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A gravity model for the guichon creek batholith Ager, Charles Arthur 1972

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A GRAVITY MODEL FOR THE GUICHON CREEK BATHOLITH by CHARLES ARTHUR AGER B.A., Sacramento State C o l l e g e , 1968 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of Geophysics We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA March, 1972 In presenting t h i s thesis i n p a r t i a l f ulfilment of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t freely available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the Head of my Department or by h i s representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of GEOPHYSICS The University of B r i t i s h Columbia Vancouver 8, Canada Date March 10, 1972 i ABSTRACT The Guichon Creek Batholith, located in south-central British Columbia, contains several large, low grade copper deposits of extreme economic importance. A three dimensional model for the batholith has been determined on the basis of a gravity survey conducted in 1971. In addition the gravity data has been compared with the f i l t e r e d aeromagnetic maps of the batholith. A striking correlation between the spatial relationship of the mineral deposits and the core of the batholith has been discovered. i i TABLE OF CONTENTS Page 1. INTRODUCTION 1 2. GEOLOGICAL SETTING 3 2.1 Geography and Topography 3 2.2 Geology 3 3. THE GRAVITY SURVEY 6 3.1 G r a v i t y Observations 6 3.2 The Survey Procedure 6 3.3 E l e v a t i o n s 8 3.4 Rock D e n s i t i e s 10 4. GRAVITY REDUCTIONS 11 4.1 D r i f t 11 4.2 L a t i t u d e E f f e c t 11 4.3 Free A i r E f f e c t 13 4.4 Bouguer E f f e c t 14 4.5 T e r r a i n E f f e c t 14 4.6 The G r a v i t y Anomaly 17 4.7 Accuracy of Results 19 5. DATA ENHANCEMENT TECHNIQUES 20 5.1 I n t e r p o l a t i o n to a Square G r i d 20 5.2 F i l t e r i n g of P o t e n t i a l F i e l d s 20 5.3 Regional-Residual Separation 23 5.4 The F i l t e r e d G r a v i t y Maps 24 6. INTERPRETATION 31 6.1 Depth Estimates 31 6.2 Consideration of G r a v i t y h a l f - w i d t h s 33 6.3 Cons i d e r a t i o n of the Second V e r t i c a l D e r i v a t i v e 33 6.4 S e l e c t i o n of D e n s i t i e s 37 6.5 Cons i d e r a t i o n of Magnetics 37 6.6 C a l c u l a t i o n of Ag f o r Model 43 7. MODEL OF THE BATHOLITH 7.1 Gross Shape 44 7.2 The C a l c u l a t e d G r a v i t y Map 44 8. SUMMARY AND CONCLUSIONS 51 REFERENCES 53 APPENDIX A 55 APPENDIX B 62 i i i LIST OF FIGURES Page Figure 1-1 Guichon B a t h o l i t h L o c a t i o n Map 2 2—1 Guichon B a t h o l i t h Geology Map 4 3- 1 G r a v i t y Survey S t a t i o n L o c a t i o n Map 7 3- ^2 Guichon B a t h o l i t h Density Plan 9 4- 1 G r a v i t y E f f e c t s 12 (a) L a t i t u d e e f f e c t (b) Free a i r e f f e c t (c) Bouguer e f f e c t (d) T e r r a i n e f f e c t 4-2 (a). T e r r a i n e f f e c t s c a l c u l a t i o n e r r o r s 16 (b) E l e v a t i o n map d i g i t i z a t i o n format 16 4- 3 Lo c a t i o n of g r a v i t y anomalies 18 5- 1 Complete Bouguer Anomaly Map 21 5-2. (a) Representation of F i l t e r i n g Process 22 (b) .Selec t i o n . o f Cutoff Wavenumber using V e r t i c a l Prism 22 (c) Regional-Residual Separation 22 5-3 U l r y c h Regional (low pass) F i l t e r 25 5-4 Regional Ag Map 26 5-5 Rosenbach Second D e r i v a t i v e F i l t e r 27 5-6 Re s i d u a l Ag Map 28 5- 7 Second D e r i v a t i v e Map 29 6- 1 Depth-Shape Estimate 32 6-2 Half-Width/2nd D e r i v a t i v e 34 6-3 Source Slope Curves 35 6-4 Data Compilation P l a n 36 6-5 T o t a l Aeromagnetic F i e l d Map 38 6-6 Regional Aeromagnetic Map 39 i v Page Figure 6-7 R e s i d u a l Aeromagnetic Map 40 6- 8 2nd V e r t i c a l D e r i v a t i v e Map 41 7- 1 Gross Shape Plan 45 7-2 C a l c u l a t e d Ag Anomaly 46 7-3 Regional Ag Map (Figure 5-4) 47 7-4 Depth/Gravity P r o f i l e AA' 48 7-5 Depth/Gravity P r o f i l e BB' 49 V ACKNOWLEDGMENTS I would l i k e to si n c e r e l y thank a l l those i n d i v i d u a l s who have con-tr i b u t e d to the accomplishment of th i s p r o ject. I am indebted to the Gravity D i v i s i o n , Ottawa, f o r supplying free instrumentation, free computer time and expert advice. In p a r t i c u l a r , I would l i k e to thank Dr. R. A. Stacey, J . B. Boyd, and R. V. Cooper for th e i r u n s e l f i s h t e c h n i c a l support during the course of the survey. I wish to thank Dr. A. Sutherland Brown and Dr. W. F. Slawson f o r i n i t i a t i n g the project, the B. C. Dept. of Mines and Petroleum Resources for t h e i r major f i n a n c i a l support, Bryan Lee for h i s excellent f i e l d assistance, and, i n p a r t i c u l a r , Dr. W. J. McMillan for the use of his geological data and for the many enjoyable discussions r e l a t i n g to the geology of the Guichon. I am e s p e c i a l l y thankful to Dr. T. J . Ulrych, supervisor of t h i s t h e s i s , for h i s guidance, .encouragement and assistance on a l l phases of th i s p r oject. This work was -supported, i n part, by a.bursary award from the National Research Council f o r - t h e year 1971-72. 1 1. INTRODUCTION The Guichon Creek B a t h o l i t h (Figure 1-1), l o c a t e d i n s o u t h - c e n t r a l B r i t i s h Columbia, has a t t r a c t e d much a t t e n t i o n i n recent years. The d i s -covery of copper ore i n the b a t h o l i t h during the 1950's l e d to a mining boom u n p a r a l l e l l e d i n the h i s t o r y of B r i t i s h Columbia. S e v e r a l l a r g e , low grade copper deposits have s i n c e been d e l i n e a t e d and brought to var i o u s stages of production. N a t u r a l l y , i n t e r e s t i n the s t r u c t u r e and the genesis of the b a t h o l i t h has been i n t e n s e . In response to t h i s demand, many d e t a i l e d geologic i n v e s t i g a t i o n s have s i n c e been undertaken by v a r i o u s workers - noteworthy s t u d i e s being the published work of Northcote (1969) and the current work of McMillan (1972). As a r e s u l t of t h i s c o l l e c t i v e e f f o r t , the surface geology of the b a t h o l i t h and i t s ore.deposits became r e l a t i v e l y w e l l known, but important questions concerning the genesis of the b a t h o l i t h remained unanswered. A three dimensional model f o r the b a t h o l i t h was d e s i r e d . For t h i s reason, a g r a v i t y survey was conducted along s e l e c t e d t r a v e r s e s over the b a t h o l i t h i n the summer of 1971. I n t e r p r e t a t i o n of the Guichon's Bouguer anomaly map has allowed a determination of the gross shape f o r the b a t h o l i t h . The proposed three dimensional model i s c o n s i s t e n t w i t h a l l known.geological and geophysical data, and i s of considerable importance i n e x p l a i n i n g the genesis of the b a t h o l i t h . FIGURE I-l 3 2. GEOLOGICAL SETTING 2.1 Geography and Topography The Guichon Creek B a t h o l i t h u n d e r l i e s an area of approximately 400 square m i l e s w i t h i n the i n t e r i o r p l a t e a u of B r i t i s h Columbia. The Guichon i s bounded by the Thompson, N i c o l a and Guichon Creek v a l l e y s , (see F i g . 1-1). The geographic co-ordinates of the center of the batho-l i t h are 50°30'N, 121°00'W. The g e n e r a l l y semi-arid climate of the region causes the veg e t a t i o n to be sparse w i t h o c c a s i o n a l t h i c k stands of timber. The e n t i r e area i s covered by deep deposits of g l a c i a l m a t e r i a l l a i d down during P l e i s t o c e n e time. The t h i c k i c e sheets over-rode the highest peaks (6000 fee t ) , rounding t h e i r tops and deepening e x i s t i n g v a l l e y s , as they moved to the southeast. The a b l a t i o n of the i c e f i e l d s r e s u l t e d i n the formation of many c o l d water lakes and swamps by the t r a p p i n g of the melt water i n scoured depressions dammed by g l a c i a l d e b r i s . As a r e s u l t , bedrock exposures are not numerous - outcrops o c c u r r i n g on.less than 3% of the b a t h o l i t h . 2.2 Geology The Guichon Creek B a t h o l i t h i s a semi-concordant dome that i s elongated s l i g h t l y west of north. I t i n t r u d e s sedimentary and v o l c a n i c s t r a t a of the Permian Cache Creek Group and Upper T r i a s s i c N i c o l a Group and i s unconformably o v e r l a i n by sedimentary and v o l c a n i c s t r a t a ranging i n age from middle J u r a s s i c to Middle T e r t i a r y . The b a t h o l i t h appears to be bounded on the east and west sides by f a u l t s of r e g i o n a l extent. In map view, Figure 2-1, the b a t h o l i t h i s composed of s e v e r a l n e a r l y c o n c e n t r i c phases which have contacts that may be sharp l o c a l l y but are 5 g e n e r a l l y g r a d a t i o n a l . Extensive potassium-argon dating has shown t h a t , w i t h i n the l i m i t s of e r r o r , a l l phases began r e t a i n i n g argon at the same time, 198 + 8 m i l l i o n years ago, (Northcote, 1969). However, geologic data i n d i c a t e that phases are p r o g r e s s i v e l y younger from the border of the b a t h o l i t h inward. The phases of the b a t h o l i t h are separable on the b a s i s of com-p o s i t i o n a l and t e x t u r a l c r i t e r i a , M c Millan (1972). From the o l d e s t to the youngest, the f o l l o w i n g phases are d i s t i n g u i s h a b l e : (1) The border, HYBRID phase, which i s h i g h l y v a r i a b l e to uniform i n composition as a r e s u l t of contamination by a d j o i n i n g country rock. I t i s t y p i c a l l y r i c h i n mafic m i n e r a l s . (2) The HIGHLAND VALLEY phase which c o n s i s t s of the Guichon and Chataway g r a n o d i o r i t e s . The Guichon g r a n o d i o r i t e has 15 percent mafic minerals which'occur as evenly d i s t r i b u t e d c l u s t e r s of anhedral g r a i n s , whereas the Chataway g r a n o d i o r i t e has 12 percent mafic minerals and i s c h a r a c t e r i z e d by hornblende c r y s t a l s . (3) The BETHELEHEM phase g r a n o d i o r i t e has 8 percent mafic minerals. I t i s c h a r a c t e r i z e d by i r r e g u l a r l y d i s t r i b u t e d coarse-grained p o i k i l i t i c hornblende c r y s t a l s i n a m a t r i x c o n t a i n i n g evenly d i s t r i b u t e d f i n e to medium-grained mafic c r y s t a l s . (4) . The core.of the b a t h o l i t h i s composed of the BETHSAIDA phase quartz monzonite which has 6 percent mafic m i n e r a l s . I t i s c h a r a c t e r i z e d by coarse-grained subhedral quartz phenocrysts and coarse-grained book-l i k e b i o t i t e phenocrysts. A p e r i o d of extensive dyke emplacement followed the i n t r u s i o n of the Bethelehem phase and a l e s s e r p e r i o d followed the Bethsaida phase. 6 3. THE GRAVITY SURVEY 3.1 Gravity Observations The gravity survey was conducted and the observations reduced according to National Standards as defined by the Gravity D i v i s i o n , Earth Physics Branch, Dept. of Energy, Mines & Resources, Ottawa, Canada. (Refer to Chapter 4 f o r d e t a i l s ) . The gravity stations were t i e d into the National Control Network, and can be compared d i r e c t l y to any other observation throughout the Canadian network. The complete Bouguer anomaly values are r e l a t i v e to Ottawa which i n turn i s t i e d to the world base point at Potsdam, East Germany. The value at Ottawa i s 980,622.00 m i l l i g a l s , 3.2 The Survey Procedure Three traverses over the c e n t r a l portion of the Guichon Creek Batho-l i t h were selected on the basis of the mapped geology and the a c c e s s i b i l i t y by four wheel drive v e h i c l e . Gravity observations were taken at one-half mile i n t e r v a l s along two east-west and one north-south l i n e (Figure 3-1). For convenience, each s t a t i o n was assigned two numbers: (1) Gravity D i v i s i o n Station Number: corresponding to the time sequence of observation; 9000 series f or base s t a t i o n s , 19,000 series f o r d e t a i l s t a t i o n s . (2) Grid Point Number: corresponding to the s p a t i a l sequence of each s t a t i o n along i n d i v i d u a l traverses. 8 The ground p o s i t i o n of each s t a t i o n was marked by a wooden hub on which was n a i l e d an i r o n cap stamped with the g r i d point number. The UTM (Universal Transverse Mercator) co-ordinates f o r each gravity s t a t i o n were scaled from 1"=1320' topographic maps covering the survey area. The azimuthal pos i t i o n s were known to an accuracy of + 150 fe e t . (See Appendix A for a l i s t i n g ) . The g r a v i t y observations were made using a Worden Master gravity meter (no. W546) with scale constant 0.39937 mgal/scale d i v i s i o n and reading accuracy of 0.10 scale d i v i s i o n s . D r i f t control was maintained by tying into a base s t a t i o n network within each four hour i n t e r v a l . The base stations were selected at convenient points and base loop t i e d to each other and to the National network usjing a LaCoste & Romberg > Model G gravity meter. Since this instrument i s approximately an order of magnitude more accurate than the Worden and has v i r t u a l l y no instrument d r i f t , observed gravity values, accurate to +0.04 m i l l i g a l s were deter-mined f o r the base network. 3.3 Elevations The elevations (above mean sea l e v e l , MSL) at each s t a t i o n were deter-mined by a l e v e l survey conducted by Mr. George New of the B. C. Dept. of Lands, Forests and Water Resources. The e l e v a t i o n s , to the top of the wooden hubs, were measured to an accuracy of + 0.10 feet using a Jena Automatic Level. (See Appendix A for d e t a i l s ) . highland valley and younger phases DENSITY P L A N GUICHON CREEK BATHOLITH CONTOUR INTERVAL = 0.03gm/cm3 SCALE l"=4mi DATE FEB*72 FIGURE 3-2 3.4 Rock D e n s i t i e s Rock samples were c o l l e c t e d from 85 outcrops along and around the survey routes. Three samples were s e l e c t e d at random from each outcrop. Bulk d e n s i t i e s were measured using a M e t t l e r Balance. The value assigned to each outcrop was the average of the three samples. These d e n s i t i e s were p l o t t e d along w i t h over 600 other measurements determined by Dr. W. J . McMillan of the B. C. Dept. of Mines. The contoured surface d e n s i t y map of the Guichon b a t h o l i t h i s shown i n Figure 3-2. Rock d e n s i t i e s g e n e r a l l y i n c r e a s e w i t h the age of each phase. How-ever, only two major d i v i s i o n s can be made on the b a s i s of d e n s i t y . They are: (1) The Hybrid phase and country rocks, p = 2.80 gm/cm3. (2) The Highland V a l l e y , Bethelehem and Bethsaida phases, p = 2.70 gm/cm3. 11 4. GRAVITY CORRECTIONS The s m a l l v a r i a t i o n s i n o b s e r v e d g r a v i t y o v e r a s u r v e y e d a r e a i n c l u d e s e v e r a l e f f e c t s t h a t a r e u n r e l a t e d t o t h e g e o l o g y . S i n c e t h e s e v a r i a t i o n s a r e o f t h e same o r d e r o f magnitude as t h e r e s i d u a l g r a v i t y v a l u e s , i t i s n e c e s s a r y t o compensate f o r t h e s e e f f e c t s b e f o r e any m e a n i n g f u l i n t e r -p r e t a t i o n o f t h e r e s i d u a l f i e l d can be made. 4.1 D r i f t ( g D ) The t e r m " d r i f t " i s used h e r e t o i n c l u d e a l l f a c t o r s t h a t cause the o b s e r v e d g r a v i t y v a l u e , a t any g i v e n s t a t i o n , t o change w i t h t h e passage o f t i m e . I n c l u d e d i n d r i f t c o r r e c t i o n s a r e i n s t r u m e n t d r i f t and t h e e f f e c t o f e a r t h t i d e s . D r i f t c o r r e c t i o n s were a p p l i e d t o each o b s e r v a t i o n . The d r i f t r a t e was assumed t o be c o n s t a n t d u r i n g each o b s e r v a t i o n i n t e r v a l between c o n -t r o l s t a t i o n s . The range o f c o r r e c t i o n s f o r the s u r v e y was + 0.01 -+ 0.65 mgal,, t h e average b e i n g + .18 m g a l . 4.2 L a t i t u d e E f f e c t (g ) Li D e f i n i t i o n s : The s p h e r o i d a l s u r f a c e w h i c h g i v e s t h e c l o s e s t o v e r a l l f i t t o mean s e a l e v e l i s c a l l e d t h e r e f e r e n c e s p h e r o i d . The d i s t r i b u t i o n o f t h e g r a v i t a t i o n a l f i e l d on t h i s r e f e r e n c e s p h e r o i d i s c a l l e d t he t h e o r e t i c a l g r a v i t y , g^. On t h e b a s i s o f d a t a e x i s t i n g i n 1930, g was a p p r o x i m a t e d t o be: JL g T = 978.049(1+0.0052884sin 2cj> - 0.0000059sin 22cf>) g a l s 4.2-1 Li where <j> = g e o c e n t r i c l a t i t u d e (a) LATITUDE EFFECT g L equator reference spheroid (b) FREE AIR EFFECT g FA reference * uci "spheroid "M 3 L (0 (d) BOUGUER EFFECT QQ TERRAIN EFFECT g T —H A ground surface bouguer plane y » • slab i 1 r t rSSd 4 M S I- ( 9 ^ 9 ^ 9 ^ 1 - 9 13 Equation 4.2-1 i s known as the I n t e r n a t i o n a l G r a v i t y Formula, 1930, and was used to c a l c u l a t e the l a t i t u d e e f f e c t (g^) at each s t a t i o n due to the e l l i p t i c i t y of the e a r t h , Figure 4 - l ( a ) . As seen from equation 4.2-1, the l a t i t u d e e f f e c t increases as one moves toward the p o l e s . 4.3 Free A i r E f f e c t ( g ^ J °FA I n . p r a c t i c e , g r a v i t y observations are taken over an i r r e g u l a r surface at d i f f e r e n t distances from the reference spheroid. In order to approximate t h e . t h e o r e t i c a l value of the earth's f i e l d at a poi n t h from the reference spheroid of radius R, we may w r i t e , s i n c e R » h: g(R+h) = g(R) + h | | = g L + h | | 4.3-1 Using McCullagh's formula f o r the g r a v i t a t i o n a l p o t e n t i a l at any p o i n t outside a spheroid of s m a l l e c c e n t r i c i t y r o t a t i n g w i t h an angular v e l o c i t y , Grant & West (1965, p.237) show that f o r the e a r t h : | | = -0.9416-0.0090cos24> + 0.68 x 10" 7h gu/foot 4.3-2 where = the v e r t i c a l gradient of the g r a v i t a t i o n a l a c c e l e r a t i o n h = s t a t i o n e l e v a t i o n above mean sea l e v e l (MSL) The product i s known as the f r e e a i r e f f e c t (g-p^) > and was used to compensate f o r v a r i a t i o n s i n g r a v i t y due to departures from the reference s p h e r o i d , Figure 4-1(b). 14 4.4' Bouguer E f f e c t (g„) a The free a i r correction ignores the a t t r a c t i o n of the enti r e mass of material that l i e s between the gravity s t a t i o n and the reference spheroid. For l o c a l surveys, the curvature of the earth (the reference spheroid) can be ignored. We can therefore approximate t h i s material by an i n f i n i t e slab which has g r a v i t a t i o n a l a t t r a c t i o n : g n = 2-rrGph = 0.01276 ph mgal/foot 4.4-1 D where G = g r a v i t a t i o n a l constant p = bulk density of slab (Bouguer density), gm/cm3 h = s t a t i o n elevation above MSL, feet The e f f e c t represented by equation 4.4-1 at the observation s t a t i o n i s known as the Bouguer e f f e c t (g„). The s e l e c t i o n of p i s somewhat d i f f i c u l t . B Unless there i s strong evidence to the contrary, such as strong c o r r e l a t i o n of Bouguer anomaly with topography, p i s usually taken to be the average c r u s t a l density, 2.67 gm/cm3 , which y i e l d s a Bouguer e f f e c t of 0.034 mgal/ foot above MSL, (refer to Figure 4 - l ( c ) ) . 4.5 Terrain E f f e c t (g T) Since the Bouguer e f f e c t ignores i r r e g u l a r i t i e s i n the surface topo-graphy, an estimate must be made f o r the e f f e c t s at a s t a t i o n due to the f i l l i n g i n of v a l l e y s by the Bouguer slab, and for the t e r r a i n mass above the Bouguer plane. This c a l c u l a t i o n requires knowledge of the t e r r a i n d e n s i t i e s as w e l l as the nature (elevations) of the ground surface. In t h i s survey, the ground surface was approximated by a network of rectangular prisms with h o r i z o n t a l dimensions A x A, increasing i n 15 dimension away from the s t a t i o n . The height (Ah) of each prism was taken to be the elevation difference between the i n t e r s e c t i o n of the center of the prism with the ground surface and the Bouguer plane. (See Figure 4-1(d)). The t e r r a i n density was taken to be equal to the Bouguer density, 2.67 gm/cm3. The actual d i g i t i z a t i o n of the elevation maps and the c a l c u l a t i o n of the t e r r a i n e f f e c t s was performed i n three stages: near, intermediate, and f a r t e r r a i n d i v i s i o n s . The f i r s t quadrant of the format used i s depicted i n Figure 4-2(b) with a summary of s p e c i f i c a t i o n s l i s t e d i n Table 4.5. To increase e f f i c i e n c y , a c o r r i d o r was d i g i t i z e d along each traverse thereby allowing use of a d i g i t i z e d elevation point f o r more than one s t a t i o n c a l c u l a t i o n . Table 4.5 Prism approximations to t e r r a i n t e r r a i n e f f e c t prism s i z e A areal 2B extent 2C map scale of elevations prism approximation formula used FAR 1 km 50 km 5 km 1:50 ,000 v e r t i c a l l i n e mass INTERMED-IATE 200 m 5 km 600 m 1:50,000 sector of hollow cylinder NEAR 100 m 66 m 33 m 600 m 200 m 66 m 200 m 66 m 0 m 1:13,200 v e r t i c a l prism TERRAIN EFFECTS CALCULATION ERRORS Id) (using approx. to a square topped prism) FIGURE A-i Nagy's (1966) exact expression 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 v e r t i c a l prism (see Appendix B) was used to cal c u l a t e the NEAR t e r r a i n e f f e c t s . At INTERMEDIATE distances from the s t a t i o n , the prism's a t t r a c t i o n was approximated by a segment of a hollow c y l i n d e r , and at FAR distances by a v e r t i c a l l i n e mass. These l a t t e r approximations were ca r r i e d out at considerable saving i n computer time and l i t t l e loss i n accuracy. As seen i n Figure 4-2(a), (after Bott, 1969), the maximum errors due to these approximations are less than 4%. According to Stacey and Stephens (1970), consideration of the t e r r a i n e f f e c t s out to a distance of 25 km (50 km x 50 km area) w i l l account f o r > 90% of the t o t a l e f f e c t . Hence, the combined e r r o r due to the prism approximations and the exclusion of t e r r a i n e f f e c t s beyond 25 km i s about 14% g^, where g^ i s the t e r r a i n e f f e c t at each s t a t i o n . Terrain e f f e c t s ranged from 1.17. to 25.60 mgal, with an average of 4.70 mgal per s t a t i o n . 4.6 The G r a v i t y Anomaly (Ag) The l a t i t u d e ( g L ) , free a i r ( g p A ) , Bouguer (g^) and t e r r a i n (g T) e f f e c t s can be combined to approximate the t h e o r e t i c a l gravity f i e l d value for the co-ordinates of the observation s t a t i o n . The difference between the actual observed gravity g^ ( d r i f t corrected) and th i s c a l -culated gravity f i e l d value i s termed the "gravity anomaly" Ag. A gravity anomaly i s further described as.follows: (a) 'Free A i r ' Anomaly,, i f Ag = g Q - ( g L - g p A> (b) 'Simple Bouguer' Anomaly, i f Ag = g Q - ( g L - g p A + g g) (c) 'Complete Bouguer' Anomaly, i f Ag = g Q - ( g L - g p A + g f i - g T) 18 I t should be s t r e s s e d that the anomalous values are In f a c t l o c a t e d  at the co-ordinates of the observation s t a t i o n s . They ARE NOT reduced to any datum, but have been correct e d f o r e f f e c t s DOWN to a datum. The datum i s g e n e r a l l y MSL f o r absolute g r a v i t y anomalies and mean e l e v a t i o n f o r r e l a t i v e g r a v i t y anomalies. I t i s th e r e f o r e c l e a r that anomaly values are l o c a t e d on an i r r e g u l a r s u r f a c e , and any mathematical treatment of the data must consider t h i s p o i n t . I f we wish to "reduce the data to a common plane", then we must e f f e c t a l o c a l c o n t i n u a t i o n of the g r a v i t y anomaly to that plane.' As pointed out by Henderson & C o r d e l l (1971) , t h i s c o r r e c t i o n can be con-s i d e r e d important i n regions of high topographic r e l i e f (5000 f e e t ) , or where high p r e c i s i o n - (1 gu) i s r e q u i r e d . (See Figure 4-3) Figure 4-3 Location..of G r a v i t y Anomalies ground surface g r a v i t y datum e o = l o c a t i o n of anomaly = l o c a l c o n t i n u a t i o n of anomaly 19 A "gravity datum" can be viewed as an a r b i t r a r y plane below which the ef f e c t s are the same for a l l stations and above which they are s t a t i o n dependent. The datum chosen for the Guichon B a t h o l i t h was the mean elevation of the observation sta t i o n s = 4,055 feet. No continuation of the f i e l d was attempted. 4.7 Accuracy of Results The following table constitutes a summary of errors involved i n ca l c u l a t i n g the Bouguer anomaly for each s t a t i o n . range of error average err o r source of error amount of error f o r survey f or survey* observation +0.1 scale d i v i s i o n s +0.04 mgal + 0.04 mgal + 0.04 mgal l a t i t u d e + 150 f e e t ~ + 0.04 mgal +0.04 mgal +0.04 mgal elevation +0.10 f e e t ~ + 0.006 mgal + 0.006 mgal +0.01 mgal t e r r a i n 14% g T +.17 to +3.58 mgal +0.66 mgal d r i f t 10% g D** +0.001 to +.065 mgal +0.02 mgal The t o t a l average err o r f o r the Bouguer anomalies i s therefore + 0.77 mgal. * average err o r i s calculated to nearest .01 mgal ** d r i f t corrections were considered to be i n error by a maximum of 10% of the e f f e c t for each s t a t i o n . 5. DATA ENHANCEMENT TECHNIQUES 5.1 Interpolation of Gravity Map to a Square Grid In order to apply standard enhancement techniques, i t i s necessary that the values be d i s t r i b u t e d on a regular g r i d . Therefore, the Ag values at the 205 survey stations together with several regional observa-tions supplied by the Gravity D i v i s i o n were d i g i t i z e d and i n t e r p o l a t e d to a 1 mi x 1 mi square' g r i d using the UBC Xpand Subroutine.* The gridded values of dimension 35 x 46 were then contoured to y i e l d the "Complete Bouguer Anomaly Map", Figure 5-1. The contours are considered meaningful only near gravity s t a t i o n s . In other regions they represent only an approximation to the anomaly f i e l d . 5.2 F i l t e r i n g of P o t e n t i a l F i e l d s As demonstrated, by. F u l l e r (1967), Clarke (1969), Ulrych (1969), i t i s convenient to view- the enhancement of p o t e n t i a l f i e l d s as the input-output r e l a t i o n of a l i n e a r system. Such an i n t e r p r e t a t i o n allows considerable c l a r i f i c a t i o n of the e f f e c t s of a p a r t i c u l a r enhancement technique.by viewing i t s wavenumber thumbprint. With the advent of the FFT (Fast Fourier Transform), Cooley and Tukey (1965), t h i s approach i s now p r a c t i c a l . Figure 5-2(a) i l l u s t r a t e s the equivalence of the f i l t e r i n g process i n the space and wavenumber domains. In the space domain, the f i l t e r e d map the value assigned to a g r i d i n t e r s e c t i o n i s set equal to the average of the nearest values i n each octant that have been weighted by 1/d, where d = distance from the data point to the g r i d i n t e r s e c t i o n . FIGURE 5-1 REPRESENTATION OF FILTERING PROCESS (a) SPACE DOMAIN A3, WAVENUMBER DOMAIN impulse response h Ag. * Ag * h transfer function h a g 0 = ag. • h Ag, SELECTION OF (b) CUTOFF WAVENUMBER USING VERTICAL PRISM ^g Ag/2 2 miles - • 25 cpm REGIONAL-RESIDUAL SEPARATION (c) Nk) idea) -Ag.(k) normalized regional residual 1 •25 cycles /mile N •50 FIGURE 5 -2 Ag Q(x,y) i s obtained by convolving (*) the input map Ag^(x,y) with the impulse response f u n c t i o n h ( x , y ) . In wavenumber space, t h i s process i s e q u i v a l e n t to m u l t i p l y i n g the F o u r i e r transform (^ ) of the input map Ag.(k ,k ) by the t r a n s f e r f u n c t i o n h(k ,k ), where: i x' y x' y ' Mk x,k y) = J J e i ( x k x + y k y ) h(x,y)dxdy -an - ° ° such that k and k are the wavenumbers i n the x and y d i r e c t i o n s x y J r e s p e c t i v e l y . The choice of the i d e a l f i l t e r i n g f u n c t i o n h depends on how one wishes to enhance the' data. Common operations on p o t e n t i a l f i e l d s are v e r t i c a l c o n t i n u a t i o n , r e g i o n a l - r e s i d u a l s e p a r a t i o n , and the second d e r i v a t i v e computation. A complete set of weighting c o e f f i c i e n t s together w i t h t h e i r frequency images f o r these operations can be found i n F u l l e r (1967). 5.3 Regional-Residual Separation The separation of r e g i o n a l (broad s c a l e ) from r e s i d u a l ( l o c a l ) anomalies can be viewed.as the c o n v o l u t i o n of the input map w i t h a low pass f i l t e r , where the c u t o f f wavenumbers may be determined by the geology of the r e g i o n . By i n s p e c t i o n of the surface geology of the Guichon B a t h o l i t h , the minimum h o r i z o n t a l dimension of any major phase of the b a t h o l i t h was taken to be two m i l e s . For a v e r t i c a l prism, t h i s corresponds to a Ag h a l f -width of about 2 m i l e s , Figure 5-2(b). Using t h i s distance as one h a l f a wavelength, the maximum c u t o f f wavenumber k^ f o r the b a t h o l i t h was c a l -c u l a t e d to be 0.25 c y c l e s / m i l e . Applying the same reasoning to the maximum dimension of the b a t h o l i t h (36 miles) , we calculated a minimum cutoff wavenumber of 1/72 cycles per mile. However, i n t h i s case, since i t i s i m p r a c t i c a l to b u i l d a short, f i l t e r with a steep leading edge which cuts o f f at 1/72 cpm, the minimum cutoff wavenumber was set at 0 cpm. Close scrutiny of the Regional Ag map edges reveals l i t t l e large scale trend, except to the east and south-east where the f i e l d i s known to overlap with neighbouring sources, (e.g. N i c o l a b a t h o l i t h ) . Therefore this 0 cpm assumption appears j u s t i f i e d . A p i c t o r i a l representation of the r e g i o n a l - r e s i d u a l separation i n the wavenumber domain i s shown.in Figure 5-2(c). 5.4 The F i l t e r e d Gravity Maps A l l f i l t e r i n g operations were performed i n the space domain by con-volving the input map with the appropriate weighting function. The plots of the f i l t e r e d maps exclude the edge e f f e c t of (L-l) p o i n t s , where L i s the f i l t e r length. Since the dimensions of the Ag map were small, 35 x 46, care was taken to s e l e c t f i l t e r operators that were short i n length and that attenuated high frequencies but were s t i l l a good approximation to the i d e a l operator at low. wavenumbers. (1) The REGIONAL Ag MAP.was calculated'by convolving the Ag map with the Ulrych (1969) four point f i l t e r . The frequency c h a r a c t e r i s t i c s and weighting c o e f f i c i e n t s f o r t h i s low pass f i l t e r are summarized i n Figure 5-3. By inspection of the map edges, a base l e v e l of -115 mgal was subtracted from the e n t i r e map. The p l o t of the regional Ag f i e l d i s Figure 5-4. It i s t h i s map that was interpretated f o r the gross shape of the b a t h o l i t h (see Chapter 6). U L R Y C H R E G I O N A L FILTER AMPLITUDE SPECTRUM K X CYCLES / MILE WEIGHTING COEFFICIENTS t -0-0084-=0-0078—00033 0 0000 I I I I ^ 0-0237—0 0088—0-0079—^00033 6 | | | >j 0-1232—0-0778—00088—0-0078 - I I I I 0-1843 —01232—O0237 —"00084 -FIRST QUADRANT (AX»lmi) FIGURE 5 - 3 REGIONAL A g ANOMALY \ ^GUICHON^ X \ BATHOLITH SCALE 1" =4 mi FEB 1972 CONTOUR INTERVAL = 5 mgal BASE LEV£L ? "115 mqal 5Q°W E FIGURE 5-4 a FIGURE 7 - 3 R O S E N B A C H SECOND DERIVATIVE FILTER AMPLITUDE SPECTRUM UJ CO UJ o K, CYCLES /MILE WEIGHTING COEFFICIENTS 0 0 0 0 — 0042 0-000 I I I -0750-^0-334 0 042 I I I 4000^0-750—-6-000 FIRST QUADRANT ( A X « l m l ) FIGURE 5-6 FIGURE 5-7 30 (2) The RESIDUAL Ag MAP was defined to be (Ag - regional Ag) and is p l o t t e d i n Figure 5-5. It contains anomalies at t r i b u t e d to structures of less than two miles i n h o r i z o n t a l dimension. Only those anomalies along the gravity traverses are considered meaningful. (3) The SECOND (VERTICAL) DERIVATIVE MAP was made by applying the Rosenbach 3 point f i l t e r , F u l l e r (1967) , to the regional Ag map and i s plo t t e d i n Figure 5-7. As we w i l l see l a t e r , t h i s map was very h e l p f u l i n determining a density model for the b a t h o l i t h . The amplitude spectrum together with the weighting c o e f f i c i e n t s for the Rosenbach f i l t e r are shown i n Figure 5-6. 31 6. INTERPRETATION 6.1 Depth Estimates An attempt was made to estimate the depth to the center of mass of the source using s p e c t r a l a n a l ysis. However, due to the short record length only a poor estimate of the power spectrum could be made and the approach was discarded a f t e r y i e l d i n g gross errors. Af t e r c a r e f u l scrutiny of the density, gravity and magnetic data, i t appeared that the b a t h o l i t h was shallow r e l a t i v e to i t s l a t e r a l extent. For t h i s reason, the t h i n s e m i - i n f i n i t e two dimensional slab model was used to ca l c u l a t e the i n i t i a l depth estimate to the center of mass of the body, where Ag = 2Gpt(Tr/2 + tan - 1 x / z ) 6.1-1 and using t h i s equation we get: where 6.1-2 z = average depth The various parameters are as shown i n Figures 6-1 and 6-2. Applying equation 6.1-2 to both sides of p r o f i l e AA' (the p r i n c i p a l p r o f i l e of the regional Ag) an average depth to the center of mass of the body was estimated to be 2.0 miles, (see Figure 6-1). Since the top of the source i s at the surface, t h i s implies a depth extent for the b a t h o l i t h of about 5 miles. 0" - 5 -I"-10-15-< g'-acH -25-"30-0-i 2 H CL XI Ag max T T |Ag' max1 D E P T H - S H A P E ESTIMATE PROFILE AA' (looking northerly) SCALE 4mi FEB 1972 highland valley and yojunger phases 5mi 33-0 mgal ^ AVERAGE 2 * 2-0mi "INITIAL" GROSS SHAPE r-0 I-K> FIGURE 6-1 33 6.2 Consideration of Gravity half-widths The half-width of the gravity p r o f i l e can be diagnostic of the gross shape of the source. For a s e m i - i n f i n i t e two dimensional s l a b , Figure 6-2, the d i r e c t i o n of slope of the edges of the source can be estimated by observing the trace of the gravity p r o f i l e half-width r e l a t i v e to the source contact. The general rule of thumb being: (1) If the half-width and source contact coincide, then the side i s v e r t i c a l . (2) I f they are not coincident, then the source slopes i n the d i r e c t i o n toward the h a l f width contour. Applying t h i s crude estimate to the Guichon, we see that the batho-l i t h slopes inward on the west and outward on the east, Figure 6-4. 6.3 Consideration of the Second V e r t i c a l Derivative Referring again to the s e m i - i n f i n i t e h o r i z o n t a l slab model, Figure 6-2, Bott (1962) has shown that the .ratio of the maximum to minimum values of the second d e r i v a t i v e s , on e i t h e r side of the zero trace and r a d i a l l y containing the anomaly high, give a measure of both the d i r e c t i o n and the amount of s l o p e - o f the source edge, ... He has shown that: (1) I f (-g" /g"„ ) > 1, the side slopes inward. max °min (2) If (-g" /g"„ ) < 1, the side slopes outward. °max mm (3) If the r a t i o of depths to the top and bottom of the slab (z^/Zy) are known, then using Bott's family of curves, Figure 6-3, the slope.of the source edge can be determined. 8 A -mm 8 a. & Ag/2 1 > p Q. a> T3 Ag HALF-WIDTH i > 9 0 ° 1 = 9 0 ° i < 90° siab source of density contrast =p HALF-WIDTH /2nd DERIVATIVE SEMI-INFINITE HORIZONTAL SLAB MODEL SCALE Arbi tra ry FEB 1972 ANGLE OF SLOPE ( i) S O U R C E S L O P E C U R V E S $ P L O T O F DERIVATIVE RATIOS FOR VARIOUS EDGES O F BATHOLITH after B o t t ( l 9 6 2 ) F E B 1972 F IGURE 6 - 3 o 03 A V H A L F - W I D T H CONTOUR O F REGIONAL A g V v DENSITY = 2-76 g m / c m 3 CONTOUR ScTJo' j V / V - 1 V V 4ml DATA COMPILATION P L A N © POSITION O F A g " = 0 ON GRAVITY T R A V E R S E SHOWING DIP O F SOURCE EDGE MAGNETIC HIGHS v» HIGHLAND NALLEY and YOUNGER P H A S E S OF B A T H O L I T H S C A L E I"-4 mi F E B , 9 ? 2 vP-FIGURE 6-4 Applying t h i s approach to the b a t h o l i t h , we note that the "zero trace" of the second derivative map (considered only along gravity traverses) outlines the Hybrid-younger phase contact rather w e l l , Figure 6-4. Consideration of the r a t i o s of derivatives on eith e r side of t h i s contact led to the following estimates: (1) west edge = slopes 70-80° east (2) south edge = slopes 70° north (3) east edge = slopes 75° east with a reversal of dip at depth to 50°W. (4) north edge = slopes v e r t i c a l with the zero trace approximating the northern boundary of the younger phases. 6.4 .Selection of Densities The 2.76 gm/cm3 density contour coincides rather w e l l with the Hybrid-younger phase boundary, Figure 6-4. Northcote (1969) calculated the mean value of the'Hybrid phase to be 2.80 gm/cm3. By inspection of the density map, Figure 3-2, the younger phases were estimated to have a bulk density of about 2.70 gm/cm3. Hence, a density contrast of Ap = -0.10 gm/cm3 was assumed for the body. 6.5 Consideration of Magnetics In an attempt to gain further i n s i g h t into the sub-surface nature of the b a t h o l i t h , published aeromagnetic maps* covering the b a t h o l i t h were d i g i t i z e d at 1 mi x .1 mi-, i n t e r v a l s over an area 68 miles by 45 miles. The r e s u l t i n g t o t a l f i e l d maps together with the reg i o n a l , r e s i d u a l and second d e r i v a t i v e maps are p l o t t e d i n Figures 6-5, 6-6, 6-7 and 6-8. The * Map sheet numbers 5209G-5212G, 5217G-5220G, GSC/BC Dept. of Mines Aeromaenetic s e r i e s . FIGURE 6-7 42 U l r y c h r e g i o n a l / r e s i d u a l and the Rosenbach second v e r t i c a l d e r i v a t i v e f i l t e r s were a p p l i e d as before. Since the magnetic s u s c e p t i b i l i t y c o n t r a s t of the b a t h o l i t h i s known to vary a p p r e c i a b l y i n the Hybrid zone and was not measured, no attempt was made to i n t e r p r e t the 1 magnetics q u a n t i t a t i v e l y . However, c e r t a i n conclusions f o l l o w from a v i s u a l examination of the data: (1) The regional'magnetic map, Figure 6-6, reveals a halo of magnetic highs surrounding the b a t h o l i t h . I f one a t t r i b u t e s these highs to be caused, at l e a s t i n p a r t , by the d i p o l e e f f e c t of the edge of the source, then the magnetics support the p o s i t i o n of the d e n s i t y  contact as the Hybrid-younger contact, Figure 6-4. (2) The e x i s t e n c e of the highs suggests that the b a t h o l i t h can be considered as a d i p o l a r source and i s t h e r e f o r e r e l a t i v e l y shallow. Since the highs are a p p r e c i a b l y of greater magnitude to the west than t o the e a s t , t h i s suggests that the b a t h o l i t h deepens to the east. This i s c o n s i s t e n t w i t h the" g r a v i t y depth and shape estimates. (3) The zero t r a c e . o f the second d e r i v a t i v e (Figure 6-8) a l s o suggests that the younger phases are- d i s t i n c t from the Hybrid zone, and that m a g n e t i c a l l y the Bethsaida phase i s ~ s e p a r a b l e from the younger phases. (4) The l i n e a r magnetic features c o i n c i d e n t w i t h the Thompson R i v e r on the west and w i t h the Guichon Creek on the east support Carr's (1963) hypothesis that the b a t h o l i t h i s f a u l t bounded. 6.6 C a l c u l a t i o n of Ag for Model On the basis of the foregoing estimates, a funnel shaped s t a r t i n g model for the b a t h o l i t h was envisaged. The " i n i t i a l " gross shape i s shown i n section for p r o f i l e AA', Figure 6-1. To f a c i l i t a t e c a l c u l a t i o n of the v e r t i c a l component of the g r a v i t a -t i o n a l e f f e c t at each s t a t i o n , the model was divided into thin h o r i z o n t a l polygonal (12 sided) sheets at depth i n t e r v a l s of 1 km. 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 each sheet was computed using the well known Talwani and Ewing (1960) method (see Appendix C). The e f f e c t f o r the body was found by evaluating the i n t e g r a l top Ae = z. V dz using Simpson's r u l e , bottom where V = e f f e c t of each sheet z = depth of each lamina (sheet) The depths and the co-ordinates of the v e r t i c e s were adjusted and the model recomputed u n t i l an rms error f i t of less than 0.90 mgal was obtained f o r the 205 g r a v i t y stations that were a c t u a l l y observed. The rms error f i t f o r a l l the 1160 gravity stations of Figure 5-4 was 3.94 mgal. The f i n a l model for the b a t h o l i t h and i t s gravity map are shown and discussed i n Chapter 7. 7. .MODEL .OF .THE BATHOLITH 7.1 Gross Shape The density model of the ba t h o l i t h which gives a good f i t to the gravity data i s shown i n Figures 7-1, 7-4 and 7-5. It can be i n t e r -preted as being a f l a t - f u n n e l shaped structure with the center of the stubby spout sub-cropping to the east but enclosing the mineralized areas of the Highland V a l l e y . The maximum depth i s about 7 kilometers, except near the ce n t r a l core where the depth i s about 12 km. If one assumes an i n i t i a l symmetric shape f o r the b a t h o l i t h , then the pole of the axis of symmetry would p l o t on the surface at co-ordinates 120°58.5'W, 50°27.9'N with a plunge of 64°/72°, as shown i n Figures 7-1, 7-4 and 7-5. This ; can be taken as support f o r the hypothesis that the b a t h o l i t h i s t i l t e d to the west-southwest. 7.2 The Calculated Gravity Map The calculated gravity map.for the b a t h o l i t h model i s shown i n Figure 7-2. For convenience;..the regional'Ag map ' i s shown again here as Figure 7-3. Care was taken to f i t the data along gravity traverses. In other areas, e s p e c i a l l y peripheral to the b a t h o l i t h source and where observations are sparse, the model represents only an estimate. In the ce n t r a l region, the -30 mgal contour could only be approxi-mated. In order to obtain a better f i t , the addition of a near surface source i s required. This feature i s of l i t t l e importance to the gross shape of the b a t h o l i t h , but may be of i n t e r e s t l o c a l l y . The large i n f l e c t i o n i n the gra v i t y contours to the north can be att r i b u t e d to the anomaly caused by the overlying Kamloops vol c a n i c s . FIGURE 7-1 C A L C U L A T E D Ag ANOMALY MODEL OF BATHOLITH S C A L E = 4mi FEB 1972 CONTOUR INTERVAL = 5 mgal FIGURE 7-2 REGIONAL A g ANOMALY \ '"GUICHON-^ BATHOLITH ^ 4. SCALE l"=4mi FEB 1972 CONTOUR INTERVAL = 5 mgal B A S E L E V £ L ? "115 mgal 50°30_ FIGURE 5-4 MODEL P R O F I L E Bcf (looking easterly) SCALE |" * 4 mi FEB 1972 -1 To include this effect, the outcrop trace of the group was approximated by a 12 sided vertical prism and i t s gravity effect calculated as before and included in the computed Ag map. The density of the volcanics was estimated from measurements on collected rock samples to be 2.60 gm/cm3. The average depth of the group was found by t r i a l and error to be about 1 kilometer, see Figure 7-5. Calculated and observed (regional) gravity anomalies together with depth profiles for sections AA' and BB' are shown in Figures 7-4 and 7-5. Along these lines the f i t is extremely good as evidenced by the comparison of the computed points with the actual Ag values. 51 8. SUMMARY AND CONCLUSIONS As shown i n Chapter 4, and contrary to popular b e l i e f , i t i s important to r e a l i z e that the gravity anomalies are i n fact located at the co-ordinates of the observation s t a t i o n . They ARE NOT reduced to any datum, but have been corrected for e f f e c t s down to a datum. It i s therefore c l e a r that the anomaly values are located on an i r r e g u l a r surface, and any mathematical treatment of the data must consider t h i s point. This i s of sp e c i a l importance i n mountainous regions. The use of l i n e a r f i l t e r operators on p o t e n t i a l f i e l d s g r e atly enhances the i n t e r p r e t a t i o n of the data and provides a useful means of anomaly separation. This i s most c l e a r l y evident on the f i l t e r e d magnetic map (Figure 6-6) where resolution of regional magnetic features i s remarkable. * Another example i s the use of the second v e r t i c a l d e r i v a t i v e map i n defining the boundary of the source (Figure 6-4) . In p a r t i c u l a r , i t suggests that the b a t h o l i t h terminates rather abruptly to the north, sub-cropping the Kamloops vol c a n i c s . On the basis of the gra v i t y and density data, only two sub-divisions of the b a t h o l i t h can be made: (a) The Hybrid phase and country rock, p = 2.80 gm/cm3, and .(b) The Highland V a l l e y , Bethlehem and Bethsaida phases, p = 2.70 gm/cm3. . An estimate of the average depth of the Kamloops volcanics overlying the north edge of the b a t h o l i t h was made from the regional Ag map. Using p = 2.60 gm/cm3, a depth of 1.0 kilometers was determined. I n t e r p r e t a t i o n of the g r a v i t y data l e d t o a d e n s i t y model f o r the b a t h o l i t h (Chapter 7). I t s gross shape can be l i k e n e d to that of a f l a t o v a l f u n n e l - l i k e s t r u c t u r e w i t h a stubby spout. The a x i s of symmetry f o r the model i s t i l t e d about 18° from the v e r t i c a l i n a west-southwest d i r e c t i o n . The maximum depth of the c e n t r a l core i s about 12 k i l o m e t e r s . Probably the most important r e s u l t of t h i s study i n terms of ore search i s shown i n Figure 7-1. Here a s t r i k i n g c o r r e l a t i o n between the s p a t i a l r e l a t i o n s h i p of the m i n e r a l deposits and the core of the b a t h o l i t h has been discovered. These r e s u l t s c l e a r l y p o i n t to the value of high p r e c i s i o n r e g i o n a l g r a v i t y s t u d i e s i n the search f o r b a t h o l i t h r e l a t e d ore d e p o s i t s . I t i s the author's view that s k i l l f u l i n t e r p r e t a t i o n of g r a v i t y -magnetic surveys using modern f i l t e r i n g techniques w i l l y i e l d a wealth of i n f o r m a t i o n p e r t i n e n t to the d i s c o v e r y of more economic ore d e p o s i t s . 53 REFERENCES Bott, M.H.P. (1959). The use of e l e c t r o n i c d i g i t a l computers for the evaluation of gravimetric t e r r a i n corrections, Geophys. Prosp. _7, 46-54. Bott, M.H.P. (1962). A simple c r i t e r i a f o r i n t e r p r e t i n g negative gr a v i t y anomalies, Geophysics, 2_7, 376-381. Bott, M.H.P., and Smithson, S.B. (1967). Gravity i n v e s t i g a t i o n s of the subsurface shape and mass d i s t r i b u t i o n s of granite b a t h o l i t h s , GSA B u l l e t i n , 78, 859-878. Blackman, R.B., and Tukey, J.W. (1958). The measurement of power spectra, Dover Pu b l i c a t i o n s , N.Y. Carr, J.M. (1963). Geology of part of the Thompson River Va l l e y between Ashcroft and Spences Bridge, M i n i s t e r of Mines and P.R., B. C., Annual report, 1962, 28-45. Clarke, G.K.C. (1969). Optimum second-derivative and downward continuation f i l t e r s , Geophysics, 34, 424-437. Cooley, J.W., and Tukey, J.W. (1965). An alogrithm f o r the machine c a l c u l a t i o n of complex f o u r i e r s e r i e s , Math. Comput. 19_, 297-301. Dobrin, M.B. (1960). Introduction to geophysical prospecting, McGraw-Hill Book Co., N.Y. Grant, F.S., and West, G.F. (1965). I n t e r p r e t a t i o n theory i n applied geophysics, McGraw-Hill Book Co., N.Y. Henderson, R.G., and C o r d e l l , L. (1971). Reduction of unevenly spaced p o t e n t i a l f i e l d data to a h o r i z o n t a l plane by means of f i n i t e harmonic s e r i e s , Geophysics, 36, 856-877. Kane, M.F. (1962). A comprehensive system of t e r r a i n corrections using a d i g i t a l computer, Geophysics, 27, 455-462. Ku, C C . , T e l f o r d , W.M. , and Lim, S.H. (1971). The use of l i n e a r f i l t e r i n g i n gravity problems, Geophysics, ^6, 1174-1203. McMillan, W.J. (1972). Personal communication. Nagy, D. (1966).. The prism method for t e r r a i n corrections using d i g i t a l computers; Pure Appl. Geophys., _63, 31-39. Northcote, K.E. (1969). Geology and geochronology of the Guichon Creek B a t h o l i t h , B. C. Dept. of Mines and P.R., B u l l e t i n No. 56. Parasnis, D.S. (1966). Mining geophysics. E l s e v i e r Publishing Co., Netherlands. 54 Stacey, R.A. , and Stephens, L.E. (1970). Procedures f o r c a l c u l a t i n g t e r r a i n corrections for gravity measurements, Publications of the Dominion Observatory, Ottawa, 39_, No. 10. Talwani, M., and Ewing, M. (1960). Rapid computation of g r a v i t a t i o n a l a t t r a c t i o n of three dimensional bodies of a r b i t r a r y shape, Geophysics, 25, 203-225. Ulrych, T.J. (1969). Wavenumber domain analysis and design of p o t e n t i a l f i e l d f i l t e r s , Proceedings of a Symposium on decision-making i n mineral exploration I I , U n i v e r s i t y of B. C. Winter, P.J., and P e r r i e r , J.A. (1968). Descriptions of gravity c o n t r o l s t a t i o n s , Dominion Observatory, Ottawa, NTS 92, July 1968. 55 APPENDIX A SUMMARY OF SURVEY RESULTS GRID GRAVITY UTM CO-ORDINATES ELEVATION OBSERVED COMPLETE POINT STATION ZONE 10 (METERS) GRAVITY g Q B. ANOMALY NO. NO. . EASTING NORTHING (FEET) (MILLIGAL) Ag (MGALS) 0 19570 620800 5603560 940.8 980946.75 - 110.16 IB 19694 621590 5603375 1652.2 980910.17 - 106.02 2 19693 622325 5603180 2324.8 980872.90 - 107.42 3 19568 623100 5603025 2672.3 980854.73 - 105.28 4 19567 624050 5602740 2999.9 980835.84 - 103.90 5 19566 624840 5602600 3323.5 980819.38 - 104.11 6 19628 625590 5602450 3803.9 980791.56 - 101.93 7 19565 626300 5602300 3885.7 980787.31 - 103.43 8 19251 627100 5602450 4064.2 980776.03 - 104.21 9 19501 627930 5602425 4052.4 980773.03 - 108.24 10 19502 628740 5602525 3976.1 980775.15 - 111.16 11 19503 629550 5602550 3862.0 980780.38 - 112.24 12 19504 630350 5602540 3840.0 980780.37 - 114.30 13 19505 631075 5602500 3811.1 980781.21 - 115.21 14 19506 631925 5602200 3836.1 980776.74 - 117.42 15 19507 632700 5601275 3794.6 980774.38 - 122.26 16A 19508 633175 5600900 3848.1 980769.23 - 122 ..64 17 19510 634325 5600350 3836.1 980764.55 - 127.89 18 19511 635100 5600150 3889.9 980758.75 - 13.0.39 19 19512 635900 5599660 3883.9 980755.87 - 133.33 20 19513 636650 5598975 3891.0 980751.84 - 134.81 21 19514 637475 5598200 3947.9 980745.37 - 137.52 22 19515 638300 5596650 3974.5 980740.10 - 141.16 23 19516 639200 5594250 3988.2 980733.39 - 146.11 24 19517 640075 5594010 3969.7 980732.51 - 148.88 25 19518 640800 5593750 3957.2 980733.66 - 148.22 26 19252 641690 5593450 3940.1 980732.14 - 150.51 27 19519 642500 5593475 3929.4 980731.74 - 151.45 56 28 19520 643225 5593550 3942.1 980732.56 - 149.31 29 19521 644025 5593200 3932.1 980733.26 - 149.36 30 19522 644850 5592950 3921.7 980734.76 - 148.41 31 19523 645600 5592400 3912.1 980733.64 - 150.07 32 19524 646425 5592390 3912.7 980734.63 - 149.27 33 . 19525 647225 5592000 3865.4 980738.28 - 148.01 34 19526 648000 5591950 3842.8 980741.74 - 145.80 35 19527 648825 5592025 3841.5 980743.49 - 144.45 36 19528 649575 5592275 3828.2 980746.58 - 142.05 37 19529 650075 5593650 3805.6 980753.34 - 136.31 38 19530 651080 5594725 3696.0 980763.30 - 134.19 39 19531 651890 5595500 3558.5 980773.96 - 126.36 < 40 19532 652650 5595725 3425.2 980782.43 - 130.30 41 19533 653525 5595150 3366.5 980785.30 - 132.44 42 19253 654225 5595050 3391.2 980785.83 - 130.66 43 19534 655000 5595250 3562.0 980780.95 - 124.60 44 19535 655700 5596100 3615.8 980780.98 - 123.76 45 19536 656500 5595975 3688.9 980780.10 - 119.99 46 19537 657325 5596000 3727.9 980780.33 - 115.00 47 19538 658175 5595525 3782.5 980777.53 - 114.72 48 19539 659050 5595250 3795.0 980776.33 - 116.24 49 19540 659900 5595150 3880.0 980772.09 -50 19541 660675 5594925 3857.9 980774.00 -51 19542 661470 5594835 3908.0 980771.92 -52 19543 662350 5594150 3913.8 980772.10 -53 19601 619575 5587025 748.8 980935.94 - 120.15 54 19602 620450 5586100 769.6 980930.46 - 118.84 55 19603 621200 5585800 1169.3 980910.07 - 109.55 56 19604 622000 5586100 1998.1 980864.46 - 118.59 57 19605 622800 5587500 3321.6 980791.14 - 117.82 58 19606 623625 5586425 3455.9 980782.91 - 113.91 59 19607 624400 5586925 3814.2 980763.17 - 116.01 60 19608 625100 5586750 4072.3 980747.01 - 119.24 61 19609 625900 5586800 4229.8 980736.88 - 118.53 57 62 19610 626675 5586775 4364.8 980727.48 - 121.16 63 19611 627710 5586050 4735.3 980701.54 - 122.66 64 19612 628375 5585425 4802.6 980697.80 - 123.93 65 19613 629000 5585475 4737.1 980702.82 - 123.57 66 19614 629825 5584650 4794.5 980700.95 - 121.07 67 19615 630625 5584350 4847.1 980701.38 - 118.01 68 19616 631450 5584625 4860.8 980701.41 - 118.18 69 19617 632225 5584775 4933.0 980696.54 - 118.44 70 19618 633025 5584700 4956.9 980694.10 - 120.64 71 19619 633850 5584725 4982.6 980690.82 - 122.18 72 19255 634575 5585025 5030.8 980683.43 - 127.17 73 19620 635420 5585210 5103.5 980674.35 - 130.39 74 19621 636200 5585300 5095.2 980671.81 - 133.18 75 19622 637000 5585425 5132.1 980667.72 - 136.74 76 19623 637825 5585875 5145.2 980664.97 - 139.81 77 19624 638625 5595975 5282.6 980654.87 - 141.30 78 19625 639375 5586125 5318.9 980651.62 - 143.06 79 19626 640125 5585350 5334.8 980649.61 - 141.18 80 19627 640950 5585150 5451.2 980641.54 - 143.21 81 19593 641775 5588000 5399.6 980644.29 - 144.02 82 19594 642500 5587056 5633.2 980629.04 - 144.00 83 19596 643300 5587050 5754.7 980620.84 - 145.24 84 19600 644100 5586825 5489.6 980637.17 - 143.47 85 19599 644875 5586700 5310.0 980648.33 - 145.32 86 19598 645550 5586425 5189.0 980655.85 - 146.78 87 19685 646475 5584050 5129.0 980658.22 - 146.14 88 19684 647275 5583700 4921.5 980671.24 - 147.64 89 19683 648125 5583125 4858.2 980675.00 - 144.91 90 19680 648875 5584100 4834.4 980677.80 - 143.38 91 19681 649625 5584450 4704.8 980686.61 - 142.63 92 19682 650375 5584600 4578.6 980695.22 - 142.41 93 19679 651200 5587100 4490.0 980704.67 - 140.29 94 19678 651950 5587050 4275.8 980719.17 - 137.93 95 19677 652925 5587025 96 19676 653250 5587025 97 19675 654325 5586625 98 19674 655125 5586075 99 19254 655925 5585650 100 19669 656850 5581050 101 19670 657675 5581500 102 19671 658450 5581825 103 19672 659175 5581950 104 19673 659975 5581375 105 19695 660700 5580825 106 19696 661425 5580475 107 19629 651550 5557400 108 19630 651825 5558275 109 19631 651775 5559100 110 19632 652050 5559900 111 19633 652075 5560675 112 19634 651850 5561325 113 19635 651550 5562050 114 19636 650775 5562950 115 19637 651150 5563725 116 19638 651525 5564375 117 19639 651825 5565350 118 19640 651400 5566100 119 19641 651375 5566875 120 19642 651725 5567725 121 19643 651950 5568500 122 19644 652175 5569300 123 19645 652450 5570075 124 19646 652650 5570875 125 19647 652750 5571675 126A 19648 651775 5572425 126B 19649 650825 5572025 126C 19650 650000 5571900 58 4125.6 980729.13 - 136.02 4063.0 980732.57 - 131.33 3582.9 980761.74 - 132.16 3227.3 980782.40 - 133.69 3189.5 980786.68 - 129.32 3323.7 980776.09 - 129.71 3621.6 980763.20 - 126.55 3916.1 980748.19 - 124.68 4102.1 980737.44 - 122.77 4190.9 980730.90 -4366.0 980719.95 -4286.0 980723.62 -1916.6 980838.89 - 131.68 1981.4 980833.11 - 136.61 2027.3 980831.07 - 136.61 2085.1 980827.11 - 137.34 2135.1 980824.36 - 137.66 2286.4 980817.52 - 133.40 2291.9 980819.40 - 130.41 2317.2 980822.07 - 125.83 2610.9 980804.70 - 129.70 2789.0 980796.48 - 128.90 2930.2 980789.96 - 128.19 3097.2 980783.01 - 124.36 3275.0 980772.70 - 126.33 3285.6 980773.67 - 125.85 3270.7 980773.04 - 122.78 3288.3 980771.62 - 124.46 3306.3 980768.65 - 131.19 3317.5 980770.33 - 127.63 3346.5 980766.88 - 132.14 3730.3 980742.22 - 132.75 4135.4 980717.90 - 131.02 4241,4 980712.36 - 134.62 59 126D 19651 649200 5572175 4398.9 980703.43 - 132.85 126E 19652 648375 5572325 4379.7 980705.00 - 134.64 127 19653 647375 5573175 4403.1 980703.26 - 135.03 128 19654 647250 5573950 4416.2 980701.91 - 137.36 129 19655 647275 5574725 4423.9 980700.89 - 135.19 130 19656 647275 5575500 4340.3 980705.49 - 139.18 131 19657 647375 5576275 4185.9 980713.88 - 138.26 132 19658 647700 5577075 4271.2 980707.71 - 141.43 133 19659 647675 5577900 4383.1 980699.90 - 140.67 134 19660 647475 5578625 4430.2 980697.43 - 142.62 135 19661 647375 5579400 4481.9 980693.73 - 142.46 136 19663 647775 5580200 4524.6 980691.59 - 140.75 137 19662 648025 5580975 4614.9 980687.23 - 142.70 138A 19664 648175 5581775 4647.6 980686.30 - 142.94 138B 19665 647050 5581775 4850.4 980673.58 - 143.30 139 19666 646400 5582500 5097.7 980658.90 - 144.03 140 19667 646100 5583300 5165.3 980655.64 - 145.73 141 19668 645950 5584100 5178.8 980655.01 - 145.39 142 19259 645575 5584875 5213.2 980653.35' - 146.04 143 19597 645550 5585700 5196.1 980654.74 - 146.14 144 19598 644875 5586700 5189.0 980655.85 - 146.53 145 19595 643875 5587250 5670.4 980626.09 - 144.12 146 19593 641775 5588000 5399.6 980644.29 - 144.02 147 19592 641875 5588800 5195.2 980657.19 - 144.72 148 19591 642200 5589625 5121.6 980661.63 - 145.14 149 19590 642775 5590425 4825.8 980679.20 - 144.66 150 19589 642975 5591125 4522.9 980697.45 - 144.88 151 39588 642600 5591900 4172.7 980719.37 - 147.46 152 19587 641075 5592825 4158.8 980722.06 - 145.93 153 19252 641690 5593450 3940.1 980732.14 - 150.51 154 19572 641350 5594325 4001.9 980731.46 - 147.03 155 19573 640750 5595050 4097.7 980728.47 - 145.18 156 19574 640500 5595850 4222.6 980722.85 - 145.11 157 19575 640775 5596675 4470.5 980709.48 — 142.87 60 158 19576 641050 5597425 4612.5 980702.70 - 141.49 159 19577 6412 75 5598250 4782.7 980693.69 - 139.79 160 19578 641925 5599025 4878.8 980690.22 - 139.87 161 19579 642025 5599850 5083.3 980679.97 - 133.96 162 19580 641300 5600600 5568.2 980649.96 - 134.99 163 19581 641175 5601375 5737.6 980641.38 - 135.21 164 19582 640825 5602175 5972.9 980628.25 - 136.82 165 19583 640700 5602975 5832.2 980637.52 - 135.95 166 19584 640075 5603725 5933.5 980627.75 - 138.75 167 19585 639200 5604500 5929.5 980631.46 - 135.54 168 19586 640075 5605350 5923.4 980633.30 - 133.59 169 19692 640300 5606125 5797.0 980642.94 - 135.71 170 19691 640275 5606925 5524.5 980661.21 - 134.85 171 19690 640225 5607750 5194.9 980682.16 - 133.96 172 19689 640250 5608510 5094.3 980689.54 - 131.92 173 19688 640275 5609300 4944.9 980700.23 - 129.21 174 19564 639730 5610100 4921.6 980703.61 - 129.70 175 19687 639650 5610800 4860.7 980710.51 - 127.84 176 19686 639510 5611625 4643.8 980728.82 - 123.49 177 19563 640225 5612480 4323.7 980751.79 - 119.48 178 19562 639675 5613250 4394.1 980748.18 - 122.53 179 19561 638150 5613975 4377.5 980747.08 - 125.11 180 19560 637990 5614710 4339.6 980751.69 - 122.30 181 19559 636480 5615510 4201.9 980762.80 - 121.14 182 19558 635200 5616260 4149.1 980767.00 - 118.86 183 19257 634425 5617175 4186.9 980767.39 - 117.18 184 19557 633950 5617850 4086.9 980775.44 - 117.68 185 19556 633975 5618660 3942.4 980783.05 - 118.75 186 19555 634000 5619425 3774.8 980792.98 - 119.56 187 19554 633700 5620280 3483.7 980814.44 - 113.69 188 19552 632900 5620940 3459.1 980817.02 - 113.70 189A 19553 632725 5621630 3239.4 980832.34 - 112.14 189B 19551 633425 5611730 3120.7 980838.78 - 112.73 190 19550 633950 5612550 2930.6 980850.55 — 113.99 61 191A 19549 634575 5623325 3145.0 980837. 52 - 113.63 19 IB 19548 635790 5623360 2700.1 980863. 29 - 113.35 192 19544 635625 5624225 2319.4 980887. 78 - 110.95 193 19545 634975 5624975 2311.7 980889. 88 - 110.82 194 19546 634125 5625750 1983.5 980911. 64 - 108.93 195 19547 633325 5626500 1408.9 980944. 46 - 107.28 62 APPENDIX B GRAVITATIONAL ATTRACTION FORMULAE The parameters for the following formulae are shown i n Figure B, where the following d e f i n i t i o n s hold for a l l formulae: G = un i v e r s a l g r a v i t a t i o n a l constant p = density of body Ag = v e r t i c a l component of 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 "gals" for cgs un i t s . V e r t i c a l Line Mass, Bott (1969) Ag = GpA 2(l/r - l / ( r 2 + A h 2 ) 2 ) Segment of a Hollow Cylinder, Bott (1969) GpA 2 2 Ahf r ( r 2 - p 2 ) x Ag PARAMETERS station \ \ \ Ah segment of hollow cylinder * f \ s t a t i o n ^ ^ vertical line mass station-station thin horizontal lamina n-gon 1-1,2,- , n body of arbitrary shape y \ lamina approximation to body z O Z i depth sect ion FIGURE B 64 Vertical Prism, Nagy (1966) Ag = Gp y 2+ vx 2+y 2 y 2+ A42+y~2+h"2 - In T 2'J1 yi+Vx^ +yJ+h2 - x.. In y 2 + V x ^ + h 2 - In y l + ^ X l + y l In x2+ Vx 2+y 2 IT7'1-2 x 2+ Vx2+y2+h - In X l + V x l + y 2 X l *^1+y2+h x 2 + ^ x 2 + y i +h sm 2 2 -1 V h + y 2 / 2 2 2 (y X2 y2 ' y2 2,, 2, V 2, 2,, 2 - l y2 y2 V x 1 + y 2 + h s i n ~ ~ ~ ~ 2,1.2, V" 2. 2.. 2 -1 y l y l 2 y l in ~ ~ ~ (yx+ Vx^y^h ) ' y^+h 2.. 2. V 2, 2^ ,2 A . - l y i + h + y i V x i + y i + h + sm — / . V 2 ^ 2^U2,V 2,L2 ( y i V x i + y i + h > V y 1 + h 65 Three Dimensional Body of Arbitrary Shape, Taiwan! and Ewing (1960) e z. top Vdz (1) "bottom n -where V = Gp J i=l --. x. x, ,., y„ y. . , rr "I / I N r 1+1 \ • / 1 \ / 1+1\ W cos ( — ) ( - ) + ( — ) ( - ) i i+1 i i+1 -i i zq , S I , / zf. S - l / i V. . -1 / i - s i n < — 7 . — T T ~ - r / T s m and S = +1 i f p, 0, S = -1 i f p. < 0 I l W = +1 i f M. ^ 0, W = -1 i f M. < 0 x x y i - y i + l r 1,1+1 x . -l X i ~ X i + l r i ? i + l q i x . - x X x+1 • i,i+1 ' i 4. y i ' y i + l — -r r. x r i , i + l f. = X X + l X + l , X x + l x + l • 1 » r i , l + l i+1 r i , i + l r i + l M. = Y i Xi+1 ( y i + l } X r. r.,, x 1+1 ( r ± + 1 ) r. 66 r. x r i+1 r i , i + l + ) 2 +(y 1-y i + 1 ) 2 J n = number of vertices of polygonal lamina. V = vertical component of the gravitational attraction per unit thickness of a thin horizontal polygonal lamina, evaluated at a point p'(0,0,z). Ag = numerical integration of equation (1); the total vertical component of the gravitational attraction found by applying Simpson's rule to a series of lamina approximating the body at depths z.. 1 

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