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Geomagnetic depth-sounding profile across central British Columbia Dragert, Herb 1970

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A GEOMAGNETIC DEPTH-SOUNDING PROFILE ACROSS CENTRAL BRITISH COLUMBIA by HERB DRAGERT B.Sc, University of Toronto, 1968 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF M. Sc. i n the Department of GEOPHYSICS We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1970 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l m a k e i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e H e a d o f my D e p a r t m e n t o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f GEOPHYSICS T h e U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8, C a n a d a D a t e Sept.30.1070 i ABSTRACT Geomagnetic depth-sounding was c a r r i e d out i n a l a r g e - s p a c e d p r o f i l e across c e n t r a l B r i t i s h Columbia i n order to map the c o n d u c t i v i t y s t r u c t u r e of the c r u s t and upper mantle i n the c e n t r a l Canadian C o r d i l l e r a . Geomagnetic v a r i o g r a p h s were s e t up from east o f Ja s p e r to P r i n c e Rupert i n two suc-c e s s i v e east-west p r o f i l e s d u r i n g the summer of 1969. Numerical a n a l y s i s o f geomagnetic storm a c t i v i t y i n d i c a t e s t h a t the d i s c o n t i n u i t y i n the a t t e n u a t i o n o f the v e r t i c a l magnetic f i e l d , as f i r s t r e p o r t e d f o r s o u t h - e a s t e r n B r i t i s h Columbia by Hyndman (1963), i s l o c a t e d i n the area o f the Rocky Mountain Trench. A l l s t a t i o n s to the west e x h i b i t t y p i c a l 'low Z' c h a r a c t e r i s t i c s and no or l i t t l e anomalous i n d u c t i o n ; s t a t i o n s to the east o f the t r e n c h d i s p l a y a s t r o n g , h i g h - f r e q u e n c y Z - v a r i a t i o n content as w e l l as anomalous f i e l d enhancement. Power s p e c t r a l and p o l a r i z a t i o n analyses show a f i r s t o r d e r agreement w i t h the two-dimensional c o n d u c t i v i t y s t r u c t u r e model proposed by Caner (1970) f o r south-western Canada. Second-order e f f e c t s suggest a more complex model c o n s i s t i n g o f two c o n d u c t i v i t y d i s c o n t i n u i t i e s : One shallow s t r u c t u r e s t r i k e s roughly NW-SE at a depth of 10 to 15 km. and may be a s s o c i a t e d w i t h the 'edge' of a hydrated l a y e r l o c a t e d at the western f r o n t o f the Rocky Mountains; a second much deeper s t r u c t u r e , t r e n d i n g approximately E-W, i s l o c a t e d south of Kootenay Lake and i s p o s s i b l y a s s o c i a t e d w i t h a s t r i k e - s l i p f e a t u r e i n the upper mantle ( L a j o i e and Caner, 1970). i i TABLE OF CONTENTS I INTRODUCTION A. Geomagnetic Depth Sounding in Western North America B. Conductivity Structure Model for Southwestern Canada II THEORY A. Outline of Geomagnetic Induction 9 B. Induction in a Lateral Conductivity Discontinuity 12 III EXPERIMENTAL PROCEDURE A. Instrumentation 17 B. Field Operation 19 C. Methods of Data Analysis (i) Power Spectral Analysis 21 ( i i ) Parkinson Plots and Vectors 23 ( i i i ) Mercator Induction Plots 24 (iv) Horizontal Field Enhancement 25 IV EXPERIMENTAL RESULTS A. East Profile (Robb-Prince George) (i) Sample Records 27 ( i i ) Spectral Analysis Results 30 ( i i i ) Induction Analysis Results 37 (iv) Interpretation 48 B. West Profile (Prince George-Prince Rupert) (i) Sample Records 55 ( i i ) Spectral Analysis Results 55 ( i i i ) Induction Analysis Results 60 (iv) Interpretation 64 V. SUGGESTIONS FOR FURTHER STUDY 66 Page 1 2 i i i P a g e V I . C O N C L U S I O N S 67 A P P E N D I C E S A . O u t l i n e o f P o w e r S p e c t r a l C a l c u l a t i o n s 68 B . P a r a m e t e r s o f I n d u c t i o n A n a l y s i s 70 C . D e t e r m i n a t i o n o f E r r o r s i n ' L e a s t S q u a r e s ' L i n e a r F u n c t i o n F i t t i n g 76 R E F E R E N C E S 78 i v LIST OF FIGURES Page 1-1 Magnetogram sections from pairs of stations between 33° and 54°N. 3 1-2 Location of GDS stations in North America up to 1966. ' 4 1-3 Location of GDS and MT stations i n western Canada up to 1969. 5 I- 4 P e t r o l o g i c a l model for western Canada, l a t i -tude 49.3°N. 7 II- 1 Electromagnetic response of i s o l a t e d i n f i n i t e e l l i p t i c a l cylinder. 14 II - 2 Electromagnetic response of i n f i n i t e c i r c u l a r cylinder coupled with s e m i - i n f i n i t e conduct-ing sub-stratum. 15 I I I - l Location of instrument s i t e s . 20 IV- l a , l b Sample of magnetogram records d i g i t i z e d and replotted from eastern p r o f i l e . 28,29 IV-2b,3b S p a t i a l and frequency dependence of power rati o s in each component for the eastern p r o f i l e . 32,33 IV-4a,4b M-ratios for several frequency bands at eastern p r o f i l e stations. 34,35 IV-5a,5b Parkinson polar diagrams for eastern p r o f i l e s t a t i o n s . 38,39 IV-6 Mercator plots of induction effects with f i t t e d sine curves for eastern p r o f i l e s tations. 40 IV-7 Averaged Mercator plots of induction e f f e c t s with f i t t e d curves for Robb and Jasper. 42 IV-8 Azimuthal dependence of the r a t i o of t o t a l horizontal f i e l d amplitudes at McBride and Jasper with respect to Prince George. 47 IV-9 Observed v e r t i c a l and horizontal induced f i e l d s and a possible 2-dimensional model of the conducting step. 50 V Page IV-10 P a r k i n s o n v e c t o r s and s t r i k e s o f proposed c o n d u c t i n g zones. 54 IV-11 Sample o f magnetogram r e c o r d s d i g i t i z e d and r e p l o t t e d from w e s t e r n p r o f i l e . 56 IV-12a Power s p e c t r a l e s t i m a t e s a t w e s t e r n p r o f i l e s t a t i o n s . 57 IV-12b S p a t i a l and f r e q u e n c y dependence o f power r a t i o s i n each component f o r the w e s t e r n p r o f i l e . 57 IV-13 M - r a t i o s f o r s e v e r a l f r e q u e n c y bands a t w e s t e r n p r o f i l e s t a t i o n s . 59 IV-14a,14b P a r k i n s o n p o l a r diagrams f o r w e s t e r n p r o f i l e s t a t i o n s . 61,62 IV-15 M e r c a t o r p l o t s o f i n d u c t i o n e f f e c t s w i t h f i t t e d s i n e c u r v e s f o r w e s t e r n p r o f i l e s t a -t i o n s . 63 v i LIST OF TABLES Page IV-1 Summary o f f i t t e d s i n e - c u r v e parameters and P a r k i n s o n v e c t o r s f o r e a s t e r n p r o f i l e . 37 IV-2 Frequency dependence o f the i n d u c e d f i e l d a t J a s p e r . 45 IV-3 Summary o f v e r t i c a l and h o r i z o n t a l i n d u c e d f i e l d s f o r the e a s t e r n p r o f i l e . 49 IV-4 Summary o f f i t t e d s i n e c u r v e parameters and P a r k i n s o n v e c t o r s f o r w e s t e r n p r o f i l e . 60 v i i ACKNOWLEDGEMENTS I wish to acknowledge the encouragement, advice and l i b e r a l supervision of Dr. G. K. C. Clarke throughout the tenure of thi s research. I am indebted to Dr. B. Caner of the V i c t o r i a Magnetic Observatory for d i r e c t i n g f i e l d opera-tions and for many useful discussions which helped in the ana-l y s i s and in t e r p r e t a t i o n of the data. The use of equipment from the Dominion Observatory and the support of the National Research Council are g r a t e f u l l y acknowledged. Personal thanks are also given to the operational s t a f f at the Computing Centre who made the endless computing a pleasant task. This work was supported in part by a University Graduate Fellowship. 1 I. INTRODUCTION A. Geomagnetic Depth Sounding i n Western North America Intense e l e c t r i c current systems, concentrated i n the auroral zones, cause strong fluctuations in the earth's geomagnetic f i e l d , thus inducing currents within the earth at depths depending on the frequency of the v a r i a t i o n . The secondary f i e l d s associated with these subsurface currents w i l l s i g n i f i c a n t l y a f f e c t the t o t a l geomagnetic f i e l d recorded at the earth's surface, and hence, deep conductivity inhomo-geneities can be revealed by measurement of the three geomag-n e t i c f i e l d components. This i s the basic p r i n c i p l e of the geomagnetic depth sounding (GDS) technique. It i s a method that has recently been used to an increasing extent i n North America i n order to determine the e l e c t r i c a l conductivity structure of the lower crust and upper mantle. The pioneering work of Schmucker (1964) i n the south-west U.S.A. revealed two conductivity anomalies of major i n -t e r e s t . The f i r s t , the ' C a l i f o r n i a coastal anomaly', i s marked by unusually strong variations i n the v e r t i c a l f i e l d (Z) cor-related with east-west v a r i a t i o n s , and was explained as the edge e f f e c t of the P a c i f i c Ocean. The second, the 'Texas inland anomaly', i s delineated by a sharp d i s c o n t i n u i t y i n the amplitude of Z fluctuations between Las Cruces and Cornudas, New Mexico. Schmucker interpreted i t s cause to be a roughly N-S s t r i k i n g step i n the top surface of the conducting mantle, 2 with a change in depth of the highly conducting sub-stratum from 160 km. i n the west to 320 km. under the eastern region. A s i m i l a r sudden inland change in the character of Z va r i a -tions \\ras subsequently observed by other investigators at lat i t u d e s further north (see Fig. 1-1). Work by Hyndman (1963), Lambert and Caner (1965) , and Caner et a l (1967) indicated the continental extent of such an inland anomaly marking the t r a n s i t i o n between the 'low I 1 stations of the western C o r d i l l e r a and the 'high I' stations l y i n g to the east. ( I i s the r a t i o of v e r t i c a l to horizontal amplitude of geomagnetic variations.) This, or at least a s i m i l a r , t r a n s i t i o n zone, shown i n small sections i n Fig . 1-2, has since been confirmed to follow roughly the l i n e of the Rocky Mountains at intermediate l a t i t u d e s (Gough and Anderson, 1968), but anomalously high I s t a t i o n s , i n d i c a t i n g low conductivity of the sub-stratum, have also been found within the C o r d i l l e r a region (Reitzel et a l , 1970). B. Conductivity Structure Model for Southwest Canada The combined work of the V i c t o r i a Magnetic Observatory and the Department of Geophysics at U.B.C. has provided d e t a i l e d GDS and MT (magnetotelluric) coverage of south-western Canada (see F i g . 1-3). This work has continued the mapping of a t r a n s i t i o n zone for the Canadian C o r d i l l e r a and also established the coastal e f f e c t at the west coast of Vancouver Island. 3 PRINCE GEORGE JASPER «£ u T. 04 0* OS G R A N D F O R K S L E T H B R I D G E P i g . I - l . M a g n e t o g r a m s e c t i o n s from p a i r s o f s t a t i o n s a t (a) l a t i t u d e 5^°N ( t h e s i s work) (b) l a t i t u d e 51°N (Caner e t al ,1967) ( c ) l a t i t u d e 4 9 . 5 ° N (Hyndman,1963) (d) l a t i t u d e 33°-35°N (Caner e t al,1967) S c a l e b a r s are 50r;time marks 1 hour. 4 F i g . 1 - 2 . L o c a t i o n of GDS s t a t i o n s i n N o r t h America up t o 1 9 6 6 . ( a f t e r Caner e t a l,1967) P i g . 1-3.Map of GDS" and MT s t a t i o n s i n w e s t e r n Canada up t o 1 9 6 9 . ( a f t e r Caner e t a l ,1971) 6 Recently, Caner (1970) has proposed a p e t r o l o g i c a l c r u s t a l model for this region based primarily on these MT and GDS r e s u l t s but also giving due consideration to geological, aeromagnetic, seismic, and heat flow data. This regional model, shown in Fig. 1-4, postulates an uppermost mantle temperature of at least 750°C at a depth of about 35 km., thus creating a moderately conducting sub-stratum under the entire C o r d i l l e r a . At the wrestern front of the Rocky Mountains and towards the west, the lower crust (from a depth of 10 to 15 km.) becomes conductive as w e l l , the most l i k e l y cause being hydra-t i o n and possible p a r t i a l melting. In addition to this large scale regional model, the 'coast e f f e c t ' at Tofino has previously been interpreted by Lambert and Caner (1965) as a combination of two d i s t i n c t e f f e c t s : 1) the conductivity contrast of the land-sea i n t e r -face and 2) inhomogeneities in the upper mantle associated with the edge of the continental shelf. Also, the strong anomaly at Kootenay Lake, f i r s t reported by Hyndman (1963), was found to be due to a sharp, east-west trending conductivity d i s c o n t i n u i t y , interpreted by Lajoie and Caner (1970) to be associated with a deep s i n i s t r a l s t r i k e - s l i p feature i n a subsequently i n e r t basement, thus creating a ' l o c a l i z e d d i s -i t o r t i o n ' of the main low I-high I t r a n s i t i o n . ^ S E L K I R K K O O T E N A Y M O U N T A I N S L A K E P U R C E L L M O U N T A I N S R O C K Y M T N . T R E N C H ( K O O T E N A Y V A L L E Y ) R O C K Y M O U N T A I N S P L A I N S 20 * 4 0 - CONDUCTIVE, HYDRATED LOWERS CRUST (PROBABLY PARTIAL MELTINGP* 60 80 \ \1I0-I5KM\^ \ \ Y V RESISTIVE RESOLUTION N x - A - x x x X>750°C X MODERATELY CONDUCTIVE UPPER MANTLE, T> 800°C, COMPOSITION UNDEFINED P i g . I - 4 . P e t r o l o g i c a l model f o r southwest Canada at l a t i t u d e 49.3°N.(after Caner,1970) 8 The purpose of this thesis was therefore twofold: to continue the GDS mapping of the I t r a n s i t i o n zone at a l a t i t u d e of 54°N, and to test the v a l i d i t y of th i s proposed model for the central Canadian C o r d i l l e r a . 9 I I . THEORY A. Outline of Geomagnetic Induction The t o t a l v a r i a t i o n a l part of the geomagnetic f i e l d observed at the earth's surface i s a function of p o s i t i o n (r) and time (t) , and can be expressed as the t o t a l vector quantity F(r,t) = F e ( r , t ) + F i n ( r , t ) + F i a ( r , t ) CD where F g = the external source f i e l d , due to ionospheric currents. -> F. = the 'normal' in t e r n a l f i e l d , due to induced i n currents flowing p a r a l l e l to the earth's surface. -*• F. = the 'anomalous' i n t e r n a l f i e l d , due to induced i a currents i n a non-horizontally s t r a t i f i e d con-d u c t i v i t y structure. Generally speaking, the problem of geomagnetic depth sounding -> i s to determine F. and F. by simultaneous measurement of in i a ' -»• F at various l o c a t i o n s , to deduce 'normal' and 'anomalous' current systems responsible for these i n t e r n a l f i e l d s , and f i n a l l y to draw conclusions about the conductivity structure c o n t r o l l i n g the pattern and strength of the induced currents. The ionospheric current systems causing the external f i e l d fluctuations are at a distance from the earth's surface much smaller than the wavelengths of the v a r i a t i o n s . Conse-quently, the magnetic induction f i e l d predominates over the r a d i a t i o n f i e l d , and the t o t a l v a r i a t i o n a l f i e l d in (1) can 10 be derived from a magnetic p o t e n t i a l function having the form: $ = Ce" v zP(x,y,v) (2) Neglecting displacement currents, the t o t a l magnetic f i e l d i s given by: ' e l w t F = 103 dW 9P dW # 3P d~z * 8x ' d~z * 9y , v2WP where W s a t i s f i e s the equation: (3) d2W dz 2 (v 2 + 4Trioja(z))W (4) and P s a t i s f i e s the r e l a t i o n : *2l + i l l + V * P . o 3x 2 9y 2 (5) and v = X/2ir , the s p a t i a l wavenumber of the source f i e l d (see Price (1962) for d e t a i l e d t h e o r e t i c a l development). For a h o r i z o n t a l l y layered earth, the conductivity a w i l l be constant within each layer of thickness h ; t h i s allows the solution of equation (4) within each layer to be expressed by: W = A e 6 z + Be" 6 z (6) 11 where 0 = v 2 + 4-rriwa (7) Combining r e l a t i o n s (6) and (3) results in the following expression for the r a t i o Fz/Fx i n each layer: Fz Z yj Fx ~ H " 6 9P 3x . 9z „ -0z Ae + Be A e G z - Be" 6 z (8) The boundary conditions for an n-layered earth (see Srivastava, 1965) leads to the r e l a t i o n : _P v z=0 " i i ' 6 z u 9x J- • fCe k,h k) k=l,n ( 9 ) where f ( 6 k , h k ) = coth O i h i + coth" 1 coth ( 6 2 h 2 + ... ...coth" 1 -g^)]} 6 n (10) 9 P Since the term P/gY i s indeterminate, simultaneously recorded data from two stations i s used to evaluate the following r a t i o : (see Caner et a l , 1967) (Z/H)station 1 _ f (v ,a>,a ,h) station 1 _ ,M (Z/H)station 2 f(v,u,a,hjstation 2 (11) M i s the power attenuation r a t i o , and i s generally the basis of simple layer i n t e r p r e t a t i o n of GDS data. 12 B. Induction in a Lateral Conductivity Discontinuity Often in areas of greatest i n t e r e s t , such as the coastal region and the low I-high I t r a n s i t i o n zone i n North America, the l a t e r a l homogeneity i n conductivity demanded by the theory outlined in section II-A i s not present. In these areas, the 'anomalous* i n t e r n a l f i e l d becomes s i g n i f i c a n t , r e s u l t i n g in azimuthally dependent geomagnetic f i e l d variations at the surface of the earth. The three-dimensional problem of a l a t e r a l conductivity d i s c o n t i n u i t y has not been solved. However, by assuming that a feature of the conductivity zone remains consistent along s t r i k e for a distance large compared to the skin depth, a two-dimensional solution i s possible. Madden and Swift (1969) showed that a gradual sloping d i s c o n t i n u i t y in the conductivity of the upper mantle w i l l r e s u l t i n a variable anisotropy (depen-dent on source f i e l d d i r e c t i o n with respect to conductor s t r i k e ) for apparent co n d u c t i v i t i e s computed from magnetotelluric obser-vations, thus permitting the location of a conductivity 'step'. Using conformal mapping techniques, Schmucker (1964) i n v e s t i -gated a two-dimensional step-discontinuity in conductivity and showed that a concentration of magnetic f i e l d l i n e s intersected the upper corner of the step for the steady-state case. Con-sequently, for a time-varying magnetic f i e l d , a concentration of current w i l l flow in the upper corner p a r a l l e l to the d i s -continuity s t r i k e , r e s u l t i n g i n strong anisotropic f i e l d en-hancement . 13 The induction of 'anomalous' f i e l d s for various two-dimensional models has been investigated by Rikitake and Whitham (1964). They derive the electromagnetic response of an i s o l a t e d i n f i n i t e e l l i p t i c a l cylinder of i n f i n i t e conductivity to a uniform horizontal inducing f i e l d perpendicular to the axis of the c y l i n d e r . (Fig. I I - l shows several examples.) To show the 'amplification e f f e c t ' of an underlying conductive layer, the case of an i n f i n i t e c i r c u l a r cylinder embedded in an i n s u l a t o r and underlain by a semi - i n f i n i t e conductor i s also investigated, and an amplification varying from 47% to 80% i s found for the representative case i l l u s t r a t e d in Fig. 11 -2 as the r a t i o of radius to depth of axis varied from 1.0 to 0.5. Symmetric and asymmetric 'conductive upheavals' in an otherwise semi - i n f i n i t e conductive layer are also examined and t h e i r response curves are found to be generally s i m i l a r to the e l l i p -t i c c y l i n d e r case. From Rikitake and Whitham's 'representative' cases alone, i t can be seen that the s i m i l a r i t y of the induced f i e l d s for models varying i n shape of cross-section, i n o r i e n t a t i o n , and i n depth w i l l introduce a strong ambiguity in any model in t e r p r e t a t i o n of observed anomalous f i e l d s . Of course, common to a l l such two-dimensional models i s the anisotropy introduced by the d i r e c t i o n of the inducing f i e l d with respect to the conductor: Maximum anomalous ef f e c t s are present when the 14 F i g . I I - l . T h e e l e c t r o m a g n e t i c response of r e p r e s e n t a t i v e i n f i n i t e e l l i p t i c a l c y l i n d e r s o f i n f i n i t e conduc-t i v i t y under a h o r i z o n t a l u n i f o r m i n d u c i n g f i e l d p e r p e n d i c u l a r t o the a x i s o f the c y l i n d e r . ( a f t e r R i k i t a k e and whitham,1964) 15 -06 H| I n d u c i n g F i e l d <r =00 P i g . I I - 2 . T h e e l e c t r o m a g n e t i c response o f a r e p r e s e n t a t i v e i n f i n i t e c i r c u l a r c y l i n d e r of i n f i n i t e c o n d u c t i v i t y w i t h a u n i f o r m i n d u c i n g f i e l d p e r p e n d i c u l a r t o the a x i s o f the c y l i n d e r f o r b o t h the c o u p l e d and the un c o u p l e d c a s e . ( a f t e r R i k i t a k e and Whitham,1964) 16 inducing f i e l d i s perpendicular to i t s s t r i k e , and no anomalous response i s expected when inducing f i e l d s are p a r a l l e l to the conductor. Consequently, both the v e r t i c a l and horizontal components of the induced f i e l d w i l l e xhibit a sinusoidal dependence on the azimuth of the inducing horizontal f i e l d , with extremum peaks occurring at directions normal to conductor s t r i k e . 17 II I . EXPERIMENTAL PROCEDURE A. Instrumentation Instruments used i n the f i e l d were of two types: (i) The Askania Geomagnetic Variograph Gv3 This variograph continuously records time variations i n the three f i e l d components D, H, and Z, using three small, fibre-suspended bar magnets which, along with t h e i r o p t i c a l systems and c a l i b r a t i o n c o i l s , comprise the three independent variometers. In addition to these three traces, a base-line, an i n t e r n a l instrument temperature l e v e l , and hourly time marks are recorded on the photographic recording paper. To ensure that temperature fluctuations remained less than 1°C, a thermostatically c o n t r o l l e d heater, which can be set at 10°, 20°, 30°, or 40°C, i s enclosed i n the variograph housing. The recording reels used were those designed and b u i l t at V i c t o r i a to allow operation with 60 hz l i n e power and non-metric chart speeds; these reels accommodate up to 10 metres of recording paper thus allowing 12 to 14 days of continuous record when a chart speed of 1 in./hr. i s used. The time-scale resolution at this speed i s l i m i t e d to about 200 sec. periods, while the minimum geomagnetic change resolvable is roughly 1 or 2y. ( i i ) The Presentey Recording Magnetometer This variometer i s a t r a n s i s t o r i z e d fluxgate mag-netometer developed at the Dominion Observatory in Ottawa, 18 based on Serson's (1957) IGY st a t i o n magnetometer. Using three orthogonal fluxgate solenoids, the three f i e l d components D, H, and Z, are measured in terms of D.C. voltage outputs of 1 v o l t per 100y in each of three channels. The three traces were recorded on two Moseley 7100B S t r i p Chart Recorders at a sensi-t i v i t y of 0.5 v o l t s / i n . which allowed a resolution of 1 to 2y. Chart capacity i s 120 feet which, at a chart speed of 2 in./hr., t h e o r e t i c a l l y allowed over 25 days of continuous record and l i m i t e d the time-scale resolution to about 100 sec. periods. F i e l d s i t e s for the Askania variographs were chosen with p a r t i c u l a r care to ensure a location which s a t i s f i e d the following demands: 1) 110V/60 hz l i n e power 2) no severe l o c a l geomagnetic f i e l d gradients 3) well removed from t r a f f i c , power l i n e s and other l o c a l magnetic disturbances 4) reasonably weatherproof 5) a s o l i d f l o o r to support the instrument For the supplementary fluxgate s i t e s , the t h i r d con-d i t i o n was usually e a s i l y met and the l a s t two conditions were unnecessary since the sensing head can be mounted well away from the control unit (100 or 200 feet) on an aluminum pipe placed in a covered p i t . The q u a l i t y of data from either instrument i s about equal, but due to repeated malfunctioning 19 of the Moseley S t r i p Chart Recorders, the Askania system proved more r e l i a b l e . B. F i e l d Operation During the f i r s t two weeks of June 1969, the 'East GDS P r o f i l e ' was set up i n order to locate the d i s c o n t i n u i t y in lower crust-upper mantle conductivity i n east central B r i t i s h Columbia. Askania variographs were set up at Robb (ROB), Jasper (JAS), McBride (MCB), and Prince George (PGE) , a flux-gate variometer recording a l l three components was set up at Valemount (VAL), and supplementary fluxgate systems recording H and Z only were i n s t a l l e d at Quesnel (QUE) and B a r k e r v i l l e (BAR) (see F i g . I I I - l ) . After an active magnetic period i n mid-June, s u f f i c i e n t data were recorded to allow v i s u a l , q u a l i -t a t i v e i d e n t i f i c a t i o n of the 'low I-high I' d i s c o n t i n u i t y , and consequently, i n spite of poor records at Valemount, the East P r o f i l e was shut down between July 10 and July 13. To complete the p r o f i l e across central B r i t i s h Columbia at approximately the same geomagnetic l a t i t u d e , the 'West GDS P r o f i l e ' was established during the t h i r d week of July with Askania stations at Prince George, Smithers (SMI), Terrace (TER), and Prince Rupert (PRP), and three-component fluxgate systems at Vanderhoof (VAN) and Burns Lake (BRN)(see Fig. I l l - 1 ) . A l l stations were located i n the 'low-I* zone and hence, no F i g . I I I - 1 . M a p o f the l o c a t i o n of i n s t r u m e n t s i t e s . 21 anomalous behaviour was expected, except for a possible small 'coastal e f f e c t ' (Parkinson, 1962) at Prince Rupert. By mid-August s u f f i c i e n t magnetic storm a c t i v i t y had been recorded, and hence, observations along the West P r o f i l e were ended by August 18. C. Methods of Data Analysis (i) Power Spectral Analysis a) Data Reduction To f a c i l i t a t e numerical analysis, several magnetically active periods of at least 15 hour length were d i g i t i z e d using the v i s u a l trace d i g i t i z e r b u i l t at the Department of Geophysics, U.B.C. This numerical data, f i r s t punched automatically onto paper tape in a binary code, was converted to a decimal format (decimal numbers with 4 s i g n i f i c a n t d i g i t s ) and stored on mag-ne t i c tape for subsequent processing. For adequate resolution of short period events (5 min.), a d i g i t i z i n g rate of about 64 points/inch was chosen, which remained reasonably constant, giving a d i g i t i z i n g i n t e r v a l of about 56 sec. After an i n i t i a l computer plot-out of the input data, a r b i t r a r y adjustments were made on the stored numerical data to eliminate obvious d i g i t i z i n g errors u n t i l the computer traces could be exactly superimposed on the i n i t i a l photographic traces. The f i n a l 'adjusted' data were considered the 'best possible' d i g i t a l representation of the actual traces, and spectral analysis was ca r r i e d out on these data. 22 b) Numerical Methods To allow d i r e c t comparison with previous work, the Tukey method of spectral analysis was employed i n a computer program adapted from one written by R . M. E l l i s of the Depart-ment of Geophysics, U.B.C. (see Appendix A). The sampling i n t e r v a l used was 56 sec. giving a folding frequency of about 0.5 cycles per minute. The maximum c o r r e l a t i o n lag used was about 10% of the sample s i z e , and since i t s absolute value was at least 100, the equivalent resolution bandwidth for power spectra calculations was .01 cycles per minute or better. The r a t i o s of the power spectral densities P V e r t i c a l / P H o r i z o n t a l ( i ' e - P Z / P H a n d P Z / P D > w e r e determined as a function of frequency at each station i n order to i d e n t i f y 'low I' and 'high I 1 s t a t i o n s . These power ra t i o s were further combined into a 'power attenuation r a t i o ' , M , (Caner et a l , 1967) where M " ' ( P Z / P H ) S T A T I O N ^ P Z / ! V R E F E R E N C E S T A T I ON This normalized, dimensionless attenuation factor i s r e l a t i v e l y independent of geomagnetic l a t i t u d e e f f e c t s , and i t s v a r i a t i o n with frequency characterizes the difference i n conductivity structure between the 'eastern' and 'western' zones. "5a 23 In a d d i t i o n t o t h i s s t a n d a r d M p a r a m e t e r , the r e l a t i v e component power r a t i o s STATION/ ( PX^ REFERENCE STATION where X = D, H, o r Z were e v a l u a t e d t o r e v e a l p o s s i b l e l a t i t u d e e f f e c t s and t o i l l u s t r a t e s e p a r a t e l y t h e r e l a t i v e v a r i a t i o n o f the i n d i v i d u a l component e n e r g i e s w i t h f r e q u e n c y from s t a t i o n t o s t a t i o n . (Note t h a t a change i n M can be b r o u g h t about by a change i n e i t h e r o r P^ .) ( i i ) P a r k i n s o n P l o t s and V e c t o r s The p o l a r p l o t method o f P a r k i n s o n (1959) was a p p l i e d t o v i s u a l l y measured a m p l i t u d e s o f s i m u l t a n e o u s e v e n t s , w i t h component f i e l d changes AD , AH , and AZ , i n o r d e r t o a s c e r t a i n the c o r r e l a t i o n between the magnitude o f AZ and the magnitude and d i r e c t i o n o f AB , the t o t a l h o r i z o n t a l f i e l d change (see Appendix B f o r an o u t l i n e o f P a r k i n s o n ' s t e c h n i q u e o f i n d u c t i o n a n a l y s i s ) . Assuming 1 quasi-random' geomagnetic s o u r c e f l u c t u a t i o n s , the p r e s e n c e o f an anomalous c o n d u c t o r w i l l cause an a z i m u t h a l dependence o f AZ on AB , the e x a c t n a t u r e o f t h i s dependence b e i n g d e t e r m i n e d by the geometry o f the c o n d u c t o r . (See, f o r example, P a r k i n s o n 1962, 1964; R i k i t a k e and Whitham, 1964; Schmucker, 1964.) The a m p l i -tude d a t a were p r o c e s s e d u s i n g a computer program d e v e l o p e d 24 from one used by Lajoie and Cannon of the Department of Geophysics, U.B.C, which gave IBM Calcomp plots of Parkinson diagrams for each s t a t i o n . ( i i i ) Mercator Induction Plots The Mercator projection of the Parkinson polar p l o t (Lajoie and Caner, 1970) was also used to give a l i n e a r scale representation of the anomalous induction e f f e c t i n the v e r t i -c a l component and i t s azimuthal dependence. The 'dip', 6 , -> of the t o t a l geomagnetic vector change, AT , measured posi-t i v e l y downward from the h o r i z o n t a l , i s plotted against <j> , the geographic azimuth of the horizontal inducing f i e l d vector, AB , measured p o s i t i v e l y east of north. (Note that the Parkinson angle 6 as defined i n Appendix B i s related to the t o t a l f i e l d dip by the equation: 6 = ir/2 - 9 .) For normal s t a t i o n s , the points on these 'induction' plots have a random d i s t r i b u t i o n , but for anomalous stations, 6 i s a function of <J> , and the azimuth where > 6 i s a minimum gives the d i r e c t i o n of the Parkinson vector, while the value of sin|6| at t h i s azimuth i s the Parkinson vector magnitude. As outlined in section II-B, under the assumption v. of a 'two-dimensional' conductor, 6 w i l l be a fundamental sinusoidal function of <j> . Consequently, using the method of least squares (Chauvenet, 1960), a sine function of the form A s i n - <$> ) o 25 was f i t t e d to the Mercator data points. The value of the amplitude A i s equivalent to the maximum absolute value of 6 , and the phase angle minus TT/2 yi e l d s the azimuth of the minimum dip, i . e . the Parkinson vector d i r e c t i o n . Root-mean-square errors associated with each of these determined parameters were also computed (see Appendix C) i n order to ascertain q u a n t i t a t i v e l y the accuracy of the s i n u s o i d - f i t to the data. Both the Mercator plots and the f i t t e d sine curve were computer generated i n the same program used for Parkinson diagrams. (iv) Horizontal F i e l d Enhancement Anomalous induction e f f e c t s , which may or may not be apparent i n the Parkinson polar p l o t s , can be revealed by an azimuthal dependence of enhancement in the horizontal f i e l d . Defining a r a t i o Rg as follows: RB = (AB)ANOMALOUS 1 f A B )REFERENCE where REFERENCE * s t* l e c ^ a n 8 e ^ n t^ i e horizontal f i e l d at a normal sta t i o n free of anomalous e f f e c t s , then Rg w i l l ->-be a simple function of $ , the azimuth of AB at the reference s t a t i o n , i f a l i n e a r , induced current system i s present nearby. (Note that the assumption of a s p a t i a l l y uniform i n -ducing f i e l d i s made.) 26 The expected form of thi s dependence w i l l again be s i n u s o i d a l , but i t w i l l have a 2<{> functional dependence since the enhancement i s p o s i t i v e for a postive or negative inducing f i e l d normal to conductor s t r i k e ; consequently, the function (R Q + RB/2) + RB/2 sin(2<f> -was least-squares f i t t e d to the data. R Q represents the average l e v e l of constant r e l a t i v e horizontal f i e l d strengths and r e f l e c t s differences i n the magnitudes of the horizontal f i e l d s due to geomagnetic l a t i t u d e e f f e c t s , l o c a l attenuation e f f e c t s , or instrumental c a l i b r a t i o n error. Rfi gives the maximum magnitude of the anomalous enhancement as a f r a c t i o n of the inducing f i e l d magnitude, and the value of <J> = + y i e l d s the d i r e c t i o n of maximum enhancement. It should be noted that the plot of R^ w i l l reveal actual anomalous enhancement only i f no single component la t i t u d e attenuation or source effects are present. I f , for instance, there i s an appreciable l a t i t u d e attenuation in H at the reference s t a t i o n , then Rg w i l l exhibit peaks coinciding with magnetic north and south of the tested s t a t i o n . 27 IV. EXPERIMENTAL RESULTS A. East P r o f i l e (Robb-Prince George) (i) Sample Records Two storm periods were analysed for this p r o f i l e : Event 1: June 16, 01:00 UT to June 17, 12:00 UT Event 2: June 19, 23:00 UT to June 20, 14:00 UT Event 1 was an extremely active and extended storm period, but i t was recorded well at only the four primary (Askania) stat i o n s ; Event 2 was well recorded at a l l seven st a t i o n s , however, i t was a much less disturbed geomagnetic period. Figs. IV-la and IV-lb show sample records from Events 1 and 2 r e s p e c t i v e l y , d i g i t i z e d and replotted at equal s e n s i t i v i t y . The character of the horizontal components i s almost i d e n t i c a l from s t a t i o n to s t a t i o n , i n d i c a t i n g a uniform source f i e l d . The s l i g h t l y reduced amplitudes i n the H component at Quesnel (geomagn. l a t . 58.79N) and B a r k e r v i l l e (geomagn. l a t . 59.0°N) and the s l i g h t l y increased H amplitudes at Robb (geomagn. l a t . 60.2°N) a l l as compared to Prince George (geomagn. l a t . 59.6°N) are most probably l a t i t u d e e f f e c t s . However, the sharper, increased-amplitude character of H at McBride (geomagn. l a t . 59.6°N) and Valemount (geomagn. l a t . 59.3°N) must be a t t r i -buted to a genuine enhancement in the north-south magnetic P i g . I V - l a . S a m p l e o f magnetogram r e c o r d s , d i g i t i z e d and r e p l o t t e d . P e r i o d : J u n e 16,22:43UT t o June 17, 0 3 : 2 3 U T . ( f r o m Event 1 ) 29 P i g . r v - l b . S a m p l e o f magnetogram r e c o r d s , d i g i t i z e d and r e p l o t t e d . P e r i o d : J u n e 20,04:56UT t o 09:53UT. (from Event 2) 30 f l u c t u a t i o n s . The character of the Z component changes as expected between P r i n c e George and Robb. The normal low-Z of the western C o r d i l l e r a i s apparent at Prin c e George, Q u e s n e l , and B a r k e r v i l l e . McBride and Valemount e x h i b i t a ' t r a n s i t i o n a l ' c h a r a c t e r i n the Z-component, whereas Jasper and Robb show the t y p i c a l high-Z amplitude v a r i a t i o n s of the 'eastern' s t a t i o n s . As i n previous GDS work i n southern B.C., the low I - high I t r a n s i t i o n zone again occurs i n the region of the Rocky Mountain Trench. Only at Jasper does the Z component show a v i s u a l l y -apparent c o r r e l a t i o n w i t h the H v a r i a t i o n s , marking Jasper as a c l e a r l y 'anomalous' s i t e . ( i i ) S p e c t r a l A n a l y s i s Results Event 1, a record of 34.9 hours, had a t o t a l of 2250 d i g i t i z e d p o i n t s , y i e l d i n g a d i g i t i z i n g i n t e r v a l of 55.8 sec. The maximum l a g used was 250 l a g - p o i n t s which gives a normalized standard e r r o r * of 33% and a r e s o l u t i o n * of .004 cy c l e s per minute. Event 2, only 15 hours i n l e n g t h , had a t o t a l of 960 d i g i t i z e d p o i n t s y i e l d i n g a d i g i t i z i n g i n t e r v a l of 56.2 sec. A maximum la g of 100 p o i n t s was used g i v i n g an e r r o r of 32% and an equi-v a l e n t r e s o l u t i o n bandwidth of .01 cy c l e s per minute. (Since the power estimates are used i n a comparative sense o n l y , a sm a l l e r standard e r r o r was s a c r i f i c e d i n r e t u r n f o r - b e t t e r r e s o l u t i o n . ) *Expressions f o r these q u a n t i t i e s assume a s t a t i o n a r y Gaussian process, and hence, t h e i r q u a n t i t a t i v e v a l i d i t y f o r these time s e r i e s i s ques t i o n a b l e . 31 The plots of the power spectral densities shown in Fig. IV-2a and Fig. IV-3a express qu a n t i t a t i v e l y the r e s u l t s of the v i s u a l trace-comparison dealt with in the previous section. The increased power of the H component at Valemount and McBride as compared to Prince George i s quite obvious and a frequency dependence of t h i s enhancement i s shown as we l l . The gradual increase i n the Z power as one moves from the western stations of Prince George and Quesnel to the eastern stations of Jasper and Robb i s also graphically apparent. This s p a t i a l and frequency dependence of the spectral power of i n d i v i d u a l components (primarily H and Z) r e l a t i v e to the corresponding components at Prince George i s better i l l u s t r a t e d i n Figs. IV-2b and IV-3b. In these diagrams, the component power r a t i o s ( p x/ p x ' where X represents D, H, or Z and the primed quantities r e f e r to Prince George) are plotted on a logarithmic scale against s t a t i o n location where the graph distances between stations i s representative of the r e l a t i v e distances between sta-tions projected onto the 59.6°N p a r a l l e l of geomagnetic l a t i t u d e . Each of these diagrams includes a plot of the geomagnetic l a t i t u d e of the instrument s i t e s in order to demonstrate possible geomag-ne t i c l a t i t u d e e f f e c t s in the r e l a t i v e strengths of f i e l d com-ponent changes. The D component power ra t i o s for both events r e f l e c t some l a t i t u d e e f f e c t s and also shoiv a s l i g h t frequency dependent enhancement at McBride. ( I n s u f f i c i e n t data prevented an analysis of the D component at Valemount.) Averaged over a l l plotted C-4 0.02 0.06 0.10 0.14 FREQUENCY, CRM. Fig.IV-2a.Power s p e c t r a l e s t i m a t e s f o r Event l , P r . George t o Robb. 2 b . S p a t i a l and f r e q u e n c y dependence of power r a t i o s i n each component f o r Event 1. Fig.IV-3a.Power s p e c t r a l e s t i m a t e s f o r Event 2,Pr. George t o Robb. 3 b . S p a t i a l and f r e q u e n c y dependence o f power r a t i o s : i n each component f o r Event 2. I 34 F I g . l V - 4 a . M - r a t l o s p l o t t e d a g a i n s t p r o j e c t e d s t a t i o n l o c a t i o n f o r E v e n t 1. 35 P i g . I V - 4 b . M - r a t i o s p l o t t e d a g a i n s t p r o j e c t e d s t a t i o n l o c a t i o n f o r E v e n t 2. 36 frequencies, the power ra t i o s for the H component at Quesnel and B a r k e r v i l l e indicate an approximate 10% and 5% attenuation in the H fluctuations respectively due to la t i t u d e e f f e c t s . The magnitude and the frequency dependence of the enhancement of the H component at the ' t r a n s i t i o n ' stations i s i l l u s t r a t e d numerically by the following. For Event 2, at McBride, H variat i o n s with a period of 47 min. and 19 min. show an ampli-tude enhancement of 17% and 32% respectively, r e l a t i v e to Prince George; at Valemount, where a s l i g h t l a t i t u d e attenuation i s expected, the same period variations show a magnitude increase of 46% and 62% respectively. The v e r t i c a l component power ra t i o s show an even greater v a r i a t i o n and the t r a n s i t i o n of low-Z to high-Z i s well i l l u s t r a t e d . (Note: For Event 2, the four western stations have e f f e c t i v e l y zero power in Z for the two higher frequencies. Conse-quently, the P z / p z ' r a t i o s for the eastern stations were taken r e l a t i v e to Valemount, with the Valemount r a t i o being a r b i t r a r i l y fixed at 2.0 i n order to posi-tion these curves reasonably' on the graph. This value represents a 'lower l i m i t ' since the high frequency Z power l e v e l at Valemount i s d e f i n i t e l y greater than that at McBride (see F i g . IV-3a), and since Valemount is t r a n s i t i o n a l l i k e McBride where an increase i n Z power ra t i o s with increasing frequency has been established in the analysis of Event 1 (see F i g . IV-2b)). 37 F i g . IV-4a and F i g . IV-4b exhibit the v a r i a t i o n of the M r a t i o s from Prince George to Robb. The normal t r a n s i t i o n from low-I to high-I stations i s shown between McBride/Valemount and Jasper. The unusual depression of the M r a t i o at the t r a n s i t i o n stations i s due to the presence of anomalous enhancement of the north-south magnetic variations with a weaker accompanying ano-malous Z induction. ( i i i ) Induction Analysis Results a) Induction E f f e c t s in AZ The Parkinson polar diagrams shown in F i g . IV-5a and Fig. IV-5b indicate that McBride, Jasper, and Robb"are a l l ano-malous to varying degrees. This same information i s more simply i l l u s t r a t e d i n the Mercator induction plots of F i g . IV-6, which also include 'best f i t ' simple sine curves whose constant para-meters y i e l d the Parkinson vector information summarized i n the following table: Station F i t t e d Sine Function Anomalous? Parkinson Vector Amplitude Phase Magnitude Direction (degr.) (degr.) (degr.) Robb 21. ± 7%* -63. ± 4.* Yes 0.36 ± .03 -153. ± 4. Jasper 32. ± 5% -57. ± 3. Yes 0.53 ± .02 -147. ± 3. McBride** 13. ± 14% 150. ± 8. Yes(weak) 0.22 ± .04 +60. ± 8. Pr. George 5. ± 31% -3. ± 17. No _ ^ _ TABLE IV-1. Summary of f i t t e d sine curve parameters and Parkinson vectors for eastern p r o f i l e . * Errors are root-mean-square errors computed in the method of least squares (see Appendix C). **Since anomalous horizontal f i e l d enhancement is s i g n i f i c a n t at McBride, these numerical results were obtained using AB from Prince George. co P i g . I V - 5 a . P a r k i n s o n p o l a r diagrams f o r e a s t e r n p r o f i l e s t a t i o n s . F i g . I V - 5 b . P a r k i n s o n p o l a r diagrams f o r e a s t e r n p r o f i l e s t a t i o n s . AZIMUTH M DCa fMf ASUttO K K i T t V I IAST Of NOCTH) JRSPER • 1M I AZIMUTH M Ota (MEASURED POSITIVE IAST Of NOtTM) 4^ O MCBRIDE • • ' M . I m* 1*1 AZIMUTH tN OCa. (MEASUREO POSITIVE EAST Of NOtTH) PR. GEORGE AZIMUTH IN OCO. (MIASURCO POSITIVI IAST C r NOtTH) F i g . I V - 6 . M e r c a t o r p l o t s o f i n d u c t i o n e f f e c t s w i t h f i t t e d s i n e . c u r v e s . ( e a s t e r n p r o f i l e ) 41 The disproportionately large error of the sine function f i t at Pr. George indicates randomly d i s t r i b u t e d data points, which j u s t i f i e s the conclusion that the s t a t i o n i s not anomalous. b) Second Order Anomalous Ef f e c t s in AZ In order to resolve more highly the functional depend-ence of the dip of the t o t a l induced f i e l d on the azimuth of the horizontal inducing f i e l d , the 6 values on the Mercator plots were averaged over 10 degree i n t e r v a l s every 5 degrees (this reduces ordinate scatter) for the two stronger anomalous st a t i o n s , Jasper and Robb. The resultant induction plots (Fig. IV-7) reveal almost i d e n t i c a l sine curves to F i g . IV-6 except for a suggestion of the presence of higher order s p a t i a l f r e -quencies. The s l i g h t amplitude reduction at the fundamental sine peaks has the mathematical appearance of a phase locked t h i r d harmonic, the addition of which to the fundamental sine curve (again using the method of least squares) re s u l t s i n the dashed l i n e of F i g . IV-7. It i s obvious that the magnitude of this possible e f f e c t i s at the 'noise l e v e l ' of observation and numerical analysis, and therefore cannot be unequivocably established with the available data. I f further i n v e s t i g a t i o n proves th i s e f f e c t to be r e a l , i t suggests an induced current system more complex than the two-dimensional model suggested by Caner (1970) for southwestern Canada. Anisotropics or inhomogeneities could cause such complexities, but perhaps the simplest explanation i s the possible presence of two separate 42 Fig.IV-7.Averaged M e r c a t o r p l o t s o f i n d u c t i o n e f f e c t s w i t h f u n d a m e n t a l s i n e c u r v e ( s o l i d l i n e ) and added t h i r d harmonic s i n e c u r v e ( d a s h e d l i n e ) . 43 conductive zones whose anomalous induced f i e l d s cause mutually induced secondary anomalous f i e l d s . 'Secondary anomalous' i s emphasized here because the primary anomalous induced f i e l d s of two separate conducting zones w i l l add in such a way as to r e s u l t in only a single Parkinson vector, which i s the resultant of the i n d i v i d u a l inductance arrows of each zone. (Note that the existence of two zones could therefore be erroneously i n -terpreted as a single conductive zone whose e f f e c t i s equivalent to the vector sum e f f e c t of the two zones.) A l l the previously mentioned induction r e s u l t s for anomalous stations have, i n e f f e c t , been integrated over a l l geomagnetic v a r i a t i o n periods ranging from 5 to 60 minutes, thus averaging out the frequency dependence of the Parkinson vector. If two d i s t i n c t i v e zones exi s t at s i g n i f i c a n t l y d i f -ferent depths, then the d i r e c t i o n and magnitude of the induc-tion vector w i l l vary with frequency as well as p o s i t i o n of the s t a t i o n with respect to the zones of conductivity. Un-fortunately, measuring amplitudes in given frequency ranges by hand i s a t r y i n g and time-consuming task; consequently, using the numerical technique outlined in Appendix B, a com-puter program was'written to evaluate the Parkinson vector information from d i g i t i z e d data. Two drawbacks of t h i s method became immediately apparent: 1) Because of the i n f l e x i b i l i t y and undiscriminating nature of a simple numerical technique, the scatter i n the induction data i s greatly increased over the hand measured data (in this case by a factor of 3) and 44 2) Because of d i g i t i z a t i o n noise, meaningful amplitudes of geomagnetic variations could not be computed for periods less than 15 minutes, r e s u l t i n g i n a lack of high frequency i n f o r -mation and a biasing towards low frequency data. Only at Jasper was the anomaly strong enough to ensure that the si z e of errors in the sine function f i t did not i n -validate the entire f i t attempt. (At Robb and McBride, the errors i n amplitude and phase of the f i t t e d function were greater than 15% and 10 degrees respectively, which were maxi-mum allowable errors for a station to be considered anomalous in the v i s u a l l y determined Parkinson vectors.) As the follow-ing table shows, even at Jasper the errors involved in the Parkinson vector are too large to allow an indisputable con-clu s i o n of frequency dependence. However, a trend is apparent, i n d i c a t i n g the possible existence of two conducting zones: one shallow, running NW-SE, drawing the Parkinson vector at Jasper towards the west, and a second, stronger, very deep anomaly s t r i k i n g E-W and thus drawing the induction vector south. 45 Mean Period Favored by Analysis* Maximum Absolute Dip of Total F i e l d (degr.) Azimuth of Parkinson Vector (degr.) 15 min. 20.4 ± 9.5% -153. ± 6. 30 min. 21.0 ± 11.91 -154. ± 7. 45 min. 22.1 ± 12.4% -155. ± 8. 60 min. 23.1 ± 13.6% -157. ± 9. 75 min. 24.7 ± 14.0% -167. ± 10. TABLE IV-2. Frequency dependence of the induced f i e l d at Jasper. *The numerical technique described i n Appendix B does not d i s t i n c t l y separate d i f f e r e n t frequencies of v a r i a t i o n , i t simply 'favours' cert a i n frequency ranges. There i s s t i l l 'contamination' from other frequencies in each range and hence the tabulated data s t i l l has an inherent 'smearing together' e f f e c t ; i . e . i t could be said to represent a minimum difference between high and low frequency r e s u l t s . The reduced dip angles of the t o t a l f i e l d compared to the f i t t e d amplitude at Jasper in Table IV-1 are probably due to the increased scatter of points , while the Parkinson vector d i r e c t i o n at Jasper l i s t e d i n Table IV-1 has high f r e -quency contributions lacking i n the computed Parkinson direc-tions of Table IV-2. (Note: The apparent lack of data at certa i n azimuths in Figs. IV-5 to IV-7 i s due to an observational bias, not a p o l a r i z a t i o n of the source f i e l d . Since the induction plots search for a v e r t i c a l component change, amplitude measurements were usually made where some change i n Z occurred. This implies that where gaps appear on the 46 graphs, the v e r t i c a l component i s n e g l i g i b l e . For such points, the t o t a l f i e l d dip angle would be e f f e c t i v e l y zero and hence they would not v i o l a t e the f i t t e d sine curves of Fig. IV-6.) c) Induction Ef f e c t s in AB Fig. IV-8 i l l u s t r a t e s the horizontal enhancement r a t i o Rg as a function of azimuth. The values of Rg have been averaged over 10 degree i n t e r v a l s every 5 degrees and a sine curve was then f i t t e d to these averaged data. Although small i n magnitude, the sinusoidal behaviour of the enhancement at McBride i s quite d e f i n i t e when compared to the Jasper Rg p l o t , which i s p r a c t i c a l l y a straight l i n e . The magnitude of maximum i n t e n s i f i c a t i o n of AB at McBride (compared to Prince George) i s 26%. This value, representing an enhancement averaged over a l l observed frequencies, i s i n good agreement with the component power r a t i o estimates of section I V - A ( i i ) , which i n -dicated an average 25% enhancement of the H component. The d i r e c t i o n of maximum increase of AB i s +55 degrees (and -125 degrees) which p r a c t i c a l l y coincides with the Parkinson vector azimuth. The error involved in the sine f i t to Rg at McBride was 10% and 6 degrees for amplitude and phase respectively, whereas an attempted sine f i t for Rg at Jasper resulted in a 54% amplitude error and a phase error of 31 degrees. 47 RELATIVE ENHANCEMENT OF THE HORIZONTAL FIELD JRSPER / PR. GEORGE o p AZIMUTH (MEASURED POSITIVE EAST OF NORTH) -iaO.0 -14).o -ito.o -60.0 ZD.I) jo.o GO.D IOO.O I i i i I i i 1 140.0 IBO.O cr hp RELATIVE ENHANCEMENT OF THE HORIZONTAL FIELD MCBRIDE / PR. GEORGE AZIMUTH (MEASURED POSITIVE EAST OF NORTH) im.D -14).0 -100.11 -60.D .20.0 20.0 80.0 100.0 1 4).0 IBO.O 1 I I I I I I I I I P i g . I V - 8 , A z i m u t h a l dependence o f R (BB) S t a t i o n B (5.B). Pr.George ( u s i n g d a t a averaged o v e r 10 degree i n t e r v a l s ) w i t h f i t t e d s i n e c u r v e . 48 (iv) Interpretation It i s concluded that the t y p i c a l low amplitude Z-va r i a t i o n s and lack of high frequency Z fluctuations i n the western C o r d i l l e r a are caused by a highly conductive layer at a depth of 10 to 15 km. as proposed by Caner (1970). The most l i k e l y cause of t h i s higher conductivity appears to be hydra-ti o n and possibly p a r t i a l melting (Hyndman and Hyndman, 1968). The eastern 'high I' regions lack this r e l a t i v e l y shallow con-ducting layer and hence show strong Z a c t i v i t y . The t r a n s i -t i o n between these two zones occurs at the western front of the Rocky Mountains, i n an area marked by the presence of anomalous induced f i e l d s . McBride and Jasper straddle a ' l i n e ' of ano-malous current flow, giving r i s e to the observed reversal of the induced v e r t i c a l f i e l d . Furthermore, the close proximity of the 'Trench' stations (McBride and Valemount) to the anomalous currents r e s u l t s in the marked horizontal f i e l d enhancement at these t r a n s i t i o n s t a t i o n s . Assuming a uniform horizontal inducing f i e l d perpen-d i c u l a r to a single i n f i n i t e conductor, the r a t i o s of the v e r t i -c a l induced to inducing f i e l d (H^/Hj) and horizontal induced to inducing f i e l d (H x/Hj, where X i s the d i r e c t i o n normal to the conductor) w i l l allow cert a i n q u a l i t a t i v e i f not quantitative conclusions to be drawn with respect to the models proposed by Rikitake and Whitham (1964). (See Section Il-b.) Table IV-3 shows the estimates for the magnitude of induction at each s t a t i o n ; these values are derived from a subjective combina-49 tion of the induction analyses and the r e l a t i v e spectral power l e v e l s . Station V e r t i c a l Induction (H z/H x) Horizontal Induction (H x/Hj) Robb - 0 . 3 8 0 .98 Jasper - 0 . 6 3 0 .95 Valemount + 0 . 30 1.60 McBride + 0 .22 1.32 Pr. George ^ 0 . 0 1.05 TABLE IV-3. Summary of v e r t i c a l and horizontal induced f i e l d s for the eastern p r o f i l e . These r a t i o s plotted against r e l a t i v e s t a t i o n distance from a NW-SE l i n e passing through McBride y i e l d the curves of F i g . IV - 9 . The shapes of the two enhancement curves reveal that the observed p r o f i l e does cross a conductor s i m i l a r to the model cases shown in F i g . I I - l . The magnitude of the observed enhance-ment at McBride and Valemount tends to be s l i g h t l y large, con-sidering that the actual conductivity i s not i n f i n i t y , and an amp l i f i c a t i o n through coupling with an underlying layer or through a concentration of current i n the upper corner of the step (shown by dark shading in the area of current flow in F i g . IV -9) i s 50 5 0 KM. • 1 T 2.0 VH, / \ Hj 9 \ INDUCING FIELD N > 1.0 0.0 LU CD 0 . 0 Q _ 1 (/) It,,, J -M.O m o QC sax 4 AREA OF INDUCED CURRENT FLOW Fig.IV-9.Observed v e r t i c a l and h o r i z o n t a l i n d u c e d f i e l d s and a p o s s i b l e 2 - d i m e n s i o n a l model o f the con-d u c t i n g step. 51 required to account for this increase. Both mechanisms are p l a u s i b l e . Coupling could occur between the 'step' current and the moderately conducting layer underlying both regions at a depth of about 35 km; concentration of current can be achieved by sharpening the step or by even reversing the slope of the step, i . e . the edge of the hydrated layer would slope p o s i t i v e l y from west to east, opposite to that indicated in F i g . IV-9. The above in t e r p r e t a t i o n i s confined to f i r s t order r e s u l t s , and i s i n agreement with Caner's proposed conductivity and p e t r o l o g i c a l model for southwestern Canada. However, the i n t e r p r e t a t i o n of some f i n e r points and second order e f f e c t s suggest a model consisting of two l a t e r a l conducting discon-t i n u i t i e s : One associated with the edge of a hydrated layer at a depth of 10 to 15 km., located at and s t r i k i n g in the same d i r e c t i o n as the western front of the Rocky Mountains; and a second, much deeper d i s c o n t i n u i t y , running approximately E-W south of Kootenay Lake, perhaps associated with a s t r i k e - s l i p feature i n the upper mantle (Lajoie and Caner, 1970). Such a model would explain the large negative peak in H^/Hj at Jasper and i t s sustained value at Robb (Fig. IV-9) without having to introduce an improbable complex step geometry. These two eastern stations are then affected by t h i s more remote, deeper di s c o n t i n u i t y which causes additional enhancement of the v e r t i c a l f i e l d (but i s too remote to af f e c t the horizontal f i e l d ) ; this deeper conductivity structure i s not apparent at the western 52 stations due to attenuation by the shallower conducting layer. It i s i n t e r e s t i n g to note that resolving the induction vectors at Jasper and Robb along directions normal to the two conduc-t i v i t y s t r i k e s y i e l d s more reasonable 'model' values of -0.42 and -0.21 for H^/I-Ij with respect to the shallow d i s c o n t i n u i t y . Furthermore, this 'dual-structure' model would explain the frequency dependence of the Parkinson vector at Jasper and the 'fine-structure' azimuthal dependence of the dip angle of the induced f i e l d at Jasper and Robb. In addition, no l o c a l change i n s t r i k e of the 'hydrated layer edge' need be invoked to explain the change in Parkinson vector d i r e c t i o n at the anomalous stati o n s . At McBride, l y i n g to the west of the 'shallow' anomaly, the induction arrow points 60° east of north, s l i g h t l y south of the d i r e c t i o n normal to the s t r i k e of the l o c a l tectonic pattern, and shows l i t t l e e f f e c t s of the deep anomaly due to the underlying attenuating layer. The d i r e c t i o n of maximum induction at Jasper (33°W of S) i s already notably affected by the deep E-W s t r i k i n g anomaly ly i n g well to the south, and i f the 27°W of S d i r e c t i o n at Robb i s considered to be s i g n i f i c a n t l y d i f f e r e n t from Jasper, i t can be explained by Robb's increased distance, and thus a reduced e f f e c t , from the NW-SE s t r i k i n g shallow anomaly. F i n a l l y , the l i n e of tran-s i t i o n stations of Golden, Valemount, and McBride indicate a 'low I - high I' t r a n s i t i o n l i n e s t r i k i n g 40°W of N, but the induction arrows at such widely scattered stations as Jasper, F i e l d (Caner et a l , 1971), and Sanca (Lajoie 1970) indicate a 53 conductivity structure running roughly 60°W of N. The 'two-conductor' model provides a simple solution to this disagree-ment in dir e c t i o n s since i t allows the observed Parkinson vectors to be vector sums of the induction arrows due to each d i s c o n t i n u i t y (see F i g . IV-10). (It must be noted that t h i s more complex model i s a hypothetical model suggested to explain secondary e f f e c t s and i s not considered 'proven' in th i s thesis.) Pig.IV-10.Parkinson v e c t o r s and s t r i k e s o f proposed c o n d u c t i n g zones. 55 IV. EXPERIMENTAL RESULTS B. West P r o f i l e (Prince George - Prince Rupert) (i) Sample Records The storm period analysed for the western C o r d i l l e r a p r o f i l e , c a l l e d Event 3, occurred from Aug. 3, 16:00 UT to Aug. 4, 16:00 UT. Samples of d i g i t i z e d records for a 6 hour period from Event 3, shown in F i g . IV-11, reveal a gradual l a t i t u d e attenuation i n a l l components, most obvious at Terrace (geomagn. l a t . 58.8°) and Prince Rupert (geomagn. l a t . 58.2°). A l l stations show very l i t t l e AZ a c t i v i t y in spite of large amplitude fluctuations i n H and D , confirming that they a l l l i e i n the 'low I' zone. ( i i ) Spectral Analysis Results Event 3, consisting of 24 hour record lengths, had a t o t a l of 1540 d i g i t i z e d points r e s u l t i n g in a d i g i t i z i n g i n t e r v a l of 56.1 sec. Maximum lag used was 150 points which gives a standard error of 32% and an equivalent resolution bandwidth of .007 cycles per minute. Fi g . IV-12a shows the power spectral densities for this event; the most s t r i k i n g feature i s the abrupt Z-power cut-off at a frequency of about .04 cpm for a l l s t a t i o n s . The power levels for the D component p r a c t i c a l l y coincide, and a small l a t i t u d e attenuation e f f e c t is noticeable. The H power leve l s for the d i f f e r e n t s i t e s track extremely well but are separated due to geomagnetic H S C A L E 2 H O U R S Pig.IV-11.Sample o f magnetogram r e c o r d s , d i g i t i z e d and r e p l o t t e d . P e r i o d : A u g . 4 , 0 0 : 0 0 U T t o 06:00UT. (fr o m E v e n t 3) a. b. 100 km. 0.02 0.06 0.10 0.14 FREQUENCY, CRM. Pig.IV-12a.Power s p e c t r a l e s t i m a t e s f o r E v e n t 3,Pr.George to P r . R u p e r t . 12b.Spatial and f r e q u e n c y dependence o f power r a t i o s i n each component f o r Event 3. 58 lat i t u d e e f f e c t s . A s l i g h t l y increased Z power l e v e l i s apparent at Smithers for frequencies between .02 and .04 cpm. The horizontal component power r a t i o plots of F i g . IV-12b have the general trend of the geomagnetic l a t i t u d e p l o t , and hence i l l u s t r a t e mainly the la t i t u d e attenuation e f f e c t , e s p e c i a l l y i n the higher frequencies. For example, for th i s storm event, the amplitudes of the II and D v a r i a t i o n s , averaged over a l l observed periods, are roughly 55% and 20% (respectively) greater at Prince George (geomagn. l a t . 59.6°N) than at Prince Rupert (geomagn. l a t . 58.2°N). However, the 47 min. and 35 min. period variations of the Z component power r a t i o s at Smithers show an amplitude increase in AZ with respect to Prince George of 53% and 10% respectively, i n d i c a t i n g either a source e f f e c t or possible anomalous induction. The plot of the power attenua-t i o n , M , i s shown in F i g . IV-13 and i t exhibits the same spectral power increase at Smithers as shown by the component power r a t i o s . Because of the severe attenuation of AZ at a l l these western-type 'low I' st a t i o n s , only the three i l l u s -trated frequency bands had s i g n i f i c a n t power l e v e l s , which leaves the frequency dependence of M unresolved. (Note: In Figs. IV-12b and IV-13, the graph distances between stations i s representative of the r e l a t i v e distance between stations projected onto the 59.0°N p a r a l l e l of geomagnetic latitude.) oq i M UO O I >-s ^ 05 H c+ < H-CD O 2 CO ci-ts' (jO H 1 • O ct-rl-CD Cb 0 5 05 H* CO ct O C _ j . CD O ct CD Cb to c!" 05 ct-t_J. b H O O 05 ct H-O 3 M = (PZ/PH ) STATION / (P Z/PH ) PRINCE GEORGE p _ In b 1 1 1 I ' l l T r U\ o o o -I—I—I I I I PRP TER SMI BRN VAN PGE o o Cn VO 60 ( i i i ) Induction Analysis Results a) Induction E f f e c t s in AZ 160 points from hand measured amplitude values were used to obtain the Parkinson polar diagrams for Pr. George, Smithers, Terrace, and Pr. Rupert (see Fig. IV-14a, 14b). A weak anomaly i s c l e a r l y observable at Pr. Rupert, while at Terrace and Smithers there are merely 'anomalous in d i c a t i o n s ' not present at the reference s t a t i o n , Prince George. Again, the Mercator induction plots of Fig . IV-15 with ' b e s t - f i t ' sine curves i l l u s t r a t e very simply the Parkinson vector i n f o r -mation summarized i n the following table. Station F i t t e d Sine Amplitude (degr.) Function Phase (degr.) Anomalous? Parkinson Magnitude Vector Direction (degr.) Pr. George 4. ± 32% -3. ± 15. No Smithers 10. ±"14% 30. ± 7. ? (.17 ± .03) (-60. ± 7.) Terrace 8. ± 15% -3. ± 7. ? (.14 ± .02) (-93. ± 7.) Pr. Rupert 12. ± 9% -4. ± 4. Yes (weak) .21 ± .02 -94 ± 4. TABLE IV-4. Summary of f i t t e d sine-curve parameters and Parkinson vectors for western p r o f i l e . Since the tabulated r e s u l t s for Prince George in Table IV-4 are almost i d e n t i c a l to those of Table IV-1, the same 'rejection-of-anomaly' c r i t e r i a was f e l t to apply to the P i g . I V - l 4 a . P a r k i n s o n p o l a r diagrams f o r w e s t e r n p r o f i l e s t a t i o n s . ts) F i g . I V - l 4 b . P a r k i n s o n p o l a r diagrams f o r w e s t e r n p r o f i l e s t a t i o n s . PR. GEORGE AZIKUTH IN DEO. ( u t A S U Z O FOSIT1VI L U T Of NOITM) ?-5-5MITHERS AZIMUTH IN D M (MEASURED FOSITIVF. IAS? OF NORTH) If-?• ?• f-TERRRCE AZIMUTH IM O t a (KIASUMO FOSITIVF, (AST OF NOUTX) PR. RUPERT AZIMUTH IN OEO. (MEASUSEO POSITIVE IAST OF NOJTX) ON P i g . I V - 1 5 . M e r c a t o r p l o t s o f i n d u c t i o n e f f e c t s w i t h f i t t e d s i n e I c u r v e s . ( w e s t e r n p r o f i l e ) 64 west p r o f i l e stations - i . e . , i f an amplitude error of 15% or greater and a phase error of 10 degrees or greater accompany the attempted sinusoidal f i t , the s t a t i o n i s considered non-anomalous. Smithers and Terrace are therefore considered 'borderline' cases, and at the most, are extremely weakly anomalous stations.' b) Induction E f f e c t s in AB The western stations were tested for possible ano-malous enhancement i n the horizontal f i e l d by evaluating Rg at Terrace, Smithers, and Pr. George, using Pr. Rupert as a reference s t a t i o n . No appreciable anomalous induction e f f e c t s were found, and only the expected l a t i t u d e enhancement of the source f i e l d at Prince George caused i t s p l o t of Rg to deviate s i g n i f i c a n t l y from a straight l i n e . (iv) Interpretation An underlying conductive layer, as outlined in part IV-A(iv), i s concluded to be present under a l l western p r o f i l e s t a t i o n s , causing the 'low I* response at each of these sta t i o n s . A possible source e f f e c t could cause the increase in the Z-power l e v e l at Smithers.(One way to resolve this would be to examine other storm periods.) The 'coast-effect' (Parkinson, 1962) i s the source of the anomalous Z induction at Pr. Rupert, being r e l a t i v e l y weak since the continental slope i s s t i l l more than 200 km. to the west; th i s e f f e c t i s also the most l i k e l y source of the anomalous indications at Terrace. 65 If the anomalous 'tendency' at Smithers i s taken as s i g n i f i c a n t , i t i s i n t e r e s t i n g to note that, assuming (from the rate of attenuation of the coastal e f f e c t between Pr. Rupert and Terrace) that about 50% of the 'anomaly' at Smithers i s s t i l l c o a s t a l , then another, f a i r l y deep conduc-t i v e zone to the northwest of Smithers and s t r i k i n g about 50° east of north would account for the d i r e c t i o n and s l i g h t mag-nitude increase of t h i s 'anomaly'. Such a zone would be roughly perpendicular to the tectonic pattern of the Skeena and Omineca Mountains, and be deep enough to cause the observed anomalous spectral po\^er increase i n the 50 min. period Z v a r i a t i o n s , and consequently, could possibly be associated with a conductivity feature in the upper mantle. (See F i g . IV-10 for Parkinson vectors and proposed conductivity structures for western pro-f i l e stations.) 66 V. SUGGESTIONS FOR FURTHER STUDY 1) Continued mapping of the low I - high I discon-t i n u i t y north of l a t i t u d e 54°N i s desirable, but may prove impractical, since at these high lat i t u d e s source e f f e c t s may e a s i l y i n v a l i d a t e the assumption of uniformity of the inducing f i e l d and furthermore, noise levels increase. The same objec-ti o n plus the problem of a completely inaccessible area would presently prevent a GDS investi g a t i o n of the area northwest of Smithers. 2) A continued inves t i g a t i o n of the Kootenay Lake anomaly i s warranted. Further GDS work could be ca r r i e d out in the area to the south and to the east of this E-W s t r i k i n g anomaly, i n order to accurately map the low I - high I discon-t i n u i t y and allow a concrete tying together of the GDS results of western Canada and the western U.S.A. 3) A c l o s e l y spaced, broad-band frequency coverage (10" 1 to 10"" cps) GDS p r o f i l e should be c a r r i e d out at the Trench low Z - high Z d i s c o n t i n u i t y , either at McBride or at Golden. Such an intense, detailed coverage coupled with the numerical solution of the step-conductivity problem in three dimensions would reveal more p r e c i s e l y the nature of the con-d u c t i v i t y step and allow depth resolution of multiple conduc-ti v e zones. 67 VI. CONCLUSIONS From th i s research i t i s concluded that the conduc-t i v i t y and p e t r o l o g i c a l model suggested by Caner (1970) for southwestern Canada i s also v a l i d for central western Canada. The coast-effect at Tofino (Lambert and Caner, 1965) i s present at Prince Rupert, and the inland 'step-conductivity' anomaly (Hyndman, 1963) i s again located near the Rocky Mountain Trench. Observed second order e f f e c t s prompt the hypothesis of two anomalous conductive zones: one shallow, at Caner's suggested depth of 10 to 15 km., s t r i k i n g roughly NW-SE, and associated with the fedge' of a hydrated layer located at the western front of the Rocky Mountains; and a second, much deeper zone running approxi-mately E-W south of Kootenay Lake, perhaps associated with a s t r i k e - s l i p feature in the upper mantle (Lajoie and Caner, 1970). These suggested separate l a t e r a l conductivity d i s c o n t i n u i t i e s have previously been interpreted as o f f s e t sections of the same structure. A s i m i l a r deep conductivity structure s t r i k i n g NE may e x i s t to the northwest of Smithers. 6 8 APPENDIX A Outline of Power Spectral Calculations (after Bendat and Piersol) Assuming a sampling i n t e r v a l h , then for N data values, ^ x n ^ > from a f i n i t e , stationary record x(t) with a mean of zero, an autocorrelation function estimate at the displacement rh i s given by: N-r R x ( r h ) = FFF I x n x n + r r=0,1,2 ,... .m n=l where r i s the lag number, and m i s the maximum lag number. An estimate of the exact power spectral density function, defined for a frequency range 0 - v - v c , i s then calculated by: G (v) = 2h x v *  m-1 R +2 Y R cos o L r r=l rrrv + R cos m irmv where v c = ^h, the cut-off frequency and RQ i s the auto-c o r r e l a t i o n estimate at zero lag. To avoid 'sidelobes' contaminating frequency bands adjoining the f i n i t e spectral window through which the data i s viewed, a Hanning 'lag window' weighting function, D , i s used to y i e l d a 'smooth' spectral density estimate: 69 D (rh) r (1 + cos H.) m J r=0 ,1,2 ,. . .m = 0 r > m Hence, the equation used for a smooth estimate of the power spectral density i s fkv 1 c m m-1 = 2h R Q + 2 I D R R R cos firrkl r=l t m J where spectral estimates are calculated at only the m+1 spe c i a l kv discrete frequencies v = m , y i e l d i n g m/2 independent spectral estimates, since spectral estimates at points less than 2 v c apart w i l l be correlated. m As can be seen in the Z power spectra of Figs. IV-2a and 3a, the Hanning window s t i l l introduces sidelobe e f f e c t s . Prewhitening can eliminate these minor e f f e c t s , but was not considered necessary since only q u a l i t a t i v e conclusions were drawn from r e l a t i v e power l e v e l s . (Where sidelobing introduced a negative power, the actual spectral power was assumed to be ne g l i g i b l e . ) 70 APPENDIX B Parameters o f I n d u c t i o n A n a l y s i s 1. P a r k i n s o n P o l a r Diagrams and P a r k i n s o n V e c t o r s L e t AD , AH , and AZ be the geomagnetic f i e l d component changes i n the u n i t v e c t o r d i r e c t i o n s D (magnetic e a s t ) , H (magnetic n o r t h ) , and Z ( v e r t i c a l p o s i t i v e down-ward) . Then the h o r i z o n t a l v e c t o r change i s g i v e n by: 2 AB = [(AD) + (AH) ] where the d i r e c t i o n o f AB i s d e f i n e d by the az i m u t h a n g l e , <j) , measured p o s i t i v e e a s t w a r d from H and n e g a t i v e westward: i . - 1 r A D n <f> = t a n [^j] The t o t a l v e c t o r change, AT , has a magnitude: AT = [ ( A B ) 2 + (AZ) 2]'" 2 and a d i r e c t i o n s p e c i f i e d by § (as above) and by 6 , the a n g l e between AT and Z , the downward v e r t i c a l : (See F i g . B l a.) 6 = t a n " 1 ^ ] ' N a. b. c. F i g . B l : a.Diagram i l l u s t r a t i n g the parameters used i n d e s c r i b i n g the magnitude and d i r e c t i o n of the geomagnetic f i e l d changes. b. E x p l a n a t i o n of p o l a r diagrams. P r e p r e s e n t s a d i r e c t i o n i n the SW-up o c t a n t . Q r e p r e s e n t s a d i r e c t i o n i n the NE-dowri o c t a n t . T h e a r c s aPb and aOb r e p r e s e n t the i n t e r s e c t i o n of a ' p r e f e r r e d p l a n e ' w i t h the u n i t s p h e r e , ( a f t e r Parkinson,1962) c. E x p l a n a t i o n of P a r k i n s o n V e c t o r . POQ i s the p r e f e r r e d p l a n e l o o k i n g n o r t h -west. ON i s the downward u n i t normal and i t s h o r i z o n t a l p r o j e c t i o n , O M ^ i s the P a r k i n s o n V e c t o r . ( i n the i l l u s t r a t e d c a s e , i t p o i n t s SW and has a magnitude of since.) 72 The angles <j) and 6 are then plotted as points on the unit sphere whose northern and southern hemisphere sur-faces are represented by the 'Schmidt equal area' projected polar c i r c l e s , the upper c i r c l e being used to plo t points cor-responding to a change with an upward (negative) v e r t i c a l com-ponent and the lower c i r c l e for a change with a downward (posi-tive) v e r t i c a l component (as shown i n F i g . BI b.) The azimuthal d i r e c t i o n i s corrected for present magnetic d e c l i n a t i o n , and hence N i n the diagram represents geographic north. The r a d i a l distances of the data points are d i r e c t l y proportional to 8 i n the 'down' c i r c l e and to TT-6 i n the 'up' c i r c l e (Parkinson, 1959). It i s generally found at anomalous locati o n s , i . e . s i t e s where l a t e r a l inhomogeneities cause an appreciable induc-ti o n e f f e c t i n the v e r t i c a l f i e l d , that for many events the vectors AT mapped on a unit sphere tend to be confined to a 'preferred plane'. Such a plane intersects the sphere in a great c i r c l e and hence manifests i t s e l f as data points f a l l i n g along two s i m i l a r arcs in the polar c i r c l e s . The d i r e c t i o n of the preferred plane i s represented by the 'Parkinson Vector' (Parkinson, 1962). Its d i r e c t i o n i n the horizontal plane i n -dicates the azimuth where maximum upward t i l t , a , occurs within the plane, and i t s magnitude i s proportional to the sine of the angle of maximum absolute t i l t . (Note that a = TT/2 - 6 M i n i m u m •) Consequently a steeply t i l t i n g pre-ferred plane w i l l have a long Parkinson vector, whereas a very 73 short Parkinson vector w i l l correspond to an almost h o r i z o n t a l plane (see F i g . B l c ) . 2. Numerical Technique of G e t t i n g Amplitudes from D i g i t i z e d Data. For any d i g i t i z e d magnetic event i n GDS data, there w i l l be three simultaneous s e r i e s > ^ k ^ ' a n <* ^ Hk^ ' where k=l to N and N i s the t o t a l number of d i g i t i z e d p o i n t s , r e p r e s e n t i n g the continuous traces of the three ortho-gonal f i e l d components. A t o t a l f i e l d value can be c a l c u l a t e d at each i t f l p o i n t , i . e . : T. = {D. 2 + Z.2 + U.2}h X X X X and hence a s e r i e s r e p r e s e n t i n g the continuous t o t a l f i e l d value can be computed. Changes i n the values of T are then e x t r a c t e d by c a l c u l a t i n g d i f f e r e n c e s between consecutive p o i n t s of a s e r i e s which i s a sub-sequence of {T^} created i n the f o l l o w i n g way. Xi i s set equal to Ti and then f o r the next r p o i n t s of the s e r i e s > where r i s an a r b i t r a r y s p e c i f i e d range of number of p o i n t s , the value |Xi - T^| i s c a l c u l a t e d ( i = 2 to 2+r). Then f o r these r absolute d i f f e r e n c e s , there w i l l be a p o i n t j , where 2 - j - 2 + r , such that 74 |Xi — Xj| i s a maximum. The value of X 2 i s then set equal to Tj ; then, for the next r number of points |X 2 - T^| , where i = j + 1 to j + r , i s again evaluated and X3 i s set equal to that T^ which gives the maximum absolute difference with X 2 ; and so on. In this way, n points of the series {T^} are chosen, forming the series {X^.} , and corresponding points i n the component series are also selected forming the subsequences {D^'} , f ^ ' } , and {H^') . Simultaneous component changes are then calculated from these subsequences by the following r e l a t i o n s : AD. = D* - D ! 1 l+l 1 z! where i = l , n-1 1 ' 1 H. 1 These simultaneous changes are then considered to be s t a t i s t i c a l l y representative of amplitudes of geomagnetic variations for periods favoured by the value of r It can be seen q u a l i t a t i v e l y that a small value of r w i l l favour short period f l u c t u a t i o n s , but since i t w i l l also include short-spaced sampling of long period tendencies, the results w i l l include low frequency information. S i m i l a r l y , a large value of r w i l l c l e a r l y favour long period response, but 'large-r' sampling can e a s i l y include high frequency peaks and thus contaminate the low frequency r e s u l t s . It i s obvious A Z i = Z i + 1 " AH. - H! + 1 -75 that this is neither a refined nor an optimum technique of getting combined amplitude-frequency information from digitized data; however, the application of more sophisticated techniques was f e l t to be not j u s t i f i e d due to the lack of reliable high frequency data, and the limited use made of the outlined numeri-cal technique. 76 APPENDIX C Determination of Errors i n 'Least-Squares' Linear Function F i t t i n g In the standard method of 'least-squares f i t t i n g ' (see Chauvenet, 1960) the quantity £ 6^  , where n i s the i number of observations and 6^  i s the difference between the i * * 1 observed and the i * " * 1 ' f i t t e d ' dependent v a r i a b l e , i s minimized. Its smallest value, which y i e l d s the most probable values of the parameters of the f i t t e d function, also repre-sents the f i n a l sum of squares of the observational errors. Consequently, a root-mean-square error i s given by e = n W. I l n-m n > m (1) where m i s the number of independent parameters i n the f i t t e d function. This 'observational error' can be considered as a measure of the mean dispersion of the observed data with respect to the f i t t e d function. The i n d i v i d u a l errors (e Y ) in the determined para-(x^) are dependent on the t o t a l observed error (c) and the r e l a t i v e weight of each parameter (p x ) in the functional k expression of the observed quantity: k=l,...m (2) 77 If the m determined parameters are consequently com-bined i n some functional expression f ( x i , Xz , . . .x^) , then e.P , the combined error in f due to small errors e in i x k x^ , can be expressed by m f 3 f 4= i 1 k=l e 3 x, x k k (3) For example, i n this thesis the function v = x s i n 0 + y cos 6 was f i t t e d to the Mercator plot induction data, and by the method of least squares the most probable values of x and y and t h e i r associated errors, e and e , were determined^ x y The f i t t e d curve, however, was expressed a n a l y t i c a l l y as a single sine function of the form v = A s i n (cj> - <j>o) (4) where A = (x 2 + y 2 ) ' 5 (amplitude) <j>o = tan _ 1(-y/x) (phase) Consequently, using r e l a t i o n (3), the errors in amplitude and phase are: £ A = { C x e x ) 2 + ( y e y ) 2 } l 2 / A ee = { ( y £ x ) 2 + ( X O ^ / A 2 o y (5) 78 REFERENCES Bendat, J . S. and P i e r s o l , A. G., 1958. Measurement and Analysis of Random Data. John Wiley and Sons, New York. Caner, B. , Cannon, W. H., and Livingstone, C. E., 1967. Geomagnetic depth sounding and upper mantle struc-ture i n the C o r d i l l e r a region of western North America. J . Geophys. Res., 72, 6335-6351. Caner, B., 1969. E l e c t r i c a l conductivity structure of the lower crust and upper mantle in western Canada. Unpublished t h e s i s , University of B r i t i s h Columbia, Vancouver. Caner, B., 1970. E l e c t r i c a l conductivity structure i n western Canada and p e t r o l o g i c a l i n t e r p r e t a t i o n . J . Geomag. and G e o e l e c , V. 22, 113-129. Caner, B., Auld, D. R., Dragert, H. , Camfield, P. A., 1971. Geomagnetic depth sounding in western Canada. In preparation; to be submitted to J . Geophys. Res. Cannon, W. H., 1967. Geomagnetic depth sounding in southern B r i t i s h Columbia and Alberta. Unpublished t h e s i s , University of B r i t i s h Columbia, Vancouver. Chauvenet, W., 1960. A Manual of Spherical and P r a c t i c a l Astronomy, Volume Two. Dover Publications, New York. 79 Gough, D. I. and Anderson, C. W., 1968. Magnetic deep sound-ings in the Rocky Mountains. Paper presented at CAP meetings, Calgary, June 5-8, 1968. Hyndman, R. D., 1963. E l e c t r i c a l conductivity inhomogeneities in the earth's upper mantle. Unpublished t h e s i s , University of B r i t i s h Columbia, Vancouver. Hyndman, R. D. and Hyndman, D. W., 1968. Water saturation and high e l e c t r i c a l conductivity i n the lower continental crust. Earth and Planet. S c i . Letters, 4, 427-432. Lajoie, J . J . , 1970. The geomagnetic v a r i a t i o n anomaly at Kootenay Lake, B.C. Unpublished t h e s i s , University of B r i t i s h Columbia, Vancouver. Lajoie, J . J. and Caner, B., 1970. Geomagnetic induction anomaly near Kootenay Lake - a s t r i k e s l i p feature in the lower crust? Submitted to Can. J . Earth S c i . Lambert, A., 1965. An anomaly i n geomagnetic variat i o n s on the west coast of B r i t i s h Columbia. Unpublished the s i s , University of B r i t i s h Columbia, Vancouver. Lambert, A. and Caner, B., 1965. Geomagnetic depth sounding and the coast e f f e c t in western Canada. Can. J . Earth S c i . , 2, 485-509. Livingstone, C. E. , 1967. Geomagnetic depth sounding i n the southwest U.S.A. and in southern B r i t i s h Columbia. Unpublished t h e s i s , University of B r i t i s h Columbia, 80 Madden, T. R. and Swift J r . , C. M., 1969. Magnetotelluric studies of the e l e c t r i c a l conductivity structure of the crust and upper mantle. Am. Geophys. Union Monograph 13, 469-479. Parkinson, W. D. , 1959. Directions of rapid geomagnetic fl u c t u a t i o n s . Geophys. J . , 2, 1-14. Parkinson, W. D. , 1962. The influence of continents and oceans on geomagnetic v a r i a t i o n s . Geophys. J . , 6, 441-449. Parkinson, W. D. , 1964. Conductivity anomalies in A u s t r a l i a and the ocean e f f e c t . J . Geomag. G e o e l e c , 15, 222-226. P r i c e , A. T. , 1962. The theory of magnetotelluric methods when the source f i e l d i s considered. J . Geophys. Res., 67, 1907-1918. R e i t z e l , J. S. , Gough, D. I., Porath, H., Anderson I I I , C. W., 1970. Geomagnetic deep sounding and upper mantle structure in the western United States. Geophys. J. , 19, 213-235. Rikitake, T. , Whitham, K., 1964. Interpretation of the A l e r t anomaly in geomagnetic v a r i a t i o n s . Can. J . Earth S c i . , 1, 35-62. 81 Rikitake, T., 1966. Electromagnetism and the Earth's i n t e r i o r . E l s e v i e r Publ. Co., Amsterdam. Schmucker, U., 1964. Anomalies of geomagnetic variations in southwestern United States. J . Geomag. Geoelec., 15, 193-221. Serson, P. H., 1957. An e l e c t r i c a l recording magnetometer. Can. J . Phys., 35, 1387-1394. Srivastava, S. P., 1965. Method of in t e r p r e t a t i o n of magneto-t e l l u r i c data when source f i e l d i s considered. J . Geophys. Res., 70, 945-954. Whitham, K., 1963. An anomaly in geomagnetic variations at Mould Bay i n the A r c t i c Archipelago of Canada. Geophys. J. , 8 , 26-43. Whitham, K., 1965. Geomagnetic v a r i a t i o n anomalies i n Canada. J. Geomag. G e o e l e c , 17 , 481-498. 

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