UBC Theses and Dissertations

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UBC Theses and Dissertations

Seismic structure across the active subduction zone of western Canada Spence, George Daniel 1984

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SEISMIC STRUCTURE ACROSS THE ACTIVE SUBDUCTION ZONE OF WESTERN CANADA by GEORGE DANIEL SPENCE M . S c . The U n i v e r s i t y Of B r i t i s h C o l u m b i a , 1976 B . S c . ( H o n . ) The U n i v e r s i t y Of C a l g a r y , 1971 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES Department Of G e o p h y s i c s And As t ronomy We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA J u l y 1984 © George D a n i e l Spence , 1984 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e head o f my d e p a r t m e n t o r by h i s o r h e r r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f U f c O p " y ^ > ^ r T L i r U H O W u j The U n i v e r s i t y o f B r i t i s h C o l u m b i a 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5 D a t e > E-6 ( 2/79^ i i F o r t h e i r c o n s t a n t s u p p o r t and c o n c e r n , I d e d i c a t e t h i s t h e s i s t o my p a r e n t s , George D . Spence and D i a n S p e n c e . i i i ABSTRACT The V a n c o u v e r I s l a n d S e i s m i c P r o j e c t (VISP) was c o n d u c t e d i n 1980 t o s t u d y the s t r u c t u r e of the s u b d u c t i n g o c e a n i c Juan de Fuca p l a t e and the o v e r r i d i n g c o n t i n e n t a l A m e r i c a p l a t e . The p r i n c i p a l s e i s m i c r e f r a c t i o n l i n e ( l i n e I ) was a 350 km o n s h o r e -o f f s h o r e p r o f i l e p e r p e n d i c u l a r t o the c o n t i n e n t a l m a r g i n . An a r r a y of 32 r e c e i v e r s was l o c a t e d on the A m e r i c a p l a t e on t h e m a i n l a n d and a c r o s s V a n c o u v e r I s l a n d , and e x t e n d e d o f f s h o r e w i t h 3 ocean b o t t o m se i smometer s ( O B S ' s ) . Two s h o t s were f i r e d a t the e a s t e r n end of the l i n e , and 17 s h o t s were l o c a t e d a l o n g t h e wes te rnmos t 100 km of the p r o f i l e . C o n t r o l f o r t h e i n t e r p r e t a t i o n of t h e o n s h o r e - o f f s h o r e p r o f i l e was p r o v i d e d by a r e v e r s e d r e f r a c t i o n p r o f i l e a l o n g the l e n g t h of Vancouver I s l a n d (McMechan and Spence 1983) and by t h e m a r i n e r e f r a c t i o n p r o f i l e r e c o r d e d on t h e O B S ' s ( W a l d r o n 1982 ) . To a i d i n the m o d e l i n g of t h e s e i s m i c s t r u c t u r e of t h i s complex r e g i o n , two p r a c t i c a l t e c h n i q u e s have been d e v e l o p e d and a p p l i e d i n the i n t e r p r e t a t i o n of l i n e I . The f i r s t p r o c e d u r e was an i t e r a t i v e i n v e r s i o n t e c h n i q u e f o r t r a v e l t i m e s from e x p l o s i o n s i n w h i c h s h o t s a t s e v e r a l l o c a t i o n s a r e r e c o r d e d on t h e same s e t of r e c e i v e r s . T r a v e l t i m e s f o r the i n i t i a l model and f o r subsequent i t e r a t i o n s a r e computed u s i n g t w o - d i m e n s i o n a l r a y t r a c i n g . The model i s r e p r e s e n t e d by one or more b l o c k s i n w h i c h the v e l o c i t y , the v e l o c i t y g r a d i e n t , and s p e c i f i e d boundary p o s i t i o n s a r e a l l o w e d t o v a r y . P e r t u r b a t i o n s t o t h e p a r a m e t e r s a r e then d e t e r m i n e d s i m u l t a n e o u s l y u s i n g a damped l e a s t s q u a r e s method . i v S e c o n d , a f a s t , e f f i c i e n t a l g o r i t h m based on a s y m p t o t i c r a y t h e o r y has been d e v e l o p e d f o r the c a l c u l a t i o n of s y n t h e t i c se i smograms t h r o u g h t w o - d i m e n s i o n a l m e d i a . The same r a y t r a c i n g scheme i s used as i n the t r a v e l t i m e i n v e r s i o n method , i n w h i c h the v e l o c i t y model i s r e p r e s e n t e d by l a r g e p o l y g o n a l b l o c k s , each w i t h a u n i f o r m v e l o c i t y g r a d i e n t . S i m p l e a n a l y t i c e x p r e s s i o n s a r e t h u s used f o r b o t h the r a y t r a c i n g and f o r the a m p l i t u d e c o m p u t a t i o n s . A m p l i t u d e s may be c a l c u l a t e d f o r head waves , r e f r a c t i o n s , p r e - c r i t i c a l and w i d e - a n g l e r e f l e c t i o n s , s u r f a c e r e f l e c t i o n s and m u l t i p l e s . The t r a v e l t i m e i n v e r s i o n p r o c e d u r e and s y n t h e t i c se i smogram a l g o r i t h m were b o t h a p p l i e d i n the i n t e r p r e t a t i o n o f t h e o n s h o r e - o f f s h o r e p r o f i l e . The ma jor f e a t u r e s o f t h e r e f r a c t i o n s t r u c t u r a l model a r e as f o l l o w s : (1) The o c e a n i c l i t h o s p h e r e d i p s a t 3° o r l e s s b e n e a t h t h e c o n t i n e n t a l s l o p e , so the bend i n t h e s u b d u c t i n g s l a b o c c u r s l a n d w a r d of t h e f o o t of the s l o p e . (2) The s u b d u c t i n g c r u s t d i p s a t 1 4 - 1 6 ° b e n e a t h the c o n t i n e n t a l s h e l f u n t i l i t pa s se s b e n e a t h the c o n t i n e n t a l Moho a t 37 km d e p t h be low w e s t e r n V a n c o u v e r I s l a n d . (3) An upper m a n t l e r e f l e c t o r may c o r r e s p o n d t o the base o f the s u b d u c t i n g l i t h o s p h e r e . (4) A segment of h i g h - v e l o c i t y m a t e r i a l above t h e downgoing c r u s t , w i t h v e l o c i t y 7.7 km/s and d e p t h range ~20-25 km, may r e p r e s e n t a remnant of s u b d u c t e d l i t h o s p h e r e , p e r h a p s d e t a c h e d when the s u b d u c t i o n zone jumped wes tward t o i t s p r e s e n t p o s i t i o n . V TABLE OF CONTENTS A b s t r a c t i i i T a b l e Of C o n t e n t s v L i s t Of T a b l e s v i i L i s t Of F i g u r e s v i i i Acknowledgements x i C h a p t e r 1. I n t r o d u c t i o n 1 1.1 T e c t o n i c S e t t i n g 3 1.2 G e o p h y s i c a l S t u d i e s 5 1.3 The V a n c o u v e r I s l a n d S e i s m i c P r o j e c t (VISP) 12 1.3.1 Program D e s c r i p t i o n 12 1 .3 .2 I n t e r p r e t a t i o n Of L i n e IV 15 1 .3 .3 I n t e r p r e t a t i o n Of M a r i n e L i n e I : OBS 1 To OBS 5 17 1.4 O u t l i n e Of The T h e s i s 21 C h a p t e r 2 . Ray T r a c i n g And T r a v e l t i m e I n v e r s i o n I n L a t e r a l l y V a r y i n g M e d i a 24 2.1 I n t r o d u c t i o n 24 2 .2 V e l o c i t y M o d e l And Ray T r a c i n g 29 2 . 3 Theory 30 2 . 3 . 1 The F o r w a r d P r o b l e m 31 2 . 3 . 2 Damped L e a s t Squares I n v e r s i o n .37 2 .4 T e s t s W i t h A r t i f i c i a l Da ta 39 C h a p t e r 3 . P r a c t i c a l S y n t h e t i c Seismograms F o r L a t e r a l l y V a r y i n g M e d i a C a l c u l a t e d By A s y m p t o t i c Ray Theory 55 3.1 I n t r o d u c t i o n 55 3 .2 V e l o c i t y M o d e l And Ray T r a c i n g 59 3 .3 C a l c u l a t i o n Of A m p l i t u d e s And S y n t h e t i c Seismograms 60 3 . 3 . 1 R e f l e c t e d And R e f r a c t e d Rays 60 3 . 3 . 2 Head Waves 65 3 . 3 . 3 A l t e r n a t i v e A p p r o a c h F o r R e f l e c t e d And D i r e c t Rays 66 3 . 3 . 4 Seismogram S y n t h e s i s 67 3 .4 R e s u l t s 68 3 .5 D i s c u s s i o n 83 C h a p t e r 4 . I n t e r p r e t a t i o n Of O n s h o r e - O f f s h o r e P r o f i l e A c r o s s V a n c o u v e r I s l a n d 85 4.1 I n t r o d u c t i o n 85 4 .2 I n t e r p r e t a t i o n Of S h o t s J1 And J2 87 4 . 3 D e s c r i p t i o n Of P S e r i e s S h o t s 94 4 .4 Ray T r a c i n g And T r a v e l t i m e I n v e r s i o n : Sho t s P 1 9 , P13 And P8 1 00 4 . 5 F i n a l O n s h o r e - o f f s h o r e R e f r a c t i o n M o d e l 107 4 . 6 A l t e r n a t e M o d e l s C o n s i s t e n t W i t h The S e i s m i c Data . . 1 3 3 4 .7 G r a v i t y Mode l A c r o s s The S u b d u c t i n g M a r g i n 140 4 .8 D i s c u s s i o n 148 R e f e r e n c e s 159 A p p e n d i c e s : A d d i t i o n a l R e c o r d S e c t i o n s 166 A . 1 Common Shot R e c o r d S e c t i o n s 166 A . 2 S e l e c t e d Common R e c e i v e r R e c o r d S e c t i o n s 181 v i i L I S T OF TABLES 2.1 P a r a m e t e r s f o r t w o - l a y e r model used t o t e s t t r a v e l t i m e i n v e r s i o n . . 4 2 2 .2 P a r a m e t e r s f o r s u b d u c t i o n zone t e s t model 50 4.1 P a r a m e t e r s a f t e r f i n a l i t e r a t i o n of t r a v e l t i m e i n v e r s i o n f o r l i n e I d a t a s e t 113 v i i i L I S T OF FIGURES 1.1 T e c t o n i c map of the c o n t i n e n t a l m a r g i n 2 1.2 G r a v i t y model a c r o s s s o u t h e r n V a n c o u v e r I s l a n d 9 1.3 L o c a t i o n map showing r e f r a c t i o n l i n e s I and IV 13 1.4 V e l o c i t y s t r u c t u r e a l o n g l i n e IV 16 1.5 A l t e r n a t i v e v e l o c i t y - d e p t h p r o f i l e s f o r l i n e IV 18 1.6 V e l o c i t y s t r u c t u r e a l o n g m a r i n e p o r t i o n of l i n e I 19 2.1 Ray p a t h changes due t o p e r t u r b a t i o n of a boundary 34 2 .2 I n f i n i t e s i m a l p e r t u r b a t i o n of a boundary e n d p o i n t 36 2 . 3 T w o - l a y e r model used t o t e s t t r a v e l t i m e i n v e r s i o n 41 2 . 4 T w o - l a y e r model t r a v e l t i m e c u r v e s a f t e r s u c c e s s i v e i t e r a t i o n s of r a y t r a c e i n v e r s i o n p r o c e d u r e 44 2 . 5 S t a r t i n g model f o r s u b d u c t i o n zone t e s t 47 2 .6 F i n a l model f o r s u b d u c t i o n zone t e s t 49 2 .7 I n i t i a l and f i n a l t r a v e l t i m e c u r v e s f o r s u b d u c t i o n zone t e s t 50 2 .8 N o n u n i q u e n e s s of models i n s u b d u c t i o n zone t e s t 53 3.1 Geometry o f t h e r a y tube a t t h e i - t h i n t e r f a c e 61 3 .2 V e r t i c a l component a m p l i t u d e s f o r a t w o - l a y e r m o d e l . . . . 7 0 3 .3 S y n t h e t i c s f o r t h e HILDERS v e l o c i t y - d e p t h model 73 3 .4 Rays and s m p l i t u d e s f o r a s i m p l e 2D model 77 3 .5 The I m p e r i a l V a l l e y v e l o c i t y - d e p t h model 78 3 .6 Rays and s y n t h e t i c s f o r t h e I m p e r i a l V a l l e y model 79 3 .7 Rays and s y n t h e t i c s f o r a s u b d u c t i o n zone model 82 4.1 Shot J1 , s y n t h e t i c s and d a t a 88 4 .2 V e l o c i t y model and r a y t r a c i n g d i a g r a m f o r shot J1 91 4 . 3 O b s e r v e d d a t a f o r s h o t s P 1 9 , P13 and P8 97 i x 4 .4 Observed d a t a r e c e i v e r s X45 and X22 98 4 . 5 Ray t r a c i n g d i a g r a m f o r s h o t s P 1 9 , P13 and P8 102 4 . 6 T r a v e l t i m e c u r v e s a f t e r one i t e r a t i o n of i n v e r s e p r o c e d u r e 105 4 .7 F i n a l v e l o c i t y model f o r l i n e I . . . . 110 4 .8 D e t a i l s of r a y t r a c e model 111 4 . 9 Ray t r a c e used i n i n v e r s e p r o c e d u r e f o r f i n a l m o d e l . . . . 1 1 2 4 .10 Shot P 1 9 , s y n t h e t i c s and d a t a 116 4.11 Shot P 1 3 , s y n t h e t i c s and d a t a 117 4 .12 Shot P 8 , s y n t h e t i c s and d a t a 118 4 .13 Shot P 2 , s y n t h e t i c s and d a t a . . . 1 1 9 4 .14 R e c e i v e r X 4 5 , s y n t h e t i c s and d a t a 120 4 .15 R e c e i v e r X 3 4 , s y n t h e t i c s and d a t a 121 4 .16 R e c e i v e r X 2 2 , s y n t h e t i c s and d a t a .122 4 .17 R e c e i v e r X 6 , s y n t h e t i c s and d a t a 123 4 .18 Shadow zones c a u s e d by c o r n e r where s u b d u c t i n g s l a b and c o n t i n e n t a l Moho meet 129 4 .19 Shot P19 and P13 s y n t h e t i c s w i t h 8 . 6 km/s be low r e f l e c t o r 1 32 4 .20 P r e l i m i n a r y model of E l l i s e t a l . . (1983) w i t h a d d i t i o n a l upper m a n t l e r e f l e c t o r 135 4.21 V e l o c i t y model w i t h k i n k i n s u b d u c t i n g o c e a n i c c r u s t . . . 1 3 7 4 .22 F i n a l g r a v i t y model a l o n g l i n e I 144 4 .23 F i n a l v e l o c i t y model and s t y l i z e d t e c t o n i c model 149 4 .24 E x t e n t of h i g h v e l o c i t y m a t e r i a l a t 20 km d e p t h 152 4 .25 Depths f rom r e f l e c t i o n s e c t i o n compared t o r e f r a c t i o n model 157 X A1 . 1 Shot J 2 , o b s e r v e d r e c o r d s e c t i o n 167 A 1 . 2 Shot P1 , o b s e r v e d r e c o r d s e c t i o n 168 A 1 . 3 Shot P 3 , o b s e r v e d r e c o r d s e c t i o n 169 A 1 . 4 Shot P 4 , o b s e r v e d r e c o r d s e c t i o n . . . 1 7 0 A 1 . 5 Shot P 5 , o b s e r v e d r e c o r d s e c t i o n 171 A 1 . 6 Shot P 6 , o b s e r v e d r e c o r d s e c t i o n .172 A 1 . 7 Shot P 9 , o b s e r v e d r e c o r d s e c t i o n 173 A1 .8 Shot P 1 0 , o b s e r v e d r e c o r d s e c t i o n 174 A1 .9 Shot P 1 2 , o b s e r v e d r e c o r d s e c t i o n 175 A 1 . 1 0 Shot P 1 4 , o b s e r v e d r e c o r d s e c t i o n 176 A1 . 1 1 Shot P 1 5 , o b s e r v e d r e c o r d s e c t i o n 177 A 1 . 1 2 Shot P 1 6 , o b s e r v e d r e c o r d s e c t i o n 178 A1 . 1 3 Shot P 1 7 , o b s e r v e d r e c o r d s e c t i o n 179 A1 .1 4 Shot P 1 8 , o b s e r v e d r e c o r d s e c t i o n 180 A2 .1 R e c e i v e r X 2 , o b s e r v e d r e c o r d s e c t i o n 182 A 2 . 2 R e c e i v e r X 1 3 , o b s e r v e d r e c o r d s e c t i o n . . . 183 A 2 . 3 R e c e i v e r X 1 5 , o b s e r v e d r e c o r d s e c t i o n 184 A 2 . 4 R e c e i v e r X 1 7 , o b s e r v e d r e c o r d s e c t i o n 185 A 2 . 5 R e c e i v e r X 1 9 , o b s e r v e d r e c o r d s e c t i o n 186 A 2 . 6 R e c e i v e r X 2 3 , o b s e r v e d r e c o r d s e c t i o n 187 A 2 . 7 R e c e i v e r X 3 1 , o b s e r v e d r e c o r d s e c t i o n 188 A 2 . 8 R e c e i v e r X 3 5 , o b s e r v e d r e c o r d s e c t i o n 189 A 2 . 9 R e c e i v e r X 4 0 , o b s e r v e d r e c o r d s e c t i o n 190 A 2 . 1 0 R e c e i v e r X 4 3 , o b s e r v e d r e c o r d s e c t i o n 191 x i ACKNOWLEDGEMENTS F i r s t and f o r e m o s t , I want t o thank my w i f e M a r i a , who d i d n e a r l y a l l t h e t y p i n g and f i n a l d i a g r a m p r e p a r a t i o n f o r t h i s t h e s i s . But m o s t l y I want t o t e n d e r my s i n c e r e t h a n k s f o r her u n w a v e r i n g m o r a l s u p p o r t , w h i c h meant so much t o me. And h a v i n g c o m p l e t e d her own d o c t o r a l t h e s i s i n the not so d i s t a n t p a s t , she p r o v i d e d a s t e r l i n g example of someone who had s u r v i v e d . Throughout my r e s e a r c h I have had the d i s t i n c t advantage o f h a v i n g two s u p e r v i s o r s , D r . R . M . C lowes and D r . R . M . E l l i s . I am g r a t e f u l t o them f o r t h e i r e n t h u s i a s t i c encouragement and a d v i c e , so c r i t i c a l i n d e f i n i n g the d i r e c t i o n of o n e ' s r e s e a r c h . I s h o u l d a l s o l i k e t o thank Ron and Bob i n g e n e r a l f o r t h e o v e r a l l p r o j e c t d e s i g n and f o r the o p p o r t u n i t y t o p a r t i c i p a t e ( r a t h e r h e a v i l y ! ) i n o r g a n i z i n g t h e l o g i s t i c s of t h e f i e l d p r o g r a m . W h i l e Ron was on s a b b a t i c a l , Bob i n p a r t i c u l a r p r o v i d e d t h e needed g u i d a n c e f o r my o r g a n i z a t i o n a l e n d e a v o r s . S i m i l a r l y , w h i l e Bob was on s a b b a t i c a l , Ron p r o v i d e d s t i m u l u s d u r i n g i n t e r p r e t a t i o n s t a g e s of the t h e s i s , as w e l l as a d v i c e i n t h e w r i t i n g o f t h e s y n t h e t i c se i smogram r o u t i n e . F i n a l l y , I f e l t I c o u l d a l m o s t a l w a y s c o u n t on Ron t o u p l i f t my s p i r i t s by g r a c i o u s l y d e c l i n i n g t o be the v i c t o r i n most of our d a r t s m a t c h e s . D i s c u s s i o n s w i t h Ken W h i t t a l l , e s p e c i a l l y r e l a t e d t o t h e s y n t h e t i c se i smogram r o u t i n e , a r e g r e a t l y a p p r e c i a t e d . Perhaps t h e g r e a t e r p a r t of t h i s t h e s i s s h o u l d be d e d i c a t e d t o K e n ' s r a y t r a c i n g c o d e , s i n c e much of my work was based upon i t . I a l s o a p p r e c i a t e t a l k s w i t h D a v i d W a l d r o n c o n c e r n i n g h i s m a r i n e x i i i n t e r p r e t a t i o n , and I am i n d e e d g r a t e f u l t h a t h i s i n t e r p r e t a t i o n was c o m p l e t e d i n t i m e t o p r o v i d e c o n t r o l f o r m i n e . As w e l l , I am t h a n k f u l l and c o n s t a n t l y amazed t h a t George McMechan was a b l e t o b r i n g t h e m a j o r i t y of h i s i n t e r p r e t a t i o n t o c o m p l e t i o n , i n c l u d i n g w r i t e - u p , w i t h i n a s i x week p e r i o d . My g r a t i t u d e a l s o goes t o Bob M e l d r u m , who I f e e l i s the t r u e c o r e of t h e s e i s m o l o g y g roup i n m a t t e r s of i n s t r u m e n t a t i o n and r e l a t e d f i e l d p r o j e c t s . I n a d d i t i o n , Bob p r o v i d e d t h e g r e a t e r p a r t of t h e m o t i v a t i o n f o r our l o n g - s t a n d i n g s e m i - r e g u l a r noon hour F r e n c h s e s s i o n s , w h i c h not o n l y were r e w a r d i n g i n t h e m s e l v e s but a l s o s u p p l i e d a needed break from t h e d e a d e n i n g e f f e c t s of g e o p h y s i c s . M e r c i , Bob . Data a c q u i s i t i o n f o r t h e V a n c o u v e r I s l a n d S e i s m i c P r o j e c t (VISP) was o n l y p o s s i b l e t h r o u g h t h e j o i n t e f f o r t of many i n d i v i d u a l s and o r g a n i z a t i o n s . F o r t h e m a r i n e phase of t h e p r o j e c t , t h e p a r t i c i p a t i o n of p e r s o n n e l f rom the P a c i f i c G e o s c i e n c e C e n t r e was i n d i s p e n s a b l e . I t was p a r t i c u l a r l y a p r i v i l e g e t o work w i t h D r . Roy Hyndman, b o t h d u r i n g t h e o r g a n i z a t i o n of t h e m a r i n e o p e r a t i o n and a t l a t e r s t a g e s i n d i s c u s s i n g my i n t e r p r e t a t i o n . O B S ' s were s u p p l i e d by the P a c i f i c G e o s c i e n c e C e n t r e and t h e A t l a n t i c G e o s c i e n c e C e n t r e . G r a t e f u l acknowledgement i s a l s o made t o t h e Department o f F i s h e r i e s and Oceans Canada f o r t h e use of t h e s h i p CSS V e c t o r and t o t h e C a n a d i a n F o r c e s t h r o u g h t h e De fense R e s e a r c h E s t a b l i s h m e n t P a c i f i c f o r t h e CFAV E n d e a v o u r . The a s s i s t a n c e of t h e F l e e t D i v i n g U n i t , P a c i f i c M a r i t i m e Command, who d e t o n a t e d t h e e x p l o s i v e s a t s e a , i s e s p e c i a l l y a p p r e c i a t e d . The onshore phase o f the p r o j e c t c o u l d not have been u n d e r t a k e n w i t h o u t t h e p a r t i c i p a t i o n of members of t h e CO-CRUST g r o u p , who p r o v i d e d e q u i p m e n t , s c i e n t i f i c , o r g a n i z a t i o n a l and f i n a n c i a l c o n t r i b u t i o n s . In p a r t i c u l a r , t h e e f f o r t s of t h e n e a r l y 30 p e o p l e who t o o k p a r t i n t h e f i e l d program a r e g r a t e f u l l y a c k n o w l e d g e d . We a r e a l s o i n d e b t e d t o the f o l l o w i n g f o r e s t companie s on V a n c o u v e r I s l a n d f o r p r o v i d i n g a c c e s s t o t h e i r a r e a s of o p e r a t i o n , a d v i c e on a c c e s s and s a f e t y and d e t a i l e d maps f o r s t a t i o n l o c a t i o n : R a y o n i e r Canada L t d . , M a c M i l l a n B l o e d e l L t d . , C a n a d i a n F o r e s t P r o d u c t s L t d . , T a h s i s C o . L t d . , Crown Z e l l e r b a c h Canada L t d . , B . C . F o r e s t P r o d u c t s L t d . , and W e s t e r n F o r e s t I n d u s t r i e s L t d . P e r s o n a l f i n a n c i a l s u p p o r t was p r o v i d e d by a P o s t g r a d u a t e S c h o l a r s h i p f rom the N a t u r a l S c i e n c e s and E n g i n e e r i n g R e s e a r c h C o u n c i l (NSERC) and by an H . R . M a c M i l l a n F a m i l y F e l l o w s h i p f rom t h e U n i v e r s i t y of B r i t i s h C o l u m b i a . P r i n c i p a l s u p p o r t f o r t h e f i e l d program was p r o v i d e d by c o n t r a c t OSU80-00137 from t h e E a r t h P h y s i c s B r a n c h of E n e r g y , M i n e s and R e s o u r c e s Canada and f rom NSERC o p e r a t i n g g r a n t s of t h e p a r t i c i p a n t s . A n a l y s i s has been s u p p o r t e d by NSERC o p e r a t i n g g r a n t s A2617 and A7707 t o R . M . E l l i s and R . M . C l o w e s , r e s p e c t i v e l y . 1 CHAPTER K_ INTRODUCTION I n Augus t 1980, CO-CRUST 1 c o n d u c t e d t h e V a n c o u v e r I s l a n d S e i s m i c P r o j e c t ( V I S P ) , a s e r i e s of r e f r a c t i o n and r e f l e c t i o n s e i s m i c e x p e r i m e n t s t h a t u t i l i z e d b o t h l a n d - b a s e d and ocean b o t t o m s e i s m o g r a p h s (OBS ' s ) w i t h e x p l o s i v e and a i r g u n energy s o u r c e s . T h i s d i s s e r t a t i o n c o n c e r n s t h e i n t e r p r e t a t i o n of the p r i n c i p a l r e f r a c t i o n p r o f i l e of t h e e x p e r i m e n t , f o r w h i c h the p u r p o s e was t o o b t a i n a s e i s m i c s t r u c t u r a l s e c t i o n t o upper m a n t l e d e p t h s f rom t h e o c e a n i c Juan de Fuca p l a t e t o t h e i n l a n d v o l c a n i c a r c of t h e c o n t i n e n t a l A m e r i c a p l a t e ( F i g . 1 . 1 ) . T o g e t h e r w i t h o t h e r g e o p h y s i c a l s t u d i e s such as s e i s m i c i t y , g r a v i t y , h e a t f l o w and m a g n e t i c s , a s e i s m i c v e l o c i t y model p l a y s a ma jor r o l e i n u n d e r s t a n d i n g t h e c o n t e m p o r a r y t e c t o n i c s and p l a t e i n t e r a c t i o n c o m p l e x i t i e s o f t h e r e g i o n . The deve lopment of a s e i s m i c / t e c t o n i c model has two i m p o r t a n t p r a c t i c a l i m p l i c a t i o n s . F i r s t , t h e r e i s t h e p o t e n t i a l f o r t h e t e c t o n i c model t o be a p p l i e d i n t h e e x p l o r a t i o n f o r h y d r o c a r b o n r e s o u r c e s on t h e c o n t i n e n t a l s h e l f , o r f o r m i n e r a l r e s o u r c e s on V a n c o u v e r I s l a n d and i n t h e C oa s t Range . In t h e p a s t , t h e d i s t r i b u t i o n of m i n e r a l d e p o s i t s was c o n s i d e r e d t o be somewhat h a p h a z a r d ; but t o d a y t h e t e c t o n i c s e t t i n g i s seen as a ma jor c o n t r o l l i n g f a c t o r i n t h e l o c a t i o n of m i n e r a l r e s o u r c e s , and methods a r e b e i n g 1 CO-CRUST ( C o n s o r t i u m f o r C r u s t a l R e c o n n a i s a n c e u s i n g S e i s m i c T e c h n i q u e s ) i n c l u d e d i n 1980 p a r t i c i p a n t s f rom t h e E a r t h P h y s i c s B r a n c h ( O t t a w a ) , P a c i f i c G e o s c i e n c e C e n t r e , A t l a n t i c G e o s c i e n c e C e n t r e , and t h e U n i v e r s i t i e s of A l b e r t a , B r i t i s h C o l u m b i a , M a n i t o b a , S a s k a t c h e w a n , and W e s t e r n O n t a r i o . F I G . 1 . 1 . T e c t o n i c map o f t h e s o u t h e r n B r i t i s h C o l u m b i a c o n t i n e n t a l m a r g i n s h o w i n g t h e m a i n l i t h o s p h e r i c b o u n d a r i e s a n d p l a t e m o t i o n s r e l a t i v e t o N o r t h A m e r i c a . Q u a t e r n a r y v o l c a n o e s a r e i n d i c a t e d by s o l i d t r i a n g l e s a n d p r o f i l e 2 i s t h e l o c a t i o n o f t h e g r a v i t y m o d e l c r o s s s e c t i o n a c r o s s s o u t h e r n V a n c o u v e r I s l a n d a s s h o w n i n F i g . 1 . 2 . TWs = T u z o W i l s o n s e a m o u n t ; P R f z = P a u l R e v e r e f r a c t u r e z o n e ; S f z = S o v a n c o f r a c t u r e z o n e . 3 d e v e l o p e d w h i c h use t h e t e c t o n i c s e t t i n g as a g u i d e t o e x p l o r a t i o n (Rona 1980; M i t c h e l l and Gar son 1981) . The second s i g n i f i c a n t a p p l i c a t i o n of a s e i s m i c / t e c t o n i c model i s i n t h e a s ses sment of e a r t h q u a k e r i s k , w h i c h a f f e c t s not o n l y a r e a s of h i g h p o p u l a t i o n d e n s i t y , but a l s o a r e a s of low p o p u l a t i o n d e n s i t y where f a c i l i t i e s r e l a t e d t o energy deve lopment may be p l a c e d . The t e c t o n i c model i s n e c e s s s a r y f o r u n d e r s t a n d i n g the s e i s m i c i t y p a t t e r n and t h u s the p r o c e s s e s g e n e r a t i n g l a r g e e a r t h q u a k e s . As w e l l , a r e a l i s t i c v e l o c i t y model i s r e q u i r e d s p e c i f i c a l l y f o r the a c c u r a t e l o c a t i o n of t h e e a r t h q u a k e s t h e m s e l v e s . 1.1 T e c t o n i c S e t t i n g In t h e Vancouver I s l a n d r e g i o n t h e p l a t e t e c t o n i c reg ime i s c o n v e r g e n t , w i t h the o c e a n i c Juan de Fuca and E x p l o r e r p l a t e s b e i n g s u b d u c t e d o b l i q u e l y b e n e a t h t h e c o n t i n e n t a l A m e r i c a p l a t e ( F i g . 1 . 1 ) . Based on m a g n e t i c anomaly p a t t e r n s , t h e p r e s e n t p e r p e n d i c u l a r c o n v e r g e n c e r a t e s a r e about 3 cm/year f o r the Juan de F u c a - A m e r i c a and l e s s t h a n 2 c m / y e a r f o r the E x p l o r e r - A m e r i c a p l a t e s ( R i d d i h o u g h 1 9 7 7 ) . The d i f f e r e n c e i s accommodated by l e f t - l a t e r a l s t r i k e - s l i p movement a l o n g the N o o t k a f a u l t zone between t h e E x p l o r e r and Juan de Fuca p l a t e s (Hyndman e t a l . 1979 ) . In terms of a b s o l u t e p l a t e m o t i o n s f i x e d t o a ho t spot frame of r e f e r e n c e , i t i s p o s s i b l e t h a t t h e E x p l o r e r p l a t e has s t o p p e d s u b d u c t i n g i n an a b s o l u t e sense ( R i d d i h o u g h 1981 ) . T h u s , b o t h the E x p l o r e r and Juan de Fuca p l a t e s a r e t o some e x t e n t b e i n g o v e r - r i d d e n by t h e s o u t h w e s t w a r d m o t i o n of the A m e r i c a p l a t e . 4 The p r e s e n t s t r u c t u r e a t t h e w e s t e r n m a r g i n of the A m e r i c a p l a t e i s c o n t r o l l e d by the p a s t p l a t e t e c t o n i c h i s t o r y a t t h a t m a r g i n , i n w h i c h e p i s o d e s of s u b d u c t i o n may have a l t e r n a t e d w i t h p e r i o d s of s t r i k e - s l i p m o t i o n ( R i d d i h o u g h 1 9 8 2 a ) . R e c e n t l y , m o d i f i c a t i o n s t o p l a t e t e c t o n i c t h e o r y have i n t r o d u c e d an a d d i t i o n a l f a c t o r . New e v i d e n c e s u g g e s t s t h a t w e s t e r n N o r t h A m e r i c a has grown by the p i e c e m e a l a d d i t i o n of b l o c k s of l i t h o s p h e r e ( v a r i a b l y c a l l e d m i c r o p l a t e s , t e r r a n e s , e x o t i c t e r r a n e s or a l l o c h t h o n o u s t e r r a n e s ) , some o f w h i c h have been c a r r i e d t h o u s a n d s of k i l o m e t e r s f rom t h e i r s i t e s o f o r i g i n . A t e r r a n e i s r e c o g n i z e d by i t s u n i q u e s t r a t i g r a p h y r e l a t i v e t o n e i g h b o r i n g t e r r a n e s and t h e c r a t o n , by d i f f e r e n t f aunas compared t o t h o s e on t h e c r a t o n , and i n some c a s e s by p a l e o m a g n e t i c r e s u l t s w h i c h i n d i c a t e t h a t t h e y have been r o t a t e d or d i s p l a c e d i n l a t i t u d e . Among t h e b e s t r e c o g n i z e d t e r r a n e s i s t h e d i s p e r s e d W r a n g e l l i a b l o c k , p i e c e s of w h i c h a r e now i n s o u t h e a s t A l a s k a , the Queen C h a r l o t t e I s l a n d s , V a n c o u v e r I s l a n d , and e a s t e r n Oregon ( Jones e t a l . 1977 ) . On V a n c o u v e r I s l a n d , m i d d l e P a l e o z o i c v o l c a n i c r o c k s ( t h e S i c k e r Group) w h i c h a r e c h a r a c t e r i s t i c of i s l a n d a r c s a r e o v e r l a i n by up t o 6000 m of b a s a l t i c p i l l o w l a v a s , f l o w s , p i l l o w b r e c c i a s and minor s e d i m e n t s of t h e upper T r i a s s i c Karmutsen F o r m a t i o n ( M u l l e r 1977 ) . P a l e o m a g n e t i c r e s u l t s f rom the Karmut sen show t h a t Vancouver I s l a n d has moved n o r t h w a r d r e l a t i v e t o the N o r t h A m e r i c a n c r a t o n by a t l e a s t 1300 km, and p o s s i b l y as much as 4900 km, s i n c e t h e l a t e T r i a s s i c ( Y o l e and I r v i n g 1980) . The Karmutsen b a s a l t p r o b a b l y r e p r e s e n t s r i f t i n g r e l a t e d t o t h e 5 commencement of n o r t h w a r d movement. I t i s p r o p o s e d t h a t W r a n g e l l i a was a c c r e t e d by m i d - C r e t a c e o u s t i m e , and s i n c e t h e n has been f r agmented by t h r u s t i n g and t r a n s l a t i o n a l o n g i n t r a p l a t e s t r i k e - s l i p f a u l t s (Coney e t a l . 1 9 8 0 ) . The g r o w t h of w e s t e r n N o r t h A m e r i c a by t e r r a n e a c c r e t i o n i s complex and p o o r l y u n d e r s t o o d . I t has been s u g g e s t e d t h a t e x o t i c t e r r a n e s have modern a n a l o g s i n some of t h e l a r g e o c e a n i c p l a t e a u s , seamounts and v o l c a n i c r i d g e s , w h i c h c o m p r i s e about 10% of the ocean f l o o r (Ben-Avraham e t a l . 1981 ) . Many of t h e p l a t e a u s a r e comparab le t o c o n t i n e n t s i n t h i c k n e s s and d e n s i t y , and would r e s i s t s u b d u c t i o n on c o l l i s i o n w i t h a c o n t i n e n t a l m a r g i n . I t i s l i k e l y t h a t t h r u s t f a u l t i n g w o u l d be a s s o c i a t e d w i t h t h e c o l l i s o n p r o c e s s , and the end r e s u l t w o u l d be new c r u s t t h i c k e n e d t o c o n t i n e n t a l p r o p o r t i o n s ( Jones e t a l . 1 9 8 2 ) . P e r h a p s t h e p r e s e n t s t r u c t u r e of V a n c o u v e r I s l a n d , as p a r t o f t h e W r a n g e l l i a t e r r a n e , r e f l e c t s such a h i s t o r y . 1.2 G e o p h y s i c a l S t u d i e s I t i s g e n e r a l l y a c c e p t e d t h a t s u b d u c t i o n has o c c u r r e d a l o n g C a n a d a ' s w e s t e r n m a r g i n o v e r t h e l a s t s e v e r a l m i l l i o n y e a r s , and t h a t i t i s c u r r e n t l y o c c u r r i n g . R i d d i h o u g h and Hyndman (1976) r e v i e w e d t h e r e l e v a n t g e o l o g i c a l and g e o p h y s i c a l d a t a w h i c h s u p p o r t t h e c a s e f o r s u b d u c t i o n . The g e o l o g i c a l i n f o r m a t i o n i n c l u d e s a s e d i m e n t a r y - f i l l e d m a r g i n t r e n c h , c o m p r e s s i v e d e f o r m a t i o n o f s e d i m e n t s a l o n g the c o n t i n e n t a l s l o p e , and t h e a c t i v e a n d e s i t i c v o l c a n i s m of t h e Cascade m o u n t a i n s . The g e o p h y s i c a l e v i d e n c e i n c l u d e s the c l a s s i c m a g n e t i c l i n e a t i o n s on t h e Juan de Fuca p l a t e , t h e h i g h - l o w p a t t e r n o f t h e g r a v i t y 6 f i e l d at the c o n t i n e n t a l margin, the change i n heat flow from low values above the downgoing p l a t e to high v a l u e s near the v o l c a n i c a r c , and the l o c a l s e i s m i c i t y . A comprehensive g e o p h y s i c a l review of the western Canada c o n t i n e n t a l margin was presented by Keen and Hyndman (1979). Rogers (1983) has d e s c r i b e d the s e i s m i c i t y p a t t e r n f o r the Vancouver Island/Puget Sound region and has produced s e i s m o t e c t o n i c models to account f o r i t . A s t r o n g c o n c e n t r a t i o n of s e i s m i c i t y occurs w i t h i n the Puget Sound area. T h i s l o c a l i z a t i o n i s p o s s i b l y the r e s u l t of phase changes i n the descending l i t h o s p h e r e i n a s s o c i a t i o n with the bend i n the c o n t i n e n t a l margin at the l a t i t u d e of Puget Sound (Rogers 1983). S e v e r a l l a r g e earthquakes have taken plac e beneath c e n t r a l Vancouver I s l a n d , near a l i n e c orresponding to the extension of the Nootka f a u l t zone. However, they may i n f a c t not be d i r e c t l y r e l a t e d to motion along the Nootka f a u l t zone because the c h a r a c t e r of the s e i s m i c i t y under Vancouver I s l a n d i s d i f f e r e n t from that i n the ocean b a s i n where the f a u l t zone i s . d e f i n e d . Rather, Rogers (1983) argued that the l a r g e earthquakes are due to the i n t e r a c t i o n of the E x p l o r e r p l a t e with the America p l a t e . Since the E x p l o r e r may have stopped subducting i n an a b s o l u t e sense (Riddihough 1981) and i s being o v e r - r i d d e n by the America p l a t e , the E x p l o r e r may produce upward pressure on the o v e r l y i n g America p l a t e . T h i s i n t e r a c t i o n would be expected to be g r e a t e s t near the southern boundary of the E x p l o r e r p l a t e where i t i s t h i c k e s t . The s e i s m i c i t y , p a r t i c u l a r l y i n the Puget Sound r e g i o n , i s d i v i d e d i n t o two d i s t i n c t groups - a shallow one with depths 7 l e s s t h a n 30 km, and a deeper one where t h e d e p t h s range from about 40 t o 70 km. The d e p t h d i s t r i b u t i o n and l o c a t i o n of e a r t h q u a k e h y p o c e n t e r s were g r e a t l y improved w i t h t h e e s t a b l i s h m e n t i n 1970 of t h e dense ne twork of s e i s m o g r a p h s i n t h e Puget Sound r e g i o n by the U n i v e r s i t y of W a s h i n g t o n . I n a c o m p i l a t i o n of t h e e a r t h q u a k e d a t a by C r o s s o n ( 1 9 8 1 ) , t h e deeper zone o f s e i s m i c i t y was seen t o be d i s t r i b u t e d a l o n g a c l a s s i c B e n i o f f z o n e , d i p p i n g under t h e c o n t i n e n t a t 1 1 ° . The W a s h i n g t o n ne twork was r e c e n t l y expanded wes tward w i t h 11 permanent s t a t i o n s i n t h e O l y m p i c P e n i n s u l a , and the r e s u l t s of Taber (1983) improved t h e d e l i n e a t i o n of t h e B e n i o f f z o n e . W i t h t h e r e c e n t u p g r a d i n g of t h e C a n a d i a n E a r t h q u a k e Data F i l e by Roger s ( 1 9 8 3 ) , a s i m i l a r d i s t r i b u t i o n of e a r t h q u a k e s was seen i n t h e s o u t h e r n V a n c o u v e r I s l a n d and s o u t h e r n G e o r g i a S t r a i t r e g i o n , where t h e B e n i o f f zone was o b s e r v e d d i p p i n g a t 12 ° t o t h e n o r t h e a s t . G e o d e t i c d a t a a l s o have p r o v i d e d d i r e c t s u p p o r t f o r c u r r e n t s u b d u c t i o n . I n a p r e c i s e l e v e l l i n g s u r v e y over a 70 y e a r p e r i o d a c r o s s w e s t e r n W a s h i n g t o n , a p a t t e r n of u p l i f t on t h e o u t e r c o a s t and s u b s i d e n c e f u r t h e r i n l a n d i s c o n s i d e r e d t o be c o n s i s t e n t w i t h t h e s u b d u c t i o n of t h e Juan de Fuca p l a t e under N o r t h A m e r i c a (Ando and B a l a z s 1979 ) . The same p a t t e r n c o n t i n u e s n o r t h w a r d i n t o t h e V a n c o u v e r I s l a n d r e g i o n ( R i d d i h o u g h 1982b) . The q u e s t i o n t h e n rema ins whether t h e s u b d u c t i o n i s o c c u r r i n g i n a s e i s m i c or an a s e i s m i c mode. Ando and B a l a z s (1979) a rgue t h a t a s e i s m i c s u b d u c t i o n i s i m p l i e d by t h e i r d o w n - t o - t h e - c o n t i n e n t c r u s t a l t i l t and by the l a c k of any l a r g e t h r u s t e a r t h q u a k e s i n W a s h i n g t o n and Oregon i n h i s t o r i c a l t i m e ( the p a s t 140 y e a r s ) . 8 A s e i s m i c s l i p i s a l s o s u g g e s t e d by t h e e n e r g y r e l e a s e c a l c u l a t i o n s of Hyndman and W e i c h e r t ( 1 9 8 3 ) , who showed t h a t t h e e a r t h q u a k e r a t e f o r Puget Sound was a t l e a s t a f a c t o r of 10 l e s s t h a n t h a t e x p e c t e d from t h e c o n v e r g e n c e r a t e . However , e v i d e n c e c o n t r a r y t o a s e i s m i c s l i p comes from g e o d e t i c s t r a i n measurements i n W a s h i n g t o n by Savage e t a l . ( 1 9 8 1 ) , who found an a c c u m u l a t i o n of c o m p r e s s i v e s t r a i n p e r p e n d i c u l a r t o the c o n t i n e n t a l m a r g i n . The d i r e c t i o n of s t r a i n a c c u m u l a t i o n i s c o n s i s t e n t w i t h s u b d u c t i o n of t h e Juan de Fuca p l a t e , but t h e s t r a i n r a t e i m p l i e s t h a t l a r g e t h r u s t e a r t h q u a k e s s h o u l d be e x p e c t e d , w h i c h i s d i f f i c u l t t o r e c o n c i l e w i t h t h e e v i d e n c e f o r a s e i s m i c s u b d u c t i o n . R i d d i h o u g h (1979) c a r r i e d out d e t a i l e d m o d e l l i n g of t h e g r a v i t y f i e l d a c r o s s t h e B r i t i s h C o l u m b i a and W a s h i n g t o n m a r g i n s . H i s s t r u c t u r a l model a l o n g p r o f i l e 2 ( F i g . 1.1) i s shown i n F i g u r e 1 .2 . In t h e c o n s t r u c t i o n of t h i s s e c t i o n , s e i s m i c c o n t r o l f rom r e f l e c t i o n , r e f r a c t i o n , and s u r f a c e wave i n t e r p r e t a t i o n s were used where a v a i l a b l e . Based on t h e r m a l a r g u m e n t s , he f u r t h e r assumed t h a t t h e d e e p e s t e a r t h q u a k e h y p o c e n t e r s i n t h e s o u t h e r n S t r a i t o f G e o r g i a - Puget Sound a r e a (50-70 km) c a n n o t l i e b e n e a t h t h e downgoing p l a t e and t h a t b e n e a t h the v o l c a n i c c h a i n t h e d e p t h t o t h e t o p o f t h e downgoing o c e a n i c l i t h o s p h e r e i s c l o s e t o 100 km, as has been found f o r o t h e r a c t i v e m a r g i n s ( B a r a z a n g i and I s a c k s 1 9 7 6 ) . The s e i s m i c c o n s t r a i n t s p l a c e d on M o h o r o v i c i c (Moho) d e p t h s i n the model o f F i g u r e 1.2 r e q u i r e f u r t h e r comment. C o n t r o l p o i n t 1 was d e t e r m i n e d from t h e s e i s m i c r e f r a c t i o n i n t e r p r e t a t i o n s of C lowes and M a l e c e k (1976) and Keen and Georgia S W NE F I G . 1 .2 . G r a v i t y model c r o s s s e c t i o n a c r o s s s o u t h e r n Vancouver I s l a n d ( f rom R i d d i h o u g h 1979 ) . G r a v i t y p r o f i l e s a re f r e e over sea and Bouguer over l a n d ; s o l i d = o b s e r v e d , dash = c a l c u l a t e d . D e n s i t i e s a r e i n grams per c u b i c c e n t i m e t r e . N o t e : 1 mGal = 10~ 5 m / s 2 . B a r s a r e s e i s m i c c o n t r o l p o i n t s ; numbers a r e s o u r c e s : ( l ) C l o w e s and Malecek ( 1 9 7 6 ) , Keen and B a r r e t t ( 1 9 7 1 ) ; (2) and (2 )Tseng ( 1 9 6 8 ) ; (3 ) W i c k e n s ( 1 9 7 7 ) ; ( 4 ) W h i t e e t a l . ( 1 9 6 8 ) ; ( 5 ) S h o u l d i c e (1971 ) . 10 B a r r e t t ( 1 9 7 1 ) . U n f o r t u n a t e l y , t h e p r o f i l e s f o r the se i n t e r p r e t a t i o n s a r e l o c a t e d a t s i g n i f i c a n t d i s t a n c e s f rom t h e p r o f i l e o f F i g u r e 1.2 and i n d i f f e r e n t t e c t o n i c e n v i r o n m e n t s ; t h e C l o w e s and M a l e c e k (1976) s t u d y i s l o c a t e d i n t h e complex E x p l o r e r R i d g e - Sovanco f r a c t u r e zone r e g i o n 200 km t o t h e n o r t h w e s t , whereas the Keen and B a r r e t t (1971) p r o f i l e s l i e o f f the n o r t h w e s t c o r n e r of F i g u r e 1 . 1 . However , Au and Clowes (1982) have i n t e r p r e t e d r e f r a c t i o n d a t a l o c a t e d near t h e Nootka f a u l t zone and on t h e Juan de Fuca p l a t e , and t h e d e p t h a s s i g n e d a t c o n t r o l p o i n t 1 i s i n agreement w i t h t h e i r r e s u l t s . F o r c o n t r o l p o i n t 4 a t the n o r t h e a s t e r n end of t h e p r o f i l e , t h e d e p t h t o t h e c o n t i n e n t a l Moho was d e t e r m i n e d by t h e r e f r a c t i o n p r o f i l e of W h i t e e t a l . ( 1 9 6 8 ) . S u b s e q u e n t l y , B e r r y and F o r s y t h (1975) i n t e r p r e t e d r e v e r s e d s e i s m i c s e c t i o n s f rom s o u t h e r n V a n c o u v e r I s l a n d t o t h e B r i t i s h C o l u m b i a i n t e r i o r , and i n t h e e a s t e r n segment of t h e i r model t h e Moho d e p t h i s g e n e r a l l y c o n s i s t e n t w i t h the Moho d e p t h o b t a i n e d by W h i t e e t a l . ( 1 9 6 8 ) . B e r r y and F o r s y t h (1975) a l s o s u g g e s t e d t h a t t h e r e i s a change i n s t r u c t u r e between V a n c o u v e r I s l a n d and t h e m a i n l a n d t h a t i s a s s o c i a t e d w i t h t h e e x i s t e n c e of a s c a t t e r i n g zone b e n e a t h t h e e a s t e r n p a r t of the S t r a i t o f G e o r g i a . S e i s m i c c o n t r o l a t p o i n t s 2 , 2 * , and 3 b e n e a t h V a n c o u v e r I s l a n d ( F i g . 1.2) i s l e s s s t r i n g e n t . C o n t r o l p o i n t 3 o f W i c k e n s (1977) i s ba sed on the i n v e r s i o n o f a r a t h e r s c a t t e r e d se t of s u r f a c e wave phase v e l o c i t i e s . Depth e r r o r s f o r t h e b o u n d a r i e s a r e d i f f i c u l t t o d e t e r m i n e , but an e r r o r of ±4 km c o u l d be a s s i g n e d as an o p t i m i s t i c e s t i m a t e . The bounds a r e somewhat a r b i t r a r y ; u s i n g t h e r e s o l u t i o n m a t r i x o b t a i n e d i n t h e 11 g e n e r a l i z e d i n v e r s e p r o c e d u r e , W i c k e n s (1977) d e f i n e d h i s bounds as the d i s t a n c e o f f t h e d i a g o n a l r e q u i r e d t o o b t a i n an a r b i t r a r y 10% d r o p - o f f i n a m p l i t u d e . I n t e r p r e t a t i o n of the r e f r a c t i o n a n a l y s i s of Tseng ( 1 9 6 8 ) , c o n t r o l p o i n t s 2 and 2 * , has p r e s e n t e d some d i f f i c u l t y . The h i g h e s t v e l o c i t i e s o b s e r v e d , even f o r s o u r c e - r e c e i v e r s e p a r a t i o n s i n e x c e s s of 300 km, a r e 7 . 1 ± 0 . 1 km/s f o r a l a y e r w i t h t h e upper boundary near 30 km. However , t h e g r a v i t y d a t a r e q u i r e d e n s i t i e s near 3 .3 g c m " 3 a t t h i s d e p t h , a v a l u e w h i c h i s n o r m a l l y c h a r a c t e r i s t i c of t h e upper m a n t l e r a t h e r t h a n t h e l o w e r c r u s t . R i d d i h o u g h (1979) c o n s i d e r e d t h i s p r o b l e m and s u g g e s t e d t h a t t h e p r o b a b l e c o n d i t i o n s above t h e downgoing l i t h o s p h e r e of low t e m p e r a t u r e , h i g h p r e s s u r e , and h y d r o u s e n v i r o n m e n t may r e s u l t i n the f o r m a t i o n of u n u s u a l metamorphic f a c i e s w i t h t h e r e q u i r e d h i g h d e n s i t y and low P-wave v e l o c i t y c h a r a c t e r i s t i c s . I n summary, adequate s e i s m i c models e x i s t of t h e o c e a n i c and c o n t i n e n t a l c r u s t s t o c o n s t r a i n t h e end p o i n t s of t h e g r a v i t y model i n F i g u r e 1 .2 . B e n e a t h V a n c o u v e r I s l a n d , o n l y weak c o n s t r a i n t s a r e p r o v i d e d by t h e s u r f a c e wave d a t a , and P-wave v e l o c i t i e s g e n e r a l l y c h a r a c t e r i s t i c of t h e upper m a n t l e have not been o b s e r v e d . However , arguments such as t h o s e of R i d d i h o u g h (1979) m e n t i o n e d a b o v e , w h i c h r a t i o n a l i z e t h e a p p a r e n t c o n f l i c t between t h e low P-wave v e l o c i t y d e t e r m i n e d from s e i s m i c d a t a and h i g h d e n s i t y r e q u i r e d by t h e g r a v i t y i n t e r p r e t a t i o n , have been made. 1 2 1.3 The V a n c o u v e r I s l a n d S e i s m i c P r o j e c t (VISP) I n l i g h t of the e v i d e n c e o u t l i n e d i n t h e p r e v i o u s s e c t i o n , t h e r e seems l i t t l e doubt of t h e e x i s t e n c e of a s u b d u c t i n g l i t h o s p h e r i c s l a b under V a n c o u v e r I s l a n d . The p u r p o s e of t h e V a n c o u v e r I s l a n d S e i s m i c P r o j e c t was t o d e t e r m i n e i f s e i s m i c r e f r a c t i o n and r e f l e c t i o n methods c o u l d p r o v i d e more d e t a i l s of t h e s u b d u c t i o n zone s t r u c t u r e . T h i s d i s s e r t a t i o n p r e s e n t s an i n t e r p r e t a t i o n of t h e p r o j e c t ' s p r i n c i p a l r e f r a c t i o n l i n e , i n w h i c h s h o t s i n t h e deep ocean were r e c o r d e d on o n s h o r e s t a t i o n s on V a n c o u v e r I s l a n d and the m a i n l a n d . C o n s t r a i n t s have been p r o v i d e d by o t h e r l i n e s of the e x p e r i m e n t , f o r w h i c h t h e i n t e r p r e t a t i o n s have been p r e s e n t e d e l s e w h e r e (McMechan and Spence 1983; W a l d r o n 1982 ) . Because of t h e i r r e l e v a n c e t o the c o m p l e t e i n t e r p r e t a t i o n of t h e o n s h o r e - o f f s h o r e l i n e , a d e s c r i p t i o n of t h e s e p r o f i l e s and of t h e s i g n i f i c a n t p o i n t s i n t h e i r i n t e r p r e t a t i o n w i l l a l s o be d e s c r i b e d h e r e . 1.3.1 Program d e s c r i p t i o n D e t a i l s o f the f u l l r e f r a c t i o n and r e f l e c t i o n p r o g r a m , i n c l u d i n g i n s t r u m e n t c h a r a c t e r i s t i c s , s h o o t i n g and r e c o r d i n g g e o m e t r i e s , and a d i s c u s s i o n of e r r o r s i n t i m i n g and s i t e l o c a t i o n , a r e t o be found i n E l l i s and C lowes (1981) and E l l i s e t a l . ( 1 9 8 3 ) . A b r i e f d e s c r i p t i o n of t h e p o r t i o n s of the program r e l e v a n t t o t h i s t h e s i s i s g i v e n b e l o w . The r e f r a c t i o n program c o n s i s t e d of f o u r p r o f i l e s ; two of them a r e shown i n F i g u r e 1 .3 . L i n e I e x t e n d e d a c r o s s Vancouver I s l a n d from t h e v o l c a n i c a r c t o t h e deep o c e a n , and l i n e IV was 13 1 . 3 . L o c a t i o n map s h o w i n g r e f r a c t i o n l i n e s I and I V , r e f l e c t i o n l i n e ( R L ) , and t h e g r a v i t y p r o f i l e (GR) B a t h y m e t r y i s i n m e t r e s . 1 4 s h o t a l o n g t h e l e n g t h of V a n c o u v e r I s l a n d a p p r o x i m a t e l y p a r a l l e l t o t h e c o n t i n e n t a l m a r g i n . Two a d d i t i o n a l l i n e s a l o n g s t r i k e were a l s o s h o t : l i n e I I i n t h e deep o c e a n , u s i n g e x p l o s i v e s and a i r g u n s o u r c e s i n t o O B S ' s , and l i n e I I I on t h e m i d - c o n t i n e n t a l s h e l f u s i n g an a i r g u n s o u r c e o n l y . I n t e r p r e t a t i o n of l i n e s I I and I I I has not y e t been c o m p l e t e d . F o r l i n e I , up t o 32 l a n d s e i s m o g r a p h s were d e p l o y e d a l o n g a 160 km r e c o r d i n g l i n e on V a n c o u v e r I s l a n d , on i s l a n d s i n t h e S t r a i t of G e o r g i a , and on t h e B r i t i s h C o l u m b i a m a i n l a n d . I n a d d i t i o n , 4 OBS ' s were d e p l o y e d i n t h e o f f s h o r e r e g i o n , a l t h o u g h o n l y d a t a f rom t h e 3 O B S ' s shown i n F i g u r e 1.3 have been i n t e r p r e t e d (Waldron 1 9 8 2 ) . Two 825 kg s h o t s (J1 and J 2 ) , s e p a r a t e d by a p p r o x i m a t e l y 7 km, were shot a t t h e e a s t e r n end of the p r o f i l e , and a s e r i e s of 17 s h o t s r a n g i n g f rom 200 t o 825 k g , d e s i g n a t e d as t h e P s e r i e s , were f i r e d o v e r t h e c o n t i n e n t a l s l o p e and ocean b a s i n i n t o the l a n d and m a r i n e d e t e c t o r s . E i g h t e e n a d d i t i o n a l 50 kg c h a r g e s were d e t o n a t e d f o r r e c o r d i n g s on t h e O B S ' s a l o n e . F i n a l l y , a c o n t i n u o u s s e i s m i c p r o f i l e (CSP) u s i n g a 5 L a i r g u n was r e c o r d e d a l o n g t h e m a r i n e p o r t i o n of l i n e I , and a 32 L a i r g u n was f i r e d a l o n g p r o f i l e s o v e r each OBS, t o d e t e r m i n e s e d i m e n t a r y s t r u c t u r e , basement d e p t h , and upper c r u s t a l s t r u c t u r e . F o r l i n e I V , 38 l a n d s e i s m o g r a p h s were d i s t r i b u t e d a l o n g the 150 km s e c t i o n N-A i n F i g u r e 1.3 and s h o t s o f 900 , 900 and 1800 kg were d e t o n a t e d a t N , A and F , r e s p e c t i v e l y . The s e i s m o g r a p h s were t h e n l o c a t e d a l o n g t h e A - F s e c t i o n of l i n e IV t o o b t a i n r e c o r d i n g s f rom 1800, 900 and 900 kg s h o t s a t N , A and F . 1 5 The r e f l e c t i o n program was composed of two p h a s e s . The f i r s t was a 10 km 1200% common d e p t h p o i n t e x p l o s i o n s u r v e y (RL i n F i g . 1 . 3 ) , d e s i g n e d t o t e s t whether c o h e r e n t r e f l e c t i o n s t o upper m a n t l e d e p t h s c o u l d be o b t a i n e d . In t h e second p h a s e , a 5 km r e f l e c t i o n s p r e a d d e p l o y e d p e r p e n d i c u l a r t o t h e c o a s t r e m a i n e d s t a t i o n a r y and i n t h e a d j a c e n t i n l e t a 32 L a i r g u n was d e t o n a t e d a l o n g a 10 km end-on p r o f i l e t o t e s t the f e a s i b i l i t y o f o b t a i n i n g deep r e f l e c t i o n d a t a u s i n g an a i r g u n s o u r c e . P o s i t i v e r e s u l t s from t h e r e f l e c t i o n e x p e r i m e n t were o b t a i n e d and have been r e p o r t e d i n C lowes e t a l . ( 1 9 8 3 a ) . 1 .3 .2 I n t e r p r e t a t i o n of l i n e IV A n a l y s i s o f l i n e IV a l o n g the a x i s of V a n c o u v e r I s l a n d has been done by McMechan and Spence ( 1 9 8 3 ) , and t h e i r r e s u l t s were a l s o summarized i n E l l i s e t a l . ( 1 9 8 3 ) . The t w o - d i m e n s i o n a l s t r u c t u r e i n t e r p r e t e d by McMechan and Spence (1983) i s shown i n F i g u r e 1 .4 . The most s i g n i f i c a n t f e a t u r e s of t h e i r i n t e r p r e t a t i o n a r e : (1) The upper 20 km of t h e model i s r e l a t i v e l y w e l l c o n s t r a i n e d . The v e l o c i t y i n c r e a s e s f rom ~ 5 . 4 km/s a t t h e s u r f a c e t o 6 .4 km/s a t 2 km d e p t h . The v e l o c i t y t h e n i n c r e a s e s t o 6 .75 km/s a t 16 km d e p t h , where a d i s c o n t i n u i t y i s p r e s e n t and t h e v e l o c i t y jumps t o 7 km/s . (2) There i s an anomaly i n t h e s t r u c t u r e j u s t s o u t h of s h o t p o i n t A a t ~23 km d e p t h ( F i g . 1 . 4 ) , where a l o c a l i z e d r e g i o n of m a n t l e - t y p e v e l o c i t y (7 .8 km/s) i s imbedded w i t h i n t h e l o w e r c r u s t . McMechan and Spence (1983) s p e c u l a t e d t h a t t h e h i g h v e l o c i t y anomaly c o u l d be a remnant o f a s u b d u c t e d s l a b . N O R T H N J ^ A X SOUTH F 5.5-6.5-10-* 20 X a s o n Q 40-•5.5-- 6.5-6.75,7.05-7.07 • • 6.75,6.95 — 6.96 6.6 '"7.8-' : -7 .6--» « • • • • 6.6 6.2, 7.46 7.5 50 i r i i 1 7 100 200 300 DISTANCE (km) MODEL RELIABILITY: G O O D MARGINAL (UNREVERSED RAYS POOR (INFERRED, OR (REVERSED DATA) " " B O T T O M , O R PARTIALLY REVERSED) NO RAYS BOTTOM) FIG. 1.4. V e l o c i t y - d e p t h s t r u c t u r e i n t e r p r e t e d from data of l i n e IV. Shot point l o c a t i o n s are i n d i c a t e d by N, A and F; i n t e r s e c t i o n with l i n e I by X. V e l o c i t i e s ( i n km/s) are shown at boundaries; where two values are p r o v i d e d these are the v e l o c i t i e s above and below the boundary; v e l o c i t y g r a d i e n t s between boundaries are l i n e a r . R e l i a b i l i t y of the contours i s i n d i c a t e d by l i n e t y pes. A l t e r n a t i v e i n t e r p r e t a t i o n s are shown i n F i g . 1.5. (Adapted from McMechan and Spence 1983). 1 7 (3) The s t r u c t u r e of the l o w e r c r u s t and upper m a n t l e i s o n l y w e a k l y c o n s t r a i n e d . Three l a t e r a l l y homogeneous model s o f t h e l o w e r c r u s t and m a n t l e ( F i g . 1.5) were c o n s i d e r e d by McMechan and Spence ( 1 9 8 3 ) . T h e i r p r e f e r r e d i n t e r p r e t a t i o n (model 2 i n F i g . 1.5) c o n t a i n e d a low v e l o c i t y zone t h r o u g h o u t t h e l o w e r c r u s t and an upper m a n t l e v e l o c i t y of 7 .5 km/s a t 37 km d e p t h . 1 . 3 . 3 I n t e r p r e t a t i o n of m a r i n e l i n e I : OBS 1 t o OBS 5 Data r e c o r d e d on OBS ' s 1, 3 and 5 f rom t h e sequence of m a r i n e d e t o n a t i o n s on l i n e I ( F i g . 1.3) y i e l d v e l o c i t y i n f o r m a t i o n about t h e o c e a n i c c r u s t as i t b e g i n s t o subduct under t h e c o n t i n e n t a l s h e l f . The t w o - d i m e n s i o n a l v e l o c i t y model i n t e r p r e t e d by W a l d r o n (1982) i s shown i n F i g u r e 1 .6 . The n e a r -s u r f a c e s t r u c t u r e was p r o v i d e d by c o n t i n u o u s s e i s m i c p r o f i l i n g a l o n g l i n e I and by a i r g u n d a t a r e c o r d e d on t h e O B S ' s , w h i l e t h e deeper s t r u c t u r e was d e t e r m i n e d by the e x p l o s i o n d a t a on t h e O B S ' s . The CSP s e c t i o n p r o v i d e s i n f o r m a t i o n on t h e basement s t r u c t u r e b e n e a t h t h e ocean b a s i n , and t h u s on sed iment t h i c k n e s s e s . The basement west of t h e c o n t i n e n t a l s l o p e i s seen t o be d i p p i n g a t 1 . 4 ° t o w a r d s t h e c o n t i n e n t . Some m u l t i c h a n n e l r e f l e c t i o n p r o f i l e s run by C h e v r o n S t a n d a r d L i m i t e d i n d i c a t e t h a t t h e basement c o n t i n u e s t o d i p b e n e a t h the c o n t i n e n t a l r i s e . The a i r g u n d a t a on OBS 1, w h i c h i s l o c a t e d i n t h e deep ocean b a s i n , d e f i n e the s t r u c t u r e t o t h e m i d - c r u s t a t a l m o s t 4 km d e p t h , where t h e v e l o c i t y i s more t h a n 6 k m / s . T h i s c o n t r a s t s w i t h t h e r e s u l t s from a i r g u n d a t a on O B S ' s 3 and 5 on t h e c o n t i n e n t a l s l o p e , where t h e maximum v e l o c i t y of 3 km/s F I G . 1 .5 . A l t e r n a t i v e v e l o c i t y - d e p t h model s f o r l i n e I V . The p r e f e r r e d i n t e r p r e t a t i o n i s p r o f i l e 2 , but s t r u c t u r e be low 20 km i s p o o r l y c o n s t r a i n e d . w D I S T A N C E (km) E CM F I G . 1.6. F i n a l v e l o c i t y s t r u c t u r e f o r the c o n t i n e n t a l m a r g i n a l o n g the mar ine p o r t i o n of l i n e I , i n t e r p r e t e d from d a t a on OBS ' s 1,3 and 5 . D o t s show t h e l o c a t i o n s of t h e O B S ' s . V e l o c i t i e s ( i n km/s) a r e g i v e n f o r the t o p of each r e g i o n , f o l l o w e d a f t e r the c o l o n by t h e v e l o c i t y g r a d i e n t ( i n km/s/km) i f one was used ( f rom W a l d r o n 1982) . 20 indicates that only sediments are being penetrated; as well, the sedimentary v e l o c i t i e s are higher than under OBS 1. The structure is constrained down to about 2 km depth by the airgun data on OBS 3, and down to almost 3 km depth for OBS 5. The marine explosions recorded on OBS 1 form the most diagnostic dataset for determining the sub-sedimentary oceanic ve l o c i t y structure down to the Moho. The assumption was made that the entire crust beneath the ocean i s dipping at the same 1.4° angle as the dip of the basement, which was observed on the CSP data. The interpretation includes a Moho at 9 km depth below OBS 1, and a 5 km constant v e l o c i t y gradient region in the lower crust within which the ve l o c i t y increases from about 6.8 to 8.0 km/s. The v e l o c i t y at the Moho was not well constrained by the marine data,but no ve l o c i t y discontinuity was required. The v e l o c i t y structure under the continental slope and shelf, as determined by data from OBS's 3 and 5, i s not as well constrained as beneath the ocean basin. Since only shallow sedimentary information was available from the OBS airgun data and basement was not observed, a trade-off existed between sedimentary v e l o c i t y and basement dip. Thus, an assumption had to be made concerning the dip of the basement and the boundaries below i t ; but presumably the dip beneath the slope and shelf is at least as great as the dip beneath the ocean basin. The explosions recorded on OBS 5 do provide ve l o c i t y information for the material above the subducting oceanic crust. The main feature of the dataset i s that the apparent ve l o c i t y remains near 5 km/s out to a distance of >30 km from the OBS, whereas the apparent v e l o c i t y for OBS's 3 and 1 reaches 6 km/s 21 a t o f f s e t s of <20 km. T h i s i m p l i e s t h a t the h i g h e r v e l o c i t y l a y e r s a r e deeper i n t h e r e g i o n of OBS 5 ; i . e . t h e r e i s an u n u s u a l t h i c k n e s s of m a t e r i a l w i t h an i n t e r m e d i a t e v e l o c i t y of about 5 k m / s . The i n f e r r e d p o s i t i o n of t h i s i n t e r m e d i a t e v e l o c i t y b l o c k a g r e e s w e l l w i t h t h a t of a m i d - M i o c e n e melange p r o p o s e d by S n a v e l y and Wagner (1981) on t h e b a s i s of m u l t i c h a n n e l r e f l e c t i o n d a t a c o l l e c t e d by the U . S . G e o l o g i c a l S u r v e y . 1.4 O u t l i n e of the t h e s i s The main c o n c e r n of t h i s t h e s i s i s t h e i n t e r p r e t a t i o n of t h e o n s h o r e - o f f s h o r e p o r t i o n of l i n e I ( F i g . 1 . 3 ) . However , a ma jor c o n t r i b u t i o n of t h e t h e s i s has a l s o been t h e deve lopment of t e c h n i q u e s t o c a r r y out the i n t e r p r e t a t i o n . To p r o v i d e t w o - d i m e n s i o n a l i n f o r m a t i o n a l o n g t h e p r o f i l e , 17 s h o t s had been f i r e d a t d i f f e r e n t l o c a t i o n s above the c o n t i n e n t a l s l o p e and deep ocean b a s i n , and were r e c o r d e d on up t o 32 s t a t i o n s on V a n c o u v e r I s l a n d and t h e m a i n l a n d . I t was t h u s n e c e s s a r y t o f i n d a model w h i c h s i m u l t a n e o u s l y f i t t h e l a r g e number of t r a v e l t i m e s c o r r e s p o n d i n g t o many d i f f e r e n t s h o t / r e c e i v e r c o m b i n a t i o n s . At p r e s e n t , t h e o n l y p r a c t i c a l method of c a l c u l a t i n g t r a v e l t i m e s t h r o u g h t w o - d i m e n s i o n a l media i s by r a y t r a c i n g , and t h e r a y t r a c i n g scheme of W h i t t a l l and Clowes (1979) has p r o v e n i t s e l f t o be b o t h f l e x i b l e and e f f i c i e n t . T h u s , a method was d e v e l o p e d w h i c h i n c o r p o r a t e d the W h i t t a l l and Clowes (1979) r a y t r a c e r i n a l e a s t - s q u a r e s i n v e r s e scheme t o f i n d v e l o c i t y models f rom s e i s m i c r e f r a c t i o n d a t a . T h i s method i s d e s c r i b e d i n C h a p t e r 2 o f t h e t h e s i s . I t p r o v i d e s 22 an o b j e c t i v e means of f i n d i n g r a y t r a c e p a r a m e t e r s such t h a t t h e t r a v e l t i m e d a t a a r e f i t i n a l e a s t - s q u a r e s s e n s e , and r e d u c e s t h e need f o r t h e l a r g e number of t r i a l - a n d - e r r o r p e r t u r b a t i o n s u s u a l l y i n v o l v e d i n r a y t r a c e m o d e l l i n g . However , i t s ma jor l i m i t a t i o n i s t h a t a t r i a l - a n d - e r r o r p r o c e d u r e , based on s u b j e c t i v e d e c i s i o n s about the n a t u r e of the r a y p a t h s between s h o t and r e c e i v e r s , i s s t i l l r e q u i r e d t o f i n d a s t a r t i n g m o d e l . I t i s p o s s i b l e t h a t d i f f e r e n t s t a r t i n g model s may even have d i f f e r e n t p a r a m e t e r i z a t i o n s , w h i c h t h u s i m p l i e s v a r i a b l e forms of t h e f i n a l m o d e l . I n a d d i t i o n t o t h e t r a v e l t i m e i n f o r m a t i o n , t h e a m p l i t u d e s of s e i s m i c r e f r a c t i o n d a t a a l s o p l a c e c o n s t r a i n t s on t h e v e l o c i t y s t r u c t u r e of t h e e a r t h . I t i s c l e a r t h a t t h e s t r u c t u r e b e n e a t h t h e o n s h o r e - o f f s h o r e l i n e I i s s t r o n g l y t w o - d i m e n s i o n a l , s i n c e o c e a n i c c r u s t i s c o n s i d e r a b l y t h i n n e r t h a n c o n t i n e n t a l c r u s t . T h u s , as d e s c r i b e d i n C h a p t e r 3 , a s y n t h e t i c se i smogram r o u t i n e f o r l a t e r a l l y - v a r y i n g media was d e v e l o p e d . I t i s based on a s y m p t o t i c r a y t h e o r y ( A R T ) , u s i n g t h e p r a c t i c a l , e f f i c i e n t r a y t r a c i n g a l g o r i t h m of W h i t t a l l and Clowes ( 1 9 7 9 ) . A l t h o u g h o t h e r t w o - d i m e n s i o n a l ART r o u t i n e s a l r e a d y e x i s t e d ( e . g . McMechan and Mooney 1980; C a s s e l l 1982) , the a d v a n t a g e s of a se i smogram r o u t i n e based on the W h i t t a l l and C lowes (1979) r a y t r a c e r a r e i t s speed of e x e c u t i o n and i t s model f l e x i b i l i t y . The l a t t e r i s e s p e c i a l l y i m p o r t a n t when i n t e r p r e t i n g a p o s s i b l y complex r e g i o n such as t h e s u b d u c t i o n zone of t h e w e s t e r n C a n a d i a n m a r g i n . I n C h a p t e r 4, the i n t e r p r e t a t i o n of the o n s h o r e - o f f s h o r e d a t a s e t i s p r e s e n t e d . The s e i s m i c c o n s t r a i n t s p r o v i d e d by the 23 i n t e r p r e t a t i o n of Waldron (1982) and McMechan and Spence (1983) were h o n o r e d , as was t h e more g e n e r a l c o n s t r a i n t t h a t t h e d a t a s h o u l d be c o n s i s t e n t w i t h a s u b d u c t i o n zone m o d e l . The i n t e r p r e t a t i o n t e c h n i q u e s i n c l u d e d a p p l i c a t i o n of t h e r a y t r a c e t r a v e l t i m e i n v e r s e p r o c e d u r e d e v e l o p e d i n C h a p t e r 2 , and t h e c a l c u l a t i o n of s y n t h e t i c se i smograms u s i n g t h e ART r o u t i n e of C h a p t e r 3 . F i n a l l y , the i n t e r p r e t e d s e i s m i c model and i t s t e c t o n i c i m p l i c a t i o n s a r e d i s c u s s e d . 24 CHAPTER 2^ RAY TRACING AND TRAVELTIME INVERSION IN LATERALLY VARYING MEDIA 2.1 I n t r o d u c t i o n Much i n f o r m a t i o n about t h e e a r t h ' s i n t e r i o r i s p r o v i d e d by t r a v e l t i m e d a t a f rom b o t h e a r t h q u a k e s and e x p l o s i o n s . L a t e r a l l y homogeneous v e l o c i t y model s have been o b t a i n e d f rom such d a t a u s i n g a number of s o p h i s t i c a t e d t e c h n i q u e s , such as e x t r e m a l i n v e r s i o n (Bes sonova e t a l . 1974) , l i n e a r i z e d i n v e r s i o n ( Johnson and G i l b e r t 1972) and l i n e a r programming i n v e r s i o n (Garmany e t a l . 1979) . However , many g e o p h y s i c a l l y i n t e r e s t i n g r e g i o n s a r e s t r o n g l y t w o - or t h r e e - d i m e n s i o n a l , s u c h as s p r e a d i n g r i d g e s , s u b d u c t i o n z o n e s , t r a n s f o r m f a u l t s and a c c r e t e d t e r r a n e s . One-d i m e n s i o n a l methods may i n f a c t be used t o i n f e r i n f o r m a t i o n about l a t e r a l l y v a r y i n g s t r u c t u r e s , i f t h e s t r u c t u r e i s u n i f o r m a l o n g s t r i k e or i f t h e l a t e r a l v a r i a t i o n i s l i m i t e d i n e x t e n t and u n i f o r m s t r u c t u r e s on e i t h e r s i d e of t h e p e r t u r b e d zone may be compared . But more d e t a i l e d i n f o r m a t i o n may be o b t a i n e d by d i r e c t l y e x a m i n i n g t h e l a t e r a l l y v a r y i n g r e g i o n , and so two- o r t h r e e - d i m e n s i o n a l i n t e r p r e t a t i o n methods a r e r e q u i r e d . Ray t r a c i n g p r o v i d e s a r e l a t i v e l y s i m p l e method f o r c a l c u l a t i n g t r a v e l t i m e s of s e i s m i c e n e r g y t h r o u g h complex g e o l o g i c a l m o d e l s . In f o r w a r d m o d e l l i n g p r o c e d u r e s , t r a v e l t i m e s c a l c u l a t e d by t h e r a y t r a c e r a r e matched t o t h e o b s e r v e d d a t a by v a r y i n g the model i n e i t h e r a t r i a l - a n d - e r r o r o r s y s t e m a t i c f a s h i o n . Numerous examples e x i s t i n t h e l i t e r a t u r e , such as J a c o b ( 1 9 7 0 ) , S o r r e l l s e t a l . ( 1 9 7 1 ) , S c o t t ( 1 9 7 3 ) , Gebrande 25 ( 1 9 7 6 ) , A r i c e t a l . (1980) and C lowes e t a l . ( 1 9 8 1 ) . Some form of r a y t r a c i n g i s a l s o r e q u i r e d f o r i n v e r s e t r a v e l t i m e m o d e l l i n g i n t w o - or t h r e e - d i m e n s i o n s . In t h e s e schemes, t h e model i s l i n e a r i z e d and p e r t u r b a t i o n s t o a s t a r t i n g v e l o c i t y model a r e t h e n e s t i m a t e d from the d a t a i n a m a t r i x i n v e r s i o n a p p r o a c h u t i l i z i n g a l e a s t square s c r i t e r i o n . C a l c u l a t i o n o f t r a v e l t i m e s i n t h e o r i g i n a l model s t i l l r e q u i r e s t h a t t h e r a y p a t h be known. I n t h r e e - d i m e n s i o n a l v e l o c i t y i n v e r s i o n s u t i l i z i n g t e l e s e i s m i c d a t a , r a y p a t h s may be c a l c u l a t e d u s i n g a t h r e e -d i m e n s i o n a l r a y t r a c e r . A l t e r n a t i v e l y , r ay p a t h s t h r o u g h a l a t e r a l l y v a r y i n g e a r t h model may be a p p r o x i m a t e d by a s suming t h e y a r e t h e same as f o r a s p h e r i c a l l y symmetr i c v e l o c i t y m o d e l . That i s , s t a r t i n g w i t h a s p h e r i c a l l y symmetr i c m o d e l , t h e v e l o c i t y i n a g i v e n b l o c k of t h e model may change f rom i t e r a t i o n t o i t e r a t i o n of t h e i n v e r s i o n p r o c e d u r e , but so l o n g as t h e l a t e r a l v a r i a t i o n s i n v e l o c i t y a r e no t l a r g e , t h e r a y p a t h i s assumed t o r e m a i n t h e same. T h i s method has been a p p l i e d i n t e l e s e i s m i c a r r a y s t u d i e s t o d e t e r m i n e t h e l a t e r a l l y v a r y i n g s t r u c t u r e b e n e a t h the a r r a y ( A k i e t a l . 1977) . I t has a l s o been a p p l i e d i n whole e a r t h s t u d i e s , where m a s s i v e numbers of ISC t r a v e l t i m e s have been used t o d e t e r m i n e l o w e r m a n t l e h e t e r o g e n e i t i e s ; examples a r e D z i e w o n s k i e t a l . ( 1 9 7 7 ) , who r e p r e s e n t e d v e l o c i t y p e r t u r b a t i o n s i n terms of s p h e r i c a l h a r m o n i c s , and C l a y t o n and Comer ( 1 9 8 3 ) , who used a t o m o g r a p h i c t e c h n i q u e . I n v e l o c i t y i n v e r s i o n s from l o c a l e a r t h q u a k e s , i t becomes more d i f f i c u l t t o a v o i d m u l t i p l e i t e r a t i o n s o f a t h r e e -d i m e n s i o n a l r a y t r a c e r . The s i t u a t i o n i s f u r t h e r c o m p l i c a t e d by 26 t h e need t o s i m u l t a n e o u s l y d e t e r m i n e the e a r t h q u a k e h y p o c e n t e r s . C r o s s o n (1976) t a c k l e d t h e p r o b l e m f o r o n e - d i m e n s i o n a l v e l o c i t y model s o n l y , p a r a m e t e r i z i n g the s t r u c t u r e i n te rms of f l a t - l y i n g c o n s t a n t v e l o c i t y l a y e r s . A k i and Lee ( 1 9 7 6 ) , i n what i s p e r h a p s t h e most w i d e l y used 3D i n v e r s i o n r o u t i n e , s u b d i v i d e d t h e f l a t l a y e r s i n t o r e c t a n g u l a r b l o c k s , and c a l c u l a t e d a v e l o c i t y p e r t u r b a t i o n f o r each b l o c k . But f o r s i m p l i c i t y i n d e t e r m i n i n g t h e r a y p a t h , t h e y used a homogeneous h a l f space as an i n i t i a l model and i t e r a t e d o n l y once f o r t h e i r l e a s t - s q u a r e s p a r a m e t e r a d j u s t m e n t s . However , Hawley e t a l . (1981) were a b l e t o e x t e n d t h e method of A k i and Lee (1976) by i n t r o d u c i n g t h r e e -d i m e n s i o n a l r a y t r a c i n g t h r o u g h t h e p l a n e l a y e r b l o c k model and t h u s r e m o v i n g t h e r e s t r i c t i o n of a homogeneous i n i t i a l m o d e l . U s i n g t h e 3D r a y t r a c e r of J u l i a n and G u b b i n s ( 1 9 7 6 ) , Spencer and G u b b i n s (1980) a p p l i e d an i t e r a t i v e i n v e r s i o n t e c h n i q u e t o s i m u l t a n e o u s l y s o l v e f o r v e l o c i t y s t r u c t u r e and h y p o c e n t e r l o c a t i o n ; t h e y assumed t h a t t h e v e l o c i t y model i n t h e r e g i o n c o u l d be d e s c r i b e d by a s i m p l e f u n c t i o n of t h e space c o o r d i n a t e s and a s m a l l number of p a r a m e t e r s . In the B a c k u s - G i l b e r t a p p r o a c h t o 3D v e l o c i t y i n v e r s i o n , d e v e l o p e d by Chou and Booker ( 1 9 8 0 ) , t h e i n v e r s i o n f o r m a l i s m does not r e q u i r e t h e e x p l i c i t form o f t h e v e l o c i t y s t r u c t u r e t o be known, but r a t h e r assumes t h a t i t i s an unknown f u n c t i o n w h i c h can be v i e w e d t h r o u g h a s m o o t h i n g window. N e v e r t h e l e s s , t h e i m p l e m e n t a t i o n r e q u i r e s s p e c i f i c r a y p a t h s a l o n g w h i c h i n t e g r a l s may be e v a l u a t e d . T h i s c h a p t e r i s c o n c e r n e d m a i n l y w i t h t h e deve lopment o f an i n v e r s i o n p r o c e d u r e f o r the t w o - d i m e n s i o n a l i n t e r p r e t a t i o n of s e i s m i c r e f r a c t i o n t r a v e l t i m e d a t a f rom e x p l o s i o n s . I n 27 e x p e r i m e n t s where m u l t i p l e s h o t s a r e r e c o r d e d on t h e same s e t of m u l t i p l e r e c e i v e r s , f o r w a r d m o d e l l i n g of t h e t r a v e l t i m e s by r a y t r a c i n g becomes cumbersome. I t i s t h u s d e s i r a b l e t o i n v e r t t h e t r a v e l t i m e d a t a f o r a v e l o c i t y m o d e l , u s i n g a p r o c e d u r e i n w h i c h p e r t u r b a t i o n s t o t h e r a y t r a c e model a r e a u t o m a t i c a l l y c a l c u l a t e d . The a d v a n t a g e s a r e : (1) many of t h e t i m e - c o n s u m i n g m a n i p u l a t i o n s of t h e f o r w a r d p r o c e d u r e a r e e l i m i n a t e d , and (2) t h e r e i s b e t t e r a s s u r a n c e of h a v i n g a model w h i c h f i t s t h e d a t a i n a l e a s t - s q u a r e s s e n s e . The r a y t r a c i n g method used i n t h e i n v e r s i o n p r o c e d u r e i s the s i m p l e , e f f i c i e n t scheme p r e s e n t e d by W h i t t a l l and C lowes ( 1 9 7 9 ) . The v e l o c i t y model i s r e p r e s e n t e d by l a r g e b l o c k s w i t h a r b i t r a r y b o u n d a r i e s , and w i t h i n each b l o c k t h e v e l o c i t y g r a d i e n t i s c o n s t a n t and of a r b i t r a r y o r i e n t a t i o n . The ma jor a d v a n t a g e s o f t h i s r a y t r a c i n g method a r e i t s speed of e x e c u t i o n and i t s f l e x i b i l i t y . Speed i s n e c e s s a r y i n i n v e r s e m o d e l l i n g because s e v e r a l i t e r a t i o n s a r e u s u a l l y r e q u i r e d and i n each i t e r a t i o n the r a y p a t h s c o r r e s p o n d i n g t o many s h o t / r e c e i v e r c o m b i n a t i o n s must be c a l c u l a t e d . F l e x i b i l i t y i n r a y t r a c i n g i s even more i m p o r t a n t i n e x p l o s i o n r e f r a c t i o n s u r v e y s t h a n i n v e l o c i t y m o d e l l i n g i n v o l v i n g e a r t h q u a k e s o u r c e s , where o n l y t h e d i r e c t ray p a t h i s u s u a l l y assumed. I n a r e f r a c t i o n i n t e r p r e t a t i o n , the c r i t i c a l f i r s t s t e p i s t o i d e n t i f y t h e a r r i v a l s , u s u a l l y as r e f l e c t i o n s f rom a p a r t i c u l a r boundary or as r e f r a c t i o n s (or head waves) i n t h e r e g i o n be low t h e b o u n d a r y . The r a y t r a c e r needs t o be s u f f i c i e n t l y f l e x i b l e t o a l l o w a d j u s t m e n t s i n the d e p t h and shape of i n t e r f a c e s and t o accommodate v e l o c i t y d i s t r i b u t i o n s v a r y i n g b o t h l a t e r a l l y and 28 v e r t i c a l l y . The need f o r f l e x i b i l i t y i s a l s o r e l a t e d t o one of t h e s h o r t c o m i n g s of r e f r a c t i o n m o d e l l i n g p r o c e d u r e s , e i t h e r f o r w a r d o r i n v e r s e , w h i c h u t i l i z e r a y t r a c i n g . That i s , t h e i d e n t i f i c a t i o n of the a r r i v a l t y p e and the n a t u r e of t h e r a y p a t h i n v o l v e s a s u b j e c t i v e d e c i s i o n about model p a r a m e t e r i z a t i o n . W i t h a d i f f e r e n t p a r a m e t e r i z a t i o n or even d i f f e r e n t s t a r t i n g v a l u e s f o r a g i v e n se t of p a r a m e t e r s , t h e f i n a l model may be d i f f e r e n t i n many s i g n i f i c a n t d e t a i l s . U n f o r t u n a t e l y , t h e r e e x i s t s no method a t p r e s e n t t o overcome t h i s f u n d a m e n t a l p r o b l e m f o r t w o - or t h r e e - d i m e n s i o n a l i n t e r p r e t a t i o n s . The i n v e r s e p r o c e d u r e d e s c r i b e d i n t h i s c h a p t e r d i f f e r s from p r e v i o u s v e l o c i t y i n v e r s i o n methods f o r l a t e r a l l y v a r y i n g media p r i m a r i l y i n t h e n a t u r e of t h e r a y t r a c e r . I n p a r t i c u l a r , t h e d e p t h o f s p e c i f i e d i n t e r f a c e s may be v a r i e d i n a d d i t i o n t o the v e l o c i t y of a r e g i o n . The i n v e r s e r o u t i n e i s most s i m i l a r t o t h a t of Wesson ( 1 9 7 1 ) , who, i n c r u s t a l i n t e r p r e t a t i o n s of e x p l o s i o n r e f r a c t i o n d a t a , a l s o used s e i s m i c r a y c o m p u t a t i o n s i n d e t e r m i n i n g l e a s t - s q u a r e s a d j u s t m e n t s t o a s e t of v e l o c i t y model p a r a m e t e r s . However , t h e v e l o c i t y model was a s i m p l e f u n c t i o n of a few p a r a m e t e r s , s i m i l a r t o t h e v e l o c i t y model of Spencer and G u b b i n s ( 1 9 8 0 ) , and so was l i m i t e d i n i t s f l e x i b i l i t y . W i t h t h e e x c e p t i o n of t h e r a y t r a c e r , the i n v e r s e r o u t i n e d i s c u s s e d i n t h i s c h a p t e r has many c h a r a c t e r i s t i c s i n common w i t h o t h e r v e l o c i t y i n v e r s i o n t e c h n i q u e s , e i t h e r i n t h e g e n e r a l t y p e of p a r a m e t e r i z a t i o n or i n t h e method used t o p e r f o r m t h e m a t r i x i n v e r s i o n . As w i l l be shown, t h e d e p t h t o a s p e c i f i c 29 boundary p l a y s a r o l e w h i c h i s i n many ways a n a l o g o u s t o the h y p o c e n t e r d e p t h i n the r o u t i n e s w h i c h s i m u l t a n e o u s l y i n v e r t f o r v e l o c i t y and e a r t h q u a k e l o c a t i o n . I n v e r s i o n i s a c c o m p l i s h e d u s i n g t h e damped l e a s t s q u a r e s t e c h n i q u e (Levenberg 1 9 4 4 ) , w h i c h i s t h e p r o c e d u r e f o l l o w e d by A k i and Lee (1976) and i s one of t h e p r o c e d u r e s c o n s i d e r e d by C r o s s o n (1976) and Spencer and G u b b i n s ( 1 9 8 0 ) . 2 .2 V e l o c i t y M o d e l and Ray T r a c i n g A c o m p l e t e d e s c r i p t i o n of t h e r a y t r a c i n g r o u t i n e i s g i v e n i n W h i t t a l l and C lowes ( 1 9 7 9 ) , and o n l y a b r i e f o u t l i n e of t h e p r o c e d u r e i s r e p e a t e d h e r e . To d e f i n e t h e v e l o c i t y s t r u c t u r e , t h e r e a r e two t y p e s of b o u n d a r i e s , model b o u n d a r i e s and d i v i d e r b o u n d a r i e s . A model boundary i s a s t r a i g h t l i n e of a r b i t r a r y d i p , a s s i g n e d a c o n s t a n t v e l o c i t y a l o n g i t s l e n g t h and a n o n - z e r o v e l o c i t y g r a d i e n t n o r m a l t o i t s l e n g t h . A d i v i d e r b o u n d a r y , a s s i g n e d a v e l o c i t y of z e r o , s e p a r a t e s a r e g i o n w i t h one v e l o c i t y and g r a d i e n t f rom a l a t e r a l l y a d j a c e n t r e g i o n w i t h a d i f f e r e n t v e l o c i t y and g r a d i e n t . B l o c k s may t h u s be d e f i n e d i n w h i c h t h e v e l o c i t y and b o t h t h e magni tude and d i r e c t i o n of t h e v e l o c i t y g r a d i e n t a r e a r b i t r a r y . The r a y p a t h w i t h i n a g i v e n b l o c k i s a c i r c u l a r a r c , f o r w h i c h t h e t r a v e l t i m e and d i s t a n c e t r a v e l l e d may be c a l c u l a t e d u s i n g v e r y s i m p l e a n a l y t i c a l e x p r e s s i o n s (Gebrande , 1976 ) . The s o u r c e may be l o c a t e d a l o n g any model b o u n d a r y , and r a y s t r a v e l l i n g upwards or downwards f rom t h e s o u r c e may be c o n s i d e r e d . I f a r a y i s i n c i d e n t t o a boundary a t an a n g l e w h i c h i s w i t h i n a s p e c i f i e d range of t h e c r i t i c a l 30 a n g l e , t h e n head waves may be p r o d u c e d . Beyond the p o i n t of i n t e r s e c t i o n of t h e c r i t i c a l r a y w i t h the b o u n d a r y , t h e head waves a r e s i m u l a t e d by s h o o t i n g c r i t i c a l l y r e f r a c t e d r a y s o f f t h e boundary a t r e g u l a r i n t e r v a l s a l o n g i t s l e n g t h . The r a y p a t h from a s p e c i f i c shot t o a s p e c i f i c r e c e i v e r must be found i n o r d e r t o c a l c u l a t e a model t r a v e l t i m e c o r r e s p o n d i n g t o t h e o b s e r v e d t r a v e l t i m e . F o r f i n d i n g r a y p a t h s , t h e W h i t t a l l and Clowes (1979) r a y t r a c e r employs a s h o o t i n g m e t h o d , i n w h i c h a shot l o c a t i o n and a range o f t a k e - o f f a n g l e s a r e s p e c i f i e d . I t was t h u s n e c e s s a r y t o e x t e n d t h e r a y t r a c e r t o p e r f o r m m u l t i p l e i t e r a t i o n s w h i c h c o n v e r g e d on t h e r e c e i v e r l o c a t i o n . F o r r e f l e c t e d and t u r n i n g r a y s , t h i s s i m p l y r e q u i r e s an e s t i m a t e of t h e r a t e t h a t the s h o t / r e c e i v e r range f o r t h e r a y changes w i t h s t a r t i n g a n g l e . F o r head waves , an e s t i m a t e i s r e q u i r e d of t h e r a t e of change of range w i t h r e s p e c t t o d i s t a n c e a l o n g t h e head wave b o u n d a r y . These e s t i m a t e s a r e t h e n u p d a t e d w i t h t h e most c u r r e n t r a y i n t h e i t e r a t i o n . 2 . 3 T h e o r y I t i s assumed t h a t t h e r e a r e sound g e o p h y s i c a l r e a s o n s f o r c h o o s i n g a p a r t i c u l a r s t a r t i n g model t o d e s c r i b e t h e v e l o c i t y s t r u c t u r e of a r e g i o n . Some of t h e r e a s o n s may be of a g e n e r a l n a t u r e , based on w e l l - e s t a b l i s h e d g e o l o g i c a l or t e c t o n i c p r i n c i p l e s s u c h as t h e e x i s t e n c e of a s u b d u c t i o n z o n e , a s e d i m e n t a r y b a s i n , or a f a u l t z o n e . C o n s t r a i n t s on t h e v e l o c i t y s t r u c t u r e may a l s o come from o t h e r r e f l e c t i o n o r r e f r a c t i o n s u r v e y s i n t h e a r e a ; f o r e x a m p l e , t h e r e may be t i e l i n e s c r o s s i n g t h e p r o f i l e t o be i n t e r p r e t e d , or t h e r e may be s m a l l e r 31 o f f s e t s u r v e y s i n the a r e a w h i c h d e s c r i b e the upper l a y e r s i n d e t a i l . F i n a l l y , the c h o i c e of c e r t a i n f e a t u r e s i n the model may be g u i d e d by a g e n e r a l e x a m i n a t i o n of the r e f r a c t i o n d a t a se t under c o n s i d e r a t i o n ; as d i s c u s s e d i n the i n t r o d u c t i o n t o t h i s c h a p t e r , a g i v e n a r r i v a l must be a s s o c i a t e d w i t h a p a r t i c u l a r boundary or a p a r t i c u l a r r e g i o n of the m o d e l . Whatever the r ea sons g u i d i n g the c h o i c e of a s t a r t i n g m o d e l , not a l l f e a t u r e s of t h e v e l o c i t y s t r u c t u r e a r e t o be d e t e r m i n e d by the i n v e r s e p r o c e d u r e . O n l y a few w e l l - c h o s e n p a r a m e t e r s , w h i c h s h o u l d be w e l l - s a m p l e d by m u l t i p l e r a y s w i t h d i f f e r e n t p a t h s , a r e a l l o w e d t o v a r y . 2 . 3 . 1 The f o r w a r d p r o b l e m In g e n e r a l , the t r a v e l t i m e T^j between the i - t h shot and the j - t h r e c e i v e r f o r a s e t of o b s e r v e d d a t a i s 1 ) where v ( x , z ) i s the a c t u a l v e l o c i t y s t r u c t u r e and ds i s the e lement of a r c l e n g t h a l o n g the r a y p a t h L^j from shot i t o r e c e i v e r j . F o r the W h i t t a l l and Clowes (1979) ray t r a c e r , the v e l o c i t y model i s s p e c i f i e d i n terms of b l o c k s w i t h c o n s t a n t v e l o c i t y g r a d i e n t and a r b i t r a r y b o u n d a r i e s . The v e l o c i t y v w i t h i n a g i v e n b l o c k i s g i v e n by v = v 0 + k z ( 2 . 2 ) where v 0 i s t h e v e l o c i t y a l o n g the t o p boundary of t h e b l o c k , k i s the v e r t i c a l v e l o c i t y g r a d i e n t , and z i s the v e r t i c a l d i s t a n c e from the t o p b o u n d a r y . Boundary p o s i t i o n i s s p e c i f i e d 32 by the c o o r d i n a t e s o f the e n d p o i n t s of the b o u n d a r y . P e r t u r b a t i o n s t o the v e l o c i t y s t r u c t u r e p r o d u c e changes i n b o t h t h e v e l o c i t y v and the r a y p a t h L;J . To f i r s t o r d e r , the t r a v e l t i m e can be a p p r o x i m a t e d u s i n g a T a y l o r s e r i e s e x p a n s i o n : T.. = T-. + I /9T \ A v 0 ( n + / 9T\ Ak. ( 2 . 3 ) + 2 / 9 T \ A h n ""\3hJn c T^j i s the c a l c u l a t e d t r a v e l t i m e t h r o u g h the s t a r t i n g m o d e l . The r a y pa s se s t h r o u g h M b l o c k s w i t h i n w h i c h v e l o c i t y i s a l l o w e d t o v a r y . Av„^ and A k m a r e t h e unknown, c o r r e c t i o n s f o r the v e l o c i t y a t t h e t o p of t h e m-th b l o c k and t h e v e l o c i t y g r a d i e n t i n t h e b l o c k . N i s the number of e n d p o i n t s c o r r e s p o n d i n g t o the v a r i a b l e b o u n d a r i e s i n t e r s e c t e d by the r a y , and A h ^ i s the unknown c o r r e c t i o n f o r the d e p t h of the n - t h boundary e n d p o i n t . The p a r t i a l d e r i v a t i v e s i n . e q u a t i o n 2 . 3 a r e c a l c u l a t e d f o r the s t a r t i n g m o d e l , and r e p r e s e n t the r a t e of change o f t r a v e l t i m e per u n i t change of pa rameter v a l u e . From e q u a t i o n s 2.1 and 2 .2 the p a r t i a l d e r i v a t i v e o f t r a v e l t i m e w i t h r e s p e c t t o v e l o c i t y a t the t o p of the m-th b l o c k i s ( 9 v 0 ) m \ 9 v 0 ( v ) ds ds (2 . 4 ) S i m i l a r l y , the p a r t i a l d e r i v a t i v e of t r a v e l t i m e w i t h r e s p e c t t o v e l o c i t y g r a d i e n t i s g i v e n by 33 ds (2 .5 ) T h u s , b o t h p a r t i a l d e r i v a t i v e s may be s i m p l y o b t a i n e d by n u m e r i c a l i n t e g r a t i o n a l o n g the r a y . The i n t e g r a t i o n was implemented f o r t h e W h i t t a l l and Clowes (1979) r a y t r a c e r by d i v i d i n g t h e c i r c u l a r r a y p a t h w i t h i n each b l o c k i n t o a l a r g e number of segments of e q u a l l e n g t h and a s suming c o n s t a n t v e l o c i t y a l o n g each segment . The p a r t i a l d e r i v a t i v e of t r a v e l t i m e w i t h r e s p e c t t o the d e p t h of the n - t h boundary e n d p o i n t was c a l c u l a t e d a n a l y t i c a l l y u s i n g a s i m p l e e x p r e s s i o n d e r i v e d from g e o m e t r i c a l a r g u m e n t s . F i g u r e 2 . 1 a shows a r a y between shot and r e c e i v e r , r e f l e c t e d a t an a n g l e a f rom a b o u n d a r y . When the boundary i s p e r t u r b e d by a d i s t a n c e dD normal t o i t s l e n g t h , the r a y p a t h between the same shot and r e c e i v e r i s c h a n g e d , but the r e f l e c t i o n p o i n t on t h e boundary remains the same; i . e . i t moves t h r o u g h space w i t h t h e b o u n d a r y . T h u s , the l e n g t h of the r a y p a t h changes by a d i s t a n c e (2 dD c o s a ) . I f t h e v e l o c i t y i m m e d i a t e l y above t h e boundary i s v ^ , t h e n the e x t r a t r a v e l t i m e dT t a k e n by the p e r t u r b e d r a y i s (2 dD c o s a / v^ ) , and 9T = 2 c o s a ( 2 . 6 ) dD v For a r e f r a c t e d ray ( F i g . 2 . 1 b ) , the c o r r e s p o n d i n g d e r i v a t i v e i s 9T = c o s a - cosff ( 2 . 7 ) 9D v , v-where a i s the i n c i d e n t a n g l e , B i s the emergent , and v,, and v^ a r e the v e l o c i t i e s a l o n g the i n c i d e n t and emergent p o r t i o n s of F I G . 2 . 1 . (a) When a boundary i s moved by an i n f i n i t e s i m a l d i s t a n c e d D , ' t h e r e f l e c t e d r a y p a t h between a f i x e d shot and r e c e i v e r i s a l s o c h a n g e d . The heavy s o l i d l i n e s show the p o s i t i o n s of boundary and r a y p a t h b e f o r e t h e p e r t u r b a t i o n , and the heavy dashed show t h e new p o s i t i o n s . The r a y p a t h i n c r e a s e s i n l e n g t h by an amount 2 dD c o s a . (b) For a r e f r a c t e d r a y , the r a y p a t h l e n g t h i n c r e a s e s by an amount dD(cosa - cos/3) . LO 35 the r a y p a t h , r e s p e c t i v e l y . Note t h a t e q u a t i o n 2 .7 i s more g e n e r a l and r e d u c e s t o e q u a t i o n 2 .6 i f the a n g l e B i s . c o n s i s t e n t l y measured from the normal below t h e b o u n d a r y . A s i m p l e g e o m e t r i c c o r r e c t i o n i s r e q u i r e d t o c o n v e r t the d e r i v a t i v e from d i s t a n c e measured normal t o a boundary t o d i s t a n c e measured v e r t i c a l l y a t a boundary e n d p o i n t ( F i g . 2 . 2 ) . I f t h e boundary e n d p o i n t s a r e a t h n and h h + 1 , then u s i n g the g e o m e t r i c r e l a t i o n s f o r dD/dh and d h / d h n shown i n F i g u r e 2 . 2 , the c h a i n r u l e may be a p p l i e d t o f i n d / 3 T \ = f cosa ~ cos/3 \ c o s ? / h - h n \ ( 2 . 8 ) where 7 i s the d i p of t h e boundary measured from the h o r i z o n t a l and h i s t h e d e p t h a t w h i c h the r a y i n t e r s e c t s t h e b o u n d a r y . A l l o f t h e s e q u a n t i t i e s a r e found by t h e ray t r a c e r , s i n c e f u l l d e t a i l s o f t h e r a y p a t h f o r t h e s t a r t i n g model a r e known. I n s i m u l t a n e o u s i n v e r s i o n s f o r v e l o c i t y and e a r t h q u a k e l o c a t i o n s , t h e p a r t i a l d e r i v a t i v e s w i t h r e s p e c t t o h y p o c e n t e r c o o r d i n a t e s may be found by t h e same g e o m e t r i c a l method . I f the i n t e r s e c t i o n p o i n t of the r a y w i t h t h e boundary were r e g a r d e d as t h e t e r m i n a t i n g p o i n t of t h e r a y ( i . e . a s o u r c e ) , then e i t h e r e q u a t i o n 2 . 6 or 2 .7 becomes 3T = c o s a ( 2 . 9 ) 3z vM where z i s t h e c o o r d i n a t e i n t h e v e r t i c a l d i r e c t i o n and c o s a i s t h e v e r t i c a l d i r e c t i o n c o s i n e . In two d i m e n s i o n s , t h e p a r t i a l d e r i v a t i v e w i t h r e s p e c t t o t h e h o r i z o n t a l c o o r d i n a t e s i m p l y i n v o l v e s t h e h o r i z o n t a l d i r e c t i o n c o s i n e . 36 F I G . 2.2. W i t h one e n d p o i n t of a boundary f i x e d , an i n f i n i t e s i m a l change d h n i n the d e p t h a t t h e o t h e r e n d p o i n t i s r e l a t e d by s i m p l e geometry t o the i n f i n i t e s i m a l change ,dD n o r m a l t o t h e boundary a t an a r b i t r a r y p o i n t a l o n g i t s l e n g t h . 37 2 . 3 . 2 Damped l e a s t s q u a r e s i n v e r s i o n E q u a t i o n 2 . 3 may be w r i t t e n i n m a t r i x n o t a t i o n as AAx = At ( 2 . 1 0 ) where A i s a m a t r i x of p a r t i a l d e r i v a t i v e s , Ax i s the s o l u t i o n v e c t o r c o n t a i n i n g the (M+N) parameter a d j u s t m e n t s , and At i s t h e t r a v e l t i m e r e s i d u a l v e c t o r , At^ j = T^j - TV- , c o r r e s p o n d i n g t o the q o b s e r v a t i o n s . The n o n - l i n e a r p r o b l e m has been l i n e a r i z e d by t h e use of e q u a t i o n 2 . 3 , and so the s o l u t i o n must be computed i t e r a t i v e l y . The c u r r e n t s o l u t i o n Ax i s a p p l i e d t o the s t a r t i n g m o d e l , r a y s a r e t r a c e d t h r o u g h the new s t a r t i n g model t o f i n d a new m a t r i x A and d a t a v e c t o r A t , and a new s e t of pa rameter a d j u s t m e n t s a r e c a l c u l a t e d . The p r o c e d u r e i s r e p e a t e d u n t i l c o n v e r g e n c e i s r e a c h e d t o w i t h i n t h e r e q u i r e d a c c u r a c y . W i t h many more t r a v e l t i m e o b s e r v a t i o n s than p a r a m e t e r s , t h e p r o b l e m i s o v e r d e t e r m i n e d . The c l a s s i c a l l e a s t - s q u a r e s s o l u t i o n of t h e o v e r d e t e r m i n e d p r o b l e m ( e q u a t i o n 2 .10 ) i n v o l v e s m i n i m i z i n g the t r a v e l t i m e r e s i d u a l s w i t h r e s p e c t t o t h e p a r a m e t e r v a r i a t i o n s . T h i s l e a d s t o the c a l c u l a t i o n of t h e n o r m a l e q u a t i o n s , A T AAx =AT At ( 2 . 1 1 ) However , d i f f i c u l t i e s a r i s e w i t h t h i s s o l u t i o n because the norma l e q u a t i o n m a t r i x A T A may be s i n g u l a r or n e a r - s i n g u l a r , due t o a f u n d a m e n t a l l a c k of c o n s t r a i n t on c e r t a i n p a r a m e t e r s . Symptoms of the l a c k of c o n s t r a i n t would be l a r g e v a r i a t i o n s i n the p a r a m e t e r s o l u t i o n from i t e r a t i o n t o i t e r a t i o n . The method used • h e r e t o overcome t h i s d i f f i c u l t y i s t o a p p l y a s t a n d a r d damped l e a s t - s q u a r e s s o l u t i o n , f i r s t d e s c r i b e d by L e v e n b e r g ( 1 9 4 4 ) ; i n the c o n t e x t of t r a v e l t i m e i n v e r s i o n , I c l o s e l y f o l l o w 38 t h e a p p r o a c h d e s c r i b e d by A k i and Lee (1976) and C r d s s o n ( 1 9 7 6 ) . L a r g e v a r i a t i o n s i n t h e p a r a m e t e r s a r e damped out by m i n i m i z i n g the w e i g h t e d sum of the t r a v e l t i m e r e s i d u a l s and the parameter s o l u t i o n v e c t o r s , l e a d i n g t o a sys tem of m o d i f i e d norma l equat i o n s , ( A T A + 0) Ax = A T At ( 2 .12 ) 0 i s a d i a g o n a l w e i g h t i n g m a t r i x , g i v e n by © = e fo2/< 0 0 a2/o, 2 0 0 \ "I ( 2 . 1 3 ) a2 i s an e s t i m a t e of the H e r e , 6 i s an o v e r a l l damping f a c t o r , v a r i a n c e of the t r a v e l t i m e r e s i d u a l s and 2 i s an e s t i m a t e of t h e v a r i a n c e of the i - t h component of the pa rameter v e c t o r . E q u a t i o n 2 .12 has as i t s s o l u t i o n the e s t i m a t e d c o r r e c t i o n v e c t o r Ax = ( A T A + 0 ) - 1 A T A t ( 2 . 1 4 ) The r e s o l u t i o n and c o v a r i a n c e m a t r i c e s a r e g i v e n by ( 2 . 1 5 ) ( 2 . 1 6 ) The magn i tude of the d i a g o n a l e lement of R i s a good measure of the r e s o l u t i o n of the c o r r e s p o n d i n g parameter ( W i g g i n s 1972) . Damping i s i n c r e a s e d by i n c r e a s i n g the magni tude of the e l e m e n t s o f 0 . S i n c e the i n d i v i d u a l w e i g h t i n g f a c t o r s a r e R = (A T A + 0) " ' A T A C = o2 ( A T A + 0 ) - ' R T i n v e r s e l y p r o p o r t i o n a l t o the v a r i a n c e parameter a d j u s t m e n t w i t h a s m a l l v a r i a n c e w i l l have a l a r g e damping f a c t o r . T h i s i s s i g n i f i c a n t s i n c e t h e magni tude of the parameter 39 a d j u s t m e n t s may d i f f e r by more than a f a c t o r of 10; f o r example , v e l o c i t y a d j u s t m e n t s may be l e s s than 0.1 km/s whereas d e p t h a d j u s t m e n t s may be s e v e r a l k i l o m e t r e s . But a pa rameter a d j u s t m e n t w i t h a s m a l l v a r i a n c e i m p l i e s t h a t a s m a l l change i n p a r a m e t e r p r o d u c e s a l a r g e change i n t r a v e l t i m e , so t h e c o r r e s p o n d i n g p a r t i a l d e r i v a t i v e i s l a r g e . As w e l l , t h e r e l a t e d d i a g o n a l e lement of the norma l e q u a t i o n s m a t r i x A T A i s l a r g e , and so a r e l a t i v e l y l a r g e damping f a c t o r i s r e q u i r e d t o have any e f f e c t on t h a t d i a g o n a l e l e m e n t . T h u s , the purpose o f the i n d i v i d u a l w e i g h t i n g f a c t o r s i s t o b a l a n c e the e f f e c t s of t h e o r d e r of magn i tude d i f f e r e n c e s i n parameter a d j u s t m e n t v a l u e s . As damping i s i n c r e a s e d , the c o v a r i a n c e v a l u e s d e c r e a s e and t h e r e s o l u t i o n v a l u e s a l s o d e c r e a s e , e x h i b i t i n g t h e s t a n d a r d t r a d e - o f f between r e s o l u t i o n and v a r i a n c e . I t i s d e s i r a b l e t o have the o v e r a l l damping f a c t o r 8 as s m a l l as p o s s i b l e t o m a i n t a i n maximum r e s o l u t i o n but l a r g e enough t o a c h i e v e r e a s o n a b l e s t a b i l i t y and v a r i a n c e e s t i m a t e s . U s u a l l y , damping may be d e c r e a s e d from i t e r a t i o n t o i t e r a t i o n of the i n v e r s i o n p r o c e d u r e . 2 .4 T e s t s w i t h A r t i f i c i a l Data T e s t i n g the ray t r a c e i n v e r s i o n p r o c e d u r e u s i n g s y n t h e t i c d a t a s e r v e s two p u r p o s e s . F i r s t , s i n c e the " t r u e " model i s known, i t i s o b v i o u s l y n e c e s s a r y t o c o n f i r m t h a t the p r o c e d u r e w i l l c o r r e c t l y r e p r o d u c e t h a t model t o w i t h i n a s p e c i f i e d degree of c e r t a i n t y . T h i s i s p a r t i c u l a r l y i m p o r t a n t t o c o n f i r m the v a l i d i t y o f t h e l i n e a r i z i n g a p p r o x i m a t i o n t o the t r a v e l t i m e ( e q u a t i o n 2 . 3 ) . S e c o n d , s y n t h e t i c t e s t s may be u s e f u l i n 40 a s s e s s i n g t h e s i g n i f i c a n c e of the r e s u l t s from r e a l d a t a . That i s , i f a s y n t h e t i c model i s used w h i c h i s as c l o s e as p o s s i b l e t o t h e model used w i t h t h e a c t u a l d a t a , t h e p e r f o r m a n c e of the i n v e r s i o n p r o c e d u r e may p r o v e a p p l i c a b l e t o t h e r e a l i n t e r p r e t a t i o n . The f i r s t t e s t of t h e r a y t r a c e i n v e r s i o n p r o c e d u r e was an a t t e m p t t o r e c o v e r a s i m p l e t w o - l a y e r model f o r w h i c h t h e d e p t h of the boundary between t h e l a y e r s v a r i e d l a t e r a l l y . F i g u r e 2 . 3 shows the s y n t h e t i c model and the r a y p a t h s used t o g e n e r a t e s y n t h e t i c " o b s e r v e d " t r a v e l t i m e s . P a r a m e t e r v a l u e s f o r t h e s y n t h e t i c model a r e g i v e n i n T a b l e 2 . 1 . The model may be c o n s i d e r e d a n a l o g o u s t o a s i m p l i f i e d c r u s t a l m o d e l . The upper l a y e r c o r r e s p o n d s t o t h e c r u s t w i t h c o n s t a n t v e l o c i t y 6 . 5 km/s , w h i l e the second l a y e r i s the m a n t l e ; t h e boundary between the l a y e r s c o r r e s p o n d s t o t h e Moho, below w h i c h the v e l o c i t y i s 8 . 0 km/s w i t h c o n s t a n t v e l o c i t y g r a d i e n t 0.01 k m / s / k m . The Moho boundary i s a t a d e p t h of a p p r o x i m a t e l y 30 km, but t h e r e a r e v a r i a t i o n s i n the Moho d e p t h as l a r g e as 3 km. S h o t s a t e i t h e r end of the model r e s u l t i n a f o r w a r d and a r e v e r s e d p r o f i l e , r e c o r d e d on 9 r e c e i v e r s spaced e v e r y 20 km between 70 km and 230 km ( F i g 2 . 3 ) . A r r i v a l s i n c l u d e d w i d e - a n g l e r e f l e c t i o n s f rom t h e boundary and t u r n i n g r a y s t h r o u g h the g r a d i e n t l a y e r . Not a l l r e c e i v e r s r e c o r d e d b o t h a r r i v a l s , e i t h e r because t h e s h o t -r e c e i v e r o f f s e t was l e s s t h a n the c r i t i c a l d i s t a n c e o r because of the e f f e c t of the c o r n e r i n t h e boundary a t 120 km, w h i c h p r o d u c e d a shadow zone f o r t h e r e f l e c t i o n s . The t o t a l number of t r a v e l t i m e o b s e r v a t i o n s was 3 1 . No random n o i s e was added t o t h e s y n t h e t i c t r a v e l t i m e s . However , the r a y t r a c i n g scheme i n v o l v e d 41 S H O T A D I S T A N C E ( K M ) 0 100 200 300 o i D I S T A N C E ( K M ) S H O T B 0 100 200 300 F I G . 2 . 3 . S i m p l e t w o - l a y e r model used t o g e n e r a t e s y n t h e t i c t r a v e l t i m e s f o r t e s t i n g the r a y t r a c e i n v e r s i o n p r o c e d u r e . V e l o c i t y g r a d i e n t s a r e 0 i n the upper l a y e r and 0.01 km/s /km i n the l o w e r l a y e r . The f i v e v a r i a b l e s v , , v 2 , h , , h 2 and h 3 , a r e t o be r e c o v e r e d i n t h e i n v e r s i o n (see T a b l e 2 . 1 ) . 42 i t e r a t i o n t o a s p e c i f i c r e c e i v e r l o c a t i o n t o w i t h i n a t o l e r a n c e of 0.1 km, and so t h e t r a v e l t i m e e r r o r due t o e r r o r i n l o c a t i o n c o u l d be as l a r g e as (0 .1 k m ) / ( 6 . 5 k m / s ) , or 15 ms. F o r t h e i n v e r s i o n p r o c e d u r e , f i v e p a r a m e t e r s of t h e model were a l l o w e d t o v a r y : the v e l o c i t y of t h e f i r s t l a y e r , t h e v e l o c i t y a t the t o p of t h e second l a y e r , and t h e d e p t h s of t h e boundary a t 0 km, 120 km and 300 km. A l t h o u g h t h e v a r i a n c e a2 of t r a v e l t i m e e r r o r s was q u i t e s m a l l , a v a l u e of 50 ms was assumed t o e v a l u a t e the p e r f o r m a n c e of t h e damping scheme. A p r i o r i gues ses were made f o r the v a l u e s of the p a r a m e t e r v a r i a n c e s t o be used i n t h e w e i g h t i n g m a t r i x , and the gues se s were c o n f i r m e d by l o o k i n g a t the subsequent s o l u t i o n . In any c a s e , e x a c t v a l u e s f o r t h e v a r i a n c e s were not r e q u i r e d , s i n c e t h e i r main purpose was t o e l i m i n a t e t h e e f f e c t of o r d e r of magn i tude d i f f e r e n c e s . A v a l u e of 0 .015 km/s was chosen as an e s t i m a t e o f t h e rms e r r o r of t h e v e l o c i t y v a r i a t i o n s . F o r a v e l o c i t y of 8 .0 km/s , t h i s i s S y n t h e t i c V a l u e S t a r t i n g V a l u e F i n a l V a l u e M o d e l R e s . o 6.50 km/s 6 .00 km/s 6 .49 km/s 0 .93 0 .007 km/s v 2 8 .00 km/s 7 .80 km/s 7 .97 km/s 0 .72 0 .013 km/s h , 33 .0 km 2 3 . 0 km 3 2 . 9 km 0 .96 0 .38 km h 2 3 0 . 0 km 2 3 . 0 km 2 9 . 3 km 0 .92 0 .46 km h 3 3 1 . 5 km 2 3 . 0 km 3 1 . 5 km 0 .99 0 .23 km TABLE 2 . 1 . S y n t h e t i c t e s t u s i n g a s i m p l e t w o - l a y e r model ( F i g . 2 . 3 ) . S y n t h e t i c m o d e l , s t a r t i n g m o d e l , and c h a r a c t e r i s t i c s o f f i n a l model a r e shown. R e s o l u t i o n and s t a n d a r d e r r o r a f o r t h e f i n a l model g i v e r e l a t i v e measures of pa rameter c e r t a i n t i e s . O v e r a l l damping f a c t o r d f o r t h e f i n a l i t e r a t i o n was 0 . 2 5 . 43 a p r e c i s i o n of about 1 p a r t i n 500 , w h i c h i s comparab le t o t h e p r e c i s i o n assumed f o r the t r a v e l t i m e s (50 ms out of a t y p i c a l t r a v e l t i m e of about 25 s ) . For d e p t h s , t h e rms e r r o r was e s t i m a t e d as ~1 km. The o v e r a l l damping c o e f f i c i e n t 6 was s e t t o 1.0 f o r t h e f i r s t i t e r a t i o n and r e d u c e d t o 0 .25 f o r subsequent i t e r a t i o n s . As a s t a r t i n g m o d e l , the Moho boundary was assumed t o be f l a t - l y i n g a t a d e p t h of 23 km, w i t h the v e l o c i t y s e t t o 6 .0 km/s above t h e boundary and 7 .8 km/s j u s t be low t h e boundary ( T a b l e 2 . 1 ) . I n F i g u r e 2 . 4 , c u r v e 1 ( l o n g dashed l i n e s ) r e p r e s e n t s t h e t r a v e l t i m e c u r v e f o r t h e s t a r t i n g m o d e l . The s y n t h e t i c t r a v e l t i m e s a r e shown by t h e s o l i d d o t s i n F i g u r e 2 . 4 , and the rms d i f f e r e n c e between t h e s t a r t i n g model t r a v e l t i m e s and t h e s y n t h e t i c t r a v e l t i m e s was 1.035 s . T h i s was r e d u c e d t o 0 .266 s a f t e r one i t e r a t i o n of t h e i n v e r s i o n p r o c e d u r e ( c u r v e 2 i n F i g . 2 . 4 ) , t o 0 .030 s a f t e r t h e second i t e r a t i o n ( c u r v e 3 i n F i g . 2 . 4 ) , and t o 0 .019 s a f t e r t h e t h i r d and f i n a l i t e r a t i o n . The f i n a l rms d i f f e r e n c e was c o m p a r a b l e t o the v a l u e of 0 .015 s due t o l o c a t i o n e r r o r i n the r a y t r a c i n g p r o c e d u r e . The f i n a l i n v e r t e d model r e p r o d u c e d t h e o r i g i n a l s y n t h e t i c model v e r y c l o s e l y , as shown i n T a b l e 2 . 1 . The d i a g o n a l e l e m e n t s of t h e r e s o l u t i o n m a t r i x and t h e s t a n d a r d e r r o r s o b t a i n e d from t h e d i a g o n a l o f t h e c o v a r i a n c e m a t r i x g i v e r e l a t i v e measures f o r t h e p a r a m e t e r c e r t a i n t i e s i n the f i n a l s o l u t i o n . The most p o o r l y d e t e r m i n e d parameter was the v e l o c i t y v 2 a t the t o p of t h e second l a y e r , a l t h o u g h the d i f f e r e n c e compared t o the s y n t h e t i c model v e l o c i t y was o n l y 0 .03 k m / s . The r e s o l u t i o n f o r t h e 44 C J W G O o crj 00-Q I E-" to SHOT A 100 200 DISTANCE (KM) 300 o 0 5 w C O ^ 00 q CO Q I S H O T B 100 200 DISTANCE (KM) 300 F I G . 2 . 4 . P e r f o r m a n c e of the i n v e r s i o n p r o c e d u r e f o r t h e t w o -l a y e r model of F i g . 2 . 3 . S o l i d d o t s a r e t h e s y n t h e t i c t r a v e l t i m e s , c u r v e 1 i s t h e s t a r t i n g model t r a v e l t i m e c u r v e , c u r v e 2 i s a f t e r t h e f i r s t i t e r a t i o n and c u r v e 3 i s a f t e r t h e t h i r d i t e r a t i o n . Rms d i f f e r e n c e between the s y n t h e t i c and c u r v e 3 t r a v e l t i m e s i s 30 ms; a f u r t h e r i t e r a t i o n r e d u c e d the d i f f e r e n c e t o 19 ms. 45 v e l o c i t y v 2 was 0 . 7 2 , compared t o v a l u e s above 0 .9 f o r t h e o t h e r p a r a m e t e r s , and the s t a n d a r d e r r o r was n e a r l y t w i c e as l a r g e as f o r the v e l o c i t y v , i n t h e t o p l a y e r . S i m i l a r l y , t h e n e x t most p o o r l y d e t e r m i n e d parameter was t h e d e p t h h 2 , w h i c h had a r e s o l u t i o n of 0 .92 and t h e l a r g e s t s t a n d a r d e r r o r ( 0 . 4 6 km) of a l l t h e d e p t h p a r a m e t e r s . The o v e r a l l damping f a c t o r 6 was 0 .25 f o r the f i n a l i t e r a t i o n . I f 8 i s r e d u c e d f o r a g i v e n i t e r a t i o n so t h a t damping i s f u r t h e r r e d u c e d , t h e n t h e s t a n d a r d t r a d e - o f f between r e s o l u t i o n and v a r i a n c e i s o b s e r v e d . F o r e x a m p l e , i f 6 was r e d u c e d t o 0.1 f o r t h e f i n a l i t e r a t i o n , t h e r e s o l u t i o n f o r parameter v 2 i n c r e a s e s t o 0 .86 w h i l e t h e s t a n d a r d e r r o r a l s o i n c r e a s e s t o 0 .013 k m / s . I n t h i s c a s e , however , p a r a m e t e r v a l u e s change o n l y s l i g h t l y and t h e rms t r a v e l t i m e d i f f e r e n c e d e c r e a s e s i n s i g n i f i c a n t l y t o 0 .018 s . A f u n d a m e n t a l l i m i t a t i o n i n the s u c c e s s of t h e i n v e r s i o n p r o c e d u r e i s the s u b j e c t i v e c h o i c e of p a r a m e t e r i z a t i o n of t h e s t a r t i n g m o d e l , i n c l u d i n g t h e c h o i c e of r a y p a t h s used t o c a l c u l a t e model t r a v e l t i m e s . F o r the t w o - l a y e r t e s t e x a m p l e , t h e t r u e model w o u l d not have been a c c u r a t e l y r e c o v e r e d i f the d e p t h parameter h 2 i n the s t a r t i n g model had been s p e c i f i e d a t a d i s t a n c e 200 km from shot A i n s t e a d of a t 120 km as i n t h e t r u e m o d e l . S i m i l a r y , i f t h e v e l o c i t y g r a d i e n t i n a l a y e r had been chosen as a v a r i a b l e pa rameter i n a d d i t i o n t o the v e l o c i t y a t the t o p of t h e l a y e r , t h e n i t w o u l d have been p o s s i b l e t o f i n d o t h e r models w h i c h a l s o f i t t h e d a t a . That i s , t h e v e l o c i t y g r a d i e n t i s a v e r y p o o r l y c o n s t r a i n e d p a r a m e t e r , e s p e c i a l l y i n the f i r s t l a y e r where a l l of t h e r a y p a t h s p e n e t r a t e t o the same d e p t h ( i . e . t h e bot tom of t h e l a y e r ) and t h e r e a r e no r a y s w h i c h 46 i n d e p e n d e n t l y sample o n l y t h e t o p of t h e l a y e r . The model may be o v e r - p a r a m e t e r i z e d not o n l y by a l l o w i n g t h e v e l o c i t y g r a d i e n t t o v a r y but a l s o by s p e c i f y i n g many v e l o c i t y b l o c k s and many boundary segments . In t h i s c a s e , a n o t h e r p r o b l e m a r i s e s i n a d d i t i o n t o t h e p r o b l e m of non-u n i q u e n e s s f o r most of t h e p a r a m e t e r s . W i t h many v a r i a b l e b l o c k s and b o u n d a r i e s , the r a y t r a c i n g becomes v e r y u n s t a b l e , s i n c e no s m o o t h i n g i s done i n t h e r a y t r a c e program e i t h e r of b o u n d a r i e s or of v e l o c i t i e s between b l o c k s . Ray p a t h s wou ld t e n d t o s c a t t e r , and i t wou ld be d i f f i c u l t t o f i n d r a y p a t h s between many s h o t s and r e c e i v e r s . That i s , t h e i n v e r s e p r o c e d u r e i s not v e r y r o b u s t because of t h e i n s t a b i l i t y of the r a y t r a c i n g . A l s o , the use of t h e i n v e r s e r o u t i n e g i v e s no added a s s u r a n c e t h a t t h e c o r r e c t c h o i c e of p a r a m e t e r i z a t i o n was made, j u s t as i n t h e case of u s i n g t h e r a y t r a c e r i n a f o r w a r d m o d e l l i n g scheme. I n t h e second t e s t of t h e r a y t r a c e i n v e r s i o n p r o c e d u r e , a model was c o n s t r u c t e d t o r e p r e s e n t t h e s u b d u c t i o n zone v e l o c i t y s t r u c t u r e b e n e a t h l i n e I of t h e V a n c o u v e r I s l a n d S e i s m i c P r o j e c t , w h i c h i s i n t e r p r e t e d i n C h a p t e r 4 . The t e s t model was v e r y s i m i l a r t o t h e p r e l i m i n a r y model of E l l i s e t a l . ( 1 9 8 3 ) , m o d i f i e d by t h e a d d i t i o n of an upper m a n t l e r e f l e c t o r (boundary 3-4 i n F i g . 2 . 5 a ) . To g e n e r a t e t h e s y n t h e t i c d a t a s e t , r a y s were t r a c e d f rom l o c a t i o n s c o r r e s p o n d i n g t o t h e t h r e e main s h o t s of t h e e x p e r i m e n t ( P 1 9 , P13 and P 8 ; see F i g . 1.3) t o t h e same 32 r e c e i v e r l o c a t i o n s as used d u r i n g t h e r e c o r d i n g of l i n e I . To a p p r o x i m a t e the e r r o r s o f a r e a l t r a v e l t i m e d a t a s e t , random G a u s s i a n n o i s e w i t h a s t a n d a r d d e v i a t i o n of 75 ms, t h e same as t h e e s t i m a t e d p i c k i n g e r r o r of the t r a v e l t i m e s , was added t o the F I G . 2 . 5 . (a) Ray p a t h s t h r o u g h a t e s t s t a r t i n g model u s i n g t h e same shot and r e c e i v e r l o c a t i o n s as i n the i n t e r p r e t a t i o n of l i n e I of t h e V a n c o u v e r I s l a n d S e i s m i c P r o j e c t . V a r i a b l e s i n the i n v e r s i o n p r o c e d u r e i n c l u d e the d e p t h of the s u b d u c t i n g Moho a t p o i n t s 1 and 2 and the d e p t h of an upper mant le r e f l e c t o r a t p o i n t s 3 and 4 . (b) V e l o c i t y - d e p t h p r o f i l e a t l o c a t i o n A on t h e r a y t r a c e m o d e l . A f i x e d m a n t l e g r a d i e n t of O . O I k m / s / k m i s assumed. O n l y the v e l o c i t y below the Moho ( p o i n t 5) i s v a r i a b l e . 48 a r t i f i c i a l d a t a . F o r t h e t e s t p r o c e d u r e , t h e a r r i v a l s t o the near o f f s e t r e c e i v e r s were m o d e l l e d as t u r n i n g r a y s t h r o u g h the m a n t l e , w h i l e the f a r o f f s e t a r r i v a l s were m o d e l l e d as r e f l e c t i o n s f rom the upper m a n t l e b o u n d a r y . F i g u r e 2 . 5 a shows t h e s t a r t i n g model and t h e r a y p a t h s t h r o u g h i t . The p a r a m e t e r s t o be r e c o v e r e d , w h i c h a r e the v a r i a b l e s i n t h e i n v e r s e method , i n c l u d e d t h e d e p t h s of t h e Moho a t p o s i t i o n s 1 and 2 , t h e d e p t h s o f t h e upper m a n t l e r e f l e c t o r a t l o c a t i o n s 3 and 4, and t h e Moho v e l o c i t y ( p o i n t 5 i n F i g . 2 . 5 b ) . A f i x e d m a n t l e v e l o c i t y g r a d i e n t o f 0.01 km/s/km was as sumed. T h i s model was a c t u a l l y not much more c o m p l i c a t e d t h a n t h e f i r s t t e s t model d i s c u s s e d p r e v i o u s l y . A l t h o u g h t h e c r u s t a l p o r t i o n s of t h e s u b d u c t i o n zone t e s t model were c o m p l e x , n e a r l y a l l p a r a m e t e r s r e l a t e d t o t h e c r u s t were c o n s i d e r e d f i x e d and d i d not e n t e r i n t o t h e i n v e r s e p r o c e d u r e . The same v a l u e s as i n t h e f i r s t t e s t were used f o r t h e e l e m e n t s of t h e w e i g h t i n g m a t r i x , t h a t i s , 0 .015 km/s f o r t h e s t a n d a r d e r r o r of t h e v e l o c i t y and 1 km f o r t h e d e p t h s . The s t a n d a r d e r r o r of t h e t i m e measurements was 75 ms, the l e v e l o f the random n o i s e added t o t h e d a t a . As b e f o r e , t h e o v e r a l l c o e f f i c i e n t 8 was s e t t o 1.0 f o r the f i r s t i t e r a t i o n and s u b s e q u e n t l y r e d u c e d t o 0 . 2 5 . The p e r f o r m a n c e of t h e i n v e r s e p r o c e d u r e i s d e m o n s t r a t e d i n F i g u r e 2 . 6 , F i g u r e 2 .7 and T a b l e 2 . 2 . F i g u r e 2 . 6 shows a b lowup of the c e n t r a l p o r t i o n of t h e v e l o c i t y m o d e l . The dashed l i n e s c o r r e s p o n d t o t h e s t a r t i n g model w h i l e t h e heavy s o l i d l i n e s o u t l i n e t h e f i n a l model a f t e r two i t e r a t i o n s . The f i n a l model compares w e l l w i t h the " t r u e " m o d e l , shown by t h e d o t t e d l i n e s , D I S T A N C E ( K M ) 7 5 1 0 0 1 2 5 1 5 0 1 7 5 A 2 0 0 2 2 5 2 5 0 4 1 1 1 I v r i , I F I G . 2 . 6 . (a) Dashed l i n e s show the boundary p o s i t i o n s of the s t a r t i n g model ( F i g . 2 . 5 ) . Heavy s o l i d l i n e s o u t l i n e the f i n a l p o s i t i o n s a f t e r two i t e r a t i o n s of t h e i n v e r s i o n p r o c e d u r e . D o t t e d l i n e s show the " t r u e " p o s i t i o n s of the s u b d u c t i n g o c e a n i c Moho and upper m a n t l e r e f l e c t o r , (b) F i n a l ( s o l i d l i n e ) , t r u e ( d o t t e d l i n e ) and s t a r t i n g (dashed l i n e ) upper m a n t l e v e l o c i t y . No change i n v e l o c i t y g r a d i e n t was p e r m i t t e d . L o c a t i o n of v e l o c i t y p r o f i l e s i s a t 50 °175 200 225 250 275 300 325 350 DISTANCE (KM) F I G . 2 . 7 . P e r f o r m a n c e of t h e r a y t r a c e i n v e r s i o n p r o c e d u r e a p p l i e d t o t h e s u b d u c t i o n zone t e s t m o d e l . Dashed l i n e s a r e t h e t r a v e l t i m e c u r v e s f o r t h e s t a r t i n g model of F i g . 2 . 5 , and s o l i d l i n e s a r e the f i n a l model t r a v e l t i m e c u r v e s a f t e r 2 i t e r a t i o n s . C r o s s e s a r e t h e s y n t h e t i c t r a v e l t i m e s , t o w h i c h 75 ms random n o i s e has been a d d e d . Rms d i f f e r e n c e beween s y n t h e t i c and model t r a v e l t i m e s i s 405 ms f o r t h e s t a r t i n g model and 74 ms f o r t h e f i n a l m o d e l . 51 t h e o n l y s i g n i f i c a n t d i f f e r e n c e b e i n g an e r r o r of about 1.6 km f o r t h e e n d p o i n t s of the upper m a n t l e r e f l e c t o r ( F i g . 2 . 6 a and T a b l e 2 . 2 ) . F i g u r e 2 .7 i n d i c a t e s how t h e t r a v e l t i m e f i t i s i m p r o v e d by t h e i n v e r s e p r o c e d u r e . F o r each of t h e t h r e e s h o t s , t h e dashed l i n e s a r e the t r a v e l t i m e c u r v e s c o r r e s p o n d i n g t o the s t a r t i n g m o d e l , t h e s o l i d l i n e s a r e the t r a v e l t i m e c u r v e s f o r t h e f i n a l m o d e l , and t h e c r o s s e s a r e t h e s y n t h e t i c " o b s e r v e d " t r a v e l t i m e s . The rms d i f f e r e n c e between s t a r t i n g model t r a v e l t i m e s and s y n t h e t i c t r a v e l t i m e s was 405 ms. T h i s was r e d u c e d t o 80 ms a f t e r one i t e r a t i o n and t o 74 ms a f t e r t h e second and f i n a l i t e r a t i o n . Subsequent i t e r a t i o n s p r o d u c e d o n l y s m a l l pa rameter p e r t u r b a t i o n s and r e d u c e d t h e rms t r a v e l t i m e d i f f e r e n c e o n l y m a r g i n a l l y ; s i n c e t h e f i n a l rms v a l u e was a l r e a d y below t h e l e v e l of t h e n o i s e , p e r t u r b a t i o n s from subsequent i t e r a t i o n s c o u l d not be c o n s i d e r e d s i g n i f i c a n t . S y n t h e t i c V a l u e S t a r t i n g V a l u e F i n a l V a l u e M o d e l R e s . a V 8.00 km/s 7 .90 km/s 8 .02 km/s 0 .94 0 .007 km/s h , 20 .0 km 16.5 km 19.5 km 0 .87 0 .66 km h 2 29 .0 km 26 .0 km 2 9 . 7 km 0 . 9 3 0 .48 km h 3 38 .0 km 42 .0 km 39 .8 km 0 . 7 3 0 .84 km h . 51 .0 km 57 .0 km 5 2 . 5 km 0 . 2 9 0 .84 km TABLE 2 . 2 . S y n t h e t i c t e s t u s i n g a s u b d u c t i o n zone model ( F i g . 2 . 5 ) . V a r i a b l e p a r a m e t e r s i n c l u d e d Moho v e l o c i t y v , d e p t h s h , and h 2 o f t h e s u b d u c t i n g Moho, and dep ths h 3 and h„ of the upper m a n t l e r e f l e c t o r . O v e r a l l damping f a c t o r 6 was 0 . 2 5 . 52 From T a b l e 2 . 2 , t h e b e s t r e s o l v e d parameter was t h e m a n t l e v e l o c i t y v , w i t h a r e s o l u t i o n of 0 . 9 4 . The l o c a t i o n of the upper m a n t l e r e f l e c t o r was v e r y p o o r l y r e s o l v e d , i n p a r t i c u l a r t h e d e p t h a t p o i n t 4 where t h e r e s o l u t i o n was 0 . 2 9 . The r e a s o n t h e r e f l e c t o r p o s i t i o n was p o o r l y d e t e r m i n e d i s because t h e t r a v e l t i m e s t o t h e f a r o f f s e t r e c e i v e r s were not v e r y s e n s i t i v e t o r e f l e c t o r d e p t h . T h i s i s e v i d e n t upon e x a m i n a t i o n of t h e p a r t i a l d e r i v a t i v e s of t r a v e l t i m e w i t h r e s p e c t t o t h e d e p t h of p o i n t 4; a 1 km change i n d e p t h t y p i c a l l y p r o d u c e s a t r a v e l t i m e change of o n l y ~15 ms, w h i c h i s s m a l l compared t o t h e random n o i s e l e v e l o f ~75 ms. On the o t h e r h a n d , t h e p o s i t i o n s of t h e Moho boundary a t p o i n t s 3 and 4 a r e b e t t e r r e s o l v e d . H e r e , a 1 km p e r t u r b a t i o n i n d e p t h c a u s e s a t r a v e l t i m e d i f f e r e n c e o f t y p i c a l l y ~60 ms. I f e e l t h a t not t o o much emphas i s s h o u l d be p l a c e d on t h e a b s o l u t e v a l u e s of t h e c o v a r i a n c e e s t i m a t e s a n d , more s p e c i f i c a l l y , t h a t t h e y s h o u l d be c o n s i d e r e d as minimum v a l u e s f o r pa rameter e s t i m a t e s . A d d i t i o n a l and p e r h a p s more s i g n i f i c a n t e r r o r s may a r i s e because of the dependence of t h e f i n a l model on the s t a r t i n g m o d e l ; i n p a r t i c u l a r , t h e r e i s no a s s u r a n c e t h a t t h e p a r a m e t e r i z a t i o n chosen i s v a l i d f o r t h e r e a l e a r t h . A s i m p l e example of the n o n - u n i q u e n e s s i m p l i e d by t h i s p r o b l e m i s shown i n F i g u r e 2 . 8 . The heavy s o l i d l i n e s i n t h e f i g u r e a r e t h e boundary p o s i t i o n s f o r t h e " t r u e " model f rom t h e p r e v i o u s s u b d u c t i o n zone t e s t , i n w h i c h t h e d e p t h of t h e c o n t i n e n t a l Moho ( the boundary e a s t of 225 km) was c o n s i d e r e d f i x e d a t 37 km. I f the c o n t i n e n t a l Moho i s changed t o 32 km d e p t h , the same s y n t h e t i c t r a v e l t i m e s a r e f i t w i t h i n the s t a t i s t i c a l e r r o r by D I S T A N C E (KM) F I G . 2 . 8 . T h r e e d i f f e r e n t m o d e l s w h i c h f i t t h e s y n t h e t i c t r a v e l t i m e s o f t h e s u b d u c t i o n z o n e t e s t m o d e l . H e a v y s o l i d l i n e s a r e t h e b o u n d a r y p o s i t i o n s a s s u m i n g a c o n t i n e n t a l Moho ( e a s t o f 225 km) f i x e d a t 37 km d e p t h . D a s h e d l i n e s a s sume a Moho f i x e d a t 32 km d e p t h , a n d d o t t e d l i n e s a s sume a Moho f i x e d a t 42 km d e p t h . 54 t h e model i n d i c a t e d by t h e dashed l i n e s i n F i g u r e 2 . 8 . S i m i l a r l y , t h e d o t t e d l i n e s show a model w h i c h f i t s t h e t r a v e l t i m e s a s suming a c o n t i n e n t a l Moho f i x e d a t 42 km d e p t h . That i s , t h e d e p t h of t h e c o n t i n e n t a l Moho c a n n o t be d e t e r m i n e d u n i q u e l y w i t h t h e o t h e r 5 p a r a m e t e r s . I f t h e Moho d e p t h had been i n c l u d e d as a v a r i a b l e parameter i n t h e i n v e r s i o n , t h e n t h e s t a r t i n g v a l u e assumed f o r the d e p t h w o u l d c o n t r o l t h e v a l u e s c a l c u l a t e d f o r the o t h e r p a r a m e t e r s . In s e c t i o n 4 .4 of C h a p t e r 4 , t h e r a y t r a c e i n v e r s i o n p r o c e d u r e i s a p p l i e d t o the t r a v e l t i m e d a t a s e t r e c o r d e d a l o n g t h e o n s h o r e - o f f s h o r e l i n e I of t h e V a n c o u v e r I s l a n d S e i s m i c P r o j e c t . The model used i s a v a r i a n t of t h e s u b d u c t i o n zone t e s t m o d e l . To i l l u s t r a t e t h e b a s i c n o n u n i q u e n e s s of t h e i n t e r p r e t e d m o d e l , two a l t e r n a t i v e models w h i c h f i t t h e o b s e r v e d t r a v e l t i m e s e q u a l l y as w e l l a r e p r e s e n t e d i n s e c t i o n 4 . 6 . One of t h e a l t e r n a t i v e model s i s t h e s u b d u c t i o n zone t e s t model i t s e l f , but w i t h the a c t u a l o b s e r v e d t r a v e l t i m e s r e p l a c i n g the s y n t h e t i c t r a v e l t i m e s of t h e p r e v i o u s e x a m p l e . 55 CHAPTER 3^ PRACTICAL SYNTHETIC SEISMOGRAMS FOR LATERALLY VARYING MEDIA CALCULATED BY ASYMPTOTIC RAY THEORY 3.1 I n t r o d u c t i o n F o r many y e a r s , s e i s m o l o g i s t s have made use of b o t h t h e k i n e m a t i c and dynamic c h a r a c t e r i s t i c s of s e i s m i c r e f r a c t i o n d a t a t o b e t t e r model t h e v e l o c i t y - v e r s u s - d e p t h s t r u c t u r e of t h e e a r t h . Such i n t e r p r e t a t i o n r e q u i r e s t h e c a l c u l a t i o n , f o r a s p e c i f i c m o d e l , o f t h e o r e t i c a l se i smograms w h i c h a r e compared t o t h e o b s e r v e d s e i s m o g r a m s . Through a t r i a l - a n d - e r r o r p r o c e s s d i f f e r e n t model s a r e p r o p o s e d , the s y n t h e t i c se ismograms a r e g e n e r a t e d , and c o m p a r i s o n s a r e made u n t i l an a c c e p t a b l e f i t has been a c h i e v e d . T h i s p r o c e d u r e of i n c o r p o r a t i n g b o t h t r a v e l t i m e and a m p l i t u d e i n f o r m a t i o n i n t o t h e i n t e r p r e t a t i o n of s e i s m i c d a t a has e n a b l e d more r e a l i s t i c models of t h e e a r t h ' s s t r u c t u r e t o be d e r i v e d . However , u n t i l v e r y r e c e n t l y the p r o c e d u r e c o u l d o n l y be a p p l i e d t o o n e - d i m e n s i o n a l e a r t h model s because t h e t h e o r e t i c a l bases f o r s y n t h e t i c se i smogram c o m p u t a t i o n assumed t h a t v e l o c i t y v a r i e d w i t h d e p t h o n l y ( e . g . H e l m b e r g e r , 1968; Fuchs and M i i l l e r , 1971; Chapman, 1978 ) . But many of t h e most i n t e r e s t i n g p r o b l e m s t o w h i c h r e f r a c t i o n s e i s m o l o g y i s a p p l i e d ( e . g . s p r e a d i n g r i d g e s , s u b d u c t i o n z o n e s , c o r d i l l e r a n s t r u c t u r e s , r i f t b a s i n s ) a r e s t r o n g l y t w o - d i m e n s i o n a l and r e q u i r e a c r o s s - s e c t i o n a l model t o d e s c r i b e them. Ray t r a c i n g f o l l o w i n g a v a r i e t y of methods has p r o v i d e d a means of c a l c u l a t i n g t r a v e l t i m e s i n l a t e r a l l y inhomogeneous media ( e . g . C e r v e n y e t a l . , 1977; J u l i a n and 56 G u b b i n s , 1977; G e b r a n d e , 1976; W h i t t a l l and C l o w e s , 1979 ) . However , e x p e r i e n c e w i t h t h e i n t e r p r e t a t i o n of o n e - d i m e n s i o n a l models i n d i c a t e s t h a t i t i s e s s e n t i a l t o have a means of c a l c u l a t i n g a m p l i t u d e s as w e l l as t r a v e l t i m e s . What i s r e q u i r e d by t h e i n t e r p r e t i n g s e i s m o l o g i s t i s an a l g o r i t h m w h i c h combines r a y t r a c i n g w i t h the g e n e r a t i o n of s y n t h e t i c se i smograms f o r t w o - d i m e n s i o n a l s t r u c t u r e s . An e f f e c t i v e a l g o r i t h m must be a b l e t o a c c e p t r e a l i s t i c s t r u c t u r e s , and r e l i a b l y g e n e r a t e s y n t h e t i c se i smograms f o r t h o s e a r r i v a l s commonly i d e n t i f i e d on t h e o b s e r v e d r e c o r d s e c t i o n s . A t the same t i m e , a p r a c t i c a l computer a l g o r i t h m must be f a s t and e c o n o m i c a l t o r u n , and s h o u l d have a s i m p l e method f o r t h e i n p u t of model p a r a m e t e r s . T h u s , the d e s i r e f o r g r e a t g e n e r a l i t y i n a computer r o u t i n e must be b a l a n c e d a g a i n s t i t s speed and s i m p l i c i t y of u s e . The most g e n e r a l of t w o - d i m e n s i o n a l s y n t h e t i c se i smogram r o u t i n e s t a k e i n t o a c c o u n t the wave n a t u r e of t h e p r o p a g a t i n g e n e r g y . Examples a r e the G a u s s i a n beam method (Cerveny e t a l . , 1982) , t h e g e n e r a l i z a t i o n of the WKBJ se ismogram t o l a t e r a l l y -v a r y i n g media (Chapman and Drummond, 1982) , and t h e v a r i o u s K i r c h o f f i n t e g r a l methods ( e . g . Haddon and B u c h e n , 1981) . In t h e s e methods , r a y t r a c i n g i s s t i l l u sed as a common f i r s t s t e p t o g e n e r a t e a f u l l sy s t em of r a y s t h r o u g h o u t t h e m o d e l . T r a v e l t i m e s a r e o b t a i n e d from r a y a r r i v a l t i m e s , and t h e c a l c u l a t i o n of a m p l i t u d e s t h e n p r o c e e d s by c o m b i n i n g many r a y s a t each r e c e i v e r u s i n g v a r i o u s w e i g h t i n g schemes . However , p r a c t i c a l , e f f i c i e n t computer a l g o r i t h m s based on t h e s e t h e o r e t i c a l methods a r e not r e a d i l y a v a i l a b l e t o t h e 57 i n t e r p r e t i n g s e i s m o l o g i s t . In t h i s c h a p t e r , t w o - d i m e n s i o n a l s y n t h e t i c se i smograms a r e c a l c u l a t e d by a d i r e c t a p p l i c a t i o n of a s y m p t o t i c r a y t h e o r y ( A R T ) . The method has t h e advantage of s i m p l i c i t y , i n t h a t a s i n g l e r a y p a t h i s used t o d e t e r m i n e t h e a m p l i t u d e of a p a r t i c u l a r a r r i v a l . A l t h o u g h t h i s c h a r a c t e r i s t i c i m p l i e s t h a t ART c a n n o t model c e r t a i n t y p e s of s i g n a l s , such as d i f f r a c t i o n s and c a u s t i c s , t h e method has p r o v e d a p p l i c a b l e i n a wide range of models and a number of ART a l g o r i t h m s have r e c e n t l y a p p e a r e d i n t h e l i t e r a t u r e . I n t h e method d e s c r i b e d by C e r v e n y e t a l . (1974) and C e r v e n y e t a l . ( 1 9 7 7 ) , a s e t of d i f f e r e n t i a l e q u a t i o n s i n v o l v i n g a m p l i t u d e p a r a m e t e r s was s o l v e d s i m u l t a n e o u s l y w i t h a s e t of d i f f e r e n t i a l e q u a t i o n s f o r t h e t r a c i n g of r a y s . Because a s o l u t i o n must be o b t a i n e d f o r each of t h e many p o i n t s a l o n g each r a y , t h e n u m e r i c a l s o l u t i o n s a r e e x c e s s i v e l y t i m e - c o n s u m i n g . McMechan and Mooney ( 1 9 8 0 ) , i n what a p p a r e n t l y was t h e f i r s t a p p l i c a t i o n of ART t o r e a l r e f r a c t i o n d a t a , c a l c u l a t e d a m p l i t u d e s by u s i n g the end p o i n t s of two n e i g h b o r i n g r a y s t o e s t i m a t e t h e e l e m e n t a r y r a y tube a r e a . However , t h e y used the r a y t r a c i n g code d e s c r i b e d i n C e r v e n y e t a l . ( 1 9 7 7 ) , w h i c h employs t h e t i m e - c o n s u m i n g p o i n t - b y - p o i n t c o m p u t a t i o n s . M a r k s (1980) and C a s s e l l (1982) a v o i d e d t h e s e cumbersome n u m e r i c a l c a l c u l a t i o n s by p a r a m e t e r i z i n g t h e v e l o c i t y model i n t o s m a l l r e c t a n g u l a r or t r i a n g u l a r r e g i o n s w i t h c o n s t a n t v e l o c i t y or c o n s t a n t v e l o c i t y g r a d i e n t , so t h a t s i m p l e a n a l y t i c a l e x p r e s s i o n s c o u l d be u s e d . F o r c a l c u l a t i n g a m p l i t u d e s , Marks (1980) used n e i g h b o r i n g r a y s t o e s t i m a t e r a y tube a r e a a t t h e r e c e i v e r f o r r e f l e c t i o n and r e f r a c t i o n p h a s e s . 58 C a s s e l l (1982) used s i m p l e e x p r e s s i o n s f o r a m p l i t u d e s of r e f l e c t e d , r e f r a c t e d and head waves i n model s w i t h homogeneous l a y e r s and p l a n e d i p p i n g b o u n d a r i e s , as g i v e n i n C e r v e n y and R a v i n d r a ( 1 9 7 1 ) . A s i m p l e , e f f i c i e n t r a y t r a c e method f o r l a t e r a l l y v a r y i n g media was p r e s e n t e d by W h i t t a l l and C lowes ( 1 9 7 9 ) . The v e l o c i t y model i s r e p r e s e n t e d by l a r g e b l o c k s w i t h a r b i t r a r y b o u n d a r i e s , and w i t h i n each b l o c k t h e v e l o c i t y g r a d i e n t i s c o n s t a n t and of a r b i t r a r y o r i e n t a t i o n . The model i s v e r y s i m p l e t o s p e c i f y and t o m o d i f y , and the a l g o r i t h m i s v e r y f a s t . The p r o c e d u r e has p r o v e d s u f f i c i e n t l y f l e x i b l e t o a l l o w i t s a p p l i c a t i o n i n a number o f r e f r a c t i o n i n t e r p r e t a t i o n s , f o r example C l o w e s e t a l . ( 1 9 8 1 ) , D e l a n d r o and Moon ( 1 9 8 2 ) , E l l i s e t a l . ( 1 9 8 3 ) , Green e t a l . (1983) and Horn e t a l . ( 1 9 8 4 ) . The w i d e s p r e a d use of the r o u t i n e has p r o v i d e d encouragement t o d e v e l o p a method of d e t e r m i n i n g a m p l i t u d e s as w e l l as t r a v e l t i m e s w i t h i n the a l g o r i t h m . I n t h i s c h a p t e r , a m p l i t u d e s a r e c a l c u l a t e d f o r t h e W h i t t a l l and Clowes (1979) r a y t r a c e r by a c o m b i n a t i o n of the ART a p p r o a c h e s a p p l i e d by M a r k s (1980) and C a s s e l l ( 1 9 8 2 ) . The a m p l i t u d e c a l c u l a t i o n adds o n l y a modest amount t o t h e c o s t of t h e r a y t r a c i n g , so t h e a d v a n t a g e s of a s i m p l e , e a s i l y m o d i f i e d i n p u t and e f f i c i e n t c o m p u t a t i o n s a r e m a i n t a i n e d . The r e s u l t i n g a l g o r i t h m i s a u s e r o r i e n t e d program f o r c a l c u l a t i n g s y n t h e t i c se i smograms i n l a t e r a l l y inhomogeneous m e d i a . 59 3.2 V e l o c i t y M o d e l and Ray T r a c i n g A b r i e f d e s c r i p t i o n of the W h i t t a l l and Clowes (1979) r a y t r a c e r i s g i v e n i n s e c t i o n 2 .2 of C h a p t e r 2 . However , e x t e n s i o n s t o t h e r o u t i n e as d e s c r i b e d i n s e c t i o n 2 .2 have been added i n the c o u r s e of d e v e l o p i n g t h e s y n t h e t i c se i smogram a l g o r i t h m . The W h i t t a l l and C lowes (1979) a l g o r i t h m was e x t e n d e d so as t o a l l o w r a y t r a c i n g f o r p r e - c r i t i c a l l y r e f l e c t e d and m u l t i p l y r e f l e c t e d waves . C o n v e r t e d phases a r e s t i l l not c o n s i d e r e d . F o r the p r e - c r i t i c a l and m u l t i p l e r e f l e c t i o n s , o n l y t h e boundary or b o u n d a r i e s a t w h i c h r e f l e c t i o n i s d e s i r e d need t o be s p e c i f i e d . At a l l o t h e r b o u n d a r i e s e n c o u n t e r e d by t h e r a y , t h e b e h a v i o r of the r a y i s c o n t r o l l e d by t h e a n g l e of i n c i d e n c e a t t h e b o u n d a r y . I f t h e i n c i d e n t a n g l e i s l e s s t h a n t h e c r i t i c a l a n g l e , t h e n the r a y r e f r a c t s t h r o u g h the b o u n d a r y ; o t h e r w i s e , i t r e f l e c t s from the b o u n d a r y . T h u s , i f no p r e - c r i t i c a l o r m u l t i p l e r e f l e c t i o n s a r e d e s i r e d , t h e n a s i n g l e s p e c i f i c a t i o n of t h e range of t a k e -o f f a n g l e s g i v e s a l l w i d e - a n g l e r e f l e c t i o n s , t u r n i n g r a y s and head waves . The c o r r e s p o n d i n g t r a v e l t i m e c u r v e i s d i v i d e d i n t o b r a n c h e s such t h a t t h e d i s t a n c e a l o n g each b r a n c h i n c r e a s e s or d e c r e a s e s m o n o t o n i c a l l y w i t h d i s t a n c e . The f a m i l y of r a y s a s s o c i a t e d w i t h each t r a v e l t i m e b r a n c h i s l a b e l l e d w i t h a u n i q u e i d e n t i f i c a t i o n number, w h i c h i s u sed i n the s y n t h e t i c se i smogram r o u t i n e f o r p u r p o s e s of i n t e r p o l a t i o n w i t h i n a g i v e n r a y f a m i l y . 60 3.3 C a l c u l a t i o n of Ampl i tudes and s y n t h e t i c seismograms 3.3.1 R e f l e c t e d and R e f r a c t e d Rays In a medium wi th an a r b i t r a r y inhomogeneous v e l o c i t y d i s t r i b u t i o n , z e r o - o r d e r a sympto t i c ray theory p r o v i d e s a c o n n e c t i o n formula between the source at M 0 and any p o i n t M for the a m p l i t u d e of a r e f l e c t e d or r e f r a c t e d wave (Cerveny and R a v i n d r a , 1971, p . 7 4 ) . N U(M) = 1 MMQMMQ ) ) 1 / 2 n / v ' ( 0 ; ) p ' (0; )\ "2RL (3.1) L \ v(M)p(M) J i=]{ v'(Oi)p(0L) J The ray geometry i s shown i n F i g u r e 3 . 1 . 0^ i s the p o i n t of i n c i d e n c e of the ray at the i - t h i n t e r f a c e i t e n c o u n t e r s . Primed q u a n t i t i e s are e v a l u a t e d on the s i d e of the i n t e r f a c e from which the ray emerges. The r e l a t i o n s h i p between P-wave v e l o c i t y v and d e n s i t y p i s approximated by ( B i r c h , 1 9 6 4 ) p = 0.252 + 0.3788v . Z o e p p r i t z ampl i tude c o f f i c i e n t s R^ for t r a n s m i s s i o n or r e f l e c t i o n are taken from Cerveny and Ravindra (1971, p . 6 3 ) , and are c a l c u l a t e d us ing a r o u t i n e d e s c r i b e d by Young and B r a i l e (1976) and C a s s e l l (1982) . The Z o e p p r i t z a l g o r i t h m assumes that the medium has a P o i s s o n ' s r a t i o of 0.25 except i f the P-wave v e l o c i t y i s l e s s than 1.5 km/s, where the m a t e r i a l i s assumed to be water w i t h a d e n s i t y of 1.0* 10 3 kg/m 3 and an S-wave v e l o c i t y of z e r o . The Z o e p p r i t z r o u t i n e a l s o a l l o w s the c a l c u l a t i o n of su r f ace r e f l e c t i o n and s u r f a c e c o n v e r s i o n c o e f f i c i e n t s i f d e s i r e d . In e q u a t i o n 3.1 the g e o m e t r i c a l sp read ing f u n c t i o n L i s FIG. 3 . 1 . Geometry of the ray tube at the source M 0 and at the i - t h i n t e r f a c e , where the point of i n t e r s e c t i o n i s . The p r o p e r t i e s of the medium are l a t e r a l l y v a r y i n g i n the x-z plane but are uniform in the y - d i r e c t i o n . 62 given by Cerveny and Ravindra (1971, p.74) as N ( da(M) V'2 n fdo(0 ) V 2 1 do(M 0)j i = l U ^ ' (0 )/ L = / da(M) 2  f do(0 ) V>2 (3.2) Here, da denotes the elementary ray tube area at p o i n t s M, M 0, or 0^ . The product term in equation (3.2) represents the i n f l u e n c e of i n t e r f a c e s on geometrical spreading (see F i g u r e 3.1). The change i n ray tube area at a given plane boundary can be ev a l u a t e d as the r a t i o of the cos i n e of the angle of in c i d e n c e to the c o s i n e of the angle of emergence (Cerveny and Ravindra, 1971, p.79). On the other hand, the f i r s t term i n equation 3.2 re p r e s e n t s the change in ray tube area between i n t e r f a c e s , which i s c a l c u l a t e d as f o l l o w s . The point M 0 i s commonly assumed to be on the u n i t sphere, w i t h i n which the v e l o c i t y i s homogeneous, so that the elementary area on the sphere i s do(M 0) = s i n 0 o dt90 d<£0 (3) where 80 and tj>0 are the angular c o o r d i n a t e s of the ray at the source: 60 i s the angle measured from the v e r t i c a l or z-d i r e c t i o n , and <j>0 i s the angle measured from the x-z plane. For a general t h r e e - d i m e n s i o n a l v e l o c i t y d i s t r i b u t i o n , an element of area on the wavefront at po i n t M i s do(M) 3r ^ 3? 30o 3t90 d0od<po where f i s the v e c t o r p o i n t i n g from the source M 0 to r e c e i v e r M. Cerveny et a l . (1974) and Wesson (1970) obtained e x p r e s s i o n s f o r the time d e r i v a t i v e s of 3r/30 o and 3r/3t9 0, which were then i n t e g r a t e d from known s t a r t i n g values to the point M. However, 63 f o r l e s s complex v e l o c i t y d i s t r i b u t i o n s , the e x p r e s s i o n s f o r da(M) s i m p l i f y , and a n a l y t i c e x p r e s s i o n s can be used i n s t e a d of t i m e - c o n s u m i n g n u m e r i c a l i n t e g r a t i o n . W i t h the a s s u m p t i o n t h a t the v e l o c i t y s t r u c t u r e i s two-d i m e n s i o n a l , v a r y i n g o n l y i n the x - z p l a n e , Marks (1980) showed t h a t H e r e , y i s t h e o u t - o f - p l a n e c o o r d i n a t e and r i s the magni tude of f . The f i r s t f a c t o r i n e q u a t i o n ( 3 . 4 ) i s the w i d t h of the r a y tube i n t h e x - z p l a n e . In our a l g o r i t h m , we e s t i m a t e dr/d60 a t each d e p a r t u r e a n g l e 80 by s h o o t i n g a second ray a t a s m a l l a n g u l a r i n c r e m e n t At90 g r e a t e r t h a n 60t and u s i n g t h e d i f f e r e n c e ' i n e p i c e n t r a l d i s t a n c e Ar t o c a l c u l a t e A r / A t 9 0 . A s i m i l a r p r o c e d u r e was f o l l o w e d by Marks ( 1 9 8 0 ) , who s p l i n e d seven r a y s a t each r e c e i v e r t o e s t i m a t e 3r/9e9 0, and by McMechan and Mooney ( 1 9 8 0 ) , who used the two r a y s a t s u c c e s s i v e d e p a r t u r e a n g l e s 80. The second f a c t o r i n e q u a t i o n 3 .4 i s the w i d t h of the ray tube i n the o u t - o f - p l a n e d i r e c t i o n . For a o n e - d i m e n s i o n a l s t r u c t u r e v a r y i n g o n l y i n the z - d i r e c t i o n , the q u a n t i t y g=3y/90 o i s s i m p l y the e p i c e n t r a l d i s t a n c e r , as d i s c u s s e d by C e r v e n y and R a v i n d r a ( 1 9 7 1 , p . 7 8 ) . But f o r l a t e r a l l y v a r y i n g m e d i a , t h e e x p r e s s i o n f o r g becomes more c o m p l e x . W i t h the second s i m p l i f y i n g a s s u m p t i o n t h a t the model i s p a r a m e t e r i z e d i n terms of b l o c k s w i t h c o n s t a n t v e l o c i t y g r a d i e n t , Marks (1980) s o l v e d f o r g by i n t e g r a t i n g an e x p r e s s i o n f o r d g / d t from C e r v e n y e t a l . (1974) t o o b t a i n ( 3 . 4 ) 64 N / 2 k - ( t - - t : . , ) ' 3y = s in t9 0 I v 0 I 2 ( 1 + t a n 2 g o i / 2 ) e ' -1 "STo v 0 i = l 2k: V (3 .5) 1 + t a n 2 0 o i , e T 2 k ^ ( t x - t • . , ) V l where N = number of b l o c k s v0i = v e l o c i t y on e n t e r i n g the i - t h b l o c k k^ = v e l o c i t y g r a d i e n t i n t h e i - t h b l o c k 0 O ; = r a y a n g l e on e n t e r i n g the i - t h b l o c k , measured w i t h r e s p e c t t o the v e l o c i t y g r a d i e n t d i r e c t i o n i n the b l o c k t i - i ' t i = t o t a l t r a v e l t i m e upon e n t e r i n g and upon l e a v i n g the i - t h b l o c k We may e x p r e s s 9y/3</>0 i n terms of the e p i c e n t r a l d i s t a n c e c a l c u l a t e d by the W h i t t a l l and Clowes (1979) r a y t r a c e r , by n o t i n g t h a t t h e d i s t a n c e r^ t r a v e l l e d w i t h i n t h e i - t h b l o c k , measured p e r p e n d i c u l a r t o t h e v e l o c i t y g r a d i e n t k , i s g i v e n by ( M a r k s , 1980) / 2 k , ( t i - t - . , ) r; = v 0 ; tantfoi e - 1 , 2 k i ( t i - t i - . , ) \ - l / 1 + t a n 2 a 0 i . e ( T~ The above e x p r e s s i o n f o r r^ may be s u b s t i t u t e d i n t o e q u a t i o n ( 3 . 5 ) , a f t e r u t i l i z i n g the t r i g o n o m e t r i c i d e n t i t y 1+tan 26 0 i/2 = ( 2 t a n 0 o ^ / 2 ) / s i n t 9 0 ^ . E q u a t i o n (3 .5) then r e d u c e s t o -N 3y_= s inc9 0 I v 0 ; r,-, (3 .6) 30o v 0 i = 1 s i n 0 o l 65 C o m b i n i n g e q u a t i o n s 3 . 3 , 3.4 and 3 . 6 , we have N do(M) = 9r cosg(M) L v n ; , r 2 ( 3 . 7 ) d o ( M 0 ) 3t90 v 0 i = l s i n t 9 0 ; w h i c h i s s u b s t i t u t e d i n t o e q u a t i o n 3 .2 f o r the g e o m e t r i c a l s p r e a d i n g f u n c t i o n L . 3 . 3 . 2 Head Waves The scheme o u t l i n e d above i s based on t h e z e r o o r d e r a s y m p t o t i c e x p a n s i o n , and i s v a l i d f o r r e f l e c t e d and r e f r a c t e d r a y s , i n c l u d i n g t u r n i n g r a y s . For head waves , w h i c h r e p r e s e n t t h e f i r s t - o r d e r c o e f f i c i e n t i n t h e r a y e x p a n s i o n , a d i f f e r e n t scheme i s u s e d . The c r i t i c a l a n g l e r a y p a t h t o w a r d and away from t h e head wave boundary i s d e s c r i b e d by the W h i t t a l l and Clowes (1979) ray t r a c e r i n terms of c i r c u l a r a r c s . W i t h i n each b l o c k , we d i v i d e the c i r c u l a r ray p a t h i n t o a l a r g e number of segments of e q u a l l e n g t h , and assume a c o n s t a n t v e l o c i t y a l o n g each segment . T h u s , t h e v e l o c i t y model i s r e - p a r a m e t e r i z e d , i n terms o f a s e r i e s of t h i n homogeneous l a y e r s , whose b o u n d a r i e s a r e p a r a l l e l w i t h i n a g i v e n b l o c k but may be n o n - p a r a l l e l from b l o c k t o b l o c k . We t h e n a p p l y e x p r e s s i o n s from C e r v e n y and R a v i n d r a (1971 , e q u a t i o n s 5 .22 and 5 .29 ) f o r the a m p l i t u d e of head waves i n a model of homogeneous l a y e r s w i t h p l a n e d i p p i n g i n t e r f a c e s : U * ( M ) = v r t ant9(Q * J s- 1 f l R * ; i w l 3 / 2 ( v R / v ) V 2 L , L j = 1 j = k k- 1 L , = / v K V / 2 n cos0(o*,-) ( 3 . 8 ) 66 where 8(0*j) = a n g l e of i n c i d e n c e a t the j - t h b o u n d a r y . 6'(0*) = a n g l e of emergence a t the j - t h b o u n d a r y . v e l o c i t y between b o u n d a r i e s ( j - 1 ) and j . l e n g t h of the j - t h segment of the r a y ( j = 1 ,2 , . . . s) . V = v e l o c i t y j u s t below the head wave boundary (boundary k ) . 1 = l e n g t h of t h e ray p a t h a l o n g t h e head wave b o u n d a r y . e s t i m a t e of dominant f r e q u e n c y head waves . The head wave c o e f f i c i e n t TK i s g i v e n by C e r v e n y and R a v i n d r a ( 1971 , p p . 108-109) as where P 3 = ( 1 - v 2 © 2 ) 1 2 and 0 = s i n c 9 ( 0 * ) / v . R * , 3 i s the t r a n s m i s s i o n c o e f f i c i e n t a t the head wave boundary f o r t h e r a y i n c i d e n t a t the c r i t i c a l a n g l e , and R 3 , i s t h e c o e f f i c i e n t f o r the emergent r a y . 3 . 3 . 3 A l t e r n a t i v e A p p r o a c h f o r R e f l e c t e d and D i r e c t Rays A l t h o u g h the p a r a m e t e r i z a t i o n of the model i n terms of t h i n homogeneous l a y e r s was made i n o r d e r to c a l c u l a t e head wave a m p l i t u d e s , the p a r a m e t e r i z a t i o n i s a l s o a p p l i c a b l e f o r c a l c u l a t i n g a m p l i t u d e s of r e f l e c t e d r a y s and of d i r e c t r a y s ( i . e . r e f r a c t e d r a y s h a v i n g no t u r n i n g p o i n t s ) . T h u s , w i t h v e r y l i t t l e added e f f o r t or c o s t , an independent check may be o b t a i n e d on t h e r e f l e c t e d and d i r e c t ray a m p l i t u d e s found by t h e p r e v i o u s method i n w h i c h an e s t i m a t e of the r a y tube a r e a i s 67 made. For a model of homogeneous l a y e r s w i t h p l a n e d i p p i n g i n t e r f a c e s , the s p r e a d i n g f u n c t i o n L i s g i v e n by ( C e r v e n y and R a v i n d r a , 1971, e q u a t i o n 2 .174) r s / s J ~1 \~1 L = \ [ L livA I l / v ; n cos[e(0.) \ 1 / 2 (3.9) [lj = 1 vTJ\J = 1 v, i * l c o s 2 0 ' (c- )] where s i s the number of r a y segments and the p r o d u c t f a c t o r e q u a l s 1 f o r j =1 . T h i s method was a p p l i e d by C a s s e l l ( 1 9 8 2 ) . The p a r a m e t e r i z a t i o n i n terms of homogeneous l a y e r s and the use of e q u a t i o n 3 .9 s h o u l d not be a p p l i e d i n t h e ca se of t u r n i n g r a y s . I f a ray c o n t a i n s a t u r n i n g p o i n t due t o the v e l o c i t y g r a d i e n t , t h e ray p a t h and i t s t r a v e l t i m e a r e w e l l a p p r o x i m a t e d by t r e a t i n g t h e ray as a r e f l e c t i o n from t h e base of a s t a c k of t h i n homogeneous l a y e r s . However , t h e a m p l i t u d e of t h e t u r n i n g r a y i s not w e l l a p p r o x i m a t e d by j u s t t h e a m p l i t u d e of the s i n g l e b a s a l r e f l e c t i o n , but r a t h e r i s due t o c o n s t r u c t i v e i n t e r f e r e n c e f rom the e n t i r e s t a c k of l a y e r s (McMechan and Mooney, 1980; W i g g i n s and H e l m b e r g e r , 1974) . 3 . 3 . 4 Seismogram S y n t h e s i s A f t e r a m p l i t u d e s f o r the d e s i r e d r e f l e c t i o n s , r e f r a c t i o n s and head waves a r e c a l c u l a t e d , s y n t h e t i c se i smograms a re g e n e r a t e d by s u p e r i m p o s i n g the d i s p l a c e m e n t s of a l l a r r i v a l s a t a p a r t i c u l a r d i s t a n c e . The se i smograms a r e p r o d u c e d a t a s e t of e q u a l l y spaced d i s t a n c e s u s i n g the same a l g o r i t h m as McMechan and Mooney ( 1 9 8 0 ) . A s s o c i a t e d w i t h each ray t h a t r e a c h e s the s u r f a c e i s a t r a v e l t i m e , an e p i c e n t r a l d i s t a n c e , a complex a m p l i t u d e and a t r a v e l t i m e b r a n c h ID number. F o r a g i v e n b r a n c h , 68 a m p l i t u d e and t r a v e l t i m e a r e l i n e a r l y i n t e r p o l a t e d t o t h e d e s i r e d d i s t a n c e . A p h a s e - s h i f t e d i m p u l s e i s t h e n c o n s t r u c t e d by a l i n e a r c o m b i n a t i o n of a u n i t i m p u l s e and i t s H i l b e r t t r a n s f o r m . The se i smogram s y n t h e s i s i s c o m p l e t e d by c o n v o l u t i o n w i t h an a p p a r e n t s o u r c e f u n c t i o n . 3 .4 R e s u l t s As a f i r s t t e s t of t h e s y n t h e t i c se i smogram r o u t i n e , r a y a m p l i t u d e s a r e c a l c u l a t e d f o r a t w o - l a y e r l a t e r a l l y homogeneous model w h i c h c o u l d r e p r e s e n t , f o r e x a m p l e , the e a r t h ' s c r u s t o v e r the m a n t l e . The f i r s t l a y e r i s 30 km t h i c k w i t h a v e l o c i t y of 6 .4 k m / s . The v e l o c i t y a t the t o p of t h e second l a y e r i s 8 . 0 k m / s , below w h i c h i s a s m a l l v e l o c i t y g r a d i e n t of 0 .0226 k m / s / k m . F i g u r e 3 . 2 a shows t h e v e r t i c a l component a m p l i t u d e s of r a y s r e f l e c t e d f rom t h e base of t h e f i r s t l a y e r and of r a y s r e f r a c t e d i n the s e c o n d l a y e r . As w e l l , a m p l i t u d e s a r e shown f o r the pure head wave t h a t wou ld p r o p a g a t e a l o n g the i n t e r f a c e between t h e l a y e r s under t h e a s s u m p t i o n t h a t t h e v e l o c i t y g r a d i e n t i s z e r o i m m e d i a t e l y be low t h e i n t e r f a c e ; t h e dominant f r e q u e n c y of t h e head wave i s assumed t o be 6 .4 H z . Because t h e v e l o c i t y model i s o n e - d i m e n s i o n a l , ART a m p l i t u d e s of r e f l e c t e d , r e f r a c t e d and head waves may a l s o be c a l c u l a t e d d i r e c t l y from s i m p l e a n a l y t i c e x p r e s s i o n s ( C e r v e n y and R a v i n d r a , 1971, F i g u r e 6 . 6 ) . As shown i n F i g u r e 3 . 2 a , the a n a l y t i c v a l u e s and t h e v a l u e s c a l c u l a t e d by our a l g o r i t h m agree v e r y w e l l . I n t h i s a l g o r i t h m we make one of two a p p r o x i m a t i o n s t o a s y m p t o t i c r a y t h e o r y , d e p e n d i n g on t h e t y p e of r a y . E i t h e r (1) we a p p r o x i m a t e 9 r / 9 0 o , t h e d e r i v a t i v e of 69 F I G . 3 . 2 . (a) V e r t i c a l component a m p l i t u d e s of r e f l e c t e d , r e f r a c t e d and head waves f o r a t w o - l a y e r m o d e l . The f i r s t l a y e r i s 30 km t h i c k and has c o n s t a n t v e l o c i t y 6 .4 k m / s ; t h e second l a y e r has v e l o c i t y 8 .0 km/s a t t h e t o p and a l i n e a r v e l o c i t y g r a d i e n t of 0 .0226 k m / s / k m . The head wave a m p l i t u d e s , c a l c u l a t e d f o r a dominant f r e q u e n c y of 6 .4 H z , a r e t h o s e t h a t w o u l d be p r o d u c e d a s suming t h a t t h e v e l o c i t y g r a d i e n t i s z e r o f o r a s h o r t d i s t a n c e i m m e d i a t e l y be low t h e i n t e r f a c e between t h e l a y e r s . The a n a l y t i c v a l u e s were c a l c u l a t e d u s i n g s i m p l e e x p r e s s i o n s f o r a l a t e r a l l y homogeneous t w o - l a y e r model and were t a k e n from C e r v e n y and R a v i n d r a ( 1 9 7 1 , F i g u r e 6 . 6 ) . No s u r f a c e c o n v e r s i o n c o e f f i c i e n t s have been i n c l u d e d . (b) V e r t i c a l component a m p l i t u d e s f o r t h e t w o - l a y e r model u s i n g t h e a l g o r i t h m s of McMechan and Mooney (1980) and C a s s e l l ( 1 9 8 2 ) . AMPLITUDE AMPLITUDE OL 71 range w i t h r e s p e c t t o s t a r t i n g a n g l e , by e s t i m a t i n g i t s v a l u e from two n e i g h b o r i n g r a y s or (2) we a p p r o x i m a t e a smooth v e l o c i t y g r a d i e n t i n a b l o c k by a l a r g e number of t h i n homogeneous l a y e r s . The agreement between the a n a l y t i c v a l u e s and t h o s e c a l c u l a t e d by our a l g o r i t h m t h u s a s s u r e s t h a t t h e e f f e c t of our a p p r o x i m a t i o n s t o ART i s m i n i m a l . F i g u r e 3 . 2 b shows a m p l i t u d e s f o r t h e t w o - l a y e r model c a l c u l a t e d u s i n g t h e a l g o r i t h m s of McMechan and Mooney (1980) and C a s s e l l ( 1 9 8 2 ) . The a m p l i t u d e v a l u e s f o r t h e C a s s e l l r o u t i n e , w h i c h was r e c e n t l y u p d a t e d , were s u p p l i e d by C a s s e l l ( p e r s . comm., 1983 ) . For b o t h a l g o r i t h m s , the a m p l i t u d e s of t h e r e f r a c t e d waves and of t h e w i d e - a n g l e r e f l e c t i o n s agree q u i t e w e l l w i t h t h e a n a l y t i c v a l u e s . However , t h e p r e - c r i t i c a l r e f l e c t i o n a m p l i t u d e s f o r the McMechan and Mooney a l g o r i t h m d i v e r g e from t h e a n a l y t i c v a l u e s , the d i f f e r e n c e becoming g r e a t e r as t h e d i s t a n c e becomes l e s s . P a r t of t h i s d i f f e r e n c e i s due t o d i f f e r e n t v a l u e s c a l c u l a t e d f o r t h e p r e - c r i t i c a l r e f l e c t i o n c o e f f i c i e n t s , w h i c h p o s s i b l y a r i s e s because t h e McMechan and Mooney r o u t i n e u se s a d i f f e r e n t v e l o c i t y / d e n s i t y r e l a t i o n s h i p t h a n the one used i n t h i s paper (McMechan, p e r s . comm., 1 9 8 3 ) . Head waves a r e no t computed by t h e McMechan and Mooney m e t h o d . The a m p l i t u d e s of t h e head waves c a l c u l a t e d by the C a s s e l l a l g o r i t h m a r e d i f f e r e n t from the a n a l y t i c v a l u e s i n F i g u r e 3 . 2 b . C a s s e l l ' s v a l u e s u n d e r e s t i m a t e t h e a n a l y t i c v a l u e s by a n e a r l y c o n s t a n t f a c t o r of about 2 . 5 . T h i s d i f f e r e n c e a r i s e s because C a s s e l l (1982) uses an a p p r o x i m a t i o n f o r t h e head wave g e o m e t r i c a l s p r e a d i n g f u n c t i o n , and not t h e e x a c t e x p r e s s i o n s f rom C e r v e n y and R a v i n d r a ( 1 9 7 1 ) . 72 F o r a more complex l a t e r a l l y homogeneous m o d e l , an a d d i t i o n a l check of our a l g o r i t h m compares t h e a m p l i t u d e s w i t h t h o s e c a l c u l a t e d by t h e r e f l e c t i v i t y method . S i n c e t h e r e f l e c t i v i t y method p r o d u c e s the f u l l wave r e s p o n s e from t h e m o d e l , t h e c o m p a r i s o n a l s o t e s t s t h e v a l i d i t y of t h e a p p r o x i m a t i o n s i n h e r e n t i n a s y m p t o t i c r a y t h e o r y . The v e l o c i t y model used i s the HILDERS model ( F i g u r e 3 .3a ) of Fuchs and M i i l l e r ( 1 9 7 1 ) . R e f l e c t i v i t y s e i smograms , shown i n F i g u r e 3 . 3 c , were o r i g i n a l l y c a l c u l a t e d f o r t h i s model by Fuchs and M i i l l e r (1971) and have been used as a b a s i s of c o m p a r i s o n i n t h e ART methods of C e r v e n y e t a l . ( 1 9 7 7 ) , McMechan and Mooney (1980) and C a s s e l l ( 1 9 8 2 ) . To d e t e r m i n e t h e r e f l e c t i v i t y r e s p o n s e , t h e v e l o c i t y g r a d i e n t i n t h e d e p t h range 11-27 km was r e p r e s e n t e d by a s t a c k of 10 homogeneous l a y e r s , and t h e deeper g r a d i e n t i n t h e d e p t h range 34-36 km was r e p r e s e n t e d by 3 l a y e r s . The CPU t i m e r e q u i r e d t o c a l c u l a t e t h e r e f l e c t i v i t y se i smograms on an Amdahl 470 V / 8 was a p p r o x i m a t e l y 3 m i n u t e s . I n F i g u r e 3 .3b t h e se i smograms c a l c u l a t e d by our p r o c e d u r e a r e d i s p l a y e d . The c a l c u l a t i o n took a p p r o x i m a t e l y 14 seconds of CPU t i m e on t h e Amdahl 470 V / 8 . The agreement w i t h t h e r e f l e c t i v i t y se i smograms ( F i g u r e 3 . 3 c ) i s s a t i s f a c t o r y f o r i n t e r p r e t a t i o n a l p u r p o s e s . The se i smograms p r o d u c e d by our a l g o r i t h m a r e a l s o c o n s i s t e n t w i t h t h o s e p r o d u c e d by o t h e r ART a l g o r i t h m s . However , f o r any ART a l g o r i t h m , r a y t h e o r y i t s e l f i s i n h e r e n t l y l i m i t e d , and so some d i f f e r e n c e s e x i s t compared t o t h e r e f l e c t i v i t y r e s u l t s . F o r e x a m p l e , a c u s p a p p e a r s on t h e ART s e c t i o n a t a p p r o x i m a t e l y 4 . 5 s and 160 km ( p o i n t C ) , where t h e a m p l i t u d e s change a b r u p t l y f rom a l a r g e v a l u e t o z e r o a t g r e a t e r 73 V (KM/S) D I S T A N C E ( K M ) F I G . 3.3. S y n t h e t i c se i smograms f o r the HILDERS v e l o c i t y - d e p t h model ( a ) . Response shown i n (b) i s the s y n t h e t i c s e c t i o n c a l c u l a t e d by our ART method , w h i l e t h a t i n (c ) i s c a l c u l a t e d by the r e f l e c t i v i t y method . A i l t r a c e s a r e m u l t i p l i e d by a f a c t o r p r o p o r t i o n a l t o t h e i r d i s t a n c e . 74 d i s t a n c e s . On t h e r e f l e c t i v i t y s e c t i o n t h e a m p l i t u d e i s s m a l l e r a t 160 km and i s n o n - z e r o a t g r e a t e r d i s t a n c e s . The c u s p i n ART o c c u r s when t h e b r a n c h of r a y s r e f l e c t e d from t h e i n t e r f a c e a t 27 km d e p t h ( b r a n c h CD) j o i n s t h e b r a n c h of t u r n i n g r a y s i n t h e g r a d i e n t zone above 27 km ( b r a n c h B C ) . The t u r n i n g r a y w h i c h j u s t g r a z e s t h e i n t e r f a c e c o r r e s p o n d s t o a s h a r p t e r m i n a t i o n of the b r a n c h e s i n ART but not i n wave t h e o r y , where non-Fermat r a y s a r e p r e s e n t i n t h e "shadow z o n e " . A second d i f f e r e n c e between t h e ART and r e f l e c t i v i t y s e c t i o n s c o n c e r n s t h e s m a l l a m p l i t u d e b r a n c h (EF) f rom a p p r o x i m a t e l y 120 t o 180 km w i t h v e l o c i t y of about 8 .0 k m / s . On t h e r e f l e c t i v i t y s e c t i o n , t h e a m p l i t u d e o f t h e b r a n c h i n c r e a s e s w i t h d i s t a n c e . The a m p l i t u d e s a r e due t o p r e - c r i t i c a l r e f l e c t i o n s f rom the l a y e r s a p p r o x i m a t i n g t h e deeper g r a d i e n t a t 34-36 km d e p t h . On t h e ART s e c t i o n , t h e b r a n c h EF has been m o d e l l e d s i m p l y as a head wave a l o n g the i n t e r f a c e a t 27 km d e p t h , and so the a m p l i t u d e d e c r e a s e s w i t h d i s t a n c e . Tha t i s , t h e r e i s no e f f e c t p r e s e n t on the ART s e c t i o n due t o t h e deeper g r a d i e n t s t r u c t u r e , s i n c e t u r n i n g r a y s w i t h i n t h i s zone o n l y r e a c h t h e s u r f a c e a t d i s t a n c e s g r e a t e r t h a n 190 km. However , by r e p l a c i n g t h e g r a d i e n t zone by one or more s m a l l s t e p d i s c o n t i n u i t i e s , t h e ART a l g o r i t h m c o u l d a l s o g e n e r a t e p r e - c r i t i c a l r e f l e c t i o n s a t d i s t a n c e s l e s s than 190 km, f o r w h i c h a m p l i t u d e s i n c r e a s e w i t h d i s t a n c e ; t h i s was done by C a s s e l l (1982) and C e r v e n y e t a l . ( 1 9 7 4 ) . A l t e r n a t i v e l y , the 8 .0 km/s b r a n c h c o u l d be m o d e l l e d f o r i n t e r p r e t a t i o n a l purpose s as t u r n i n g r a y s p r o d u c e d by a weak v e l o c i t y g r a d i e n t i n the e n t i r e r e g i o n below 27 km d e p t h . I n F i g u r e 3 . 4 , r a y s and v e r t i c a l component a m p l i t u d e s a r e 75 d i s p l a y e d f o r a s i m p l e l a t e r a l l y v a r y i n g m o d e l . The model ( F i g u r e 3 .4a ) c o n s i s t s of a b l o c k o f c o n s t a n t v e l o c i t y 5 .0 km/s next t o a d i p p i n g l a y e r i n w h i c h t h e v e l o c i t y a t t h e upper d i p p i n g boundary i s 6 .0 k m / s . The d i p p i n g l a y e r has a c o n s t a n t v e l o c i t y g r a d i e n t of 0 .08 km/s/km p e r p e n d i c u l a r t o t h e b o u n d a r y . The model i s a c t u a l l y l a t e r a l l y homogeneous but has been t i l t e d c l o c k w i s e f rom t h e v e r t i c a l by 3 0 ° . The c a l c u l a t i o n of r a y a m p l i t u d e s t h u s e x e r c i s e s the t w o - d i m e n s i o n a l a s p e c t s of our a l g o r i t h m , and the a m p l i t u d e v a l u e s have been c h e c k e d a g a i n s t e x a c t ART a n a l y t i c a l v a l u e s d e t e r m i n e d f o r t h e c o r r e s p o n d i n g o n e - d i m e n s i o n a l m o d e l . As shown i n F i g u r e 3 . 4 b , t h e agreement i s e x c e l l e n t , t h e p r o g r a m - c a l c u l a t e d v a l u e s d i f f e r i n g from t h e a n a l y t i c v a l u e s by l e s s t h a n 0.1% f o r the s e t of r a y s shown i n F i g u r e 3 . 4 a . A more complex l a t e r a l l y v a r y i n g m o d e l , t h e I m p e r i a l V a l l e y model d i s c u s s e d i n McMechan and Mooney ( 1 9 8 0 ) , i s shown i n F i g u r e 3 . 5 . I n t h e r a y t r a c i n g r o u t i n e employed by McMechan and Mooney ( 1 9 8 0 ) , l a t e r a l as w e l l as v e r t i c a l v e l o c i t y g r a d i e n t s a r e a l l o w e d . In t h e W h i t t a l l and Clowes (1979) r a y t r a c i n g r o u t i n e u t i l i z e d i n our a l g o r i t h m , t h e v e l o c i t y g r a d i e n t s w i t h i n a g i v e n b l o c k a r e u n i f o r m and p e r p e n d i c u l a r t o one of the b l o c k b o u n d a r i e s . Thus t h e l a t e r a l v e l o c i t y g r a d i e n t s i n t h e I m p e r i a l V a l l e y model a r e a p p r o x i m a t e d i n F i g u r e 3 .5 by c r u d e l y d i v i d i n g each of t h e 3 t o p l a y e r s i n t o e i t h e r 2 or 3 b l o c k s . I n F i g u r e 3 . 6 a , we d i s p l a y r a y p a t h s t h r o u g h our I m p e r i a l V a l l e y m o d e l , and i n F i g u r e 3 .6b t h e c o r r e s p o n d i n g s y n t h e t i c se i smogram s e c t i o n c a l c u l a t e d by our a l g o r i t h m i s shown. F i g u r e 3 .6c c o n t a i n s t h e s y n t h e t i c se i smograms f o r t h e I m p e r i a l V a l l e y 76 F I G . 3 . 4 . (a) Ray t r a c i n g d i a g r a m f o r a s i m p l e t w o - d i m e n s i o n a l m o d e l . The two dashed l i n e s r e p r e s e n t t h e b o u n d a r i e s of a l a y e r d i p p i n g a t 3 0 ° , w i t h i n w h i c h t h e v e l o c i t y i n c r e a s e s l i n e a r l y f rom 6 .0 km/s a t t h e upper boundary t o 8 .0 km/s a t t h e l o w e r b o u n d a r y . The r e g i o n above t h e d i p p i n g l a y e r has c o n s t a n t v e l o c i t y 5 .0 k m / s . The model i s a c t u a l l y l a t e r a l l y homogeneous but t i l t e d from t h e v e r t i c a l by 3 0 ° . (b) V e r t i c a l component a m p l i t u d e s f o r t h e model i n ( a ) . The s o l i d l i n e r e p r e s e n t s t h e a m p l i t u d e s c a l c u l a t e d by t h e t w o -d i m e n s i o n a l s y n t h e t i c se i smogram r o u t i n e . The c r o s s e s a r e t h e e x a c t ART v a l u e s d e t e r m i n e d f o r t h e e q u i v a l e n t l a t e r a l l y homogeneous model u s i n g s i m p l e a n a l y t i c e x p r e s s i o n s . A m p l i t u d e s , w h i c h a r e r e l a t i v e t o t h e a m p l i t u d e on t h e u n i t s p h e r e , s h o u l d be m u l t i p l i e d by 1 0 ~ 3 . D I S T A N C E ( K M ) 0 2 0 4 0 6 0 8 0 1 0 0 0 2 0 4 0 6 0 8 0 1 0 0 D I S T A N C E ( K M ) DISTANCE (KM) 0 20 40 60 80 o 1.8 ; 0.71 I 2.0 ; 0.775 IO t z — — ZI5T;X5IZ — 333EpI«SI ZZ _ 5.65 ; 0.035 I 5.65 ; 0.022 in _ 7.2 ; 0.05 o ca F I G . 3 . 5 . The I m p e r i a l V a l l e y model s i m i l a r t o t h a t used by McMechan and Mooney ( 1 9 8 0 ) . L a t e r a l v e l o c i t y g r a d i e n t s i n the t o p 3 l a y e r s have been a p p r o x i m a t e d by d i v i d i n g each l a y e r i n t o b l o c k s . V e l o c i t i e s (km/s) a r e g i v e n f o r the t o p - J of each l a y e r f o l l o w e d a f t e r t h e s e m i c o l o n by t h e v e l o c i t y 0 0 g r a d i e n t ( k m / s / k m ) . 79 DISTANCE (KM) 20 40 60 80 DISTANCE (KM) F I G . 3 . 6 . (a) Ray p a t h s t h r o u g h the I m p e r i a l V a l l e y model of F i g u r e 3 . 5 . (b) S y n t h e t i c se ismograms c a l c u l a t e d by our a l g o r i t h m . (c ) S y n t h e t i c se ismograms c a l c u l a t e d by t h e r o u t i n e of McMechan and Mooney (1980) f o r t h e i r I m p e r i a l V a l l e y m o d e l , i n w h i c h l a t e r a l l y v a r y i n g v e l o c i t y g r a d i e n t s a r e a l l o w e d . A m p l i t u d e s c a l i n g i n (b) and (c ) i s p r o p o r t i o n a l t o square r o o t o f d i s t a n c e . 80 model c a l c u l a t e d by t h e r o u t i n e of McMechan and Mooney ( 1 9 8 0 ) . The se i smograms d e t e r m i n e d by our r o u t i n e ( F i g u r e 3 .6b) agree c l o s e l y w i t h t h o s e d e t e r m i n e d by t h e McMechan and Mooney (1980) a l g o r i t h m ( F i g u r e 3 . 6 c ) . The c o r r e s p o n d i n g CPU t i m e s t o c a l c u l a t e r a y a m p l i t u d e s on an Amdahl V / 8 were 5 seconds and 19 seconds r e s p e c t i v e l y , w i t h an a d d i t i o n a l 8 seconds f o r each t o p r o d u c e t h e s e i smograms . The t y p e s of a r r i v a l s m o d e l l e d i n c l u d e p r e - and p o s t - c r i t i c a l r e f l e c t i o n s , t u r n i n g r a y s i n 5 l a y e r s , and t h e f r e e - s u r f a c e m u l t i p l e s PP and P P P . An i m p o r t a n t a s p e c t of t h e s y n t h e t i c se i smogram a l g o r i t h m i s t h a t i t a l l o w s t h e m o d e l l i n g of complex s t r u c t u r e s . An example i s shown i n F i g u r e 3 . 7 . The d a t a upon w h i c h t h e model i s based and p r e l i m i n a r y i n t e r p r e t a t i o n s of t h e d a t a a r e d i s c u s s e d i n E l l i s e t a l . (1983) and C lowes e t a l . ( 1 9 8 3 b ) . The main purpose o f p r e s e n t i n g t h i s example i s no t t o show agreement between o b s e r v a t i o n s and s y n t h e t i c s or t o d i s c u s s t h e i n t e r p r e t a t i o n , but r a t h e r t o i l l u s t r a t e t h e type of l a t e r a l changes i n s t r u c t u r e t h a t can a r i s e i n s e i s m i c r e f r a c t i o n i n t e r p r e t a t i o n s , e s p e c i a l l y i n r e g i o n s where t e c t o n i c a c t i v i t y has o c c u r r e d . The model i n F i g u r e 3 .7 d e p i c t s t h e s u b d u c t i o n zone a c r o s s t h e m a r g i n between t h e o c e a n i c Juan de Fuca p l a t e and t h e c o n t i n e n t a l A m e r i c a p l a t e i n t h e r e g i o n of V a n c o u v e r I s l a n d . The l a r g e t w o - d i m e n s i o n a l v a r i a t i o n s i n s t r u c t u r e a r e n e c e s s a r y because o f t h e g r e a t d i f f e r e n c e between o c e a n i c and c o n t i n e n t a l c r u s t a l t h i c k n e s s e s , each of w h i c h i s c o n t r o l l e d w i t h i n l i m i t s by o t h e r i n d e p e n d e n t i n t e r p r e t a t i o n s . The most i m p o r t a n t f e a t u r e s of t h e model a r e t h u s t h e d e t a i l s o f t h e t r a n s i t i o n between o c e a n i c and c o n t i n e n t a l c r u s t s . These 81 F I G . 3.7. (a) S c h e m a t i c d i a g r a m of t h e s u b d u c t i o n zone between t h e o c e a n i c Juan de Fuca p l a t e and the c o n t i n e n t a l A m e r i c a p l a t e i n t h e r e g i o n of V a n c o u v e r I s l a n d . The range of v e l o c i t i e s i n km/s i s i n d i c a t e d f o r each l a y e r . The d i a g r a m does not i n c l u d e the d e t a i l s o f a l l l a y e r s o r b l o c k s t h a t were used f o r the r a y t r a c i n g , (b) Ray t r a c i n g d i a g r a m f o r t h e V a n c o u v e r I s l a n d s u b d u c t i o n m o d e l . (c ) S y n t h e t i c se i smograms f o r the s u b d u c t i o n m o d e l . F a r - o f f s e t a r r i v a l s a r e r e f l e c t i o n s from t h e d i p p i n g upper m a n t l e h o r i z o n . N e a r - o f f s e t a r r i v a l s i n c l u d e t u r n i n g r a y s i n the upper m a n t l e , and l a r g e upper m a n t l e r e f l e c t i o n s as s e c o n d a r y a r r i v a l s . o w CO CD -i n CO \ Q I CO < <r -r < <r <r c . nttt 180 200 220 240 260 280 300 320 DISTANCE FROM P19 (KM) 340 360 83 include: (1) the shallow-dipping high-velocity finger (7.8 km/s) at 20-26 km depth over the distance range 150-240 km, and (2) the upper mantle v e l o c i t i e s of 8.0-8.3 km/s below the subducting oceanic crust. The subducting oceanic crust i s i t s e l f not well-defined, since a l l rays take a similar amount of time to pass through i t and this time i s only a small portion of the t o t a l traveltime. Only three types of rays - two sets of r e f l e c t i o n s and one set of turning rays - are traced (Figure 3.7b) because these represent the a r r i v a l s of most interest for the interpretation. The resultant seismograms are thus very simple (Figure 3.7c), but model the kinematic and dynamic c h a r a c t e r i s t i c s of the observed data reasonably well. 3 . 5 Di scussion A fast, p r a c t i c a l method of c a l c u l a t i n g asymptotic ray theory amplitudes has been implemented u t i l i z i n g an e f f i c i e n t technique for ray tracing through l a t e r a l l y varying structures. The types of a r r i v a l s which may be modelled include head waves, refractions, p r e - c r i t i c a l and wide-angle r e f l e c t i o n s , surface r e f l e c t i o n s and multiples. Amplitudes calculated by t h i s method in a one-dimensional medium are consistent with those determined by the r e f l e c t i v i t y method, with the exception of c e r t a i n types of a r r i v a l s a r i s i n g from wave phenomena which any asymptotic ray theory method cannot d i r e c t l y handle. However, t h i s l i m i t a t i o n is overshadowed by the c a p a b i l i t y of the routine to be applied in two-dimensional structures. The routine i s intended as a p r a c t i c a l tool for use by interpreters of seismic refraction data. In comparison with 84 o t h e r a s y m p t o t i c r a y t h e o r y methods , t h e major a d v a n t a g e s of t h e a l g o r i t h m a r e i t s speed and ease of u s e . These c h a r a c t e r i s t i c s a r i s e because of t h e n a t u r e of t h e v e l o c i t y m o d e l , w h i c h i s d e f i n e d by a r b i t r a r y p o l y g o n a l b l o c k s , each w i t h i t s own v e l o c i t y and l i n e a r v e l o c i t y g r a d i e n t . Such model s p e c i f i c a t i o n i s p a r t i c u l a r l y a p p r o p r i a t e f o r some t y p e s of t e c t o n i c f e a t u r e s , e . g . wedges or f a u l t b l o c k s . On t h e o t h e r h a n d , t h e p a r a m e t e r i z a t i o n i s somewhat l i m i t i n g f o r model s where t h e v e l o c i t y or i t s g r a d i e n t v a r y c o n t i n u o u s l y i n a l a t e r a l s e n s e , e . g . a p a s s i v e c o n t i n e n t a l m a r g i n p r o b l e m . However , such models can be a d e q u a t e l y a p p r o x i m a t e d by s e v e r a l l a t e r a l l y a d j a c e n t b l o c k s . A scheme w h i c h a u t o m a t i c a l l y d i v i d e s a b l o c k i n t o s e v e r a l s u b - b l o c k s c o u l d be i n c o r p o r a t e d i n t o the program w i t h o u t g r e a t d i f f i c u l t y . A number of m o d i f i c a t i o n s t o t h e a l g o r i t h m c o u l d be implemented t o f u r t h e r enhance i t s a p p l i c a b i l i t y . To compensate f o r l i m i t a t i o n s i n r a y t h e o r y , i t i s p o s s i b l e t o i n c o r p o r a t e a d d i t i o n s t o ART w h i c h a c c o u n t f o r c e r t a i n t y p e s of wave b e h a v i o r . These i n c l u d e c o r r e c t i o n s t o r a y t h e o r y a m p l i t u d e s i n t h e r e g i o n o f c r i t i c a l p o i n t s and c a u s t i c s , and h i g h f r e q u e n c y a p p r o x i m a t i o n s f o r waves such as d i f f r a c t i o n s . On a more p r a c t i c a l b a s i s , t h e program c o u l d be a d a p t e d f o r i n t e r a c t i v e u s e , where speed i s a p r i m a r y r e q u i r e m e n t . Changes t o t h e i n p u t v e l o c i t y s t r u c t u r e c o u l d t h u s be made even more q u i c k l y , and t h e e f f e c t of t h e change on the a m p l i t u d e and t r a v e l t i m e b e h a v i o r seen w i t h i n a few s e c o n d s . 85 CHAPTER INTERPRETATION OF ONSHORE-OFFSHORE PROFILE ACROSS VANCOUVER ISLAND 4.1 I n t r o d u c t i o n S e i s m i c r e f r a c t i o n l i n e I was d i r e c t e d a c r o s s the s t r i k e of t h e B r i t i s h C o l u m b i a c o n t i n e n t a l m a r g i n (see F i g . 1 . 3 ) . The o n s h o r e - o f f s h o r e l i n e p r o v i d e s t h e b a s i c d a t a t o t e s t the s t r u c t u r a l model of R i d d i h o u g h ( 1 9 7 9 ) , i n w h i c h t h e o c e a n i c Juan de Fuca p l a t e s u b d u c t s b e n e a t h t h e c o n t i n e n t a l A m e r i c a p l a t e . S e v e n t e e n , s h o t s ( the P s e r i e s ) were f i r e d o v e r t h e c o n t i n e n t a l s l o p e and ocean b a s i n , and were r e c o r d e d on an a r r a y of 32 l a n d s e i s m o g r a p h s l o c a t e d on V a n c o u v e r I s l a n d and t h e B r i t i s h C o l u m b i a m a i n l a n d . An a d d i t i o n a l two s h o t s s e p a r a t e d by ~7 km ( s h o t s J1 and J2 ) were f i r e d a t s h o t p o i n t s near t h e e a s t e r n end of t h e p r o f i l e . F o r t h e o c e a n i c s h o t s / t h e minimum s h o t - r e c e i v e r d i s t a n c e was 93 km and t h e maximum was 350 km. S i n c e o c e a n i c c r u s t t y p i c a l l y has a t h i c k n e s s of about 10 km or l e s s , r a y s f rom t h e o c e a n i c s h o t s a r e e x p e c t e d t o t r a v e l t h r o u g h upper m a n t l e m a t e r i a l f o r a t l e a s t a p o r t i o n of t h e i r p a t h s . T h u s , t h e i n t e r p r e t a t i o n of l i n e I p r o v i d e s i n f o r m a t i o n about upper m a n t l e v e l o c i t y and t h e l o c a t i o n of t h e c o n t a c t between upper m a n t l e and c r u s t a l m a t e r i a l . The d i s t r i b u t i o n of s h o t s and r e c e i v e r s a l o n g l i n e I a l l o w s a t w o - d i m e n s i o n a l i n t e r p r e t a t i o n t o be made of t h e s u b d u c t i o n zone v e l o c i t y s t r u c t u r e . I n t h i s t h e s i s , d a t a a r e d i s p l a y e d e i t h e r as common shot g a t h e r s o r common r e c e i v e r g a t h e r s . I n common shot g a t h e r s , r e c o r d i n g s on a l l 32 r e c e i v e r s f rom a 86 p a r t i c u l a r s h o t a r e shown and t h e v a r i a t i o n i n t h e d a t a f rom r e c e i v e r t o r e c e i v e r t e n d s t o p r o v i d e i n f o r m a t i o n about t h e s t r u c t u r e b e n e a t h the r e c e i v e r s . On common r e c e i v e r g a t h e r s , t h e se i smograms f rom a l l 17 s h o t s r e c o r d e d on a p a r t i c u l a r r e c e i v e r a r e d i s p l a y e d ; i n t h i s ca se t h e v a r i a t i o n from shot t o s h o t t e l l s us more about t h e s t r u c t u r e b e n e a t h t h e s h o t s . F u r t h e r m o r e , we may a l r e a d y have i n d e p e n d e n t i n f o r m a t i o n about t h e uppermost l a y e r s b e n e a t h t h e s h o t s and b e n e a t h t h e r e c e i v e r s , so t h e i n t e r p r e t a t i o n i s t h e n r e d u c e d t o f i n d i n g t h e v a r i a t i o n i n t h e s t r u c t u r e of t h e deeper l a y e r s . For t h e i n t e r p r e t a t i o n o f the o n s h o r e - o f f s h o r e p o r t i o n of l i n e I , the uppermost l a y e r s about w h i c h i n f o r m a t i o n i s known i n c l u d e much of the o c e a n i c c r u s t (Waldron 1982) and a p o r t i o n of t h e c o n t i n e n t a l c r u s t (McMechan and Spence 1 9 8 3 ) . F o r t h e o c e a n i c c r u s t , t h e s t r u c t u r e t o about 9 km d e p t h was r e l a t i v e l y w e l l - d e t e r m i n e d b e n e a t h t h e deep o c e a n i c b a s i n and somewhat l e s s c o n s t r a i n e d under the c o n t i n e n t a l s l o p e , where t h i c k s e d i m e n t s and a p o s s i b l e l o w - v e l o c i t y melange were f o u n d . F o r the c o n t i n e n t a l c r u s t , the s t r u c t u r e was c o n t r o l l e d a t i t s i n t e r s e c t i o n p o i n t w i t h l i n e I V , w h i c h was r o u g h l y p a r a l l e l t o t h e c o n t i n e n t a l m a r g i n and p e r p e n d i c u l a r t o l i n e I ( F i g . 1 . 3 ) . H e r e , t h e upper c o n t i n e n t a l c r u s t was w e l l - d e t e r m i n e d t o a d e p t h of about 20 km w h i l e t h e l o w e r c o n t i n e n t a l c r u s t was p o o r l y c o n s t r a i n e d . The p r e f e r r e d i n t e r p r e t a t i o n f o r t h e l o w e r c r u s t i n c l u d e d a l o w - v e l o c i t y zone and a c r u s t a l t h i c k n e s s of 37 km; however , a l t e r n a t i v e i n t e r p r e t a t i o n s a l l o w e d t h e t h i c k n e s s t o be as l a r g e as 52 km. 87 4 . 2 I n t e r p r e t a t i o n of s h o t s J1 and J2 S h o t s J1 and J 2 , w h i c h were d e t o n a t e d i n a deep i n l e t and r e c o r d e d on t h e l a n d r e c e i v e r s , p r o v i d e a d d i t i o n a l c o n t r o l f o r t h e c o n t i n e n t a l c r u s t a l s t r u c t u r e . S i n c e t h e maximum s h o t -r e c e i v e r o f f s e t was l e s s than 170 km, o n l y upper c r u s t a l i n f o r m a t i o n i s o b t a i n e d f rom t h e s e s h o t s . The s e i s m i c s e c t i o n f o r shot J1 i s shown i n F i g u r e 4 . 1 b ; a m p l i t u d e s a r e m u l t i p l i e d by a f a c t o r p r o p o r t i o n a l t o d i s t a n c e . The s e c t i o n f o r shot J2 i s v e r y s i m i l a r (see A p p e n d i x 1, F i g . A 1 . 1 ) , a l t h o u g h t h e r e a p p e a r s t o be some i n d i c a t i o n of c l i p p i n g even on some of the more d i s t a n t t r a c e s . F o r b o t h s h o t s J1 and J 2 , t h e s h o t s and r e c e i v e r s have been c o r r e c t e d t o sea l e v e l by u s i n g a r e p l a c e m e n t v e l o c i t y of 5 . 5 km/s f o r b o t h t h e w a t e r - c o l u m n and t h e near s u r f a c e m a t e r i a l a t the r e c e i v e r s . Because o f t h e s i m i l a r i t y of t h e s h o t J1 and J2 r e c o r d s e c t i o n s , an i n t e r p r e t a t i o n f o r t h e s h o t J1 d a t a w i l l a l s o be v a l i d f o r t h e shot J2 d a t a . A p r e l i m i n a r y i n t e r p r e t a t i o n of f i r s t a r r i v a l t r a v e l t i m e s f o r shot J1 was p r e s e n t e d i n E l l i s e t a l . ( 1 9 8 3 ) . An i n i t i a l o n e - d i m e n s i o n a l s t a r t i n g model was d e t e r m i n e d by a l i n e a r programming i n v e r s i o n of t h e f i r s t a r r i v a l t i m e s (Garmany e t a l . 1 9 7 9 ) . The i n i t i a l model was t h e n m o d i f i e d u s i n g t h e t w o -d i m e n s i o n a l r a y t r a c i n g r o u t i n e of W h i t t a l l and Clowes ( 1 9 7 9 ) , f o r w h i c h t h e p r e f e r r e d model of McMechan and Spence (1983) was i n c o r p o r a t e d west of t h e i n t e r s e c t i o n p o i n t of l i n e s I and I V . The i n t e r p r e t a t i o n of shot J1 p r e s e n t e d i n E l l i s e t a l . (1983) has been f u r t h e r r e f i n e d i n an e f f o r t t o model a m p l i t u d e s and t o a c c o u n t f o r s e c o n d a r y a r r i v a l s . I n p a r t i c u l a r , an a t t e m p t 88 F I G . 4 . 1 . S y n t h e t i c se ismograms and o b s e r v e d d a t a f o r s h o t J 1 , w h i c h i s l o c a t e d on the r i g h t hand s i d e of the s e c t i o n s . The f i r s t a r r i v a l t r a v e l t i m e p i c k s a r e i n d i c a t e d by a r r o w h e a d s . The t h e o r e t i c a l t r a v e l t i m e c u r v e from the s y n t h e t i c se i smograms i s s u p e r i m p o s e d on the o b s e r v e d r e c o r d s e c t i o n . The dashed l i n e c o r r e s p o n d s t o r e f l e c t i o n s from the base of the 6 .7 km/s c o n s t a n t v e l o c i t y l a y e r i n F i g . 4 . 2 . A l l a m p l i t u d e s have been m u l t i p l i e d by a f a c t o r p r o p o r t i o n a l t o d i s t a n c e . The d i s t a n c e s c a l e i n (a) and the t o p s c a l e i n (b) a r e measured r e l a t i v e t o shot P 1 9 , the wes ternmost of t h e P s e r i e s s h o t s i n the deep o c e a n . 89 was made t o model t h e l o w - a m p l i t u d e f i r s t a r r i v a l s and the h i g h e r a m p l i t u d e second a r r i v a l s o c c u r r i n g a t d i s t a n c e s from shot J1 g r e a t e r than about 110 km ( F i g . 4 . 1 b ) . The a p p a r e n t v e l o c i t y of the f i r s t a r r i v a l p h a s e , w h i c h i s d e n o t e d by a da shed l i n e i n F i g u r e 4 . 1 , i s about 6 .7 km/s w h i l e t h e a p p a r e n t v e l o c i t y o f the s e c o n d a r y phase i s about 6 .5 k m / s . A s i m i l a r s e t of a r r i v a l s , but w i t h v e l o c i t i e s 6 .9 km/s and 6 . 7 5 k m / s , had been found f o r some of t h e V a n c o u v e r I s l a n d s h o t s a l o n g l i n e IV (McMechan and Spence 1983) . The f i n a l v e l o c i t y model f o r shot J1 i s shown i n F i g u r e 4 . 2 a . West of 240 km, the McMechan and Spence (1983) i n t e r p r e t a t i o n i s i n c o r p o r a t e d i n t h e m o d e l , e x c e p t f o r t h e p o r t i o n be low ~16 km w h i c h o r i g i n a t e s from t h e i n t e r p r e t a t i o n of t h e P s e r i e s s h o t s c o n s i d e r e d i n t h e f o l l o w i n g s e c t i o n . I n F i g u r e 4 . 2 b , r a y s a r e t r a c e d t h r o u g h o u t t h e m o d e l , and t h e t h e o r e t i c a l model t r a v e l t i m e s a r e s u p e r i m p o s e d on t h e J1 r e c o r d s e c t i o n i n F i g u r e 4 . 1 b . S y n t h e t i c se ismograms c o r r e s p o n d i n g t o t h e t r a c e d r a y s were c a l c u l a t e d u s i n g the r o u t i n e d e s c r i b e d i n C h a p t e r 3 of t h i s t h e s i s and by Spence et a l . ( 1 9 8 4 ) , and a r e d i s p l a y e d i n F i g u r e 4 . 1 a . I n t h e i n t e r p r e t e d m o d e l , t h e v e l o c i t y of t h e near s u r f a c e m a t e r i a l i s 5 . 3 k m / s , somewhat l e s s t h a n t h a t d e t e r m i n e d on V a n c o u v e r I s l a n d by McMechan and Spence ( 1 9 8 3 ) . The v e l o c i t y of t h e upper l a y e r s i s d e t e r m i n e d by t h e f i r s t a r r i v a l s a t r e c e i v e r s near shot J 1 . T h i s p o r t i o n of the model i s p o o r l y c o n s t r a i n e d because r a y p a t h s were not r e v e r s e d i n t h i s r e g i o n and because the r e c e i v e r s were f a r from t h e i n t e r s e c t i o n w i t h l i n e I V , where some t w o - d i m e n s i o n a l c o n t r o l was a v a i l a b l e . F o r 90 F I G . 4 . 2 . V e l o c i t y model d e t e r m i n e d from shot J1 d a t a , and r a y p a t h s t r a c e d t h r o u g h the m o d e l . I n t e r p r e t a t i o n of McMechan and Spence (1983) t o a d e p t h of 16 km i s used west of 240 km d i s t a n c e . D e t a i l s i n t h e model be low t h a t d e p t h a r e d e r i v e d fom i n t e r p r e t a t i o n of t h e P s e r i e s s h o t s . D i s t a n c e s a r e measured r e l a t i v e t o shot P 1 9 , t h e wes ternmost shot i n t h e deep ocean b a s i n . The a r rowheads i n d i c a t e t h e west and e a s t c o a s t s of V a n c o u v e r I s l a n d . V e l o c i t i e s (km/s) a r e g i v e n f o r t h e t o p of each b l o c k , f o l l o w e d a f t e r the c o l o n by the v e l o c i t y g r a d i e n t (km/s/km) i f one was u s e d . DEPTH (KM) DEPTH (KM) 16 92 s i m p l i c i t y , t h e r e g i o n from 1.0 km t o 3 .5 km was m o d e l l e d as a c o n s t a n t v e l o c i t y l a y e r w i t h v e l o c i t y j u s t o v e r 6 k m / s , so t h a t a r r i v a l s i n t h e d i s t a n c e range of 20-50 km from J1 c o r r e s p o n d e d t o r e f l e c t i o n s f rom t h e bot tom of t h i s l a y e r . But because of t h e i n d e t e r m i n a c y , d i f f e r e n t v e l o c i t y s t r u c t u r e s wou ld a l s o be v a l i d ; f o r e x a m p l e , t h e upper 3 o r 4 km o f t h e model c o u l d have been m o d e l l e d e q u a l l y as w e l l by a l a y e r w i t h c o n s t a n t v e l o c i t y g r a d i e n t , w i t h the f i r s t a r r i v a l s c o r r e s p o n d i n g t o t u r n i n g r a y s . Below 3 .5 km d e p t h i n the i n t e r p r e t e d m o d e l , t h e v e l o c i t y i n c r e a s e s f rom 6 . 3 3 km/s w i t h a v e l o c i t y g r a d i e n t o f 0 .018 k m / s / k m . T u r n i n g r a y s i n t h i s r e g i o n form the f i r s t a r r i v a l s i n the d i s t a n c e range of 50-120 km from J 1 , and a r e t h e s e c o n d a r y , l a r g e a m p l i t u d e a r r i v a l s p a s t 120 km. The i n t e r p r e t a t i o n of the s m a l l a m p l i t u d e p r i m a r y a r r i v a l s p a s t 120 km i s somewhat s p e c u l a t i v e . They were i n t e r p r e t e d i n a f a s h i o n s i m i l a r t o t h a t employed by McMechan and Spence (1983) f o r l i n e IV on V a n c o u v e r I s l a n d . T h e r e , a s m a l l a m p l i t u d e f i r s t a r r i v a l phase w i t h v e l o c i t y 6 .95 km/s was m o d e l l e d as t u r n i n g r a y s below a d i s c o n t i n u i t y a t 16 km d e p t h , a c r o s s w h i c h t h e v e l o c i t y i n c r e a s e d from 6 .75 km/s t o 6 . 9 5 km/s ( F i g . 1 . 5 ) . F o r shot J 1 , a d i s c o n t i n u i t y i s s i m i l a r l y i n f e r r e d , a c r o s s w h i c h v e l o c i t y i n c r e a s e s from 6 . 4 - 6 . 5 km/s t o 6 .7 k m / s , and t h e s m a l l a m p l i t u d e phase i s i n t e r p r e t e d as a s e t of a r r i v a l s w h i c h t u r n back t o t h e s u r f a c e w i t h i n the r e g i o n of 6 .7 km/s v e l o c i t y . In t h e r a y t r a c i n g d i a g r a m of F i g u r e 4 . 2 b , t h e s e a r r i v a l s a r e f o r c o n v e n i e n c e m o d e l l e d as r e f l e c t i o n s f rom t h e bo t tom of t h e 6 .7 km/s v e l o c i t y r e g i o n ; but w i t h a s m a l l g r a d i e n t i n t h e r e g i o n , t h e c o r r e s p o n d i n g t u r n i n g r a y s t o t h e g r e a t e r o f f s e t d i s t a n c e s 93 would a l s o have s m a l l a m p l i t u d e s and a l m o s t t h e same t r a v e l t i m e s as t h e r e f l e c t i o n s . The t o p of t h e 6 .7 km/s c o n s t a n t v e l o c i t y zone i s i n f e r r e d t o be s h a l l o w e r i n t h e e a s t t h a n i n t h e w e s t . The d e p t h i n the e a s t i s 8 km and i s c o n t r o l l e d by t h e l o c a t i o n of t h e c r o s s o v e r p o i n t between t h e p r i m a r y and s e c o n d a r y a r r i v a l s w h i c h o c c u r s 120 km from t h e s h o t ( a t 240 km i n t h e model of F i g u r e 4 . 2 ) . I f t h e d e p t h was g r e a t e r , t h e n t h e t r a v e l t i m e s f o r t h e r e f l e c t i o n s w o u l d be g r e a t e r , and t h e c r o s s o v e r p o i n t w o u l d be a t an even g r e a t e r d i s t a n c e f rom t h e s h o t . The d i s c o n t i n u i t y needs t o be deeper a t i t s w e s t e r n end because t h e l a r g e a m p l i t u d e t u r n i n g r a y s above t h e b o u n d a r y , w h i c h a r e p r e s e n t i n t h e d a t a out t o t h e maximum s h o t - r e c e i v e r o f f s e t , need t o p e n e t r a t e t o d e p t h s near 14 km. The t o p of t h e 6 .7 km/s v e l o c i t y r e g i o n has been m o d e l l e d as a d i s c o n t i n u i t y , but c o u l d j u s t as w e l l be a nar row g r a d i e n t z o n e . On t h e s y n t h e t i c r e c o r d s e c t i o n ( F i g . 4 . 2 a ) , t h e r e f l e c t i o n s f rom t h e d i s c o n t i n u i t y a r e s u f f i c i e n t l y c l o s e i n t r a v e l t i m e t o t h e t u r n i n g r a y s above the d i s c o n t i n u i t y t h a t t h e i r waveforms o v e r l a p . That i s , the r e f l e c t i o n s a r e no t e x p e c t e d t o form a v e r y d i s t i n c t phase w h i c h can be e a s i l y i d e n t i f i e d on the o b s e r v e d r e c o r d s e c t i o n ( F i g . 4 . 2 b ) , and t h u s t h e r e i s no t d i r e c t s u p p o r t f o r t h e e x i s t e n c e of t h e d i s c o n t i n u i t y . T h i s c o n t r a s t s w i t h the e v i d e n c e on V a n c o u v e r I s l a n d f o r t h e e x i s t e n c e o f the d i s c o n t i n u i t y a t ~16 km d e p t h i n t h e i n t e r p r e t a t i o n of McMechan and Spence ( 1 9 8 3 ) , where r e f l e c t i o n s were more e a s i l y p i c k e d on some ( t h o u g h not a l l ) o f t h e o b s e r v e d r e c o r d s e c t i o n s . 94 P e r h a p s one of the more i n t e r e s t i n g f e a t u r e s of the J1 d a t a s e t i s what i s not seen i n t h e d a t a : no ma jor o f f s e t or p e r t u r b a t i o n of t r a v e l t i m e s or a m p l i t u d e s i s o b s e r v e d on c r o s s i n g the S t r a i t of G e o r g i a , w h i c h c o r r e s p o n d s t o the d i s t a n c e range 60-95 km from shot J1 ( F i g . 4 . 1 b ) . T h i s i m p l i e s t h a t down t o a d e p t h of a l m o s t 14 km t h e r e i s no e v i d e n c e f o r a ma jor v e l o c i t y d i s c o n t i n u i t y a c r o s s G e o r g i a S t r a i t . T h u s , the i n f e r r e d f a u l t ( M u l l e r 1977) s e p a r a t i n g t h e C o a s t P l u t o n i c Complex on t h e m a i n l a n d from t h e I n s u l a r B e l t on V a n c o u v e r I s l a n d i s not o b s e r v a b l e i n terms of v e l o c i t y c o n t r a s t . An i n t e r p r e t a t i o n of a d e t a i l e d sonobuoy r e f r a c t i o n s u r v e y a c r o s s G e o r g i a S t r a i t (Whi te and Clowes 1984) a l s o c o n c l u d e d t h a t t h e r e was no s e i s m i c e v i d e n c e f o r such a f a u l t down t o d e p t h s of 3 t o 4 km. 4 . 3 D e s c r i p t i o n of P s e r i e s s h o t s The 17 P s h o t s were c o r r e c t e d f o r sea b o t t o m t o p o g r a p h y and d e t o n a t i o n d e p t h by p l a c i n g a l l s h o t s a t an e q u i v a l e n t datum d e p t h of 2600 m. I n a d d i t i o n t o a t i m e c o r r e c t i o n , t h i s a l s o i n v o l v e d a d i s t a n c e o f f s e t of e a c h shot t o w a r d t h e r e c e i v e r s . The c o r r e c t i o n s were found by r a y t r a c i n g from each shot t o t h e datum d e p t h t h r o u g h the model of W a l d r o n ( 1 9 8 2 ) , who d e t e r m i n e d t h e s e d i m e n t a r y s t r u c t u r e a l o n g t h e m a r i n e p o r t i o n of l i n e I u s i n g CSP and OBS d a t a . The t o p o g r a p h i c v a r i a t i o n was o n l y s i g n i f i c a n t f o r t h e f i r s t s i x s h o t s on the c o n t i n e n t a l s l o p e ( s h o t s P1 t o P6) where t h e water d e p t h ranged f rom 500 t o 2100 m; f o r the r e m a i n i n g s h o t s i n t h e ocean b a s i n (P8 t o P 1 9 ) , d e p t h s were between 2425 and 2625 m. V a r i a t i o n i n t o p o g r a p h y a t 95 t h e r e c e i v e r s was c o r r e c t e d i n t h e same manner as f o r shot J 1 , by a d j u s t i n g r e c e i v e r e l e v a t i o n t o sea l e v e l u s i n g a v e l o c i t y of 5 . 5 k m / s . A c o r r e c t i o n f o r basement t o p o g r a p h y and v a r y i n g t h i c k n e s s of s e d i m e n t s was a l s o c a l c u l a t e d f o r t h e 11 s h o t s i n t h e ocean b a s i n , where t h e s e d i m e n t a r y s t r u c t u r e down t o t h e basement was w e l l - d e t e r m i n e d i n the i n t e r p r e t a t i o n of Waldron ( 1 9 8 2 ) . The c o r r e c t i o n s were found by e q u a l i z i n g t h e sed iment t h i c k n e s s t o 1 km and the sed iment v e l o c i t y t o 1 . 8 k m / s . No basement c o r r e c t i o n was p e r f o r m e d f o r s h o t s P1 t o P6 on t h e c o n t i n e n t a l s l o p e . F i g u r e 4 . 3 d i s p l a y s t h e r e c o r d s e c t i o n s f o r t h r e e r e p r e s e n t a t i v e s h o t s i n t h e ocean b a s i n . A l l s e c t i o n s show t r u e a m p l i t u d e s m u l t i p l i e d by a f a c t o r p r o p o r t i o n a l t o s h o t / r e c e i v e r d i s t a n c e , and c o r r e c t e d f o r c h a r g e s i z e u s i n g t h e W 2 / 3 r e l a t i o n s h i p between c h a r g e w e i g h t and a m p l i t u d e d e t e r m i n e d e x p e r i m e n t a l l y by 0 ' B r i e n ( 1 9 6 0 ) . S h o t s P19 and P13 a r e 825 kg c h a r g e s , and shot P8 i s 200 k g . On a l l t h r e e r e c o r d s e c t i o n s , t h e gap i n t h e m i d d l e c o r r e s p o n d s t o t h e l o c a t i o n of G e o r g i a S t r a i t (265-285 km from shot P 1 9 ) . Common r e c e i v e r g a t h e r s f o r two l a n d s e i s m o g r a p h s t a t i o n s , X45 on t h e m a i n l a n d a t t h e e a s t e r n end of t h e p r o f i l e and X22 l o c a t e d on V a n c o u v e r I s l a n d ~15 km west of G e o r g i a S t r a i t , a r e shown i n F i g u r e 4 . 4 . Note t h a t t h e wes ternmost s h o t P19 i s on t h e l e f t of t h e common r e c e i v e r s e c t i o n s , i . e . t h e s h o t / r e c e i v e r d i s t a n c e i n c r e a s e s from r i g h t t o l e f t . The most p r o m i n e n t phases i n t h e e n t i r e d a t a s e t a r e the l a r g e a m p l i t u d e f i r s t a r r i v a l s f rom t h e ocean b a s i n s h o t s r e c o r d e d on t h e s t a t i o n s t o t h e e a s t of G e o r g i a S t r a i t (see 96 F I G . 4 . 3 . O b s e r v e d r e c o r d s e c t i o n s f o r s h o t s P 1 9 , P13 and P 8 . R e c o r d s e c t i o n s a r e t r u e a m p l i t u d e , so t h a t a m p l i t u d e s may be compared from shot t o s h o t . A l l a m p l i t u d e s have been m u l t i p l i e d by a f a c t o r p r o p o r t i o n a l t o d i s t a n c e . T r a v e l t i m e p i c k s a r e i n d i c a t e d by a r r o w h e a d s , and i n c l u d e s e c o n d a r y a r r i v a l s f o r s h o t s P19 and P 1 3 . Times and d i s t a n c e s a r e a d j u s t e d t o p l a c e t h e s h o t a t a d e p t h of 2 .6 km, and t o c o r r e c t t h e sed iment l a y e r t o a t h i c k n e s s of 1 km and v e l o c i t y of 1.8 k m / s . The gap near t h e m i d d l e of a l l s e c t i o n s i n d i c a t e s the l o c a t i o n o f G e o r g i a S t r a i t (a t 265-285 km from s h o t P i 9 ) . 98 S H O T / R E C E I V E R D I S T A N C E (KM) F I G . 4 . 4 . Observed r e c o r d s e c t i o n s showing a l l s h o t s ( t h r e e a r e i d e n t i f i e d ) r e c o r d e d on r e c e i v e r s X45 and X 2 2 , w h i c h a r e l o c a t e d t o the r i g h t of the s e c t i o n s . Record s e c t i o n s a r e t r u e a m p l i t u d e , w i t h a l l a m p l i t u d e s m u l t i p l i e d by a f a c t o r p r o p o r t i o n a l t o d i s t a n c e . Times and d i s t a n c e s a r e a d j u s t e d t o p l a c e the s h o t s a t 2 .6 km d e p t h , and f o r s h o t s P19-P8 t o c o r r e c t the sed iment l a y e r t o a t h i c k n e s s of 1 km and v e l o c i t y of 1.8 k m / s . 99 s h o t s P19 and P13 i n F i g u r e 4 . 3 and r e c e i v e r X45 i n F i g u r e 4 . 4 ) . These a r r i v a l s have an e x c e l l e n t s i g n a l - t o - n o i s e r a t i o and a s h a r p o n s e t , w i t h an a p p a r e n t v e l o c i t y of 8 . 1 - 8 . 2 km/s a c r o s s t h e r e c e i v e r s ( F i g . 4 .3 ) and a r e v e r s e d a p p a r e n t v e l o c i t y of 8 . 3 - 8 . 5 km/s a c r o s s t h e s h o t s ( F i g . 4 . 4 ) . The l a r g e a m p l i t u d e s from t h e s e more d i s t a n t ocean b a s i n s h o t s c o n t r a s t m a r k e d l y w i t h the d i m i n i s h e d a m p l i t u d e s f rom the c l o s e r s h o t s P1-P6 on t h e c o n t i n e n t a l s l o p e , as seen f o r r e c e i v e r X45 i n F i g u r e 4 . 4 . Because t h e a m p l i t u d e s f o r s h o t s P1-P6 a r e q u i t e s m a l l , i t i s d i f f i c u l t t o p i c k the a p p a r e n t v e l o c i t i e s a c r o s s t h e s e s h o t s , but an e s t i m a t e i s about 8 k m / s . F o r t h e s t a t i o n s on V a n c o u v e r I s l a n d , w h i c h a r e c l o s e r t o t h e s h o t s t h a n the m a i n l a n d s t a t i o n s , t h e d a t a q u a l i t y i s p o o r e r t h a n t h a t o f t h e p r o m i n e n t phases seen on t h e m a i n l a n d s t a t i o n s . The s i g n a l s a r e l e s s c o n s i s t e n t f rom t r a c e - t o - t r a c e , h a v i n g a more complex wave form and l o w e r s i g n a l - t o - n o i s e r a t i o . However , a second a r r i v a l can be d i s c e r n e d on some of t h e V a n c o u v e r I s l a n d s t a t i o n s , and i t s a m p l i t u d e i s somewhat l a r g e r t h a n t h a t of t h e p r i m a r y a r r i v a l . The b e s t examples o f t h e s e a r r i v a l s a r e seen on s h o t P13 ( F i g . 4 . 3 ) and r e c e i v e r X22 ( s h o t s P13 t o P 1 9 , F i g . 4 . 4 ) . A c o n s i s t e n t c h a r a c t e r i s t i c of t h e s e c o n d a r y a r r i v a l s i s t h a t t h e i r t r a v e l t i m e s a p p r o a c h t h e p r i m a r y a r r i v a l t r a v e l t i m e s f o r g r e a t e r s h o t / r e c e i v e r o f f s e t s . The a p p a r e n t v e l o c i t y of t h e f i r s t a r r i v a l s a c r o s s the V a n c o u v e r I s l a n d r e c e i v e r s i s 7 . 5 - 7 . 7 km/s ( F i g . 4 . 3 ) , w h i l e t h a t of t h e second a r r i v a l s i s n e a r l y 8 k m / s . The a p p a r e n t v e l o c i t y of t h e f i r s t a r r i v a l s a c r o s s t h e s h o t s f o r a V a n c o u v e r I s l a n d s t a t i o n i s ~ 8 . 3 km/s ( F i g . 4 . 4 ) , w h i c h i s comparab le t o 100 t h a t f o r a m a i n l a n d s t a t i o n , w h i l e the s e c o n d a r y a r r i v a l a p p a r e n t v e l o c i t y a p p r o a c h e s 9 k m / s . F i n a l l y , t h e most p r o m i n e n t t r a v e l t i m e c h a r a c t e r i s t i c of t h e d a t a i s a t r a v e l t i m e d e l a y of about 1 s o c c u r r i n g on a l l s h o t s f o r the s t a t i o n s e a s t of G e o r g i a S t r a i t r e l a t i v e t o t h e s t a t i o n s west of G e o r g i a S t r a i t . The a c t u a l l o c a t i o n where t h e d e l a y o c c u r s i s t h e same on a l l s h o t r e c o r d s e c t i o n s and i s not dependent on s h o t / r e c e i v e r o f f s e t . T h i s i s s u g g e s t i v e of a f i x e d s t r u c t u r a l f e a t u r e i n t h e m o d e l , such as a f a u l t , r a t h e r t h a n s i m p l y a d e p t h - d e p e n d e n t f e a t u r e such as a l o w - v e l o c i t y z o n e . But f rom t h e i n t e r p r e t a t i o n of shot J 1 , we know t h a t t h e r e i s no ma jor t w o - d i m e n s i o n a l d i s r u p t i o n i n s t r u c t u r e b e n e a t h G e o r g i a S t r a i t down t o a d e p t h of 14 km. T h u s , the s t r u c t u r a l f e a t u r e c a u s i n g t h e t r a v e l t i m e o f f s e t must be a t g r e a t e r d e p t h s . 4 .4 Ray t r a c i n g and t r a v e l t i m e i n v e r s i o n : s h o t s P 1 9 , PI 3 and P8 The 17 s h o t s of t h e P s e r i e s r e c o r d e d on up t o 32 r e c e i v e r s form a l a r g e number of s h o t - r e c e i v e r c o m b i n a t i o n s , e s p e c i a l l y when s e c o n d a r y a r r i v a l s a r e c o n s i d e r e d . A model of t h e d a t a s h o u l d s i m u l t a n e o u s l y f i t a l l t h e t r a v e l t i m e s . To a c h i e v e t h i s , the r a y t r a c e i n v e r s i o n p r o c e d u r e d e s c r i b e d i n C h a p t e r 2 was a p p l i e d . I n t h i s p r o c e d u r e , t w o - d i m e n s i o n a l r a y t r a c i n g i s used t o d e t e r m i n e t r a v e l t i m e s and t h e p a r t i a l d e r i v a t i v e s of t r a v e l t i m e w i t h r e s p e c t t o s e l e c t e d p a r a m e t e r s o f t h e v e l o c i t y m o d e l . A d j u s t m e n t s t o the model a r e then found u s i n g the damped l e a s t - s q u a r e s m a t r i x i n v e r s i o n t e c h n i q u e . Of t h e 17 s h o t s i n t h e P s e r i e s , ocean b a s i n s h o t s P 1 9 , P13 and P8 were s e l e c t e d i n t h e r a y t r a c e i n v e r s i o n p r o c e d u r e . None 101 of the c o n t i n e n t a l s l o p e s h o t s P1-P6 were used because c o n s i s t e n t a r r i v a l s were d i f f i c u l t t o p i c k and because s e d i m e n t a r y and upper c r u s t a l s t r u c t u r e s ( i n c l u d i n g a p o s s i b l y t h i c k low v e l o c i t y melange) were not as w e l l c o n s t r a i n e d as t h e ocean b a s i n s t r u c t u r e i n the i n t e r p r e t a t i o n o f W a l d r o n ( 1 9 8 2 ) . O n l y t h e t h r e e s h o t s P 1 9 , P13 and P8 were used because (1) s h o t s P19 and P13 were t h e l a r g e s t c h a r g e s and t h e i r a r r i v a l s t h e b e s t r e c o r d e d , and (2) f i r s t a r r i v a l t r a v e l t i m e s show no major o f f s e t s f rom shot P8 t o shot P 1 9 , and so i t was f e l t t h a t the t h r e e s h o t s a d e q u a t e l y r e p r e s e n t e d t h e v a r i a t i o n among a l l the ocean b a s i n s h o t s . In t h e f o l l o w i n g e x a m p l e , the b e h a v i o r of t h e r a y t r a c e i n v e r s i o n p r o c e d u r e i s d e m o n s t r a t e d u s i n g a model w h i c h i s c l o s e t o t h e f i n a l o n s h o r e - o f f s h o r e r e f r a c t i o n m o d e l . The deve lopment of the model and t h e d e t a i l s o f t h e f i n a l model w i l l be d i s c u s s e d i n l a t e r s e c t i o n s . F i g u r e 4 . 5 shows r a y p a t h s t h r o u g h t h e model f rom the s h o t s t o t h e r e c e i v e r s . The o b s e r v e d t r a v e l t i m e s w h i c h were used i n t h e i n v e r s e p r o c e d u r e a r e marked by a r rowheads on t h e P 1 9 , P13 and P8 r e c o r d s e c t i o n s i n F i g u r e 4 . 3 . In t h i s e x a m p l e , t u r n i n g r a y s t h r o u g h t h e upper m a n t l e g i v e r i s e t o t h e f i r s t a r r i v a l s a t t h e near s t a t i o n s , r e f l e c t i o n s from an upper m a n t l e h o r i z o n form t h e second a r r i v a l s , and r e f l e c t i o n s f rom t h e same h o r i z o n c o r r e s p o n d t o t h e s o l e a r r i v a l s a t t h e f a r s t a t i o n s . O n l y s i x p a r a m e t e r s of t h e s t r u c t u r e shown i n F i g u r e 4 . 5 a r e a l l o w e d t o v a r y : the v e l o c i t y i n r e g i o n I where the t u r n i n g r a y p a t h s t o the near r e c e i v e r s a r e l o c a t e d , t h e v e l o c i t y i n r e g i o n I I where r a y p a t h s t o t h e f a r r e c e i v e r s a r e l o c a t e d , and CD F I G . 4 . 5 . Ray p a t h s t h r o u g h a p r e l i m i n a r y model f o r s h o t s P19 , P13 and P 8 . Observed t r a v e l t i m e p i c k s shown i n F i g . 4 . 3 a r e used i n the ray t r a c e i n v e r s e p r o c e d u r e , by w h i c h a d j u s t m e n t s t o s p e c i f i e d ray t r a c e p a r a m e t e r s a r e a u t o m a t i c a l l y c a l c u l a t e d so t h a t model t r a v e l t i m e s f i t o b s e r v e d t r a v e l t i m e s . P a r a m e t e r s t h a t a r e a d j u s t e d a r e upper m a n t l e v e l o c i t i e s i n r e g i o n s I and I I , and t h e d e p t h s of b o u n d a r i e s o a t p o i n t s A , B , C and D. Arrowheads i n d i c a t e t h e c o a s t s of Vancouver M I s l a n d . V e r t i c a l e x a g g e r a t i o n i s 3 : 1 . 103 the d e p t h s a t f o u r p o i n t s A , B, C and D w h i c h r e p r e s e n t t h e ends of two b o u n d a r i e s i n t h e m o d e l . V a r i a t i o n s i n t h e s e p a r a m e t e r s a f f e c t t h e t r a v e l t i m e s t h r o u g h the model i n d i f f e r e n t ways . For e x a m p l e , i f t h e v e l o c i t y i n c r e a s e s i n one of t h e r e g i o n s , t h e n the t o t a l t r a v e l t i m e d e c r e a s e s and t h e a p p a r e n t v e l o c i t y i n c r e a s e s i n b o t h t h e f o r w a r d and r e v e r s e d i r e c t i o n s . I f t h e r e f l e c t i n g boundary becomes d e e p e r , t h e n t h e t o t a l t r a v e l t i m e s f o r t h e r e f l e c t i o n s a l s o i n c r e a s e . I f the d i p of t h e boundary i n c r e a s e s , t h e n the a p p a r e n t v e l o c i t y a c r o s s t h e r e c e i v e r s becomes s m a l l e r and t h e a p p a r e n t v e l o c i t y a c r o s s t h e s h o t s becomes l a r g e r ; however , f o r the p a r t i c u l a r s e t of r a y s shown i n F i g u r e 4 . 5 , t h e change i n a p p a r e n t v e l o c i t y a c r o s s t h e r e c e i v e r s wou ld be s m a l l e r t h a n t h a t a c r o s s t h e s h o t s , because t h e r e f l e c t i n g p o i n t s f o r a l l r a y s from a s h o t t o i t s r e c e i v e r s a l l l i e w i t h i n a v e r y s m a l l r e g i o n on t h e b o u n d a r y . The p e r f o r m a n c e of t h e r a y t r a c e i n v e r s e r o u t i n e i s shown i n F i g u r e 4 . 6 . The p e r t u r b a t i o n s d e t e r m i n e d from a s i n g l e i t e r a t i o n o f t h e r o u t i n e were a p p l i e d t o t h e i n i t i a l m o d e l , and f i n a l model t r a v e l t i m e s were t h e n found by r e t r a c i n g the r a y s . In each p a n e l of F i g u r e 4 . 6 , the c r o s s e s i n d i c a t e t h e o b s e r v e d t r a v e l t i m e s , t h e dashed l i n e r e p r e s e n t s the i n i t i a l model t r a v e l t i m e s , and the s o l i d l i n e r e p r e s e n t s t h e f i n a l model t r a v e l t i m e s . F o r t h e i n i t i a l m o d e l , t h e r e s i d u a l between o b s e r v e d and c a l c u l a t e d t r a v e l t i m e s had an rms v a l u e of 222 ms, due m a i n l y t o t h e m i s f i t i n t r a v e l t i m e s t o t h e f a r s t a t i o n s . The rms t r a v e l t i m e r e s i d u a l f o r t h e f i n a l model was 79 ms, w h i c h i s c l o s e t o t h e e s t i m a t e d e r r o r on t h e o b s e r v e d t r a v e l t i m e p i c k s of ~75 ms. 1 04 F I G . 4 . 6 . P e r f o r m a n c e of t h e r a y t r a c e i n v e r s i o n p r o c e d u r e i s i n d i c a t e d by t h e t r a v e l t i m e f i t b e f o r e and a f t e r the p r o c e d u r e i s a p p l i e d . O b s e r v e d t r a v e l t i m e s a r e shown by c r o s s e s f o r f i r s t a r r i v a l s and p l u s s i g n s f o r s e c o n d a r y a r r i v a l s . The dashed l i n e s f o r each shot a r e t h e t r a v e l t i m e c u r v e s f o r t h e i n i t i a l model o f F i g 4 . 5 ; t h e rms r e s i d u a l i s 222 ms. The s o l i d l i n e s a r e the t r a v e l t i m e c u r v e s f o r the f i n a l model a f t e r the p a r a m e t e r a d j u s t m e n t s have been a p p l i e d ; the rms r e s i d u a l i s 79 ms. 1 0 5 DISTANCE (KM) 106 The changes i n p a r a m e t e r s f o r t h e i t e r a t i o n shown i n F i g u r e 4 .6 were as f o l l o w s : T h u s , t h e most s i g n i f i c a n t changes were t h e i n c r e a s e i n t h e v e l o c i t y of r e g i o n I I and t h e d e c r e a s e i n d i p of t h e r e f l e c t i n g boundary ( i . e . p o i n t A became deeper and p o i n t B s h a l l o w e r ) . The v e l o c i t y i n c r e a s e d i n o r d e r t o reduce t h e t o t a l t r a v e l t i m e t o the f a r s t a t i o n s . Because a l a r g e r model v e l o c i t y a l s o i m p l i e d a l a r g e r a p p a r e n t v e l o c i t y , t h e d i p of the r e f l e c t i o n d e c r e a s e d t o c o u n t e r b a l a n c e t h e v e l o c i t y c h a n g e , i . e . t o a c t i n such a way as t o reduce t h e a p p a r e n t v e l o c i t y a c r o s s the s h o t s . I t s h o u l d be c l e a r t h a t the l o g i c c o u l d become q u i t e c o n v o l u t e d i f a manual o r t r i a l - a n d - e r r o r method were used t o f i n d t h e p r o p e r a d j u s t m e n t s t o a r a y t r a c e m o d e l . U s i n g the r a y t r a c e i n v e r s i o n p r o c e d u r e , l e a s t - s q u a r e a d j u s t m e n t s a r e a u t o m a t i c a l l y c a l c u l a t e d w h i c h e n a b l e us t o d i r e c t l y f i n d a r a y t r a c e model w h i c h f i t s t h e d a t a . T h i s has t h e f o l l o w i n g a d v a n t a g e s : (1) we a r e a s s u r e d t h a t t h e model and o b s e r v e d d a t a agree i n an o b j e c t i v e l e a s t - s q u a r e s - s e n s e , and not i n a more s u b j e c t i v e manner w h i c h would be i n v o l v e d i n a manual p r o c e d u r e , and (2) compared t o a s t r i c t l y t r i a l - a n d - e r r o r method , we a r e a b l e t o t e s t a much l a r g e r range of s t a r t i n g model s w i t h d i f f e r e n t c h o i c e s of e i t h e r f i x e d or v a r i a b l e p a r a m e t e r s . v e l o c i t y , r e g i o n I v e l o c i t y , r e g i o n I I +0.045 km/s +0.107 km/s d e p t h , p o i n t A d e p t h , p o i n t B d e p t h , p o i n t C d e p t h , p o i n t D A h c Ah^ +2.11 km - 2 . 9 9 km +1.39 km +0.21 km 1 07 4 . 5 F i n a l o n s h o r e - o f f s h o r e r e f r a c t i o n model 4 . 5 . 1 I n t e r p r e t a t i o n p r o c e d u r e As d e s c r i b e d i n the p r e v i o u s s e c t i o n , t h e method of f i t t i n g t r a v e l t i m e s f o r m u l t i p l e s h o t s and m u l t i p l e r e c e i v e r s i s l a r g e l y au tomated t h r o u g h t h e r a y t r a c e i n v e r s i o n p r o c e d u r e . However , once a s a t i s f a c t o r y t r a v e l t i m e f i t i s o b t a i n e d , m o d i f i c a t i o n s t o t h e c o r r e s p o n d i n g model may s t i l l be d e s i r e d i n o r d e r t o o b t a i n a b e t t e r f i t t o t h e a m p l i t u d e s on t h e o b s e r v e d s e c t i o n s . Changes may a l s o be i n t r o d u c e d i n o r d e r t o t r y d i f f e r e n t s t a r t i n g models and so f i n d a l t e r n a t e model s w h i c h a l s o f i t t h e d a t a ; such a l t e r n a t e models w i l l be d i s c u s s e d i n t h e f o l l o w i n g s e c t i o n . Whatever t h e r e a s o n f o r t h e c h a n g e , t h e major d i f f i c u l t y t h a t a r i s e s i s r e l a t e d t o t h e s t a b i l i t y of t h e r a y t r a c i n g . That i s , t h e change may have t h e r e s u l t t h a t t h e r a y p a t h from shot t o r e c e i v e r no l o n g e r e x i s t s . T h i s w o u l d o c c u r , f o r e x a m p l e , i f the "shadow z o n e " due t o a low v e l o c i t y zone o r t o a c o r n e r moved o v e r t h e r e c e i v e r , o r i f t h e c r i t i c a l p o i n t on a boundary was changed so t h a t t h e c o r r e s p o n d i n g c r i t i c a l r a y s u r f a c e d beyond t h e r e c e i v e r . A m p l i t u d e s t h r o u g h t w o - d i m e n s i o n a l s t r u c t u r e s were c a l c u l a t e d w i t h t h e a s y m p t o t i c r a y t h e o r y a l g o r i t h m of Spence e t a l . ( 1 9 8 4 ) , a l s o d e s c r i b e d i n C h a p t e r 3 . The a l g o r i t h m i n c o r p o r a t e s a m o d i f i e d v e r s i o n of the r a y t r a c i n g r o u t i n e of W h i t t a l l and Clowes ( 1 9 7 9 ) , and so the i d e n t i c a l model i n p u t f i l e may be used f o r b o t h t h e r a y t r a c e i n v e r s i o n p r o c e d u r e and t h e a m p l i t u d e a l g o r i t h m . To o b t a i n a model w h i c h f i t s b o t h a m p l i t u d e s and t r a v e l t i m e s , t h e two r o u t i n e s a r e a p p l i e d i n 108 c o n j u n c t i o n . For example , s t a r t i n g w i t h a model t h a t f i t s t h e t r a v e l t i m e s , changes may be made such t h a t t h e a m p l i t u d e f i t i m p r o v e s , w h i c h a l s o has the l i k e l y s i d e e f f e c t t h a t t h e t r a v e l t i m e f i t d e t e r i o r a t e s . U s i n g the r a y t r a c e i n v e r s i o n p r o c e d u r e , a d j u s t m e n t s a r e then found so t h a t model and o b s e r v e d t r a v e l t i m e s a g a i n m a t c h , i n t h e hope t h a t the a m p l i t u d e b e h a v i o r i s no t much a f f e c t e d . I n p r a c t i c e , a m p l i t u d e s a r e not v e r y s e n s i t i v e t o s m a l l changes i n t h e o v e r a l l v e l o c i t y of a b l o c k , whereas t r a v e l t i m e s n a t u r a l l y a r e . On t h e o t h e r h a n d , a m p l i t u d e s may be a l t e r e d by v a r y i n g t h e v e l o c i t y g r a d i e n t i n a b l o c k , t h e v e l o c i t y c o n t r a s t a c r o s s a b o u n d a r y , and t h e a n g l e a t w h i c h a r a y and a boundary i n t e r s e c t . A m p l i t u d e v a r i a t i o n s were m o d e l l e d f o r d i f f e r e n t a r r i v a l s on the same t r a c e and f o r d i f f e r e n t t r a c e s on t h e same r e c o r d s e c t i o n . However , o n l y t h e g e n e r a l a m p l i t u d e t r e n d s between d i f f e r e n t g roups of t r a c e s were m o d e l l e d , and not t h e i n d i v i d u a l v a r i a t i o n s f rom t r a c e t o t r a c e . The d e t a i l e d t r a c e - t o - t r a c e v a r i a t i o n s were not c o n s i d e r e d because of u n c e r t a i n t i e s b o t h i n the d a t a and i n the m o d e l l i n g p r o c e d u r e . F o r t h e d a t a , some of the v a r i a t i o n s i n a m p l i t u d e from r e c e i v e r t o r e c e i v e r c o u l d be c aused by s i t e - d e p e n d e n t c h a r a c t e r i s t i c s . For a g i v e n m o d e l , t h e c a l c u l a t i o n of a m p l i t u d e s was l i m i t e d by the use of a s y m p t o t i c r a y t h e o r y , w h i c h cannot d i r e c t l y h a n d l e wave phenomena, and by p o s s i b l e e f f e c t s f rom unknown t w o - or t h r e e - d i m e n s i o n a l s t r u c t u r e s . The f i n a l o n s h o r e - o f f s h o r e r e f r a c t i o n model i s d i s p l a y e d i n F i g u r e 4 . 7 . I n F i g u r e 4 . 8 , the f u l l d e t a i l s o f t h e v e l o c i t y model a r e g i v e n , i n c l u d i n g the v e l o c i t i e s and v e l o c i t y g r a d i e n t s 109 of a l l b l o c k s i n t h e m o d e l . The f i n a l r ay t r a c e t h r o u g h t h e model f o r s h o t s P 1 9 , P13 and P8 i s shown i n F i g u r e 4 . 9 . The rms t r a v e l t i m e r e s i d u a l f o r the t h r e e s h o t s i s 79 ms. I f a f u r t h e r i t e r a t i o n of the r a y t r a c e i n v e r s i o n p r o c e d u r e i s a p p l i e d , t h e r e s i d u a l i s r e d u c e d i n s i g n i f i c a n t l y t o 78 ms. From t h e v a l u e s of r e s o l u t i o n and s t a n d a r d e r r o r f o r t h e f i n a l i t e r a t i o n of t h e i n v e r s i o n p r o c e d u r e ( T a b l e 4 . 1 ) , t h e most p o o r l y d e t e r m i n e d p a r a m e t e r i s t h e d e p t h h A a t p o i n t A ( F i g . 4 .5 ) on t h e upper m a n t l e r e f l e c t o r . The r e s o l u t i o n i s 0 .46 and t h e s t a n d a r d e r r o r i s n e a r l y 1 km. T h i s i s c o n s i s t e n t w i t h t h e r e s u l t s from t h e s u b d u c t i o n zone t e s t model i n s e c t i o n 2 .4 of C h a p t e r 2 , where the poor r e s o l u t i o n of t h e upper m a n t l e r e f l e c t o r was r e l a t e d t o the l a c k o f s e n s i t i v i t y of t r a v e l t i m e w i t h r e s p e c t t o t h e d e p t h of t h e r e f l e c t o r . I t s h o u l d a g a i n be e m p h a s i z e d t h a t t h e s t a n d a r d e r r o r s g i v e n i n T a b l e 4.1 s h o u l d not be c o n s i d e r e d as a b s o l u t e measures of c e r t a i n t y f o r t h e p a r a m e t e r s . As w i l l be shown i n s e c t i o n 4 . 6 , t h e r e a r e a l t e r n a t e models w i t h s l i g h t l y d i f f e r e n t p a r a m e t e r i z a t i o n s w h i c h a l s o s a t i s f y t h e o b s e r v e d t r a v e l t i m e s , and the e q u i v a l e n t p a r a m e t e r s f o r t h e v a r i o u s model s d i f f e r by amounts g r e a t e r t h a n t h e c a l c u l a t e d s t a n d a r d e r r o r s . The f i n a l model a l s o i n c o r p o r a t e s a m p l i t u d e i n f o r m a t i o n from t h e c o n t i n e n t a l s l o p e s h o t s P 1 - P 6 , as w e l l as f rom t h e main ocean b a s i n s h o t s P 1 9 , P13 and P 8 . O n l y t h e o b s e r v e d t r a v e l t i m e s from t h e ocean b a s i n s h o t s were i n c l u d e d i n t h e r a y t r a c e i n v e r s i o n p r o c e d u r e . To o b t a i n a t r a v e l t i m e f i t f o r t h e c o n t i n e n t a l s l o p e s h o t s , t h e s h a l l o w s t r u c t u r e b e n e a t h t h e s h o t s was v a r i e d i n a t r i a l - a n d - e r r o r manner , w h i c h had no e f f e c t on w o cs Y DISTANCE (KM) 100 Vancouver Island 200 T I T Mainland 300 F I G . 4 . 7 . F i n a l v e l o c i t y model i n t e r p r e t e d from the o n s h o r e - o f f s h o r e d a t a s e t a l o n g l i n e I. Numbers i n d i c a t e t h e v e l o c i t i e s (km/s) a t the s h a l l o w e s t and deepes t p o i n t s i n each b l o c k . CS i s the l o c a t i o n of the f o o t of the c o n t i n e n t a l s l o p e . O c e a n i c c r u s t a l model was d e t e r m i n e d by Waldron ( 1 9 8 2 ) . The s u b d u c t i n g ocean c r u s t i s a r b i t r a r i l y r e p r e s e n t e d by o n l y a s i n g l e l a y e r be low about 30 km d e p t h . C o n t i n e n t a l c r u s t a l model was c o n s t r a i n e d by the p r e f e r r e d l o w - v e l o c i t y zone i n t e r p r e t a t i o n o f McMechan and Spence (1983) w h i c h a p p l i e s a t the i n t e r s e c t i o n of l i n e I and l i n e IV (230 km from shot P19) . D I S T A N C E ( K M ) 0 1 0 0 2 0 0 3 0 0 F I G . 4.8. D e t a i l s o f the v e l o c i t y model shown i n F i g . 4.7. V e l o c i t i e s (km/s) a r e g i v e n f o r t h e t o p of each b l o c k , f o l l o w e d a f t e r the c o l o n by t h e v e l o c i t y g r a d i e n t (km/s/km) i f one was u s e d . co F I G . 4 . 9 . Ray p a t h s from s h o t s P 1 9 , P13 and P8 t h r o u g h the f i n a l v e l o c i t y model shown on F i g . 4 .7 and F i g . 4 . 8 . The rms r e s i d u a l f o r the t h r e e s h o t s i s 79 ms; i f a f u r t h e r i t e r a t i o n of the r a y t r a c e i n v e r s i o n p r o c e d u r e i s a p p l i e d , the r e s i d u a l i s r e d u c e d i n s i g n i f i c a n t l y t o 78 ms. 1 13 Parameter F i n a l V a l u e R e s o l u t i o n S t a n d a r d E r r o r v i 7 . 97 km/s 0. 68 0. 013 km/s 8 . 1 6 km/s 0 93 0. 007 km/s " A 27 .5 km 0 46 0 93 km * H 39 .6 km 0 .83 0 67 km h c 1 7 .3 km 0 .90 0 .54 km 18 .9 km 0 .93 0 .45 km TABLE 4 . 1 . Pa rameter v a l u e s , r e s o l u t i o n and s t a n d a r d e r r o r f o r t h e f i n a l i t e r a t i o n of t h e r a y t r a c e i n v e r s i o n p r o c e d u r e , a p p l i e d t o the t r a v e l t i m e d a t a s e t of t h e o n s h o r e - o f f s h o r e l i n e I. ( F i g . 4 . 9 ) . R e s o l u t i o n and s t a n d a r d e r r o r g i v e a p p r o x i m a t e r e l a t i v e measures of c e r t a i n t y f o r t h e p a r a m e t e r s . The o v e r a l l damping f a c t o r 6 was 0 . 2 5 . t h e t r a v e l t i m e f i t f o r s h o t s P 1 9 , P13 and P 8 . T r a v e l t i m e s from t h e c o n t i n e n t a l s l o p e s h o t s were not i n c l u d e d i n t h e more automated r a y t r a c e i n v e r s i o n p r o c e d u r e because of t h e poor d a t a q u a l i t y f rom t h e s h o t s , and because o c e a n i c c r u s t a l s t r u c t u r e i n the i n t e r p r e t a t i o n of W a l d r o n (1982) was not as w e l l - c o n s t r a i n e d b e n e a t h t h e c o n t i n e n t a l s l o p e and s h e l f as b e n e a t h t h e deep ocean b a s i n . I n F i g u r e 4 . 8 , t h e melange has been m o d i f i e d s l i g h t l y f rom t h a t shown i n F i g u r e 1 .6 , w h i c h was d e r i v e d by W a l d r o n ( 1 9 8 2 ) . The major change was a r e d u c t i o n i n t h e v e l o c i t y g r a d i e n t w i t h i n the melange f rom 0 .2 km/s /km t o 0 .04 k m / s / k m . W i t h t h i s c h a n g e , a b e t t e r f i t was o b t a i n e d f o r t h e d a t a r e c o r d e d on OBS 5 ( l o c a t e d a t 125 km i n F i g . 4 . 8 ) , compared t o t h e i n t e r p r e t a t i o n p r e s e n t e d by W a l d r o n ( 1 9 8 2 ) ; t h a t i s , t h e a m p l i t u d e s of t u r n i n g r a y s w i t h i n t h e melange t o OBS 5 were r e d u c e d and t h u s compared more f a v o r a b l y w i t h the d a t a . An a d d i t i o n a l c o s m e t i c change t o 1 1 4 the model of F i g u r e 1.6 was t h a t an e x t r a l a y e r was added a t the base of t h e melange above t h e lower ocean c r u s t . The ocean c r u s t s t i l l a p p e a r s t o t h i n benea th t h e melange ( F i g . 4 . 7 ) . T h i s e f f e c t i s r e l a t e d t o t h e f o r m a t i o n of t h e melange i t s e l f ; as a r e s p o n s e t o t h e i r r e s i s t a n c e t o s u b d u c t i o n , t h e upper l a y e r s a r e compres sed and deformed and t h e i r v e l o c i t y i s r e d u c e d (Waldron 1 982) . I n t h e f i n a l r ay t r a c e d i a g r a m f o r the r a y t r a c e i n v e r s i o n p r o c e d u r e ( F i g . 4 . 9 ) , i t s h o u l d be n o t e d t h a t t u r n i n g r a y s a r e used t o t h e m a i n l a n d r e c e i v e r s , i n c o n t r a s t t o t h e r e f l e c t e d r a y s i n S e c t i o n 4 .4 where the r a y t r a c e p r o c e d u r e was f i r s t d e m o n s t r a t e d . I n terms of t r a v e l t i m e s , t h e two t y p e s of r a y s a r e a l m o s t e q u i v a l e n t , w i t h a maximum t i m e d i f f e r e n c e of ~150 ms f o r shot P 8 . The major d i f f e r e n c e between t h e ray t y p e s i s t h a t t u r n i n g r a y s t o the f a r s t a t i o n s a r e much more u n s t a b l e w i t h r e s p e c t t o changes i n t h e r a y t r a c e m o d e l , s i n c e t h e y i n t e r s e c t t h e c o n t i n e n t a l Moho a t a s h a l l o w e r a n g l e t h a n t h e r e f l e c t e d r a y s . T h u s , much of the deve lopment of t h e r a y t r a c e model was done u s i n g r e f l e c t e d r a y s as t h e o n l y a r r i v a l s a t t h e f a r r e c e i v e r s . However , no c l a i m i s made t h a t b o t h t h e t u r n i n g and r e f l e c t e d r a y s can be s e p a r a t e l y o b s e r v e d a t t h e m a i n l a n d s t a t i o n s . E i t h e r c o u l d be r e c o r d e d and would c o n t r i b u t e t o t h e o b s e r v e d a r r i v a l s . 4 . 5 . 2 S y n t h e t i c se ismograms f o r t h e f i n a l model F i g u r e s 4 .10 t o 4 .17 c o n t a i n t h e o r e t i c a l and o b s e r v e d v e r t i c a l component se ismograms f o r r e p r e s e n t a t i v e s h o t s and r e p r e s e n t a t i v e r e c e i v e r s . The s y n t h e t i c se i smograms were 1 1 5 c a l c u l a t e d u s i n g the f i n a l r e f r a c t i o n model of F i g u r e 4 . 7 , and the t h e o r e t i c a l t r a v e l t i m e s of the s y n t h e t i c s a r e s u p e r i m p o s e d on the o b s e r v e d r e c o r d s e c t i o n s . B o t h o b s e r v e d and s y n t h e t i c se i smograms a r e m u l t i p l i e d by a f a c t o r p r o p o r t i o n a l t o d i s t a n c e . A l l r e c o r d s e c t i o n s a r e t r u e a m p l i t u d e , so a m p l i t u d e s may t h u s be compared from t r a c e - t o - t r a c e . I n a d d i t i o n , a m p l i t u d e s may be compared between shot r e c o r d s e c t i o n s and between r e c e i v e r r e c o r d s e c t i o n s . The s e c t i o n s a r e p r e s e n t e d u n f i l t e r e d ( e x c e p t f o r a 1 Hz l o w c u t f i l t e r on t h e o b s e r v e d r e c o r d s e c t i o n f o r r e c e i v e r X 3 4 ) , s i n c e f i l t e r i n g d i d not appear t o s i g n i f i c a n t l y enhance e i t h e r f i r s t b r e a k s or c o n t i n u i t y of a r r i v a l s f rom t r a c e - t o - t r a c e . On F i g u r e s 4 . 10 t o 4 . 1 7 , t h e l o c a t i o n of a se i smogram may be r e f e r r e d e i t h e r t o i t s a p p r o p r i a t e s h o t / r e c e i v e r d i s t a n c e , or t o i t s l o c a t i o n on t h e f i n a l v e l o c i t y model w h i c h has t h e l o c a t i o n of sho t P19 as i t s o r i g i n ; b o t h d i s t a n c e s c a l e s a r e p r e s e n t e d . The main c h a r a c t e r i s t i c s of t h e s y n t h e t i c se i smograms and t h e i r r e l a t e d f e a t u r e s on t h e f i n a l v e l o c i t y model a r e as f o l l o w s : (1) T u r n i n g r a y s t h r o u g h t h e upper m a n t l e g i v e r i s e t o t h e f i r s t a r r i v a l s a t a l l r e c e i v e r s . The v e l o c i t y a t t h e Moho of t h e s u b d u c t i n g s l a b i s a p p r o x i m a t e l y 8 . 0 km/s , w i t h a v e l o c i t y g r a d i e n t p e r p e n d i c u l a r t o the Moho of 0.01 k m / s . As i n t h e p r e l i m i n a r y i n t e r p r e t a t i o n of E l l i s e t a l . ( 1 9 8 3 ) , the v a l u e of the g r a d i e n t i s not w e l l - c o n s t r a i n e d . The v a l u e used i s comparab le t o t h a t g i v e n by S t e i n m e t z e t a l . (1977) f o r l i t h o s p h e r e b e n e a t h 9 Ma o c e a n i c c r u s t and by Fuchs (1979) f o r l i t h o s p h e r e b e n e a t h c o n t i n e n t s . 1 16 CO 9 to oo \ Q T 1 1 r— SHOT P19 2 0 0 2 0 0 2 4 0 2 8 0 3 2 0 D I S T A N C E F R O M P 1 9 ( K M ) 2 4 0 2 8 0 3 2 0 3 6 0 3 8 0 CVJ 180 2 2 0 2 6 0 3 0 0 S H O T / R E C E I V E R D I S T A N C E (KM) 3 4 0 F I G . 4 . 1 0 . S y n t h e t i c se i smograms and o b s e r v e d d a t a f o r shot P 1 9 . Mode l t r a v e l t i m e s from the s y n t h e t i c se i smograms a r e s u p e r i m p o s e d on the o b s e r v e d r e c o r d s e c t i o n . P r i m a r y a r r i v a l s a r e t u r n i n g r a y s t h r o u g h the m a n t l e . Secondary a r r i v a l s c o r r e s p o n d t o r a y s r e f l e c t e d from an upper m a n t l e b o u n d a r y , w i t h the v e l o c i t y be low the boundary . s m a l l e r , t h a n t h e v e l o c i t y a b o v e . For shot P 1 9 , the model t r a v e l t i m e s t o the m a i n l a n d s t a t i o n s (290-350 km) a r e a l m o s t t h e same f o r b o t h t u r n i n g r a y s and r e f l e c t e d r a y s . 4 . 1 1 . S y n t h e t i c se i smograms and o b s e r v e d d a t a f o r s h o t P 1 3 , l o c a t e d 40 km e a s t of sho t P 1 9 . See c a p t i o n f o r F i g 4 . 1 0 . 118 w co -Q co I — I — r — SHOT P8 i i 1" 200 200 240 280 320 DISTANCE FROM P19 (KM) 240 280 320 380 380 CM 125 165 205 245 SHOT/RECEIVER DISTANCE (KM) 285 F I G . 4 . 1 2 . S y n t h e t i c s e i s m o g r a m s a n d o b s e r v e d d a t a f o r s h o t P 8 , l o c a t e d 67 km e a s t o f s h o t P 1 9 . See c a p t i o n f o r F i g . 4 . 1 0 . On t h e s y n t h e t i c s e i s m o g r a m s , n o t e t h a t t h e f i r s t a r r i v a l b r a n c h t o t h e m a i n l a n d s t a t i o n s i s t r u n c a t e d ; t h e s e a r r i v a l s a r e t u r n i n g r a y s t h r o u g h t h e u p p e r m a n t l e , some o f w h i c h a r e b l o c k e d by t h e c o r n e r - f o r m e d a t t h e i n t e r s e c t i o n o f c o n t i n e n t a l Moho a n d s u b d u c t i n g o c e a n i c c r u s t ( s e e F i g . 4 . 1 8 ) . 119 O co-J 00 9 io eo CO 1 — i — r SHOT P 2 < < «> 4 > 200 200 95 •r < «r <• <r* <r «r-240 280 320 DISTANCE FROM P19 (KM) 240 280 320 360 380 135 1?5 215 SHOT/RECEIVER DISTANCE (KM) 255 4 . 1 3 . S y n t h e t i c se i smograms and o b s e r v e d d a t a f o r s h o t P 2 , l o c a t e d 99 km e a s t of s h o t P 1 9 . See c a p t i o n f o r F i g . 4 . 1 0 . On t h e s y n t h e t i c s e i smograms , the o n l y b r a n c h p r e s e n t a t the m a i n l a n d s t a t i o n s i s t h e b r a n c h of r a y s r e f l e c t e d a t t h e upper m a n t l e b o u n d a r y . A l l t u r n i n g r a y s t o t h e m a i n l a n d s t a t i o n s a r e b l o c k e d by t h e c o r n e r formed a f the i n t e r s e c t i o n of c o n t i n e n t a l Moho and s u b d u c t i n g o c e a n i c c r u s t ( see F i g . 4 . 1 8 ) . 120 w co -9 m oo \ i r i i I i MAINLAND RECEIVER X45 25 50 75 DISTANCE FKOM P19 (KM) 25 50 75 100 100 CM 355 335 315 295 DISTANCE (KM) 275 255 F I G . 4 . 1 4 . S y n t h e t i c ' s e i s m o g r a m s and o b s e r v e d d a t a f o r m a i n l a n d r e c e i v e r X 4 5 , l o c a t e d a t the e a s t e r n m o s t end o f the o n s h o r e - o f f s h o r e p r o f i l e . See c a p t i o n f o r F i g . 4 . 1 0 . The f i r s t a r r i v a l b r a n c h of t u r n i n g r a y s i s t r u n c a t e d (no a r r i v a l s beyond 99 km on the s y n t h e t i c s e c t i o n ) due t o t h e e f f e c t o f the c o r n e r where t h e c o n t i n e n t a l Moho meets the s u b d u c t i n g o c e a n i c c r u s t (see F i g . 4 . 1 8 ) . The s e c o n d a r y a r r i v a l b r a n c h of r e f l e c t e d r a y s i s a l s o t r u n c a t e d ; but t h i s i s due t o a p o o r l y c o n t r o l l e d f e a t u r e of t h e v e l o c i t y model ( F i g . 4 . 7 ) , i n w h i c h t h e d i p of the r e f l e c t o r e a s t of about 200 km d i s t a n c e from P19 s u d d e n l y i n c r e a s e s . 121 O W 00 co -H m i co P C3 MAINLAND RECEIVER X34 o 25 75 DISTANCE FROM P19 (KM) 25 50 75 100 100 CM 310 290 270 250 230 SH0T/RECEIVER DISTANCE (KM) 210 F I G . 4 . 1 5 . S y n t h e t i c se i smograms and o b s e r v e d d a t a f o r m a i n l a n d r e c e i v e r X 3 4 . See c a p t i o n f o r F i g . 4 . 1 0 . Note t h a t the f i r s t a r r i v a l b r a n c h of t u r n i n g r a y s i s t r u n c a t e d due t o t h e e f f e c t o f t h e i n t e r s e c t i o n o f t h e c o n t i n e n t a l Moho and s u b d u c t i n g o c e a n i c c r u s t ( see F i g . 4 . 1 8 ) . 122 SHOT/RECEIVER DISTANCE (KM) F I G . 4 . 1 6 . S y n t h e t i c se i smograms and o b s e r v e d d a t a f o r m a i n l a n d r e c e i v e r X 2 2 . See c a p t i o n f o r F i g . 4 . 1 0 . 123 SHOT/RECEIVER DISTANCE (PCM) F I G . 4 . 1 7 . S y n t h e t i c se i smograms and o b s e r v e d d a t a f o r m a i n l a n d r e c e i v e r X 6 . See c a p t i o n for . F i g . 4 . 1 0 . 1 24 I t was hoped t h a t the a m p l i t u d e m o d e l l i n g wou ld p r o v i d e more c o n t r o l on t h e m a n t l e g r a d i e n t , a t l e a s t on t h e r e l a t i v e v a l u e s between s h a l l o w e r and deeper m a n t l e , s i n c e t h e two r e g i o n s were sampled by d i f f e r e n t r a y p a t h s (see r a y t r a c e d i a g r a m , F i g . 4 . 9 ) . However , as d i s c u s s e d b e l o w , t h e s h a l l o w m a n t l e g r a d i e n t was not t h e d e c i s i v e f a c t o r i n d e t e r m i n i n g t h e a m p l i t u d e s of t h e t u r n i n g r a y a r r i v a l s t o t h e near s t a t i o n s , and so t h e g r a d i e n t was not w e l l - c o n t r o l l e d by t h e a m p l i t u d e s . (2) An anomalous f e a t u r e i n the v e l o c i t y m o d e l , and a f e a t u r e t h r o u g h w h i c h a l l r a y s t o t h e V a n c o u v e r I s l a n d s t a t i o n s p a s s , i s t h e m a n t l e - l i k e s l i v e r a t ~20 km d e p t h above t h e downgoing o c e a n i c c r u s t ( F i g s . 4 .7 t o 4 . 9 ) . The s l i v e r v e l o c i t y of 7 .7 km/s was d e t e r m i n e d m a i n l y by a m p l i t u d e c o n s i d e r a t i o n s , i n p a r t i c u l a r f o r t h e n e a r e s t o f f s e t s h o t s . A m p l i t u d e s a r e s e n s i t i v e t o t h e v a l u e of s l i v e r v e l o c i t y because t h e v e l o c i t y c o n t r o l s t h e r a y p a t h a n g l e t h r o u g h t h e s l i v e r , and r a y p a t h a n g l e s a r e near z e r o . T h u s , a d e c r e a s e i n v e l o c i t y i m p l i e s t h a t ray p a t h s a r e d i r e c t e d more s t e e p l y towards t h e s u r f a c e and a r e s u l t a n t i n c r e a s e i n a m p l i t u d e . On t h e o t h e r h a n d , an i n c r e a s e i n v e l o c i t y may r e s u l t i n r a y p a t h s t h a t a r e d i r e c t e d downwards , n e v e r t o i n t e r s e c t t h e upper boundary of t h e s l i v e r or t o r e a c h the s u r f a c e . T h i s e f f e c t i s most p r o n o u n c e d f o r t h e n e a r e s t o f f s e t s h o t s , w h i c h have the s t e e p e s t downward a n g l e t h r o u g h t h e m a n t l e below t h e ocean c r u s t . (3) F o r t h e o c e a n i c b a s i n s h o t s , t h e a p p a r e n t v e l o c i t y of t u r n i n g r a y s a c r o s s t h e m a i n l a n d r e c e i v e r s i s a p p r o x i m a t e l y 8.1 k m / s . S i n c e t h i s i s t h e v e l o c i t y of m a n t l e m a t e r i a l , i t i m p l i e s t h a t t h e d i p of t h e boundary t h r o u g h w h i c h r a y s e n t e r the 1 25 c o n t i n e n t a l c r u s t i s near z e r o . That i s , the boundary i s i n t e r p r e t e d as a p p r o x i m a t e l y f l a t - l y i n g c o n t i n e n t a l Moho, and not a boundary r e l a t e d t o the s u b d u c t i n g o c e a n i c c r u s t . T h i s c o n t r a s t s w i t h t h e r e s u l t s of Taber (1983) f o r a s i m i l a r o n s h o r e - o f f s h o r e p r o f i l e a c r o s s s t h e W a s h i n g t o n m a r g i n o n l y 250-300 km s o u t h of t h e V a n c o u v e r I s l a n d p r o f i l e . Taber (1983) found an a p p a r e n t v e l o c i t y of 7 .4 km/s a c r o s s h i s m a i n l a n d r e c e i v e r s f rom deep ocean s h o t s and i n t e r p r e t e d a s u b d u c t i n g o c e a n i c Moho d i p p i n g a t ~ 9 ° . (4) F o r the ocean b a s i n s h o t s , t h e a p p a r e n t v e l o c i t y of t u r n i n g r a y s a c r o s s t h e V a n c o u v e r I s l a n d r e c e i v e r s i s 7 . 5 - 7 . 7 km/s ( F i g s . 4 .10 t o 4 . 1 2 ) . T h i s a p p a r e n t v e l o c i t y i s c o n t r o l l e d p r i m a r i l y by t h e h i g h - v e l o c i t y s l i v e r above t h e downgoing c r u s t . That i s , w i t h a s l i v e r v e l o c i t y of 7 .7 k m / s , t h e o b s e r v e d a p p a r e n t v e l o c i t y i m p l i e s t h a t t h e d i p of the upper boundary of t h e m a n t l e s l i v e r i s near z e r o . (5) The t r a v e l t i m e o f f s e t of ~1 s seen f o r t h e f i r s t a r r i v a l s on shot p r o f i l e s a c r o s s G e o r g i a S t r a i t ( F i g s . 4 .10 t o 4 .13 ) i s c a u s e d by d i f f e r e n t r a y p a t h s t o the V a n c o u v e r I s l a n d s t a t i o n s compared t o t h e m a i n l a n d s t a t i o n s . F o r t h e V a n c o u v e r I s l a n d a r r i v a l s , r a y s pas s t h r o u g h t h e h i g h - v e l o c i t y s l i v e r b e n e a t h w e s t e r n V a n c o u v e r I s l a n d and t h e i n n e r c o n t i n e n t a l s h e l f a t d e p t h s as s h a l l o w as 20 km. These a r r i v a l s a r e t h u s advanced i n t r a v e l t i m e compared t o t h e m a i n l a n d a r r i v a l s , w h i c h must e n t e r the c o n t i n e n t a l c r u s t t h r o u g h t h e Moho a t 37 km d e p t h . (6) F o r a g i v e n r e c e i v e r , t h e a p p a r e n t v e l o c i t y o f t u r n i n g r a y s a c r o s s t h e ocean b a s i n s h o t s i s 8 . 3 - 8 . 5 km/s , o n l y s l i g h t l y h i g h e r t h a n m a n t l e v e l o c i t y . T h i s i s c o n s i s t e n t w i t h a s h a l l o w 126 d i p of < 2 ° f o r t h e o c e a n i c c r u s t a l l a y e r s west of the c o n t i n e n t a l r i s e . The d i p of the c r u s t a l l a y e r s was c o n s t r a i n e d by t h e m a r i n e i n t e r p r e t a t i o n of W a l d r o n (1982) f o r the o c e a n i c c r u s t . (7) The f i r s t break a p p a r e n t v e l o c i t y a c r o s s t h e c o n t i n e n t a l s h o t s P1-P6 on t h e r e c e i v e r g a t h e r s i s d i f f i c u l t t o p i c k , but a p p e a r s t o be a p p r o x i m a t e l y 8 .0 k m / s . T h i s a p p a r e n t v e l o c i t y i s s e n s i t i v e p r i m a r i l y t o t h e d i p a t t h e base of t h e s u b - s e d i m e n t melange b l o c k b e n e a t h s h o t s P 1 - P 6 , l a b e l l e d w i t h v e l o c i t y 4 . 8 - 5 . 3 km/s i n the v e l o c i t y model of F i g u r e 4 . 7 . Assuming t h a t o c e a n i c l a y e r s a r e p a r a l l e l t o t h e base of t h e me lange , t h e a p p a r e n t v e l o c i t y t h e r e b y p r o v i d e s c o n t r o l on t h e d i p of t h e Moho b e n e a t h s h o t s P 1 - P 6 . On the s y n t h e t i c p r o f i l e s ( F i g s . 4 .14 t o 4 . 1 7 ) , t h e a p p a r e n t v e l o c i t y may a c t u a l l y be somewhat l a r g e r t h a n i n t h e o b s e r v e d d a t a ; so b e n e a t h s h o t s P i -pe, t h e base of t h e melange and t h e o c e a n i c l a y e r s s h o u l d p r o b a b l y d i p a t a s m a l l e r a n g l e t h a n shown i n t h e v e l o c i t y model of F i g u r e 4 . 7 . However , t h e i m p o r t a n t i m p l i c a t i o n i s t h a t t h e p o i n t a t w h i c h t h e s u b d u c t i n g o c e a n i c s l a b s i g n i f i c a n t l y i n c r e a s e s i n d i p must o c c u r e a s t of t h e c o n t i n e n t a l s l o p e . T h i s i s c o n s i s t e n t w i t h t h e r e s u l t s of Taber (1983) i n an o n s h o r e -o f f s h o r e e x p e r i m e n t a c r o s s t h e W a s h i n g t o n m a r g i n . Taber (1983) o b s e r v e d an i n c r e a s e i n a p p a r e n t v e l o c i t y from 8 km/s f o r t h e more w e s t e r l y s h o t s t o 11 km/s f o r the e a s t e r l y s h o t s . He i n t e r p r e t e d t h i s i n c r e a s e as d i r e c t e v i d e n c e of t h e bend i n the s u b d u c t i n g s l a b a t a p o i n t n e a r l y 50 km l a n d w a r d of the b e g i n n i n g of t h e c o n t i n e n t a l s l o p e . (8) The a m p l i t u d e s of t h e f i r s t a r r i v a l s a t t h e m a i n l a n d 1 27 r e c e i v e r s a r e l a r g e from t h e ocean b a s i n s h o t s (see s h o t s P19 and P13) and r e l a t i v e l y s m a l l f rom t h e c o n t i n e n t a l s l o p e s h o t s (see s h o t P2 and r e c e i v e r X 4 5 ) . The r e d u c e d a m p l i t u d e s c o u l d p o s s i b l y be due t o l a r g e a t t e n u a t i o n l o s s e s from t h e t h i c k and p r o b a b l y c o m p l e x l y deformed c o n t i n e n t a l s l o p e s e d i m e n t s . However , d e c r e a s e d a m p l i t u d e s a r e a l s o e x p e c t e d due t o s t r u c t u r a l f e a t u r e s i n t h e v e l o c i t y m o d e l . F i g u r e 4 .18 shows t u r n i n g r a y s f rom a c o n t i n e n t a l s l o p e shot t o t h e m a i n l a n d r e c e i v e r s , and t h e r e v e r s e s e t of r a y s from a m a i n l a n d r e c e i v e r t o t h e c o n t i n e n t a l s l o p e and ocean b a s i n . A l l r a y s a r e s e p a r a t e d by e q u i - a n g u l a r i n c r e m e n t s , and f o r e a c h s e t of r a y s t h e r e i s a "shadow z o n e " due t o t h e c o r n e r where the c o n t i n e n t a l Moho meets the s u b d u c t i n g o c e a n i c c r u s t . No t u r n i n g r a y a r r i v a l s o c c u r w i t h i n t h e shadow z o n e ; t h u s , on t h e s y n t h e t i c s e c t i o n f o r s h o t P2 ( F i g . 4 . 1 3 ) , t h e r e i s no t u r n i n g r a y b r a n c h p r e s e n t , and t h e b r a n c h i s t r u n c a t e d on t h e s y n t h e t i c s f o r s h o t P8 ( F i g . 4 . 1 2 ) , r e c e i v e r X45 ( F i g . 4 . 1 3 ) , and r e c e i v e r X34 ( F i g 4 . 1 4 ) . However , due t o t h e wave n a t u r e of the p r o p a g a t i n g e n e r g y , d i f f r a c t i o n s would be p r e d i c t e d w i t h i n t h e shadow z o n e , so t h a t r e d u c e d a m p l i t u d e a r r i v a l s a r e e x p e c t e d w i t h i n t h e r e g i o n . (9) Secondary a r r i v a l s a t t h e V a n c o u v e r I s l a n d s t a t i o n s , w h i c h a r e most c l e a r l y seen on t h e o b s e r v e d s e c t i o n s f o r s h o t P13 ( F i g . 4 . 11 ) and r e c e i v e r X22 ( F i g . 4 . 1 6 ) , a r e i n t e r p r e t e d as r e f l e c t i o n s f rom an upper m a n t l e r e f l e c t o r . R e c e i v e r X6 ( F i g . 4 .17 ) a l s o shows e v i d e n c e of a s e c o n d a r y a r r i v a l , a l t h o u g h t h e model t r a v e l t i m e s a r e somewhat l a t e compared t o t h e o b s e r v e d t r a v e l t i m e s . However , the d i f f e r e n c e i s not c o n s i d e r e d s e r i o u s s i n c e i t s magni tude i s not t o o much l a r g e r t h a n t h e a v e r a g e 128 F I G . 4 . 1 8 . Ray p a t h s showing shadow zones due t o t h e c o r n e r a t 215 km d i s t a n c e and 37 km d e p t h , where t h e s u b d u c t i n g o c e a n i c c r u s t i n t e r s e c t s t h e c o n t i n e n t a l Moho. Arrowheads i n d i c a t e t h e c o a s t s of V a n c o u v e r I s l a n d , (a) A c o n t i n e n t a l s l o p e s h o t a t 85 km d i s t a n c e p r o d u c e s a shadow zone o v e r the d i s t a n c e range 285-335 km. (b) A r e c e i v e r a t 305 km d i s t a n c e r e c o r d s no a r r i v a l s f rom s h o t s on t h e c o n t i n e n t a l s l o p e e a s t o f 70 km d i s t a n c e . D E P T H ( K M ) D E P T H ( K M ) 6 0 4 0 2 0 0 6 0 4 0 2 0 0 i i L n I 1 i — 1 : r i m — 62 I 130 p i c k i n g e r r o r f o r a l l a r r i v a l s (~75 ms) and because o n l y the s e c o n d a r y a r r i v a l t i m e s f o r s h o t s P13 and P19 (and not r e c e i v e r X6) were used i n the r a y t r a c e i n v e r s i o n p r o c e d u r e w h i c h d e t e r m i n e d t h e o v e r a l l t r a v e l t i m e f i t . The a m p l i t u d e s of w i d e - a n g l e r e f l e c t i o n s a r e not v e r y s e n s i t i v e t o t h e magni tude of t h e v e l o c i t y c o n t r a s t a t the boundary from w h i c h they a r e r e f l e c t e d ( B r a i l e and S m i t h 1975) . However , t h e a m p l i t u d e s do depend on whether t h e v e l o c i t y c o n t r a s t i s p o s i t i v e or n e g a t i v e , w i t h l a r g e r a m p l i t u d e s p r o d u c e d f rom a p o s i t i v e c o n t r a s t . F i g u r e 4 . 1 9 shows the s y n t h e t i c s f o r s h o t s P19 and P13 t h r o u g h a model i d e n t i c a l t o t h e f i n a l model e x c e p t t h a t t h e v e l o c i t y below t h e r e f l e c t o r i s 8 . 6 km/s i n s t e a d of 7 .7 k m / s . When compared t o t h e s y n t h e t i c s and o b s e r v e d d a t a i n F i g u r e s 4 .10 and 4 . 1 1 , i t i s seen t h a t the r e f l e c t e d a r r i v a l s a t the V a n c o u v e r I s l a n d s t a t i o n s i n F i g u r e 4 .19 a r e t o o l a r g e i n c o m p a r i s o n t o t h e a r r i v a l s a t t h e m a i n l a n d s t a t i o n s . I t i s on t h i s b a s i s t h a t a low v e l o c i t y o f 7 .7 km/s i s t h e p r e f e r r e d v e l o c i t y i n t h e f i n a l model f o r t h e r e g i o n below t h e upper m a n t l e r e f l e c t o r . (10) Upper m a n t l e r e f l e c t i o n s t o the m a i n l a n d r e c e i v e r s have been i n c l u d e d on a l l s y n t h e t i c s e c t i o n s . Based on t h e d a t a , t h e y a r e no t n e c e s s a r y t o t h e m o d e l l i n g , s i n c e o n l y r e f l e c t i o n s t o t h e V a n c o u v e r I s l a n d r e c e i v e r s a r e o b s e r v e d as d i s t i n c t a r r i v a l s . However , r e f l e c t i o n s t o t h e f a r s t a t i o n s a r e p o s s i b l e a r r i v a l s and so t h e y a r e i n c l u d e d f o r c o m p l e t e n e s s and t o show t h e i r p o s s i b l e e f f e c t as an a d d i t i o n a l a r r i v a l a t a t i m e s l i g h t l y d e l a y e d from t h a t of t h e m a n t l e t u r n i n g r a y . But i t s h o u l d be emphas i zed t h a t t h e e x i s t e n c e of t h e upper m a n t l e 131 F I G . 4 . 1 9 . S y n t h e t i c se i smograms f o r s h o t s P19 and P13 f o r r a y s t h r o u g h t h e same v e l o c i t y model as t h e f i n a l model ( F i g . 4 . 7 ) , e x c e p t t h a t t h e v e l o c i t y be low t h e upper m a n t l e r e f l e c t o r i s 8 . 6 km/s i n s t e a d of 7 .7 k m / s . The a m p l i t u d e s of the r e f l e c t i o n s a t t h e V a n c o u v e r I s l a n d s t a t i o n s , w h i c h a r e the s e c o n d a r y a r r i v a l s f o r d i s t a n c e s 200-260 km from shot P 1 9 , a r e t o o l a r g e i n c o m p a r i s o n w i t h t h e o b s e r v e d r e c o r d s e c t i o n s ( F i g . 4 . 3 ) . V - 8 .6 KM/S o w to co-in -oo \ Q I co SHOT PI9 (- 4 4 > > > 4> 180 200 220 240 260 280 300 320 340 360 o w CO co <-! m i oo \ Q I E- ^ CO SHOT PI3 i — ± . ZTTi 180 200 220 240 260 280 300 320 340 360 D I S T A N C E F R O M P 1 9 (KM) 133 boundary i s s p e c u l a t i v e f o r d i s t a n c e s g r e a t e r t h a n 110 km, w h i c h c o r r e s p o n d s t o t h e r e f l e c t i o n p o i n t f o r t h e e a s t e r n m o s t V a n c o u v e r I s l a n d s t a t i o n (see r a y t r a c e d i a g r a m , F i g . 4 . 9 ) . W i t h t h e v e l o c i t y be low t h e r e f l e c t i n g boundary l o w e r t h a n t h e v e l o c i t y a b o v e , t h e phase of r e f l e c t i o n i s o p p o s i t e t o t h a t of t h e m a n t l e t u r n i n g r a y . T h u s , f o r s h o t P19 ( F i g . 4 . 1 0 ) , where t h e a r r i v a l t i m e s of t h e r e f l e c t e d and t u r n i n g r a y s d i f f e r by l e s s t h a n 20 ms, t h e e f f e c t of the r e f l e c t i o n on t h e s y n t h e t i c s i s t o d e c r e a s e t h e a m p l i t u d e of t h e t u r n i n g r a y a l o n e . F o r shot P13 ( F i g . 4 . 1 1 ) , t h e d i f f e r e n c e i s ~75 ms a n d , a s suming a s o u r c e w a v e l e t o f l e n g t h 200 ms, t h e combined a r r i v a l i s e l o n g a t e d and has a main peak a m p l i t u d e l a r g e r t h a n t h a t of t h e t u r n i n g r a y a l o n e . F o r s h o t P8 ( F i g . 4 . 1 2 ) , t h e r e f l e c t e d and t u r n i n g r a y w a v e l e t s s t a r t t o s e p a r a t e , a l t h o u g h t h e r e f l e c t e d r a y i s t h e o n l y a r r i v a l on t h e s y n t h e t i c s a t 290 and 300 km d i s t a n c e f rom P19 because t h e t u r n i n g r a y e x p e c t e d a t t h o s e d i s t a n c e s i s s t o p p e d by t h e c o r n e r between t h e c o n t i n e n t a l Moho and t h e s u b d u c t i n g ocean c r u s t . F o r shot P2 ( F i g . 4 . 1 3 ) , t h e r e f l e c t e d wave i s t h e o n l y a r r i v a l on the s y n t h e t i c s , w i t h t h e t u r n i n g r a y b e i n g c o m p l e t e l y b l o c k e d by the c o r n e r . 4 . 6 A l t e r n a t e model s c o n s i s t e n t w i t h t h e s e i s m i c d a t a I n t h e f i n a l o n s h o r e - o f f s h o r e model d i s c u s s e d i n t h e p r e v i o u s s e c t i o n , c e r t a i n f e a t u r e s were i n t r o d u c e d w h i c h were not c o n t r o l l e d by the r e f r a c t i o n s e i s m i c d a t a but r a t h e r were s u g g e s t e d by more g e n e r a l t e c t o n i c or g e o l o g i c a l p r i n c i p l e s . I n p a r t i c u l a r , most f e a t u r e s o f the downgoing o c e a n i c c r u s t and even i t s v e r y e x i s t e n c e i n t h e model a r e not n e c e s s a r y t o 1 34 s a t i s f y t h e r e f r a c t i o n s e i s m i c c o n s t r a i n t s , but a r e i n c l u d e d because the w e i g h t of the o t h e r g e o p h y s i c a l e v i d e n c e , b o t h l o c a l l y and w o r l d w i d e , l e n d s s t r o n g s u p p o r t t o i t s p r e s e n c e (Keen and Hyndman 1979 ) . The u n c e r t a i n t y of t h e c h a r a c t e r i s t i c s of t h e downgoing c r u s t i n t h e s e i s m i c model w i l l be i l l u s t r a t e d w i t h two a l t e r n a t e models w h i c h f i t t h e t r a v e l t i m e s f o r P 1 9 , P13 and P8 e q u a l l y as w e l l as t h e f i n a l model and have s i m i l a r a m p l i t u d e b e h a v i o r . The purpose of p r e s e n t i n g two a l t e r n a t i v e models i s t o show t h e v a r i a b i l i t y p e r m i t t e d by t h e s e i s m i c d a t a and a l s o t o emphas ize t h o s e f e a t u r e s common t o a l l m o d e l s . The s i m p l e s t model c o n s i s t e n t w i t h t h e s e i s m i c d a t a i s e s s e n t i a l l y t h e p r e l i m i n a r y model of E l l i s e t a l . (1983) m o d i f i e d by t h e a d d i t i o n of an upper m a n t l e r e f l e c t o r ( F i g . 4 . 2 0 ) . The o c e a n i c c r u s t i s shown as t e r m i n a t i n g a g a i n s t t h e c o n t i n e n t a l c r u s t , and t h e s t r u c t u r e be low V a n c o u v e r I s l a n d as d e t e r m i n e d by McMechan and Spence (1983) i s e x t r a p o l a t e d t o t h e r e g i o n be low t h e c o n t i n e n t a l s h e l f . The f e a t u r e s of the p r e l i m i n a r y model ( F i g . 4 .20 ) i n common w i t h t h e f i n a l model ( F i g . 4 . 7 ) a r e (1) t h e m a n t l e v e l o c i t y and g r a d i e n t ( 8 . 0 km/s and 0.01 k m / s / k m ) , (2) a f l a t - l y i n g c o n t i n e n t a l Moho a t a d e p t h of 40 km or l e s s , (3) t h e geometry o f t h e upper m a n t l e r e f l e c t o r ( the d e p t h of t h e boundary when e x t r a p o l a t e d b e n e a t h P 1 9 i s ~22 km f o r t h e p r e l i m i n a r y model and ~25 km f o r t h e f i n a l m o d e l , and t h e c o r r e s p o n d i n g d i p s a r e ~ 8 ° and ~ 7 ° ) , and (4) a s h a l l o w h i g h -v e l o c i t y pathway a t d e p t h s of 30 km and l e s s b e n e a t h w e s t e r n Vancouver I s l a n d and t h e c o n t i n e n t a l s h e l f . The ma jor d i f f e r e n c e between t h e m o d e l s , a p a r t from t h e t e r m i n a t i o n o f the o c e a n i c c r u s t , i s t h a t t h e h i g h - v e l o c i t y pathway i n t h e f i n a l model F I G . 4 . 2 0 . The p r e l i m i n a r y v e l o c i t y m o d e l o f E l l i s e t a l . ( 1 9 8 3 ) , m o d i f i e d by t h e a d d i t i o n o f a n u p p e r m a n t l e r e f l e c t o r . The o c e a n i c l a y e r s a r e shown t e r m i n a t i n g a g a i n s t t h e c o n t i n e n t a l c r u s t a l l a y e r s . T h e r a y t r a c e i n v e r s i o n p r o c e d u r e h a s b e e n a p p l i e d t o t h e m o d e l , a n d t h e m o d e l t r a v e l t i m e s f o r s h o t s P 1 9 , P 1 3 a n d P8 f i t t h e o b s e r v e d t r a v e l t i m e s w i t h an rms r e s i d u a l o f 73 m s , e q u i v a l e n t t o t h a t f o r t h e f i n a l m o d e l . 1 36 a p p e a r s as a s l i v e r of m a n t l e m a t e r i a l a t 20-25 km d e p t h , whereas i n t h e p r e l i m i n a r y model t h e d e p t h t o m a n t l e s u d d e n l y i n c r e a s e s from ~29 km t o ~39 km i n a f a u l t - l i k e f e a t u r e under c e n t r a l V a n c o u v e r I s l a n d . To b e t t e r s a t i s f y t e c t o n i c p r i n c i p l e s , t h e p r e l i m i n a r y model may be m o d i f i e d by r e q u i r i n g t h a t t h e o c e a n i c c r u s t s h o u l d be c o n t i n u o u s l y s u b d u c t i n g t h r o u g h o u t t h e r e g i o n , i n s t e a d of t e r m i n a t i n g a b r u p t l y a g a i n s t t h e c o n t i n e n t a l c r u s t . I n t h e i n t e r m e d i a t e model of F i g u r e 4 . 2 1 , the o c e a n i c l a y e r s a r e e x t r a p o l a t e d e a s t w a r d , i n s t e a d of t h e c o n t i n e n t a l l a y e r s b e i n g e x t r a p o l a t e d wes tward as i n t h e p r e l i m i n a r y model o f F i g u r e 4 . 2 0 . Because t h e s l a b of s u b d u c t i n g o c e a n i c c r u s t i s p a r a l l e l -s i d e d , a l l r a y s t o a s e t of r e c e i v e r s a r e a f f e c t e d e q u a l l y , and t h e major s t r u c t u r a l c h a r a c t e r i s t i c s of t h e p r e l i m i n a r y model a r e no t s i g n i f i c a n t l y c h a n g e d . D i p s of b o u n d a r i e s a r e c o m p a r a b l e i n t h e two m o d e l s , and t h e sudden i n c r e a s e i n t h i c k n e s s of t h e c o n t i n e n t a l c r u s t b e n e a t h c e n t r a l V a n c o u v e r I s l a n d a p p e a r s as a k i n k i n the s u b d u c t i n g o c e a n i c c r u s t . The i n t e r m e d i a t e model a l s o i n c o r p o r a t e s c o n s i d e r a t i o n s f rom p r e s s u r e - t e m p e r a t u r e d a t a t h a t b a s a l t i n t h e . o c e a n i c . c r u s t t r a n s f o r m s t o e c l o g i t e , w i t h a s s o c i a t e d i n c r e a s e s i n d e n s i t y and v e l o c i t y t o v a l u e s g r e a t e r t h a n t h o s e o f n o r m a l m a n t l e . The s t a b i l i t y f i e l d o f b a s a l t -e c l o g i t e as shown by Grow and Bowin (1975 , F i g . 5) i n d i c a t e s t h a t t h e phase change o c c u r s a t d e p t h s as s h a l l o w as 30 km. T h u s , an e l e v a t e d v e l o c i t y of 8 .2 km/s i s u sed i n the i n t e r m e d i a t e model f o r t h e p o r t i o n of o c e a n i c c r u s t be low a p p r o x i m a t e l y 30 km d e p t h . I t s h o u l d be n o t e d t h a t t h i s e f f e c t i s not i n c o r p o r a t e d i n t h e f i n a l r e f r a c t i o n m o d e l , s i n c e t h e r e W DISTANCE (KM) V a n c o u v e r I s l Q n d M d n l a n d E 0 100 200 300 F I G . 4 . 2 1 . I n t e r m e d i a t e v e l o c i t y model i n w h i c h t h e o c e a n i c l a y e r s d e t e r m i n e d by Waldron (1982) a r e e x t r a p o l a t e d under the c o n t i n e n t a l c r u s t . The r a y t r a c e i n v e r s i o n p r o c e d u r e has been a p p l i e d t o the m o d e l , and t h e rms r e s i d u a l f o r s h o t s P 1 9 , P 1 3 and P8 was 75 ms, e q u i v a l e n t t o t h a t f o r the f i n a l m o d e l . 138 i s c o n t r o v e r s y r e g a r d i n g t h e d e p t h a t w h i c h t h e phase t r a n s f o r m a t i o n o c c u r s . In p a r t i c u l a r , Fukao e t a l . (1983) p r e s e n t e d more d i r e c t s e i s m o l o g i c a l e v i d e n c e t h a t the s u b d u c t i n g o c e a n i c c r u s t r ema ins u n t r a n s f o r m e d down t o a d e p t h of about 60 km. The s h a l l o w e r phase change i s i n c l u d e d i n t h e i n t e r m e d i a t e model o n l y t o i l l u s t r a t e t h a t i t i s no t i n c o n s i s t e n t w i t h t h e o n s h o r e - o f f s h o r e d a t a . A l t h o u g h t h e i n t e r m e d i a t e model has a c o n t i n u o u s o c e a n i c c r u s t and i s g e n e r a l l y c o n s i s t e n t w i t h t h e s e i s m i c d a t a , t h e r e a r e s t i l l some d i f f i c u l t i e s w i t h t h e m o d e l . The main p r o b l e m i s t h e e x i s t e n c e of the k i n k i n t h e downgoing c r u s t . The k i n k may p e r h a p s be i n t e r p r e t e d as a n o r m a l f a u l t i n t h e ocean c r u s t , downthrown towards t h e c o n t i n e n t , and i n some s u b d u c t i o n zones such as t h e A l e u t i a n a r c (Spence 1 9 7 7 ) , n o r m a l f a u l t i n g has been s u g g e s t e d as a d e s c e n t mechanism f o r t h e s l a b . However , i t i s d i f f i c u l t t o a c c e p t a f a u l t w i t h a t h r o w of ~10 km, e s p e c i a l l y s i n c e t h e r e i s no s u b s t a n t i a l s e i s m i c i t y a s s o c i a t e d w i t h t h e f a u l t , i . e . i n t h e d e p t h range 20-30 km b e n e a t h c e n t r a l V a n c o u v e r I s l a n d . A n o t h e r p r o b l e m w i t h t h e i n t e r m e d i a t e model i s t h a t i t i s no t t o t a l l y c o n s i s t e n t w i t h t h e l o w e r c r u s t a l p o r t i o n of t h e McMechan and Spence (1983) model f o r l i n e IV a l o n g t h e l e n g t h of V a n c o u v e r I s l a n d . A l t h o u g h t h e models a r e c o n s i s t e n t where l i n e IV and t h e o n s h o r e - o f f s h o r e l i n e I i n t e r s e c t ( a t a p o i n t 230 km from shot P 1 9 ; see l o c a t i o n map, F i g 1 . 3 ) , t h e bend i n t h e m i d d l e of l i n e IV cause s t h e deeper r a y p a t h s f rom the s o u t h e r n s h o t p o i n t t o t h e n o r t h e r n r e c e i v e r s t o c r o s s l i n e I a t d i s t a n c e s up t o 20-25 km west of t h e i n t e r s e c t i o n p o i n t . T h u s , t h e c o n t i n e n t a l Moho and the l o w - v e l o c i t y zone above t h e Moho 139 s h o u l d e x t e n d as f a r west as ~205 km from s h o t P 1 9 . I f t h i s e x i s t e d i n t h e i n t e r m e d i a t e " k i n k " m o d e l , t h e n the k i n k i n t h e downgoing c r u s t would become a b r e a k , and t h e d e s i r e d c o n t i n u i t y of t h e o c e a n i c c r u s t wou ld be l o s t . The two models e v o l v e d i n t o the f i n a l model ( F i g . 4 . 7 ) m a i n l y by i n v o k i n g t h e r e q u i r e m e n t t h a t t h e s u b d u c t i n g o c e a n i c c r u s t be c o n t i n u o u s . W i t h t h i s r e q u i r e m e n t , w h i c h i s i t s e l f not n e c e s s a r y t o s a t i s f y the r e f r a c t i o n d a t a but r a t h e r i s i m p l i e d by more g e n e r a l p r i n c i p l e s , a s l i v e r of h i g h - v e l o c i t y m a t e r i a l must t h e n be i n t r o d u c e d above t h e s u b d u c t i n g c r u s t on t h e b a s i s o f t h e s e i s m i c c o n s t r a i n t s . In p a r t i c u l a r , t h e s h a l l o w h i g h -v e l o c i t y pathway i s r e q u i r e d t o a l l o w a r r i v a l s a t the V a n c o u v e r I s l a n d s t a t i o n s t o be advanced by ~1 s r e l a t i v e t o t h e a r r i v a l s a t t h e m a i n l a n d s t a t i o n s . In b o t h a l t e r n a t e models and i n t h e f i n a l model d i s c u s s e d i n s e c t i o n 4 . 5 , the d e p t h of the c o n t i n e n t a l Moho was f i x e d a t a v a l u e near 40 km. A l t h o u g h t h i s d e p t h i s c o n s t r a i n e d by t h e p r e f e r r e d i n t e r p r e t a t i o n of McMechan and Spence ( 1 9 8 3 ) , a l t e r n a t e i n t e r p r e t a t i o n s of the l i n e IV d a t a s e t a l l o w the Moho t o be as deep as 52 km ( F i g . 1 . 5 ) . I f a Moho d e p t h >40 km were used i n t h e o n s h o r e - o f f s h o r e i n t e r p r e t a t i o n , t h e n a ma jor e f f e c t on t h e f i n a l model wou ld be a l a r g e r shadow z o n e , due t o t h e c o r n e r where t h e s u b d u c t i n g ocean c r u s t meets t h e c o n t i n e n t a l Moho, f o r t h e t u r n i n g r a y s t o t h e f a r o f f s e t r e c e i v e r s ( F i g . 4 . 1 8 ) . I t i s d i f f i c u l t t o q u a n t i f y t h e i m p l i c a t i o n s of a l a r g e r shadow z o n e , s i n c e a 2D se i smogram r o u t i n e i n c l u d i n g d i f f r a c t i o n a r r i v a l s w o u l d be r e q u i r e d . However , i t i s my i m p r e s s i o n t h a t the s i z e of the c u r r e n t shadow zone i s s u f f i c i e n t l y l a r g e ; w i t h 140 a l a r g e r shadow z o n e , t o o many r e c e i v e r s w o u l d be w i t h o u t t u r n i n g r a y a r r i v a l s . N e v e r t h e l e s s , i t i s s t i l l p o s s i b l e t o model t h e d a t a u s i n g o n l y r e f l e c t i o n s t o the f a r - o f f s e t s t a t i o n s ( a l t h o u g h the f i t d e t e r i o r a t e s because a m p l i t u d e s a t the f a r s t a t i o n s w o u l d be too s m a l l ) . T h u s , w i t h a deeper c o n t i n e n t a l Moho, t h e e f f e c t on t h e r e m a i n d e r of t h e model w i l l be s i m i l a r t o t h a t shown i n F i g u r e 2 . 8 , i n w h i c h d i f f e r e n t Moho d e p t h s were used i n t h e s u b d u c t i o n zone t e s t m o d e l . That i s , a deeper Moho i m p l i e s a f a s t e r m a n t l e v e l o c i t y and a l s o a s h a l l o w e r d e p t h f o r the upper m a n t l e r e f l e c t o r . 4 .7 G r a v i t y model a c r o s s t h e s u b d u c t i n g m a r g i n As d i s c u s s e d i n t h e i n t r o d u c t o r y c h a p t e r , t h e g r a v i t y anomaly d a t a i n t h e P a c i f i c N o r t h w e s t e x h i b i t a l o w - h i g h c o u p l e w h i c h i s s i m i l a r t o o t h e r s u b d u c t i o n z o n e s . The g r a v i t y low n o r m a l l y c o r r e s p o n d s t o t h e t r e n c h and t h e h i g h t o the a r c -t r e n c h gap , w h i c h i n t h e P a c i f i c N o r t h w e s t i n c l u d e s a l l o f V a n c o u v e r I s l a n d . The V a n c o u v e r I s l a n d " g r a v i t y - s e i s m i c c o n f l i c t " , w h i c h was the main c o n c e r n o f R i d d i h o u g h ( 1 9 7 9 ) , a r i s e s because t h e g r a v i t y h i g h demands a r e l a t i v e l y t h i n c r u s t i n w h i c h m a t e r i a l w i t h m a n t l e d e n s i t y o c c u r s a t d e p t h s of 30 km or l e s s , whereas s e i s m i c i n t e r p r e t a t i o n s on V a n c o u v e r I s l a n d sugges t t h a t t h e c r u s t i s much t h i c k e r . The i n t e r p r e t a t i o n of McMechan and Spence ( 1 9 8 3 ) , i n w h i c h the minimum c r u s t a l t h i c k n e s s b e n e a t h V a n c o u v e r I s l a n d i s 37 km, p r o v i d e s t h e ma jor s e i s m i c e v i d e n c e w h i c h c o n s t r a i n s t h e c r u s t t o be t h i c k e r t h a n t h a t i m p l i e d by t h e g r a v i t y d a t a . The o n s h o r e - o f f s h o r e s e i s m i c model must o b v i o u s l y be c o n s i s t e n t w i t h 141 the i n t e r p r e t a t i o n of McMechan and Spence ( 1 9 8 3 ) , and so i t can i m m e d i a t e l y be r e c o g n i z e d t h a t a g r a v i t y model a l o n g t h e c r o s s -i s l a n d p r o f i l e w i l l not b r i n g about a s t r a i g h t f o r w a r d r e s o l u t i o n of t h e g r a v i t y - s e i s m i c c o n f l i c t . However , because o f t h e p r e s e n c e of t h e h i g h - v e l o c i t y s l i v e r b e n e a t h w e s t e r n V a n c o u v e r I s l a n d i n t h e 20-25 km d e p t h r a n g e , i t can be q u a l i t a t i v e l y s t a t e d t h a t p e r h a p s t h e s e v e r i t y of t h e c o n f l i c t w i l l be r e d u c e d . The l i m i t a t i o n of t h e c r o s s - i s l a n d model i n r e s o l v i n g the c o n f l i c t i s t h a t t h e h i g h - v e l o c i t y s l i v e r does not e x t e n d e a s t w a r d s s u f f i c i e n t l y f a r . The r e s o l u t i o n of t h e c o n f l i c t r e q u i r e s s p e c i a l a rguments w h i c h j u s t i f y the e x i s t e n c e of anomalous l o w e r c r u s t a l m a t e r i a l w i t h h i g h d e n s i t y and low c o m p r e s s i o n a l v e l o c i t y . R i d d i h o u g h (1979) p o i n t e d t o known b a s i c metamorphic r o c k s w i t h t h e r e q u i r e d p r o p e r t i e s , and s u g g e s t e d t h a t t h e anomalous m a t e r i a l c o u l d o r i g i n a t e i n t h e wedge of m a t e r i a l above t h e downgoing l i t h o s p h e r e due t o e x p e c t e d c o n d i t i o n s of low t e m p e r a t u r e , h i g h p r e s s u r e and h y d r o u s e n v i r o n m e n t . T h u s , the i m p l i c a t i o n of t h i s s o l u t i o n i s t h a t t h e s e i s m i c Moho, w h i c h marks a v e l o c i t y c o n t r a s t , does not c o r r e s p o n d t o a d i s c o n t i n u i t y m a r k i n g a d e n s i t y c o n t r a s t . 4 . 7 . 1 Method The o b s e r v e d g r a v i t y p r o f i l e a l o n g a l i n e v e r y c l o s e t o t h e o n s h o r e - o f f s h o r e p r o f i l e was q u a n t i t a t i v e l y m o d e l l e d u t i l i z i n g t h e c o n s t r a i n t s of t h e c r o s s - i s l a n d s e i s m i c model and t h e c o n c e p t t h a t t h e l o w e r c r u s t may c o n t a i n anomalous h i g h - d e n s i t y , l o w - v e l o c i t y m a t e r i a l . The o b s e r v e d g r a v i t y v a l u e s (dashed l i n e s 142 i n F i g s . 4 .22b and 4 . 2 2 c ) and t h e ocean bot tom t o p o g r a p h y a l o n g the l i n e were s u p p l i e d by R i d d i h o u g h ( p e r s . comm. 1982 ) . The i n t e r p r e t e d c r o s s - i s l a n d g r a v i t y model i s shown i n F i g u r e 4 . 2 2 a . The model i n c o r p o r a t e s most f e a t u r e s of the g r a v i t y model of W a l d r o n ( 1 9 8 2 ) , w h i c h was based on h i s m a r i n e s e i s m i c i n t e r p r e t a t i o n f o r t h e p o r t i o n of t h e ocean c r u s t as f a r e a s t as t h e t o p of t h e c o n t i n e n t a l s l o p e . A few minor m o d i f i c a t i o n s were made t o W a l d r o n ' s g r a v i t y m o d e l ; t h e number of s e d i m e n t a r y b l o c k s was r e d u c e d , and an upper c r u s t a l d e n s i t y of 2 .72 g c m " 3 was u s e d , i n s t e a d of 2 .62 g c m - 3 . The l a t t e r change a r o s e because o u t s i d e t h e r e g i o n of t h e ocean c r u s t and s h e l f W a l d r o n (1982) used t h e same model as R i d d i h o u g h ( 1 9 7 9 ) , i n w h i c h t h e p o s i t i o n s of a number of b o u n d a r i e s ( i n c l u d i n g t h e base of t h e l i t h o s p h e r e ) were s l i g h t l y d i f f e r e n t from t h o s e i m p l i e d by t h e c r o s s - i s l a n d s e i s m i c i n t e r p r e t a t i o n . D e n s i t i e s i n o t h e r r e g i o n s of the c r o s s - i s l a n d g r a v i t y model a r e t h e same as i n R i d d i h o u g h ( 1 9 7 9 ) : c r u s t a l d e n s i t y i s 2 .92 g c m " 3 , l i t h o s p h e r e m a n t l e i s 3 .34 g c m " 3 , o c e a n i c a s t h e n o s p h e r e i s 3 .295 g c m " 3 , c o n t i n e n t a l a s t h e n o s p h e r e i s 3 .285 g c m " 3 , and t h e anomalous m a t e r i a l above t h e downgoing l i t h o s p h e r e i s a s s i g n e d a d e n s i t y of 3 .30 g c m " 3 . F i n a l l y , t h e s l i v e r of h i g h - v e l o c i t y m a t e r i a l embedded i n t h e c o n t i n e n t a l c r u s t i s g i v e n a d e n s i t y of 3 .28 g c m " 3 , somewhat l e s s t h a n n o r m a l m a n t l e d e n s i t y . As i n t h e i n t e r p r e t a t i o n of R i d d i h o u g h ( 1 9 7 9 ) , t h e d e n s i t y of t h e downgoing o c e a n i c c r u s t i s assumed t o i n c r e a s e t o t h e d e n s i t y of t h e s u r r o u n d i n g m a n t l e . The c r u s t a l d e n s i t y w o u l d be e x p e c t e d t o i n c r e a s e beyond t h a t of normal l i t h o s p h e r e due t o t h e b a s a l t / e c l o g i t e phase t r a n s i t i o n . But i n t h e g r a v i t y m o d e l , 143 F I G . 4 . 2 2 . (a) D e n s i t y m o d e l , w i t h d e n s i t i e s i n g c m - 3 , based on t h e o b s e r v e d g r a v i t y and on t h e f i n a l v e l o c i t y model f o r t h e o n s h o r e - o f f s h o r e p r o f i l e . Ar rowheads i n d i c a t e c o a s t s of V a n c o u v e r I s l a n d . The shaded r e g i o n i s t h e p o r t i o n of t h e l o w e r s e i s m i c c r u s t w i t h an anomalous l o w - v e l o c i t y h i g h -d e n s i t y r e l a t i o n s h i p . The h o r i z o n t a l dashed l i n e a t t h e base of t h i s r e g i o n i s t h e s e i s m i c Moho a t 37 km d e p t h . (b) O b s e r v e d g r a v i t y v a l u e s (dashed l i n e ) and t h e o r e t i c a l g r a v i t y v a l u e s ( s o l i d l i n e ) f o r w h i c h the shaded r e g i o n of t h e d e n s i t y model i s a s s i g n e d a d e n s i t y of 3 .30 g c m - 3 . (c ) O b s e r v e d g r a v i t y v a l u e s (dashed l i n e ) and t h e o r e t i c a l g r a v i t y v a l u e s ( s o l i d l i n e ) f o r w h i c h t h e shaded r e g i o n of t h e d e n s i t y model i s a s s i g n e d a d e n s i t y of 2 .92 g c m " 3 , t h e n o r m a l d e n s i t y e x p e c t e d f o r c r u s t a l m a t e r i a l . The m i s f i t i l l u s t r a t e s t h e b a s i c g r a v i t y - s e i s m i c c o n f l i c t . 144 1 45 as i n t h e s e i s m i c v e l o c i t y m o d e l , t h e d e p t h a t w h i c h the phase change o c c u r s i s assumed t o be 60 km or g r e a t e r . In any c a s e , even i f the o c e a n i c c r u s t were a s s i g n e d an e l e v a t e d d e n s i t y of 3 .56 g c m " 3 be low 30 km d e p t h , t h e g r a v i t y e f f e c t due t o t h e i n c r e a s e d d e n s i t y wou ld be s m a l l and have a much l o n g e r w a v e l e n g t h t h a n t h a t i n the o b s e r v e d g r a v i t y d a t a . The base of t h e l i t h o s p h e r e b e n e a t h t h e w e s t e r n ocean b a s i n was assumed t o c o r r e s p o n d t o t h e upper m a n t l e r e f l e c t o r i n t h e s e i s m i c v e l o c i t y m o d e l . B e n e a t h shot P19 the d e p t h of the r e f l e c t o r i s 25 km ( a l t h o u g h i t c o u l d be as deep as 31 km w i t h o u t a l t e r i n g any p a r t of the s e i s m i c model t h r o u g h w h i c h r a y s t r a v e l ) . W i t h 2 . 6 km of wate r and ~1 km of s e d i m e n t s , l i t h o s p h e r i c t h i c k n e s s i s ~ 2 1 . 5 km. T h i s v a l u e i s s l i g h t l y l a r g e r t h a n t h e e x p e c t e d t h i c k n e s s of a r o u n d 20 km f o r the l i t h o s p h e r e (aged 6-9 Ma a t t h e c o n t i n e n t a l m a r g i n ) , based on the a g e - t h i c k n e s s r e l a t i o n s h i p o f Y o s h i i e t a l . ( 1 9 7 6 ) . The t o p of t h e s u b d u c t i n g l i t h o s p h e r e was e x t r a p o l a t e d t o 100 km d e p t h b e n e a t h t h e v o l c a n i c c h a i n , w h i c h i s i n a c c o r d w i t h i t s d e p t h i n o t h e r a c t i v e m a r g i n s ( B a r a z a n g i and I s a c k s 1976 ) . E a s t of t h e Coa s t M o u n t a i n s , a v a l u e of 33 km was used f o r the Moho d e p t h ( B e r r y and F o r s y t h 1975) . Below t h e Moho i n t h i s r e g i o n , a s t h e n o s p h e r i c d e n s i t i e s were used f o r t h e m a n t l e ; l i t h o s p h e r i c m a n t l e was assumed t o be a b s e n t ( F u l t o n and W a l c o t t 1975; R i d d i h o u g h 1 9 7 9 ) . The s t r u c t u r e s a t t h e edges of the model were e x t e n d e d out t o ± 3 0 0 0 km and down t o 200 km d e p t h , so t h a t t h e e f f e c t of m a t e r i a l o u t s i d e t h e s e l i m i t s c o u l d be s a f e l y assumed t o be n e g l i g i b l e . The g r a v i t y f i e l d due t o t h e s t r u c t u r a l model was 1 46 c a l c u l a t e d u s i n g a s t a n d a r d t w o - d i m e n s i o n a l a l g o r i t h m based on T a l w a r i i e t a l . ( 1 9 5 9 ) . The model p a r a m e t e r s w h i c h were v a r i e d i n o r d e r t o match t h e o b s e r v e d and c a l c u l a t e d g r a v i t y p r o f i l e s were m a i n l y : (1) t h e d e p t h t o t h e t o p of the anomalous wedge w i t h d e n s i t y 3 .30 g c m " 3 , and the d e p t h t o t h e n e a r b y c o n t i n e n t a l Moho o v e r t h e d i s t a n c e range 250-400 km, and (2) t h e b o u n d a r i e s of t h e s e d i m e n t a r y b l o c k s i n the d i s t a n c e range 110-200 km, much of w h i c h c o r r e s p o n d s t o the s e d i m e n t s of T o f i n o B a s i n . 4 . 7 . 2 I n t e r p r e t a t i o n The f i n a l g r a v i t y model i s shown i n F i g u r e 4 . 2 2 a . The shaded r e g i o n i n t h e f i g u r e c o r r e s p o n d s t o t h a t p o r t i o n of t h e l o w e r s e i s m i c c r u s t w i t h an anomalous h i g h - d e n s i t y l o w - v e l o c i t y r e l a t i o n s h i p , and i s a s s i g n e d a d e n s i t y o f 3 .30 g c m " 3 f o r t h e f i n a l m o d e l . The c o r r e s p o n d i n g t h e o r e t i c a l g r a v i t y v a l u e s a r e d i s p l a y e d i n F i g u r e 4 . 2 2 b , t o g e t h e r w i t h t h e o b s e r v e d g r a v i t y v a l u e s a l o n g the p r o f i l e . F i g u r e 4 .22c shows t h e t h e o r e t i c a l g r a v i t y v a l u e s when a l l of t h e l o w e r s e i s m i c c r u s t , i n c l u d i n g t h e shaded r e g i o n , i s a s s i g n e d a norma l c r u s t a l d e n s i t y of 2 .92 g c m " 3 . T h u s , t h e d i s a g r e e m e n t between t h e s e t h e o r e t i c a l v a l u e s and t h e o b s e r v e d g r a v i t y i l l u s t r a t e s t h e c u r r e n t e x t e n t of t h e g r a v i t y - s e i s m i c c o n f l i c t . F o r t h e f i n a l g r a v i t y m o d e l , most of t h e f e a t u r e s of t h e g r a v i t y p r o f i l e above t h e ocean b a s i n and c o n t i n e n t a l s h e l f a r e due t o r e l a t i v e l y n e a r - s u r f a c e e f f e c t s . As i n t h e i n t e r p r e t a t i o n of Waldron ( 1 9 8 2 ) , t h e wes ternmost g r a v i t y low ( F i g . 4 . 2 2 b ) r e f l e c t s t h e ocean b a s i n s e d i m e n t s i n c r e a s i n g i n t h i c k n e s s t o w a r d s the s h e l f . The g r a v i t y h i g h o v e r t h e o u t e r s h e l f i s due 147 t o d e c r e a s i n g water d e p t h a l o n g t h e c o n t i n e n t a l s l o p e and a l s o t o g r e a t e r sed iment d e n s i t i e s t h e r e . The n e g a t i v e anomaly over the main p o r t i o n of t h e s h e l f i s r e l a t e d m a i n l y t o t h e s e d i m e n t s i n T o f i n o B a s i n , w h i c h i n c r e a s e i n t h i c k n e s s t o w a r d s t h e c e n t e r of t h e b a s i n and may a l s o be l e s s dense t h a n on t h e o u t e r s h e l f . As w e l l , a c o n t r i b u t i o n t o t h e g r a v i t y low a r i s e s f rom the i n c r e a s i n g c r u s t a l t h i c k n e s s i n t h i s r e g i o n , as the downgoing l i t h o s p h e r i c s l a b b e g i n s t o bend more s t e e p l y . The main g r a v i t y h i g h , w h i c h e x t e n d s a c r o s s V a n c o u v e r I s l a n d t o a p o i n t e a s t of G e o r g i a S t r a i t , may be e x p l a i n e d i n terms of p o c k e t s of h i g h - d e n s i t y m a t e r i a l imbedded i n the l o w e r ( s e i s m i c ) c r u s t . That i s , p a r t of t h e p o s i t i v e anomaly i s due t o the s l i v e r of h i g h - d e n s i t y m a n t l e under w e s t e r n V a n c o u v e r I s l a n d i n the d e p t h range 20-25 km, and p a r t i s due t o anomalous h i g h -d e n s i t y l o w - v e l o c i t y m a t e r i a l b e n e a t h e a s t e r n V a n c o u v e r I s l a n d and p a r t of t h e m a i n l a n d . The anomalous m a t e r i a l ( the shaded zone i n F i g . 4 .23a ) e x t e n d s above the s e i s m i c Moho w i t h a maximum t h i c k n e s s of o n l y 9 km. T h u s , perhaps t h e main r e s u l t of t h e g r a v i t y m o d e l l i n g i s t h a t t h e s i z e of t h e anomalous zone has been r e d u c e d r e l a t i v e t o t h a t of R i d d i h o u g h ( 1 9 7 9 ) . O b v i o u s l y , o t h e r d i s t r i b u t i o n s of h i g h - d e n s i t y m a t e r i a l i n t h e l o w e r c r u s t w i l l a l s o s a t i s f y t h e g r a v i t y d a t a . F o r e x a m p l e , an even b e t t e r match between o b s e r v e d and c a l c u l a t e d v a l u e s wou ld be o b t a i n e d i f t h e h i g h - d e n s i t y s l i v e r a t 20-25 km d e p t h were e x t e n d e d e a s t w a r d s . However , t h i s i s not p e r m i t t e d on the b a s i s of t h e r e f r a c t i o n d a t a , u n l e s s t h e e x t e n d e d s l i v e r had a p e c u l i a r c o n f i g u r a t i o n out of t h e p l a n e of t h e c r o s s - i s l a n d p r o f i l e or were f r agmented so as t o be u n d e t e c t a b l e a t the 1 48 w a v e l e n g t h s o f s e i s m i c e n e r g y . 4 .8 D i s c u s s i o n The ma jor o b j e c t i v e of t h e o n s h o r e - o f f s h o r e s t u d y was t o o b t a i n a t w o - d i m e n s i o n a l v e l o c i t y model t o upper m a n t l e d e p t h s a c r o s s the m a r g i n where the o c e a n i c Juan de Fuca p l a t e s u b d u c t s b e n e a t h the c o n t i n e n t a l A m e r i c a p l a t e . F i g u r e 4 . 2 3 shows the r e s u l t a n t v e l o c i t y model t o g e t h e r w i t h a s t y l i z e d t e c t o n i c model t a k e n from t h e t r a n s - C o r d i l l e r a T r a n s e c t B2 of Monger e t a l . ( 1 9 8 4 ) , l o c a t e d a l o n g a l i n e c l o s e t o t h e l o c a t i o n of the o n s h o r e - o f f s h o r e p r o f i l e . The t e c t o n i c model i n c o r p o r a t e s t h e s p e c u l a t i v e c o n c e p t t h a t a s semblages c o r r e s p o n d i n g t o o l d e r t e r r a n e s a r e v e r t i c a l l y s t a c k e d and a r e u n d e r l a i n by t h e c u r r e n t l y d e s c e n d i n g o c e a n i c p l a t e . The model i s based on s u r f a c e g e o l o g y , o t h e r g e o p h y s i c s and a l s o on t h e s e i s m i c r e s u l t s f rom t h i s t h e s i s , w h i c h has p r o v i d e d a r e p r e s e n t a t i o n of t h e geometry o f t h e s u b d u c t i n g l i t h o s p h e r i c p l a t e i n c l u d i n g p o s s i b l e c o m p l e x i t i e s a s s o c i a t e d w i t h t h e s u b d u c t i o n z o n e . The f i n a l v e l o c i t y model i s a c t u a l l y a c o m p o s i t e m o d e l , r e q u i r i n g t h e i n t e r p r e t a t i o n o f s e v e r a l a s s o c i a t e d s e i s m i c d a t a s e t s . The v e l o c i t y s t r u c t u r e of t h e o c e a n i c c r u s t , i n c l u d i n g the p r e s e n c e of a r e l a t i v e l y l o w - v e l o c i t y melange b e n e a t h t h e o u t e r c o n t i n e n t a l s h e l f , was d e t e r m i n e d by W a l d r o n (1982) i n a mar ine r e f r a c t i o n i n t e r p r e t a t i o n . The b a s i c s e i s m i c s t r u c t u r e of the c o n t i n e n t a l c r u s t was e s t a b l i s h e d by McMechan and Spence (1983) i n t h e i n t e r p r e t a t i o n of a r e f r a c t i o n l i n e a l o n g the l e n g t h of V a n c o u v e r I s l a n d ; t h e most i m p o r t a n t f e a t u r e of t h e i n t e r p r e t a t i o n was a p r e f e r r e d v a l u e of 37 km f o r t h e c r u s t a l 60-J HO) (OZ) HOH, OZETTE MELANGES WR) WRANGELLIA CRESCENT AGE in Ma PACIFIC RIM F I G . 4 .23 . F i n a l v e l o c i t y model for the o n s h o r e - o f f s h o r e p r o f i l e and s t y l i z e d t e c t o n i c c r o s s s e c t i o n m o d i f i e d from the t r a n s - C o r d i l l e r a T r a n s e c t B2 of Monger et a l . (1984) No v e r t i c a l e x a g g e r a t i o n . vo 150 t h i c k n e s s , w h i c h a l s o i m p l i e d the e x i s t e n c e of a l o w - v e l o c i t y zone i n t h e l o w e r c r u s t . W i t h t h e o c e a n i c and c o n t i n e n t a l s t r u c t u r e s as known q u a n t i t i e s , t h e i n t e r p r e t a t i o n of t h e o n s h o r e - o f f s h o r e p r o f i l e a c r o s s V a n c o u v e r I s l a n d was a b l e t o e x t e n d t h e c r u s t a l models t o the upper m a n t l e r e g i o n . A l t h o u g h the s u b d u c t i n g o c e a n i c c r u s t was not d i r e c t l y o b s e r v e d , t h e o n s h o r e - o f f s h o r e d a t a s e t p r o v i d e s some i n d i r e c t c o n t r o l on t h e d i p of t h e o c e a n i c c r u s t and the p o i n t a t w h i c h i t bends t o d i v e under t h e c o n t i n e n t a l c r u s t . The c o n t r o l l i n g i n f o r m a t i o n i s t h a t t h e d i p a t the base of t h e melange u n i t i s r e l a t i v e l y s m a l l ( 3 ° o r l e s s ) under a l l s h o t s on t h e o u t e r c o n t i n e n t a l s h e l f . T h u s , a s suming t h e o t h e r o c e a n i c l a y e r s d i p a t t h e same a n g l e as t h e base of t h e me lange , the bend i n t h e s u b d u c t i n g s l a b must o c c u r l a n d w a r d of t h e e a s t e r n m o s t s h o t , w h i c h i s 35 km e a s t of t h e f o o t of t h e c o n t i n e n t a l s l o p e . T h i s c o n c l u s i o n i s c o n s i s t e n t w i t h t h e r e s u l t s of Taber ( 1 9 8 3 ) , who more d i r e c t l y o b s e r v e d t h e bend i n t h e s l a b a t a p o i n t n e a r l y 50 km l a n d w a r d of the b e g i n n i n g of t h e s l o p e a t t h e W a s h i n g t o n c o n t i n e n t a l m a r g i n . Taber (1983) s u g g e s t e d t h a t l a r g e r a t e s of s e d i m e n t a t i o n caused the f o o t of t h e s l o p e t o move s e a w a r d s , and a l s o r e s u l t e d i n t h e l a c k of an ocean bot tom t r e n c h . W i t h t h e d e p t h of t h e t o p of t h e o c e a n i c c r u s t a p p r o x i m a t e l y known under t h e c o n t i n e n t a l s l o p e , t h e d i p of t h e s l a b under t h e c o n t i n e n t a l s h e l f may be d e t e r m i n e d because t h e d e p t h of t h e s l a b under w e s t e r n V a n c o u v e r I s l a n d can be no s h a l l o w e r t h a n 37 km, the c o n t i n e n t a l Moho d e p t h found by McMechan and Spence ( 1 9 8 3 ) . The average d i p i s 1 4 - 1 6 ° , w h i c h i s l a r g e r t h a n the v a l u e of 9 - 1 1 ° found by Taber (1983) from s e i s m i c i t y s t u d i e s and from an 151 o n s h o r e - o f f s h o r e r e f r a c t i o n p r o f i l e o f f the c o a s t of W a s h i n g t o n . However , r e l a t i v e l y s m a l l d i f f e r e n c e s i n s t r u c t u r e a r e p e r h a p s t o be e x p e c t e d , s i n c e the s t u d i e s of Taber (1983) were l o c a t e d t o t h e s o u t h of a bend i n t h e c o n t i n e n t a l m a r g i n a t the l a t i t u d e of Puget Sound ( F i g . 1 . 1 ) , w h i l e t h e p r e s e n t s t u d y i s t o t h e n o r t h of t h e b e n d . The base o f t h e s u b d u c t i n g l i t h o s p h e r e i n t h e r e g i o n can be a s s o c i a t e d w i t h t h e upper m a n t l e r e f l e c t o r i n the v e l o c i t y m o d e l , d i v i d i n g o c e a n i c upper m a n t l e from o c e a n i c a s t h e n o s p h e r e ( F i g . 4 . 2 3 ) . F o r l i t h o s p h e r e of age 9 Ma, t h e e x p e c t e d t h i c k n e s s i s about 20 km, and t h i s c o r r e s p o n d s r e a s o n a b l y w e l l w i t h the d e p t h of t h e upper m a n t l e r e f l e c t o r . As w e l l , the p r e f e r r e d v e l o c i t y be low t h e boundary i s l e s s t h a n t h e v e l o c i t y a b o v e , w h i c h i s c o n s i s t e n t w i t h the e x p e c t e d r e l a t i v e v e l o c i t i e s of l i t h o s p h e r e and a s t h e n o s p h e r e . The s u b d u c t i o n zone i n t h e V a n c o u v e r I s l a n d r e g i o n a p p e a r s t o be c o m p l i c a t e d by an anomalous f e a t u r e above the downgoing o c e a n i c c r u s t . On the b a s i s of t h e o n s h o r e - o f f s h o r e r e f r a c t i o n d a t a s e t , a s l i v e r of m a t e r i a l w i t h m a n t l e - t y p e v e l o c i t i e s ( 7 . 7 km/s) i s p r e s e n t a t t h e 20-25 km d e p t h range b e n e a t h w e s t e r n V a n c o u v e r I s l a n d and t h e i n n e r c o n t i n e n t a l s h e l f . A s i m i l a r l o c a l i z e d r e g i o n of h i g h - v e l o c i t y m a t e r i a l a t 20 km d e p t h was i n d e p e n d e n t l y p r e d i c t e d from t h e r e f r a c t i o n d a t a s e t a l o n g V a n c o u v e r I s l a n d , i n t e r p r e t e d by McMechan and Spence (1983) ( F i g . 1 . 4 ) . A map v i e w showing t h e l o c a t i o n o f t h e s e h i g h -v e l o c i t y r e g i o n s and t h e i r p o s s i b l e i n t e r c o n n e c t i o n i s shown i n F i g u r e 4 . 2 4 . B e n e a t h the s o u t h e r n t i p of V a n c o u v e r I s l a n d , w e s t e r n W a s h i n g t o n and w e s t e r n O r e g o n , L a n g s t o n (1981) found a 152 F I G . 4 . 2 4 . Shaded r e g i o n shows the p o s s i b l e e x t e n t of p o c k e t s of h i g h - v e l o c i t y m a t e r i a l l y i n g a t 20 km d e p t h benea th V a n c o u v e r I s l a n d . The boundary of the shaded r e g i o n i s i n d i c a t e d by a s o l i d l i n e where i t s l o c a t i o n i s r e a s o n a b l y w e l l - c o n t r o l l e d , and by a dashed l i n e where i t s l o c a t i o n i s s p s c u l a t i v e . 1 53 r e g i o n of m a n t l e - t y p e v e l o c i t y a t 16 km d e p t h , below w h i c h was a l o w - v e l o c i t y zone and a second r e g i o n of h i g h v e l o c i t y s t a r t i n g a t 40 km d e p t h . He i n t e r p r e t e d t h e s h a l l o w h i g h - v e l o c i t y r e g i o n as o l d e r i n d i g e n o u s m a n t l e and t h e l o w e r one as m a n t l e r e l a t e d t o t h e c u r r e n t l y s u b d u c t i n g ocean l i t h o s p h e r e . S i m i l a r arguments may a p p l y f o r t h e s h a l l o w , h i g h - v e l o c i t y r e g i o n s benea th V a n c o u v e r I s l a n d . That i s , t h e s p e c u l a t i o n can be made t h a t the f e a t u r e s a r e remnants of a s u b d u c t e d s l a b , p e r h a p s s t r a n d e d i n t h e p a s t when t h e l o c u s of s u b d u c t i o n jumped w e s t w a r d . Such a r e o r g a n i z a t i o n of s u b d u c t i o n geometry has been s u g g e s t e d t o e x p l a i n the e x i s t e n c e of T o f i n o B a s i n on t h e c o n t i n e n t a l s h e l f , w h i c h may t h e n have been t h e former t r e n c h ( D i c k i n s o n 1976; R i d d i h o u g h 1 9 7 9 ) . The seaward jumping of a s u b d u c t i o n zone may be r e l a t e d t o t h e a r r i v a l of an a c c r e t e d t e r r a n e a t the c o n t i n e n t a l m a r g i n ( Jones e t a l . 1 9 8 2 ) . At t h e same t i m e , t h r u s t f a u l t i n g a s s o c i a t e d w i t h t h e c o l l i s i o n p r o c e s s t e n d s t o t h i c k e n t h e c r u s t t o c o n t i n e n t a l p r o p o r t i o n s . I n t h e t e c t o n i c model of 4 . 2 3 b , s e v e r a l a d j a c e n t a c c r e t e d t e r r a n e s a r e r e p r e s e n t e d . These i n c l u d e the W r a n g e l l i a t e r r a n e WR on V a n c o u v e r I s l a n d and t h e m a i n l a n d ( Jones e t a l . 1977; M u l l e r 1977) , t h e P a c i f i c Rim Complex PR on t h e wes ternmost c o a s t of V a n c o u v e r I s l a n d and e x t r a p o l a t e d o f f s h o r e ( M u l l e r 1977) , t h e O z e t t e and Hoh melanges OZ and HO under t h e o u t e r c o n t i n e n t a l s h e l f and s l o p e ( S n a v e l y and Wagner 1981 ; W a l d r o n 1 9 8 2 ) , and a f ragment o f C r e s c e n t v o l c a n i c s CR i d e n t i f i e d as a d e t a c h e d s l a b of Eocene o c e a n i c c r u s t ( Y o r a t h and C u r r i e 1980; Y o r a t h 1980 ) . The t e r r a n e s form d i s t i n c t u n i t s l a t e r a l l y , but i n a d d i t i o n t h e s p e c u l a t i o n has 1 54 been made t h a t t h e t h r u s t f a u l t i n g has r e s u l t e d i n v e r t i c a l s t a c k i n g of the t e r r a n e s as w e l l (Monger e t a l . 1984) . T h u s , b e n e a t h W r a n g e l l i a t h e r e might be a f r agmented m i x t u r e of s e v e r a l t e r r a n e s , i n c l u d i n g P a c i f i c Rim p l u s more w e s t e r l y t e r r a n e s such as C r e s c e n t and O z e t t e ( F i g . 4 . 2 3 b ) . Compared t o t h e v e l o c i t y model f rom t h e o n s h o r e - o f f s h o r e r e f r a c t i o n p r o f i l e ( F i g . 4 . 2 3 a ) , t h e s p e c u l a t i v e r e g i o n below W r a n g e l l i a c o r r e s p o n d s t o the l o w - v e l o c i t y zone i n the l o w e r " c o n t i n e n t a l " c r u s t and a l s o i n c l u d e s the h i g h - v e l o c i t y s l i v e r above t h e s u b d u c t i n g o c e a n i c c r u s t . The s e i s m i c l o w - v e l o c i t y zone may t h u s be made up of p o c k e t s of s u b d u c t e d or u n d e r t h r u s t m a t e r i a l from a number of t e r r a n e s , and the low v e l o c i t i e s may r e s u l t f rom the m e l a n g e - l i k e n a t u r e of t h e r e g i o n . The s l i v e r , w h i c h i s most l i k e l y m a n t l e m a t e r i a l but a l s o may c o n s i s t of h i g h - v e l o c i t y l o w e r c r u s t a l m a t e r i a l , may be a l a r g e f ragment e q u i v a l e n t t o the d e t a c h e d s l a b of o c e a n i c c r u s t benea th the c o n t i n e n t a l s h e l f (CR i n F i g . 4 . 2 3 b ) . The i n t e r p r e t a t i o n of t h e o n s h o r e - o f f s h o r e r e f r a c t i o n d a t a has added s i g n i f i c a n t d e t a i l s t o t h e o r i g i n a l s u b d u c t i o n zone model of R i d d i h o u g h ( 1 9 7 9 ) , w h i c h was based on g r a v i t y , heat f l o w and l i m i t e d s e i s m i c d a t a . However , a g r a v i t y i n t e r p r e t a t i o n c o n s t r a i n e d by t h e new s e i s m i c model l e a d s t o s i m i l a r c o n c l u s i o n s as t h o s e of R i d d i h o u g h ( 1 9 7 9 ) . The main c o n c l u s i o n from t h e g r a v i t y m o d e l l i n g i s t h a t s p e c i a l h i g h - d e n s i t y l o w -v e l o c i t y m a t e r i a l i s r e q u i r e d i n some p o r t i o n s of t h e l o w e r c r u s t . R i d d i h o u g h (1979) has s u g g e s t e d t h a t t h e f o r m a t i o n of the anomalous m a t e r i a l may be due t o c o n d i t i o n s of h i g h p r e s s u r e , low t e m p e r a t u r e and h y d r o u s e n v i r o n m e n t above t h e s u b d u c t i n g 155 c r u s t . I n the new s e i s m i c m o d e l , a s l i v e r of m a n t l e m a t e r i a l , w i t h a n o r m a l v e l o c i t y - d e n s i t y r e l a t i o n s h i p , was found i n the l o w e r c r u s t b e n e a t h w e s t e r n V a n c o u v e r I s l a n d . T h u s , t h e s i z e of the anomalous z o n e , r e l a t i v e t o t h a t of R i d d i h o u g h ( 1 9 7 9 ) , has been r e d u c e d t o a p o c k e t o f m a t e r i a l above t h e s e i s m i c Moho w i t h a maximum t h i c k n e s s of o n l y 8 km ( F i g . 4 . 2 2 a ) . An a l t e r n a t i v e o r i g i n f o r t h e u n u s u a l h i g h - d e n s i t y l o w -v e l o c i t y m a t e r i a l may p e r h a p s be found i n t h e s p e c u l a t i v e t e c t o n i c model d i s c u s s e d p r e v i o u s l y . The p r o p e r t i e s of the anomalous m a t e r i a l may not be due t o t h e c u r r e n t e n v i r o n m e n t above t h e s u b d u c t i n g s l a b , but r a t h e r t h e m a t e r i a l had formed e l s e w h e r e and been t r a n s p o r t e d t o t h e r e g i o n as p a r t of an a c c r e t e d t e r r a n e , some of w h i c h was t h r u s t under t h e s t a c k of t e r r a n e s a l r e a d y i n p l a c e . I f a c c r e t e d t e r r a n e s i n f a c t have t h e i r modern a n a l o g i n some of t h e p l a t e a u s p r e s e n t i n t o d a y ' s o c e a n s , t h e n the o r i g i n of the anomalous m a t e r i a l i s r e l a t e d t o the o r i g i n of t h e o c e a n i c p l a t e a u s , the c r u s t a l s t r u c t u r e of w h i c h i s i n t e r m e d i a t e between c o n t i n e n t a l and o c e a n i c c r u s t a l s t r u c t u r e (Ben-Avraham e t a l . 1 9 8 1 ) . That i s , t h e g r a v i t y -s e i s m i c c o n f l i c t i n t h e V a n c o u v e r I s l a n d r e g i o n i s a n o t h e r m a n i f e s t a t i o n of t h e c o m p l e x i t y t h a t can a r i s e i n p r o c e s s e s i n v o l v i n g t h e g e n e r a t i o n and a c c r e t i o n of e x o t i c t e r r a n e s . As s u g g e s t e d by McMechan and Spence (1983) and E l l i s e t a l . ( 1 9 8 3 ) , f u t u r e s t u d i e s s h o u l d i n c l u d e r e f l e c t i o n p r o f i l i n g f o r d e l i n e a t i n g many of t h e d e t a i l s of t h e s e i s m i c r e f r a c t i o n m o d e l . A f e a s i b i l i t y s t u d y has a l r e a d y been c a r r i e d o u t , as p a r t of the V a n c o u v e r I s l a n d S e i s m i c P r o j e c t , t o d e t e r m i n e whether c o h e r e n t r e f l e c t i o n s t o upper m a n t l e d e p t h s c o u l d be a c q u i r e d i n t h i s 1 56 t e c t o n i c reg ime (Clowes e t a l . 1983a ) . The program i n c l u d e d a 10 km 1200% common d e p t h p o i n t e x p l o s i o n s u r v e y ; t h e l o c a t i o n of t h e r e f l e c t i o n l i n e (RL i n F i g s . 1.3 and 4 .24 ) was v e r y c l o s e t o t h e o n s h o r e - o f f s h o r e l i n e I . Two c l e a r r e f l e c t i o n s were p r e s e n t a c r o s s the r e c o r d s e c t i o n near 4 .4 s and 7 .0 s two-way t r a v e l t i m e , and two bands of c o h e r e n t energy were o b s e r v e d near 9 . 5 s and 10.8 s . These two-way t r a v e l t i m e s have been c o n v e r t e d t o d e p t h u s i n g t h e r e f r a c t i o n v e l o c i t y m o d e l , and the c o r r e s p o n d i n g d e p t h s a r e shown s u p e r i m p o s e d on the r e f r a c t i o n model i n F i g u r e 4 . 2 5 . The uppermost r e f l e c t o r A c o r r e l a t e s w e l l w i t h the r e f r a c t o r a t 16 km d e p t h d e t e r m i n e d by McMechan and Spence ( 1 9 8 3 ) . The second r e f l e c t o r C near 24 km d e p t h c o u l d c o r r e s p o n d w i t h t h e base of t h e h i g h - v e l o c i t y s l i v e r , a l t h o u g h i t s h o u l d be kept i n mind t h a t t h i s boundary was no t w e l l -c o n s t r a i n e d i n t h e r e f r a c t i o n m o d e l . The t h i r d p o s s i b l e r e f l e c t o r D a t 31 km d e p t h l i e s i n t h e m i d d l e of t h e c r u s t a l l o w - v e l o c i t y zone of McMechan and Spence ( 1 9 8 3 ) . The deepes t r e f l e c t o r E a t 37 km d e p t h p o s s i b l y c o r r e l a t e s w i t h e i t h e r t h e c o n t i n e n t a l Moho o r the t o p of t h e s u b d u c t i n g o c e a n i c c r u s t . The a v a i l a b i l i t y of a s e i s m i c r e f r a c t i o n model and t h e e n c o u r a g i n g r e s u l t s of t h e r e f l e c t i o n f e a s i b i l i t y s t u d y has l e d t h e C a n a d i a n L i t h o p r o b e S t e e r i n g Committee t o d e s i g n a t e V a n c o u v e r I s l a n d as the s i t e of a major V i b r o s e i s 1 r e f l e c t i o n program t o be c a r r i e d out i n May-June 1984. The program i n c l u d e s a t l e a s t 150 km of 3000%-coverage p r o f i l e s , the m a j o r i t y of w h i c h i s a p r o f i l e a c r o s s V a n c o u v e r I s l a n d f o l l o w i n g e s s e n t i a l l y c o p y r i g h t C o n t i n e n t a l O i l Company Vancouver Island F I G . 4 . 2 5 . E n l a r g e m e n t of t h e f i n a l v e l o c i t y model under Vancouver I s l a n d . RL i n d i c a t e s t h e l o c a t i o n of t h e 10 km e x p l o s i o n r e f l e c t i o n l i n e , a l s o shown on t h e l o c a t i o n map ( F i g s . 1.3 o r 4 . 2 4 ) . The e q u i v a l e n t d e p t h s of r e f l e c t o r s A , C , D and E on t h e r e f l e c t i o n r e c o r d s e c t i o n a r e super imposed on the m o d e l . _ 1 58 t h e same l i n e as the c r o s s - i s l a n d r e f r a c t i o n p r o f i l e . T h i s h i g h -r e s o l u t i o n s t u d y may t h u s p r o v i d e n e a r l y immedia te c o n f i r m a t i o n (or r e p u d i a t i o n ) of many of t h e f e a t u r e s of t h e r e f r a c t i o n m o d e l . 159 REFERENCES A k i , K . and W . H . K . Lee ( 1 9 7 6 ) . D e t e r m i n a t i o n of t h r e e -d i m e n s i o n a l v e l o c i t y a n o m a l i e s under a s e i s m i c a r r a y u s i n g f i r s t P a r r i v a l t i m e s f rom l o c a l e a r t h q u a k e s , 1. A homogeneous i n i t i a l m o d e l , J . G e o p h y s . R e s . 8J_, 4381-4399 . A k i , K . , A . C h r i s t o f f e r s s o n and E . S . Husebye ( 1 9 7 7 ) . D e t e r m i n a t i o n of the t h r e e - d i m e n s i o n a l s e i s m i c s t r u c t u r e of t h e l i t h o s p h e r e , J . G e o p h y s . R e s . 8^, 277-296 . A n d o , M . and E . I . B a l a z s ( 1 9 7 9 ) . G e o d e t i c e v i d e n c e f o r a s e i s m i c s u b d u c t i o n of t h e Juan de Fuca p l a t e , J . G e o p h y s . R e s . 84 , 3023-3028 . A r i c , K . , R. G u t d e u t s c h and A . S a i l o r ( 1 9 8 0 ) . C o m p u t a t i o n of t r a v e l t i m e s and r a y s i n a medium of t w o - d i m e n s i o n a l v e l o c i t y d i s t r i b u t i o n , P u r e A p p l . Geophys . 118, 7 9 6 - 8 0 6 . A u , D . and R . M . C lowes ( 1 9 8 2 ) . C r u s t a l s t r u c t u r e f rom an OBS s u r v e y of the Nootka f a u l t zone o f f w e s t e r n Canada , G e o p h y s . J . j_68, 2 7 - 4 8 . B a r a z a n g i , M . and B . L . I s a c k s ( 1 9 7 6 ) . S p a t i a l d i s t r i b u t i o n of e a r t h q u a k e s and s u b d u c t i o n of t h e Nazca p l a t e b e n e a t h S o u t h A m e r i c a , G e o l o g y 4 , 6 8 6 - 6 9 2 . Ben-Avraham, Z . , A . N u r , D . J o n e s and A . Cox ( 1 9 81 ) - C o n t i n e n t a l a c c r e t i o n : f rom o c e a n i c p l a t e a u s t o a l l o c t h o n o u s t e r r a n e s , S c i e n c e 213 , 4 7 - 5 4 . B e r r y , M . J . and D . A . F o r s y t h ( 1 9 7 5 ) . S t r u c t u r e of t h e C a n a d i a n C o r d i l l e r a f rom s e i s m i c r e f r a c t i o n and o t h e r d a t a , C a n . J . E a r t h S c i . J_2, 182-208. B e s s o n o v a , E . N . , Y . M . F i s h m a n , V . Z . R y a b o y i and G . N . S i t n i k o v a ( 1 9 7 4 ) . The t a u method f o r i n v e r s i o n of t r a v e l t i m e s - I . Deep s e i s m i c s o u n d i n g d a t a , G e o p h y s . J . 3_6, 377-398 . B i r c h , F . ( 1 9 6 4 ) . D e n s i t y and c o m p o s i t i o n of the m a n t l e and c o r e , J . G e o p h y s . R e s . 69 , 4377-4387 . B r a i l e , L . W . and R . B . S m i t h ( 1 9 7 5 ) . G u i d e t o t h e i n t e r p r e t a t i o n of c r u s t a l r e f r a c t i o n p r o f i l e s , G e o p h y s . J . £ 0 , 145-176 . C a s s e l l , B . R . ( 1 9 8 2 ) . A method f o r c a l c u l a t i n g s y n t h e t i c se i smograms i n l a t e r a l l y v a r y i n g m e d i a , G e o p h y s . J . 69 , 339-354 . C e r v e n y , V . and R. R a v i n d r a ( 1 9 7 1 ) . Theory of S e i s m i c Head  Waves, U n i v e r s i t y of T o r o n t o P r e s s , T o r o n t o 312 p p . C e r v e n y , V . J . Langer and I . P s e n c i k ( 1 9 7 4 ) . C o m p u t a t i o n of g e o m e t r i c a l s p r e a d i n g of s e i s m i c body waves i n l a t e r a l l y inhomogeneous media w i t h c u r v e d i n t e r f a c e s , G e o p h y s . J . 38 , 9 - 1 9 . 160 Cerveny, V., I. Molotkov, and I. Psencik (1977). Ray Method in  Seismology, C h a r l e s U n i v e r s i t y Press, Prague, 214 pp. Cerveny, V., M.M. Popov, and I. Psencik (1982). 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S t e i n m e t z , L . , R . B . W h i t m a r s h and V . S . M o r e i r a ( 1 9 7 7 ) . Upper m a n t l e s t r u c t u r e b e n e a t h t h e M i d - A t l a n t i c R i d g e , n o r t h of t h e A z o r e s based on o b s e r v a t i o n s of c o m p r e s s i o n a l waves , G e o p h y s . J . 50 , 3 5 3 - 3 8 0 . T a b e r , J . J . J r . ( 1 9 8 3 ) . C r u s t a l s t r u c t u r e and s e i s m i c i t y of the W a s h i n g t o n c o n t i n e n t a l m a r g i n , P h . D . t h e s i s , U n i v e r s i t y of W a s h i n g t o n , 159pp. T a l w a n i , M . , L . W o r z e l and M . Landi sman ( 1 9 5 9 ) . R a p i d g r a v i t y c a l c u l a t i o n s f o r 2 - d i m e n s i o n a l b o d i e s w i t h a p p l i c a t i o n t o t h e M e n d o c i n o submar ine f r a c t u r e z o n e , J . G e o p h y s . R e s . 64 , 4 9 - 5 9 . T s e n g , K . H . ( 1 9 6 8 ) . A new model f o r t h e c r u s t i n t h e v i c i n i t y of V a n c o u v e r I s l a n d , M . S c . t h e s i s , U n i v e r s i t y o f B r i t i s h 165 C o l u m b i a , 83pp . W a l d r o n , D . A . ( 1 9 8 2 ) . S t r u c t u r a l c h a r a c t e r i s t i c s of a s u b d u c t i n g o c e a n i c p l a t e , M . S c . t h e s i s , U n i v e r s i t y o f B r i t i s h C o l u m b i a , 121pp. Wesson , R . L . ( 1 9 7 0 ) . A t i m e i n t e g r a t i o n method f o r c o m p u t a t i o n o f t h e i n t e n s i t i e s of s e i s m i c r a y s , B u l l . S e i s m . S o c . Am. 6 0 , 307-316 . Wesson , R . L . ( 1 9 7 1 ) . T r a v e l - t i m e i n v e r s i o n f o r l a t e r a l l y inhomogeneous c r u s t a l v e l o c i t y m o d e l s , B u l l . S e i s m . S o c . Am. 6j_, 7 2 9 - 7 4 6 . W h i t e , D . J . and R . M . Clowes ( 1 9 8 4 ) . S e i s m i c i n v e s t i g a t i o n of the Coas t P l u t o n i c C o m p l e x - I n s u l a r B e l t boundary b e n e a t h G e o r g i a S t r a i t , C a n . J . E a r t h S c i . ( a c c e p t e d ) . W h i t e , W . R . H . , M . N . Bone and W . G . M i l n e ( 1 9 6 8 ) . S e i s m i c r e f r a c t i o n s u r v e y s i n B r i t i s h C o l u m b i a : a p r e l i m i n a r y i n t e r p r e t a t i o n , AGU Monograph J_2, 8 1 - 9 3 . W h i t t a l l , K . P . and R . M . C lowes ( 1 9 7 9 ) . A s i m p l e , e f f i c i e n t method f o r t h e c a l c u l a t i o n of t r a v e l t i m e s and r a y p a t h s i n l a t e r a l l y inhomogeneous m e d i a , J . C a n . S o c . E x p l . G e o p h y s . 15, 2 1 - 2 9 . W i c k e n s , A . J . ( 1 9 7 7 ) . The upper m a n t l e of s o u t h e r n B r i t i s h C o l u m b i a , C a n . J . E a r t h S c i . J_4, 1100-1115 . W i g g i n s , R . A . ( 1 9 7 2 ) . The g e n e r a l l i n e a r i n v e r s e p r o b l e m : I m p l i c a t i o n of s u r f a c e waves and f r e e o s c i l l a t i o n s f o r e a r t h s t r u c t u r e , R e v . G e o p h y s . Space P h y s . J_0, 2 5 1 - 2 8 5 . W i g g i n s , R . A . and D . V . H e l m b e r g e r ( 1 9 7 4 ) . S y n t h e t i c se ismogram c o m p u t a t i o n by e x p a n s i o n i n g e n e r a l r a y s , G e o p h y s . J . 37 , 7 3 - 9 0 . Y o l e , R .W. and E . I r v i n g ( 1 9 8 0 ) . D i s p l a c e m e n t of V a n c o u v e r I s l a n d : p a l e o m a g n e t i c e v i d e n c e from the Karmutsen F o r m a t i o n , C a n . J . E a r t h S c i . JJ7, 1210-1228. Y o r a t h , C . J . ( 1 9 8 0 ) . The A p o l l o s t r u c t u r e i n T o f i n o B a s i n , C a n a d i a n P a c i f i c c o n t i n e n t a l s h e l f , C a n . J . E a r t h S c i . 17, 7 5 8 - 7 7 5 . Y o r a t h , C . J . and R . G . C u r r i e ( 1 9 8 0 ) . Some a s p e c t s of t h e g e o l o g y and s t r u c t u r a l s t y l e of t h e V a n c o u v e r I s l a n d c o n t i n e n t a l m a r g i n , G e o l o g i c a l A s s o c i a t i o n of Canada , A n n u a l M e e t i n g , H a l i f a x , N . S . , Program w i t h A b s t r a c t s 5 , p . 8 8 . Y o s h i i , T . , Y . Kono and K . I t o ( 1 9 7 6 ) . T h i c k e n i n g of t h e o c e a n i c l i t h o s p h e r e , AGU Monograph J_9, 423-430 . Y o u n g , G . B . and L . W . B r a i l e ( 1 9 7 6 ) . A computer program f o r t h e a p p l i c a t i o n of Z o e p p r i t z ' s a m p l i t u d e e q u a t i o n s and K n o t t ' s energy e q u a t i o n s , B u l l . S e i s m . S o c . Am. 66 , 1881-1885. 166 APPENDICES: ADDITIONAL RECORD SECTIONS A . 1 Common Shot R e c o r d S e c t i o n s The f o l l o w i n g 14 f i g u r e s r e p r e s e n t t h e o b s e r v e d r e c o r d s e c t i o n s f o r a l l s h o t s of t h e V a n c o u v e r I s l a n d S e i s m i c P r o j e c t o t h e r t h a n s h o t s J 1 , P 1 9 , P 1 3 , P8 and P 2 , f o r w h i c h r e c o r d s e c t i o n s were p r e s e n t e d i n C h a p t e r 4 . P i c k s on the main r e c o r d s e c t i o n s were made i n a manner c o n s i s t e n t w i t h t h e s e c t i o n s i n t h i s a p p e n d i x . That i s , t h e main s e c t i o n s a r e r e p r e s e n t a t i v e of the f u l l V I S P d a t a s e t shown h e r e . A m p l i t u d e s on a l l s e c t i o n s may be compared between s h o t s . A l l a m p l i t u d e s have been m u l t i p l i e d by a f a c t o r p r o p o r t i o n a l t o d i s t a n c e . Times and d i s t a n c e s a r e a d j u s t e d t o p l a c e the s h o t a t a d e p t h of 2 . 6 km, and t o c o r r e c t t h e sed iment l a y e r t o a t h i c k n e s s of 1 km and v e l o c i t y of 1.8 k m / s . The gap near t h e m i d d l e of a l l s e c t i o n s i n d i c a t e s t h e l o c a t i o n of G e o r g i a S t r a i t (a t 265-285 km from shot P 1 9 ) . 170 130 90 50 SH OT/RECEIVER DISTANCE (KM) F I G . A l . l . Observed r e c o r d s e c t i o n f o r s h o t J2. 130 170 210 SHOT/RECEIVER DISTANCE (KM) 250 F I G . A 1 . 2 . Observed r e c o r d s e c t i o n f o r shot P 1 , 104 km from shot P 1 9 . co 100 140 180 220 260 SHOT/RECEIVER DISTANCE (KM) F I G . A 1 . 3 . Observed r e c o r d s e c t i o n f o r s h o t P 3 , 94 km from shot P 1 9 . 105 145 185 225 265 SHOT/RECEIVER DISTANCE (KM) F I G . A 1 . 4 . Observed r e c o r d s e c t i o n f o r s h o t P 4 , 89 km from shot P 1 9 . 110 150 190 230 SHOT/RECEIVER DISTANCE (KM) 270 F I G . A 1 . 5 . Observed r e c o r d s e c t i o n f o r s h o t P 5 , 83 km from shot P 1 9 . 115 155 195 235 275 SHOT/RECEIVER DISTANCE (KM) F I G . A 1 . 6 . Observed r e c o r d s e c t i o n f o r shot P 6 , 78 km from shot P 1 9 . ^ ' • ' — — I • — ' — 1 — ' — f ' ' • •' ' ' 1 r f 130 170 210 250 290 SHOT/RECEIVER DISTANCE (KM) F I G . A 1 . 7 . Observed r e c o r d s e c t i o n f o r shot P 9 , 63 km from shot P 1 9 . O J 135 175 215 255 SHOT/RECEIVER DISTANCE (KM) 295 F I G . A 1 . 8 . Observed r e c o r d s e c t i o n f o r shot P 1 0 , 57 km from shot P 1 9 . ^ n r " •—" —j • - » — 1 — c — 1 —f-*— i » i i i—« i * j— 145 185 225 265 305 SHOT/RECEIVER DISTANCE (KM) F I G . A 1 . 9 . Observed r e c o r d s e c t i o n f o r shot P 1 2 , 47 km from shot P 1 9 . 155 195 235 275 SHOT/RECEIVER DISTANCE (KM) F I G . A L I O . Observed r e c o r d s e c t i o n f o r shot P 1 4 , 36 km from shot 200 240 280 SHOT/RECEIVER DISTANCE (KM) Observed r e c o r d s e c t i o n f o r shot P 1 5 , 31 km from 165 205 245 285 SHOT/RECEIVER DISTANCE (KM) F I G . A l . l 2 . Observed r e c o r d s e c t i o n f o r shot P 1 6 , 26 km from s 175 215 255 295 335 SHOT/RECEIVER DISTANCE (KM) F I G . A 1 . 1 3 . Observed r e c o r d s e c t i o n f o r shot P 1 7 , 21 km from shot P 1 9 . VD 185 225 265 305 345 S H O T / R E C E I V E R DISTANCE (KM) F I G . A 1 . 1 4 . Observed r e c o r d s e c t i o n f o r shot P 1 8 , 10 km from shot P 1 9 . CO o 181 A . 2 S e l e c t e d Common R e c e i v e r R e c o r d S e c t i o n s The f o l l o w i n g 1 0 f i g u r e s a r e s e l e c t e d samples of o b s e r v e d r e c o r d s e c t i o n s showing a l l 17 s h o t s r e c o r d e d on a g i v e n r e c e i v e r . Shot P 1 9 i s on t h e l e f t and s h o t P1 i s on t h e r i g h t (P7 and P11 were m i s f i r e s and so a r e m i s s i n g ) . A m p l i t u d e s may be compared beween a l l r e c e i v e r s , and a l l a m p l i t u d e s have been m u l t i p l i e d by a f a c t o r p r o p o r t i o n a l t o d i s t a n c e . Times and d i s t a n c e s a r e a d j u s t e d t o p l a c e t h e s h o t s a t 2 .6 km d e p t h , and f o r s h o t s P19-P8 t o c o r r e c t t h e s e d i m e n t l a y e r t o a t h i c k n e s s of 1 km and v e l o c i t y of 1.8 k m / s . SHOT/RECEIVER DISTANCE (KM) F I G . A 2 . 4 . Observed r e c o r d s e c t i o n f o r r e c e i v e r X 1 7 . CD O l SHOT/RECEIVER DISTANCE (KM) F I G . A 2 . 6 . Observed r e c o r d s e c t i o n f o r r e c e i v e r X 2 3 . -CO SHOT/RECEIVER DISTANCE (KM) F I G . A 2 . 7 . Observed r e c o r d s e c t i o n f o r r e c e i v e r X31 . _ CO CO SHOT/RECEIVER DISTANCE (KM) F I G . A2.8. Observed r e c o r d s e c t i o n f o r r e c e i v e r X 3 5 . SHOT/RECEIVER DISTANCE (KM) F I G . A 2 . 1 0 . Observed r e c o r d s e c t i o n f o r r e c e i v e r X 4 3 . PUBLICATIONS E l l i s , R.M. G.D. Spence, R.M. Clowes, O.A. Waldron, I.F. Jones, A.G. Green, D.A. Forsyth, J.A. Mair, M.J. Berry, R.F. Mereu, E.R. Kanasewich, G.L. Cumming, Z. Hajnal, R.D. Hyndman, G.A. McMechan, and B.D. Loncarevic (1983). The Vancouver Island Seismic Project: A CO-CRUST onshore-offshore study of a convergent margin, Can. J . Earth Sci. 20, 719-741. McMechan, G.A. and G.D. Spence (1983). P-wave velocity structure of the Earth's crust beneath Vancouver Island, Can. J . Earth Sci. 20, 742-752. Spence, G.D., R.M. Clowes and R.M. E l l i s (1977). Depth l imits on the Moho discontinuity in the southern Rocky Mountain Trench, Canada, Bul l . Seism. Soc. Am. 67, 543-546. Spence, G.D., R.M. E l l i s and R.M. Clowes (1977). Gravity evidence against a high-angle fault crossing the Rocky Mountain Trench near Radium, Brit ish Columbia, Can. J . Earth Sci. IA, 25-31. Spence, G.D., K.P. Whittall and R.M. Clowes (1984). Practical synthetic seismograms for lateral ly varying media calculated by asymptotic ray theory, Bul l . Seism. Soc. Am. (in press). 

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