spectral amplification in a sediment filled valley exhibiting clear basin-edge-induced waves

7/30/2019 Spectral Amplification in a Sediment Filled Valley Exhibiting Clear Basin-edge-Induced Waves

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Bulletin of the Seismological Society of America, Vol. 86, No. 4, pp. 991-1005, August 1996

Spectral Am plif ication in a Sediment-Filled V alley E xhibiting C learBas in-Edge-Induced Waves

b y E d w a r d H . F i e ld

Abs t r a c t v a r i o u s s i t e - r e s p o n s e e s t i m a t e s a r e p r e s e n t e d f o r a l i n e a r a r r a y d e p l o y e di n t h e C o a c h e l l a V a l l e y , C a l i f o r n ia , d u r i n g t h e 1 9 9 2 L a n d e r s / B i g B e a r a f t e r s h o c ks e q u e n c e . T h i s s y s t e m a t i c c o m p a r i s o n i s u n i q u e i n th a t t h e r e s p o n s e o f th e s i te i sc l e a r ly d o m i n a t e d b y b a s i n - e d g e - i n d u c e d w a v e s . A v e r a g e s e d i m e n t t o b e d r o c k s p e c -t r a l r a t i o s f o r l o n g S - w a v e w i n d o w s , w h i c h i n c l u d e t h e b a s i n - e d g e - i n d u c e d w a v e s ,e x h i b i t a m p l i f i c a t i o n f a c t o rs a s h i g h a s - 1 8 , b e l o w 7 H z . T h e d e e p b a s i n s tr u c t u re ,w h i c h g i v e s r i s e t o t h e o b v i o u s m u l t i - d i m e n s i o n a l e f f e c t s , p r o d u c e s a f u n d a m e n t a lr e s o n a n t p e a k t h a t s h i f t s b e t w e e n b a s i n s i t e s ( f r o m 0 . 2 3 t o 0 . 4 8 H z ) a s t h e d e p t h t ob e d r o c k c h a n g e s . A b o v e 0 . 6 H z , w h e r e t h e l a r g e s t a m p l i f i c a t i o n s o c c u r , t h e r e s p o n s ei s r e m a r k a b l y s i m i la r b e t w e e n s i te s a n d a p p e a r s t o b e d o m i n a t e d b y a n e a r - s u r fa c el a y e r t h a t i s r e l a t i v e l y u n i f o r m a c r o s s t h e v a l l e y . T h e a p p a r e n t f u n d a m e n t a l r e s o n a n tf r e q u e n c y o f t h is l a y e r i s b e t w e e n 0 . 8 a n d 1 H z . S e d i m e n t t o b e d r o c k s p e c t r a l ra t i o sc o m p u t e d u s i n g s h o r t er w i n d o w s t h a t e x c l u d e t he b a s i n - e d g e - i n d u c e d w a v e s i m p l yt h a t t h e m u l t i - d i m e n s i o n a l e f f e c t s a re s ig n i f ic a n t o n l y b e l o w - 4 H z , w h e r e t h e yi n c r e a s e a m p l i f ic a t i o n s b y a n a p p r o x i m a t e f a c t o r o f 2 . S p e c t r a l r a t i o s c o m p u t e d u s i n gc o d a w i n d o w s , t a k e n a t t w i c e t h e S - w a v e t r a v e l t i m e , e x h i b i t a m p l i f i c a t i o n s t h a t a r ea n a v e r a g e f a c t o r o f 1 . 7 g r e a t e r , b e t w e e n 1 a n d 4 H z , t h a n t h o s e o f t h e S - w a v ee s t im a t e s . T h i s d i s c r e p a n c y d o e s n o t i m p r o v e b y t a k in g c o d a w i n d o w s l a te r a t fo u rt i m e s t h e S - w a v e t r a v e l t i m e . H o r i z o n t a l - t o v e r t i c a l - c o m p o n e n t S - w a v e s p e c t r a l r a -t i o s d o n o t a g r e e w i t h t h e s e d i m e n t t o b e d r o c k r a t i o s . H o w e v e r , t h e y d o e x h i b i t ac l e a r p e a k a t t h e f u n d a m e n t a l r e s o n a n t f r e q u e n c y o f t h e d e e p b a s i n s t r u c tu r e . S e d i -m e n t t o b e d r o c k s p e c t r a l r a ti o s o f a m b i e n t s e i s m i c n o i s e a r e a l s o i n c o n s i s te n t w i t ht h e S - w a v e e s t i m a t e s . H o w e v e r , h o r i z o n t a l t o v e r t i c a l n o i s e r a t io s e x h i b i t c le a r p e a k sn e a r t h e f u n d a m e n t a l r e s o n a n t f r e q u e n c i e s o f b o t h t h e d e e p b a s i n s tr u c t u r e ( b e l o w0 . 6 H z ) a n d t h e s u s p e c t e d n e a r - s u r f a c e l a y e r ( b e t w e e n 0 . 8 a n d 1 H z ) . T h e r e f o r e ,a m b i e n t - n o i s e d a t a a p p e a r t o p r o v i d e v a l u a b l e c o n s t r a i n t s o n t h e b a s i n s t r u c t u r e .O n g o i n g e f f o r ts i n v o l v e m u l ti - d im e n s i o n a l m o d e l i n g o f th e o b s e r v e d b a s i n - e d g e -i n d u c e d p h a s e s a n d r e s o n a n t f r e q u e n c i e s .

I n t r o d u c t i o nThe st rong influence of near-surface geological condi -

t ions, in the form o f sedime nt amplification or site respon se,has been apparent f rom the da mage dist ribution of manydestructive earthquakes. The long l ist of exam ples starts atleast as far back as the great Japan ear thquake of 1891, forwhich Milne (1898, p . 82) wrote that " . . . dest ruct ion wasmarked on every p l ane be twee n Tokyo and N agoya , a d is -tance o f 200 mi les, whi le those wh o from the dividing rangeslooked do wn upo n the clouds of dust and smo ke r is ing f romfallen and burning towns, themselves suffered l i t t le if anydamage." Modern examples include the 1985 Michoacanearthquake in Mexico (e.g., Celebi e t a l . , 1987); the 1988Spi tak ear thquake in Armenia (e.g . , Borcherdt e t a l . , 1989);

the 1989 Loma Prieta (e.g., Hough e t a l . , 1990) and the 1994Northridge (e.g., EERI, 1994) earthquakes in California; andthe Hyog o-Ke n Nanbu (Kobe) Ear thquake in Japan (e.g .,EERI, 1995).

There are man y factors that influence the wa y a site willresponse to earthquake ground motion [see Aki (1988), Akiand Irikura (1991), and Bard (1994) for seminal reviews].In addit ion to the 1D structure, these include (1) the sourcelocation, w hich influences the angle, azimuth, and type ofincident waves; (2) the prevalence of energy foc used or scat-tered from lateral heterogeneit ies, such as surface wa vesgenerated at the edge of a basin that propagate as energytrapped within the sediments; and (3) the degree to which

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sed i ment s beha ve non l i nea r l y , whi ch causes t he r e sponse t od e p e n d o n t h e l e v e l o f i n p u t m o t i o n .

E f f o r t s t o mak e t he i nc l us i on o f s i te e f f ec t s in s e i smi ch a z a r d a s s e s s m e n ts m o r e s o p h i st ic a t e d h a v e b e e n h a m p e r e dby o ur l i mi t ed under s t and i ng o f t hese comp l i ca t i ng f ac t o r s .P a r t o f t he p r ob l em i s t ha t t he concep t o f s i t e r e sponse i so f t en vague , s i nce i ts d i s t i nc t ion f r om pa t h e f f ec t s is som e-wha t a r t if i c ia l and a r b i t r a r y . F or exam pl e , i n t he en g i nee r i ngcommuni t y , i t i s common t o r ega r d t he s i t e e f f ec t a s t hei n f l uence o f t he uppe r 30 m. However , s e i smol og i s t s o f t ent h i n k o f s u r f a c e w a v e s g e n e r a t e d a t t h e b o u n d a r y o f a s e d i-m e n t a r y b a s i n ( w h i c h m a y h a v e d i m e n s i o n s o f s e v e r a l k i -l ome t e r s ) a s a s i t e e f f ec t . T he r e f o r e , i t is i mp or t an t t ha t themea n i ng o f s i te r e sponse be c l ea r l y de fi ned .

F or haza r d a s ses sment , a p r ac t i ca l de fi n i t ion woul dseem t o be t he un i que behav i o r o f a s i t e , r e l a t i ve t o o t he rs i te s , t ha t pe r s i s ts g i ven a l l ( o r mos t ) o f t he po t en t i a l sour cesof ea r t hquake g r ound mot i on i n t he r eg i on . F or such a de f -i n i t i on t o be use f u l , t he va r i ab i l i t y o f t he r e sponse a t anypar t i cu l a r s i te , w i t h r e spec t t o t he d i f f e r en t po t en t i a l ea rt h -quake sour ces , mus t be l e s s t han t he d i f f e r ences be t wee n t hedis t inguished s i tes (Aki , 1988) .

G i ven t h i s de f i n i t i on , wha t i s t he bes t way t o e s t i ma t eor p r ed i c t s i t e r e sponse? T heor e t i ca l appr oaches a r e i ns tr uc -t i ve , a l t hough conduc t i ng t he neces sa r y s ens i t i v i t y t e s t s( w i t h r e spec t t o d i f f e r en t loca t i ons and s i zes o f pos s i b l eeven t s ) and unce r t a i n t y ana l yses ( w i t h r e spec t to our l i mi t edknow l edge o f t he E a r t h ' s s t r uc t u re ) i s usua l l y i mpr ac t i ca l.I dea l l y , one woul d l i ke t o compar e empi r i ca l obse r va t i ons

f r om eve r y po t en t i a l even t a t eve r y s i t e o f i n te r e s t, wh i ch i sobv i o us l y no t pos s i b l e . E m pi r i ca l s t ud i e s t yp i ca l l y u ti l i ze t hea f t e r shocks f o l l owi ng a l a r ge ev en t t o i n f e r t he r e l a t i ve r e -sponse o f va r i ous s i te s. F or ex ampl e , H ar t ze l l e t a l . ( 1996)r ecen t l y pe r f o r med a gene r a l i zed i nve r s i on f o r t he s i t e r e -sponse o f 90 s i t e s us i ng a f t e r shocks o f the Nor t h r i dge ea r t h -quake . S i mi l a r l y , Gao e t a l . ( 1996) demons t r a t ed t ha t d i f -f e r i ng l eve l s o f dam age be t w een ne i gh bor i ng s i t e s in S an t aM oni ca dur i ng t he Nor t h r i dge ea r t hquake can be a t t r i bu t edt o bas i n - edge e f f ec t s . As s t r e s sed by Gao e t a l . (1996) , ther esu l ts o f t hese s t ud i e s pe r t a i n t o sour ces l oca t ed w i t h i n theNor t h r i dge a f t e r shock zone , and i t is no t c l ea r whe t he r t heywi l l app l y t o o t he r sour ce l oca t i ons a s we l l . I n f ac t , accor d-i ng t o t he d e f i n i ti on o f s i te r e sponse g i ven above , i t i s ques -t i onab l e whe t he r such o bse r ved d i f f e r ences be t ween s i t e sshou l d be r e f e r r ed t o a s s i t e r e sponse . T h e d i f f e r ences cou l dr esu l t mor e f r om r eg i ona l pa t h e f f ec t s spec i f i c t o t he Nor t h -r i dge a f t e r shock zone . A l t e r na t i ve l y , one cou l d r e f e r t o t hed i f f e r ences a s s i t e e f fec t s , ye t ack now l edge t ha t t he r e sponsemay be i n t r i ns i ca l l y va r i ab l e g i ven o t he r sour ce l oca t i ons .Regar d l e s s o f whi ch de f i n i t i on one chooses , t he obse r vedd i f f e r ences be t w een s i t e s may ap p l y on l y t o t he Nor t h r i dgee a r t h q u a k e s e q u e n c e , w h i c h w e a r e n o w l e s s c o n c e r n e dabout i n t e r ms o f haza r d a s ses sment . T h i s p r ob l em i s en -demi c t o many empi r i ca l s i t e - r e sponse s t ud i e s . I t does no td i mi n i sh t he i r va l ue , how ever ; t o t he con t r a r y , i t is i mpor t an tt ha t many such s t ud i e s a r e conduc t ed us i ng da t a f r om d i f -

f e t i ng so ur ce r eg i ons so t ha t pe r s i s t en t d i f f e r ences be t we enneighbor ing s i tes , and the int r ins ic var iabi l i ty a t each s i te ,can be a sce r t a ined .

One w i de l y used t echn i qu e f o r e s ti ma t i ng s i t e r e sponsei nvo l ves us i ng S - wave coda ( e .g . , T su j i u r a , 1978 ; P h i l l i psand Aki , 1986 ; M ayed a e t a l . , 1991; Ka t o e t a l . , 1995; Suand Aki , 1995) . T he o r i g i na l mo t i ve f o r th i s me t hod was t ot ake advan t age o f t he r e l a t i ve l y abundan t ve r t i ca l - compo-nen t ne t wor k da t a t ha t is gene r a l l y c l i pped on t he d i r ec t a r -r i va ls . How ever , t he mo s t appea l i ng a sp ec t o f th i s appr oachi s t ha t s ince t he coda i s t houg h t t o be com posed o f s ca t te r edene r gy comi ng i n f r om a va r i e t y o f d i r ec t i ons ( Aki andChoue t , 1975) , the s i t e - r e sponse e s t i ma t e mi gh t na t u r a l l y re -f l ec t an ave r age ove r va r i ous sour ce l oca t i ons . Unf or t u -na t e l y , t he r e i s some d i sagr eem ent a s t o whe t he r coda s i t e -r e sponse e s t i ma t es a r e cons i s t en t w i t h t he s i t e r e sponse o fd i r e c t S w a v e s ; w h i l e s o m e h a v e f o u n d a g r e e m e n t b e tw e e nthe two (e .g. , Tsuj iura , 1978; Kato e t a l . , 1995) , o t he r s haveno t ( e .g . , M ar ghe r i t i e t a l . , 1994; S eek i ns e t a l . , 1995; S teidle t a l . , 1995; thi s s tudy) .

C l ea r l y , mor e bas i c r e sea r ch i s neede d i n o r de r t o mak eour i nc l us i on o f s i t e r e sponse i n haza r d a s ses sment s mor esophis t icated. In thi s a r t ic le , I present s om e resul t s of a s i te-r e sponse s t udy conduc t ed i n t he Coache l l a Va l l ey nea r I n -dio, Cal i fornia . This s i te i s of par t icular interes t in that i tr ep r esen t s a case wher e t he r e sponse i s c l ea r l y dom i na t ed bybas i n - e dge - i n duce d wave s ( i n a t l ea s t a 2D sense ) . F ur t he r -mor e , s i nce t he phases a r e gene r a t ed a t the edge o f the bas i nboun ded by a f au lt , t he r e su l t s shou l d he l p e l uc i da t e t he haz -a r d i n mor e den se l y popu l a t ed f au l t - bounded bas i ns ( such a st hose unde r l y i ng t he L os Ange l es r eg i on) .

M ul t i - d i mens i ona l s i te e f f ec t s have been i n f e r r ed i n s ev-e r a l s t ud i e s , o f t en f r om t he f ac t t ha t one - d i mens i ona l mod-e l i ng cou l d no t p r ed i c t obse r ved ampl i t udes o r dur a t i ons( e .g . , K i ng and T u cker , 1984 ; Ka wase , 1987) , o r f r om a r r ay-data analys i s (e .g. , Hor ike, 1988; Frankel e t a l . , 1991; Spu-d i ch and I i da , 1993). D i r ec t obse r va t i ons o f bas i n - edg e -i n d u c e d w a v e s h a v e b e e n l e s s c o m m o n , a n d t h e s e h a v e u s u -a l l y been o f l onge r - pe r i od ( 2 t o 10 sec ) su r f ace - wave mod es( e .g . , Hanks , 1975 ; Koyama e t a L , 1988; V i da l e and He l m-be r ge r , 1988 ; Ha t ayama e t a L , 1995) . However , shor t e r -pe r i od ( - - 1 s ec ) s ca t t e r ed phases have a l so been obse r ved(e .g. , Kinoshi ta , 1985; Gao e t a l . , 1996; thi s s tudy) , andm o d e l i n g a t te m p t s o f t h e s e h a v e s o m e t i m e s b e e n r e m a r k a b l ysucces s f u l ( e.g ., S c r i vne r and H e l mb er ge r , 1994) .

T he p ur pose o f t h is a r t i c le i s t o p r esen t va r i ous empi r -ical es t imates of spect ra l ampl i f icat ion for a s i te that i sc l e a r ly d o m i n a t e d b y b a s i n - e d g e - i n d u c e d w a v e s . A d e t a il e di n t e r p r e t a ti on o f t hese and o t he r obse r va t i ons i n t e r ms o f t heva l l ey s t r uc t u r e i s p r e sen t ed e l s ewher e ( F i e l d , 1995) , ande f f o rt s to m o d e l t h e b a s i n - e d g e - i n d u c e d w a v e s w i ll b e t h et op i c o f a f u t u r e pub l i ca t i on . Her e , s ed i ment t o bedr ockspec t r a l r a t i os comput ed us i ng l ong ( 40 sec ) S - wave wi n-dows a r e p r esen t ed f o r a l l o f t he s i t e s . T o i nves t i ga t e t hei n f l uence o f t he obv i ous 2D e f f ec t s , t hese l ong- wi ndow es -t i ma t es a r e t hen compar ed wi t h s ed i ment t o bedr ock r a t i os


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S p e c t r a l A m p l i f i c a t io n i n a S e d i m e n t - F i l l e d V a l l e y E x h i b i t i n g C l e a r B a s i n - E d g e - I n d u c e d W a v e s 993

o b t a i n e d u s i n g s h o r t e r S - w a v e w i n d o w s t h a t e x c l u d e t h ebas i n - edge - i nduced phases . I n add i t i on , compar i sons a r emad e wi t h s ed i ment t o bedr ock sp ec t r a l r a t i os ob t a i ned f r omt h e c o d a a n d f r o m a m b i e n t - n o i s e m e a s u r e m e n t s . F i n a l l y ,s i t e - re sponse e s t i ma t es o b t a i ned f r om hor i zon t a l - t o ve r t ica l -c o m p o n e n t s p e c tr a l ra t io s o f b o t h S w a v e s ( L e r m o a n dChav ez - Gar c i a , 1993) and ambi en t no i se ( Nakam ur a , 1989)a r e a l so exami ned . T he r e su l t s o f t hese compar i sons a r ep l aced wi t h i n t he co n t ex t o f p r ev i ous f i nd i ngs i n t he d i scus-s ion sect ion.

S i nce t he a f t e r shocks exami ned i n t h i s s t udy r epr esen tr e l a t i ve l y we ak mo t i on , t he w i de l y deba t ed i s sue o f non-l i nea r s i te r e sponse i s no t addr es sed h e r e . Reade r s i n t e r e s t edi n t h i s t op i c a r e r e f e r r ed t o Ber esnev e t a l . ( 1995) f o r a b r i e fr e v i e w a n d r e c e n t c a s e s t u d y , a n d t o W e n n e r b e r g (1 9 9 6 ) a n dChi n and Aki ( 1996) f o r a l i ve l y deba t e .

C o a c h e l la V a l l e y D e p l o y m e n tO n t h e d a y f o l l o w i n g t h e 2 8 J u n e 1 9 9 2 L a n d e r s ( M 7 . 3)

and B i g Bea r ( M 6 .4 ) ea r t hquakes , a s i t e - re sponse s t udy wasi n i t ia t ed i n t he Coach e l l a Va l l ey unde r suppor t f r om t he Na-t i ona l Cen t e r f o r E a r t hquake E ngi nee r i ng Resea r ch [ s eeF i e l d e t a l . ( 1992) f o r a p r e l i mi na r y r epor t ]. A r eg i ona l ma pshowi ng t he a f t e r shock zone and s t udy a r ea is g i ven i n F ig -ur e l a .

T h e d e p l o y m e n t w a s c o n s t r u c te d t o a d d r e s s f o u r c u r-r en t l y unr eso l ve d ques t i ons w i t h r e spec t to s ed i men t ampl i -f i cat i on : ( 1 ) T o wh a t ex t en t a r e nea r b y bedr ock- s i t e r ecor d-i ngs r epr esen t a t i ve o f t he g r oundmot i on i npu t a t t he baseof t he s ed i ment s , and can t h i s sour ce o f unce r t a i n t y be i so -l a t ed f r om an i n t r i ns i c va r i ab i l it y i n t he s i te r e sponse i t s e lf ?( 2 ) T o wha t ex t en t do su r f ace waves gene r a t ed a t t he va l l eyedges i n f l uence g r ound m ot i on w i t h i n t he s ed i ment s ( so -ca l l ed t wo- o r t h r ee - d i men s i ona l e f f ec t s ) ? ( 3 ) How w e l l canone p r ed i c t s ed i ment ampl i f i ca t i on us i ng ambi en t s e i smi cn o i s e ? ( 4 ) T o w h a t e x t e n t d o t h e s e d i m e n t s b e h a v e n o n -l i nea r l y dur i ng s t r ong g r ound mot i on?

E i gh t s i te s wer e occup i ed dur i ng t he 10- day expe r i me nt( F i g . l b , T ab l e 1 ). T he ove r a l l dep l oym ent was i n t he f o r mo f a l i n e a r a r r a y s t r e t c h i n g f r o m a n o u t c r o p o f M e s o z o i cgr an i t e on t he nor t heas t s i de o f t he va l l ey ( s i t e ROKE nea rF a r g o C a n y o n ) , a c r o s s t h e Q u a t e r n a r y s e d im e n t s o c c u p y i n gthe val ley (s i tes JEFF, FIRE, JEAN, FRED, and GOLF) , andend i ng o n equ i va l en t M e sozo i c g r an i te a t t he sou t hwes t s i deof t he va l l ey ( s i t e ROKW nea r L a Qui n t a ) . An ad d i t iona l r ocks i t e (ROKN) was a l so oc cup i ed o n t he wes t s i de o f t he va l l eydur i ng pa r t o f t he expe r i ment . E ach s i t e was equ i pped wi t ha t h r e e - c o m p o n e n t s e t o f e i t h e r K i n e m e t r i c 5 - s e c v e l o c i t ysensor s ( S H - 1 , S V- 1 ) , T e r r a T ech no l o gy f o r ce - ba l ance d ac -ce l e r om et e r s (F BAs) , o r bo t h . T hese w er e pa i r ed w i t h E DAP RS 4 d i g i t a l r ecor de r s . E xc ep t wher e o t he r wi se no t ed , a l l o ft he da t a p r esen t ed i n t h i s a r t i c l e wer e r ecor ded wi t h t he 5 -sec ve l oc i t y s ensor s . A l t hough 227 a s soc i a t ed even t s wer er ecor ded dur i ng t he expe r i ment , 101 o f t hese wer e chosen

f o r a n a l y s i s h e r e b e c a u s e t h e y w e r e r e c o r d e d a t b o t h t h er e f e r ence s i t e ( ROKW ) and a t l ea s t one o f t he s ed i m ent s i te s .T hes e 101 even t s a r e l i s ted i n T ab l e 2 , and t he i r ep i cen t e r sa r e p l o t ted i n F i gur e l a .

I n add i t i on t o t he a f t e r sho ck r ecor d i ngs , ambi en t s e is -m i c n o i s e m e a s u r e m e n t s w e r e o b t a i n e d w i th t h e 5 - s e c v e -loci ty sensors a t f ive of the s i tes (ROKW, GOLF, FRED,JE AN, and ROKN) i n o r de r t o addr es s t he ques t i on o f howwel l amb i en t s e i smi c no i se can be used t o p r ed i c t ea r t hquakes i t e r e sponse . F i na l l y , s i nce we d i d no t r ecor d any g r oundmot i on t ha t mi gh t be h i gh enough t o exc i t e a s i gn i f i can tnon l i nea r r e sponse , S S A - l s w er e i ns t a ll ed on a s emi - pe r -man en t bas i s a t ROKW , F RE D, and F I RE to r ecor d an y f u t u r es t ro n g g r o u n d m o t i o n . T h e W o r k i n g G r o u p o n S o u t h e r n C al -i f o r n i a P r obab i l i t i e s ( 1995) has p l aced a 22% chance o fr u p t u re b e f o r e 2 0 2 4 f o r t h e C o a c h e l l a V a l l e y s e g m e n t o f th eS an Andr eas F au l t .

C o a c h e l l a V a l l e y S t r u c t u r eT h e Coach e l l a Va l l ey cons t it u t e s the nor t he r n ex t ens i on

of t he S a l t on T r ough i n sou t he r n Ca l i f o r n i a . Unf or t una t e l y ,t he s ed i ment a r y s t r uc t u r e benea t h t he va l l ey su r f ace i s no tw e l l k n o w n ( B i e h l e r e t a l . , 1964; S y l ves t e r and S mi t h ,1976) . T he ma i n s t r uc t u r a l cons t r a i n t s come f r om gr av i t yd a ta . W h i l e t h e p i o n e e r i n g w o r k w a s c o n d u c t e d b y B i e h l e r( 1964) , a mor e r ece n t g r av i t y - da t a compi l a t i on and i nve r s i onh a s b e e n c o n d u c t e d b y B o b J a c k e n s a t t h e U n i t e d S t a t e sGeol og i ca l S ur vey ( pe r sona l comm.) . Bo t h s t ud i e s sugges tt ha t t he bas i n i s a ha l f - g r aben t i l t ed t owar d t he nor t heas t . Aschemat i c c r os s s ec t i on based on t he J ackens da t a i s showni n F i gur e l c , whi ch i mpl i e s t ha t t he s ed i ment s g r adua l l yt h i cken i n go i ng f r om t he sou t hwes t edge a t ROKW andr each a ma xi m um t h i ckness o f 5 ___ 1 km j us t be f o r e t hes t eep bas i n edge a t t he S an And r eas F au l t ( S AF ). T he g r av i t yda t a do no t r e so l ve any s i gn i f i can t s ed i ment t h i cknessesnor t heas t o f t he S A F , even t ho ugh t hey a r e p r esen t i n t hes u r f a c e - g e o lo g y m a p i n F i g u r e l b . D a m t e ( 1 9 9 5 ) r e c e n t lyp r e s e n t e d a c r o s s s e c t i o n b a s e d o n g r a v i ty m e a s u r e m e n t s f o rt h e n o r th w e s t e r n M e c c a H i ll s a re a ( - 1 5 k m s o u t h e a st o fI nd i o , a s show n i n F i g . l b ) t ha t i s cons i s t en t w i t h t he r e su l tso f J ackens . Un f or t una t e l y , t he g r av i t y s t ud ie s canno t r e so l veany s t r uc t u r e w i t h i n t he s ed i ment s .

De t a i l ed map pi ng i n t he I nd i o H i l l s a r ea (e .g ., P openoe ,1 9 5 9 ; R y m e r e t a l . , 1987) and mappi ng , dense g r av i t y , andsha l l ow r e f r ac t i on p r of i l e s i n t he M ecca H i l ls ( e .g . , S y l ves t e rand S mi t h , 1976 ; P o t t e r , 1992 ; Rymer , 1994) sugges t t ha tt he r eg i on jus t nor t heas t o f the S AF is com pose d o f anas t o -mo s i ng h i gh- ang l e f au l t s w i t h a s soc i a t ed f o l d i ng . T he r e f o r e ,whi l e t he su r f ace s ed i m ent s m ay be r e l a t i ve l y t h in nor t heas to f t he S AF , t hese s t ud i e s , and i ndeed t he v e r y ex i s t ence o ft he I nd i o H i l l s and M ecca H i l l s f au lt s , sugges t t ha t t he nor t h -e a s t b o u n d a r y o f th e b a s i n m a y b e v e r y c o m p l e x . T h e d e p t hex t en t o f t h i s comp l ex i t y r ema i ns unce r t a i n .


4/15

9 9 4 E .H . F i e lda

24300` 243" 30' 244' 00`

34"30 '

34" 00'

33 ~ 30'

34" 30 '

34'00`

33" 30'

b243"00 ' 243" 30'

243.6 E

D Quaternary,DuneSandNonmarine ediments(Pleistocene)

U-]l l

Quatem,'u , Alluvium& Lake Deposits

Mesozoic Granit ic Rocks

A s ~ROKW GOLF FRED JEAN FIRE JEFF

244" 00`

244,0 E33.8 N

33.6 N

A tROKN_ _ &

F i g u r e 1. (a) Regional map showing after-shock epicenters (stars) and recording si tes ( tri-angles) . The Coachella Valley is the f iat regionnorthwest of the Salton Sea. The thin solidl ines represent mapped faults . (b) Simplif iedgeological map o f the study area (outl ined bythe rectangular box in Fig. la ) based on theCal i fo rn ia Div i s ion o f Mines and GeologySanta Ana Sheet . The tr iangles mark the de-ployment locations. (c) Schematic sediment-basement contact cross sect ion for the dashedl ine A-A ' in F igure lb . Th is i s based on aninversion (Bob Jackens, wri t ten correspon-dence) of 2-kin-grid gravity data using a den-si ty/depth function based on well informationthroughout Nevada and f rom bas ins a long theSan And reas Fault . Jackens believes that whilethe absolute depths are uncertain (about _ 1km at the deepest locations) , the relat ive depthsare accurate. The tr iangles mark the approxi-mate points w here the stat ion locations projectonto the dashed l ine. Note that the inversiondoes no t resolve any signif icant sediment thick-nesses nor theas t o f the San A ndreas Fau l t .


5/15

Spe c t ra l Am p l i f ic a t ion in a Se dim e n t -F i l l e d Val l e y Ex hib i t ing C le ar Bas in-Edg e - Indu c e d Wa v e s 9 95

T a b l e 1Station Locations

Site Latitude LongitudeROKW 33.6672 243.7161FRED 33.6881 243.7438FIRE 33.7081 243.7856JEFF 33.745 4 243.83 82

ROKE 33.7450 243.9004GOLF 33.6812 243.7288JEAN 33.7006 243.7679ROKN 33.7021 243.6994

T i m e S e r ie s O b s e r v a t i o n sF i g u r e 2 s h o w s a n e x a m p l e t i m e s e r i es f o r a m a g n i t u d e

4 . 4 ev en t . T h e d i r ec t P an d S w av es a r e am p l i f i ed a t t h esed im en t s i t e s r e l a t i v e t o t h e ro ck s i t e s . H o w ev er , t h e l a rg es ta m p l i t u d e s a r e p r o d u c e d b y a p h a s e t h a t a p p e a r s t o p ro p a g a t ea c r o s s t h e v a l l e y f r o m t h e n o r t h e a s t e d g e ( t o w a r d R O K W ).T h e S - w a v e a r r i v a l -t i m e d e l a y s a c r o s s t h e a r r a y a r e c o n s i st e n tw i th t h e b as in m o d e l su g g es t ed b y t h e g rav i ty d a t a . T h a t i s ,t h e l a rg e d e l ay a t F IR E re l a t i v e t o JE FF an d th e sh o r t en in g o fd e l a y t i m e s a t s i te s b e t w e e n F I R E a nd R O K W a r e c o n s i s te n tw i t h t h e h a l f - g r a b e n m o d e l d e p i c t e d i n F ig u r e l c .

N o te t h e an o m alo u s r i n g in g b eh av io r a t s i t e JE F F , e s -p e c i a l l y o n t h e v e r t i c a l c o m p o n e n t . A l t h o u g h o u t s i d e o f t h em ain b as in su g g es t ed b y t h e g rav i ty d a t a (F ig . l c ) , t h i s s i t ew as ac tu a l l y l o ca t ed o n t h e In d io H i l l s F au l t . T h e re fo re , t h ea n o m a l o u s b e h a v i o r a t J E F F m a y b e r e l a t e d t o f a u l t - z o n ew a v e - g u i d e e f f e c t s , a s o b s e r v e d e l s e w h e r e ( e . g . , L i e t a l . ,1 9 9 4 ), o r t o t h e g en e ra l co m p lex i ty o f t h i s r eg io n , a s d i s -c u s s e d a b o v e .T h e r e l a t i v e ly l a rg e -am p l i t u d e a r r i v a l s fo l l o w in g th e d i-r e c t S w a v e s a t t h e m a i n b a s i n s i t e s w e r e o b s e r v e d c o n s i s -t e n t ly a m o n g t h e a f t e r s h o c k s . F o r e x a m p l e , a s i n F i g u r e 2 ,t h e h i g h e s t a m p l i t u d e o b s e r v e d a t F RE D w a s o f t e n p r o d u c e db y a p h ase a r r i v in g - -1 2 sec a f t e r t h e d i r ec t S w av e o n t h en o r th co m p o n en t ( t h i s a r r i v a l i s sh ad ed in F ig . 2 ) . S h o w n inF i g u r e 3 i s t h e p e a k a m p l i t u d e o f t h is p h a s e ( d e t e r m i n e df r o m v e l o c i t y s e i s m o g r a m s f i l te r e d b e l o w 2 . 5 H z ) , r e l a t iv eto t h a t o f t h e d i r ec t S w av e , a s a fu n c t io n o f ep i cen t r a l l o -ca t i o n ( see ca p t io n fo r d e t a i l s ) . T h i s p lo t sh o w s th a t t h e l a rg -e s t e x c i t a t i o n s a r e g e n e r a l l y p r o d u c e d b y L a n d e r s a f t e r -s h o c k s l o c a t e d ju s t s o u t h o f t h e m a i n s h o c k e p i c e n t e r b u t t ha tr e l a t i v e am p l i t u d es g rea t e r t h an u n i ty a l so o ccu r fo r o th e re v e n t l o c a t i o n s ( i n c lu d i n g s o m e o f t h e B i g B e a r a f t e r -sh o ck s ) . N o s ig n i f i can t d ep en d en ce o n h y p o cen t r a l d ep th i so b s e r v e d . T h e a v e r a g e r e l a t i ve a m p l i t u d e a m o n g a l l o f th eev en t s p lo t t ed i n F ig u re 3 i s 1 .9 , w h ereas t h e a v e rag e r e l a t i v ea m p l i t u d e m e a s u r e d i n a n i d e n t i ca l m a n o r a t R O K W i s 0 .4 7 .

E i g h t e e n o f t h e a f t e r s h o c k s e x h i b i te d b o t h s t r o ng a p -p a r e n t b a s i n - e d g e - i n d u c e d w a v e s a n d r e m a r k a b l y s i m i l a rw av efo rm s ( t h ese ev en t s a r e p lo t t ed w i th so l i d s t a r s i n F ig .3 an d a r e u n d e r l i n ed i n T ab le 1 ) . A l l 1 8 a r e L an d er s a f t e r -sh o ck s , w i th 1 5 o f t h em c lu s t e r in g n ea r 2 4 3 . 6 E an d 3 4 . 0 7

N . S t ack s o f t h ese ev en t s a r e sh o w n in F ig u re 4 s t a r t i n g a t1 .5 sec b e fo re t h e S -w a v e a r r i v a l ( s ee t h e cap t io n fo r p ro -

ces s in g d e t a i l s ) . S in ce t h e b as in s i t e s a r e d o m in a t ed b y en -e r g y p r o p a g a t i n g f r o m t h e n o r t h e a s t e d g e , t h e h o r i z o n t a lc o m p o n e n t s h a v e b e e n r o t a t e d i nt o a c o o r d i n a te s y s t e m p a r -a l l e l an d p e rp en d icu l a r t o t h e v a l l ey ax i s (N 4 5 W ) . V ar io u si n d i vi d u a l p h a s e s c a n b e s e e n f o l l o w i n g t h e S w a v e s i n F i g -u r e 4 . F o r e x a m p l e , t h e v a l l e y - a x i s p e r p e n d i c u l a r c o m p o n e n ta t JEA N ex h ib i t s t h r ee d i s t i n c t a r r i v a l s a t ab o u t 6 , 8 , an d 1 2s e c a f t e r th e S w a v e . T h e f i rs t m a y r e p r e s e n t a w a v e t h a t h a sp r o p a g a t e d d i r e c t ly f r o m t h e b a s i n e d g e , a n d t h e s e c o n d a n dt h ir d a r r i v a l s m a y r e p r e s e n t p h a s e s t h a t h a v e r e f l e c t e d o n c ea n d t w i c e , r e s p e c t i v e l y, f r o m t h e t o p a n d b o t t o m o f t h e b a s i nl ay e r . B y th e t im e th ey g e t t o t h e s i t e G O L F , t h ese p h aseso v e r l ap t o su ch a d eg ree t h a t i t i s p ro b ab ly m o re i n s t ru c t i v et o t h in k o f t h e m a s a s u r f a c e w a v e .

A s sh o w n in F i e ld (1 9 9 5 ), t h e a r r i v a l t im es o f m a n y o ft h e s e p h a s e s c a n b e p r e d i c t e d u s i n g a s i m p l e m o d e l w h e r et h e w a v e s a r e s c a t t er e d f r o m t h e b a s i n e d g e i m p l i e d b y t h eg rav i ty d a t a ( a t t h e S A F ; F ig . l c ) . H o w ev er , a s d i scu ssed i nth a t a r t i c l e an d su m m ar i zed l a t e r h e re , an i n t e rp re t a t i o n m u -tu a l l y co n s i s t en t am o n g th i s an d o th e r s t ru c tu ra l co n s t r a in t s( e . g ., t h e g rav i ty - d a t a d ep th s , t h e sp ec t r a l an a ly ses p resen t edin t h i s a r ti c l e ) h as n o t y e t b een o b t a in ed . T h e re fo re , a d e -t a i l ed ex p lan a t io n o f t h e v a r io u s o b se r v ed p h ases i s n o t a t -t e m p t e d h e r e b u t p o s t p o n e d u n t i l t h e a n a l y s i s o f o n g o i n gm u l t i - d i m e n s i o n a l m o d e l i n g i s c o m p l e t e .

I n s p i t e o f o u r i n c o m p l e t e u n d e r s t a n d i n g o f t h e t i m es e r ie s , t h e o b s e r v a t i o n s a r e c l e a r l y d o m i n a t e d b y w a v e s s c a t -t e r ed f ro m th e n o r th eas t b as in ed g e ( a t t h e S A F ) . T h e ab u n -d a n c e o f a f t e r s h o c k d a t a , a n d t he p r e s e n c e o f n e a r b y b e d r o c ks i t e s , p ro v id es t h e u n iq u e o p p o r tu n i ty t o ex am in e v a r io u ses t im a te s o f sp ec t r a l am p l i f i ca t i o n in a v a l l ey t h a t ex h ib i t s as t ro n g m u l t i -d im en s io n a l r e sp o n se ( i n a t l ea s t a 2 D sen se ) .

O b s e r v e d S p e c t r a l A m p l i f i c a t i o nS e d i m e n t t o B e d r o c k S p e c t r a l R a t i o sL o g -av e rag e sp ec t r a l r a t i o s , r e l a t i v e t o t h e b ed ro ck s i t e

R O K W , w e r e c o m p u t e d f o r e a c h s i t e u s in g 4 0 - s e c w i n d o w ss t a r t i n g 1 sec b e fo re t h e S -w av e a r r i v a l . A g a in , s i n ce t h eb a s i n s i t e s a r e d o m i n a t e d b y e n e r g y p r o p a g a t i n g f r o m t h en o r t h e a s t e d g e , t h e h o r iz o n t a l c o m p o n e n t s h a v e b e e n r o t a t e din to a co o rd in a t e sy s t em p a ra l l e l an d p e rp en d icu l a r t o t h ev a l l ey ax i s (N 4 5 W ) . T h e r e su l t s a r e sh o w n in F ig u re 5 .B e f o r e t a k i n g t h e r a ti o s , e a c h s p e c t r u m w a s s m o o t h e d w i t ha b o x c a r w i n d o w o f w i d t h t h a t i n c re a s e d g e o m e t r i c a l l y w i t hf r eq u e n cy (0 . 0 5 H z a t 0 .1 H z , 0 . 2 H z a t 1 H z , an d 0 . 3 4 H za t 1 0 H z) . F u r th e rm o re , d a t a w e re ex c lu d e d i f t h e sp ec t r a lam p l i t u d e o f t h e s ig n a l w as n o t t h r ee t im es g rea t e r t h an t h a to f t h e p r e - e v e n t n o i s e ( s c a l e d t o a c c o u n t f o r p o s s i b l e d i f f e r-en ces i n w in d o w l en g th s ) . I n fo rm a t io n o n t h e 1 01 a f t e r -s h o c k s u s e d i s g i v e n i n T a b l e 2 , w h i c h a l s o s h o w s w h i c hs t a t i o n s r eco rd ed each ev en t .

R O K W w a s c h o s e n a s t h e r e f e r e n c e s i t e s i n c e i t r e c o r d e d


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9 9 6 E . H . F i el d

T a b l e 2Th e Land ers/Big Bear aftershocks used in this study. Al l occurred in July of 1992 . Th e event inform ation i s from the Southern

Cal i fornia Seismic Network. The aster isks indicate that the event was recorded at that s i te . The underl ined events are those used inthe stacks shown in Figure 4 .

Event Mag D epth Lat i tude Longitude(d:hr:min:sec) ( M L ) ( k m ) (degrees) (degrees) R O K W G O L F F R E D J E A N F I R E J E F F R O K E R O K N

01:07:40 :29 3 .6 9 .00 34.332 243.538 * - - * - - - - * - -01:19:36 :28 3 .2 0 .35 34.171 243.589 * - - - - - - * - - - -01:20:53 :56 3 .0 1 .42 34.281 243.269 * - - - - - - * - - - -0 2 :1 6 : 05 : 3 7 2 .6 1 .5 9 3 4 .3 2 6 24 3 .5 4 0 * - - * . . . .0 2 :1 6 : 32 : 4 6 3 .2 0 . 1 4 3 4 .3 4 0 24 3 .3 3 0 * - - * . . . .0 2 :1 7 : 01 : 5 6 2 .5 9 . 3 7 3 4 .2 4 5 24 3 .6 3 6 * - - * . . . .0 2 :1 7 : 56 : 3 8 2 .9 0 . 6 1 3 4 .2 6 1 24 3 .2 3 9 * - - * . . . .02:23:08 :50 2 .6 3 .59 34.105 243.589 * - - * - - - - - - *02:23:57 :05 2 .7 1 .83 34.069 243.626 * - - * - - - - - - *0 3 :0 1 : 05 : 5 0 2 .5 4 .7 1 3 4 .0 0 8 24 3 .6 5 1 * . . . . . *0 3 :0 1 : 18 : 3 5 2 .8 0 .0 1 3 4 .2 4 4 24 3 .6 1 1 * - - * . . . .03:03:51 :22 2 .9 2 .14 34.063 243.634 * - - * - - * * *03:04:15 :50 3 .0 10.8 34.209 243.230 * - - * - - * * *0 3 :0 4 : 54 : 1 4 2 .4 1 .1 9 3 4 .1 5 1 24 3 .5 7 2 * . . . . * *03:05:28 :06 2 .6 3 .42 34.249 243.277 * - - * - - - - - - *03:05:55 :42 3 .3 2 .98 34.018 243.652 * - - * - - * * *0 3 :0 6 : 27 : 3 2 2 .5 3 . 0 4 3 4 .4 2 4 24 3 .4 8 9 * . . . . * - -0 3 :1 9 : 46 : 4 4 2 .8 1 .8 6 3 4 .0 4 7 24 3 .6 4 9 * . . . . * *03:19:49 :56 3 .7 2 .48 34.122 243.588 * - - * - - * * *03:20:38 :06 2 .8 0 .72 34.022 243.644 * - - * - - * * - -03:20:52 :46 2 .9 0 .00 34.291 243.280 * - - * - - * * - -03:21:18 :22 3 .6 4 .84 34.619 243.357 * - - * - - * * *03:21:52 :20 3 .3 1 .98 34.055 243.620 * - - * - - * * *0 3 :2 2 : 52 : 5 1 2 .9 3 . 7 4 3 4 .1 9 9 24 3 .1 3 1 * . . . . . *04:00:12 :09 3 .0 1 .33 33.993 243.627 * - - - - - - * * - -04:02:32 :00 3 .3 2 .77 34.089 243.144 * - - - - - - * * *0 4 :0 3 : 29 : 0 4 2 .9 1 .7 3 3 4 .1 0 3 24 3 .1 4 4 * . . . . * *04:04:41 :43 2 .6 3 .64 34.078 243.622 * - - - - - - * * *04:04:48 :50 3 .3 2 .83 33.927 243.673 * - - - - - - * * *0 4 :0 4 : 54 : 1 5 3 .1 2 .8 5 3 4 .2 2 2 24 3 .2 2 7 * . . . . * *0 4 :0 5 : 29 : 5 1 2 .8 8 . 5 0 3 4 .4 1 9 24 3 .5 2 4 * . . . . * *0 4 :0 5 : 48 : 4 2 2 .8 4 .3 0 3 4 .2 5 5 24 3 .5 6 4 * . . . . * *04:05:52 :04 3 .1 1 .73 34.091 243.621 * - - - - - - * * *04:06:09 :52 3 .1 2 .97 34.089 243.144 * - - * - - - - * *04:06:22 :02 2 .6 6 .00 34.246 243.215 * - - * - - - - * *04:07:11 :54 2 .9 4 .64 34.180 243.568 * - - * - - - - * *04:08:08 :08 2 .7 2 .78 34.070 243.634 * - - * - - * * *04:08:25 :31 2 .6 1 .12 34.131 243.602 * - - * - - - - * *0 4 :0 8 : 56 : 4 6 2 .6 5 .1 4 3 4 .3 9 0 24 3 .5 3 5 * . . . . * *0 4 :0 9 : 23 : 4 0 2 .8 1 .0 0 3 4 .5 6 5 24 3 .4 7 9 * . . . . * - -04:09:36: 01 3 .3 3 .41 34.293 243.114 * - - * - - * * - -0 4 :1 0 : 33 : 4 0 3 .4 7 .0 9 3 4 .3 1 1 24 3 .5 7 2 * - - * . . . .04:14:03: 39 2 .8 3 .11 33.978 243.721 * - - * - - * - - - -04:17:16: 24 2 .8 2 .43 33.873 243.743 * - - * - - - - * *05:01:58: 18 3 .2 7 .80 34.314 243.546 * - - * - - * - - - -05:03:23: 12 2 .4 3 .80 33.929 243.669 * * * * * - - - -05 : 0 4: 4 5: 4 4 3 .0 4 .2 3 3 4 .6 4 5 24 3 .3 4 6 * * * . . . .05:05:49: 38 3 .1 3 .20 33.945 243.601 * * * * * - - - -05:11:14: 38 3 .7 2 .53 34.068 243.636 * * * * * - - - -05:11:28 :22 3 .0 9 .44 34.170 243.180 * * * * * - - - -0 5 :1 1 : 34 : 1 1 2 .9 4 .4 2 3 4 .2 0 4 24 3 .1 3 3 * * * . . . .05:11:58 :12 2 .6 0 .00 33.957 243.661 * * * * * - - - -05:12:01 :54 3 .2 7 .46 34.245 243.210 * * * * - - - - - -0 5 :1 9 : 31 : 2 2 2 .3 1 0. 0 3 4 .1 4 1 24 3 .1 3 6 * - - * . . . .05 . :22:3 3:45 4 .3 0 .00 34.583 243.696 * - - * * * - - - -06:00:15 :30 3 .0 4 .77 34.101 243.602 * - - * * * - - - -0 6 :0 0 : 44 : 4 7 2 .9 3 . 9 4 3 4 .4 7 1 24 3 .5 3 8 * - - * . . . .06:01:11 :37 3 .5 2 .56 34.222 243.137 * - - * * * - - - -06:02:13 :58 3 .4 0 .01 34.564 243.717 * - - - - - - * - - - -

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Spe c t ra l Am pl i f i c a t ion in a Se dim e nt -F i l l e d Val l e y Ex hib i t ing C le ar Bas in-Edge - Induc e d Wav e s 99 7T a b l e 2

C o n t i n u e dEvent Mag Depth Latitude Longitude

(d:hr:min:sec) (ML) (km) (degrees) (degrees) ROKW GOLF FRED JEAN FIRE JEFF ROKE ROKN0 6 : 0 2 : 5 9 : 2 6 2 . 6 4 . 4 1 3 4 . 1 7 4 2 4 3 . 5 6 8 * * * . . . . .0 6 : 0 4 : 4 8 : 3 4 2 . 6 1 0 . 2 3 4 . 0 5 2 2 4 3 . 5 7 2 * * * * * - - - - - -0 6 : 0 6 : 0 0 : 4 4 3 . 2 2 . 8 2 3 4 . 1 0 1 2 4 3 . 6 1 7 * * * * . . . .0 6 : 1 1 : 0 3 : 1 3 3 . 1 1 0 . 7 3 4 . 1 6 5 2 4 3 . 1 7 2 * * * * . . . .0 6 : 1 1 : 3 5 : 3 3 2 . 9 1 0 .1 3 4 . 0 9 3 2 4 3 . 5 5 4 * - - * * * - - - - - -0 6 : 1 1 : 3 8 : 0 3 3 . 2 9 . 2 5 3 4 . 0 9 4 2 4 3 . 5 5 2 * * * . . . . .0 6 : 1 1 : 4 2 : 5 3 3 . 2 5 . 6 7 3 4 . 1 2 7 2 4 3 . 0 8 4 * * * * * - - - - - -0 6 : 1 1 : 4 6 : 3 4 3 . 3 1 . 99 3 4 . 2 2 1 2 4 3 . 2 5 5 * - - * * * - - - - - -0 6 : 1 1 : 5 9 : 3 3 2 . 4 2 . 6 0 3 4 . 1 3 1 2 4 3 . 5 9 5 * - - * . . . . .0 6 : 1 2 : 0 0 : 5 9 4 . 4 1 . 7 9 3 4 . 0 9 2 2 4 3 . 6 3 1 * * * * * - - - - - -0 6 : 1 2 : 2 6 : 1 2 3 . 2 1 . 7 1 3 4 . 0 4 7 2 4 3 . 6 3 5 * * * * * - - - - - -0 6 : 1 2 : 4 8 : 2 5 3 . 5 4 . 4 0 3 4 . 3 1 2 2 4 3 . 5 4 2 * - - * * * - - - - - -0 6 : 1 3 : 1 5 : 0 9 2 . 9 5 . 0 0 3 4 . 2 3 8 2 4 3 . 1 4 3 * * * * . . . .0 6 : 1 4 : 1 9 : 4 5 3 . 0 3 . 8 5 3 4 . 3 7 0 2 4 3 . 5 3 4 * - - * . . . . .0 6 : 1 8 : 0 6 : 3 6 3 . 2 0 . 4 8 3 4 . 4 5 7 2 4 3 . 5 2 4 * - - * * * - - - - - -0 6 : 1 8 : 2 7 : 2 7 3 . 6 1 . 11 3 4 . 1 5 2 2 4 3 . 5 9 4 * - - * * * - - - - - -0 6 : 1 9 : 4 1 : 3 7 4 . 3 3 . 2 7 3 4 . 0 8 2 2 4 3 . 6 2 2 * - - * * * - - - - - -0 6 : 2 0 : 5 6 : 5 2 2 . 9 3 . 3 8 3 4 . 0 9 9 2 4 3 . 6 1 9 * - - * * . . . .0 7 : 0 1 : 4 5 : 3 8 3 . 3 5 . 5 1 3 4 . 2 3 2 2 4 3 . 1 0 6 * - - * * * - - - - - -0 7 : 0 8 : 2 1 : 0 3 3 . 1 3 . 2 4 3 4 . 0 6 9 2 4 3 . 6 1 9 * * * * * - - - - - -0 7 : 0 8 : 3 8 : 0 3 3 . 5 1 . 7 6 3 4 . 2 1 0 2 4 3 . 2 3 4 * * * * . . . .0 7 : 1 3 : 3 8 : 0 3 3 . 4 0 . 0 1 3 4 . 2 3 0 2 4 3 . 1 6 8 * * * * . . . .0 7 : 1 3 : 5 3 : 2 8 3 . 4 0 . 4 6 3 4 . 3 9 8 2 4 3 . 5 3 6 * * * . . . . .0 7 : 1 4 : 5 1 : 5 5 3 . 0 0 . 0 0 3 4 . 2 9 9 2 4 3 . 5 2 9 * * * . . . . .0 7 : 1 6 : 1 7 : 5 4 3 . 1 0 . 9 0 3 4 . 2 4 7 2 4 3 . 2 8 5 * * * . . . . .0 7 : 1 6 : 4 7 : 3 5 3 . 2 0 . 8 0 3 4 . 4 3 1 2 4 3 . 5 2 1 * * . . . . . .0 7 : 2 1 : 0 1 : 1 0 3 . 6 7 . 7 8 3 3 . 9 5 2 2 4 3 . 6 4 3 * * * * * - - - - - -0 7 : 2 2 : 0 9 : 2 8 3 . 4 2 . 5 3 3 4 . 3 4 1 2 4 3 . 5 3 3 * * * * * - - - - - -0 7 : 2 2 : 2 1 : 4 5 3 .1 0 . 3 2 3 4 . 2 7 3 2 4 3 . 2 7 5 * * * . . . . .0 8 : 0 2 : 2 3 : 1 1 4 . 7 6 . 0 0 3 4 . 5 7 6 2 4 3 . 6 6 4 * * * * * - - - - - -0 8 : 0 8 : 0 5 : 3 8 3 . 3 1 0 . 5 3 4 . 6 0 5 2 4 3 . 6 4 9 * * * * * - - - - - -0 9 : 0 0 : 2 2 : 2 9 2 . 7 7 . 3 9 3 3 . 9 5 4 2 4 3 . 6 4 2 * * * . . . . .0 9 : 0 1 : 4 3 : 5 7 3 . 4 0 . 0 1 3 4 . 2 3 9 2 4 3 . 1 6 3 * * * . . . . *0 9 : 0 2 : 3 4 : 3 5 3 . 5 0 . 6 6 3 4 . 2 2 4 2 4 3 . 1 5 6 * * * . . . . *0 9 : 0 2 : 3 4 : 3 6 3 . 3 0 . 0 0 3 4 . 1 4 1 2 4 3 . 5 7 7 * * * . . . . *0 9 : 0 2 : 5 6 : 5 0 3 .1 0 . 3 2 3 4 . 2 2 6 2 4 3 . 1 5 3 * * * . . . . *0 9 : 0 2 : 5 6 : 5 4 2 . 9 0 . 0 0 3 4 . 2 2 7 2 4 3 . 1 4 9 * * * . . . . *0 9 : 0 3 : 1 4 : 1 8 3 . 1 1 .8 1 3 4 . 4 2 5 2 4 3 . 5 1 8 * * * . . . . *0 9 : 0 5 : 3 7 : 3 7 2 . 5 1 0 . 9 3 4 . 1 8 2 2 4 3 . 1 3 3 * * * . . . . .0 9 : 2 2 : 4 5 : 4 5 2 . 6 0 . 8 9 3 4 . 0 9 1 2 4 3 . 6 2 9 * . . . . . . .1 0 : 0 3 : 4 0 : 1 5 3 . 0 1 . 1 6 3 4 . 3 2 5 2 4 3 . 3 4 9 * - - * . . . . *1 0 : 0 5 : 4 8 : 4 3 3 . 3 3 . 6 2 3 4 . 1 0 8 2 4 3 . 6 0 0 * - - * * - - - - - - *

m o r e e v e n t s t h a n t h e o t h e r r o c k s i t e s . A s i g n i f i c a n t s i t e r e -s p o n s e a t R O K W c a n n o t b e r u l e d o u t , s o t h e s p e c t r a l r a t i o sm a y r e p r e s e n t r e l a t iv e r a t h e r t h a n a b s o l u t e s i t e r e s p o n s e .S i n c e s i t e e f f e c t s o n b e d r o c k a r e g e n e r a l l y s i g n i f i c a n t a th i g h e r f r e q u e n c i e s , r e s u l t s a r e s h o w n h e r e o n ly b e l o w 1 0 H z( w h i c h i s a l s o t h e f r e q u e n c y r a n g e o f e n g i n e e r i n g i n t e r e s t ) .

F i g u r e 5 r e v e a l s o v e r a l l a m p l i f i c a t i o n a t t h e s e d i m e n ts i t e s f o r f r e q u e n c i e s u p t o - 7 H z , w i t h p e ak v a l u e s r e a c h i n ga s h i g h a s a f a c t o r o f 1 8 . T h e f i r s t p r o m i n e n t p e a k a t t h em a i n b a s i n s i t e s ( t h o s e s o u t h w e s t o f t h e S a n A n d r e a s F a u l t :F I R E , J E A N , G O L F , a n d F R E D ) o c c u r s b e l o w - - 0 . 6 H z . T h ef r e q u e n c y o f t h i s p e a k i n c r e a s e s f r o m 0 . 2 3 + 0 . 0 7 H z a tF I R E t o 0 . 4 8 _+ 0 . 0 6 H z a t G O L F , w h i c h i s qualitativelyc o n s i s t e n t w i t h t h e f u n d a m e n t a l r e s o n a n t f r e q u e n c y s h i f t e x -

p e c t e d f r o m t h e g r a v i t y m o d e l i n F i g u r e l c . A b o v e - 0 . 6 H z ,t h e s p ec t r a l r a t i o s l o o k q u i t e s i m i l a r b e t w e e n t h e m a i n b a s i ns i t e s ; i n f a c t , t h e d i f f e r e n c e b e t w e e n c o m p o n e n t s i s g r e a t e r .T h a t i s , a l l o f t h e s e s i t e s h a v e s t a t i s t i c a l l y e q u i v a l e n t s p e c t r a la m p l i f i c a t io n s , o n a n y p a r t i c u la r c o m p o n e n t , w h i c h i s s u r -p r i s i n g g i v e n d i f f e r en c e s s e e n i n t h e t i m e - d o m a i n o b s e r v a -t i o n s ( F i g s . 2 a n d 4 ) . T h e m a i n d i f f e r e n c e b e t w e e n t h e t w oh o r i z o n t a l c o m p o n e n t s i s a p r o m i n e n t p e a k a t - 2 . 4 H z s e e ni n t h e d i r e c t i o n p a r a l l e l t o t h e v a l l e y a x i s , w h i c h i s n o t p r e s -e n t i n t h e p e r p e n d i c u l a r d i r e c t io n . F u r t h e r m o r e , t h e e s t i m a t e sf o r t h e a x i s - p a r a l le l c o m p o n e n t h a v e p e a k s n e a r 0 . 8 , 2 . 4 , 4 . 0 ,a n d s o m e t i m e s 5 . 6 a n d 7 .2 H z ( e s p e c i a l ly a t J E A N ) , w h i c hl o o k c o n s p i c u o u s l y l i k e t h e S H r e s o n a n t f r e q u e n c i e s o f as i n g l e l a y e r o v e r a h a l f - s p a c e . T h a t t h i s c o m p o n e n t s h o u l d


8/15

998 E.H. Field

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Figure 2. The time series observed across the lin-ear array for a magni tude 4.4 aftershock (event06:12:00:59 in Table 2). All of these records wereobtained with the 5-sec velocity sensors, except forthose at JEFF and ROKN, which are integrated accel-eration (FBA) data. The epicentral distance and back-azimuth, with respect to ROKW, are --48 km andN9W, respectively. The seismograms are offset bythe distance of the site from the San Andreas Fault(SAF). Note that the east-component record at ROKEis only digital noise. The light solid lines connect theP- and S-wave arrival times between the two rock sites(ROKW and ROKE).

exhibit an SH-looking response is not surprising since thevalley-parallel direction corresponds to SH motion for en-ergy scattered from the basin edge. What is surprising is thatthe spectral amplifications look one-dimensional when thetime series do not. As discussed more later, one possibleexplanation for the similarity in response above 0.6 Hz isthat there is a shallower near-surface layer that is relativelyuniform (i.e., one dimensional) between the main basin sites.The fundamental resonance of this layer could be responsi-ble for the highest amplitude peak observed near 0.8 to 1.0Hz in the horizontal-component ratios. The effect of thedeeper basin structure would then be to channel more energytoward this shallow layer.

Figure 5 also reveals a significant response at the sedi-ment site JEFF, located outside of the main part of the basin

(northeast of the SAF). Of particular interest is the anomal-ously large response on the vertical component, which maybe related to its being positioned on the Indio Hills Fault.The bedrock site ROKN, located on the same side of thevalley as the reference site ROKW, exhibits no significantrelative site response. This gives some confidence thatROKW might represent an adequate reference site, althoughit remains possible that both of these sites have a significant,yet similar, site response. The other bedrock site, ROKE,located on the northeast side of the valley, exhibits relativeamplifications of up to a fac tor of 3. This small amplificationcould result for two possible reasons. One is that we werenot able to locate this site direc tly on bedrock, but rather onshallow sediments within 15 m of bedrock. Another is thatthis site, by virtue of being on the opposite side of the SAF,is on a separate lithospheric plate, so the path effects mightdiffer.

The observation in Figure 5 that all of the main basinsites exhibit similar site response above 0.6 Hz, yet differ-ences between components, was observed for the other typesof estimates discussed below. Therefore, in what follows,only the results for site FRED will be shown as a represen-tative example. The same geometrically increasing smooth-ing width has been applied to all spectral estimates, and theearthquake data were always excluded if the amplitudeswere not greater than 3 times that of the pre-event noise.Results for site JEFF will not be shown since this site exhibitsanomalous behavior presumably related to its location onthe Indio Hills Fault (which, although interesting, is not thefocus of this article).

Sediment to Bedrock Spectral Ratioswith Short WindowsIn Figure 6, sediment to bedrock spectral ratios for the

40-sec windows (reproduced from Fig. 5) are compared withthose for 9-sec S-wave windows that just exclude the basin-edge-induc ed waves. While both estimates exhibit some ofthe same apparent resonances, the basin-edge-inducedwaves increase the relative amplification by a factor of -2on average between 0.2 and 2.5 Hz and by up to a factor of3 at some individual frequencies. Above --4 Hz, the twoestimates are consistent, implying that the basin-edge-in-duced waves are significant only at lower frequencies.

Sediment to Be drock Spectral Ratios o f S-Wave CodaAverage spectral ratios computed from 10-sec windowsof coda, taken at both two and four times the S-wave prop-

agation time (2T and 4Ts, respectively), are shown in Figure7 along with the direct S-wave spectral ratios (reproducedfrom Fig. 5). The coda-estimate amplitudes are generallygreater than the direct S-wave estimates below - 5 Hz forthe earlier (2Ts) windows and below --3 Hz for the later(4Ts) windows. Although the frequency range of disagree-ment is less for the later coda windows, the amplitude dis-crepancy at lower frequency is larger. The discrepancy forthe earlier coda windows (2Ts) is about a factor of 1.7 on


9/15

Spe c t ra l Am p l i f ic a t ion in a Se dim e nt -F i l l e d Val l e y Ex hib i t ing C le ar Bas in -Edg e - Induc e d Wa v e s 9 9 9

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Fig ure 3. Amplitude of the phase arriving12 sec after the direct S wave on the north com -ponent at FRED (shaded in Fig. 2), relative tothe direct S-wave amplitude, as a function ofepicentral location. The relative amplitudeswere determ ined by filtering the particle-veloc-ity seismograms below 2.5 Hz (third-orderButterworth filter), measuring the peak ampli-tudes that occurred in a 5-sec window centeredon both the S-w ave arrival and 12 sec later, andthen dividing the latter amplitude by the for-mer. The filled stars represent those 18 eventsused to make the stacks shown in Figure 4(note that most plot on top o f each other).

a v e r a g e b e t w e e n 1 a n d 4 H z , w i t h d i f f e r e n c e s g r e a t e r t h a na f ac to r o f 2. 5 a t so m e in d iv id u a l f r eq u en c i e s . T h i s am p l i -t u d e d i s c r e p a n c y w a s a l s o s e e n f o r c o d a e s t i m a t e s c o m p u t e dfo r w in d o w s s t a r t i n g a t a co n s t an t t im e l ag o f 3 5 sec (w h ichi s - -2 T s fo r th e m o s t d i s t an t ev en t ) . A s d i sc u ssed m o re l a t e r ,t h is a m p l i t u d e d i s c r e p a n c y m a y b e r e l a t e d t o p r o lo n g e d r e -v e rb e ra t i o n s w i th in t h e b as in .

H o r i z o n t a l - to V e r t i c a l - C o m p o n e n t S p e c t r a l R a t i oso f S W a v e sA v e r a g e h o r i z o n ta l - t o v e r t i c a l - c o m p o n e n t ( h / v ) s p e c -

t r a l- r a ti o s i t e - r e s p o n s e e s t i m a t e s w e r e a l s o c o m p u t e d u s i n g4 0 - sec S -w av e w in d o w s . T h e r e su l t s fo r s i te FR E D a re sh o w nin F ig u re 8 , a lo n g w i th t h e sed im en t t o b ed ro ck sp ec t r a lr a t i o s r ep ro d u ced f ro m F ig u re 5 . I n co n t r a s t t o t h e r e su l ts o fs o m e p r e v i o u s s t u d i e s ( L e r m o a n d C h a v e z - G a r c i a , 1 9 9 3 ;F i e ld an d J aco b , 1 9 95 ), t h e h /v r a t i o s l o o k n o th in g l i k e t h es e d i m e n t t o b e d r o c k r a t i os . T h e r e i s , h o w e v e r , a c l e a r p e a ka t 0 . 2 4 _ + 0 . 0 4 H z th a t i s n ea r t h e fu n d am en ta l r e so n an tf r e q u e n c y a p p a r e n t i n t h e s e d i m e n t t o b e d r o c k r a t io s . T h eresu l t s fo r t h e o th e r m a in b as in s i t e s l o o k s im i l a r , ex ce p t t h el o w - f r e q u e n c y p e a k s h i f ts s y s t e m a t i c a l l y f r o m 0 . 1 6 + 0 . 02H z a t F IR E to 0 . 4 2 + 0 . 0 5 a t G O LF . T h i s sh i f t is co n s i s t en tw i th t h a t s een i n t h e sed im en t t o b ed r o ck sp ec t r a l ra t i o s (F ig.5 ) an d w i th t h e n o t io n t h a t i t r e f l ec t s a sh i f t i n t h e fu n d a -

m e n t a l r e s o n a n t f r e q u e n c y a s t h e d e e p - b a s i n s e d i m e n t s t hi nt o w a r d t h e s o u t h w e s t e d g e .

A m b i e n t - N o i s e S p e c t r a l R a t i osS e d i m e n t t o b e d r o c k s p e c t r a l r a t io s o f a m b i e n t s e i s m i c

n o i s e a r e c o m p a r e d i n F i g u r e 9 w i t h t h e S - w a v e s e d i m e n t t ob e d r o c k r a t i o s ( r e p r o d u c e d f r o m F i g . 5 ). A l s o s h o w n a r e h /vs p e c t r a l ra t i os o f t h e n o i s e . T h e s e n o i s e e s t i m a t e s w e r e c o m -p u t e d f r o m 1 6 c o n s e c u ti v e 4 0 - s e c w i n d o w s o b t a i n e d s i m u l -t an eo u s ly a t b o th s i t e s j u s t a f t e r m id n ig h t . A l th o u g h th e re i ss o m e a g r e e m e n t b e t w e e n t h e h o r i z o n t a l - c o m p o n e n t s e d i -m e n t t o b e d r o c k r a ti o s be l o w - 0 . 9 H z , a b o v e 1 H z t h e a m -p l i t u d es o f t h e n o i se r a t i o s a r e u p t o f i v e t im es g rea t e r t h ant h e S - w a v e e s t i m a t e s . T h e a g r e e m e n t i s w o r s e f o r t h e v e r -t i c a l - c o m p o n e n t s e d i m e n t t o b e d r o c k r a t io s .

T h e h /v n o i se r a t i o s i n F ig u re 9 l o o k n o th in g l i k e t h e S -w a v e r e s u lt s . H o w e v e r , t h e r e i s a p r o m i n e n t p e a k n e a r 0 . 2 5_ + 0 . 0 4 H z th a t ex h ib i t s a sh i f t i n f r eq u en cy a t t h e o th e rm a in b as in s i t e s (n o t sh o w n ) . T h ese p eak f r eq u en c i e s a r es t a t i s t i ca l l y eq u iv a l en t t o t h o se o b se rv ed in t h e S -w av e h /vra t i o s . A g a in , t h ese p ro b ab ly r e f l ec t t h e fu n d am en ta l r e so -n an t f r eq u en cy o f t h e d eep e r b as in s t ru c tu re . T h e re i s a l so as e c o n d a r y p e a k n e a r 1 H z i n t h e h / v n o i s e r a t i o s t h a t is p r e s -en t a t t h e sam e f r eq u en cy a t t h e o th e r m a in b as in s i t e s (n o ts h o w n ) . T h e r e f o r e , i t m a y w e l l c o r r e s p o n d t o t h e f u n d a m e n -


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1000 E.H. F ie ld

1"


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Spectral Amplification in a Sediment-Filled Valley Exhibiting Clear Basin-Edge-Induced Waves 1001

Para llel Pe rp en di cu lar Vertical1 8 -

15-.~ 12-~ 9

6

f i i l l t l l l I I l l l l l l l I I | l l l l l t I I I l l | I l l0.1 1.0 l0 O.1 1.0frequency (H z ) frequencyHz)I I I I Itl l l I I I I Itl l llO 0.1 1.0 10frequency (Hz)

Figu re 6. Comparison of average sedimentto bedro ck spectral ratios at FRED for 9-sec S-wave windows (solid line), which do not in-clude the basin-edge-induced waves, withthose of the 40-sec windows (dashed line, re-produced from Fig. 5). In both cases, the w in-dows started 1 sec before the S-w ave arrival.The shaded regions represent the 95% confi-dence limits.

Parallel Perpendicular

15

! ~ i i I I I I I l l l l l | l ! t l i l l | l l0.1 1.0 10 0.1 1.0frequency (H z) frequencyHz)

Vertical

1 I I I IIII I I I [ | IJl ll10 0.1 1.0 I0frequency (Hz)

Fig ure 7. Average sediment to bedrockspectral ratios f or site FRED comp uted from1 0 - s e c coda wind ows taken at twice (solid line)and four times (dot-dashed line) the S-wavepropagation time. Shown for comparison arethe 40-sec S-wave ratios (dashed line) repro-duced from Figure 5. The shaded regions rep-resent the 95 % confidence limits (to avoid clut-ter, no uncertainties are shown fo r the ratios ofcoda windows taken at four times the S-wavepropagation time).

Parallel Perpendicular,8]3

0.1 I 1 1 1 1 1 1 1 I I 1 t | t t 1 11.0 I0 0.I 1.0 I0frequency (H z ) frequ ency Hz)Fig ure 8. Comparison of average horizontal- tovertical-co mpone nt spectral ratios (solid line) with thesediment to bedrock spectral ratios (dashed line, re-produced from Fig. 5) for 40-sec S-wave windows(starting 1 sec before the arrival) at site FRED. Theshaded regions represent the 95% confidence limits.

be low 0 .6 Hz , wh ich sh i f ts toward h igher f requency in goingfrom FIRE (0 .23 + 0 .07 Hz) toward GOLF (0 .48 + 0 .06Hz) . S ince both gravi ty da ta and S-w ave a rr iva l - t ime d i ffe r-ences seen be twee n these s i tes (Figs. lc and 2 , respec t ive ly)suggest that the sediments thin in this direction, this low-frequen cy peak l ike ly represents fundamen ta l reverbera t ionsof the basin . Abov e 0 .6 Hz , w here the la rgest ampl i f icat ionsoccur , the response is remarkably simi la r be tween the mainbasin s i tes (a l though d i ffe rent be tween components) . Fur-thermore , the co mpo nent o f mot io n para l lel to the va l ley axishas prominent p eaks near odd mul t ip les of 0 .8 Hz , which

suggests the one-dimensiona l S H response of a s ingle layer.This s imi la r ity in response be tween basin s i tes i s surpr is inggiven the obvious mul t i -d imensiona l e ffec ts observed in thet ime domain . The present in te rpre ta t ion involves a re la t ive lysha l low near-surface layer tha t i s re lat ive ly uniform ( i.e ., onedimensiona l) ac ross the basin . The fund amenta l resonan t f re -quency of th is layer , which g ives r i se to the la rgest ampl i -f ica t ion fac tors , appears to be be tw een 0 .8 and 1 .0 Hz .

By com paring the spec t ral ra t ios of long S-wav e win-dows (40 sec) wi th those of rela t ive ly short windows (9 sec)tha t exc lude the basin-edge- induced waves, the mul t i -d i -mensiona l e ffec ts a re found to be inf luent ia l a t f requenc iesbe low -4 Hz . Abov e 4 Hz , the sca t te red energy appears tobe comple te ly a t tenua ted by the va l ley sediments . At lowerfrequenc ies, the basin-edge- induced waves increase the am-pl i f ica t ion leve ls by an approxim ate fac tor of 2 (on averagebe tween 0 .2 and 2 .5 Hz) . Knowing the threshold f requencywhere mul t i -d imensiona l e ffec ts a re no longer s ignif icantwi l l be useful in theore t ica l model ing since computa t iona lconst ra in ts usua l ly govern the h ighest f requency tha t can beconsidered .

Sediment to bedrock spec t ra l ra t io est imates obta inedusing coda waves show signif icant ly grea te r ampl i f ica t ionfac tors than those obta ined from the 40-sec S-wave seg-ments . This i s espec ia l ly t rue be tween 1 and 4 Hz , wherethe d isc repancy is a fac tor of 1 .7 on average and up to afac tor of 2 .5 a t some frequenc ies. Suc h an inconsistency be-tween d i rec t S wave and coda est imates a t sediment s i tes hasbeen observed in a t least three o ther s tudies (Margher i t i etal., 1994; Seekins et aI., 1995; Steidl et al., 1995) , which


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1002 E.H . Field

e~

Parallel50_-

0 . 1 I I I I l t l l l I I I I I I l l l

0.1 1.0 10frequency (Hz)

Perpendicular

I I ~ t l l t l I I I I I I l ~ l0.1 1.0frequency (Hz)

Vertical. ~

.......... " i I I I I H I I f t l l l l l lI0 0.1 1.0 10frequency (Hz)

Figure 9. Average spectral ratios at FREDcomputed using sixteen 40-sec window s of am-bient seismic noise. The dot-dashed line rep-resents those taken with respect to the bedrocksite (ROKW), and the solid line represents thosetaken with respect to the vertical component(Nakamura's estimate). For comparison, theaverage S-wave sediment to bedrock ratios (re-produced from Fig. 5) are shown with thedashed line. The shaded regions represent the95% confidence limits.

cal ls into ques t ion the re l iabi l i ty of applying coda-amplif i -cat ion factors . Howev er, there are a t leas t two s tudies show-ing cons is tency betw een the two at sediment s i tes (Tsuj iura ,1978; Kato et al., 1995), leaving the issue unresolved. Asfirs t sugges ted by Phil l ips and Aki (1986), the discrepancym ay be re la ted to the p ro longed reve rbe ra t ion o f ene rgy a tthe sediment s i tes . There is , however, an a l ternat ive expla-nat ion. Coda es t imates are bel ieved to reflect the averageresponse for energy incident a t a varie ty of angles and azi-muths , whereas the direct S-wave es t imates in this s tudyrepresen t the re sponse to w aves em ana t ing f rom the Lande rs /Big Bear aftershock sequence. Therefore , i t is poss ible thatthe coda es t imates accurate ly reflect the average responseexpected g iven a varie ty of source locat ions , which could belarger than the es t imates obta ined for the l imited source lo-cat ions avai lable in this s tudy. Unfortunate ly, n ei ther one ofthese explanat ions c an be ruled out here . I t is interes t ing tonote , however, that the coda-amp lif icat ion factor of --9 .0 forthe vert ical compo nent , avera ged between 1 and 4 Hz, agreeswith that of the direct S-wave es t imate for the horizontalcomponent . S ince most of the previous coda-amplif icat ions tudies we re based on vert ical-co mpon ent data (e .g. , Phil l ipsand Aki , 1986; Mayeda et al., 1991; Su and Aki, 1995), thisagreement implies that these previous resul ts may be appl i-cable to horizontal-co mpon ent S-wave amplif icat ion factors .

For several sediment s i tes in Mexico, Lermo andChav ez-G arcia (1993) found that h/v spectra l ra t ios of Swaves rev ealed the frequenc y and amplif icat ion factor of thefundamental resonant frequency observed in sediment tobedrock spectra l ra t ios . F ie ld and Jacob (1995) found thatsuch h/v ra t ios revealed the overal l frequency-dependentcharacter of s i te response, including several higher-modepeaks , but that the ampli tudes w ere off by a frequency-in-dependent scal ing factor of - 1 .6. Other more recent s tudieshave found general ly mixed, yet encouraging, resul ts(Lache t et al., 1995; Seekins et al., 1995; Malagnini et al.,1996). These es t imates are sometim es referred to as receiver-funct ion-type es t imates (F ie ld and Jacob, 1995) because ofthe analo gy with the so-cal led s tudies that ut i l ize te leseismicP waves to infer crus ta l and upper mantle s t ructure (Lang-ston, 1979; Owens et al., 1984). The success of this methodappears to be based on the fact that sediments have re la t ivelyl i t tle influence on the vert ical ground motion (predominan tly

P waves converted from S waves). Therefore , the vert icalcom ponen t m ay prov ide a conven ien t e s t im a te o f the sourceand path effects (a t leas t for the frequencies where the sed-iments are s ignif icant ly amplifying).

In this s tudy, the h/v spectra l ra t ios of S waves looknothing l ike the sediment to bedro ck ra t ios . This may be dueto the ve rt i ca l com ponen t be ing dom ina ted by bas in -edge -induced wav es ra ther than S- to -P convers ions a t the bedrockcontact below the s i te . There is , howev er, a prominen t peakat low frequency with a shif t between s i tes as the depth tobedrock changes . This sugges ts the peak is re la ted to thefundame ntal resonant frequen cy of the bas in. The frequencyof this peak is general ly abou t 0.8 t imes that observed in thesediment to bedr ock ra t ios , a l though giv en the uncerta inties ,this difference ma y not be s ta t is t ica lly s ignif icant . Therefore ,while the h/v spectra l ra t ios of S waves do not agree withthe sedimen t to bedrock ra t ios , they do a ppear to reveal thefundamental resonant frequency of the deep bas in s t ructure .

Although sediment to bedrock ra t ios of ambient se ismicno ise do no t co m pare favorab ly wi th those ob ta ined f rom Swaves , the h/v noise ra t ios appear to reveal resonant fre-quencies . Many recent s tudies , both observat ional (Naka-mura, 1989; Omachi et al., 1991; Field and Jacob, 1993;Lerm o and Chavez -Garc ia , 1994 ; Yam anaka et al., 1994;Field et al., 1995; Field and Jacob, 1995; Seekins et aL,1995) and theoret ical (F ie ld and Jacob, 1993; Lermo andChavez-Garcia , 1994; Lachet and Bard, 1995), have shownthat h/v ra t ios of ambient se ismic noise can reveal the fun-damental resonant frequency of sediment deposi ts . This isoften referred to as Nakamura ' s es t imate , named after thefirs t person to demonstra te the method empirical ly (Naka-mura, 1989). However, s ince the peak a t the fundamentalresonant frequency is thought to be a manifes ta t ion of Ray-le igh-wave pa r t i c le m ot ion (Le rm o and Chavez -Garc ia ,1994; Lachet and Bard, 1994), h/v noise ratios are also re-ferred to as "e l l ipt ic i ty" es t imates in the l i tera ture (Yaman -aka et al., 1994).

The h/v noise ra t ios observed in this s tudy have twopeaks . The f i rs t occurs below 0.6 Hz, which is s ta t is t ica l lyequivalent to that observed in the h/v S-waves ra t ios . Thispeak a lso has the associa ted shif t in frequency between themain bas in s i tes , implying that i t too reflects the fundam entalresonant frequen cy of the deep bas in s t ructure . There is a lso


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Spe c t ra l Am pl i f i c a t ion in a Se dim e n t -F i l l e d Val l e y Ex hib i t ing C le ar Bas in-Ed ge - Ind uc e d Wa v e s 1003

a s e c o n d a r y p e a k i n t h e h / v n o i s e r a t io s n e a r 1 H z t h a t d o e sn o t s h i f t in f r e q u e n c y b e t w e e n t h e m a i n b a s i n s i t e s. T h i s m a yr e f l e c t t h e f u n d a m e n t a l r e s o n a n t f r e q u e n c y o f t h e i n f e r r e ds h a l l o w n e a r - s u r f a c e l a y e r ( t h a t i s r e l a t i v e l y u n i f o r m b e -tw een s i t e s ) . T h e re fo re , w h i l e t h e n o i se d a t a d o n o t l o o kp ro m is in g i n t e rm s o f d i r ec t l y p red i c t i n g s i t e r e sp o n se , t h eh / v n o i s e r a t i o s a p p e a r t o r e v e a l t h e f u n d a m e n t a l r e s o n a n tf r eq u en c i e s o f tw o w id e ly d i f f e r en t s i ze sca l e s , th a t o f th ed e e p e r b a s i n a n d t h a t o f t he i n f e r r e d s h a l l o w u n i f o r m n e a r -s u r f a c e l a y e r . T h i s i n f o r m a t i o n p r o v i d e s v a l u a b l e c o n s t r a in t so n th e b as in s t ru c tu re .

T h e f u n d a m e n t a l r e s o n a n t f r e q u e n c y o f a s e d i m e n t s i t ei s g e n e r a l l y e q u a l t o t h e a v e r a g e S - w a v e v e l o c i t y d i v i de d b yfo u r t im es t h e sed im en t t h i ck n ess ( t h e so -ca l l ed "q u a r t e r -w a v e l e n g t h " r u l e) . T h e r e f o r e , i f c o n s t ra i n t s c a n b e p l a c e d o ne i th e r t h e sed im en t t h i ck n ess o r t h e S -w av e v e lo c i t y , t h ent h e o t h e r c a n b e d e t e r m i n e d f r o m t h e o b s e r v e d r e s o n a n t f r e -q u e n c y . E f f o r t s t o d e t e r m i n e t h e b a s i n s t r uc t u r e f r o m s u c hco n s id e ra t i o n s a r e d e t a i l ed e l sew h ere (F i e ld , 1 9 9 5 ) . U n fo r -tu n a t e ly , a m u tu a l ly co n s i s t en t p i c tu re h as n o t y e t em erg ed .F o r ex am p le , t h e g rav i ty d a t a (F ig . l c ) su g g es t s a d ep th t ob a s e m e n t o f 5 _ 1 k m a t F IR E . W i t h t h e o b s e r v e d r e s o n a n tf r e q u e n c y o f - - 0 . 2 3 H z a n d t h e q u a r t e r w a v e l e n g t h r u le , t hi st r a n s la t e s i n t o a n u n r e a l i st i c a l ly h i g h a v e r a g e S - w a v e v e l o c -i t y o f 3 . 7 t o 5 . 5 k m /sec . T h e re fo re , e i t h e r t h e g rav i ty -d a t ad e p t h e s t i m a t e s h a v e a g r o s s s y s t e m a t i c e r r o r o r t h e i m p e -d a n c e c o n t r a s t g i v i n g r i s e t o t he o b s e r v e d r e s o n a n c e i s s o m e -w h e r e a b o v e t h e b a s e m e n t c o n t a c t w i th i n t h e s e d i m e n t s .

B y m a k i n g v a r i o u s a s s u m p t i o n s , o n e c a n t r y t o e s ti m a t es h e a r - w a v e v e l o c i t i e s f r o m t h e a r r i v a l t i m e d e l a y s s e e n i nF i g u r e 2 o r f r o m t h e v a r i o u s p h a s e s s e e n i n t he s h e a r - w a v es t ack s i n F ig u re 4 (F i e ld , 1 9 9 5 ) . G iv en o b se rv a t io n a l u n ce r -t a i nt i e s a n d t h e r a n g e o f a s s u m p t i o n s o n e c a n m a k e , t h e a v -e r a g e s h e a r - w a v e v e l o c i t y e s ti m a t e s v a r y b e t w e e n - - 0 . 4 a n d- -0 . 9 k m /sec . W i th t h e q u a r t e r -w av e l en g th ru l e , t h i s t r an s -l a t e s i n to an im p ed an ce -co n t r a s t d ep th b e tw een 0 . 5 an d 1 . 1k m a t F IR E (F i e ld , 1 9 9 5 ). C o n s t r a in in g t h e av e rag e -v e lo c i t y /d e p t h t r a d e - o f f f o r t h e r e l a t i v e l y s h a l l ow u n i f o r m l a y e r i n -f e r r e d b e t w e e n t h e s i te s i s e v e n m o r e p r o b l e m a t i c . A t t h i sp o in t , t h e re i s n o i n d ep en d en t ev id en ce fo r i t s ex i s t en ce , j u s tt h e p e r s is t e n t p e a k s a t o d d m u l t i p le s o f 0 .8 H z a t t h e m a i nb as in s i te s .

A l t h o u g h t h e a b s o l u t e d e p t h a n d S - w a v e v e l o c i t i e s i nth e b as in a r e n o t y e t k n o w n , t h e r e l a t i v e ch an g e i n d ep th t ob a s e m e n t i s w e l l c o n s t r a i n e d f r o m t h e o b s e r v e d s h i f t in r e s -o n an t f r eq u en c i e s , a r r i v a l t im e d e l ay s i n t h e d i r ec t S -w av e ,t h e g r a v i t y d a ta , a n d P - t o S - w a v e c o n v e r s i o n s a t t he b a s e -m en t co n t ac t (F i e ld , 1 9 9 5 ) . C lea r ly , b o reh o le an d /o r r e f r ac -t i o n / r e f l ec t i o n s tu d i e s w o u ld p ro v id e ad d i t i o n a l co n s t r a in t san d , t h e re fo re , m ay b e p u r su ed in t h e fu tu re . I n t h e m ean -t i m e , i t is h o p e d t h a t o n g o i n g m u l t i - d i m e n s i o n a l m o d e l i n go f t h e b a s i n r e s p o n s e w i l l s i m u l t a n e o u s l y p r o v i d e a d d i t io n a lc o n s t r a in t s o n t h e s t r u c t u r e a n d m a k e s e n s e o f r e s o n a n tp eak s , a r r i v a l t im es , p a r t i c l e m o t io n , an d H i lb e r t - t r an s fo rmef fec t s s een i n t h e o b s e rv a t io n s . I f a s a t i s f ac to ry f it can b eo b ta in ed , t h en t h e im p o r t an t q u es t i o n o f h o w v a r i ab l e t h e

r e s p o n s e i s w i t h r e s p e c t t o o t h e r s o u r c e l o c a t i o n s c a n b eex p lo red w i th ad d i t i o n a l s im u la t i o n s .

C o n c l u s i o n sS ev e ra l co n c lu s io n s can b e m ad e r eg a rd in g t h i s s i t e t h a t

ex h ib i t s a c l ea r m u l t i -d im en s io n a l r e sp o n se ( i n a t l ea s t a 2 Ds e n s e) . F i r s t, b y c o m p a r i n g s e d i m e n t t o b e d r o c k s p e c t r a l r a -t i o s o f l o n g S - w a v e w i n d o w s w i t h r e l a t i v e l y s h or t w i n d o w s ,t h e b a s i n - e d g e - i n d u c e d w a v e s a r e f o u n d t o b e s i g n i f i c a n to n l y b e l o w - - 4 H z , w h e r e t h e y b o o s t s p e c t ra l a m p l i f ic a t i o n s( o n a v e r a g e b e t w e e n 0 . 2 a n d 2 .5 H z ) b y a n a p p r o x i m a t ef a c t o r o f 2 . T h e r e f o r e , m u l t i - d im e n s i o n a l e f f e c t s m i g h t b ea p p r o x i m a t e l y a c c o u n t e d f o r b y a p p l y i n g a f a c t o r o f 2 t o1 D -b ased p red i c t i o n s a t t h o se f r eq u en c i e s . S eco n d , s i t e -r e s p o n s e e s t i m a t e s b a s e d o n c o d a w a v e s s i g n i f ic a n t ly o v e r -e s t i m a t e a m p l i t u d e s b e l o w 3 t o 4 H z ( b y u p t o a f a c t o r o f2 . 5 ) . T h i r d , s e d i m e n t t o b e d r o c k r a t i o s o f a m b i e n t n o i s es h o w l i t t l e a g r e e m e n t w i t h t h o s e b a s e d o n S w a v e s . S i m i -l a r ly , h / v r a t io s o f b o t h S - w a v e d a t a a n d a m b i e n t n o i s e d on o t c o m p a r e f a v o r a b l y w i t h s e d i m e n t t o b e d r o c k S - w a v e ra -t i o s , ex cep t i n i d en t i fy in g fu n d am en ta l r e so n an t f r eq u en c i e sth a t can p ro v id e v a lu ab l e s t ru c tu ra l co n s t r a in t s . T h ese co n -c lu s io n s ap p ly t o a sp ec i f i c s e t o f s i t e s an d so u rces (w eak -m o t i o n L a n d e r s / B i g B e a r a f t e r s ho c k s ) , s o a d d i t io n a l s t u d i esw i l l b e n eed ed b e fo re g en e ra l i z in g t o o th e r s i t e s , t o o th e rso u rce l o ca t i o n s , an d to s t ro n g g ro u n d m o t io n .

A c k n o w l e d g m e n t sI would l ike to thank Klans Jacob for ob tain ing the in i t i a l f inancial sup-

p o r t f o r t h is p ro j ec t. P au l F r i b e rg , N o e l B a r s t o w , an d D o u g J o h n s o n w e rea l l v i ta l p a r t i c ip an t s i n t h e f i e l d d ep l o y m en t , an d A m y C l em en t h e l p ed w i t hd a t a p ro ces s i n g an d p r e l i m i n a ry an a l y s i s . I am a l s o g r a t e fu l to K e i A k i ,S u s an H o u g h , Y u t ak a N ak am u ra , an d P au l S p u d i ch fo r r ev i ew i n g th i sm an u s c r i p t , e s p ec i a l l y P au l, w h o s e co m m en t s l ed t o a s i g n i f i can t r ev i s io n .F i n a ll y , I w o u l d l i k e t o t h an k G eo f f r ey E l y , w h o s e a s s i s t an ce s av ed m eh o u r s i n p r ep a r i n g F ig u re l a (m ad e w i t h G M T ) , an d B o b J ack en s fo r s h a r i n gh i s g r av i t y - i n v e r s io n r e s u lt s . T h e d a t a co l l ec t i o n an d p ro ces s i n g w as s u p -p o r t ed b y t h e N a t i o n a l C en t e r f o r E a r t h q u ak e E n g i n ee r i n g R es ea rch G ran tN u m b er N C E E R -9 2 -1 0 0 2 , an d t h e r e s ea r ch w as s u p p o r t ed b y th e S o u t h e rnC a l i fo rn ia E a r t h q u ak e C en t e r (S C E C ), w h i ch i s f u n d ed b y t h e N a t i o n a l S c i -en ce F o u n d a t i o n u n d e r co o p e ra t i v e ag reem en t E A R -8 9 2 0 1 3 6 an d U n i t edS t a t e s G eo l o g i ca l S u rv ey co o p e ra t i v e ag reem en t 1 4 -0 8 -00 0 1 -A 0 8 9 9 . T h i si s SCEC publ icat ion nu mbe r 227 .

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spectral amplification in a sediment filled valley exhibiting clear basin-edge-induced waves

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