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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, University 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 thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1965 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of Bri t i sh Columbia, I agree that the Library shall make i t freely available for reference and study* 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 is 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 Brit ish Columbia, Vancouver 8, Canada Date flPZlL °l ? / ^ g i ABSTRACT Pour portable magnetometer stations were set up at in t e r v a l s of 80 - 100 kilometers along an east-west p r o f i l e running from Tofino on the west coast of Vancouver Island to Abbotsford on the mainland i n order to study the s p a t i a l dependence of the coastal anomaly,, These were supplemented by records from the permanent V i c t o r i a Magnetic Observatory, The Tofino-Abbotsford chain extends and p a r t l y overlaps an e a r l i e r chain of stations set up to search f o r geomagnetic anomalies, along an east-west p r o f i l e from Lethbridge, Alberta to Vancouver, B r i t i s h Columbia, The coastal anomaly recorded at Tofino Is observed exclusively i n the v e r t i c a l component, diminishing rapidly inland and reaching i t s maximum value when the inducing f i e l d changes i n approximately an east-west d i r e c t i o n with a frequency between one and two cycles per hour. The horizontal and v e r t i c a l variations are i n a r a t i o of two to one at the coast which Is i n agreement with induction r a t i o s calculated at coastlines In Au 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 li m i t e d s p a t i a l extent of the anomaly indicate a rather shallow conductivity discontinuity, at most 100 kilometers deep, running approximately p a r a l l e l to the continental s h e l f l i n e . Since at the maximum response frequency the upper mantle beneath the ocean.is l a r g e l y shielded by the overlying wedge of sea water, the anomaly i s thought to be mostly due to the conductivity contrast between the deep ocean and the continent. The diurnal geomagnetic variations I i which pass through the surface layers v i r t u a l l y unattenuated show at l e a s t a twenty f i v e percent enhancement i n the v e r t i c a l component from Abbotsford to Tofino. This anomaly perhaps r e f l e c t s a change i n upper mantle conductivity more accurately than does the higher frequency Tofino anomaly„ At a s t i l l higher frequency of three cycles per hour where the Tofino anomaly i s already reduced, there i s a small anomaly i n the v e r t i c a l component at Westham Island on the east side of Georgia S t r a i t which i s completely absent at lower frequencies,, The influence of a shallow body of sea water such as Georgia S t r a i t i s expected-to be small. Hence t h i s anomaly i s probably due to a conductivity structure beneath the S t r a i t i n the crust or upper mantle. v i i i ACKNOWLEDGEMENTS i I am pleased to acknowledge the invaluable assistance and welcome c r i t i c i s m given by Mr, Bernard Caner, Director of the V i c t o r i a Geomagnetic Observatory. I am also indebted to Professor J„A, Jacobs f o r h i s kind and patient supervision and to Dr, T, Watanabe who provided useful discussion and c r i t i c i s m of the the o r e t i c a l part of t h i s t h e s i s . Many thanks go to Mr. D. Weichert who assisted with the data analysis and to others i n the Department of Geophysics who gave help when i t was needed. The work i n t h i s thesis was p a r t i a l l y supported by the National Research Council. i l l TABLE OF CONTENTS Page I INTRODUCTION 1 A Coastal Geomagnetic Anomalies 1 B Possible Explanations of the Anomalies 3 C Electromagnetic Induction i n the Earth 5 D Theoretical Conductivity Models 6 E Experimental Conductivity Models 10 II THEORY 13 A Natural Geomagnetic Variations 1 3 1„ Normal Variations 13 2. Anomalous Variations 14 3. Separation of the F i e l d into an Internal and an External Part 14 B Induction Analysis 16 1. The General Theory of Induction - 1 6 2» Induction by a Periodic Linear Current i n an I n f i n i t e l y Conducting Half Space 22 C The E f f e c t of an Ocean on Geomagnetic Variations 24 1. Relation between E l e c t r i c Currents and Magnetic F i e l d s In a Thin Uniformly Conducting Sheet 24 2* The Edge E f f e c t of a Current Sheet 29 3. The Free Decay of E l e c t r i c Currents i n the Oceans 31 4„ The Shielding E f f e c t of an Oceanic Layer 31 5, The E f f e c t of the Conducting Mantle on E l e c t r i c Currents i n the Oceans 33 III EXPERIMENTAL PROCEDURE 34 A Askania Variographs 34 B I n s t a l l a t i o n and Maintenance of the Variographs 34 C Confidence Limits 3 5 D Processing of Records 36 IV METHOD OF ANALYSIS 37 A Fourier Analysis 37 iv B Polar Diagrams 3 9 C S t a t i s t i c a l Analysis 4 2 1, The Precision of a Mean Value 4 2 2. The Significance of a Mean Value 4 3 V RESULTS AND ANALYSIS 4 5 A D i r e c t i o n a l Dependence of the Anomaly 4 9 B Sp a t i a l Dependence of the Anomaly 5 9 L Variations with a Period of Forty Pive Minutes 60 2 „ V ariations with a Period of Twenty Minutes 62 C Frequency Dependence of the Anomaly 6 4 D Daily Geomagnetic Variations 64 ' I Discussion of Results 6 8 VI CONCLUSIONS ?0 V FIGURES Page 1. Generalized S e c t i o n Across a Stable C o n t i n e n t a l Margin 3 2. E l e c t r i c Currents 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 Uniformly Conducting Sheet 29 3. Method of P l o t t i n g a P o l a r Diagram 40 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 44 5 . A Comparison of Magnetograms Showing an Enhancement i n the V e r t i c a l Component at Tofino as Compared to V i c t o r i a 46 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 Tofino and V i c t o r i a on January 10, 1964 47 7. A Comparison 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 Component of the Disturbance Recorded at Tofino and V i c t o r i a on January 10, 1964 48 80 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 Tofino on January 10, 1964 50 9 . 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 2 Components f o r Magnetic Disturbance Recorded at V i c t o r i a on January 10, 1964 51 10. Sine and Coaine 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 River on July 3, 1964 52 11. 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 Component© f o r Magnetic Disturbance Recorded at West-h-am Island on March 5, 1964 53 12. 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 Abbotiford en jun§ l l , 1964 54 13• Polar Diagram f o r Tofino at 30 minute to 60 minute P s r i e d i 53 14. Polar Diagram f o r Tofino at 20 minute to 25 minute Ptrieds 56 15. Polar Diagram f o r V i c t o r i a at 30 minute to 60 minute Periods 57 v i Page l6o Polar Diagram f o r V i c t o r i a at 20 minute to 25 minute Periods 5° 17. Frequency Dependence of the Tofino 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 at the Diurnal and Semi-Diurnal Periods 65 19. Amplitude of V e r t i c a l Variations along the East-West P r o f i l e Normalized with Abbotsford Values; Compared with an Elevation P r o f i l e and a Crustal Structure P r o f i l e 67 v i i TABLES Page l o Location and De t a i l s of the Variograph Stations 71 2o Mean Values of V e r t i c a l and Horizontal Changes Relative to Abbotsford values (Based on Nine Magnetic Disturbances) 71 3 8 Comparison of V e r t i c a l Component Spectral Densities ( i n Gamma-minutes) at Tofino, F r a n k l i n River and V i c t o r i a as a Function of Frequency 72 4„ Comparison of Spectral Densities f o r the Daily Variations 72 5o Comparison along the P r o f i l e of the Spectral Densities ( i n Gamma-minutes) Representing the V e r t i c a l Change Z and the Total Horizontal Change H t together with the Ratio z/H t 73 6c Comparison along the P r o f i l e of the Spectral Densities ( i n Gamma-minutes) Representing the V e r t i c a l Change i n an East-West Di r e c t i o n S together with the Ratio Z/S 75 APPENDICES I Fourier Analysis II Magnetograms 76 79 1 I INTRODUCTION A Coastal Geomagnetic Anomalies This thesis i s concerned with an anomaly In the v e r t i c a l component variations of the geomagnetic f i e l d which was examined with four portable Askanla magnetometers set up along an east- 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 coastline, together with records from the V i c t o r i a Magnetic Observatory. Similar v e r t i c a l anomalies have been measured at coastlines i n many part3 of the world and seem to be correlated with the horizontal magnetic f i e l d variations i n a d i r e c t i o n approximately perpendicular to the coastline. Parkinson ( 2 4 ) has analyzed a large number of magnetograms from coastal stations a l l over the world and f i n d s that there i s a strong tendency f o r the Vectors representing changes i n the geomagnetic f i e l d to l i e on or close to a plane. At coastal stations t h i s plane t i l t s upward towards the nearest deep ocean^ the only exceptions being at a few stations where the structure of the continental shelf i s complicated. S i m i l a r l y , R i k i t a k e ^ 1 ) and h i s co-workers have studied int 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 Island and have found that i t i s best observed when the inducing f i e l d changes i n a north™south d i r e c t i o n approximately perpendicular to the s h e l f l i n e south of the i s l a n d . Along the C a l i f o r n i a coastline Schmucker^^) n a s recorded anomalously large v e r t i c a l components (z) i n long period Sq 2 i and short period bay type variations, together with s l i g h t l y reduced horizontal variations (D,H) at the shorter periods. The v e r t i c a l anomaly there i s also correlated with horizontal changes perpendicular 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 coastal regions have furnished i n t e r e s t i n g r e s u l t s . In p e r t i c u l a r , Mason and H i l l ( 2 0 ) found that the d a i l y range of geomagnetic t o t a l force variations was conspicuously greater (over the continental shelf i n the north east A t l a n t i c than at the shore by a factor of two. Off the west coast of I t a l y at Ponza Island (Simeon and 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 horizontal variations which i s absent at stations In central I t a l y , In the A r c t i c (Zh'igalov^ 1^) measurements from an ice f l o e i d r i f t i n g across the continental shelf into deeper water showed v e r t i c a l component variations of diminishing amplitude as the sea depth increased, e s p e c i a l l y f o r short period fluctuations, of the order of minutes. At Mirny i n the Antarctic Mansurov^^) has reported an increase i n v e r t i c a l component variations at the coastline and an increase i n horizontal variations on the ice just seaward of the c o a s t l i n e . The r a t i o of v e r t i c a l to horizontal variations on the land near the coast Increased as the period decreased to the order of seconds. This r e s u l t i s consistent with the frequency dependence of t h i s r a t i o at the coastal stations of Westham Island 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 , e t a l < 1 0 > ) . 3 B Possible Explanations of the Anomalies A l l these coastal phenomena can be included 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 m a t e r i a l , i t has been suggested ( P a r k i n s o n ^ C h a p m a n and R i k l t a k e ^ ) ) ak§ and Yokayamav • $ 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 dust i n g ©§©§ftsa 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© M§sast ©££@@trt 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 ©e§ana fh© MehereviHiU d i s c o n t i n u i t y d i p s Continent ©f g©atin©nt and Ocean Sea Level Shells Unconsolidated Sediments Ultrobasic mantle rocks Figure 1. Generalized Section Across a Stable Continental Margin, af t e r J.A. Jacobs, R.D. Russell, and J.T. Wilson. sharply downward (Hess^ 1*^, D i e t z ^ 1 2 ) ) as the t r a n s i t i o n i s approached from ocean to continent, and according to heat flow 4 measurements, there i s a marked, difference between the c o n s t i - tution of the upper part of the mantle beneath the two regions ( J a c o b s ^ 1 ^ ) so that a conductivity d i s c o n t i n u i t y i s not unlikely,, Furthermore, seismic studies show a decrease i n shear v e l o c i t y at shallower depths under the oceans than under the continents (Dorman, et a l ^ 1 ^ ) . Such a decrease i n v e l o c i t y has been (14) attributed by Gutenberg ' to the e f f e c t of increasing tempera- tures on the e l a s t i c constants of the rocks. Hence, the i s o - therms i n the mantle beneath the continents could very well r i s e closer to the surface on passing into the shallower oceanic mantle providing increased e l e c t r i c a l conductivity due to ioni c conduction 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 conductivity anomaly i n the upper mantle as a possible source f o r the "coast e f f e c t " . (47) By such arguments, Schmucker has proposed that the v e r t i c a l conductivity d i s c o n t i n u i t y which was found at a depth of the order of 100km under continental North America (Niblett, et a l ^ 2 2 ) , C a n t w e l l ^ ) , S r i v a s t a v a ^ 0 ) ) may be at much shallower depths under the oceans r e s u l t i n g i n a large conductivity step i n the upper mantle beneath the continental shelf l i n e . This conductivity step might roughly p a r a l l e l the upper boundary of the low v e l o c i t y layer, although i t i s doubtful (Rikitake^-^)) that the low v e l o c i t y layer i t s e l f i s an- extensive highly conducting layer extending over large parts of the earth. Studies of heat flow anomalies i n the eastern P a c i f i c (Von Herzen and Uyeda^-^)) lend strong support to arguments 5 f o r the possible existence of high temperature thermal sources at 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 zones. In f a c t , i t has been proposed ( R i k i t a k e ^ * ^ ) that a highly conducting loop which could be composed of high temperature mater ia l provides an explanation f o r the Japanese "coast e f f e c t " anomaly. Although such proposals f u r n i s h plausible reasons f o r expecting a coastal anomaly which Is independent of the mapped geology, i t i s s t i l l not c l e a r whether the "coast e f fec t" i s due to eddy currents i n the conducting oceans or due to the upper mantle conductivity structure at the coast. I f i t i s a hybrid e f f e c t due to both the conductivity 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 eliminated i n order to study the deeper conductivity anomaly. C Electromagnetic Induction i n the Earth The distance from the earth's surface to the closed e l e c t r i c current systems, generally believed to be the cause of transient magnetic f i e l d s , i s very small compared with the wavelength of the f i e l d s , so the magnetic induction f i e l d predominates over the r a d i a t i o n f i e l d and the geomagnetic fl u c t u a t i o n s may be derived from a p o t e n t i a l function. The p o t e n t i a l can be ex- pressed i n a series of spherical harmonics and i s found to consist of an external part and a part of i n t e r n a l o r i g i n . The i n t e r n a l f i e l d i s assumed to be caused s o l e l y by induction (9) In the earth by the external f i e l d (Chapman and Bartels ' ). 6 The strength and. d i s t r i b u t i o n of the induced earth currents must, therefore, depend on the conductivity d i s t r i b u t i o n and also on the nature of the inducing f i e l d . Hence, i n order to study the conductivity d i s t r i b u t i o n within the earth, i d e a l l y , a separation of the transient surface f i e l d s into external and i n t e r n a l parts must be made. This should be over a large region comparable i n extent to the entire earth's surface or over a region of more li m i t e d extent, depending on whether the average conductivity within the earth as a whole or l o c a l conductivity d i s t r i b u t i o n s are being considered. Different methods of separating the f i e l d over an area of the earth's surface small enough to be treated as plane, have been described by Siebert and K e r t z ^ 8 ^ , Schmucker^ 5^ and W e a v e r . R i k i t a k e ^ 0 ^ has approximated the potentials of i n t e r n a l and external o r i g i n due to a magnetic disturbance by two p a i r s of r a d i a l l y opposed dipoles, one outside the Earth and one inside the Earth, i n the region of the Asian continent. D ^Theoretical Conductivity Models Theoretical calculations have been c a r r i e d out i n attempts to correlate the behaviour of the time dependent part of the geomagnetic f i e l d over the earths surface with the conductivity d i s t r i b u t i o n within the earth. Information about the e l e c t r i c a l state of the earth can be obtained, as i n t h i s thesis, by an analysis, at a given 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 natural geomagnetic fl u c t u a t i o n s over the region 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 horizontal components of the natural 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 earth's surface ( C a g n i a r d ^ , Wait^^O, Price^°)) o so f a r , however, no success has been achieved i n c a l c u l a t i n g the conductivity d i s t r i b u t i o n d i r e c t l y from such information on the natural geomagnetic f l u c t u a t i o n s . Rather, the d i s t r i b u t i o n of con- ducting material i s Inferred by comparing the measured surface f i e l d with that calculated f o r an assumed model conductivity d i s t r i b u t i o n often based on seismic, gravity and geological information. The world wide average of the r a t i o of i n t e r n a l to external parts of the solar (Sq) and lunar (L) d a i l y magnetic variations was found to be consistent with a s p h e r i c a l l y symmetric earth model consisting of a uniform "core" with conductivity 3 .6 x 1 0 - 1 3 e m u . surrounded by a non-conducting outer s h e l l (Chapman(6), Chapman and Whitehead(7)). Later, the theory of induction i n a conducting sphere was extended to a consideration of the i n t e r n a l and external parts of the magnetic storm time variations (Dg T). This, i n turn, led to the treatment of an earth model i n which the conductivity i n the "core" varied as r " m ( L a h i r i and Price (18) ) (where r i s the earth's radius and m an integer) 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 variations and the storm time v a r i a t i o n s . The solution re- quired a worldwide increase i n conductivity at a depth of about 8 700 kilometers together with a surface conductivity d i s t r i b u t i o n suggesting the Influence of the highly conducting oceans. (Chapman and Whitehead^), L a h i r i and P r i c e ^ 1 ^ ) ) . However, on the basis of more numerous and r e l i a b l e data, new analyses of the amplitude r a t i o and phase difference between the external and i n t e r n a l parts suggest that the depth of the uniform conducting core should be at 400km with a conductivity of -12 5 x 10 emu. This new uniform core model overcomes the d i s - crepancy between the induction f i e l d from Sq and Dgip. More l o c a l i z e d analyses have revealed a large increase i n conductivity at depths as shallow as 100 kilometers beneath the North American continent (Srivastava(50), N i b l e t t ^ 2 2 ) , Cantwell(^)) and recent work i n C a l i f o r n i a (Schmucker^^^) suggests a more gradual t r a n s i t i o n from lower to higher conductivity values i n order to explain the observed induction due to both long and short period v a r i a t i o n s . The practice of assuming a highly conducting core whose spherical surface e x i s t s at a c e r t a i n depth below the earth's surface would, therefore, seem to be u n r e a l i s t i c , since the depth and r a p i d i t y of the major conductivity increase In the upper mantle appears to vary from place to place. Using the theory of induction of e l e c t r i c currents i n non- uniform t h i n sheets and s h e l l s ( P r i c e ^ 2 ^ ) , Ashour( x)), Rikitake (36, 37) studied electromagnetic induction caused, by d a i l y variations i n a hemispherical ocean underlain by a concentric sphere of uniform conductivity and also induction 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 induction of e l e c t r i c currents i n an ocean model represent the f i r s t attempts to approximate geomagnetic variations by considering a spherical earth model whose l a t e r a l surface conductivity variations resemble those of the earth's upper layers. Rikitake's solutions showed that electromagnetic coupling between the ocean and the conducting part of the earth's mantle reduced the expected anomaly i n geomagnetic bays to a value l e s s than f o r t y percent of the Inducing f i e l d and reduced the anomaly In the d a i l y variations due to a hemispherical ocean to an almost negligable value. Recently, however, i t has been shown (Roden^ 2)), on the basis of a f l a t ocean model, that i n the case of d a i l y variations, e l e c t r i c currents i n the mantle can have but l i t t l e e f f e c t i n reducing the anomaly within distances from the edge of the ocean which are comparable to the depth at which the currents are flowing. The problem of induction i n a spherical earth model with complex boundary conditions near the surface i s a p r o h i b i t i v e one and l a t e l y more in t e r e s t has been shown i n the interpre- tat i o n of l o c a l anomalies involving simple t h e o r e t i c a l model cal c u l a t i o n s i n which the s p h e r i c i t y of the earth i s neglected and the earth i s treated as a semi-infinite plate conductor. The basic theory of the magnetotelluric method (Cagniard^)) has been extended to. the case where the earth contains-'a v e r t i c a l d i s c o n t i n u i t y i n conductivity. ( d ' E r c e v i l l e and K u n e t z , R a n k i n ^ ? ) ) . Because of i t s relevance to the 1 0 i n t e r p r e t a t i o n of the "coast e f f e c t " at micropulsation f r e - quencies, t h i s v e r t i c a l f a u l t problem has been studied further (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 theory of the magnetotelluric method (Wait^-^, Price ( 3 0 ) ) regarding the nature and d i s t r i b u t i o n of the source f i e l d . However, no exact solution has been obtained. The C a l i f o r n i a coastal anomaly of bay type disturbances has been treated t h e o r e t i c a l l y as the r e s u l t of a perturbation of the large-scale, 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 conductivity (47) d i s t r i b u t i o n (Sehmuckerv ). A relaxation method developed by Price( 2®), taking into account the mutual induction between a conducting surface layer of varying thickness and a core of i n f i n i t e conductivity, furnished a d i s t r i b u t i o n of the anomaly which followed the observed data c l o s e l y . 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 variations r e s u l t from the edge of an oceanic current sheet at the surface and from currents flowing i n the upper mantle beneath the continental surface layers. Similar t h e o r e t i c a l c a l c u l a t i o n s using conformal mapping methods, based on a model consisting of a large conductivity step close to the earth's surface, give a similar s p a t i a l d i s t r i b u t i o n . Both of these models predict the observed increase i n the anomaly as the frequency of the geomagnetic variati o n s increases to the order of one cycle per hour. E Experimental Conductivity Models Theoretical investigations must involve vastly s i m p l i f i e d conductivity 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 i n solving induction problems with highly complex boundary conditions,, 11 On the other hand, coastline and subsurface i r r e g u l a r i t i e s may- be taken into account to some extent i n laboratory model studies. In p a r t i c u l a r , experimental proof was obtained f o r the enhance- ment of v e r t i c a l geomagnetic variations at the edge of a hemi- spherical ocean, and the anomalous e f f e c t s of a conducting loop beneath Japan were investigated experimentally. (Nagata, et a l ^ 2 1 ) ) . More recently experiments performed with a f l a t , copper sheet model of the P a c i f i c Ocean i n the neighbourhood of Japan (Rodenv> ') have yielded a d i s t r i b u t i o n of diurnal and semi diurnal f i e l d s which agree q u a l i t a t i v e l y with observa- ti o n s . In A u s t r a l i a (Parkinson^ 2-^) experiments have been performed on an earth model In which the oceans are represented by sheets of copper bent to l i e on the surface of a sphere and a uniform highly conducting core at a depth of 600 kilometers i s simulated by a sphere of aluminium. The primary f i e l d i s introduced by a c o i l of wire wound i n the form of the current function thought to produce bays, and held outside the sphere i n a p o s i t i o n corresponding to the ionosphere. Preliminary r e s u l t s show that f o r bay type disturbances 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 with observations at the coastline, but the conductors modify the f i e l d much les s than the conductors present i n the earth. Measurements i n the i n t e r i o r of the continent indicate that the uniform highly conducting core should be at a much shallower depth. It would seem, then, that the oceans are responsible f o r at least part of 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 devised which gives a quantitative explanation f o r the anomaly at a l l frequencies. 13 II THEORY A Natural Geomagnetic Variations It i s believed that transient geomagnetic variations are caused by the in t e r a c t i o n of solar p a r t i c l e s with the earth's magnetic f i e l d . Analysis of these variations, both periodic and Irregular, at d i f f e r e n t points on the earth's surface provides a too l f o r the study of the e l e c t r i c state of the earth. Changes i n the t o t a l magnetic force vector are usually measured continu- a l l y In the form of the three components D, H and Z each of which i s recorded on a magnetogram. A l l three components undergo smooth and regular variat i o n s with a period of approximately one day. These d a i l y variations may be separated into the solar d a i l y v a r i a t i o n (S). which depends mainly on lati t u d e and l o c a l time and the much smaller lunar d a l l y v a r i a t i o n (L). Storm and bay type disturbances are superimposed on these periodic variations and commence at almost the same Instant at a l l points on the earth's surface. Bay type disturbances, which l a s t f o r about one half to two hours, show up on magnetograms as a deviation from the normal periodic d a i l y v a r i a t i o n , gradually Increasing to a maximum value and then decreasing smoothly back to the undis- turbed level. Certain phases of weak magnetic storms provide use- f u l features, although they are usually more i r r e g u l a r and less e a s i l y analyzed than bays. 1* Normal Variations Geomagnetic variations may be represented by a time dependent disturbance vector P(t) with components D(t), H(t) and Z(t) 14 which, In general, are functions of p o s i t i o n P and frequency OJ. The disturbance vector consists of parts of both an i n t e r n a l and an external origin, i . e . we can write f~(t) = F^(P,^J) + F{(P1u>) . A common assumption i s that the magnetic permeabilityJU i s unity (cgs units) and that the i n t e r n a l part arises s o l e l y from i n - duction by the external part i n the conducting earth. If the conductivity d i s t r i b u t i o n In the earth 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 variations are said to be "normal" and Fit) = F»W « K*(pM + F t n t e " ) 2. Anomalous Variations L a t e r a l conductivity inhomogeneities may r e s u l t i n a de- formation of the i n t e r n a l current system responsible f o r the normal i n t e r n a l part p^N(P, coj giving r i s e to an anomalous i n - ternal component F Q̂(p,w) which varies from station to station. For simple conductivity structures where mutual induction can be ignored the t o t a l i n t e r n a l part may then be written as and the t o t a l disturbance vector as Rt) = Fenfcw) + Rn(P,w) + P^(P,u>) • Induction analysis leads one to expect a c o r r e l a t i o n between the anomalous variations F{a(P>u;) and the t o t a l normal variations R(t) - FeniM + F i n ( P ^ ) -. 3 . Separation of the F i e l d into an Internal and an External Part If the inducing f i e l d i s e s s e n t i a l l y uniform, any differences 15 i n geomagnetic variations observed at adjacent stations can be assumed to be due to an i n t e r n a l anomalous part. However, If the external inducing f i e l d i s not uniform, the i n t e r n a l and external parts must be separated i n order to determine the i n - duced secondary f i e l d s associated with the conductivity anomaly. Assuming that the displacement current can be ignored, the magnetic variations may be derived from a p o t e n t i a l function. The potentials due to i n t e r n a l and external e l e c t r i c currents may be repres- sented as Fourier i n t e g r a l s involving spectral densities which decay exponentially with depth (see Induction Analysis, equation (22)) as follows: o r~ A Z r- e tj\ cos A y + £ Lh sin A e cos Ay + e 7* s in Ay dA , z > o dA , z > o where Z Is 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 horizontal f i e l d v a r i a t i o n H T. The c o e f f i c i e n t s E^F^, e-^f^ are spectral densities and 2TT/K i s the s p a t i a l wavelength. The f i e l d components at the earth's surface Z = 0 are given by Z(3)= - ^ e - ^ i ^ fr(Eh-e,)co5Ay +(F>-/Jsfn *y]dA H TM= - ^ O i e _ A j l { = f[(-E*-eA)s;nAB + (h+h)coS d * 16 A Fourier Analysis 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 variations which are determined by measurement. oo r r o CO The spectral densities ^ F ^ e ^ . , ^ i n the expressions f o r the i n t e r n a l and external potentials may be found by equating the corresponding spectral densities i n the expressions f o r Z(y) and HT(ij) . Thus B t W = F»- ^ B H r(A)= -E^+e, Hence, the i n t e r n a l and external contributions to the magnetic variations at the earth's surface may be calculated. B Induction Analysis The current system which i s the source of the magnetic variations i s assumed to vary p e r i o d i c a l l y with time. A l l the f i e l d vectors contain a time factor e 1 , and a l l time deriva- t i v e s may thus be replaced by ito. 1. The General Theory of Induction Using the electromagnetic system of u n i t s Maxwell's f i e l d equations are: 17 cfiv E = curl Tt = A ^ fi c 0 4 IT K E + Cur I E = - i t ! i t ( i ) (2) (3) where the permeabilityJJL i s taken as unity everywhere, K i s the conductivity of the medium, and jO the charge density. These equations are applied to the regions above and within a semi i n f i n i t e conductor which approximates conditions above and below the earth's surface. z 1 - i i / / / / / / / l l l l l l 1 It i s assumed that there i s no space charge i n the region above the conductor and that any charge d i s t r i b u t i o n inside the con- ductor w i l l be rapidly dispersed, so that we can write p-0 everywhere and div E = O 1 (5) Taking the c u r l of equation (4) and combining i t with equation (3) gives = 1 4 - i r K c o f 4- (i CJ) E (6) For slowly i varying f i e l d s and/or high conductivity ^ C<4TTKCO 18 Hence, i n s i d e the conductor e q u a t i o n (6) reduces to the d i f f u s i o n e quation _ 2 , Y E = i 4 T T K t o E ( 7) Above the conductor the c o n d u c t i v i t y K i s n e g l i g i b l e and the displacement term can be n e g l e c t e d s i n c e the i n d u c t i o n at f i e l d dominates the r a d i a t i o n f i e l d i n r e g i o n s w e l l w i t h i n one wavelength of the source. Both terms on the r i g h t hand si d e of e q u a t i o n (6) can thus be n e g l e c t e d and i n the r e g i o n above the conductor, e q u a t i o n (6) reduces to L a p l a c e ' s e q u a t i o n . i V ' E = o (8) With- the above s i m p l i f i c a t i o n s e q u a t i o n (3) becomes c u r l H = 0 and hence H = - grad SI where SI s a t i s f i e s L a p l a c e ' s e q u a t i o n s i n c e d i v I f = 0. T h e r e f o r e , the magnetic f i e l d may be expressed as the g r a d i e n t of a s c a l a r p o t e n t i a l i n the r e g i o n above the conductor. The problem now i s to f i n d f i e l d v e c t o r s E and If which s a t i s f y equations (5) and (7) i n s i d e the conductor, e q u a t i o n (8) above the conductor and the u s u a l boundary c o n d i t i o n s at the s u r f a c e . S u b s t i t u t i n g E= Z(z)F£,y) i n t o equations ( 5 ) , (7) and (8) y i e l d s V ^ V JE (9) W Z L d z * - J ( 1 0 ) 19 -z>°> Z-f +. =Lf = - .1 F (ii) The Form of Z(z) Above and Within the Conductor The c o e f f i c i e n t s of p" on the right hand side of equations (10) and (11) must be constant, since the l e f t hand sides contain no Z dependence. Therefore l e t Z > 0 , - ± = - ^ (12) Z & z a and Z<0 , - ^ r + -14TTKGJ = - ?\2 Z hzx Solutions of equations (12) and (13) are: (13) Z>o, Z " A e W + fie^ (14) 8z z<o , Z = a e (15) where 9 l = }\2 + i 4 TT K u> l e . 6 - j j , [ { ( 4 W + A*)t ̂ ] + ^ [ { ( 4 . T r t C c o )+ ,'X^. A1] The solution (15) s a t i s f i e s the condition that ZW-»0 as Z - » - * < The Form of F(x,y) Above and Within the Conductor Equation (9) y i e l d s an expression f o r F*(x,y) which holds above and within the conductor. Let F z s O so that O X c»ij Then F - ( f . - i ? , 0 ) ( 1 6 ) 2 0 where by equations ( 1 0 ) and ( 1 1 ) + & + h a P = O ( 1 7 ) The Form of E and H Above and Within the Conductor Above the Conductor ( z > o ) : From expressions (14) and (16) E - ( A e*z+ 8 e"* z)( i ? , - £ P , o) <l8> c)y <=>7C Equation (4) gives an expression f o r the magnetic f i e l d H i n terms of the e l e c t r i c f i e l d p _ Z ( £ P , - , 0 ) , { w H = C u r l Z ( £ \ - i P , 0 ) ^ az Sx &z. a y v dx* a^*' / By equation ( 1 7 ) t h i s becomes and on using equation ( l 4 ) H = -A r d [ ( A e ^ e e ^ ) ? w ] ( 1 9 ) Within the Conductor ( z < o ) : From expressions ( 1 5 ) and ( 1 6 ) E - * « ( f f , - a p , o ) ( 2 0 ) 21 Once again equation (4) gives an expression f o r the magnetic f i e l d 3 - _ _ L ( 9 a e i f , 6 a e d P , K P a e J ( 2 i ) The Scalar Magnetic Potential Above the conductor, H = - grad Si and thus by comparison with expression (19) 7\z ^ -Az where J l = - ( A e + B e ) P ( * , y ^ ) (22) 7\A = _ p and A £ - B 10) \ tJ The term involving n e corresponds to the f i e l d due to sources i n the region above the conductor, whereas the term B -Az e corresponds to the f i e l d of the induced currents inside the conductor. Boundary Conditions The tangential components of E and H are continuous at Z = 0 . Thus, the tangential components of E given by equations (l8) and (20) and the tangential components of H given by equations (19) and (21) may be equated at Z = 0 giving + Q = a (23) and A - £>) = @<x (24) Written 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 - - t c j ( R - B ) - (25) - i w (ft + B) = (26) 22 Combining these expressions gives the value of B i n terms of A, vi z V 8 + A / where 0 2 = A Z + i 4 T T K 6 0 . Thus, the boundary conditions at the earth's surface require an image source beneath the surface with a strength depending on the conductivity K of the earth, the frequency of the variations oo and the s p a t i a l wavelength 2ir/A . 2. Induction by a Periodic Linear Current i n an I n f i n i t e l y Conducting Half Space. Linear Current Source Image Current Source t e flowing p a r a l l e l to the x- axis i n a po s i t i v e d i r e c t i o n at a height h above the earth's surface. The magnetic po t e n t i a l of t h i s l i n e current i s given by , which may be represented by Fourier's i n t e g r a l theorem as The po t e n t i a l of the induced f i e l d a r i ses from an image source 23 with s t r e n g t h / 6 - \ \ J , and thus the po t e n t i a l due to i n t e r n a l currents may be represented by SI In the case of an i n f i n i t e l y conducting half space 8-* 0 + h become.s unity and the image current source appears as a l i n e current of strength I at a depth -h flowing i n the opposite d i r e c t i o n to the external source. The mirror image approximation may also be applied i n the case of a f i n i t e l y conducting h o r i - z o ntally s t r a t i f i e d earth so long as high frequency variations are considered so that 8 i s very large and 0 -^ once again approaches unity. The external and induced v e r t i c a l variations at the surface are: Z (2=o) = - ? f t e (z=o) = -2 \ I 6 < U j t sin ^ d* and Therefore Z e = - Z { at 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 at the surface of an i n f i n i t e l y conducting half-space. The external and induced horizontal v a r i a t i o n s at the surface are: \\ (z=o)= - M e ( z = o ) = -2 f I e i u t f t ^ cos h% dh 24 and H. (z.0) = - S J l x ^ s o ) = -2 J I e C a i t e ̂  c o s A 3 Therefore H e y = H v ' y at Z = 0 and the t o t a l h o r i z o n t a l v a r i a t i o n i s 2. H e y 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 earth i s f i n i t e and i n the case of longer p e r i o d bay type d i s - turbances, the image source w i l l be weaker than a m i r r o r image, the v e r t i c a l component w i l l not be completely c a n c e l l e d and the h o r i z o n t a l component w i l l be increased l e s s than t w o - f o l d . C The E f f e c t of an Ocean on Geomagnetic V a r i a t i o n s The boundary between ocean and continent represents an obvious 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 - sponsible f o r an anomalous i n t e r n a l magnetic f i e l d . The anomaly may be studi e d as the edge e f f e c t of a la r g e scale system of eddy cu r r e n t s Induced i n a t h i n sheet of uniform c o n d u c t i v i t y repre- s e n t i n g the ocean. Since the depth of a la r g e ocean i s n e g l i g a b l y small compared to i t s h o r i z o n t a l dimens:io..ns, the c u r r e n t s would be expected to c i r c u l a t e i n l a r g e eddies f l o w i n g p a r a l l e l to the ocean f l o o r . 1. R e l a t i o n between E l e c t r i c Currents and Magnetic F i e l d s i n a Thin Uniformly Conducting sheet K=o /////////// K = 0 . / / / / / / / / / / / / d 25 Neglecting the displacement current as i n part B, the relevant f i e l d equations are: curl H - 4 T T T ( ! ) curl E = - d f f ( 2 ) £t di'v H = 0 " (3) t = KE" (4) where the permeability [/. i s taken as unity (cgs units) and K i s the conductivity of the t h i n sheet. Above and below the sheet x = o , so that c u r l 1? = 0 and hence H* = - grad Si (5) where Si s a t i s f i e s Laplace's equation. If the thickness of the sheet i s i n f i n i t e s i m a l , the currents w i l l flow p a r a l l e l to. the surface of the sheet and the normal component of the magnetic f i e l d and the tangential component E t of the e l e c t r i c f i e l d have the same magnitude and d i r e c t i o n on both sides of the sheet.- Integrating equation (4) over the thickness of the sheet • f T d z = J K E dz = tt \ K d z —̂  —* i e . l t = E t < r , ( 6) d d where ~ J i dz. and G~ - j K dz are the t o t a l sheet current i n t e n s i t y per unit length at a point on the surface and the t o t a l conductivity per unit length. Applying equation ( l ) to a small volume element enclosing part of the thi n sheet, 26 f(r Curl H dV = jj 4.TT 1 (7) using the i d e n t i t y f curl dV = r?><'adS JJ J J. and the d e f i n i t i o n of t o t a l sheet current i n t e n s i t y per unit length, equation (7) reduces to By shrinking the volume while s t i l l enclosing the sheet, we can write _^ , s ^ r _ i e . T t = J _ f i x ( H + - H _ ) (8) where tt i s the unit vector i n the po s i t i v e Z d i r e c t i o n , H + i s the t o t a l f i e l d above the sheet and H„ the f i e l d below. Applying equation (2) to a small c i r c u i t i n the surface of the sheet at Z = 0, gives curl E t « - $ H dt which together with equations (6) and (8) y i e l d s 27 Curl [TTX(17 +-H1)] = - 4 T T ^ £>H ht Taking the scalar product of both sides of t h i s equation with rf, we obtain the boundary equation dW ( T T + - T L ) = - 4 i r < T ^JHz (9) a t Now H^- H_ = - greed ( J l + - (52-) and where and are the magnetic potentials of i n t e r n a l and external o r i g i n . Since we have: The magnetic p o t e n t i a l of the induced currents 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 sides of the sheet, the potentials on one side being the negative of the potentials on the other. so that at Z = 0 J " l ^ = - Si. and ^ J l - Therefore equation (10) becomes f\ - H = -2 f i ^ J U + ; i J l + ) ( i i ) where i and ^ are unit vectors i n the x and y d i r e c t i o n s . 28 Substituting t h i s into equation (9) together with 1-1= <)S£ we obtain + will = z i r r i r ^ + + i i ^ i " and since must s a t i s f y Laplace's equation, t h i s boundary equation becomes 52 J (12) Let the inducing p o t e n t i a l f i e l d be of the form SI - e e Then the induced f i e l d above the sheet w i l l be of the form Sli= k e - > Z e i u t P ( z , y ) (13) so that SI' as. as - oo and SX\ —* 0 By substituting SI? and Sl>\ into the boundary equation (12), k = Zif<r \ t o A + 2TT<T\U> The modulus of k gives the r a t i o of the magnitudes of and and the argument of k gives the phase s h i f t of the induced f i e l d r e l a t i v e to the inducing f i e l d . The e l e c t r i c current i n t e n s i t y per unit length 1-t i n the sheet can now be expressed i n terms of the inducing f i e l d H e. Substituting equation (13) into (11) we have 29 which i n turn may be substituted into equation (8) to give 2TT The e l e c t r i c current per unit length at a point i n the sheet i s , therefore, l i n e a r l y correlated with the component of the external inducing magnetic f i e l d v a r i a t i o n perpendicular to I t . 2. The Edge E f f e c t of a Current Sheet Neglecting the e f f e c t of the ocean boundary i n modifying the e l e c t r i c currents, and tr e a t i n g the current sheet as uniform right up to the edge, provides a s i m p l i f i e d picture of.the s p a t i a l d i s t r i b u t i o n of the associated v e r t i c a l magnetic f i e l d s . Mutual induction between the current sheet and any conductivity d i s t r i b u t i o n beneath i t i s also neglected. Z Inducing Field / / / y Z / / / A/ / Y/ A/}/ Inducing Field Figure 2 E l e c t r i c Currents and t h e i r Associated Magnetic F i e l d s at the Edge of a Uniformly Conducting Sheet. 30 The v e r t i c a l magnetic f i e l d at a point (y,z) due to a l i n e current of i n f i n i t e length i n a d i r e c t i o n perpendicular to the y- axis and of strength dtj' situated at a point ( y % 0 ) i s given by The e f f e c t of a current sheet of i n f i n i t e length, extending from y = 0 to y = -W, may be approximated by integrating the v e r t i c a l f i e l d s contributed by a number of such l i n e currents perpendicular to the y-axis and i n the plane of the thi n conductor. Hence, the v e r t i c a l f i e l d due to the sheet i s given by I »3 i . e . '3 2.TT using equation (14) This expression gives 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 , edge-effect, anomaly, v i z 1) The v e r t i c a l anomaly increases as the ocean i s approached, reaching a maximum at the coa s t l i n e . 2) The anomaly Is l i n e a r l y correlated with the horizontal inducing f i e l d perpendicular to the coast l i n e . When the f i e l d changes toward the ocean the anomalous v e r t i c a l change i s po s i t i v e (upward), and when the f i e l d changes toward the land the anomalous v e r t i c a l change i s negative 31 (downward).The expression f o r H z i s indeterminate at z =0, y = 0 because of the mathematical nature of the model, 3. The Free Decay of E l e c t r i c Currents i n the Oceans If the e l e c t r i c currents are excited i n an ocean and l e f t to decay, they w i l l do so exponentially with a time constant which depends on the t o t a l conductivity of the ocean. The theory of e l e c t r i c currents i n a uniformly conducting disc (Ashour^"^) shows that the time ^ required f o r the current density to be reduced to i/e of i t s i n i t i a l value i s given by "C = 2.34 a//° where a i s the radius of the disc and J> i s the surface resistance per uni t length. Taking the conductivity K of sea water to be 4 x lO'^emu, the radius of the P a c i f i c Ocean 4000km., and the average depth 4 km., the above formula gives a free decay time of approximately four or f i v e hours. Although bottom i r r e g u l a r i t i e s may reduce t h i s decay time to a smaller value, i t i s evident that the P a c i f i c Ocean w i l l sustain e l e c t r i c currents induced by bay type disturbances of one or two hours duration. A curcular eddy current In the r e l a t i v e l y shallow Georgia S t r a i t between Vancouver Island and the mainland would decay i n just a few seconds, so that i n t h i s case a v e r t i c a l anomaly caused s o l e l y by the sea water Is Impossible f o r variations with a period greater than a few minutes. 4. The Shielding E f f e c t of an Oceanic Layer The. magnetic f i e l d s of the Induced currents i n an ocean tend to cancel the source f i e l d beneath the layer. I t has been shown i n section C l that the Inducing and induced f i e l d s above 32 a t h i n conducting sheet are related by the following equation i l l (*) - k Sl\-z) where i _ ^ .. K = 2 Tr CT 1 1 0 A l s o = - J i i c - ^ ) so that below the sheet the f i e l d i s given by and the t o t a l f i e l d there i s : Hence V -fc3- +. 4- TT 2 a*2" CO 1 / and the amplitude of the f i e l d v ariations below the sheet i s reduced to a f r a c t i o n 7\ of the external f i e l d . I t i s reasonable to suppose that spherical harmonics up to the tenth degree are s u f f i c i e n t to describe the f i e l d of a bay type disturbance i n mid l a t i t u d e s . Hence one can set an upper l i m i t on the value of A and a corresponding lower l i m i t on the attenuation of the external f i e l d as i t passes through a layer of ocean, three kilometers thick, i n the v i c i n i t y of Vancouver Island. Setting the s p a t i a l wavelength 2tr/h equal -8 _, to 2TTR/IO where R i s the earth's radius gives A- '-£>x/0 c»m Assuming that the conductivity K of sea water i s 4 x 10--1-1emu, the corresponding harmonic of the incident f i e l d w i l l be reduced beneath the oceanic layer to ten percent of i t s value above the 33 ocean, f o r variations with a period of f o r t y - f i v e minutes. This 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 i n that i t neglects the ef f e c t of a possible highly conducting region i n the upper mantle beneath the ocean. Also, we are not e n t i r e l y j u s t i f i e d In assuming that the source of the magnetic variations i s a station- ary e l e c t r i c current system varying p e r i o d i c a l l y with time, since there i s now reason to believe (Rostoker, private communi- cation) that the system i s quite l i k e l y to d r i f t r e l a t i v e to the earth's surface giving the source f i e l d a t r a v e l l i n g wave nature. 5. The E f f e c t of the Conducting Mantle on E l e c t r i c Currents i n the Oceans There i s a rapid increase i n e l e c t r i c a l conductivity i n the v i c i n i t y of the upper mantle which may be represented t h e o r e t i - c a l l y by a highly conducting core i n the earth's i n t e r i o r . E l e c t r i c currents which are induced there are responsible f o r magnetic f i e l d s which suppress the induction of currents i n the surface layers. Therefore, i f the conducting region begins at a shallow depth, as might be expected beneath the oceans, mutual induction w i l l reduce both the Intensity of the oceanic current sheet and i t s shielding e f f e c t on the layers below. 34 II I EXPERIMENTAL PROCEDURE A Askanla Variographs The Askanla variograph i s a portable Instrument consisting of three variometer u n i t s f o r recording the d e c l i n a t i o n D, the horizontal 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 device f o r recording time marks, the temperature and a base l i n e . The instrument i s housed i n a heat insulated case and a heater and thermostat are provided to keep the inside temperature at a constant l e v e l . The suspension f i b r e s carrying the magnet systems can a l l be adjusted f o r complete temperature compensation, i n case temperature fl u c t u a t i o n s are permitted by the thermostat. Scale values f o r the three systems are determined by passing a known current through Helmholtz c o i l s mounted on each variometer and noting the d e f l e c t i o n . 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 drive. The drive operated poorly on 60 cycle l i n e power, causing a number of records to be l o s t . The recording magazine holds a ten meter r o l l of photographic recording paper which l a s t s f o r about twenty days operating at a speed of 24m.m./hour. B I n s t a l l a t i o n and Maintenance of the Variographs The instruments, with the exception of the Westham Island variograph, were located indoors i n reasonably non-magnetic buildings where 60 cycle, 110-115 v o l t power was a v a i l a b l e . The Tofino and Abbotsford stations were operated with the 35 assistance of the Department of Transport personnel and the Frank l i n River station was housed i n a b u i l d i n g provided by the courtesy of the MacMillan, Bloedel and Powell River Company. The instrument on Westham Island was located i n a plywood shelter at the R.C.A.F. telemetry station. A l l the s i t e s were checked with a portable Barrlnger 6M-102 proton precession magnetometer, and only those with low s p a t i a l gradients (< 5 K per meter) were used. , The chronometers which provided the hourly time marks were set within a few seconds by W.W.V. short wave time signals. Records were also kept of the gain and loss of each chronometer so that corrections could be applied to the time marks i n the event of an error greater than one minute. A c a l i b r a t i o n check of a l l three components was c a r r i e d out f o r each r o l l of photo- graphic f i l m used i n the variographs. C Confidence Limits The 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$. The magnetometer d e f l e c t i o n caused by c a l i b r a t i n g currents can be measured to within about ±0.3m.m., i . e . about ±1$ of the d e f l e c t i o n . Unknown facto r s include: the meter c a l i b r a t i o n (probably better 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; inaccurate meter reading under d i f f i c u l t f i e l d conditions (probably under 1%). The o v e r a l l accuracy of magnetogram features should, therefore, be better than -3 to 5$. For the purpose of t h i s survey, the instrumental confidence 36 l i m i t s have been a r b i t r a r i l y set at 5%, i . e . differences i n amplitute recorded at d i f f e r e n t stations are considered (instrumentally) s i g n i f i c a n t only i f they exceed 5$ . D Processing of Records The photographic recording paper i n the variographs was changed approximately once every two weeks and developing was done using f a c i l i t i e s at the V i c t o r i a Geomagnetic Observatory. Data f o r the Fourier Analysis of bays was obtained from the records (as shown below) by marking off each of the three components at 2.5 minute i n t e r v a l s and d i g i t i z i n g by means of a template. i i i i i i l i i i m m i i m i ! HIIIMIIIIIIIIIIIIIIII IIIIIIIIIIIIIIIIIIIIMI This spacing allows the c a l c u l a t i o n of Fourier c o e f f i c i e n t s f o r frequencies up to six cycles per hour. Dally variat i o n s were analyzed by d i g i t i z i n g the records at twenty minute i n t e r v a l s . 37 IV METHOD OP ANALYSIS A Fourier Analysis The analysis i s based on the c a l c u l a t i o n of the spectral d e n s i t i e s of each of the three components D,H, Z of a p a r t i c u l a r magnetic disturbance. A d i g i t a l computer program based on Simpson's i n t e r p o l a t i o n rule furnished the Fourier components fo r each of several bay type magnetic disturbances f o r frequen- ci e s from .001 cycles per minute to .061 cycles per minute. Ideally, a spectral analysis allows each of the three time dependent components D, H, Z of a disturbance to be expressed as a sum of simple harmonic time functions + 00 +oo fit) = r r ft (CJ) Cos c j t d w r f J -00 B(co) sin u>t dui where the frequency functions B(w) and f\ (,ui) are the sine and cosine spectral d e n s i t i e s (defined i n Appendix 11). Since Maxwell's f i e l d equations are l i n e a r , each of the Fourier components $Jit) = f\(u>)clu> c o s o j t + B ( < o ) d u S i n co t ° r f t o t t ) = C(^) dco Cos ((A - e-J) where C(OJ) = / A(w)* + Bi^f a n d 1^ = may be treated separately as l i n e a r l y polarized harmonic waves of frequency to Incident on the earth's surface, and then the p r i n c i p l e of superposition applied. Henceforth, the sine and cosine spectral densities w i l l be used i n place of the Fourier 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. Therefore, the Fourier component (at a frequencyco) of the t o t a l magnetic disturbance at the earth's surface can be written as the vector sum of three orthogonal harmonic terms F^Ot) = j C2C^')cos('wt-£2)4._J.CH(w)cos(tj-fc-gH)+k C D M c o s ( w t - £ B ) i n the d i r e c t i o n s of the three geomagnetic components Z, H, D. The corresponding external Inducing disturbance i s an e l l i p t i - c a l l y polarized harmonic o s c i l l a t i o n of frequency to i n a plane p a r a l l e l to the earth's surface, comprised of l i n e a r harmonic o s c i l l a t i o n s i n the D and H d i r e c t i o n s . For a two dimensional anomalous zone, the anomalous part of the v e r t i c a l magnetic disturbance z A at the earth's surface i s correlated with the component of the horizontal disturbance perpendicular to the s t r i k e of the zone, denoted by S. H Thus where 39 The l i n e a r horizontal disturbance S consists of parts of both external and i n t e r n a l o r i g i n and may i t s e l f contain an anoma- lous part varying with distance from the anomalous zone. If the assumption of two dimensionality i s not j u s t i f i e d , the approximate magnitude of the horizontal disturbance i s given by A study of the s p a t i a l dependence and frequency dependence of of the depth and extent of the conductivity anomaly. B Polar Diagrams Polar diagrams provide a means of t e s t i n g a possible 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 horizontal 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 (Parkin- son (23) ). The upper c i r c l e of the diagram i s used to plot points corresponding to 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 points are plotted as i n a Schmidt equal area projection, the r a d i a l distance of each point from the centre depending on the r a t i o of the v e r t i c a l change to the horizontal change and the asimuthal angle ^ of each point depending on the geographic d i r e c t i o n of the horizontal change. A point at the centre of the diagram represents a change i n the magnetic f i e l d i n a v e r t i c a l d i r e c t i o n . the quantities Z , S, Z A/S and ftp permits a l i m i t i n g estimate 40 Figure 3 Method of P l o t t i n g a Polar Diagram A Fourier Analysis breaks down a magnetic disturbance into in-phase and out-of-phase sinusoidal o s c i l l a t i o n s of the form Z ^ ( t ) = R 2 ( c o ) c o s o t + B 2 ( ^ ) Sin c j t The horizontal change at a p a r t i c u l a r frequency can be regarded as the sum of two out. of phase l i n e a r o s c i l l a t i o n s of the form 5 ^ (<o) = ( R H (w) f Rj^w)) cos S sf„ (") = ( B H (w) + Bj>(w)) Sfnoot 41 with asimuthal d i r e c t i o n s d) = - t a n ' 1 A » M rcos -—r » r Sin • r e l a t i v e to the d i r e c t i o n of D. When the conductivity i s r e l a t i v e l y large as i t i s i n the oceans, i t seems reasonable to assume that there i s in-phase induction (Hyndman^)), s o that one i s j u s t i f i e d i n attempting to correlate each of the horizontal l i n e a r o s c i l l a t i o n s SCos(<*•>) and (w) with the corresponding in-phase v e r t i c a l o s c i l l a t i o n s A z(p) and on a polar diagram. Hence, the Fourier analysis of one magnetic disturbance y i e l d s two points on the polar diagram defined by flt(w) , S c o s C w) a n d B t (w) > Ssin C w) corres- ponding to the frequency CO . i f the anomalous zone i s two dimensional, the points from the Fourier Analysis of a number of disturbances w i l l be scattered along a great c i r c l e (Fig. 3) which w i l l be symmetrical about the d i r e c t i o n of best c o r r e l a t i o n , perpendicular to »the s t r i k e of the anomalous zone. The c o r r e l a - t i o n at each st a t i o n can then be expressed by the Induction c o e f f i c i e n t C = Z/S. The scatter of the points which may vary with frequency w i l l be enhanced If there i s any out of phase Induction and i f the inducing wave contains too large an 42 uncompensated v e r t i c a l component. In such cases, the d i r e c t i o n a l dependence, indicated by the pos i t i o n of the great c i r c l e on the diagram, may become obscured and no induction c o e f f i c i e n t can be defined f o r the sta t i o n . C S t a t i s t i c a l Analysis 1. The Pre c i s i o n of a Mean Value The mean value of a geomagnetic variable, such as Z, at a p a r t i c u l a r station can be estimated by sampling a number of geomagnetic disturbances. The p r e c i s i o n of the mean value obtained from such a sample of n disturbances as an estimate of the long term mean value i s given by the standard error S.E. = * V V " " w h e r e l s t n e standard deviation of a long series of observations. Using data from one sample, we can approximate tf" by y ~ _ z The probable error P.E. of a mean value i s defined as the value of the deviation from the true long 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 ha l f the occasions The probable accuracy of a l l the mean values calculated i n so that the S.E. = P.E. = 0.6745 (S.E.) 43 t h i s thesis are given i n terms of the probable error P.E. 2. The Significance of a Mean Value "Students" t test provides 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 postulated value Z", assuming that the long-term d i s t r i b u t i o n of values of Z i s nearly normal. The value of t i s defined by t = 2-Z' S.E. and Student" has calculated the p r o b a b i l i t y of exceeding any value of t derived from a random sample of n events. Adopting a confidence l e v e l of twenty percent requires that the calcu- lated value of t be smaller than that value which has a one i n f i v e chance of occuring i n any random sample; otherwise the data shows a s i g n i f i c a n t deviation from the postulated mean value and a new mean value must be sought. Figure 4. Location Map Showing Sites of Recording Stations 45 V RESULTS AND ANALYSIS. The s i t e s of the stations used i n the analysis are shown i n F i g . 4 . Tofino, Franklin River, Westham Island and Abbots- ford were occupied by Askania variographs. V i c t o r i a i s a per- manent magnetic observatory. Two of these stations (Abbotsford and Westham Island) overlap the p r o f i l e recorded by Hyndman^1^) . Hyndman's analysis showed that the amplitude of the variations i n both the horizontal and v e r t i c a l components was e s s e n t i a l l y constant from Westham Island as f a r inland as Grand Forks (longtitude l l 8 ° 3 0 « ) . This means that Abbotsford and Westham Island can be used as representative inland stations. A p a r t i c u l a r example of a geomagnetic disturbance, recorded simultaneously at Tofino and V i c t o r i a on Jan. 10th , 1964, i s shown i n F i g . 5 where the Z, H and D components have been re- drawn to the same scale. A two to one enhancement i n the ver- t i c a l component at Tofino as compared to V i c t o r i a shows up c l e a r l y , whereas the H and D components are e s s e n t i a l l y i d e n t i c a l . This disturbance was d i g i t i z e d at two and one half minute i n t e r v a l s and a Fourier analysis was c a r r i e d out on the v e r t i c a l component at the two stations. The sine and cosine spectral densities B z ( " ) , f\z (w) and the amplitude spectral d e n s i t i e s CZ({S) were plotted as a function of frequency showing a two to one enhancement of Tofino values over V i c t o r i a values covering v i r t u a l l y the entire frequency range from .001 cycles per minute to .061 cycles per minute (Figs. 6 , 7 ) . A plot of the r a t i o C z ( a > ) T 0 F I N 0 / C z ( w ) V I C T ^ (Fig. 7) gives a better i n d i c a t i o n of the frequency dependence 46 of the Tofino anomaly and shows a peak at .036 cycles per minute (period ~ 30 min.) with another smaller peak at .053 cycles per minute ( p e r i o d ^ 20 min.). 3 Figure 6 A Comparison of the Sine and Cosine Spectral Densities of the V e r t i c a l Component of the Disturbance Recorded at Tofino and V i c t o r i a on January 10, 1964 o1—1 .001 .007 .013 .019 .025 .031 .037 FREQUENCY IN CYCLES PER MINUTE Figure 7 A Comparison of the Amplitude Spectral Densities of the V e r t i c a l Figure (. J o m p o i i e n t Q f t h e D i s t u r b a n c e Recorded at Tofino and V i c t o r i a on January 10, 1964 4 9 A D i r e c t i o n a l Dependence of the Anomaly Nine bay type disturbances were recorded and d i g i t i z e d , covering the period Jan. 10th to July 3 r d , 1964. A Fourier Analysis was c a r r i e d out f o r each of the three components Z, H, D at a l l the stations operating at the time of each disturbance. One representative disturbance f o r each of the f i v e stations was then chosen i n order to look f o r a possible c o r r e l a t i o n between the v e r t i c a l and horizontal v a r i a t i o n s . A plot of the Z, H and D sine and cosine spectral densities f o r the f i v e stations shows a c o r r e l a t i o n mostly between the Z and D components, becoming most pronounced at Tofino over the frequency range from one to two cycles per hour (Figs. 8 to 1 2 ) . A confirmation of t h i s result was obtained i n the form of a polar diagram (Fig. 13)• Points representing magnetic variations with frequencies between one and two cycles per hour were derived from the spectral densities of six magnetic disturbances recorded at Tofino. They show a tendency f o r the f i e l d to change upward when It 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 horizontal change i s north or 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 are only a l i m i t e d number of points, a c o r r e l a t i o n i n approximately an east-west d i r e c t i o n i s indicated. The change vectors repre- sented on the"polar diagram are scattered about a plane i n c l i n e d upward towards the west at an angle of about 30° to the h o r i - zontal, corresponding to an induction c o e f f i c i e n t C = Z/S of 0 . 5 . Points representing f i e l d changes with frequencies outside the 05  1000,- COSINE TERMS co UJ < CO UJ CO •z. UJ Q < cr i -o UJ Q_ CO -1600 ro .01 02 D3 0 4 05 .06 .01 .02 .03 .04 .05 .06 .07 FREQUENCY IN CYCLES PER MINUTE Figure 10 Sine and Cosine Spectral Densities of the D, H and Z Components f o r Magnetic Disturbance Recorded at- Franklin River on July 3* 1964 900 r 600h SINE TERMS COSINE TERMS co UJ I < < CO LU 300 -300h c -600h co UJ Q < CC 1- o UJ CL CO -900H -1200 -1500 -I800L .01 .02 .03 .04 .05 .06 FREQUENCY IN CYCLES PER MINUTE Pifiu-e II Sine and Cosine Spectral Densities of the D, H and Z components f o r Figure i i Magnetic Disturbance Recorded at Westham Island on March 5, 1964 VJ1 to SINE TERMS COSINE TERMS "02 03 04 05 06 '-*0i 02 03 04 05 0 6 1)7 FREQUENCY IN CYCLES PER MINUTE Figure 12 Sine and Cosine Spectral Densities of the D? H, and Z Components f o r Magnetic- Disturbance Recorded at Abbotsford on June 11 s 1964 VJl     59 range one to two cycles per hour, not included on t h i s polar diagram, deviated considerably from t h i s pattern, Indicating that the coastal anomaly i s most c l e a r l y defined i n t h i s frequency range. The Z, H and D sine and cosine spectral densities f o r Tofino at a frequency of about three cycles per hour show that the Z component i s not correlated with the D or H component alone but probably with a combination of both. A polar diagram plotted f o r Tofino at the higher 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 perpendicular to the Vancouver Island coastline, but the scatter i n the points i s greater than at the lower frequencies making i t d i f f i c u l t to define a preferred plane (Fig. 14). Polar diagrams plotted f o r V i c t o r i a were based e s s e n t i a l l y on the same magnetic disturbances that were u t i l i z e d i n the Tofino diagrams. The c o r r e l a t i o n at frequencies of one to two cycles per hour at V i c t o r i a appears to be more north-east, south- west rather than east-west as at Tofino with a great deal more scatter than on the corresponding Tofino diagram (Fig. 15)° At a frequency of three cycles per hour the c o r r e l a t i o n i s not clear (Fig„ 16)„ B S p a t i a l Dependence of the Anomaly The stations occupied along the east west p r o f i l e provided a means of measuring the,coastal anomaly at distances of 50, 120, 240, and 300km„ east of the one hundred fathom l i n e o f f the west coast of Vancouver Island. The s p a t i a l dependence i s best studied 60 by analyzing magnetic disturbances recorded simultaneously at a l l stations on the p r o f i l e . However, each magnetic disturbance was recorded only at two or three of the stations, because of frequent instrument f a i l u r e s , mainly i n the drive unit, and l o c a l a r t i f i c i a l disturbances at the Tofino station. In addition, the two stations at the eastern end of the p r o f i l e were at no time occupied simultaneously. Thus, comparisons of the v e r t i c a l and horizontal variations between two stations on the p r o f i l e could sometimes be made only I n d i r e c t l y with reference to the V i c t o r i a s t a t i o n . 1. Variations with a Period of Forty Five Minutes The v e r t i c a l variations, z, at t h i s period are apparently correlated with the component of the horizontal disturbance i n an east-west d i r e c t i o n , S. A study of the change of Z and S with distance along the p r o f i l e i l l u s t r a t e s the s p a t i a l dependence of the anomaly. The amplitude spectral d ensities Cz(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 and the east-west horizontal v a r i a t i o n S i s defined using the sine and cosine spectral d e n s i t i e s A H ( W ) , B H ^ ) * A^O 0) A N D (H) of the H and D components. V e r t i c a l Component Amplitude spectral densities, C (OJ) f at frequencies of .021, .023 and .025 cycles per minute represent v a r i a t i o n s with a period of approximately f o r t y f i v e minutes. A comparison of along the p r o f i l e at these frequencies, f o r the same magnetic disturbance, furnishes a f a i r l y consistent pattern (Table 6 ) . 61 For the six magnetic features studied, the values of' Z decrease from Tofino to the Westham Island and Abbotsford stations, the value at Tofino being as much as one hundred percent—larger than at Westham Island. A mean value of Z was calculated f o r each station by normalizing the v e r t i c a l component of each disturbance by the corresponding v e r t i c a l component at Abbotsford (Table 2 ) . ( i n some cases t h i s was calculated i n d i r e c t l y by comparison with V i c t o r i a values.) This mean value of Z decreases steeply from Tofino to Frankl i n River and then l e s s steeply towards the repre- sentative inland stations of Westham Island and Abbotsford (Fig. 19) , the l a t t e r stations being equivalent If a confidence l e v e l of twenty percent i s accepted. An important point i s that the Tofino anomaly diminishes to les s than hal f i t s value over the 70 kilometer distance from Tofino to Franklin River. On the average V i c t o r i a values do not d i f f e r s i g n i f i c a n t l y from Abbots- ford values. Horizontal Components The component of the horizontal v a r i a t i o n In an east-west d i r e c t i o n , S, at a period of f o r t y f i v e minutes, i n general decreases coastward with the exception that In some cases Frank- l i n River has a s l i g h t l y smaller value than Tofino (Table 6 ) . The value of S at Tofino, however, Is consistently about f i v e to ten percent smaller than at Westham Island. With reference to Abbotsford a mean value of S was calculated f o r each station with a probable error of three percent (Table 2). The decrease of ten percent i n the mean value of S from Abbotsford to Tofino i s 62 consistent with the expected decrease with distance from the Auroral Zone. If the source of geomagnetic bays i s assumed to be a l i n e a r current approximately 2000km. from the p r o f i l e , the horizontal component f a l l s off i n inverse r a t i o to the square of the distance from the source (Van'yan and Kharin(52)y and hence d S = _ ̂  d r = _ S 2± r3 r Tofino i s about 100 kilometers further from the Auroral Zone than Abbotsford, so that d S = „ 2 d r = - 2 ( » 0 0 ) a -0.1 5 r 2000 Thus, a decrease of ten percent i n the value of S i s expected, independent of an i n t e r n a l anomaly. In the l i g h t of these con- siderations, no anomaly i s apparent i n the horizontal component. The Induction C o e f f i c i e n t Z/S The c o r r e l a t i o n exhibited by the Tofino polar diagram f o r frequencies between one and two cycles per hour j u s t i f i e s the c a l c u l a t i o n of an induction c o e f f i c i e n t C = Z/S at a period of f o r t y - f i v e minutes. The mean of the Z/S r a t i o s given i n (Table 6) i s 0.5 i .03 which i s consistent with the 30° t i l t of the preferred plane on the polar diagram and comparable to the values obtained (25) by Parkinson x ' i n A u s t r a l i a . 2. Variations with a Period of Twenty Minutes The scatter of the Tofino polar diagram at a frequency of 63 three cycles 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 variations with a horizontal disturbance vector i n a p a r t i c u l a r d i r e c t i o n . V e r t i c a l Component Amplitude spectral densities C (co) at frequencies of .047, .049, .051 , and .053 cycles per minute were used to represent variations with a period of approximately twenty minutes. The v e r t i c a l component at Tofino i s t y p i c a l l y larger than at Franklin River but, Instead of there being a smooth trend to smaller values further inland, values at V i c t o r i a , Westham Island and Abbotsford are In general larger than at F r a n k l i n River, but usually not so large as at Tofino (Table 5 ) . As at the lower frequency a mean value of Z, based on eight magnetic features, was calculated f o r each station r e l a t i v e to corresponding Abbotsford values (Table 2 ) . The plot of Z as a function of distance from the coast shows the Tofino anomaly and also suggests a v e r t i c a l anomaly i n the region of Westham Island (Fig. 19)« The larger probable errors at t h i s frequency imply that the suggested trends are not as consistently reproducible as at the lower frequencies. Nevertheless, the enhancement of Westham Island over Abbotsford which i s absent at the lower frequencies i s s t a t i s t i c a l l y 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 conductivity inhomogeneity„ Horizontal Component The t o t a l horizontal v a r i a t i o n H t i s , i n general, larger inland, the amplitudes at Westham Island being about twenty percent larger than at Tofino and the amplitude at F r a n k l i n River usually from ten to twenty percent larger (Table 5). Here again, the horizontal variations are expected to diminish with increasing distance from the Auroral Zone. Hence, we conclude as before, that no appreciable i n t e r n a l anomaly shows up i n the horizontal component from Tofino to Abbotsford. C Frequency Dependence of the Anomaly The v e r t i c a l amplitude spectral densities, Cz (ui) s at Tofino and F r a n k l i n River were compared with the corresponding values at V i c t o r i a (Table 3). The values of Z T O F ^ / Z ! V I C . derived from six magnetic disturbances showed a s t a t i s t i c a l l y s i g n i f i c a n t deviation from a postulated value ^ T O F y / 2 y ( C . = / over the entire range of periods from twenty minutes to three hours. The values of -ZVf?ft^/ZTy,c derived from f i v e magnetic disturbances did not deviate s i g n i f i c a n t l y from a r a t i o of unity over the same frequency range, and a comparison between V i c t o r i a and Abbotsford at these frequencies based on six magnetic features showed no s i g n i f i c a n t difference. The mean values of ~Z--^QV.^/^vic. and Z. p^y/Z^x. were plotted as a function of period and the points f i t t e d with a smooth curve (Fig. 17). The r e s u l t s indicate that the anomaly reaches a maximum at a period of t h i r t y minutes to one hour, a period at which the e f f e c t i v e o v e r a l l conductivity contrast i s apparently greatest<, D Daily Geomagnetic Variations A Fourier analysis of six t y hours of simultaneous magnetic 2.0h 1.8 1.6 1.4 1.2 1.0 0.8L 65 RATIO OF SPECTRAL DENSITIES AS A FUNCTION OF PERIOD 20 30 60 100 120 PERIOD IN MINUTES Figure 17. Frequency Dependence of the Tofino Anomaly 180 4 § 500 co 400 U J t oo 300 LU O _J < cr & UJ Q_ CO 200 100 48 24 18 15 PERIOD IN HOURS Figure 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 at the Diurnal and Semi-Diurnal Periods 66 records at Tofino, F r a n k l i n River, V i c t o r i a , and Abbotsford yielded well defined peaks at periods of twelve and twenty-four hours, allowing a comparison of the diurnal and semi diurnal geomagnetic variations at these four stations. Additional analyses of simultaneous records were not possible because of l o c a l disturbances on the Tofino records, so that these r e s u l t s must be considered as preliminary. There are no convincing trends i n the horizontal components of the semi diurnal variations, but there i s a six percent increase i n the diurnal horizontal component from Abbotsford to the coast (Table 4). However, the v e r t i c a l variations f o r both the diurnal and semi diurnal com- ponents decrease eastward along the p r o f i l e Tofino, F r a n k l i n River, Abbotsford, the amplitude of the Vancouver Island stations, including V i c t o r i a , being twenty to t h i r t y percent larger than at Abbotsford on the mainland. The marked difference i n the v e r t i c a l d a i l y variations between Abbotsford and the more western stations indicated i n the above preliminary analysis had been mentioned i n an e a r l i e r (16) study by Hyndman% . Consequently, a more thorough analysis based on one hundred and twenty-six consecutive hours of simultaneous magnetic records was c a r r i e d out i n order to compare the v e r t i c a l variations at the V i c t o r i a and Abbotsford stations. The r e s u l t s show a twenty f i v e percent enhancement of V i c t o r i a over Abbotsford i n the diurnal v e r t i c a l variations, diminishing to a ten percent enhancement i n the semi diurnal v e r t i c a l v a r i a t i o n s (Fig. 18)„ V i c t o r i a does not d i f f e r appreciably from Abbotsford at higher frequencies. ; 2 I 0 - l h -2 CO a: 3 UJ 3 - SEISMIC PROFILE -20 X fc-30 LU Q -40 -50 1.8 1.6 1.4 1.2 1.0 0.8 0.6 67 ELEVATION PROFILE 49° 10' 130° 129° 128° I27°V'I26°. 49° 30 , LATITUDE TbF I F ^ ^ ^ ' A K T 5.9 KM/SEC. 8.1 KM/SEC. V \ 6.8 KM /SEC. \ \ \ \ \ AMPLITUDE OF VERTICAL GEOMAGNETIC VARIATIONS PERIOD — 45 MIN. — 20 MIN. -I _L TOP _»— 130' 129° I28c 127* I26e 125° 124° 123° 122° Figure 19. Amplitude of V e r t i c a l Variations along the East-West P r o f i l e Normalized with Abbotsford Values; Compared with an Elevation P r o f i l e and a Crustal Structure P r o f i l e (adapted from W.R.H. White and J.C. Savage) 68 E Discussion of Results The v e r t i c a l anomaly at Tofino reaches a maximum at a frequency between one and two cycles per hour and i s characterized by an induction c o e f f i c i e n t of 0.5. The polar diagram plotted f o r t h i s range of frequencies suggests a two dimensional conductivity di s c o n t i n u i t y running approximately i n a north-south d i r e c t i o n . Although the diagram at a higher frequency of three cycles per hour seems to indicate a s h i f t i n the d i r e c t i o n a l dependence (more perpendicular to the co a s t l i n e ) , such a s h i f t cannot be considered s i g n i f i c a n t because of the limited number of points and the scatter on the diagrams. I t i s clear, however, that at the maximum response frequency the d i r e c t i o n a l dependence i s consistent with that expected at the edge of an oceanic current sheet and/or above a two dimensional conductivity step i n the upper mantle•running approximately p a r a l l e l to the continental s h e l f l i n e . Since the anomaly diminishes to an almost n e g l i g i b l e value at a distance of 100 kilometers from the coastline (Pig. 19) i t i s not expected to be caused by a conductivity step deeper than 100 kilometers beneath the surface. Furthermore, unless the upper surface of the step i s at a shallow depth, perhaps i n the v i c i n i t y of the Mohorovicic discontinuity, most of the e l e c t r i c currents w i l l flow i n the ocean rather than i n the mantle beneath. U n t i l one can accurately measure the e l e c t r i c currents flowing i n the deep ocean or the amplitude of geomagnetic variati o n s beneath the oceanic layer, i t i s d i f f i c u l t to estimate the contribution of subsurface changes i n conductivity at the coast- l i n e . 69 The twenty-five percent increase i n the v e r t i c a l diurnal variations from the mainland to Vancouver Island must be inde- pendent of surface layers and most l i k e l y does r e f l e c t some kind of l a t e r a l subsurface change i n conductivity deep i n the upper mantle which may be associated with a systematic difference i n the nature of the upper mantle beneath oceans and continents„ The possible v e r t i c a l anomaly at three cycles per hour at Westham Island may be due to a r e l a t i v e l y shallow conductivity inhomogeneity, since i t i s absent at a lower frequency of one to two cycles per hour. The l i m i t e d s p a t i a l extent of the coastal anomaly rules out mutual induction between, the P a c i f i c Ocean and the sea water i n Georgia S t r a i t , and the t o t a l conductivity of the sea water Is not large enough to sustain e l e c t r i c currents fo r longer than a few seconds. However, the Georgia S t r a i t depression at the south end of the l a r g e l y submerged coastal trough between Vancouver Island and the mainland i s underlain to a depth of f i v e kilometers by c l a s t i c sediments of late Mesozoic and early Cenozoic age (White and Savage(5^)). Consequently., i t i s at l e a s t plausible to suppose that the o v e r a l l conductivity of the depression r e l a t i v e to the mainland rocks i s large enough to cause a small v e r t i c a l anomaly. At ;the same time, a deeper subcrustal source Is not ruled out. 70 VI CONCLUSIONS With reference to Pig. 19 which shows the magnitude and extent of the v e r t i c a l anomaly, an elevation p r o f i l e f o r the region, and a c r u s t a l structure p r o f i l e based on seismic and gravity data (White and Savage^o 1)^ i t i s believed that: (a) The major portion of the coastal anomaly at one to two cycles per hour i s caused by e l e c t r i c currents flowing i n the ocean beyond the continental s h e l f l i n e , unless there i s a l a t e r a l conductivity contrast at a depth of 100km or l e s s which i s large enough to compete with the contrast between ocean and continent. (b) The extent of the diurnal "anomaly" i s consistent with a conductivity d i s c o n t i n u i t y deep i n the upper mantle. (c) The possible Inland anomaly at a higher frequency of three cycles per hour i s so heavily dependent on shallow structure that no consistent trends compatible with the large scale c r u s t a l model can be postulated. TABLES STATION INSTRUMENT GEOGRAPHIC LONGITUDE LATITUDE APPROX. ELEVATION (FT) DURATION OF OBSERVATIONS TOFINO ASKANIA 125°47'W 49°5'N 40 Dec 16/63 to July 10/64 FRANKLIN RIVER ASKANIA 124°48'W lf9°6'N 100 May 16/64 to July 10/64 VICTORIA ASKANIA 123°25'W 48°31'N 600 Sept 1/63 to May 12/64 VICTORIA RUSKA 123°25'W 48°31'N 600 Continuous WESTHAM ISLAND ASKANIA 123°11'W 49°6'N 10 Nov I/63 to June 5/64 ABBOTSFORD ASKANIA 122°21'W 49°1"N 200 June 5/64 to July 12/64 Table 1 Location and Deta i l s of the Variograph Stations FREQUENCY .RANGE .021 C.P.M. to .025 C.P.M. TOP FRA WES ABB .047 C.P.M. to .053 C.P.M. TOF FRA WES ABB Z COMPONENT 1.8*0.1 1.1±.04 0 . 9 * . 0 7 1.0 Z COMPONENT 1.4*0.1 0.80±.08 1 . 2 * 0 . 1 1.0 S COMPONENT 0 . 9 * . 0 3 0.9±.02 1.0±.04 1 .0 H t COMPONENT 0 . 9 * . 0 5 1 . 0 * . 0 3 1.1*.09 1.0 VIC 1.1*0.09 VIC 1 . 0 * 0 . 1 Table 2 Mean Values of V e r t i c a l and Horizontal Changes Relative to Abbotsford Values (Based on Nine Magnetic Disturbances) FREQUENCY IN JAN. 10, 1964 ] VLARCH 5, 1964 MAY 24, 1964 JUNE 19, 1964 CYCLES PER MIN TOF VIC J?OF VIC TOF FRA VIC FRA VIC .005 760 420 550 340 2790 2740 2890 3610 3840 .009 1010 520 680 430 2540 2150 2000 2420 2650 .017 760 370 1050 540 810 530 560 1400 1450 .023 860 410 850 410 580 450 450 720 750 .033 460 170 110 40 370 340 340 i 4 o 60 .041 240 100 360 170 130 80 90 420 470 .049 150 70 70 50 170 170 170 180 240 MAY 25, 1964 MAY 27, 1964 JUNE 21, 1964 TOF FRA VIC TOF FRA VIC TOF FRA VIC .005 4160 4100 4520 1940 1720 1580 920 970 1060 .009 2880 2780 2940 930 610 560 450 550 066O .017 400 350 400 69O 500 400 230 170 1170 .023 460 360 460 250 170 100 220 170 170 .033 360 200 270 160 130 90 120 90 100 .041 220 260 300 140 80 60 130 130 160 .049 210 160 200 80 70 40 40 30 40 Table 3 Comparison of V e r t i c a l Component Spectral Densities ( i n Gamma-minutes) at Tofino, Franklin River and V i c t o r i a as a Function of Frequency. VERTICAL COMPONENT TOF FRA VIC ABB DIURNAL SEMI DIURNAL 525 333 490 285 508 290 406 278 TOTAL HORIZONTAL COMPONENT DIURNAL SEMI DIURNAL 876 670 854 679 825 648 830 687 Table 4 Comparison of Spectral Densities f o r the Dai l y Variations (Based on 60 hrs. of Continuous Records from 1500 U.T. June 19/64 to 9300 U.T. June 22/64) .047 CYCLES PER MINUTE DATE OP Z COMPONENT VIC* H<_ COMPONENT Z/H* RATIO FEATURE TOP FRA WES ABB TOP FRA WES ABB VIC* TOF FRA WES ABB VIC* JAN. 10 140 70 270 360 0 . 5 0 . 2 MARCH 5 130 80 40 450 510 440 0 . 3 0 . 2 0 . 1 MAY 24 190 150 180 180 90 100 130 120 2.0 1.4 1.4 1.5 APRIL 29 40 10 190 190 0 . 2 0 . 1 MAY 25 270 240 310 300 290 240 0 . 9 0 . 8 1.3 MAY 27 90 50 60 290 180 180 290 0 . 3 0 . 3 0 . 2 JUNE 21 70 50 70 50 150 170 170 0 . 4 0 . 3 0 . 4 0 . 3 JUNE 10 150 160 180 320 370 290 0 . 5 0 . 4 0 . 6 JULY 3 10 30 100 80 0 . 1 0 . 4 .049 CYCLES PER MINUTE JAN 10 150 70 280 310 0 . 5 0 . 2 MARCH 5 70 20 50 230 270 220 0 . 3 0 .1 0 . 2 MAY 24 170 170 210 170 90 100 120 120 1.9 1.6 1.8 1.5 APRIL 29 10 20 150 130 0.1 0 . 1 MAY 25 210 160 200 200 250 240 1.1 0 . 6 0 . 9 MAY 27 .86 70 40 140 110 120 0 . 6 0 . 6 0 . 3 JUNE 21 40 30 60 40 140 150 190 160 0 . 3 0 . 2 0 . 3 0 . 2 JUNE 10 180 170 240 360 420 350 0 . 5 0 . 4 0 . 7 JULY 3 10 30 90 80 0.1 0 . 3 Table 5 Comparison along the P r o f i l e of the Spectral Densities ( i n Gamma-minutes) Representing the V e r t i c a l Change Z and the Total Horizontal Change H t together with the Ratio Z/Ht ( V i c t o r i a Not Included i n the P r o f i l e ) .051 CYCLES PER MINUTE DATE OP Z COMPONENT COMPONENT Z/Ht RATIO FEATURE TOP FRA WES ABB VIC* TOP PRA WES ABB VIC* TOP T PRA WES ABB VIC* JAN 10 160 60 290 180 250 0 . 5 •0.3 MARCH 5 50 60 7.0 140 140 0 . 4 0 . 3 0 . 5 MAY 24 170 150 170 150 60 70 80 90 2.6 2.1 2.1 1.7 APRIL 29 50 50 140 110 0 . 3 0 . 4 MAY 25 290 240 250 240 330 340 1.2 0 . 7 0 . 7 MAY 27 100 80 70 170 180 170 0 . 6 0 . 5 0 . 4 JUNE 21 30 30 20 40 100 100 130 110 0 . 3 0 . 3 0 . 1 0 . 4 JUNE 10 160 170 200 370 460 310 0 . 4 0 . 4 0 . 6 JULY 3 10 20 90 80 0 . 1 0 . 2 .053 CYCLES PER MINUTE JAN 10 140 60 290 200 0 . 5 0 . 3 MARCH 5 100 110 70 260 300 260 0 . 4 0 . 4 0 . 3 MAY 24 90 70 100 80 150 150 140 120 0 . 6 0 . 5 0 . 8 0 . 7 APRIL 29 70 60 140 120 0 . 5 0 . 5 MAY 25 370 320 340 290 350 350 1.3 0 . 9 1.0 MAY 27 70 30 40 210 210 220 0 . 3 0 . 2 0 . 2 JUNE 21 40 40 30 50 70 80 80 60 0 . 6 0 . 5 0 . 4 0 . 9 JUNE 10 160 200 150 290 370 250 0 . 5 0 . 5 0 . 6 JULY 3 10 10 80 70 0 . 2 0 . 1 Table 5 (continued) ,021 CYCLES PER MINUTE DATE OP Z COMPONENT ABB * S COMPONENT ABB Z/S RATIO ABB * FEATURE Tub ERA WES VIC TOP FKA WES VIC TOP FKA WES VIC JAN 10 840 390 1500 1620 0 .6 0 . 2 MARCH 5 1100 600 560 1970 880 2060 1890 0 . 6 0 .3 0 . 3 MAY 24 550 460 420 550 890 920 890 0 . 6 0 . 5 0 • 5 0 . 6 MAY 25 380 190 50 1450 1450 1470 0 . 3 0 . 1 0 MAY 27 210 90 50 760 800 760 0 . 3 0 . 1 0 .1 JUNE 21 150 80 110 50 410 390 460 430 0 . 4 0 . 2 0 . 2 0 .1 JUNE 10 1290 1350 1290 1700 1820 1650 0 . 8 0 . 7 0 . 8 JULY 3 400 390 490 570 0 . 8 0 . 7 .023 CYCLES PER MINUTE JAN 10 860 410 1460 1540 0 . 6 0 . 3 MARCH 5 850 400 410 1670 1730 1590 0.5 0 .2 0 . 3 MAY 24 580 450 350 450 860 880 930 820 0 . 7 0 . 5 0 .4 0 . 6 MAY 25 46o 360 460 1160 1160 1110 0 . 4 0.3 0 . 4 MAYJ. 27 i. 250 170 100 720 800 720 0 . 3 0 . 2 0 . 1 JUNE 21 220 170 140 170 320 300 360 340 0 . 7 0 . 6 0 . 4 0 . 5 JUNE 10 720 680 750 l l 8 0 1140 1070 0 . 6 0 . 6 0 . 7 JULY 3 330 340 450 470 0 . 7 0 . 7 .025 CYCLES PER MINUTE JAN 10 840 390 1390 1390 0 . 6 0 . 3 MARCH 5 580 240 240 1280 1300 1200 0 . 5 0 .2 0 . 2 MAY 24 370 250 220 200 670 700 74o 640 0 . 6 0 . 4 0 .3 0 . 3 MAY 25 760 640 710 820 800 660 0 . 9 0 . 8 1.1 MAY 27 240 140 120 640 750 640 0 . 4 0 . 2 0 , 2 JUNE 21 250 210 160 220 270 250 300 280 0 . 9 0 . 9 0 .5 0 . 8 JUNE 10 310 240 390 490 480 420 0 . 6 0 . 5 0 . 9 JULY 3 260 280 450 410 0 . 6 0 . 7 Table 6 Comparison along the P r o f i l e of the Spectral Densities ( i n Gamma-minutes) Representing the V e r t i c a l Change Z and the Horizontal Change i n an East-. West Direction S together with the Ratio Z/S 76 APPENDIX I FOURIER ANALYSIS 1. A function f ( t ) can be expanded i n any i n t e r v a l (-T, T) so long as i t s a t i s f i e s the D i r i c h l e t condition i n the'interval | f ( t ) | d t converges. The function may be developed oo -oo i n a Fourier Series OO where and -fCt) = i k + ^ Q « C o s Tfrt + b„ Sin nut 2 . nsi 7 - r>=i T -T4 * ^ T T J :f to d : - T T J T - T ^ ( x ) cos hir x dac T I f Writing - T f (*) s , n n 1 r x d x T T 2ir J - T oo > T rT. IT L J - T - T The i n t e r v a l (-T,T) may be expanded to (-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 +00 fft) ~ 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 -* J -00 The cosine and sine spectral d e n s i t i e s and B(w) are 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 that f(t) = [ ft (co) cos cot + B(co) siVut] d -00 CO 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 expone n t i a l form + ~ - gn i r t Kt) = 2 c n e T wh e r e I fa) + UVTTZ e T -ot> 2 T As before t h i s reduces to an i n t e g r a l form i n the l i m i t asT -»oo i . e . - icot C (co) e dco -oo where and 2TT + 00 -00 1 cox •iuit Hence, f ( t ) may be synthesized by a sum of terms e covering a l l angular frequencies i n the continuous i n f i n i t e range (-00,00). These terms have i n f i n i t e s i m a l amplitudes given by the expression 78 | C(w) 1 dco . The amplitude density spectrum 1 C(u>) | i s , therefore, not the actual amplitude c h a r a c t e r i s t i c of f ( t ) , but rather a c h a r a c t e r i s t i c which shows r e l a t i v e magnitude only. > TOFINO VICTORIA WESTHAM ISLAND § Recorded March 5, 1964 0100 to 0300 U.T. VICTORIA WESTHAM ISLAND Recorded A p r i l 29, 1964 0100 to 0300 U.T. TOFINO FRANKLIN RIVER VICTORIA W E S T H A M ISLAND Recorded May 24, 1964 0600 to 0900 U.T. 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