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Gravity and seismic studies in the southern Rocky Mountain trench Spence, George D. 1976

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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 <o ^  (41 h i ABS!I.fi A CI as one of three e x p l a n a t i o n s of a prominent t i n e d elay i n the 6.5 km/s branch of t h e i r s e i s m i c r e f r a c t i o n survey i n the Rocky Mountain Trench, Eennett et a l (1975) suggested a h i g h -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 Radium. I f the d e n s i t y c o n t r a s t between basement and cover rocks i s 0.1 g/cm 3, a g r a v i t y anomaly of approximately 18 mgal should be observed.„ To t e s t the f a u l t h y p o t h e s i s , a g r a v i t y survey has been c a r r i e d out i n and adjacent to the t r e n c h i n the Radium area. The r e s u l t a n t data are not c o n s i s t e n t with the proposed f a u l t model. The p r i n c i p a l f e a t u r e of the data i s a pronounced low which c o i n c i d e s with the t r e n c h throughout the survey area. The lew i s due to Cenozoic f i l l and i n t e r p r e t a t i o n by two-dimensional modelling i n d i c a t e s the t h i c k n e s s of f i l l i s about 550 m to the north and 420 m to the south of Radium. , An a n a l y s i s has a l s o been performed of the shear-wave data recorded d u r i n g the s e i s m i c survey of Bennett e t a l (1975) . Although the q u a l i t y of the S save data i s poor, they show c o n s i s t e n t behavior with the P save data. There i s weak evidence suggesting 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..The corresponding P o i s s c n ' s r a t i o s are 0.30 and 0.28-0.32. To determine maximum and minimum depth l i m i t s to the Hcho allowed by the s e i s m i c data, an extremal a n a l y s i s was performed on both the P and S wave r e c o r d s e c t i o n s . From the P wave dat a , the l i m i t s on c r u s t a l t h i c k n e s s beneath the Rocky Mountain Trench are 52 km and 60 km; from the S wave data, the l i m i t s are 47 km and 59 km. i i I s a r e s u l t of these a d d i t i o n a l s t u d i e s , the tao a l t e r n a t i v e hypotheses of Bennett e t a l (1975) t o e x p l a 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 . .These are (1) the e x i s t e n c e of a c r u s t a l low v e l o c i t y zone and (2) a major deformation of the basement and o v e r l y i n g rocks due to the t r e n c h being an a n c i e n t zone of weakness which c o i n c i d e s with the western l i m i t of the c o n t i n e n t a l Precambrian c r a t o n . As r e f l e c t i o n s from the top of the low v e l o c i t y zone are not observed by Bennett et a l (1975), the second a l t e r n a t i v e i s p r e f e r r e d . i i i TABLE 0? CONTENTS page ABSTRACT i TABLE OF CONTENTS i i i LIST OF TABLES v LIST OF FIGURES v i ACKNOWLEEGEVENTS v i i i CHAPTER 1. INTRODUCTION 1.1 General D e s c r i p t i o n 1 1.2 Formation of the Trench 2 1.3 The R e f r a c t i o n P r o f i l e and P Save I n t e r p r e t a t i o n cf Bennett e t a l (1975) 4 1.4 Mo t i v a t i o n and O r g a n i z a t i o n of the Th e s i s 10 CHAPTER 2. A GRAVITY TEST FOR A HIGH ANGLE FAULT CROSSING THE ROCKY MOUNTAIN TRENCH. NEAR RADIUM 2.1 G e o l o g i c a l S e t t i n g 2.2 F i e l d Program 2.3 Data Reduction 2.4 I n t e r p r e t a t i o n cf the G r a v i t y Data CHAPTER 3. SEISMIC REFRACTION SURVEY ALONG THE ROCKY MOUNTAIN TRENCH 3.1 Data C o l l e c t i o n 28 3.2 L i m i t s fox C r u s t a l Thickness as Determined from the P Wave Record S e c t i o n of Bennett et a l (1975) 29 3.3 The S Have Record S e c t i o n s : Data A n a l y s i s 35 3.3.1 P r e l i m i n a r y data r e d u c t i o n 35 3.3.2 P o l a r i z a t i o n f i l t e r i n g 36 3.4 The S Have Record S e c t i o n s : I n t e r p r e t a t i o n 40 3.4.1 General f e a t u r e s of the record s e c t i o n s 40 3.4.2 S t r u c t u r e based on shear a r r i v a l s 48 3.4.2a Low v e l o c i t y zone s t r u c t u r e 49 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 50 CHAPTER 4. DISCUSSION 4.1 Formation of the Trench by Block F a u l t i n g 56 4.2 C r n s t a l Thickness 57 4.3 C r u s t a l S t r u c t u r e 58 CHAPTER 5. SUMMARY AND CONCLUSIONS 60 REFERENCES 62 15 18 19 21 APPENDIX 1 RECALCULATION OF THE FAULT. PARAMETERS EENNETT ET AL (1975) . APPENDIX 2 GRAVITY PROCEDURES AND DATA PROCESSING APPENDIX 3 ¥1ECHERT-HERGLOTZ INTEGRATION AND THE DETERMINATION OF DEPTH LIMITS APPENDIX 4 ENHANCEMENT CF SV PHASES BY POLARIZATION FILTERING V LIST Of TABLES Table Page I Average d e n s i t i e s of water s a t u r a t e d rock samples from Radium area 19 I I Seismic c r u s t a l s t r u c t u r e i n the Canadian C o r d i l l e r a 31 I I I Weighting c o e f f i c i e n t s of a p r a c t i c a l low pass f i l t e r 73 v i L I S ! OF FIGURES F i g u r e Page 1 The southern Rocky Mountain Trench , 6 2a 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 f a u l t i n t e r p r e t a t i o n of Bennett et a l (1975) . 9 b 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 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) . 3 Basement f a u l t s t r u c t u r e of Bennett et a l (1975) and corresponding t h e o r e t i c a l g r a v i t y p r o f i l e . 11 4 S wave a r r i v a l s a t s i t e B5. 14 5 Geologic map of Radium area i n southeastern B r i t i s h Columbia. 17 6 Scheme f o r d i g i t i z i n g e l e v a t i o n s used i n t e r r a i n c o r r e c t i o n s . 20 T e r r a i n - c o r r e c t e d Bouguer anomaly g r a v i t y map of Radium area i n southern B r i t i s h Columbia. 23 G r a v i t y p r o f i l e s a c r o s s Rocky Mountain Trench i n Radium area. 24 9 Geologic models based cn g r a v i t y i n t e r p r e t a t i o n f o r the north and south p r o f i l e s shown cn Figure 7., 26 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 - d e l t a curves (B) corresponding to minimum and maximum Mono depths, as deduced from P wave record s e c t i o n . 33 11 Minimum depth and maximum depth t r a v e l time curves on P wave record s e c t i o n . ,, 34 12 Angles of i n c i d e n c e of s e i s m i c energy. 38 13 Seismic s i g n a l at c.5 before 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 . , 39 14 V e r t i c 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 . , 41 15 R a d i a l component bandpass f i l t e r e d r e c o r d section.„ . • 42 16 Transverse component bandpass f i l t e r e d r ecord s e c t i o n with no c o r r e c t i o n f o r geometrical spreading., 43 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 , r e c o r d s e c t i o n , c o n t a i n i n g SV motion only, P o r t i o n s of v e r t i c a l bandpass and SV-only p o l a r i z a t i o n f i l t e r e d r e c o r d s e c t i o n s c o n t a i n i n g wide angle r e f l e c t i o n s from Mono. F i t of t r a v e l times to SV-only r e c o r d s e c t i o n f o r low v e l o c i t y zone i n t e r p r e t a t i o n and Mono extremal depth i n t e r p r e t a t i o n s . , V e l o c i t y - d e p t h s t r u c t u r e s f o r P wave and S wave i n t e r p r e t a t i o n s . V e l o c i t y - d e p t h s t r u c t u r e s corresponding t o minimum and maximum Moho depths, deduced from S wave r e c o r d s e c t i o n . P - d e l t a curve showing the area which d e f i n e s the time f o r a ray p c to t r a v e l a d i s t a n c e A e . The p - d e l t a envelope and paths i n v o l v e d i n the maximization of depth. Extremal curves d e f i n e d i n the T-A plane w i t h i n the T-A l i m i t envelope. , v i i i ACKNOWLEDGEMENTS I would l i k e to thank Drs, R.M. Clowes and R.M. E l l i s f o r t h e i r guidance duri n g t h i s r e s e a r c h p r o j e c t and a l s o f o r t h e i r a d v i c e and a p p r a i s a l during the w r i t i n g of the t h e s i s . A l s o a p p r e c i a t e d are d i s c u s s i o n s with Hat Y e d l i n , Bob Cl a y t o n and John c. Davies, and the help of Ed Haddington and La r r y L i n e s d u r i n g the g r a v i t y f i e l d p r o j e c t . As w e l l , I thank Dr. B.A. l i g g i n s f o r the use of h i s a i e c h e r t - H e r g l o t z program. The loan of Lacoste-Bcmberg gravimeter G88 by the U n i v e r s i t y of Western Ontario i s g r a t e f u l l y acknowledged. The G r a v i t y D i v i s i o n , Earth P h y s i c s Branch provided advice and a s s i s t a n c e a t s e v e r a l stages of the g r a v i t y f i e l d program. T h i s study has been supported by the N a t i o n a l Research C o u n c i l c f Canada Grant A-2617. ( 1. INTRODUCTION 3il GEa-EBai; ;l3lSGRIgT:ION The Bocky Mountain Trench i s a l o n g , narrow intermontane v a l l e y extending approximately 1600 km from Montana to the Yukon. The only break i n i t s c o n t i n u i t y i s a gap of about 160 km near the Big Bend of the Eraser R i v e r ; to the north the trend i s S 33 I and to the south the tr e n d i s M 35 W. Along both the northern and southern s e c t i o n s , the l o c u s of the t r e n c h i s the d i v i d i n g l i n e between the Rocky Mountain Thrust B e l t on the e a s t and the Omineca C r y s t a l l i n e B e l t cn the west. To the e a s t , the Rocky Mountains c o n s i s t mainly of sedimentary, m i o g e o c l i n a l r o c k s . No g r a n i t i c i n t r u s i o n s occur i n the Rockies, and r e g i o n a l metamorphism i s r e s t r i c t e d to a b e l t on the west s i d e of the Rockies between 52°N and 57°N. The c h a r a c t e r i s t i c s t y l e of deformation i s c o n c e n t r i c f o l d i n g and northeastward t h r u s t f a u l t i n g . , I n c o n t r a s t , the mountains i n the Omineca B e l t west of the trench c o n t a i n many metamorphic and i n t r u s i v e rocks and, i n a d d i t i o n , mixed v o l c a n i c s are found. ;The s t r u c t u r a l s t y l e i n the Omineca B e l t , u n l i k e t h a t i n the Rockies, i s complex and l a c k s e a s i l y r e c o g n i z a b l e t r e n d s as a r e s u l t o f the widespread metamorphism, i n t r u s i o n s and deformation., The Rocky Mountain Trench i s a l s o a d i v i d i n g l i n e between s i g n i f i c a n t g e o p h y s i c a l c o n t r a s t s , Haines et a l (1971) showed th a t the trench i s the boundary between broad, high-amplitude aeromagnetic anomalies.to the east and l o n g , narrow n o r t h w e s t e r l y t r e n d i n g anomalies to the west. Geomagnetic data 2 of Caner et a l (1971) and Dragert (1973) indicated a highly conductive lower crust west of the trench in contrast with a r e s i s t i v e lower crust to the east. Stacey (1972) and Berry and Forsyth (1975) interpreted trans-Cordilleran gravity data by using a model of the crust i n which c r u s t a l thickness was controlled by Cordilleran seismic surveys. Their r e s u l t s suggested that density of the crust and/or upper mantle decreases i n the area west of the t r e n C f l » 4 * 2 QI- IJ3.I TRENCH The debate about the o r i g i n of the Rocky Mountain Trench centres mainly on whether i t i s an erosional feature or a str u c t u r a l feature. Controversy arises because the trench may be due to both erosion and str u c t u r a l control, and because di f f e r e n t sections of the trench may have had di f f e r e n t o r i g i n s . For example, there i s strong evidence i n the southern part for block f a u l t i n g along the eastern margin (Leech 1966; Garland et a l , 1961) , while the trench near 52*N i s considered to be an erosional valley excavated along a f a u l t zone (Leech 1966 ) . Some form of s t r u c t u r a l control must c e r t a i n l y be necessary to explain the remarkable length of the trench and to explain the contrasting geological and geophysical c h a r a c t e r i s t i c s across the trench, with the advent of the plate-tectonic model of the Canadian C o r d i l l e r a i n recent years, i t has been proposed that the Rocky Mountain Trench marks the edge of the Precambrian continental craton (Berry et a l , 1971; Monger et a l , 1972; Wheeler and Gabrielse, 1972). In t h i s model, the region above the ancient continental margin i s a major zone of c r u s t a l weakness , and block f a u l t i n g (at l e a s t i n the south) r e s u l t e d when the motion of the P a c i f i c p l a t e changed from subduction t o trans f o r m motion along the Queen C h a r l o t t e - F a i r w e a t h e r F a u l t . G e o l o g i c a l support f o r the t e c t o n i c model and i t s r e l a t e d p r o p o s a l concerning the r o l e o f the t r e n c h has been given by Monger e t a l (1972) and Wheeler and G a b r i e l s e (1972). T h i s model e x p l a i n s the nature of the rocks on d i f f e r e n t s i d e s of the tr e n c h . For example^ many of the sedimentary rocks t o the east are m i o g e o c l i n a l sediments deposited over the edge of the c o n t i n e n t ; the mixed v o l c a n i c s to the west are i s l a n d a r c rocks formed when a p l a t e subducted near the western boundary of the Omineca B e l t ; and b a s a l t and u l t r a m a f i c s west of the Omineca B e l t are oceanic c r u s t a l rocks. The t e c t o n i c model can a l s o e x p l a i n the d i f f e r e n t s t r u c t u r e s across the t r e n c h . That i s , metamorphism and deformation i n the Omineca B e l t o c c u r r e d when a hot, e a s t e r l y - s p r e a d i n g i n f r a s t r u c t u r e was d e f l e c t e d upward at a hinge zone marking the edge of the c r a t o n and l o c a t e d approximately at the present l o c u s of the Rocky Mountain Trench ( P r i c e and Mountjoy, 1970); and the t h r u s t i n g i n the Rockies was caused by the r e l a t e d u p l i f t i n the Omineca B e i t and subseguent g r a v i t a t i o n a l spreading to the e a s t , , G e o p h y s i c a l support f o r the c r a t o n ending at the t r e n c h has been summarized by Berry et a l (1971) . Perhaps the isost d i r e c t evidence i s the c o n t r a s t i n aeromagnetic anomalies a c r o s s the t r e n c h , because-the broad, high amplitude anomalies east of the t r e n c h are c h a r a c t e r i s t i c of S h i e l d r e g i o n s (Haines et a l , 1971). a l s o s i g n i f i c a n t , however, are the l a r g e c o n d u c t i v i t y i n the lower c r u s t (Caner et a l , 1971) and the decreased d e n s i t y i n 4 the c r u s t or upper mantle (Stacey 1972) found west of the t r e n c h . These e f f e c t s are e x p l a i n e d by the presence t h e r e at one time of a subducting s l a b or of o c e a n i c c r u s t : the r e s u l t a n t high temperature and h y d r a t i o n would cause both the i n c r e a s e d c o n d u c t i v i t y and decreased d e n s i t y . However, i t i s by no means completely accepted t h a t the t r e n c h marks the edge.of the Precambrian c r a t o n . In the southern t r e n c h near 49°15*, B a l l y et a l (1966) obtained s e i s m i c r e f l e c t i o n s from beneath the P u r c e l l Mountains , which c o u l d be i n t e r p r e t e d a s c o m i n g from a westerly d i p p i n g basement. /Working i n the n o r t h e r n Columbia Mountains, Campbell (1973) presented arguments that the basement ( e i t h e r c r a t o n i c or P u r c e l l ) has been v e r t i c a l l y u p l i f t e d i n both the Omineca C r y s t a l l i n e B e l t and the main Ranges of the Rocky Mountains. Thus, the i m p l i c a t i o n i s t h a t the Rocky Mountain Trench does not mark a s p e c i a l boundary of e i t h e r u p l i f t or basement* but that the basement was i n v o l v e d i n the deformation f r o n the Omineca B e l t to the f a u l t s s e p a r a t i n g the Main from the Front Ranges. l i l THF REFRlCTICg PROFILE AND P HAVE ISTEBPHET&TIQN Ql 11 J i JJ9751 Upon d i s c o v e r i n g t h a t l a r g e b l a s t s from open p i t c o a l mines near Sparwood (Figure 1) acted as good inexpensive sources of s e i s m i c energy, Bennett e t a l (1975) c a r r i e d out an unreversed s e i s m i c r e f r a c t i o n survey along the southern Rocky Mountain Trench . T h e i r aim, i n view of the c o n t r o v e r s y about the s i g n i f i c a n c e of the t r e n c h , was to o b t a i n i n f o r m a t i o n on the deep s t r u c t u r e i n and adjacent to the trench,/The r e s u l t s of 5 Figure 1. The Southern Bocky Mountain Trench Geologic setting and location of 1972-1973 seismic recording s i t e s (inset a f t e r Douglas 1970) Explanation of symbols: A portable seismic recording system (Kaiser shot only) k portable seismic recording system (Kaiser and Fording shots) © Mica array component shot point • town physiographic outline of trench .«.._,- provincial boundary . — r i v e r 6 7 t h i s study provided the major m o t i v a t i o n f o r t h e present t h e s i s , and so are reviewed i n d e t a i l . The l o c a t i o n s of shot p o i n t s and r e c o r d i n g s i t e s are shown i n F i g u r e 1. The p r o f i l e ran from 80 km to 540 km from the shot p o i n t s a t the K a i s e r and Fording open p i t c o a l mines.,Note that the p r o f i l e entered the trench i n the v i c i n i t y of Radium, about 130 km from the shot p o i n t s . On t h e i r P wave record s e c t i o n , Bennett e t a l (1975) i n t e r p r e t e d a number of s t r u c t u r e s which were based on a r r i v a l s i d e n t i f i e d with a high degree of c o n f i d e n c e . Assuming t h a t the average upper c r u s t v e l o c i t y i s 5.7 km/s, the depth t o the basement immediately e a s t of the t r e n c h was c a l c u l a t e d as 6.5 km. T h i s was based on the i d e n t i f i c a t i o n of a 6.5-6.6 km/s phase i n t e r p r e t e d as the (Pg) a r r i v a l from the top of the Precambrian basement. The v e l o c i t y of the Mohcrovocic d i s c o n t i n u i t y (M d i s c o n t i n u i t y , or Moho) was found to be 8.22 (±.04) km/s, as evidenced by a (Pn) phase which had t h a t v e l o c i t y and which was i n a s s o c i a t i o n with a curved branch of l a r g e secondary a r r i v a l s i d e n t i f i e d as the wide angle r e f l e c t i o n s from the Moho. F i n a l l y , a 7 km t h i c k low v e l o c i t y zone was i n t e r p r e t e d on the b a s i s of a second 8.22 km/s phase, which was delayed by 0.5 s from the Pn phase and had much l a r g e r amplitudes. However, the depth to the Precambrian basement w i t h i n the t r e n c h i t s e l f and the depth t o the Moho cou l d not be determined unambiguously because of a prominent 1.7 s time delay a s s o c i a t e d with the Pg branch a t about 150 km. Three i n t e r p r e t a t i o n s were proposed t o e x p l a i n the delay. The f i r s t and p r e f e r r e d i n t e r p r e t a t i o n was a high-angle 8 c r u s t a l f a u l t , o b l i q u e t o the t r e n c h near Radium, as shown i n the v e l o c i t y - d e p t h p l o t of F i g u r e 2a, the basement to the south of Radium had a depth of 6.5 km and the depth to Hoho was 51 km; to the n o r t h the corresponding values were 12.1 and 58 km. Subsequent r e c a l c u l a t i o n of the f a u l t parameters by t h i s author shows that the expected f a u l t throw due to the 1,7 s-time delay should be even g r e a t e r : at the basement, the f a u l t throw s h c u l d be 18 km i n s t e a d of the 5.6 km c a l c u l a t e d by Bennett e t a l (1975) . The d e t a i l e d c a l c u l a t i o n of t h i s c o r r e c t i o n to the r e s u l t s of Bennett e t a l (1975) i s found i n Appendix 1, The second p r o p o s a l t o e x p l a i n the time delay was a c r u s t a l low v e l o c i t y zone beginning 3 km beneath the basement and having a depth extent of 9 to 15 km. The v e l o c i t y - d e p t h p l o t c orresponding to t h i s i n t e r p r e t a t i o n i s shown i n F i g u r e 2b. A d i f f i c u l t y with t h i s e x p l a n a t i o n was t h a t there were no r e f l e c t i o n s • f r o m the base of the c r u s t a l low v e l o c i t y zone present on the observed record s e c t i o n ; such r e f l e c t i o n s were expected froia c a l c u l a t i o n s of t h e o r e t i c a l s y n t h e t i c seismograms. In F i g u r e 2b, the low v e l o c i t y zone beneath the ffoho i s not r e l a t e d t o the 1.7 s time delay but, as e x p l a i n e d e a r l i e r i n t h i s s e c t i o n , i s based on a branch delayed from the Pn phase ; t h i s low v e l o c i t y zone should a l s o appear beneath the Moho i n the f a u l t s t r u c t u r e s of F i g u r e 2a. The t h i r d s u g g e s t i o n of Bennett e t a l (1975) was t h a t the basement u n d e r l y i n g the Rocky Mountains ends at the t r e n c h , which r e p r e s e n t s the western t e r m i n a t i o n of the c o n t i n e n t a l Precambrian c r a t o n . The s e i s m i c head wave cannot be maintained as a coherent wave package a f t e r i t has passed i n t o the r e g i o n 9 •CO. DEPTH (KM) Figure 2a. Velocity-depth structure for the f a u l t i n t e r p r e t a t i o n of Bennett et a l (1975) . Dashed l i n e shows the upfault structure south of Radium, s o l i d l i n e shows the downfault structure north of Radium. DEPTH (KM) Figure 2b. Velocity-depth structure for the low v e l o c i t y zone int e r p r e t a t i o n of Eennett et a l (1975) . The low velo c i t y zone beneath the Moho should also appear beneath the Moho in Figure 2a. 10 of c r u s t a l d i s r u p t i o n , but becomes s c a t t e r e d o r d i f f r a c t e d , r e s u l t i n g i n the weak and p o o r l y d e f i n e d f i r s t a r r i v a l data observed as the delayed branch. T h i s e x p l a n a t i o n f o r the s e i s m i c anomaly i s only a g u a l i t a t i v e one as a g u a n t i t a t i v e one i s very d i f f i c u l t . IxB. JOTJIJfIC.J j£JJ) OBGfiNIZATION OF •THE ' The f i r s t area of i n v e s t i g a t i o n i n t h i s t h e s i s concerns the p r e f e r r e d i n t e r p r e t a t i o n of Bennett et a l (1975) of a major c r u s t a l f a u l t near Badium. The i n t e r p r e t e d f a u l t s t r u c t u r e at the basement s u r f a c e i s shown i n the lower p o r t i o n of F i g u r e 3; an e q u i v a l e n t f a u l t was a l s o i n t e r p r e t e d a t the Moho. I f the basement f a u l t e x i s t s , then there would be a l a t e r a l c o n t r a s t between the c r y s t a l l i n e basement rocks and the l i g h t e r cover rocks of the upper c r u s t . The corresponding d e n s i t y c o n t r a s t can be c a l c u l a t e d from the v e l o c i t y model of Bennett e t a l (1975), i n which the cover rocks have an (assumed) average v e l o c i t y of 5.7 km/s and the basement has v e l o c i t y 6.5 km/s. Using the v e l o c i t y - d e n s i t y curves of Drake (Grant and West, 1965), the d e n s i t y c o n t r a s t i s about 0.13 g / c a 3 . Thus, the f a u l t i n t e r p r e t a t i o n with i t s a s s o c i a t e d l a t e r a l d e n s i t y c o n t r a s t i m p l i e s a v a r i a t i o n i n g r a v i t y above the f a u l t . The t h e o r e t i c a l g r a v i t y v a r i a t i o n i s shown i n the top p o r t i o n of F i g u r e 3, f o r which a value of 0.1 g/cm 3 has been used as a c o n s e r v a t i v e e stimate of the d e n s i t y c o n t r a s t The g r a v i t y e f f e c t of the f a u l t was c a l c u l a t e d by:determining the g r a v i t y anomaly due to a s e m i - i n f i n i t e s l a t c f t h i c k n e s s h = 5.6 km, that i s , the s l a b formed by the p o r t i o n of the basement below N O R T H £5 — T25 0 g ^ ^ T r o G h A g =19 mgal D I S T A N C E F R O M F A U L T (km) 20 -10 0 10 —I 1 1 1 20 —i— 30 —•— 40 — ' S O U T H upper crust lower crust (basement) \ 6.5.km Figure 3. 12 6.5 km and above 12.1 km. The maximum anomaly or such a semi-i n f i n i t e s l a b i s 2npGh, where G i s the u n i v e r s a l g r a v i t y c o n s t a n t . The r e l a t i v e v a r i a t i o n of g r a v i t y with d i s t a n c e was obtained f r o a the form curves of U e t t l e t o n (1971) i n which the t h e o r e t i c a l g r a v i t y of a f a u l t with a r b i t r a r y t h i c k n e s s and depth i s p l o t t e d as a f u n c t i o n of d i s t a n c e from the f a u l t . The g r a v i t y curve i n F i g u r e 3 does not i n c l u d e the e f f e c t o f the f a u l t a t the Moho. However, because the Moho i s deep (over 50 km ), the g r a v i t y e f f e c t of the Moho f a u l t i s not as l a r g e as t h a t from the basement f a u l t ; a l s o , the v a r i a t i o n with h o r i z o n t a l d i s t a n c e i s almost l i n e a r and would thus appear on l y as a r e g i o n a l t r e n d . From Figure 3, then, the i n t e r p r e t a t i o n of a c r u s t a l f a u l t with a 5.6 km throw r e g u i r e s a g r a v i t y anomaly of approximately 19 mgai over a r e g i o n 30 km to e i t h e r s i d e of the f a u l t ; f o r a f a u l t with a throw of 18 km, which i s the c o r r e c t e d value f o r the f a u l t of Bennett et a l (1975), the correspondxng g r a v i t y anomaly i s 54 mgal. The l a r g e magnitude anomaly and c h a r a c t e r i s t i c shape of the g r a v i t y v a r i a t i o n should be e v i d e n t i n g r a v i t y measurements over the proposed f a u l t . Thus, to t e s t the v a l i d i t y of the f a u l t model, a g r a v i t y survey was c a r r i e d out i n and adjacent to the trench along a 60 km s t r i p c e n t r e d near Radium. The second major study r e p o r t e d i n t h i s thesxs concerns the S wave data recorded i n 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 e t a l (1975) . i n S wave a n a l y s i s of these data seemed p a r t i c u l a r l y a t t r a c t i v e because prominent S waves were present on a number of s e i s m i c r e c o r d s ; an example of a c l e a r S wave 13 a r r i v a l , as i t appeared before any f i l t e r i n g had been a p p l i e d , i s shown i n F i g u r e 4. As w e l l , most of the s e i s m i c s t a t i o n s recorded a l l t h r e e components of motion, so t h a t p o l a r i z a t i o n f i l t e r i n g c o u l d be performed to separate the S waves from l a t e P phases. These two s t u d i e s - the g r a v i t y survey and the S wave a n a l y s i s - form the core of the t h e s i s . Both s t u d i e s have a r i s e n from the wcrk of Bennett et a l (1975), and so a c l o s e examination of t h e i r P wave record s e c t i o n i s a l s o i n c l u d e d i n the t h e s i s ; t h i s examination has enabled l i m i t s to be obtained f o r c r u s t a l t h i c k n e s s beneath the t r e n c h . The g r a v i t y and s e i s m i c s t u d i e s are not, however, independent o f each o t h e r , s i n c e t h e i r main concern i s the s t r u c t u r e and o r i g i n of the t r e n c h . Thus, an important aspect of t h i s t h e s i s i s to attempt to i n t e g r a t e these s t u d i e s together with other g e o l o g i c a l and g e o p h y s i c a l i n f o r m a t i o n about the nature of the Bocky Mountain Trench . 15 2 i i U J 1 ?os a HIGH ANGLE FAULT CJfiSSING THF IjOGKY HOJJNTAlN TJENCH J l i l JMIJ3H 2±} GEOLGGIGAL SETTING The Bocky Mountain Trench near Radium separates the western ranges of the Bocky Mountains from the P u r c e l l Mountains (Figure 5). ,To the eas t of Badium , the Bockies are c h a r a c t e r i z e d by f o l d s with v e r t i c a l a x i a l planes and steep a s s o c i a t e d f a u l t s , and even f u r t h e r east the c h a r a c t e r i s t i c s t y l e of deformation changes t c t h r u s t f a u l t i n g . To the west the P u r c e l l A n t i c l i n o r i u m i s composed of Precambrian sediments. The Precambrian i s d i v i d e d i n t o the P u r c e l l sediments and the younger Windermere sediments, separated by an unconformity marking the East Kootenay orogeny, which occurred more than 800 m.y. ago. The s t r u c t u r a l i m p l i c a t i o n of the c o n t a c t between c o n t r a s t i n g Precambrian and P a l e o z o i c rocks i s the e x i s t e n c e of the (reverse) Bocky Mountain Trench f a u l t (Figure 5), which i s a l s o c a l l e d the P u r c e l l f a u l t . The average e l e v a t i o n of the t r e n c h f l o o r i s about 780 m. A few outcrops of Precambrian age are exposed between the western edge and c e n t r e of the t r e n c h , but the majority of the f l o o r there and elsewhere i s covered with Cenozoic sediments. In the trench n o r t h of Radium, Steamboat Mountain r i s e s t o a maximum e l e v a t i o n of 1800 m above sea l e v e l . The Mount Forster-Steamboat reverse f a u l t (Beesor 1973) s t r i k e s t r a n s v e r s e t o the t r e n c h a c r o s s the P u r c e l l Boundary S y n c l i n e on Steamboat Mountain and the Mount F o r s t e r S y n c l i n e i n the b o r d e r i n g mountains to the Cl.6' i Figure 5. Geologic map of Radium area in southeastern B r i t i s h Columbia. Numbers are densities in g/cm3 of rock samples. The inset shows the location of the map area i n re l a t i o n to the pr i n c i p a l tectonic elements of the C o r d i l l e r a . 17 18 5).,On Steamboat Mountain, i t s e p a r a t e s Precambrian northern t i p from P a l e o z o i c rocks on the south. 2 A2 FIFID EJCGBAJ The g r a v i t y survey was c a r r i e d out i n the summer of 1974 using lacoste-Romberg gravimeter G88 with a s c a l e constant of 0.99886 mgal/div. The area covered was the t r e n c h and adjacent r e g i o n s a c c e s s i b l e by road from 50.3°N to 50,8° N (see F i g u r e 7 ) . 469 s t a t i o n s at spacings of approximately 1 km were occ u p i e d . A temporary base s t a t i o n was e s t a b l i s h e d and t i e d to the N a t i o n a l G r a v i t y Network s t a t i o n s at B r i s c o ( s t a t i o n 9071-54), Fairmont (9043-68) and Invermere (9072-54). I n i t i a l and f i n a l r e a d i n g s were made each day a t one of these base s t a t i o n s . S t a t i o n l o c a t i o n s normally were obtained w i t h i n ±100 m using 1:50,000 topo g r a p h i c maps, although i n a few cases 1:31,680 and 1:126,720 maps were used and the e r r o r i n l o c a t i n g the s t a t i o n s v a r i e d a c c o r d i n g l y . V e r t i c a l c o n t r o l was provided by benchmarks and monument posts of the Department of Energy, Mines and Resources. E l e v a t i o n s were obtained a t other l o c a t i o n s with a matched p a i r of aneroid a l t i m e t e r s which were t i e d to a c o n t r o l s t a t i o n at-approximately 2 hour i n t e r v a l s . Due t o r a p i d pressure changes i n the mountainous t e r r a i n , d r i f t s of up t o 30 m were recorded. The corresponding e r r o r i n e l e v a t i o n s may be as l a r g e as ±5 m y i e l d i n g an a s s o c i a t e d maximum e r r o r i n the g r a v i t y value of about 1 mgal,, Rock samples were c o l l e c t e d where p o s s i b l e , . U n f o r t u n a t e l y few are a v a i l a b l e i n the t r e n c h f l o o r due to c o v e r i n g by d e t r i t u s . The l o c a t i o n s of sampling s i t e s and the water-west (Figure rocks on the 19 s a t u r a t e d d e n s i t i e s of the 'samples are shown i n F i g u r e 5. A summary of the average d e n s i t i e s of rock samples i s given i n Table I.,The mean d e n s i t y of the Precambrian samples i s Table I. Average d e n s i t i e s of water-saturated rock samples from Eadium area. The e r r o r values i n d i c a t e approximate ranges of the measured d e n s i t i e s . , Age Density Number of (g/cm 3) samples P a l e o z o i c 2.74 ±.11 26 Precambrian: Hindermere 2.67 ±.11 28 -P u r c e l l 2.72 ±.10 14 2.69 g / c i 3 and of the P a l e o z o i c i s 2.74 g/cm 3. The d e n s i t y cf Cenozoic f i l l i s presumed to be 2.2 g/cni 3, although i t may be as low as 2.1 or as high as 2.4 g/cm 3. These f i g u r e s f o r the d e n s i t y of unconsolidated sediments were the e s t i m a t e s used by Garland e t a l (1961) i n a g r a v i t y i n t e r p r e t a t i o n f u r t h e r south i n the Rocky Mountain Trench; they were i n i t i a l l y obtained from the Handbook of P h y s i c a l Constajnts (1942). 2 i J MTA REJD0CT1GN The Bouguer anomaly was determined on the b a s i s of the Geodetic Reference System (1967) arid a Bouguer d e n s i t y of 2.67 g/cm 3. The formulas used to c a l c u l a t e the l a t i t u d e , e l e v a t i o n and "Bouguer s l a b " c o r r e c t i o n s are given i n Appendix 2.,The t e r r a i n c o r r e c t i o n f o r each s t a t i o n i n v o l v e d the d i g i t i z a t i o n o f e l e v a t i o n s from 1:50,000 maps. A 0.25 km g r i d of e l e v a t i o n s was ; •;. . 20 o b t a i n e d by d i g i t i z i n g the maps a c c o r d i n g t o the scheme shown i n F i g u r e 6. The program d e s c r i b e d by Ager (1972) was then used t o F i g u r e 6. Scheme f o r d i g i t i z i n g e l e v a t i o n s used i n t e r r a i n c o r r e c t i o n s . -e--e--e- -e-c0.5 km ' 0.25 km -e-X p o i n t s where e l e v a t i o n i s d i g i t i z e d from map O p o i n t s where e l e v a t i o n i s the average o f the s u r r o unding U p o i n t s determine the t e r r a i n c o r r e c t i o n f o r d i s t a n c e s to 25 km. F o r . s t a t i o n s w i t h i n the Bocky Mountain Trench {approximately 50%) , the i n n e r zone t e r r a i n c o r r e c t i o n , i n the range 0 to 0.25 km, was c a l c u l a t e d f o l l o w i n g Kane (1962) with e l e v a t i o n d a t a from the 1:31,660 Columbia B i v e r E a s i n maps. A d i s c u s s i o n o f t h e s i g n i f i c a n c e of t e r r a i n c o r r e c t i o n s and g e n e r a l methods used t o c a l c u l a t e them may a l s o be found i n Appendix 2. The t o t a l t e r r a i n c o r r e c t i o n had values of about 5 mgal w i t h i n t h e v a l l e y , i n c r e a s i n g to as l a r g e as 20 mgal near the w a l l s of the t r e n c h . The e r r o r i n t e r r a i n c o r r e c t i o n i n s i m i l i a r c i r c u m s t a n c e s i s e s t i m a t e d by Ager (1972) to be ±158. The t o t a l e r r o r i n the g r a v i t y value f o r s t a t i o n s w i t h i n the t r e n c h i s l e s s than 21 ±2 mgal while f o r s t a t i o n s having very l a r g e t e r r a i n c o r r e c t i o n s the e r r o r may be as l a r g e as ±4 mgal. The complete Bouguer map was low-pass f i l t e r e d to reduce the e f f e c t of s p u r i o u s e r r o r s and near s u r f a c e geology (see Appendix 2). The c u t - o f f freguency of the f i l t e r was chosen t o be 0.20 cycles/km based on a power spectrum a n a l y s i s which showed the p r i n c i p a l • wave numbers to be l e s s than t h i s value. The f i l t e r e d map i s shown i n F i g u r e 7. 2 AJi IfiSlSIIMiSflJS 01 1 U GBAVUI MM The most prominent f e a t u r e of the f i l t e r e d Bouguer anomaly map i s the trough which l i e s along the east w a l l of the t r e n c h . As shown i n the p r o f i l e s of F i g u r e 8, the anomaly i s about -9 mgal north of Radium and -7 mgal to the south., The a s s o c i a t e d e r r o r i n these values i s estimated to be ±1-2 mgal. T h i s e r r o r may appear to be s m a l l , c o n s i d e r i n g t h a t the e r r o r i n the Bouguer anomaly values near the w a l l s c f the t r e n c h i s ±4 mgal., However, the p r o f i l e s i n F i g u r e 8 are across a f i l t e r e d map, so that some of the e r r o r at i n d i v i d u a l s t a t i o n s i s smoothed out and a g r a v i t y value at a given l o c a t i o n on the map i s then much l i k e a 'mean' value. A l s o , most of the Bouguer g r a v i t y e r r o r comes from the t e r r a i n c o r r e c t i o n i n which s y s t e m a t i c e r r o r s are i n v o l v e d . For example, i f the t e r r a i n c o r r e c t i o n i s over? estimated at one l o c a t i o n , i t i s over-estimated at a nearby l o c a t i o n . Thus the d i f f e r e n c e between Bouguer g r a v i t y v a l u e s at those l o c a t i o n s i s l e s s than the e r r o r on the i n d i v i d u a l v a l u e s . . Keeping i n mind the comments on the nature of the e r r o r , i t s hould be noted that the north-south d i f f e r e n c e ^ i n the r e l i e f 22 F i g u r e 7, T e r r a i n - c o r r e c t e d Bouguer anomaly g r a v i t y map of Radium area i n southern B r i t i s h Columbia. The data were l o w - p a s s . f i l t e r e d with a c u t o f f freguency of 0.20 cycles/km. 23 2 C T 10' - 116° 00' 50" 2 4 8 8 T" IR) NORTH PROFILE RCROSS TRENCH — r 10 15 — r so —r 25 i 30 8 cr LD I - I O £ 8 -8 cr UJ o i (B) CENTRE PROFILE ACROSS TRENCH T" 10 - r 15 20 IC) SOUTH PROFILE RCROSS TRENCH C' 10 - r is 20 - r 2S 2S -1 30 - 1 30 8 8. i ID) PROFILE DQVN CENTRE OF TRENCH 10 20 1 30 40 SO I 60 F i g u r e 8. G r a v i t y p r o f i l e s a c r o s s Rocky Mountain Trench i n Radium a r e a . 25 of the gravity trough, as shown i n Figure 8D, i s a r e a l e f f e c t , The gravity changes guite rapidly i n the north-south d i r e c t i o n around Radium, but there i s no corresponding major topographic change so the north-south gravity difference does not ar i s e from the t e r r a i n correction error. The trough on the gravity map i s interpreted as being due to l i g h t , unconsolidated material of Cenozoic age overlying the bedrock. To determine the form of the underlying bedrock surface, a two-dimensional modelling program based on the algorithm described by Taiwan! et a l (1959) was used. The regional trend was estimated and removed for the p r o f i l e s of Figure 81 and 8C and the residual anomaly f i t t e d by a n-sided polygon. Good f i t s were obtained as shown i n Figure 9, for which, following Garland et a l (1961), -0.5 g/cm3 was used as the best estimate of density contrast. At the. deepest point, the maximum depth to bedrock i s 550 m i n the north and 420 m i n the south and the width of the f i l l i s about 8 km, When we consider the ±2 mgal error in gravity r e l i e f , the range in values of depths i s 425-675 m i n the north and 3 00-54 0 m i n the south. Also, i f a di f f e r e n t value for density contrast were used,the depths would vary proportionately. The values for the thickness of f i l l agree well with the estimate of Garland and Tanner (1957) whose p r o f i l e through Radium (corresponding to Figure 9B) yielded a thickness of 550 m, assuming a density contrast of -0.7 g/cm3 . The 5 mgal positive anomaly about 13 km south-east of Radium (Figure 7) can be explained on the basis of density contrasts. From Figure 5 we note that the rock densities i n t h i s 2 6 D ISTANCE (KM) 0 5 10 15 20 25 (A) NORTH PROFILE AND GRAVITY MODEL (B) SOUTH PROFILE AND GRAVITY MODEL F i g u r e 9. G e o l o g i c models b a s e d cn g r a v i t y i n t e r p r e t a t i o n f o r t h e n o r t h and s o u t h p r o f i l e s shown on F i g u assumed d e n s i t y c o n t r a s t i s -0,5 g/cm3. r e 7. The 27 r e g i o n average over 2*8 g/cm 3 which i s more than t h a t of adjacent regions by g r e a t e r than 0.1 g/cm 3. She 4 mgal p o s i t i v e anomaly at the southern t i p of Steamboat Mountain c o u l d a l s o p o s s i b l y be due to ne a r - s u r f a c e rock d e n s i t y c o n t r a s t s , although t h e r e are too few measurements at t h i s l o c a t i o n to support or d i s c l a i m such a p o s s i b i l i t y . ,However, the s i n g l e measurement made th e r e does give a r e l a t i v e l y l a r g e d e n s i t y of almost 2.8 g/cm 3i Other l o c a l anomalies on the g r a v i t y map, on the order of 2 mgal, could be due e i t h e r t o the ±2-4 mgal e r r o r i n the g r a v i t y values or t o l o c a l sediment of about 100 m above bedrock., No evidence e x i s t s f o r a basement f a u l t t r a n s v e r s e to the tr e n c h as proposed by Bennett e t a l (1975) . E v e n with a d e n s i t y c o n t r a s t of only 0,1 g/cm 3 the anomaly from north t o south f o r a f a u l t with a throw of 5.6 km should be 18 mgal with a c l e a r l y d e f i n e d maximum g r a d i e n t near Badium. As shown by F i g u r e 7 such a f e a t u r e does not e x i s t i n the observed data, A comparison of the g r a v i t y r e s u l t s with other surveys i n the t r e n c h w i l l be postponed u n t i l Chapter 4 , At t h i s time the s i g n i f i c a n c e of these and other r e s u l t s determined i n the course of the t h e s i s w i l l a l s o be d i s c u s s e d . 28 l i SlISMIC BEFEACTION SJJ RVEY ALONG THE RCCKY MOUNTAIN TEENCH As reported by Bennett et a l (1975), the University of B r i t i s h Columbia, during the summers of 1972 and 1973, recorded an unreversed seismic r e f r a c t i o n p r o f i l e along the southern Rocky Mountain Trench from 50° N to 53°N. Large blasts from open p i t coal mines near Sparwood sere used as energy sources for the survey. The r e f r a c t i o n l i n e (Figure 1) ran 540 km northwest from the mines and entered the trench in the v i c i n i t y of Badium, B.C., approximately 130 km from the shot points. Blasts were recorded from the Kaiser Besources Ltd open p i t mine near Sparwood, B.C., and the Fording Coal Ltd operations 50 km to the north. Shot sizes ranged from about 25,000 to 250,000 kg. The method of f i r i n g was the " r i p p l e - f i r e " technigue i n which a pattern of shots i s l a i d out with up to several tens of milliseconds delay between each detonation. This method p a r t i a l l y accounted for the weak f i r s t a r r i v a l P data and r e l a t i v e l y large S wave data at distances greater than about 400 km. 3±1 MM COLLECTION Three portable FM recording systems, designated A, B and C, were used i n the survey. Each system recorded on analog tape output from three 1-Hz seismometers, providing v e r t i c a l , r a d i a l and transverse components. In addition, the Mica telemetered array was in operation by the f a l l of 1972. The array recorded only the v e r t i c a l component at four s i t e s located on peaks 29 o v e r l o o k i n g the Bocky Mountain Trench (Thompson THO; Dainard DAI; Cummings COM; and Tabernacle TAB; see F i g u r e 1). The data on analog tape were l a t e r d i g i t i z e d at a d i g i t i z i n g r a t e of 85 Hz ( 0,012 s ) , F u r t h e r d e t a i l s on i n s t r u m e n t a t i o n and on f i e l d procedure can be found i n Bennett (1973) . A l t o g e t h e r twelve b l a s t s were r e c o r d e d , numbered from 2 to 13, Records sere i d e n t i f i e d by the system name f o l l o w e d by the shot number. The Mica array recorded s i g n a l s from the l a s t f i v e b l a s t s , thus p r o v i d i n g 20 v e r t i c a l seismograras with 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 s . The p o r t a b l e systems provided 24 v e r t i c a l , 25 r a d i a l and 19 t r a n s v e r s e seismograms. . A l l three components were obtained only at 18 s i t e s . 3_j_2 l i m i t s f o r C r u s t a l Thickness as Determined from the I i f i y e Becord S e c t i o n of Bennett et a I (1975) The major f e a t u r e f o r which d i f f i c u l t y was encountered i n the E wave i n t e r p r e t a t i o n of Bennett et a l (1975) was the . prominent time delay on the Pg branch. However, even i f we d i s c a r d the d e t a i l e d c r u s t a l models used t o e x p l a i n t h i s delay and assume the Pg branch i s completely missing, there i s s t i l l u s e f u l i n f o r m a t i o n i n the r e c o r d s e c t i o n : the t r a v e l times of the Moho r e f l e c t i o n and r e f r a c t i o n branches are w e l l - d e f i n e d w i t h i n l i m i t s , and the En v e l o c i t y can be measured p r e c i s e l y . ,In p a r t i c u l a r , such a • p a r t i a l 1 r e c o r d s e c t i o n s t i l l enables depth l i m i t s t o the Moho to be c a l c u l a t e d . . In p l a c e of the missing c r u s t a l i n f o r m a t i o n , we assume f o r the c r u s t a simple l a t e r a l l y homogeneous two-layer s t r u c t u r e . , Such a c r u s t thus r e p r e s e n t s an average of the r e a l and p o s s i b l y inhomogenecus s t r u c t u r e . V e l o c i t y and t h i c k n e s s l i m i t s f o r the l a y e r s are determined by examining r e s u l t s of other C o r d i l l e r a n s e i s m i c r e f r a c t i o n surveys (see Table I I ) . Thus i n the f o l l o w i n g a n a l y s i s , the minumum average upper c r u s t v e l o c i t y was chosen as 5.0 km/s to a maximum depth of 12 km, below which the lower c r u s t has minimum v e l o c i t y of 6.0 km/s. The maximum upper c r u s t v e l o c i t y was 6.0 km/s f o r a minimum depth of 3 km, below which the lower c r u s t has maximum average v e l o c i t y 7.0 km/s., The method-used i n determining the depth l i m i t s i s an extremal a n a l y s i s technique s i m i l a r t o t h a t o u t l i n e d i n McMechan and Wiggins (1972) and Wiggins et a l (1973) . ,A d e s c r i p t i o n of the procedure, as a p p l i e d t o a model with a two-layer c r u s t and upper mantle, may be found i n appendix 3. The b a s i c t o o l i n v o l v e d i s the HEG1TZ computer r o u t i n e of H.A. Wiggins, which uses S i e c h e r t - H e r g l o t z i n t e g r a t i o n to produce v e l o c i t y - d e p t h and t r a v e l t i m e vs. d i s t a n c e (T-A) curves by i n v e r t i n g a s e t of ray parameter vs. d i s t a n c e (p-A) v a l u e s . In the extremal technique, a p -A l i m i t envelope i s determined. The dete r m i n a t i o n of the envelope i s c o n s t r a i n e d by the f o l l o w i n g : (1) the v e l o c i t y c f the Moho r e f r a c t i o n branch and the corresponding ray parameter value are f i x e d , (2) the t r a v e l times f o r the Moho r e f r a c t i o n and r e f l e c t i o n branches must not l i e . o u t s i d e of approximate e r r o r l i m i t s p i cked on the re c o r d s e c t i o n , and (3) the v e l o c i t i e s and depths must be wi t h i n the l i m i t s chosen f o r the c r u s t a l l a y e r s . ' R e s u l t s of the extremal p e r t u r b a t i o n s are shown i n F i g u r e s 10 and 11. In F i g u r e 10* i s shown the minimum and maximum v e l o c i t y - d e p t h models, and i n Fi g u r e 11 the corresponding T -A 31 Table I I Seismic C r u s t a l S t r u c t u r e i n the Canadian C o r d i l l e r a , i n r e l a t i o n to the Rocky Mountain Trench (RMT) . , l o c a t i o n a c r o s s RMT at 49 30» (lamb and Smith, 1962) j u s t west of RMT at 49* ( B a l l y e t a l , 1966) 15 • Depth to Bottom of Layer (km) 1.5 (pC P u r c e l l ) 1.0 Greenbush l a k e , B.Cv, t o near Idaho-Washington border (Hales and Nation, 1973) Greenbush L. t o S w i f t Current, Sask. (Chandra and Gumming, 1972) 0. 2 4.7 15. y 21. 37. 5 (mantle) 20. 31. , 49. , (mantle) V e l o c i t y (km/s) 2.3-3.3 5.2-5.5 5.2 (assumed) 3. 5.9, g r a d i e n t to 6.0 6.0, g r a d i e n t t o 5.8 5.8 6.4 8. , 6.0 6.5 7.2 8.2 no r t h and south from M e r r i t t , B.C. (White e t a l , 1968) Greenbush I. to B i r d I. on Queen C h a r l o t t e I s . (Forsyth et a l , 1974) Greenbush I. t o N i t i n a t , Van. I s . , to R i p l e y Bay, to B i r d I . , and t o McCleod L. (Berry and F o r s y t h , 1975) 3. , 30, (mantle) (mantle) 3.5 24. „• 36. .. (mantle) >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 <i) c P ; < o ro *— P P -< B (0 P ' r-< H-ro & r. c: o 3 M P - P < rt' (ft U ' •c CI' r t O t r rt (-'• , , O P * » P J Vi O t i -Hi ro P J C C o a c i-i 0 ) < r t ro r t *—• (D Ct-r t r l P J p> < 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 <Q O (!) D O tt> B 3 <fc r t r t t i t r 01 n a a> 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) <n m to co „ ro CD CD ro ro CD ro ro CD O ro CO o CO o a CO ro o CO D CO ro To CD l-cn -Pi CD e<7 oor (_> 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. 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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<p E E &<p 69 = •0.810.3 sin2<^ mgal/km, where E £ i s the mean Earth r a d i u s (6371 km). l i . J i e e a i r Anomaly And E l e v a t i o n C o r r e c t i o n As the d i s t a n c e from the centre of the Earth i s i n c r e a s e d , g r a v i t y becomes l e s s . The v e r t i c a l g r a d i e n t of g r a v i t y , or the e l e v a t i o n c o r r e c t i o n , i s found to be (Grant and West, 1965) dg - 0.3086 mgal/m dz The f r e e a i r anomaly i s FA = 9 0 " l9t ~ dg h) dz which i s thus the d i f f e r e n c e between the observed g r a v i t y and the t h e o r e t i c a l g r a v i t y at a d i s t a n c e h meters above the r e f e r e n c e s p h e r o i d . 4. Simjale Bouguer A n S l S l l And Bouguer -Correction We can approximate the c r u s t a l rock between the g r a v i t y s t a t i o n and the r e f e r e n c e spheroid as a i n f i n i t e s l a b of t h i c k n e s s h. The g r a v i t a t i o n a l a t t r a c t i o n of the s l a b i s known as the Bouguer c o r r e c t i o n and equals 2TT^Gh, where G i s the g r a v i t a t i o n a l constant and f i s the d e n s i t y of c r u s t a l rock.. Assuming j? = 2.67 g/cm 3, the c o r r e c t i o n i s 2fTfG = 0.1119 mgal/m The simple Bouguer anomaly i s BA £ = g c - (g t - dg h +-liroGh). dz 70 5 A Ccffl£let e Bo jug uer A n c a a ly. And -T ex/gain C o r r e c t i o n An i n f i n i t e s l a b of rock between the s t a t i o n and the r e f e r e n c e spheroid i s only an approximation, s i n c e the top s u r f a c e of the c r u s t a l rock i s not f l a t but has many i r r e g u l a r i t i e s i n i t . The e f f e c t of the i r r e g u l a r i t i e s i s always t o decrease the g r a v i t a t i o n a l a t t r a c t i o n i n comparison with the i n f i n i t e s l a b : v a l l e y s i n the s l a b mean l e s s r o ck e x e r t i n g a downward f o r c e , and mountains above the l e v e l o f the s l a b imply more rock e x e r t i n g an upward f o r c e . An e x c e l l e n t review of procedures used t o c a l c u l a t e t h i s t e r r a i n e f f e c t i s found i n Stacey and Stevens (1970). They can be grouped i n t o e i t h e r a prism method or a p i e - s l i c e method. In the prism method, e l e v a t i o n s on topographic maps are d i g i t i z e d so t h a t a g r i d of r e c t a n g u l a r v e r t i c a l prisms i s obta i n e d . An exact e x p r e s s i o n f o r the g r a v i t a t i o n a l a t t r a c t i o n of a prism i s known, so the t o t a l g r a v i t a t i o n a l a t t r a c t i o n of a l l the prisms surrounding a s t a t i o n may be c a l c u l a t e d . , Larger prisms and approximate expressions f o r the a t t r a c t i o n of a prism can be u t i l i z e d , e s p e c i a l l y a t g r e a t e r d i s t a n c e s from the s t a t i o n , i n order t o reduce computer time. Such e x p r e s s i o n s i n c l u d e those f o r a s e c t i o n o f a hollow c y l i n d e r , a s e c t i o n of a c y l i n d e r with an i n v e r t e d cone removed, and a v e r t i c a l l i n e mass. T e r r a i n c o r r e c t i o n s i n t h i s t h e s i s were c a l c u l a t e d using the prism method; a d e s c r i p t i o n of the program i s given i n Ager (1972). In the p i e - s l i c e method, e l e v a t i o n contour l i n e s on the topographic maps are d i g i t i z e d . One then a p p l i e s the e x p r e s s i o n f o r the g r a v i t a t i o n a l a t t r a c t i o n of a pie-shaped s l i c e c e n tered 71 on the s t a t i o n and between two contour l i n e s . With the t e r r a i n c o r r e c t i o n c a l c u l a t e d as g T c , the g r a v i t a t i o n a l a t t r a c t i o n of the c r u s t a l rock i s (27T^Gh-gTc) and the complete Bouguer anomaly i s B l c - g 0 - - (g t - dg h + 2npGh - g r c ) dz The complete Bouguer anomaly i s zero f o r an earth o f uniform d e n s i t y . T h i s i s because observed g r a v i t y on the i r r e g u l a r s u r f a c e of such an e a r t h i s completely accounted f o r by c o n t r i b u t i o n s from (1) the t h e o r e t i c a l 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 , <2) the e l e v a t i o n c o r r e c t i o n and (3) the a t t r a c t i o n of the c r u s t a l rock. Non-zero Bouguer anomaly values thus map v a r i a t i o n s e i t h e r i n d e n s i t y or i n t h i c k n e s s of l a y e r s beneath the s u r f a c e . , 6jt is* £§ss f i l t e r i n g > 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 ) <q 2-p 0 2)'^ where the ray having parameter p 0 bottoms at depth Y ( p c ) . The depth i s an i n t e g r a l which f o l l o w s the same path as f ( p 0 ) , t h a t i s , along the p - A curve above the r e f e r e n c e value p D . For X (p c) the i n t e g r a n d i s A(g)# while f o r Y (p 0) the integ r a n d i s A( g ) / (g 2""P 0 2 ) / ^ T h i s means t h a t f o r values of g very c l o s e to p6 the c o n t r i b u t i o n t o the i n t e g r a l Y(p e) i s much gr e a t e r than f o r g f a r away from p 0,,As a r e s u l t , p e r t u r b a t i o n s i n the shape of the p-A curve near the re f e r e n c e value p D have a much g r e a t e r e f f e c t on depth than p e r t u r b a t i o n s f a r away from p 0 . The qu e s t i o n now a r i s e s as to what p e r t u r b a t i o n s can be made which w i l l produce the extremal depths corresponding to ray parameter p e . The f o l l o w i n g a n a l y s i s i s s i m i l a r , although mere l i m i t e d , than the extremal i n v e r s i o n techniques d e s c r i b e d by Hctfechan and Wiggins (1972) and Wiggins et a l (1973) ..From a record s e c t i o n , u n c e r t a i n t i e s can be determined f o r the t r a v e l time and d i s t a n c e measurements, so t h a t the T - A curve i s r e s t r i c t e d to l i e w i t h i n a s p e c i f i e d envelope. An e g i i i v a l e n t envelope can then be c o n s t r u c t e d f o r the p - A curve; an example of such an envelope i s given by the s t r i p e d area i n F i g u r e 2 2 . C o n s i d e r i n g f i r s t the' fflaximizatlon•of depth, one sees from equation ( 2 .2 ) t h a t A ( g ) must be made as l a r g e as p o s s i b l e over the path from p o t o p W ( l x. J o r e e x a c t l y , because of the weighting f a c t o r i n the i n t e g r a n d , A ( q ) must be as l a r g e as p o s s i b l e near A F i g u r e 22 The p-A envelope and paths i n v o l v e d i n the j a x i m i z a t i o n of depth. > 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.<?and p.so; F i g u r e 21). That i s , the o n l y phases present on the re c o r d s e c t i o n are the Moho r e f r a c t i o n branch and the wide-angle r e f l e c t i o n branch..Also, the r e f e r e n c e value p 0 i s the parameter of the ray which r e f r a c t s along the Moho, so t h a t the s m a l l e s t d i s t a n c e f o r which p Q i s d e f i n e d ( i . e . A o i n Fi g u r e 21) i s the c r i t i c a l d i s t a n c e . With these assumptions, the c o n s t r u c t i o n of the p -A envelope and the r e l a t e d extremal i n v e r s i o n proceeds as o u t l i n e d below. Q u a n t i t a t i v e c a l c u l a t i o n s i n v o l v e the HfiGLTZ computer r o u t i n e of B. A. Wiggins, which performs the i n v e r s i o n of p - A values t c a v e l o c i t y - d e p t h model and a l s o c a l c u l a t e s the corresponding T -A v a l u e s . , 78 (1) C o n s t r u c t an envelope i n the T - A plane f o r the Mono r e f r a c t i o n and r e f l e c t i o n branches ( s t r i p e d area i n F i g u r e 23). The p o s i t i o n s of curves w i t h i n t h i s envelope whica.gj.ve maximum or minimum depths can be determined approximately. For maximum depth,-, i t i s d e s i r e d t h a t f o r a given d i s t a n c e A on the r e f l e c t i o n branch the r e l a t e d p value be as s m a l l as p o s s i b l e f o r the p o r t i o n of the path before c r o s s o v e r ( i . e . p s h o u l d l i e along the r i g h t hand s i d e of the p - A e n v e l o p e ) . H e n c e , dX /dA should be as s m a l l as p o s s i b l e , o r , the t i m e , i n t e r v a l d l between any two f i x e d d i s t a n c e s should be as s m a l l as p o s s i b l e . . I n F i g u r e 23, then, the l e f t nand'side of the maximum depth T - A curve i s at the top of the T - A envelope, and t h e r i g a t hand s i d e i s at the bottom of the envelope. For the minimum depth the s i t u a t i o n i s v i c e - v e r s a . (2) M i s s i n g branches must be c o n s t r a i n e d t o have p h y s i c a l l y reasonable v e l o c i t i e s . Thus, as i n F i g u r e 22, c o n s t r a i n upper c r u s t ray parameters to l i e between maximum and minimum v a l u e s p and p , and lower c r u s t ray parameters between p. and p. . T h i s forms the h o r i z o n t a l s e c t i o n s of the p-A envelope.. (3) From the T~ A envelope determine the maximum (minimum) c r i t i c a l d i s t a n c e A e f o r the r e f e r e n c e ray parameter p Q . (4) Choose a r b i t r a r y p - A v a l u e s f o r the r e f l e c t i o n branches and using HRGLTZ c a l c u l a t e the T - A v a l u e s . For the Moho . r e f l e c t i o n branch, compare d i f f e r e n c e s between the c a l c u l a t e d t r a v e l times with a l l o w a b l e d i f f e r e n c e s o b t a i n e d from the T - A envelope and p e r t u r b the p - A curve u n t i l the d i f f e r e n c e s match. For maximization, the r e s u l t a n t T - A curve then corresponds to path 1 i n F i g u r e 22 (except f o r the basement r e f l e c t i o n b r a n c h). 79 Note that a r e s t r i c t i o n on the c h o i c e of p - A values i s t h a t the curve cannot be n e a r - h o r i z o n t a l f o r a r e c e d i n g branch, or e l s e a non- s i n g l e valued f u n c t i o n w i l l r e s u l t . (5) S t a r t i n g at high p va l u e s , change the p - A . values so they l i e cn the opposite s i d e of the p - A envelope. ;The envelope f o r the basement r e f l e c t i o n branch on the p - A curve can now be d e f i n e d by en s u r i n g t h a t the basement depth c a l c u l a t e d by HRGLTZ i s not o u t s i d e any p h y s i c a l l y reasonable r e s t r i c t i o n s on i t s depth. When t r a v e l times f o r the Moho branches f i t , c r o s s over and stay oh the other s i d e of the l i m i t curve. For maximization, the p - A curve then corresponds t o path 2 i n Fig u r e 22. 80 APPENDIX 4 ENHANCEMENT P.F SV -PHASES BY gOIABI2AfTGJ ElXTEBIiG An important c h a r a c t e r i s t i c of P and SV motion i s 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 . Both are i n the v e r t i c a l - r a d i a l plane, but P motion i s i n the propagation d i r e c t i o n while SV motion i s p e r p e n d i c u l a r t o the propagation d i r e c t i o n . S i g n a l generated noise (e.g., c o n v e r s i o n s of P and S body waves to s u r f a c e waves, or r e f l e c t i o n s and r e f r a c t i o n s a t inhomogeneities or topographic i r r e g u l a r i t i e s ) i s r e c t i l i n e a r as w e l l ; however, because of the nature o f the inhomogeneities, p o l a r i z a t i o n d i r e c t i o n s are random. Background noise i s e i t h e r e l l i p t i c a l l y p o l a r i z e d (mainly B a y l e i g h waves from microseismic a c t i v i t y ) or random (e.g., c u l t u r a l n o i s e c r noise from n a t u r a l sources such as r i v e r s or wind through t r e e s ) . - T h u s , a f i l t e r which passes only r e c t i l i n e a r motion i n the v e r t i c a l - r a d i a l plane should enhance only the P and SV motion and some s i g n a l generated no i s e . SV motion may then be separated by using knowledge of i t s w e l l d e f i n e d d i r e c t i o n i n space. One type of p o l a r i z a t i o n f i l t e r i s the BEMODE f i l t e r (Basham 1967). I t computes the c r o s s c o r r e l a t i o n f u n c t i o n efc) between v e r t i c a l and r a d i a l t r a c e s , and then convolves the even part of c (-c) with the o r i g i n a l time s e r i e s . B e c t i l i n e a r motion i s enhanced, because i t i s observed t h a t the even p a r t of c (r) i s l a r g e r e l a t i v e to the odd part f o r r e c t i l i n e a r motion and s m a l l f o r e l l i p t i c a l l y p o l a r i z e d motion. SV motion i s d i s c r i m i n a t e d from P motion by c a l c u l a t i n g at time t the product of v e r t i c a l and r a d i a l components z (t) and r ( t ) . For SV motion, z ( t ) * r ( t ) < 0 . 81 Both the components are set to zero i f the above i n e q u a l i t y i s net t r u e . The r e s u l t a n t r e c o r d s can then be low pass f i l t e r e d to remove sharp edges. The p o l a r i z a t i o n f i l t e r used i n t h i s t h e s i s was f i r s t d e s c r i b e d by F l i n n (1965) , with f u r t h e r a p p l i c a t i o n and i n t e r p r e t a t i o n by M o n t a l b e t t i and Kanasewich (1970) and Souriau and Veinante (1975) . The HEBOBE f i l t e r was not u t i l i z e d because the f i l t e r of F l i n n (1965) was l e s s complicated and time consuming and p h y s i c a l l y more a p p e a l i n g . , In the f o l l o w i n g d e s c r i p t i o n of t h i s f i l t e r , a n a l y s i s i s done on l y i n two dimensions, the v e r t i c a l - r a d i a l plane; i t could be e a s i l y extended t o th r e e dimensions, i f d e s i r e d . In a d d i t i o n , i t i s assumed t h a t the angle of i n c i d e n c e i s known, and the plane has been r o t a t e d so t h a t SV motion w i l l t h e o r e t i c a l l y l i e along the new v e r t i c a l d i r e c t i o n and P motion along the r a d i a l d i r e c t i o n . Over one c y c l e of the p a r t i c l e motion, one can g e n e r a l l y f i t an e l l i p s e t o the path of the motion.„In the f i l t e r of F l i n n (1965) , the p r i n c i p a l axes of the e l l i p s e and t h e i r d i r e c t i o n s i n space are found by an a n a l y s i s of the c o v a r i a n c e matrix f o r the s e t of H o b s e r v a t i o n s i n a s p e c i f i e d time window. In the t h e s i s , the l e n g t h of the window was taken as the time f o r one c y c l e of the p a r t i c l e motion. , The c o v a r i a n c e between U o b s e r v a t i o n s of two random v a r i a b l e s x and y i s d e f i n e d by Cov[x,y] =± li^-m,) (y,-m ) where m and m are means of the v a r i a b l e s . The g u a n t i t y Cov[x,x] i s j u s t the variance c f x. l e t x be a vector of 82 v a r i a b l e s x and y, and m=®x i+m^i be the v e c t o r s of means. The co v a r i a n c e or d i s p e r s i o n matrix f o r the s e t of N p o i n t s (x^,y^.) i s given by A/ The s u p e r s c r i p t T i n d i c a t e s the transpose of the v e c t o r . The matrix can thus be w r i t t e n as i (x A -my) iJi-my)) = /Var[x] Cov[x,y ] \ Cov[x,y ] Var[x] ^ The p r o p e r t i e s of t h i s c o v a r i a n c e matrix D i n E u c l i d i a n v e c t o r space are i n t i m a t e l y r e l a t e d to the p r o p e r t i e s of an e l l i p s o i d i n E u c l i d i a n geometric space. ,In p a r t i c u l a r , the eigenvalues of D f o r a two-dimensicnal space are simply the squared l e n g t h s of the major and minor serai-axes o f the e l l i p s e , and the corresponding e i g e n v e c t o r s are v e c t o r s i n the d i r e c t i o n s of the axes (Dempster 1969, pp. 137-138). > 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 = <v?, v R) . Thus, v,\ = 1 <3. 1) T h e r e f o r e , 83 - O - o Z2-1 ZH \ZS E2-1 The only n o n - t r i v i a l s o l u t i o n i s when the determinant of the matrix on the LHS i s z e r o , i . e . , 22-1 ZE Zfi R2-1 There are two s o l u t i o n f o r 1, 1, = (Z2 + B2 + d)/2 (3.2) lx = (Z2 + E2 - d)/2 (3.3) where d •= ( (Z2-B2) 2 + 4ZB 2)' /* The e i g e n v e c t o r s v are those v e c t o r s s a t i s f y i n g (3 .1) , when e i t h e r 1, or l x i s s u b s t i t u t e d f o r 1. I f we s p e c i f y t h a t the magnitudes.of the e i g e n v e c t o r s be normalized t o 1 ( i . e. v^ 2+v R 2= 1) , then the components of v are d i r e c t i o n c o s i n e s . A f t e r some a l g e b r a , we o b t a i n f o r one of the e i g e n v e c t o r s (Souriau and Veinante 1975) • v • = (cos a, cos b) c o s 2 a = (Z2 - L2 + d)/2d (3.4) c o s 2 b = (B2 - Z2 + d)/2d (3.5) where a and b are the angles between the ve c t o r and the v e r t i c a l and r a d i a l axes, r e s p e c t i v e l y . The other e i g e n v e c t o r v ^ i s at r i g h t angles to* v,, : Hence, the length cf the p r i n c i p a l axes o f the e l l i p s e are given by eguations (3.2) and (3,3) and t h e i r d i r e c t i o n s by eguations (3.4) or (3 ,5 ) . I f the p a r t i c l e motion i s h i g h l y r e c t i l i n e a r , then the e l l i p s e i s elongated, while completely u n p o l a r i z e d motion i s d e s c r i b e d by a c i r c l e . The r a t i o of the 8a p r i n c i p a l axes i s thus a measure of the degree of r e c t i l i n e a r i t y . In p a r t i c u l a r , i f 1, i s the l a r g e s t e i g e n v a l u e , then G, (t) = 1 - l a / l , (3.6) i s a f u n c t i o n which i s n e a r l y 1 when one of the p r i n c i p a l axes i s much l a r g e r than the oth e r , and ne a r l y 0 when the axes have the same s i z e . The f u n c t i o n i s computed over a s p e c i f i c time window centered at time t . I t i s a t i m e - v a r y i n g f u n c t i o n because i t i s r e c a l c u l a t e d f o r every d i g i t i z e d time along the e n t i r e r e c o r d . M u l t i p l i c a t i o n of the v e r t i c a l and r a d i a l r e c o r d s by the f u n c t i o n G, (t) thus r e s u l t s i n a time s e r i e s i n which only r e c t i l i n e a r motion i s present. As mentioned b e f o r e , the v e r t i c a l a x i s i s i c the same d i r e c t i o n as SV motion. Eguation (3,4) give s the angle a between the v e r t i c a l and the p o l a r i z a t i o n d i r e c t i o n of the p a r t i c l e motion, so t h a t f u n c t i o n G a ( t ) = cos a = < (Z2 -12 + d)/2d)' / : L i s 1 f o r SV p o l a r i z a t i o n and 0 f o r P p o l a r i z a t i o n . Hence, m u l t i p l i c a t i o n of the v e r t i c a l by G a ( t ) attenuates any p o l a r i z e d motion which i s not i n the SV d i r e c t i o n , so t h a t the v e r t i c a l d i r e c t i o n c o n t a i n s onlv, SV motion. S i m i l a r l y , m u l t i p l i c a t i o n of the r a d i a l by G 3 ( t ) = cos b = ( (R2 - Z2 + d)/2d)' / x causes the r a d i a l component to c o n t a i n only P motion. In p r a c t i c e , the f u n c t i o n s G , (t) , G^Jt) and G 3 ( t ) are f i r s t smoothed by averaging them over a time window egual t o about h a l f of the o r i g i n a l window l e n g t h ( M o n t a l b e t t i and Kanasewich 1970). 

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