 38.0 H 0.03 0.02 0.05 4523 Oroville Seismo Sta 1051 R 8.0 C 0.11 0.10 0.12 8,15,3923 Marysville 1291 S 30.0 C 0.07 0.06 0.04 8,15,3923 Chico 1292 S 31.0 C 0.08 0.06 0.03 8,15, 3923 Paradise KEWG Trans 1293 R 32.0 C 0.04 0.03 0.03 8,15,3924 Panaluu 2803 S 27.0 C 0.12 0.10 0.05 8,4724 I-Iilo, Cloud Phys Lab 2808 R 45.0 C 0.22 0.11 0.10 8,4724 Honokaa 2809 76.0 A 0.11 0.09 0.04 4725 Karakyr, USSR 9110 R 3.5 C 0.752 0.668 1.324 8,1126 Goleta UCSB Phys Plant 885 S 7.7 C 0.39 0.24 0.14 8,15, 3426 Goleta UCSB North Hall 5093 S 7.7 C 0.44 0.27 0.11 8,3426 St. Barbara Courthouse 283 S 9.8 C 0.21 0.10 0.07 8,15,3426 St. Barbara Freitas 5137 S I0.1 C 0.22 0.11 0.06 8,3426 Goleta Substation 9022 R 11.8 C 0.28 0.24 0.09 8,1526 Gibraltar Dam R Abut 941 R 18.1 C 0.04 0.04 0.03 826 Cachuma Dam Toe 106 R 25.9 C 0.07 0.03 0.02 8,3427 Tabas S 3.0 C 0.942 0.875 0.737 2627 Dayhook S 17.0 A 0 . 3 9 1 0.379 0.184 2627 Boshrooyeh S 28.0 A 0.116 0.110 0.082 2627 Ferdows S 11 0. 0 A 0.106 0.099 0.053 4127 Khezri S 160.0 A 0.026 0.024 0.024 4127 Bajestan S 160 .0 A 0 .0 91 0.068 0.030 4127 Sedeh S 17 0. 0 A 0.027 0.024 0.027 4127 Birjand S 175.0 A 0.019 0.016 4127 Kashmer S 250.0 A 0.036 0.034 0.032 4128 Long Valley Dam L.Abut 1444 R 7.6 C 0.26 0.17 0.17 8,1828 Bishop 1008 S 27.1 C 0.06 0.03 0.03 8,1828 Mammoth Lakes H.S. 1490 S 29.0 C 0.07 0.05 0.04 8,1828 Benton, Jct 6 120 1325 S 34.2 C 0.06 0.06 0.04 8,1829 Icy Bay 2734 S 38.3 C 0.16 0.11 0.07 8,15,2729 Yakutat 2728 S 92.7 A 0.09 0.06 0.02 1530 Coyote Creek 1445 S 3.9 C 0.23 0.16 0.10 8,15,3330 Gilroy Sta 6 1413 R 4.0 C 0.42 0.34 0.17 8,15,3330 Gilroy Sta 4 1411 S 4.9 C 0.26 0.24 0.44 8,15,3330 Gilroy Sta 3 1410 S 6.3 C 0.27 0.26 0.15 8,15,3330 Gilroy Sta 2 1409 S 8.0 C 0.26 0.20 0.18 8,15,33

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APPENDIX. PEAK ACCELERATION DATASta Dist3 Peak Acc. g)Eqk Station Name No. 1 G 2 km) Ref4 H1 I-I2 V Sources530 Gilroy Sta 1 1408 R 8.9 C 0.13 0.10 0.08 8,15,3330 San Juan Bautista 1377 S 14.4 C 0.I1 0.09 0.12 8,15,3330 SailJuan Bautista Over 1492 S 16.2 C 0.12 0.08 0.06 8 ,15,3330 Halls Valley 1422 S 24.8 C 0.05 0.04 0.03 8,15,3330 Salinas 1414 S 35.0 A 0.10 0.10 0.06 3330 Bear Valley Sta 12 1481 37.3 A 0.09 0.08 0.07 33,4231 E1 Centro Sta 7 5028 S 0.2 C 0.52 0.36 0.65 8,15,4931 Meloland FF 5155 S 0.2 C 0.318 0.296 0. 23 1 15,19,4931 MelolandFooting 5155 S 0.2 C 0.326 0.279 0.172 8,1931 Meloland Abut 1 5155 S 0.2 C 0.422 0.277 0.274 8,1931 Meloland Abut 3 5155 S 0.2 C 0.385 0.35 0.25l 8,1931 E1Centro Sta 5 952 S 1.0 C 0.56 0.40 0 . 7 1 8,15 ,4931 E1Centro Sta 6 942 S 1.4 C 0.72 0.45 1 . 7 4 8,15 ,4931 Bonds Comer 5054 S 2.8 C 0.81 0.66 0.47 8,15,4931 E1Centro Sta 8 958 S 3.5 C 0.64 0.50 0.55 8,1 5,4931 E1Centro Sta4 955 S 4.4 C 0.61 0.38 0.32 8,1 5,4931 Dogwood Rd 5165 S 4.8 C 0.51 0.37 0.93 8,15,4931 Aeropuerto 6616 S 5.2 A 0.316 0.240 0.179 15 ,4931 E1Centro Sta 9 117 S 5.8 C 0.40 0.27 0.38 8,15,4931 Brawley Airport 5060 S 7.0 C 0.22 0.17 0.18 8,15,4931 ICSB 5090 S 7.0 C 0.35 0.32 0.19 8,4931 ICSBfree-field 5154 S 7.0 C 0 . 2 4 3 0.237 0.270 8,15,4931 Holtville P.O. 5055 S 7.3 C 0.26 0.22 0 . 3 1 8,15,4931 E1Centro Sta 10 412 S 8.2 C 0.23 0.20 0.15 8,15,4931 E1Centro Sta 3 5057 S 9.3 C 0.27 0.22 0.15 8,15,4931 MexicaliSAHOP 6619 S 9.8 A 0.459 0. 31 1 0.332 15,4931 Calexico Fire Sta 5053 S 10.1 C 0.28 0.22 0 . 2 1 8,15,4931 El Centro Sta 2 5115 S 10.2 C 0.43 0.33 0.17 8,1 5,4931 E1Cenlro Sta 11 5058 S 12.2 C 0.38 0.38 0.16 8,15,4931 WestmorlandF.S. 5169 S 12.6 C 0.106 0. 08 1 0.090 8,15,4931 Parachute Test Site 5051 S 13.1 C 0.20 0.11 0.18 8,15,4931 Cucapah 6617 S 13.8 A 0.310 0. 11 5 15~4931 EICentro Sta 1 5056 S 16.4 C 0.15 0.15 0.10 8,15,4931 EICentro Sta 12 931 S 18.0 C 0.15 0.11 0.08 8,1 5,4931 Chihuahua 6621 S 18.4 A 0.267 0.263 0.215 15 ,4 931 El Centro Sta 13 5059 S 21.5 C 0.15 0.12 0.06 8,15,4931 Calipatria Fire Sta 5061 S 22.2 C 0.13 0.09 0.07 8,15,4931 Compuertas 6622 S 23.7 A 0.188 0.149 0.066 15,4 931 Cerro Prieto 6604 R 24.0 A 0.167 0.149 0.198 15,4 931 Superstition Mtn. 286 R 24.5 C 0.21 0.12 0.09 8,15,4931 Salton Sea 5062 S 28.0 C 0.06 0.06 0.03 8,15,4931 Plaster City 5052 S 30.5 C 0.07 0.05 0.03 8,15,4931 Delta 6605 S 33.0 A 0.349 0.235 0.152 15,4 931 Niland 724 S 34.0 C 0.10 0.07 0.03 8,15,4931 Victoria 6610 S 44.0 A 0 .1 6 3 0.122 0.056 15,4931 Cochella Canal 4 5066 S 47.7 C 0.14 0.I 1 0.04 8,15,4931 Ocotillo Wells 5050 S 60.0 A 0.05 0.04 0.03 15,4931 Yuma, Arizona 2316 S 64.0 A 0.03 0.03 0.02 15,4932 Holtville P.O. 5055 S 9.0 H 0.264 0.116 0.042 15,4 932 El Centro Sta 6 942 S 10.1 H 0 .2 6 3 0.175 0.080 15, 4932 El Centro Sta 7 5028 S 10.2 H 0.230 0.147 0.086 15,4 932 Dogwood Rd 5165 S 10.6 H 0.147 0.146 0.103 15,4 932 E1 Centro Sta 5 952 S 10.9 H 0.286 0.235 0.117 15 ,4932 E1Centro Sta 8 958 S 10.9 H 0.157 0.128 0.056 15,4932 E1CentroSta4 955 S 11.6 H 0.237 0.168 0.079 15,4932 El Centro Sta 9 117 S 11.6 H 0.133 0.078 0.086 15 ,4 932 E1Centxo Sta 10 412 S 13.0 H 0.055 0. 05 1 0.026 1 5,4932 Calexico Fire Sta 5053 S 13.2 H 0.097 0. 07 1 0.034 15,49

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57 N. A. ABRAHAMSON AND J. J. LITEHISER

APPENDIX. PEAK ACCELERATION DATASta Dist3 Peak Acc. (g)Eqk Station Name No. 1 G 2 ~m) Ref4 H1 H2 V Sources532 Bonds Corner 5054 S 13.7 H 0.129 0.074 0.052 15 ,4 932 E1Centro Sta 11 5058 S 15.4 H 0.192 0.098 0,063 15 ,4 932 El Centro Sta 3 5057 S 15.7 H 0.147 0.103 0,039 15 ,4 932 E1Centro Sta 2 5115 S 18.3 H 0.154 0.089 0.054 1 5,4932 E1 Cenlxo Sta 1 5056 S 24.4 H 0.060 0. 03 3 0 .033 15 ,4932 Brawley Airport 5060 S 25.5 H 0.057 0. 04 5 0.043 15,4933 San Ramon, Kodak Bldg 1418 S 17.6 A 0.15 0.06 0.03 15,20,4233 San Ramon, 2241 SRV 1383 S 18.5 A 0 . 05 3 0,042 0.018 15,20,4233 Antioch 1308 S 22.3 A 0.04 0.01 0 . 0 3 15,20,4233 Tracy 1298 S 29.6 A 0.094 0.055 0.039 15,20,4233 Fremont, Mission SJ 1299 S 34.1 A 0.063 0.051 0.028 15,20,4233 APEEL Sta 3E 1219 R 41.1 A 0.077 0.060 0. 02 3 15,20,4233 Halls Valley 1422 S 45.4 A 0.078 0.055 0.028 20,4234 FagundezRanch 8.9 A 0.254 0.217 0.095 15 ,2 034 Morgan Temtory Park 12.9 A 0.272 0.189 0.078 15,2034 San Ramon, Kodak Bldg 1418 S 19.4 A 0.28 0.09 0.04 15,20,4234 San Ramon, 2241 SRV 1383 S 23.9 A 0 . 0 5 3 0.042 0.018 15,20,4234 Antioch Contra Loma 27.7 A 0.04 0.03 0.01 15,2034 Fremont, Mission SJ 1299 S 30.1 A 0.11 0.04 0.02 15,20,4234 Antioch 1308 S 31.9 A 0.110 0.048 0.018 15,20,4234 APEEL Sta 3E 1219 R 38.7 A 0.076 0.044 0.016 15,20,4235 TerwiUigerValley 5045 8.3 H 0 . 1 2 3 0.088 0.063 15, 2835 Pinyon Flat Obs 5044 13.4 H 0 . 1 3 3 0.118 0.058 15,2835 Anza Fire Sta 5160 S 13.5 H 0 . 0 7 3 0.067 0.04 1 15,28,4235 blurkey Creek Park 5043 21.4 H 0.097 0.076 0.101 15, 2835 Rancho de Anza 5047 21.4 H 0.096 0.096 0 .051 15 ,2 835 Puerl aLaCruz 933 S 26.0 H 0 . 1 8 1 0. 11 4 0.090 28,4235 Palm Desert 5132 S 30.1 H 0 . 0 9 4 0.072 0.054 28 ,4 235 Thousand Palms 5068 36.4 I4 0.082 0.050 0.049 15 ,2 835 Sage 901 R 36.6 I4 0 .1 1 1 0.084 0.174 28 ,4 235 Cranston Forest Sta 5042 36.8 14 0.110 0. 09 4 0.038 15,2835 lndio, So Cal Gas 5067 39.0 14 0.094 0.060 0.020 15 ,2 835 Borrego Air Ranch 5049 41.8 14 0.040 0.032 0.016 15,2 835 San Jacinto 5006 44.0 H 0 .0 4 7 0.044 0.064 2835 North Palm Springs 5070 44.8 H 0.022 0.017 0.028 15 ,2 835 Hemet City Lib 5091 46.5 H 0.057 0.046 0.058 2835 San Jacinto 5005 47.5 I-I 0.080 0.062 0.052 2835 Fun Valley 5069 48.1 H 0 . 0 3 3 0. 02 8 0. 01 1 15,2835 Cabozon P.O. 5073 49.6 H 0.017 0.016 0 .011 15, 2835 White Water Cyn Trout 5072 53.4 H 0.022 0.016 0.022 15 ,2 836 Convict Lake 1324 S 1.0 A 0.464 0.428 0.433 40,42,4336 Mammoth Lakes 14.S. 1490 S 3.2 A 0.327 0.237 0.264 40,42,4336 Long VaUey dam, dnstr 1444 R 3.2 A 0. 11 0.069 0.075 40,42,4336 MonoLake 1323 S 35.0 A 0.079 0.057 0.044 40,42,4337 Convict lake 1324 S 8.9 14 0.06 0.04 0.04 40,42,4338 Convict Lake 1324 S 1.0 A 0.20 0.17 0.14 40,42,4338 Mammoth Lakes H.S. 1490 S 3.2 A 0.43 0.37 0.27 40,42,4338 Long Valley dam, dn str 1444 R 3.2 A 0.04 0.01 0.02 40,42,4339 Convict Lake 1324 S 1.0 A 0,239 0. 19 3 0.197 40,42,4339 Long Valley dam, dnst r 1444 R 3.2 A 0. 11 0.062 0.075 40,42,4340 Convict Lake 1324 S 1.0 A 0.49 0.38 0.35 40,42,4341 Convict Lake 1324 S 1.0 A 0 .3 3 1 0.267 0.197 40,42,4341 Long Valley dam, dn str 1444 R 3.2 A 0 .2 4 3 0.172 0.09 40,42,4341 Paradise Lodge 12.0 A 0.119 0.090 0.09 40,42,4341 Benton 1325 S 33.0 A 0.177 0 . 11 0.068 40,42,4341 Bishop 1008 S 34.0 A 0.078 0. 04 1 0.024 40,42,4342 Victoria 6610 S 7.3 A 0.848 0.786 1.00 142 CerroPrieto 6604 S 10.0 A 0 . 6 7 5 0.575 0.307 1

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APPENDIX. PEAK ACCELERATION DATASta Dist3 Peak Acc. g)Eqk Station Name No.1 G2 Ion) Ref H1 H2 V Sources5

42 Chihuahua 6621 S 15.0 A 0.154 0.070 0.097 142 Cucap ah 6617 S 21.0 A 0.076 0.060 142 SAHOP 6619 S 31.0 A 0.073 0.060 0.043 142 Aeropuerto 6616 S 33.0 A 0 . 03 1 0. 02 3 0.019 142 MexicaliHospital 6624 35.0 A 0.047 0.045 0.033 142 Bonds Comer 5054 S 38.0 A 0.13 0.12 0.03 1,2842 Calexico 5053 S 41.0 A 0 . 04 1 0. 04 1 0.031 1,2842 E1Centro Sta 11 5058 S 55.0 A 0. 05 1 0. 04 1 0.010 1,2843 Butler Valley Sta 2 1112 R 66.0 A 0.10 0.08 0.04 2944 Average of 26 records 1 S 21.0 A 0.129 0.105 0.046 5145 Westmorland F.S. 5169 S 5.3 A 0.49 0.39 0.80 8,2145 Salton Sea 5062 S 5.8 A 0.20 0.19 0.22 8,2345 Brawley Airport 5060 S 16.1 A 0.18 0.16 0.11 8,2345 Superstition Mtn 286 R 16.5 A 0.11 0.09 0.06 8,2345 Parachute Test Site 5051 S 17.0 A 0.23 0.16 0.16 8,2345 El Centro Sta 2 5115 S 30.0 A 0.05 0.03 0.02 8,2345 E1Centro Sta 5 952 S 30.0 A 0.06 0.05 0.01 8,2345 E1Centro Sta 1 5056 S 31.0 A 0.06 0.05 0.03 8,2345 El Centro Sta 6 942 S 31.0 A 0.06 0.05 0.03 8,2345 E1Centro Sta 7 5028 S 31.0 A 0.05 0.03 0.01 8,2345 E1Centro Sta 9 117 S 31.0 A 0.04 0.03 0.04 8,2345 E1Centro Sta 10 412 S 31.0 A 0.04 0.03 0.02 8,2345 E1 Centro Sta 3 5057 S 32.0 A 0.03 0.02 0.02 8,2345 E1Centro Sta4 955 S 32.0 A 0.02 0.02 0.01 8,2345 E1Centro Sta 8 958 S 32.0 A 0.05 0.05 0.03 8,2345 Piaster City 5052 S 32.0 A 0.03 0.02 0.01 8,2345 E1 Cenlro Diff Array 5165 S 34.0 A 0.08 0.05 0.02 8,2345 E1 Centro Sta 11 5058 S 34.0 A 0.06 0.05 0.04 8,2345 E1Centro Sta 12 931 S 36.0 A 0.05 0.05 0.02 8,2345 E1Centxo Sta 13 5059 S 38.0 A 0.03 0.03 0.01 8,2345 Holtville 5055 S 38.0 A 0.03 0.03 0.02 , 8,2345 Niland 724 S 48.0 A 0.19 0.11 0.13 8,2145 Calexico 5053 S 69.0 A 0.02 0.02 0.01 8,2346 PVPP Bsmt 1162 S 25.8 H 0.08 0.06 0.03 3046 PVPP Switchyard 1162 S 25.8 H 0.11 0.09 0.05 3047 Long Valley Dam,L. Abut 1444 R 23.6 H 0.09 0.06 0.06 3148 PVPP Switchyard 1162 S 6.8 A 0.54 0.46 0.38 3148 PVPP Basement 1162 S 6.8 A 0.31 0.28 0.22 3148 Parkfield VC 2E R 23.9 A 0.179 0.122 0.067 6,2248 Cantua Creek School S 25.9 A 0.288 0.226 0.114 6,2248 ParkfieldVC 1E 26.2 A 0.232 0.178 0.084 6,2248 Par kfieldFZ16 28.1 A 0.184 0.144 0.062 6,2248 Slack Canyon R 28.7 A 0 . 1 7 3 0.137 0.053 6,2248 Parkfield VC 1W 28.9 A 0.090 0.086 0.070 6,2248 Park fie ldFZ15 29.6 A 0.194 0. 12 5 0.084 6,2248 Parkfield VC 2W 30.1 A 0.089 0.079 0.058 6,2248 Par kfieldFZ14 30.1 A 0.275 0.264 0.097 6,2248 ParkfieldFZ12 30.4 A 0.113 0.110 0.071 6,2248 ParkfieldFZ 8 31.6 A 0.134 0.116 0.054 6,2248 Parkfield VC 3W R 31.7 A 0.139 0. 10 1 0.056 6,2248 Parkfi eld FZ10 R 31.7 A 0 . 1 3 3 0.075 0.046 6,2248 Parkfield GH 3E 32.1 A 0.095 0.072 0.055 6,2248 ParkfieldFZ 7 32.7 A 0.122 0.120 0.055 6,2248 Parkfi eld FZ9 32.8 A 0 .0 51 0.050 0.027 6,2248 Parkfield SC 4E R 33.9 A 0.074 0.065 0.029 6,2248 Parkfield VC 4W 34.0 A 0.057 0.039 0.028 6,2248 Parkfield FZ 6 34.4 A 0.057 0.056 0.028 6,2248 Parkfield GH 2E 35.2 A 0.082 0.077 0.039 6,22

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57 N. A. ABRAHAMSON AND J. J. LITEHISERAPPENDIX. PEAK ACCELERATION DATASta Dist3 Peak Acc. g)Eqk Station Name No. 1 G 2 ~km) Ref4 H1 1-12 V Sources5

48 Parkfield FZ 11 35.6 A 0.087 0.079 0.043 6,2248 ParkfieldFZ4 36.3 A 0.122 0.067 0.047 6,2248 Parkfield SC 3E 36.4 A 0 . 15 1 0.107 0.034 6,2248 Parkfield VC 5W 36.6 A 0.065 0.049 6,2248 ParkfieldGH 1W 37.1 A 0.122 0.066 0.035 6,2248 Parkfield GH 2W 39.0 A 0.084 0.075 0.037 6,2248 Parkfield FZ 3 S 39.6 A 0.164 0.140 0.050 6,2248 Parkfield SC 2E R 39.8 A 0.089 0.062 0.033 6,2248 Parkfield VC 6W 40.5 A 0.078 0.054 0.038 6,2248 Parkfield GH 3W R 40.8 A . 0.138 0.123 0.067 6,2248 ParkfieldSC IE 41.2 A 0.127 0.105 0.069 6,2248 ParkfieldFZ2 S 41.3 A 0.135 0.119 0.041 6,2248 Parkfield GH 4W 42.8 A 0.099 0.056 0.030 6,2248 ParkfieldC 3E R 43.5 A 0.046 0.044 0.027 6,2248 Parkfield GH 5W 45.2 A 0.073 0.055 0.035 6,2248 Par kfi eld FZ1 S 45.2 A 0.143 0.112 0.041 6,2248 Parkfield C 2E R 45.4 A 0.039 0.027 0.017 6,2248 ParkfieldC IE 46.4 A 0.093 0. 09 1 0.059 6,2248 Parkfield C 2WA 47.3 A 0.114 0. 11 1 0.044 6,2248 Parkfield C 3W 48.1 A 0.099 0.084 0.034 6,2248 Parkfield C 4W 49.0 A 0.133 0.133 0.041 6,2248 Parkfield GH 6W 49.3 A 0.069 0.064 0.036 6,2248 Parkfield C 4AW 50.1 A 0 . 0 7 1 0.052 0.025 6,2248 Parkfield C 5W 51.2 A 0.140 0.13.6 0.034 6,2248 Parkfield C 6W 52.7 A 0.133 0.096 0.034 6,2248 Parkfield C 8W 54.2 A 0 . 1 0 1 0.099 0.027 6,2248 ParkfieldC 12W 58.2 A 0.047 0.044 0.022 6,2248 Bear Valley Sta. 10 1479 S 70.9 A 0.06 0.04 0.02 31,4248 Bear Valley Sta. 12 1481 S 85.7 A 0.08 0.08 0.03 31,4248 L.Success Dam,down str. 1484 120.7 A 0.09 0.04 0.01 3149 Anticline Rdge,FF R 12.6 H 0.56 0.56 0.30 3149 Anticline Rdge,pad R 12.6 H 0.48 0.47 0.37 3149 Anticline Ridge, Palmer Av S 12.7 H 0.28 0.21 0.12 349 Oil Flds Fire Sta.,FF R 12.7 H 0.25 0.18 0.16 3149 Palmer Av. R 12.8 H 0.26 0.22 0.10 3149 OilCity R 13.2 H 0.30 0.24 0.10 3149 Skunk Hollow R 13.5 H 0.15 0.12 0.12 3149 Oilfields-Skunk Hollow S 13.8 FI 0.35 0.30 0.23 349 Coalinga CI-IP S 15.7 H 0.13 0.11 0.08 349 PVPP Basement 1162 S 16.3 H 0.14 0.05 0.04 3149 PVPP Switchyard 1162 S 16.3 H 0.22 0.10 0.11 3149 Burnett Co. S 16.6 H 0.09 0.08 0.07 3149 Sulphur Baths R 18.9 H 0.02 0.01 0.01 349 Harris Ranch S 19.8 H 0.15 0.08 0.07 350 Average of 35 records 1 S 35.4 H 0.047 0.037 0.026 5151 OilCity R 10.1 H 0.09 0.09 0.09 3151 Transmitter HI. 11.4 H 0.06 0.06 0.04 3151 Anticline Rdge,FF R 12.2 H 0.06 0.06 0.02 3151 Burnett Co. S 15.6 H 0.20 0.14 0.07 3151 PVPP Switchyard 1162 S 20.6 H 0.05 0.04 0.02 3152 Average of 23 records 1 S 11 1. 0 A 0.026 0.022 0.009 5153 Average of 30 records 1 S 10 8. 0 A 0.052 0.040 0.013 5154 Long Valley Fire Sta. 12.9 H 0.05 0.04 0.02 3154 Long Valley Dam,L Abut 1444 R 16.8 H 0.08 0.07 0.05 31,4255 Oil City R 10.5 H 0.38 0.37 0.21 3155 Transmitter HI. 11.3 H 0.20 0.19 0.12 3155 Anticline Rdge,FF R 11.7 H 0.39 0.28 0.12 3155 AnticlineRdge,pad R 11.7 H 0.42 0.24 0.11 31

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APPENDIX. PEAK ACCELERATION DATASta Dist3 Peak Acc. g)Eqk Station Name No. 1 G 2 km) Ref H1 H2 V Sources555 Oil Flds Fire Sta.,FF R 12.8 H 0.09 0.09 0.07 3155 Oil Flds Fire Sta.,pad R 12.8 H 0.09 0.09 0.07 3155 Skunk Hollow R 13.9 H 0.17 0.14 0.15 3155 Coalinga CHP S 14.4 H 0.18 0.17 0.09 355 Palmer Av. R 14.5 H 0.20 0.12 0.07 3155 Burnett Co. S 15.2 H 0.14 0.10 0.08 3155 Sulphur Baths R 16.0 H 0.07 0.07 0.04 355 PVPP Switchyard 1162 S 18.9 H 0.06 0.03 0.03 3156 OilCity R 10.9 H 0.30 0.25 0.12 3156 Anticline Rdge,pad R 12.3 H 0.51 0.34 0.22 3156 Transmitter HI. 12.3 H 0.30 0.25 0.08 3156 Coalinga CHP) S 12.8 H 0.21 0.13 0.11 356 Burnett Co. S 13.4 H 0.17 0.11 0.04 3156 Oil Flds Fire St.,FF R 13.7 H 0.14 0.13 0.04 3156 Oil Flds Fire St.,pad R 13.7 H 0.16 0.13 0.04 3156 Sulphur Baths R 13.8 H 0.06 0.02 0.03 356 Palmer Av. R 14.5 H 0.33 0.30 0.08 3156 Skunk Hollow R 15.4 H 0.15 0.09 0.04 3157 Oil City R 10.5 H 0.37 0.24 0.22 3157 TransmitterH1. 11.6 H 0.39 0.28 0.12 3157 Anticline Rdge,FF R 11.7 H 0.59 0.55 0.30 3157 Anticline Rdge,pad R 11.7 H 0.56 0.43 0.29 3157 Coalinga CHP S 12.8 H 0.71 0.48 0.38 357 OilF lds Fire Sta.,FF R 13.0 H 0.15 0.10 0.06 3157 Oil Flds Fire Sta,,pad R 13.0 H 0.18 0.12 0.06 3157 Burnett Co. S 13.5 H 0.66 0.39 0.26 3157 PalmerAv. R 13.9 H 0.18 0.15 0.17 3157 Sulphur Baths R 14.2 H 0.19 0.18 0.17 357 Skunk Hollow R 14.6 H 0.14 0.06 0.09 3158 Oil Flds Fire Sta.,Ff R 7.1 H 0.14 0.09 0.09 3158 Oil Flds Fire Sta.,pad R 7.1 H 0.17 0.12 0.07 3158 Skunk Hollow R 8.1 I-I 0.10 0.09 0.05 3158 Anticline Rdge,field R 8.1 H 0.23 0.18 0.05 3158 AnticlineRdge.pad R 8.1 H 0.20 0.18 0.09 3158 Anticline Rdge,nonh R 8.1 FI 0.29 0.17 0.06 3158 Anticline Rdge,south R 8.1 H 0.08 0.06 0.04 3158 PVPP Switchyard 1162 S 10.1 H 0.08 0.07 0.08 3158 PVPP Free Field 1162 S 10.1 H 0.06 0.04 0.05 3158 Oil City R 10.1 H 0.09 0.07 0.04 3159 Average of 33 records 1 S 83.0 A 0.034 0.028 0.009 5160 TRA-670 S 89.0 A 0.023 0.022 0.019 1460 TRA-642 S 90.0 A 0.030 0.029 0.018 1460 CPP-601-2 92.0 A 0.044 0.038 0.038 1460 CPP-610 93.0 A 0.078 0.058 0.035 1460 TAN-719 S 94.0 A 0.050 0.040 0.016 1460 PBF-620-2 R 97.0 A 0 .0 5 1 0.050 0.032 1460 ANL-767 110.0 A 0.033 0.032 0.031 1460 ANL-768 110.0 A 0.048 0.038 0.028 1461 Smith Ranch 21.4 A 0.08 0.06 0.04 3162 Coyote Creek Dam 1017 3.2 N 1.29 0.72 0.40 25,4262 Halls Valley 1422 S 3.2 N 0.31 0.13 0.11 25,4262 Anderson Dam 3.8 N 0.409 0. 30 1 0. 20 1 25,4262 Gilroy Sta 6 1413 R 11.6 N 0.34 0.23 0.43 25,4262 SJinterchange 12.2 N 0.123 0.083 0.082 25 ,4 262 Gilroy Sta 4 1411 S 12.6 N 0.37 0.23 0.40 25,4262 Gilroy Sta 7 13.7 N 0.19 0. 11 0.46 25,4262 Gilroy Sta 3 1410 S 14.4 N 0.20 0.20 0.40 25,4262 Gilroy Sta 2 1409 S 14.9 N 0.22 0.16 0.61 25,42

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576 N. A. ABRAHAMSON AND J. J. LITEHISERAPPENDIX. PEAK ACCELERATION DATA

Sta Dist3 Peak Acc. (g)Eqk Station Name No. 1 G 2 ~km) Ref H1 H2 V Sourees562 SJ Town Park Towers 1507 S 15.4 N 0.06 0.06 0.05 25,4262 Gilroy Gavilan Col. 1250 15.9 N 0.12 0.10 0.12 25,4262 SJ Great Western 1506 S 15.9 N 0.06 0.06 0.04 25,4262 Gilroy Sta 1 1408 R 16.0 N 0.10 0.08 0.I0 25,4262 SJ Santa Clara Co Bldg 1508 S 16.7 N 0.04 0.03 0.02 25,4262 Agnes Hospital 1301 S 23.0 N 0.04 0.04 0.03 25,4262 Corralitos Eureka Cyn Rd 1251 S 24.1 N 0.12 0.09 0.07 25,4262 Lexington Dam 1415 25.0 N 0.02 0.02 0.01 25,4262 Saratoga West Vly Col 1460 27.0 N 0.10 0.04 0.03 25,4262 Hollister Diff Array 27.9 N 0.094 0.089 0.222 25,4262 Watsonville Tel Bldg 29.5 N 0.11 0.06 0.09 25,4262 San Juan Bautista F.S. S 29.9 N 0.04 0.03 0.06 25,4262 Livermore VA 1226 S 30.7 N 0.022 0.016 0 .011 25,4262 Fremont Mission San Jose 1299 S 31.6 N 0.03 0.02 0.02 25,4262 HollisterWarehouse 32.1 N 0.11 0.06 0.31 25,4262 Hollis terCityHaU 1028 S 32.2 N 0.078 0.077 0.425 25 ,4 262 San Justo DAM R Abut 33.2 N 0.076 0.059 0.060 25,4262 San Justo Dam L Abut 34.4 N 0.074 0.038 0.034 25 ,4 262 Hollister Damler Res. 35.9 N 0.078 0.060 0.076 25,4262 Palo Alto 1900 Embarcadero 1469 37.0 N 0.03 0.03 0.02 25,4262 Palo Alto VA 1227 S 38.0 N 0.022 0.022 0.018 25,4 262 BelmontEnvirotech Bldg 1467 39.2 N 0.02 0.02 0.01 25,4262 Capitola 1376 S 39.2 N 0.15 0.10 0.05 25,4262 Stanford Quad 41.1 N 0.027 0. 02 3 0.022 25,4262 Stanford SLAC Survey Hill 43.3 N 0.027 0.016 0.020 25, 4262 Stanford SLAC Testlab 44.0 N 0.032 0. 03 1 0.022 25,4262 Hayward CSUH 1524 45.6 N 0.02 0.01 0.01 25,4262 San Ramon Kodak Bldg 1418 S 46.5 N 0.03 0.02 0.02 25,4262 Apeel 2E 1121 S 47.3 N 0.03 0.03 0.02 25,4262 Santa Cruz UCSC Lick Obs 1384 R 47.3 N 0.07 0.04 0.04 25,4262 Apeel 1E 1180 S 47.7 N 0.04 0.03 0.02 25,4262 Salinas John Work St 1414 S 50.0 N 0.04 0.03 0.06 25,4262 Redwood City Canada Col. 1468 50.3 N 0.01 0.01 0.01 25,4263 Dickey, Idaho 17.9 H 0.33 0.16 0.19 3264 Bishop Paradise Lodge R 5.0 A 0.24 0.20 0.20 3764 Crowley Lake S 12.9 A 0.15 0.11 0.09 3764 Long Valley Dam R 13.7 A 0.08 0.08 0.06 3764 McGeeCreek,surface S 16.6 A 0.11 0.10 0.09 3264 Bishop 873 N Main St S 18.2 A 0.07 0.04 0.03 3764 Bishop LAWP 1008 S 18.8 A 0.06 0.04 0.04 3764 Convict Creek 1324 S 22.1 A 0.06 0.06 0.04 3764 Mammoth Lakes Sheriff R 27.8 A 0.04 0.02 0.02 3764 Chalfant Zack Ranch S 29.6 A 0.10 0.09 0.05 3764 Mammoth Lakes H.S. S 32.9 A 0.04 0.03 0.03 3764 Mammoth Lakes H.S. (FF-) S 32.9 A 0.05 0.03 0.03 3764 Benton 1325 S 40.6 A 0.03 0.03 0.03 3764 Tinemaha Dam R 54.0 A 0.01 0.01 0.01 3765 Average of 33 records 1 S 45.0 H 0.076 0.050 0.022 5166 CaletadeComp os R 7.2 A 0.144 0. 14 1 0.091 266 LaVilli ta R 12.0 A 0.127 0.124 0.059 266 LaUnion R 16.0 A 0.169 0. 15 1 0.131 266 Zihuatanejo R 25.0 A 0.164 0.105 0.106 266 Papanoa R 45.0 A 0.112 0.102 0.081 266 EI Suchil R 93.0 A 0.092 0.072 0.041 266 Atoyac R 115.0 A 0.060 0.054 0.061 266 E1Cayaco R 132.0 A 0.049 0.042 0.024 266 Coyuca R 157.0 A 0.040 0.036 0.020 266 Xaltianguis R 184.0 A 0.025 0.018 0.020 2

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ATTENU ATION OF VERTICAL PEAK ACCELERATION 577

APPENDIX. PEAK ACCELERATION DATASta Dist3 Peak Acc. g)Eqk Station Name No.1 G 2 km) Ref H1 I4_2 V Sources566 LaVenta R 174. 0 A 0 .0 2 1 0.018 0.016 266 Cerro de Piedra R 189.0 A 0.025 0.015 0.015 266 E1Ocotito R 194 .0 A 0 .0 5 1 0.030 0.020 266 Los Mesas R 212.0 A 0.022 0.018 0.019 266 CUMV, Ciudad U., Mex. City R 400.0 A 0.040 0.035 0.020 3566 CUIP, Ciudad U., Mex. City R 400.0 A 0.035 0.029 0.021 3566 CUO1, Ciudad U., Mex. City R 400.0 A 0.035 0.028 0.022 3566 SCT, Sec. de Com. y Trans. S 400.0 A 0 . 17 1 0.100 0.037 3666 CAF, Cent. de Abastos Frig S 400.0 A 0.097 0.082 0.028 3666 CAO, Cent. deAbastos Ofic S 400.0 A 0 . 08 1 0.070 0.037 3667 Zihuatanejo R 15.0 A 0.132 0.122 0.092 267 Papanoa R 15.0 A 0.204 0.204 0.153 267 LaUnion R 26.0 A 0.077 0.049 0.059 267 E1Suchil R 51.0 A 0 .0 81 0. 05 1 0.041 267 LaVil lita R 56.0 A 0 .0 41 0.034 0.020 267 Atoyac R 72.0 A 0 .0 81 0.075 0.074 267 E1Cayaco R 89.0 A 0 .0 61 0.044 0.021 267 Coyuca R 112. 0 A 0 .0 5 1 0.04 1 0.031 267 Xaitianguis R 146.0 A 0.015 0. 01 1 0.018 267 LaVenta R 146 .0 A 0.018 0. 01 3 0.014 267 Cerro dePiedra R 161.0 A 0.01

abrahamsonand litehiser 1989 equation

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