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Analytical and analogue methods of studying electromagnetic variations at the earth's surface Dosso, Harry William 1967

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The U n i v e r s i t y of B r i t i s h  Columbia  FACULTY OF GRADUATE STUDIES PROGRAMME OF THE FINAL ORAL  EXAMINATION  FOR THE DEGREE OF DOCTOR OF PHILOSOPHY of HARRY W... DOS SO B.A.,  The U n i v e r s i t y of B r i t i s h  Columbia,"1955  M.Sc,  The U n i v e r s i t y of B r i t i s h Columbia, 1957 WEDNESDAY, MAY 3, 1967 AT 10:30 A.M.  IN ROOM 206, CHEMICAL ENGINEERING  BUILDING  COMMITTEE IN CHARGE Chairman:  B. N. Moyls  R. W. B u r l i n g R. M. E l l i s J . A. Jacobs  M. W. Ovenden R. D. R u s s e l l T. Watanabe  E x t e r n a l Examiner: D. I . Gough U n i v e r s i t y of A l b e r t a Edmonton, A l b e r t a Research S u p e r v i s o r :  J . A. Jacobs  ANALYTICAL AND  ANALOGUE METHODS OF  ELECTROMAGNETIC VARIATIONS AT THE  STUDYING •  EARTH'S SURFACE  ABSTRACT The r e s e a r c h d e s c r i b e d i n t h i s t h e s i s d e a l s w i t h both mathematical ..and analogue, .methods of s t u d y i n g e l e c t r o m a g n e t i c . v a r i a t i o n s at the e a r t h ' s s u r f a c e . F i e l d components .are s t u d i e d f o r f r e q u e n c i e s i n the range 10 ^ - 10^ cps and f o r e a r t h c o n d u c t i v i t i e s i n the range 1 0 " - 10" emu. 1 6  1 0  E x p r e s s i o n s are ..developed f o r the . e l e c t r i c . and .magn e t i c . . f i e l d components .at the s u r f a c e and w i t h i n the upper l a y e r of a...hori.zontalLy . . s t r a t i f i e d . . f l a t . c o n d u c t i n g e a r t h i n the f i e l d of i n c i d e n t plane waves. Amplitudes and phase angles are o b t a i n e d f o r v a r i o u s f r e q u e n c i e s , angles of i n c i d e n c e , l a y e r t h i c k n e s s e s , depths, and conductivities. As an e x t e n s i o n of t h i s problem, e x p r e s s i o n s f o r a m u l t i l a y e r e a r t h (n l a y e r s ) are d e v e l oped and e v a l u a t e d . Each of s e v e r a l t h i c k l a y e r s i s d i v i d e d i n t o a s u f f i c i e n t number of s u b l a y e r s , w i t h changing c o n d u c t i v i t y , to r e p r e s e n t , to a good a p p r o x i mation, a continuous change i n c o n d u c t i v i t y . The c o n d u c t i v i t y d i s t r i b u t i o n s used are of i n t e r e s t i n geophysics. The r e s u l t s f o r the plane wave model, i n d i c a t e that the amplitudes and phase, angles are s t r o n g l y a f f e c t e d by the c o n d u c t i v i t y s t r u c t u r e . The e l e c t r i c and magnetic f i e l d s at the s u r f a c e of a f l a t homogeneous c o n d u c t i n g e a r t h i n the near f i e l d of an o s c i l l a t i n g l i n e c u r r e n t are. s t u d i e d . The equations f o r the amplitudes and phase angles developed by Law and Fannin (1961) are used f o r the c a l c u l a t i o n s . Amplitudes and phase angles are o b t a i n e d f o r v a r i o u s f r e q u e n c i e s , c o n d u c t i v i t i e s , source h e i g h t s , and l o c a t i o n s w i t h r e s p e c t to the overhead c u r r e n t . The r e s u l t s i n d i c a t e that the v e r t i c a l to h o r i z o n t a l magnetic f i e l d r a t i o s are i n the range of e x p e r i m e n t a l l y observed, v a l u e s . An analogue model s u i t a b l e f o r s t u d y i n g the behaviour of the n a t u r a l geomagnetic and t e l l u r i c f i e l d v a r i a t i o n s f o r v a r i o u s g e o l o g i c a l s t r u c t u r e s was c o n s t r u c t e d . Two types -of f i e l d sources were used - an o s c i l l a t i n g sheet  c u r r e n t and an o s c i l l a t i n g l i n e c u r r e n t . Amplitudes and phase angles f o r the h o r i z o n t a l e l e c t r i c , h o r i z o n t a l magnetic, and v e r t i c a l magnetic f i e l d components are o b t a i n e d and d i s c u s s e d f o r v a r i o u s g e o l o g i c a l s t r u c t u r e s i n c l u d i n g a f l a t l a y e r e d e a r t h , c y l i n d r i c a l bodies embedded i n the s u r f a c e l a y e r , v e r t i c a l f a u l t s and dykes, sea mounts and c o n d u c t i n g domes, c o a s t l i n e s t r u c t u r e s ( s e a - l a n d i n t e r f a c e and an u p w e l l i n g i n a h i g h c o n d u c t i v i t y zone w i t h i n the m a n t l e ) , and i s l a n d s i n an ocean c h a n n e l . The r e s u l t s o b t a i n e d f o r the c o a s t l i n e s t r u c t u r e s and i s l a n d s i n an ocean channel tend to support the proposed s t r u c t u r e s suggested by v a r i o u s workers (Schmucker 1964, Lambert and Caner 1965, Lokken and Maclure 1966.) i n d e s c r i b i n g the experimentally observed c o a s t a l magnetic f i e l d anomalies. The analogue model c o n s t r u c t e d and used f o r t h i s work r e a d i l y lends i t s e l f to s t u d y i n g a wide range of g e o l o g i c a l s t r u c t u r e s f o r a v a r i e t y of source f i e l d s i n a d d i t i o n to those used here „  GRADUATE STUDIES Field  of Study:  Geomagnetism  Advanced Geophysics P r i n c i p l e s of E a r t h Geomagnetism and Plasma Waves  Science  Aeronomy  J . A.  Jacobs  W.  Slawson  F.  T. Watanabe T. Watanabe  PUBLICATIONS 6 7  s h o r t .pedagogical a r t i c l e s (not l i s t e d below) P a c i f i c Naval L a b o r a t o r y Reports (not l i s t e d below)  Singh, P.P., Dosso, H.W., and G r i f f i t h s , G.M., 1959. The e n e r g i e s and r e l a t i v e p a i r p r o d u c t i o n c r o s s s e c t i o n s f o r Zn&5 and Na22. .gamma r a y s . Can. J . Phys. _37, 1055. Dosso, H.W., 1962. The magnetic f i e l d at the s u r f a c e of a s t r a t i f i e d f l a t conductor i n the f i e l d of plane waves w i t h a p p l i c a t i o n to g e o p h y s i c s . Can. J . Phys. 40, 1583. Dosso, H.W., 1965. The e l e c t r i c and magnetic f i e l d s i n a s t r a t i f i e d f l a t conductor f o r i n c i d e n t plane waves. Can. J . Phys. 43, 898. Dosso, H.W., 1966. A plane wave analogue model f o r stud} ing electromagnetic v a r i a t i o n s . Can. J . Phys. 44, 68. Dosso, H.W., 1966. A m u l t i - l a y e r c o n d u c t i n g e a r t h i n the f i e l d of p l a n e waves. Can. J . Phys. 44, 81. Dosso, H.W., 1966. Further r e s u l t s f o r a multi-layer c o n d u c t i n g e a r t h i n the f i e l d of plane waves. Can. J . Phys. 44, 1197. Dosso, H.W., 1966. Analogue model measurements f o r e l e c t r o m a g n e t i c v a r i a t i o n s near v e r t i c a l f a u l t s and dykes. Can. J . E a r t h S c i . 3, 287. Dosso, H.W., 1966. The e l e c t r i c and magnetic f i e l d s at' the s u r f a c e of a f l a t c o n d u c t i n g e a r t h i n the near f i e l d of an o s c i l l a t i n g l i n e c u r r e n t . Can. J . Phys. 44, 1923. Dosso, H.W., 1966. Analogue model measurements f o r e l e c t r o m a g n e t i c v a r i a t i o n s near a c o a s t l i n e . Can. J . E a r t h S c i . 3, 917.  (i)  ANALYTICAL  AND  ELECTROMAGNETIC  ANALOGUE  METHODS  VARIATIONS  AT  THE  OF  STUDYING  EARTH'S  SURFACE  by  HARRY B.A.  ( H o n s . ) ,  M . S c ,  A  WILLIAM  U n i v e r s i t y  U n i v e r s i t y  THESIS THE  of  SUBMITTED  DOCTOR  i n  of  OF  the  B r i t i s h  B r i t i s h  IN  REQUIREMENTS  DOSSO  Columbia,  PARTIAL FOR  THE  Columbia,  FULFILMENT DEGREE  1955  1957  OF  OF  PHILOSOPHY  Department of  GEOPHYSICS  We  a c c e p t  r e q u i r e d  THE  t h i s  t h e s i s  as  conforming  to  s t a n d a r d  UNIVERSITY  OF  A p r i l ,  ! (c)  Harry  William  BRITISH  COLUMBIA  1967 Dosso  1967  the  In presenting  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements  f o r an advanced degree a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I agree that  d i e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and  study.  I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e  copying of t h i s  t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d t y t h e Head o f my Department o r by h i s r e p r e s e n t a t i v e s .  I t i s understood t h a t  or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l w i t h o u t my w r i t t e n p e r m i s s i o n .  Department o f  ' Geophysics  The U n i v e r s i t y o f B r i t i s h Col-umbia Vancouver 8, Canada Date  May, < 1967  copying  g a i n s h a l l n o t be a l l o w e d  ( i i )  ABSTRACT  T h i s models  f o r  t h e s i s  s t u d y i n g  s u r f a c e .  The  the  10  i n  range the  d e a l s  range  components  c y c l e s / s e c -  to  10"^  E x p r e s s i o n s magnetic  f i e l d  l a y e r  a  the  of  f i e l d  amplitudes q u e n c i e s , and  i n c i d e n t  and  phase of  e v a l u a t e d .  a  s u f f i c i e n t  number  r e p r e s e n t  to  c o n d u c t i v i t y . i n t e r e s t model  i n  s t r o n g l y  f l a t  a  an  f l a t  l a y e r  e x t e n s i o n e a r t h  (n  t h i c k  of  The  w i t h  -results  (1961)  used  f o r  are  angles the  f o r  a  and a  change  used  are  i n of  wave are  s t r u c t u r e .  i n  near  c a l c u l a t i o n s .  e x -  c o n d u c t i v i t y ,  angles  at  developed  f r e -  i n t o  plane  phase  ;  developed  d i v i d e d  f i e l d s  s t u d i e d .  of  problem,  the  i n  depths,  continuous  f o r  upper  e a r t h  v a r i o u s  are  i s  the  r e s u l t s  changing  and  magnetic e a r t h  and  w i t h i n  d i s t r i b u t i o n s  amplitudes  c o n d u c t i n g  and  t h i s  l a y e r s  and  phase  i n  c o n d u c t i v i t i e s  e l e c t r i c  l a y e r s )  e l e c t r i c  and  e a r t h ' s  f r e q u e n c i e s  t h i c k n e s s e s ,  c o n d u c t i v i t y  c u r r e n t  analogue  the  c o n d u c t i n g  o b t a i n e d  the  l i n e  f o r  E x t e n s i v e  a p p r o x i m a t i o n  the  and  a t  e a r t h  the  surfaee  by  amplitudes are  are  c o n d u c t i v i t y  that  homogeneous  o s c i l l a t i n g  the  s u b l a y e r s ,  good  f o r  f o r  waves.  angles  g e o p h y s i c s .  a f f e c t e d The  plane  s e v e r a l  of  The  i n d i c a t e  at  m u l t i l a y e r  Each' of  s t u d i e d  s t r a t i f i e d  As  v a r i a t i o n s  and  developed  i n c i d e n c e ,  c o n d u c t i v i t i e s . f o r  m a t h e m a t i c a l  emu.  0  components  a n g l e s  p r e s s i o n s  to  are  h o r i z o n t a l l y of  are  J  ^0  10"^  both  e l e c t r o m a g n e t i c  f i e l d to  w i t h  the  The by  the  s u r f a c e  f i e l d  equations  Law  and  E x t e n s i v e  of f o r  of  a  an the  F a n n i n r e s u l t s  of  (ill) amplitudes and  phase angles are o b t a i n e d f o r v a r i o u s  quencies, c o n d u c t i v i t i e s , source h e i g h t s , respect  to the overhead c u r r e n t .  The  and  fre-  locations with  r e s u l t s i n d i c a t e that  the v e r t i c a l to h o r i z o n t a l magnetic f i e l d r a t i o s are i n the range of e x p e r i m e n t a l l y  observed  values.  - An analogue model s u i t a b l e f o r studying of the n a t u r a l geomagnetic and various of f i e l d  the  behavior  t e l l u r i c f i e l d variations for  g e o l o g i c a l s t r u c t u r e s was  constructed.  The  two  types  sources used were an o s c i l l a t i n g sheet c u r r e n t  an o s c i l l a t i n g l i n e c u r r e n t . amplitudes and  measurements of  phase angles f o r the h o r i z o n t a l e l e c t r i c ,  h o r i z o n t a l magnetic, and ents are o b t a i n e d and structures  Extensive  the v e r t i c a l magnetic f i e l d  discussed  f o r various  i n c l u d i n g a f l a t layered earth,  an u p w e l l i n g  w i t h i n the mantle), and  cylindrical and  suggested by v a r i o u s  (sea-  i n a high-conductivity  i s l a n d s i n an ocean channel.  i n an ocean channel tend to support the proposed  islands structures  i n describing  m e n t a l l y observed c o a s t a l magnetic f i e l d anomalies. analogue model c o n s t r u c t e d to studying  zone The  workers (Schmucker 196^-, Lambert  Caner 1965? Lokken and Maclure 1966)  bodies  dykes,  r e s u l t s o b t a i n e d f o r the c o a s t l i n e s t r u c t u r e s and  lends i t s e l f  compon-  conducting domes, c o a s t l i n e s t r u c t u r e s  l a n d i n t e r f a c e and  the  geological  embedded i n the s u r f a c e l a y e r , v e r t i c a l f a u l t s sea mounts and  and  and  the  experi-  The •  and used f o r t h i s work r e a d i l y  a wide range of g e o l o g i c a l s t r u c t -  ures f o r a v a r i e t y of source f i e l d s i n a d d i t i o n to the ones used here.  (iv)  Page  ABSTRACT  i i  L I S T OF ILLUSTRATIONS  vi  LIST- OF TABLES  xvi  ACKNOWLEDGEMENTS CHAPTER 1  xvii 1  INTRODUCTION  i  CHABTER 2  1.1  H i s t o r i c a l Review  1.2  Object of the Thesis  15  MATHEMATICAL MODELS  18  2.1  A Simple Layered Conducting E a r t h i n t h e F i e l d o f P l a n e Waves  18  2.1.1  Introduction  18  2.1.2  Mathematical Analysis  19  2.1.3  Discussion  28  2.2  2.3  of Results  A Complex L a y e r e d C o n d u c t i n g E a r t h i n t h e F i e l d o f P l a n e Waves  $h  2.2.1  Introduction  5*+  2.2.2  Mathematical Analysis  55  2.2.3  Discussion  58  of Results  A Homogeneous C o n d u c t i n g E a r t h i n the F i e l d of a L i n e Current  68  2.3.1  68  2.3.2 2.3.3  Introduction •Mathematical Analysis Discussion  of Results  72 72  (v)  CHAPTER 3  Page  ANALOGUE MODELS 3.1  Sheet C u r r e n t Source  87  3.1=1  Introduction  87  3.1.2  Mathematical Analysis  89  3.1.3  M o d e l D e s c r i p t i o n and • Measurement Techniques  91  3.1A 3.2  87  Discussion  of Results  L i n e C u r r e n t Source  17*f  3.2.1  Introduction  3.2.2  Mathematical Analysis  3.2.3 3.2.!+  • Model D e s c r i p t i o n Discussion  99  of Results  '['Jh 175" 175 176  CHAPTER h • SUMMARY AND CONCLUSIONS  202  BIBLIOGRAPHY  206  (vi) L I S T OF ILLUSTRATIONS Figure 1.  M o d e l u s e d i n t h e p l a n e wave p r o b l e m .  2.  The a m p l i t u d e s  (a)-(c)  and t h e phase a n g l e s (1)  a f u n c t i o n o f 6 f o r f=1 c y c l e / s e c ,  (2) 1 0 ~ \ (3) 1 0 ~ ^ a n d (If) 1 0 ~ 1  3.  11  1  emu, a n d (1) 9=5, (2)  10, (3) 25, (k) k5,  85°.  (5) 65,  S k i n d e p t h as a f u n c t i o n o f f r e q u e n c y f o r a of  5.  o=10~ ,  The r a t i o R as a f u n c t i o n o f f r e q u e n c y f o r o=10"' ^ a n d (6)  k.  as  emu.  1 6  1  (d)  range  conductivities.  The a m p l i t u d e s H ,  H  x  H  y 5  z ?  f u n c t i o n s o f © f o r o =1 0~ 2  and the r a t i o R as o^=10"  1  1  emu,  6  f=1  c y c l e / s e c , a n d d = .1 o5 cm. 2  6. • The d e p e n d e n c e o f H  H  z  incidence  f o r o = 1 0 ~ \ y ^ ~°^^  and l a y e r t h i c k n e s s a n d f=1 c y c l e / s e c .  7.  on t h e a n g l e o f  z  1  2  as a f u n c t i o n o f f a n d d  ci  =  Q  e m U  f o r $=50 , p  2  ( a ) - d = 1 0 ~ \ - d =.l'0"" ,- ( b ) o = 1 0 ~ , d = 1 0 ~ 1  16  2  8. < E  z  1 6  2  3  3  a s a f u n c t i o n o f f f o r 6= +5 , 0 = 1 0 ~ 1  emu, (1) d =10 2  (5)  d *10 2  ?  (6)  3  '  P  2  1  ,  1  l I f  emu.  o^iO"  1 6  (2) 10 -,- (3) 10-, • (lf>- 10^; o = 1 0 ~ , 3  10 ,  (7)  3  15  IO**", (8)  10?; o  =10-™,'  (9) d =10, ( 1 0 ) M 0 , (11). 10^, (12). 10^; d = 1 0 ~ , (13) d =10, (1^) 1 0 , (15) 1 0 ^ , (16) 10^ cm. 3  2  3  2  9-  H  z  1 3  3  a s a f u n c t i o n o f f f o r 9=>+5 , o = 1 0 " " , o = 1 0 ~ p  emu,  (-1) d = 1 0 , ' (2) 3  2  10^, (3)  16  2  10 , 6  (h)  10?;  3  11  o =10" 3  1 3  (5) d = 1 0 , ( 6 ) 1 0 (7) 1 0 , (8) 1 0 ; o , = 1 0 ~ ^ , (9) d = 1 0 (10) 10^, (11) 1 0 , (12) 107 cm. 3  0  10.  H  z  5  3  9  6  5  7  6  3  as a f u n c t i o n o f d  2  f o r f=1 ,  a n d 6=i+5 , (A) o = 1 0 ~ " , d . = 1 0 ~ -11 ' ~> d =10 emu. P  9  3  16 1 6  cycles/sec  emu, (B)  d =10~ . 1 6  o  (vii) Figure 11.  0  Page Z  as a f u n c t i o n o f d d =10~  1 1  (A)  (B) d = 1 0 "  1 6  2  2  12.  f o r f=1  2  cycle/sec,  ©= 5° k  ,  d =10- °,  10~ ^,  10"  ?  10~  1 3  ,  d =10~  10~  10~ \  10"  1 5  1  1  3  1 1  3  5  ,  1 3  l l f  1  -+3  5  emu, emu.  The a m p l i t u d e s ( a )  a n d t h e p h a s e a n g l e s ( b ) as 11 1Ua f u n c t i o n of z f o r d = x 1 0 , d =10 emu,  k6  L  2  d =2x10  cm, d y  l f  2  13.  H  0 0  ?  -~  3  =1  c  v  c  l  e  /  s  e  c  )  a  n  ©=-+5°.  d  as a f u n c t i o n o f f f o r d = 1 0 , d^=1 . 6 x 1 0 ^ cm,  if 7  3  z  2  z=0, a n d © = 5 ° . k  1*f.  H „ as a f u n c t i o n o f f f o r d = 1 0 ~ 0^=10  >  emu, z=0, 6=^5  d =0,  (1)  (2)  2  10 ,  1oV  15-  H_  (a)  (10)  and Q  cycle/sec, 10"  ih) (6)  10" io~  (8)  10~  (10) 16.  H_  1 1  (a)  , C o , d ^ : (1)  , ,  i o " , (5) 10- V(7)  ,  10~  ,  10-  1 6  ,  1 1  1 6  d =ro- 5  (5)  10~  1  3  1 1  3  1 1  ,  ,  1 6  c< 5  d^s d = 1 0  (8) a n d <*>  1 6 1 1  1 6  , ,  ( )  i o ~ 1 1  10"  l I + ?  ,  1 6 1 6  1 6  10' 10"  ,'  10' 10 - 1~ , ' 1 0 - , i o " \ ' f10' o" ,' 10 , 1 100 " ,, 10' 1(T \ L  1 V  1 6  1  ,  l I f  1 l f  l I f  1  0  f o r z=0.  52  ©=^-5 , a n d t h e dj=10  2  1  59  emu.  1 1  2  (7)  10io~  as a f u n c t i o n o f d  2  10"  1  (9) 1 0 -  cycle/sec,  3  , 10~ \  -16,-  10~  (b)  1 1  1 1  1  and d = 1 0 ~  ;  1 1  1 1  cm, f=1  CD  (a)  1 l +  10~  a n d <*  ^o\,  cm, a n d t h e  , ' (3) - 1 0 -"1 V, ' 1 00 ~-  io~ io~  1  following dp,  H  10"  , ,  1 1  1*8  a s a f u n c t i o n o f z f o r f=1  10"  1 6  10~  (b)  10" ^,  1 6  (8)  2  2  2  ,  and  10 ,  (7)  1 l f  1 0 ^ cm.  ,  d-j-d^lO  17.  (6) 1 0 ,  ©=^5°? d = 1 0 , d^=2x10  following d (2)  0  ,  (h) 1 0 ^ ;  3  2  3  o  10 ,  (3)  2  d = 8 x 1 0 ^ cm, (5) d = 0 , (9)  d.=10~ ^ L 3 , d^=1:.:6x10 cm, 1 1  o  - . 1 6  z  \ (3) i c H 3 ,  ,  (k)  1 6  1 3  ,  (10)  (b.) a s - a f u n c t i o n o f d n  LL  0  1  2  , 1  6  3  10-  Q  -  d =l'0~ - ,'  , 0 ^ = 1 0 " , ' (6)  (9) 1 0 ~  1  1 2  emu.  f o r z=d ,  53  Q  d^-d =10 cm, f=1 c y c l e / s e c , ©=+5 and t h e ~> -16 -11 f o l l o w i n g dp, d , d ^ : d =10 , d^=10 , i  9  ?  3  2  ( 1 ) d = 1 0 " 5 emu, (2) 1  3  (5)  10"  (7)  10~  1 1  ; andd =10~ 2  1 5  ,  (8)  10~  l L f  ,  10" 1 1  ,  l I f  ,  d^lO"  (9) 1 0 ~  10~  (3) 1 3  1  ,  6  ,  1 3  (6)  (10)  ,  (^)  10~  d =10~ 3  10-  1 2  1 6  ,  emu.  1 2  ,  (viii) Figure 18.  Model used i n the c a l c u l a t i o n s f o r a complex layered earth.  19.  Complex l a y e r e d  conductor.  20. "  Model used i n c a l c u l a t i n g  'equivalent'  conductivities. 21.  Model used i n the l i n e c u r r e n t  problem.  22.  H  o f y f o r 0=1 O * "  y  (a) and 0  (b) as f u n c t i o n s  y  1 6  emu, h=2x10 cm, a n d (1) f=10~ , (2) 1'0", 7  3  (3) 10" , \k)  2  1, a n d (5) 10 c y c l e s / s e c .  1  16  23. - H  z  (a) and  •• ( b ) as• f u n c t i o n s  o f y f o r d=10'  emu, h=2x10? cm, a n d (1) f = 1 0 , (2) 10^ , 2  _ 3  (3) 1 0 ~ , Xk) 1 , a n d (5) 10- c y c l e s / s e c - . 1  2k.  E • (a) and ^  x  ( b ) a s f u n c t i o n s o f y f o r o=10"  16  emu, h=2x10? cm, a n d (1) f=10~ , (2) 10~ , 3  (3) 10" , ik)  1, a n d (5) 10 c y c l e s / s e c .  1  25.  H  y  (a) and H  2  z  ( b ) a s f u n c t i o n s o f y f o r d=10"  11  emu, h=2x10 cm, a n d (1) f = 1 0 ~ , (2) 10~ , 7  2  3  (3) 10" , (!+) 1, a n d (5) 10 c y c l e s / s e c . 1  26.  E  x  ( a ) a n d 0^, 0 , ^ Z  f o r o=10~ (2) 1 0 , r2  27.  11  x  (b) as f u n c t i o n s  of y  emu, h= 2x10 cm, a n d (1) f=10~ , 7  3  (3) 1 0 ~ , Xh) 1, a n d (5) 10 c y c l e s / s e c . 1  H . ( a ) a n d H_ ( b ) ats f u n c t i o n s o f y f o r f=10"" J ' 7 16 c y c l e s / s e c , h=2x10' cm, a n d (1) o=10 ,  1  (2) 10" , (3) 10"™, ( i f ) 10" , (5) 10" , (6) 10 \, a n d (7) 10~ emu. 15  13  r1  28.  E  x  12  10  (a) and 0 , 0 y  ( b ) a s f u n c t i o n s o f y f o r f=10~  1  Z  c y c l e s / s e c , h=2x10 cm, a n d (1) o = i 0 ~ , (2) 10~ ^ (3) 1 ( T \ l O ^ , (5) 10" , ( 6 ) 10" , a n d (7) 1'0" emu. 1  10  29.  H  y  (h)  ( a ) , H_ ( b ) -1  f=10  5  7  1 3  12  11  a n d 0_ ( c ) a s a f u n c t i o n o f y f o r . -16 . • 7  c y c l e s / s e c , o=10  emu, a n d (1) h=10',  (2) 2x10 , (3) 3x10 , a n d (>+) lfx10 cm. 7  1  1 6  7  7  (ix) Figure 30.  Page  H  a s a f u n c t i o n o f f r e q u e n c y f o r h=10'  z  (a)  0=1  CT ,' 16  a n d (1+)  Diagram of  the analogue  Diagram of  the model l a y e r e d c o n d u c t o r .  7  8x10  cm.  7  model.  and m a g n e t i c  93  33.  The e l e c t r i c  3k.  B l o c k d i a g r a m o f t h e model measurements  35 •  B_  (a)  and H  f o r f=3x10  E  (a)  y=0,  and H LL  f o r f=6x10 along 37.  (1)  ^ ~ Py  y=0,l +  (k)  cm.  E  d^=1  (k)  y=0.  graphite  105  cylinder  106  traverses y=3R/2 cm.  (k)  c y l i n d e r f o r d^=1  (a)-(b), ^=6x10^ (2) R,  cylinder  traverses  cm, a n d  graphite  98  3 R / 2 cm.  (3) y=R/2,  cycles/sec  and (1)  3R/2  (3) R/2,  (2) y=R,  (c)-(d),  cm, a n d  95  system.  graphite  for a vertical  vertical  x  cm, f = 3 x 1 0  38.  (b)  J  d^=1  cycles/sec,  a  <  (2) R,  93  f i e l d detectors.  for a vertical  cycles/sec,  along- (1) 36.  (b)  85  y=10 ,  (3)  L  x10 ,  emu, a n d ( 1 )  cm, 7  (2) 2 x 1 0 , 7  31.  (b) d = 1 0 "  1 1  7  (3) R/2,  108  cycles/sec  and  f o r t r a v e r s e s a l o n g ( a ) y=0, ( b ) y=R, H. f o r x y t r a v e r s e s a l o n g ( c ) y=0$ ( d ) y=R, f o r a v e r t i c a l  108  v  LL  graphite (1) 39-  E  v  d ^ l , (a)  3x10  Vl.  8 . 6 , (3) h•  (2)  f o r f=3x10 cycles/sec,  vertical hO.  c y l i n d e r f o r f=3x10  cycles/sec,  16.2-, and (>+)  23>.8 cm.  cycles/sec, (d)-(e)  6x10  and  for  (b)-(c)  cycles/sec,  c o n c r e t e c y l i n d e r f o r d^=1  cm a n d  for  109 a  traverses  a l o n g ( 1 ) y=0, (2) R (3) R/2, a n d ( h ) 3R/2. E „ (a) and H (b) f o r a h o r i z o n t a l g r a p h i t e c y l i n d e r x y and E „ (c) f o r a h o r i z o n t a l c o n c r e t e c y l i n d e r f o r f=3x1 CP" c y c l e s / s e c ' , d^=1 cm, a n d t r a v e r s e s a l o n g y=0. ?  H ,  H  (e)  f o r the H p o l a r i z a t i o n f o r a g r a p h i t e  y  z  (a),'E  w=23 cm.  x  ( b ) , \|/ -0 x  y  (c),  0 -0 z  y  (d)  and E / H x  dyke  y  with  111  11"+  (x) Figure 'te.  Page  Hy, H  (a),  z  (e)  dyke w i t h  w = 2 3  r  3 .  E  Y  (a)  for  x  E  with (if) k I  f.  E  x  x  (c) E ^ H y ,  y  y  (d),  z  116  graphite  cm. (b)  1 1 8  and  z  y  the E p o l a r i z a t i o n f o r a g r a p h i t e cm, a n d  w = 2 9  H /H  f o r the E p o l a r i z a t i o n f o r a  i  for  d=1  ( 1 )  ( 2 )  ,  6,  ( 3 )  dyke  and  1 1 ,  16 cm. (a)  t h e H p o l a r i z a t i o n w i t h d = 5 cm f o r  for  ( 1 )  w=5,  and  ( 7 )  ( 2 )  1 0 ,  ( 3 )  100 cm; H , y  polarization with and  t -0  t h e H p o l a r i z a t i o n , H- , H ,  .  (c)  (b),  x  and, 0„?-fr Z  7  k  E  (3)  i f 5 . • Hy, H  z  1 5 ,  H  z  d = 2 9  (  L  )  (b)  2 0 ,  and E  cm, f o r  5 cm f o r a g r a p h i t e (a), E  and 4>  (b),  x  for  ( 5 )  (c)  x  (6)  2 5 ,  for  3 0 ,  the  w = 0 . 2 ,  ( 1 )  1 2 0 E 1 ,  ( 2 )  dyke.  H /Hy (c)  ^ -$  z  x  (d),  y  the H p o l a r i z a t i o n f o r a  E^Hy  (e),  1 2 2  graphite  y cylinder with traverses If6.  d=7.6  along  y=0,  (2)  R/2, (3)  R cm.  x  ?  z  (  y  7  d = 7 . 6  cm a n d  R=30. iL  d  )  ' V y graphite  cm f o r  0  (  e  )  x'  •"  X  7  y  1  for a c y l i n d r i c a l graphite d=7.6 and  cm a n d  R = 3 0 .  ( 2 )x=R/2  +  i  s h e l l 2 cm t h i c k  cm f o r  traverses  along  x=R-1 ,  cm a n d ( 2 )  3  1 2 5  ( 1 )  x = 0 ,  cm.  R=30„ f l  x=R  The a m p l i t u d e s an i n v e r t e d  2  with  H , H , E_, H / H . a n d E / H . f o r t h e E p o l a r i z a t i o n y z x" z y x y f o r a c y l i n d r i c a l g r a p h i t e s h e l l 2 cm t h i c k w i t h d = 7 o 6  1  traverses  a l o n g ( - 1 ) x = 0 , ( 2 ) R / 2 , a n d ( 3 ) R cm. H , H_, E , H /H , a n d E /H f o r the E p o l a r i z a t i o n 7  !+9.  cm f o r  k  H  z  cylinder with  If8.  R = 3 0 o  Hy, H (a), E (b) H /H (c), V y and 0 - # „ f o r the E p o l a r i z a t i o n f o r a £  If7-.  (1)  cm, a n d  cm f o r  traverses  along  (1)  cm. and phase a n g l e s f o r  traverses  over  t r u n c a t e d c o n e f o r the: E p o l a r i z a t i o n .  and f r e q u e n c i e s  126  ;  (a)  3x10  , (b)  10  cycles/sec.  1 3 3  (xi) F i g u r e 50;  T h e a m p l i t u d e s an  i n v e r t e d  and 51•  wedge  (a)  wedge  (a)  58.  10  (b)  a n d  t h e wedge  and  (b)  a n d f=10  (a)  t h e wedge  and  (b)  LL  a n d  a n g l e s  t h e wedge  and  (b)  e x t e n d i n g  3  f=10  (a)  t h e wedge  and  (b)  alone  a n d phase 3  c y c l e s / s e c .  f o r t r a v e r s e s  over  a n d f r e q u e n c i e s  f o r t r a v e r s e s  over  a n d f r e q u e n c i e s  f o r t r a v e r s e s  o v e r  a n d f r e q u e n c i e s  a n g l e s  e x t e n d i n g alone  a l o n e  a n g l e s  p o l a r i z -  f o r t r a v e r s e s cm beyond 1  o v e r  a l o n e  f o r t h e E  edge, (2).  p o l a r i z over  t h e b l o c k  t h e b l o c k  edge, (2)..  t h e b l o c k  t h e b l o c k  ( I ) ,  o v e r  f o r t r a v e r s e s  ?  (2).  p o l a r i z -  f o r t h e E  cm beyond  10  edge,  t h e b l o c k  • t h e b l o c k  angles  10  f o r t h e E  cm beyond  (-1),  over  a l o n e  f o r t r a v e r s e s  10  p o l a r i z -  t h e b l o c k  t h e b l o c k  (1),  (1)  f o r t h e E  cm beyond  10  c y c l e s / s e c  t h e wedge  p o l a r i z a t i o n  f o r t r a v e r s e s  c y c l e s / s e c  e x t e n d i n g  t h e wedge  a n d  alone  a n d phase  T h e a m p l i t u d e s  a n g l e s  c y c l e s / s e c  f=3x10  (a)  alone  a n d phase  t h e wedge  over  c y c l e s / s e c .  e x t e n d i n g  T h e a m p l i t u d e s  a t i o n  a n g l e s  c y c l e s / s e c  t h e wedge  • T h e a m p l i t u d e s  3  c y c l e s / s e c .  cycles/sec*.  a n d phase  f=3x10  (a)  a t i o n  a n g l e s  p o l a r i z a t i o n  f o r t r a v e r s e s  10-  over  c y c l e s / s e c .  a n d phase  • T h e a m p l i t u d e s  a t i o n  (b)  3x10  p o l a r i z a t i o n 3  10  3  f o r t h e H  f o r t h e H p o l a r i z a t i o n  3x10^,  a t i o n  57-  10  (b)  5  T h e a m p l i t u d e s a  56.  3  a n g l e s  cone  a n d phase  f o r t h eE  3x10  (b)  p o l a r i z a t i o n  10^  (b)  T h e a m p l i t u d e s a  55-  f o r t h e E  3x10^,'  3x10 ,  a n d phase  f o r t r a v e r s e s  f o r t h e E  3  t r u n c a t e d (a)  a n g l e s  cone  a n d phase  f r e q u e n c i e s  wedge  • (a)  k  (a)  T h e a m p l i t u d e s a  5.  f r e q u e n c i e s  i n v e r t e d  and  53.  t r u n c a t e d  T h e a m p l i t u d e s an  52.  a n d phase  a l o n e  edge, (2).  (xii) Figure 59 •  Page  The a m p l i t u d e s a n d p h a s e ation for traverses  angles  f o r the E p o l a r i z -  o v e r t h e wedge w i t h t h e wedge  edge d i r e c t i y o v e r t h e b l o c k edge and (a) 60.  3x1 oV  (b)  I O  3  frequencies  cycles/sec*.  The a m p l i t u d e s a n d p h a s e ation for traverses  angles  f o r the E p o l a r i z -  o v e r t h e wedge w i t h t h e  edge e x t e n d i n g 10 cm b e y o n d t h e wedge edge frequencies 61.  (a)  3x10  (b)  s  The a m p l i t u d e s a n d p h a s e ation for traverses  10°  (a) 62.  3x10  , (b)  10  o v e r t h e wedge  63.  10  3  frequencies  f o r the H p o l a r i z frequencies  cycles/sec.  ation for traverses  angles  f o r the H p o l a r i z -  o v e r t h e wedge w i t h t h e  edge e x t e n d i n g 10 cm b e y o n d t h e wedge edge (a)  157  o v e r t h e wedge w i t h t h e wedge  The a m p l i t u d e s a n d p h a s e  frequencies  155  extending  edge d i r e c t l y o v e r t h e b l o c k edge a n d (b)  and  cycles/sec.  ation for traverses 3x10^,  block  f o r the H p o l a r i z -  angles  The a m p l i t u d e s and p h a s e a n g l e s  . (a)  153  cycles/sec.  10 cm b e y o n d t h e b l o c k edge a n d 3  151  3x10  (b)  s  10-  158  block and  cycles/sec.  3  6^-.  Map o f T e x a d a I s l a n d and t h e S t r a i t o f G e o r g i a .  160  65.  The a m p l i t u d e s a n d p h a s e  163  ation for 66.  t r a v e r s e 0 and (b)  (a)  (a)  t r a v e r s e 3 and (b)  (a)  t r a v e r s e 0 and (b)  t r a v e r s e 3 and (b)  traverse  traverse  frequencies  (a)  3x10  ?  - (b)  for  ) 1  10  cycles/sec.  166  1„ 167  5.  for traverses  y d i r e c t i o n o v e r a g r a p h i t e cone )1  16*+  t r a v e r s e 5«  f o r the H p o l a r i z -  69. • The a m p l i t u d e s a n d p h a s e a n g l e s the  1„  f o r the H p o l a r i z -  The a m p l i t u d e s a n d p h a s e a n g l e s ation for  traverse  f o r the E p o l a r i z -  The a m p l i t u d e s and p h a s e a n g l e s ation for  68.  f o r the E p o l a r i z -  The a m p l i t u d e s and p h a s e a n g l e s ation for  67.  (a)  angles  in  170  ( x i i i )  F i g u r e  Page  The a m p l i t u d e s  70. ,  t h e  x  d i r e c t i o n  f r e q u e n c i e s 71.  y  The a m p l i t u d e s f o r  73.  (a)  a n o v e r h e a d  The a m p l i t u d e s c u r r e n t an  over ,  3x10  o v e r  f o r  a n g l e s  (b)  a  a n g l e s  o s c i l l a t i n g  i n  t r u n c a t e d  7*+.  The a m p l i t u d e s c u r r e n t an  i n v e r t e d  The a m p l i t u d e s c u r r e n t an  3x10  5  i n  i n  t h e  3x10 , 3  76.  - T h e a m p l i t u d e s c u r r e n t  i n  p o l a r i z a t i o n (b) 77«  k  10  78.  10  3  10  3  d i r e c t i o n  179 over  f o r  t h e  f o r  y  a  d i r e c t i o n cone  10^  180 o v e r  f o r  c y c l e s / s e c - .  a n g l e s t h e  l i n e  f o r  x  a  l i n e  d i r e c t i o n cone  182 over  f o r  ?  (b)  c y c l e s / s e c .  10^  a n g l e s  over  a  f o r a  wedge (a)  l i n e  f o r  18U-  t h e E  k  3x10  5  a n g l e s  over  a  a n d f r e q u e n c i e s  f o r  wedge (a)  a  l i n e  f o r  185  t h e E  3x10 , 3  c y c l e s / s e c . a n d phase  a n d t r a v e r s e s  p o l a r i z a t i o n (b)  l i n e  O  a n d phase  a n d t r a v e r s e s  The a m p l i t u d e s c u r r e n t  178  c y c l e s / s e c o  p o l a r i z a t i o n (b)  d i r e c t i o n  c y c l e s / s e c .  10  a n d frequencies--  The a m p l i t u d e s c u r r e n t  a  cone  g r a p h i t e  a n d phase  a n d t r a v e r s e s  f o r  y  f o r  a n g l e s  (b)  a n d phase  3x10  173  c u r r e n t .  y  g r a p h i t e  t r u n c a t e d (a)  cone  l i n e  k  f r e q u e n c i e s  i n  f o r  t r a v e r s e s  t h e  a n g l e s  (b)  a n d phase  a n d t r a v e r s e s  i n v e r t e d  172  k  t r u n c a t e d (a)  i n  c y c l e s / s e c .  g r a p h i t e  a n d t r a v e r s e s  f r e q u e n c i e s 75-  (a)  f o r  J  k  f r e q u e n c i e s  cone  c o n c r e t e 10  t r a v e r s e s  c y c l e s / s e c .  10  t r a v e r s e s  a n d phase  f o r  g r a p h i t e  (b)  3x10  a n d t r a v e r s e s  i n v e r t e d  a  a n d phase  d i r e c t i o n  f r e q u e n c i e s 72.  (a)  The a m p l i t u d e s the  a n d phase  a n g l e s  over  a  a n d f r e q u e n c i e s  c y c l e s / s e c .  f o r  wedge (a)  a  l i n e  f o r  3x10^,  t h e H  186  ( x i v )  F i g u r e 79-  Page  T h e a m p l i t u d e s  a n d phase  angles  f o r t h e E  p o l a r i z -  188  L. a t i o n f o r  a n d a  t r a v e r s e s  beyond  T h e a m p l i t u d e s  c u r r e n t  over  t h e b l o c k  t h e b l o c k  (1), 80.  l i n e  ( a )  w i t h  f=3x10  t h e wedge  edge,  a n d (b)  a l o n e  c y c l e s / s e c  e x t e n d i n g  t h e wedge  10  cm  alone  (2).  a n d phase  angles  f o r t h e E  p o l a r i z -  189  LL  a t i o n f o r  a n d a  t r a v e r s e s  beyond  T h e a m p l i t u d e s a t i o n f o r  a n d a  beyond  82.  T h e a m p l i t u d e s a t i o n f o r  a n d a  (1),  T h e a m p l i t u d e s c u r r e n t the  b l o c k  w i t h  edge  edge,  e x t e n d i n g  t h e wedge  angles w i t h  10  cm  alone  f=3x10  a n d (b) (2).>  ( a )  edge,  f o r t h e E  t h e wedge  c u r r e n t  alone  J  p o l a r i z -  190  c y c l e s / s e c -  e x t e n d i n g  t h e wedge  10  cm  alone  • a n g l e s w i t h  f o r t h e E  f=10  t h e wedge a n d (b)  3  p o l a r i z -  191  c y c l e s / s e c  e x t e n d i n g  t h e wedge  10  cm  alone  (2).  a n d phase  a n d t h e E  wedge  (a)  over  c y c l e s / s e c  (2).  a n d phase  t h e b l o c k  t h e b l o c k  a n d Ob)  c u r r e n t  a l o n e  f=10  t h e wedge  edge,  over  l i n e  t r a v e r s e s  beyond  83.  b l o c k  w i t h  a n d phase  t h e b l o c k  ( 1 ) , t h e  ( a )  a l o n e  l i n e  t r a v e r s e s  c u r r e n t  over  t h e b l o c k  t h e b l o c k  (1), 81.  l i n e  angles  p o l a r i z a t i o n  t h e wedge  edge  a n d f r e q u e n c i e s  f o r a  l i n e  193  f o r t r a v e r s e s d i r e c t l y  (a)  3x1 o \  over (b)  over t h e  10^  c y c l e s / s e c . 8^.  ' T h e amplitudes c u r r e n t the  a n d phase  a n d t h e E  wedge  w i t h  angles  p o l a r i z a t i o n  t h e b l o c k  edge  f o r a  l i n e  19^  f o r t r a v e r s e s e x t e n d i n g  10  o v e r  cm LL  beyond (b) 85.  10  t h e wedge 3  a n d f r e q u e n c i e s  ( a )  3x10  ,  c y c l e s / s e c .  T h e a m p l i t u d e s c u r r e n t  edge  a n d phase  angles  a n d t h e H p o l a r i z a t i o n  f o r a  l i n e  f o r t r a v e r s e s  196 over  (xv) Figure  Page  a wedge e x t e n d i n g 10 cm b e y o n d t h e b l o c k edge and f r e q u e n c i e s (a)  (b)  3x1o\  10  3  cycles/sec.  The a m p l i t u d e s a n d p h a s e a n g l e s f o r a l i n e  86.  197  c u r r e n t and the H p o l a r i z a t i o n f o r t r a v e r s e s o v e r t h e wedge w i t h t h e wedge edge d i r e c t l y o v e r t h e b l o c k edge a n d f r e q u e n c i e s ( a )  3x10  , (b)  10  J  cycles/sec. The a m p l i t u d e s a n d p h a s e a n g l e s f o r a l i n e  87.  198  c u r r e n t and the H p o l a r i z a t i o n f o r t r a v e r s e s o v e r t h e wedge w i t h t h e b l o c k edge e x t e n d i n g 10 cm b e y o n d t h e wedge edge a n d f r e q u e n c i e s ( a ) 3x10^, • 88.  (b)  10  3  cycles/sec.  The a m p l i t u d e s a n d p h a s e a n g l e s f o r t h e E p o l a r i z a t i o n and a l i n e for  c u r r e n t w i t h f=3x10  lf  cycles/sec  t r a v e r s e s o v e r t h e wedge w i t h t h e b l o c k edge  e x t e n d i n g 10 cm b e y o n d t h e wedge edge f o r wedge edge p o s i t i o n s ( a ) y = r-5  ?  ( b ) y = -^0  cm.  :  200  (xvi) L I S T OF TABLES Table I. II. III. IV..  Page The e f f e c t o f v a r y i n g  VI.  VIII.  61 62  Conductivity decreasing  w i t h depth.  63  Conductivity decreasing  w i t h depth below a  65  sea.  C o n d u c t i v i t y i n c r e a s i n g w i t h depth,,  69  Conductivity decreasing  70  conducting VII.  sublayers.  Conductivity increasing with depth.  conducting V.  t h e number o f  below a u n i f o r m  sea.  Model dimensions.  103  Geophysical dimensions.  103  ( x v i i )  ACKNOWLEDGEMENTS  I t c u s s i o n s  i s  a  w i t h  p l e a s u r e  Dr.  J o  A.  to  acknowledge  J a c o b s  a s p e c t s  of  t h i s  r e s e a r c h .  I  f o r  c a r e f u l  r e v i e w i n g  of  h i s  indebted  to  p a r t s  the  of I  w i t h and  Dr.Dr.  Dr.  T.  J .  E s q u i m a l t ,  Dr.  w i s h the and  to  T.  h e l p f u l  Watanabe  thank  Dr.  m a n u s c r i p t . Dr.  R.  d i s -  M.  J . I  E l l i s  on  v a r i o u s  A.  am  J a c o b s a l s o  f o r  r e v i e w i n g  m a n u s c r i p t .  would J .  Watanabe  and  the  a l s o  l i k e  Lokken,  Ei T.  Weaver  B.  C ,  Dr.  of  and  to S.  the  Mr.  acknowledge  B.  Z.  Mack,  P a c i f i c Caner  u s e f u l  Dr.  K.  N a v a l of  the  d i s c u s s i o n s  C.  M a c l u r e ,  L a b o r a t o r y , V i c t o r i a  M a g n e t i c  O b s e r v a t o r y I wife,-  i n  have  M a r t h a ,  g r e a t l y  throughout  I  w i s h  to  t y p i n g  t h i s  t h e s i s .  T h i s  a p p r e c i a t e d  thank  r e s e a r c h  Defence  R e s e a r c h  C o u n c i l  of  Board  Canada.  the Mrs.  was of  time M.  the of  t h i s  G e l l i n g  supported Canada  encouragement  and  by  my  r e s e a r c h .  f o r  her  g r a n t s  the  of  c a r e f u l  from  N a t i o n a l  work  the R e s e a r c h  1 Chapter  1.  INTRODUCTION  1.1  H i s t o r i c a l The  served i n  a t  n a t u r a l l y  t h e  t h e  source, these  c o n d u c t i v i t y p l a y s  a n  nature  o f  s t r u c t u r e  o f  The o f  was  f i e l d s f l a t by  source  o f  P r i c e  as  t o  a t i o n .  determined between and  w i t h  p a i r s  K i k u c h i  a  i s  a s  o f  b e t t e r  o b -  i n t e r e s t  w e l l  w e l l  known  a s  t h e  t h e nature t h i s  o f n a t u r a l  understanding  v a r i a t i o n s  o b t a i n i n g  and  as  o f  a  o f  t h e  t h e  o f  subsurface  t h e  a t  t e l l u r i c  r e q u i r e s movable  a  e l e c t r o d e s  both  f o r  g e n e r a l  method  f o r  r e f e r e n c e  embedded  (1950)  time  source and  was  Chapman  and P r i c e a t t e n t i o n  used  and  was e x p l o r i n  g r a d i e n t s  p o t e n t i a l  a r e  d i f f e r e n c e s  e a r t h .  suggested  done  (1939).  g e o l o g i c a l  s t a t i o n  t h e  t h a t  a n a l y s i s  P o t e n t i a l  i n  s u r f a c e ,  s p h e r i c a l  (1922),  and L a h i r i  measuring  a n d Tikhonov  e a r t h ' s  v a r i o u s  o f  d i s t r i -  from  e f f e c t s  s t a t i o n . b y  e a r t h ,  t h e  c o n s i d e r a b l e  !  t h e  S i n c e  and Whitehead  1920 s  t h e  t h e  o n  S c h u s t e r .  e a r l y  (1929, 1930),  s u r f a c e  (1950)  v a r i a t i o n s  d i s t r i b u t i o n s  Chapman  i n  i n f o r m a t i o n  w i t h i n  t h e  Some  t h e o f  to  i n v e s t i g a t e d  method  a t  e a r t h ,  u n d e r s t a n d i n g  by  P r i c e  t h e u s e  c o n j u n c t i o n  a f f e c t i n g  1889  (1919)?  This  I t  i n  c o n d u c t i v i t y  c o n d u c t i v i t y  B e g i n n i n g g i v e n  o f  e a r l y  have  (193O),  studies,,  these  t h e magnetic  s t r u c t u r e s .  Chapman  c o n t i n u i n g  t h e  l e a d s  o f  o f  v a r i a t i o n s  e a r t h .  e l e c t r i c a l  and  i n c r e a s e d  p o s s i b i l i t y  workers  a r e  o f  r o l e  background  t h e  c o n s i d e r e d  many  e a r t h  s t r u c t u r e  A n  t h e  measurements  t h e  important  v a r i a t i o n s .  b u t i o n  o f  e l e c t r o m a g n e t i c  and m a g n e t o t e l l u r i c  e l e c t r o m a g n e t i c the  o c c u r r i n g  s u r f a c e  geomagnetic  that  Review  B o t h  that  t h e  Kato  2 e l e c t r i c a l c o u l d and  c h a r a c t e r i s t i c s  be determined  t e l l u r i c  theory waves  o f  t h i s  C a g n i a r d ' s source  e s s e n t i a l l y h o r i z o n t a l  method  d i s t a n c e  c o n s i s t s e l e c t r i c  n a t u r a l  The  e l e c t r i c  f i e l d  r a t i o  o f  f u n c t i o n i v i t y ence  o f  i n f i n i t e  f i e l d  a l s o  i s measured  a t  o f  p r o v i d e s  f r e q u e n c y  o f  (1951)? o f  d i f f e r e n c e s  t o  t h e s i g n i f i c a n c e  o f  a s  r e l a t e d  m a g n e t o t e l l u r i c  method  h a s been  of  method  o f  success  a s a  t h e  g r a d i e n t • T h e  f i e l d  mag-  o n t h e  d i f f e r -  a l s o  t r e a t e d r a t i o s  a  c o n d u c t -  T h e phase i s  T h e  a s  a n d L i p s k a i a  w i t h  o f  s u r f a c e .  s u r f a c e .  f i e l d s  t h e subsurface  h o r i z -  components  t h e e a r t h .  amplitude  e x p l o r i n g  o f  p o t e n t i a l  have  a  i n t h e  t h e e a r t h ' s  l a y e r s .  used  t o  be  m a g n e t o t e l l u r i c  t h e magnetic  (1953)  t h e f i e l d s  depth"  f i e l d  i n f o r m a t i o n  i n  o f t h e  o b s e r v a t i o n  T h e  Tikhonov  a n d L i p s k a i a -  t o  o f  W a i t  t h e l i m i t a t i o n s  t h a t  t h e  plane  conductor.  " s k i n  a n d magnetic  t h e s t r u c t u r e .  f o r  t h e e a r t h ' s  i n h o r i z o n t a l  t h e e l e c t r i c  a t  a s a  o n t h e s u r f a c e  f i e l d  method  measurements  f i e l d  i s measured  a  magnetic  t h e e l e c t r i c  d i a g n o s t i c  o f  o f  depth.  simultaneous  o u t l i n e d  r e q u i r e s  t h e o r d e r  geomagnetic  t h e dimensions  t h e p o i n t  e l e c t r o m a g n e t i c  between  a s p e c t s  theory  a n d h o r i z o n t a l  d i s t r i b u t i o n  R i k i t a k e  o f  o f  two p o i n t s  n e t i c  from  t o  o f  s t r u c t u r e  (1953)  s t r a t i f i e d  d i s c u s s e d  r e s p e c t  C a g n i a r d ' s  c o n d u c t o r  between  w i t h  c o n s t a n t  the  m a g n e t o t e l l u r i c  have  c r u s t a l  a n a l y s i s  C a g n i a r d  h o r i z o n t a l l y  (1962)  r e s u l t s  f i e l d .  u n i f o r m  v a r i a t i o n s .  o n a  a n d P r i c e  k  t h e e a r t h ' s  t h e combined  s o - c a l l e d  i n c i d e n t  (195 )  o n t a l  f i e l d  b y  o f  v a r i o u s  a n d  s t r u c t u r e . v a r y i n g  t h e s u b s u r f a c e  (1952)  phase T h e  degrees n a t u r e  5  3  of  the  make  eartho  The  p o s s i b l e  some  wide  range  study  of  of  the  f r e q u e n c i e s e a r t h ' s  p r o v i d e d  s t r u c t u r e  by  even  n a t u r e  to  great  depths. A t i n  the  s t u d y i n g  the  d i s t r i b u t i o n three  p r e s e n t problem  i n  magnetic  v a r i a t i o n s .  the  T h i s  to  g i v e  tudes  of  the  phase  d i f f e r e n c e s  f o r i n  i s  more  d i r e c t i o n  a t l  ,  .  (frequency  range  Pc  where  the  source  a  l a r g e  are  term i n  f i e l d  e a r t h ' s  the  the  e a r t h ' s  v a r i a t i o n s e l e c t r i c  the  range  from  and  method  i n  from  about  10  m i c r o p u l s a t i o n s  the  three  may  and  c a l l e d  0.1  the  f i e l d  w h i l e  d e s c r i b e d  be  c y c l e s / s e c i n  h o r i z -  m i c r o p u l s a t i o n s  f i e l d .  have  g r a d i e n t  d y k e s ) .  magnetic  about  the  T h i s  h o r i z o n t a l  known  geomagnetic  and  f i e l d s .  d i s c o n t i n u i t i e s f a u l t s ,  a m p l i -  c o n d u c t i v i t y  m a g n e t o t e l l u r i c  where  ( c o a s t l i n e ,  The  are  The  the  components  type  p u l s a t i o n s  i n t o  than  the  r e l a t i v e  w e l l  i n  geomagnetic  and  both  s e v e r a l  p r e s e n t  p u l s a t i o n s  i n  of  the  e l e c t r o m a g n e t i c from  The  f i e l d  of  observed  e l e c t r i c the  a n a l y s i s  n a t u r a l  used  c o n d u c t i v i t y  v a r i a t i o n s  f l u c t u a t i o n s  c l a s s i f i e d  e a r t h  the  measurements  v e r t i c a l  commonly  e l e c t r o m a g n e t i c  a s s o c i a t e d  The  and  o r  the  the  more  and  d i s t r i b u t i o n .  problems  o c c u r  the  w i d e l y  to  the  on  of  employs  method  f i e l d s  based  d i a g n o s t i c  e x i s t s  " m i c r o p u l s a t i o n s r e f e r s  i s  a p p r o p r i a t e  c o n d u c t i v i t y  s t u d i e d  are  c e r t a i n  Among  source  s p a t i a l  w i t h i n  s t u d y i n g  o n t a l  method a  another  components  h o r i z o n t a l  d i s t r i b u t i o n  of  e a r t h  f i e l d  s t a t i o n s  method  time  The  p e r i o d s  second to  to  JOT-* p a s t  P t ,  as  10  m i c r o -  these  of  minutes  c y c l e s / s e c ) .  commonly  and  the  main  c a t e g o r i e s :  P c ,  (continuous  pulsations.)  m i c r o p u l s a t i o n s  been  Pg. are  a  h  continuous  s e r i e s  (much  than  l e s s  s e v e r a l  h o u r s .  between  10  o f  geomagnetic  1y,  1y  The  range  and 60  s e c  =  v a r i a t i o n s  1 0 " ^ gauss) o f  i n  s m a l l  a n d l a s t i n g  p e r i o d s  ( r o u g h l y  o f  f o r  t h e  as  l o n g  P c ' s tends  f r e q u e n c y  amplitude,  to  range  a s  be 0.1  t o  —2 1.6  x  10  c y c l e s / s e c ) . . The  s e r i e s  o f  P t  damped  o s c i l l a t i o n s the  ( p u l s a t i o n  t o  range  be  2.5  The  between x  10  o f  t h e P t  m i c r o p u l s a t i o n s  those  o f  t h e  type  The of  Pg  ( g i a n t  o s c i l l a t i o n s  and  P t  tend  types  t o  be  b u t  o f  (1Oy  much  l o n g e r  o t h e r  range  two  made  geomagnetic o t h e r s  t o  e x t e n s i v e  t o  p e r i o d s s e c  o f  i n  g e n e r a l  l e s s  than  10 m i n u t e s ,  a m p l i -  than  l y *  than  o r  i n  The  l a r g e r  m i c r o p u l s a t i o n s  a m p l i t u d e s  these  ( r o u g h l y  c y c l e s / s e c ) .  The p e r i o d s  .10 °  c y c l e s / s e c ) ,  (1963)  r e v i e w s  m i c r o p u l s a t i o n s .  d i v i d i n g  Pc,  P t ,  the  I n t e r n a t i o n a l  Pg  (1  100  s e p a r a t e  a r e  those  o f  a  s e r i e s  o f  t h e Pc  t h e Pg  r o u g h l y  type  i n  t h e  ' —^  [ e . g . M a t s u s h i t a  a n d P g ,  were  l a r g e r  and Westphal  c l a s s i f i c a t i o n  t h e r e  s t i l l  o f  a r e  than  those  o f  t h e  t y p e s .  Jacobs r e c e n t l y  10  a r e  g r e a t e r ) .  —2 f r e q u e n c y  10  p u l s a t i o n s )  much o r  a r e  range  *+0 a n d  t o  tudes  Pc  m i c r o p u l s a t i o n s  o s c i l l a t i o n s .  tends  f r e q u e n c y  t r a i n )  was t o o  many  a  types  great  these i t  9  broad.  o f  c l a s s i f i c a t i o n i n d i c a t e d .  c l a s s i f i c a t i o n  t h e  s t a t e  v a r i e t y  i n t o  ( I . G . Y o )  v a r i a t i o n s A s o f  a  :  r e s u l t  have  knowledge  a s  was p o i n t e d  I n f o r m a t i o n Y e a r  (196*t) o f  works,  m i c r o p u l s a t i o n s  G e o p h y s i c a l  more  o f  I n  (1963)]  and J a c o b s  w e l l o u t  three  as  o f i n  t h a t  t h e  c a t e g o r i e s ,  c o l l e c t e d  d u r i n g  i n d i c a t e d  t h a t  than o f  n o n - u n i f o r m  t h e P c , P t , t h i s  and  broad  n o t a t i o n s  a n d  5 d e f i n i t i o n s  developed  attempt  a t  v i e w  encouraging  o f  f o r m a l i z i n g  hoc  committee  and  Aeronomy  and  Geophysics  o f  August,  of  geomagnetic  were  b y  these  •  T(sec)  Pc Pc Pc  3 h  Pc  i n  2 5  energy  t o  b e i n g  i n t e r a c t i o n  t h e  t h e  charged  p a r t i c l e s  e a r t h ' s  magnetic  r e n t s ,  c a u s i n g  e a r t h ' s to  systems f i e l d  and  t h e t o  i s  energy, o f  t h e  f i e l d ,  p o s i t i o n s  i n  v a r i a t i o n s  a t  t h e  t h e  i n  n o t a t i o n  has  been  m i c r o p u l s a t i o n s  f ( s e c "  1 -1+0  t h e  e a r t h ' s t h e  and  The  s u r f a c e  b e l i e v e d  o f  s u n , w i t h  t h e  f a r  v a r i o u s  r e l a t i o n s h i p s u r f a c e  o f  c u r a t  t h e  workers  such  between  and  t h e  t h e  e l e c t r i c  been  ionosphere  t h e  r e a c h i n g  o b s e r v a b l e  by  a r e  t h a t  t h e  made  )  1-0.025  source  i o n o s p h e r i c  1  0.025-0.006  d i s t u r b a n c e s  t h e  e a r t h ' s  and  f o l l o w s :  1+0-150  from  ionosphere  have  B e r k e l e y  ( s e c )  e a r t h ,  e m i t t e d  r e s u l t s  Geodesy  P c - ( c o n t i n u o u s  as  now commonly  S t u d i e s  determine  a t  t h e  e l e c t r o m a g n e t i c  s u r f a c e .  determine  I t  T  P i 1  o u t s i d e  s u n .  a r e  P i2  observed  o f  m i c r o p u l s a t i o n s ) .  P i  0.1-0.022  o r i g i n a t e  o f  )  5-0.2  M i c r o p u l s a t i o n s b e l i e v e d  c a t e g o r i e s ;  a d  a t  was adopted  Geomagnetic  a n  Geomagnetism  U n i o n  h e l d  t h e  by  o f  c l a s s i f i c a t i o n  0.2-0.1  5-10 10-1+5 1+5-1 50 150-600  assembly  two c a t e g o r i e s  1  w i t h  was made  I n t e r n a t i o n a l  ( i r r e g u l a r  f ( s e c "  0.2-5  usage  (196*+)°  A n  and n o t a t i o n  w h i c h  two main  phenomena.  A s s o c i a t i o n  g e n e r a l  a l  and P i  1  1  t h e  r e s u l t i n g  e t  i n t o  micropulsations )  Pc  a t  m i c r o p u l s a t i o n s  Jacobs  s u b d i v i s i o n s  symbolism  I n t e r n a t i o n a l  The  1963.  d i f f e r e n t  c o n s i s t e n t  ( I . U . G . G . )  c l a s s i f i e d  PC  more  t h e  t h e  t h e  (I.A.G'.A.)  i n  d i s c u s s e d  f o r  c u r r e n t  magnetic  i o n o s p h e r i c  6  c u r r e n t  systems  (1960?  Zmuda  o t h e r s ) . w i l l  Campbell  both  1961,  observed  o h t h e n a t u r e  i n t h e ionosphere) t h e e a r t h .  These  an  t o  i n v e s t i g a t e  b o t h  t h a t  f t t e m p t  o f  t h e i n t e r i o r  In  r e c e n t  t o  e x p l a i n  hydromagnetic and  Westphal  p a p e r s ) . a t i n g t h e  I t  l i n e s .  waves  1 96*+,  (e.gv, -  many  a  propagate  e l e c t r o m a g n e t i c e l e c t r o m a g n e t i c  where  they  a l s o  w i l l  secondary  propagate  waves as  a l s o  t h a t  along-  f l i p i d  t o  r e s u l t  geomagnetic  these  waves,  o r i g i n -  a l o n g  magnetic  unable-  pass t o  A l f v e n  l i n e s  i n t o  over  f i e l d through  transformed  t h e  i o n o s p h e r e . s u r f a c e  m i c r o p u l s a t i o n s .  waves  e n t e r i n g  a s w e l l waves)  waves  I t  t h e  a s g i v i n g  w h i c h  o b l i q u e l y  t o l o w e r  i n e l e c t r o m a g n e t i c  a r e  t h e e a r t h ' s  b u t t r a v e l  from  t o propagate  t h e e a r t h ,  be r e f l e c t e d  m i c r o p u l s a t i o n s  i n  o f  Jacobs  1962,  r e g i o n s  hydromagnetic  t h e f i e l d  i n terms  a r e g i v e n  a s geomagnetic  l i n e s ,  i n a n  d i s t a n t  o f  i n  source  r a d i i  t r a v e l  ( m o d i f i e d  done  a n dWatanabe  a s they  waves  i n p a r t  waves  p e r p e n d i c u l a r  waves  t h e  e a r t h  waves,  d i s t r i -  a n d magnetic  m i c r o p u l s a t i o n s  o f  t o p o l a r  observed  b e l i e v e d  ionosphere to  are-  ( c u r r e n t  o f  hydromagnetic  a n d atmosphere  These  is-  number  s u r f a c e  a r e s t u d i e d  h a s been  r e f e r e n c e s t h a t  a n d many  e a r t h .  work  Jacobs  T h e hydromagnetic  (  t h e  much  i s b e l i e v e d  ionosphere  i n t o  o f  v a r i a t i o n s t h e n a t u r e  geomagnetic  i n o u t e r s p a c e  e a r t h ,  the  y e a r s  t h e source  a n d o n t h e e l e c t r i c  o f  and  1962,  Bomke  1960,  Hasegawa  a t t h e e a r t h ' s  o f  p r o p e r t i e s attempt  1960),  a n d Sinno  a n d Rees  T h e v a r i a t i o n s  depend  b u t i o n  ( e . g . Jacobs  do n o t t o , o r  l a t i t u d e s . w h i c h  t h e e a r t h ' s  r i s e  a r e  These observed  s u r f a c e .  7 The general source the  a n a l y s i s  c o m p l i c a t e d o f  understood  t o a l l o w  e i t h e r  i n  t h e c o n d u c t i v i t y  i n  mind  many cases  w i t h  p l a u s i b l e  a  d u c t i n g  source and  o f  v e r y  S e v e r a l wave  based  i s  sources-  (1953) based  assumption  have  ?  P r i c e  knowledge  problem f o r  c o n d u c t i v i t y s p e c i a l  i n f o r m a t i o n  o n  s t r u c t u r e s . f i e l d s o f  u s u a l l y  i n -  a  c o n -  h o r i z o n t a l l y sources  ( r e q u i r i n g  v e r y  f l a t  l a y e r e d  s t u d i e d a  c u r r e n t  t h e a n a l y s i s  o f  much  used  o n t h e plane  theory  k  o f  o s c i l l a t i n g  o n t h e assumption  C a g n i a r d ' s  195  types  models a n d  c o n s i s t i n g  o r a  t h i s  b y  many  d i s t a n t  s h e e t ) ,  d i p o l e s ,  c u r r e n t s .  Cagniard'smethod  depth  W i t h  some  source  s t r u c t u r e  w e l l  a t t r i b u t e d  f o r these  y i e l d  o f  o f  inhomogeneities  sources  t h e r e s u l t s  s t u d i e s  t o be  t h e  a n d c o n d u c t i v i t y  e a r t h  l a r g e  f i e l d  o f t h e  d i s t r i b u t i o n  m a t h e m a t i c a l  measurements  - F o r s i m p l i c i t y , o f t e n  o f  t o  i n  n o t s u f f i c i e n t l y  t h e e a r t h -  s t u d i e d  i n f i n i t e  a r e : plane  o f  o r  i s  t h e nature  t h e v a r i a t i o n s  s p e c i f i c  f i e l d s  e a r t h .  o r a  o f  Comparisons  s i m p l i f i e d  l i n e  have  f i e l d  both  r e s p e c t s  t h e source  m a t h e m a t i c a l  e a r t h  workers  :  source  c o n d u c t i n g  o f  assuming  a c t u a l  The  a r e i n many  s t r u c t u r e  workers  t h a t  measurements  a n d t h e c o n d u c t i v i t y  a s p e c t s  t h e nature  d i s t r i b u t i o n s .  v o l v e d  b y t h e f a c t  i n t e r i o r  to  cases  m i c r o p u l s a t i o n :  t h e v a r i a t i o n s  e a r t h ' s  s p e c i a l  o f  a  theory wave  d i s c u s s e d W a i t  (1962  m a g n e t o t e l l u r i c  f i e l d  plane o f  wave  t h e  o f  b y v a r i o u s a )  measurements source  f i e l d .  Refinements  t h e plane workers  h a s reviewed  f i e l d s  i s  m a g n e t o t e l l u r i c  assumption.  a n d t h e l i m i t a t i o n s  been  1962).  o f  o f  a n d t h e  t o  wave ( e . g . W a i t  t h e s t a t e  o f  m a g n e t o t e l l u r i c  8 methodo  He  p r e t a t i o n the  of  c u r v e s .  c h o i c e  method.  i n c l u d e d  o f  c o n d i t i o n s As  methods,  f i e l d  number  o f  p a r t  range  5  e l e c t r o m a g n e t i c i t y i n  o f  the  a b l e  using-  the  p l a n e  component.  a t  f i e l d  v a r y i n g  and  c o n d u c t i v i t i e s  component  times  should  o f  g r e a t e r  o n  used  to  of  power  on  a  i n c i d e n c e  i n d i c a t e  L a b o r a t o r y v e r t i c a l t h a t  to  the  spectrum  t e c h n i q u e s  y e a r s  v e r t i c a l  i n  h o r i z o n t a l by  as  the  w i t h  the  Dosso  and  wide  range  magnitude  i n d i c a t e  and  horir-  w e l l  as  t h a t i n  the terms  of  p r e d i c t i o n  of  h o r i z o n t a l  (1961)  Lokken  o f  of  plane  the  wave  v e r t i c a l by  the  i s  e a r t h  f r e q u e n c i e s  made  t h a t  components the  c o n s i d e r -  c o n d u c t i n g  Measurements  o t h e r s  p r e d i c t e d  c o n d u c t i v e  homogeneous  s m a l l .  and  the  a p p r o x i m a t e l y  a  s t u d i e d  a p p l y i n g  assumption  and  t h a t  of  The  by  a  f r e q u e n c y  a n a l y s i s  o u t  f l a t  the  f o r  r e s u l t s  f r o m  k  r e c e n t  t h e  compared  c a r r i e d  be  I n  d e s c r i b e d  component  f i e l d s  s t u d y i n g  u s i n g  e a r t h  i n  v a r i o u s  (196 )  purpose  to  method.  the  indeed  than  He  be  i n c i d e n t  angles  N a v a l  r a t i o  may  C a l c u l a t i o n s  f o r  the  measurements  v e r t i c a l  plane  w i t h  g i v e n  e x a m i n a t i o n  by  E l l i s  f i e l d  measurements.  been  m a g n e t o t e l l u r i c  m a g n e t o t e l l u r i c A l b e r t a .  d i s c u s s e d  m a g n e t o t e l l u r i c  a n a l y z e d ,  measurements  f i e l d  f o r  tude  C e n t r a l  depth.  i n c i d e n t  waves  of  t h e  the  i n t e r -  k  d e t a i l e d  o f  he  i n  e a r t h  (196 )  Watanabe  a  e l e c t r o m a g n e t i c  v a r i a t i o n s  s m a l l  P a c i f i c  i n  made  study,  m a g n e t o t e l l u r i c  waves  v e r y  t h i s  l a y e r e d  used  v a l i d i t y  c y c l e s / s e c ,  has  magnetic  magnetic-  a  the  a t t e n t i o n  z o n t a l  o f  o f  paper  c o n d i t i o n s  the  f i e l d  e a r t h  a n a l y z i n g  r e c e n t  measurements  to  number  (196-2) h a s  n a t u r a l  0.001  a  f o r  s t a t i o n s  e a r t h ' s  l a r g e  boundary  method.  the  I n  S r i v a s t a v a  the  a  the  a m p l i -  about model.  10  3  9 One e x p e c t s  t h e v e r t i c a l component t o be h i g h l y d e p e n d e n t  inhomogeneities structure.  and s t r a t i f i c a t i o n p l a n e s w i t h i n t h e  Measurements  made n e a r c o a s t a l r e g i o n s ,  l a r g e c o n d u c t i v i t y g r a d i e n t a n d deep l y i n g exist,  uniform geological structure is 1960,  1^62,  Parkinson  t o f f e l e t a l 1961, 196^,  earth's where a  inhomogeneities  y i e l d l a r g e a m p l i t u d e s o f t h e v e r t i c a l component  compared w i t h v e r t i c a l c o m p o n e n t s  1959,  1962,  Schmucker  even f o r i n l a n d  t h a n p r e d i c t e d b y t h e p l a n e wave m o d e l . however,  This  Jacobs  stations  i s much l a r g e r  The p l a n e  wave  r e a d i l y lend i t s e l f to studying  m a t i c a l l y the e f f e c t of inhomogeneities substratum.  and  Chris-  The v e r t i c a l t o h o r i z o n t a l  where u n i f o r m h o r i z o n t a l l a y e r s a r e l i k e l y ,  model does,  i n l a n d where a  S h a n d e t a l 1959,  1  r a t i o , however,  i n the  mathe-  conducting  a s p e c t o f t h e p l a n e wave m o d e l w i l l  treated l a t e r i n this  when  ( D u f f u s e t a l 1959?  196 *, S r i v a s t a v a  L a m b e r t and C a n e r 1965)»  magnetic f i e l d  at stations  likely  on  be  work.  A v a r i e t y of d i p o l e f i e l d s f o r a f l a t  homogeneous  c o n d u c t i n g e a r t h o r f o r a h o r i z o n t a l l y s t r a t i f i e d e a r t h have been t r e a t e d and d i s c u s s e d W a i t 1951,  1958,  Quon 1963,  s t u d i e d the response a flat  W e a v e r 1965).  Wait  Quon O963)  sources  (1962  o f an o s c i l l a t i n g magnetic d i p o l e  e a r t h w i t h the c o n d u c t i v i t y v a r y i n g  with depth. dipole  i n the l i t e r a t u r e (e.g. Wolf  19^6,  a) over  exponentially  gave an e x t e n s i v e t r e a t m e n t f o r  o v e r a c o n d u c t i n g e a r t h . - He d e a l t w i t h b o t h  v e r t i c a l and h o r i z o n t a l e l e c t r i c two l a y e r c o n d u c t i n g f l a t  earth.  and m a g n e t i c d i p o l e s o v e r Weaver  (1965) t r e a t e d t h e  a  10 problem of  the f i e l d of a magnetic  dipole situated in  u p p e r l a y e r o f a s e m i - i n f i n i t e two l a y e r e a r t h . a p p l i c a t i o n to a d i p o l e s i t u a t e d i n the sea. ical  investigations  infinite people  L i e n 1953, W a i t  theoret-  semivarious  1953, W a i t and C a m p b e l l 1953).  (1966)  s t u d i e d the  electromagnetic  o f a d i p o l e o v e r a homogeneous a n i s t r o p i c h a l f  He d e v e l o p e d e x p r e s s i o n s  The g e n e r a l  theory of electromagnetic i n d u c t i o n i n a t r e a t e d by P r i c e  As a n i l l u s t r a t i v e e x a m p l e , he e x a m i n e d t h e  case of an o s c i l l a t i n g l i n e c u r r e n t . 1962)  finite  dimensions.  special  I n a more r e c e n t  he s t u d i e d t h e e f f e c t o f a g e n e r a l s o u r c e Srivastava  considered.  He n o t e s  t h a t phase a n g l e s a r e v e r y  i n determining the c o n d u c t i v i t y d i s t r i b u t i o n s made a t t h e e a r t h ' s  surface.  Weaver  He o b t a i n e d g e n e r a l s o l u t i o n s  f i e l d components  of  from  of field  significant measurements  extended the  o f P r i c e (1950, 1962) f o r a u n i f o r m c o n d u c t o r conductor.  work  (1965) o u t l i n e d a m e t h o d  i n t e r p r e t a t i o n o f m a g n e t o t e l l u r i c d a t a when t h e s o u r c e is  for  sources.  s e m i - i n f i n i t e homogeneous c o n d u c t o r was  (Price  space.  f o r the e l e c t r o m a g n e t i c f i e l d s  b o t h v e r t i c a l and h o r i z o n t a l d i p o l e  (1950).  has  Earlier  of d i p o l e sources s i t u a t e d i n a  In a recent paper Wait fields  This  c o n d u c t i n g medium h a v e b e e n c a r r i e d o u t b y  (e.g.  the  to a  f o r the  work  two-layer magnetic  i n the upper l a y e r of a t w o - l a y e r  conductor.  The s p e c i a l c a s e o f a n o s c i l l a t i n g l i n e c u r r e n t a b o v e a c o n d u c t i n g e a r t h has  b e e n t r e a t e d b y Law a n d F a n n i n  c a r r i e d out c a l c u l a t i o n s f o r a plane conducting near f i e l d of a l i n e source  situated at a height  (1961). earth i n of 2 x  They the 10  y  11 meters o b t a i n i n g v e r t i c a l t o h o r i z o n t a l magnetic f i e l d r a n g i n g from 0 t o 0.5 f o r an a n g u l a r f r e q u e n c y radians/sec.  ratios  o f 0.3  These r e s u l t s a r e i n t h e range o f e x p e r i m e n t -  a l l y observed v a l u e s .  Weaver (1961) has extended t h i s  line  c u r r e n t model t o a p p l y t o more d i s t a n t p o i n t s on t h e e a r t h ' s s u r f a c e by c o n s i d e r i n g a c y l i n d r i c a l e a r t h i n t h e n e a r f i e l d of a r a d i a t i n g l i n e c u r r e n t .  The v a l u e s he o b t a i n e d compare  f a v o r a b l y w i t h those o f Law and F a n n i n  (1961) i n t h e r e g i o n  where t h e p l a n e e a r t h a s s u m p t i o n i s v a l i d .  Results f o r the  l i n e c u r r e n t source f o r a wide range o f f r e q u e n c i e s ^  conduct-  i v i t i e s , and source h e i g h t s w i l l be t r e a t e d l a t e r i n t h i s work. The  e f f e c t o f the gross f e a t u r e s o f the e a r t h on the  electromagnetic  v a r i a t i o n s a t the earth's surface f o r a given  assumed source f i e l d c a n be s t u d i e d by assuming a s i m p l e  con-  d u c t i v i t y s t r u c t u r e f o r t h e e a r t h as was d i s c u s s e d i n t h e preceding paragraphs.  However, t h e e a r t h ' s c r u s t i s p r o b a b l y  more d i s t i n g u i s h e d by i r r e g u l a r i t i e s t h a n by r e g u l a r i t i e s * Although  l a y e r e d s t r u c t u r e s do e x i s t , o t h e r s t r u c t u r e s o f  c o n s i d e r a b l e i n t e r e s t i n geophysics  a t t h e p r e s e n t time a r e  those h a v i n g d i s c o n t i n u i t i e s o r c o n d u c t i v i t y g r a d i e n t s i n t h e h o r i z o n t a l d i r e c t i o n such as v e r t i c a l f a u l t s , d y k e s , and e a r t h sea i n t e r f a c e s . Some a n a l y t i c a l work i n v o l v i n g v e r t i c a l  fault  s t r u c t u r e s and s i m p l i f i e d source f i e l d s has been done. . d ' E r c e v i l l e and K u n e t z (1962) have s t u d i e d t h e case o f t h e m a g n e t i c f i e l d everywhere p a r a l l e l t o t h e t r a c e o f t h e f a u l t * R a n k i n (1962) has extended t h e work o f d ' E r c e v i l l e and K u n e t z to  t h e case o f a dyke d i s c o n t i n u i t y . To s t u d y t h e enhancement  12 of  t h e v e r t i c a l  (1963)  Weaver where  normal  c o a s t a l were  magnetic  c o n s i d e r e d t o  v e r t i c a l  t o  i n f i n i t e  i n t e r f a c e .  I n  magnetic  f a u l t .  • This-' enhancement  ponent  h a s been  a t i o n s  ( f o r example,  a l s o  c o a s t a l the  c o n d u c t i v i t y d u c t i v i t y  suggest  magnetic i s  n o t due t o g r e a t e r  than  10  f a c e  was found  problems much  b y  t h e ocean  w i t h i n  i n c l u d i n g  t h e i r  n e a r  observed  depths.  t o  more  o f  p a r t i c u l a r l y  problem,  such  study. a  i n  terms  t h e  c o n t r a s t  o f  o f  deep  h i g h  c o n -  (1965)  t h e  v e r t i c a l  f r e q u e n c i e s  inhomogeneities  f r e q u e n c i e s  a s w e l l  s t r u c t u r e s  - One method  s c a l e d  s i m i l i t u d e u s e f u l  i n  a t  (periods  l e s s  t h e l a n d - s e a  i n t e r -  i m p o r t a n t .  c o a s t l i n e  t h e u s e o f  p r i n c i p l e  be  i n v o l v i n g  due t o  F o r h i g h e r  c e r t a i n  a n d Caner  f o r t h e l o w e r  com-  i n v e s t i g -  i n a  o f  h o r i -  o f t h e  components  enhancement  t h e c o a s t l i n e  t h e  r e f e r e n c e s  h a s d e s c r i b e d  Lambert  l a n d  f i e l d  e a r l i e r  a n u p w e l l i n g  t h e mantle.  t h a t  t h e o r e t i c a l  f i e l d  a  o f t h e  magnetic  a n d inhomogeneities  m i n . ) t h e c o n d u c t i v i t y  The  i s  k  t h e s e a b u t r a t h e r  much  bear  o f  t h a t  f i e l d  (196 )  e v e r y -  s e a a n d  t h e t r a c e  where  1961,  f i e l d  s i d e  h e assumed  a c r o s s  r e g i o n s ,  r e p r e s e n t i n g  B o t h  o n e i t h e r  v a r i o u s  t h e magnetic  s t r u c t u r e  zone  o f  R i k i t a k e  i n  f a u l t  t h e v e r t i c a l  Schmucker  anomalies e f f e c t  depth  c o a s t a l  t h e magnetic  v e r t i c a l  was c o n s t a n t o f  i n  s e a a n d l a n d .  i n  t h e s u b j e c t  q u o t e d ) .  edge  a l s o  f i e l d  a  o f  t h e a n a l y s i s  z o n t a l  are  o f  s e p a r a t i n g  be  component  t h e case  t h e t r a c e  boundary  t a k e n  f i e l d  model  a s f a u l t s o f  19 1)• k  w h i c h  g e o l o g i c a l  a n d dykes,  s t u d y i n g  employing  ( S t r a t t o n  f o r problems  a s o t h e r  these  t h e w e l l T h i s  c a n  problems known  method  do n o t r e a d i l y  i s y i e l d  t o  13 a n a l y t i c a l s e a l e d  s o l u t i o n .  models  a s  m a g n e t o t e l l u r i c  (1953). f i e l d both  The  and  ( e . g .  conducted u n i f o r m  t h e  such  a  f i e l d and  d i p o l e  The model  t i n f o i l .  t h e  t i n f o i l  sphere  ( t r a n s m i t t e r )  was  assumption  c o n d u c t i n g  • The  study  t h e  w h i c h  a r e n o t  s e v e r a l  sphere  g r e a t e s t  amenable  the  u s u a l  when  The  l a t e r  problem.  The  i s  i n  problem  o f  a  S i n c e  s c a l e  response  o f  a n a l y t i c a l t h e  t h a t o f  work, t h e  t h e  used  sphere  j u s t i f y  i s  s o l u t i o n s  response  o f  medium  i s  a  being  w i t h To  c a n be  medium  f o r  a b l e  f o r  i s  t o  geometries s i m p l i f y  c o n d u c t i n g  c o n d u c t i n g .  a  f o r  t h e o r e t i c a l  bodies  s u i t a b l e  to  measurements  surrounding  medium  i n  sphere  s o l u t i o n . o f  a n d  source  bodies  problem  were  thick,,  a g a i n s t  c o n d u c t i n g  i s  sphere  e x a c t  models  s c a l e d  The f i e l d  "the m o d e l  checked  a  a p p l i e d  he  t h e  s t u d i e d  (1932)  n o n - c o n d u c t i n g  1953)?  o f  u n i f o r m  c o n d u c t i n g  from  t h e  a i d o f  h o l l o w  s u r f a c e .  f a r  a  a n  depths  o f  C a g n i a r d  been  t h e  i n  theory and  S l i c h t e r  a  s k i n  s o l i d  i n  surrounding t h i s  o f  f i e l d .  be  o f  response  t h e  discus-sed  t o  a n a l y s i s  assumption  c o n d u c t i n g .  t h e  v a l u e  e l e c t r o m a g n e t i c  t h e o r e t i c a l  near  (Wait  c a n r e a d i l y  the  a  immersed  w i t h  f r e q u e n c i e s  l i k e  u n i f o r m  a n a l y t i c a l l y  geometry  was  have  sphere  c o n s i s t e d source  o n l y  a  i n  source  l a r g e  s u f f i c i e n t l y  o f  sphere  1932).  The  behaved  f l o w  a  s t r u c t u r e s b y  e x p e r i m e n t a l l y  o n  c u r r e n t s  m o d i f i e d  a  study  w h i c h  v a l u e s .  o f  t h e  t r e a t e d  c o n d u c t i n g  model  t h e  t h i s  a  were  S l i c h t e r  hence  o b t a i n e d  f a c t o r s  o f  p r e s e n t e d  g e o l o g i c a l  1953?  w i t h  t h a t  t o  March  f i e l d .  c o a t e d  a  s c a l i n g  t h e o r e t i c a l l y  model  the  a p p l i e d  problems  i n  (1937)  • Hubhert  i s  sphere non--  s i g n i f i c a n t l y The  s t u d y i n g  s e m i . - i n f i n i t e  model  t h i s p l a n e  Ik has  been  s t e e l  s t u d i e d  sheet  z o n t a l  to  a  c o u l d  n o n - c o n d u c t i n g p r o v i d e d  by  an  d i s c s  overhead  s i m i l a r  to  In  a  of  of  s i d e .  s c a l e d  the  l o o p  - The  He  the  o r  source  h o r i -  b u t t i n g  l a y e r  c o n d u c t i n g  over  i n  a  an  dyke  w i t h  f i e l d s  were  systems.  response  of  a  s t u d i e d  diameters  s i t u a t e d  c u r r e n t .  The  s e m i r - i n f i n i t e  i n  l a y e r  p o s i t i o n ,  loop  model.  s t a i n l e s s  sheet,  c o n d u c t i n g  a  v e r t i c a l  v a r i o u s  a  a  r e p r e s e n t  and  l a r g e  The  v e r t i c a l  e i t h e r  a  c o n d u c t i n g  o r  s t u d i e d  h o r i z o n t a l t h a t  a  c o u l d  ( 1 9 6 1 )  u s i n g  a  l a y e r ,  on  used  h a l f V p l a n e .  r e p r e s e n t  h o r i z o n t a l  f i e l d  h o r i z o n t a l  i t  media  D o u l o f f d i p o l e  a  medium.  p o s i t i o n  He  ( 1 9 6 0 ) .  n o n - c o n d u c t i n g  n o n - c o n d u c t i n g i n c l i n e d  West  r e p r e s e n t  p o s i t i o n  a g a i n s t  by  plane  d i s c  i n  a  v e r t i c a l i n  the  response s t u d i e d  and  f i e l d  was  by  of  v e r y  West  ( 1 9 6 0 ) .  Y o s t i c a l l y i n  a  w i t h  l a y e r e d  m e t a l s i n g  and  to  f i e l d s  w i t h  t i m i n g  s t a c k s  r e f l e c t e d  The s e q u e l  to  making  f i e l d  et  a i d  of  s c a l e d  a  e a r t h .  a l  l a y e r s  i n  of  s h e e t s .  as  were a  model, used  by  m e t a l  have  ( 1 9 5 2 )  They  ;  c o n d u c t i n g  markers  c u r r e n t  d i s p l a y e d  f u n c t i o n  of  t r a n s i e n t s sheets  the  p u l s e s  The  an  time  of  i n  a  t h e o r e t generated  v a r i o u s  e a r t h .  response  on  s t u d i e d  The  e x c i t -  h o r i z o n t a l s i g n a l  t o g e t h e r  o s c i l l o s c o p e , f o l l o w i n g  loop  the  and  the  c u r r e n t  s t u d i e d . work  t h a t  employed  Y o s t  s u p p l i e d  f i e l d s ,  were  and  c o n d u c t i n g  were  the  p u l s e ,  the  r e p r e s e n t  over  i t  ( 1 9 5 2 )  a  of  of  O r s i n g e r  Y o s t  model  ( 1 9 5 2 )  l i k e  measurements  the to  and and one  Van  N o s t r a n d  Y o s t  et  d e s c r i b e d  determine  a l by  depths  ( 1 9 5  k  )  ( 1 9 5 2 ) ,  the i n  was i n  l a t t e r a  a t h a t i n  l a y e r e d  15 earth.  The metal sheets i n the model were a d j u s t e d by t r i a l  and e r r o r to g i v e , as n e a r l y as p o s s i b l e , the same s i g n a l as that o b t a i n e d  from the f u l l s c a l e f i e l d measurements.  t h i s way an analogue o f the l a y e r e d e a r t h was  In  constructed.  T h e i r r e s u l t s f o r measurements a t v a r i o u s l o c a t i o n s agreed w i t h subsequent d r i l l h o l e measurements to w i t h i n an  accuracy  of 5%o Roden (196^) has d e s c r i b e d a model f o r i n v e s t i g a t i n g the- e f f e c t o f i r r e g u l a r i t i e s i n the shape of the c o a s t l i n e on magnetic d i u r n a l v a r i a t i o n s . • He used a t h i n copper sheet to represent  the ocean.  cause observable  He concluded  t h a t the ocean edge should  enhancement o f the magnetic f i e l d f o r v a r i a t -  ions w i t h p e r i o d s as long as 2h hours. Rankin; (19,60) and Rankin e t a l (1965) d e s c r i b e d a m a g n e t o t e l l u r i c model c o n s i s t i n g e s s e n t i a l l y o f an o s c i l l a t i n g l i n e c u r r e n t over a conducting represented  s a l t water s o l u t i o n , which  the upper l a y e r o f a model e a r t h .  Some' magneto-  t e l l u r i c model measurements were obtained f o r f a u l t s and dykes.  A model somewhat s i m i l a r to Rankin's (1960),; but  designed cussed  to provide c o n s i d e r a b l y more i n f o r m a t i o n , i s disr-  l a t e r i n t h i s work.  T h i s model i s p a r t i c u l a r l y  a b l e f o r s t u d y i n g some i n t e r e s t i n g problems o f  suit-  conducting  s-tructures surrounded by media of lower c o n d u c t i v i t y . 1 .2  Object o f the -Thesis There are f o u r o b j e c t i v e s of t h i s t h e s i s .  o b j e c t i v e i s to develop and evaluate mathematical  The f i r s t expressions  16  f o r  the  e l e c t r o m a g n e t i c  and  w i t h i n  d u c t i n g works t h i s  the  e a r t h  i n  the  upper u s i n g  such  components.  In  components  range  of  and  work be  o s c i l l a t i n g  phase  angles)  f o r  the  overhead  c u r r e n t .  of  the  assumption  those be  a  the  l i n e  The  to  l i n e  be  i n  wide  the  f o r  wide  t h i c k n e s s e s , v a l u e s ,  of  near  the  a  plane v a r i a t i o n s and  at  a  of  an  plane  ( a m p l i -  f r e q u e n c i e s , w i t h on  f o r  the  some  f i e l d  of  components  of  model  the  a  problem  i n f o r m a t i o n  c u r r e n t  model  f o r  i n d i v -  homogeneous  l o c a t i o n s  v a r i a t i o n s  c u r r e n t  of  of  the  l a y e r  the  range  and  f o r  f o r  of  a s s e s s e d .  e v a l u a t i n g  r e s u l t s  r a t i o s  c a l c u l a t e d  study  e a r t h  A g a i n ,  a s p e c t s  e l e c t r o m a g n e t i c  can  i s  a  and  e v a l u a t e d  e f f e c t  c o n -  S i m i l a r  assumption  the  s u r f a c e  s t r a t i f i e d  s p e c i a l  waves  the  the  h e i g h t s ,  e l e c t r o m a g n e t i c  a s s e s s e d . f o r  of  by  w i t h  and  the  model.  i n c i d e n c e ,  l a y e r s  c u r r e n t  to  be  of  at  e x p r e s s i o n s  From  o b j e c t i v e  source  can  of  a d d i t i o n ,  c o n d u c t i v i t i e s ,  o c c u r r i n g  g e n e r a l  c o n d u c t i n g  l i n e  d e a l  o c c u r r i n g  c o n d u c t i n g second  source  i n c i d e n t  v a l i d i t y  In  homogeneous  and  to  angles  both  h o r i z o n t a l l y  o b t a i n e d  n a t u r a l l y  o b t a i n e d .  The  tudes  the  f o r  inhomogeneous  plane  tend  normal  w i l l  a  wave  c o n d u c t i v i t i e s . on  model be  as  components  of  plane  f r e q u e n c i e s ,  i n f o r m a t i o n  can  a  t h i s  i d u a l  wave  l a y e r  l i t e r a t u r e  problem  depths,  f i e l d  r e s p e c t  the  v a l i d i t y  n a t u r a l l y  e a r t h ' s wave  s p e c i a l  s u r f a c e  model  and  cases  can;  compared. The  analogue u r e s )  t h i r d  model  s u i t a b l e  o b j e c t i v e  ( i n c l u d i n g f o r  i s  to  s u i t a b l y  s t u d y i n g  d e s i g n s c a l e d  and  c o n s t r u c t  g e o l o g i c a l  e l e c t r o m a g n e t i c  an s t r u c t -  v a r i a t i o n s .  The  17 measurements  will  i n c l u d e t h e a m p l i t u d e s and phase a n g l e s  the v e r t i c a l magnetic f i e l d as w e l l as  those of  electric  f o r both sheet  and m a g n e t i c f i e l d c o m p o n e n t s  and l i n e c u r r e n t  the h o r i z o n t a l current  sources.  The f o u r t h o b j e c t i v e i s  to use  study a v a r i e t y of g e o p h y s i c a l problems geological structures.  The r e s u l t s  i n f o r m a t i o n on s e v e r a l problems problem.  of  t h i s analogue model to involving  should provide  i n c l u d i n g the  typical new  coastline  18 Chapter  2.  2.1  A  MATHEMATICAL  S i m p l e  L a y e r e d  C o n d u c t i n g  of  2.V.1  n a t u r a l  comparison  geomagnetic  method  f o r  s t r u c t u r e . magnetic g e n e r a l the  the  n a t u r a l  and  v a r i a t i o n s determined  the  of  the  there  of  the  e l e c t r i c  the  methods and  T h i s magnetic  s t r a t i f i e d p r e s s i o n s  f i e l d s  f l a t f o r  the  e l e c t r i c  f o r  v a r i o u s  and  The  the a t  e a r t h  the  the  the  F i e l d  i n  magnetic  the  methods of  the  magnetic  of  p r e s e n t  f i e l d and  f i e l d s a n g l e s  and  the used  One  to  i s  based  f i e l d  of  i n v o l v e s  components  by  e a r t h .  components  o t h e r  d e a l s  and of  are  c o n d u c t i v i t i e s .  i n  and  the the  t h e i r  measurements l a y e r s  of  f o r u n i f o r m  f i e l d .  phase  of  w i t h i n  h o r i z o n t a l  work  s u r f a c e  i s  f i e l d s  e a r t h .  The  e l e c t r o -  s u r f a c e  commonly  f i e l d  f i e l d  c r u s t a l  o c c u r r i n g  source  the  p r o v i d e s  e a r t h ' s  c o n d u c t i v i t y  two  of  v a r i a t i o n s  the  i n d u c i n g  the  phases  e a r t h ' s  of  assumes  a m p l i t u d e  and  on  a n a l y s i s  the  f r e q u e n c i e s ,  depths,  at  magnetic  u n i f o r m of  f i e l d  v a r i a t i o n s .  n o r m a l l y a  p a r t  are  and  n a t u r a l l y  n a t u r e  three  and  dependence.  c o n d u c t i v i t y  the  s t r u c t u r e  e l e c t r o m a g n e t i c  above  of  e l e c t r i c a l  f r e q u e n c y  n e s s e s ,  t e l l u r i c  i n f o r m a t i o n  c o n d u c t i v i t y  h o r i z o n t a l  and  i n  Waves  a m p l i t u d e s  observed by  p r e s e n t  a n a l y s i s  the  b e h a v i o r  d i s t r i b u t i o n  study  of  o b t a i n i n g The  A t  on  P l a n e  E a r t h  I n t r o d u c t i o n A  a  MODELS  i n  the  plane of  w i t h  upper  waves.  the  o b t a i n e d  i n c i d e n c e , The  the  e l e c t r i c l a y e r E x -  components and l a y e r  of  of  e v a l u a t e d t h i c k -  c o n d u c t i v i t i e s  a  19 d  =  10~  to  10  c y c l e s / s e c  10"  1 6  s t u d i e d  C o n s i d e r time, the  t r a v e l i n g  s u r f a c e  c o n s i s t s 3,  k  media (j  and  are  of'  - M a t h e m a t i c a l  2.1.2  2,  emu  =  of  ) ,  be  2,  If),  where  magnetic  p e r m e a b i l i t y  same  as  t h a t  system  of  i n  m a t h e m a t i c a l  the  expressed The  u n i t s  w i l l  of  be  f i e l d  w i l l  In  (2)  •  (3)  • -  each  •  d  -  of  i n c i d e n t  upon  i n  the  the  space.  • The  the  the  c o n s t a n t ,  i s  The  assumed  to  G a u s s i a n  e x p r e s s e d  i n  emu)  r e s u l t s  w i l l  be  commonly  gauss  f o u r  d j  r e s p e c t i v e l y .  conductors  more  (media  The  e^,  A l t h o u g h  i n  l a y e r s  d i e l e c t r i c  g r a p h i c a l  used  c o n d u c t o r  detfth.  ( c o n d u c t i v i t y  g i v e n  w h i l e  i n the  g e o p h y s i c s . e l e c t r i c  v o l t s / m e t e r . M a x w e l l ' s  equations  i  +  <Wdc E 2  V.H s i d e  10*  and  c o n s t a n t s  are  of  e  §f)  =  must  be  s a t i s f i e d . ,  0,  =0,  V.E  (If)  right-harid  to  3  i n  i s o t r o p i c  c o n d u c t i v i t y  are be  i n  medium  VxH  pc,  a n a l y s i s ,  magnetic  g i v e n  the  used  w h i c h  be  1Cf  harmonic  c o n d u c t o r .  by  f r e e  u n i t s  w i l l  =  wave  1),  i n f i n i t e  each  i n  f i e l d  The  e, and  of  f l a t  l a y e r  c h a r a c t e r i z e d  3,  f  g e o p h y s i c s .  (medium  homogeneous,  t h i r d  p e r m e a b i l i t y ,  the  space  f l a t ,  the  i n  e l e c t r o m a g n e t i c  f r e e  magnetic  be  i n t e r e s t  s t r a t i f i e d  three  f r e q u e n c i e s  A n a l y s i s  plane  i n a  w i t h  can 1?  of  a  the  =  e q u a t i o n  0. (3)  i s  s e t  equal  to  zero  s i n c e  20 we  are  the  c o n s i d e r i n g  e l e c t r i c  wave  i n  and  medium  c h a r g e - f r e e  magnetic  f i e l d  s a t i s f y i n g  1  media.  I t  v e c t o r s  these  i s  e a s i l y  shown  f o r  the  i n c i d e n t  equations  can  be  that plane  expressed  as  (5)  H  (6)  where and  E„ o  and o  1  are  H  magnetic  1  f i e l d  =  E  =  H  the  Q  Q  exp  i d L j i i ^ . r  +  cot),  exp  K ^ n ^ . r  +  cot),  amplitudes  v e c t o r s  of  the  r e s p e c t i v e l y ,  i n c i d e n t i  =  e l e c t r i c  ,  ^-1  co i s  the  .A angular of  frequency,  propagation,  r  n^ ^ i s k.j  (7)  i s  the =  —  the  u n i t  p o s i t i o n jj„j e  ij  1  co  v e c t o r v e c t o r  -  i^+Tr^  i n  the  from  a  c  d i r e c t i o n f i x e d  co  o r i g i n ,  ,  10 and  c  i s  the  v e l o c i t y  c m / s e c ) .  The  1 9^1)  are  r e l a t e d  by  f i e l d  v e c t o r s  f o r  The as  (5)  and  v a r i a t i o n  exp(icot),  us  F i g .  and  2,  The  plane  the  f r e e  magnetic  f i e l d  f a c t o r  space  f i e l d  r e f l e c t e d  a l l  t h i s  i n  x  (3  v e c t o r s  10 ( S t r a t t o n ,  wave  have  the  v e c t o r s  w i l l  c o n t a i n  w i l l  be  same  suppressed  i n  form the  time  the  development.  L e t i n  l i g h t  and  S i n c e  (6).  f o l l o w i n g  shown  e l e c t r i c  of  and  c o n s i d e r 1  w i t h of  The  w i t h the  a  the  r i g h t - h a n d e d o r i g i n  conducting  i n c i d e n c e r e s u l t a n t  i s  the  f i e l d  at  the  l a y e r s yz  c o - o r d i n a t e i n t e r f a c e p a r a l l e l  system  of  to  as  media  the  xy  1 plane,  plane.  v e c t o r s  i n  each  medium  are  the  21  F i g u r e  1 .  < Model  used  i n  the  plane  wave  problem.  22 complex  v e c t o r  r e f l e c t e d  plane  =  (9)  sums  o f  t h e f i e l d  waves,  + H \  2  v e c t o r s  o f  t h e i n c i d e n t  a n d  i . e .  = l \ expCik^n^ . r ) + B ^ expCik^n^ . r ) ,  and  =  (10)  E ^  +  By  -* Cy  where  ky  k j  d e f i n e d  i s  E  j2  =  C  D..  i n  ( j  (9)  a n d (10)  equations  (5)  a n d (6),  o f  f i e l d  i n f i n i t e v e c t o r s  normal the  t o  plane  I n c i d e n t In x  component  of  primes  (11)  the  x  =  i  k  - j  1,  n  - j - | - r )  '  2,  H  Q  Magnetic  =  E  a n d a  ( S t r a t t o n ,  system  t h i s  normal  U s i n g  t o  t h e components t h e  o f  magnetic  i n t o  a  component  t h e Plane  o f  a n d z  primes  i n c i d e n c e  p a r a l l e l  t o  g i v e s  r e p r e s e n t  a n d t h e  t h e  double  t h e plane  o f i n -  n o t a t i o n  =  k . , ( y s i n 9^  +  z  c o s  9.,),  .  k . n . p . r  =  k . ( y s i n 9.  -  z  c o s  9.)?  components  t h e  components  k ^ n ^ . r  o f  t o  I n c i d e n c e  a., =  =  component  p a r a l l e l  p o l a r i z a t i o n  a n d t h e y  L e t t h e s i n g l e  t h e plane  h  k  o u r c o - o r d i n a t e  f i e l d  medium  19 1). t o  t h e magnetic  i n  s i n c e  a n d t h e  a n d  I n  a s d e f i n e d  r e s o l v e d  Normal  f i e l d .  ,  Q  v e c t o r s  (7)].  a r e zero  c a n be  i n c i d e n c e  e x p ( i k ^ n ^ . r ) ,  [equation  F i e l d  o f  -j  a r e complex  M-)  , C j  D  t h e e l e c t r i c  medium  o f  +  \  3,  w a y a s k^  B o t h  i n c i d e n c e  components  a n d z  P (  a n d B ^ a n d  each  r e p r e s e n t  c i d e n c e .  y  i n  t h e e l e c t r i c  components  x  =  depth.  t h e plane o f  e  t h e same  equations  i s  j  t h e complex o f  magnetic  t h e complex  f i e l d  e l e c t r i c  v e c t o r s  f i e l d  a n d t h e  v e c t o r s  i n  t h e f o u r m e d i a become (13)  (Hj)  (1 )  (Ej)  (15)  (Ej) ' =  k  = Aj exp(ioj)- +  x  = [- C*j e x p C i a j . ) + D'j e x p ( i P j ) ]  z  [C'j e x p ( i a ^ ) + D*j e x p ( i P j ) ]  The c o m p l e x c o n s t a n t s  of  (13)  i n equations  mined u s i n g the boundary components  exp(iPj),  conditions  the e l e c t r i c  cos  sin  (15)  to  9^,  Qy  c a n be d e t e r -  that the t a n g e n t i a l  and m a g n e t i c f i e l d s a r e  continuous,  A p p l y i n g these boundary  c o n d i t i o n s a t z = d ^ , we f i n d  (16)  B'  = m«A»  that  ,  where khCos9., - k - , c o s 9 ^ (17) If  we l e t  (18)  Y-| = e x p ( i 2 k d c o s 9 > + m^  (19)  y  3  2  2  3  = exp(i2k d cos9 ) 3  2  3  5  - m^ ,  t h e n a t z = d,  (20)  B2  = m A 2  2  ,  where  (21) At z  (22)  m  =0  2  =  Y^k^cos9 Y^k cos9 3  - Y2^2 ^3 + Y k K cos9. c o s  2  2  2  0 2  exp(i2k d co s9 ) 2  2  2  2h  where k cos©^  f  (23)  2  k , cos©2(1-m2)  -  m, - — — - — • k cos©^ 2  I t  Cl+mp  f o l l o w s  —  (1+m )  k^cos© (-1-m )  +  2  2  2  t h a t  (21+)  Then  u s i n g  e q u a t i o n  ( H  ( 2 5 )  )  2  = A ] [T^TJ  x  A f t e r  d e t e r m i n i n g  u s i n g  equations  (26)  ( E  C  ( E  )  2  I n c i d e n t  =  y  )  z  -C"  ,  2  )  +  m^  t h e e l e c t r i c a r e g i v e n  +  m  f i e l d  e x  P(  2^  ± a  e x p ( i p  f i e l d  ) ]  2  components  b y  ~  m  2  e  x  P (  i  P 2 ^  C  9  )  +  n u e x p ( i B  9  k  F i e l d  f o r these  S  6  k -5-  ) ]  2 /  a n dt h ex  O  1 »  2  [ e x p ( i a  p o l a r i z a t i o n  P a r a l l e l g i v e s  t o t h e P l a n e  t h ey  component components  a n dz  o f  s i n e  I n c i d e n c e  components  o f t h e e l e c t r i c i n t h e f o u r  ( H j )  (29)  (R\.)  z  =  [A'j e x p C i a j )  =  [-A'j e x p ( i a j )  ( E j )  x  +  B'j e x p ( i P j ) ]  o f t h e  f i e l d .  media  +  = C j e x p ( i a j )  B'j e x p ( i P j ) ]  -  D j  c o s  c a n b e  6.,  s i n 6 j ,  e x p ( i P j ) .  1  2  a s  (28)  (30)  1  Magnetic  equations  w r i t t e n  L"  [j~^J  / l t i j \ r  = C1  T h i s  The  2  a n d (15)  (1*+)  V  magnetic  [ e x p ( i a  a n dD  2  = 2 ,  /l-m'\ 2  (27)  f o r j  (13)  25  I n s t a t e d  we  m a g n e t i c  a d d i t i o n h a v e  t h a t  f i e l d  c o n d i t i o n s  we  t o  i s  t h e b o u n d a r y  f o r c o n s t a n t  c o n t i n u o u s .  f i n d  t h a t  a t  c o n d i t i o n s  u. t h e n o r m a l  A g a i n =  3  =  sinQ^cosQ^  -  sin9^cosQ^  sin6 cos©  +  3^9^0039.^  (3D  B  m  3  A  component  a p p l y i n g  z  p r e v i o u s l y  t h e  o f  t h e  b o u n d a r y  ,  3  where  -_;M  (32)  m = 3  I f  3  k  3  3  Y  (3 )  Yh. = e x p ( i 2 k d c o s 9 )  k  t h e n  3  = exp(i2k d cos9 > + m 3  a t  z  =  B  m  it  2  3  2  11,1!  = m A  2  2  Y sin9 cos9v 3  - m  3  ,  3  =  Y sin9 cos9 2  3  ,  2  Yk in9 cos9 s  2  3  =  3  d ,  -II  (36)  z  2  3  (35)  3  + Yh. i ®3 s  n  C 0 S  2  ®2  exp(i2k d cos9 ) 2  0 _ M  (37)  B  II , It  = m A  1  1  1  ,  where  sin9.j c o s 9 ( 1 + m ) - sin92Cos9.| (1-mp 2  (38)  f o l l o w s  2  s i n 9 cos9 (1+m ') + 31^20039.! (1-m ) ' 1  I t  3  we l e t  (33)  A t  exp(i2k d cos© ).  t h a t  2  2  2  2  2  26  / 1+m"\  Hence  u s i n g  (MO)  (H ) 2  e q u a t i o n s  =  y  A!,  and  (28)  (j^n-j  1  cose.  f o r  (29)  [ e x p ( i a  2  )  j  =  +  2,  e x p ( i B  2  ) ]  cos  e  ,  1  /1-m"\ ( H  (M-1)  2  )  =  z  - A "  A f t e r  d e t e r m i n i n g  u s i n g  e q u a t i o n  (M-2)  (E ) 2  C  and  2  D  the  2  reduces  (30)  =  x  [ e x p ( i a  I  1  cj  2  )  and  of  the  (M-2)  v a r y i n g  are  the  [ e x p ( i a  9  i n  the  upper  waves  i n  the  yz  The  (M-3)  k ^ s i n  and  magnetic  -  ) ]  s i n  e  l  are  and  components l a y e r  e x p ( i B  mX  the  the  f o r  ) ]  ^ complex  equations  of  9  (26),  v a r y i n g  plane  compon-  e  1  and  Phase  r e l a t i o n s h i p s  =  k  2  s i n  ©  2  =  of  the  x,  y,  ( S t r a t t o n ,  k ^ s i n  ©^  =  (27)  e l e c t r i c  e l e c t r o m a g n e t i c  p l a n e .  the  l  component  ^  (M-1)  f i e l d  c o n d u c t i n g  A m p l i t u d e  U s i n g  )  ^  (M-0)  complex  f i e l d  f i e l d  2  - m " \  2  ents  e x p ( i B  2  to  HT  (25),  m  e l e c t r i c  1-m y E q u a t i o n s  -  z  Components  19M-1) k ^ s i n  ©^  ,  27  ( 6)  k^COS©  k  ©2?  a  the  n  d  ^1+  e l e c t r i c  m  a  y  b  = -Ji^  k  e  e  o f  S i n c e  t h e a m p l i t u d e s  waves  a n dhence  t h e modulus  H' O  <  k  n  a  H  H  H  from  H  "  Q  ,  2  3  d  a n dE  Q  m j , m"  components o f  t h e complex  e q u a t i o n s  (25)  exp(i0 )  = H  exp(i<j>  = H  0  )  x  V  E a c h  mayb e e x p r e s s e d  a r e d e s c r i p t i v e  v  2  a n dm ^  5  ?  o f i n  q u a n t i t i e s .  o f  a s f a r a s computations  1  ( H  t h e i n c i d e n t a r e concerned, a n d ( 1)  C+0),  k  a s  exp(i<o ), x  |  y  H"  0  •«  Z  sin e )  a n d argument  "  H" o  e  2  f i e l d  H  2 V  < 2>  t  ( 2>x|  H  ( 8)  i  t o express  < 2>x  L  m  a r b i t r a r y  i s c o n v e n i e n t  ( 7)  i  a n dmagnetic  terms  i t  l  - k  H"  )  exp(i<?>  ),  o  and  (*+2)y ( 2 6 ) ,  e q u a t i o n s  a n d  ( 2>x  (27)  a s  E  (50)  (51)«  E' o  E"0 " < 2>z E  (52)-  where  "  "S  t h e modulus  e x p ( i |  E  (  x  )  = E  1  o  2 M  B  E"0  < 2> | E  Z  exp(i\|r  ) =  exp(i\|r  )  i s t h e amplitude  o f  E  = E  x  x  e x p d ^ ) x' r  y  exp(i\jr  •),  e x p ( i ^  ),  t h e component  a n d  t h e  28 argument  i s  amplitudes r e l a t i v e  and  are  are  to  give  (52)  the  a  angle.  E x p r e s s e d  d i m e n s i o n l e s s  the  the  i n  phase  i n c i d e n t  f i e l d  and  f i e l d  components  convenient  form  f o r  upper  c a l c u l a t i n g  a l l  the  components  except  the  f i e l d  component  are  continuous  at  f r e e  f a c e ,  these  e l e c t r i c not  of  f i e l d  component  i n t e r e s t  u n i f o r m  i n  l a y e r  i n f i n i t e  depth  d-  R e s u l t s  = oo.  f o l l o w i n g  2.1.3  tudes k  are  of  a::  these  computer  angles  depths,  and  s t u d i e d  were  p u l s a t i o n ;  of  was  the  angles  r e s p e c t i v e l y  and  e l e c t r o m a g n e t i c  s p e c i a l  the  v e r t i c a l i s  i n  cases  depth,  and  of  (1)  are  °°  g e n e r a l (1)  a  (2)  c o n d u c t i n g  cases  a  s i n g l e e a r t h  and  s  of  (2)  d i s c u s s e d  emu.  l o w e r f i e l d  w r i t t e n  to  e v a l u a t e  components  as  g i v e n  computations of  c o n d u c t i v i t i e s .  10"  s u r f a c e  i n t e r -  i n  the  R e s u l t s  E x t e n s i v e  to  The  sea.  e l e c t r i c  s p a c e - e a r t h  0).  s e t t i n g  v a r i o u s  programme  10""  =  l a y e r  c o n d u c t i n g  c a l c u l a t i n g  e a r t h ' s The  a  to  e l e c t r o m a g -  v e r t i c a l  homogeneous  by  A  (51)"  (z  i n f i n i t e  of  f r e q u e n c i e s ,  =  the  D i s c u s s i o n  phase  f o r  i n  the  (V7)  (2.1.3).  v a r i o u s  0  at  o b t a i n e d  f o r  the  s u r f a c e  o v e r l y i n g  s e c t i o n  and to  ( 7)  earth,  depths  s u i t a b l e  g e o p h y s i c s .  c o n d u c t i n g  c o n d u c t i n g  v a r i o u s  e a r t h ' s  measured  c o n d u c t i n g  the  s i n c e  the  are  i n  A l s o ,  at  angles  the  Equations  components  are  form..,  components.  f i e l d  equations  t h i s  phase  n e t i c  components  at  the  i n  f The  i n c i d e n c e ,  The -  were  10  f r e q u e n c i e s •  J  to  \0  J  f r e q u e n c i e s  frequency  range  v a r i a t i o n s .  of  by  c a r r i e d l a y e r and  the  a m p l i -  equations  out  f o r  t h i c k n e s s e s , c o n d u c t i v i t i e s  c y c l e s / s e c are  the  w i t h i n e a r t h ' s  and the  m i c r o -  n a t u r a l  29 In media  g  and  c o n s t a n t , range  of  the  -  computations f o r  0  e,  was  • F o r  become  i m p o r t a n t ,  case  (a)  of  the  f i e l d  out  a  f l a t  e  The  not  =  e  f o r  Q  a l l  d i e l e c t r i c  important  (Dosso  and  c y c l e s / s e c  has  a  l a r g e  i n  t h i s  L o k k e n ,  10  ti  does  v a l u e  i n  f o r  a  as  i n  work  wave  on  t h i s  and  (f  to  1 0~  3  the  e a r t h  problem  f r e q u e n c y  the  s o u r c e ,  c o n d u c t i n g  A l t h o u g h  =  Depth  i n f o r m a t i o n plane  F o r  (51)°  e n t i r e  t h i s  I n f i n i t e  homogeneous  to  the  of  g e n e r a l  f i r s t .  (*+7)  emu),  as  f i e l d  r e l a t i v e  w h i l e  the  i n  u n i t s  =  i s  F i g u r e s  s u r f a c e  of  a  wave  shown  2(a)  -  e l e c t r i c  the  of  g i v e n  r e l a t i v e  d  of  =  2  co  computations c o n d u c t i v i t y 10  t y p i c a l  c y c l e s / s e c ,  3  r e s u l t s ,  i n  c o n v e r s i o n u n i t  the  to  show  and  magnetic  f r e q u e n c y  MKS  the  the  u n i t s are  f a c t o r MKS  f a c t o r  be  e l e c t r i c ( v o l t s / m e t e r )  g i v e n  f o r  u n i t (c  w i l l  i n  c o n v e r t i n g  i s  c/10  ,  )  f o r  the  10"  graphs.  (d)  depend  r e s u l t s  a m p l i t u d e s  c o n v e r s i o n on  conductor  source  few  f o l l o w i n g  The  The  a  are  g a u s s i a n .  10  the  the  (gauss).  f i e l d  of  a l l  f i e l d  f i e l d x  3  o n l y  a m p l i t u d e s  magnetic  e l e c t r i c  plane  f o r  10  Here,  angles  i t  ,  11 to  e l e c t r i c  i s  E a r t h  some  s t u d i e d  i n t e r e s t  10  c  of  was  1 f\  where  i t  i f  JJ,  u s e d .  than  components  equations  c a r r i e d  g a u s s i a n  to  problem  i n  the  p a r t i c u l a r l y  o r d e r  was  shown.  g r e a t e r  o b t a i n  of  (j, =  c o n d u c t i v i t i e s  In  used  were  s i n c e  C o n d u c t i n g  depth  =  and  v a l u e s  water.  i n f i n i t e  d  v a r i e d  Homogeneous  s i m p l i f i e d  ranges  space  f r e q u e n c i e s  of  b e h a v i o r  were  not  f r e q u e n c i e s  1961).  the  f r e e  the  how  on 1  the  amplitudes  f i e l d the  and  components  angle  c y c l e / s e c  of f o r  phase  a t  i n c i d e n c e the  the f o r  c o n d u c t -  30  F i g u r e a  T h e a m p l i t u d e s  2.  f u n c t i o n  (3)  10"  1 5  ,  o f  G  f o r  ( a ) - ( c )  f=1  a n d (1+) 1 0 "  1 6  a n d t h e phase  cycle/sec-,  emu.  (1)  angles  o=10" , 1 1  (2)  (d)  10~  1  31 1Cf  i v i t i e s v e r t i c a l F o r  the  w i t h  , 1 (T ^, 10" ^  e l e c t r i c  P  •  E„  has  F i g .  6,  component  was  i t s  2(b)  more  maximum  i t  can  be  E  and  from  16  emu.  f o r  E  are  curves  seen  Z'  and  (1)  t h a t  H .  angle  H_  i t  i s  s i m p l y  equations  an  A l t h o u g h  computed  c o m p l i c a t e d .  v a l u e  From  5°.  L  here,  a l t h o u g h  appears  a p p r o x i m a t e l y i n  f i e l d  s t u d i e d  cos  y  r e l a t i o n s h i p  i v i t y ,  10~  1  ?  problem  E„ x  and  1  1  1  and  f o r  each  and as  shown.  the  (h2)  c o n d u c t -  i n c i d e n c e  (3),  v a r i e s  not  r e l a t e d ,  (26)  of  the  of  and  (2)  d~"^.  (•+)  T h i s  z was  found  10  c y c l e s / s e c .  3  E  x  and  a n g l e s  H  be  the  case  As  can  z  are  a l s o  do  not  depend  a n g u l a r the  to  form  f o r  be  s i m p l y  dependence  same  f o r  on  f o r a l l  the  seen  f r e q u e n c y from  r e l a t e d .  the a l l  e q u a t i o n s H  x  ,  H  c o n d u c t i v i t y the  o t h e r  range  o r  components  f r e q u e n c i e s  ,  =  (M-1)  and  a l l  10~  to  and  (M-2)  the  phase  3  f r e q u e n c y .  and  and  f  phase  The  a n g l e s  has  c o n d u c t i v i t i e s  e o n s i a e r e d . In  s t u d y i n g  m i c r o p u l s a t i o n ions  can  be  rrgnga,  e x p l a i n e d  e a r t h .  If  r e g i o n s  where  compare  f a v o u r a b l y  In  f i e l d  geomagnetic  t h i s  i t i n  a  u n i f o r m w i t h  magnetic  l o c a t i o n s  such  s t r u c t u r e  i s  ( C h r i s t o f f e l  as  et  were  v a l u e s i t  R a l s t o n ,  a l ,  of  i s  v a l i d ,  1961).  t h a t  i n c i d e n t  to  by  study  i s a  A l b e r t a ,  where  a  r a t i o s  up  A m p l i t u d e  r a t i o s  R  s h o u l d model.  v e r t i c a l  made  to =  the i n  wave  at  u n i f o r m  y i e l d  on  l i k e l y  the  the  v a r i a t -  made  plane  Measurements  i n  the  measurements  s t r u c t u r e  common  l i k e l y ,  waves  p r e d i c t e d  r a t i o .  e s p e c i a l l y  assumed  plane  g e o l o g i c a l  f i e l d  c o n s i d e r e d  sometimes  terms  assumption  measurements,  h o r i z o n t a l  i s  v a r i a t i o n s ,  to  i n l a n d  g e o l o g i c a l about  H  (H z  2  +  0.1 H )""^ 2  x  y  -1 as  a  f u n c t i o n  of  f r e q u e n c y  f o r  an  e a r t h  c o n d u c t i v i t y  d  =  10  % y  32 emu 1  and  v a r i o u s  c y c l e / s e c  v a r i o u s f i e l d  a n g l e s  be  and  from  the  r a t i o of  F i g .  square  on  t h a t  3>  f o r  of  the  C h r i s t o f f e l  et  a l  i n  d e c r e a s e s  g e n e r a l ,  One  of  (1961)  C o n d u c t i n g  the  a c t u a l  model  to  f i e l d study  substratum. e i t i e s  i n  s i m i l a r plane  One  wave  o t h e r model  c o n d u c t o r s . v a r y i n g  The  = oo  was  components  and  phase  S i n c e  F i e l d  O v e r l y i n g  i s  t y p i c a l r a t i o s s t r u c t -  apparent as  made  t h a t  the  the by  r a t i o ,  a:  Homogeneous  Depth  wave  model  p r e d i c t s  magnetic  f i e l d  r a t i o  of  i t  f o r  a  i s  of  t h a t plane  of  a  i n f i n i t e i n  a n g l e s  c o n d u c t i v i t i e s  i n t e r e s t  the wave as  i s  ( k 7)  computed  d i s c u s s e d  r e f e r e n c e  to  i n  " s k i n  to f o r the  observed  the  t h i s  c o n d u c t i n g  inhomogen-  would  be  c u r r e n t s .  a  The  l a y e r e d  h o r i z o n t a l  s t u d i e d  s m a l l e r  use  s t u d y i n g  o v e r l y i n g  e q u a t i o n s were  l i n e  i s  of  source  to  much  to  i n  e f f e c t  c o n d u c t i n g  depth  a  than  i n h o m o g e n e i t i e s  c o n d u c t i v i t y  f r e q u e n t  the  w i t h  v a r i e s  z  i n d i c a t e  I n f i n i t e  e x p e c t  used  H  I t  measurements  i t s e l f  of  model.  model  l e n d s  problem  and  wave  r e a d i l y  e a r t h  r a t i o  f o r  l a y e r e d  such  and  k  A t  h o r i z o n t a l  s o u r c e s  t h i c k n e s s  t h i s  10~  3-  amplitude  f i e l d  c o n d u c t i n g  quencies  of  e f f e c t  e f f e c t  of  P i g .  observed  wave  o t h e r s  i n  f r e q u e n c y .  plane  c o n d u c t i v i t y  f o r  plane  L a y e r  would  of  plane  measurements, the  the  b a s i s  and  E a r t h  shown  neighborhood  t h a t  w i t h  are  Comparing  a  the  v e r t i c a l - t o - h o r i z o n t a l i n  the  f r e q u e n c y .  C o n d u c t i n g A l t h o u g h  i n  the  assumption  r o o t  (b)  i s  i n c i d e n c e  suggests  e x p l a i n e d  the  of  i n c i d e n c e .  measurements  cannot ure  angles  -  l a y e r  of  homogeneous here.  (51)* the  F o r The  same  p r e v i o u s  depth"  (the  t h i s f i e l d f r e -  s e c t i o n . -amplitude  F i g u r e  (2)  3. 10,  The  (3)  r a t i o  25  ( ) k  5  R  as k  5,  a  (5)  f u n c t i o n  65  s  and  of (6)  frequency  85°.  f o r  o=10~  1 3  emu,  and  (1)  9=5,  3 of  a  wave  depth)  i s  w i l l  a t t e n u a t e d be  made  depth  as  a  g i v e n  i n  F i g .  h.  F i g u r e  5  ents  of  f u n c t i o n  the  h o r i z o n t a l  of  the  plane  the  same  i t i e s .  of  magnetic  the  a l l  i v i t i e s , i n  the  H  f o l l o w i n g  not  be  t h a t  the  r a t i o  v a r i o u s  the  f i e l d  and  the  r a t i o  R  of  on  angle  a n g u l a r  are  w  the  dependence  l a y e r  s i m p l y  H  y  R,  s k i n  of  was  to  three  compon-  v e r t i c a l i n c i d e n c e  found and  H_  i s  to  be  c o n d u c t i v -  they  are  not  z  ,  found  and  f i g u r e s  t r e a t e d  s k i n  showing  the  t h i c k n e s s e s r e l a t e d  a  c o n d u c t i v i t i e s  of  to  l a y e r i n  be  d e t a i l  i s  v e r y  s e c t i o n .  i n  t h i s  s m a l l .  a g a i n ,  i n  t h i s  s e c t i o n .  6,  the  r a t h e r  s t u d i e d  i n  the  f o l l o w i n g  As  can  be  seen  component  i s  s t r o n g l y  dependent o c c u r s .  emu  note  the  H  0=10  We  a n g l e s  than  f r e q u e n c y ,  c o n d u c t i v i t y  phase  shown  t h i c k n e s s ,  and  d i s c o n t i n u i t y  The  be  l a y e r  d u c t i v i t y ,  c o n d u c t i v i t y  not  i n  changes  F i g .  w i l l  c o n d u c t -  h o r i z o n t a l  by  from  a l l  the  u n a f f e c t e d  f i g u r e s  f o r  s e c t i o n .  S i n c e  are  z  same  t h i c k n e s s e s ,  t h i s  i n  the  components  i c a l  graph  a m p l i t u d e s  E  f r e q u e n c i e s  w i l l  f o r  a  y and  x  work,  i n  the  x h e r e .  0.368  =  how  The  and  1/e  t h i s  f r e q u e n c y  f r e q u e n c i e s ,  S i n c e  shown  f a c t o r  components depend  waves.  f o r  a  throughout  shows  to  by  k  on The  c o r r e s p o n d i n g  r a t i o  R  c o n -  i s  magnitude  of  the  the  at  w h i c h  depth  c o n d u c t i n g to  t h a t  l a y e r  of  v e r t the  has  f r e s h  —16 w a t e r  w h i l e  the  c o r r e s p o n d i n g The f r e q u e n c y i n  F i g .  7.  to  r e g i o n t h a t  dependence  range The  f c r  below c f of  dry H_  v a r i o u s  l a y e r  has  a  c o n d u c t i v i t y  a  -  emu  10"  e a r t h . on  the  l a y e r  t h i c k n e s s  i s  f r e q u e n c y  t h i c k n e s s e s a  s t r o n g  over i s  a  l a r g e  brought  f a c t o r  i n  out  d e t e r -  a  35  '  «  10"  2  l  I  I  10  f  F i g u r e range  h. of  • S k i n  depth  as  i  I—  10  2  4  CYCLES/SEC  a  c o n d u c t i v i t i e s .  f u n c t i o n  of  f r e q u e n c y  f o r  a  36  9 DEGREES  F i g u r e  5.  The  f u n c t i o n s and  d =10^ o  o f  amplitudes Q  cm.  f o r  H  d =-10~' 2  , l f  H ,  , d  3  H  z  ,  = 1 0 ~  and 1  6  the  emu,  r a t i o f=1  R  as  c y c l e / s e c ,  37  H,  40  20  60  80  0 DEGREES  F i g u r e and f=1  6 l a y e r  The  dependence  t h i c k n e s s  c y c l e / s e c .  f o r  of-  H  z  on  the  angle  0-^=10"^  of  i n c i d e n c e  emu,  and  f F i g u r e  (b)  7.  H  O =1CH 2  f  CYCLES/SEC a s a 6  3  f u n c t i o n  ' q.=10"  1 l f  o f  emu.  f  a n d  d  2  f o r 3=50°,  CYCLES / SEC  ( a ) c =10~ 2  l I f  ,  <j.=10" , 1 6  39 mining depth root  the ( d  of  f r e q u e n c y = OP)  2  the  dependence  i n  o f  R"  the  c o n d u c t i v i t y  not  f r e q u e n c y  i v i t y  f o r  s m a l l e r  v e r t i c a l of  i s  a l l  The  s t r o n g l y and  dependence  i t s  of  z  v a r i e s  as  show  H  from an  then i s 9  t h a t f o r  and  i f  l a y e r  combinat-  both  f r e q u e n c y  H  e f f e c t  H  v a r y  s u r f a c e  the  z  curves  does  and  f o r  s u r f a c e  i n  z  t h a t  9  cases  out  depth  d e t a i l e d  the  some  the  square  and  8  i f  t h a t  i n f i n i t e  the  important  shows  l a y e r  of  more  F i g s .  brought  a f f e c t  on  the  t h i c k n e s s ,  c o n s i d e r e d  c o n d u c t i v i t y . v e r y  l a y e r  shown  T h i s  depths  s i n g l e  has  a l s o  F i g u r e  8.  a  9  e v i d e n t  c o n d u c t i v i t y ,  component  the  i s  I t  H  and  8  substratum  F i g .  c o m b i n a t i o n s  d e t a i l  the  (b)  l a y e r  f r e q u e n c y .  i n  11  I t  l a y e r s .  w i t h  and  f r e q u e n c y ,  of  F o r  F i g u r e s  g r e a t e r  and  the  the  the v a r y  7,  w i t h has  s u r f a c e  has  3,  7(a)  c o n d u c t i v i t i e s .  s h a l l o w  2,  on  z  of  does  F i g s .  f r e q u e n c y .  i o n  l a y e r  dependence.  l a y e r  the  c o n d u c t -  amplitude  dependence. t h i c k n e s s  of  G r e a t e r  f o r  f r e -  z quencies  1,  and  Curves  show  h  16  c y c l e s / s e c  i s  p r o v i d e d  i n  F i g .  1i A  s u r f a c e  l a y e r  has  same  the  c y c l e s / s e c , be  v a l u e  the  substratum,  i n f i n i t e  f o r  whereas  d i f f e r e n t  approaches  f o r  c  the  each  the  are  v a l u e s  "1 A emu  r a n g i n g  curves i f  10  from  f r e q u e n c y B  show  the  and IOi n  o b t a i n e d  f o r  a  1  =  cm  to  the  of  F o r  the  l a r g e  s i n g l e  10" 10  range  f r e q u e n c y  c o n d u c t i v i t i e s  i n t e r c h a n g e d .  ^  c ,  emu  h  cm,  1  and H_  z  to  16  dependence s u r f a c e d  2  ,  H  c o n d u c t i n g  to  l a y e r  z  l a y e r  depth.  F i g u r e  11  shows  f a c e  l a y e r  t h i c k n e s s  f o r  i o n s  f o r  f r e q u e n c y  of  a  =  2  t h i c k n e s s e s  q u i t e  and  of  t h a t ,  10.  how  a 1  the  phase  v a r i e t y  of  c y c l e / s e c .  <j>„ z  depends  c o n d u c t i v i t y F o r  s m a l l  and  on  the  s u r -  c o m b i n a t l a r g e  d  9  ?  ho  f  F i g u r e 8.  o =10~ 3  16  d =10" ^, 1  3  CYCLES / SEC  , d =10~ emu,- ( 1 ) d =10, (2) 1 0 , (3) 1 o \ (h) 10 $  H  z  as a f u n c t i o n o f f f o r e ^  0  11  2  3  2  (5) d = 1 0 , (6) 1 0 , (7.) 10^", (8) 1 0 * ; d = 1 0 ~ , 3  2  3  (9) d = 1 0 , ( 1 0 ) 1 0 , (11) 10**, (12) 10^5 d = 1 0 " , (13)> d =10,- (1*+)> 1o3, (15)' 10^, ( 1 6 ) 10* cm. 3  2  2  ?  5  3  1 3  lIf  k  f  F i g u r e  9. • H  0 =10"  1 1  3  z  a s a  e m u , (1)  CYCLES / SEC  f u n c t i o n  d =10 . 3  2  O = 1 0 ~ , - (5) d = 1 0 3 , 1 3  3  2  0 =10~ ^,. (9) 1  3  d =10 2  1  3 s  (6) (10)  o f  f  (2) 10 , 5  f o r  10^  s  (7)  e= 5°  o =10"  k  (3) 10  10^, (11)  10 , 6  (8)  6 3  10 , 6  l b  2  s  (h)  s  10 ; 7  10 ;  (12)  7  10 c m . 7  Figure  10. • H  and e= 5°, k  a s a f u n c t i o n o f dp f o r f = 1 , (A) o = 1 0 ~  0 ^ = 1 0 - ^ emu.  2  1 1  ,  o =10~^ 3  6  L  emu, ( B )  ,  16  cycles/sec  o =10~ 2  1 6  ,  ^3  d F i g u r e  11 „  <p„ a s a  f u n c t i o n  cm  0  o f  cL-, f o r f=1  (A)  d = 1 C ~ * , d- =1(T , 10~ *, 1 0 ~  (B)  d = 1 C f , d.=10" , 10~ ,  16  1  1  ll+  2  1 6  2  11  1 3  K T ^ , 1  ?  c y c l e / s e c ,  10~  1 3  emu,  10~ * e m u . 1  ©=  h a s a  v a l u e  o f  225°.  s i n g l e  l a y e r  o f  i n f i n i t e  0_  Zs  a  225°  when  l a y e r  i s  s h i f t s  there l e s s  t o  than  v a l u e s  a  s k i n  g r e a t e r  225°  d  than  g r e a t e r  t h e d i f f e r e n c e  tude  t h e maximum  w h i c h  t h i s  magnitude  phase o f  c o m b i n a t i o n ness  r e q u i r e d  (c)  phase  l a y e r s  t h i c k  d  change  I t  phase  change  f o r maximum  o f  a n d B  was found f o r a  change  eous  e l e c t r o m a g n e t i c  phase  u l a r  P h y s i c a l  e a r t h  a n g l e s  i n  when  N a v a l  L a b o r a t o r y )  phase  changes  made  a s a  emphasis  i n f i n i t e  a s a t  a n d some f u n c t i o n i s  t h e c o n d u c t i v i t y  p l a c e d o f  o f  depth  l a y e r  i n  f r e q u e n c y .  i n  o t h e r  homogen-  here. t h e  a r e o f i s  i n  The upper  a m p l i t u d e s p a r t i c -  an. o c e a n .  v a r i a t i o n s  on, t h e c a s e  s e a w a t e r ,  t h i c k -  o n  a;i  The  l a y e r  o n  t h e  c o n d u c t i v i t y  t r e a t e d  l a b o r a t o r i e s  i n f o r m a t i o n  f o r  a l t h o u g h  depend  f o r p o i n t s  f i e l d  m a g n i -  Homogeneous  i s  c o n d u c t i n g  b y v a r i o u s  t h a t  t h e l a y e r  t h e s u r f a c e .  magnetic  t h e  t h e range  o v e r l y i n g  c o n d u c t i n g  phase  t h e  i n h o m o g e n e i t i e s  depth  computed  t h e upper o f  o f  t h a t  g i v e n  does  two l a y e r s  t h e upper  measurements  a r e being  o f  were  a s w e l l  ocean  A l t h o u g h  o f  f i e l d s  l a y e r  i n t e r e s t  t h e e f f e c t  t h e problem  c o n d u c t i n g  c o n d u c t i n g  study  The  t h e g r e a t e r  t h e f r e q u e n c y ,  phase  s u r f a c e  show  a n d t h e g r e a t e r  o c c u r s .  independent  A  from  a n d to! V a l u e s ,  2  a n d d^  2  a n d t h e  f o r  Zi  g r e a t l y  G*  i f  0„  o f  ( s e e F i g . k).  Curves  between  t h e v a l u e  d e p a r t s  0  225°  > dy  2  change  f u r t h e r  c o n d u c t i v i t y ,  has  i f  depth  w i t h  Two C o n d u c t i n g L a y e r s Qverlyifag a n C o n d u c t i n g B a r t h o f I n f i n i t e Bepth To  and  depth.  than  t h e maximum i s  agrees  a r e two c o n d u c t i n g  s m a l l e r  o f  T h i s  ( e . g .  i n t h e P a c i f i c  t h e attenuation,  t h e s e a i s where  o f  a n d  i n t e r e s t .  t h e upper  c o n d u c t i v i t i e s  l a y e r a r e  M-5 a l s o  c o n s i d e r e d .  S i n c e  a l l  cases  c o n s i d e r e d  i l y  taken  as  The c o n d u c t i n g the  phase  u a t i o n  of  H  E„  w e l l  as  n o s t i c are  on  depth  i s  shown  depth  shown  H  the  hence The  the  the  E„  at  z  J  out  the to  e f f e c t  of  s u r f a c e shown  i n  f o r  F i g .  w i t h  the  same  i s  a r b i t r a r -  very  f o r  and  1  s h a l l o w  l a n d on  masses  frequency  The  f o r  p l a y s  v a r i o u s  c o n d u c t i v i t y  a  the  are  ,  ,  and  l a y e r  are H  f r e -  as  d i a g and  x  o n l y  Ey H  the  c o n d u c t i n g 1  the  i s  to  32 two  depths  dominant w h i c h  might  dependence  t h i c k n e s s e s  and  r o l e .  frequency  upper  l a y e r  upper  s k i n  those The  l a r g e  l a y e r of  H  range  of  e a r t h .  over  E  each  w h i l e  case  terms  t h i c k n e s s the  ,  the  s e c t i o n .  t h i s  l a y e r  on  of  f r e q u e n c i e s  on  H  to  v a l u e s  and  components  r e l a t e d  i n  of  a t t e n -  s u r f a c e  l a y e r .  frequency In  The  depend  s e m i - i n f i n i t e  13"  l a y e r  the  does  t h i s  the  c o n s i d e r a b l y  s t r u c t u r e ,  i n  i n  dependence  1 2 ( b ) .  i s  upper  simply  s e m i - i n f i n i t e  the  t h i c k n e s s e s  s m a l l  F i g .  H  These  lower a  F i g .  depth  and  are  and  depth  c o n d u c t i v i t i e s  the  f i g u r e s  over i n  f a c t ,  E„  the  c y c l e s / s e c 1 *'.  a l l  of  i n  w i t h  y A l t h o u g h  c o n d u c t i v i t y  remaining  s u r f a c e  10  f o r  p l a c e  and  frequency.  and  c o n d u c t i v i t i e s  H  i n c i d e n c e  12(a)  x Hg= z  and  same  H  c o n d u c t i v i t y  on  l o w e r  p o s s i b l e  E . y  of  c o n d u c t i v i t y  i n  be  10  x  ,  e n t i r e  i s  a r e ,  v  each  a t t e n u a t i o n  the  the  c y c l e s / s e c l a y e r s  the  the  at  z  are the  The on  E  S i n c e  i n  f o r  f o r  the  not.  takes  angles  depend of  that  F i g .  on  of  i s  +5°»  i n  and  dependence  angle  shown  H  depend  the  i s  c o n s i d e r e d , quency  a n g u l a r  l a y e r  than  and  here,  a t t e n u a t i o n  w i t h  g r e a t e r  L  the  of  range i s  l a y e r  brought  i s  -11 dp  =  10  emu,  the  c o n d u c t i v i t y  of  sea  water.  Curves  1  and  -r  Z F i g u r e d  2  =  k  12. x 1 ( T  cm  Z  The amplitudes 1  1  ,  o =10" 3  l  i  +  emu  (a) 3  and t h e phase  d =2x1Q 2  l +  cm, d  angles  =QO  ?  f=i  (b)  as  cm a  c y c l e / s e c ,  f u n c t i o n  o f  and-e=l+5°.  z  f o r  k  F i g u r e  z=0,  13.  • H  as  z  a n d 0= 5°. k  a  7  f u n c t i o n  of  f  f o r  d =10- , 2  3  d^= 1 . 6 x 1 0  cm,  J+8  F i g u r e  1  d ^ l O "  L  1  .  H  z  emu,  6  as  a  z=0,  f u n c t i o n  o f  0=M-5°,  d =1 3  (3)  1 0  3  ,  (h)  1 0 ^ ;  and  d = 8 x 1 0 *  (7)  1 0  2  ,  (8)  1 0  (9)  1 0 \  3  ,  f  f o r  d =10  .6x10^  3  (10)  cm,  ,  2  cm,  (5)  1 0 * cm.  (1)  d =0, 2  ^ = 1 0 d =0, 2  (6)  (2)  10,  1 0  2  h9 v a r y  10  p a r t has  of  a p p r o x i m a t e l y  as  the  range.  zero  w i t h  the  hence  curve f o r  t h i c k n e s s ,  w h i l e  s k i n  f o r  the  i n f i n i t e  f r e q u e n c y  depth  s t r u c t u r e l a y e r the  10,  as  a  equal  to  of  d^»  and  hence  l a y e r can  a  a  simple  F o r depth  to  a  deeper and  hence  of  l a y e r  curve  s u r f a c e  f o r  the  10,  f r e q u e n c i e s  the  curves  of  F i g .  c o n d u c t i n g  k  and  d^.  F o r  s k i n  depth  s t r u c t u r e c o n d u c t i v i t y  l a y e r  i s  s e m i - i n f i n i t e  s u r f a c e  l a y e r .  frequency  s t r u c t u r e  i s ,  much  c y c l e / s e c ,  1  s i n g l e  the  1,  compared  s e m i -  w i t h  above  of  t h a t  a  the  s e m i - i n f i n i t e  to  the  s i n g l e  f o r  l a y e r  s h a l l o w  than  equal  from  s u r f a c e  that  c o n d u c t i v i t y  i n  As  depend-  g e n e r a l ,  not  one. i s  evident  i s  than  d u c t i v i t y  f o r  p a r t i c u l a r l y if  phase  s k i n a l l  l a y e r  5  w i t h  angles  shown.,  s h a l l o w  v e r y  are  depth  f o r  a  Important  when 9  5  s i n g l e  h i g h l y  6  t h a t ,  s t r u c t u r e of  the  l a y e r  w i t h  on as  i n d i c a t e d .  the a  the  lower  c o n -  of  and  the  2  l o w e r l a y e r s  w i t h  the  s t r u c t u r e  f u n c t i o n Curves  i m l a y e r s  A l t h o u g h  10.  dependent  1  an two  s u r f a c e  curves  a  upper  f o r  s h a l l o w  f o r  has  That  a t t e n u a t i o n i s  (b)  i n d i c a t e d .  comparing  and  l a y e r  and  t h i c k n e s s  s t r u c t u r e s  i s  15(a)  c o n d u c t i v i t y  combined  l i t t l e  s u r f a c e  F i g s .  the  the  e v i d e n t  and.  from  l a y e r , The  a  s e m i - i n f i n i t e  the  much  of  frequency  c y c l e / s e c ,  1  a  e f f e c t .  cases  equal  i s  as  p o r t a n t  and  below  c y c l e / s e c ,  1  l a y e r  behaves  s u r f a c e  8,  i s  the  1,  that  the  a g a i n  s h a l l o w  w i t h  second  n e a r l y  l a y e r  t h r e e - l a y e r  I t  l e s s  curve  of  s t r u c t u r e  seen  f o r  root  f r e q u e n c i e s  s i n g l e  s k i n  the  w i t h  be  ence a  t h a t  the  c o n d u c t i v i t y  above  behaves  square F o r  very  s u r f a c e  a g a i n  than  i s  w i t h  f r e q u e n c i e s  deeper  the  2,  of  7  5  i s 3  amplitude f o r depth and  a l l i n 10,  270  icr 3  250to LU LU  H,  cr o  LU Q r4  230-  1,8  10  3,7 4  10,-5  210-  -lO-  taj 10  (b)  10  I0  3  I0  3  Z cm F i g u r e  15°  H  d =2x10  cm,  0  10  1 4  \  10' •1M 10' =16  !  10  (a)  1 6  a n d <j>  (b)  2  a s a  a n d t h e f o l l o w i n g 5  10~ , -16' 10  Z cm  (3)  10  ,  (6)1 0 " -16 (9) 10 1  6  10  o  f u n c t i o n 9  ,  d _ ,  , 10-1H-,-  0  ,  ( L l )  o f  z  f o r f=1  .. (1) 1 0  1  '" 1<T \ -ll+ -H  -lO  (7) 1 0 "  10~ \  (10) 1 0 "  5  1 1  1 0  ,  1 6  ?  1 0  10- ^, 1  ,  5  (  1 0 "  1  10- , 1 0 ~ 11  9=1+5°  10-  1  1 1  S  10~ \ 1  0  c y c l e / s e c  5  )  1 6  , 10  ( 2 ) 10" -16  \ (8)  1 1  d  emu.  10"  1 1  ,  51 which  r e f e r  to  s t r u c t u r e  w i t h  the  lower  s e m i - i n f i n i t e  l a y e r  —11 h i g h l y  c o n d u c t i n g The  l a y e r give  i s  s p e c i a l  shown  the of  the  amplitude l a y e r  F i g s .  curves  and (z  1  and  l i t t l e  e f f e c t  however,  i t s  curves  6  when  to  10,  phase  i t  i s  presence the  at  the  same  16  t h i c k n e s s  the  w h i l e  at  the  much  Figs.17(a) i n t e r f a c e  that  17 l e s s  the  than  l a y e r  the  a  i s  as  (b) a  and  f u n c t -  (b)  g i v e  of  the  f i r s t  It  can  be  second s k i n  as  second  and  s u r f a c e  important,  s u r f a c e  of  16(a)  s t r u c t u r e .  and  i s  a t t e n u a t i o n .  F i g u r e s  17.  angle  angle  F i g s .  when  some  c o n s t a n t and  f o r  i n  t h i c k ;  show  ?  t h i c k n e s s ,  d^) 5  of 16  phase  =  to  emu)  case  s u r f a c e - l a y e r  second  has  i n  amplitude  i o n  from  (10  i s  s h a l l o w  and  seen  l a y e r  depth  seen  from  and  h i g h l y  — 11 c o n d u c t i n g  (sea  water,  almost  i d e n t i c a l  to  depths  much  than  f o r  l e s s  s u r f a c e - l a y e r  seen  e a r l i e r  than  a  s k i n  l a y e r s  i s On  i s  seen  g r e a t e r  hence  the  16(a)  and  (b)  f o r  but  they  d i f f e r  s k i n  depth.  than  and  i s  a  (b)  are  s u r f a c e - l a y e r r a d i c a l l y We  s m a l l  f o r  depths  s i m i l a r i t y  f o r  s h a l l o w  have  l e s s s u r f a c e  e x p e c t e d . the  b a s i s  f o r  e l e c t r i c  the  the  f i e l d  c o n d u c t i n g of  of  the  the  r e s u l t s  d i s c u s s e d  i n  wave  model  the  amplitudes  magnetic  f i e l d  components  plane  v e r t i c a l  a l t h o u g h  s t r u c t u r e ,  depths  depth,  depth  z o n t a l  t h a t ,  s k i n  a t t e n u a t i o n  of  s t r u c t u r e  a  F i g u r e s  ^^•(a.) a n d  F i g s ,  the  t h a t  upper  emu).  t h a t  angles  the  10  components l a y e r  conductor.  these  are It  components  a t t e n u a t i o n  w i t h  both  at  s t r o n g l y i s are  of  the  and  the  h o r i -  s u r f a c e  and  i n  on  a l s o  s e n s i t i v e  the  i t phase  i n t e r e s t  i n  s e c t i o n , and  dependent-  r a t h e r  depth  t h i s  s u r f a c e  the to  note to  l a y e r  f o r  o cm  Q  11  w  O  Q  o  -J- n ON  O  CD  H (D \  ON  w  O (D  I -  VJT. <D N «•» II  ON  IV) —II>.^ ^op _ o.1.00p pp* s  U)  ON  ^-v  —  - p(D  »  Hj  CO  >>—'  O  -&  1  - f c t ESI  v-^  O  H O  w  — H*  Hj  —* ! O  • • s  vn.  -'  N  1  , -° cmO CO ^  ^  O  i  —  c+  Q  -rro  O 0  — Q. OU) ! 1  I  ro  O  ro Q ^ -T  Pi  \0  o -I*•O->I• OI NoII  o -*  w |V)  OJ  —  -J.  1  ON-*  ^ a, o p -r 1 ^ & 11 p, -  2  IV)  o. o II II -->• -or o -° » o  O IV) I1  -  1  I —1 1  B  H3  2£  <£ DEGREES ro z  5h these  components  A  2.2  i s  Complex  r a t h e r  Layered  s m a l l .  Conducting Plane  F o r o f t e n i n g  s i m p l i c i t y ,  based  on  l a y e r s .  the  However,  inhomogeneous more  the  m a g n e t o t e l l u r i c A l b e r t a ,  o b t a i n e d  r e s u l t s  to  m a t e r i a l  becomes  i v i t y . t r i e  T h i s  and  c o n d u c t i n g  F i e l d  of  In d i p o l e  c o n s i d e r e d e n t i a l l y  a  w i t h  at  that  f u n c t i o n .  a  the  w i t h  depth.  the  whose  the  response  Two  cases  s u r f a c e  d e a l s  a  a  of  f u n c t i o n s  be  rock depths c o n d u c t -  the  elec-.  a p p r o x i m a t i o n , i s  d e s c r i b e d  g e o p h y s i c s .  an  o s c i l l a t i n g e a r t h .  c o n d u c t i v i t y c o n s i d e r e d  c o u l d  m u l t i l a y e r  f u n c t i o n s  f l a t  w i t h  the  w i t h  at  have  great  i n  s t r a t i f i e d whose  at  good  c o n d u c t i v i t y  i n t e r e s t  the  i n c r e a s e  of  t o  made  c o n d u c t i v i t y  to  these  A p p l y i n g  (1960)  because  work  3  e f f e c t  c o n d u c t i v i t y  c o n d u c t i v i t y  e a r t h  some  whereas  tend  present  of  c o n d u c t i n g  the  measurements  i n  the  d r i e r ,  are  c o n t i n u o u s l y  study i n  to  depth  r e p r e s e n t s  The  to  i s  c o n d u c t -  d i s t r i b u t i o n s .  decrease  should  conductor  s t u d y i n g  over  of  homogeneous  s i n c e  s u r f a c e  r a p i d l y  measurements  S a y n - W i t t g e n s t e i n  a  the  f i e l d s  c o n s i d e r e d  s e v e r a l  a n a l y s i s  and  f i e l d  i n t e r e s t  p r o g r e s s i v e l y  s t r u c t u r e  continuous  quencies  near  of  l a y e r s ,  i n d i c a t i n g  s e c t i o n  inhomogeneous  of  of  temperature  magnetic  of  c o n d u c t i v i t y  method  decrease  i n c r e a s i n g  i s  N i b l e t t  R e l a t i v e l y  expected  the  i t  r e a l i s t i c  Meanook,  a  the  Waves  a n a l y s i s  c o n d u c t i n g  be  depth.  the  assumption  may  an  i n  I n t r o d u c t i o n  2.2.1  of  E a r t h  by  and  by  f r e -  magnetic Wait-  (1962  v a r i e d him.  are  b)  exponused  55 h e r e ; .0  these +  [1  kz  e x p ( -  c o n s t a n t s i n  a  have  d (1 Other  -  d  d (1  +  k z ) ,  0  2 . 2 . 2  k  and  (n-1  f i e l d  conductor  s o l v i n g f i v e  e v i d e n t  o b t a i n e d . f o l l o w s  f o r  l a y e r s  the  mathematics  w i l l  not  i n g of  harmonic i n  a  f r e e  l a y e r s  (media  i n  depth.  e^s  |j, • ,  d.  f l a t  2,  The (j  =•  a  the  d i s c u s s e d  form  o(z)  =  c o n s t a n t s .  work  are  e x p ( a z ) ] ,  f o r  d(z)  =  i n  -  -  s  n  media  1 ,  -  -  ?  of  i n  becomes media  of  t h i s  are  problem the  e l e c t r o m a g n e t i c  i n c i d e n t  are  c h a r a c t e r i z e d magnetic  the  F i g .  homogeneous, l a s t  ,  CD  upon  i n  w i t h  The  then  here.  n),  n ) .  n  f r e q u e n c y  the  and  2 . 1 . 2 ,  plane  shown  t h r e e 2 . 1 . 2 ) .  r e l a t i o n  case  used  the  f o u r  a n a l y s i s  a  as  of  f o r  and  conductor  ( S e c t i o n  d e t a i l  and  f l a t ,  e l e c t r i c  m u l t i l a y e r  the  was  conductor n-1  the  t u r n  angular 1)  f o r  r e c u r r e n c e  g i v e n  w i t h  of  3?  =  p o s i t i v e  p o s i t i v e  e a r l i e r i n  as  (medium  c o n s i s t s  has  e x t e n s i o n  c o n s i d e r i n g  time  space  s t r a t i f i e d  conductor  be  a g a i n i n  an  m a t h e m a t i c a l  procedure  wave  ).  equations  same  are  kz  t r e a t e d  the  We  kz  t h i s  as  e x p r e s s i o n s  S i n c e  +  d(z)  f u n c t i o n  p r e s e n t  e x p r e s s i o n s  problem  the  the  +  are  and  A n a l y s i s  M a x w e l l ' s  and  a)  are  [1  k  az)  Another  p  Q  e x p ( -  Q  and  '„  i n  s i m p l y  c o n d u c t i n g  d  (1962  c  components  f o l l o w  a  d (1  a n a l y t i c a l  l a y e r s )  l a y e r  •=  =  M a t h e m a t i c a l  magnetic  f o r  W a i t  d(z)  and  The  In  by  d(z)  s  =  cm  c o n s i d e r e d  exp(az)  Q  where  where  f u n c t i o n s  o(z)  d(z)  dimensions  a r t i c l e  kz)""P,  +  Q  form  a z ) ] ,  w i t h  r e v i e w  the  t r a v e l s u r f a c e The  18.  i s o t r o p i c l a y e r by  the  i n f i n i t e c o n s t a n t s  p e r m e a b i l i t y  of  56 of  e a c h  c o n d u c t i n g  F o l l o w i n g  t h e  method  the  s i m p l i f i e d  (53)  k\.  f o r  j  ents  =  =2, i n  t h e  ( E  (5 ) k  2  i s  u s e d  e x p r e s s i o n  c  3,  l a y e r  ^  -  i  ^  - ,  u p p e r  ~  2  n-,  assumed  be  f o r  p r o p a g a t i o n  t h e  e l e c t r i c  c o n d u c t i n g  =  ^ y  (  c a n be  (56)>  ( E )  (57K  ( H  2  |exp[-zv (1 +i ) ]  -  2  )  x  jexp[-zv (1 + 2  / W ' \ ( H  (58)  2  -•Hj^^Jjexp[-zv (1 +  where  ^•(LL^S^CO -  =  d u c t i v i t y and to  f a l l  i s  2  2  o f  f r e e  t h e  -  iWjj,^  space  i s  f r e q u e n c y .  components  i s  e x p [ z v ( 1 + i ) ]j c o s 6 2  m  2  ( U i ) ]j ^  exp[zv (1 + i ) fj  ,  2  2  1  n o t  i ) ] - m ^  c co)"^ =  ^  2  z e r o , • The  v  2  time  i n c l u d e d .  =  J 2u  exp[zv (1 + i ) ] J 2  JJ,^ e ^ J  d  2  v a r i a t i o n The  c o s©  2  s i n c e f  -,  i  =  t h e J  exp(icot)  a p p r o x i m a t i o n  -1  ,  1  e ,  s i n  ,  6,, ,  s i n  exp"[zv <1-+i)]j  2  2  =>  .  .  y  z  k^  +  ) = H ^ j ^ ^ J | e x p [ - z v ( 1 +i)]+m '  (59)«-(H ) > 2  i ) ]  a s :  2  e x p { z v  2  • =  2  compon-  exp[zv (1 +i ) ] J  m£  m  j^exp[-zv (1+ i ) ] + m ^  = E Q H ^ I  Z  u s i n g  f i e l d  e x p r e s s e d  2  = -o(^4)  a n d  space*  c o n s t a n t  m a g n e t i c  [exp[-zv (1 +i ) ] - -  x  f r e e  (-iWLtjdvto)^  and  l a y e r  o f  2.1.2)  ( S e c t i o n  2  ( 5 5 )  t h a t  e a r l i e r  i W ^ d ^ c o ) *  t h e  ) =  t o  1  c o n ,  common i n d i c a t e d  57 i n  e q u a t i o n  i e s  i s v a l i d  (53)  c o n s i d e r e d  s m a l l e r  than  i n t h i s  W ^ . o . c J J  c o n d u c t i v i t y  ranges  i n  (5 )  e q u a t i o n s  o f  s i n c e  i n t e r e s t  2  f o r  -  2  u (1-i)(1+m») 2  ( a ^ ^ m ! (62)-  +  1  work  =  2 ,  t h e v a r i o u s  ( 6 3 )  ) ^ ^ ( q ^  r  m !  +  O-m")  c o s©  (1-m»)  c o s ©., '  1  n-1 ,  w i t h  a  = e p[-2d.v.  J  +  1  terms  +• (1-m£)  1  X y o 7  1  exp[-2d.v.(1 + i ) ] J  35  magnitude  (l-mvp  m"=m'= I J  j  o f  F o r t h e f r e q u e n c y a n d  1 ^"u (1-i)(1+m^)cos ©  1  i s o r d e r s  2  =  a n d c o n d u c t i v i t -  a r e g i v e n b y :  (59)  2  m  p  i n t h i s  u (1-i)(H-m ')  (61-)-  [i-e-co J V  u (-1<-i-) ( I r t - m p c o s ©.j -  t  m  work  co f o r a l l c a s e s .  t o  L  (60)  2  f o r t h e f r e q u e n c i e s  m ! = 1  m! =  X  + 1  0  ( l  +  f o r j =  J  n .  i ) ]  ( 6 l f )  and  (65)  u  S i n c e  t h e a m p l i t u d e s  waves  a n dhence  i t the  i s a g a i n form  E  e a r l i e r  =  a n dH  a r b i t r a r y  c o n v e n i e n t  g i v e n  Q  2  c  Q  ^ ( o  2  / f )  a r e d e s c r i p t i v e  o f  a s f a r a s computations  t o express  e q u a t i o n s  b y equations  C+7)  t o  (5*+) (52).  t h e i n c i d e n t a r e concerned, " t o (59)  i n  58 2.2..3  D i s c u s s i o n N u m e r i c a l  e l e c t r i c  and  of  v a l u e s  magnetic  v a r i o u s  c o n d u c t i v i t y  i e s  f r e q u e n c i e s  and  p r e v i o u s l y :  d  c y c l e s / s e c . c o n s i s t i n g w i t h  a  shown  The of  i n  The  the  F o r  compared  w i t h The  l a y e r s a  are a r e  way  f o r  one  l a y e r s case  l a y e r s  each  e x p ( - a z ) ,  same  emu  and  f  of  f o r  case  d i v i d e d  the  f i r s t  the  o n e - l a y e r  r e s u l t s  f o r  the  to  depth,  N  1  i n  a  a  c o n d u c t o r  case  were  = 1 ,  10,  p r o f i l e ,  i n  d  =•  10  f o r  100, w i t h  —11  a  p r o f i l e  300, D^  1 0  determined emu,  and  by a  -16 the  c o n d u c t i v i t y  f i l e  c o n s i s t s  w i t h  a  of  i s a  10  s t r u c t u r e s how  many  to  N^  behave  as  a  c a l c u l a t i o n s number  of  F o r  t h i s  c o n d u c t i n g  f u n c t i o n  chosen  s u b -  =  o  s u c h  d  t h a t  a t  z  =  c o n d u c t i n g  1 0  y  cm.  l a y e r  of  The  second  i n f i n i t e  p r o -  d e p t h  —1 6 c o n d u c t i v i t y  of  10  Q  1 emu  s i n g l e  are  1 , 0 0 0 ) .  the  t h a t  p r o f i l e s .  v a r y i n g  has  i s  i n  o b t a i n e d  700, cm,  y  p r o f i l e  f u n c t i o n  a  as  e q u a l l y  each  f a s h i o n *  f o r  500,  =  are  c o n d u c t i v i t y *  out  3  p r o f i l e s ,  c o n d u c t o r  continuous  1 0  p r o f i l e ^  determine  the  whose  c a r r i e d  c o n d u c t i v i t i e s  where  a  and  f  c o n d u c t i v i t y To  used  c o n d u c t o r ,  each,  homogeneous  form.  1  f o r  i n  the  c o n d u c t i v i t -  s e v e r a l  r e s u l t s  v a r i o u s  p r o f i l e  v a r i e s  The  l a y e r  of f o r  those  M-5°.  c o n d u c t i v i t y  s t u d i e d ,  t a b u l a r  as  10"-^  w i t h i n  the  The  =  i n t o  f u n c t i o n  f o r  i n  i s  phases  s u r f a c e  computed.  i n c i d e n c e i s  and  the  the  v a l u e s  f i r s t  w i t h  16  at  are  s u b l a y e r s  g i v e n  Q  s p e c i a l  the  of  The  g i v e n  ( i . e .  were  c o n d u c t i v i t y  r e q u i r e d  of  10"  l a y e r s ,  s i m i l a r  f u n c t i o n  to  amplitudes  components  c o n s i d e r e d  c o n d u c t i v i t y d  the  p r o f i l e s  11  19.  v a l u e  s t u d i e d  f o r  f i e l d  angle  n-1  F i g .  p r o f i l e .  i n  10~  d i f f e r e n t  spaced. has  =  R e s u l t s  emu.  The  r e s u l t s  are  g i v e n  i n  59  INCIDENT  REFLECTED  WAVE  WAVE X  MEDIUM (free  I  space)  MEDIUM 2 (conductor) MEDIUM 3 (conductor)  1 d  MEDIUM N (conductor of infinite depth) F i g u r e 18. l a y e r e d  Model e a r t h .  used  i n  \\  n-|l I  the  *  w  Z  •  t  \  c a l c u l a t i o n s  f o r  a  free space  0*2  I  d  Profile I N, sub-layers crAz)  4  Profile II N sub-layers 2  <r U) b  Profile TXT N sub-layers 3  (z) d  F i g u r e  19-  • Complex  l a y e r e d  n  r D=oo  c o n d u c t o r .  <r  0  complex  60  Table  I.  beyond  I t  can  be  l a y e r s  300  c a l c u l a t i o n s  puted,  o n l y  t r e a t e d E_. y  are  much  H_  s i m p l y  a l l  i n t e r e s t  p a r t i c u l a r out  the  v a l u e s to  of  H x and  H_, z  e f f e c t  on  H  and  f o r  v a r i o u s  Table  II.  The  s t r u c t u r e  t h i c k  d i v i d e d  i n t o  Zi  phase  H  the  f o l l o w i n g  angles  were  s t u d i e d  are y  p l a c e  l a y e r s .  cases  i s  of  Q  very  com-  are  c o n s t a n t ,  E  s m a l l  x not  and  and of  the  c o n s i s t s  l a y e r s The  f u n c t i o n s  c o n d u c t i v i t y  i n c r e a s i n g  Zi  c o n d u c t i v i t y  300  substratum.  c o n d u c t i v i t y  E_  A l l  300  and  takes  e x p e r i m e n t a l l y .  d e p t h  i n f i n i t e  f o r  and  change  case.  v a r i o u s  Zi  w i t h  l i t t l e  components  f o r  r e l a t e d  v e r y  c a r r i e d  the  0_  The  t h a t  t h i s  been  and  below.  The  f o r  have  A l t h o u g h  seen  d i s t r i b u t i o n s  of  of  a  equal  c o n s t a n t s ,  f o r  s u r f a c e  Nos.  1 -  k  and  shown  l a y e r  t h i c k n e s s e s  are  k  i s  a  chosen  ,  10  cm  7  and  a  used  to  be  at  the  i n  s e m i -  i n  the  such  -1 ^ that to  the  c o n d u c t i v i t y  -11  from  emu  10--  s u r f a c e  7 emu  10  the  i n c r e a s e s  r e s u l t s  at  a  d e p t h  of  f o r  a  homogeneous  cm.  10'  F o r  purposes  c o n d u c t i n g  of  s u r f a c e  comparison,  l a y e r  w i t h  -1 5 c o n d u c t i v i t y  10  y  emu  and  a  s e m i - i n f i n i t e  emu  are  g i v e n  substratum  w i t h  —11 c o n d u c t i v i t y and  a ,  used  maximum A g a i n  at  f o r  5  10 i n x  No.  are  5  10^  purposes  such  i n  that  cm  and  then  of  comparison,  the  From the  w i t h  the  a  c o n d u c t i v i t y  r e s u l t s  c o n d u c t i v i t y  amplitude  and  Table  l i s t e d  v a r i a t i o n  phase III  i n  of  The  c o n s t a n t s ,  to  10~ ^ 1  r e s u l t s  a  e m u  f o r  k  reaches  ^  ^Q7  a CNIO  a  homogeneous  i n  No.  "5  10  y  emu  Table  II,  has  marked  a  6.  c o n d u c t i v i t y  r e t u r n s  -1 medium  No. the  i t  are  given  i s  r e a d i l y  e f f e c t  on  seen both  7° that the  angle.  shows  the  e f f e c t  of  d e c r e a s i n g  c o n d u c t i v i t y  61  TABLE The  e f f e c t  o f v a r y i n g  6  x  N  1  1  6  y  y  1 .03x10~* M-6.6  10  100  300  500  700  1000  1  O-K  1. +5xio~* 1  226.6°  s u b l a y e r s .  H  y  <  2.00 0  1M 0  7.27x1O"  11  183.1°  11  >+.05x10"* 2.3^  5.73x1'0"* 182„3°  h.21x10"* 2.28  5.95x10"* 182.3°  M-.2M-X10~*  n  it  2.87x10"  11  182.3°  11  2.98x10~ 182.3  6  6  n  11  2.27  6.00x10~* 182.3°  11  ti  ^.25x10"* 2.27  6.02x10"* 182.3°  n  11  M-.26x1  6.03x10~*  =•  10"  y  c m  ?  0  3.00x10~ 182.3°  6  3.01x10~ 182.3°  6  11  ti  3.02x1O"  2  emu.  =  °°>  d  a  =  1 0  ~  6  • 182.3°  182.3°  D  226.6° 6  11  10  6  1 .81X10" 183.1°  11  =  z  0°  3.62x10~*  0"*  H  *x  2.56x10"* 3.81  2.27  D  * x  o f  0  * x  1  t h enumber  E (10- c)  E (10" c)  I  1 1  e x p ( - a z ) 9  a  =  1 .15xio~  lIf s  62 TABLE C o n d u c t i v i t y  f No  '  10"  3  =  i n c r e a s i n g  sec"''  f  =  0° z  z  H  I I  H  v  1 s e c  w i t h  depth  -1  f  0° ^z  z  10  =  H  3  sec"^  z  ^z  1  1 .86x10"  259.2°  lf.7 x10" ' 2^-0.8°  2.28x10~  22^.7°  2  6.75x10~  2^0.1°  7.00x10'"^  2lf1 A °  9.95x1O"  3  250.1°  3  1 .05x10~  2^7.5°  1.85X10~  L  2^7.0°  2.19x10"  230.1+°  h  7-30x10"  2lf0.1°  1.05x10"^  253.7°  7.05x1O"  267.0°  5  2.35x10"  2^-3.9°  7A5X10"  266.h°  7.00x1O"  6  2.27x10~  265 0 6°  7 = 65x10" 223.k°  2.31x10~  223.7°  7  2-36x10~5  225.0  7- 5xio"  225.0°  2.31x10"  223.7  6  7  6  8  8  6  k  1  (cm)  D  2  (cm)  N  6  k  0  k  TABLE  D  L|  I I  k  3  3  2  2  300  10" ^  e x p ( a z ) ,  »  11  11  10~ ^  (1+kz),  »  11  11  10~ ^  (1+kz ),  »  11  11  10" ^[1+kz  it  11  10  ..  1  t.  !  1  1  1  1  _ 1 ?  [1+kz  268.8°  0  o (emu)  c (emu)  1  oo  „  2  (continued)  10  7  2  b  o=9-21x10~  7  k=1 .00x10~  it  10  k=1.00, a =6.91x10~  e x p ( a z ) ] .  7  e x p ( - a z ) ] ,  1<T* 1(T * 1  11  tt  k=1.00x10-3  2  1  10  n  k= 0.0, a=1.98x10" k  10-  11  io" * 1  63 TABLE C o n d u c t i v i t y  ,. f  No.  10"•3  = H  s e c "  d e c r e a s i n g  f  1  ^z  z  I I I  1  =  H  s e c -1  2.82x10 •7  203  2  •6 5-65x10"  189.8°  7.00x10"  6  3  2.36x10"•5  225.0°  7.50x10"  L  k  2.36x10"•7  225.0°  7-95x10"  7 0 95x10"  A °  TABLE  D  1  D  (cm)  10  7  2  (cm)  oo  N  I I I  depth  f  6  H  •11 '10"  1  0° ^z  z  k  225.0°  229.1°  2.36x1o"  k  225.0°  22 „9°  2.30x1o"  2  223.6°  225.0°  2.36x1o~  k  225.0°  (continued)  d (emu)  a  300  s e c "  2.36x1o"  o (emu)  1  3  22^.8°  k  6  10  =  0° ^z  z  1  r  w i t h  exp(-az)  II  II  tt  10"°  1 1  (1+kz)"  it  it  ti  10"°  1 1  (1+kz)"  it  it  1  1  2;  b  ?  a=9° 21x10"  ,  k=1 . 0 0 x 1 0 "  7  tt  . k=9» 90x10"  6  it  11 10"  7  tt  6h as  a  f u n c t i o n  b u t i o n s . cm  The  t h i c k  um.  of  depth  s t r u c t u r e  d i v i d e d  The  i n t o  c o n s t a n t s  c o n d u c t i v i t y  f o r  a g a i n  decreases  d i f f e r e n t  c o n s i s t s  l a y e r s  300  k  three  and  a  from  10  and  are -11  c o n d u c t i v i t y  of  a  a  l a y e r  s e m i - i n f i n i t e  chosen emu  s u r f a c e  at  to  be  the  d i s t r i 10^  s u b s t r a t -  such  that  s u r f a c e  to  the  -1  10  5 '  7 emu  at  a  depth  of  cm.  10  The  c o n d u c t i v i t y  of  the  homogeneous  -11 substratum s t r o n g l y the  i s  emu.  10  dependent  frequency.  l a y e r  w i t h  both  a  c o n d u c t i v i t y  the  same  s t r u c t u r e  are  by  as  Table  IV  d e a l s  a  l a y e r  i s  much  homogeneous  water.  chosen The  d u c t i v i t y f u n c t i o n  homogeneous  g i v e n as  w i t h  have  a  as i n  c o n d u c t i v i t y  each  being  determined  Table  IV.  i n  •A g a i n  the  a  of  magnitude. c o n d u c t i v i t y  to  t h a t  s u r f a c e of  sea  the  c o n -  c o n d u c t i v i t y  and  k  are  chosen  such  cm  to  that  the  c o n d u c t i v i t y  - 1 5 10  from  emu  10  at  10  6 emu  y  decreases  to  ' h  -11' be  the  The  k.  l a y e r s ,  300  and  s u r f a c e  homogeneous  equal  i n t o by  No.  of  The  are  s u r f a c e  d e c r e a s i n g  l a y e r .  d i v i d e d  the  III,  of  i s  g i v e n  Table  a  below  phase  d i s t r i b u t i o n  of  orders  l a y e r  of  that  l a y e r  and  c o n d u c t i n g  s e v e r a l  c o n d u c t i n g  to  amplitude  c o n d u c t i v i t y  f o r  d i f f e r  below  the  the  R e s u l t s  m u l t i l a y e r v a l u e s  on  A g a i n  a t  cm.  The  s e m i - i n f i n i t e  emu.  The  homogeneous  10  substratum  has  a  -1 5 c o n d u c t i v i t y the In  e f f e c t  of  of  comparing  seen  t h a t  10  making H  f o r  -1-3  frequency  a f f e c t e d  due  to  the  f a c t i n  Nos.  a  a l l  cm  l e s s  f o r  at  10  H_  z  not  than  y  t h a t sea  by  the water.  w i t h  of  the  s e n s i t i v e  10  3  the  the  depth  below f o r  f o r  the the  t h i s  sea;has  s t r u c t u r e  r e s u l t s  c y c l e s / s e c  s t r u c t u r e  s k i n  to  c o n d u c t i n g  below.  No.  i t  amplitude sea.  T h i s  frequency  i s  i s i s i s l e s s  65 TABLE C o n d u c t i v i t y  d e c r e a s i n g  u n i f o r m  f  f  z  0° *z  1  2.09x10"•6  183.9°  2 3  No  •  H  depth  below  a  s e a  secr  f  1  0°  z  H  ^z  10  =  -1  3  sec  0°  z  7 «55X1 0">5 221.9°  2.36x1 o  - l f  225.0°  1.15x1 o"•5 200.1°  1 .90x10"  181+.1  2.36x1 o  _ l +  225.0°  8» 65x10"•7 195.1°  •5 188.9° 1 .25x10" •6 225.0° 7.55x1o"  2.36x1 o  - I f  225.0°  TABLE  1  1  =  H  h 2.77x10"•7 195=1°  D  w i t h  c o n d u c t i n g  10"•3' s e c " ^  =  IV  D  2  D  2.36x1 o"^ 225.0°  (continued)  ^  (cm)(cm)(cm)  10^ 10  IV  0  N  1  6  00  300  »  "•  "  "  11  11  u  II  II  I!  g  a  (  e  m  10~ "  u  11  )  d  1 0~  1  1  b  (  e  exp [ - a  m  u  ° c  )  Cz-D.,)  10~ [ 1 + k ( z - D 11  1  ) ] ~  ] 1  ,a=9.303x10"  ,k=1 .01x10"  2  10~ [1+k(z-D )]~ ,k=1.00x10"^ 11  II  1  0"  2  6  (  e  m  u  )  10~ * 1  "  66  On  the  b a s i s  amplitudes  and  phases  components  are  s t r o n g l y  c o n d u c t i n g  medium'.  are  ones  i v i t y  t h a t  of  of  A n o t h e r problem eous  of  c o n s i s t e d  geneous  l a y e r s the  same  t h i c k n e s s .  model  i n c r e m e n t i n g The the  r e f e r  q u a n t i t i e s e l e c t r i c the  z  and  f o r  f r e q u e n c i e s t a b u l a r and  r e f e r  to  of  F i g . -  the  v a r i o u s  f  10~  are  The  S  i ,  f o r  the  a m p l i t u d e s ,  r e p r e s e n t e d  by  the  f i e l d  3  H,  0-,  of  the  by  f o r  homo-  compon-  a  phases  i n  F i g .  were i s  the  • A l t h o u g h  u s i n g t h r e e -  w h i l e  and  D  20.  are  and The  d i s c u s s i o n unprimed a l l  computed,  d i s c u s s e d  a n g l e s , o  the  f i e l d  s t r u c t u r e s  phase  The  inhomogeneous  c y c l e s / s e c -  1.0  of  l a y e r s  w h i l e  case.  c o n d u c t i v i t y and  inhomogen-  f o l l o w i n g  case  components  e a r t h  c o n d u c t o r s .  the  i n  magnetic  the  s t e p s .  and  m u l t i l a y e r  the  and  shown  c o n d u c t o r  of  c o n d u c t -  determined  i s  20  of  components  s m a l l  used  f i e l d  c o n d u c t i n g  of  were  f i e l d  the  s t u d i e d  the  c o n d u c t i v i t y  models  f i e l d  the  3  the  amplitudes  system  the  form.  depths  :  magnetic  =  r e p l a c i n g  i n  t h a t  s t r u c t u r e .  homogeneous  the the  conductor i n  d e s c r i b i n g  inhomogeneous  c o n d u c t i v i t y  homogeneous  component  r e s u l t s  f o r  seen  d i s t r i b u t i o n s  amplitudes  the  i s  inhomogeneity  inhomogeneous  the  the  i n  c o n d u c t i v i t i e s  c o o r d i n a t e  the  i s  computing  the  the  c r u s t a l  the  f o r  (51)  q u a n t i t i e s to  of  w h i c h  to  homogeneous  primed  p l a u s i b l e e a r t h ' s  as  by  i t  e l e c t r o m a g n e t i c  c o n d u c t i v i t y  d e t e r m i n i n g  - The  and  v a r y i n g  a f f e c t e d  here  of  same  (V7)  the  o b t a i n e d ,  ' e q u i v a l e n t '  f o r  were  l a y e r  the  by  problem  equations-  be  i n t e r e s t  ents  of  a s p e c t  conductors  r e s u l t s  The  ;  might  p a r t s  of  the o n l y  below.  s t u d i e d g i v e n  • f o r  i n  c o n d u c t i v i t i e s r e s p e c t i v e l y .  The  Profile I N| s u b - l a y e r s  *1L  4> r  Layer  I  J  I  - D,' Profile H N sub-layers a : (Z)  L a y e r IT  2  I r  t  F i g u r e  20.  Model-  J  D=a>  used  Layer HI D = a>  i n  c a l c u l a t i n g  e q u i v a l e n t '  c o n d u c t i v i t i e s .  68 Table w i t h  V  d e a l s  c o n d u c t i v i t y  substratum.  w i t h  an  i n c r e a s i n g  R e s u l t s  inhomogeneous w i t h  are  g i v e n  300  l a y e r s ,  depth  f o r  z  =  and  N  s u r f a c e  and  a  l a y e r  s e m i - i n f i n i t e  0,  =  D  10 , 7  =  2  °°,  -11 o  -  b  emu,  10  d i f f e r e n t  were  = ocy N  2  =  VI  o  sea  c a r r i e d &  =  10  inhomogeneous s k i n  -11  l a y e r s .  300  w i t h  an  d e c r e a s i n g  and  a  w i t h  f o r  emu,  z  c  -  Q  S i n c e  =  the  c o n d u c t i n g f o r  f  substratum  p l a y s  the  dominant  are  0'  c o n d u c t i n g  sea  almost i s  the  c o n d u c t i v i t y  are  almost • I t  VI f o r  t h a t two  angles  2.3  i s  q u i t e  A  =  10  -1^  10  J  are  pal'©  s u f f i c i e n t l y s t r u c t u r e  below  =  10  emu,  N  1  each  and  F o r t h i c k  below  a  and  f to  l a y e r  u n i f o r m The  c a l c u l a t -  cm,  D  =  l a y e r ,  1  c o n d u c t i n g v e r y  c y c l e s / s e c ,  -3  i d e n t i c a l .  apparent  i n  i t  from  i s  g e n e r a l  the  =  2  sea  much  the  cm,  10  and  and  the  l e s s  than  the  =  c y c l e s / s e c  10  3  a c t  a  s e m i - i n f i n i t e  hence  a g a i n  to  as  a  the  phase  angles  s h i e l d  phase  the f o r  angles  the  i n  Tables  same  s t r u c t u r e s  the  V  and  amplitudes phase  d i f f e r e n t .  Conducting a  g i v e n  o b t a i n  c o n d u c t i v i t y q u i t e  Homogeneous  r e s u l t s  p o s s i b l e  d i f f e r e n t  of  2.3.1  f i v e  i d e n t i c a l .  a l t h o u g h  are  f o r  s u r f a c e  substratum.  ,  l a y e r  t h i c k  and  depth  s h a l l o w  depth  4>„  l a y e r  1  inhomogeneous  s e m i - i n f i n i t e  out  -  2  d i s t r i b u t i o n s .  d e a l s  c o n d u c t i v i t y  c o n d u c t i n g ions  =  1  c o n d u c t i v i t y  Table w i t h  N  L i n e  B a r t h  i n  the  Near  F i e l d  C u r r e n t  I n t r o d u c t i o n A l t h o u g h  the  plane  wave  model  r e a d i l y  lends  i t s e l f  to  TABLE  V  C o n d u c t i v i t y i n c r e a s i n g , w i t h depth  N o  -(sec- -) 1  d (emu)  cl  2I+3.O  M^M-xtO^  2MO.-8 225,0  "  10  2:28x10~  22M-.7 223.7  "  1 .88x10~ 259.2 6  3  2  3  3  d -'•{••emu)  a  z  10° 1  10~ 1 10•  6.75x1O" 2M0.1 7.00x10"* 2Vl A 9«95-x10~ 250.1 7  3  22h.h 225.0 22h.h  1 0 " * e x p ( a z ) a=9«21x10~ 1  1 .60x10'•13 2A5x10~ * 1 .02x10 •15  7  5  1  1 .23x10-12 1 .13x10'•13 5.50x10'>15  10~ *(1+kz), k=1.00x10~ 1  3  11 II  1.05x10" 2M-7.5 225.h 10" *(1+kz ) k=1.00x10" 10 u 1.85x10"^ 2M7.O 225.0 2.19x10" 230.h 223.8  10" 1 10 3  3  H  6  1  5.67x10~ 1 .62x10" 1 .11 x10"•15 13  2  ?  :  2  10r 1 10,3  •8 2M-0.1 225.0 10" *[1+kz e x p ( a z ) ] k=1 .00;a=6.91xiO" 1 .OM-xlO" 7.30x10" 11 1.05x10'=5 253»7 225.0 5.09x10~ it 1 .10x10 ' 7.05x10~ 267.0 225»6  10~ 1 10,3  2.35x10~  3  3  1  7  10  5  12  3  8  7.1+5x10~ 7.00x10r3  6  2M-3.9 225.0 266.k 225.0 288.8 22M-.6  10" *[1+kz e x p ( - a z ) ] ^=^0.0^=1-98X10" ! .01x10" 1 .00x10-11 it 1 .12x10.-A ti 1  6  9  TABLE C o n d u c t i v i t y  N  o  1  '  ( s e c "  10 1 10  _3  3  10" 1 10  2.09x10" 6.30x10" . 0x10'  ' 183.9 210.2 225.0  185-3 213.3 225.0  10""  1.15x10"^ 1.89x10"^ .38x10~  200.1 180.0 225.6  200.2  10*'  8.65x10"* 1 .23x1 o~5  195.1 181.5 225.1  195.3 203.8 225.0  k  3  3  K°  H  z  v  6  10"" 1 10  3  3  below  z  )  6  3  2  1  decreasing  7  L  k  7  6  k.kOxl0"  7  V I  1  1  a uniform  c o n d u c t i n g s e a  e x p [ - a ( z - D  (emu)  d  l 3  1  )•],  it  d£(emu)  a=9-30x10"*  6  -1 2 1 .11 x1 0 ' * 9-27x10" 1.00x1O" 3.96x1 o 1.99x10~ 1 .00x10 12  11  11  1 1  [1+k(z-D )]- , 1  1  k=1 .01x1 O"*  2  11  193.5 225.0  13  it  10"*  1 1  -11  [1+k(z-D )]- , 1  tt 11  - 1 l f  2  k=1 .00x10"^  1 .1 9x10" 1.30x10" 1.00x1O  13  12  -11  71 s t u d y i n g i n  a n a l y t i c a l l y  t h e c o n d u c t i v i t y  f o r  t h e magnitude  v e r t i c a l the  s t r u c t u r e ,  o f  plane  wave  magnitude  i n  t h e case  c o n s i d e r  model  s m a l l e r o f  P r i c e f i n i t e  dimensions  i n g  e a r t h .  i n g  e a r t h  has  been  p r e d i c t s than  o t h e r  (1962.)  over  o f  f i e l d  t h e equations  o f  t h e  r a t i o s  i n f i e l d  I t  i n t e r e s t  a  i s o f wave  o f  a  orders  measurements a s w e l l  g e n e r a l  t o  source  homogeneous  a n o s c i l l a t i n g  c o n d u c t -  f l a t  c o n d u c t -  l i n e  c u r r e n t  (1961).  a n dF a n n i n  f o r t h e f i e l d  e a r l i e r ,  f i e l d .  s e m i - i n f i n i t e  b y Law  observed  s e v e r a l  observed  s e m i - i n f i n i t e  case  i n d e t a i l  o f  account  A s d i s c u s s e d  t h e e f f e c t  a  inhomogeneities  i n g e n e r a l  r a t i o s  plane  s t u d i e d  i n t h e near  developed  cannot  amplitude  e a r t h . a  c e r t a i n  f i e l d .  those  than  • T h e s p e c i a l  t r e a t e d  i t  magnetic  t h e r e a l  f i e l d s  o f  t h e amplitude  t o h o r i z o n t a l  of  of  t h e e f f e c t  components  They  a n d  o b t a i n e d  7  r e s u l t s  f o r a  r a d i a n s / s e c ,  0.3  T h e i r  r e s u l t s  r a d i a n s / s e c component t h a t of  source  o f  a n d a  have  s e c t i o n  components  c o n d u c t i n g h e i g h t s ,  e a r t h  d e a l s  o f  1 .25  ranging  These  frequency x  10  f r e q u e n c y  t h e v e r t i c a l  f i e l d .  observed  c m , a  10'  f o r a  a magnitude  t h e h o r i z o n t a l  T h i s  x  2  t h a t  c y c l e s / s e c )  (1 .9'  c o u l d  o f  c o n d u c t i v i t y  demonstrated  e x p e r i m e n t a l l y  f i e l d  h e i g h t  J  o f  magnetic from  r e s u l t s  0  o f  emu. 0.3 f i e l d  t o 0.5  o f  a r e i n t h e  range  v a l u e s . w i t h  t h e e l e c t r i c  f o r a n i o n o s p h e r i c f o r a wide  a n d c o n d u c t i v i t i e s .  range  o f  l i n e  a n d magnetic  c u r r e n t  f r e q u e n c i e s ,  a n d a  f l a t  source  72 M a t h e m a t i c a l  2.3.2  The  m a t h e m a t i c a l  (1961)  F a n n i n  a s s o c i a t e d  f o r  w i t h  homogeneous  used  components  i n  S i n c e  t h e i r  would  r e q u i r e here.  q u e n c i e s , p r e s e n t The  work.  e x p r e s s e d  i s  computer  program  phase  a n g l e s  of  and  assumed  to  f i e l d L  r e l a t i v e  the  components  to  used  i s  a g a i n  (52),  a m p l i t u d e s  T h e i r the  not  f o r  the  the  f r e -  i n t e r e s t  shown w i t h  i n  m a g n e t i c ,  and  i s  the  d i m e n s i o n l e s s  where  the  m o d u l i  the  components  .  express  the  x  the 21  and  E  i n  F i g .  time to  and  r e p r o d -  i n  of  f i e l d  l e n g t h y  e v a l u a t e  c o n v e n i e n t  h o r i z o n t a l  a  f u n c t i o n s .  are  of  h a r m o n i c a l l y  components to  ( 7)  they  w r i t t e n  i s  here.  r a t h e r  h e i g h t s  above  express  was  system  v a r y  the  equations  and  components  S t r u v e  n e c e s s a r i l y  source  c o o r d i n a t e  e l e c t r i c ,  the  are  and  Law  c u r r e n t  reproduced  B e s s e l  d e f i n i n g  e q u a t i o n s  be  l i n e  H a n k e l ,  h o r i z o n t a l  are  not  by  f i e l d  of  I t  i n  o s c i l l a t i n g  numerous  magnetic  magnetic  c a l c u l a t i o n s ,  exp(icot).  used  as  and  out  p r e s e n t  equations  The  c a r r i e d  the  I  v e r t i c a l  H  i n  w i l l  c o n d u c t i v i t i e s  c u r r e n t  the  e l e c t r i c  e a r t h  f i n a l  and  a n a l y s i s  h o r i z o n t a l  terms  • A  a m p l i t u d e s  the  a  f l a t  solution;,  uced  A n a l y s i s  ,  form  Ry,  f o r  a  and c u r r e n t  Zi  of  c o n s t a n t  a m p l i t u d e  and  the  arguments  ty  ,  phase  angles  r e l a t i v e  D i s c u s s i o n  2.3.3  N u m e r i c a l f i e l d the  components  c o n d u c t i n g  s p h e r i c  l i n e  f r e q u e n c i e s  of  f o r  e a r t h  ~  1CT  3  t h e i r  r e s p e c t i v e  and  are  0  y  the  z  phases  a t  the  s o u r c e .  R e s u l t s  v a l u e s  c u r r e n t (f  to  ,  0  x  a  f o r  range  were  of  a m p l i t u d e s p o i n t s  computed  h e i g h t s to  the  10  (h  f o r  =•• 10  7  and  a l o n g a to  c y c l e s / s e c ) ,  wide h  x  and  the  phases  s u r f a c e  range 10  7  of  of  cm),  e a r t h  the of  i o n o c u r r e n t  c o n d u c t -  73  LINE SOURCE (x,o,-h)  IMAGE  SOURCE  (x,o,h) F i g u r e  21.  Model  u s e d  i n  t h e  l i n e  c u r r e n t  problem.  7  i v i t i e s  (d  10"  to  10  emu).  g r a p h i c a l  r e s u l t s ,  i n  o r d e r  to  the  measurements  model  v a l u e s  =  k  f o r  of  v o l t s / m  i n  u n i t s  the  of  v  ,  and  f o r  the  22,  phases  *  ,  e a r l i e r  comparisons  C h a p t e r  the  3,  g i v e n  magnetic  f i e l d  show  amplitudes  w i t h  n u m e r i c a l i n  u n i t s  amplitudes  are  2k  f o r  \k  z  1  the  the  H  ,  H  f r e q u e n c i e s  f  and  z  =  10" , 3  x  -1 Tj. 10  ,  :  i s  the  are  and  0_,  y  10  a l l  amplitudes  the  and  23,  x  -2  i n  i n  gauss.  F i g u r e s E  those  f i e l d  as  f a c i l i t a t e  d i s c u s s e d  e l e c t r i c  w h i l e  Here  the  and  1,  d i s t a n c e  v e r t i c a l l y source  along  below  h e i g h t  c y c l e s / s e c  10  i s  the  the  l i n e  h  2  =  x  as  e a r t h ' s source cm  10^  a  f u n c t i o n  s u r f a c e as  from  shown  and  the  of  i n  y.  the  Here  y  p o s i t i o n  Fig.-21.  c o n d u c t i v i t y  The of  the  —16 e a r t h  i s  emu.  10"  I t  i s  apparent  t h a t  f o r  a  c o n d u c t i v i t y  of  —16 10" H„ y  i s  emu H and E are s t r o n g l y dependent on f r e q u e n c y w h i l e l e s s s e n s i t i v e . S i n c e H i s much more a f f e c t e d by a z  change the  J  i n  f r e q u e n c y  h o r i z o n t a l  than  magnetic  dependent  on  f r e q u e n c y  i n c r e a s e s .  r e s u l t s an  frequency,  d i s c u s s e d  i n c r e a s i n g  w i t h  e a r l i e r  25  and  H  ,  f i e l d  - This  f u n c t i o n  F i g u r e s  i s  r a t i o  components the  r a t i o  d i f f e r s  1  where  of 26  the  the  w i l l  v e r t i c a l  a l s o  d e c r e a s i n g  from  i t  of  was  the  plane  found  t h a t  be  to  s t r o n g l y  as  the  wave  model  the  r a t i o  i s  frequency. d e a l  w i t h  the  case  where  the  c o n d u c t -  —16 i n g  e a r t h  (d  =•  emu)  10"  has  been  r e p l a c e d  by  a  c o n d u c t i n g  —11 sea  (d-  emu)  =10  amplitudes i t  can  be  i n  the  two  and seen  of  phase t h a t  cases.  i n f i n i t e  angles the  F o r  depth.  w i t h  those  f r e q u e n c y f r e q u e n c i e s  In of  comparing F i g s .  dependence up  to  1  i s  22,  these 23  v e r y  c y c l e / s e c  and  2k,  d i f f e r e n t H  i s  10  10° h  b X  10  8  0  12  8  16  Y(l0 cm)  20  24  7  2 2 . H _ ( a ) a n d cp ( b ) a s f u n c t i o n s o f y f o r ( 1 ) f ==1i -0n - 3 ' ( 2 ) i o " , "(3) 1 0 , ( ) 1 , a n d (5) 10  F i g u r e  2  16  Y ( I 0 cm)  7  ?  12  r  1  k  -16 d=1C r  ID  emu,  c y c l e s / s e c .  ^7 c m , a n d h=2x10  F i g u r e and  23.  (1)  H  z  ( a )  f=iO~ , 3  a n d 4-  (b)  a s f u n c t i o n s  o f  (-2) 1 G ~ - < 3 ) 1G" , (if) 1, 2  1  r  y  f o r  a n d  0=10"  ( 5 ) 10  1  6  emu,  h=2x10  c y c l e s / s e c .  7  cm  F i g u r e and  2k.  •E  x  (a)  a n d ^  (b)  x  a s f u n c t i o n s  o f  (1) f=10~ , (2) 10~ , (3) 10~ , (k) 1 , 3  2  1  y  f o r  a n d  0=10  (5) 1-0  emu,  h=2x10'  c y c l e s / s e c .  c m ,  -<1 CO  8  8  12 16 Y (I0 cm)  12 16 Y(l0 cm)  24  7  7  Figure 25. H (a) and R" (b) as functions of y f o r o=10~ emu, h=2x10 cm, and (1) f=10-3 <2) 10" , ( 3 ) 10" , <*+)-1, and (5) 10 cycles/sec. 11  y  z  5  2  1  7  140 I  I  120  »  l  •  I  co  UJ UJ tr o UJ 4 0  3,4,5 = 2 =  vO  20  3.4  (b)  5  1  1  IO"T— —L 1  8  0  12  I 20  16  •  24  I  '  8  12  and  26. (1)  E  (a)-  x  f=10  J  ,  and (2)  I  •  16  1  20  24  Y (10 cm)  Y (I0 cm)  7  7  F i g u r e  •  xf> ,  <J> ,  1 0 " °,  (3)  Z  ^  x  (b)  1 ("T , 1  as (k)  f u n c t i o n s 1,  and  (5)  o f  y 10  f o r  0=10  ^11  c y c l e s / s e c .  emu,  ^7  h=2x10'  cm,  80  independent v a r i e s F i g s .  a s f  -1/2  25(a)  ( l e s s than  than  w h i l e  E  f o ra l l  0.05  [ F i g .  t h ec o n d u c t i n g The  a s f  o f H  v a l u e s  26(b)]  a s a f u n c t i o n  o f F i g .  v a r i e s  1/2 '  2.5(a)],  H_  z .  A s can  t o H  b e seen  i s much  e a r t h  f o ra l l  ( a sl a r g e  components  o f frequency  and  a s 0.5K  show  p o s i t i o n  from  s m a l l e r  o f y ) f o r t h ec o n d u c t i n g  f o r t h ec o n d u c t i n g  angles  change  ,  [curves  a n d( b ) , t h e r a t i o  i t was  phase  of  o f frequency  sea T h e  very  l i t t l e  : i n t h e case  sea.  e f f e c t  o f t h ec o n d u c t i v i t y  out  i n g r e a t e r  d e t a i l  f o r  t h ec o n d u c t i v i t y  i n F i g s . range  and  27  o* =  o f t h ee a r t h  10"^  R e s u l t s  2.8.  t o lO""  1  emu  0  i s  brought  a r e shown f o ra  7 source As a  h e i g h t  seen  from  change  do  show  o f 2 x F i g .  27(a),  d e c r e a s i n g  and  H  changes  10  —1 h-  and  x  E  from  v a r y those  a p p r o x i m a t e l y o f F i g s .  25(b)  a f f e c t e d b y  27(b)  and  28(a)]  g r e a t e r  both  F o r c o n d u c t i v i t i e s  7  than  2 x  From  these  c m b o t h R~  10'  z  / 2  a s d and  o f c o n d u c t i v i t y ,  i n c r e a s e s .  -1 and  s t r o n g l y  c y c l e s / s e c .  J \ .  a s a f u n c t i o n  emu  o f 0.1  E ^ [Figs.  Z  a s t h ec o n d u c t i v i t y  than  a frequency  R V i s n o tv e r y  i n c o n d u c t i v i t y . l a r g e  g r e a t e r  c ma n d  10-  • . 26(a)  i t can  r e s u l t s a n d  b e seen  that f o r  —11 a  conducting  quency  sea  H _ v a r i e s  (d =  emu)  10  a p p r o x i m a t e l y  and  as  a  s u f f i c i e n t l y -1 / 2  (df)  •  w h i l e  a s f '  a p p r o x i m a t e l y The f i e l d s  i s t r e a t e d  c y c l e s / s e c , 3 on  x  e f f e c t  v  10^,  and  t h es o u r c e  h  x  1 d~  .  o f t h es o u r c e i n Fig,,  0 = 1 0 " 10^  h e i g h t ,  f r e -  E. . v a r i e s A.  Z  1/2  low  emu cm..  R e s u l t s  29and H  ,  h e i g h t  source  w i t h  magnetic  a r eg i v e n  h e i g h t s  although  i n c r e a s e s  o n the  not  h  =  f o rf 1 0 ' ,  s t r o n g l y  i n c r e a s i n g  = 0 . 1 2 x  1 0 ' ,  dependent  source  h e i g h t  10'  10"  ro i  o ^ ^ S v  —  ;  10  (a) .  . I . I 0  8  4  and  (7)  H  27  Y  U)  U - 1 0 - 1 6 , 10  l  u  emu.  .  I  12 Y  Figure  I  (  ,  °  7  .  16  c  m  1 0  .  20  24  0  4  8  16  12  >  a n d H , (b) (2)  I  20  24  Y(l0 cm) 7  as f u n c t i o n s  -15, ( ) 3  1 0 ^ \ (!>)  of j 1  0  f o r f=l<T  ^ 3 ,  ( 5 )  1 ( r  1  cycles/sec,  12  ( f i )  10  -11  h=2 10? X  C  m  F i g u r e  28._  h=2xl0 (6.)  7  •  (a)  a n d c/y,  <£  z  (b)  a s f u n c t i o n s  c m a n d (1.) 0=10-16, (2) 1 0 ~ , 1 5  1 0 " , a n d (7) 1 0 " 1 1  1 0  emu.  o f  y  (3) 1 0 " , l k  f o r  f=10~'  (>f) 10" , 1 3  c y c l e s / s e c ,  (5) 1 0 " , 1 2  0  4  8  12  16  20  24  0  4  8  12  Y(l0 cm)  d = i C ~  291  6  •Hy (a),- K emu, a n d  z  20  24  Y(l0 cm)  7  F i g u r e  16  7  ( b ) ,  a n d 0-  ( c )  a s a  f u n c t i o n  (1) h=10^, (2) 2x10 , (3) 3x10 , 7  7  o f  y  f o r f=10  a n d (h)  c y c l e s / s e c ,  ^fx10  7  c m .  8>f f o r  p o s i t i o n s  than  x  k  10  of  H y,  x '  E  A t  i s  z  R"  ^ x  a  n  ^y  d  how  =  EL  d  =  of  r  of  w i t h  as  r a p i d l y  the  source  i n c r e a s i n g  show  they  the a  cm.  7  d i s t a n c e  computed  e  10  of  and  sea  y.  I t  i s  emu  H_  v a r i e s  f r e q u e n c i e s  z  w h i l e  e v i d e n t  (d  of =  from  almost  y  source  ( l e s s h e i g h t  a p p r o x i m a t e l y f o r  shown  7  x  12  l a r g e r  h e i g h t *  not  10'  v a l u e s  A l t h o u g h  h e r e .  dependence, f r e q u e n c y  F i g .  f o r  d r y  30 e a r t h  11 emu),  10  F i g s .  a p p r o x i m a t e l y  b e i n g  the  source  f r e q u e n c y  w a t e r  s m a l l  h e i g h t ;  are  f u n c t i o n  F o r  as  —  emu)  1 f\  10  e  x  h  d e c r e a s e s  z  v a r i e s  z  10  v a l u e s  w  than  h o r i z o n t a l  f u r t h e r  1 f\ (d  a  i n c r e a s e s  To shows  H  independent  z  ?  g r e a t e r  cm),  7  i n c r e a s e s . cm,  x  30(a) as  f  f o r and  —1  independent  '  /?  of  s e v e r a l (b)  f o r  t h a t the  f o r  h i g h e r  f r e q u e n c y  f o r  11 the  l o w e r  f r e q u e n c i e s .  F o r  a  =  emu,  10  however,  F i g .  30(b)  - 1 /2 shows  t h a t  H  z  v a r i e s  as  f  '  f o r  the  e n t i r e  b a s i s  of  r e s u l t s  o b t a i n e d  be  t h a t  f r e q u e n c y  range  c o n s i d e r e d . On and  phase  a n g l e s  components ance  f r o m  are the  component source  the  i s  l o c a t i o n z  / H y  not  are  The  I f  are  one  the  i n  g e n e r a l  q u i t e  as  s o u r c e . to  the  t h r e e  f i e l d  h o r i z o n t a l  d i s t -  as  The  changes  and  r a t i o s  h o r i z o n t a l  on  f r e q u e n c y , on  E ^ H y  l i n e  the and  frequency*  l o c a t i o n .  o s c i l l a t i n g  c u r r e n t s  o r  the  dependent  i n  f i e l d  c o n d u c t i v i t y ,  dependent  w e l l  a m p l i t u d e s  magnetic  f i e l d  s t r o n g l y  s e n s i t i v e  source  assumes  the  the  f r e q u e n c y ,  magnetic  h e i g h t ,  to  on  h o r i z o n t a l to  the  a l t h o u g h  dependent  s e n s i t i v e  source  and  seen  v e r t i c a l  r e s p e c t  hence  c o n d u c t i v i t y ,  s o u r c e ,  v e r y  and  w i t h  can  s t r o n g l y  l i n e  f i e l d  c o n d u c t i v i t y  H  a l l  h e i g h t .  e l e c t r i c  i t  f o r  i n  the  f  F i g u r e • (b>  CYCLES / S E C  30.- H 0=10" 11  a s a  h=10 (1) y=10 ,- (2) 2x1O , (3) ^ x  f u n c t i o n  emu, a n d  f  o f  frequency  7  f o r 7  7  CYCLES/SEC  cm,'(a) l O  7  ,  a n d  o=i0" ^, (>+-) 8x10 1  7  c m .  86 i o n o s p h e r e as a s o u r c e o f  the e l e c t r o m a g n e t i c v a r i a t i o n s  the e a r t h , t h e n measurements the e a r t h ' s  on  o f t h e f i e l d c o m p o n e n t s made a t  s u r f a c e s h o u l d be d e p e n d e n t o n t h e s o u r c e  quency,  t h e s o u r c e p o s i t i o n , and t h e c o n d u c t i v i t y o f  earth.  In  the case of the r e a l e a r t h inhomogeneities  frethe i n the  c o n d u c t i v i t y s t r u c t u r e would c o n s i d e r a b l y modify the a m p l i tudes and phases o f t h e f i e l d  components.  87 Chapter  ANALOGUE  3-  3-1  Sheet  .3... 1... 1  ..  C u r r e n t  b e h a v i o r  v a r i a t i o n s  determined  by  of  the  observed  the  nature  of  of  the  In  we  c o n s i d e r e d  Chapter  2  plane  wave  l a r g e  c u r r e n t  o b t a i n e d e a r t h ' s  s u r f a c e  the  the  a l s o  e a r t h ' s  c o n d u c t i v i t y r e a d i l y  to  i n  that  should  be  f o r  an  i n  the  g e n e r a l  f o r  v e r y  c o n d u c t i v i t y  • The  problem  sheet  s o u r c e s ,  f o r  i n  on  of  e a r t h .  or  i t  v e r y r e s u l t s  at  the  two  was  the  the  a  The  the  a  s o u r c e s .  a l s o  v e r t i c a l  f i e l d s  observed  d i s c o n t i n u i t i e s  d i r e c t i o n  does  found  not  i n  submit  as  treatment.  d e a l s  the  e f f e c t  the  observed  l a y e r s ,  g e n e r a l  the  w i t h i n  source»  d i f f e r e n t  i n  by  source  f i e l d s  c o n d u c t i n g  i s  and  f i e l d  c u r r e n t  q u i t e  i n  f i e l d  of  e l e c t r o m a g r  s u r f a c e  d i s t a n t  v a r y i n g  h o r i z o n t a l  c h a p t e r  s t u d y i n g  types  important  s u r f a c e .  e a r t h ' s source  l i n e  the  h o r i z o n t a l  had  a  o c c u r r i n g  c o n d u c t i v i t y  two  a  m a t h e m a t i c a l  T h i s model  and  d i s c o n t i n u i t i e s  d i r e c t i o n  the  r e q u i r i n g  i n d i c a t e d  the  e l e c t r i c a l  sheet,,  c o n s i d e r i n g  t h a t  at  source  n a t u r a l l y  at  d i s t r i b u t i o n  In  Source  I n t r o d u c t i o n The  n e t i c  MODELS  w i t h  problem  c u r r e n t  an of  analogue  method  c o n d u c t i v i t y and  (3°1)  l i n e  u s i n g  a  d i s c o n t i n u i t i e s  c u r r e n t  (3.2)  s o u r c e s . The i s  one  time.  of  problem  of  c o n s i d e r a b l e  Among  the  e l e c t r o m a g n e t i c  h o r i z o n t a l i n t e r e s t  f e a t u r e s f i e l d  of  c o n d u c t i v i t y  i n  geophysics  i n t e r e s t  components  i n  i s  the  the  d i s c o n t i n u i t i e s at  the  b e h a v i o r  neighborhood  p r e s e n t of of  the a  88 c o a s t l i n e  as  w e l l  and  i n  the  i s  dykes  commonly  i n d u c i n g the  Kunetz  a  of  somewhat  the  r e a l  case  h i s  r e s u l t s  i s  Caner  i n  and the  e f f e c t "  normal  the  to  r e s u l t s ocean  the  i n c r e a s e s  support  plane  the  waves  a n a l y s i s  o r  a  the  of  f l o o r  be  and  observed  a  dyke  of  the f a u l t .  expected  of  the  as  the  and  d i s -  the  l a n d  f o r  i n t e r f a c e ,  v e r t i c a l  mag-  d i s c o n t i n u i t y  enhancement  c o a s t l i n e s  to  d ' E r c e v i l l e  t r a c e  would  u n i f o r m  p a r a l l e l  ( 1 9 6 2 ) c o n s i d e r e d  s h a r p l y  of  by  f a u l t s  the  f i e l d  case  amplitude  neighborhood  i s  means w i t h  s i m i l i t u d e  f a c t o r s  were  a  a  l i n e  r e p r e s e n t e d  the  e l e c t r i c a  p r e s e n t  to  s c a l e d  of  model  u s i n g  19 ^ 1 ) »  by  of  (Lambert  upper the  over  l a y e r  the  a  of  model  the  e a r t h . r a t i o  f i e l d )  e a r t h .  The  to  the  t h i s and  study  f o r  model  the  " c o a s t  R a n k i n  s a l t • T h e y  p r i n c i p l e s  s c a l i n g et  c o n s i s t i n g  c o n d u c t i n g  magnetic  designed  as  w e l l - k n o w n  ( 1 9 5 3 ) °  m a g n e t o t e l l u r i c  model  such  M a g n e t o t e l l u r i c  C a g n i a r d  c u r r e n t  h o r i z o n t a l  was  problems  m a g n e t o t e l l u r i c  t w o - l a y e r work  s t u d y i n g  t r e a t e d  d e s c r i b e d  measurements  of  ( S t r a t t o n  o s c i l l a t i n g  above  of  Weaver  s h e l v i n g t h a t  s i m p l i c i t y ,  s t u d i e d  to  v e r t i c a l  4 9 6 5 ) .  One  have  a  of  magnetic  was  extended  d i f f e r e n t  i n d i c a t e  approached,  the  f a u l t  f i e l d  f i e l d . c o m p o n e n t  component  of  of  of  ( 1 9 6 2 ) .  magnetic  F o r  assumption  case  was  neighborhood  c r u s t .  the  R a n k i n  A l t h o u g h  n e t i c  the  ver^ti_cal I t  by  the  on The  ( 1 9 6 2 ) . o  c o n t i n u i t y case  based  of  i n  e a r t h ' s  f i e l d .  t r a c e  as  a l  of  ( 1 9 6 5 )  an  s o l u t i o n  w h i c h  d i s c u s s e d  ( h o r i z o n t a l a  l i n e  used  v e r t i c a l  c u r r e n t  in.  the  to  h o r i z o n t a l  89 magnetic r a t i o  f i e l d  f o r  r a t i o  v a r i o u s  as  w e l l  f i e l d  as  the  m a g n e t o t e l l u r i c  f i e l d  sources  and  a  s u i t a b l y  s c a l e d  g e o l o g i c a l  s t r u c t u r e s .  of  h o r i z o n t a l  e l e c t r i c ,  the  v e r t i c a l a t i o n s , The  magnetic a n g l e s  p r e s e n t  u r e s F o r  i n a  the  sheet  t e l l u r i c v a l u e s  f i e l d  of  f i e l d of  and  expected  on  The t h i s  model  of  s i m i l i t u d e  equations  as  the  V  x  i s  making  (68)  (69)  e q u a t i o n s  x  H'  the  may  a  based  E«  -  be  on  of  l a r g e  plane  a n g l e s  and  the  p o l a r i z -  are  measured.  e a r t h  l a r g e  e x t e n t ,  should  s t r u c t dimensions.  the  magneto-  approximate  wave  the  [equations  +  J  f o r  f i e l d  £  the  assumption.  -  and  (1)  P = HoV  =  W d c E '  Q  f i e l d  (2)]:  =  0  01  e x p r e s s e d  e  f a c t o r s  p r i n c i p l e  M a x w e l l ' s  i n  d i m e n s i o n l e s s  s u b s t i t u t i o n s  E'  s c a l i n g  0 ,  | f ' =  §f^-  the  w e l l - k n o w n  C o n s i d e r  1 9VI).  c These  of  model  c u r r e n t  angles  phase  v a r i o u s  f i e l d s  the  development  e a r l i e r  V  (67)  sheet  b a s i s  ( S t r a t t o n  (66)  w i t h  and  m a g n e t i c ,  the  source  of  A n a l y s i s  problem  g i v e n  a  phase  m a t h e m a t i c a l  i n  and  f o r  s u f f i c i e n t l y  the  M a t h e m a t i c a l  3.1.2  h o r i z o n t a l  d e a l s of  range  a m p l i t u d e s  components  (3.1)  c u r r e n t  r a t i o s  the  i n c i d e n c e ,  s e c t i o n near  The  wide  E ,  e  H'  =  e  o e' K  =  h_H,  d  =  °o ' S  form  by  90 (70)  •  where  d  B y  and  e  the  e l e c t r i c  Q  ,  H, h  Q  d i e l e c t r i c i v e l y .  ,  =  d D,  K^,  K  g  5  S,  LL ,  e  o  ,  d  q  f i e l d ,  =  0  D  and  T  are  d  ?  and  Q  magnetic  c o n s t a n t ,  E q u a t i o n s  t  Q  t  t  Q  d i m e n s i o n l e s s a r e  f i e l d ,  and  the  l e n g t h ,  then  (67)  (71)  x  (72)  V x H - p |f  E  -  T  q u a n t i t i e s ,  q u a n t i t i e s  of  p e r m e a b i l i t y ,  and  time  r e s p e c t -  become  0  a |f =  +  u n i t  magnetic  c o n d u c t i v i t y ,  (66)  T ,  E  0  =  where  (73).  - - ^ f r )  ,  V 0/  O  >=^f  fe  and (75)  The  .  Q  s o l u t i o n s  under  a  and  a r e  y  n e t i c  (h^)°  *f = W c d d S  change  to i n  equations s c a l e  i n v a r i a n t .  boundary  v a l u e  i f  0  and  (71) the  • Hence problem  an  w i l l  (72)  d i m e n s i o n l e s s a c t u a l  can  be  be  i n v a r i a n t  q u a n t i t i e s  g e o p h y s i c a l  r e p r e s e n t e d  by  <st,  p,  e l e c t r o m a g a  s c a l e d  model. If have  the  we  f r e e  d i r e c t space  our  a t t e n t i o n  v a l u e s ,  and  to  problems  e l i m i n a t e  e  o / h  where 0  f r o m  e  and  e q u a t -  p,  91 i o n s  (73)  to  (75)?  for  i n v a r i a n c e  and  do  =  t h e n  u n d e r  c o n s t a n t ,  a  f  i s  t h e  refer  to  a c t u a l  refer  t o  m o d e l  p r e s s e d  i t s  d i m e n s i o n s ,  M o d e l The 31. a n  on  a  w e r e  f r a m e  c o n s t a n t  we  t h e n  s u f f i c i e n t  are  t h a t  d f  c o n d i t i o n s  =  c o n s t a n t ,  ,  now  l e t  p r i m e d  a n d  u n p r i m e d  (11)  e q u a t i o n  m o d e l  o f  a b o u t  t h e  t h a t  i t  a l t e r  t h e w i r e  c o u l d t h e  p r o v i d e d  m  to  C o p p e r  f r o m  w i l l  h a v e  a n d  "symbols  c a n  symbols  be  e x -  s h e e t  l o n g  h e a v y  bus  2.^  m  a r r a y . be  a n g l e by  < T h e  a  w i t h  1 5C>-W  t h e  o r  g e o p h y s i c a l  same  2.M+ bus  o f  w i r e s  1  b a r s to  r e t u r n  l o w e r e d  M c i n t o s h  to  a t  the  t h e  was  o f  w i d e .  ends  r e s p e c t  the by  the  f r a m e  t e c h n i q u e  p r o v i d e d  m  o f  m o d e l  cm  ' The the b r a s s  the  power  shown  p a r a l l e l ends  frame  as  o f  bus  i n  a m p l i f i e r  t h e  a n d  e x t h e n  a b o u t s u c h  h o r i z o n t a l .  h e l d  w i r e s  b a r s  w e l l  i n  f l o w i n g  s e p a r a t i o n  c o n d u c t o r  r e a d i l y  i s  c u r r e n t  s u p p o r t e d  t h e  p r o b l e m  s o l u t i o n s .  measurement  a t t a c h e d  w i t h  r a i s e d  the  b r a s s  a n d  b e y o n d  c i r c u i t  t h e n  was  b r a s s  b a r s  .  2  a r r a n g e m e n t  h o r i z o n t a l  h>8,8  o ' f ' d '  s a t i s f i e d ,  c u r r e n t  a t t a c h e d  c o m p l e t e d  i s  e x p e r i m e n t a l  a r r a y  t e n d e d  s c a l e  d i m e n s i o n s  =  2  d e s c r i p t i o n  T h e  f r a m e .  was  (72)  s c a l e d  3.1.3  i n  a n d  as  c o n d i t i o n  F i g .  i n  I f  g e o p h y s i c a l  o f d  and  =  f r e q u e n c y .  (77)  to  change  o f d  where  n e c e s s a r y  o r  (76)  If  the  7.6 a  as T h e  u way  t i l t e d power  c o n n e c t e d  92 d i r e c t l y to the l o o p as shown i n F i g . 31 . ' The l o o p was  c u r r e n t i n the  maximized by adding a c a p a c i t o r to make a  c i r c u i t as shown i n F i g . - 31.  The  c u r r e n t was  resonant  monitored  by  measuring the v o l t a g e across a r e s i s t i v e element o f the l o o p . F o r the measurements d e s c r i b e d i n t h i s work, the sheet was  kept In a h o r i z o n t a l p o s i t i o n 1.25  current  m above the  s u r f a c e of the s a l t s o l u t i o n i n a plywood tank 2.¥+  m  1.68  concrete  m and O.76  f l o o r and  m deep. - To minimize e f f e c t s of the  the e a r t h below, the bottom of the tank was  w i t h a 5-cm  by  lined  l a y e r of g r a p h i t e i n the form of machined rods  o f square c r o s s s e c t i o n . • F o r measurements made l a t e r i n t h i s work the ends o f the tank p e r p e n d i c u l a r to the d i r e c t i o n o f the e l e c t r i c f i e l d of the source were l i n e d w i t h  graphite.  T h i s reduced the edge e f f e c t s , ' T h i s * p o i n t w i l l be t r e a t e d l a t e r i n t h i s work.  The  s a l t s o l u t i o n over the  l a y e r i n the tank represented  the upper conducting  the r e a l e a r t h problem. - F i g u r e 32  the g r a p h i t e l i n i n g  the tank forming The  wide and  the upper l a y e r  ( c o n d u c t i v i t y d'^) at' the bottom o f  the lower l a y e r .  d e t e c t o r c a r r i e r , to which the f i e l d  were attached, 2 cm  layer i n  shows the l a y e r e d conductor  w i t h the s a l t water ( c o n d u c t i v i t y ov,) forming and  graphite  c o n s i s t e d of a l u c i t e p l a t e 100 thick.  the r i g i d laminated  The  detectors  cm l o n g , 15  cm  c a r r i e r , though f r e e to move along  plywood beam above the tank, was  secured  to the beam by means of a l u c i t e r a i l glued to the beam.  The  r a i l , w i t h a T-shaped c r o s s s e c t i o n , mated w i t h a s l o t o f  the  same c r o s s s e c t i o n extending  the f u l l l e n g t h of the  carrier.  F i g u r e  32.  Diagram  of  the  model  l a y e r e d  c o n d u c t o r .  9^ S m a l l  n y l o n  along  t h e beam  beam a t  a n d i n  f i x e d  S i n c e  c a r r i e r  s o l u t i o n geared uous  o r Y  s u i t a b l e  f o r  r e q u i r e d  e i g h t  .provided  by  a  s l i d i n g  beam.  • A  a  the  on  by  l u c i t e  a d j u s t e d  t o The  c o n s i s t e d  graph l u c i t e  To  o f  c a r t r i d g e tube  1.91  a  f o r  by  w i r e  c o n t i n -  a  speed  t r a v e r s e  d . c .  was  and  f a s t e n e d  t h e  a  making  to  t h e  p o t e n t i a l  w i r e .  t h e  f i e l d  l u c i t e  d e t e c t o r s ,  tubes,  d e t e c t o r ,  i t  and secured o f  were  t h e d e t e c t o r  f i e l d  d e t e c t o r  by  diameter  c o i l s s i d e  secured  and h e l d  magnetic t w i n  from i n  a n d 35  each  was s i m p l y  depths  s i d e  s a l t  t r a v e r s e s  c a r r i e r  water  mounted  t h e  d r i v e n  a t  d i f f e r e n t  o f  t o  t h e X - Y p l o t t e r t h e  t h e  locate  a l l o w e d  along  p r o v i d e d  The h e i g h t  p a i r  cm i n  t o  i n  tank.  t o  o f  system,  move  p o s i t i o n e d  t h e  s u r f a c e  to  t o  p a r a l l e l  A . c o m p l e t e  r e s i s t a n c e  separate  h o r i z o n t a l  be  o f  t h e beam,  a t t a c h e d  t h e p l a t e  f o r  t h e  used.  and magnetic  screws.  a l l o w  a t  and b e l t  b a t t e r y  p o s i t i o n  l e n g t h  was drawn  r e s i s t a n c e  through  s e t  t h e  t o  i t  h o l e s  was p o s s i b l e  The X - i n p u t  storage  end o f  c a r r i e r  a n X - Y p l o t t e r  c a r r i e r  w i t h  t h e  • P o s i t i o n i n g  i t  end o f  o n  a l l o w e d  any l o c a t i o n  p o i n t  one  s l i d e r  e l e c t r i c  c a r r i e r . t h e h o l e  33  brass  t h e  i n  3-1),  minutes.  along  mounted  The  c o n t a c t  The  (Fig<. •  t h e K - Y p l o t t e r  6 - v o l t  g r a d i e n t  t o  r e c o r d i n g  tank.  t h e  moved  on  c a r r i e r  t h e f u l l  .A p u l l e y  mounted  automatic t h e  over  a x i s  t h e  a l l o w e d  be  tank.  to  f r i c t i o n , ,  any d e s i r e d  the  motor  across  c a r r i e r  c o u l d  a t  i n  l i t t l e  i n t e r v a l s  beam  t h e X  a t t a c h e d  w i t h  t h e  1-cm  t h e  e i t h e r the  r o l l e r s  a  t h e  i n  G15^  i n s e r t e d  v e r t i c a l l y was  t h e  r e a d i l y  tank.  shown  i n F i g .  O L E .• p h o n o -  s e a l e d  cm l o n g .  to  end o f  - E a c h  c o i l  a  95  DIFFERENTIAL AMPLIFIER  T V  I TWIN  V -  COILS  1  t  SIGNAL  ( NOISE, C A B L E P I C K U P , E T C . )  V  I  UNWANTED  o u  out  tt  < 2" v  V =V+ v 2  v  l  2  )  DIFFERENTIAL AMPLIFIER  V, = V + v ,  LrrFigure-  --1J  ELECTRIC  3 3 . - The e l e c t r i c  PROBE  a n d magnetic  f i e l d  d e t e c t o r s .  96 was 0 . 6 ? signals  cm l o n g and 0.57  cm i n d i a m e t e r . - To remove  f r o m t h e d e t e c t o r s and c o n n e c t i n g l e a d s ,  c o i l s were c o n n e c t e d i n s e r i e s  unwanted  the  two  i n a way t o p r o v i d e a  input to a d i f f e r e n t i a l a m p l i f i e r .  suitable  The l e a d f r o m t h e  outer  l a y e r o f e a c h c o i l was c o n n e c t e d t o t h e s h i e l d o f a t w o c o n d u c t o r l o w p i c k - u p c a b l e ( I n t e r - 8 Weave P e r f e c t i o n M i c a cable)  a n d t h e o t h e r ends o f  means o f t h e two c o n d u c t o r s input of the low noise  the c o i l s were c o n n e c t e d , of  by  the c a b l e , to the d i f f e r e n t i a l  battery operated Princeton Applied  R e s e a r c h m o d e l CR^f d i f f e r e n t i a l a m p l i f i e r .  A 70 cm c a b l e  c o n n e c t e d t h e d e t e c t o r t o t h e a m p l i f i e r w h i c h was mounted one end o f  t h e d e t e c t o r c a r r i e r . • The a m p l i f i e r t h u s  t o g e t h e r w i t h the probe w h i l e t r a v e r s e s  moved  w e r e made a c r o s s  t a n k . ' The p r e s e n c e o f t h e a m p l i f i e r h a d a n e g l i g i b l e on t h e f i e l d a t t h e s u r f a c e o f  insensitive  the  effect  the s a l t s o l u t i o n . • Although  t h e a m p l i f i e r was s i t u a t e d i n a r e l a t i v e l y i n t e n s e magnetic f i e l d ,  on  i t s w e l l designed  s h i e l d i n g made i t  electroquite  t o t h e f i e l d . • The o u t p u t f r o m t h e a m p l i f i e r was  connected by a 9 m two-conductor  s h i e l d e d cable to the d i f f e r -  e n t i a l i n p u t o f a T e k t r o n i x 502 o s c i l l o s c o p e where i t  was  f u r t h e r a m p l i f i e d . - The a m p l i t u d e o f t h e o u t p u t f r o m t h e o s c i l l o s c o p e was m e a s u r e d b y a n A . C . H e w l e t t - P a c k a r d 3+U-0r-A ;  l  DVM a n d t h e p h a s e a n g l e was m e a s u r e d by a n A d - Y u  52^-A3 -  d i g i t a l p h a s e c o m p u t e r whose o u t p u t was d i s p l a y e d o n a H e w l e t t - P a c k a r d 3¥+0-A DVM. • A r e f e r e n c e s i g n a l o f p h a s e a n g l e was p r o v i d e d b y a s m a l l c o i l  fixed  situated at a fixed  p o s i t i o n n e a r t h e f i e l d s o u r c e . • The a m p l i t u d e s  and phase  97 angles  d i s p l a y e d on the meters  point,  o r a l t e r n a t i v e l y an analogue  traverses digital  c o u l d be o b t a i n e d u s i n g  to analogue  recorder.  c o u l d be r e c o r d e d f o r recording for  each  complete  a Hewlett-Packard  580-A  c o n v e r t e r and a M o s e l y M o d e l 3 X-Y  The i n s t r u m e n t a r r a n g e m e n t  The v e r t i c a l m a g n e t i c  is  shown i n F i g ,  3 » k  f i e l d d e t e c t o r , shown i n F i g .  33", was c o n s t r u c t e d i n t h e same way a s  the h o r i z o n t a l  magnetic  f i e l d d e t e c t o r , e x c e p t t h a t the t w i n c o i l s were o r i e n t e d w i t h t h e i r axes  i n the v e r t i c a l d i r e c t i o n .  Both magnetic  field  d e t e c t o r s w e r e c a l i b r a t e d f o r t h e f r e q u e n c y r a n g e o f -1-30 k-c/sec w i t h a m o d e l 350 B e l l G a u s s m e t e r . e x t r a p o l a t e d t o 60 The a v e r a g e face of the s a l t  The c a l i b r a t i o n was  kc/sec. h o r i z o n t a l e l e c t r i c f i e l d along  the  s o l u t i o n was d e t e r m i n e d by m e a s u r i n g  v o l t a g e d i f f e r e n c e between p o i n t s  ]  cm a p a r t . • To  sur-  the remove  signals  common t o b o t h p r o b e s  and to m i n i m i z e the e f f e c t o f  signals  induced i n the l e a d s ,  t h e d e t e c t o r was d e s i g n e d  to  provide a s u i t a b l e i n p u t to the d i f f e r e n t i a l a m p l i f i e r .  The •  detector consisted of  end  three probes  mounted i n the s e a l e d  o f a l u c i t e t u b e (1.91)cm d i a m e t e r a n d 35 cm l o n g ) points  just protruding  making  c o n t a c t w i t h the s u r f a c e of  outer probes,  through  t h e s e a l e d ends o f  w i t h the the tube  and  t h e s a l t s o l u t i o n . • The  two  1 A 8 cm a p a r t , w e r e j o i n e d t o t h e two l e a d s  t h e s h i e l d e d c a b l e ( I n t e r - 8 Weave)  connected to the d i f f e r -  e n t i a l a m p l i f i e r , w h i l e the t h i r d probe, between the o u t e r probes,  of  a t the  midpoint  was c o n n e c t e d t o t h e c a b l e  shield.  T h u s ' t h e t h i r d p r o b e p r o v i d e d a common r e f e r e n c e p o t e n t i a l f o r  DUAL-BEAM  AMPLITUDE  SCOPE TEKTRONIX 502  PHASE  ANGLE  DIGITAL P H A S E COMPUTER A D - Y U 524A2  DIFF. AMPLIFIER! PA.R.-CR4A  DIGITAL VOLTMETER HP 3 4 4 0 A (AC)  DIGITAL VOLTMETER HP 3 4 4 0 A  PHASE REFERENCE X-Y  RECORDER MOSELEY  MODEL  N0.3  DIGITAL-ANALOG I CONVERTER HP 5 8 0 A  DETECTOR  i-gure  • Block-  (D C)  diagram  of  the  model  measurements  system.  99 the  two  a b l e  i n p u t  phase the  o u t e r  probes,,  to  the  angles  measured  f i e l d  shown here  i n i s  the  t e n d i n g  32i  one  o f  l a y e r  w i t h  of  the  tank.  end  i f  e f f e c t s - The  measured  f l a t  i n  o^  The  t h a t  and  However,  ;  i s  X  l a y e r e d  t h i s  hence  the  the  model  w i l l  be  of  i n f i n i t e c u r r e n t  i n  sheet  h o r i z o n t a l ents  the  '.should  X  was  Y  way  as  a  s u i t -  amplitudes d e s c r i b e d  a  d i r e c t i o n s ,  the  l a y e r l a y e r  of i s  • The  being  s t r a t i f i e d  s a l t  i s  d i s c u s s i o n  problem  Og  the  and f o r  o f  m o d e l l e d  i n  the the  s o l u t i o n  l i n i n g  model be  a r e  does i s  f i e l d  the  bottom  h i g h  c o n -  p e n e t r a t e  i n f i n i t e  m o d e l l e d  of  l a y e r  the  n o t  n o t  e x -  upper  and  s u f f i c i e n t l y  f i e l d  i s  e a r t h ,  model,  g r a p h i t e  cannot  dimensions  i n  e x a c t l y .  s u f f i c i e n t l y  l a r g e ,  the  s m a l l . of  the  and  the  H  f o r same  and Y o f  model w i t h  was  t e s t e d  by  c a l c u l a t e d  comparing  v a l u e s  the  u s i n g  y  (50)  e l e c t r i c have  • The  the  In  l a y e r .  E  and of  i n  and  problem  v a l i d i t y  system  used  e l e c t r o m a g n e t i c  below  (U-8)  same  c u r r e n t .  x  equations  the  h o r i z o n t a l  t h e  second  the  v a l u e s  a m p l i f i e r .  g e o p h y s i c a l  c o n d u c t i v i t y  r e g i o n s  e x t e n t  system  sheet  c o n d u c t i v i t y  d u c t i v i t y to  a  i n f i n i t e l y  i o n o s p h e r i c  i n  p r e s e n t e d  R e s u l t s  - The  l a r g e  w i t h  o f  c o o r d i n a t e  F i g .  arrangement  s i g n a l s .  3 . 1 . h D i s c u s s i o n The  t h i s  d i f f e r e n t i a l  were  magnetic  and  plane  c o n d u c t i v i t y  d i r e c t i o n s .  s u f f i c i e n t l y and  v a l u e s  waves  the  - I t  l a r g e  h o r i z o n t a l  p r e d i c t e d  f o r  i n c i d e n t as was  the  assumed  dimensions  plane  a  model  magnetic a  on  b u t t h a t  that  f i e l d  wave  t w o -  t h e the  compon-  s o u r c e .  100 O n l y t h e r e l a t i v e a m p l i t u d e s c a n be o b t a i n e d b y c a l c u l a t i o n , s i n c e the amplitude of the i n c i d e n t f i e l d i s S i n c e H„ f r o m t h e m o d e l m e a s u r e m e n t s  an unknown.  was q u i t e i n s e n s i t i v e  to  edge e f f e c t s , i t was, u s e d as a b a s i s f o r c o m p a r i n g t h e c a l culated values  o f t h e f i e l d components w i t h t h e  values. - Solutions  to Maxwell's  equations  measured  f o r p l a n e waves  i n c i d e n t on a h o r i z o n t a l l y s t r a t i f i e d c o n d u c t o r p r o v i d e r e l a t i o n s h i p between E  a n d H . • The v a l u e o f H  as  a  measured  jf  tr  f o r t h e m o d e l c a n t h e n be u s e d t o p r e d i c t a v a l u e f o r E It  was f o u n d t h a t t h e v a l u e p r e d i c t e d f o r E„ a g r e e d  c l o s e l y w i t h the value determined f o r E  .  very  from the model  measurements  f o r p o i n t s w e l l removed f r o m t h e e d g e s o f t h e . h t a n k , • The v a l u e s a g r e e d t o w i t h i n 2% a t ' 3 x 1 0 cycles/sec . k  and t o w i t h i n h % a t ' 6 x 1 0  cycles/sec.  The p h a s e  angle  measurements  a l s o agreed to w i t h i n a few p e r c e n t . • D e t a i l e d  measurements  w e r e made o f b o t h E  and H .  It  was f o u n d  H-__ was e s s e n t i a l l y c o n s t a n t o v e r t h e e n t i r e s u r f a c e while E  varied less  that  area,  t h a n -2% o v e r a c e n t r a l r e g i o n 130  cm  l o n g a n d 50 cm w i d e when t h e t a n k was s i t u a t e d c e n t r a l l y below the c u r r e n t sheet w i t h the l o n g dimension i n the e c t i o n of the e l e c t r i c graphical results  field.  i n a l l the  t o f o l l o w i n d i c a t e the measured v a l u e s  t h e a m p l i t u d e s and phase a n g l e s ducting layers.  The b r o k e n l i n e s  dir-  It  will  the X d i r e c t i o n decreases  of  f o r uniform horizontal con-  be n o t e d t h a t t h e e l e c t r i c f i e l d r a p i d l y n e a r t h e edge o f t h e  in  tank.  The edge e f f e c t s w e r e g r e a t l y r e d u c e d i n some o f t h e l a t e r work,  b y l i n i n g t h e end o f t h e t a n k w i t h g r a p h i t e r o d s .  In  101 the e a r l y measurements -(Figs „ 35 to *f8)  the ends o f the tank  were n o t l i n e d w i t h g r a p h i t e . - The v e r t i c a l magnetic f i e l d H„ was a l s o s t u d i e d i n great d e t a i l f o r u n i f o r m conducting l a y e r s . Various  types o f s c a l e d s t r u c t u r e s , r e p r e s e n t i n g  s t r u c t u r e s such as f a u l t s , dykes, sea c o a s t s ,  geological  e t c . , were  p l a c e d i n the s a l t s o l u t i o n . • Departure o f the amplitudes and phase angles from the o r i g i n a l values the s t r u c t u r e  can he a t t r i b u t e d to  introduced.  • The m a t e r i a l s used f o r the v a r i o u s g r a p h i t e and concrete.  s t r u c t u r e s were  The c o n d u c t i v i t y o f g r a p h i t e was taken  to be 1.2 x 10""^ emu, w h i l e t h a t o f concrete \CT^§  emu  u  was assumed to be  ' The c o n d u c t i v i t y o f the s a l t s o l u t i o n was measured  to be 2.1 x l b ~ ^ emu. • The v a r i o u s 1 <  types o f g r a p h i t e s t r u c t -  ures used i n t h i s work were machined from l a r g e blocks  and  graphite  sheets.  • The s c a l i n g f a c t o r s i n v o l v e d s a t i s f y equation (77)'. The  c o n d u c t i v i t i e s o f the model s t r u c t u r e s f o r a l l measure-  ments a r e 10^ g r e a t e r  than those f o r the g e o p h y s i c a l  problem.  -10 The  s a l t s o l u t i o n , o f c o n d u c t i v i t y 2.1 x 10  emu represents _i < a l a y e r o f e a r t h having a c o n d u c t i v i t y o f 2.1 x 10 emu, w h i l e the g r a p h i t e s t r u c t u r e , o f c o n d u c t i v i t y 1.2 x 10"^ emu, 5  y  -11 ' corresponds to sea water o f c o n d u c t i v i t y 1.2 x 10 Several  em.  s e t s o f s c a l i n g f a c t o r s f o r the frequency and l i n e a r  dimensions were used depending on the p a r t i c u l a r problem studied. It  i s convenient to express the f i e l d  E„\ e x p ( \ i i r , * I L e x p ( i * ), and H !  components as  exp(ic/> -), where the modulus  102 is  t h e a m p l i t u d e o f t h e component a n d t h e a r g u m e n t  phase  angle.  This  notation is  C h a p t e r 2.  The s y m b o l s  represent,  respectively,  d , R, W, a n d a w i l l  be u s e d t o  the depth, r a d i u s ,  w i d t h , and c ,  2  represent,  structure,  respectively,  the s a l t  graphite layer.  a  n  °3  d  the depth of water over the  the con-  s o l u t i o n , and t h e c o n d u c t i v i t y o f  The m o d e l r e s u l t s  in  con-  2  the t o t a l depth of water i n the tank,  d u c t i v i t y of  the  c o n s i s t e n t w i t h that used  d u c t i v i t y of the model s t r u c t u r e , w h i l e d^, d , will  is  the  w i l l now be d i s c u s s e d  in  detail. For discussion the sheet  c y l i n d r i c a l structures,  s t r u c t u r e s , ' (<s) seamount  coastline structures,  (d),  to the e l e c t r i c and (e)  (b)  f a u l t and  (d)  for  following  island  dyke  structures,  and c o n d u c t i n g dome s t r u c t u r e s .  h o r i z o n t a l f i e l d components allel  t h e model measurements  c u r r e n t source are d i v i d e d i n t o the  groups: • (a)  and (e)  purposes  In  (a)  are treated f o r traverses  f i e l d of the source,  while in  par-  (b),  t h e v e r t i c a l m a g n e t i c f i e l d component a n d  h o r i z o n t a l f i e l d components  for traverses  p e r p e n d i c u l a r to the e l e c t r i c  the  (c),>  the  b o t h p a r a l l e l and  f i e l d of the source  are  presented. (a)  Cylindrical. Structures The m o d e l d i m e n s i o n s  geophysical  dimensions  i n Tables VII  and V I I I  The s t r u c t u r e s of various  lengths  i n v o l v e d and t h e  used i n F i g s .  corresponding  35 t o *f0 a r e  summarized  respectively. studied i n Figs.  35 t o *+0 a r e  w i t h a d i a m e t e r o f 30.h  cm.  The  cylinders results  TABLE Model  f ( s e c "  Case  Two  l a y e r s  C y l i n d e r  3x1  1  )  d  1  (cm)  6 x 1 0 ^  b\  it.  it  dimensions  d (cm)  R(cm)  2  31  "  G e o p h y s i c a l  Two  f ' ( s e c "  l a y e r s  C y l i n d e r  1  )  0.3 ,  0 . 6  it  «  :  d ^ c m )  d-^Ccm.)  -  3.15X10  1 0  5  - -  2  0  2 x i O "  6  2 . 1 x 1 0 " 1 0 ~  ?  1  6  1  1 . 2 x 1 0 "  0  6  ti  ••-  VIII dimensions  R'(cm)^  6  -i  d^(emu)  d (emu)  -  30.1+  TABLE  Case  d(emu)  -  .5  1  VII  >  •.  3.0^+xlO  6  d'(emu') -  1  ^ x l O " "  d^emu)  1  1  , 1 0 ~  2 . 1 x 1 0 ~ 2  1  1  d^(emu)  ^  1  .21x10""  1 1  10V shown i n F i g s , 35 to 39 a r e f o r v e r t i c a l c y l i n d e r s immersed i n the s a l t s o l u t i o n w i t h the a x i s o f the c y l i n d e r i n each case along the z - a x i s o f the c o o r d i n a t e system shown i n F i g . 3 2 . F i g u r e kO d e a l s w i t h c y l i n d e r s having t h e i r axes p a r a l l e l to the y - a x i s .  The depth o f the s a l t s o l u t i o n used f o r these  measurements was 3 1 ° 5 cmo ' The two model f r e q u e n c i e s used k k were 3 x 1 0 c y c l e s / s e c and 6 x 1 0 cycles/sec. F i g u r e 35 shows the behavior o f E  x  and Hy as a  f u n c t i o n o f p o s i t i o n f o r f = 3 x 10^ c y c l e s / s e c f o r the case of d^ = 1  cm over a v e r t i c a l g r a p h i t e c y l i n d e r . • F o r y = 0  and y = R / 2 , E__ changes v e r y r a p i d l y i n the neighborhood o f the edge o f the c y l i n d e r . < The change i n E „ would be even g r e a t e r i f the depth o f water over the c y l i n d e r were decreased.  This' s t r u c t u r e on a g e o p h y s i c a l s c a l e would  correspond to a deep c i r c u l a r sea surrounded by e a r t h w i t h a v e r t i c a l earth-sea' i n t e r f a c e .  The value o f E„ d i r e c t l y over  the c y l i n d e r a t y = 0 agrees to w i t h i n a few percent o f ."the: J value c a l c u l a t e d f o r plane waves u s i n g Maxwell's equations f o r the case o f 1 cm o f s a l t s o l u t i o n over a s e m i ^ - i n f i n i t e H  a l s o shows some change i n the neighbor-  hood o f the i n t e r f a c e .  U n l i k e E , H y does n o t become constant  layer of graphite.  x  d i r e c t l y over the c y l i n d e r f o r y = 0. k F i g u r e 36 shows the behavior o f E  x  and H  c y c l e s / s e c ^ a n d the same s t r u c t u r e as f o r F i g . 35° a r e v e r y s i m i l a r except t h a t H  y  forf  =10  The curves  shows s l i g h t l y more change.  Measurements made f o r a wide range o f f r e q u e n c i e s (10  to 1 0  c y c l e s / s e c ) , but not shown here, i n d i c a t e d t h a t the g r a p h i t e  y  tn  o  b x  0  X  °  CM  T—'—i— —i—'—i— —i— —i— —i—i—i— —i—»—i— —r 1  1  1  1  i*-2R-^ -i I i I i I i I i I i L • i • -100 - 8 0 - 6 0 - 4 0 - 2 0 0 20 40 X cm  F i g u r e  35-  E  v  (a)  and  H  (b)  f o r  f=3x10 c y c l e s / s e c , d^=1 (1) y=0, (2) R , (3) R/2, (1+)  f o r  cm, 3R/2  a  1  1  v e r t i c a l and cm.  (b) J 60  J  L 80  100  g r a p h i t e  t r a v e r s e s  a l o n g  c y l i n d e r  10$  3 ~  2  A 2  /  N  |\  V  >  1° CD  ~x3 LU  -i—i—I—i—i—i—i  1—i—I—i—I—i—I—i—I  -100 -80 -60 -40 -20 0  1—I—'—I—i  1—r  20 40 60 80 100  X cm  3 2 </>  Z3  O  fr-2R-*  s°  1—i—|—i—|—i—|—i—|—i—|—i—|—i—|—i—|—'—|—>—|—r  id x  2 (b) i_l i I i_ 20 40 60 80 100  *-2R—*  _L  -100 -80 -60 -40 -20  0  J  X cm  F i g u r e  36;  E  y  ( a ) a n dH  c y c l e s / s e c ,  v  ( b ) f o r a v e r t i c a l  f o r  f=6x10  (1)  y = 0 , (2) y = R , (3) y = R / 2 ,  g r a p h i t e  d ^ 1 c m , a n d t r a v e r s e s  ( I f ) y=3R/2 c m .  a l o n g  c y l i n d e r  10? c y l i n d e r s were not  e n t i r e l y homogeneous.  At some f r e q u e n c i e s  the shape of the curves i n the neighborhood of the edge changed s l i g h t l y i f the c y l i n d e r was  rotated  cylinder to a  new  position. Figure  37  displays  components of the f i e l d  the d i f f e r e n c e i n phase of the  studied.  ^  — <p • i s the phase d i f f e r -  x  ence between the h o r i z o n t a l e l e c t r i c and magnetic f i e l d .  Figures37(a) and  be  and  the  horizontal  (b) show the behavior of in: F i g , 35?  phase angle f o r the case d e s c r i b e d 37(c)  (d) r e f e r to the case d e s c r i b e d  3)ji F i g . 36.  than f o r f = 3 x  cycles/sec  the  while F i g s .  seen t h a t the phase d i f f e r e n c e , undergoes a much  change f o r f = 6 x 10  two  It  can  greater 10  cycles/sec -The  dependence o f E„ and H,_ ,on the depth of the x  s o l u t i o n over the g r a p h i t e f = 3 x 10^  cycles/sec  salt  y  c y l i n d e r f o r y = 0 and y = R at i n F i g . 38.  i s brought out  seen t h a t changing the depth of the -cylinder g r e a t l y affects' E  I t can  s a l t s o l u t i o n over  i n the neighborhood of  1  be  the  the  cylinder. - Figure  39 d e a l s w i t h the case of a v e r t i c a l  c y l i n d e r submerged i n the Figure  39(a)  shows E  s a l t s o l u t i o n w i t h d^ = 1  as a f u n c t i o n of p o s i t i o n f o r -A-  over the c y l i n d e r .  Measurements o f E  concrete cm  u  traverses  were a l s o made f o r a -X.  k  frequency of 6 x 1 0  cycles/sec^  but  l i t t l e from measurements f o r 3 x 1 0 are n o t  shown* • S i n c e H  was  s i n c e they d i f f e r e d v e r y cycles/sec  the  results  not a t a l l a f f e c t e d by the .  c o n c r e t e c y l i n d e r , the r e s u l t s f o r H  are not  shown. •- The  108  CO LU UJ  or  (b)  (a)  LU  I  o  i I i i i l i i i  j i | i | i | i | i 0 20 40 60 80  1  X cm  i i i  i 1 i l i  1  37 (d) | i j i i • i • i . 0 20 40 60 80  'E >  b x  CO  If)  x LU  ' J (a) 1  i I i l i i • I i  l  i  1  i  i i > i  1  i  l*R-»l  in 3 O  ^  1  H  U  y  O X CM  H  (c) 1  1  0  1  1  1  20  1  40  1  1  60  1  y (0  38 1  1  80  0  1  1 . 1  20  1  1  40 60  1  1 .  80  X cm Figure 37. - t x " ° % f o r a vertical f=3x10  Lf  cycles/sec  (a)-(b),  g r a p h i t e c y l i n d e r f o r d ^ l cm,  f=6x10^" c y c l e s / s e c  (c)-(-d),.  and  ( 1 ) y=0,< ( 2 ) R, ( 3 ) R / 2 , a n d (1+) 3 R / 2 cm. Figure 38.  E  x  f o r traverses along  traverses along  ( c ) y=0, ( d ) y=R, f o r a v e r t i c a l  c y l i n d e r f o r f=3x10 (3)  16.2,  ( a ) y = 0 , ( b ) y=R, H  and A )  l f  c y c l e s / s e c , and (1) d  2 3 . 8  cm.  l =  y  for .  graphite  1 , (2) 8.6,  109  -, 0  39.  F i g u r e  3x10  k  1  20  (a)  R,-  c y l i n d e r  (3) R / 2  3  1  1  4 0  1  1  6 0  j  1  1  80  X cm  0  1  |  20  1  1  1  1  4 0  x  f o r d^=1 a n d {k)  cm a n d traverses  3R/2.  y  1r  1  60  f=3x10^" c y c l e s / s e c , - ty -<P ( d ) - ( e ) 6x10 c y c l e s / s e c , f o  f o r  c y c l e s / s e c , •  concrete  (2)  •  1  1  8 0  f o r r a  along  ( b ) - ( c ) v e r t i c a l (1)  y=0,  110 conductivity of concrete i s  s u f f i c i e n t l y low that the  of concrete i n v o l v e d here i s depth.:  The c o n c r e t e a c t s  the conducting cylinder is  depth  a very small f r a c t i o n of a  essentially like  a large cavity  s o l u t i o n , and t h e enhancement o f E  due t o t h e l a r g e  skin  over  conductivity contrast.  the  H  is  n o t shown s i n c e  i t i s n o t a t a l l a f f e c t e d by t h e  concrete  cylinder.  This  s t r u c t u r e on a g e o p h y s i c a l  would  correspond  t o a b o d y o f v e r y l o w c o n d u c t i v i t y embedded  the e a r t h . • F i g s . 3 9 ( b ) and ( c ) ty x  $  f o r f = 3 x 10  y  show t h e p h a s e  t h a t the phase  K  cycles/sec. ' In  -  <p u n d e r g o e s  a much  comparing FigsL  graphite  k  0(a)  (e)  greater  t h a n i t does f o r f = 3 x  37 a n d 39, i t i s  of the concrete  and (b)  10  interesting  d i f f e r e n c e s i n the neighborhood  i n the neighborhood • Figures  As over  g r a p h i t e c y l i n d e r a r e q u i t e d i f f e r e n t from the phase ences  (e)  h  cycles/sec  t o n o t e t h a t the phase  cycles/sec.  evident from Figs.39(b) -  d i f f e r e n c e ty L.  change f o r f = 6 x 10  and  differences for traverses  cylinder, i t is  in  difference  while Figs.39(d)  d i f f e r e n c e f o r f = 6 x 10  was t h e c a s e f o r t h e p h a s e the graphite  show t h e p h a s e  cycles/sec  k  scale  in  of  the  differ-  cylinder.  d e a l w i t h the case of  c y l i n d e r i+5 cm l o n g p o s i t i o n e d w i t h i t s  the  axis  parallel  LL  to the y - a x i s This  w i t h d^ = 1 cm a n d f = 2 x 10  s t r u c t u r e on a g e o p h y s i c a l  highly  conducting  of the e a r t h .  H  cycles/sec.  scale could correspond  c y l i n d r i c a l body l o c a t e d n e a r t h e is  very l i t t l e  E  decreases  a f f e c t e d by t h e  to a  surface  graphite  v  c y l i n d e r , whereas  approached. •F i g u r e  MX-c)  r a p i d l y as  the c y l i n d e r  indicates a very large  is  enhancement  111  1—i—I—i—l—i—I—i—I—i—|—'—I— —I— —I—' 1  -100 -80  -60  -40  -20  -100  -60  -40  -20  -80  0  X  0 X  F i g u r e  1+0.  • E  c y l - i n d e r - -andf=3x10  LL  • (a) E  and • -(c)-  H  y  • (b)  f o r  a  cm  f o r  I  1  1  20  40  60  80  100  20  40  60  80  100  cm  a  h o r i z o n t a l  h o r i z o n t a l  c o n c r e t e  g r a p h i t e c y l i n d e r  X  c y c l e s / s e c ,  d-.,=1  cm,  and  t r a v e r s e s  along  y=0.  f o r  112  of: E „ when t h e h o r i z o n t a l g r a p h i t e c y l i n d e r i s .A.  concrete c y l i n d e r . - H all  sensitive  f o r d-.j = 0.1  i s n o t shown,  to t h i s cm. • I n  structure. this  case E  r e p l a c e d by a  since i t is  again not  M e a s u r e m e n t s w e r e made x  at  also  d i r e c t l y over the c y l i n d e r  i n c r e a s e d by a f a c t o r o f k a b o v e t h e v a l u e o b t a i n e d f o r d\j = 1 cm. On t h e b a s i s o f apparent that i f  the r e s u l t s  discussed  so f a r , i t  t h e g r a p h i t e and c o n c r e t e c y l i n d e r s  repres-;-  e n t e d c y l i n d r i c a l b o d i e s -embedded i n t h e e a r t h , b o t h E \|r -, -ty i n t h e n e i g h b o r h o o d x  different for a highly resistive cylinder.  It  of  t h e c y l i n d e r s w o u l d be  conducting c y l i n d e r f o r a is  also  is  and very  highly  evident t h a t the depth below  t h e s u r f a c e of, the e a r t h w o u l d have an i m p o r t a n t e f f e c t on the value of E  a t the  surface.  -X.  Ob)  F a u l t a n d Dyke In  (a)  Structures  o n l y t h e h o r i z o n t a l f i e l d components  verses p a r a l l e l to the e l e c t r i c considered. w e l l as  In  (b)  f i e l d of the source  for  tra-  were  t h e v e r t i c a l m a g n e t i c f i e l d component  t h e h o r i z o n t a l f i e l d component a r e i n c l u d e d f o r  as  tra-  v e r s e s b o t h p a r a l l e l ( i n t h e x d i r e c t i o n ) t o and p e r p e n d i c ular  ( i n the y d i r e c t i o n ) to the e l e c t r i c  f i e l d of  thus p e r m i t t i n g the study of both p o l a r i z a t i o n s f o r  the  source,  the  v e r t i c a l f a u l t and dyke p r o b l e m s . - F o r a l l measurements m o d e l f r e q u e n c y was 3 x 1 0  cycles/sec,  the depth of the  s o l u t i o n o v e r the submerged s t r u c t u r e a p p r o x i m a t e l y 0 . 0 5 and t h e t o t a l d e p t h o f the s a l t s o l u t i o n i n the t a n k i s  the salt cm, 61 cm.  113 The s c a l i n g f a c t o r s  involved again s a t i s f y equation  (77)?  w i t h t h e c o n d u c t i v i t y and t h e f r e q u e n c y e a c h a f a c t o r o f greater,  and t h e l i n e a r d i m e n s i o n s  a f a c t o r of  1Cr  smaller,  t h a n - t h o s e " f o r t h e g e o p h y s i c a l p r o b l e m , ' The s y m b o l s a  and W a g a i n r e p r e s e n t , width of the g r a p h i t e  1Cr  d , ' R,  r e s p e c t i v e l y , the depth, r a d i u s  and  structure.  The m o d e l m e a s u r e m e n t s  f o r the i n c i d e n t magnetic  f i e l d p a r a l l e l t o t h e d y k e d i s c o n t i n u i t y -(H p o l a r i z a t i o n ) d e s c r i b e d i n F i g - . h \ . • The g r a p h i t e d y k e i s 23 cm w i d e . - I t s it  l e n g t h , 102 cm, i s  s u f f i c i e n t l y great  c a n be c o n s i d e r e d i n f i n i t e l y l o n g f o r t h e  g e o p h y s i c a l d i m e n s i o n . - As  is  and that -  corresponding  c a n be s e e n f r o m F i g .  shows a s m a l l g r a d u a l i n c r e a s e a s H  61 cm deep  are  the dyke i s  L  1 (a),  H„  approached-*  v e r y s m a l l , b u t d o e s become m e a s u r a b l e n e a r t h e i n t e r -  faces. ' It  c a n be s e e n f r o m F i g . » M ( b )  that E  changes  very  l i t t l e up t o a b o u t 1 cm f r o m t h e d i s c o n t i n u i t i e s and  then  decreases  r a p i d l y to v e r y s m a l l values  the  dyke. - I t  is  dyke, i t s  presence  d i r e c t l y over  r a t h e r i n t e r e s t i n g to note t h a t f o r t h i s i s n o t d e t e c t a b l e on t h e b a s i s o f  f i e l d measurement u n t i l  M(c)  phase d i f f e r e n c e s , ^  x  and (d)  show t h e b e h a v i o r o f  A • a n d <$> • . y  a change i n phase angle i s  ^  cp . • I t  is  change  apparent  is  points 1  x  y  considered i n magnetotelluric  shown i n F i g . ' M (-e).  show some c h a n g e a t p o i n t s  that  i n E„» » The r a t i o E / H , x  the q u a n t i t y u s u a l l y  the  y  o b s e r v a b l e a t more d i s t a n t  w h e r e t h e r e i s no o b s e r v a b l e  analyses,  electric  p o i n t s very near the d i s c o n t i n u i t y  are reached. - Figures  which i s  deep  We n o t e t h a t E ^ R y  does  q u i t e remote f r o m the i n t e r f a c e .  11  k  *  H.  b X  in IS M  0 'E  8  b  6  X.  O CD  4  x LU  (b)  i  1  i i i —r 1  1  1  - 1 -  !—  -100 -80 -60 -40 -20 co  i i i i• i  1  1  1  1  0 20 X cm  40  60  80 100  160"  S  70  Q  •6-^60 J  20  1.0  i  I i  40  L  60  J  80  i  L  20  40  J  i  60  I  80  i_  -5*0.8 E > 0.6! cn S 0.4 LU - KJ  C  (e) — i — i — | — i — | — i — | — i — |  T^?  -100 -80 -60 -40 -20  0 20 X cm  • Hy,(e)  H  z  (-a)y  E  x  -  -  (b),<  f o r t h e H- p o l a r i z a t i o n  f o r a  -j—i—i—i—i—i—|—i—i—  40  60  80 100  ( ^ y ^ H y g r a p h i t e  dyke  (d)  a n d - E ^ H y  w i t h  w=23  c m .  115 T h i s  i s  due  even  f o r  t o  t h e f a c t  p o i n t s F i g u r e  p a r a l l e l  t o  w e l l  dyke  f r o m  w i t h  t h e  t h e  made  f o r  t r a v e r s e s  e v i d e n t  F i g . 2(a)  t h a t  k  a  (E  e l e c t r i c  y change u l a r  i n  i n t e r e s t  i n c r e a s e of  t h e neighborhood  r i g h t  o v e r  2.5  t h e  The b e h a v i o r  p o l a r i z a t i o n  f o r  shown  t h i s  v a l u e o f  E  ,  show  I t a  d i s c o n t i n u i t y . H  a s  t h e  p o l a r i z a t i o n  Of  p a r t i c -  a  l a r g e  about  o f  a  a  f a c t o r  homogeneous  i n F i g . 2(b),  i s  k  from  E  b y  case  shown  i n F i g . Vl ( b ) .  i s  l a r g e  undergoes  i n c r e a s i n g f o r  w i t h  z  t h a t  i n t e r f a c e ,  r e f e r e n c e  d i f f e r e n t  t h e  t h e o b s e r v a t i o n  a t  t h e  c o n d u c t o r . q u i t e  i s  o f  f i e l d  t h e y - a x i s . a n d EL  EL  i n c r e a s e  p o l a r i z a t i o n ) ,  a l o n g  both  g r a d u a l  i n t e r f a c e .  i n c i d e n t  d i s c o n t i n u i t y  measurements f r o m  undergoes  EL  removed  d e a l s  k2  t h e  t h a t  t h a t  f o r  undergoes  a  t h e  H  f a i r l y  .X. g r a d u a l  d e c r e a s e ,  i n t e r f a c e , dyke.  a n d reaches  A g a i n ,  The  r a t i o s  the  f a c t  f r o m  a t t h e  i n  a r e  t h a t  c o n d u c t i n g u n i t y  b e g i n n i n g  t h e  2  dyke  z  dyke.  t h e measurements  f o r as  a  dyke,  shown  g r a p h i t e .  a  maximum cm i n  d i s c o n t i n u i t y .  i s  approached  t h e  r a t i o  i n F i g . '  k  The maximum  T h i s  a n d f a l l s were  would  2 ( a ) ,  w h i c h  y  (2x10^  i n t e r f a c e I f  w e l l  v a l u e s  ^-2(d).  EL/EL ,  reaches  cm  s m a l l  i n F i g .  r a t i o  l a y e r s ,  about  v e r y  p o i n t s  removed  d i r e c t l y  from over  t h e t h e  g e o p h y s i c a tl h ap nr o bt lhe em ,a m tp hl iet ur da et si o st h Ee m s/ E e Ll v e s .  shown t h e  a t  be  would v a l u e  Of  s p e c i a l  i s  v e r y  v a l u e  t h e  made  o f  H  t o /EL  o f  f o r  a  f a u l t ,  d i f f e r e n t  would,  u n i f o r m  problem)  s t e e p l y  r a p i d l y  l o w e r  f o r  i s  a p p r o x i m a t e l y  r i s e s  v e r y  somewhat f a l l  s m a l l  g e o p h y s i c a l  r a t i o o f f  i n t e r e s t  v a l u e s  a s  over  t h e  t h e  r a t h e r  than  s i n c e  EL.,  over  t h e  however,  have  116  _  "Oh  H  4  x  T  N  b  >  4  X  2U  E  0  b x  4  (a) T— —r  i—•—r  1  o (0  (b)  UJ  —i—i—|—i—|—i—i—i—|—i—i—i—i—i—i—i—i—i—i—•—i—  -100 -80 -60 -40 -20  0 20 cm  Y  ->—I— —I—  40  T—|  1  20 F i g u r e and w i t h  hZ. 0 -0 z  H y  y  ?  H  40  z  (a),,  60 80 E  ( e ) f o r t h e E  w=23 c m .  x  60  Y cm  ( b ) ,  ^ -0 x  y  1  20  40  ( c ) ,  E  0  p o l a r i z a t i o n  80 100  x  f o r a  1—1—|—  60 / H  y  5  <  80  E /E J  g r a p h i t e  Z  ( d ) , dyke  117 a p p r o x i m a t e l y  the  would  t h a t  the  suggest  maximum  e a r t h - s e a '  same f o r  v a l u e  o f  ty„  0  —  x and  (e).  shows  H  i n t e r f a c e ,  d i f f e r e n c e s ,  -$ - -  the  the z  / H y ,  and  i t  f o r be  f o r  the  measurements  fc,  dyke.  c o n s i d e r e d  a p p r o x i m a t e l y  <j> • -  are  shown  T h i s c y c l e s / s e e )  (0.3  a t  a  v e r t i c a l  1.  - The  phase  i n  F i g s .  2(c)  k  y  undergoes  e f f e c t s  has  f r e q u e n c y  would  V  as  <y 0y  z  v a l u e  of  the  a  p a r t i c u l a r l y  dyke  a t  p o i n t s  l a r g e  f a r  change  removed  and  from  the  dyke. To  study  the  e f f e c t  the  f i e l d  components,  and  t h e  p o l a r i z a t i o n s  f o r  f o u r  k-3  E  d i f f e r e n t  c o r r e s p o n d  and  ( >  16  k  maximum  to  cm.  v a l u e  F o r of  E  the  measurements f o r  dyke  the  t h a t  dykes  depths.  depths t h e  H  n e a r  (1)  depth  were  the  made  f o r  dyke b o t h  of  c o n s t a n t  w i d t h  - The  numbered  curves  1  cm,  dyke  6  (2)  p o l a r i z a t i o n the  of  cm,  [ F i g .  d i s c o n t i n u i t y  H  cm)  i n 11  ]  on  the  (29  (3)  3(a)  k  has  F i g . cm,  the  i s  s t r o n g l y  .A. dependent becomes  on  the  deeper,  depth the  of  the  shape  of  c o n d u c t i n g the  curve  dyke.  f o r  E  • As  the  dyke  approaches  t h a t  -A.  shown  i n  show  no  f a l l  o f f  F i g .  k  as  s h a r p l y  a t  the  i n t e r f a c e .  shown  t r a v e r s e d . f o r  p o s i t i o n e d o f  s i n c e  t r a v e r s e s p a r a l l e l  H  but  the  i n  they  • F i g u r e s  and  H  dyke  showed k  3(b)  made  to  the  the  a l o n g  approached,  Hy  and  (c) the  y - a x i s . w i t h  dyke,-  i s  n e g l i g i b l e  and  i n c r e a s e  deep  d e a l  H  f o r  w i t h  F i g .  i n c r e a s i n g  but  as  the  a c r o s s k  3(b)  would  case  the E  dyke  p o l a r -  the the  dyke  would  t h i s  change  y - a x i s In  z  E„  dykes maximum  depth.  E  Zt  J  shown  i n f i n i t e l y  a l l  was  as  an  a t  not  v a l u e s  F o r  i n c r e a s e  a r e  i z a t i o n  1 (b).  F i g . ^  changes  k  3(-c),  are  , A  not  i s  a l s o  as  g r e a t  a f f e c t e d as  they  by are  the f o r  dyke t h e  depth, H  p o l a r -  118  -  E  _  >  -—w—»  I  'E 12 >  "  X  2  o CD  CO  LU  s  X  (a) -I00 -80 -60 -40 -20  0 X  _  20  40  60  80  100  cm  IO  <r 9 x  8  m  e  6  N  >% x I  (b) i- • i  '' I  <  '//////*?////  O X  o  to>< LU  -T—i—|—i—|—i—|—I—|—i—|—i—I—r—\—r—y  -100 -80 -60 -40 -20  0  Y  Figure  k  3.  E • (a)  20 40 60  f o r t h e H p o l a r i z a t i o n , H__f H  (c) f o r the E p o l a r i z a t i o n f o r a graphite d=1,  (b) and E „  J  •A.  a n d (-1)  80 100  cm  (2.)  (3)  11, and  (K)  16 cm.  d y k e w i t h w=29 cm.  119 i z a t i o n 3(b)  k  shown  a n d  i n F i g .  (c)  To  s i n c e  study  i t  o f  dyke  c o n s t a n t  a n d t h e w i d t h  p o l a r i z a t i o n  (1)  5 c m , (2)  (6)  30  maximum  10  v a l u e  i n t e r f a c e  i s  s t r u c t u r e  f o r  respond  t o  a  a  (3)  cm,  (7)  o f  i n  7?  v e r t i c a l  s i d e s  o f  t h e dyke  f i e l d  a t  one i n t e r f a c e  f a c e .  F i g u r e s  a  depth  (3) Hy  5 cm.  I t  a n d E  i n  z  w i t h  dyke  maximum ent.  o f  f o r  s m a l l  29  three  v a l u e s  have dyke  d i r e c t l y  2  a t  w i t h o f  w i d t h s over  M+Cb)  c o n s i d e r e d  t h e dyke.  would a  c o r -  c o n d u c t The and t h e i n t e r -  cm, t h a t  (2)  1  f o r  cm, a n d  t h e v a l u e s  d i s c o n t i n u i t y almost a r e v e r y i s  would  those does  o f  o f v a r y  t h e  same  d i f f e r -  f u r t h e r  c o n s i d e r a b l e  v a l u e t o  The  p o l a r i z a t i o n  w i d t h a  t h e dyke  t h e second  w i d t h s  show  t h e  f a r a p a r t  have  t h e dyke  s i m i l a r  t h a t  i n t e r f a c e .  0.2  f o r H  t h e maximum shape  (1)  t h e dyke  t h e dyke  would  w i t h  t h e E  a  o f  s h a l l o w  i n f i n i t e l y  F i g .  a n d 3  f o r H  a  t h e  a s  3«  25 c m ,  s c a l e ,  10  o f  a s  a  cm deep  d e a l  from  t h a t  t h e dyke,  would  t h e  (c)  though  expect  o f  b y  curve  w i t h  t h e dyke.  n o t a f f e c t e d  seen  Curves  o f  F i g s .  k e p t  d e a l s  i n d i c a t e  10^  cm a n d w i d t h s  t h e curve  over  i s  was  (5)  cm,  t h e g e o p h y s i c a l  a n d  even  20  o n  x  w i t h  cm a n d w i d t h s  t h e w i d t h  a r e e s s e n t i a l l y  f(b)  ¥f(a)  o n  5  i n  components  t h e dyke  The r e s u l t s  t h e neighborhood  • One would  curve  l  5  (h)  a p p r o x i m a t e l y  c a n be  v a l u e s ,  d i r e c t l y  H_  k  w i d t h .  i n c r e a s e d ,  the  o f  o f  cm,  f a u l t  c o n t r a s t  o f  shown  e x a c t l y  t h e neighborhood  dependent curve  15  n o t  t h e f i e l d  F i g u r e  depth  cm.  100 E  o f  v a r i e d .  i s  h  almost  t h e depth  dyke  i v i t y  dyke  c o i n c i d e d  w i d t h ,  f o r  cm, a n d  Curve  t h e b e h a v i o r  f u n c t i o n  H  3 ( a ) .  k  decrease  d e c r e a s e , F i g .  decrease  The e l e c t r i c  k  a n d  3 ( b ) *  t o  f i e l d ,  v e r y a s  120  1  — i — • — i — • — i — — r  •  1  -100  -80 -60  i  •  - 4 0 - 2 0  X  i C)  cm  i—"—r ' i • i ' i 20 40 60 8 0 100  >-  •>-  CP  3 - J  I  2 - |  O  X  If)  'J  1-  X ;—1—i—|—i—i—i—i—i—I— —l 1  1  I •' I  1  i  '  i ' i  o  X o <x> CD  X  i . i . i . -100 - 8 0 - 6 0  u  F i g u r e  k  L  K  E  x  (a)  " ^ ^ ^ - 4 0 -20  f o r t h e H  0 20 Y cm  40  p o l a r i z a t i o n  — i —1 0l 0—  60  80  w i t h  d=5  cm f o r  (1)w=5,- (-2)10, (3)15, ( )20y (5)25, (6)30, a n d (7)100 c m ; k  H  y  ,  f o r  H  z  (b)  a n d E  x  ( c )  (-1)w=0.2,' (2)1,  f o r t h e E  a n d  (3)5 c m  p o l a r i z a t i o n f o r a  w i t h  g r a p h i t e  d=29 c m ,  dyke.  12.1  shown  i n P i g . M + ( - c •)•,'•  p o i n t  o u t that-  f o r t h e v e r y  w o u l d  probably-  have  s e p a r a t i o n minimum more  d e a l s y  and H  H  f o r curve  R  i m a t e l y  o f  l i t t l e  some-  with,  v a l u e  o f E  w h i l e  the'maximum  v  curves  f o r curve  1  v a l u e  f r o m  o f  2 and 3  v  t h e c y l i n d e r  y  =  k  h a s  F i g u r e R/2 .  *+5 (3)  A l t h o u g h  R y  dyke  f o rt h e  ^ ( a ) t h a t  f o r a  i n t h e neighborhood  f o r a  f i e l d  dyke  k  o f  30a)»'  o f t h e  i s  q u i t e  approx-?-  b y comparing  o f F i g . -  curve  f o r curves  a n d 3  2  1  T h e maximum  i s a p p r o x i m a t e l y  5(b)  i t s  a n d  3  s h a l l o w  c a nb e s e e n  o f E  measurements  cm i n d i a m e t e r a n d  F i g *  t h a t  o f fig.  f o r  (2)  r  ••  3.  t h e e l e c t r i c  than  ' T h i s  Q  - T h e  c o r r e s p o n d  system.  f o r a  change  f o r t h e c y l i n d e r  Figo' ^ 5 ( h )  o f  probe  usedc  t h e c y l i n d e r .  change  - T h e b e h a v i o r  depth.  =  o f  c a nb e s e e n  do show  e q u a l  y  (-1)  t h e r a d i u s  i t  s u r f a c e  s h o u l d  t h e curve  s  p r o b a b l y  30»h  o u r c o o r d i n a t e  a l o n g  were  t h e r e s u l t s  c y l i n d e r  T h e upper  v e r y  t h e y  show  g r a p h i t e  i s  d i s c o n t i n u i t y .  o f  a n d h6  5  k  -1)  ' W e  s m a l l e r  v a l u e  p o l a r i z a t i o n ,  d i f f e r e n t  a  t o t h e minimum  showed  c y l i n d e r  i f  would  t r a v e r s e s  where  shape  w i d t h .  (curve  a n d 2  v e r t i c a l  w i t h  dyke  1  a t t h e 'o r i g i n  =- R ,  d i f f e r e n t  f o r curves  cm i n height0  c e n t e r  n a r r o w  dyke  d e t e c t o r  •'Figures-  7.6  w i t h  f i e l d  v a l u e s  a  a  changes  f o r t h e e l e c t r i c  c l o s e l y  a c r o s s  a l s o  o f  13.5  Fig.'  .X.  ^3(a)  8  i s about  0  '  Curve  Hv/H; z y  remains  ences  a n d E ^ / H y a r e g i v e n  r  The g i v e n  e s s e n t i a l l y  r e s u l t s  i n F i g . 6. L  1  zero  a l o n g  i n Figs•„  f o r t r a v e r s e s I n  *+5(c)  f o r F i g .  comparing  k  y  =  i s .n o t shown 0.  5Ca)'  a l o n g  -  • T h e phase  d i r e c t i o n a r e  f o r H  a n dH  y F i g .  k  6(a)  w i t h  those  l a b e l l e d  curve  3  d i f f e r s  ( c ) .  t h e x  t h e curves  s i n c e  i n F i g . 3(b).$ k  o f  ^ i t i s  122  r  i  0  20  i  i  »  40  i  i  60  [  »  80  0 X  F i g u r e  >+5,  Hy-j-H-  (a),  (e)...» a n d  cfr - c &  . f o r  c y l i n d e r  w i t h  d=y.6  (1) y = 0 ,  (2) R / 2  5  E  the  <3)  x  H  •( b ) .  i  1  - H  z  / H  and  R  cm.  R=30 , . 1 +  i  •  20  i  40  i  i  i  i  60  i  80  cm y  - ( e v H j ^ y  p o l a r i z a t i o n  cm,  •  cm  (d),  f o r  a  f o r  t r a v e r s e s  E ^ H y  g r a p h i t e along  123  0  20  40  60  80  0 Y  0  20  40  60  20  40  60  80  20  40  60  80  cm  80  0 Y cm  F i g u r e (e)  h6.  . h y  and  4> -0  c y l i n d e r  (1)  x=0,-  z  H y  w i t h  (-2)'  z  f o r  (a), t h e  d=7.6  R/2,  E  cm  and  x  E  (c),  E  p o l a r i z a t i o n  f o r  a  R=30.  f o r  t r a v e r s e s  (b),  and  (3)  R  H  cm.  z  / H  k  y  cm  x  / H  y  (d),  g r a p h i t e a l o n g  12 e v i d e n t  t h a t  the  f o r  the  dyke  d i s c o n t i n u i t y  the  c y l i n d e r  s i m i l a r o f  E  to  i s  dyke. imum  x  =  c u r v e s . (f).  by  of  The  the  E  phase  f o r  of  the  5  and  k  same k  i c a l  "scale  r i n g  dyke  R e s u l t s  f o r  x  they  s o l i d  g r a p h i t e  are  v e r y  d i f f e r e n c e s  are  shown  Y  0  ••.-  10  cm  ;  were  those  and  (1)  f o r  a t t a i n s  a  The  edge  b e h a v i o r  f o r  the  v e r y  as  v e r y  r e a c h i n g  f o r  a  i n  to  F i g s .  l a r g e  a  max-  t r a v e r s e  s i m i l a r  homogeneous  the  E  x  6(e)  and  d e p a r t u r e s  f r o m  k  c o n d u c t o r  s h e l l  and  h e i g h t  c y l i n d e r  i n  i n  w i d t h  maximum  k  to  almost  f o r  (3)  x  R  i n d i c a t e t h i s  v a l u e  =•  t h a t  H  and  d i s c u s s e d of  k  k  the  i n d i c a t e d  to  T  x  =  1  cm  the  H  the  a p p r o x i m a t e l y  shown f o r  r e s u l t s  ( )  =  x o f  than  q u i t e  e a r l i e r .  not  F i g .  b e h a v i o r  are  depth.  those  k  0.5-  k  R.  1  and  f o r  the  The  8 F i g -  H  r a t i o  the  f o r  s i m i l a r  The  F i g s .  geophys-  w h i l e  and  s h e l l  i n  the  i n  as  and  c o n d u c t i n g  are  same  R/2,  a  cm  t h i c k ,  used  On  10^  shows  7  cm  2  8.  d i r e c t i o n  c y l i n d r i c a l  f o r  dykes  x  <F i g u r e  x  7'6  the  (2)  and  7  c o r r e s p o n d  a l o n g be  the  and  and  curves  narrow  c o u l d  =0  f o r  as  F i g s .  x  (c)  d i f f e r e n t  c y l i n d e r .  a  the  a- c y l i n d r i c a l  c y l i n d e r .  r e s u l t s  q u i t e  of  t h a t  f o r  found  shows  7(a-)-  y  case  c y l i n d e r  shows  TT  s t r u c t u r e  a l o n g  k  0  z  d e s c r i b e d  t r a v e r s e s  ures  a p p r e c i a b l e , -  f o r  i s  c y l i n d e r  the  t r a v e r s e s  s i n c e  the  becomes  the  than  6(b)  k  i n d i c a t i n g  f o r  components  g r e a t e r  F i g .  curves  d i a m e t e r  t h i s 2  3 ( c ) ,  same  o f  1  f i e l d  l i n e .  a r e  6,  c o n s i d e r a b l y  ' C u r v e k  magnetic  / H x • y  Measurements of  the  near  -  the  broken  the  z  v a l u e  v a l u e s  i s  F i g . '  H '/H  O.35  0.  - The  The  the  o f  2  r a t i o  v a l u e  of  d i s c o n t i n u i t y .  curve  • The  along  enhancement  e s s e n t i a l l y ••  JL  k  H  i s s o l i d  to H  z  / H y  b e h a v i o r  125  I'  8  g x in  Hy  6  • —'  4  N  X_  >%  X  -  2 0  A1  2  t * i •  i  • H—* 6 _ 777WA O X  CD x LU  / t- — " ~ i • H—>  \ ' 1  1' 1  I  H 1  1  z  1  1  1  I  Ex  _fx  1/  4  o  Hy  "2  2  20  40  60 80  20  0  40 60 80  Y cm  1— —i— —I—'—I— —l—»" 1  20  0  F i g u r e i o n cm  k7'. f o r a  H  y  5  H  z  r  E  x  , - H  z  / H  60 80  y  ,  a n dE  Y  x  0  cm  / H  y  20  1  40 60 .80  f o rt h eE  g r a p h i t e  s h e l l  2  cm f o r t r a v e r s e s  along  (1)x=0,  c y l i n d r i c a l  a n d R=30A  40  1  c mt h i c k  p o l a r i z a t -  w i t h  d=7„6  a n d (2)x=R/2c m .  126  X.  Hy  1  H„  " ^ ^ - 2  4 -  x  " H-  If)  • tway/i *-R*  ^  2-  Hz ^  •  -  1  i  i • i  i  1  1  j  1  l  -  1 '1  I  I  1  1  10  I  E  >  8  o x o o>  6  <?  Vi  E  x  4  to LU  20  40  60  80  1—i—i—•—|—i—i— —r 1  0  20  40  60  80  Y  0 cm  20  r  1—  I  0  20  40  1  Y cm  F i g u r e i o n cm  <H  h&. f o r a  a n d  y  ,  ;  R" .  &  E  x  .  c y l i n d r i c a l  R=30.  L  H  z  40  60  I  1  80  1  60  / H , a n d E / H f o r t h e E y x y  g r a p h i t e  s h e l l  2  cm t h i c k  cm f o r t r a v e r s e s  along  (1)x=R<-1  ?  I  1  80  p o l a r i z a t w i t h  6=7.6  (2)x=R c m .  127 of  E ^ R y  except than and  i s  v e r y  t h a t  i t  the  was  to  / H  r a t i o  i n t e r f a c e be  as  f o r  of  l a r g e  a  c y c l e s / s e c . a  v e r t i c a l  the  depth  s k i n  f a u l t s  If  of on  than  i n t e r f a c e  f o r  i s  i n t e r f a c e ,  a  and  The  model  the  c u r v a t u r e  t h e  next  u s i n g ent  s l o p i n g t h i s  t y p i c a l  ocean  Caner  the  west  0.3  f o r  f r e q u e n c i e s  In  t h e i r  c o a s t  a  of i n  t h a t  a  l a r g e  expected the  neighborhood  e a r t h - s e a  be  c o u l d  of  0.3 by  l e s s  s i n c e  s h a l l o w  compared  w i t h  a  r e s u l t s  i n d i c a t e  that  the  i n  much  s m a l l e r  a  the  than  s t i l l  f o r  r e a l  a  a l s o  a f f e c t  v e r t i c a l  the  neighborhood s t a t i o n ,  r a t i o s , ,  the  ••  are  In  s t u d i e d  to  represrby  H  z  / H y ,  a p p r o x i m a t e l y  0.01  a l t h o u g h  from  t h a t  f i e l d s .  cones  be  of  r a t i o .  r e p o r t e d  amplitude to  e a r t h - s e a  i n d i c a t e  t r u n c a t e d  I s l a n d  s h a l l o w  s m a l l e r  Measurements  d i s t a n c e  the  i n t e r f a c e  c o n s i d e r a b l y  r a t h e r  and  at  r a t i o  e a r t h - s e a - i n t e r f a c e s  Vancouver  c o n s i d e r a b l e  very  the  be  i n d i c a t e  t h e ' r e c o r d i n g  are  t h a t  would  f l o o r .  the  s h e l l  amplitudes  and  c y l i n d e r  wedges  (1965)  f o r  was  the  (c),  R  be  ' Furthermore,  c o a s t l i n e  and  work,  should  r e s u l t  f o r  • The  =  appear  the  model  the  Lambert  c o a s t ,  would  c y l i n d e r  c y l i n d r i c a l  y  should  i n  i n t e r f a c e  g r a p h i t e  s h e l v i n g  would  should  f a u l t s .  measurements  machined  the  r a t i o  f o r  8  f a u l t ,  The  the  c y l i n d e r . k  r e l a t i v e l y  l a n d .  deep  s e c t i o n  i t  approximates  i s  s o l i d  c y l i n d e r .  f r e q u e n c i e s  the  of  F i g .  s o l i d  r a t i o  the  i n s i d e  s o l i d  i n  v e r t i c a l  sea  of  the  f o r  p o l a r i z a t i o n  the  dry  v a l u e  E  one  the  l a r g e r  the  f o r  f a u l t ,  depth  maximum  the  1  t h a t  r e s u l t s ,  deep  as  i s  shown  f o r  these  to  over  r a t i o s  those  From H  r a t i o  d i r e c t l y  amplitude  s i m i l a r  s i m i l a r  c y c l e s / s e c - . l o c a t e d  c o n t i n e n t a l  at  the shelf,.  128 and  hence  w e l l  One  c o u l d  expect  e n t a l  a  the  n e t i c  somewhat  s t e e p e r  l a r g e r  r e s u l t s  i n d i c a t e  w i t h  r e s p e c t  to  r o l e  i n  • Of  i n d i c a t e  e a r t h - s e a  r a t i o  n e a r e r  the  e l e c t r i c  i n  h i s  a n a l y t i c a l  the'  f i e l d  f o r  i s  y  r a t i o  . A l t h o u g h ments  h i s  v a l u e  i n d i c a t e ,  s i m i l a r  to  the  • In  the  i n t e r f a c e .  the  c o n t i n -  to  be  the  p o l a r i z a t i o n  s t r u c t u r e n e t i c  v e r y  f o r  f i e l d s ,  c o n t i n u i t i e s  the  E  to  r a t h e r  the  o t h e r  f o r  the  E  f a u l t .  2.6  the  the  model  p o l a r i z a t i o n  f a u l t The  at  L  e l e c t r o m a g -  (1962),  ' Weaver  v e r t i c a l  h i g h e r h i s  than  computed  from of  the the  changes  problem,  maximum  the  v a l u e  i n t e r f a c e .  hand  model  curve  f i e l d  changes  b e h a v i o r  i s  s t r u c t u r e  of  i s  more  s e n s i t i v e  p o l a r i z a t i o n  than  f o r  ?  v e r y  experiment.  s h a l l o w to  measure-  i s  e l e c t r i c  i n  > The  the  model  i n s e n s i t i v e  p o l a r i z a t i o n .  on  the  f o r  the  an  y  b e h a v i o r  s e n s i t i v e  t h a t  was  o b t a i n e d  the  and  of  the  f a c t  p o l a r i z a t i o n  p l a y s  of  c o n s t a n t .  T  z  nature  g e n e r a l ,  was Hv/H _  the  b e h a v i o r  the  somewhat  r e s u l t s  found H  i s  to  of  H  t h a t  c o n s t a n t  p a r a l l e l  t h a t  the  i s  not  treatment  assumption  o b t a i n e d  H  a l s o  d i s c o n t i n u i t y  the  i n t e r e s t  t h a t  of  the  d e t e r m i n i n g  v a r i a t i o n s .  r e s u l t s  he  the  model  f i e l d  important  made  f r o m  s h e l f . • The  of  removed  the  i n  the to  H  f o r  s h a l l o w magd i s -  p o l a r i z -  a t i o n . (c)  i s  -  the  Caner  C o a s t l i n e  S t  Among  problems  the  c o a s t l i n e 1965)  ruetures  anomaly.  i n d i c a t e  t h a t  of  c o n t i n u i n g ,  ' E x p e r i m e n t a l the  enhancement  i n t e r e s t r e s u l t s of  the  i n  geophysics  -(Lambert v e r t i c a l  and  129 magnetic be  a c c o u n t e d  Lambert ment to  f i e l d  component  f o r o n  a n d C a n e r  n e a r  (1965)  t h e c o a s t l i n e  g r e a t e r  depths,  zone  i n t e r f a c e .  • Schmucker  anomaly  P a c i f i c  Ocean  h i g h l y some  d u c t i v i t y i n  t h e mantle  (196 ) k  anomalies  t o  s t r u c t u r e s ,  s t e p  model  r e p r e s e n t i n g  zone  w i t h i n  and  form  o f  manner, by  s e c t i o n  ( s l o p i n g  l i n i n g  e l e c t r i c  o f  o f  t h e  w i t h i n  t h e  He  1  a t t r i b u t e s  i n  c o n -  c o n d u c t i v -  combinations  c o n d u c t i v i t y  o f  t h e  t h e deep  a  h e  o f  inhomoc o n s i d e r s  h i g h l y  a  model s c a l e d  t h e f l o o r  o f t h a t  study  a  c o n d u c t i n g  a 5-cm  square  c r o s s  t h e edge  ends  o f  t h e source)  a n d e a r t h l a y e r  o f  e f f e c t s  e a r t h - s e a  s t r u c t u r e s ,  e a r l i e r , below,  g r a p h i t e  s e c t i o n .  t h e tank w i t h  o f  mantle  - A s was d i s c u s s e d  w i t h  t h e v e r t i c a l o f  w i t h  t h e s e .  rods  was found  f i e l d  t h e u p w e l l i n g  o f  o f  i n h o m o g e n e i t i e s  i n t e r f a c e s ) ,  was l i n e d  machined i t  i n  h i g h l y  C a l i f o r n i a  e f f e c t  m a n t l e .  a n d some-to  l y i n g  d e a l s  t h e e f f e c t s  t h e tank  t h e  i n d u c t i o n  l y i n g  a  a t  m a n t l e .  c o m b i n a t i o n s  m i n i m i z e  o f  t h e d i f f e r e n c e s  a n d deep  ' F o r t h e deep  i n t e r f a c e s -  t h e edge  i n h o m o g e n e i t i e s t o  i s n o t due  t h e s e a s i d e  t h e upper  l a y e r s ,  geneities'.  t h e  o f  some  i n t e r m e d i a t e ,  This,  o n  enhance-  i n h o m o g e n e i t i e s  h a s d e s c r i b e d  due t o  r e g i o n s  f r e q u e n c i e s t o  cannot  s e a a l o n e .  t h e observed  t h e u p w e l l i n g  a n d i t s effect" upon  t h e s u r f a c e  s u r f a c e ,  t h a t  b u t r a t h e r t o  i n t e r f a c e  t h e c o n d u c t i n g  f o r t h e l o w e r  a s b e i n g  c o n d u c t i n g  i n l a n d  i t i e s  w i t h i n  o f  suggest  namely,  c o n d u c t i n g  c o a s t a l  a n e a r t h - s e a  t h e b a s i s  t h e e a r t h - s e a - i n t e r f a c e  much  of  n e a r  - I n  c o u l d  be  t o  t h e  i n t h e t h e  t o  form  same  reduced  ( p e r p e n d i c u l a r  g r a p h i t e  bottom  a  t o t h e g r a p h i t e  130 w a l l .  T h i s  has  the  e f f e c t  of  making  tank  e x t e n t .  The  e l e c t r i c  f i e l d  i n  r i g h t  to  the  g r a p h i t e  w a l l ,  whereas  w i t h o u t  f i e l d  begins  cm  the  r a p i d l y  a l l y  as  i t  i s  e a r l i e r  below  the  s o u r c e  the  p o s i t i o n  the  y - d i r e c t i o n tank,  In  v e r t i c a l  v e r t i c a l had  a  the  c e n t e r  of  the  model  o r d e r  to and  as  the  a t  tank,  same  was  turned  w i t h  the  e l e c t r i c  f i e l d ,  and  t h a t  appeared  n e a r  the  about  tank  o r  the one 2  m  f o r  i n now  e l e c t r i c  f a l l s  o f f  e i t h e r  by  i t  i s  a v o i d i n g the  s e t  minimum  l o n g o f f  i n  end  of  the  by  1.7  m  tank. was  f o r  v e r t i c a l  the  c e n t r a l  angle  of  the  change  l o c a t e d to  the  n e a r  l o c a t e r e g i o n .  In  l a r g e  s t r u c t -  r e v e r s a l  r e g i o n ,  p e r p e n d i c u l a r r e s p e c t magnetic  t h i s  a v a i l a b l e  a c r o s s  phase  not  phase  w i t h  the  n o n - s y m m e t r i c a l  of  dimension  i n  the  r e v e r s a l  some  - In  of  T h i s  phase  the  t h i s  way  phase  d e s i r a b l e  c e n t e r  the  s i d e  the  d i m e n s i o n  • F o r  s t r u c t u r e s  f o r  l o n g  h a l f  180°.  t h i s  space  the  s y m m e t r i c -  t r a v e r s e s  p o i n t s  l a r g e  near  time  tank  so  and  s o u r c e .  measurements  and  too  the  source  the  l o c a t e d  w i t h  minimum  changes  wedges  a t on  t h i s  a p p r e c i a b l e  the  l a r g e r  i s i u n i f o r m  i t  edge  was  the  f i e l d  v a l u e  making  s t r u c t u r e s have  of  magnetic  f i e l d  when  such  f i e l d  through  tank  c u r r e n t )  s y m m e t r i c a l l y  magnetic  s t r u c t u r e s  x - d i r e c t i o n  from  the  (sheet  minimum  p a s s i n g  troublesome  work  e l e c t r i c  i n c r e a s i n g  l i n e .  30  seem  approached.  the  to  u r e s  decrease  • In  p a r a l l e l  i s  to  the  the  way  f o r  a  to  to  the  f i e l d  r e g i o n  making  of  measure^-  ments. G r a p h i t e c a t e d  cone  p l a c e d  s t r u c t u r e s i n  the  i n  s a l t  the  form  s o l u t i o n  of  wedges  were  used  and to  a  t r u n -  r e p r e s e n t  131 oceans. depth  • L a r g e  i n t h e tank  h i g h l y  s c a l i n g  a r e t a k e n  p h y s i c a l  i n g  w i t h  d / d '  =  3  o f  a n df  /  were  g e o p h y s i c a l  problem.  0.3,  c o a s t l i n e - m a n t l e  1/(5  =  x  k  a n d  a n d  f o r t h e  f a c t o r s  ' F i g u r e s  i n v o l v e  10  k  geo-  f o r t h e t o  9  s c a l i n g  l i n e a r d e a l -  5? k  f a c t o r s  f r e q u e n c i e s  f  used,  L  correspond  c y c l e s / s e c  s c a l i n g  1oVo.O .  =  k  c o r r e s p o n d  0.000  c y c l e s / s e c ,  t o 6 , § , d e a l i n g  55  i n v o l v e /  J  a n d 0.01  •F i g u r e s  used  (77)•  f o r a l l measure-  those  T h e model  0.03,  a n d f  e q u a t i o n  "3  problem,  f r e q u e n c i e s  0.00 , 0.0012,  u s e d .  .  10^/1  0.1,  10^)  than  o f  mantle.  s a t i s f y  s c a l i n g  0  o f  model  =  LL  f r e q u e n c i e s  d / d '  o f  a p p r o p r i a t e  t h e u p w e l l i n g  s t r u c t u r e s  i n t e r f a c e ,  f  t h e  t h e e a r t h ' s  i n v o l v e d  Two s e t s  a t  r e p r e s e n t  t o b e 1Cr g r e a t e r  10 , 1 0 , 3 x 1 0 ° ,  x  t o  t h e model  t h e e a r t h - s e a  1/10^  p l a c e d  w i t h i n  a n d f r e q u e n c y  LL  =  used  f a c t o r s  problem.  dimensions  b l o c k s  zones  c o n d u c t i v i t i e s  ments  f  were  c o n d u c t i n g The  The  g r a p h i t e  i n t h e  w i t h t h e  f a c t o r s F o r t h i s  t o f r e q u e n c i e s  c y c l e s / s e c  t o  i n t h e  case t h e  0.012,  o f  g e o p h y s i c a l  problem. • F i g u r e s g r a p h i t e i o n . the  cone  k  9  w i t h  - T h e d i a m e t e r d i a m e t e r  g r a p h i t e  f r o m  s t r u c t u r e  o f  of  km f r o m  d e a l  i t s base o f  zero  t h e base  a  depth  t o  a t  a n i n v e r t e d  t r u n c a t e d  t h e s u r f a c e  o f  o f  w a s 30A  t h e cone  e n d 5  c m .  t h e t r u n c a t e d  c i r c u l a r  t h e shore.  p a r a l l e l  w i t h  a t  t h e t r u n c a t e d  r e p r e s e n t s  from  t r a v e r s e s  51  t h e base  s l o p i n g 12.7  t o  s e a 30.h  t h e shore  a n d p e r p e n d i c u l a r  t o  s o l u t -  c m ,a n d  T h e t h i c k n e s s e n d w a s 2.5 km i n  t o 2.5  •Measurements  t h e s a l t  c m .  T h e  diameter,  km a t a  were  o f t h e  made  d i s t a n c e b o t h  t h e e l e c t r i c  f o r  f i e l d  132 LL  of 3  the x  s o u r c e . and  10^  The  f r e q u e n c i e s  c y c l e s / s e c .  10-^  used  were  - F i g u r e s  k  f  =  9(a)  and  and  r e s p e c t i v e l y , f o r  3  x  and  F i g .  f i e l d t h a t  the  of  w i t h  s o u r c e .  the  o f  the  cone.  s i d e  of  d e c r e a s i n g  s i d e  of  the  is- a l s o  f i e l d .  - To  i n d u c i n g  the  on  e i t h e r  the  cone.  hand,  d i d  edges  of  cone  t h a t  seen  F i g s .  i n t e r f a c e  a n g l e  xlr f o r  decreases  L  9  f o r the  whereas  n a t u r e 50,'  of E„  cone the  a  changes  i n  d e c r e a s e s .  • On  the  a  an  of  was  cone  was  of  a t  R" ,  on  of  z  on  b a s i s  of  on  the on  the  a t  i s a  source  s i d e s  and  as  n e a r  near  '  change change  the  the  T h i s As near i n  phase  f r e q u e n c y  d e c r e a s e  0„  the  o t h e r  i m p o r t a n t .  The  of  d e c r e a s -  the  l a r g e  the  the  p o s i t i o n .  i n c r e a s e s T r  the  phase  enhancement  s t u d i e d .  $  of  f i e l d  shape  both  the  v a r i o u s  l o c a t e d  b o t h  undergoes  50  a f f e c t  of  9  e l e c t r i c  the  on  source  L  and  k9  d e c r e a s e  the  the  enhancement  i n d u c i n g  somewhat  F i g .  d e c r e a s e  p l a c e d  the  the  n o n - u n i f o r m i t y  y f r e q u e n c y  to  does  asymmetry  e f f e c t  f i e l d  B o t h  n o n - u n i f o r m i t y  f r e q u e n c y  e l e c t r i c  and  ,  measurements  neighborhood  shows  p o s i t i o n ,  depend  each  the  g e n e r a l  w i t h  and  The  show  the  F i g s .  f i e l d  h o r i z o n t a l  showed  the  d i d  the  the  H-  change  i n d i c a t e s f r o m  w i t h  A l t h o u g h  the  < When  from  the  f i e l d  the  t r u n c a t e d  tank.  i n  example,  to  show  p e r p e n d i c u l a r  source  f i e l d .  examine  s i d e ,  not  the  10  c y c l e s / s e c  10  r e s p e c t i v e l y .  components f o r  (b)  apparent  h o r i z o n t a l  the  p o s i t i o n ,  i n g  of  - H ,  f u r t h e r  i n  i s  a t t r i b u t e d  f i e l d ,  l o c a t i o n s  the  - I t  i n c r e a s i n g  curves  and  50(a)  ,  LL  and  3x10  t r a v e r s e s  f i e l d  edge  f o r  c y c l e s / s e c  n o n - u n i f o r m i t y  b e h a v i o r  c e n t r a l  angles F i g s .  10^  d e a l  50  t h e  w h i l e  and  10^  of  phase  10  (b)  Li. a m p l i t u d e s  x  3  LL  as  the  z the  r e s u l t s  g i v e n  i n  133  F i g u r e o v e r and  k  9. an  • The  amplitudes  i n v e r t e d  f r e q u e n c i e s  and  t r u n c a t e d (a)  3-X-10"", 1  phase  cone (b)  f o r  10^  angles the  E  f o r  t r a v e r s e s  p o l a r i z a t i o n  c y c l e s / s e c .  13^  -p-,—|—i—|—.—|—i |—i 20 4 0 6 0 8 0 100  w  —i—r-1—|—i—i—i—j i—f— 2 0 4 0 6 0 8 0 100  Y cm F i g u r e over and  50.  • T h eamplitudes  a n i n v e r t e d f r e q u e n c i e s  a n dp h a s e  t r u n c a t e d ( a )  3x10^,  cone ( b )  angles  f o r t h eE  10^  f o r t r a v e r s e s p o l a r i z a t i o n  c y c l e s / s e c .  135 F i g s .  k  and  9  amplitudes g r a p h i t e  10  are  cone  i n t e r f a c e  i t  50  ir„,  however,  the  i n d i c a t e  s l o p i n g  to  and  H  borhood a b l e  a f o r  of  f o r  F i g u r e t r a v e r s e s  a  of  f o r  h a r d l y  l a r g e  t h a t  u n t i l  t h a t  i s  km  sea  would f i e l d  to  the  the  l o w 30.  v e r y  e l e c t r i c  km  k  l o w  a l l .  i n  v e r y  and  f i e l d  the as E  and  f r e q u e n c i e s .  the  have  a  and  the  and  e f f e c t  i n  phase  of  The  diameter  l i t t l e  i t - would  a m p l i t u d e s  near  as  a t  c y c l e s / s e c  0.1  f i e l d  t r u n c a t e d  f r e q u e n c i e s  of  p a r a l l e l  of  have  f r e q u e n c i e s the  magnetic  p o i n t s  a t  a l t h o u g h  g i v e s  as  f r e q u e n c i e s  c y c l e s / s e c ,  51  f a r  o b s e r v a b l e  changes  c i r c u l a r  2.5  as  presence  e l e c t r o m a g n e t i c  0.01  e f f e c t  the  and  cone  depth  t h a t  o b s e r v a b l e  undergo  r e s u l t s  H  not  reached,  c y c l e s / s e c  3  apparent  concerned, i s  are  i s  on  n e i g h c o n s i d e r -  h i g h e r . angles  f o r  s o u r c e .  F i g u r e  LL  g i v e s  51(a)  the  r e s u l t s  f o r  10  J  c y c l e s / s e c .  x  10  3  c y c l e s / s e c  3  f o r  x  3  Measurements but  are  n o t  c y c l e s / s e c  10  were  shown  a l s o  h e r e .  and  made H  but  no  goes  a  o v e r  the  cone  change  f o r  a  g r a d u a l  decreases i s  H  the  f r e q u e n c y of  the  • F o r  10  i n t e r f a c e a  the  presence  E  a t  the  i n t e r f a c e  r i g h t  f r e q u e n c y  d e c r e a s e s . cone,  - B o t h a r e  and  Q  Z  h i g h l y  ty  i n  <t>_ d e c r e a s e s  w i t h  decrease  change  i n  ty  i n c r e a s e s  w i t h  a  r e s u l t s  o f  F i g .  51  as  w e l l  as  of  x  the  i n  those  F i g s .  a  s m a l l  u n d e r -  approached, 10  then  c y c l e s / s e c ,  3  cone.  The  as  e n -  the  neighborhood  f r e q u e n c y i n  of  H_  dependent.  d e c r e a s e  and  10  c y c l e s / s e c ,  10  i n c r e a s e s i n  ,  of the  frequency  change  3  i s  frequency  by  .A.  of  51(b)  LL  c y c l e s / s e c .  3  a f f e c t e d  o f  t r u n c a t e d  as  cone.  hancement  the  a  f r e q u e n c y  i n c r e a s e  over  h a r d l y  Zi.  f o r  f o r  shows 7  i n c r e a s e  F i g .  • The w h i l e  frequency. k9  of  and  the The  50  136  10  H  'O  V  X  200  CD  i— —i— —i—•—r 1  o  X 00  1  16  -M-  80  OJ  40 'E <*>  0  X 00  -40  'o '> LU  M  'Q x  2  S  I  xT"  20  40  E  »»  - i — I — i — i — r  60  80  CD ro  (a)  I  i X  I  20  cm  i—|—i—|—i  40  60  |—i—r—  80  100  200H,  160  • i •—r  i—<—r  N  x  ^UaJS*  rji  'O  E  120  16  5-12  e o  8  X O *"">< LU  E i — | — — i — r * H — I — i — I — i  20  Figure  40  60  80  100  51 »• •' The a m p l i t u d e s  o v e r an I n v e r t e d  X cm  and phase  ^Uaf ,  40  angles  |  •  60  for  I  (b)  |  80  -  100  traverses  t r u n c a t e d cone f o r t h e H p o l a r i z a t i o n k  and f r e q u e n c i e s  20  |  (a)  3x10  (b)  10  3 J  cycles/sec.  137 i n d i c a t e t h a t the v e r t i c a l magnetic f i e l d  i s l i t t l e affected  by the presence o f t h i s model sea f o r f r e q u e n c i e s o f c y c l e s / s e c , but i s c o n s i d e r a b l y a f f e c t e d a t h i g h e r  0.01  frequencies.  The h o r i z o n t a l magnetic f i e l d on the o t h e r hand, f o r t r a v e r s e s along a diameter i n the d i r e c t i o n o f the e l e c t r i c f i e l d , i s e s s e n t i a l l y u n a f f e c t e d f o r the frequency  range s t u d i e d . • The  h o r i z o n t a l e l e c t r i c f i e l d i s much a f f e c t e d by the presence of the model sea a t a l l f r e q u e n c i e s . - To f u r t h e r study  the e f f e c t o f the earth-sea  f a c e a g r a p h i t e wedge s l o p i n g from 0.1  cm to 2.5  h o r i z o n t a l d i s t a n c e o f 50 cm w i t h a constant t h i s was used to represent  inter-  cm i n a  t h i c k n e s s beyond  the s h e l v i n g ocean f l o o r . ' The •  width o f the wedge was 60 cm, - This' wedge, w i t h the plane s u r f a c e a t the s u r f a c e o f the s a l t s o l u t i o n and the s l o p i n g s u r f a c e submerged, was a s c a l e d model o f the ocean on the west coast o f Vancouver I s l a n d ( T o f l n o a r e a ) . p a r t o f the wedge represented begins  the c o n t i n e n t a l slope which  about 25 km from the shore and f a l l s from a depth o f  abouti.*0.1 50 km.  The s l o p i n g  km to  2,5  km i n a h o r i z o n t a l d i s t a n c e o f about  The depth o f the ocean beyond the c o n t i n e n t a l slope  i s about 2.5 km.  The g r a p h i t e wedge, which i s a model o f  the ocean, d i d not i n c l u d e the f i r s t 25 km o f the ocean tinental shelf).  A model o f the c o n t i n e n t a l s h e l f would  r e q u i r e a very t h i n sheet o f g r a p h i t e shallow water) extending wedge.  (con-  ( r e p r e s e n t i n g the very  25 cm beyond the sharp edge o f the  138 Measurements a t  T o f i n o  i s  near  s l o p e  have  been  t h e c o a s t  i s about  e r a b l e f i e l d  made  k m .  25  o f  a t T o f i n o  measurements  t h e n a t u r a l b y Lambert  a n dhence  enhancement r a t i o  o f  magnetic  above  c a na i d i n s t u d y i n g  i n d i c a t e d  t o h o r i z o n t a l  t h e v a l u e  T o f i n o  t o t h e c o n t i n e n t a l  measurements  t h e v e r t i c a l  v a r i a t i o n s  01 965)•  a n dCaner  t h e d i s t a n c e  T h e i r  f i e l d  f u r t h e r  t h e e f f e c t  a  c o n s i d -  magnetic  i n l a n d .  o f  a  Model  s e a - l a n d  i n t e r f a c e . F i g u r e s t r a v e r s e s  over  corresponds  of  E  (wedge  a n dF i g .  p e r p e n d i c u l a r  i v e l y  52(a),  5  ( b ) , 53(a),  t h a t  52  a n d 53  f i e l d g i v e ,  3  x  a  d e a l  o f  t h e  s o u r c e ) . r e s p e c t -  c y c l e s / s e c .  J  a n dmagnetic  f i e l d  (wedge  t h e r e s u l t s 10  l i n e w i t h  t o t h e e l e c t r i c  t h e H p o l a r i z a t i o n  f o r  t h i s  F i g u r e s  10  t h e e l e c t r i c  problem  a n d s e aa l o n g  a n d (b)  3 x 1 0 ,  made  o n l a n d  p a r a l l e l  w i t h  k  measurements  t h e g e o p h y s i c a l  made  edge  w i t h  t o t h e e l e c t r i c  f o r f r e q u e n c i e s  apparent  I n  d e a l  t o t h e c o a s t l i n e .  p o l a r i z a t i o n  F i g u r e s  i s  t h e wedge.  t h e s o u r c e ) ,  edge  a n d 5^  53  t o measurements  p e r p e n d i c u l a r the  52,  f i e l d s  I t  a r e a f f e c t e d LL  by  t h e g r a p h i t e  Hy  a n dH  show  z  d e c r e a s i n g s l i g h t l y  wedge.  c o n s i d e r a b l e  a s t h e wedge  over  o f F i g s .  wedge  i s somewhat  source t h e n  f i e l d .  f a l l s  l o c a t i o n s  H  9  10  change  near  a n d 50)  cm f r o m  c y c l e s / s e c ,  10  t h e wedge  w i t h H y  i n c r e a s i n g  o u t e a r l i e r o f H  ( i nt h e  n e a r  o n t h e n o n - u n i f o r m i t y  s h a r p l y s m a l l  x  3  t h e b e h a v i o r  dependent  t o v e r y  o f  a n d then  A s w a sp o i n t e d  i n c r e a s e s  z  r a p i d l y beyond  k  f r e q u e n c y  i s approached  t h e wedge.  d i s c u s s i o n edge  F o r a  a s t h e wedge  v a l u e s  t h e wedge  over  edge  i s  t h e o f t h e  approached  t h e wedge.  F o r  H__ a n d H _ s h o w n o y  z  139  - i — T — | — i — | — i — | — i — |  20  40  60  80  100  1—|—i—i—i—|—i—|—i—r vy  Y cm  F i g u r e over  a  ^ . Ca)'  wedge  f o r  100  t h e E  Ycm  ,  (b)  1(T  20  a n d phase-  p o l a r i z a t i o n  h  LL  3x10  80  T h e . a m p l i t u d e s  52-  U'.  60  60  1  1  40  40  80  100  —•—i—'—i— —i— —r  -i—•—i— —i—•—i—•—i—•  20  20  c y c l e s / s e c .  1  40  60  angles  f o r  a n d  80  100  t r a v e r s e s  f r e q u e n c i e s  1U0  i— —i— —i—'—i—•—i— 1  20  1  —•—i— —i— —i—'—i— —r 1  1  40 60 80  100  Y cm  1  1  2 0 4 0 6 0 8 0 100  / /  %  "~ ~ Ls'  /  ~  ~~  T  H -I  F i g u r e over (a)  1  20  1  1  1  1  1  1  T  1  " T h ea m p l i t u d e s  53-  a wedge  3x10 , 3  1  4 0 6 0 8 0 100  f o rt h eE  ( h )  10  3  Ycm  p o l a r i z a t i o n  c y c l e s / s e c .  (b)  20  a n d phase  y  4 0 6 0 8 0 100  angles  f o r t r a v e r s e s  a n d f r e q u e n c i e s  11 k  20  F i g u r e over (a)  The  5*+. a  40  wedge  3*1o\  (b)  60  80  I00  amplitudes f o r 10  the 3  H  and  X  cm  20  phase  p o l a r i z a t i o n  c y c l e s / s e c .  40  60  angles  f o r  and  80  I00  t r a v e r s e s  f r e q u e n c i e s  -|!+2 a p p r e c i a b l e change due to the wedge. 0  However, the phase  angle  i s a f f e c t e d by the wedge a t l o c a t i o n s as f a r as 30 cm from  the wedge edge. • F o r the H p o l a r i z a t i o n , as shown i n F i g . Hy. a g a i n i n c r e a s e s over the wedge. cycles/sec H  y  F o r a frequency  5  k 5  o f 3 x 10  i s a f f e c t e d by the wedge a t l o c a t i o n s as f a r as  30 cm from the edge.  H  z  begins  to i n c r e a s e a t a d i s t a n c e  s l i g h t l y g r e a t e r than 10 cm from the edge, reaches a maximum about 1 cm beyond the edge, and then f a l l s at  to v e r y s m a l l  a d i s t a n c e o f about 15 cm beyond the edge.  E  values  begins to  r i s e r a p i d l y 20 cm from the edge, reaches a maximum value d i r e c t l y over the edge o f the wedge, and then f a l l s small values ^  x  1 cm beyond the edge.  The phase angles  to v e r y <* and  a r e e s s e n t i a l l y u n a f f e c t e d by the wedge as the edge i s  approached, they then change r a p i d l y r i g h t a t the', edge. As ;  can be seen from F i g s . 52 and 53 the magnetic f i e l d are l e s s a f f e c t e d by the wedge as the frequency 10^ c y c l e s / s e c , which corresponds to 0.01  components  decreases.  c y c l e s / s e c i n the  g e o p h y s i c a l s c a l e , the wedge has o n l y a s m a l l e f f e c t on H H_.  At  I t i s .apparent from._the—results T o r t h i s model  or  sea-land  i n t e r f a c e t h a t the. enhancement o f the amplitude r a t i o s o f the v e r t i c a l to h o r i z o n t a l magnetic f i e l d observed i n c o a s t a l regions cannot be a t t r i b u t e d to the earth-seal i n t e r f a c e F o r f r e q u e n c i e s i n the neighborhood o f 0.01  alone.  c ycles/seC' the  sea should have o n l y a s m a l l e f f e c t f o r a l l l o c a t i o n s .  At  higher frequencies  the s e a - e a r t h i n t e r f a c e should have a  g r e a t e r e f f e c t on H  y  and H  z  but o n l y f o r l o c a t i o n s near the  c o n t i n e n t a l s l o p e . • I n most cases l o c a t i o n s on l a n d would be  13 k  too-  d i s t a n t  from  t h e c o n t i n e n t a l  slope  f o r H„  a n d H„ • z  y much be  a f f e c t e d .  expected  slope  a )  lower  o f  a  t h i n n e r  c o n d u c t i n g earth S' l i n e s .  t h a t than  i n  K  In u s i n g  s u r f a c e the  o f  a  g r a p h i t e t h e s a l t  i n v a r i o u s  below. e r e s t  S i n c e t o  i n  study  d i s c u s s e d  i n  under  s e a l i n g  f a c t o r s  study  a t  p o s i t i o n s t h i s  i s  be much  c o n d u c t i n g  upper  e a r t h ' s much  • H i g h l y  n e a r e r  a n d near  due t o  t h e  f o r t h e  a n d t h e  c o a s t a l  t h e  c o a s t -  anomalies t h e edge  m a t e r i a l  t h e u p w e l l i n g a t  i n e f f e c t  i n t h e  d i s t a n c e  • A  g r a p h i t e  wedge  ;  t o  i t  lower  t h e s c a l i n g  dimensions, r e s p e c t i v e l y  a n d t h e d / d  ;  below  f  •f  t h e  wedge was  t h e g r a p h i t e  problem  f r e q u e n c i e s  modelled  r e p r e s e n t i n g  T h e g r a p h i t e  r e s p e c t  measurements,  were  was  s u i t a b l e  w i t h  o f  mantle  a  c o a s t l i n e - m a n t l e  The l i n e a r used  important  c r u s t  o f  under  c o n d u c t i n g  t h e oceans  t h e s u r f a c e .  t h e b e h a v i o r  ;  o f  t h e e f f e c t  t h e c o n t i n e n t s .  a s being  s o l u t i o n .  t h e wedge  m o d i f i e d .  c o n t i n e n t a l  s t e p .  b l o c k s  s e a was suspended  p l a c e d  were  o f  t h e p r e s e n t  l a r g e  however  t h e mantle  h i g h l y  may hence  v a r i a t i o n s  t h e form  o f  h a s d e s c r i b e d  (196 )  f i e l d  w i t h i n  t h e ocean  under  t h e s e a a n d t h e u p w e l l i n g  mantle  t h e  f u r t h e r  t h e e a r t h ' s  t h e mantle  f o r r e g i o n s  • Schmucker  magnetic  c o u l d  from  p a r t i c u l a r l y  p e n e t r a t e  known  i n  s u r f a c e  1  zone  become  t h e ocean  zones  i n  d i s t a n c e s  - The u p w e l l i n g  w h i c h  i s w e l l  under  s h i f t s  problem  c o n d u c t i n g  should  f r e q u e n c i e s - I t  l a r g e  t h e s e a - c o a s t  m a t e r i a l  c r u s t .  phase  be  0  w a s modelled„  mantle  the  r e l a t i v e l y  study  u p w e l l i n g  ocean  of  a t  ( F i g . 52 To  the  • S i g n i f i c a n t  t o  step  i s  o f i n t ^  than  those  f a e t o r s  frequency  4^^^~4#^--and  1¥+ f/f  = 1 0 ^ / O . O . • W i t h - t h e s e f a c t o r s t h e wedge u s e d h e r e  1  to  k  r e p r e s e n t t h e s e a was one f i f t h t h e s i z e o f t h e one u s e d e a r l i e r . - The wedge s l o p e d t o 0.5  cm t h i c k n e s s  d i s t a n c e o f 10 cm a n d h a d a c o n s t a n t b e y o n d . - The 0.5 2.5  cm t h i c k n e s s  km o c e a n d e p t h .  Large  in a horizontal  thickness  o f 0.5  cm  of graphite represented  graphite blocks  (1 f o o t  the  cubes)  were s t a c k e d t o r e p r e s e n t c o n d u c t i n g zones w i t h i n the m a n t l e . The t o p f l a t  s u r f a c e o f t h e a s s e m b l e d g r a p h i t e b l o c k was  3 cm b e l o w t h e s u r f a c e o f represents  the s a l t s o l u t i o n .  This  depth  a d e p t h o f 15 km i n t h e g e o p h y s i c a l p r o b l e m .  d e p t h o f w a t e r between the upper s u r f a c e of the  The  1  conducting  b l o c k a n d t h e l o w e r s u r f a c e o f t h e f l a t p a r t o f t h e wedge was 2.5  cm.  T h e s t e p - h e i g h t was 61 cm. k  k  quene-ies u s e d 3 x 10 , 10 correspond  The m o d e l f r e -  o  o  , 3 x 10 , a n d TO-*  cycles/see  t o f r e q u e n c i e s o f 0.012, 0.00k, 0.0012, a n d  0.000*+ c y c l e s / s e c  i n the geophysical problem.  The  c u r r e n t was k e p t a t t h e o r i g i n a l p o s i t i o n , 1.25 s u r f a c e of the s a l t Figure for  traverses  parallel  55(a)  m above the .  solution. shows t h e a m p l i t u d e s and p h a s e  angles  o v e r t h e wedge w i t h t h e wedge and b l o c k  to the e l e c t r i c  f i e l d of the source k  f o r a m o d e l f r e q u e n c y o f 3 x 10 wedge e x t e n d s  sheet  (E p o l a r i z a t i o n )  cycles/sec.  10 cm b e y o n d t h e b l o c k e d g e .  p h y s i c a l problem t h i s would correspond  edges  The edge o f In  the  to the ocean  the  geoextending  50 km b e y o n d t h e edge o f t h e c o n d u c t i n g m a n t l e . •• F i g u r e 55(D)  gives  the r e s u l t s  f o r t h e wedge (-1)  s e p a r a t e l y . - In comparing the curves  and the b l o c k  of Fig.  55(a)  with  (2) those  i 5 k  20  40  60  i—j—r—r—i—i—i—j—»—j—i  20  F i g u r e  -55.  ;  40  60  80  I00  80  100  T h e a m p l i t u d e s  p o l a r i z a t i o n  a n d  f=3x1cA  (a)-  t h e wedge  e x t e n d i n g  Cb)  t h e wedge  a l o n e  (-1),  Y cm  40  60  80  I00  • — i — i — i — j — i — r — B — i — > — j —  20  K/  a n d phase  angles  c y c l e s / s e c 10  20  60  t h e b l o c k  a l o n e  8 0 100  f o r t h e E  f o r t r a v e r s e s  cm beyond  t h e b l o c k  40  (-2).  over  edge,  a n d  14-6  of  F i g .  b l o c k  55(b)  can  the  be  r e l a t i v e  a s s e s s e d -  importance  I t  i s  of  apparent  the  wedge  and  of  model  the  t h a t  f o r  a  fre?*  wedge  and  the  b l o c k  i n f l u e n c i n g  the  b e h a v i o r  LL  quency  of  s t r u c t u r e of  the  *  3  p l a y  f i e l d  suggest  an  f o r  both  10  e x c e p t  t h a t  quencies  x  a t  and  correspond  l o w e r  a p p r e c i a b l y  by  the  s t r u c t u r e .  E  on.  the  wedge  and  angles  are  goes  v e r y  a  phase  f r e q u e n c i e s the  the  l a r g e <p_  55  to  i s  than  58  a  an  and  would  of  the  0.01'  u p w e l l i n g  important  e f f e c t  on  the  c o a s t l i n e .  d e a l  58  w i t h  the  f r e q u e n c i e s  we  c y c l e s / s e c  J  x,  h  l O " ^ ,  i n  the  f r e q u e n c i e s wedge the  but  o t h e r  block,  same  have  problem  been  f o r  r a p i d  a f f e c t e d i s  the  can  and  a l l  as  changed  case  H  z  i s  near  are  not  l a r g e  changes  f o r  c o n c l u d e  ty  that  much  A l l  f o r  the  L f  see  b l o c k  ty  the  more the  by  the  edge.  a t  From  .  We  by  s t r u c t u r e s ,  p o i n t s  10~  a f f e c t e d  wedge  f r e -  a f f e c t e d  a f f e c t e d  the  x  k-  problem.  s t r o n g l y  both  These  and  f r e q u e n c i e s .  by  a t  10"^,  s t i l l  hand  undergoes  x  g e o p h y s i c a l Hy  change  r e s p e c t i v e l y .  1.2  are  somewhat  a l s o  and  s t r u c t u r e  F i g s .  1 0 to  a f f e c t e d  angle  have  T h i s  neighborhood  i n t e r f a c e  model  r e s p e c t i v e l y  the  a n g l e s .  O  10~%  c y c l e s / s e c t h a t  the  i n  the  near  and  the  phase  i n  below  57?  5  O  3  the  e a r t h - s e a  v a r i a t i o n s 56  ,  r o l e  and  zones  • F i g u r e s 55  both  f r e q u e n c i e s  c o n d u c t i n g  LL  to  important  the  e l e c t r o m a g n e t i c  F i g .  c y c l e s / s e c  components  t h a t  c y c l e s / s e c mantle  10  both  phase u n d e r The  h i g h e r  d i s t a n t r e s u l t s  f r e q u e n c i e s  i n  from, of the  —2 neighborhood  of  f a c e  u p w e l l i n g  i n  and  the  d e t e r m i n i n g  10  the  c y c l e s / s e c ,  both  c o n d u c t i n g  b e h a v i o r  of  the  zone  the  e a r t h - s e a  should  n a t u r a l l y  be  i n t e r -  important  o c c u r r i n g  17 L  20  40  60  80  I00  20  Y cm  40  60  80  I00  H-  -I  F i g u r e  56.  1  20  1  The  p o l a r i z a t i o n  1  40  1  1  60  1  1  80  a m p l i t u d e s LL  and  f=10  T—]—-T  100  and  K  ,  Y cm phase  c y c l e s / s e c  ' (a)  the  wedge  e x t e n d i n g  (b)  the  wedge  a l o n e  (1),  10  cm  the  1  '  1  angles f o r  beyond b l o c k  1  20  J  40  T  j~  60  f o r  80  the  t r a v e r s e s the  alone  E  over  b l o c k  edge,  (2).  •  and  18 k  1  -I  20  1  1  40  1  1  1  1  60  l—•—i—>—i— —i—'—r—  T  1  80  2~0  I00 Y  20  4'o  6b  8b  ibo  40  1  60  80  -  100  cm  '  s'o'  f o r  the  2b " 40 ' 60  v  ido  Y cm F i g u r e  57'  The  p o l a r i z a t i o n  a m p l i t u d e s and  and  f=3x10-3  (a)  the  wedge  e x t e n d i n g  (b)  the  wedge  alone  (1),  phase  angles  c y c l e s / s e c 10  cm the  f o r  beyond b l o c k  the  a l o n e  t r a v e r s e s b l o c k (2).  E o v e r  edge,  and  19 k  T—|  1  20  F i g u r e  58.  1  40  The  p o l a r i z a t i o n  1  1  1  60  1  1  I  80  a m p l i t u d e s and  f=10  1  '  3  (a)  the  wedge  e x t e n d i n g  (b)  the  wedge  a l o n e  (1),  1  and  phase  c y c l e s / s e c 10  1  „ 20 Y cm  100  cm the  1  1  1  40  60  angles  f o r  f o r  beyond b l o c k  1  1  1  the  t r a v e r s e s the  a l o n e  b l o c k (2).  1  1  80  100  E o v e r  edge,  and  1 5 0  magnetic  v a r i a t i o n s ,  c y c l e s / s e c have be  a n  o n l y  mantle  f o r  examine  by  the  and  H„  o n l y  57(a)  and H  H  maximum  d i r e c t l y  s m a l l  v a l u e s  wedge  edge,  then  removed the  as  o v e r  near  the  the 55  mantle  to  the  a  maximum  s l i g h t l y  the  b l o c k  and  • To  f u r t h e r model  c o n s i d e r  h i g h e r  a f f e c t e d  edge  i s  the  by  even  f o r  I t  i s  apparent  quencies  at  t h e  i n g l y  by  p o i n t s  the  t h i s w e l l  from  wedge  l o w e r  the  over  shows- a  phase  to  to  the  c o n s t a n t  a t  \Lr  s t r u c t u r e removed  55  F i g s . has  but  r i s e  from to  Zs  the  58  t h a t  c o n s i d e r a b l e  f r e q u e n c i e s  the  b l o c k  edge  w e l l  a r e  0  the  on  s t r u c t u r e  edge,  as n o t  y  the  e f f e c t  the  d e c r e a s e  l a r g e  o f  a t  a t  p o i n t s  and  shows  0,  a  v e r y  b l o c k  g r a d u a l  a n g l e s  and  r e a c h i n g  x a f f e c t e d  a g a i n  f r e -  b l o c k  f a l l s  begins  d i r e c t l y  • B„  • The  then  - H  becomes  o f  approached,  edge,  edge.  edge.  approached.  the  wedge  r e a c h i n g  much  should  c o n d u c t i n g  58,  the  s h o u l d  f i e l d  combined  A t  10  e l e c t r i c  s t u d i e d .  f o r  wedge  b l o c k  i s  range  c o n s i d e r a b l y  the  f r o m  wedge  a r e  the  u p w e l l i n g  58(a).  beyond  d e c r e a s e s  the  in> F i g s .  and  r e g i o n s  i n c r e a s e s  z  and  x  k  2  f o r  wedge.  s e a  near  w i t h i n  h o r i z o n t a l  dependence  y s t r u c t u r e  zones  The  b l o c k )  56(a),  b o t h  f r e q u e n c i e s  f r e q u e n c y  f r e q u e n c y  55(a),  quencies  e f f e c t .  whole  (wedge  f o r  c o n d u c t i n g  both  the  the  s t r u c t u r e F i g s .  the  i m p o r t a n t  a f f e c t e d  w h i l e  changes s t r u c t u r e .  frer-  h i g h e r IL_ y  and  but  H_  z  becomes  i n c r e a s -  i m p o r t a n t . - To  study  how  the  a f f e c t  the  f i e l d  the  b l o c k  was  changed.  d i r e c t l y  ;  above  The the  r e s u l t s b l o c k  r e l a t i v e  p o s i t i o n s  components i n  F i g . - 59  edge,  w h i l e  t h e  of  the  p o s i t i o n  a r e  f o r  the  the  r e s u l t s  wedge o f  wedge i n  t h e  and wedge  edge  F i g .  60  151  20  40  60  80  20  I00  40  60  80  I00  Ycm F i g u r e  59v  • The  . p o l a r i z a t i o n edge (a)  a m p l i t u d e s f o r  d i r e c t l y 3x1 c\  (b)  and  t r a v e r s e s  o v e r  the  phase  over  b l o c k  the  edge  1 c y c l e s / s e c .  angles wedge  and  f o r w i t h  t h e the  f r e q u e n c i e s  E wedge  152 are f o r the b l o c k edge extending  10  cm beyond the wedge edge.  In the r e a l e a r t h problem the s t r u c t u r e f o r F i g . 59 would r e p r e s e n t the s i t u a t i o n where the edge of the mantle conducting  zone \wsfis d i r e c t l y below the s h o r e l i n e , while F i g . 60 r  would r e p r e s e n t occurred  50 km  the case where the conducting inland.  F i g u r e 59(a)  mantle-step  d e a l s w i t h a model fre*>  1+ quency of 3 x 10 frequency  of 10^  c y c l e s / s e c and F i g . 59(b) cycles/sec.  f r e q u e n c i e s of 10 The  and  Measurements were a l s o made f o r  3 x 10  c y c l e s / s e c but are not shown.  J  changes i n the amplitudes and phase angles  l a t t e r f r e q u e n c i e s were i n t e r m e d i a t e In F i g s . 59(a)  and  (b).  F i g u r e 59(a)  i n c r e a s e a t d i s t a n c e s as g£eat as 20 structure. for  deals with a  to those  falls  r e s u l t s shown  shows t h a t H  z  begins  cm from t h i §dg§ of  F o r t h i g e o p h y s i c a l problem, t h i s i n d i e a t i s  f r i q u e a e i e s i n t h i neighborhood of 0.01  begins  f o r these  to shew enhanced values  100  km  eyele§/§ee,  to  the that H  g  from the s h o r e l i n e , then  to very s m a l l values over the sea f o r regions beyond the  continental slope.  .  F i g u r e 59(b)  shows t h a t f o r f r e q u e n c i e s  as  -Li  low as H- x 10  i c y c l e s / s e c both Hy and H  by the c o a s t l i n e - m a n t l e  z  are l i t t l e a f f e c t e d  s t r u c t u r e u n t i l p o i n t s d i r e c t l y over  the s t r u c t u r e are reached.  In the g e o p h y s i c a l problem H  H„ f o r the s t r u c t u r e modelled i n F i g .  59(b), should be  a f f e c t e d by the presence of the ocean and  and  little  the u p w e l l i n g  con-  d u c t i n g zones of the mantle f o r p o i n t s on l a n d near the coast.  From* the r e s u l t s shown i n F i g . ' 60 i t i s apparent  t h a t the coast e f f e c t f o r H i n l a n d (as f a r as 1 50 km)  z  w i l l be observed much f a r t h e r  f o r frequencies  i n the neighborhood  153  20  40  60  80  I00  20  40  60  80  I00  w  cm  Ycm  20  40  60  80  20  40  60  80  F i g u r e 6 0 . > The a m p l i t u d e s and p h a s e a n g l e s p o l a r i z a t i o n for traverses 3x1 O^,' ( b )  <1()3  o v e r t h e wedge w i t h t h e  cycles/sec.  DO  f o r the E  edge e x t e n d i n g 10 cm b e y o n d t h e wedge edge and (a)  I00  block  frequencies  i5 of-0.01 cycles/sec i f  k  the u p w e l l i n g mantle conducting  extends w e l l beyond the s h o r e l i n e . the neighborhood  zone  At lower frequencies  of h x 10"^ cycles/sec, H  z  would b e g i n  d e c r e a s e a t a p p r o x i m a t e l y 50 km f r o m t h e s h o r e  in to  ( d i r e c t l y over  t h e m a n t l e stefc) a n d m a i n t a i n a c o n s t a n t v a l u e a t p o i n t s  over  t h e s e a b e y o n d 50 km f r o m t h e s h o r e . * A t t h i s f r e q u e n c y  the  sea has  con-  very l i t t l e  d u c t i n g zone i s  i n f l u e n c e , but the, u p w e l l i n g mantle  important.  5 9 ( a ) , ' a n d 60(a)  A comparison of F i g s .  shows t h a t 0  i n the r e l a t i v e p o s i t i o n s evident from F i g s .  Z  is  quite sensitive  55(a), to  changes  o f t h e wedge a n d b l o c k . • I t  is  55 t o 60 t h a t t h e r e l a t i v e p o s i t i o n s  of  t h e c o n d u c t i n g s t e p and t h e ocean c o a s t have an i m p o r t a n t e f f e c t o n t h e b e h a v i o r o f t h e a m p l i t u d e s and p h a s e a n g l e s the  of  components. Figures  6 1 , 6 2 , a n d 63 d e a l w i t h t h e H p o l a r i z a t i o n  (wedge edge p a r a l l e l source).  Figure  61 shows t h e r e s u l t s  the  f o r model f r e q u e n c i e s  O  LL  3 x 10  to the h o r i z o n t a l magnetic f i e l d of  and 1 0  J  c y c l e s / s e c f o r t h e wedge e x t e n d i n g 10 cm  beyond the b l o c k edge. b o t h f r e q u e n c i e s as  EL undergoes  the s t r u c t u r e i s  a gradual increase  for  a p p r o a c h e d w h i l e EL shows  z a slight  e n h a n c e m e n t n e a r t h e wedge edge a n d t h e n d e c r e a s e s  smaller values  o v e r t h e wedge. ' E  t h e wedge i s  approached then f a l l s  small values  o v e r t h e wedge.  ty- n e a r t h e wedge i n c r e a s e s phase  angle  1  as  increases  very r a p i d l y  extremely sharply  The c h a n g e  i n the phase  to  in Figs.  z  61(a)  the frequency decreases.  a n d ( b ) we s e e t h a t i t s  very  angle  0__ i s n o t a t a l l a f f e c t e d b y t h e s t r u c t u r e .  comparing A  as  The In  behavior  to  155  20  T  40  - 1  60  1  80  (a)  WM7M  —i— —r  100  v  X cm  20  40  60  8 0 100  ' 'V  _ •  1  1  1  •  l  *  i  1  i  i  EZZZZZzZZZZ^I W7777777A  J  . 4  (b)  LU  i  20  F i g u r e  6 1 .  *  i  1  i  4 0 60  f o r t r a v e r s e s  b l o c k  edge  i  over  - i — i — i — | —  1  8 0 100  T h e amplitudes  a t i o n  1  40  X cm  a n d phase  angles  t h e wedge  extending  a n d f r e q u e n c i e s  (a)  3x10^,  (b)  i— —i—>—r~ 1  60  8 0 100  f o r t h e H  p o l a r i z -  10 cm beyond  10-^ c y c l e s / s e c .  t h e  156 near the s t r u c t u r e i s frequency  dependent. • F i g u r e 62 shows  the r e s u l t s f o r the wedge edge d i r e c t l y over the mantle edge w h i l e F i g . 63 d e a l s w i t h the b l o c k edge extending the wedge edge.  The  behavior  of- H , y  s i m i l a r to t h a t i n d i c a t e d i n F i g . 61.  H, z  0  The  y  and  Q  10 cm beyond Z  i s very  behavior of- E ,, JL  however, i s q u i t e s e n s i t i v e to the r e l a t i v e p o s i t i o n s of wedge edge and b l o c k edge. model f r e q u e n c i e s of 10  the  R e s u l t s were a l s o o b t a i n e d f o r  and 3 x IO-*  c y c l e s / s e c but are  shown s i n c e they i n d i c a t e d no l a r g e departure  not  from the  r e s u l t s f o r the other f r e q u e n c i e s a l r e a d y d i s c u s s e d .  In  general,, the r e s u l t s f o r the H p o l a r i z a t i o n i n d i c a t e t h a t magnetic f i e l d  components undergo o n l y s m a l l changes as  s t r u c t u r e i s approached w h i l e the h o r i z o n t a l e l e c t r i c  the  the  field  i s v e r y s e n s i t i v e to the c o n d u c t i v i t y s t r u c t u r e . Measurements were a l s o made f o r the top f l a t o f the b l o c k s t r u c t u r e 1.5  cm below the s u r f a c e of the  s o l u t i o n . - In the g e o p h y s i c a l problem, t h i s depth a-depth of 7 ° 5 km«  surface salt  represents  S i n c e a l l the r e s u l t s f o r t h i s case were  almost i d e n t i c a l to those f o r the 3 cm depth d i s c u s s e d i n d e t a i l i n t h i s work, they are not shown. The  r e s u l t s of t h i s work on model c o a s t l i n e s t r u c t -  ures i n d i c a t e t h a t , i n g e n e r a l , f o r f r e q u e n c i e s i n the neighborhood of 0.01  c y c l e s / s e c ' the s l o p i n g s e a - e a r t h  f a c e should have an important  inter-  e f f e c t on the H" /Hy r a t i o z  near the c o a s t but t h a t an u p w e l l i n g h i g h l y conducting  very mantle  s t r u c t u r e near the coast would become i n c r e a s i n g l y more important  at decreasing frequencies.  I t appears t h a t the  157  cn  K  2  E>  CO  200 160  H,  I  2* ' l  o X  oo 16  t7 / M  5tl2  r r m m  CvJ  /  '  I  '  I  LS  120  '  f  80  f  40  c? 8 O s  0 -40  4  1777777}  LU  I  '  20  I  '  i  —  i  40 60  —  (a)  i — i — i — i — i — i — i — i — > — i —  r  8 0 100  X cm  20  4 0 6 0 8 0 100  3*  b x 2 ID  x  N  "y •  I 1  b — —r x cr> ro |6 1  '  i  i •  •  i  i •  i  i  € IE >  h  e  X  O  4  UJ  20  F i g u r e 62„  T—•—n—i  40  60  • mrnn '"i"  i  80 100  1  v  i  X cm  i  20  i  i  40  The a m p l i t u d e s and phase a n g l e s  i  (b) i  •—i—r—r  60 80 100 f o r the H  p o l a r i z a t i o n f o r t r a v e r s e s o v e r t h e wedge w i t h t h e wedge edge d i r e c t l y o v e r t h e b l o c k edge a n d f r e q u e n c i e s (a)  3x1 o \  (<b) 1C-3 c y c l e s / s e c .  158  H  ro  %  200  & 2  160 cn 10 O  1  I  1  V II co 16  '  1  i— —i—i—i—»  '20  1  80  MS  U77rrm  <f> 4 0 0  E  <*> 8 o x „ oq 4  -40 (a)  x  T— —I 1  LU  20  40 60  8 0 100  —1—I—I—1—I—I—I—•—I—  '  1— —r 60 8 0 100  20  X cm  40  l — ' — i —  1  F i g u r e  63.  • T h e amplitudes  p o l a r i z a t i o n edge (a)  3x1o\  a n dphase  f o r t r a v e r s e s  extending (b)  10 10^  X cm  cm beyond  over  20  c y c l e s / s e c .  40  angles  t h e wedge  t h e wedge  6 0 8 0 DO  edge  1  60  — r - - — r  8 0 100  f o r t h e H w i t h  t h e b l o c k  a n d f r e q u e n c i e s  159 e x p e r i m e n t a l l y  o b s e r v e d  enhancement  o f  the  H  z  / H y  r a t i o  a t  f r e l a t i v e l y i n  p a r t ,  The  l a r g e  to  the  r e s u l t s  (196*+)  i n  d i s t a n c e s u p w e l l i n g  o b t a i n e d  d e s c r i b i n g  v a r i a t i o n s ;  f r o m  • I n  o f  h e r e  c o a s t a l the  r a t i o  t h e  (1965)  be  e x p l a i n e d ,  c o n d u c t i n g  (d)  •  i s l a n d s  zone  w i t h i n  Ialand some  i n  a  w a t e r  G e o r g i a  w h i c h  o n  the  s i d e  c a n  o f  r e a d i l y T h e  t h i s  m o d e l  r e g i o n p r e s e n t  s c i e n t i s t s T h e  m o d e l  ments u s e d a t  w a t e r  was  b u o y e d  v a r i o u s  i n s t r u m e n t s  by  the  a t t r i b u t e d , the  b y  m a n t l e . S c h m u c k e r  m a g n e t i c  i n d i c a t e  b y  L a m b e r t  s u g g e s t ,  by  a n  f i e l d t h a t  a n d  C a n e r  u p w e l l i n g  s u c h by  as  the  a r e  the  o n  a r e  p r o b l e m  f o u n d  B r i t i s h  I s l a n d  c h a n n e l  i s  the  C o l u m b i a  the  s u c h  i n  o t h e r  t h a t  o f  a  s m a l l  S t r a i t M a i n l a n d  s i d e . s c a l e d  The m o d e l  made. o f  t h e  i n c l u d e s  t e c h n i q u e t h e  t h e  - T h i s  as  P a c i f i c  a  P a c i f i c  G e o r g i a  I s l a n d .  r e s u l t  o f  j u s t  was  i n  t h e  v i c i n i t y  p r i o r  r e c o r d e d  the  t o t a l  m a g n e t i c o f  f i e l d  c h o s e n 6h  s t u d i e d  T e x a d a  a t  the  u s i n g  the  w i t h  E s q u i m a l t ,  to i n  f o r  shows  c o l l a b o r a t i o n  L a b o r a t o r y  make  a r e a  F i g u r e  L a b o r a t o r y  made  N a v a l to  o f  r e g i o n  N a v a l  were  magnetometers p o i n t s  S t r a i t T e x a d a  m o d e l l e d .  measurements  made  i n  i n  u s e d  r e s u l t s  i n t e r e s t  V a n c o u v e r  s e c t i o n  a t  m o d e l  o b t a i n e d  t h e y  zone  be  m a n t l e .  b o u n d e d  a n d  t h i s  be  m o d e l  the  c h a n n e l ,  i s  s t u d y  t h a t  m o d e l  as  e x p e r i m e n t a l  o f  d i m e n s i o n s  z  c o u l d  S t r u e t u r e s  Of  one  H y / H  the  a n o m a l i e s  a d d i t i o n ,  o f  c o a s t  c o n d u c t i n g  s u p p o r t  measurements c o u l d  a  the  f i e l d May  f i e l d  m e a s u r e -  1966.  T h e y  measurements  I s l a n d ;  v a r i a t i o n s  B . C .  a n d  t h e i r n o t  the  VANCOUVER  F i g u r e  6 +„ 1  - Map  of  Texada  I s l a n d  and  the  ISLAND  S t r a i t  of  G e o r g i a .  161 components.  Simultaneous  r e f e r e n c e  s t a t i o n  l e v e l )  Texada  on  The sheet T h i s  of  of  g r a p h i t e  120  sheet  sheets  t o g e t h e r  cement  of  used.  These  S u r p r i s e  the  was end  i n  the  to  r e p r e s e n t  i n  F i g .  k  to  end.  the  c o a s t s  machining  was  done  i n  and  to  the a  used  (a)  and  i n  c h a p t e r ,  The s a l t the  sheet.  f o r  both  normal show  i n  E  to  0  and 7  i n  H  the  the  H  65  cementing  sheet  above  the  sea  A  of  t h i n  and  e l e c t r i c  The  6 . k  to  0.1  66  show  f i e l d  p o l a r i z a t i o n  i n  f i l m  the  the  to  ocean.  those  the  model  E  at  the  T h i s  sander. used  i n  c o r r e s -  s u r f a c e  s o l u t i o n  and made  f o r  on  the  ( t r a v e r s e s  w h i l e  p a r a l l e l  the  f i e l d s  the  t r a v e r s e s  of  10^  g e o p h y s i c a l  p o l a r i z a t i o n source)  of  covered  magnetic  frequency  c y c l e s / s e c  of  t h i c k n e s s  as  of  were  model  the  shown  s c a l e .  e l e c t r i c  p o l a r i z a t i o n s  F i g .  same  h o l e s ,  g r a p h i t e  c i r c u l a r  suspended  the  The  was  s e r i o u s  i s l a n d s  speed  g e o p h y s i c a l  tank.  no  shaped  s m a l l  epoxy  g r a p h i t e  of  cm  1  s m a l l e r  depth  the  w i t h  was  as  a p p r o p r i a t e  are  t h i c k .  c o n d u c t i n g  sheet.  low  l a r g e cm  O.k-  p r e s e n t e d  o t h e r  a  f o u r  S u i t a b l y  v a r y i n g  sheet  corresponds  F i g u r e s to  the  the  and  c o n d u c t i v i t y  the  here  Measurements  c y c l e s / s e c s c a l e .  on  g r a p h i t e  the  l a b e l l e d  68  cm  s o l u t i o n  t h e i r  f e e t  e l e c t r i c a l l y  s m a l l  f a c t o r s  10^  at  r e q u i r e d  wide,  g r a p h i t e  s c a l i n g  to  by  the  and  the  u s i n g  t h i s  cm  L  measurements.  The  ponding  made  (1000  i s l a n d s  same  i n  machined  r e p r e s e n t  3  • An  the  I s l a n d  cut  and  l o n g ,  j o i n t s  Texada  f u r t h e r  (b)  Mountain  c o n s t r u c t e d  model  were  6 ,  was  epoxy  sea  cm  a p p r o x i m a t e l y  problems  were  I s l a n d .  model  l a r g e  sheet  near  measurements  to  ( t r a v e r s e s F i g s . the  67  and  e l e c t r i c  162 field- of  the s o u r c e ) .  graphite sheet i s  In- F i g s .  65 t o 68 t h e p o s i t i o n o f  i n d i c a t e d w i t h V-.I.  I s l a n d s i d e and B v C.  i n d i c a t i n g the  i n d i c a t i n g the Mainland  through  and (b)  0 and 1 a r e  r e s p e c t i v e l y . - Traverse  the r e f e r e n c e s t a t i o n p o s i t i o n ( S u r p r i s e  Figure  65 shows t h a t EL i s  sides  as  C.  values  o v e r t h e s h a l l o w s e a , and t h e n i n c r e a s e s  ial  change as  and (b)  undergoes  E  smaller  slightly  shows e n h a n c e m e n t o v e r  undergoes Both 0  the I s l a n d i s  the  a large increase  and  Z  undergo  a  as  as  substant-  traversed.  for traverses  3 a n d 5 a r e shown i n  r e s p e c t i v e l y . - The r e s u l t s  very s i m i l a r to those of E  ;  crossed.  The r e s u l t s 66(a)  approached, f a l l s to  approached. - H  s e a n e a r t h e two c o a s t s . Texada I s l a n d i s  is  measure-  e n h a n c e d o n b o t h t h e V-.I.'  and- B.  Texada I s l a n d i s  the coast  0 passes  Mountain)  u s e d by t h e P a c i f i c N a v a l L a b o r a t o r y i n t h e i r f i e l d ments.  Vancouver  side.  The a m p l i t u d e s a n d p h a s e s f o r t r a v e r s e s shown i n F i g s 6 5 ( a )  the  Figs.  f o r traverse 3 are  t r a v e r s e 0 w i t h the exceptions  a s m a l l e r c h a n g e as> T e x a d a I s l a n d i s  that  crossed  and  - JL •  \k  a l a r g e r change as ;  t h e B.  j  CL c o a s t l i n e i s  crossed. - Tra-  • JL  verse  5 (Fig.  crosses  66 b )  does n o t pass o v e r T e x a d a I s l a n d ,  a much s m a l l e r i s l a n d . H a r w o o d I s l a n d . .  e s t i n g t h a t Hy a n d H for  the t r a v e r s e s  t h e i r behavior i s presence of  z  It  but  is  tfLn^fps-  b e h a v e a l m o s t i n t h e same manner  over Texada I s l a n d .  This- i n d i c a t e s  a f f e c t e d more b y t h e c o a s t s  the i s l a n d s .  E  is  t h a n by  as that the  r a t h e r d i f f e r e n t , i t now shows  JL  enhancement i n c r o s s i n g Harwood I s l a n d and i s  little  by Texada I s l a n d .  t h e change  The p h a s e  curves  emphasize  affected in  163  Fig-tire  6-5 „  The  p o l a r i z a t i o n  amplitudes for-  (a)  and  t r a v e r s e  phase 0  and  angles (b)  f o r  the  t r a v e r s e  E 1 »  16>+  20  Figure  40  60  80  6 6 . * The a m p l i t u d e s  polarization for  (a)  100  v  Y cm  and phase  traverse  20  40  angles  3 and (b)  60  80  f o r the E  traverse  5°  100  165 s t r u c t u r e c r o s s  and  Texada The  t r a v e r s e s and  (b)  are  s i g n i f i c a n t l y  I s l a n d  and  a m p l i t u d e s  0.  1,  and  and  3?  b o t h  H  are  v e r y  t h i s  p o l a r i z a t i o n o  The  as  and  l a r g e  H„  I t  as  ^-O .  c r o s s  E  i s  as  the  the  v e r y  sea  and  c r o s s e d . c o a s t l i n e s change  are  i n  a n g l e  shores  takes  ty  by  f a l l s  f o r  the  the  68(a)  i n of  t r a v e r s e s  F i g . * a l l  problem  were but  6k  the  model  Ry  v e r y  and  r i s e s  v e r y of  the  Harwood  s h a r p l y over  i s l a n d s  u n u s u a l l y  do  c u r v e s ,  z  v a l u e s  • An  i s  w h i c h H  s e n s i t i v e  t r a v e r s i n g  b)  v e r y  s m a l l  f o r  change  68  v e r y  i s l a n d s .  made are  a l s o  not  f o r  shown  measurements  measurements  a p p r e c i a b l e  n e a r  e l e c t r i c  sharp  a  ( F i g .  5  t h a t  s t r u c t u r e  to  are the  l a r g e  I s l a n d  made  the  o t h e r  h e r e , are  t r a v e r s e s  s i n c e  covered  i n d i c a t e  changes  i n  both  t h a t H  and  f o r  the by  main  the  b o t h f i e l d  d e c r e a s e s h a r p l y  c o a s t l i n e s  o n l y  E„  E  f o r  the  as  the  c o a s t l i n e s  over  the  ocean,  f o r  the  f o u r  showing  E  c o u l d  be  p o l a r i z a t i o n . should  approached some  g e o p h y s i c -  z  p o l a r i z a t i o n are  the  H_  y  The  f i g u r e s  d i s c u s s e d .  The  e x p e c t e d  (b),  undergo  the  shores  a l s o  67(a),  t r a v e r s e s  I t  to  f o r  the  t r a v e r s e  to  p o l a r i z a t i o n  these  does  z  curves  i s  ty  i n  from  s t r u c t u r e .  as  H  F i g s .  c o n t r a s t  w h i c h  5)°  i n d i c a t e d  a l  of  p l a c e  Measurements  f e a t u r e s  a g a i n  f o r  $  t r a v e r s e s  n o t .  a f f e c t e d  the  In the  i n  angle  approached,  phase  and  ( t r a v e r s e  to  i n c r e a s e s  The  from  I s l a n d .  s e n s i t i v e  c o a s t s  phase  f o r  the  apparent  curve  d i f f e r e n t  Texada  i s  do  f o r  shown  l i t t l e  The  0  c o n s i d e r a b l y not  *  w h i c h  phases  are  5  r e s p e c t i v e l y .  y  those  d i f f e r e n t  and  show  a  then  f a l l  enhancement  n e a r  166  -i—i—'—i— —i—i—i— —r 1  20 E  V  9  2 X  40  80  l—•—i— —i— —i—•—r 20 40 60 80 100 1  100  X cm  1  >  BJCJ—  2  60  1  H  HVI.  200  Y  fsl i  •  i  i  i—>—r—  * 16  *  160  H,  120  80  Y  40 0  'o  -40 '  Figur-e  67.  |  20  i  The  p o l a r i z a t i o n  f o r  (a)  and  t r a v e r s e  HVI.  (b)  i i | i i ' j i 40 60 8 0 100  a m p l i t u d e s  BJOT  —i—i—|—i—|—i—|—i—|—  X cm 2 0  phase 0  and  40  angles (b)  60  f o r  80  the  t r a v e r s e  100  H 1.  167  F i g u r e  68*  The  p o l a r i z a t i o n  amplitudes f o r  (a)  and  t r a v e r s e  phase 3  and  angles (b)  f o r  the  t r a v e r s e  H 5.  168 islands.  It  should r i s e  f o r t h e ' H- p o l a r i z a t i o n o  s t e e p l y as B o t h <*  the coast i s  a n d \l/  z  s h o u l d show  consider?-  x  1  a b l e change' f o r b b t h p o l a r i z a t i o n s „  approached  The f i e l d  measurements  made i n t h e T e x a d a I s l a n d r e g i o n ( L o k k e n a n d M a c l u r e , indicate netic  s m a l l changes i n the a m p l i t u d e o f  f i e l d variations  1966)  the r e s u l t a n t  and changes i n phase a n g l e  mag-  somewhat  l a r g e r t h a n t h o s e p r e d i c t e d by t h e model measurements. - Much of  the m i c r o p u l s a t i o n s  quency l o w e r t h a n O d  activity  t h e y r e c o r d e d was a t a  cycles/sec  • One w o u l d e x p e c t  faults  and a p o s s i b l e u p w e l l i n g o f m a n t l e c o n d u c t i n g zones coastal region,  in  w e l l i n g of  i n the' p r e v i o u s  appears  sections).  In  t h a t t h e r e s u l t s o b t a i n e d by t h e P a c i f i c  of the e a r t h - s e a - I n t e r f a c e inhomogeneities  Seamount this  general  Naval  the combined  effect  a t t h e c o a s t l i n e s and i s l a n d s , ,  i n the f o r m o f f a u l t s and u p w e l l i n g o f  mantle c o n d u c t i n g zones a t g r e a t e r  In  (see  .The f a u l t s a n d u p -  f o r lower frequencies.  L a b o r a t o r y c a n be e x p l a i n e d i n t e r m s o f  (e)  both  t h e c o n d u c t i n g z o n e s w i t h i n t h e m a n t l e w o u l d become  i n c r e a s i n g l y more I m p o r t a n t it  the  and s u c h s t r u c t u r e would g r e a t l y a f f e c t  t h e v e r t i c a l m a g n e t i c f i e l d a m p l i t u d e and phase a n g l e the results  fre-  and  the  depths.  a n d - C o n d u c t i n g -Dome' S t r u c t u r e s s e c t i o n measurements  r e p r e s e n t i n g seamounts  f o r model  and c o n d u c t i n g domes a r e  briefly.  Elevations  mountains  to small islands. >Since  structures treated  of the ocean bottom v a r y from  c a n i c h i l l s o r mountains)  submarine  seamounts- ( s u b m e r g e d  w i l l have a c o n d u c t i v i t y l o w e r  volthan  169 t h a t  of  sea  anomalies i o n s  water,  i n  the  measured  S i m i l a r l y , s u r f a c e  of  and  anomalies  o c c u r r i n g  the  s u r f a c e  s u r f a c e . n e a r • In  l a n d i n  t h i s  diameter  a t  the  same  diameter  l e v e l  g r a p h i t e and  cone  30.*+ k m  used  f o r  the  c o n c r e t e . than  would  F i g u r e d i r e c t i o n  the  s o u r c e .  quency  of  as  base  s u r f a c e  a t  a  the  of  shows  the  69(a)  c y c l e s / s e c  10  water  The  a  g r a d i e n t s , the  e a r t h ' s  3  i n  same  30.  cm  k  c o n d u c t i n g cm  k  h i g h  apex  the  dome  i s  and  The  the  tank. km  30A  used  about  and  of  The h i g h  geometry  m a t e r i a l  was  was l o w e r  10^  s o l u t i o n . over  the  h o r i z o n t a l the  w h i l e  h i g h  cone.  c o n c r e t e  g i v e s  a t  c y l i n d e r  the  s a l t  below  e x p e c t e d . cm  the  The  t r a v e r s e s po  be  30A  base.  v a r i a t -  domes)  v a r i a t i o n s  c o n d u c t i n g  s t r u c t u r e .  and  e x p e c t e d .  r e p r e s e n t  of of  be s a l t  c o u l d  to  e x i s t  c o n d u c t i v i t y  g r a p h i t e  r e p r e s e n t  p a r a l l e l  x  a  the  the  F i g u r e  3  on  c o n c e n t r a t e d  69  to  cone  used  c o n d u c t i v i t y  the  the  domes  was  s e t  seamount  of  o r  r i s e  g r a p h i t e  diameter  The  t h a t  was  w i t h  i n  a  base  of  might  e l e c t r o m a g n e t i c  work  cone  was  g i v e  w i l l  e l e c t r o m a g n e t i c  ( m i n e r a l  c o n d u c t i n g  T h i s  cone  domes  would  dome. the  ocean  the  the  g r a d i e n t s  n a t u r a l l y  c o n d u c t i n g  the  i n  a t  c o n d u c t i v i t y  g r a p h i t e  magnetic  r e s u l t s 69(b)  f o r  shows  a  cone  i n  f i e l d  of  model  f r e -  the  r e s u l t s  -  LL  f o r  a  f r e q u e n c y  amplitudes presence ent  of  of  the  g r a p h i t e  of  of  the  the  10 three  cone.  magnetic  cone.  c y c l e s / s e c .  A t  components  are  The  f i e l d  B o t h -ty  phase i s  and  angle  these  a f f e c t e d of  a p p r e c i a b l y are  0  f r e q u e n c i e s  the  by  the  v e r t i c a l  i n f l u e n c e d  e s s e n t i a l l y  the  by  componthe  u n a f f e c t e d .  y Measurements  were  a l s o  made  f o r  model  f r e q u e n c i e s  of  3  x  10^  170  F i g u r e i n (a)  The  69,  the3x10%  y  a m p l i t u d e s  d i r e c t i o n (b)  10^  o v e r  and a  phase  a n g l e s  g r a p h i t e  c y c l e s / s e c .  cone  f o r  t r a v e r s e s  f o r  f r e q u e n c i e s  171 a n d 10^ c y c l e s / s e c b u t t h e r e s u l t s a r e n o t p r e s e n t e d h e r e . Both H ies.  and H  y  show much l e s s  z  Measurements  change a t t h e s e l o w e r f r e q u e n c -  for traverses p a r a l l e l  to the h o r i z o n t a l k  electric  f i e l d of the source f o r model f r e q u e n c i e s o f 3 x  a n d 10  c y c l e s / s e c a r e shown i n F i g s .  ively.  These  results  respect-  i n d i c a t e t h a t H_ i s n o t a t a l l a f f e c t e d  by the cone f o r t h i s , p o l a r i z a t i o n . cone, w h i l e E  and (b)  70(a)  10  H  is  enhanced o v e r  the  f a l l s v e r y s h a r p l y a n d r e a c h e s a minimum JL  d i r e c t l y o v e r t h e c o n e . - The p h a s e a n g l e s a f f e c t e d by the g r a p h i t e - Measurements parallel  are not n o t i c e a b l y  cone.  f o r t h e m o d e l l e d seamount f o r  traverses  t o the magnetic f i e l d o f the s o u r c e , and f o r model LL  f r e q u e n c i e s o f 3 x 10 a n d 10 g i v e n i n F i g s . 71(a) a n d ( b ) .  0  cycles/sec r e s p e c t i v e l y , are N e i t h e r H„ n o r H a r e a t a l l y z a f f e c t e d b y t h e c o n c r e t e c o n e . - E now u n d e r g o e s a s h a r p J  JL  enhancement d i r e c t l y o v e r t h e c o n e .  The p h a s e a n g l e s  a g a i n n o t a p p r e c i a b l y a f f e c t e d by the c o n e . for E  traverses  are  Measurements  i n t h e x - d i r e c t i o n a r e n o t shown,  since  only  was s e n s i t i v e t o t h e s t r u c t u r e . JL  • The r e s u l t s o f F i g s . ies  69-71  suggest that f o r frequenc-  i n the neighborhood of 0 . 3 c y c l e s / s e c , anomalies i n  electric  and magnetic f i e l d ,  e x i s t a t the e a r t h ' s while anomalies measurements  though i n g e n e r a l s m a l l ,  s u r f a c e n e a r submerged c o n d u c t i n g  i n the e l e c t r i c  should domes,  f i e l d only, are i n d i c a t e d f o r  a t t h e s u r f a c e o f t h e sea n e a r seamounts  merged s m a l l i s l a n d s . • I n h o m o g e n e i t i e s d i s t r i b u t i o n i n seamount r e g i o n s  the  or  sub-  i n the c o n d u c t i v i t y  w o u l d l i k e l y be p r e s e n t  at  1 72  10 •o x CD CO  2  H  I  cn  1  i  'O  i  1  i  i  1  1  1 6 0 z  i  r  8 0  1  «  E  x  3  >  2  ~T™ °  r  CM  E  o X LU oo  ^  120  1  00  cvi  :  -40  •  (a)  , 1  20  40  60  80  20  100  X cn  H  ro  '° 2 x 09 CD  L  cn  1  1  1  1  1  1  1  1  x  cm  E  T  r  x  4 0  7  •40-  *  (b) "i  I  "  20  I  i l—'—l—'—I—'  40  60  80  ' — i — | — i — | — i — | — i — | — i  100  F i g u r e  The  70.  the  x  3x10^,  a m p l i t u d e s  d i r e c t i o n (h)  10^  o v e r  and a  20  w  X  (a)  *  0  I -  100  120  1  1  2  LU  i n  80  80  3  X  60  160  'o x m 4 pS >»  'o  40  200  -  ro  3  7  phase  60  80  . 100  cm a n g l e s  g r a p h i t e  c y c l e s / s e c .  4 0  cone  f o r  t r a v e r s e s  f o r  f r e q u e n c i e s  173  H  'o  .  X  — — ^ ^ y ^ H  OJ  —  oo  l  |  1  |  l  |  i  |  2 0 0  I60  z  l  •  ion l£U  |  8  80  r  OJ  4>° T  MO  e  7  4  o  co  H — * ^  2  —*  40 (a)  UJ  i  °  i  20  i  j  40  i  j  60  •  i  80  i  i  100  i  > w  Y cm  i  20  •  i  40 H  v  2  X  —  i - ^ .  c  Hp""  CO  12 |  i  i  i  |  i  i  i  |  i  jf Is >  60  <  i  80  r  1 A H  7  r  X  -  80  *°  •  -40 (b)  o  1  20  |a)  100  0  X  i n  i  e  'o  F i g u r e  >  •  \dU  "3» 8  0  i  160  i  CM  'o o>  2  •  • The  71.  the 3x1  y o\  I  40  1  10^  1  80  a m p l i t u d e s  d i r e c t i o n (b)  1  60  over  100  and a  "1  Y cm  phase  angles  c o n c r e t e  c y c l e s / s e c .  20  cone,  40  60  I "  80  I  100  f o r  t r a v e r s e s  f o r  f r e q u e n c i e s  17  g r e a t e r depths,  K  i n the form of f a u l t s and u p w e l l i n g s of con-  d u c t i n g zones i n the mantle, c o u l d be  and hence s u b s t a n t i a l  anomalies  expected. Measurements were a l s o made w i t h the c u r r e n t sheet  i n c l i n e d a t 1 0 ° and 2 0 ° w i t h r e s p e c t to the h o r i z o n t a l f o r the seamount and conducting dome s t r u c t u r e s as w e l l as f o r some of the s t r u c t u r e s d i s c u s s e d e a r l i e r . of  the components near the s t r u c t u r e s was  a l t e r e d by changing  S i n c e the behavior not a p p r e c i a b l y  the angle of i n c i d e n c e , none of the  r e s u l t s are shown. 3.2  Line Current  3.2.1  Introduction In  Source  s e c t i o n 2 . 3 the problem of a homogeneous conducting  e a r t h i n the near f i e l d of an o s c i l l a t i n g l i n e c u r r e n t was s t u d i e d . - In comparing the r e s u l t s f o r the l i n e c u r r e n t source w i t h those f o r the plane wave source i t i s found that although the h o r i z o n t a l e l e c t r i c and the h o r i z o n t a l magnetic the two  fields for  sources are v e r y s i m i l a r , the v e r t i c a l magnetic  components were q u i t e d i f f e r e n t .  field  The r a t i o H„/H„ f o r the z y  plane wave source i s s e v e r a l orders of magnitude s m a l l e r than values observed e x p e r i m e n t a l l y a t the e a r t h ' s s u r f a c e , w h i l e the r a t i o of the components f o r the l i n e c u r r e n t source i s w i t h i n the range of e x p e r i m e n t a l l y observed v a l u e s . as f o r the plane wave source, the problem  of d i s c o n t i n u i t i e s  i n c o n d u c t i v i t y In the h o r i z o n t a l d i r e c t i o n does not submit to mathematical '^rsajtmeht.  Again,  readily  1 7 5  T h i s s e c t i o n d e a l s w i t h an analogue method f o r studyi n g problems o f c o n d u c t i v i t y d i s c o n t i n u i t i e s f o r an overhead o s c i l l a t i n g l i n e current„  S e v e r a l o f the problems s t u d i e d  f o r the sheet c u r r e n t source w i l l be s t u d i e d f o r the l i n e c u r r e n t source as w e l l . 3.2.-2  • Ma themsdkcal • • A h a l y s i s • The mathematical  f o r the model problem assumption  development o f the s c a l i n g  given i n section  3 o 1 » 2  factors  makes no  on the type o f source f i e l d , and hence i s d i r e c t l y  a p p l i c a b l e to a l i n e c u r r e n t model a s i w e l l * • The n e c e s s a r y and- s u f f i c i e n t c o n d i t i o n f o r i n v a r i a n c e under a change i n s c a l e -Is a g a i n g i v e n by e q u a t i o n (77) = 3.2.3  • Mod-el -Descri-T>tion- and^-Mea-surement Technique • The e x p e r i m e n t a l arrangement i s the same as t h a t  d i s c u s s e d f o r the sheet c u r r e n t source w i t h the e x c e p t i o n t h a t the a r r a y o f wires used f o r the sheet c u r r e n t was r e ^ p l a c e d by a s i n g l e copper r o d 3 / 8 i n c h i n diameter. < T h i s copper r o d was l o c a t e d a t the same h e i g h t ( U 2 5 m) as the c u r r e n t sheet source above the s u r f a c e o f the s a l t  solution.  The tank was a g a i n s e t o f f c e n t e r w i t h r e s p e c t to the over^head l i n e source i n o r d e r t h a t the minimum i n H  z  near one end o f the tank* - The minimum H_ appears  should occur directly  below the l i n e c u r r e n t , and the phase 4> r e v e r s e s a t t h i s z  p o i n t . • As was p o i n t e d out e a r l i e r ^ troublesome  t h i s phase change i s  when making measurements over s t r u c t u r e i f the  s t r u c t u r e i s l o c a t e d too near t h i s phase r e v e r s a l r e g i o n *  176 Ail  the measurements d i s c u s s e d  i n the f o l l o w i n g s e c t i o n s were  made f o r s t r u c t u r e s w e l l removed from t h i s phase r e v e r s a l region. 3.2.  k  Discussion- of The  coordinate  Results system used i n the d i s c u s s i o n here i s c u r r e n t model ( F i g . 3 2 ) .  the same as t h a t f o r the sheet geophysical  problem being modelled here i s t h a t of a f l a t  h o r i z o n t a l e a r t h i n the f i e l d of an i o n o s p h e r i c l i n e The  s a l t s o l u t i o n i n the tank represented  geneous f l a t • The  The  current.  a l a y e r of a homo-  earth. v a l i d i t y of the model was  t e s t e d by comparing  measured values of the amplitudes with c a l c u l a t e d values a s e m i - i n f i n i t e , f l a t conducting c a l c u l a t e d values was c u r r e n t sheet for  earth.  The  the for  agreement w i t h  not q u i t e as good as i n the oase of  source. - At 3-x  10  c y c l e s / s e c the r a t i o  the the  B^Hy  the model measurements agreed to w i t h i n 6$ w i t h the com-  puted values  f o r p o i n t s d i r e c t l y below the l i n e source.  The  c a l c u l a t i o n s assume a homogeneous conductor of i n f i n i t e  depth  extending i n f i n i t e l y i n the h o r i z o n t a l d i r e c t i o n s while  the  model has a l a y e r of s a l t s o l u t i o n with a l a y e r of g r a p h i t e below.  A l s o the edge e f f e c t s cannot be i n c l u d e d i n the  culations.  The  v e r t i c a l magnetic f i e l d as measured by  calthe  model a t p o i n t s w e l l removed from the p o s i t i o n d i r e c t l y below the source,  i s c o n s i d e r a b l y l a r g e r than t h a t p r e d i c t e d by  c a l c u l a t i o n s . • The The  the  edge e f f e c t s i n p a r t account f o r t h i s .  r e t u r n loop f o r the l i n e c u r r e n t source,  which was  loc-  177 ated about 7 m from the edge o f the tank, a l s o i n c r e a s e s the v e r t i c a l magnetic f i e l d . the curves  In g e n e r a l , however, the shape o f  g i v i n g the amplitudes as a f u n c t i o n o f p o s i t i o n  agree w e l l w i t h the c a l c u l a t e d ones.  F i g u r e 72 gives the  model measurements o f the amplitudes f o r t r a v e r s e s normal to the d i r e c t i o n o f the l i n e c u r r e n t f o r a frequency  o f 3 x 10  c y c l e s / s e c and a water depth o f 6h,h cm. A l t h o u g h v a r i o u s s t r u c t u r e s were s t u d i e d ' u s i n g the l i n e c u r r e n t model, o n l y c o a s t l i n e s t r u c t u r e s w i l l be d i s cussed  i n d e t a i l here.  In o r d e r to f a c i l i t a t e comparison  with measurements made f o r the sheet c u r r e n t source, the s t r u c t u r e s were l o c a t e d a t the same p o s i t i o n s as those f o r the sheet c u r r e n t  source.  Coastline Structures Measurements f o r the i n v e r t e d t r u n c a t e d g r a p h i t e cone are shown i n F i g s . 73 to 75.  The s c a l i n g f a c t o r s i n v o l v e d  are the same as those used f o r the t r u n c a t e d cone i n the f i e l d o f the sheet c u r r e n t d i s c u s s e d e a r l i e r The  L  9 to 51)•  o n l y change i s t h a t the sheet c u r r e n t has been r e p l a c e d  by a l i n e c u r r e n t .  F i g u r e s 73(a) and (b) show the amplitudes  h and phase angles f o r 3 x 1 0 w h i l e F i g s . 7Ma) and  (Figs.  h  and 10  cycles/sec respectively,  and (b) show the measurements f o r 3 x 10^  10^ c y c l e s / s e c r e s p e c t i v e l y .  Both F i g . 73 and F i g . 7  k  d e a l w i t h t r a v e r s e s p e r p e n d i c u l a r to the e l e c t r i c f i e l d of the source.  As was the case f o r F i g s . h9 and 50, the non-  u n i f o r m i t y o f the source f i e l d a g a i n a l s o a f f e c t s the  -\1  co  F i g u r e  72.  The  o s c i l l a t i n g  amplitudes  l i n e  c u r r e n t .  f o r  t r a v e r s e s  i n  the  y  d i r e c t i o n  f o r  an  overhead  179  -I—|  20  1 — | — i |  40  60  I  1—i—I—r  8 0 I00  Y cm  T — I — i — | — i — i — i — i — i — | — r  20  F i g u r e  a n d t r a v e r s e s  i n v e r t e d !  (a)  60  8 0 I00  The a m p l i t u d e s  73.  c u r r e n t  40  t r u n c a t e d  3x10 ' L|  ?  (b)  10^  i n  Y cm  a n d phase t h e  g r a p h i t e  y cone  c y c l e s / s e c .  20  40  60  8 0 I00  20' 4 0  60  80  a n g l e s  d i r e c t i o n f o r  f o r  a  o v e r  f r e q u e n c i e s  l i n e a n  I00  180  i — i — i — i — " — i — i — i — i — i — i  F i g u r e  L  60  80  100  20  40  60  80  100  and  i n v e r t e d (a)  40  The  7-  c u r r e n t  20  a m p l i t u d e s  t r a v e r s e s  t r u n c a t e d  3x10 , 3  (b)  10^  i n  and  Y cm  20  40  60  80  20  40  60  80  f o r  a  Y cm y  cone  c y c l e s / s e c .  — i — i — i — i — i — j — i — i — i — i —  w  phase  the  g r a p h i t e  1  angles  d i r e c t i o n f o r  over  f r e q u e n c i e s .  -  l i n e an  100  100  181 behavior o f the f i e l d components edge of the. cone.  i n the neighborhood of the  EL,, as b e f o r e , shows a decrease on the  s i d e o f the d e c r e a s i n g h o r i z o n t a l f i e l d and an enhancement the s i d e of the i n c r e a s i n g f i e l d .  on  In comparing F i g s . 73 and  7k w i t h F i g s . k9 and 50 we see that E L and H E undergo somey z what l a r g e r changes near the cone edges f o r the l i n e c u r r e n t source than i s i n d i c a t e d f o r the sheet c u r r e n t source.  The  r a t i o H_/H„ i s approximately u n i t y near the cone edge on the Z  y  s i d e o f the d e c r e a s i n g h o r i z o n t a l f i e l d f o r the l i n e c u r r e n t source w h i l e the r a t i o i s much l e s s than u n i t y f o r the sheet c u r r e n t source. * The phase angles 0,. and <j>_ are very s i m i l a r V z  for  the two sources, w h i l e the phase a n g l e ty undergoes x  g r e a t e r changes f o r the l i n e c u r r e n t source than i t does f o r the sheet c u r r e n t source. F i g u r e 75 g i v e s the amplitudes and phase angles f o r t r a v e r s e s p a r a l l e l to the e l e c t r i c f i e l d o f the source. F i g u r e 75( ) &  g i v e s the r e s u l t s f o r 3 x 1 0 cycles/sec.  c y c l e s / s e c and  Fig.  75(b) those f o r 10^  Comparing F i g . 75 w i t h  Fig.  51 we see t h a t the behavior of the amplitudes and phase  angles f o r the two f i e l d sources i s very s i m i l a r . H /H z  The  ratio  i s a g a i n n e a r e r u n i t y f o r the l i n e c u r r e n t source.  F o r a frequency o f 3 x 10  c y c l e s / s e c , ty undergoes l a r g e r  changes f o r the l i n e c u r r e n t source, whereas f o r a frequency of  10^ c y c l e s / s e c , ty undergoes a l a r g e r change f o r the x  sheet c u r r e n t source. To study f u r t h e r the e f f e c t o f a s l o p i n g earth-sea i n t e r f a c e , measurements  were made f o r the g r a p h i t e wedge i n  182  cm  X  F i g u r e  75.  c u r r e n t i n v e r t e d (a)  • The and  amplitudes  t r a v e r s e s  t r u n c a t e d  3x1-o\' ( b )  1C-3  i n  and  phase  the  g r a p h i t e  x cone  c y c l e s / s e c .  angles  d i r e c t i o n f o r  f o r  a  over  f r e q u e n c i e s  l i n e an  183 t h e f i e l d o f the l i n e c u r r e n t .  The s e a l i n g f a c t o r s and the  p h y s i c a l arrangement were the same as those used f o r the sheet c u r r e n t source  ( P i g s . 52 t o 5 ) • k  F i g u r e s 76 and 77 show the  E p o l a r i z a t i o n (wedge edge p a r a l l e l to the e l e c t r i c f i e l d o f the s o u r c e ) , and' F i g . 78 shows t h e H p o l a r i z a t i o n (wedge edge p e r p e n d i c u l a r t o the e l e c t r i c f i e l d o f the s o u r c e ) . - F i g u r e s 76(a),  ( b ) , 77(a), and (b) g i v e the r e s u l t s r e s p e c t i v e l y f o r  f r e q u e n c i e s 3 x 1 o \ 1 0 , 3 x 10^, and 10^ c y c l e s / s e c . F o r k  the H p o l a r i z a t i o n . F i g s . 78(a) and (b) show the r e s u l t s LL  r e s p e c t i v e l y f o r f r e q u e n c i e s 3 x 10  0  and 1 0  J  cycles/sec.  In >  comparing the amplitudes and phase angles near the wedge edge for  the overhead l i n e c u r r e n t source  ( F i g s . 52 t o 5 ) w i t h L  those f o r the overhead sheet c u r r e n t source  ( F i g s . 76 to 78)  we see t h a t f o r t h i s s t r u c t u r e a l s o the behavior s i m i l a r f o r the two f i e l d being  sources,  is  very  the main d i f f e r e n c e a g a i n  t h a t the r a t i o H /Hy i s much l a r g e r f o r the l i n e z  r e n t source  than f o r the sheet c u r r e n t source.  cur-  Smaller  H /Hy r a t i o s would be o b t a i n e d f o r the l i n e c u r r e n t problem z  if  the wedge edge were s i t u a t e d nearer  z o n t a l l y ) where the v e r t i c a l f i e l d  to the source  o f the source  (hori-  i s smaller.  These r e s u l t s i n d i c a t e t h a t f o r c e r t a i n l o c a t i o n s an overhead l i n e c u r r e n t source  should r e s u l t i n a l a r g e r H /Hy, r a t i o z  near sea-land i n t e r f a c e s than would be the case f o r a l a r g e sheet  current. The  e f f e c t o f the u p w e l l i n g o f a conducting  zone  w i t h i n the e a r t h ' s mantle under the ocean was s t u d i e d f o r the l i n e c u r r e n t model u s i n g the wedge and b l o c k s t r u c t u r e  F i g u r e r e n t  76. and  The  amplitudes  t r a v e r s e s  f r e q u e n c i e s  (a)  over  3x1O^,  and  phase  a  wedge  (b)  10^  f o r  angles the  E  c y c l e s / s e c .  f o r  a  l i n e  p o l a r i z a t i o n  c u r and  185  i—i—i—i—i—i—i—i—i—i—i  20  F i g u r e r e n t  40  60  77o  < The  and  t r a v e r s e s  f r e q u e n c i e s  80  100  amplitudes  (a)  over  3x10 , 3  1  —i—i—i—i—i—i—i—i—i—r—  Y cm  and  phase  a  wedge  (b)  10  3  f o r  20  40  angles the  E  c y c l e s / s e c .  60  f o r  80  a  100  l i n e  p o l a r i z a t i o n  c u r and  186  F i g u r e r e n t  78. and  The  a m p l i t u d e s  t r a v e r s e s  frequencies-  (a)  3x1  over C-\  and a  (b)  phase  wedge 1Cp  f o r  angles t h e  H  c y c l e s / s e c .  f o r  a  l i n e  c u r -  p o l a r i z a t i o n  and  187  d e s c r i b e d f a c t o r s  e a r l i e r  were  f o r  the  the  same  79(a)  v e r s e s  o v e r  the  wedge  w i t h  to  e l e c t r i c  f i e l d  o f  m o d e l  f r e q u e n c y  wedge  e x t e n d s  o f  the  edge.  - I n  u r e s  the  wedge  81  a n d  82  t h a t  the  (E  b e y o n d  w i t h  the  e d g e . the  i n  f o r  edges-  edge  o f  • T h i s  i s  o f  F i g .  the  63). t r a -  p a r a l l e l f o r  a  the a  m o d e l  m a n t l e  g i v e s  the  s e p a r a t e l y .  (2)  3  10^,  c a s e  to  r e l a t i v e  79(b)  p r o b l e m  a r e the  a n g l e s  c o n d u c t i n g  b l o c k same  f r e q u e n c i e s - As  The  s c a l i n g  55  p o l a r i z a t i o n )  b l o c k , '  the  The  ( F i g s .  b l o c k  i n d i c a t i o n  the  a n d  r e s p e c t i v e l y .  p h a s e a n d  b l o c k  some  (1)  l#0del  a n d  wedge  the  a n d  d e a l  e a r l i e r  s o u r c e  km  50  wedge  p r o b l e m .  c y c l e s / s e c .  o b t a i n  the  c y c l e s / s e c  the  b e y o n d  f o r  80,  e x c e p t  o f  u s e d  the  10  e x t e n d i n g to  c u r r e n t  a m p l i t u d e s  x  3  cm  o r d e r  i m p o r t a n c e r e s u l t s  o f  10  o c e a n  the  t h o s e  F i g u r e  t h e  shows  as  s h e e t  o f  as  F i g . ' 7 9  10^,  x  the  Pig--  10^  a n d  s h e e t  c u r r e n t  problem, we see that f o r the lower frequencies- Hy and H are z  n o t  a f f e c t e d  a p p r e c i a b l y  a f f e c t e d  by  b o t h  wedge  I f  t h e  we  w i t h  c o m p a r e P i g s .  i v e l y , t h e  i t  55, i s  e f f e c t f o r . t h e s o u r c e  o n  r  a n d  s h e e t [ c u r v e s  a n d  i n  t h a n  f o r  c u r r e n t  the  l a b e l l e d  f r e q u e n c i e s  (2)  f o r  seems  l i n e  s o u r c e .  s t r o n g l y  >H  f o r  H  s t u d i e d .  c u r r e n t  s o u r c e )  r e s p e c t -  the to  i n Zi  by  s o u r c e )  much  f o r  a f f e c t e d  c u r r e n t  o f  Hy,  a n d  g r e a t e r l i n e  have  c u r r e n t  z  somewhat  ( l i n e  82  enhancement  i s  s t i l l  a l l  g e n e r a l , i t  a r e  i s  a n d  the  b u t  • E „  ( s h e e t  58  t h a t  i s ,  f o r  p a r t i c u l a r , H _ z  wedge  81,  80,  57?  s o u r c e i n  b l o c k  79,  edges  the  s t r u c t u r e .  the  a p p a r e n t  edge H, y  a n d  56,  c u r r e n t  b l o c k  b l o c k  Figs-.  s t r u c t u r e  s h e e t T h e  the  b y  the  f o r  a  v e r y  55  o v e r  s o u r c e . d i f f e r e n t  t h a n  s h e e t  z  the  c u r r e n t  s o u r c e  F i g s .  H  i t  h a d  c u r r e n t to  58]  u n d e r -  188  o  ^ > ^ H y IN  O  I20  -  . r ^ ^ ^ ^  —r—|—1—i  r-i  i  |  i  8  |  0  i 4 0  \ A +  X  00  cvi  i  3  '-  *0  1 /  > CM  x  ' 1/ / /07 ^/ IS  00  H  UJ  I  4 0 6 0 8 0 100  •  79-  4  and  t r a v e r s e s b l o c k  1  - The  4 0  o v e r  6 0  a m p l i t u d e s  a l i n e  edge,  Y cm  —<—i— —i— 20  a t i o n  (/ / / 0" / ^ IS  *  20  F i g u r e  - 8 0'  c u r r e n t  8 0  v  Y cm  a n dp h a s e  ( a ) t h ewedge  a n d ( b ) t h ewedge  f  I  !  20  "1—1  1111  4 0 6 0 8 0 100  '  r  100  w i t h  I  =  2 0  a n g l e s 3x10^  e x t e n d i n g alone  4 0  6 0  f o r the  8 0 100  E  p o l a r i z -  c y c l e s / s e c f o r 10  c mbeyond t h e  (1), t h eb l o c k  a l o n e  (2).  189  F i g u r e  80.  20  40  60  80  I00  20  40  60  80  I00  • The  a m p l i t u d e s  and  v  Y  cm  v  Y  cm  phase  20  40  60  80  I00  20  40  60  80  I00  angles  f o r  the  E  p o l a r i z -  LL  a t i o n  and  t r a v e r s e s b l o c k  a  l i n e  o v e r  edge,  and  c u r r e n t  (a) (b)  the the  w i t h  wedge wedge  f  =  c y c l e s / s e c  10  e x t e n d i n g a l o n e  (4),  10  cm the  f o r  beyond b l o c k  the a l o n e  (2).  190  1 I I <Tl I IT  x o  U7V72 I  20  > i  1  E  (a) l— —I— —i—' 1  81.  40 60 80 100  ' T h eamplitudes  a t i o n .. a n d .  a l i n e  t r a v e r s e s  over  b l o c k  edge,  - i — i — | — i — | — i — i — i — | —  1  ' 2b ' 4b ' 60 ' 8b ' F i g u r e  c u r r e n t  \l t i crl I IS  x ^-40  160' Y  a n d phase w i t h  (-a) t h e w e d g e  a n d (>b) t h e w e d g e  Y c m 20  f=3x10  extending a l o n e  -i— —i— —i—•—i— —r 1  cm  angles 3  40 60 80 100  20  1  40 60 80 100  f o r t h eE  c y c l e s / s e c 10  (1),  1  p o l a r i z -  f o r  cm beyond t h e b l o c k  t h e a l o n e  (2).  191  'O x  2  ID  X £ 42 3x o  5.  y / / 7 I I.  T7TW77[  K V M t k |"l|'Tli|  I  |  |  |  |  |  |  20  40  60  80  20  40  60  8 0 100  1  OO  i  i  Y cm. 20  j  i  40  i  i i i • i 60 80 100  i—•—i— —i—•—i—•—r 1  F i g u r e a t i o n  8 2 . • The a m p l i t u d e s a n d a  t r a v e r s e s b l o c k  l i n e  o v e r  edge,  c u r r e n t  (a)  a n d (b)  20  Y cm  a n d phase w i t h  t h e wedge t h e wedge  f  =  40  angles  e x t e n d i n g (1),  10  8 0 DO  f o r t h e E  c y c l e s / s e c  10^  alone  60  p o l a r i z -  f o r  cm beyond t h e b l o c k  t h e alone  ( 2 ) .  192 g o e s a s h a r p i n c r e a s e d i r e c t l y o v e r t h e b l o c k edge w h i c h  is  n o t t h e c a s e f o r the, l i n e  the  wedge e d g e ' H  is  c u r r e n t source<»  enhanced f o r b o t h f i e l d  D i r e c t l y over sources,, but the  enhancement f o r t h e s h e e t c u r r e n t s o u r c e i s shows l e s s  c h a n g e n e a r t h e s t r u c t u r e edges  current source  greater. - H , too, f o r the  t h a n i t d o e s f o r t h e s h e e t c u r r e n t s o u r c e . • The  r e s u l t i n g a m p l i t u d e s f o r the combined s t r u c t u r e s block, Figs.  79(a),  8 0 ( a ) , 81 ( a )  80(a)  consid-  to h o r i z o n t a l  f i e l d s f o r the l i n e c u r r e n t source reach values ?  and 8 2 ( a ) ] whereas  greater  s h e e t c u r r e n t s o u r c e . • The p h a s e a n g l e <j>_ t e n d s t o  are the  undergo  a n d t h e p h a s e a n g l e \jr s m a l l e r c h a n g e s  for  x  the sheet c u r r e n t source than f o r the l i n e  than  the r a t i o s  than u n i t y f o r a l l p o i n t s along the t r a v e r s e s f o r  l a r g e r changes  and  Another d i f f e r e n c e i s  that the amplitude r a t i o s of the v e r t i c a l  u n i t y •{Figs. 7 9 ( a )  [wedge  and 8 2 ( a ) ] a r e hence  e r a b l y d i f f e r e n t f o r t h e two s o u r c e s .  less  line  current  source.  • To s t u d y how t h e r e l a t i v e p o s i t i o n s o f t h e wedge b l o c k a f f e c t t h e f i e l d components f o r a l i n e  current  source,  t h e p o s i t i o n o f t h e wedge was c h a n g e d ( a s was done f o r sheet c u r r e n t source, F i g s .  59 t o 6 0 ) .  The r e s u l t s  and  the  i n F i g . 83  a r e f o r t h e wedge edge d i r e c t l y o v e r t h e b l o c k e d g e , w h i l e t h e results  in Fig.  oh a r e f o r t h e b l o c k edge e x t e n d i n g 10 cm  b e y o n d t h e wedge e d g e . - F i g u r e s  83(a) a n d 8 ( a ) k  are f o r a  m o d e l f r e q u e n c y o f 3 x 10^ c y c l e s / s e c w h i l e F i g s .  83(h)  and  8 Cb) show t h e r e s u l t s f o r a f r e q u e n c y o f 10^ c y c l e s / s e c . k  :  comparing the r e s u l t s o f F i g s . w i t h the r e s u l t s of F i g s .  83 a n d oh ( l i n e c u r r e n t  In  source)  59 a n d 60 ( s h e e t c u r r e n t s o u r c e )  we  193  F i g u r e  c u r r e n t wedge and  The  83.  and  w i t h  amplitudes  the the  f r e q u e n c i e s  E  and  phase  p o l a r i z a t i o n  wedge (a)  edge 3x10  f o r  d i r e c t l y ,  (b)  10  J  angles  f o r  a  l i n e  t r a v e r s e s o o v e r  the  over  edge  the  b l o c k  c y c l e s / s e c .  19  >  9  2  x  CO  H  k  »  T7T77A  V/*///\  UJ  ' 20 ' 4*0 ' 6'0' 80 '  l6o'  '  Y cm  i  20  '  (a)  j—•—i—•—i—•  40  60  80  I  100  'O X «>  ro Cn CM  'o CD  ro*  4  'E >  ro  H  'o x o  mrrn  UJ  F i g u r e  edge  N  s  ->—i— —i— —i— —i— —i— 20 40 60 80 100 1  8^1-^  c u r r e n t wedge  x 1  1  • The amplitudes  1  t h e b l o c k  a n d f r e q u e n c i e s  edge (a)  1/ /  v r w r n  —I—•—i—•—i— —i—'—r~ 20 40 60 80 100 Y cm  f o r  angles  f o r a  t r a v e r s e s  extending  10  ,• ( b )  10  3x10  (b) 1  a n d phase  a n d t h e E- p o l a r i z a t i o n  w i t h  -40  over  cm beyond J  l i n e t h e t h e  c y c l e s / s e c .  wedge  195 a g a i n see t h a t a l t h o u g h t h e r e i s  a considerable s i m i l a r i t y i n  t h e c u r v e s f o r t h e two s o u r c e f i e l d s , t h e e n h a n c e m e n t of- H a n d H_ o v e r t h e s t r u c t u r e e d g e s i s the l i n e  c u r r e n t source than f o r the sheet c u r r e n t  The g e n e r a l o b s e r v a t i o n s discussed  w i t h r e s p e c t t o f r e q u e n c y dependence  c u r r e n t p r o b l e m as  • Figures  well.  85, 86, a n d 87 show t h e H p o l a r i z a t i o n  (wedge edge p a r a l l e l  to the h o r i z o n t a l magnetic f i e l d of  - F i g u r e 85 g i v e s  t h e r e s u l t s f o r t h e wedge  e x t e n d i n g 10 cm b e y o n d t h e b l o c k edge.' F i g .  edge the  87 t h o s e  t h e b l o c k edge e x t e n d i n g 10 cm b e y o n d t h e wedge e d g e *  model f r e q u e n c i e s u s e d f o r t h e measurements t o 87 w e r e 3 x 10  and 1 0  J  t o 87 ( l i n e c u r r e n t s o u r c e )  cycles/sec. with Figs.  i d e n t i c a l i n t h e two c a s e s ; wedge e d g e ,  is  E,  85  In comparing F i g s .  85  61  t o 63 ( s h e e t  l i n e current source,  cur-  is  almost  however, d i r e c t l y over  c u r r e n t s o u r c e . • The H /H'  than u n i t y f o r a l l p o s i t i o n s  rent source.  z  a b o u t 30$ l a r g e r f o r t h e s h e e t c u r r e n t  than f o r the l i n e  The  shown i n F i g s .  r e n t s o u r c e ) , we s e e t h a t t h e b e h a v i o r o f Hy. a n d H  less  the  86 t h o s e f o r  wedge edge d i r e c t l y o v e r t h e b l o c k e d g e , a n d F i g . for  source.  i n the r e s u l t s f o r the sheet c u r r e n t problem a p p l y  t o the l i n e  source).  considerably smaller for  ratios,  the  source though  and f r e q u e n c i e s f o r  the  are l a r g e r than those f o r the sheet  The b e h a v i o r o f t h e p h a s e a n g l e s  is  cur-  very  s i m i l a r f o r t h e two s o u r c e f i e l d s , w i t h t h e e x c e p t i o n t h a t ty LL  f o r a f r e q u e n c y o f 3 x 10  c y c l e s / s e c , undergoes  much g r e a t e r  changes d i r e c t l y o v e r t h e s t r u c t u r e edges f o r t h e l i n e  current  s o u r c e t h a n f o r t h e s h e e t c u r r e n t s o u r c e . ' As was f o u n d f o r  1  196  'o  200  _  X cvi  —i—|—I-T-  'o  E  cvi  5l2 > CM  'O  l  |  1  2  '  1  -  +  ' > / / /a / / S  .0  i°  9  •  60  80  100  20  40  60  80  100  amplitudes  the cm  10 Ob)  H  3  and  V ~"4>  40 E  • S / /  M  the  X cm  X cm  phase  p o l a r i z a t i o n  beyond 10  *x  7  *  rr/ /  1/  M/I  (a)  .*  40  and  extending  •  E  20  The  85.  3-x10  80  -40  _ x_  ^  c u r r e n t  120  0  8  00  (a)  H  '  X  F i g u r e  I60  /V*. y -  :  f o r  b l o c k  c y c l e s / s e c .  20  80  100  20 ' 4 0 ' 60 ' 8 0  100  angles  40  f o r  t r a v e r s e s  edge  and  60  a over  l i n e a  wedge  f r e q u e n c i e s  197  ro  1^ si  200  H.  160  I H,  ro  1—r  120  "i— —i—'—i— —r 1  1  E-  80 -  T E T Z m U T  4>°  'g  40 -  7  0  -40  'E 8  UJ CJ"*  g  20  CD 4  40  t—|  60  1  1  1  1  8 0 100  1  >/ A / / I i—i—i—r  X cm  20  40  T—i—r  60  (a)  8 0 100  CM  'O  x 2  CD ro  -  Hz  CM  ' 1  o X  i  i  i  I  *  i  16  <T>  ro  X  s  4  (b)  uT 20  Figure'  60  8 0 100  86-. • T h e a m p l i t u d e s  c u r r e n t wedge and  40  I—r  cm  a n d phase  a n d t h e H p o l a r i z a t i o n  with,  t h e wedge  f r e q u e n c i e s  (a)  T—|—i—|—i—|—i—|—i—r—  edge 3x1O^,  40  angles  60  10^  over  8 0 100  f o r a  f o r t r a v e r s e s  d i r e c t l y (b)  20  l i n e  over  t h e b l o c k  c y c l e s / s e c .  t h e edge  198  CP  200  i  CD  OJ  _  *~lsl  io  I60  H,  CP  I  •  i  •  i  i  I20  'o  80  co 16  VP7T7\  CO  5.  w  o  co  40  I2 8  4  UJ  —T 20  '  'XT 1 '  40  F  I 60  1  1 ' 1 80 100 1  l6o  20 " 40 ' 60 ' 80 '  F i g u r e  1/ /  -40  87.  > The  a m p l i t u d e s  r e n t  and  the  w i t h  the  b l o c k  H  and  p o l a r i z a t i o n edge  X  cm  „ X  cm  e x t e n d i n g  f r e q u e n c i e s  (a)  3x10  W  i — 20  1  7  — i — 40  cm  10  1  (a)  1  — i — 60  40'  60  a n g l e s  t r a v e r s e s beyond  f o r o v e r the  O  LL  and  7  20'  phase f o r  g7>*  ,  (b)  10  0  c y c l e s / s e c .  1  — i — 80  — i — 100  1  80  a  100  l i n e the  c u r -  wedge  wedge  edge  199 the sheet c u r r e n t source, i t i s apparent t h a t the r e l a t i v e p o s i t i o n s o f the wedge and b l o c k f o r the overhead l i n e c u r r e n t source a f f e c t the behavior o f the amplitudes and phases i n the neighborhood In  o f the s t r u c t u r e s .  o r d e r to compare the measurements f o r the two f i e l d  sources (sheet c u r r e n t and l i n e c u r r e n t ) i d e n t i c a l  structures  and l o c a t i o n s i n the tank were used f o r both problems — o n l y d i f f e r e n c e was a change i n source f i e l d .  the  However, some  t e s t s were made to study how the f i e l d components were a f f e c t e d by changing the s t r u c t u r e p o s i t i o n ,  In p a r t i c u l a r ,  o b s e r v a t i o n s were made on the e f f e c t which a change i n the h o r i z o n t a l d i s t a n c e to the overhead l i n e c u r r e n t had on the behavior o f the components.  F i g u r e 8*+(a) ( d i s c u s s e d  earlier)  shows the r e s u l t s f o r the wedge edge l o c a t e d a t y = 5 k  h o r i z o n t a l d i s t a n c e o f 95 cm from the p o s i t i o n  cm ( a -  directly  below the l i n e c u r r e n t ) f o r a frequency o f 3 x 10  cycles/sec-.  F i g u r e 88(a) shows the r e s u l t s f o r the same s t r u c t u r e but w i t h the wedge edge a t y » +5  cm (*+5  cm from the p o s i t i o n  d i r e c t l y below the l i n e c u r r e n t ) , w h i l e F i g . 88(b) shows the r e s u l t s when the wedge edge i s d i r e c t l y below the l i n e c u r r e n t . < H „ and p a r t i c u l a r l y H_ show much i n c r e a s e d eny z hancement d i r e c t l y over the edges o f the s t r u c t u r e as the s t r u c t u r e i s moved n e a r e r to the l o c a t i o n d i r e c t l y below the l i n e current.  F i g u r e 8 (a) shows that the enhancement o f H„ k  i s approximately the same over the wedge edge as i t i s over the b l o c k edge, w h i l e F i g . 88(b) shows a much l a r g e r enhancement over the b l o c k edge than i t does over the wedge edge.  200  "O X o  cvi cn f 'O  X  oo  CM  >  '2  x  00  UJ  0 V /  mrm  MS  -i—,—i—|—i—i—i—i—•—i—»  0  -20  inrm  40 20  40 60  • v  (a)  i—i—i—i—«—i—i—i—•—r~  0  -20  n r n  Y cm  20  40 60  T—•—r  • 60 -40 -20 F i g u r e  88.  > T h e a m p l i t u d e s  p o l a r i z a t i o n f o r  Y cm  t r a v e r s e s  e x t e n d i n g  10  p o s i t i o n s  (a)  a n d a over  l i n e  =  c u r r e n t  t h e wedge  cm beyond y  a n d phase  -5,'  w i t h  w i t h  t h e wedge (b)  y  =  a n g l e s  ~h0  f o r t h e E  f=3x10  t h e b l o c k edge c m .  k  c y c l e s / s e c edge  f o r wedge  edge  201  The phase angle </>_ a l s o shows c o n s i d e r a b l e change. • F o r the Z  v e r t i c a l source h e i g h t used here, the wedge tends to s h i e l d somewhat the b l o c k edge from the c y l i n d r i c a l source f i e l d f o r the arrangement o f F i g *  88(h)  9  w h i l e t h i s i s n o t the case  when the s t r u c t u r e i s n e a r e r the p o i n t d i r e c t l y below the source. • The-, change i n the enhancement over the wedge edge i s much l e s s  s  relatively,  than i s the change d i r e c t l y  t h e b l o c k edge.- < The b e h a v i o r o f both H  z  and R y  s  over  when the  s t r u c t u r e i s near the p o i n t d i r e c t l y below the l i n e c u r r e n t source, i s v e r y s i m i l a r overhead  to t h a t observed e a r l i e r f o r the  sheet c u r r e n t source [e.g.'Pig. 60(a)]» • I t i s  apparent from' F i g s «  8 Ca) 88(a) k  9  zontal position relative  5  and- (••&), t h a t the h o r i -  to the overhead l i n e c u r r e n t i s a  v e r y important f a c t o r i n determining the behavior o f the oag«* no-tic f i e l d component!  u  202 Chapter  k  »  SUMMARY  The of  the  p r e s e n t  e f f e c t  e l e c t r i c a l have  on  n e t i c  the  a  c e r t a i n  b e h a v i o r  v a r i a t i o n s and  v a r i e t y  of  of  c o n d u c t i v i t i e s i n  f i e l d  l a y e r  a  the  of  f i e l d  amplitudes  f r e q u e n c i e s , and  phase  a n g l e s  been a t  plane  of f o r  a  from  the  r e s u l t s  o b t a i n e d ,  z o n t a l l y  l a y e r e d  c o n d u c t i n g  l a r g e  r a t i o  s t r u c t u r e wave a  i s  source  plane  wave  a t  f i e l d . source  f l a t  c r u s t  B o t h  source have  f i e l d s  been c y c l e s / s e c )  used  been  l a y e r  the  are  of  cannot  be  a  w i t h i n  e a r t h  S i n c e  i n  s t u d y i n g  f i e l d  i s  f r e q u e n t l y  u p p e r  e a r t h  i n  r e s u l t s f o r  of  v a r i o u s  i n  depths,  c o n s i s t i n g I t  changes  l a y e r e d  and  the  t h i c k n e s s e s ,  i s i n  a f f e c t  s u r f a c e ,  e x p l a i n e d  e l e c t r i c  c o n d u c t i n g  s t r o n g l y  e a r t h ' s  where  and  l a y e r s .  a l t h o u g h  e a r t h  the  o b t a i n e d  c o n d u c t i n g  that  f o r  E x t e n s i v e  c o n d u c t i n g  H_/H__ o b s e r v e d z y l i k e l y ,  s u r f a c e  have  f l a t  u n i f o r m  angles  the  i n c i d e n c e ,  and  phase  s u r f a c e .  emu)  and  e l e c t r o m a g -  (10"°^ t o 10^  developed  waves.  angles  two  and  e a r t h ' s  s e v e r a l  10  s t r a t i f i e d  one,  tudes  t h r e e  f o r  to  components  c o n d u c t i v i t i e s  e a r t h ' s  d i s t r i b u t i o n s  (10  have  i n c i d e n t  and  the  f r e q u e n c i e s  h o r i z o n t a l l y of  sources  o c c u r r i n g  n a t u r a l l y  the  u n d e r s t a n d i n g  g e o p h y s i c s .  E x p r e s s i o n s magnetic  c u r r e n t  the  c o n d u c t i v i t y  and  the  i n  models  The  to  d i s t r i b u t i o n s  analogue  d e t a i l .  i n t e r e s t  i o n o s p h e r i c  at  i n  s p e c i a l  c o n t r i b u t e s  observed  t r e a t e d the  CONCLUSIONS  r e s e a r c h  c o n d u c t i v i t y  m a t h e m a t i c a l and  t h a t  AND  e v i d e n t a  h o r i -  the  the  of  a m p l i -  r e l a t i v e l y  g e o l o g i c a l terms  geomagnetic assumed,  of  a  plane  v a r i a t i o n s the  r e s u l t s  203  d i s c u s s e d  in-  i n d i c a t i o n l a y e r e d  t h i s  of  work  the  e a r t h  are  e f f e c t  would  an  e x t e n s i o n  c o n s i s t i n g  of  s e v e r a l  E a c h  of  number to  a  and.  1  of  S e v e r a l  c o n d u c t i v i t y  t r e a t e d  i n  problem^ l a y e r s ,  when  w i t h  homogeneous  an  and  components-  an  change  i n t e r e s t  f o r  t h i s  and  comparison  the  plane  c o n d u c t i n g  s u r f a c e f i e l d  of  was  a  (amplitudes  and  w i t h  r e s p e c t  to  c u r r e n t .  l i n e  c u r r e n t  model  to  h o r i z o n t a l  p e r i m e n t a l l y  observed,  o b t a i n e d ,  i s  i t  magnetic v a l u e s .  e v i d e n t  n e t i c  v a r i a t i o n s  were  f i e l d  components  a t  r a t i o s  an  the  t h a t  of  - From i f  a  the  s u r f a c e  on  e a r t h  i n -  the  a  wide  and  the  the  of  of  t h i s the  of  e x -  r e s u l t s e l e c t r o m a g -  c u r r e n t ,  should  range  f o r  range  the  the  l o c a t i o n s  r e s u l t s  of  i n  i n  e v a l u a t i n g  d e t a i l e d  l i n e  three  e a r t h .  amplitudes  source  i o n o s p h e r i c e a r t h ' s  f o r  i n  e a r t h  e f f e c t  have  b y  - The  f i e l d s  were  a n a l y t i c a l l y ,  h e i g h t s ,  the  r e p r e s e n t  and  the  l a y e r s  angles)  source  y i e l d  to  c o n d u c t i v i t y .  two of  c u r r e n t ,  c o n d u c t i v i t i e s , overhead  s u f f i c i e n t  geophysics  c o n d u c t i n g  l i n e  phase  a  i n  been  l a y e r s ) .  c o n d u c t i n g  f r e q u e n c i e s ,  v e r t i c a l  a  e a r t h  have  (n  i n  f o r  s t u d i e d  homogeneous  o s c i l l a t i n g  the  i n  m u l t i l a y e r e d  assessment  source  of  i n t o  r e s u l t s  second  f i e l d  r e s u l t s  e a r t h  the  A  near  some  c o n d u c t i n g  c o n d u c t i v i t y ,  continuous  homogeneous  a  g i v e  e x p r e s s i o n s  d i v i d e d  of  a  w i t h  a t  of  was  changing  a  The  f i e l d s  problem  they  d i s t r i b u t i o n  of  m u l t i l a y e r  f u n c t i o n s  r e s u l t i n g  the  problem l a y e r s ,  a  l a y e r s  compared  a l l o w  the  f o r  a p p r o x i m a t i o n  d e t a i l .  s i n c e  c o n d u c t i v i t y  u n i f o r m  t h i c k  s u b l a y e r s ,  good  to  e v a l u a t e d  s e v e r a l  the  i n t e r e s t  have.  • As  developed  of  be  then  the  s t r o n g l y  20^  d e p e n d e n t on- t h e s o u r c e f r e q u e n c y ,  the source p o s i t i o n ,  the c o n d u c t i v i t y of  comparing these  ;  the e a r t h .  In  w i t h t h o s e f o r t h e p l a n e wave s o u r c e , i t i s fields the- two  a t the e a r t h ' s sources,  results  clear that  the  s u r f a c e s h o u l d be q u i t e d i f f e r e n t f o r  1  • An analogue model s u i t a b l e f o r s t u d y i n g of n a t u r a l - geomagnetic various  and  and t e l l u r i c  the  behavior  f i e l d variations  for  g e o l o g i c a l s t r u c t u r e s was d e s i g n e d and c o n s t r u c t e d .  The two t y p e s o f f i e l d  sources  u s e d were an o s c i l l a t i n g  sheet  c u r r e n t a n d a n o s c i l l a t i n g l i n e c u r r e n t , • The m o d e l was d e s i g n e d i n s u c h a way' t h a t o t h e r s o u r c e s , and m a g n e t i c d i p o l e s , will  s u c h as  electric  c o u l d be u s e d a s w e l l * . • D i p o l e  be s t u d i e d a s a c o n t i n u a t i o n o f t h i s p r e s e n t E x t e n s i v e measurements  have been t r e a t e d f o r v a r i o u s  work.  o f a m p l i t u d e s and phase geological structures  i n t h e s u r f a c e l a y e r , v e r t i c a l f a u l t s and d y k e s ,  the- t w o . s o u r c e s  embedded  sea  mounts  c o a s t l i n e s t r u c t u r e s (sea-land intern-  f a c e s and an u p w e l l i n g i n a h i g h - c o n d u c t i n g m a n t l e ) , and i s l a n d s  angles  including  a- f l a t l a y e r e d e a r t h , c y l i n d r i c a l c o n d u c t i n g b o d i e s  a n d c o n d u c t i n g domes,  sources  i n an ocean c h a n n e l  (sheet  ! 0  zone w i t h i n t h e Measurements  c u r r e n t and. l i n e c u r r e n t ) w e r e  for compared  a n d some s i g n i f i c a n t d i f f e r e n c e s i n t h e a m p l i t u d e s a n d p h a s e s f o r t h e two s o u r c e s  found,, i n d i c a t i n g t h a t t h e s o u r c e  d i s t r i b u t i o n i n the g e o p h y s i c a l problem p l a y s  field  an i m p o r t a n t  r o l e i n d e t e r m i n i n g t h e b e h a v i o r o f t h e f i e l d components the earth*s  surface  0  ' Measurements  f o r the l i n e  at  current  source demonstrated t h a t the behavior of the f i e l d  variations  2 0 5  n e a r the  d i s c o n t i n u i t i e s o v e r h e a d  c o a s t l i n e s u p p o r t  l i n e  and  s t r u c t u r e s  p l a i n i n g  e x p e r i m e n t a l l y  .''iQmalies  0  ;  I n  o-senting  e a r t h ' s  a n  m a n t l e  w o u l d  do  r e s u l t s m o d e l wide  n o t  o b t a i n e d  i n t e r e s t  and  i t o f a  i n  d i s c u s s e d  i n  t h i s  work  range  o f  g e o l o g i c a l  r e a d i l y  f o r  the t e n d  v a r i o u s  w o r k e r s  i n  m a g n e t i c t h a t  e f f e c t  to e x -  f i e l d  a, m o d e l  c o n d u c t i n g  to  s t r u c t u r e  zone  o n  i n  the  the  c o a s t l i n e s .  s u i t a b l y  s t u d y i n g to  d i s t a n c e  c h a n n e l  s i g n i f i c a n t n e a r  the  o c e a n  f o u n d  h i g h l y  o n  o b t a i n e d  c o a s t a l  was a  a n  by  e m p l o y i n g  s u b m i t  u s e d  f i e l d s .  i n  o b s e r v e d  h a v e  methods  r e a d i l y  r e s u l t s  p o s t u l a t e d  v a r i a t i o n s  c o n s i d e r a b l e  d e p e n d e n t  i s l a n d s  u p w e l l i n g  - A n a l o g u e  w h i c h  The  p a r t i c u l a r ,  e l e c t r o m a g n e t i c  of  s t r o n g l y  c u r r e n t .  s t r u c t u r e s  the  i s  g e o p h y s i c a l  a n a l y t i c a l d e m o n s t r a t e l e n d s  s t r u c t u r e s  s c a l e d  t h a t  a  to  a r e  p r o b l e m s  s o l u t i o n .  i t s e l f  f o r  m o d e l s  the  - The  a n a l o g u e  s t u d y i n g  v a r i e t y  of  •  a  s o u r c e  206 BIBLIOGRAPHY  Bomke,  H.  to  A .  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