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Anomaly in geomagnetic variations on the west coast of British Columbia Lambert, Anthony 1965

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AN ANOMALY IN GEOMAGNETIC VARIATIONS ON THE WEST COAST OP BRITISH COLUMBIA  by ANTHONY LAMBERT B.Sc,  U n i v e r s i t y of B r i t i s h Columbia, 1963  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE  REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of GEOPHYSICS  We accept t h i s t h e s i s as conforming r e q u i r e d standard  THE  t o the  UNIVERSITY OF BRITISH COLUMBIA April,  1965  In presenting this thesis i n p a r t i a l fulfilment of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library shall make i t available for reference and study*  freely  I further agree that per-  mission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives.  It i s understood that copying or publi-  cation of this thesis for financial gain shall not be allowed without my written permission*  Department of  GEOPHYSICS  The University of B r i t i s h Columbia, Vancouver 8, Canada Date  flPZlL  °l?  /^g  i ABSTRACT Pour p o r t a b l e magnetometer s t a t i o n s were s e t up a t i n t e r v a l s of 80 - 100 k i l o m e t e r s a l o n g an east-west  profile  running from T o f i n o on the west coast of Vancouver I s l a n d to Abbotsford on the mainland i n order t o study the s p a t i a l dependence of the c o a s t a l anomaly,,  These were supplemented  by r e c o r d s from the permanent V i c t o r i a Magnetic  Observatory,  The T o f i n o - A b b o t s f o r d c h a i n extends and p a r t l y o v e r l a p s an e a r l i e r c h a i n o f s t a t i o n s s e t up t o search f o r geomagnetic anomalies, a l o n g an east-west  p r o f i l e from L e t h b r i d g e , A l b e r t a  to Vancouver, B r i t i s h Columbia, at T o f i n o I s observed  The c o a s t a l anomaly recorded  e x c l u s i v e l y i n the v e r t i c a l component,  d i m i n i s h i n g r a p i d l y i n l a n d and r e a c h i n g i t s maximum value when the i n d u c i n g f i e l d changes i n approximately  an east-west  d i r e c t i o n w i t h a frequency between one and two c y c l e s per hour. The h o r i z o n t a l and v e r t i c a l v a r i a t i o n s are i n a r a t i o of two t o one  a t the coast which I s i n agreement with i n d u c t i o n r a t i o s  c a l c u l a t e d a t c o a s t l i n e s I n A u s t r a l i a and C a l i f o r n i a ,  The  d i r e c t i o n a l dependence and l i m i t e d s p a t i a l extent of the anomaly i n d i c a t e a r a t h e r shallow c o n d u c t i v i t y d i s c o n t i n u i t y , at most 100 k i l o m e t e r s deep, running approximately the c o n t i n e n t a l s h e l f l i n e . frequency  Since at the maximum  p a r a l l e l to response  the upper mantle beneath the o c e a n . i s l a r g e l y s h i e l d e d  by the o v e r l y i n g wedge of sea water, the anomaly i s thought t o be mostly due to the c o n d u c t i v i t y c o n t r a s t between the deep ocean and the c o n t i n e n t .  The d i u r n a l geomagnetic  variations  Ii which pass through the  s u r f a c e l a y e r s v i r t u a l l y unattenuated  show at l e a s t a twenty f i v e percent component from Abbotsford reflects  T h i s anomaly perhaps  frequency T o f i n o anomaly„  At a  frequency of three c y c l e s per hour where the  anomaly i s a l r e a d y  Tofino  s i d e of  Georgia S t r a i t which i s completely absent at lower  frequencies,,  i n f l u e n c e of a shallow body of sea water such as Georgia  Strait due  still  reduced, there i s a small anomaly i n the  v e r t i c a l component at Westham I s l a n d on the east  The  vertical  a change i n upper mantle c o n d u c t i v i t y more a c c u r a t e l y  than does the h i g h e r higher  to T o f i n o .  enhancement i n the  i s expected-to be  small.  Hence t h i s anomaly i s p r o b a b l y  to a c o n d u c t i v i t y s t r u c t u r e beneath the S t r a i t  or upper mantle.  i n the  crust  viii  ACKNOWLEDGEMENTS  i I am p l e a s e d  t o acknowledge the i n v a l u a b l e a s s i s t a n c e and  welcome c r i t i c i s m g i v e n by Mr, Bernard Caner, D i r e c t o r of the V i c t o r i a Geomagnetic Observatory. J„A,  I am a l s o indebted  to Professor  Jacobs f o r h i s k i n d and p a t i e n t s u p e r v i s i o n and t o Dr, T,  Watanabe who p r o v i d e d  u s e f u l d i s c u s s i o n and c r i t i c i s m of the  t h e o r e t i c a l p a r t of t h i s t h e s i s .  Many thanks go t o Mr. D.  Weichert who a s s i s t e d with the data a n a l y s i s and t o others i n the Department of Geophysics who gave help when i t was needed. The  work i n t h i s t h e s i s was p a r t i a l l y supported by the N a t i o n a l  Research C o u n c i l .  ill  TABLE OF CONTENTS I  Page 1  INTRODUCTION A  C o a s t a l Geomagnetic Anomalies  1  B  P o s s i b l e E x p l a n a t i o n s of the Anomalies  3  C  Electromagnetic  D  T h e o r e t i c a l C o n d u c t i v i t y Models  E  Experimental  II  Induction i n t h e Earth  C o n d u c t i v i t y Models  THEORY A  5 6 10 13  N a t u r a l Geomagnetic V a r i a t i o n s 1„ Normal V a r i a t i o n s 2. Anomalous V a r i a t i o n s 3 . S e p a r a t i o n of the F i e l d i n t o an I n t e r n a l and an E x t e r n a l Part  13 13 14  Induction Analysis 1. The General Theory o f I n d u c t i o n 2» I n d u c t i o n by a P e r i o d i c L i n e a r Current i n an I n f i n i t e l y Conducting H a l f Space  16 16  The E f f e c t of an Ocean on Geomagnetic V a r i a t i o n s 1. R e l a t i o n between E l e c t r i c C u r r e n t s and Magnetic F i e l d s I n a T h i n U n i f o r m l y Conducting Sheet 2* The Edge E f f e c t of a Current Sheet 3. The Free Decay of E l e c t r i c C u r r e n t s i n the Oceans 4„ The S h i e l d i n g E f f e c t of an Oceanic Layer 5, The E f f e c t o f the Conducting Mantle on E l e c t r i c C u r r e n t s i n the Oceans  24 24 29 31 31  EXPERIMENTAL PROCEDURE  34  A  Askania V a r i o g r a p h s  34  B  I n s t a l l a t i o n and Maintenance o f t h e V a r i o g r a p h s  34  C  Confidence  35  D  P r o c e s s i n g o f Records  B  C  III  IV A  Limits  14  22  33  36  METHOD OF ANALYSIS  37  Fourier Analysis  37  iv  B  P o l a r Diagrams  39  C  S t a t i s t i c a l Analysis 1, The P r e c i s i o n of a Mean Value 2. The S i g n i f i c a n c e of a Mean Value  42 42 43  V  VI  RESULTS AND ANALYSIS  45  A  D i r e c t i o n a l Dependence of the Anomaly  49  B  S p a t i a l Dependence of the Anomaly L V a r i a t i o n s with a P e r i o d of F o r t y P i v e Minutes 2„ V a r i a t i o n s with a P e r i o d of Twenty Minutes  59 60 62  C  Frequency Dependence of the Anomaly  64  D  D a i l y Geomagnetic V a r i a t i o n s  64 '  I  D i s c u s s i o n of R e s u l t s  68  CONCLUSIONS  ?0  V  FIGURES 1.  Generalized Section Across a Stable C o n t i n e n t a l Margin  2.  Electric  Page 3  C u r r e n t s and t h e i r A s s o c i a t e d Magnetic  F i e l d s a t t h e Edge of a U n i f o r m l y C o n d u c t i n g Sheet  29  3.  Method o f P l o t t i n g a P o l a r Diagram  40  4. 5.  L o c a t i o n Map Showing S i t e s o f R e c o r d i n g S t a t i o n s A Comparison of Magnetograms Showing an Enhancement i n t h e V e r t i c a l Component a t T o f i n o as Compared to V i c t o r i a  44  6.  7.  8  0  9.  46  A Comparison o f t h e S i n e and C o s i n e S p e c t r a l D e n s i t i e s of the V e r t i c a l Component of t h e D i s t u r b a n c e Recorded a t T o f i n o and V i c t o r i a on January 10, 1964  47  A Comparison of t h e Amplitude S p e c t r a l D e n s i t i e s of the V e r t i c a l Component o f t h e D i s t u r b a n c e Recorded a t T o f i n o and V i c t o r i a on J a n u a r y 10, 1964  48  S i n e and C o s i n e S p e c t r a l D e n s i t i e s o f t h e D, H and Z components f o r Magnetic D i s t u r b a n c e Recorded a t T o f i n o on January 10, 1964  50  S i n e and C o s i n e S p e c t r a l D e n s i t i e s of t h e D, H and 2 Components f o r Magnetic D i s t u r b a n c e Recorded at V i c t o r i a on January 10, 1964  51  10.  S i n e and Coaine S p e c t r a l D e n s i t i e s o f t h e D, H and Z Components f o r Magnetic D i s t u r b a n c e Recorded at F r a n k l i n R i v e r on J u l y 3, 1964 52  11.  S i n e and Cosine S p e c t r a l D e n s i t i e s of the D, H and Z Component© f o r Magnetic D i s t u r b a n c e Recorded a t West-h-am I s l a n d on March 5, 1964  53  Sine and C o s i n e S p e c t r a l D e n s i t i e s of t h e D,» H and Z Components f o r Magnetic D i s t u r b a n c e Recorded a t A b b o t i f o r d en jun§ l l , 1964  54  P o l a r Diagram f o r Tofino at 30 minute to 60 minute Psriedi  53  14.  P o l a r Diagram f o r Tofino at 20 minute to 25 minute Ptrieds  56  15.  P o l a r Diagram f o r V i c t o r i a at 30 minute to 60 minute Periods  57  12.  13•  vi Page l6o  P o l a r Diagram f o r V i c t o r i a Periods  at 20 minute to 25 minute 5°  17.  Frequency Dependence of the T o f i n o Anomaly  65  18.  Enhancement of V i c t o r i a over Abbotsford i n the V e r t i c a l Components a t the D i u r n a l and Semi-Diurnal Periods  65  Amplitude of V e r t i c a l V a r i a t i o n s along the East-West P r o f i l e Normalized with Abbotsford Values; Compared w i t h an E l e v a t i o n P r o f i l e and a C r u s t a l S t r u c t u r e Profile  67  19.  vii  TABLES Page 71  lo  Location  2o  Mean V a l u e s o f V e r t i c a l and H o r i z o n t a l Changes R e l a t i v e t o Abbotsford values (Based on Nine Magnetic Disturbances)  71  Comparison of V e r t i c a l Component S p e c t r a l D e n s i t i e s ( i n Gamma-minutes) a t T o f i n o , F r a n k l i n R i v e r and V i c t o r i a as a F u n c t i o n of Frequency  72  Comparison of S p e c t r a l D e n s i t i e s f o r the D a i l y Variations  72  Comparison along the P r o f i l e of the S p e c t r a l D e n s i t i e s ( i n Gamma-minutes) R e p r e s e n t i n g the V e r t i c a l Change Z and the T o t a l H o r i z o n t a l Change H together w i t h the Ratio z/H  73  Comparison along the P r o f i l e of the S p e c t r a l D e n s i t i e s ( i n Gamma-minutes) R e p r e s e n t i n g the V e r t i c a l Change i n an East-West D i r e c t i o n S together with the R a t i o Z/S  75  3  8  4„ 5o  and D e t a i l s of the V a r i o g r a p h S t a t i o n s  t  t  6c  APPENDICES I II  Fourier  Analysis  Magnetograms  76 79  1  I  INTRODUCTION  A  C o a s t a l Geomagnetic Anomalies T h i s t h e s i s i s concerned  with an anomaly In the  component v a r i a t i o n s of the geomagnetic f i e l d  vertical  which was  examined  w i t h f o u r p o r t a b l e Askanla magnetometers set up a l o n g an e a s t west p r o f i l e  i n the v i c i n i t y of the B r i t i s h Columbia  together w i t h r e c o r d s from the V i c t o r i a Magnetic  coastline,  Observatory.  S i m i l a r v e r t i c a l anomalies have been measured a t c o a s t l i n e s i n many p a r t 3 of the world and h o r i z o n t a l magnetic f i e l d p e r p e n d i c u l a r to the  seem to be c o r r e l a t e d with  variations i n a direction  the  approximately  coastline.  Parkinson ( 2 4 )  has analyzed a l a r g e number of magnetograms from c o a s t a l s t a t i o n s a l l over the world and f i n d s t h a t there i s a s t r o n g tendency f o r the V e c t o r s r e p r e s e n t i n g changes i n the geomagnetic f i e l d  to l i e on or c l o s e to a p l a n e .  At  coastal  s t a t i o n s t h i s plane t i l t s upward towards the n e a r e s t deep ocean^ the o n l y e x c e p t i o n s b e i n g at a few of  s t a t i o n s where the s t r u c t u r e  the c o n t i n e n t a l s h e l f i s c o m p l i c a t e d . S i m i l a r l y , R i k i t a k e ^ ) and h i s co-workers have s t u d i e d 1  i n t e n s i v e l y the v e r t i c a l anomaly i n geomagnetic bays measured on the main Japanese I s l a n d and have found observed  when the i n d u c i n g f i e l d  d i r e c t i o n approximately of  the  t h a t i t i s best  changes i n a north™south  p e r p e n d i c u l a r to the s h e l f l i n e  south  island.  Along the C a l i f o r n i a c o a s t l i n e Schmucker^^)  n  a  s  recorded  anomalously l a r g e v e r t i c a l components ( z ) i n l o n g p e r i o d Sq  2  and  i type v a r i a t i o n s , together with  short p e r i o d bay  reduced h o r i z o n t a l v a r i a t i o n s The  (D,H)  at the  shorter  slightly periods.  v e r t i c a l anomaly there i s a l s o c o r r e l a t e d w i t h h o r i z o n t a l  changes p e r p e n d i c u l a r to the C a l i f o r n i a c o a s t l i n e . Other measurements i n c o a s t a l r e g i o n s have interesting results.  In p e r t i c u l a r , Mason and  furnished Hill(  2 0  ) found  that the d a i l y range of geomagnetic t o t a l f o r c e v a r i a t i o n s c o n s p i c u o u s l y g r e a t e r (over the c o n t i n e n t a l east A t l a n t i c than at the  s h e l f i n the  shore by a f a c t o r of two.  west c o a s t of I t a l y at Ponza I s l a n d  (Simeon and  was  north  Off  the  Sposito(49))  there i s a s t a r t l i n g p a r a l l e l i s m between the v e r t i c a l  and  h o r i z o n t a l v a r i a t i o n s which i s absent at s t a t i o n s In c e n t r a l Italy, In the A r c t i c ( Z h ' i g a l o v ^ ^ ) measurements from an i c e f l o e 1  i  d r i f t i n g a c r o s s the c o n t i n e n t a l  s h e l f i n t o deeper water showed  v e r t i c a l component v a r i a t i o n s of d i m i n i s h i n g sea depth i n c r e a s e d ,  amplitude as  e s p e c i a l l y f o r short p e r i o d  the  fluctuations,  of the order of minutes. At M i r n y i n the A n t a r c t i c M a n s u r o v ^ ^ ) has increase  reported  an  i n v e r t i c a l component v a r i a t i o n s at the c o a s t l i n e  an i n c r e a s e  i n h o r i z o n t a l v a r i a t i o n s on the  the c o a s t l i n e .  The  i c e j u s t seaward of  r a t i o of v e r t i c a l to h o r i z o n t a l  on the l a n d near the coast Increased as the p e r i o d the order of seconds.  and  This result i s consistent  variations decreased to  with  the  frequency dependence of t h i s r a t i o at the c o a s t a l s t a t i o n s of Westham I s l a n d and V i c t o r i a In B r i t i s h Columbia ( C h r i s t o f f e l , etal<  1 0  >).  3  B  P o s s i b l e E x p l a n a t i o n s of the Anomalies  A l l these c o a s t a l phenomena can be i n c l u d e d under the general term "coast e f f e c t " and although some of them may be caused by l o c a l i z e d subterranean d i s t r i b u t i o n s of conducting material,  i t has been suggested  ( P a r k i n s o n ^ C h a p m a n and  ak§ and Yokayama • $ R i k l t a k e ^ ) ) v  they §©uld p©t?hap§te©ae@eunt§d f©i? by th© aa©mal©us raagftitle f i e l d s predueed by ©l©etrle Querents indue©d i n the more d u s t i n g ©§©§fts  a  An©th©r" p©iiibl© and fat?fflgr©int©resting explanation,* a l far" a i Upp©r" Maritl© studi©§ 13?© e©neern©d^ i s that th© §sast M  ©££@@t  rt  i i I t l©a§t p a r t l y du© t© a l a t e r a l 6©nduetlvity  Sis@©fitiftulty l a th© §ru§t and/©? upp©r aantl© i t th© fe©«adary ©f g©atin©nt and ©e§an  fh© MehereviHiU d i s c o n t i n u i t y d i p s  a  Ocean Sea Level  Continent  Shells  Unconsolidated Sediments  Ultrobasic mantle rocks F i g u r e 1.  G e n e r a l i z e d S e c t i o n A c r o s s a S t a b l e C o n t i n e n t a l Margin, a f t e r J.A. Jacobs, R.D. R u s s e l l , and J.T. W i l s o n .  s h a r p l y downward ( H e s s ^ * ^ , D i e t z ^ ) ) as the t r a n s i t i o n i s 1  1 2  approached from ocean t o c o n t i n e n t , and a c c o r d i n g t o heat f l o w  4  measurements, there  i s a marked, d i f f e r e n c e between the c o n s t i -  t u t i o n of the upper p a r t of the mantle beneath the two regions ( J a c o b s ^ ^ ) so t h a t a c o n d u c t i v i t y d i s c o n t i n u i t y i s not unlikely,, 1  Furthermore, seismic at  shallower  s t u d i e s show a decrease i n shear v e l o c i t y  depths under the oceans than under the c o n t i n e n t s  (Dorman, e t a l ^ ^ ) . 1  Such a decrease i n v e l o c i t y has been (14)  a t t r i b u t e d by Gutenberg  ' t o the e f f e c t of i n c r e a s i n g tempera-  t u r e s on the e l a s t i c constants  of the r o c k s .  therms i n the mantle beneath the c o n t i n e n t s c l o s e r t o the s u r f a c e on p a s s i n g  Hence, the i s o c o u l d very w e l l  i n t o the shallower  oceanic  p r o v i d i n g i n c r e a s e d e l e c t r i c a l c o n d u c t i v i t y due t o i o n i c at  a shallower  l e v e l and r e s u l t i n g i n a l a t e r a l  rise mantle  conduction  conductivity  anomaly i n the upper mantle as a p o s s i b l e source f o r the "coast effect". (47) By  such arguments, Schmucker  has proposed t h a t the  v e r t i c 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 y which was found a t a depth of the order et  al^  2 2  ),  of 100km under c o n t i n e n t a l North America ( N i b l e t t ,  Cantwell^),  Srivastava^ )) 0  may be a t much  shallower  depths under the oceans r e s u l t i n g i n a l a r g e c o n d u c t i v i t y i n the upper mantle beneath the c o n t i n e n t a l s h e l f l i n e . c o n d u c t i v i t y step might roughly  step This  p a r a l l e l the upper boundary of  the low v e l o c i t y l a y e r , although i t i s d o u b t f u l  (Rikitake^-^))  that the low v e l o c i t y l a y e r i t s e l f i s an- e x t e n s i v e  highly  conducting l a y e r extending over l a r g e p a r t s of the e a r t h . Studies  o f heat flow anomalies i n the e a s t e r n  (Von Herzen and Uyeda^-^)) l e n d s t r o n g  Pacific  support t o arguments  5  for at  the p o s s i b l e e x i s t e n c e  of h i g h temperature thermal sources  r e l a t i v e l y shallow depths beneath the oceans e s p e c i a l l y i n  orogenic  In f a c t , i t  zones.  has been proposed  (Rikitake^*^)  that a h i g h l y conducting loop which c o u l d be composed of temperature m a t e r i a l p r o v i d e s  an e x p l a n a t i o n  f o r the  high  Japanese  "coast e f f e c t " anomaly. Although such p r o p o s a l s expecting  a c o a s t a l anomaly which Is  geology, i t i s i s due  f u r n i s h p l a u s i b l e reasons f o r independent of the mapped  s t i l l not c l e a r whether the  "coast  effect"  to eddy c u r r e n t s i n the c o n d u c t i n g oceans or due  upper mantle c o n d u c t i v i t y s t r u c t u r e at the c o a s t . h y b r i d e f f e c t due  If  to  it  the  is a  to both the 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 of  ocean and upper mantle then the ocean water e f f e c t would have to be e l i m i n a t e d  i n order to study the deeper c o n d u c t i v i t y  anomaly. C  Electromagnetic The  current  Induction  i n the  d i s t a n c e from the e a r t h ' s  the f i e l d s ,  i s very  electric  the cause of t r a n s i e n t  small compared w i t h the wavelength of  so the magnetic i n d u c t i o n f i e l d predominates over  the r a d i a t i o n f i e l d  and  the geomagnetic f l u c t u a t i o n s may  d e r i v e d from a p o t e n t i a l f u n c t i o n .  The  internal field  be  p o t e n t i a l can be  i n a s e r i e s of s p h e r i c a l harmonics and  c o n s i s t of an e x t e r n a l p a r t and The  surface to the c l o s e d  systems, g e n e r a l l y b e l i e v e d to be  magnetic f i e l d s ,  pressed  Earth  ex-  i s found to  a p a r t of i n t e r n a l o r i g i n .  i s assumed to be caused s o l e l y by  In the e a r t h by the e x t e r n a l f i e l d  induction  (9)  (Chapman and B a r t e l s ' ).  6  The  s t r e n g t h and. d i s t r i b u t i o n of the induced  earth  currents  must, t h e r e f o r e , depend on the c o n d u c t i v i t y d i s t r i b u t i o n a l s o on the nature of the i n d u c i n g f i e l d .  and  Hence, i n order  study the c o n d u c t i v i t y d i s t r i b u t i o n w i t h i n the e a r t h ,  to  ideally,  a s e p a r a t i o n of the t r a n s i e n t surface f i e l d s i n t o e x t e r n a l and  i n t e r n a l p a r t s must be made.  r e g i o n comparable i n extent  T h i s should be over a l a r g e  t o the e n t i r e e a r t h ' s  surface  or  over a r e g i o n of more l i m i t e d extent, depending on whether the average c o n d u c t i v i t y w i t h i n the e a r t h as a whole or c o n d u c t i v i t y d i s t r i b u t i o n s are being c o n s i d e r e d .  local  Different  methods of s e p a r a t i n g the f i e l d over an area of the earth's small enough to be t r e a t e d as plane, S i e b e r t and  Kertz^ ^, 8  have been d e s c r i b e d  S c h m u c k e r ^ ^ and W e a v e r . 5  has approximated the p o t e n t i a l s of i n t e r n a l and due  to a magnetic d i s t u r b a n c e  d i p o l e s , one  o u t s i d e the E a r t h and  r e g i o n of the A s i a n D  by two  surface  by  Rikitake^ ^ 0  external  origin  p a i r s of r a d i a l l y opposed  one  i n s i d e the E a r t h , i n the  continent.  ^ T h e o r e t i c a l C o n d u c t i v i t y Models T h e o r e t i c a l c a l c u l a t i o n s have been c a r r i e d out i n attempts  to c o r r e l a t e the behaviour of the time dependent p a r t of geomagnetic f i e l d over the e a r t h s d i s t r i b u t i o n w i t h i n the e a r t h .  the  s u r f a c e with the c o n d u c t i v i t y  Information  s t a t e of the e a r t h can be obtained,  about the  electrical  as i n t h i s t h e s i s , by  an  a n a l y s i s , at a g i v e n frequency, of the r e l a t i v e amplitudes arid phases of the three magnetic f i e l d components Z, H and D of  the  n a t u r a l geomagnetic f l u c t u a t i o n s over the r e g i o n of i n t e r e s t ,  or  7  through an examination of the v a r i a t i o n with frequency of  the  h o r i z o n t a l components of the n a t u r a l time dependent magnetic and  e l e c t r i c f i e l d s at a p a r t i c u l a r l o c a t i o n on the  surface no  (Cagniard^,  Wait^^O, P r i c e ^ ° ) )  so f a r , however,  o  success has been achieved i n c a l c u l a t i n g the  d i s t r i b u t i o n d i r e c t l y from such i n f o r m a t i o n geomagnetic f l u c t u a t i o n s .  earth's  conductivity  on the  natural  Rather, the d i s t r i b u t i o n of con-  d u c t i n g m a t e r i a l i s I n f e r r e d by comparing the measured  surface  f i e l d w i t h that c a l c u l a t e d f o r an assumed model c o n d u c t i v i t y d i s t r i b u t i o n o f t e n based on seismic,  g r a v i t y and  geological  information. The  world wide average of the r a t i o of i n t e r n a l to  e x t e r n a l p a r t s of the v a r i a t i o n s was  s o l a r (Sq)  and  lunar  (L) d a i l y magnetic  found to be c o n s i s t e n t with a s p h e r i c a l l y  symmetric e a r t h model c o n s i s t i n g of a u n i f o r m "core" c o n d u c t i v i t y 3.6 outer  shell  the theory  x 10 3emu. - 1  with  surrounded by a non-conducting  (Chapman(6), Chapman and Whitehead(7)). of i n d u c t i o n i n a conducting sphere was  Later, extended  to a c o n s i d e r a t i o n of the i n t e r n a l and  e x t e r n a l p a r t s of  magnetic storm time v a r i a t i o n s ( D g ) .  T h i s , i n t u r n , l e d to  T  the  the treatment of an e a r t h model i n which the c o n d u c t i v i t y i n the  "core" v a r i e d as r "  m  ( L a h i r i and  Price  (18) ) (where r i s the earth's  r a d i u s and m an i n t e g e r ) i n order  that t h e o r e t i c a l  r e s u l t s might be compatible with both the observed d a i l y v a r i a t i o n s and  the  storm time v a r i a t i o n s .  q u i r e d a worldwide i n c r e a s e  The  s o l u t i o n re-  i n c o n d u c t i v i t y at a depth of about  8  700  kilometers  suggesting  the  together  with a s u r f a c e c o n d u c t i v i t y  Influence  of the h i g h l y conducting oceans.  (Chapman and W h i t e h e a d ^ ) , L a h i r i and the b a s i s of more numerous and the amplitude r a t i o and and  Price^ ^)).  However, on  1  r e l i a b l e data,  new  analyses  phase d i f f e r e n c e between the  i n t e r n a l p a r t s suggest that the depth of the  c o n d u c t i n g core  distribution  of  external  uniform  should  be at 400km w i t h a c o n d u c t i v i t y of  T h i s new  u n i f o r m core model overcomes the  -12 5 x 10  emu.  crepancy between the i n d u c t i o n f i e l d from Sq and Dgip. l o c a l i z e d analyses  have r e v e a l e d  at depths as shallow as 100 continent  (Srivastava(50),  work i n C a l i f o r n i a  a large increase  kilometers 2 2  period v a r i a t i o n s .  i n conductivity  Cantwell(^))  (Schmucker^^^) suggests a more  The  and  recent  gradual  c o n d u c t i v i t y values  to e x p l a i n the observed i n d u c t i o n due  More  beneath the North American  Niblett^ ),  t r a n s i t i o n from lower to h i g h e r  dis-  i n order  to both l o n g and  short  p r a c t i c e of assuming a h i g h l y conducting  core whose s p h e r i c a l surface e x i s t s at a c e r t a i n depth below the e a r t h ' s  s u r f a c e would, t h e r e f o r e ,  s i n c e the depth and  seem to be  unrealistic,  r a p i d i t y of the major c o n d u c t i v i t y  In the upper mantle appears to vary from p l a c e to U s i n g the theory  37)  place.  of i n d u c t i o n of e l e c t r i c c u r r e n t s i n non-  u n i f o r m t h i n sheets and (36,  increase  shells ( P r i c e ^ ^ ) , Ashour( )), Rikitake 2  s t u d i e d electromagnetic  v a r i a t i o n s i n a hemispherical  x  i n d u c t i o n caused, by  ocean u n d e r l a i n by a  sphere of u n i f o r m c o n d u c t i v i t y and  daily  concentric  a l s o i n d u c t i o n caused by  geomagnetic bays i n a semi c y l i n d r i c a l ocean.  His  analyses  9 and  that of de Wett who  considered  the i n d u c t i o n of  c u r r e n t s i n an ocean model represent  electric  the f i r s t attempts to  approximate geomagnetic v a r i a t i o n s by c o n s i d e r i n g a s p h e r i c a l e a r t h model whose l a t e r a l s u r f a c e c o n d u c t i v i t y v a r i a t i o n s resemble those of the e a r t h ' s upper l a y e r s . showed t h a t e l e c t r o m a g n e t i c conducting  Rikitake's solutions  c o u p l i n g between the ocean and  p a r t of the e a r t h ' s mantle reduced the  expected  anomaly i n geomagnetic bays to a value l e s s than f o r t y of the Inducing v a r i a t i o n s due value.  field  and  reduced the anomaly In the  to a h e m i s p h e r i c a l  Recently,  percent  daily  ocean to an almost n e g l i g a b l e  however, i t has been shown ( R o d e n ^ ) ) ,  the b a s i s of a f l a t  on  2  ocean model, t h a t i n the case of  daily  v a r i a t i o n s , e l e c t r i c c u r r e n t s i n the mantle can have but e f f e c t i n reducing  the  little  the anomaly w i t h i n d i s t a n c e s from the edge  of the ocean which are comparable to the depth at which the c u r r e n t s are The  flowing.  problem of i n d u c t i o n i n a s p h e r i c a l e a r t h model with  complex boundary c o n d i t i o n s near the one  and  surface i s a p r o h i b i t i v e  l a t e l y more i n t e r e s t has been shown i n the i n t e r p r e -  t a t i o n of l o c a l anomalies i n v o l v i n g simple c a l c u l a t i o n s i n which the  t h e o r e t i c a l model  s p h e r i c i t y of the e a r t h i s n e g l e c t e d  and  the e a r t h i s t r e a t e d as a s e m i - i n f i n i t e p l a t e conductor.  The  b a s i c theory of the m a g n e t o t e l l u r i c  method  has been extended t o . the case where the e a r t h vertical discontinuity i n conductivity. K u n e t z ,  Rankin^?)).  (Cagniard^)) contains-'a  (d'Erceville  Because of i t s relevance  to  and the  10  i n t e r p r e t a t i o n of the  "coast e f f e c t " at m i c r o p u l s a t i o n  fre-  quencies, t h i s v e r t i c a l f a u l t problem has been s t u d i e d f u r t h e r (Weaver(55)^ C o o d e ^ ) i n the l i g h t of c r i t i c i s m s of the of the m a g n e t o t e l l u r i c  theory  method ( W a i t ^ - ^ , P r i c e (30)  ) the nature and exact  d i s t r i b u t i o n of the  s o l u t i o n has been obtained.  anomaly  of bay  type d i s t u r b a n c e s  regarding  source f i e l d .  However, no  The  coastal  California  has been t r e a t e d t h e o r e t i c a l l y  as the r e s u l t of a p e r t u r b a t i o n of the l a r g e - s c a l e , uniform induction process i n a h o r i z o n t a l l y s t r a t i f i e d (47) distribution  (Sehmucker  v  ).  conductivity  A r e l a x a t i o n method developed  by P r i c e ( ® ) , t a k i n g i n t o account the mutual i n d u c t i o n between 2  a conducting surface  l a y e r of v a r y i n g t h i c k n e s s and  a core  i n f i n i t e c o n d u c t i v i t y , f u r n i s h e d a d i s t r i b u t i o n of the which f o l l o w e d  the observed data c l o s e l y .  of  anomaly  In t h i s t h e o r e t i c a l  model the anomalous v e r t i c a l v a r i a t i o n s r e s u l t from the edge of an oceanic  current  sheet at the  surface and  from c u r r e n t s  i n the upper mantle beneath the c o n t i n e n t a l surface  flowing  layers.  S i m i l a r t h e o r e t i c a l c a l c u l a t i o n s u s i n g conformal mapping methods, based on a model c o n s i s t i n g of a l a r g e c o n d u c t i v i t y step to the e a r t h ' s  surface,  give a s i m i l a r s p a t i a l  close  distribution.  Both of these models p r e d i c t the observed i n c r e a s e  i n the  anomaly as the frequency of the geomagnetic v a r i a t i o n s i n c r e a s e s to the order E  of one  c y c l e per  Experimental C o n d u c t i v i t y  hour. Models  T h e o r e t i c a l i n v e s t i g a t i o n s must i n v o l v e v a s t l y s i m p l i f i e d c o n d u c t i v i t y d i s t r i b u t i o n s because of the extreme d i f f i c u l t y  in  s o l v i n g i n d u c t i o n problems with h i g h l y complex boundary conditions,,  11  On the other hand, c o a s t l i n e and subsurface i r r e g u l a r i t i e s maybe taken i n t o account  to some extent i n l a b o r a t o r y model s t u d i e s .  In p a r t i c u l a r , experimental proof was o b t a i n e d f o r the enhancement of v e r t i c a l geomagnetic v a r i a t i o n s a t the edge of a hemis p h e r i c a l ocean, and the anomalous e f f e c t s o f a c o n d u c t i n g loop beneath Japan were i n v e s t i g a t e d e x p e r i m e n t a l l y . al^  2 1  )).  copper of and  More r e c e n t l y experiments  sheet model o f the P a c i f i c  Japan (Roden  v>  performed  (Nagata, e t  with a f l a t ,  Ocean i n the neighbourhood  ') have y i e l d e d a d i s t r i b u t i o n o f d i u r n a l  semi d i u r n a l f i e l d s which agree q u a l i t a t i v e l y w i t h  tions.  In A u s t r a l i a  performed  ( P a r k i n s o n ^ - ^ ) experiments 2  observa-  have been  on an e a r t h model In which the oceans are represented  by sheets of copper bent t o l i e on the s u r f a c e of a sphere and a u n i f o r m h i g h l y conducting core a t a depth of 600 k i l o m e t e r s i s simulated by a sphere of aluminium.  The primary f i e l d i s  i n t r o d u c e d by a c o i l of wire wound i n the form of the c u r r e n t f u n c t i o n thought  t o produce bays,  and h e l d o u t s i d e the sphere  i n a p o s i t i o n c o r r e s p o n d i n g t o the ionosphere.  Preliminary  r e s u l t s show t h a t f o r bay type d i s t u r b a n c e s the copper  oceans  have an e f f e c t which agrees q u a l i t a t i v e l y w i t h o b s e r v a t i o n s a t the c o a s t l i n e , but the conductors modify the conductors present i n the e a r t h . of  the f i e l d much l e s s  than  Measurements i n the i n t e r i o r  the c o n t i n e n t i n d i c a t e t h a t the u n i f o r m h i g h l y c o n d u c t i n g core  should be a t a much shallower  depth.  I t would seem, then, t h a t the oceans are r e s p o n s i b l e f o r at  l e a s t p a r t o f the "coast e f f e c t " but no r e a l i s t i c  ocean  12  model, mathematical or experimental,  has yet been d e v i s e d  which g i v e s a q u a n t i t a t i v e e x p l a n a t i o n f o r the anomaly at all  frequencies.  13  II A  THEORY N a t u r a l Geomagnetic V a r i a t i o n s I t i s b e l i e v e d t h a t t r a n s i e n t geomagnetic v a r i a t i o n s are  caused  by the i n t e r a c t i o n o f s o l a r p a r t i c l e s with the e a r t h ' s  magnetic f i e l d .  A n a l y s i s of these v a r i a t i o n s , both p e r i o d i c and  I r r e g u l a r , a t d i f f e r e n t p o i n t s on the e a r t h ' s s u r f a c e p r o v i d e s a t o o l f o r the study of the e l e c t r i c  s t a t e of the e a r t h .  Changes  i n the t o t a l magnetic f o r c e v e c t o r are u s u a l l y measured c o n t i n u a l l y In the form o f the three components D, H and Z each of which i s recorded on a magnetogram.  A l l three components undergo smooth  and r e g u l a r v a r i a t i o n s with a p e r i o d of approximately  one day.  These d a i l y v a r i a t i o n s may be separated i n t o the s o l a r  daily  v a r i a t i o n (S). which depends mainly on l a t i t u d e and l o c a l and  the much s m a l l e r l u n a r d a l l y v a r i a t i o n  (L).  Storm and bay  type d i s t u r b a n c e s are superimposed on these p e r i o d i c and commence a t almost earth's surface.  time  variations  the same I n s t a n t a t a l l p o i n t s on the  Bay type d i s t u r b a n c e s , which l a s t f o r about  one h a l f to two hours,  show up on magnetograms as a d e v i a t i o n  from the normal p e r i o d i c d a i l y v a r i a t i o n , g r a d u a l l y I n c r e a s i n g to  a maximum value and then d e c r e a s i n g smoothly back t o the u n d i s -  turbed l e v e l . C e r t a i n phases of weak magnetic storms p r o v i d e usef u l f e a t u r e s , although they are u s u a l l y more i r r e g u l a r and l e s s e a s i l y analyzed than bays.  1*  Normal V a r i a t i o n s Geomagnetic v a r i a t i o n s may be represented by a time  dependent  d i s t u r b a n c e v e c t o r P ( t ) with components D ( t ) , H ( t ) and Z ( t )  14  which, I n g e n e r a l , are f u n c t i o n s of p o s i t i o n P and frequency O J . The  disturbance  v e c t o r c o n s i s t s of p a r t s of both an i n t e r n a l and f~(t) = F^(P,^J) + F{(P u>) .  an e x t e r n a l o r i g i n , i . e . we can w r i t e  1  A common assumption i s t h a t the magnetic p e r m e a b i l i t y J U  i s unity  (cgs u n i t s ) and t h a t the i n t e r n a l p a r t a r i s e s s o l e l y from i n d u c t i o n by the e x t e r n a l p a r t i n the conducting  earth.  I f the  c o n d u c t i v i t y d i s t r i b u t i o n In the e a r t h i s h o r i z o n t a l l y s t r a t i f i e d , the geomagnetic v a r i a t i o n s are s a i d t o be "normal" and  Fit) 2.  = F»W «  K*( M p  +  Ftnte")  Anomalous V a r i a t i o n s L a t e r a l c o n d u c t i v i t y inhomogeneities may r e s u l t i n a de-  formation  o f the i n t e r n a l c u r r e n t  normal i n t e r n a l p a r t t e r n a l component For  simple  ignored  and  system r e s p o n s i b l e f o r the  p^ (P, coj g i v i n g r i s e t o an anomalous i n N  F^ (p,w) Q  which v a r i e s from s t a t i o n t o s t a t i o n .  c o n d u c t i v i t y s t r u c t u r e s where mutual i n d u c t i o n can be  the t o t a l i n t e r n a l p a r t may then be w r i t t e n as  the t o t a l d i s t u r b a n c e  v e c t o r as  Rt) = Fenfcw) + Rn(P,w)  +  P^(P,u>) •  I n d u c t i o n a n a l y s i s l e a d s one t o expect a c o r r e l a t i o n between the anomalous v a r i a t i o n s  F{ (P>u;)  R(t) 3.  Separation  a  FeniM  and the t o t a l normal v a r i a t i o n s  + F i n ( P ^ ) -.  of the F i e l d i n t o an I n t e r n a l and an E x t e r n a l P a r t  I f the i n d u c i n g f i e l d i s e s s e n t i a l l y uniform, any d i f f e r e n c e s  15  i n geomagnetic v a r i a t i o n s observed at adjacent assumed t o be due  s t a t i o n s can  to an i n t e r n a l anomalous p a r t .  the e x t e r n a l i n d u c i n g f i e l d e x t e r n a l p a r t s must be  be  However, I f  i s not uniform, the i n t e r n a l and  separated  i n order  to determine the i n -  duced secondary f i e l d s a s s o c i a t e d with the c o n d u c t i v i t y anomaly. Assuming t h a t the displacement c u r r e n t can be ignored, v a r i a t i o n s may due  be d e r i v e d from a p o t e n t i a l f u n c t i o n .  to i n t e r n a l and  e x t e r n a l e l e c t r i c c u r r e n t s may  be  the magnetic The  potentials  repres-  sented as F o u r i e r i n t e g r a l s i n v o l v i n g s p e c t r a l d e n s i t i e s which decay e x p o n e n t i a l l y with depth (see I n d u c t i o n (22)) as  Analysis,  equation  follows:  r~  tj\  e  AZ  cos A y  +  cos Ay  +  r-  Lh sin A  £  dA  ,  dA  ,  z>  o  o  e  e  7*  s i n Ay  z>o  where Z I s measured v e r t i c a l l y upward and  Y i n the d i r e c t i o n of  the t o t a l h o r i z o n t a l f i e l d  The  variation H . T  e-^f^ are  s p e c t r a l d e n s i t i e s and  The  components at the e a r t h ' s  field  Z( )= 3  - ^ e - ^ i ^  H M= -^Oie_ T  Ajl  {  =  2TT/K  i s the  coefficients  E^F^,  s p a t i a l wavelength.  s u r f a c e Z = 0 are given  by  fr(E -e,)co5Ay +(F>-/Jsfn *y]dA h  f[(-E*-e )s;nAB + (h+h) A  coS  d  *  16  A F o u r i e r A n a l y s i s can be c a r r i e d out on the s p a t i a l dependence of  the Z and Hip v a r i a t i o n s which are determined  by measurement.  oo  r  r  o CO  The  spectral densities  ^ F^e^.,^  i n the e x p r e s s i o n s f o r  the i n t e r n a l and e x t e r n a l p o t e n t i a l s may  be found by  equating  the c o r r e s p o n d i n g s p e c t r a l d e n s i t i e s i n the e x p r e s s i o n s f o r Z(y) and  H (ij) .  Thus  T  B W t  =  F»- ^  B (A)= H r  -E^+e,  Hence, the i n t e r n a l and e x t e r n a l c o n t r i b u t i o n s to the magnetic v a r i a t i o n s a t the e a r t h ' s s u r f a c e may B  be  calculated.  Induction Analysis The c u r r e n t system which i s the source of the magnetic  v a r i a t i o n s i s assumed to vary p e r i o d i c a l l y w i t h time. field  v e c t o r s c o n t a i n a time f a c t o r  t i v e s may 1.  The  e  1 ,  A l l the  and a l l time  deriva-  thus be r e p l a c e d by i t o .  General Theory of I n d u c t i o n  Using the e l e c t r o m a g n e t i c system of u n i t s Maxwell's equations are:  field  17  cfiv  E  =  A ^ fi  (i)  c  0 curl Tt  =  Cur I E  =  4 IT  (2) K  E  (3)  +  - i t ! it  where the p e r m e a b i l i t y J J L i s taken as u n i t y everywhere, the c o n d u c t i v i t y of the medium, and jO These equations  K  is  the charge d e n s i t y .  are a p p l i e d to the r e g i o n s above and  within a  semi i n f i n i t e conductor which approximates c o n d i t i o n s above below the e a r t h ' s  surface.  z  -  1  i  i  llllll  / / / / / / /  I t i s assumed t h a t there i s no the conductor and ductor  w i l l be  (3)  E = (4)  so t h a t we O  and  can w r i t e  p-0 (5)  1  combining i t with  equation  gives =  For  charge d i s t r i b u t i o n i n s i d e the con-  div  the c u r l of e q u a t i o n  1  space charge i n the r e g i o n above  rapidly dispersed,  everywhere and Taking  t h a t any  and  1 4 - i r K c o f 4-  (i CJ)  E  s l o w l y i v a r y i n g f i e l d s and/or h i g h c o n d u c t i v i t y  (6)  ^  C<4TTKCO  18  Hence,  inside  the conductor  equation  _ 2  E  conductor  displacement  (6)  reduces  to the  diffusion  ,  Y  Above t h e  equation  =  the  term  i  4TT  E  Kto  () 7  conductivity K i s negligible c a n be n e g l e c t e d  and  the  s i n c e the i n d u c t i o n  at field  dominates the  wavelength of the equation  (6)  conductor,  can  where  SI  (6)  and  satisfy  reduces  equations  to Laplace's  equation  H = - grad  may  above t h e c o n d u c t o r  the  surface.  (7)  and  (5),  V  (7)  ^  W  r e g i o n above  (3)  becomes  SI s i n c e d i v If  expressed  as the  0. gradient  conductor.  vectors E  field  =  and If w h i c h  the conductor,  equation  E= Z(z)F£,y)  and  L  the  the u s u a l boundary c o n d i t i o n s a t  (8)  V  Z  be  inside  Substituting  equations  side of  equation.  r e g i o n above t h e  i s to f i n d and  one  (8)  i n the  (5)  r i g h t hand  = o  the magnetic f i e l d  p r o b l e m now  the  i n the  s a t i s f i e s Laplace's equation  (8)  into  n e g l e c t e d and  hence  a scalar potential The  i n regions well within  B o t h t e r m s on  simplifications  H = 0  Therefore, of  t h u s be  V' E  above  curl  source.  equation  i With- t h e  radiation field  yields  JE  dz*-  (9)  J  (  1  0  )  19  -z>°> Z-f +. =Lf  =  - .1  F  (ii)  The Form of Z ( z ) Above and W i t h i n the Conductor The c o e f f i c i e n t s of p" on the r i g h t hand s i d e of equations (10) and (11) must be constant, s i n c e the l e f t hand s i d e s c o n t a i n no Z dependence.  Therefore l e t  Z>0,  - ±  Z  and Z<0  ,  -^r  Z  S o l u t i o n s of equations  Z>o,  l  e  .  9 6  =  l  hz  x  =  - ^  (12)  a  + -14TTKGJ =  - ?\  2  (13)  (12) and (13) a r e :  Z " A e  W  +  fie^  (14)  8z  z<o , where  &z  Z= ae  (15)  }\ + i 4 TT K u> 2  - jj, [ { ( 4 W +  A*)t ^ ] +^[{(4.TrtCco)+ 'X^. A ] ,  The s o l u t i o n (15) s a t i s f i e s the c o n d i t i o n t h a t Z W - » 0 as  1  Z-»-*<  The Form of F(x,y) Above and W i t h i n the Conductor Equation  (9) y i e l d s an e x p r e s s i o n f o r F*(x,y) which h o l d s  above and w i t h i n the conductor.  OX  Let  F sO z  so t h a t  c»ij  Then  F - ( f . - i ? , 0)  ( 1 6 )  20  where by equations  ( 1 0 ) and ( 1 1 )  + &  +  h P a  = O  (17)  The Form of E and H Above and W i t h i n the Conductor Above the Conductor  (z>o):  From e x p r e s s i o n s (14)  and  (16)  E - ( A e* + 8 e"* )( i ? , - £ P , o) z  c)y  Equation  (4)  <>  z  l8  <=>7C  g i v e s an e x p r e s s i o n f o r the magnetic f i e l d p _  terms of the e l e c t r i c f i e l d  ,  {  w  H  =  By e q u a t i o n ( 1 7 ) t h i s  and on u s i n g e q u a t i o n  Sx  &z. a  v y  dx*  a^*' /  becomes  (l4)  H = -A d [ ( A e ^ e e ^ ) ? w ] r  W i t h i n the Conductor  , 0 )  Z (£\-iP,0)  Curl  ^ az  Z ( £P , -  H in  (19)  (z<o):  From e x p r e s s i o n s ( 1 5 ) and ( 1 6 )  E  -  *«  (ff,-ap,o)  (20)  21  Once a g a i n e q u a t i o n (4) field  g i v e s an e x p r e s s i o n f o r the  3 -  ( 9 a e  _ _ L  The S c a l a r Magnetic  i f , 6 a e  K  dP,  where  J  (  i)  2  and thus by comparison  with  (19)  expression  Jl  P a e  Potential  Above the conductor, H = - grad Si  7\z  =  - ( A e  7\A  _p  =  ^  +  Be  and  -Az  )  P(*,y^)  A £  -  (22)  B  \ tJ  10)  The  magnetic  n e  term i n v o l v i n g  corresponds to the f i e l d  due  to  sources i n the r e g i o n above the conductor, whereas the term -Az e corresponds to the f i e l d of the induced  B  c u r r e n t s i n s i d e the conductor. Boundary C o n d i t i o n s The t a n g e n t i a l components of E and H are continuous at Z = 0 . Thus, the t a n g e n t i a l components of E g i v e n by equations ( l 8 ) and  (20)  (19)  and  and the t a n g e n t i a l components of H g i v e n by equations (21)  may  be equated at Z = 0 g i v i n g  + Q and  =  A - £>) =  a  @<x  (23) (24)  W r i t t e n i n terms of the c o e f f i c i e n t s A and B these y i e l d  --tcj(R-B) -  (25)  - i w (ft + B ) =  (26)  22  Combining these e x p r e s s i o n s g i v e s the value of B i n terms of A, viz V8+  where  A /  0  =  2  A + Z  i4TTK60  .  Thus, the boundary c o n d i t i o n s at the e a r t h ' s s u r f a c e r e q u i r e an image source beneath the s u r f a c e with a s t r e n g t h depending on the c o n d u c t i v i t y K of the e a r t h , the frequency  of the v a r i a t i o n s  oo  and the s p a t i a l wavelength 2ir/A .  2.  I n d u c t i o n by a P e r i o d i c L i n e a r Current i n an I n f i n i t e l y Conducting H a l f Space.  Linear Current Source  Image Current Source  t  e  f l o w i n g p a r a l l e l to the x-  a x i s i n a p o s i t i v e d i r e c t i o n at a h e i g h t h above the e a r t h ' s surface.  The magnetic p o t e n t i a l of t h i s l i n e c u r r e n t i s g i v e n by , which may  be  represented by F o u r i e r ' s i n t e g r a l theorem as  The p o t e n t i a l of the induced f i e l d a r i s e s from an image  source  23  with  strength/6-\\  J  , and thus the p o t e n t i a l due t o i n t e r n a l  c u r r e n t s may be represented  by  SI In the case of an i n f i n i t e l y conducting become.s u n i t y and the image c u r r e n t  h a l f space  8-* 0+ h  source appears as a l i n e  c u r r e n t of s t r e n g t h I a t a depth -h f l o w i n g i n the opposite d i r e c t i o n to the e x t e r n a l source.  The m i r r o r image approximation  may a l s o be a p p l i e d i n the case of a f i n i t e l y conducting  hori-  z o n t a l l y s t r a t i f i e d e a r t h so l o n g as h i g h frequency v a r i a t i o n s are considered  so t h a t 8  approaches u n i t y .  i s very l a r g e and 0 -^  The e x t e r n a l and induced  once again vertical variations  at the s u r f a c e a r e :  Z  (2=o) = - ? f t e (z=o) = -2  \ I  <  U  j  6  t  sin ^ d *  and  Therefore Z e  -Z{  =  a t Z = 0 and the t o t a l v e r t i c a l v a r i a t i o n  i s zero a t the s u r f a c e of an i n f i n i t e l y conducting The e x t e r n a l and induced  \\  h o r i z o n t a l v a r i a t i o n s a t the s u r f a c e a r e :  (z=o)= - M ( z = o ) = -2 e  half-space.  f Ie  i u t  ft^  cos h%  dh  24  and  H. (z. ) = - S J l x ^ s o ) = - 2 0  H e y = Hv'y  Therefore is  2. H e y  J  I  e  C  a  i  t  e ^  cos  A  3  a t Z = 0 and t h e t o t a l h o r i z o n t a l v a r i a t i o n  at the surface.  I n r e a l i t y , the c o n d u c t i v i t y of the  e a r t h i s f i n i t e and i n t h e case o f l o n g e r p e r i o d bay type d i s turbances,  t h e image source w i l l be weaker t h a n a m i r r o r image,  the v e r t i c a l component w i l l n o t be c o m p l e t e l y  c a n c e l l e d and t h e  h o r i z o n t a l component w i l l be i n c r e a s e d l e s s t h a n t w o - f o l d . C  The E f f e c t o f an Ocean on Geomagnetic V a r i a t i o n s The  boundary between ocean and c o n t i n e n t  represents  an  o b v i o u s 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 y which w i l l be r e s p o n s i b l e f o r an anomalous i n t e r n a l magnetic f i e l d .  The anomaly  may be s t u d i e d as t h e edge e f f e c t o f a l a r g e s c a l e system o f eddy c u r r e n t s Induced i n a t h i n sheet o f u n i f o r m s e n t i n g t h e ocean.  c o n d u c t i v i t y repre-  S i n c e t h e depth o f a l a r g e ocean i s n e g l i g a b l y  s m a l l compared t o i t s h o r i z o n t a l dimens:io..ns, t h e c u r r e n t s would be e x p e c t e d t o c i r c u l a t e i n l a r g e e d d i e s f l o w i n g p a r a l l e l t o t h e ocean f l o o r . 1.  R e l a t i o n between E l e c t r i c C u r r e n t s T h i n U n i f o r m l y C o n d u c t i n g sheet  and M a g n e t i c F i e l d s i n a  K=o  ///////////  .//////////// d K=0  25  Neglecting field  the displacement c u r r e n t as i n p a r t B, the r e l e v a n t  equations a r e : curl  H  4TTT  -  (!)  curl E = - d f f  ( 2 )  £t di'v  "  H  =  0  t  =  KE"  where the p e r m e a b i l i t y [/.  (3) (4)  i s taken as u n i t y  i s the c o n d u c t i v i t y of the t h i n Above and below the sheet  (cgs u n i t s ) and K  sheet. , so t h a t c u r l 1? = 0 and  x = o  hence H* = - grad Si where  Si  (5)  s a t i s f i e s Laplace's  sheet i s i n f i n i t e s i m a l ,  equation.  I f the t h i c k n e s s of the  the c u r r e n t s w i l l flow p a r a l l e l to. the  s u r f a c e of the sheet and the normal component field the  and the t a n g e n t i a l component E  t  of the magnetic  of the e l e c t r i c f i e l d have  same magnitude and d i r e c t i o n on both s i d e s of the sheet.-  I n t e g r a t i n g e q u a t i o n (4)  f  Tdz  J  =  —^ ie.  l ~  where  over the t h i c k n e s s  dz  K E  =  t \ t  of the sheet •  K dz  —* =  E  t  d J  i  t dz.  the t o t a l sheet c u r r e n t  <  ,  r  ( ) 6  d  and  G~ -  j  K dz  i n t e n s i t y p e r u n i t l e n g t h at a p o i n t  on the surface and the t o t a l c o n d u c t i v i t y per u n i t Applying  are  length.  e q u a t i o n ( l ) t o a small volume element e n c l o s i n g  of the t h i n  sheet,  part  26  f(r  Curl  H dV  u s i n g the i d e n t i t y  and  =  4.TT 1  jj  f curl JJ J  (7)  dV =  r?><'adS J.  the d e f i n i t i o n of t o t a l sheet c u r r e n t i n t e n s i t y per u n i t  length, equation  (7) reduces t o  By s h r i n k i n g the volume while can w r i t e  ie. where  _^  T tt  t  ,  s  s t i l l e n c l o s i n g the sheet, ^  r  _  = J_fix(H -H_)  i s the t o t a l f i e l d  (8)  +  i s the u n i t  we  v e c t o r i n the p o s i t i v e  Z direction,  H  +  above the sheet and H„ the f i e l d below.  Applying equation  (2) t o a small c i r c u i t  of the sheet a t Z = 0, g i v e s  which together with equations  curl E  t  i n the s u r f a c e  « - $H dt  (6) and (8) y i e l d s  27  Curl  [TTX(17 -H1)] = +  -4TT ^  £>H ht  Taking the s c a l a r product of both s i d e s of t h i s e q u a t i o n w i t h rf, we  o b t a i n the boundary e q u a t i o n  (TT -TL) =  dW  +  -4ir<T  ^JHz  (9)  at Now  H^-  H_  and  =  - greed ( J l + - (52-)  where  and  of i n t e r n a l and e x t e r n a l o r i g i n .  are the magnetic p o t e n t i a l s Since  we  have:  The magnetic p o t e n t i a l of the induced c u r r e n t s i n a sheet at Z = o w i l l have the same d i s t r i b u t i o n on both s i d e s of the the p o t e n t i a l s on one  sheet,  s i d e b e i n g the n e g a t i v e of the p o t e n t i a l s  on the o t h e r .  so t h a t at Z = 0  J"l ^  and  where  -H  =  i  and  Si.  -  ^  T h e r e f o r e equation  f\  =  J  l  -  (10) becomes  -2  fi ^JU  ^  are u n i t v e c t o r s i n the x and y d i r e c t i o n s .  +  ; iJl+)  (ii)  28  <)S£  S u b s t i t u t i n g t h i s i n t o e q u a t i o n (9) together with 1-1=  + will  we o b t a i n  and s i n c e  =  z i r r  i  r ^ + +  i i ^ i "  must s a t i s f y L a p l a c e ' s equation, t h i s boundary  e q u a t i o n becomes  (12) J  52 Let  the i n d u c i n g p o t e n t i a l f i e l d  SI -  e  e  Then the induced f i e l d  Sli= so t h a t  and  k  e  be of the form  -  >  above the sheet w i l l  Z  i  u  P(z,y)  t  e  SI' 0  as  By s u b s t i t u t i n g SI?  k  (13) - oo  as.  SX\ —*  be of the form  and Sl>\  =  i n t o the boundary e q u a t i o n ( 1 2 ) , Zif<r \ t o  A  +  2TT<T\U>  The modulus of k g i v e s the r a t i o of the magnitudes of and the argument of k g i v e s the phase s h i f t field  r e l a t i v e to the i n d u c i n g f i e l d .  i n t e n s i t y per u n i t l e n g t h  1-t  i n terms of the i n d u c i n g f i e l d into  (11) we have  of the induced  The e l e c t r i c c u r r e n t  i n the sheet can now be H. e  and  expressed  S u b s t i t u t i n g e q u a t i o n (13)  29  which i n t u r n may be s u b s t i t u t e d i n t o e q u a t i o n (8) t o give  2TT The e l e c t r i c c u r r e n t per u n i t l e n g t h a t a p o i n t i n the sheet is,  therefore,  l i n e a r l y c o r r e l a t e d w i t h the component of the  e x t e r n a l i n d u c i n g magnetic f i e l d  v a r i a t i o n perpendicular  2.  Sheet  The Edge E f f e c t of a Current Neglecting  the e f f e c t of the ocean boundary i n m o d i f y i n g  the e l e c t r i c c u r r e n t s ,  and t r e a t i n g the c u r r e n t  r i g h t up t o the edge, p r o v i d e s  Mutual i n d u c t i o n between the c u r r e n t d i s t r i b u t i o n beneath i t i s a l s o  sheet as uniform  a s i m p l i f i e d p i c t u r e of.the  d i s t r i b u t i o n of the a s s o c i a t e d v e r t i c a l magnetic  spatial  fields.  sheet and any c o n d u c t i v i t y  neglected.  Z  / /  to I t .  Inducing Field  y  /  Z Inducing Field  / / / A/ / Y/ A/}/ Figure  2  E l e c t r i c C u r r e n t s and t h e i r A s s o c i a t e d Magnetic F i e l d s at the Edge of a U n i f o r m l y Conducting Sheet.  30  The  v e r t i c a l magnetic f i e l d  at a point  (y,z) due t o a l i n e  c u r r e n t of i n f i n i t e l e n g t h i n a d i r e c t i o n p e r p e n d i c u l a r a x i s and o f s t r e n g t h  dtj'  s i t u a t e d at a p o i n t  t o the y-  (y%0) i s  given by  The  e f f e c t of a c u r r e n t  sheet  of i n f i n i t e l e n g t h , extending  from  y = 0 t o y = -W, may be approximated by i n t e g r a t i n g the v e r t i c a l f i e l d s c o n t r i b u t e d by a number of such l i n e c u r r e n t s  perpendicular  to the y - a x i s and i n the plane o f the t h i n conductor. Hence, the v e r t i c a l f i e l d  due to the sheet  i s g i v e n by  I »3 i.e. u s i n g equation (14)  '3  2.TT This expression  g i v e s the expected s p a t i a l dependence and d i r e c t i o n a l  dependence of the v e r t i c a l , e d g e - e f f e c t , 1)  anomaly, v i z  The v e r t i c a l anomaly i n c r e a s e s as the ocean i s approached,  r e a c h i n g a maximum a t the c o a s t l i n e . 2)  The anomaly I s l i n e a r l y c o r r e l a t e d with the h o r i z o n t a l  inducing f i e l d  perpendicular  When the f i e l d  t o the c o a s t l i n e .  changes toward the ocean the anomalous  v e r t i c a l change i s p o s i t i v e (upward), and when the f i e l d toward the l a n d the anomalous v e r t i c a l change i s negative  changes  31  (downward).The e x p r e s s i o n f o r H  z  y = 0 because of the mathematical 3.  The Free Decay of E l e c t r i c  i s indeterminate at z  =0,  nature of the model,  C u r r e n t s i n the Oceans  I f the e l e c t r i c c u r r e n t s are e x c i t e d i n an ocean and  left  to decay, they w i l l do so e x p o n e n t i a l l y w i t h a time constant which depends on the t o t a l c o n d u c t i v i t y of the ocean. of e l e c t r i c c u r r e n t s i n a u n i f o r m l y c o n d u c t i n g d i s c shows t h a t the time ^ reduced to  i/e  The  theory  (Ashour^"^)  r e q u i r e d f o r the c u r r e n t d e n s i t y to be  of i t s i n i t i a l value i s g i v e n by  "C = 2.34  a//°  where a i s the r a d i u s of the d i s c and J> i s the s u r f a c e r e s i s t a n c e per u n i t l e n g t h .  Taking the c o n d u c t i v i t y K of sea water to be  4 x lO'^emu, the r a d i u s of the P a c i f i c average  depth 4 km.,  Although bottom  irregularities  reduce t h i s decay time to a s m a l l e r value, i t i s e v i d e n t t h a t  the P a c i f i c  Ocean w i l l  s u s t a i n e l e c t r i c c u r r e n t s induced by  type d i s t u r b a n c e s of one or two hours d u r a t i o n . c u r r e n t In the r e l a t i v e l y  i n t h i s case a v e r t i c a l anomaly caused  A c u r c u l a r eddy  a few  solely  seconds,  The. magnetic  of an Oceanic  f i e l d s of the Induced  tend to c a n c e l the source f i e l d beneath  so that  by the sea water I s  Impossible f o r v a r i a t i o n s with a p e r i o d g r e a t e r than a few  The S h i e l d i n g E f f e c t  bay  shallow Georgia S t r a i t between Vancouver  I s l a n d and the mainland would decay i n j u s t  4.  the  the above formula g i v e s a f r e e decay time  of approximately f o u r or f i v e hours. may  Ocean 4000km., and  minutes.  Layer c u r r e n t s i n an ocean the l a y e r .  I t has been  shown i n s e c t i o n C l t h a t the Inducing and induced f i e l d s above  32  a t h i n c o n d u c t i n g sheet are r e l a t e d by the f o l l o w i n g e q u a t i o n  i l l (*) where  i K  =  Sl\-z)  k _  ^  ..  2  Tr CT  110  = - Jiic-^)  A l s o  so t h a t below the sheet the f i e l d and the t o t a l f i e l d  i s g i v e n by  there i s :  Hence V  and the amplitude  -fc- +. 43  a*" 2  CO  1  /  of the f i e l d v a r i a t i o n s below the sheet i s  reduced to a f r a c t i o n  of  2  TT  the e x t e r n a l f i e l d .  7\  I t i s reasonable to suppose t h a t s p h e r i c a l  harmonics up to the t e n t h degree are s u f f i c i e n t to d e s c r i b e the f i e l d of a bay type d i s t u r b a n c e i n mid l a t i t u d e s . set  an upper l i m i t on the value of A  Hence one  and a c o r r e s p o n d i n g  l i m i t on the a t t e n u a t i o n of the e x t e r n a l f i e l d  lower  as i t passes  through a l a y e r of ocean, three k i l o m e t e r s t h i c k , i n the of Vancouver I s l a n d .  S e t t i n g the s p a t i a l wavelength  vicinity equal  2tr/h  -8  to 2TTR/IO where R i s the e a r t h ' s r a d i u s g i v e s  can  A-  _,  '-£>x/0  c»m  Assuming t h a t the c o n d u c t i v i t y K of sea water i s 4 x 10 - - emu, -  the c o r r e s p o n d i n g harmonic of the i n c i d e n t f i e l d w i l l  be  1  1  reduced  beneath the oceanic l a y e r to ten percent of i t s value above the  33  ocean, f o r v a r i a t i o n s w i t h a p e r i o d of f o r t y - f i v e minutes. c a l c u l a t i o n i s , however, u n r e a l i s t i c  This  i n that i t n e g l e c t s the  e f f e c t of a p o s s i b l e h i g h l y conducting r e g i o n i n the upper mantle beneath the ocean.  A l s o , we are not e n t i r e l y j u s t i f i e d In  assuming t h a t the source of the magnetic v a r i a t i o n s i s a s t a t i o n ary e l e c t r i c c u r r e n t s i n c e there  system v a r y i n g p e r i o d i c a l l y w i t h time,  i s now reason t o b e l i e v e  (Rostoker, p r i v a t e communi-  c a t i o n ) t h a t the system i s q u i t e l i k e l y to d r i f t earth's 5.  r e l a t i v e t o the  s u r f a c e g i v i n g the source f i e l d a t r a v e l l i n g wave n a t u r e .  The E f f e c t of the Conducting Mantle on E l e c t r i c C u r r e n t s i n the Oceans There i s a r a p i d i n c r e a s e  i n e l e c t r i c a l c o n d u c t i v i t y i n the  v i c i n i t y of the upper mantle which may be represented c a l l y by a h i g h l y c o n d u c t i n g core  i n the e a r t h ' s  theoreti-  interior.  E l e c t r i c c u r r e n t s which are induced there are r e s p o n s i b l e f o r magnetic f i e l d s which suppress the i n d u c t i o n of c u r r e n t s surface  layers.  Therefore,  i n the  i f the conducting r e g i o n begins a t a  shallow depth, as might be expected beneath the oceans, mutual i n d u c t i o n w i l l reduce both the I n t e n s i t y of the oceanic sheet and i t s s h i e l d i n g e f f e c t on the l a y e r s below.  current  34  III A  EXPERIMENTAL PROCEDURE Askanla V a r i o g r a p h s The Askanla v a r i o g r a p h i s a p o r t a b l e Instrument  consisting  of three variometer u n i t s f o r r e c o r d i n g the d e c l i n a t i o n D,  the  h o r i z o n t a l i n t e n s i t y H and the v e r t i c a l i n t e n s i t y Z, and a d e v i c e f o r r e c o r d i n g time marks, the temperature The  and a base l i n e .  instrument i s housed i n a heat i n s u l a t e d case and a h e a t e r  and thermostat are p r o v i d e d t o keep the i n s i d e temperature a constant l e v e l .  The  suspension f i b r e s c a r r y i n g the magnet  systems can a l l be a d j u s t e d f o r complete i n case temperature  at  temperature  f l u c t u a t i o n s are p e r m i t t e d by the  S c a l e v a l u e s f o r the three systems are determined known c u r r e n t through Helmholtz and n o t i n g the d e f l e c t i o n .  compensation, thermostat.  by p a s s i n g a  c o i l s mounted on each  variometer  Movements of the systems are  recorded by an o p t i c a l system on photographic paper which i s advanced by a 50c/s synchronous  motor d r i v e .  The d r i v e  operated  p o o r l y on 60 c y c l e l i n e power, c a u s i n g a number of r e c o r d s to be l o s t .  The  photographic  r e c o r d i n g magazine h o l d s a ten meter r o l l of r e c o r d i n g paper which l a s t s f o r about twenty days  o p e r a t i n g at a speed of 24m.m./hour. B  I n s t a l l a t i o n and Maintenance of the V a r i o g r a p h s The instruments, with the e x c e p t i o n of the Westham I s l a n d  v a r i o g r a p h , were l o c a t e d i n d o o r s i n reasonably non-magnetic b u i l d i n g s where 60 c y c l e , 110-115 v o l t power was  available.  The T o f i n o and A b b o t s f o r d s t a t i o n s were operated with the  35  a s s i s t a n c e of the Department of T r a n s p o r t p e r s o n n e l  and  the  F r a n k l i n R i v e r s t a t i o n was  housed i n a b u i l d i n g p r o v i d e d by  c o u r t e s y of the MacMillan,  B l o e d e l and Powell R i v e r Company.  The  instrument  on Westham I s l a n d was  the  l o c a t e d i n a plywood  s h e l t e r at the R.C.A.F. t e l e m e t r y s t a t i o n .  A l l the  sites  were checked with a p o r t a b l e B a r r l n g e r 6M-102 p r o t o n p r e c e s s i o n magnetometer, and o n l y those with low  s p a t i a l g r a d i e n t s (< 5 K  per meter) were used. The  ,  chronometers which p r o v i d e d the h o u r l y time marks  were set w i t h i n a few  seconds by W.W.V. short wave time  signals.  Records were a l s o kept of the g a i n and l o s s of each chronometer so t h a t c o r r e c t i o n s c o u l d be a p p l i e d to the time marks i n the event of  of an e r r o r g r e a t e r than one minute.  a l l three components was  graphic f i l m used i n the C  Confidence The  A c a l i b r a t i o n check  c a r r i e d out f o r each r o l l of photo-  variographs.  Limits  Helmholtz c o i l f a c t o r s used i n the c a l i b r a t i o n of the  instruments  are accurate to ±1$.  The magnetometer d e f l e c t i o n  caused by c a l i b r a t i n g c u r r e n t s can be measured to w i t h i n about ±0.3m.m., i . e . about ±1$ of the d e f l e c t i o n . include:  the meter c a l i b r a t i o n  Unknown f a c t o r s  (probably b e t t e r than  *1#);  n o n - l i n e a r i t i e s i n d e f l e c t i o n of the order of 1$ over the range of  the magnetogram; i n a c c u r a t e meter r e a d i n g under  f i e l d c o n d i t i o n s (probably under 1%).  The  difficult  o v e r a l l accuracy  magnetogram f e a t u r e s should, t h e r e f o r e , be b e t t e r than -3 to For the purpose of t h i s survey,  the i n s t r u m e n t a l  confidence  of 5$.  36  l i m i t s have been a r b i t r a r i l y set at 5%, amplitute recorded at d i f f e r e n t  i.e. differences i n  s t a t i o n s are c o n s i d e r e d  ( i n s t r u m e n t a l l y ) s i g n i f i c a n t o n l y i f they exceed D  5$.  P r o c e s s i n g of Records The  photographic  changed approximately  r e c o r d i n g paper i n the v a r i o g r a p h s once every two weeks and d e v e l o p i n g  done u s i n g f a c i l i t i e s a t the V i c t o r i a Geomagnetic Data f o r the F o u r i e r A n a l y s i s of bays was  was was  Observatory.  o b t a i n e d from the  r e c o r d s (as shown below) by marking o f f each of the three components at 2.5 a  minute i n t e r v a l s and d i g i t i z i n g by means of  template.  i i i i i i l i i i m m i i m i ! HIIIMIIIIIIIIIIIIIIII IIIIIIIIIIIIIIIIIIIIMI  T h i s s p a c i n g a l l o w s the c a l c u l a t i o n of F o u r i e r c o e f f i c i e n t s f o r f r e q u e n c i e s up to s i x c y c l e s per hour.  D a l l y v a r i a t i o n s were  analyzed by d i g i t i z i n g the r e c o r d s at twenty minute  intervals.  37  IV A  METHOD OP ANALYSIS Fourier The  Analysis  a n a l y s i s i s based on the c a l c u l a t i o n o f the s p e c t r a l  d e n s i t i e s o f each o f the three components D,H, Z of a p a r t i c u l a r magnetic d i s t u r b a n c e .  A digital  computer program based on  Simpson's i n t e r p o l a t i o n r u l e f u r n i s h e d the F o u r i e r components for  each o f s e v e r a l bay type magnetic d i s t u r b a n c e s  f o r frequen-  c i e s from .001 c y c l e s p e r minute t o .061 c y c l e s p e r minute. I d e a l l y , a s p e c t r a l a n a l y s i s allows each o f the t h r e e dependent components D, H, Z o f a d i s t u r b a n c e as a sum o f simple harmonic time + 00  t o be expressed  functions +oo  r  fit)  time  r  sin u>t dui  B(co)  ft (CJ) Cos c j t d w r f  = J  -00 where the frequency f u n c t i o n s and  cosine  and f\ (,ui)  B(w)  a r e the sine  s p e c t r a l d e n s i t i e s ( d e f i n e d i n Appendix 1 1 ) .  Since  Maxwell's f i e l d e q u a t i o n s a r e l i n e a r , each o f the F o u r i e r components  $Jit) °  r  where  =  ftott) = C(OJ) =  f\(u>)clu>  cosojt+  C ( ^ ) d c o Cos ((A  / A(w)* + Bi^f  a  n  S i n cot  - e-J) 1^  d  B(<o)du  =  may be t r e a t e d s e p a r a t e l y as l i n e a r l y p o l a r i z e d harmonic waves of f r e q u e n c y to I n c i d e n t  on the e a r t h ' s  p r i n c i p l e of s u p e r p o s i t i o n a p p l i e d . cosine  spectral densities  s u r f a c e , and then the  Henceforth, the sine and w i l l be used i n p l a c e  of the F o u r i e r c o e f f i c i e n t s B(co)dto , A(co)dto and the amplitudes  38  of the harmonic waves. a frequencyco)  T h e r e f o r e , the F o u r i e r component (at  of the t o t a l magnetic d i s t u r b a n c e at the e a r t h ' s  s u r f a c e can be w r i t t e n as the v e c t o r sum  of three  orthogonal  harmonic terms  F^Ot) = j C C^')cos('wt-£ )4._J.CH( )cos(tj-fc-g )+k w  2  H  2  C Mcos(wt-£ ) D  B  i n the d i r e c t i o n s of the t h r e e geomagnetic components Z, H, The  c o r r e s p o n d i n g e x t e r n a l Inducing d i s t u r b a n c e i s an  c a l l y p o l a r i z e d harmonic o s c i l l a t i o n of frequency p a r a l l e l t o the e a r t h ' s s u r f a c e , comprised oscillations  i n a plane harmonic  i n the D and H d i r e c t i o n s .  F o r a two of  ellipti-  to  of l i n e a r  D.  dimensional anomalous zone, the anomalous p a r t  the v e r t i c a l magnetic d i s t u r b a n c e z  A  at the e a r t h ' s s u r f a c e  i s c o r r e l a t e d w i t h the component of the h o r i z o n t a l d i s t u r b a n c e p e r p e n d i c u l a r t o the s t r i k e H  Thus  where  of the zone, denoted by  S.  39 The  l i n e a r h o r i z o n t a l disturbance  S c o n s i s t s of p a r t s of both  e x t e r n a l and i n t e r n a l o r i g i n and may i t s e l f c o n t a i n an anomal o u s p a r t v a r y i n g with d i s t a n c e from the anomalous zone.  If  the assumption o f two d i m e n s i o n a l i t y i s not j u s t i f i e d , the approximate magnitude of the h o r i z o n t a l d i s t u r b a n c e  i s given by  A study of the s p a t i a l dependence and frequency dependence of the q u a n t i t i e s Z , S, Z /S and ftp p e r m i t s a l i m i t i n g A  of the depth and extent B  estimate  of the c o n d u c t i v i t y anomaly.  P o l a r Diagrams P o l a r diagrams p r o v i d e  a means of t e s t i n g a p o s s i b l e  c o r r e l a t i o n between the v e r t i c a l v a r i a t i o n s and the component of the h o r i z o n t a l v a r i a t i o n s i n a p a r t i c u l a r d i r e c t i o n ( P a r k i n son (23) ).  The upper c i r c l e of the diagram i s used t o p l o t  p o i n t s corresponding  t o a change with an upward v e r t i c a l com-  ponent and the lower c i r c l e f o r a change with a downward v e r t i c a l component.  The p o i n t s a r e p l o t t e d as i n a Schmidt  equal area p r o j e c t i o n , the r a d i a l d i s t a n c e of each p o i n t from the c e n t r e depending on the r a t i o of the v e r t i c a l change t o the h o r i z o n t a l change and the asimuthal  angle ^  o f each p o i n t  depending on the geographic d i r e c t i o n of the h o r i z o n t a l change. A p o i n t a t the c e n t r e of the diagram r e p r e s e n t s the magnetic f i e l d i n a v e r t i c a l  direction.  a change i n  40  Figure 3  Method of P l o t t i n g a P o l a r Diagram  A F o u r i e r A n a l y s i s breaks down a magnetic d i s t u r b a n c e i n t o in-phase and out-of-phase s i n u s o i d a l o s c i l l a t i o n s of the form  Z ^ ( t ) = R ( c o ) c o s o t + B ( ^ ) Sin cjt 2  2  The h o r i z o n t a l change at a p a r t i c u l a r frequency regarded as the sum the  form  5 ^  of two out. of phase l i n e a r o s c i l l a t i o n s of (<o)  =  S f„ (") = s  can be  ( R (w) H  f  Rj^w))  ( B (w)  +  Bj>(w)) Sfnoot  H  cos  41  w i t h asimuthal  d) = rcos  directions  -tan'  r Sin  r e l a t i v e to the  d i r e c t i o n of D.  A » M -—r »  1  •  When the c o n d u c t i v i t y i s  r e l a t i v e l y l a r g e as i t i s i n the oceans, i t seems reasonable to  assume t h a t t h e r e i s in-phase  t h a t one  is justified  induction (Hyndman^)),  i n attempting  the c o r r e s p o n d i n g in-phase  to c o r r e l a t e each of the  S(<*•>)  horizontal linear oscillations  C o s  fl (w) t  , S  s C) w  c o  ponding to the frequency CO . dimensional,  with  A (p)  a  n  d  p o i n t s on the p o l a r diagram B  (w) > Ssin C ) w  t  corres-  i f the anomalous zone i s two  the p o i n t s from the F o u r i e r A n a l y s i s of a number  of d i s t u r b a n c e s w i l l be s c a t t e r e d a l o n g a great c i r c l e which w i l l be  and  z  Hence, the F o u r i e r a n a l y s i s of  one magnetic d i s t u r b a n c e y i e l d s two d e f i n e d by  (w)  and  vertical oscillations  on a p o l a r diagram.  s o  symmetrical  about the d i r e c t i o n of best  p e r p e n d i c u l a r to »the s t r i k e of the anomalous zone. t i o n at each s t a t i o n can then be expressed c o e f f i c i e n t C = Z/S.  The  by the  ( F i g . 3) correlation,  The  correla-  Induction  s c a t t e r of the p o i n t s which may  vary  w i t h frequency w i l l be enhanced I f there i s any out of phase I n d u c t i o n and i f the i n d u c i n g wave c o n t a i n s too l a r g e an  42  uncompensated v e r t i c a l component.  I n such cases, the d i r e c t i o n a l  dependence, i n d i c a t e d by the p o s i t i o n of the great c i r c l e on the diagram, may become obscured  and no i n d u c t i o n c o e f f i c i e n t  can be d e f i n e d f o r the s t a t i o n . C  S t a t i s t i c a l Analysis  1.  The P r e c i s i o n of a Mean Value The mean value of a geomagnetic v a r i a b l e ,  such as Z, at  a p a r t i c u l a r s t a t i o n can be estimated by sampling of geomagnetic d i s t u r b a n c e s .  a number  The p r e c i s i o n of the mean value  o b t a i n e d from such a sample of n d i s t u r b a n c e s as an estimate of the l o n g term mean value i s g i v e n by the standard e r r o r S.E.  =  *VV""  w h e r e  l  s  l o n g s e r i e s of o b s e r v a t i o n s . can approximate  so t h a t the  The  tf"  t  n  e  standard d e v i a t i o n o f a  Using data from one sample, we  by  y  ~  _  z  S.E. =  probable e r r o r P.E. o f a mean value i s d e f i n e d as the value  of the d e v i a t i o n from the t r u e l o n g term.mean which, i n a normal d i s t r i b u t i o n , w i l l be exceeded on h a l f the o c c a s i o n s P.E.  The  = 0.6745 (S.E.)  probable accuracy of a l l the mean v a l u e s c a l c u l a t e d i n  43  t h i s t h e s i s a r e g i v e n i n terms of the probable 2.  e r r o r P.E.  The S i g n i f i c a n c e of a Mean Value "Students"  t t e s t p r o v i d e s a method f o r t e s t i n g whether  a sample mean Z d i f f e r s s i g n i f i c a n t l y from some p o s t u l a t e d value Z", assuming t h a t the long-term d i s t r i b u t i o n of v a l u e s of Z i s n e a r l y normal.  The value o f t i s d e f i n e d by t = 2-Z' S.E.  and Student" has c a l c u l a t e d the p r o b a b i l i t y of exceeding any value of t d e r i v e d from a random sample of n events.  Adopting  a c o n f i d e n c e l e v e l of twenty percent r e q u i r e s t h a t the c a l c u l a t e d value of t be s m a l l e r than t h a t value which has a one i n f i v e chance of o c c u r i n g i n any random sample;  otherwise  the data shows a s i g n i f i c a n t d e v i a t i o n from the p o s t u l a t e d mean value and a new mean value must be sought.  F i g u r e 4. L o c a t i o n Map  Showing S i t e s of Recording S t a t i o n s  45  V  RESULTS AND The  ANALYSIS.  s i t e s of the  i n F i g . 4.  s t a t i o n s used i n the a n a l y s i s are shown  T o f i n o , F r a n k l i n R i v e r , Westham I s l a n d and  f o r d were occupied by Askania v a r i o g r a p h s . manent magnetic o b s e r v a t o r y . and  Westham I s l a n d )  overlap  Two  V i c t o r i a i s a per-  of these s t a t i o n s  (Abbotsford  the p r o f i l e recorded by Hyndman^ ^) . 1  Hyndman's a n a l y s i s showed that the amplitude of the i n both the h o r i z o n t a l and  Abbots-  v e r t i c a l components was  variations essentially  constant from Westham I s l a n d as f a r i n l a n d as Grand F o r k s (longtitude l l 8 ° 3 0 « ) .  T h i s means that Abbotsford and  I s l a n d can be used as r e p r e s e n t a t i v e  Westham  inland stations.  A p a r t i c u l a r example of a geomagnetic d i s t u r b a n c e , s i m u l t a n e o u s l y at T o f i n o  and V i c t o r i a on Jan.  shown i n F i g . 5 where the Z, drawn to the  same s c a l e .  H and  A two  10th,  recorded  1964,  is  D components have been r e -  to one  enhancement i n the  ver-  t i c a l component at T o f i n o as compared to V i c t o r i a shows up  clearly,  whereas the H and  This  disturbance and  z  d i g i t i z e d at two  a F o u r i e r a n a l y s i s was  at the f\  was  D components are e s s e n t i a l l y i d e n t i c a l .  two  (w)  and  stations.  The  and  one  c a r r i e d out sine and  h a l f minute i n t e r v a l s  on the v e r t i c a l component  cosine  frequency range from .001 minute ( F i g s . 6 , 7 ) .  Z  to one  T o f i n o v a l u e s over V i c t o r i a v a l u e s c o v e r i n g  ( F i g . 7)  C ({S)  the amplitude s p e c t r a l d e n s i t i e s  as a f u n c t i o n of frequency showing a two  B ("),  spectral densities  enhancement of  .061  A p l o t of the r a t i o C ( a > ) z  were p l o t t e d  v i r t u a l l y the  c y c l e s per minute to  z  T 0 F I N 0  entire  cycles  per  / C (w) z  V I C T  g i v e s a b e t t e r i n d i c a t i o n of the frequency dependence  ^  46 of the T o f i n o anomaly and shows a peak a t .036 c y c l e s per minute ( p e r i o d ~ 30 min.) w i t h another s m a l l e r peak a t .053 c y c l e s per minute ( p e r i o d ^ 20 min.).  3  Figure 6  A Comparison of the Sine and Cosine S p e c t r a l D e n s i t i e s of the V e r t i c a l Component of the Disturbance Recorded at T o f i n o and V i c t o r i a on January 10,  1964  o— 1  1  .001  .013  .007  .019  .025  FREQUENCY F i g u r e 7 A Comparison F i g u r e (. J o  m  p  o  i  i  e  n  t  Q  f  January 10,  t  IN  .031  CYCLES  PER  .037 MINUTE  of the Amplitude S p e c t r a l D e n s i t i e s of the V e r t i c a l t u r b a n c e Recorded a t T o f i n o and V i c t o r i a on  h  e  D i s  1964  4  A  9  D i r e c t i o n a l Dependence of the Anomaly Nine bay  type d i s t u r b a n c e s were recorded  c o v e r i n g the p e r i o d Jan. 10th A n a l y s i s was  to J u l y 3 r d ,  and  1964.  digitized, A Fourier  c a r r i e d out f o r each of the three components Z,  H,  D at a l l the s t a t i o n s o p e r a t i n g at the time of each  disturbance.  One  stations  representative disturbance  f o r each of the f i v e  was  then chosen i n order to l o o k f o r a p o s s i b l e c o r r e l a t i o n between the v e r t i c a l and h o r i z o n t a l v a r i a t i o n s . D s i n e and  A p l o t of the Z, H  c o s i n e s p e c t r a l d e n s i t i e s f o r the f i v e  and  s t a t i o n s shows  a c o r r e l a t i o n mostly between the Z and D components, becoming most pronounced at T o f i n o over the frequency two  c y c l e s per hour ( F i g s . 8 to  obtained  i n the form of  P o i n t s r e p r e s e n t i n g magnetic v a r i a t i o n s  w i t h f r e q u e n c i e s between one  and  two  c y c l e s per hour were d e r i v e d  from the s p e c t r a l d e n s i t i e s of s i x magnetic d i s t u r b a n c e s at  Tofino.  to  12).  A c o n f i r m a t i o n of t h i s r e s u l t was a p o l a r diagram ( F i g . 13)•  range from one  They show a tendency f o r the f i e l d  recorded  to change upward  when I t changes to the west and downward when i t changes to the east.  When the d i r e c t i o n of the h o r i z o n t a l change i s n o r t h  south,  very l i t t l e  v e r t i c a l v a r i a t i o n occurs.  Although there  o n l y a l i m i t e d number of p o i n t s , a c o r r e l a t i o n i n an east-west d i r e c t i o n i s i n d i c a t e d . sented  The  change v e c t o r s  zontal, corresponding  of about 30°  to the  repreinclined hori-  to an i n d u c t i o n c o e f f i c i e n t C = Z/S  Points representing f i e l d  are  approximately  on t h e " p o l a r diagram are s c a t t e r e d about a plane  upward towards the west at an angle  or  changes w i t h f r e q u e n c i e s o u t s i d e  of  0.5.  the  05  1000,-  COSINE  TERMS  co UJ  <  CO UJ CO  ro  •z. UJ Q  < cr io  UJ Q_ CO  -1600  .01  02  D3  04  05  FREQUENCY  .06 IN  CYCLES  .01 PER  .02  .03  .04  .05  .06  .07  MINUTE  F i g u r e 10 Sine and Cosine S p e c t r a l D e n s i t i e s of the D, H and Z Components f o r Magnetic Disturbance Recorded at- F r a n k l i n R i v e r on J u l y 3* 1964  900  COSINE  SINE TERMS  r  TERMS  600h co  UJ  300  I  < < CO LU  c  -300h VJ1  to  -600h  co UJ Q  < CC 1o UJ CL CO  -900H  -1200  -1500 -I800  L  .01  .02  .03  .04  .05  FREQUENCY  .06 IN  CYCLES  PER  MINUTE  Pifiu-e I I Sine and Cosine S p e c t r a l D e n s i t i e s of the D, H and Z components f o r F i g u r e i i Magnetic Disturbance Recorded a t Westham I s l a n d on March 5, 1964  SINE  COSINE TERMS  TERMS  VJl  "02  03  04  05  FREQUENCY F i g u r e 12  06 IN  '-*0i CYCLES  PER  02  03  04  05  06  MINUTE  Sine and Cosine S p e c t r a l D e n s i t i e s of the D H, and Z Components f o r Magnetic- Disturbance Recorded a t Abbotsford on June 11 1964 ?  s  1)7  59  range one  to two  c y c l e s per hour, not  i n c l u d e d on t h i s p o l a r  diagram, d e v i a t e d c o n s i d e r a b l y from t h i s p a t t e r n , I n d i c a t i n g that the c o a s t a l anomaly i s most c l e a r l y d e f i n e d i n t h i s frequency range. The  Z, H and D s i n e and  cosine  spectral d e n s i t i e s f o r Tofino  at a frequency of about three c y c l e s per hour show t h a t the  Z  component i s not c o r r e l a t e d with the D or H component alone  but  probably  with a combination of both.  A p o l a r diagram p l o t t e d  f o r T o f i n o at the h i g h e r frequency shows a c o r r e l a t i o n i n a north-east,  south-west d i r e c t i o n approximately p e r p e n d i c u l a r  the Vancouver I s l a n d c o a s t l i n e , but  to  the s c a t t e r i n the p o i n t s i s  g r e a t e r than at the lower f r e q u e n c i e s making i t d i f f i c u l t  to  d e f i n e a p r e f e r r e d plane ( F i g . 14). P o l a r diagrams p l o t t e d f o r V i c t o r i a were based on the  same magnetic d i s t u r b a n c e s  T o f i n o diagrams.  The  essentially  t h a t were u t i l i z e d i n the  c o r r e l a t i o n at f r e q u e n c i e s  of one  to  c y c l e s per hour at V i c t o r i a appears to be more n o r t h - e a s t ,  two south-  west r a t h e r than east-west as at T o f i n o with a great d e a l more s c a t t e r than on the corresponding  T o f i n o diagram ( F i g . 15)°  At  a frequency of three c y c l e s per hour the c o r r e l a t i o n i s not clear B  (Fig„  16)„  S p a t i a l Dependence of the Anomaly The  s t a t i o n s occupied  along the east west p r o f i l e  provided  a means of measuring t h e , c o a s t a l anomaly at d i s t a n c e s of 50, 240,  and  300km„ e a s t of the one  coast of Vancouver I s l a n d .  The  120,  hundred fathom l i n e o f f the west s p a t i a l dependence i s best  studied  60  by a n a l y z i n g magnetic d i s t u r b a n c e s recorded s t a t i o n s on the p r o f i l e . recorded  o n l y at two  frequent instrument  simultaneously  However, each magnetic d i s t u r b a n c e  was  or t h r e e of the s t a t i o n s , because of failures,  mainly  i n the d r i v e u n i t ,  l o c a l a r t i f i c i a l d i s t u r b a n c e s at the T o f i n o s t a t i o n . the two  at a l l  and  In a d d i t i o n ,  s t a t i o n s at the e a s t e r n end of the p r o f i l e were at no  time occupied  simultaneously.  Thus, comparisons of the  and h o r i z o n t a l v a r i a t i o n s between two  s t a t i o n s on the  vertical  profile  c o u l d sometimes be made o n l y I n d i r e c t l y with r e f e r e n c e to the Victoria 1.  station.  V a r i a t i o n s with a P e r i o d of F o r t y F i v e Minutes The  v e r t i c a l v a r i a t i o n s , z, at t h i s p e r i o d are  apparently  c o r r e l a t e d with the component of the h o r i z o n t a l d i s t u r b a n c e i n an east-west d i r e c t i o n , S. d i s t a n c e along the p r o f i l e of  the anomaly.  The  A study of the change of Z and i l l u s t r a t e s the s p a t i a l  amplitude  z  h o r i z o n t a l v a r i a t i o n S i s d e f i n e d u s i n g the W  H  dependence  s p e c t r a l d e n s i t i e s C (a>) represent  the v e r t i c a l v a r i a t i o n , Z, at each frequency to  spectral densities A ( ) ,  S with  B H ^ ) * A^O )  the east-west  sine and A N D  0  and  (H)  cosine of the  H and D components. Vertical  Component  Amplitude s p e c t r a l d e n s i t i e s , C (OJ) .023 and  f  at f r e q u e n c i e s of  .021,  .025 c y c l e s per minute r e p r e s e n t v a r i a t i o n s with a p e r i o d  of approximately along the p r o f i l e  f o r t y f i v e minutes.  A comparison of  at these f r e q u e n c i e s , f o r the same magnetic  d i s t u r b a n c e , f u r n i s h e s a f a i r l y c o n s i s t e n t p a t t e r n (Table 6 ) .  61  For the s i x magnetic f e a t u r e s s t u d i e d , the v a l u e s of' Z decrease from T o f i n o t o the Westham I s l a n d and Abbotsford  s t a t i o n s , the  value at T o f i n o b e i n g as much as one hundred p e r c e n t — l a r g e r than at Westham I s l a n d .  A mean value of Z was c a l c u l a t e d f o r each  s t a t i o n by n o r m a l i z i n g the v e r t i c a l component of each d i s t u r b a n c e by the c o r r e s p o n d i n g v e r t i c a l component at A b b o t s f o r d  (Table 2 ) .  ( i n some cases t h i s was c a l c u l a t e d i n d i r e c t l y by comparison w i t h V i c t o r i a values.)  T h i s mean value of Z decreases  s t e e p l y from  T o f i n o to F r a n k l i n R i v e r and then l e s s s t e e p l y towards the r e p r e s e n t a t i v e i n l a n d s t a t i o n s of Westham I s l a n d and Abbotsford (Fig. 19),  the l a t t e r s t a t i o n s b e i n g e q u i v a l e n t I f a confidence  l e v e l of twenty percent i s accepted.  An  important  point i s that  the T o f i n o anomaly d i m i n i s h e s t o l e s s than h a l f i t s value  over  the 70 k i l o m e t e r d i s t a n c e from T o f i n o to F r a n k l i n R i v e r .  On the  average V i c t o r i a values do not d i f f e r ford  s i g n i f i c a n t l y from Abbots-  values.  H o r i z o n t a l Components The  component of the h o r i z o n t a l v a r i a t i o n In an east-west  direction, decreases  S, a t a p e r i o d of f o r t y f i v e minutes, i n g e n e r a l coastward  w i t h the e x c e p t i o n t h a t I n some cases Frank-  l i n R i v e r has a s l i g h t l y s m a l l e r value than T o f i n o (Table 6 ) . The  value of S a t T o f i n o , however, I s c o n s i s t e n t l y about f i v e to  t e n percent  s m a l l e r than a t Westham I s l a n d .  With r e f e r e n c e t o  Abbotsford a mean value of S was c a l c u l a t e d f o r each s t a t i o n with a probable e r r o r o f t h r e e percent  (Table 2 ) .  percent i n the mean value of S from Abbotsford  The decrease to T o f i n o i s  of t e n  62  c o n s i s t e n t w i t h the expected A u r o r a l Zone.  decrease w i t h d i s t a n c e from  the  I f the source of geomagnetic bays i s assumed to  be a l i n e a r c u r r e n t approximately  2000km. from the p r o f i l e ,  the  h o r i z o n t a l component f a l l s o f f i n i n v e r s e r a t i o to the square the d i s t a n c e from the source  and hence  d  S  (Van'yan and  _ ^  =  d  r  =  _ S  of  Kharin(52)y  2± r  3  r  T o f i n o i s about 100 k i l o m e t e r s f u r t h e r from the A u r o r a l Zone than Abbotsford,  so t h a t  dS 5  „2dr  =  -2  r  Thus, a decrease independent  =  ( »00) 2000  of ten percent i n the value of S i s expected,  of an i n t e r n a l anomaly.  s i d e r a t i o n s , no anomaly i s apparent The  Induction C o e f f i c i e n t The  -0.1  a  In the l i g h t of these  i n the h o r i z o n t a l component.  Z/S  c o r r e l a t i o n e x h i b i t e d by the T o f i n o p o l a r diagram f o r  f r e q u e n c i e s between one and two  c y c l e s per hour j u s t i f i e s  c a l c u l a t i o n of an i n d u c t i o n c o e f f i c i e n t C = Z/S f o r t y - f i v e minutes. i s 0.5  i  con-  The mean of the Z/S  the  at a p e r i o d of  r a t i o s g i v e n i n (Table 6)  .03 which i s c o n s i s t e n t with the 30° t i l t  of the p r e f e r r e d  plane on the p o l a r diagram and comparable to the v a l u e s obtained (25)  by P a r k i n s o n 2.  x  ' i n Australia.  V a r i a t i o n s with a P e r i o d of Twenty Minutes The s c a t t e r of the T o f i n o p o l a r diagram at a frequency of  63  three c y c l e s per hour i s too great to j u s t i f y c o r r e l a t i n g  the  v e r t i c a l v a r i a t i o n s with a h o r i z o n t a l d i s t u r b a n c e v e c t o r i n a particular  direction.  V e r t i c a l Component Amplitude s p e c t r a l d e n s i t i e s .049,  .051,  and  .053  C (co) at f r e q u e n c i e s of  .047,  c y c l e s per minute were used to r e p r e s e n t  v a r i a t i o n s w i t h a p e r i o d of approximately  twenty minutes.  The  v e r t i c a l component at T o f i n o i s t y p i c a l l y l a r g e r than at F r a n k l i n R i v e r but, Instead of there b e i n g a smooth t r e n d to s m a l l e r values f u r t h e r i n l a n d , v a l u e s a t V i c t o r i a , Westham I s l a n d and Abbotsford are In g e n e r a l l a r g e r than at F r a n k l i n R i v e r , but u s u a l l y not frequency was  so l a r g e as a t T o f i n o (Table 5 ) .  As at the  lower  a mean value of Z, based on e i g h t magnetic f e a t u r e s ,  c a l c u l a t e d f o r each s t a t i o n r e l a t i v e to  Abbotsford  v a l u e s (Table 2 ) .  The  corresponding  p l o t of Z as a f u n c t i o n of  d i s t a n c e from the coast shows the T o f i n o anomaly and a l s o  suggests  a v e r t i c a l anomaly i n the r e g i o n of Westham I s l a n d ( F i g . 19)« The  l a r g e r probable  suggested  e r r o r s at t h i s frequency  imply t h a t the  t r e n d s are not as c o n s i s t e n t l y r e p r o d u c i b l e as at the  lower f r e q u e n c i e s .  Nevertheless,  the enhancement of Westham  I s l a n d over Abbotsford which i s absent statistically  at the lower f r e q u e n c i e s i s  s i g n i f i c a n t and most l i k e l y does r e f l e c t a  r e l a t i v e l y shallow c o n d u c t i v i t y inhomogeneity„ H o r i z o n t a l Component The  total horizontal variation H  i n l a n d , the amplitudes  t  i s , i n general,  larger  at Westham I s l a n d b e i n g about twenty percent  l a r g e r than at T o f i n o and  the amplitude at F r a n k l i n R i v e r  u s u a l l y from ten to twenty percent  l a r g e r (Table 5 ) .  Here  again,  the h o r i z o n t a l v a r i a t i o n s are expected to d i m i n i s h with i n c r e a s i n g d i s t a n c e from the A u r o r a l Zone. no a p p r e c i a b l e  i n t e r n a l anomaly shows up  component from T o f i n o to C  Hence, we  conclude as b e f o r e ,  i n the h o r i z o n t a l  Abbotsford.  Frequency Dependence of the Anomaly v e r t i c a l amplitude s p e c t r a l d e n s i t i e s , C  The  T o f i n o and F r a n k l i n R i v e r were compared with the v a l u e s at V i c t o r i a  (Table 3 ) .  The  v a l u e s of  d e r i v e d from s i x magnetic d i s t u r b a n c e s  z  (ui)  corresponding  showed a  statistically  ^TOFy/2y  over the e n t i r e range of p e r i o d s from twenty minutes to hours.  The  disturbances over the  values of  .  =  /  three  c  s i g n i f i c a n t l y from a r a t i o of u n i t y  same frequency range, and  a comparison between V i c t o r i a  at these f r e q u e n c i e s based on s i x magnetic  f e a t u r e s showed no  significant difference.  The mean values of  ~Z--^ .^/^vic. QV  p l o t t e d as a f u n c t i o n of p e r i o d and curve  ( C  -ZVf?ft^/ZTy, d e r i v e d from f i v e magnetic  d i d not d e v i a t e  Abbotsford  at  s  ZTOF^/Z!VIC.  s i g n i f i c a n t d e v i a t i o n from a p o s t u l a t e d value  and  that  (Fig. 17).  The  and  Z. p^y/Z^x.  were  the p o i n t s f i t t e d with a smooth  r e s u l t s i n d i c a t e t h a t the anomaly reaches  a maximum at a p e r i o d of t h i r t y minutes to one  hour, a p e r i o d  at which the e f f e c t i v e o v e r a l l c o n d u c t i v i t y c o n t r a s t i s a p p a r e n t l y greatest<, D  D a i l y Geomagnetic V a r i a t i o n s A F o u r i e r a n a l y s i s of s i x t y hours of simultaneous magnetic  65  RATIO OF SPECTRAL DENSITIES AS A FUNCTION OF PERIOD 2.0h 1.8 1.6 1.4 1.2 1.0 0.8  L  F i g u r e 17.  20  30  60 PERIOD IN MINUTES  100 120  180  Frequency Dependence of the T o f i n o Anomaly  4  § 500 co 400 UJ  t  oo 300 LU O  200 _J < cr 100 & UJ Q_ CO  F i g u r e 18.  48  24 18 15 PERIOD IN HOURS  Enhancement of V i c t o r i a over Abbotsford V e r t i c a l Components a t the D i u r n a l and Periods  i n the Semi-Diurnal  66  r e c o r d s at T o f i n o , F r a n k l i n R i v e r , V i c t o r i a ,  and  Abbotsford  y i e l d e d w e l l d e f i n e d peaks at p e r i o d s of twelve  and  hours,  semi d i u r n a l  a l l o w i n g a comparison of the d i u r n a l and  geomagnetic v a r i a t i o n s at these f o u r s t a t i o n s . a n a l y s e s of simultaneous  twenty-four  Additional  r e c o r d s were not p o s s i b l e because of  l o c a l d i s t u r b a n c e s on the T o f i n o r e c o r d s , so t h a t these must be c o n s i d e r e d as p r e l i m i n a r y .  results  There are no c o n v i n c i n g t r e n d s  i n the h o r i z o n t a l components of the semi d i u r n a l  variations,  but there i s a s i x percent i n c r e a s e i n the d i u r n a l h o r i z o n t a l component from Abbotsford  to the coast (Table 4 ) .  v e r t i c a l v a r i a t i o n s f o r both the d i u r n a l and ponents decrease  semi d i u r n a l com-  eastward a l o n g the p r o f i l e T o f i n o , F r a n k l i n  R i v e r , Abbotsford,  the amplitude  including Victoria, at Abbotsford  However, the  of the Vancouver I s l a n d s t a t i o n s ,  b e i n g twenty to t h i r t y percent l a r g e r  than  on the mainland.  The marked d i f f e r e n c e i n the v e r t i c a l d a i l y  variations  between Abbotsford and the more western s t a t i o n s i n d i c a t e d i n the above p r e l i m i n a r y a n a l y s i s had been mentioned i n an  earlier  (16) study by Hyndman  %  .  Consequently,  a more thorough a n a l y s i s  based on one hundred and twenty-six c o n s e c u t i v e hours of simultaneous  magnetic r e c o r d s was  c a r r i e d out i n order to compare  the v e r t i c a l v a r i a t i o n s at the V i c t o r i a The  and Abbotsford  r e s u l t s show a twenty f i v e percent enhancement of  over Abbotsford  Victoria  i n the d i u r n a l v e r t i c a l v a r i a t i o n s , d i m i n i s h i n g  to a t e n percent enhancement i n the semi d i u r n a l variations  stations.  ( F i g . 18)„  Victoria  vertical  does not d i f f e r a p p r e c i a b l y  from Abbotsford at h i g h e r f r e q u e n c i e s .  ;  67  ELEVATION PROFILE  2 I 0  130°  129°  128°  49° 10' , LATITUDE 49° 30  I27°V'I26°.  TbF  IF^^^'AKT  -lh -2 CO  a:  3  UJ  - SEISMIC PROFILE  3 -20  8.1 KM/SEC.  X fc-30  5.9 KM/SEC. V  \  6.8 KM /SEC. \  \  \  LU Q  \  -40  \  -50 1.8 1.6 1.4 1.2  AMPLITUDE OF VERTICAL GEOMAGNETIC VARIATIONS PERIOD — 45 MIN. — 20 MIN.  -I  1.0 0.8 0.6  _L  130'  TOP  129°  I28  c  127*  _»— I26 e  125°  124°  123°  122°  F i g u r e 19. Amplitude of V e r t i c a l V a r i a t i o n s along the East-West P r o f i l e Normalized w i t h Abbotsford V a l u e s ; Compared w i t h an E l e v a t i o n P r o f i l e and a C r u s t a l S t r u c t u r e P r o f i l e (adapted from W.R.H. White and J.C. Savage)  68  E  D i s c u s s i o n of R e s u l t s The  v e r t i c a l anomaly a t T o f i n o reaches a maximum a t a  frequency between one and two c y c l e s per hour and i s c h a r a c t e r i z e d by an i n d u c t i o n c o e f f i c i e n t o f 0.5.  The p o l a r diagram p l o t t e d f o r  t h i s range of f r e q u e n c i e s suggests a two dimensional c o n d u c t i v i t y d i s c o n t i n u i t y running approximately Although  i n a north-south  direction.  the diagram at a h i g h e r frequency of three c y c l e s per  hour seems t o i n d i c a t e a s h i f t i n the d i r e c t i o n a l dependence (more p e r p e n d i c u l a r t o the c o a s t l i n e ) ,  such a s h i f t cannot be  c o n s i d e r e d s i g n i f i c a n t because of the l i m i t e d number of p o i n t s and the s c a t t e r on the diagrams. the maximum response  I t i s c l e a r , however, that at  frequency the d i r e c t i o n a l dependence i s  c o n s i s t e n t w i t h t h a t expected  at the edge of an oceanic c u r r e n t  sheet and/or above a two dimensional c o n d u c t i v i t y step i n the upper mantle•running shelfline.  approximately p a r a l l e l to the c o n t i n e n t a l  Since the anomaly d i m i n i s h e s to an almost  negligible  value a t a d i s t a n c e of 100 k i l o m e t e r s from the c o a s t l i n e it  i s not expected  ( P i g . 19)  to be caused by a c o n d u c t i v i t y step deeper  than 100 k i l o m e t e r s beneath the s u r f a c e .  Furthermore,  upper s u r f a c e o f the step i s a t a shallow depth,  u n l e s s the  perhaps i n the  v i c i n i t y of the Mohorovicic d i s c o n t i n u i t y , most of the e l e c t r i c c u r r e n t s w i l l flow i n the ocean r a t h e r than i n the mantle beneath. U n t i l one can a c c u r a t e l y measure the e l e c t r i c c u r r e n t s f l o w i n g i n the deep ocean o r the amplitude  of geomagnetic  beneath the oceanic l a y e r , i t i s d i f f i c u l t  variations  to estimate the  c o n t r i b u t i o n of subsurface changes i n c o n d u c t i v i t y at the c o a s t line .  69  The  twenty-five  percent  increase  i n the v e r t i c a l d i u r n a l  v a r i a t i o n s from the mainland to Vancouver I s l a n d must be pendent of s u r f a c e  l a y e r s and  most l i k e l y does r e f l e c t  inde-  some k i n d  of l a t e r a l subsurface change i n c o n d u c t i v i t y deep i n the upper mantle which may  be a s s o c i a t e d with a systematic  difference in  the nature of the upper mantle beneath oceans and The  continents„  p o s s i b l e v e r t i c a l anomaly at three c y c l e s per hour at  Westham I s l a n d may  be due  to a r e l a t i v e l y shallow c o n d u c t i v i t y  inhomogeneity, s i n c e i t i s absent at a lower frequency of one two  c y c l e s per hour.  The  limited  s p a t i a l extent  of the  anomaly r u l e s out mutual i n d u c t i o n between, the P a c i f i c the  sea water i n Georgia S t r a i t , and  the  sea water Is not  f o r longer  than a few  depression  at the  south end  However, the Georgia  and it  e a r l y Cenozoic age  by c l a s t i c  Strait  (White and  Savage(5^)).  to cause a small v e r t i c a l anomaly. ruled  out.  to  sediments of l a t e Mesozoic  r e l a t i v e to the mainland rocks  s u b c r u s t a l source Is not  currents  the mainland i s u n d e r l a i n  Consequently.,  i s at l e a s t p l a u s i b l e to suppose that the o v e r a l l  of the d e p r e s s i o n  Ocean and  of the l a r g e l y submerged c o a s t a l  trough between Vancouver I s l a n d and a depth of f i v e k i l o m e t e r s  coastal  the t o t a l c o n d u c t i v i t y of  l a r g e enough to s u s t a i n e l e c t r i c seconds.  to  conductivity  i s l a r g e enough  A t t h e same time, a deeper ;  70  VI  CONCLUSIONS With r e f e r e n c e  t o P i g . 19 which shows the magnitude and  extent o f the v e r t i c a l anomaly, an e l e v a t i o n p r o f i l e f o r the region,  and a c r u s t a l s t r u c t u r e p r o f i l e based on seismic and  g r a v i t y data (a)  (White and S a v a g e ^ o ) ^ 1  i t i s believed  that:  The major p o r t i o n of the c o a s t a l anomaly a t one t o two  c y c l e s p e r hour i s caused by e l e c t r i c c u r r e n t s  flowing  ocean beyond the c o n t i n e n t a l  there  conductivity contrast  shelfline,  i s a lateral  a t a depth of 100km or l e s s which i s l a r g e  enough t o compete with the c o n t r a s t (b)  unless  i n the  between ocean and c o n t i n e n t .  The extent of the d i u r n a l "anomaly" i s c o n s i s t e n t with a  c o n d u c t i v i t y d i s c o n t i n u i t y deep i n the upper mantle. (c)  The p o s s i b l e Inland  anomaly a t a h i g h e r frequency of three  c y c l e s p e r hour i s so h e a v i l y dependent on shallow t h a t no c o n s i s t e n t model can be  t r e n d s compatible with the l a r g e  postulated.  structure scale  crustal  TABLES APPROX. ELEVATION (FT)  STATION  INSTRUMENT  GEOGRAPHIC LONGITUDE LATITUDE  TOFINO  ASKANIA  125°47'W  49°5'N  40  Dec 16/63 t o J u l y 10/64  FRANKLIN RIVER  ASKANIA  124°48'W  lf9°6'N  100  May 16/64 t o J u l y 10/64  VICTORIA  ASKANIA  123°25'W  48°31'N  600  Sept 1/63 t o May 12/64  VICTORIA  RUSKA  123°25'W  48°31'N  600  Continuous  WESTHAM ISLAND  ASKANIA  123°11'W  49°6'N  10  ABBOTSFORD  ASKANIA  122°21'W  49°1"N  200  Table 1  Nov I / 6 3 t o June 5/64 June 5/64 t o J u l y 12/64  L o c a t i o n and D e t a i l s of the Variograph S t a t i o n s  FREQUENCY .RANGE  .021 C.P.M. t o .025 C.P.M. TOP FRA WES ABB  Z COMPONENT  1.8*0.1  1.1±.04  0.9*.07  1.0  Z COMPONENT  S COMPONENT  0.9*.03  0.9±.02  1.0±.04  1.0  H  Table 2  DURATION OF OBSERVATIONS  t  COMPONENT  .047 C.P.M. t o . 0 5 3 C.P.M. TOF FRA WES  ABB  1.4*0.1  0.80±.08  1.2*0.1  1.0  0.9*.05  1.0*.03  1.1*.09  1.0  VIC  VIC  1.1*0.09  1.0*0.1  Mean Values of V e r t i c a l and H o r i z o n t a l Changes R e l a t i v e t o Abbotsford Values (Based on Nine Magnetic D i s t u r b a n c e s )  FREQUENCY IN CYCLES PER MIN  JAN. 10, 1964 VIC TOF  760  .005  1010  .009  760 860  .017  .023  .033  460 240  .041 .049  150  ]VLARCH 5, 1964 J?OF  420  410  .023 .033 .041  170  100  70  430  360 70  170 50  460  360  2940 400 460 270  220 210  .049  Table 3  4520  2780 350 200  260 160  810 580 370 130 170  540 410 40  300  200  1940  930 69O 250 160  140  80  1720 610 500 170 130 80 70  2740  2540  MAY 27, 1964 TOF FRA VIC  4100  360  2790  680 1050  850 110  4160  2880 400  340  550  520 370  MAY 25, 1964 FRA VIC TOF  .005 .009 .017  VIC  MAY 24, 1964 FRA TOF VIC  1580 560  400 100 90 60  40  2150  530 450 340  80 170  JUNE 19, 1964 FRA VIC  2890  3610  2000  2420 1400 720  560 450  340  90 170  i4o  420  180  3840 2650 1450 750  60  470 240  JUNE 21, 1964 TOF FRA VIC 920  450 230  220 120  130  40  970 550 170  170 90  130  30  1060 066O 1170 170 100  160  40  Comparison of V e r t i c a l Component S p e c t r a l D e n s i t i e s ( i n Gamma-minutes) at T o f i n o , F r a n k l i n R i v e r and V i c t o r i a as a F u n c t i o n of Frequency.  VERTICAL COMPONENT  TOF  FRA  VIC  ABB  DIURNAL SEMI DIURNAL  525 333  490 285  508 290  406 278  876 670  854 679  825  830 687  TOTAL HORIZONTAL COMPONENT DIURNAL SEMI DIURNAL Table 4  648  Comparison of S p e c t r a l D e n s i t i e s f o r the D a i l y V a r i a t i o n s (Based on 60 h r s . of Continuous Records from 1500 U.T. June 19/64 t o 9300 U.T. June 22/64)  .047 CYCLES PER MINUTE DATE OP FEATURE  Z COMPONENT TOP FRA WES  JAN. 10 MARCH 5 MAY 24 APRIL 29 MAY 25 MAY 27 JUNE 21 JUNE 10 JULY 3  140  130 190  270 90 70  150 240  ABB  70  80 180 40  50 50 150 10  VIC* 40  70 160 30  180 10 310 60 50 180  H<_ COMPONENT TOP FRA WES  270 450 90 300 290 150  100 290 180 170 320 100  ABB  VIC*  360  510 130 190  440  120 190  240  180 370 80  290 170 290  Z/H* RATIO TOF FRA WES  0.5 0.3 2.0 0.9 0.3 0.4  1.4 0.8 0.3 0.3 0.5 0.1  ABB  0.2 1.4 0.2 0.4 0.4 0.4  VIC*  0.2 0.1 1.5 0.1 1.3 0.2 0.3 0.6  .049 CYCLES PER MINUTE JAN 10 MARCH 5 MAY 24 APRIL 29 MAY 25 MAY 27 JUNE 21 JUNE 10 JULY 3 Table 5  150 70 170 210 .86  40  170 160 70 30 180 10  70 50 170 20 200  20 210 10 60 170 30  40  40  240  280 230 90 200  140 140  100 250 110 150 360 90  310 220 120 130  270 120 150  240  190  420  80  120 160 350  0.5 0.3 1.9 1.1 0.6 0.3  1.6 0.6 0.6 0.2 0.5 0.1  0.1 1.8 0.1 0.3 0.4 0.3  0.2 0.2 1.5 0.1 0.9 0.3 0.2 0.7  Comparison along the P r o f i l e of the S p e c t r a l D e n s i t i e s ( i n Gamma-minutes) Representing the V e r t i c a l Change Z and the T o t a l H o r i z o n t a l Change H t o g e t h e r w i t h the R a t i o Z/H ( V i c t o r i a Not Included i n the P r o f i l e ) t  t  .051 CYCLES PER MINUTE DATE OP FEATURE  Z COMPONENT TOP FRA WES  JAN 10 MARCH 5 MAY 24 APRIL 29 MAY 25 MAY 27 JUNE 21 JUNE 10 JULY 3  160 50 170 290 100 30  150 240  ABB  60 170 50  80 30 160 10  20 170 20  VIC*  60 7.0 150 50 250 70 40  200  COMPONENT TOP PRA WES  290  140  60  70  240  330 180 100 370 90  170 100  ABB  VIC*  250  180 80  140  140  130 460 80  90 110 340 170 110 310  Z/H TOP  0.5 0.4 2.6 1.2 0.6 0.3  t T  RATIO PRA WES  2.1 0.7 0.5 0.3 0.4 0.1  ABB  VIC* •0.3  0.3 2.1 0.3 0.1 0.4 0.2  0.5 1.7 0.4 0.7 0.4 0.4 0.6  .053 CYCLES PER MINUTE JAN 10 MARCH 5 MAY 24 APRIL 29 MAY 25 MAY 27 JUNE 21 JUNE 10 JULY 3  140  100 90  370 70  40  110 70 100 70 320 30 40  160 10  Table 5 (continued)  60 70  80 60  30 200 10  340 40  50 150  290 260 150 290 210 70  150 350 210 80 290 80  300  140 140  80 370 70  200 260 120 120 350 220  60  250  0.5 0.4 0.6 1.3 0.3 0.6  0.5 0.9 0.2 0.5 0.5 0.2  0.4 0.8 0.5 0.4 0.5 0.1  0.3 0.3 0.7 0.5 1.0 0.2 0.9 0.6  ,021 CYCLES PER MINUTE DATE OP FEATURE JAN 10 MARCH 5 MAY 24 MAY 25 MAY 27 JUNE 21 JUNE 10 JULY 3 .023  840 1100 550 380 210 150  CYCLES  JAN 10 MARCH 5 MAY 24 MAY 25 MAYJ. 27 i. JUNE 21 JUNE 10 JULY 3 .025  Z COMPONENT Tub ERA WES  460 190 90 80 1290 400  600 420  ABB  VIC  *  S COMPONENT TOP FKA WES  ABB  VIC  Z/S RATIO TOP FKA WES  1620 1890 890 1470 760 430 1650  0.6 0.6 0.6 0.3 0.3 0.4  410 410 450 460 100 170 750  1460 1540 1670 1730 1590 860 880 930 820 1110 1160 1160 720 800 720 320 300 360 340 1140 1070 ll80 450 470  0.6 0.5 0.7 0.4 0.3 0.7  390 240 200 710 120 220 390  1390 1280 670 820 640 270  0.6 0.5 0.6 0.9 0.4 0.9  390 560 550 50 50 110 50 1350 1290 390  1500 1970 2060 890 880 920 1450 1450 760 800 410 390 460 1700 1820 490 570  0.5 0.1 0.1 0.2 0.8 0.8  ABB  0 .3 0 •5 0.2 0.7 0.7  VIC  0.2 0.3 0.6 0 0.1 0.1 0.8  PER MINUTE  860 850 580 46o 250 220  450 360 170 170 720 330  400 350 140 680 340  0.5 0.3 0.2 0.6 0.6 0.7  0 .2 0 .4 0.4 0.6 0.7  0.3 0.3 0.6 0.4 0.1 0.5 0.7  CYCLES PER MINUTE  JAN 10 MARCH 5 MAY 24 MAY 25 MAY 27 JUNE 21 JUNE 10 JULY 3 Table 6  840 580 370 760 240 250  250 640 140 210 310 260  240 220 160 240 280  1300 700 74o 800 750 250 490 450  1390 1200 640 660 640 300 280 480 420 410  0.4 0.8 0.2 0.9 0.6 0.6  0 .2 0 .3 0.5 0.5 0.7  Comparison along the P r o f i l e of the S p e c t r a l D e n s i t i e s ( i n Gamma-minutes) Representing the V e r t i c a l Change Z and the H o r i z o n t a l Change i n an E a s t - . West D i r e c t i o n S together with the R a t i o Z/S  0.3 0.2 0.3 1.1 0,2 0.8 0.9  *  76  APPENDIX I 1.  FOURIER ANALYSIS  A f u n c t i o n f ( t ) can be expanded i n any i n t e r v a l  (-T, T)  so l o n g as i t s a t i s f i e s the D i r i c h l e t c o n d i t i o n i n t h e ' i n t e r v a l | f ( t ) | d t converges.  oo -oo  i n a Fourier  OO  Series  -fCt) = i k + 2 .  where  The f u n c t i o n may be developed  -T4  *  ^  ^ « nsi Q  C  o  s  Tfrt 7-  +  r>=i  b„ Sin n u t T  T  and  T  :f to d : J  -T  T  T  f Writing  hir x  ^(x) cos  J  T  -T  I  dac  f (*)  s  ,  n  n  1  r  x  T  -T  dx  T  oo  2ir  rT.  J  >  IT  T  L J  -T  - T  -T  The i n t e r v a l  (-T,T) may be expanded t o (-00,00) by l e t t i n g T - > 00 ,  so that  o and i n the l i m i t  -t-00  +00  ~  fft)  +00  J ifr) cos cox d x ] Coscot + £^  J f (x) sin w j c d x j s i n t o t ]  _oo  -00  -00  The c o s i n e and sine s p e c t r a l d e n s i t i e s  -*  and B(w) are  J  77  d e f i n e d as f o l l o w s : +co A (oo)  =  J _  f  $fc)coso3xdx  -co +00  B(cu) = _L f fez) sfhtoxdx -00  so t h a t  [ ft (co) cos cot + B(co) s i V u t ] d CO  f(t) = -00  2.  The F o u r i e r S e r i e s f o r f ( t ) may a l s o be w r i t t e n i n an  e x p o n e n t i a l form +  ~  -gnirt  Kt) = 2 c e -ot>  n  wh e r e  T  + UVTTZ  I  fa)  e  T  2T  As b e f o r e t h i s reduces t o an i n t e g r a l form i n the l i m i t a s T - » o o  i.e.  - icot C  (co)  e  dco  -oo  where  + 00 1 cox  2TT -00  and  Hence, f ( t ) may be s y n t h e s i z e d by a sum o f terms  •iuit  e  covering  a l l angular frequencies i n the continuous  i n f i n i t e range  These terms have i n f i n i t e s i m a l a m p l i t u d e s  g i v e n by t h e e x p r e s s i o n  (-00,00).  78  | C(w) 1 dco  .  The amplitude d e n s i t y spectrum  not the a c t u a l amplitude c h a r a c t e r i s t i c a characteristic  1 C(u>) |  i s , therefore,  of f ( t ) , but  which shows r e l a t i v e magnitude o n l y .  rather  >  TOFINO  VICTORIA  Recorded March 5,  1964  WESTHAM  0100 to 0300 U.T.  ISLAND  §  VICTORIA  Recorded A p r i l 29, 1964  WESTHAM  0100 t o 0300 U.T.  ISLAND  TOFINO  FRANKLIN  VICTORIA  Recorded May  24,  1964  WESTHAM  0600 to 0900  U.T.  RIVER  ISLAND  TOFINO  FRANKLIN  R e c o r d e d May  25, 1964  RIVER  0800 t o 1100 U.T.  VICTORIA  TOFINO  FRANKLIN  Recorded May 2 7 , 1 9 6 4  VICTORIA  RIVER  0700  t o 1 0 0 0 U.T.  FRANKLIN  RIVER  ABBOTSFORD  VICTORIA  Recorded June 10, 1964  0900 t o 1200 U.T.  TOFINO  Recorded June 21,  "  1964  FRANKLIN  0800 t o 1100  RIVER  U.T.  ABBOTSFORD  F R A N K L I N RIVER  Recorded  July  3,  1964  0700 t o 0900 U . T .  87  REFERENCES  1.  Ashour, A. A., The I n d u c t i o n of E l e c t r i c C u r r e n t s i n a Uniform C i r c u l a r D i s k . Q.J. Mech. Appl. Math., 3, 119 (1950)  2.  Brooks, C.E.P., N. C a r r u t h e r s . , Handbook of S t a t i s t i c a l Methods i n Meteorology. London: H.M.S.O. (1953)  3.  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