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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  o f 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 t h e s i s as conforming required  t o the  standard  THE UNIVERSITY OF BRITISH COLUMBIA September, 1970  In  presenting  an  advanced  the  Library  I  further  for  degree shall  agree  scholarly  by  his  of  this  written  this  thesis  in  at  University  the  make  that  it  p u r p o s e s may  for  for  is  financial  of  Sept.30.1070  of  Columbia,  British  by  gain  Columbia  for  the  understood  GEOPHYSICS  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, C a n a d a  of  extensive  be g r a n t e d  It  fulfilment  available  permission.  Department  Date  freely  permission  representatives. thesis  partial  shall  requirements  reference copying  Head o f  that  not  the  copying  be a l l o w e d  agree  and  of my  I  this  that  study. thesis  Department or  for  or  publication  without  my  i  ABSTRACT  G e o m a g n e t i c d e p t h - s o u n d i n g was c a r r i e d o u t i n a large-spaced t o map in  profile  across  the c o n d u c t i v i t y  structure  cessive  east-west p r o f i l e s  Numerical indicates vertical British  of Jasper  that  o f geomagnetic  the d i s c o n t i n u i t y  magnetic  field,  C o l u m b i a by Hyndman  typical  reported  storm  stations  A l l stations  high-frequency  to the east  Z-variation  activity  i n the area  t o the west  o f the trench  content  as w e l l  o f the  f o r south-eastern  'low Z' c h a r a c t e r i s t i c s and no o r l i t t l e  induction;  suc-  o f 1969.  (1963), i s l o c a t e d  t h e Rocky M o u n t a i n T r e n c h .  i n two  i n the attenuation  as f i r s t  mantle  variographs  Rupert  t h e summer  i n order  and u p p e r  Geomagnetic  to Prince  during  analysis  Columbia  of the crust  the c e n t r a l Canadian C o r d i l l e r a .  were s e t up f r o m e a s t  of  central British  exhibit  anomalous  display  a  as anomalous  strong, field  enhancement.  Power s p e c t r a l and p o l a r i z a t i o n a n a l y s e s first  order  structure Canada.  agreement w i t h  the two-dimensional  model p r o p o s e d by C a n e r  structure  o f two c o n d u c t i v i t y  a more complex  discontinuities:  with  the  o f t h e Rocky M o u n t a i n s ;  western  structure,  feature  model  One  shallow  s t r i k e s r o u g h l y NW-SE a t a d e p t h o f 10 t o 15 km. and  may be a s s o c i a t e d  Kootenay  conductivity  (1970) f o r s o u t h - w e s t e r n  Second-order e f f e c t s suggest  consisting  show a  front  trending  t h e 'edge' o f a h y d r a t e d  approximately  Lake and i s p o s s i b l y i n the upper mantle  E-W,  located at  a s e c o n d much  i s located  associated  (Lajoie  layer  with  and C a n e r ,  a  deeper  south o f  strike-slip 1970).  ii  TABLE OF CONTENTS I  II  III  A.  Geomagnetic Depth Sounding in Western North America  1  B.  Conductivity Structure Model for Southwestern Canada  2  THEORY A.  Outline of Geomagnetic Induction  B.  Induction in a Lateral Conductivity Discontinuity 12  A.  Instrumentation  17  B.  F i e l d Operation  19  C.  Methods of Data Analysis Power Spectral Analysis Parkinson Plots and Vectors Mercator Induction Plots Horizontal F i e l d Enhancement  21 23 24 25  EXPERIMENTAL RESULTS A.  East P r o f i l e (i) (ii) (iii) (iv)  B.  (Robb-Prince George)  Sample Records Spectral Analysis Results Induction Analysis Results Interpretation  West P r o f i l e (i) (ii) (iii) (iv)  V.  9  EXPERIMENTAL PROCEDURE  (i) (ii) (iii) (iv) IV  Page  INTRODUCTION  (Prince George-Prince Rupert)  Sample Records Spectral Analysis Results Induction Analysis Results Interpretation  SUGGESTIONS FOR  27 30 37 48  FURTHER STUDY  55 55 60 64 66  i i i  Page VI  .  CONCLUSIONS  67  APPENDICES A.  Outline  B.  Parameters  C.  Determination of Errors Linear Function F i t t i n g  REFERENCES  of  Power of  Spectral  Induction  Calculations  Analysis in  'Least  68 70  Squares'  76 78  iv  LIST OF FIGURES Page 1-1 1-2 1-3 I- 4 II- 1 II- 2  Magnetogram s e c t i o n s from p a i r s o f s t a t i o n s between 33° and 54°N.  3  L o c a t i o n o f GDS s t a t i o n s i n North America to 1966.  4  up '  L o c a t i o n o f GDS and MT s t a t i o n s i n western Canada up to 1969.  5  P e t r o l o g i c a l model f o r western Canada, tude 49.3°N.  7  E l e c t r o m a g n e t i c response o f i s o l a t e d e l l i p t i c a l cylinder.  lati-  infinite 14  E l e c t r o m a g n e t i c response o f i n f i n i t e c i r c u l a r c y l i n d e r coupled w i t h s e m i - i n f i n i t e conducti n g sub-stratum.  15  III- l  L o c a t i o n o f instrument s i t e s .  20  IV- l a , l b  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 e a s t e r n p r o f i l e .  28,29  S p a t i a l and frequency dependence o f power r a t i o s i n each component f o r the e a s t e r n profile.  32,33  M - r a t i o s f o r s e v e r a l frequency bands at eastern p r o f i l e s t a t i o n s .  34,35  Parkinson p o l a r diagrams stations.  38,39  IV-2b,3b  IV-4a,4b IV-5a,5b IV-6  IV-7 IV-8  IV-9  f o r eastern p r o f i l e  Mercator 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 curves f o r e a s t e r n p r o f i l e stations.  40  Averaged Mercator 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 curves f o r Robb and J a s p e r .  42  Azimuthal dependence o f the r a t i o o f t o t a l h o r i z o n t a l f i e l d amplitudes at McBride and J a s p e r w i t h r e s p e c t to P r i n c e George.  47  Observed v e r t i c a l and h o r i z o n t a l induced f i e l d s and a p o s s i b l e 2-dimensional model of the conducting s t e p .  50  V  Page IV-10 IV-11 IV-12a IV-12b  IV-13 IV-14a,14b IV-15  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 p r o p o s e d c o n d u c t i n g zones.  54  Sample o f m a g n e t o g r a m 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  Power s p e c t r a l stations.  57  estimates at western p r o f i l e  S p a t i a l and f r e q u e n c y d e p e n d e n c e o f p o w e r r a t i o s i n e a c h component f o r t h e w e s t e r n profile.  57  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 western p r o f i l e stations.  59  Parkinson polar stations.  61,62  diagrams  f o r western p r o f i l e  Mercator plots of induction effects with f i t t e d sine curves f o r western p r o f i l e s t a tions.  63  vi  L I S T OF TABLES  Page IV-1  IV-2  IV-3  IV-4  Summary o f f i t t e d s i n e - c u r v e p a r a m e t e r s 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  Frequency dependence o f t h e i n d u c e d at J a s p e r .  field 45  Summary o f v e r t i c a l and h o r i z o n t a l f i e l d s f o r the eastern p r o f i l e .  induced  Summary o f f i t t e d s i n e c u r v e p a r a m e t e r s and Parkinson vectors f o r western p r o f i l e .  49  60  vii ACKNOWLEDGEMENTS  I wish to acknowledge the encouragement, and  liberal  s u p e r v i s i o n o f Dr. G. K. C. C l a r k e  the tenure o f t h i s r e s e a r c h .  I am indebted  advice  throughout  to Dr. B. Caner  o f the V i c t o r i a Magnetic Observatory f o r d i r e c t i n g f i e l d t i o n s and f o r many u s e f u l d i s c u s s i o n s which helped lysis  and i n t e r p r e t a t i o n o f the d a t a .  opera-  i n the ana-  The use o f equipment  from the Dominion Observatory and the support  o f the N a t i o n a l  Research C o u n c i l are g r a t e f u l l y acknowledged.  Personal  thanks  are a l s o given t o the o p e r a t i o n a l s t a f f a t the Computing Centre who made the endless  computing a p l e a s a n t  supported i n p a r t by a U n i v e r s i t y Graduate  task.  T h i s work was  Fellowship.  1  I.  INTRODUCTION A.  Geomagnetic  Depth Sounding i n Western North America  Intense e l e c t r i c c u r r e n t systems, c o n c e n t r a t e d i n the  a u r o r a l zones, cause s t r o n g f l u c t u a t i o n s i n the e a r t h ' s  geomagnetic at  field,  depths depending on the frequency o f the v a r i a t i o n .  secondary f i e l d s will at  thus i n d u c i n g c u r r e n t s w i t h i n the e a r t h The  a s s o c i a t e d w i t h these s u b s u r f a c e c u r r e n t s  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  the e a r t h ' s s u r f a c e , and hence, deep c o n d u c t i v i t y inhomo-  g e n e i t i e s can be r e v e a l e d by measurement o f the three geomagnetic field  components.  T h i s i s the b a s i c p r i n c i p l e o f the  geomagnetic  depth sounding (GDS)  technique.  I t i s a method  t h a t has r e c e n t l y been used to an i n c r e a s i n g extent i n North America i n o r d e r to determine the e l e c t r i c a l  conductivity  s t r u c t u r e of the lower c r u s t and upper mantle. The p i o n e e r i n g work o f Schmucker (1964) i n the southwest U.S.A. r e v e a l e d two c o n d u c t i v i t y anomalies o f major i n terest.  The f i r s t ,  the ' C a l i f o r n i a c o a s t a l anomaly', i s marked  by u n u s u a l l y s t r o n g v a r i a t i o n s i n the v e r t i c a l r e l a t e d w i t h east-west v a r i a t i o n s , and was edge e f f e c t o f the P a c i f i c Ocean.  field  (Z) cor-  e x p l a i n e d as the  The second, the  'Texas  i n l a n d anomaly', i s d e l i n e a t e d by a sharp d i s c o n t i n u i t y i n the amplitude o f Z f l u c t u a t i o n s between Las Cruces and  Cornudas,  New  Mexico.  Schmucker i n t e r p r e t e d i t s cause to be a r o u g h l y  N-S  striking  step i n the top s u r f a c e o f the c o n d u c t i n g mantle,  2  w i t h a change i n depth o f the h i g h l y conducting  sub-stratum  from 160 km. i n the west to 320 km. under the e a s t e r n A s i m i l a r sudden i n l a n d change i n the c h a r a c t e r  region.  of Z varia-  t i o n s \\ras subsequently observed by other i n v e s t i g a t o r s at l a t i t u d e s further north  (see F i g . 1-1).  Work by Hyndman  (1963),  Lambert and Caner (1965) , and Caner et a l (1967) i n d i c a t e d the continental  e x t e n t o f such an i n l a n d anomaly marking the  t r a n s i t i o n between the 'low I and  the 'high  1  s t a t i o n s o f the western C o r d i l l e r a  I' s t a t i o n s l y i n g t o the e a s t .  (  I  i s the r a t i o  o f v e r t i c a l t o h o r i z o n t a l amplitude o f geomagnetic v a r i a t i o n s . ) T h i s , o r a t l e a s t a s i m i l a r , t r a n s i t i o n zone, shown i n small sections the  i n F i g . 1-2, has s i n c e been confirmed t o f o l l o w  l i n e o f the Rocky Mountains a t i n t e r m e d i a t e  latitudes  (Gough and Anderson, 1968), but anomalously high indicating  Model f o r Southwest Canada  combined work o f the V i c t o r i a Magnetic Observatory  (magnetotelluric)  F i g . 1-3).  transition the  Structure  ( R e i t z e l et a l , 1970).  the Department o f Geophysics at U.B.C. has p r o v i d e d  GDS and MT (see  the C o r d i l l e r a r e g i o n  Conductivity The  and  I stations,  low c o n d u c t i v i t y o f the sub-stratum, have a l s o been  found w i t h i n  B.  roughly  detailed  coverage o f south-western Canada  This work has c o n t i n u e d the mapping o f a  zone f o r the Canadian C o r d i l l e r a and a l s o  c o a s t a l e f f e c t at the west coast  o f Vancouver  established  Island.  3  PRINCE GEORGE  «£ u T.  04  GRAND  0*  FORKS  Pig.I-l.Magnetogram (a) l a t i t u d e (b) l a t i t u d e (c) l a t i t u d e (d) l a t i t u d e Scale bars  JASPER  OS  LETHBRIDGE  s e c t i o n s from p a i r s of s t a t i o n s 5^°N ( t h e s i s w o r k ) 51°N ( C a n e r e t a l , 1 9 6 7 ) 4 9 . 5 ° N (Hyndman,1963) 33°-35°N ( C a n e r e t al,1967) a r e 50r;time marks 1 hour.  at  4  F i g . 1 - 2 . L o c a t i o n o f GDS s t a t i o n s i n N o r t h A m e r i c a t o 1 9 6 6 . ( a f t e r Caner e t al,1967)  up  P i g . 1-3.Map o f GDS" and MT s t a t i o n s i n w e s t e r n C a n a d a up 1 9 6 9 . ( a f t e r Caner e t al,1971)  to  6  R e c e n t l y , 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 f o r t h i s r e g i o n based p r i m a r i l y on r e s u l t s but  a l s o g i v i n g due  aeromagnetic, s e i s m i c ,  and  model, shown i n F i g . 1-4,  these MT  consideration  GDS  to g e o l o g i c a l ,  heat flow d a t a . postulates  and  This  regional  an uppermost mantle  temperature o f at l e a s t 750°C at a depth of about 35 km., c r e a t i n g a moderately conducting sub-stratum under the Cordillera.  At  entire  the wrestern f r o n t of the Rocky Mountains  towards the west, the  lower c r u s t  thus  and  (from a depth of 10 to 15  km.)  becomes c o n d u c t i v e as w e l l , the most l i k e l y cause being hydrat i o n and  possible p a r t i a l  melting.  In a d d i t i o n to t h i s l a r g e s c a l e r e g i o n a l model, the by  'coast  e f f e c t ' at T o f i n o has  Lambert and  Caner (1965) as a combination o f two  effects:  1) the  face and  2)  conductivity contrast  of the  continental  anomaly at Kootenay Lake, f i r s t found to be  due  shelf. reported  L a j o i e and  a s s o c i a t e d w i t h a deep s i n i s t r a l  associated  A l s o , the  strong  by Hyndman  to a sharp, east-west t r e n d i n g  d i s c o n t i n u i t y , i n t e r p r e t e d by  distinct  land-sea i n t e r -  inhomogeneities i n the upper mantle  w i t h the edge of the  was  p r e v i o u s l y been i n t e r p r e t e d  (1963), conductivity  Caner (1970) to  strike-slip  feature  be  in a  subsequently i n e r t basement, thus c r e a t i n g 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 . ^  SELKIRK MOUNTAINS  \ 20 *40 60  KOOTENAY LAKE  PURCELL MOUNTAINS  \1I0-I5KM\^ \  - CONDUCTIVE, HYDRATED LOWERS CRUST (PROBABLY PARTIAL MELTINGP*  ROCKY MTN. TRENCH (KOOTENAY VALLEY)  ROCKY MOUNTAINS  \ Y V RESISTIVE RESOLUTION  - A  x  x  x  X  N  PLAINS  x  >750°C  X  MODERATELY CONDUCTIVE UPPER MANTLE, T > 8 0 0 ° C , COMPOSITION UNDEFINED  80  P i g . I - 4 . P e t r o l o g i c a l model f o r southwest Canada a t l a t i t u d e 49.3°N.(after Caner,1970)  8  The purpose o f t h i s t h e s i s was  therefore  to continue the GDS mapping of the I t r a n s i t i o n latitude  o f 54°N, and to t e s t  model f o r the c e n t r a l  twofold:  zone at a  the v a l i d i t y o f t h i s proposed  Canadian C o r d i l l e r a .  9  II.  THEORY A.  O u t l i n e of Geomagnetic The  t o t a l v a r i a t i o n a l p a r t of the geomagnetic  observed at the e a r t h ' s and  time  Induction  (t) , and  field  s u r f a c e i s a f u n c t i o n of p o s i t i o n (r)  can be expressed as the t o t a l v e c t o r  quantity  F(r,t) = F ( r , t ) + F ( r , t ) + F ( r , t ) e  where  F  i n  = the e x t e r n a l source f i e l d , due  g  CD  i a  to  ionospheric  currents. ->  F. = the in  'normal' i n t e r n a l f i e l d , due  currents -*•  F. = the ia  flowing p a r a l l e l  to  to the earth's  'anomalous' i n t e r n a l f i e l d , due  currents  induced  to  surface. induced  in a non-horizontally s t r a t i f i e d  con-  ductivity structure. Generally  speaking, the problem of geomagnetic depth sounding  i s to determine  F. in  ->  and  F. ia  by simultaneous measurement of '  -»•  F  at v a r i o u s  l o c a t i o n s , to deduce 'normal' and  'anomalous'  c u r r e n t systems r e s p o n s i b l e f o r these i n t e r n a l f i e l d s , finally  to draw c o n c l u s i o n s  controlling  the p a t t e r n and  The field  ionospheric  about the  conductivity structure  s t r e n g t h of the  induced  c u r r e n t systems causing  f l u c t u a t i o n s are at a d i s t a n c e  currents.  the  from the earth's  much s m a l l e r than the wavelengths of the v a r i a t i o n s . quently,  and  external surface Conse-  the magnetic i n d u c t i o n f i e l d predominates over  radiation f i e l d ,  and  the t o t a l v a r i a t i o n a l  field  i n (1)  the can  10  be d e r i v e d  from a magnetic p o t e n t i a l f u n c t i o n having  the form:  $ = Ce" P(x,y,v) vz  Neglecting  (2)  displacement c u r r e n t s , the t o t a l magnetic f i e l d i s  g i v e n by:  ' e  F =  where  W  l  w  dW 9P dW 3P d~z * 8x ' d~z * 9y  t  #  103  satisfies  , v WP  (3)  2  the equation:  dW 2  dz and  P  satisfies  (v  +  2  +  +  3x  v = X/2ir  (see P r i c e  (4)  * .o  (5)  the r e l a t i o n :  *2l i l l and  4Trioja(z))W  2  2  9y  V  P  2  , the s p a t i a l wavenumber o f the source  field  ( 1 9 6 2 ) f o r 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 l a y e r e d e a r t h , the c o n d u c t i v i t y  a  w i l l be constant  allows  w i t h i n each l a y e r of t h i c k n e s s  the s o l u t i o n o f equation  h  ; this  ( 4 ) w i t h i n each l a y e r to be  expressed by:  W = Ae  6 z  + Be"  6 z  (6)  11  where  0 = v  Combining  relations  (6) and (3) r e s u l t s  e x p r e s s i o n f o r the r a t i o  Fz/Fx  i n the f o l l o w i n g  i n each  layer:  . 9z „ -0z Ae + Be  Fz Z yj Fx ~ H " 6  The boundary  (7)  + 4-rriwa  2  9P 3x  Ae  G z  - Be"  (8)  6 z  c o n d i t i o n s f o r an n - l a y e r e d e a r t h (see S r i v a s t a v a ,  1965) leads t o the r e l a t i o n :  _P z=0 " z  where  f(6 ,h ) k  k  u  v  i i ' 9x  J- • fCe ,h )  6  = coth O i h i  k  + coth"  k=l,n  k  coth  1  ...coth"  1  (9)  (6 h 2  2  + ...  -g^)]} 6  n  (10)  9P Since the term  P/gY  i s indeterminate, simultaneously  recorded  data from two s t a t i o n s i s used to e v a l u a t e the f o l l o w i n g r a t i o : (see Caner e t a l , 1967) ( Z / H ) s t a t i o n 1 _ f (v ,a>,a ,h) s t a t i o n 1 _ ,M (Z/H)station 2 f(v,u,a,hjstation2  M  (11)  i s the power a t t e n u a t i o n r a t i o , and i s g e n e r a l l y the b a s i s  o f simple  l a y e r i n t e r p r e t a t i o n o f GDS  data.  12  B.  Induction  in a Lateral Conductivity  Often i n areas of g r e a t e s t c o a s t a l region America, the the  theory  areas,  the  resulting at  the  and  I-high  i s not p r e s e n t .  In these  '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 , i n azimuthally of the  dependent geomagnetic f i e l d v a r i a t i o n s  earth.  three-dimensional  d i s c o n t i n u i t y has of the  problem o f a l a t e r a l  not been s o l v e d .  However, by  conductivity  assuming  c o n d u c t i v i t y zone remains c o n s i s t e n t  for a distance  showed t h a t a gradual  that  along  l a r g e compared to the s k i n depth, a  dimensional s o l u t i o n i s p o s s i b l e .  Madden and  Swift  s l o p i n g d i s c o n t i n u i t y i n the  o f the upper mantle w i l l  two-  (1969) conductivity  r e s u l t i n a v a r i a b l e anisotropy  dent on source f i e l d d i r e c t i o n w i t h r e s p e c t for  the  I t r a n s i t i o n zone i n North  o u t l i n e d i n s e c t i o n II-A  The  strike  low  i n t e r e s t , such as  l a t e r a l homogeneity i n c o n d u c t i v i t y demanded by  surface  a feature  the  Discontinuity  (depen-  to conductor s t r i k e )  apparent c o n d u c t i v i t i e s computed from m a g n e t o t e l l u r i c  v a t i o n s , thus p e r m i t t i n g  the  l o c a t i o n of a c o n d u c t i v i t y  Using conformal mapping t e c h n i q u e s ,  obser'step'.  Schmucker (1964) i n v e s t i -  gated a two-dimensional s t e p - d i s c o n t i n u i t y i n c o n d u c t i v i t y showed that a c o n c e n t r a t i o n the upper corner sequently,  of magnetic f i e l d  of the step  for a time-varying  of current w i l l  flow  f o r the s t e a d y - s t a t e magnetic f i e l d ,  i n the upper corner  c o n t i n u i t y s t r i k e , r e s u l t i n g i n strong hancement .  lines  a  parallel  and  intersected  case.  Con-  concentration to the  anisotropic f i e l d  disen-  13  The  induction  d i m e n s i o n a l models has (1964).  They d e r i v e  infinite  elliptical  of  'anomalous' f i e l d s  been i n v e s t i g a t e d by R i k i t a k e  c y l i n d e r of i n f i n i t e  conductivity  f i e l d perpendicular  the  cylinder.  the  ' a m p l i f i c a t i o n e f f e c t ' of an u n d e r l y i n g  the  case o f an i n f i n i t e  is  as the  by  a semi - i n f i n i t e  an a m p l i f i c a t i o n v a r y i n g representative  r a t i o of r a d i u s  To  of  show  conductive  layer,  conductor i s a l s o from 47%  case i l l u s t r a t e d  to  80%  i n F i g . 11 -2  to depth o f a x i s v a r i e d from 1.0  Symmetric and  asymmetric  semi - i n f i n i t e  c o n d u c t i v e l a y e r are  response curves are  axis  c i r c u l a r c y l i n d e r embedded i n an  underlain  found f o r the  Whitham  to a  to the  ( F i g . I I - l shows s e v e r a l examples.)  i n v e s t i g a t e d , and  and  two-  the e l e c t r o m a g n e t i c response o f an i s o l a t e d  uniform h o r i z o n t a l inducing  i n s u l a t o r and  for various  'conductive upheavals' i n an  found to be  a l s o examined and  generally  to  0.5.  otherwise their  s i m i l a r to the  ellip-  t i c c y l i n d e r case. From R i k i t a k e a l o n e , i t can be  and  Whitham's  seen t h a t the  for  models v a r y i n g  and  i n depth w i l l  'representative'  s i m i l a r i t y o f the  introduce  a strong  ambiguity i n any  to a l l such two-dimensional models i s the the  d i r e c t i o n of the  conductor:  induced  fields  i n shape of c r o s s - s e c t i o n , i n o r i e n t a t i o n ,  i n t e r p r e t a t i o n of observed anomalous f i e l d s .  by  cases  inducing  model  Of c o u r s e , common  anisotropy  f i e l d with respect  introduced to  the  Maximum anomalous e f f e c t s are p r e s e n t when the  14  F i g . I I - l . T h e electromagnetic 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 conduct 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 perpendicular t o the a x i s of 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| Inducing  <r  Field  =00  Pig.II-2.The e l e c t r o m a g n e t i c response of 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 with a uniform inducing f i e l d perpendicular t o the a x i s o f t h e c y l i n d e r f o r b o t h t h e c o u p l e d and t h e u n 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 p e r p e n d i c u l a r to i t s s t r i k e , and no anomalous  response i s expected when i n d u c i n g f i e l d s are p a r a l l e l conductor.  Consequently, both the v e r t i c a l and  components o f the induced f i e l d w i l l  horizontal  exhibit a sinusoidal  dependence on the azimuth o f the i n d u c i n g h o r i z o n t a l w i t h extremum peaks o c c u r r i n g at d i r e c t i o n s normal strike.  to the  field,  to conductor  17  III.  EXPERIMENTAL PROCEDURE A.  Instrumentation Instruments  (i)  used i n the f i e l d were of two  The A s k a n i a Geomagnetic V a r i o g r a p h  types:  Gv3  T h i s v a r i o g r a p h c o n t i n u o u s l y r e c o r d s time in  the t h r e e f i e l d  components D, H, and Z, u s i n g three s m a l l ,  f i b r e - s u s p e n d e d bar magnets which,  along w i t h t h e i r  systems and c a l i b r a t i o n c o i l s , comprise variometers.  variations  the t h r e e  optical  independent  In a d d i t i o n to these t h r e e t r a c e s , a b a s e - l i n e ,  an i n t e r n a l instrument temperature  l e v e l , and h o u r l y time  marks are r e c o r d e d on the p h o t o g r a p h i c r e c o r d i n g paper. ensure  t h a t temperature  f l u c t u a t i o n s remained  l e s s than  To 1°C,  a t h e r m o s t a t i c a l l y c o n t r o l l e d h e a t e r , which can be s e t at 10°,  20°, 30°, or 40°C, i s e n c l o s e d i n the v a r i o g r a p h h o u s i n g .  The  r e c o r d i n g r e e l s used were those designed and b u i l t at  V i c t o r i a to allow o p e r a t i o n w i t h 60 hz l i n e power and  non-  m e t r i c c h a r t speeds; these r e e l s accommodate up to 10 metres of  r e c o r d i n g paper thus a l l o w i n g 12 to 14 days of continuous  r e c o r d when a c h a r t speed of 1 i n . / h r . i s used. s c a l e r e s o l u t i o n at t h i s speed  The  i s l i m i t e d to about  time200  sec.  p e r i o d s , w h i l e the minimum geomagnetic change r e s o l v a b l e i s r o u g h l y 1 or (ii)  The  2y.  Presentey Recording Magnetometer This variometer i s a t r a n s i s t o r i z e d  netometer  f l u x g a t e mag-  developed at the Dominion Observatory i n Ottawa,  18  based on Serson's orthogonal H,  and  (1957) IGY  s t a t i o n magnetometer.  f l u x g a t e s o l e n o i d s , the three f i e l d  Z, are measured i n terms of D.C.  per 100y  i n each of three channels.  components  v o l t a g e outputs  The  o f 0.5  three D,  of 1 v o l t  t h r e e t r a c e s were  recorded on two Moseley 7100B S t r i p Chart Recorders tivity  Using  at a s e n s i -  v o l t s / i n . which allowed a r e s o l u t i o n of 1 to  Chart c a p a c i t y i s 120  2y.  f e e t which, at a c h a r t speed o f 2 i n . / h r . ,  t h e o r e t i c a l l y allowed over 25 days of continuous l i m i t e d the t i m e - s c a l e r e s o l u t i o n to about 100 Field sites  record  and  sec. p e r i o d s .  f o r the Askania v a r i o g r a p h s were chosen  w i t h p a r t i c u l a r care to ensure a l o c a t i o n which s a t i s f i e d  the  f o l l o w i n g demands: 1) 110V/60 hz l i n e power 2) no  severe  l o c a l geomagnetic f i e l d  3) w e l l removed from t r a f f i c ,  gradients  power l i n e s and  other  l o c a l magnetic d i s t u r b a n c e s 4) r e a s o n a b l y 5) a s o l i d  weatherproof  f l o o r to support  the  instrument  For the supplementary f l u x g a t e s i t e s , the t h i r d d i t i o n was  u s u a l l y e a s i l y met  were unnecessary  conditions  s i n c e the s e n s i n g head can be mounted w e l l  away from the c o n t r o l u n i t  (100  pipe p l a c e d i n a covered p i t . instrument  and the l a s t two  con-  or 200 The  i s about e q u a l , but due  f e e t ) on an aluminum  q u a l i t y of data from e i t h e r to repeated m a l f u n c t i o n i n g  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.  Field  Operation  During the f i r s t GDS  P r o f i l e ' was  two weeks of June 1969,  s e t up i n order to l o c a t e the  the  'East  discontinuity  i n lower c r u s t - u p p e r mantle c o n d u c t i v i t y i n east c e n t r a l Columbia. Jasper  A s k a n i a v a r i o g r a p h s were s e t up at Robb (ROB),  (JAS), McBride  (MCB), and P r i n c e George (PGE) , a  gate v a r i o m e t e r r e c o r d i n g a l l three components was Valemount  (VAL), and supplementary  H and  Z only were i n s t a l l e d  (BAR)  (see F i g . I I I - l ) .  mid-June, s u f f i c i e n t tative  P r o f i l e was  s e t up at  f l u x g a t e systems r e c o r d i n g  at Quesnel  (QUE)  and  Barkerville  A f t e r an a c t i v e magnetic p e r i o d i n  o f the  'low  quali-  I-high I' d i s c o n t i n u i t y ,  and  i n s p i t e of poor records at Valemount, the East  shut down between J u l y 10 and J u l y  To complete the p r o f i l e approximately  P r o f i l e ' was  flux-  data were recorded to allow v i s u a l ,  identification  consequently,  at  British  13.  across c e n t r a l B r i t i s h  the same geomagnetic l a t i t u d e ,  the  Columbia  'West  GDS  e s t a b l i s h e d during the t h i r d week of J u l y w i t h  A s k a n i a s t a t i o n s at P r i n c e George, Smithers and P r i n c e Rupert at Vanderhoof (VAN)  (PRP),  (SMI), T e r r a c e  (TER),  and three-component f l u x g a t e systems  and Burns Lake (BRN)(see F i g . I l l - 1 ) .  s t a t i o n s were l o c a t e d i n the  'low-I*  zone and hence, no  All  F i g . I I I - 1 . M a p of the l o c a t i o n of i n s t r u m e n t  sites.  21  anomalous behaviour was expected, except f o r a p o s s i b l e 'coastal e f f e c t '  (Parkinson,  1962) at P r i n c e Rupert.  August s u f f i c i e n t magnetic storm a c t i v i t y had been and  hence, o b s e r v a t i o n s  along  small  By mid-  recorded,  the West P r o f i l e were ended by  August 18.  C.  Methods o f Data A n a l y s i s (i)  Power S p e c t r a l A n a l y s i s a) Data Reduction  To  f a c i l i t a t e numerical  active periods  This numerical  data,  numbers with  first  punched a u t o m a t i c a l l y  t o a decimal format  For adequate r e s o l u t i o n  (5 min.), a d i g i t i z i n g  r a t e o f about  64 p o i n t s / i n c h was chosen, which remained reasonably giving a d i g i t i z i n g  i n t e r v a l o f about 56 sec.  computer p l o t - o u t o f the input data, made on the s t o r e d numerical errors u n t i l  data  were c o n s i d e r e d  constant,  A f t e r an i n i t i a l  a r b i t r a r y adjustments were  t o e l i m i n a t e obvious  the computer t r a c e s c o u l d be e x a c t l y  on the i n i t i a l  onto  4 s i g n i f i c a n t d i g i t s ) and s t o r e d on mag-  n e t i c tape f o r subsequent p r o c e s s i n g . o f s h o r t p e r i o d events  using  at the Department of Geophysics,  paper tape i n a b i n a r y code, was converted (decimal  magnetically  o f at l e a s t 15 hour l e n g t h were d i g i t i z e d  the v i s u a l t r a c e d i g i t i z e r b u i l t U.B.C.  analysis, several  photographic t r a c e s .  The f i n a l  the 'best p o s s i b l e ' d i g i t a l  digitizing  superimposed  'adjusted'  data  representation of  the a c t u a l t r a c e s , and s p e c t r a l a n a l y s i s was c a r r i e d out on these  data.  22  b) To  Numerical Methods  allow d i r e c t comparison w i t h p r e v i o u s work, the  Tukey method o f s p e c t r a l a n a l y s i s was employed i n a computer by R . M. E l l i s  program adapted from one w r i t t e n  ment o f Geophysics, U.B.C. (see Appendix A ) . i n t e r v a l used was 56 sec. 0.5 c y c l e s  per minute.  The maximum c o r r e l a t i o n l a g used was  at l e a s t 100, the e q u i v a l e n t  P  i t s a b s o l u t e value was  r e s o l u t i o n bandwidth f o r power  c a l c u l a t i o n s was .01 c y c l e s The  per minute or b e t t e r .  r a t i o s o f the power s p e c t r a l  Vertical Horizontal / P  The sampling  g i v i n g a f o l d i n g frequency o f about  about 10% o f the sample s i z e , and s i n c e  spectra  ( i  determined as a f u n c t i o n  ' e  P  Z  / P  H  a  n  d  P  Z  / P  densities D  >  w  e  r  e  o f frequency at each s t a t i o n i n order  to i d e n t i f y 'low I' and 'high I  1  stations.  These power r a t i o s  were f u r t h e r combined i n t o a 'power a t t e n u a t i o n (Caner  o f the Depart-  ratio',  M  ,  e t a l , 1967) where  M  "'  (  P  Z  /  P  H ) S T A T I O N ^  P  Z  /  !  V REFERENCE  This normalized, dimensionless attenuation  S T A T I ON  factor i s r e l a t i v e l y  independent o f 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 w i t h frequency c h a r a c t e r i z e s structure  the d i f f e r e n c e  i n conductivity  between the 'eastern' and 'western' zones.  "5a  23  In relative  a d d i t i o n to t h i s  component power  standard  M  parameter,  the  ratios  STATION/ ( X^ REFERENCE STATION P  where  X = D,  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  effects  illustrate  s e p a r a t e l y the r e l a t i v e v a r i a t i o n  component e n e r g i e s w i t h f r e q u e n c y (Note in  t h a t a change i n  either  or  (ii)  visually  ascertain  change  technique  AD  ,  (1959) was  of simultaneous AH  AB  of i n d u c t i o n a n a l y s i s ) .  , and  AZ  will  Rikitake  Assuming  1  events, with  and  and  Parkinson's  quasi-random' o f an AZ  dependence b e i n g d e t e r m i n e d  anomalous on  AB  by  the  (See, f o r example, P a r k i n s o n  W h i t h a m , 1964;  d a t a were p r o c e s s e d  AZ  to  horizontal  c a u s e an a z i m u t h a l d e p e n d e n c e o f of this  applied  , i n order  , the t o t a l  f l u c t u a t i o n s , the presence  geometry o f the conductor.  tude  Vectors  ( s e e A p p e n d i x B f o r an o u t l i n e o f  the exact n a t u r e  1964;  and  d i r e c t i o n of  geomagnetic source conductor  a change  the c o r r e l a t i o n between the magnitude of  t h e m a g n i t u d e and field  station.  .)  measured amplitudes changes  to  individual  a b o u t by  p o l a r p l o t method o f P a r k i n s o n  component f i e l d  or Z  and  of the  s t a t i o n to  c a n be b r o u g h t  Parkinson Plots  The to  P^  M  from  H,  S c h m u c k e r , 1964.)  u s i n g a computer program  The  ,  1962, ampli-  developed  24  from one  used by  L a j o i e and  Cannon of the Department  Geophysics, U.B.C, which gave IBM  of  Calcomp p l o t s of P a r k i n s o n  diagrams f o r each s t a t i o n . (iii)  Mercator Induction  The ( L a j o i e and  Plots  Mercator p r o j e c t i o n of the P a r k i n s o n p o l a r p l o t  Caner, 1970)  representation  of the  c a l component and  was  a l s o used to give  anomalous i n d u c t i o n  a l i n e a r scale  e f f e c t i n the  i t s azimuthal dependence.  The  verti-  'dip',  6  ,  ->  o f the  t o t a l geomagnetic v e c t o r  change,  AT  , measured p o s i <j>  t i v e l y downward from the h o r i z o n t a l , i s p l o t t e d a g a i n s t the  geographic azimuth of the h o r i z o n t a l i n d u c i n g  AB  , measured p o s i t i v e l y east  P a r k i n s o n angle the  total field  6  as d e f i n e d  dip by  a random d i s t r i b u t i o n , but <J>  , and  the d i r e c t i o n of the sin|6|  the  (Note that  6 = ir/2  the  on these  - 9 .)  For  ' i n d u c t i o n ' p l o t s have  f o r anomalous s t a t i o n s , azimuth where > 6  6  is a  i s a minimum  Parkinson v e c t o r , w h i l e the v a l u e  at t h i s azimuth i s the Parkinson v e c t o r As  vector,  i n Appendix B i s r e l a t e d to  the e q u a t i o n :  normal s t a t i o n s , the p o i n t s  f u n c t i o n of  of n o r t h .  field  gives  of  magnitude.  o u t l i n e d i n s e c t i o n II-B, under the  assumption  v. of a 'two-dimensional' conductor, s i n u s o i d a l f u n c t i o n of o f l e a s t squares  <j> .  6  w i l l be  a fundamental  Consequently, u s i n g  the method  (Chauvenet, 1960), a s i n e f u n c t i o n o f  form A sin  ,  - <$> ) o  the  25  was f i t t e d  t o the Mercator  amplitude  A  of of  6  data p o i n t s .  The value o f the  i s e q u i v a l e n t t o the maximum a b s o l u t e value  , and the phase angle minus  TT/2 y i e l d s the azimuth  the minimum d i p , i . e . the Parkinson v e c t o r d i r e c t i o n .  mean-square e r r o r s a s s o c i a t e d w i t h each o f these parameters were a l s o computed  Root-  determined  (see Appendix C) i n order to  a s c e r t a i n q u a n t i t a t i v e l y the accuracy o f the s i n u s o i d - f i t t o the d a t a .  Both the Mercator  were computer generated  p l o t s and the f i t t e d  i n the same program used  s i n e curve f o r Parkinson  diagrams. (iv)  H o r i z o n t a l F i e l d Enhancement  Anomalous i n d u c t i o n e f f e c t s , which may or may n o t be apparent  i n the Parkinson p o l a r p l o t s , can be r e v e a l e d by  an azimuthal dependence o f enhancement i n the h o r i z o n t a l Defining a ratio  R  where at  B  Rg  =  (AB)  field.  as f o l l o w s :  ANOMALOUS  REFERENCE  *  s t  *  l e  c  ^  a n  1  8  fAB)  e  REFERENCE  ^  n t  ^  i e  horizontal  a normal s t a t i o n f r e e o f anomalous e f f e c t s , then  field Rg  will  ->-  be a simple f u n c t i o n o f  $  , the azimuth  of  AB  a t the  r e f e r e n c e s t a t i o n , i f a l i n e a r , induced c u r r e n t system i s p r e s e n t nearby.  (Note t h a t the assumption  ducing f i e l d i s made.)  o f a s p a t i a l l y uniform i n -  26  The expected form o f t h i 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<{> f u n c t i o n a l dependence s i n c e the enhancement i s p o s i t i v e f o r a p o s t i v e or n e g a t i v e inducing the  f i e l d normal to conductor s t r i k e ;  function  (R  was  least-squares  Q  + R /2) + R /2 sin(2<f> B  fitted  average l e v e l o f constant and  consequently,  B  to the data.  R  r e p r e s e n t s the  Q  relative horizontal f i e l d  strengths  r e f l e c t s d i f f e r e n c e s i n the magnitudes o f the h o r i z o n t a l  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 e f f e c t s , or i n s t r u m e n t a l  calibration error.  R  fi  attenuation g i v e s the  maximum magnitude o f the anomalous enhancement as a f r a c t i o n o f the i n d u c i n g f i e l d magnitude, and the value o f <J>  =  +  y i e l d s the d i r e c t i o n o f maximum enhancement.  I t should be noted t h a t the p l o t o f  R^  will  reveal actual  anomalous enhancement only i f no s i n g l e component a t t e n u a t i o n or source there  e f f e c t s are p r e s e n t .  I f , f o r instance,  i s an a p p r e c i a b l e l a t i t u d e a t t e n u a t i o n i n H  reference  s t a t i o n , then  magnetic n o r t h and south  Rg  will  latitude  at the  e x h i b i t peaks c o i n c i d i n g with  o f the t e s t e d  station.  27  IV.  EXPERIMENTAL RESULTS A.  East P r o f i l e (i)  Sample  Two  (Robb-Prince George) Records  storm p e r i o d s were a n a l y s e d f o r t h i s  profile:  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 but i t was  an extremely a c t i v e and extended  storm p e r i o d ,  r e c o r d e d w e l l at o n l y the f o u r primary  s t a t i o n s ; Event 2 was however, i t was  w e l l r e c o r d e d at a l l seven  a much l e s s d i s t u r b e d geomagnetic  (Askania) stations, period.  F i g s . I V - l a and IV-lb show sample r e c o r d s 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 r e p l o t t e d at equal s e n s i t i v i t y . The identical  c h a r a c t e r o f the h o r i z o n t a l components i s almost  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  field.  The s l i g h t l y reduced amplitudes i n the H component at  Quesnel  (geomagn. l a t . 58.7 N) and B a r k e r v i l l e  59.0°N) and the s l i g h t l y lat.  9  (geomagn. l a t .  i n c r e a s e d H amplitudes at Robb (geomagn.  60.2°N) a l l as compared to P r i n c e George (geomagn. l a t .  59.6°N) are most p r o b a b l y l a t i t u d e e f f e c t s .  However, the  s h a r p e r , i n c r e a s e d - a m p l i t u d e c h a r a c t e r o f H at McBride lat.  59.6°N) and Valemount  (geomagn.  (geomagn. l a t . 59.3°N) must be  buted to a genuine enhancement i n the n o r t h - s o u t h magnetic  attri-  P i g . I V - l a . S a m p l e o f m a g n e t o g r a m 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 1 6 , 2 2 : 4 3 U T t o J u n e 17, 03:23UT.(from Event 1 )  29  P i g . r v - l b . S a m p l e o f m a g n e t o g r a m 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. ( f r o m E v e n t 2)  30  fluctuations.  The c h a r a c t e r o f the Z component changes as  e x p e c t e d between P r i n c e George and Robb.  The normal  low-Z  o f t h e w e s t e r n C o r d i l l e r a i s apparent a t P r i n c e George, and B a r k e r v i l l e .  M c B r i d e and Valemount  c h a r a c t e r i n the Z-component, whereas  Quesnel,  exhibit a 'transitional'  J a s p e r and Robb show t h e  t y p i c a l high-Z a m p l i t u d e v a r i a t i o n s o f t h e ' e a s t e r n '  stations.  As i n p r e v i o u s GDS work i n s o u t h e r n B.C., t h e low I - h i g h I t r a n s i t i o n zone a g a i n o c c u r s i n t h e r e g i o n o f t h e Rocky M o u n t a i n Trench.  Only a t J a s p e r does t h e Z component show a v i s u a l l y -  a p p a r e n t c o r r e l a t i o n w i t h t h e H v a r i a t i o n s , marking J a s p e r as a clearly  'anomalous' (ii)  site.  Spectral Analysis Results  Event 1, a r e c o r d o f 34.9 h o u r s , had a t o t a l o f 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 o f 55.8 s e c . The maximum l a g used was 250 l a g - p o i n t s w h i c h g i v e s a n o r m a l i z e d s t a n d a r d e r r o r * o f 33% and a r e s o l u t i o n * o f .004 c y c l e s p e r m i n u t e . Event 2, o n l y 15 hours i n l e n g t h , had a t o t a l o f 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 o f 56.2 s e c .  A maximum  l a g o f 100 p o i n t s was used g i v i n g an e r r o r o f 32% and an e q u i v a l e n t r e s o l u t i o n bandwidth o f .01 c y c l e s p e r m i n u t e .  (Since  the power e s t i m a t e s are used i n a c o m p a r a t i v e sense o n l y , a s m a l l e r s t a n d a r d e r r o r was s a c r i f i c e d i n r e t u r n  for-better  resolution.)  * E x p r e s s i o n s f o r t h e s e q u a n t i t i e s assume a s t a t i o n a r y G a u s s i a n p r o c e s s , 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 q u e s t i o n a b l e .  31  The Fig.  p l o t s of the power s p e c t r a l d e n s i t i e s  IV-2a and  F i g . IV-3a express q u a n t i t a t i v e l y  shown i n  the  results  the  v i s u a l trace-comparison d e a l t w i t h i n the p r e v i o u s  The  increased  George i s q u i t e  obvious and  dependence of t h i s enhancement i s shown as w e l l . increase  i n the  of P r i n c e and  Z power as one  George and  s p a t i a l and  eastern stations  ratios  p  p  quantities scale  IV-3b.  ( x / x ' where  ( p r i m a r i l y H and  tions projected  onto the  r e p r e s e n t s D,  H,  of the  spectral  illustrated  component power  or Z and  George) are p l o t t e d on  the a  primed  logarithmic  graph d i s t a n c e s between  r e l a t i v e d i s t a n c e s between s t a -  59.6°N p a r a l l e l of geomagnetic l a t i t u d e .  Each o f these diagrams i n c l u d e s of the  of J a s p e r  George i s b e t t e r  s t a t i o n l o c a t i o n where the  i s representative  stations  Z) r e l a t i v e to  In these diagrams, the  r e f e r to P r i n c e  against  stations  X  gradual  frequency dependence of the  c o r r e s p o n d i n g components at P r i n c e IV-2b and  The  apparent.  power o f i n d i v i d u a l components  in Figs.  McBride  a frequency  moves from the western  Quesnel to the  Robb i s a l s o g r a p h i c a l l y This  the  section.  power of the H component at Valemount and  as compared to P r i n c e  of  a p l o t of the  geomagnetic l a t i t u d e  instrument s i t e s i n order to demonstrate p o s s i b l e  n e t i c l a t i t u d e e f f e c t s i n the  geomag-  r e l a t i v e s t r e n g t h s of f i e l d com-  ponent changes. The  D component power r a t i o s f o r both events  some l a t i t u d e e f f e c t s and enhancement at McBride. of the  reflect  a l s o shoiv a s l i g h t frequency dependent ( I n s u f f i c i e n t data prevented an  D component at Valemount.)  analysis  Averaged over a l l p l o t t e d  C-4  0.02  0.06  0.10  FREQUENCY,  CRM.  0.14  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 d e p e n d e n c e o f power r a t i o s i n e a c h component f o r E v e n t 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 d e p e n d e n c e o f p o w e r r a t i o s i n e a c h component f o r E v e n t 2.  : I  34  FIg.lV-4a.M-ratlos plotted f o r E v e n t 1.  against projected  station  location  35  Pig.IV-4b.M-ratios plotted f o r E v e n t 2.  against projected station  location  36  f r e q u e n c i e s , the power r a t i o s f o r the H component at Quesnel B a r k e r v i l l e i n d i c a t e an approximate 10% the H f l u c t u a t i o n s r e s p e c t i v e l y due magnitude and  the frequency  the H component at the n u m e r i c a l l y by the v a r i a t i o n s with  and  5% a t t e n u a t i o n i n  to l a t i t u d e e f f e c t s .  dependence o f the enhancement of  following.  For Event 2, at McBride, H  a p e r i o d of 47 min. and  32%  and  19 min.  show an  latitude attenuation i s  expected, the same p e r i o d v a r i a t i o n s show a magnitude 62%  respectively.  The  (Note:  the t r a n s i t i o n  zero power i n Z f o r the two the  Pz/ z' p  higher  ratios  tion  these  represents  Conse-  f o r the e a s t e r n s t a t i o n s  a r b i t r a r i l y f i x e d at 2.0 curves r e a s o n a b l y ' a 'lower l i m i t '  effectively  frequencies.  were taken r e l a t i v e to Valemount, with r a t i o being  of  illustrated.  For Event 2, the f o u r western s t a t i o n s have  quently,  increase  v e r t i c a l component power  r a t i o s show an even g r e a t e r v a r i a t i o n and low-Z to high-Z i s w e l l  ampli-  r e s p e c t i v e l y , r e l a t i v e to P r i n c e  George; at Valemount, where a s l i g h t  and  The  'transition' stations is i l l u s t r a t e d  tude enhancement o f 17%  o f 46%  and  the Valemount  i n order  on the graph.  to p o s i This  value  s i n c e the high frequency  Z  power l e v e l at Valemount i s d e f i n i t e l y g r e a t e r than t h a t at McBride  (see F i g . IV-3a),  transitional r a t i o s with  and  s i n c e Valemount i s  l i k e McBride where an i n c r e a s e i n Z power i n c r e a s i n g frequency  has  i n the a n a l y s i s of Event 1 (see F i g .  been e s t a b l i s h e d IV-2b)).  37  Fig. M ratios  IV-4a and F i g . IV-4b e x h i b i t  from P r i n c e George to Robb.  the v a r i a t i o n of the  The normal t r a n s i t i o n  low-I to h i g h - I s t a t i o n s i s shown between McBride/Valemount Jasper.  The  unusual  s t a t i o n s i s due north-south  d e p r e s s i o n of the M r a t i o at the  to the presence  from and  transition  o f anomalous enhancement of the  magnetic v a r i a t i o n s with a weaker accompanying ano-  malous Z i n d u c t i o n . (iii) a)  Induction E f f e c t s The  Fig.  Induction A n a l y s i s Results in  AZ  P a r k i n s o n p o l a r diagrams shown i n F i g . IV-5a  and  IV-5b i n d i c a t e t h a t McBride, J a s p e r , and Robb"are a l l ano-  malous to v a r y i n g degrees.  This same i n f o r m a t i o n i s more simply  illustrated  i n d u c t i o n p l o t s o f F i g . IV-6,  i n the Mercator  a l s o i n c l u d e 'best f i t '  simple  s i n e curves whose constant  which para-  meters y i e l d the Parkinson v e c t o r i n f o r m a t i o n summarized i n the following  table:  Station  F i t t e d Sine F u n c t i o n Phase Amplitude (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  ± 8.  -3. ±  17.  Pr. George 5. ± 31% TABLE IV-1.  Anomalous?  Parkinson Vector Magnitude D i r e c t i o n (degr.)  +60.  No  _ ^  Summary o f f i t t e d s i n e curve parameters and Parkinson v e c t o r s f o r e a s t e r n p r o f i l e .  * E r r o r s are root-mean-square e r r o r s computed i n the method o f l e a s t squares (see Appendix C ) . **Since anomalous h o r i z o n t a l f i e l d enhancement i s s i g n i f i c a n t at McBride, these n u m e r i c a l r e s u l t s were o b t a i n e d u s i n g AB from P r i n c e George.  _  co  Pig.IV-5a.Parkinson p o l a r diagrams f o r e a s t e r n p r o f i l e  stations.  Fig.IV-5b.Parkinson p o l a r diagrams f o r e a s t e r n p r o f i l e  stations.  JRSPER  •  AZIMUTH M DCa  fMf ASUttO K K i T t V I IAST Of NOCTH)  AZIMUTH M Ota  1M  I  (MEASURED POSITIVE IAST Of NOtTM)  4^  O PR. GEORGE  MCBRIDE  • •  AZIMUTH tN OCa.  ' M.I  m*  1*1  (MEASUREO POSITIVE EAST Of NOtTH)  AZIMUTH IN OCO. (MIASURCO POSITIVI IAST C r NOtTH)  Fig.IV-6.Mercator p l o t s of i n d u c t i o n e f f e c t s with f i t t e d . curves.(eastern profile)  sine  41  The fit  d i s p r o p o r t i o n a t e l y l a r g e e r r o r of the  function  at Pr. George i n d i c a t e s randomly d i s t r i b u t e d data p o i n t s ,  which j u s t i f i e s b)  sine  the  conclusion  that the s t a t i o n i s not  Second Order Anomalous E f f e c t s i n In order  AZ  to r e s o l v e more h i g h l y the  ence o f the d i p o f the  total  the h o r i z o n t a l i n d u c i n g  induced f i e l d  field,  the  anomalous.  6  f u n c t i o n a l depend-  on the  values  azimuth of  on the Mercator  p l o t s were averaged over 10 degree i n t e r v a l s every 5 degrees ( t h i s reduces o r d i n a t e s t a t i o n s , J a s p e r and IV-7) for  Robb.  The  quencies.  The  s i n e peaks has  stronger  anomalous  resultant induction plots (Fig.  o f the presence o f h i g h e r  slight  amplitude r e d u c t i o n  order at the  (again u s i n g  a d d i t i o n o f which to the  except  spatial  fre-  fundamental  the mathematical appearance of a phase  t h i r d harmonic, the  locked  fundamental s i n e  the method of l e a s t squares) r e s u l t s i n the  dashed l i n e o f F i g . IV-7.  I t i s obvious t h a t the magnitude of  t h i s p o s s i b l e e f f e c t i s at the and  two  r e v e a l almost i d e n t i c a l s i n e curves to F i g . IV-6  a suggestion  curve  s c a t t e r ) f o r the  n u m e r i c a l a n a l y s i s , and  e s t a b l i s h e d w i t h the  'noise  l e v e l ' of  therefore  cannot be  a v a i l a b l e data.  proves t h i s e f f e c t to be  observation unequivocably  If further investigation  r e a l , i t suggests an induced  current  system more complex than the two-dimensional model suggested by Caner (1970) f o r southwestern Canada.  Anisotropics  inhomogeneities c o u l d cause such c o m p l e x i t i e s , the  simplest  explanation  but  or  perhaps  i s the p o s s i b l e presence of two  separate  42  Fig.IV-7.Averaged Mercator p l o t s of 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 sine curve(dashed l i n e ) .  43  c o n d u c t i v e zones whose anomalous induced f i e l d s cause induced secondary  anomalous f i e l d s .  emphasized here because the primary two  separate conducting zones w i l l  result  'Secondary  mutually  anomalous' i s  anomalous induced f i e l d s add i n such a way  as to  i n o n l y a s i n g l e P a r k i n s o n v e c t o r , which i s the  o f the i n d i v i d u a l  inductance arrows o f each  the e x i s t e n c e o f two  zone.  All  resultant  (Note  that  zones c o u l d t h e r e f o r e be e r r o n e o u s l y i n -  t e r p r e t e d as a s i n g l e c o n d u c t i v e zone whose e f f e c t to the v e c t o r sum  of  e f f e c t o f the two  i s equivalent  zones.)  the p r e v i o u s l y mentioned i n d u c t i o n r e s u l t s f o r  anomalous s t a t i o n s have, i n e f f e c t , been i n t e g r a t e d over a l l geomagnetic v a r i a t i o n p e r i o d s r a n g i n g from 5 to 60  minutes,  thus a v e r a g i n g out the frequency dependence o f the  Parkinson  vector.  I f two  distinctive  zones e x i s t at s i g n i f i c a n t l y  dif-  f e r e n t depths, then the d i r e c t i o n and magnitude o f the induct i o n v e c t o r w i l l vary with frequency as w e l l as p o s i t i o n of the s t a t i o n w i t h r e s p e c t to the zones of c o n d u c t i v i t y . f o r t u n a t e l y , measuring  amplitudes  i n g i v e n frequency  Un-  ranges  by hand i s a t r y i n g and time-consuming t a s k ; consequently, u s i n g the n u m e r i c a l technique o u t l i n e d p u t e r program was'written  i n Appendix B, a com-  to e v a l u a t e the P a r k i n s o n v e c t o r  i n f o r m a t i o n from d i g i t i z e d d a t a .  Two  became immediately  Because of the  apparent:  1)  drawbacks of t h i s method  and u n d i s c r i m i n a t i n g nature of a simple numerical  inflexibility technique,  the s c a t t e r i n the i n d u c t i o n data i s g r e a t l y i n c r e a s e d over the hand measured data  ( i n t h i s case by a f a c t o r of 3)  and  44  2)  Because of d i g i t i z a t i o n n o i s e , meaningful  amplitudes  of  geomagnetic v a r i a t i o n s c o u l d not be computed f o r p e r i o d s than 15 minutes, mation and  resulting  i n a l a c k of h i g h frequency  a b i a s i n g towards low Only  at J a s p e r was  frequency  less  infor-  data.  the anomaly s t r o n g enough to  ensure  t h a t the s i z e of e r r o r s i n the s i n e f u n c t i o n f i t d i d not i n v a l i d a t e the e n t i r e f i t attempt. e r r o r s i n amplitude g r e a t e r than 15% mum  and  (At Robb and McBride,  and phase of the f i t t e d 10 degrees  the  f u n c t i o n were  r e s p e c t i v e l y , which were maxi-  a l l o w a b l e e r r o r s f o r a s t a t i o n to be c o n s i d e r e d anomalous  i n the v i s u a l l y determined  Parkinson v e c t o r s . )  As the f o l l o w -  ing t a b l e shows, even at J a s p e r the e r r o r s i n v o l v e d i n the P a r k i n s o n v e c t o r are too l a r g e to allow an i n d i s p u t a b l e conc l u s i o n o f frequency dependence.  However, a t r e n d i s apparent,  i n d i c a t i n g the p o s s i b l e e x i s t e n c e of two one  conducting  zones:  s h a l l o w , running NW-SE, drawing the Parkinson v e c t o r at  J a s p e r towards the west, and anomaly s t r i k i n g E-W south.  a second,  s t r o n g e r , very deep  and thus drawing the i n d u c t i o n v e c t o r  45  Mean P e r i o d Maximum Absolute Azimuth o f Parkinson Favored by A n a l y s i s * Dip o f T o t a l F i e l d V e c t o r (degr.) (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 o f the induced at J a s p e r .  field  *The n u m e r i c a l technique d e s c r i b e d 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 f r e q u e n c i e s o f v a r i a t i o n , i t simply ' f a v o u r s ' c e r t a i n frequency ranges. There i s s t i l l 'contamination' from other f r e q u e n c i e s i n each range and hence the t a b u l a t e d data s t i l l has an i n h e r e n t 'smearing t o g e t h e r ' e f f e c t ; i . e . i t c o u l d be s a i d to r e p r e s e n t a minimum d i f f e r e n c e between h i g h and low frequency r e s u l t s . The to due  the f i t t e d  reduced  d i p angles o f the t o t a l  amplitude  at J a s p e r i n Table  field  compared  IV-1 are p r o b a b l y  t o the i n c r e a s e d s c a t t e r o f p o i n t s , w h i l e the P a r k i n s o n  v e c t o r d i r e c t i o n at J a s p e r l i s t e d i n Table IV-1 has h i g h quency c o n t r i b u t i o n s l a c k i n g i n the computed P a r k i n s o n  fre-  direc-  t i o n s o f Table IV-2. (Note:  The apparent IV-5  l a c k o f data at c e r t a i n azimuths i n F i g s .  t o IV-7 i s due to an o b s e r v a t i o n a l b i a s , not a  p o l a r i z a t i o n o f the source f i e l d .  Since the i n d u c t i o n  p l o t s search f o r a v e r t i c a l component change,  amplitude  measurements were u s u a l l y made where some change i n Z occurred.  T h i s i m p l i e s 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 .  such p o i n t s , the t o t a l effectively  For  f i e l d d i p angle would be  zero and hence they would not v i o l a t e the  f i t t e d s i n e curves o f F i g . IV-6.) c)  Induction E f f e c t s  i n AB  F i g . IV-8 i l l u s t r a t e s ratio  Rg  the h o r i z o n t a l enhancement  as a f u n c t i o n o f azimuth.  The v a l u e s o f  Rg  have  been averaged over 10 degree  i n t e r v a l s every 5 degrees and  a s i n e curve was then f i t t e d  t o these averaged d a t a .  Although  s m a l l i n magnitude, the s i n u s o i d a l behaviour o f the enhancement at McBride  i s q u i t e d e f i n i t e when compared to the J a s p e r  p l o t , which i s p r a c t i c a l l y a s t r a i g h t maximum i n t e n s i f i c a t i o n o f George) i s 26%.  AB  line.  a t McBride  Rg  The magnitude o f (compared t o P r i n c e  T h i s v a l u e , r e p r e s e n t i n g an enhancement  averaged  over a l l observed f r e q u e n c i e s , i s i n good agreement w i t h the component power r a t i o estimates o f s e c t i o n I V - A ( i i ) , which i n d i c a t e d an average  25% enhancement o f the H component.  d i r e c t i o n o f maximum i n c r e a s e o f  AB  i s +55 degrees  The  (and -125  degrees) which p r a c t i c a l l y c o i n c i d e s w i t h the Parkinson v e c t o r azimuth. was  The e r r o r i n v o l v e d i n the s i n e f i t to  10% and 6 degrees  whereas an attempted 54%  f o r amplitude and phase s i n e f i t f o r Rg  Rg  a t McBride  respectively,  at J a s p e r r e s u l t e d i n a  amplitude e r r o r and a phase e r r o r o f 31 degrees.  47  RELATIVE ENHANCEMENT OF THE HORIZONTAL FIELD JRSPER  / PR. GEORGE  op  -iaO.0 I  -14).o i  AZIMUTH (MEASURED POSITIVE EAST OF NORTH) -ito.o -60.0 ZD.I) jo.o GO.D i i I i i  IOO.O 1  140.0  IBO.O  RELATIVE ENHANCEMENT OF THE HORIZONTAL FIELD MCBRIDE /  PR. GEORGE  cr  hp  im.D 1  -14).0 I  AZIMUTH (MEASURED POSITIVE EAST OF NORTH)  Pig.IV-8,Azimuthal  -100.11 I  -60.D I  .20.0 I  20.0  80.0 I  I  dependence o f R  (using data with f i t t e d  B  100.0 I  1 4).0 I  IBO.O I  (BB) S t a t i o n (5.B).  Pr.George averaged o v e r 10 degree i n t e r v a l s ) sine curve.  48  (iv)  Interpretation  It i s concluded t h a t the t y p i c a l low amplitude v a r i a t i o n s and western  Z-  l a c k of high frequency Z f l u c t u a t i o n s i n the  C o r d i l l e r a are caused by a h i g h l y c o n d u c t i v e l a y e r at  a depth o f 10 to 15 km. l i k e l y cause  as proposed  by Caner (1970).  of t h i s h i g h e r c o n d u c t i v i t y appears  The most  to be  hydra-  t i o n and p o s s i b l y p a r t i a l m e l t i n g (Hyndman and Hyndman, 1968). The  e a s t e r n 'high I' r e g i o n s l a c k t h i s r e l a t i v e l y s h a l l o w con-  d u c t i n g l a y e r and hence show s t r o n g Z a c t i v i t y . t i o n between these two  The  transi-  zones occurs at the western  f r o n t o f the  Rocky Mountains,  i n an area marked by the presence  o f anomalous  induced f i e l d s .  McBride  and J a s p e r s t r a d d l e a ' l i n e ' of ano-  malous c u r r e n t flow, g i v i n g r i s e to the observed r e v e r s a l the induced v e r t i c a l o f the  field.  'Trench' s t a t i o n s  Furthermore,  (McBride  the c l o s e p r o x i m i t y  and Valemount) to the anomalous  currents results  i n the marked h o r i z o n t a l f i e l d  these t r a n s i t i o n  stations.  Assuming a u n i f o r m h o r i z o n t a l d i c u l a r to a s i n g l e i n f i n i t e cal  induced to i n d u c i n g f i e l d  inducing f i e l d conductor) w i l l  ( H / H j , where x  of  enhancement at  inducing f i e l d  perpen-  conductor, the r a t i o s of the  verti-  (H^/Hj) and h o r i z o n t a l induced to X  i s the d i r e c t i o n normal to the  allow c e r t a i n q u a l i t a t i v e  i f not  quantitative  c o n c l u s i o n s to be drawn w i t h r e s p e c t to the models proposed R i k i t a k e and Whitham (1964).  (See S e c t i o n I l - b . )  Table  IV-3  shows the e s t i m a t e s f o r the magnitude o f i n d u c t i o n at each s t a t i o n ; these values are d e r i v e d from a s u b j e c t i v e  by  combina-  49  t i o n o f the  i n d u c t i o n analyses  and  the r e l a t i v e s p e c t r a l power  levels.  Station  V e r t i c a l Induction (H /H ) z  x  H o r i z o n t a l Induction (H /Hj) x  Robb  -0.38  0.98  Jasper  -0.63  0.95  Valemount  +  0.30  1.60  McBride  +  0.22  1.32  Pr. George  ^0.0  TABLE IV-3.  1.05  Summary of v e r t i c a l and h o r i z o n t a l f i e l d s f o r the e a s t e r n p r o f i l e .  induced  These r a t i o s p l o t t e d a g a i n s t r e l a t i v e s t a t i o n from a NW-SE l i n e p a s s i n g Fig. IV-9.  The  distance  through McBride y i e l d the curves  shapes of the two  enhancement curves  of  reveal that  the observed p r o f i l e does c r o s s a conductor s i m i l a r to the model cases  shown i n 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 s i d e r i n g t h a t the a c t u a l c o n d u c t i v i t y i s not  l a r g e , con-  infinity,  a m p l i f i c a t i o n through c o u p l i n g w i t h an u n d e r l y i n g  and  l a y e r or through  a c o n c e n t r a t i o n of c u r r e n t i n the upper corner of the step by dark shading  an  i n the area of c u r r e n t flow i n F i g . I V - 9 )  (shown is  50  5 0 KM. •  VH,  /  1  T  2.0  \  1.0 Hj  0.0 9\ INDUCING FIELD >  LU CD 0.  N  0Q_1  (/)  It,,, J  -M.O m  o  QC  4  sax  AREA OF INDUCED CURRENT FLOW  F i g . I V - 9 . O b s e r v e d 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 m o d e l o f t h e c o n d u c t i n g step.  51  r e q u i r e d to account f o r t h i s plausible. and  Coupling  the moderately conducting  sharpening  concentration  of c u r r e n t can be  l a y e r would slope  IV-9.  above i n t e r p r e t a t i o n i s c o n f i n e d to f i r s t  order  i s i n agreement w i t h Caner's proposed c o n d u c t i v i t y  i n t e r p r e t a t i o n of some f i n e r p o i n t s and suggest a model c o n s i s t i n g o f two  at  the  positively  to t h a t i n d i c a t e d i n F i g .  and p e t r o l o g i c a l model f o r southwestern Canada.  tinuities:  One  a s s o c i a t e d with  a depth o f 10 to 15 km.,  However, the  second order  lateral  effects  conducting  discon-  the edge of a hydrated  l o c a t e d at and  striking  layer  i n the same  d i r e c t i o n as the western f r o n t o f the Rocky Mountains; and second, much deeper d i s c o n t i n u i t y , running south  approximately  o f Kootenay Lake, perhaps a s s o c i a t e d with  f e a t u r e i n the upper mantle ( L a j o i e and model would e x p l a i n the l a r g e n e g a t i v e and  i t s s u s t a i n e d value  introduce  at  achieved  the step or by even r e v e r s i n g the slope of  from west to e a s t , o p p o s i t e  r e s u l t s , and  'step' c u r r e n t  l a y e r u n d e r l y i n g both r e g i o n s  s t e p , i . e . the edge of the hydrated  The  Both mechanisms are  c o u l d occur between the  a depth of about 35 km; by  increase.  at Robb ( F i g . IV-9)  H^/Hj  without  an improbable complex step geometry.  E-W  a strike-slip  Caner, 1970). peak i n  a  Such a at  Jasper  having  These  to  two  e a s t e r n s t a t i o n s are then a f f e c t e d by t h i s more remote, deeper d i s c o n t i n u i t y which causes a d d i t i o n a l enhancement of the field  (but i s too remote to a f f e c t the h o r i z o n t a l f i e l d ) ;  deeper c o n d u c t i v i t y s t r u c t u r e i s not  vertical this  apparent at the western  52  s t a t i o n s due  to a t t e n u a t i o n by the s h a l l o w e r conducting  layer.  It  i s i n t e r e s t i n g to note t h a t r e s o l v i n g the i n d u c t i o n v e c t o r s  at  J a s p e r and Robb along d i r e c t i o n s normal to the two  tivity and  s t r i k e s y i e l d s more reasonable  -0.21  for  H^/I-Ij  'model' values of  w i t h r e s p e c t to the shallow  Furthermore,  this  conduc-0.42  discontinuity.  ' d u a l - s t r u c t u r e ' model would e x p l a i n  the frequency dependence o f the Parkinson v e c t o r at J a s p e r the  ' f i n e - s t r u c t u r e ' azimuthal dependence of the d i p angle of  the induced  field  at J a s p e r and Robb.  change i n s t r i k e of the to  and  'hydrated  In a d d i t i o n , no  l a y e r edge' need be  local invoked  e x p l a i n the change i n Parkinson v e c t o r d i r e c t i o n at the  anomalous s t a t i o n s .  At McBride,  l y i n g to the west o f the  'shallow' anomaly, the i n d u c t i o n arrow p o i n t s 60° east o f n o r t h , 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 the l o c a l t e c t o n i c p a t t e r n , and shows l i t t l e anomaly due of  a f f e c t e d by the deep E-W south, and  e f f e c t s of the deep  to the u n d e r l y i n g a t t e n u a t i n g l a y e r .  maximum i n d u c t i o n at J a s p e r  of  The  direction  (33°W o f S) i s a l r e a d y n o t a b l y  s t r i k i n g anomaly l y i n g w e l l to the  i f the 27°W of S d i r e c t i o n at Robb i s c o n s i d e r e d 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 J a s p e r , i t can be e x p l a i n e d  by Robb's i n c r e a s e d d i s t a n c e , and thus a reduced the NW-SE s t r i k i n g shallow anomaly.  effect,  from  F i n a l l y , the l i n e of t r a n -  s i t i o n s t a t i o n s o f Golden, Valemount, and McBride i n d i c a t e a 'low  I - h i g h I' t r a n s i t i o n  line striking  40°W of N, but  the  i n d u c t i o n arrows at such w i d e l y s c a t t e r e d s t a t i o n s as J a s p e r , Field  (Caner et a l , 1971), and Sanca ( L a j o i e 1970)  indicate a  53  c o n d u c t i v i t y s t r u c t u r e running roughly conductor' model p r o v i d e s  a simple s o l u t i o n to t h i s  ment i n d i r e c t i o n s s i n c e i t allows vectors  to be v e c t o r  discontinuity  60°W o f N.  The  'two-  disagree-  the observed P a r k i n s o n  sums o f the i n d u c t i o n arrows due to each  (see F i g . IV-10).  ( I t must be noted t h a t  this  more complex model i s a h y p o t h e t i c a l model suggested to e x p l a i n secondary e f f e c t s and i s not c o n s i d e r e d  'proven' i n t h i s  thesis.)  P i g . I V - 1 0 . 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 p r o p o s e d zones.  conducting  55  IV.  EXPERIMENTAL RESULTS B.  West P r o f i l e (i)  Aug.  4,  period  storm p e r i o d analysed  c a l l e d Event 3, occurred 16:00  UT.  from Aug.  3, 16:00  (ii)  P r i n c e Rupert  little  amplitude f l u c t u a t i o n s i n 'low  H  AZ and  activity D  in s p i t e of large  , confirming  sec.  gives  e r r o r of 32%  a standard .007  Maximum l a g used was and  150  an e q u i v a l e n t  c y c l e s per minute.  feature  i s the  .04  for a l l stations.  lengths,  had  p o i n t s which resolution  F i g . IV-12a shows the striking  abrupt Z-power c u t - o f f at a frequency of about  c o i n c i d e , and  is noticeable.  they  Results  power s p e c t r a l d e n s i t i e s f o r t h i s event; the most  practically  that  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 o f 56.1  cpm  Terrace  (geomagn. l a t . 58.2°).  Event 3, c o n s i s t i n g of 24 hour r e c o r d  bandwidth o f  gradual  I' zone.  Spectral Analysis  a t o t a l of 1540  to  i n a l l components, most obvious at  s t a t i o n s show very  l i e i n the  UT  f o r a 6 hour  from Event 3, shown i n F i g . IV-11, r e v e a l a  (geomagn. l a t . 58.8°) and  all  f o r the western C o r d i l l e r a  Samples of d i g i t i z e d records  l a t i t u d e attenuation  All  Rupert)  Sample Records  The profile,  ( P r i n c e George - P r i n c e  The  The  power l e v e l s f o r the D component  a small  l a t i t u d e attenuation  effect  H power l e v e l s f o r the d i f f e r e n t s i t e s  t r a c k extremely w e l l but  are separated  due  to geomagnetic  H  S C A L E  2  HOURS  P i g . I V - 1 1 . S a m p l e o f m a g n e t o g r a m 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. ( f r o m E v e n t 3)  b.  a. 100 km.  0.02  0.06 0.10 FREQUENCY, CRM.  0.14  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 Pr.Rupert. 1 2 b . S p a t i a l and f r e q u e n c y d e p e n d e n c e o f p o w e r r a t i o s i n e a c h component f o r E v e n t 3.  58  latitude effects.  A slightly  i n c r e a s e d Z power l e v e l i s  apparent at Smithers f o r f r e q u e n c i e s between The h o r i z o n t a l component IV-12b have the g e n e r a l  .02 and .04  cpm.  power r a t i o p l o t s o f F i g .  trend o f the geomagnetic l a t i t u d e  and hence i l l u s t r a t e mainly the l a t i t u d e a t t e n u a t i o n e s p e c i a l l y i n the h i g h e r  frequencies.  plot,  effect,  For example, f o r t h i s  storm event, the amplitudes o f the II and D v a r i a t i o n s , averaged over a l l observed p e r i o d s , are roughly  55% and 20% ( r e s p e c t i v e l y )  g r e a t e r at P r i n c e George (geomagn. l a t . 59.6°N) than at P r i n c e Rupert  (geomagn.  l a t . 58.2°N).  However,  min. p e r i o d v a r i a t i o n s o f the Z component show an amplitude i n c r e a s e i n  AZ  the 47 min. and 35 power r a t i o s at Smithers  w i t h r e s p e c t to P r i n c e George  o f 53% and 10% r e s p e c t i v e l y , i n d i c a t i n g e i t h e r a source  effect  or p o s s i b l e anomalous i n d u c t i o n .  attenua-  tion,  M  The p l o t o f the power  , i s shown i n F i g . IV-13 and i t e x h i b i t s the same  s p e c t r a l power  i n c r e a s e at Smithers as shown by the component  power r a t i o s .  Because of the severe  all  these western-type  t r a t e d frequency  AZ  'low I' s t a t i o n s , only the three  at illus-  bands had s i g n i f i c a n t power l e v e l s , which  leaves the frequency (Note:  attenuation of  dependence of  M  unresolved.  In F i g s . IV-12b and IV-13, the graph d i s t a n c e s s t a t i o n s i s r e p r e s e n t a t i v e of the r e l a t i v e  between  distance  between s t a t i o n s p r o j e c t e d onto the 59.0°N p a r a l l e l of geomagnetic l a t i t u d e . )  M  =  ( P Z / P H ) STATION /  oq  p In 1  i M  UO  1  _ b 1  I ' l l  ( P / P H ) PRINCE  GEORGE  Z  T  r  U\ o  -I—I—I  o  I  I  o  I  PRP  O I >-s ^ 05  H c+ < HCD O 2 CO ci-  ts'  (jO H • O ctrlCD 1  TER  Cb  05  SMI Cn VO  05 H* CO ct  O  BRN  C_j.  CD O ct CD Cb to c!" 05 ctt_J.  VAN  b  o o  H  O O 05  ct  HO  3  PGE  60  (iii) a)  Induction A n a l y s i s Results  Induction E f f e c t s 160  i n AZ  p o i n t s from hand measured amplitude  values were  used t o o b t a i n the Parkinson p o l a r diagrams f o r P r . George, Smithers,  T e r r a c e , and P r . Rupert  weak anomaly i s c l e a r l y observable T e r r a c e and Smithers  (see F i g . IV-14a, 14b). A at P r . Rupert, w h i l e at  there are merely  'anomalous  indications'  not p r e s e n t at the r e f e r e n c e s t a t i o n , P r i n c e George. the Mercator s i n e curves  i n d u c t i o n p l o t s o f F i g . IV-15 w i t h  Again,  'best-fit'  i l l u s t r a t e very simply the Parkinson v e c t o r  infor-  mation summarized i n the f o l l o w i n g t a b l e .  Station  Pr. George Smithers Terrace Pr. Rupert  F i t t e d Sine F u n c t i o n Amplitude Phase (degr.) (degr.) 4. ± 32% 10. ±"14% 8. ± 15% 12.  TABLE IV-4.  ±  9%  Anomalous?  -3. ± 15.  No  30.  Parkinson V e c t o r Magnitude Direction (degr.)  ±  7.  ?  (.17 ± .03) (-60.  ± 7.)  -3. ±  7.  ?  (.14 ± .02) (-93.  ± 7.)  -4. ±  4. Yes  (weak)  .21  ± .02  -94  Summary o f f i t t e d s i n e - c u r v e parameters and Parkinson v e c t o r s f o r western p r o f i l e .  Since the t a b u l a t e d r e s u l t s f o r P r i n c e George i n Table  IV-4 are almost  i d e n t i c a l to those o f Table  same ' r e j e c t i o n - o f - a n o m a l y ' c r i t e r i a was f e l t  IV-1, the  to apply to the  ± 4.  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 western p r o f i l e  stations.  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 western p r o f i l e  stations.  PR. GEORGE  5MITHERS  ?-  5AZIKUTH IN DEO. ( u t A S U Z O FOSIT1VI L U T Of NOITM)  AZIMUTH IN D M  (MEASURED FOSITIVF. I A S ? OF NORTH)  ON  TERRRCE  PR. RUPERT  If-  ?• ?• fAZIMUTH IM O t a  ( K I A S U M O FOSITIVF, (AST OF NOUTX)  AZIMUTH  I N OEO. (MEASUSEO POSITIVE IAST OF NOJTX)  Pig.IV-15.Mercator plots of induction e f f e c t s with f i t t e d curves.(western p r o f i l e )  sine  I  64  west p r o f i l e g r e a t e r and  s t a t i o n s - i . e . , i f an amplitude e r r o r of 15%  or  a phase e r r o r o f 10 degrees or g r e a t e r accompany  the attempted s i n u s o i d a l f i t , the s t a t i o n i s c o n s i d e r e d anomalous.  Smithers and  'borderline' cases,  and  Ter r a c e  are t h e r e f o r e  non-  considered  at the most, are extremely weakly  anomalous s t a t i o n s . ' b)  Induction E f f e c t s i n  AB  The western s t a t i o n s were t e s t e d f o r p o s s i b l e anomalous enhancement i n the h o r i z o n t a l f i e l d by e v a l u a t i n g at  T e r r a c e , Smithers,  reference s t a t i o n . were found, and source  field  and  No  Pr. George, u s i n g Pr. Rupert as a  appreciable  at P r i n c e George caused i t s p l o t o f  Rg  to d e v i a t e  line.  conductive  p a r t I V - A ( i v ) , i s concluded p r o f i l e s t a t i o n s , causing  to be present  the  A p o s s i b l e source  l a y e r , as o u t l i n e d i n  'low  under a l l western  I* response at each of  e f f e c t c o u l d cause the  in  the Z-power l e v e l at Smithers.(One way  be  to examine other storm p e r i o d s . )  The  to r e s o l v e t h i s would ' c o a s t - e f f e c t ' (Parkinson,  i s the source  being  r e l a t i v e l y weak s i n c e the c o n t i n e n t a l slope i s s t i l l  source  km.  these  increase  1962)  than 200  the  Interpretation  An u n d e r l y i n g  stations.  anomalous i n d u c t i o n e f f e c t s  only the expected l a t i t u d e enhancement of  s i g n i f i c a n t l y from a s t r a i g h t (iv)  Rg  of the anomalous Z i n d u c t i o n at Pr. Rupert,  to the west; t h i s e f f e c t  of the anomalous i n d i c a t i o n s at  i s a l s o the most Terrace.  more  likely  65  I f 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 t h a t , (from the r a t e of a t t e n u a t i o n  o f the c o a s t a l e f f e c t between  Pr. Rupert and T e r r a c e ) that about Smithers i s s t i l l  assuming  50% o f the 'anomaly' at  c o a s t a l , then another, f a i r l y deep  t i v e zone to the northwest o f Smithers and s t r i k i n g  conducabout  50°  east o f n o r t h would account f o r the d i r e c t i o n and s l i g h t magnitude  increase  perpendicular Mountains,  of t h i s  'anomaly'.  Such a zone would be r o u g h l y  t o the t e c t o n i c p a t t e r n  o f the Skeena and Omineca  and be deep enough to cause the observed anomalous  s p e c t r a l po\^er i n c r e a s e  i n the 50 min. p e r i o d  Z v a r i a t i o n s , and  c o n s e q u e n t l y , c o u l d p o s s i b l y be a s s o c i a t e d w i t h a c o n d u c t i v i t y feature  i n the upper mantle.  vectors  and proposed c o n d u c t i v i t y s t r u c t u r e s f o r western pro-  file  stations.)  (See F i g . IV-10  f o r Parkinson  66  V.  SUGGESTIONS FOR FURTHER STUDY 1)  Continued  mapping o f the low I - h i g h I d i s c o n -  t i n u i t y north of l a t i t u d e  54°N i s d e s i r a b l e , but may prove  i m p r a c t i c a l , s i n c e at these h i g h l a t i t u d e s source e f f e c t s may easily field  invalidate  the assumption o f u n i f o r m i t y o f the i n d u c i n g  and furthermore, n o i s e l e v e l s  increase.  t i o n p l u s the problem o f a completely p r e s e n t l y prevent of  The same objec-  inaccessible  a GDS i n v e s t i g a t i o n o f the area  area would northwest  Smithers. 2)  A continued  anomaly i s warranted.  i n v e s t i g a t i o n o f the Kootenay Lake  F u r t h e r GDS work c o u l d be c a r r i e d out  i n the a r e a t o the south and to the east o f t h i s E-W  striking  anomaly, i n o r d e r t o a c c u r a t e l y map the low I - h i g h I d i s c o n t i n u i t y and a l l o w a c o n c r e t e t y i n g t o g e t h e r o f the GDS r e s u l t s o f western Canada and the western U.S.A. 3) (10"  A c l o s e l y spaced, broad-band frequency  t o 10"" cps) GDS p r o f i l e  1  Trench  should be c a r r i e d out at the  low Z - h i g h Z d i s c o n t i n u i t y , e i t h e r a t McBride o r at  Golden. numerical  Such an i n t e n s e , d e t a i l e d coverage  coupled w i t h the  s o l u t i o n o f the s t e p - c o n d u c t i v i t y problem i n t h r e e  dimensions would r e v e a l more p r e c i s e l y the nature d u c t i v i t y step and allow depth tive  coverage  zones.  o f the con-  r e s o l u t i o n o f m u l t i p l e conduc-  67  VI.  CONCLUSIONS From t h i s r e s e a r c h i t i s concluded that the conduc-  tivity  and p e t r o l o g i c a l model suggested by Caner  southwestern Canada i s a l s o v a l i d The c o a s t - e f f e c t at T o f i n o at P r i n c e  (1970) f o r  f o r c e n t r a l western Canada.  (Lambert and Caner, 1965) i s p r e s e n t  Rupert, and the i n l a n d  'step-conductivity'  anomaly  (Hyndman, 1963) i s again l o c a t e d near the Rocky Mountain Trench. Observed second o r d e r e f f e c t s prompt the h y p o t h e s i s o f two anomalous c o n d u c t i v e zones:  one s h a l l o w , at Caner's suggested depth o f  10 to 15 km., s t r i k i n g r o u g h l y NW-SE, and a s s o c i a t e d w i t h the fedge' of a h y d r a t e d 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; and a second, much deeper zone running a p p r o x i mately E-W south o f Kootenay Lake, perhaps a s s o c i a t e d w i t h a strike-slip  feature  i n the upper mantle  ( L a j o i e and Caner,  1970).  These suggested s e p a r a t e l a t e r a l 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 have p r e v i o u s l y been i n t e r p r e t e d as o f f s e t s e c t i o n s o f the same structure.  A s i m i l a r deep c o n d u c t i v i t y s t r u c t u r e  NE may e x i s t t o the northwest o f Smithers.  striking  68  APPENDIX A O u t l i n e o f Power S p e c t r a l  Calculations  ( a f t e r Bendat and P i e r s o l )  Assuming a sampling values,  ^  x n  ^  interval  > from a f i n i t e ,  h  , then f o r N  stationary record  data  x ( t ) with  a mean o f z e r o , an a u t o c o r r e l a t i o n f u n c t i o n estimate at the displacement  rh  i s g i v e n by: N-r  R  where  r  x  (  r  h  )  =  I n n r n=l  FFF  x  r=0,1,2 ,... .m  x  +  i s the l a g number, and  m  i s the maximum l a g number.  An estimate o f the exact power s p e c t r a l d e n s i t y f u n c t i o n , d e f i n e d f o r a frequency range  0 - v - v  , i s then  c  c a l c u l a t e d by: m-1 G (v) = 2h x ** v  where  v  c  R  o  +2  L  Y  r=l  R cos rrrv r  irmv  + R cos m  = ^h, the c u t - o f f frequency and  R  Q  i s the auto-  c o r r e l a t i o n estimate at zero l a g . To a v o i d ' s i d e l o b e s ' contaminating a d j o i n i n g the f i n i t e viewed, a Hanning  frequency bands  s p e c t r a l window through which the data i s  ' l a g window' w e i g h t i n g f u n c t i o n ,  used t o y i e l d a 'smooth' s p e c t r a l d e n s i t y e s t i m a t e :  D  ,is  69  D  r  (1 + cos H.) m  (rh)  r=0 ,1,2 ,. . .m  J  = 0  r > m  Hence, the equation  used f o r a smooth estimate o f  the power s p e c t r a l d e n s i t y i s  fkv m  1  c  m-1 =  2h  R  Q  +  I  2  D  r=l  R  R  R  cos  firrkl t m J  where s p e c t r a l estimates  are c a l c u l a t e d a t only the m+1 special kv d i s c r e t e frequencies v = , yielding m/2 independent m s p e c t r a l e s t i m a t e s , s i n c e s p e c t r a l estimates at p o i n t s l e s s than c m  2 v  a p a r t w i l l be c o r r e l a t e d . As can be seen i n the  and  3a, the Hanning window s t i l l  Prewhitening  power s p e c t r a of F i g s . IV-2a  introduces  sidelobe  effects.  can e l i m i n a t e these minor e f f e c t s , but was not  c o n s i d e r e d necessary  s i n c e only q u a l i t a t i v e c o n c l u s i o n s were  drawn from r e l a t i v e power l e v e l s . a negative  Z  (Where s i d e l o b i n g i n t r o d u c e d  power, the a c t u a l s p e c t r a l power was assumed t o be  negligible.)  70  APPENDIX B Parameters of Induction A n a l y s i s  1.  P a r k i n s o n P o l a r D i a g r a m s and P a r k i n s o n Let  component  AD  ,  AH  , and  AZ  Vectors  be t h e g e o m a g n e t i c  changes i n the u n i t v e c t o r d i r e c t i o n s ( m a g n e t i c n o r t h ) , and  Z  (magnetic  east),  H  ward) .  Then t h e h o r i z o n t a l v e c t o r c h a n g e i s g i v e n b y :  <j)  the d i r e c t i o n of  , measured p o s i t i v e  AB  i s d e f i n e d by t h e a z i m u t h  eastward from  i  .  - 1  <f> = t a n  The t o t a l  v e c t o r change,  AT  angle between Fig.  s p e c i f i e d by AT  and  Z  H  angle,  and n e g a t i v e w e s t w a r d :  rADn  [^j]  + (AZ) ]'"  2  2  §  2  ( a s a b o v e ) and by  , t h e downward v e r t i c a l :  B l a.)  6 =  down-  , has a magnitude:  AT = [ ( A B )  and a d i r e c t i o n  positive  + (AH) 2 ]  AB = [(AD)  where  (vertical  D  field  tan" ^]' 1  6  , the (See  N  a. Fig.Bl:  b.  c.  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 d i r e c t i o n of the geomagnetic f i e l d changes.  and  b. E x p l a n a t i o n o f p o l a r d i a g r a m s . P r e p r e s e n t s a d i r e c t i o n i n t h e 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 t h e 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 t h e i n t e r s e c t i o n o f a ' p r e f e r r e d p l a n e ' w i t h t h e 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 o f P a r k i n s o n V e c t o r . POQ i s t h e 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 w e s t . ON i s t h e downward u n i t n o r m a l 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 ^ is t h e P a r k i n s o n V e c t o r . ( i n t h e 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 h a s a m a g n i t u d e o f since.)  72  The  angles  <j)  and  6  are then p l o t t e d as p o i n t s  on the u n i t sphere whose n o r t h e r n and southern hemisphere surfaces are r e p r e s e n t e d by the  'Schmidt equal area' p r o j e c t e d  p o l a r c i r c l e s , the upper c i r c l e being used responding  to p l o t p o i n t s cor-  to a change w i t h an upward (negative) v e r t i c a l  ponent and the lower c i r c l e tive) vertical  component  f o r a change w i t h a downward  (as shown i n F i g . BI b.)  The  (posi-  azimuthal  d i r e c t i o n i s c o r r e c t e d f o r present magnetic d e c l i n a t i o n , hence  N  i n the diagram r e p r e s e n t s geographic n o r t h .  d i s t a n c e s o f the data p o i n t s are d i r e c t l y i n the  'down' c i r c l e  and to  TT-6  i n the  com-  and  The  p r o p o r t i o n a l to 'up'  circle  radial 8  (Parkinson,  1959). I t i s g e n e r a l l y found at anomalous l o c a t i o n s , i . e . sites tion  where l a t e r a l effect  vectors  AT  i n the v e r t i c a l  along two  field,  cause an a p p r e c i a b l e induct h a t f o r many events  mapped on a u n i t sphere  'preferred plane'. great c i r c l e  inhomogeneities  Such a plane  and hence m a n i f e s t s  tend to be c o n f i n e d to a  i n t e r s e c t s the sphere itself  in a  as data p o i n t s f a l l i n g  s i m i l a r arcs i n the p o l a r c i r c l e s .  the p r e f e r r e d plane i s r e p r e s e n t e d by the ( P a r k i n s o n , 1962).  the  The  d i r e c t i o n of  'Parkinson V e c t o r '  I t s d i r e c t i o n i n the h o r i z o n t a l plane i n -  d i c a t e s the azimuth where maximum upward t i l t ,  a  , occurs  w i t h i n the p l a n e , and i t s magnitude i s p r o p o r t i o n a l to the s i n e of the angle o f maximum a b s o l u t e t i l t . a = TT/2 - 6  M i n i m u m  •)  Consequently  (Note t h a t  a steeply t i l t i n g  pre-  f e r r e d plane w i l l have a long Parkinson v e c t o r , whereas a very  73  short Parkinson vector w i l l plane 2.  correspond  to an almost  horizontal  (see F i g . B l c ) .  Numerical  Technique o f G e t t i n g A m p l i t u d e s  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 w i l l be t h r e e s i m u l t a n e o u s  series  where  i s the t o t a l number o f  k=l  to  N  and  N  >  p o i n t s , r e p r e s e n t i n g the c o n t i n u o u s gonal f i e l d at each  i  t f l  components.  ^k^  data, there '  a n <  *  ^ k^ H  '  digitized  t r a c e s o f the t h r e e o r t h o -  A t o t a l f i e l d v a l u e can be  calculated  point, i.e.:  T. = {D. X  + Z.  2  X  X  and hence a s e r i e s  +  2  U. }  2 h  X  r e p r e s e n t i n g the c o n t i n u o u s  f i e l d v a l u e can be computed.  total  Changes i n the v a l u e s o f  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 c o n s e c u t i v e points of a s e r i e s  w h i c h i s a sub-sequence o f  c r e a t e d i n the f o l l o w i n g  way.  Xi  i s set equal to  p o i n t s o f the s e r i e s  Ti  and then f o r the n e x t  > where  r  range o f number o f p o i n t s , the v a l u e ( i = 2 t o 2+r). Then f o r these w i l l be a p o i n t  j  , where  r  {T^}  i s an a r b i t r a r y |Xi  - T^|  r specified  i s calculated  absolute d i f f e r e n c e s , there  2 - j - 2 + r  , such t h a t  74  |Xi  — Xj|  to  Tj  where set  i s a maximum.  The value o f  ; then, f o r the next i = j + 1  to  equal to that  j  T^  r  2  i s then s e t equal  number o f p o i n t s  |X  r , i s again e v a l u a t e d and  +  2  - T^|  ,  X3 i s  which g i v e s the maximum a b s o l u t e d i f f e r e n c e  with  X  ; and so on.  {T^}  are chosen, forming the s e r i e s  2  X  In t h i s way,  n  p o i n t s o f the s e r i e s  {X^.} , and c o r r e s p o n d i n g  p o i n t s i n the component s e r i e s are a l s o s e l e c t e d forming the subsequences  {D^'}  ,  f^'}  , and  {H^')  .  Simultaneous  component changes are then c a l c u l a t e d from these by the f o l l o w i n g  relations:  AD. = D* 1 l+l A  i  Z  AH.  =  Z  i 1 " +  - H!  D!  1  z!  where  1  be s t a t i s t i c a l l y  i = l , n-1 '  1  + 1  - H. 1  These simultaneous  variations  subsequences  changes are then c o n s i d e r e d t o  r e p r e s e n t a t i v e o f amplitudes o f geomagnetic  f o r p e r i o d s favoured by the value o f  r  be seen q u a l i t a t i v e l y t h a t a s m a l l v a l u e o f  r  s h o r t p e r i o d f l u c t u a t i o n s , but s i n c e i t w i l l  also  I t can  will  favour  include  s h o r t - s p a c e d sampling o f long p e r i o d t e n d e n c i e s , the r e s u l t s will  i n c l u d e low frequency i n f o r m a t i o n .  value o f  r  will  clearly  favour long p e r i o d response, but  ' l a r g e - r ' sampling can e a s i l y thus contaminate  S i m i l a r l y , a large  i n c l u d e h i g h frequency peaks and  the low frequency r e s u l t s .  I t i s obvious  75  that t h i s i s neither a refined nor an optimum technique of getting combined amplitude-frequency  information from d i g i t i z e d  data; however, the application of more sophisticated was  techniques  f e l t to be not j u s t i f i e d due to the lack of r e l i a b l e high  frequency data, and the limited use made of the outlined numerical technique.  76  APPENDIX C Determination  of E r r o r s i n  Linear Function  'Least-Squares' Fitting  In the standard method o f ' l e a s t - s q u a r e s (see Chauvenet, 1960)  the q u a n t i t y  number o f o b s e r v a t i o n s i**  observed  1  minimized.  and  and  the i * " *  1  6^  £ 6^ i  n  'fitted'  dependent v a r i a b l e , i s  I t s s m a l l e s t v a l u e , which y i e l d s the most  final  sum  i s the  i s the d i f f e r e n c e between the  v a l u e s o f the parameters o f the f i t t e d sents the  , where  fitting'  probable  f u n c t i o n , also repre-  of squares of the o b s e r v a t i o n a l e r r o r s .  Consequently, a root-mean-square e r r o r i s given n  by  W. e =  where  m  function.  I  n-m  n > m  l  i s the number o f independent parameters i n the This  ' o b s e r v a t i o n a l e r r o r ' can be c o n s i d e r e d  measure o f the mean d i s p e r s i o n o f the observed to  (1)  fitted as a  data w i t h  respect  the f i t t e d f u n c t i o n . The  (x^)  individual errors  are dependent on the t o t a l  r e l a t i v e weight of each parameter  (e  Y  )  i n the determined  observed (p  )  x  error  (c)  and  the  i n the f u n c t i o n a l  k  e x p r e s s i o n o f the observed  para-  quantity:  k=l,...m  (2)  77  I f the  m  determined parameters  f ( x i , Xz ,  b i n e d i n some f u n c t i o n a l e x p r e s s i o n e.P i  , the combined e r r o r i n  x^  , can be expressed by  4= 1  For  f  f3f  m  i  3 k=l x  are consequently com. . .x^)  due to s m a l l e r r o r s  , then ex  in  (3)  ex,  k  k  k  example, i n t h i s t h e s i s the f u n c t i o n  v = x s i n 0 + y cos 6  was f i t t e d  to the Mercator p l o t  i n d u c t i o n d a t a , and by the  method o f l e a s t squares the most probable v a l u e s o f  x  y  determined^  The  and t h e i r a s s o c i a t e d e r r o r s , fitted  e x  and  e y  , were  and  c u r v e , however, was expressed a n a l y t i c a l l y as a  s i n g l e s i n e f u n c t i o n o f the form  v  where  A = (x  =  + y )'  2  2  A  (cj>  sin  -  <j> )  (amplitude)  5  <j> = t a n ( - y / x )  (phase)  _ 1  o  Consequently, u s i n g r e l a t i o n  (4)  o  ( 3 ) , the e r r o r s  i n amplitude and  phase a r e : £  e  A  e  =  =  o  {  C  { (  x  e  x  y x £  )  2  ) 2  +  +  (y  e  ) 2 } l 2 / A y  (5)  ( X O ^ / A y  2  78  REFERENCES Bendat, J . S. and P i e r s o l , A. G., 1958. Analysis  o f Random Data.  Measurement and  John Wiley and Sons,  New York. Caner, B. , Cannon, W. H., and L i v i n g s t o n e , Geomagnetic ture  depth sounding and upper mantle s t r u c -  i n the C o r d i l l e r a r e g i o n  America. Caner, B., 1969.  C. E., 1967.  J . Geophys. Electrical  o f western North  Res., 72, 6335-6351.  c o n d u c t i v i t y s t r u c t u r e o f the  lower c r u s t and upper mantle i n western  Canada.  Unpublished t h e s i s , U n i v e r s i t y o f B r i t i s h  Columbia,  Vancouver. Caner, B., 1970.  E l e c t r i c a l conductivity structure  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 .  i n western J . Geomag.  and G e o e l e c , V. 22, 113-129. Caner, B., A u l d , D. R., D r a g e r t , H. , C a m f i e l d , P. A., 1971. Geomagnetic  depth sounding i n western Canada.  preparation; Cannon, W. H., 1967.  In  to be submitted t o J . Geophys. Res. 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