GRAVITY AND SEISMIC STUDIES IN THE SOUTHERN ROCKY MOUNTAIN TRENCH - by George D. . Spence B.Sc, University of Calgary, 19 71 p A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in the Department of Geophysics and Astronomy We accept t h i s thesis as conforming to the required standard The University Of B r i t i s h Columbia May, 1976 (G) George D. Spence, 1976 In presenting th i s thes is in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree ly ava i lab le for reference and study. I further agree that permission for extensive copying of th i s thesis for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t ion of this thesis for f inanc ia l gain sha l l not be allowed without my writ ten permission. Department of ^ZX>^J^<>(C<> Q-.vi.ik AfkronowiLf The Univers i ty of Br i t i sh 'Co lumbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date (\uA 40 km, (under RHT) (mantle) 5.2 6.1 8,1 (north of C l i n t o n , B.C.) 7.8 (south of C l i n t o n , B.C.) 5.6 6.2 6.2# g r a d i e n t to 8.0 8.0 6.5 8.0 32 curves are superimposed on the P wave r e c o r d s e c t i o n of Bennett e t a l (1975) . Note t h a t the average upjjer c r u s t v e l o c i t i e s (Figure 10A) are approximately egual to the maximum or minimum v e l o c i t i e s s p e c i f i e d p r e v i o u s l y . The lower c r u s t v e l o c i t i e s , however, are not e g u a l t o the e x t r e m a l l y allowed values but l i e somewhere i n between. The reason t h a t the lower c r u s t a l v e l o c i t i e s are not extremal may be deduced from Figure 10B , which shows the p-£ curves corresponding to the maximum and minimum depths- In t h i s p l o t , the curves f o r the upper c r u s t branches and the Moho r e f l e c t i o n branch o u t l i n e p o r t i o n s of the p-^ l i m i t envelope. The basement r e f r a c t i o n brancn, however, does not form part of the envelope but r a t h e r i s the c r o s s - o v e r curve from one s i d e of the envelope to the other; f o r f u r t h e r d e t a i l s on the p-A l i m i t envelope and the c r o s s - o v e r c u r v e , see Appendix 3. From the v e l o c i t y - d e p t h p l o t s , i t can ,be seen t h a t the Moho depth l i m i t s are 52 km and 60 -km. T h i s r e s u l t i s c o n s i s t e n t with the low v e l o c i t y zone i n t e r p r e t a t i o n of Bennett et a l (1975),, where the c r u s t a l t h i c k n e s s was 56 km. As mentioned.previously, the depth l i m i t s were c a l c u l a t e d under the assumption of a two-layer c r u s t . The a c t u a l c r u s t a l s t r u c t u r e c o u l d i n g e n e r a l vary from the assumed s t r u c t u r e i n three ways: (1) t h e r e might be more than 2 l a y e r s , or (2) the c r u s t a l v e l o c i t i e s might vary l a t e r a l l y , or (3) the c r u s t a l t h i c k n e s s might vary l a t e r a l l y . I f t h e r e are more l a y e r s or i f v e l o c i t i e s change l a t e r a l l y , the c a l c u l a t e d depth l i m i t s remain v a l i d upper and lower bounds f o r the c r u s t a l t h i c k n e s s ; t h i s i s because i t i s s t i l l u n l i k e l y that the a c t u a l v e l o c i t i e s w i l l l i e 33 T 1 1 1 1 r J i i 1 1 1 1 i J 0 10 2 0 3 0 40 5 0 6 0 70 BO D E P T H ( K M ) T 1 1 1 1 r 1^ 1 1 1 I I I I I 1_ I <=* - 5 0 100 1 5 0 2 0 0 2 5 0 3 0 0 3 S 0 4 3 0 4 5 0 5 0 0 D I S T A N C E ( K M ) F i g u r e 10. V e l o c i t y - d e p t h s t r u c t u r e (A) and p-A curves (B) g i v i n g minimum ( s o l i d curves) and maximum (dashed curves) Moho depths, as deduced from P wave r e c o r d s e c t i o n of Eennett et a l (1975) . c r l o l 2 -10 rt S H H -S CJ (!) H -B O C C a H ro ro rt Er c T ; ro H o H B H -• O D J O trt o < ro i— 1 vO -J cn • • O l C O o REDUCED TRAVEL TIME T-D/6.5 (SEC) -6 -4 -2 0 2 4 6 10 12 14 co C D CD CD M C D CDl C O C D l \ J C D C D r o C D a C O X I (-> m C O r o C D C O CD] C O cn CD C O C O o o C D -li. r o o .£> C D J\ C D C D C D O cri o C D cn r o CD cn x i O CO C Q C O " X I C O C O I —• — \r*\/Kj\f\f\ly\^w\r^^ o u t s i d e of the assumed v e l o c i t y l i m i t s . I f the c r u s t a l t h i c k n e s s v a r i e s l a t e r a l l y , the meaning of the depth l i m i t s i s t h a t they r e p r e s e n t bounds on an average c r u s t a l t h i c k n e s s , so t h a t , f o r i n s t a n c e , the c r u s t might be t h i c k e r than the maximum depth l i m i t at some places and t h i n n e r at other p l a c e s . 3 A3 THE S WAVJ IICGBD SEGTIGJSl BAT A ANALYSIS JAIAJ JEESliJiJiLEI S§l§ Beducticn S wave data were a l s o recorded along with P wave data i n the s e i s m i c p r o f i l e of Eennett et a l (1975) . At the s t a r t of the S wave a n a l y s i s , then, much of the i n i t i a l data treatment had a l r e a d y been performed by Bennett (1973), i n the course of c a r r y i n g out t h e i r P wave i n t e r p r e t a i q n s . For example, the data was i n d i g i t i z e d and demultiplexed form, with the a v a i l a b l e components f o r each s i t e p l u s a time channel s t o r e d on d i g i t a l tape . O r i g i n times, shot l o c a t i o n s and s i t e l o c a t i o n s had been determined. As w e l l , i n i t i a l amplitude f a c t o r s based on a m p l i f i e r s e t t i n g s and v e l o c i t y s e n s i t i v i t y curves had been c a l c u l a t e d . . In g e n e r a l / t h e r e l a t i v e v a r i a t i o n of S amplitudes from shot to shot was about the same as f o r P amplitudes, with the S being approximately 1.5 times larger..However, a n o t i c e a b l e e x c e p t i o n was shot 8, where the S was 3 times l a r g e r . T h i s was probably due to a source e f f e c t . Thus, the shot f a c t o r s which were determined i n the P wave a n a l y s i s of Bennett e t a l (1975) had t o be r e c a l c u l a t e d , s i n c e S wave amplitudes were l a r g e r than P wave amplitudes. The shot f a c t o r c o r r e c t s f o r v a r i a t i o n s i n s i g n a l amplitude due t o 36 d i f f e r e n t shot s i z e s , a c c o r d i n g l y , the maximum S wave amplitudes were pi c k e d on records from the Canadian Standard Seismograph Network s t a t i o n PNT and used as the shot f a c t o r s . T h e r e a f t e r , power s p e c t r a were c a l c u l a t e d f o r a few seconds of the S wave data and compared with t h e s p e c t r a o f background nois e p r i o r to the f i r s t P wave onset. The spectra.showed t h a t the dominant s i g n a l f r e q u e n c i e s were g e n e r a l l y between 1 and 3 Hz, and so nois e o u t s i d e t h i s freguency band was atte n u a t e d by a f o u r t h - o r d e r zero-phase Butterworth bandpass f i l t e r . The S wave f r e g u e n c i e s were s m a l l e r than the P wave f r e g u e n c i e s f o r the same sh o t : P wave energy u s u a l l y l a y i n the range from 2 t o 4 Hz. 3*.3±2 p o l a r i z a t i o n f i l t e r i n g Both compressional and shear wave motion are c h a r a c t e r i z e d by t h e i r r e c t i l i n e a r p o l a r i z a t i o n . To enhance the shear wave motion, a p o l a r i z a t i o n f i l t e r was used which enhanced not j u s t r e c t i l i n e a r l y p o l a r i z e d motion; but motion which was r e c t i l i n e a r i n a p a r t i c u l a r d i r e c t i o n i n space. Passing only r e c t i l i n e a r motion thereby attenuated e l l i p t i c a l l y p o l a r i z e d and random no i s e . In a d d i t i o n , ' t u n i n g ' the f i l t e r to the d i r e c t i o n o f the SV motion attenuated P motion and s i g n a l - g e n e r a t e d noise (such as r e f l e c t i o n s or r e f r a c t i o n s from ne a r - s u r f a c e d i s c o n t i n u i t i e s ) . For the Bocky Mountain Trench S wave data, only v e r t i c a l and r a d i a l components were used i n the p o l a r i z a t i o n f i l t e r i n g . T h i s was because only 18 s i t e s r e c o r d e d the t r a n s v e r s e component along with the v e r t i c a l and r a d i a l , while 24 s i t e s recorded both 37 v e r t i c a l and r a d i a l . P r i o r to the p o l a r i z a t i o n f i l t e r i n g , the propagation d i r e c t i o n of the i n c i d e n t s e i s m i c wave was determined. P a r t i c l e motion diagrams were made i n the v e r t i c a l - r a d i a l plane over approximately 1.5 s a f t e r the f i r s t P a r r i v a l . The angles of i n c i d e n c e c f the waves-and estimates of the corresponding e r r o r were measured d i r e c t l y on the p a r t i c l e motion diagrams and are o shown i n F i g u r e 12. The average angle of i n c i d e n c e i s 46.5 . However, the angle v a r i e s from 24° t o 62° and t h e r e appears t o be no r e g u l a r v a r i a t i o n i n the angle as the -distance from the shot i s i n c r e a s e d , T h i s i s probably because the i n c i d e n t angle depends very s t r o n g l y on the near s u r f a c e l a y e r which can vary c o n s i d e r a b l y from s i t e to s i t e . Using the measured angles of i n c i d e n c e , the v e r t i c a l and r a d i a l components were r o t a t e d so t h a t the new r a d i a l d i r e c t i o n was d e f i n e d by the d i r e c t i o n of P motion and the new v e r t i c a l d i r e c t i o n was d e f i n e d as p e r p e n d i c u l a r to the P d i r e c t i o n . , I n r o t a t i n g the e n t i r e r e c o r d with the angle of i n c i d e n c e measured from the f i r s t P motion, i t i s assumed t h a t l a t e r P a r r i v a l s have the same d i r e c t i o n as the f i r s t and t h a t SV motion i s p e r p e n d i c u l a r to t h i s d i r e c t i o n . A p o l a r i z a t i o n f i l t e r , s i m i l a r to t h a t d e s c r i b e d by F l i n n (1965), M o n t a l b e t t i and Kahasewich (1970) and Souriau and veinante (19.75), was then a p p l i e d to the new v e r t i c a l and r a d i a l components. The f i l t e r uses a p r i n c i p a l component technigue to determine the p r i n c i p a l axes of the p a r t i c l e motion and t h e i r d i r e c t i o n s i n space at d i f f e r e n t times along the r e c o r d (see Appendix 4). F i g u r e 13 i s an example of the use of the p o l a r i z a t i o n 6 0 LU Q S40-z LU 9 u LL o LU _ l CD z < 2 0 AZ A3 B3 CI3 C4 BI3 B/2 4 A4 A6 A5 cz I -r C5 B4 BZ I CG A7 B5 CIZ A8 B8 AI3 All v e r t r a d 1 0 0 2 0 0 3 0 0 D I S T A N C E ( K M ) 4 0 0 5 0 0 Figure 12. Angles of incidence of seismic energy as measured' from p a r t i c l e motion diagrams. BRNDPRSS FILTERED 3 9 F i g u r e 13..Seismic s i g n a l at C5 b e f o r e and a f t e r p o l a r i z a t i o n f i l t e r i n g . 40 f i l t e r a t s i t e C5. The upper two t r a c e s are the o r i g i n a l bandpass f i l t e r e d v e r t i c a l and r a d i a l components. The f i r s t l a r g e amplitude a r r i v a l , at about 2 s a f t e r the beginning of the t r a c e , i s v e r y probably a * g l i t c h ' due to a s p u r i o u s s i g n a l i n the system i n s t r u m e n t a t i o n ; the g l i t c h i s even more obvious on the t r a n s v e r s e component, not shown here.,The lower two t r a c e s i n F i g u r e 13 are the r o t a t e d v e r t i c a l and r a d i a l , a f t e r p o l a r i z a t i o n ' f i l t e r i n g - . h a s been a p p l i e d . Note that because of the r o t a t i o n , the v e r t i c a l now c o n t a i n s some of the high frequency s i g n a l from the g l i t c h on the r a d i a l . More important, i t should be noted t h a t the a r r i v a l at about 5 s on the r o t a t e d v e r t i c a l (which c o n t a i n s only SV motion) i s g r e a t l y enhanced r e l a t i v e t o the ether p a r t s of the r e c o r d . Hence, t h i s a r r i v a l i s i d e n t i f i e d as the f i r s t s i g n i f i c a n t SV a r r i v a l . The energy . before 5 s i s then mostly P energy, as evidenced by the l a r g e amplitudes on the r o t a t e d r a d i a l component. 1 I i i 31J' J J M l BECGHD SJCTIGNJl I S H I f 1ITAIION 3x4^1 General Features Cf The jRecprd S e c t i o n s F i g u r e s 14 to 17 show r e c o r d s e c t i o n s normalized f o r instrument response and shot s i z e and reduced to a v e l o c i t y of 3.5 km/s. F i g u r e s 14, 15 and 16 are the v e r t i c a l , r a d i a l and t r a n s v e r s e bandpass f i l t e r e d s e c t i o n s . F i g u r e 17 i s the r o t a t e d v e r t i c a l p o l a r i z a t i o n f i l t e r e d s e c t i o n , f o r which.SV motion only has been p a s s e d . J S i n c e only 24 s i t e s recorded both v e r t i c a l and r a d i a l components, on l y 24 of the t r a c e s i n Figure 17 are p o l a r i z a t i o n f i l t e r e d ; the remaining t r a c e s are the 20 bandpass CM I CJ UJ LO OO CMf \ a i CML I Q CD[ UJ I CJ ZD a UJ COL cc i fM l i i to I A3 B2 C 1 3 C 1 2 R4 B5 C5 H5 T f l l l TR13 CU13 B8 TH1! TH9 R12 _j • i i i _ i i l i i_ 40 F i g u r e 80 120 160 200 240 280 320 DISTANCE (KM) 360 400 440 480 520 14. V e r t i c a l component bandpass f i l t e r e d record s e c t i o n , with d i s t a n c e squared c o r r e c t i o n for geometrical spreading. I CDl A3 82 CI 3 CI 2 A4 B5 C5 fl5 C7 RI2 _ i I I l _ 40 80 120 160 200 240 280 320 - - • • DISTANCE (KM) 360 400 440 480 520 £ ] 3 F i g u r e 15. R a d i a l component bandpass, f i l t e r e d r e c o r d s e c t i o n , with d i s t a n c e squared c o r r e c t i o n f o r g e o m e t r i c a l s p r e a d i n g . N3 c 1-1 CTv o o HI 1-1 t-I (u n a (D CO o < r t ft) H * O D f-h O o o i-! a B 3 a. I—1 T ) X! (/) n iD h-h CD H -Ch (-> r t 3 (I .o r-i • (D P i t i rt) O O r l P i to ft) n r t H " O 3 r t XT 3 O -4 REDUCED TRAVEL TIME T-D/3.5 (SEC) -2 0 2 4 6 8 ro o CD CD 8 roh. CO —i X) ro c\ir a i rs iL i S T 1 cc a C D L U J I o 3 > a U J col cc I i I to | I 2 o A12 Figure 40 17 . _ i I i i _ 80 120 160 200 360 400 440 480 J1J3 520 240 280 320 DISTANCE (KM) Rotated v e r t i c a l p o l a r i z a t i o n f i l t e r e d s e c t i o n , containing SV motion onl y , p l o t t e d with distance squared c o r r e c t i o n for geometrical spreading, 4 > 45 f i l t e r e d v e r t i c a l r e c o r d s obtained from the Mica a r r a y . Each r e c o r d on F i g u r e s 14, 15 and 17 was m u l t i p l i e d by r 2 , where r i s the e p i c e n t r a l d i s t a n c e f o r the s i t e . T h i s c o r r e c t e d f o r geo m e t r i c a l spreading of the head wave , and so enhanced the s m a l l a r r i v a l s at l a r g e d i s t a n c e s . The t r a n s v e r s e s e c t i o n ( f i g u r e 16) i s p l o t t e d with no such c o r r e c t i o n f o r spreading. The bandpass f i l t e r e d v e r t i c a l and r a d i a l s e c t i o n s (Figures 14 and 15) are i n c l u d e d p r i m a r i l y f o r completeness i n the p r e s e n t a t i o n of the data. No i n t e r p r e t a t i o n w i l l be made from them. However, s i n c e the p o l a r i z a t i o n f i l t e r i s a n o n - l i n e a r f i l t e r and n o n - l i n e a r o p e r a t i o n s can d i s t o r t s i g n a l waveforms, the o r i g i n a l bandpass f i l t e r e d r e c o r d s are i n c l u d e d f o r comparison purposes. , The f o l l o w i n g f e a t u r e s are noteworthy: (1) On a l l r e c o r d s e c t i o n s , t h e r e i s a general i n c r e a s e i n amplitudes s t a r t i n g at a reduced t r a v e l time o f about 0 s. The i n c r e a s e suggests the a r r i v a l of S phases. However, i t i s d i f f i c u l t to p i c k many phases t h a t are coherent over s e v e r a l r e c o r d s , and t h i s f a c t must be kept i n mind when c o n s i d e r i n g the s i g n i f i c a n c e of the r e s u l t s from the S wave analyses. ,• (2) In the r e g i o n from 200 t o 280 km on the SV-only s e c t i o n (Figure 17), the f i r s t major SV a r r i v a l s have been i n t e r p r e t e d as the wide-angle r e f l e c t i o n s from the Moho..Records f o r t h i s d i s t a n c e range from the bandpass f i l t e r e d r e c o r d s e c t i o n and from the p o l a r i z a t i o n f i l t e r e d SV s e c t i o n are reproduced i n Fi g u r e 18, and we see here the most n o t i c e a b l e e f f e c t of the p o l a r i z a t i o n f i l t e r i n g . On the bandpass s e c t i o n the f i r s t l a r g e , a r r i v a l i s around 3 s, while i n the SV s e c t i o n the f i r s t a r r i v a l c t-i CD CD CD O O n O rt n H-L I W CD n o r t H> H * O 3 < CD to n r t O 0) o o a r t M H* tr 3 ai H - 3 3 CH fu * (I) H- M CD & 3 D> O i 3 >o W I—1 < CD I O H 3 CD ( - ' H i - * : CD 73 O O r t H -O 3 0) r l to N H i H O 3 O tr O r t H -O 3. H> H * I—' r t CD t i CD p . - i REDUCED TRAVEL TIME T - D / 3 . 5 1 3 5 7 (SEC; C D O a V — I CO —I J D ZZL O m M •Z2 CO ^ a r o c o o - 1 CO o a i—i CO —I H J -z. O m c o 2 o CO a CD J D a X ) co m rn rn 73 9 C 3 I — X ) a rn TO m a cn 9* 47 i s at about 5 to 6 s . T h i s i s e s p e c i a l l y prominent f o r s i t e s C4, C5, and AS, although r e c o r d B5 i s a n o t i c e a b l e e x c e p t i o n . That i s , the f i r s t l a r g e a r r i v a l on t h i s p o r t i o n of the bandpass s e c t i o n i s a c t u a l l y P motion, p o s s i b l y an upper c r u s t a l S t o P c o n v e r s i o n of the Moho wide angle r e f l e c t i o n S waves. Thus, the p o l a r i z a t i o n f i l t e r i n g has attenuated the P motion so t h a t the S waves, which are almost b u r i e d i n the P waves, are enhanced. (3) On the bandpass f i l t e r e d t r a n s v e r s e s e c t i o n (Figure 16) , a phase can be picked having an a r r i v a l time of about 1 s over the d i s t a n c e range from 80 to 130 km. I t s apparent v e l o c i t y i s 3.5 km/s. The j u s t i f i c a t i o n f o r p i c k i n g the phase i s not s t r o n g , a r i s i n g mainly from the very c l e a r a r r i v a l at s i t e E3, the suggestion of a c h a r a c t e r change a t s i t e A3, and the freguency change (to lower f r e g u e n c i e s ) at s i t e A2. Evidence f o r t h i s phase i s a l s o seen on the v e r t i c a l SV-only s e c t i o n (Figure 17) , where there i s a s m a l l a r r i v a l at about 1 s f o r s i t e s A3, B2, and A2. The phase has been i n t e r p r e t e d as the Sg a r r i v a l from the top of the Precambrian basement. I t i s the S wave e g u i v a l e n t of the Pg phase picked by Bennett e t a l (1975), which had a v e l o c i t y of 6.5 km/s. (4) Cn the SV-only s e c t i o n (Figure 17) th e r e i s (very weak) evidence f o r a Sn phase, the shear head wave along the Moho. The j u s t i f i c a t i o n f o r the i d e n t i f i c a t i o n o f the phase comes p r i m a r i l y from the Mica r e c o r d s , which could not be p o l a r i z a t i o n f i l t e r e d . I n s p e c t i o n of the r e c o r d s e c t i o n i n d i c a t e s t h a t the Sn branch might p o s s i b l y l i e along one of two l i n e s : one j o i n s the i n c r e a s e i n amplitude on record.B6 with t h e . i n c r e a s e on C09; the other connects the i n c r e a s e s i n amplitudes f o r r e c o r d s TA11, TA9 48 and the DA group at 370 km. The corresponding apparent v e l o c i t i e s are-4.5 km/s and 4,2 k/s; the p i c k s f o r the 4.5 km/s phase appear s l i g h t l y mere r e l i a b l e than f o r the 4.2 km/s phase., (5) Cn the bandpass v e r t i c a l s e c t i o n (Figure 14) and the SV-only s e c t i o n (Figure 17), the most prominent a r r i v a l s from s i t e s A8 to A13 a c t u a l l y occur s e v e r a l seconds l a t e r than the phase i d e n t i f i e d as Sn. On Figure 17, these l a r g e a r r i v a l s f a l l along a l i n e from A8 at about 0.5 s to .A 1.3 at -2 s, and so have an apparent v e l o c i t y of 3.7 km/s. No i n t e r p r e t a t i o n of t h i s phase was made. I t was not thought to be a basement a r r i v a l because the amplitudes were too l a r g e c o n s i d e r i n g the d i s t a n c e from the shot p o i n t s , and i t was not thought t o be a Moho r e f r a c t i o n because i t s v e l o c i t y was too s m a l l and t r a v e l times too l a t e . 3±H±2 S t r u c t u r e Based On Shear Have -••Arrivals Where both P and S wave data are a v a i l a b l e , the i n t e r p r e t e d l a y e r t h i c k n e s s e s and depths f o r both P and S v e l o c i t y models should be the same. In the Bocky Mountain Trench s e i s m i c survey, the q u a l i t y of the P wave data i s much b e t t e r than that of the S wave data. Thus, i n t e r p r e t a t i o n s of the S wave data are s t r o n g l y c o n s t r a i n e d by the e x i s t i n g i n t e r p r e t a t i o n s of the P wave data. In p a r t i c u l a r , two types of models are considered i n the S i n t e r p r e t a t i o n , each t r y i n g to be c o n s i s t e n t with the time delay prominent on the Pg branch of the P wave r e c o r d s e c t i o n , ,In the f i r s t , c r u s t a l low v e l o c i t y zones are present beneath the : Precambrian basement and beneath the Moho. In the second, the basement i s assumed t o disappear west of the t r e n c h ; f o r t h i s 49 c a s e , the i n t e r p r e t a t i o n i s concerned with d i s c u s s i n g depth l i m i t s f o r the Moho and corresponding l i m i t s f o r the Sn v e l o c i t y . In e i t h e r i n t e r p r e t a t i o n o f the S save data, we can o b t a i n approximate expected values f o r the S v e l o c i t i e s from the P wave v e l o c i t i e s measured by Eennett e t a l (1975) . ,Compressional and shear v e l o c i t i e s are r e l a t e d by Poisson's r a t i o ; the r a t i o may be expressed as C F = (cxx-2 ^) /2 (d - ^) , where o/ and (3 are P and S v e l o c i t i e s , r e s p e c t i v e l y . , F o r most rocks of the E a r t h , Poisson's r e l a t i o n , which says t h a t cr = 0. 25 or t h a t cx = J3^0 i s approximately t r u e . /Thus, given P v e l o c i t i e s of 6.5 km/s at the basement and 8.2 km/s at the Moho, the corresponding S v e l o c i t i e s expected are 3.75 km/s and 4.73 km/s. 3.4.2a Low v e l o c i t y zone s t r u c t u r e The i n t e r p r e t a t i o n , t e c h n i g u e i n v o l v e d the use of the . program HEGLTZ, as with the P interpretation.,,The Sn v e l o c i t y was chosen to be 4.5 km/s , because t h i s v e l o c i t y was based on s l i g h t l y more r e l i a b l e p i c k s than those f o r the 4.2 km/sec phase, and because a 4.2 km/s Moho v e l o c i t y was anomalously low when compared with the S v e l o c i t y d e r i v e d from a P o i s s o n * s r a t i o of 0.25. The remaining S v e l o c i t i e s f o r the c r u s t a l l a y e r were determined by u t i l i z i n g the c o n s t r a i n t s t h a t (1) the depths to the basement, to the low v e l o c i t y zone and to the Moho were f i x e d by the P wave model, (2) the c o r r e c t t r a v e l times f o r the S wave Moho wide angle r e f l e c t i o n branch had to be s a t i s i f i e d , and (3) the Sg branch should have a reduced t r a v e l time of about 1 s. In order to s a t i s f y the above c o n s t r a i n t s , the time delay 50 caused by the sub-basement low v e l o c i t y zone was found t o be 2.2 s; i n comparison, the corresponding time delay on the P wave r e c o r d s e c t i o n was 1.7 s. The det e r m i n a t i o n of the time delay f o r the sub-Moho low v e l o c i t y zone was r a t h e r a r b i t r a r y , because of the poor p i c k s f o r the Sn phase; the delay on the P wave rec o r d s e c t i o n was 0.5 s , so the delay f o r S data was chosen to be 0.8 s. As given by the dash-dotted l i n e : i n F i g u r e 19, the t r a v e l time curve f o r the low v e l o c i t y zone i n t e r p r e t a t i o n i s superimposed on the SV only record s e c t i o n . , A s can be seen, good f i t s were obtained f o r the Sg branch before 150 km and f o r the Moho r e f l e c t i o n branch. The corresponding v e l o c i t y - d e p t h s t r u c t u r e f o r the S low v e l o c i t y zone i n t e r p r e t a t i o n i s given by the s o l i d l i n e i n F i g u r e 20a; the dashed l i n e i n t h i s p l o t shows a P wave low v e l o c i t y zone model obtained by Bennett e t a l (1975) . ; I n the S model> the v e l o c i t y i n c r e a s e s from 3.3 km/s near the s u r f a c e to 3.5 km/s at a depth of 6 km (the Precambrian basement) . .The.' low v e l o c i t y zone 3 km beneath the basement has a v e l o c i t y of 3.3 km/s, and t h i s v e l o c i t y i n c r e a s e s t o 4.5 km/s at a depth of 56 km (the Moho). The low v e l o c i t y zone 7 km beneath the Moho has a v e l o c i t y of 4.35 km/s. The f i g u r e s i n br a c k e t s are the values f o r P o i s s c n ' s r a t i o f o r the d i f f e r e n t l a y e r s . ., 3.4.2b Depth l i m i t s f o r the Moho and Sn v e l o c i t y l i m i t s Se can determine l i m i t s on the c r u s t a l t h i c k n e s s i f we ign o r e d e t a i l e d c r u s t a l s t r u c t u r e and assume t h a t the c r u s t a l branches on the s e i s m i c s e c t i o n are completely missing. In t h i s extremal a n a l y s i s , a two-layer c r u s t i s assumed. Maximum and 51 Figure 19. F i t of t r a v e l times to SV-only record section. Dash-dotted l i n e i s t r a v e l time curve for low velocity zone interpretation. Dashed i s t r a v e l time curve corresponding to Moho minimum depth, and s o l i d l i n e i s curve corresponding to Moho maximum depth. DISTANCE (KM) 53 Figure 20a. Velocity-depth structures for low velocity zone interpretation. Dashed l i n e i s P wave interpretation of Bennett et a l (1975) . Solid l i n e i s S wave interpretation deduced from S wave record section with the constraint that layer thicknesses and depths are the same as for the P wave interpretation. Numbers i n parentheses are Poisson's r a t i o s for the layers. Figure 20b. Velocity-depth structures for minimum Moho depth (dashed curve) and maximum Moho depth (solid curve), as deduced from S wave record section. 55 minimum t h i c k n e s s e s of the upper l a y e r were taken to be the same as i n the P wave a n a l y s i s . Since no S wave s t u d i e s had been performed i n the Canadian C o r d i l l e r a , S wave v e l o c i t y l i m i t s f o r ( the c r u s t a l l a y e r s were determined from the P wave v e l o c i t y l i m i t s , by assuming a Poisson's r a t i o of 0.25. Unlike the Pn v e l o c i t y i n the P wave a n a l y s i s , however, the Sn v e l o c i t y was not w e l l d e f i n e d . N e v e r t h e l e s s , the extremal technigue e a s i l y accommodated t h i s d i f f e r e n c e : the maximum Sn v e l o c i t y determined from the r e c o r d s e c t i o n (4.5 km/s) was used t o produce the maximum depth, and the minimum Sn v e l o c i t y (4.2 km/s) was used to produce the minimum depth. In F i g u r e s 19 and 20 are al s o presented the r e s u l t s of determining Moho depth l i m i t s i n the manner o u t l i n e d i n Appendix 2./These were found using shear wave data alone; t h a t i s , they are independent of the P wave record s e c t i o n . -The s o l i d l i n e i n F i g u r e 19 shows the t r a v e l time curve corresponding t o the maximum Moho depths and the dashed l i n e shows the t r a v e l time curve c o r r e s p o n d i n g to the minimum depth. Only the Moho r e f r a c t i o n and r e f l e c t i o n branches of the t r a v e l time curves are presented; the omitted c r u s t a l branches are only s i g n i f i c a n t i n t h a t the v e l o c i t i e s c orresponding t o these tranches r e p r e s e n t the upper and lower l i m i t s chosen f o r the l a y e r s . The major r e s u l t o f the extremal a n a l y s i s i s gi v e n by the s o l i d and dashed l i n e s on the v e l o c i t y - d e p t h p l o t (Figure 20b): the Moho depth l i m i t s , as obtained from the S wave i n f o r m a t i o n alone, are 47 km and 59 km. 56 ik,filSGOSSION HJLI IQiMUQM. JSl 3SJ 1B E N C H BY B I O C K ZML1M§ Near-surface f e a t u r e s of the Becky Mountain Trench near Badium have been determined from a d e t a i l e d g r a v i t y survey..The most prominent f e a t u r e i s an 8 km wide bedrock t r e n c h which i s estimated to be about 5 5 0 m deep to the north of Badium and 4 2 0 m deep to the south, and which i s f i l l e d with u n c o n s o l i d a t e d Cenozoic sediments. The presence o f the deep bedrock t r e n c h c o u l d be due t o block f a u l t i n g which, i n the t e c t o n i c model of the C o r d i l l e r a , was r e l a t e d to Cenozoic northeastward e x t e n s i o n i n the c r u s t (Wheeler and G a b r i e l s e , 1 9 7 2 ). The change i n depth of the t r e n c h at Badium i n d i c a t e s t h a t the block to the north has been dewndropped f u r t h e r than the block to the south. Other evidence a l s o e x i s t s f o r block f a u l t i n g i n the southern p a r t cf the t r e n c h . The g r a v i t y r e s u l t s of Garland e t a l ( 1 9 6 1 ) i n d i c a t e d t h r e e s e d i m e n t - f i l l e d b a s i n s i n the t r e n c h between l a t i t u d e s 4 9 A 1 0 ' N and 4 9 ° 4 0 « N ; from north to south, the depth of the b a s i n s are 4 2 5 m, 7 0 0 m, and 9 0 0 - 1 3 0 0 m. In s e i s m i c p r o f i l e s a c r o s s the t r e n c h near 4 9 ° 1 5 ' N , Lamb and Smith ( 1 9 6 2 ) found that the depth t o bedrock i s a c t u a l l y about 1 5 0 0 m. Leech ( 1 9 6 6 ) c i t e d the above r e s u l t s of deep bedrock depressions along with other g e o l o g i c a l evidence as support f o r h a l f - g r a b e n f a u l t i n g i n the southern t r e n c h at a normal f a u l t on the e a s t e r n m a r g i n . / F i n a l l y , Clague ( 1 9 7 4 ) has analysed Miocene s i l t s i n the southern t r e n c h and proposed that major block f a u l t i n g had already occurred by Miocene time, although 6 0 0 m of displacement on the e a s t boundary f a u l t o c c u r r e d a f t e r Miocene. 57 Leech (1965) suggests t h a t block f a u l t i n g took p l a c e only south of the Windermere s e c t i o n of the t r e n c h . However, from the r e s u l t s of the present g r a v i t y survey, i t i s proposed t h a t block f a u l t i n g o c c u r r e d at l e a s t as f a r north as S p i l l i m a c h e e n . iU2 CROSTAL 1 J I G K N E S S From the Bocky Mountain Trench s e i s m i c data, l i m i t s have been c a l c u l a t e d f o r the depth t o t h e Moho beneath the t r e n c h . . A n a l y s i s of the P wave data i n d i c a t e d t h at the c r u s t a l t h i c k n e s s i s between 52 km and 60 km. A s i m i l a r a n a l y s i s of the S wave data suggested t h a t the t h i c k n e s s i s between 47 km and 59 km. The P wave and S wave r e s u l t s are c o n s i s t e n t with each other; i t should be noted, however, that more emphasis should be placed on the P wave r e s u l t s because of the poorer g u a l i t y of the S wave data. 1 The r e s u l t s of the Bocky Mountain Trench survey p r o v i d e the most d i r e c t support f o r a t h i c k c r u s t beneath the t r e n c h . Other g e o p h y s i c a l surveys which have been c a r r i e d out across or nearby the t r e n c h are a l s o i n general agreement with such a t h i c k c r u s t . The l a r g e s c a l e g r a v i t y p r o f i l e a c r o s s the C o r d i l l e r a of Stacey (1972) produced models i n which the c r u s t a l t h i c k n e s s beneath the Rockies was about 60 km. As w e l l , the geomagnetic depth sounding p r o f i l e across the t r e n c h of Dragert (1973) r e g u i r e d a h i g h l y conductive l a y e r e a s t of the trench a t a depth of 40-50 km. In a s e i s m i c r e f r a c t i o n survey across the tr e n c h and east i n t o A l b e r t a , Chandra and Cumming (1972) found t h a t the depth to the Moho under the trench i s about 49 km. Berry and 58 F o r s y t h (1975) have s y n t h e s i z e d the r e s u l t s of s e v e r a l s e i s m i c r e f r a c t i o n surveys i n regions west of the Bocky Mountain Trench at the western edge of the omineca B e l t , they obtained a c r u s t a l t h i c k n e s s of about 37 km, with a g e n e r a l trend of t h i c k e n i n g toward the t r e n c h ; a t Greenbush Lake, 100 -km west of the t r e n c h , they estimated c r u s t a l t h i c k n e s s as 40 km. Hx» CBSSTAL SfBOGTUBE The Bocky Mountain Trench S wave s e i s m i c data have provided weak evidence f o r a basement r e f r a c t o r v e l o c i t y of 3.5 km/s and a Moho r e f r a c t o r v e l o c i t y of 4.2-4.5 km/s; these correspond to Poisson's r a t i o s of 0.30 and 0.28-0.32. The S wave data are a l s o c o n s i s t e n t with the low v e l o c i t y zone i n t e r p r e t a t i o n of Bennett e t a l (1975) . I n t h i s case, sub-basement and sub-Moho low v e l o c i t y zones have S wave v e l o c i t i e s o f 3.3 km/s and'4.35 km/s, r e s p e c t i v e l y , and corresponding Poisson's r a t i o s of 0.26 and 0.27. In g e n e r a l , the Poisson's r a t i o s obtained from the S wave data are higher than the value of 0.25, which i s the approximation o f t e n assumed f o r purposes of computational s i m p l i c i t y . High Poisson's r a t i o s have a l s o been measured i n the r e g i o n of the Hasatch Front by B r a i l e et a l (1974) and K e l l e r et a l (1975). In t h e i r models, the r a t i o v a r i e d between 0.24 and 0.33, which i s s i m i l a r to the v a r i a t i o n f o r the Bocky Mountain Trench survey. However, i n the Wasatch Front surveys, a c r u s t a l low v e l o c i t y zone was obtained f o r which Poisson's r a t i o had a value of 0.31, which i s higher than t h a t f o r the suggested Bocky Mountain Trench c r u s t a l low v e l o c i t y zone . 59 The g r a v i t y i n t e r p r e t a t i o n - and S wave s e i s m i c a n a l y s i s r e p o r t e d i n t h i s t h e s i s have provided a d d i t i o n a l i n f o r m a t i o n on the t h r e e i n t e r p r e t a t i o n s of Bennett e t a l (1975) t o e x p l a i n the time delay i n t h e i r P wave s e i s m i c data.,The i m p l i c a t i o n f o r each of these i n t e r p r e t a t i o n s i s d i s c u s s e d below: (1) The p r o p o s i t i o n of a high angle c r u s t a l f a u l t c r o s s i n g the t r e n c h near Badium i s not supported by the g r a v i t y r e s u l t s . The l a r g e g r a v i t y anomaly expected from such a f a u l t was not observed, and thus the e x i s t e n c e of the f a u l t i s made untenable. , (2) The S wave data are c o n s i s t e n t with t h e i n t e r p r e t a t i o n of a c r u s t a l low v e l o c i t y zone .However, the d i f f i c u l t i e s with t h i s i n t e r p r e t a t i o n d e s c r i b e d by Bennett et a l (1975) - mainly the disagreement of a p o r t i o n of the s y n t h e t i c r e c o r d s e c t i o n with the observed data - s t i l l e x i s t . (3) Extremal a n a l y s i s of the Bocky Mountain Trench s e i s m i c data, which i n d i c a t e s t h a t the c r u s t a l t h i c k n e s s beneath the tr e n c h i s between 47 km and 60 km, can be i n t e r p r e t e d as i n d i r e c t support f o r the hypothesis t h a t the t r e n c h marks the c r a t c n i c boundary, That i s , the t h i c k c r u s t agrees with the s e i s m i c r e s u l t s of Berry and Fors y t h (1975), who f i n d t h a t t h a t the c r u s t t h i c k e n s eastward from the F r a s e r River to the tr e n c h and who suggest t h a t the t h i c k e n i n g i s compatible with an a n c i e n t s l a b subducting near the edge of the Precambrian c r a t o n . 60 5 A SUMJJSY ANjD CONGIOSIOjNS The s e i s m i c r e f r a c t i o n survey and P wave i n t e r p r e t a t i o n o f Bennett et a l (1975) has l e d to two f u r t h e r g e o p h y s i c a l s t u d i e s i n the southern Bocky Mountain Trench . F i r s t , a g r a v i t y survey was c a r r i e d out i n and adjacent to trench near Badium, B.C., t o t e s t the e x i s t e n c e o f a high angle c r u s t a l f a u l t o b l i g u e to the trench near Badium, which was one of three i n t e r p r e t a t i o n s of Bennett et a l (1975) to e x p l a i n a prominent time delay i n the Pg branch of t h e i r s e i s m i c data. Second, an a n a l y s i s was performed of the S Wave data recorded d u r i n g the sei s m i c survey,,In a d d i t i o n , an extremal a n a l y s i s technique was a p p l i e d to the s e i s m i c data, so t h a t depth l i m i t s to the Moho beneath the trench c o u l d be determined. The g r a v i t y and s e i s m i c s t u d i e s have l e d to the f o l l o w i n g c o n c l u s i o n s : (1) There i s no evidence from the g r a v i t y r e s u l t s f o r the high angle c r u s t a l f a u l t c r o s s i n g the tr e n c h near Badium. (2) the g r a v i t y survey i n d i c a t e s a deep bedrock t r e n c h along the len g t h of the Bocky Mountain Trench ..The bedrock t r e n c h , i n which the depth at the deepest p o i n t i s about 550 m to the north of Badium and 420 m to the south, c o u l d be due to block f a u l t i n g . (3) l i m i t s on c r u s t a l t h i c k n e s s along the tr e n c h are 47 km and 60 km. T h i s r e s u l t i s based on extremal a n a l y s i s of r e f l e c t i o n and r e f r a c t i o n branches on l y on both P and S wave re c o r d s e c t i o n s . (4) Although the q u a l i t y c f the S wave data i s poor, t h e r e i s weak evidence suggesting an Sg v e l o c i t y of 3.5 km/s and an Sn 61 v e l o c i t y c f 4.2-4.5 km/s. The corresponding P o i s s o ^ s r a t i o s are 0.30 and 0.28-0.32. Thus, the S wave v e l o c i t i e s are low i n comparison with those c a l c u l a t e d with the approximation t h a t P c i s s o n ' s r a t i o i s 0.25. 2he S wave data are a l s o c o n s i s t e n t with the sub-basement low v e l o c i t y zone i n t e r p r e t a t i o n of Bennett et a l (1975) . , The two a l t e r n a t i v e hypotheses to e x p l a i n the time delay i n the s e i s m i c data must be r e c o n s i d e r e d . .Although the c r u s t a l . 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 i s c o n s i s t e n t with the t r a v e l time analyses of both the P and S wave d a t a , i t i s thought by Bennett e t a l (1975) t o be u n r e a l i s t i c because of the t h i c k n e s s of the zone and the imperfect f i t of the s y n t h e t i c s e c t i o n . Thus, the most a t t r a c t i v e i n t e r p r e t a t i o n i s the p r o p o s i t i o n t h a t the t r e n c h c o i n c i d e s with the western l i m i t of the c r a t o n . , To t e s t the hypothesis t h a t the t r e n c h marks the edge of the c r a t o n , a s e i s m i c r e f l e c t i o n survey across the t r e n c h would be i n f o r m a t i v e . A l i k e l y area to c a r r y out the survey would be around Badium, because t h i s i s the r e g i o n where the s e i s m i c r e f r a c t i o n p r o f i l e of Bennett et a l (1975) entered the t r e n c h and where: t h e i r apparent basem«nt branch disappeared. A u s e f u l r e f l e c t i o n survey could a l s o be c a r r i e d out along a l i n e p a r a l l e l and e a s t of the t r e n c h and along another l i n e p a r a l l e l and west of the t r e n c h . A c o m p l i c a t i o n of i n t e r p r e t i n g s e i s m i c r e s u l t s west of the t r e n c h , i f i n f a c t basement r e f l e c t i o n s were observed t h e r e , would be to decide whether the r e f l e c t i o n s came from the Precambrian c r a t o n i c casement or from the c r y s t a l l i n e P u r c e l l basement (whose sediments were deposited over the edge of the c r a t o n i n l a t e r Precambrian t i m e ) . 62 REFERENCES Ager, CA, 1972. A gravity model for the Guichon Creek batholith. Onpubl, M.Sc. .Thesis, Univ. B r i t i s h Columbia, Vancouver, B r i t i s h Columbia., Bally, A . M . , Gordy, P.L., and Stewart, G.A. 1966. Structure, seismic data and orogenic evolution of Southern Canadian Rocky Mountains. B u l l . Can. Soc. .Petrol* Geol., 14, pp. 337-381. ~ Basham, P. W. 1967. Time domain studies of short period teleseismic P phases. Onpubl. M.Sc. Thesis, Univ. B r i t i s h Columbia, Vancouver, B r i t i s h Columbia. Bennett, G.T. 1973. A seismic r e f r a c t i o n survey along the southern Rocky Mountain Trench. Onpubl. ,M.Sc. Thesis, Univ. B r i t i s h Columbia, Vancouver, B r i t i s h Columbia. Bennett, G,T.# Clowes,- R.M., and E l l i s , R.M. 1975. A seismic r e f r a c t i o n survey along the southern Bocky Mountain Trench, Canada^ B u l l 1 :,Seism. rSocv Am. , 65, pp. 37-54. Berry, M.J. And Forsyth, C.A. 1975. Structure of the Canadian C o r d i l l e r a from seismic r e f r a c t i o n and other data. Can A li. Ji££h S c i i # 12, pp. 182-208. Berry, M,J., Jacoby, W.B;y Niblett, E.B., and Stacey, R.A. 1971. A review of geophysical studies i n the Canadian C o r d i l l e r a . Can.. J t Earth S c i A , 8, pp. 788-801. B r a i l e , 1.8.,, Smith, B. E., Keller, G. B,, Welch, B.M., and Meyer, R.M. 1974. Crustal structure across the Wasatch Front from detailed seismic r e f r a c t i o n studies. Geop.hy.Sg. S e s j . , 79, pp. 2669-2677. Campbell, B.B. 1973, Structural cross-section and tectonic model of the southern Canadian C o r d i l l e r a . .-Can,, , J fi -Ear.th Sci^., JO, pp. 1607-1620. Caner, H.B., Auld, D*E., Dragert, H., and Camfield, P. A. 1971. Geomagnetic depth-rsounding and crustal structure in western Canada. J. gegghys. Bes^., 76, pp.7181-7201. Chandra, N.N*# and Cumming, G.L. 1972. Seismic re f r a c t i o n studies i n western Canada. Can. Earth Sci^., 9, pp. . 1099-1109. Clague, J.J. 1974. The St. Eugene formation and the development of the southern Bocky Mountain Trench. ,Ca.nA.J1., Earth S c i . , 11, pp.916-938. Clement, W.G. 1973, Basic p r i n c i p l e s of two-dimensional f i l t e r i n g . Geoghys,. Prose,.» Z l * PP.,125-145, 63 Dempster, A.P. 1969. Elements of Continuous M u l t i v a r i a t e A n a l y s i s . Addison-Wesley, Beading, Mass, Douglas, B.J.W., ed.,1970, Geology and Economic M i n e r a l s of Canada. Canada G e o l A Survey. E c o n ^ G e o l o g y Bepti!f. vNo A ...1 • Dragert, H. 1973, Broad-band geomagnetic depth-sounding along an anomalous p r o f i l e i n the Canadian C o r d i l l e r a , Unpubl.... Ph.D. T h e s i s , Univ. B r i t i s h Columbia., F l i n n , E.A. 1965. S i g n a l a n a l y s i s using r e c t i l i n e a r i t y and d i r e c t i o n of p a r t i c l e motion. l P r g c A I J L E i E i . E x , 5,3, pp., 1874-1876. • F o r s y t h , D.A., B e r r y , M.J., and E l l i s , B. M. 19 74. A r e f r a c t i o n survey a c r o s s the Canadian C o r d i l l e r a at 53 N. £an. J± Sci,., 11, pp. 533-548. Garland, G,D,, Kanasewich, E.B,, and Thompson, T.L.,1961, G r a v i t y measurements over the southern Rocky Mountain Trench area of B.C. , j £ Geojshjrs., Bes^, 66, pp. 2495-2505, Garland, G.D. And Tanner, J.G. 1957, I n v e s t i g a t i o n s of g r a v i t y and i s o s t a c y i n the southern Canadian C o r d i l l e r a , P u b l A SbSi» 11> pp. 169-222. Geodetic Reference System 1967. S p e c i a l P u b l i c a t i o n No. 3, I n t . Assn. Geod., P a r i s , France. Grant, F.S, And West, G.F, 1965, I n t e r p r e t a t i o n Theory i n Applied Geophysics. McGraw-Hill, New York, New York, 584 p. ... Haines, G,V., Hannaford, W,, and Riddihough, R.P, 1971. Magnetic anomalies over B r i t i s h Columbia and the adjacent P a c i f i c Ocean. Can. .. J v E a r t h Sci.., 8, pp. 387-391. Hales, A* L. ...And ' Nation, J.B, 1973, A s e i s m i c r e f r a c t i o n survey i n the Northern Bocky Mountains: More evidence f o r an i n t e r m e d i a t e c r u s t a l l a y e r , Geophys, J f . pp.381-399. Handbook of P h y s i c a l Constants. ,. 1942. ., Geol., ..Soc. v ' A m e r j L'rSgecial £a£§r NOi 36i. Kane, M.F. 1962. A comprehensive system of t e r r a i n c o r r e c t i o n s using a d i g i t a l computer. Geo£hy.sics, 27, pp. 455-462. K e l l e r . , G.R., Smith, R.B., and B r a i l e , L.W. ,1975, C r u s t a l s t r u c t u r e along the Great Basin-Colorado P l a t e a u t r a n s i t i o n from s e i s m i c r e f r a c t i o n s t u d i e s . .J,t. Ge,op.hysA, Bes A , 80, pp. 1093-1098. Lamb, A,T, And Smith,D.W. 1962. R e f r a c t i o n p r o f i l e s over the southern Bocky Mountain Trench area of B.C. J t Alta^. Soc. P e t r o l G e o l i , JO, pp. 428-437. 6.4 Leech, G.B. 1965. D i s c u s s i o n of "the Kocky Mountain Trench .: a problem"„ Can. J - E a r t h S c i . , 2, pp . 4 05-4 10.-Leech, G.B. 1966. The Bocky Mountain Trench , i n I'he Morld r i f t System.. Geol Surv Can.. Pa^er 66-44, pp. 307-329. McMechan, G.A. And Wiggins, R. A. 1972. Depth l i m i t s i n body wave i n v e r s i o n . Geoghys. J . , 28, pp. 459-473. . Monger, G.S-fl., Souther, J.G-, and G a b r i e l s e , H. 1972. E v o l u t i o n of the Canadian C o r d i l l e r a : a p l a t e - t e c t o n i c model. Am. ^ i . S c i . 2 . , 272, pp. 577-602. M o n t a i b e t t i , J . E. And Kanasewich, E.B. ,1970. Enhancement of t e l e s e i s m i c body phases with a p o l a r i z a t i o n f i l t e r . GgQRklSi. d± / 11 * PP • 119-12 9. N e t t l e t o n , L.L. 1971. Elementary G r a v i t y and Magnetics f o r G e o l o g i s t s and S e i s m o l o g i s t s . S o c i e t y of E x p l o r a t i o n G s o p h y s i c i s t s , T u l s a , Oklahoma, 121 p. P r i c e , B.A. .And Mountjoy, E.W. 1970. Ge o l o g i c s t r u c t u r e of the Canadian Bocky Mountains between Bow and Athabasca fiivers. Geol. Assoc. . Canjj.: S|ec. Pa£€r No., f6, pp. 7-25. Beesor, J.E. 1973. Geology of the Lardeau map-area, e a s t - h a l f , B r i t i s h Columbia. Geol.. Surv.- Can.. Memoir 369, 129 p. Souriau, M. And Veinante, J,. I. 1975. Three adaptive f i l t e r s f o r the d e t e c t i o n cf body waves, with a p p l i c a t i o n to deep se i s m i c sounding. Bull.>.Sgisju^ggfia -'A^SL*- -33, pp. 1393-1432. , Stacey, fi.A. 1972. G r a v i t y anomalies, c r u s t a l s t r u c t u r e and p l a t e t e c t o n i c s i n the Canadian C o r d i l l e r a . Cat. J . Earth Sci^., J.0, pp. 615-628. Stacey, B.A. And Stevens, L.E. 1970. Procedures f o r c a l c u l a t i n g t e r r a i n c o r r a c t i o n s f o r g r a v i t y measurements. Publ., Pom. 29, pp. 349-363. Talwani, M., Worzel, J v l . , and Landisman, M. 1959. ,,fiapid g r a v i t y computations f o r two-dimensional bodies with a p p l i c a t i o n to the Mendocino submarine f r a c t u r e zone. J . Geojahys.. Bes., 64, pp. 49-59. ~ Dlrych,T. 1969, Savenumber domain a n a l y s i s and design of p o t e n t i a l f i e l d f i l t e r s . Proceedings of a symposium on d e c i s i o n making i n mineral e x p l o r a t i o n I I . U a a v . B r i t i s h Columbia. 65 Wheeler, J.Q, And Gabrielse, fl. 1372, The Canadian s t r u c t u r a l province, i n Variations i n tectonic styles in Canada* S§2i*; ,kM~>2£s. / C a j J i x S £ § £ J L pp. 1-72. White. W.R.H., Bone, and Milne,, W.G. . 1968. Seismic r e f r a c t i o n surveys in B r i t i s h Columbia- a preliminary interpretation. A j ^ G ^ pp.. 81-93. Wiggins, R.A., McMechan, G.A., and Toksoz, M.N. 1973. Range of earth structure non-unigueness implied by body wave observations. Rev^. Geoghvs. Sgace Phy,s.,' XI* PP- 87-113, APPENDIX J RECALCULATION CF THE FAULT PAEAilETEeS OF EENNETT ET AL J19751 In a s e i s m i c r e f r a c t i o n survey along the southern Rocky Mountain Trench , Bennett et a l (1S75) observed a 1.7 s time delay cn the basement (Pg) branch of t h e i r r e c o r d s e c t i o n ; the v e l o c i t y of the Pg branch was 6.5 km/s, the average v e l o c i t y of the upper c r u s t was assumed to be 5.7 km/s, and the depth t o the basement near the shot p o i n t s was c a l c u l a t e d as 6.5 km. The time delay can be e x p l a i n e d as being due to a f a u l t . . T o determine the f a u l t parameters, t r a v e l times to a given d i s t a n c e are c a l c u l a t e d f o r a model i n which the depth t o the basement i s h Q(=6.5 km) throughout (Model A) and f o r a model i n which the basement i s downfaulted by h km (Model B) . Model A Model B When the ray i n Model B t r a v e l s ( a 2 + h 2) , the r a y i n Model A only t r a v e l s a d i s t a n c e a. Both t r a v e l with a v e l o c i t y V, , so the time d i f f e r e n c e i s AT; = (a.a + hz)"* - a V, Hhen the ray i n Model B t r a v e l s Ax at v e l o c i t y V , , the r a y i n Model A t r a v e l s a d i s t a n c e Aa at v e l o c i t y V, • Thus, the time d i f f e r e n c e i s 67 A"C = - Aa. = h - h tan i f V e V, V 0coo i c V, where i i s the c r i t i c a l angle. Thus, the t o t a l time d i f f e r e n c e between B and A i s 1/2. A f = h - h tan i , + ( a 2 + h 2) - a (1) V.cos i & V, V, From the r e c o r d s e c t i o n of Bennett, et a l (1975), A t = 1.7 s V = 6.5 km/s ' Vo = 5.7 km/s a = 130 km We know th a t f o r a c r i t i c a l l y r e f r a c t e d r a y , s i n i e = V£/V; =5. 7/6. 5, and so ic= 61 . S u b s t i t u t i n g i n t o (1) and s o l v i n g f o r h, we f i n d t h a t the throw of the f a u l t i s h-13 km. That i s , the f a u l t model of Bennett et a l (1975) should have the u p f a u l t bdseiaeiit depth as. 6.5 sm and the do w-n f a u l t depth as 24.5 km. Tiia e r r o r i n the c a l c u l a t i o n s of Bennett et a l (1975) was t h a t the A a p o r t i o n of the path f o r the r a y an Model A was not i n c l u d e d . In the preceding a n a l y s i s , the d i f f e r e n c e i n l e n g t h of the upper l a y e r ray paths has been n e g l e c t e d . In Model A t h e angle of i n c i d e n c e o f the downgcing ray i s the c r i t i c a l a n g l e i . In Model B the angle of i n c i d e n c e i s somewhat l e s s tnan i . However, a d e t a i l e d c a l c u l a t i o n of the l e n g t h of tne co r r e s p o n d i n g ray paths shows that the path l e n g t n s a r e very n e a r l y the same. 68 1!J?IJDIX 2 GBAVITY EBGCJDUfilS JNB DATA FB0GE5SI1JG IJ. Observed Gravity. The observed g r a v i t y g 0 at a d e t a i l s t a t i o n i s determined by t a k i n g the d i f f e r e n c e i n gravimeter readings ( a f t e r compensating f o r gravimeter d r i f t ) between the d e t a i l s t a t i o n and a base s t a t i o n o f the N a t i o n a l G r a v i t y Net of Canada. , Absolute g r a v i t y v a l u e s at the base s t a t i o n s are known, so the a b s o l u t e g r a v i t y value at a d e t a i l s t a t i o n i s then e a s i l y found. I f should be noted t h a t the base s t a t i o n g r a v i t y v a l u e s used i n the survey of t h i s t h e s i s were those of the r e a d j u s t e d N a t i o n a l G r a v i t y Net , which was changed i n May, 1974 so as to be c o n s i s t e n t with the r e c e n t l y adopted I n t e r n a t i o n a l G r a v i t y S t a n d a r d i z a t i o n Net 1971. ; 2± T h e o r e t i c a l G r a v i t y The t h e o r e t i c a l g r a v i t y i s the value of g r a v i t y on the r e f e r e n c e s p h e r o i d , the s u r f a c e which g i v e s the c l o s e s t o v e r a l l f i t to mean sea l e v e l . T h e o r e t i c a l g r a v i t y i s c a l c u a t e d on the b a s i s of the Geodetic Beference System 1967: g t = 978.03185 {1 + 0.005278895sin2^+0.000023462sin*jf>) g a l s , where (p i s the s t a t i o n l a t i t u d e i n degrees. I t should be noted t h a t t h i s formula was adopted f o r use i n Canada i n May, 1974. As one moves toward the p o l e s , g r a v i t y i n c r e a s e s because the e a r t h i s f l a t t e n e d at the p o l e s . The change i n t h e o r e t i c a l g r a v i t y with north-south d i s t a n c e s i s given by Mt - _J Mt ~ 1 dg t ds *" B icp) d

The f i l t e r i n g of a g r a v i t y map g(x,y) can be viewed as the c o n v o l u t i o n of the map with an impulse response f u n c t i o n h (x, y) . The b a s i c procedures i n v o l v e d i n performing a two-dimensional c o n v o l u t i o n are g i v e n by Clement (1S73), along with i n t e r p r e t a t i o n s of the two-dimensional d i s c r e t e F o u r i e r t r a n s f o r m , z-transform and freguency a l i a s i n g . Low pass f i l t e r i n g i s used to remove or i s o l a t e h i g h wavenumber components from the g r a v i t y map. The highest wavenumbers are u s u a l l y due to g e o l o g i c a l , t o p o g r a p h i c a l or i n s t r u m e n t a l n o i s e ; t h a t i s , v a r i a t i o n s due to e r r o r i n r e a d i n g the gravimeter or to l o c a l i z e d geology"or topography surrounding a s t a t i o n have wavelengths l e s s than the s t a t i o n s p a c i n g , and 72 these correspond to very high wavenumbers. The lowest wavenumbers are due to r e g i o n a l or l a r g e s c a l e f e a t u r e s on the map, while intermediate values are a s s o c i a t e d with l o c a l f e a t u r e s . Thus, the c u t o f f wavenumber of the low pass f i l t e r determines the s c a l e of the geology present on the f i l t e r e d map., The f i l t e r may be designed i n a manner d e s c r i b e d by Ul r y c h (1969) .'The c u t o f f wavenumber i s chosen by examining the geology of the r e g i o n i n c o n j u n c t i o n with a power spectrum of the map. A boxcar f u n c t i o n i s formed such that wavenumbers below the c u t o f f are passed with u n i t gain and wavenumbers above the c u t o f f are passed with 0 g a i n . . T h i s boxcar f u n c t i o n i s the i d e a l r e p r e s e n t a t i o n of the f i l t e r i n the wavenumber domain and i t s F o u r i e r transform, which has i n f i n i t e l e n g t h , the i d e a l impulse response f u n c t i o n i n the space domain. ;To smooth the edges of the boxcar and at the same time to form a p r a c t i c a l f i l t e r of f i n i t e l e n g t h , the i d e a l impulse response i s m u l t i p l i e d by a c o s i n e b e l l of the d e s i r e d l e n g t h . The r e s u l t a n t smoothed boxcar i s then normalized such t h a t the maximum gain at wavenumbers (0,0) i s 1.0. As an example of a low pass f i l t e r , the c o e f f i c e n t s of the p r a c t i c a l f i l t e r used on the complete Bouguer anomaly map of Chapter 2 are given i n Table I I I . The g r i d spacing of the map and thus of the f i l t e r i s 1 km; the Nyguist waveumber i s thereby kwy<3=1/2Ax=1/2Ay=0.5 cycles/km., The f i l t e r i s given i n one guadrant o n l y . Since the boxcar i s symmetric i n the wavenumber domain, the f i l t e r f u n c t i o n i s symmetric and so i s r e f l e c t e d i n t o the other guadrants. For a f i l t e r of length 1 a c t i n g on a map of dimensions M*H, the f i l t e r e d map i s s m a l l e r than the in p u t map by L-1 p o i n t s on a l l fable III . n Weighting coefficients of a practical low pass f i l t e r . Cutoff wavenumber i s 0.20 cycles/km; length i s 1=4,. -f-( A x = 1 k m ) 1 h 0. 1747 0. 1112 0.0170 f -0.0064 0.1112 0.1703 0.0104 -0.0036 0.0170 0.0104 0.0014 -0.0003 -0.0064 -0.0036 -0.0003 0.0 edges. Thus, i f the input map i s 50*70 (the dimensions of the Bouguer map in Chapter 2), application of the practical f i l t e r shown above results i n a f i l t e r e d map of dimensions 44*64, 74 APPENDIX 3 IMCHEE5-ijElGLOIZ !J!I<2MI 121 £Jg£ THE DETEJ3JIJATICJJ 01 DEPfH LIMITS Observations concerning the propagation o f s e i s m i c energy are g e n e r a l l y made i n terms of t r a v e l time I t o a d i s t a n c e A . , However, i t i s o f t e n convenient to perform c a l c u l a t i o n s using the ray parameter p, which i s d e f i n e d as the d i s t a n c e d e r i v a t i v e of the t r a v e l time, dT/dA. I t i s a l s o given as p=r*sin i / v , where r i s the d i s t a n c e from the c e n t e r of the e a r t h , i i s the angle between the ray and the r a d i u s v e c t o r and v i s the v e l o c i t y . The t r a v e l time to a d i s t a n c e A 0 can be expressed as I ( A J = f % ( A ) d A = P A + f *A(g) d g (2 .1) = p 0A o + - U ( P o ) where p m a x i s the maximum p value t h a t can be ob t a i n e d and p e i s the ray parameter value at the d i s t a n c e A Q (Higgins et a l , 1973). As shown i n f i g u r e 2 1 , the t r a v e l time i s thus the area., beneath the p - A curve and above the r e f e r e n c e value p P A A = P. A(q)dq =T(p ) Figure] 2 1 . P- curve showing the area which d e f i n e s the time f o r a ray p to t r a v e l a d i s t a n c e . In terms o_f models d i s c u s s e d i n t h i s t h e s i s , 'a 1 r e p r e s e n t s the surface v e l o c i t y branch, • b* the basement wide angle r e f l e c t i o n branch, ' c* the basement r e f r a c t i o n bxanch, 'd* the Moho wide angle r e f l e c t i o n branch and 'e;» the Moho r e f r a c t i o n branch. (area A ) plus the area of the r e c t a n g l e p o A 0 ( area B ). The Wiechert-Herglctz i n t e g r a l provides a means of d i r e c t l y i n v e r t i n g t r a v e l time o b s e r v a t i o n s t o a v e l o c i t y - d e p t h model. I t s form i s . P l » » X A ( g ) d g ( 2 . 2 ) I ^maximum depth curve minimum depth curve A F i g u r e 23. Extremal curves d e f i n e d i n the T-A plane .within the T-A l i m i t envelope. T r a v e l times are shown reduced by a v e l o c i t y 77 20, because of the weighting i n the integ r a n d of e q u a t i o n (2.2). The maximum depth then corresponds to i n t e g r a t i n g as much as p o s s i b l e along the r i g h t hand s i d e of the p -A envelope. However, i f the i n t e g r a t i o n were along the r i g h t hand s i d e f o r the e n t i r e path (path 1 i n F i g u r e 22), the t r a v e l times would be too l a r g e , s i n c e t r a v e l time i s the area under the p-A curve.,Thus at some p o i n t i t i s necessary t c c r o s s over t o the opp o s i t e s i d e o f the envelope, and t h i s c r o s s o v e r should be as f a r away from p 0 as p o s s i b l e (path'2 i n Fig u r e 22). For minimiz a t i o n o f depth, one i n t e g r a t e s over the l e f t hand s i d e of the p -A envelope, u n t i l t r a v e l time r e s t r i c t i o n s f o r c e the path to c r o s s over t o the r i g h t hand s i d e . In p r a c t i c e , the c o n s t r u c t i o n of the p -A envelope, e s p e c i a l l y along any r e f l e c t i o n branches, i s not s t r a i g h t forward* The f o l l o w i n g d i s c u s s i o n g i v e s d e t a i l s of i t s c o n s t r u c t i o n f o r the type of data c o n s i d e r e d i n the main body of the t h e s i s (Chapter 3, p.2. An eigenvalue 1 of a matrix D i s d e f i n e d such that D v = 1 v where v i s an e i g e n v e c t o r of D. For the case where x and y are the v e r t i c a l and r a d i a l components of p a r t i c l e motion, l e t Z2 and 82 r e p r e s e n t the v a r i a n c e s of the v e r t i c a l and r a d i a l , r e s p e c t i v e l y , and ZR the co v a r i a n c e between the two. A l s o l e t 2 =