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An investigation of the magnetotelluric method for determining subsurface resistivities. Srivastava, Surat Prasad 1962

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Y  AN INVESTIGATION OF THE MAGNETOTELLURIC METHOD FOR DETERMINING  SUBSURFACE  RESISTIVITIES  by SURAT PRASAD SRIVASTAVA B , S c . ( H o n s ) , I n d i a n I n s t i t u t e o f T e c h n o l o g y , K h a r a g p u r , 1958 M.Tech., I n d i a n I n s t i t u t e o f T e c h n o l o g y , K h a r a g p u r , 1960  A T H E S I S SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF in  PHILOSOPHY  t h e Department of Physics  We a c c e p t t h i s t h e s i s  as c o n f o r m i n g t o t h e  required standard  THE UNIVERSITY OF B R I T I S H November,  1962  COLUMBIA  i i i  In  presenting  requirements of  British  it  freely  agree for  that  that  for  thesis  available  o r by h i s  of  O c t o b e r 9,  that  fulfilment at  the  extensive  thesis  shall  permission.  Zoology  1964  Columbia,  of  the  University  Library shall  copying  representative. this  the  and study.  may b e g r a n t e d  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, C a n a d a  Date  degree  reference  for  purposes  my w r i t t e n  Department  agree  for  permission  p u b l i c a t i o n of  without  in partial  an advanced  Columbia., I  scholarly  Department  this  by  the  It  is  not  be  I of  make  further this  Head o f  thesis my  understood allowed  ABSTRACT  The m a g n e t o t e l l u r i c method, which depends upon t h e determination  of impedance v a l u e s over a wide frequency  range  (0.001-1 cps) from a p a i r of o r t h o g o n a l e l e c t r i c and magnetic f i e l d components, has been used i n the past by s e v e r a l i n v e s t i g a t o r s t o determine the r e s i s t i v i t y of t h e c r u s t and upper mantle.  Because o f the d i v e r s i t y of t h e r e s u l t s  obtained by the m a g n e t o t e l l u r i c method i t was f e l t to examine the method c r i t i c a l l y and unambiguous r e s u l t s . was  necessary  i n order t o o b t a i n u s e f u l  To c a r r y t h i s out an i n v e s t i g a t i o n  made of the m a g n e t o t e l l u r i c f i e l d recorded  simultaneously  at s i x s t a t i o n s i n c e n t r a l A l b e r t a d u r i n g August 1961. The i n v e s t i g a t i o n i s d i v i d e d i n t o f i v e main s e c t i o n s ; the r e c o r d i n g of t h e m a g n e t o t e l l u r i c f i e l d , t h e a n a l y s i s o f the f i e l d r e c o r d s by v a r i o u s methods, the e v a l u a t i o n o f the v a l i d i t y of t h e d i f f e r e n t assumptions made i n the m a g n e t o t e l l u r i c method, the d e t e r m i n a t i o n o f s u b s u r f a c e r e s i s t i v i t i e s , and the i n v e s t i g a t i o n o f inhomogeneous and a n i s o t r o p i c b o d i e s . Continuous r e c o r d i n g s o f Ey, H  x  and H  z  were made d u r i n g  August 1961 f o r two weeks a t s i x s t a t i o n s , each 100 km apart and o r i e n t e d i n a north-south (113.5° W l o n g i t u d e ) .  approximately  direction  I n a d d i t i o n two e x t r a components  E  x >  Hy were recorded at the central station, Beiseker. Estimates of the wave impedance E / H y  x  were obtained by  inspection of quasi-sinusoidal events on the records from Meanook and Cardston.  Using Cagniard's method an estimate  of the subsurface r e s i s t i v i t y  p was made at Meanook.  No  estimate could be made at Cardston because of the large scatter of points i n the plot of E / H y  x  against period T,  Subsurface inhomogeneities near Cardston are believed to be the main cause of t h i s scattering. At Beiseker, power spectra of selected lengths of records were computed and from them the r a t i o s E / H and y  E /H x  x  were obtained i n order to estimate subsurface r e s i s -  y  tivities.  In addition a method for interpreting anisotropic  bodies has been suggested and used at Beiseker to explain the differences which exist between the r a t i o s E /HL and V  E /H . x  y  A comparison between the various methods suggested by d i f f e r e n t investigators to interpret magnetotelluric data has been made and i t has been shown with the help of t h e o r e t i c a l models that these methods have no advantage over the curve matching method suggested by Cagniard.  Moreover,  i t has been shown that such methods may give ambiguous r e s u l t s i f applied to the interpretation of high frequency ( > 0.005 cps) magnetotelluric data. In order to judge the v a l i d i t y of the basic assumption  -iv-  of Cagniard's method, v i z . t h a t the h o r i z o n t a l g r a d i e n t s of the f i e l d v e c t o r s a r e n e g l i g i b l e compared t o v e r t i c a l g r a d i e n t s , power s p e c t r a of c o r r e s p o n d i n g l e n g t h s of r e c o r d s , used f o r the e s t i m a t i o n of the r e s i s t i v i t i e s , were computed at a l l s i x s t a t i o n s f o r the components Hx and Hz.  Micro-  p u l s a t i o n a c t i v i t y which e x h i b i t e d h i g h coherence  o f Hx at  a l l s i x s t a t i o n s y i e l d e d the l e a s t s c a t t e r i n the p l o t as was expected.  By c a r e f u l l y s e l e c t i n g  b a s i s o f t h i s and other coherence  P  vs T  data on the  c r i t e r i a i t i s believed  that a r e l i a b l e i n d i c a t i o n has been o b t a i n e d of a marked decrease i n the r e s i s t i v i t y i n the uppfer p a r t of the E a r t h ' s mantle.  xiv  ACKNOWLEDGEMENTS  It i s my pleasure to acknowledge the help I have received from Professor J. A. Jacobs.  During the period when this  research was conducted he has been a constant source of encouragement and advice.  In addition I wish to thank him  for reviewing the manuscript  critically.  I would also l i k e to thank Professor S. H. Ward, Department of Mineral Technology, University of C a l i f o r n i a , Berkeley, for allowing me to work with him for a short time and without whose help a part of t h i s thesis might not have been accomplished. I also thank J. M. Ozard, student from the University of Western Ontario, and N. E. Goldstein, student from the University of C a l i f o r n i a , f o r help with the computations. I g r a t e f u l l y acknowledge the help received from the s t a f f s of the Computation Centers of the University of B r i t i s h Columbia and the University of C a l i f o r n i a .  The constant interest shown  by Dr. T. Watanabe and others i n the Institute of Earth Sciences during t h i s invesgigation i s appreciated.  I also thank  V. M. Brawn f o r reading my manuscript. This work was f i n a n c i a l l y supported by the o f f i c e of Naval Research under Contract No. 3116(00).  -V-  TABLE OF CONTENTS  CHAPTER I  INTRODUCTION 1.1  Aim of the t h e s i s  1  1.2  Early investigations  1  1.3  The m a g n e t o t e l l u r i c  1.4  D i f f i c u l t i e s i n the i n t e r p r e t a t i o n of magnetotelluric  1.5 II  III  Outline  method  data  6  14  of the t h e s i s  17  FIELD OPERATIONS  19  2.1  Purpose  19  2.2  Geology of the a r e a  21  2.3  Description  28  of the f i e l d o p e r a t i o n s  RECORDING OF MAGNETOTELLURIC SIGNALS  33  3.1  U n i v e r s i t y of B r i t i s h Columbia equipment  33  3.2  U n i v e r s i t y of A l b e r t a equipment  41  3.3  P a c i f i c Naval L a b o r a t o r y equipment  42  3.4  U n i v e r s i t y of C a l i f o r n i a  43  3.5  F i e l d procedure  equipment  51  -vi-  IV  V  METHODS OF ANALYSIS 4.1  General  56  4.2  Visual correlation analysis  58  4.3  Power s p e c t r a l a n a l y s i s  61  4.4  Error analysis  70  78  5.1  General  78  5.2  Harmonically varying f i e l d s  80  5.3  Horizontal  space v a r i a t i o n o f the  magnetic f i e l d 5.4  INTERPRETATION OF THE MAGNETOTELLURIC DATA 6.1. General 6.2  93 97 97  Determination of the d i s t r i b u t i o n of r e s i s t i v i t y  6.3  82  R e l a t i v e magnitudes of the v e r t i c a l and h o r i z o n t a l magnetic f i e l d components  103  Combined a n a l y s i s o f Meanook and Beiseker data  VII  y  JUSTIFICATION OF THE ASSUMPTIONS IN THE MAGNETOTELLURIC METHOD  VI  56  ANISOTROPY AND INHOMOGENEITY  139 147  7.1  General  147  7.2  Method of a n a l y s i s  153  7.3  Determination o f k and 9 a t B e i s e k e r  160  7.4  Error analysis  175  -vii-  VIII  RESULTS AND CONCLUSIONS 8.1  General  8.2  R e s i s t i v i t y r e s u l t s a t Meanook,  181 181  Beiseker, and Cardston  181  8.3  Anisotropy r e s u l t s at Beiseker  187  8.4  Conclusions  192  APPENDIX A  RESULTS OF THE POWER SPECTRAL COMPUTATIONS A-I A-II  194  Magnetic  196  Magnetotelluric  202  B  STATISTICAL ANALYSIS  213  C  IMPEDANCE VALUE FOR AN INHOMOGENEOUS MEDIUM  220  D  IMPEDANCE VALUE FOR AN ANISOTROPIC MEDIUM  222  BIBLIOGRAPHY  224  -viii-  LIST OF ILLUSTRATIONS  Figure 1.1  Apparent r e s i s t i v i t y vs p e r i o d different  2.1  Map  o b t a i n e d by  investigators i n d i f f e r e n t regions  10  showing the l o c a t i o n o f the d i f f e r e n t  stations  22  2.2  Main s t r u c t u r a l elements of western Canada  24  2.3  Precambrian s u b s u r f a c e map  26  2.4  Lithology  of the Precambrian basement as  i n f e r r e d from w e l l samples and g r a v i t y anomalies  27  2.5  Geological  29  3.1  B l o c k diagram showing the arrangement  cross  s e c t i o n along the s i x s t a t i o n s  d i f f e r e n t recording  of the  units  32  3.2  C r o s s s e c t i o n of the magnetic d e t e c t o r  34  3.3  Galvanometer  36  3.4  Photocell  3.5  Frequency response of the h o r i z o n t a l vertical British  3.6  a m p l i f i e r layout  a m p l i f i e r and impedance changer  magnetic d e t e c t o r s  38  and  ( U n i v e r s i t y of  Columbia) used at Meanook  Frequency response of the h o r i z o n t a l magnetic d e t e c t o r s used at B e i s e k e r  (Pacific  40 (X and  Y)  Naval L a b o r a t o r y ) 44  XX  3.7  Frequency response of the v e r t i c a l detector  3.8  magnetic  used at Beiseker  45  Cross s e c t i o n of copper-copper s u l f a t e electrode  47  3.9  Circuit  diagram f o r the E a r t h  3.10  Frequency response of the Earth recording  4.1  4.2  filter  50  current  system  52  T y p i c a l example o f n o r t h - s o u t h at  current  magnetic  records  the s i x s t a t i o n s  60  R e l a t i o n s h i p between t h e p o t e n t i a l d i f f e r e n c e t o be m e a s u r e d and t h e l e n g t h  (M N 1  1  of detector  line  - 100 m)  -  5.1  T y p i c a l E and H s i n u s o i d a l m i c r o p u l s a t i o n s  5.2  Latitude distribution north-south  (H ) X  and v e r t i c a l  (H ) Z  Power d e n s i t y v s f r e q u e n c y f o r t h e m a g n e t i c omponent  5.4  Power d e n s i t y  magnetic 84  north-south  at the s i x s t a t i o n s  85  vs frequency f o r v e r t i c a l  m a g n e t i c component a t t h e s i x s t a t i o n s 5.5  Power d e n s i t y  86  and c o h e r e n c y v s f r e q u e n c y a t  s t a t i o n #3 f o r n o r t h - s o u t h 5.6  Latitude distribution  m a g n e t i c component  Latitude  distribution  (HJJ) and v e r t i c a l  88  o f power d e n s i t y f o r  R, and HL f o r e v e n t s o f 30 s e c p e r i o d 5.7  81  of amplitudes of  components f o r e v e n t s o f 30 s e c p e r i o d 5.3  73  of amplitude of  (H ) Z  e v e n t s o f 90 s e c p e r i o d  90 north-south  m a g n e t i c components f o r 92  -X5.8  R a t i o of v e r t i c a l  (H ) t o h o r i z o n t a l (Hjj.) z  magnetic f i e l d components as a f u n c t i o n of p e r i o d at B e i s e k e r 6.1(a)  95  M a g n e t o t e l l u r i c two l a y e r  standard  r e s i s t i v i t y curves 6.1(b)  99  M a g n e t o t e l l u r i c two l a y e r standard  phase  angle curves 6.2  E/H  6.3  (E/H)  y  x  vs l/v/~T o  100 f o r s t a t i o n #6, Meanook  vs frequency  (0-.64 cps) f o r a t h r e e  l a y e r e d E a r t h model 6.4  (E/H)  2  106  112  vs frequency  (0-.03 cps) f o r a t h r e e  l a y e r e d E a r t h model  113  o  6.5  (E/H)  vs frequency f o r a two l a y e r e d E a r t h model  6.6  Apparent r e s i s t i v i t y vs p e r i o d , s t a t i o n #6, Meanook  6.7  119  Power d e n s i t y and coherency vs frequency at s t a t i o n #3 f o r E-W  magnetic and N-S  electric  components 6.8  116  124  Power d e n s i t y and coherency vs frequency a t s t a t i o n #3 f o r N-S magnetic and E-W  electric  components 6.9(a)  125  Apparent r e s i s t i v i t y vs p e r i o d , s t a t i o n #3,  Beiseker  (from E /H ) y  127  x  6.9(b)  Phase angle between E  y  and H  x  vs p e r i o d  128  6.10(a) Apparent r e s i s t i v i t y vs p e r i o d , s t a t i o n #3, Beiseker  (from ^ / H y )  129  -xi-  6.10(b) P h a s e a n g l e between Ex and H 6.11  (E/H)  6.12  E /H  6.13  Apparent r e s i s t i v i t y  y  vs p e r i o d  130  v s f r e q u e n c y a t s t a t i o n #3, B e i s e k e r  2  x  y  vs p e r i o d ,  s t a t i o n #1, C a r d s t o n vs period,  136  s t a t i o n #1,  Cardston 6.14  138  Master curves of apparent r e s i s t i v i t y f o r magnetotelluric  soundings over  a three  layer  Earth 6.15  140  Apparent and  7.1  vs p e r i o d  f o r Meanook 143  Theoretical magnetotelluric contact,  P l o t o f E/H o v e r poorly  7.3  resistivity  Beiseker  vertical 7.2  132  H field  sounding  parallel  across  t o the s t r i k e  a highly conducting  and a  c o n d u c t i n g dyke  Orientation respect  149  150  of the anisbtropy  axes w i t h  t o measuring axes o f s i g n a l and randomly o r i e n t e d  155  7.4  Addition  noise  7.5  T y p i c a l example o f n o r t h - s o u t h and e a s t - w e s t  162  m a g n e t i c components a t B e i s e k e r  163  7.6  V a r i a t i o n o f E/H a l o n g  the s i x s t a t i o n s  165  7.7  V a r i a t i o n o f E/H a l o n g  the s i x s t a t i o n s  for  90 s e c p e r i o d  7.8  Resistivity  7.9  Example o f t h e d i r e c t i o n o f p o l a r i s a t i o n o f electric  i n t e r p r e t a t i o n - Cooking Lake  and m a g n e t i c f i e l d s  166 168  171  -xii-  7.10  Example of the d i r e c t i o n of p o l a r i s a t i o n electric  7.11  of  and magnetic f i e l d s , f o r 25 sec p e r i o d  Apparent r e s i s t i v i t y vs p e r i o d f o r Meanook (from Ej/Hy)  7.12  172  174  Change i n the apparent r e s i s t i v i t y v a l u e s at Meanook o b t a i n e d from data taken at d i f f e r e n t times  176  8.1  R e s i s t i v i t y vs depth p l o t f o r d i f f e r e n t models  185  8.2  Diagram showing the o r i e n t a t i o n  of the  a n i s o t r o p y axes and the d i r e c t i o n of polarisation  of E and H f i e l d s  190  -xiii-  L I S T OF TABLES  Table 4.1  Table time  containing the d i f f e r e n t  frequency  l a g and t h e maximum f r e q u e n c y  power s p e c t r u m e s t i m a t e s  8 0 % r a n g e o f t h e power s p e c t r a l  6.1  Apparent deviation  a t which  c o u l d be made  4.2  resistivity,  bauds,  Ey/H  x  P  o f t h e mean o f  69  density estimates  and s t a n d a r d at different  p e r i o d s a t Meanook 6.2  Apparent r e s i s t i v i t y , between E  v  105 coherency  and H „ a t d i f f e r e n t  and p h a s e  angle  periods at  Beiseker 6.3  121  Apparent r e s i s t i v i t y , between E  x  and H  y  coherency  at different  and p h a s e  angle  periods at  Beiseker 6.4  122  Apparent r e s i s t i v i t y , deviation  Ey/H  x  and s t a n d a r d  o f i t s mean a t d i f f e r e n t  periods at  Cardston 7.1  Direction  76  134 of p o l a r i s a t i o n  magnetic f i e l d s  of e l e c t r i c  and 178  CHAPTER I  INTRODUCTION  1.1  Aim of t h e t h e s i s Because o f t h e d i v e r s i t y of the r e s i s t i v i t y  obtained  results  i n t h e past by the m a g n e t o t e l l u r i c method, i t was  f e l t necessary t o examine t h i s method c r i t i c a l l y i n order t o o b t a i n u s e f u l and unambiguous r e s u l t s .  T h i s i s t h e main aim  of t h e 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 .  To c a r r y i t out  an i n v e s t i g a t i o n has been made of t h e m a g n e t o t e l l u r i c recorded  simultaneously  field  at s i x stations i n Central Alberta  d u r i n g August 1961. The i n v e s t i g a t i o n i s d i v i d e d i n t o f i v e main s e c t i o n s ; t h e r e c o r d i n g of t h e m a g n e t o t e l l u r i c  field,  the a n a l y s i s of f i e l d r e c o r d s by v a r i o u s methods, the e v a l u a t i o n of the v a l i d i t y o f t h e d i f f e r e n t  assumptions  made i n t h e m a g n e t o t e l l u r i c method, t h e d e t e r m i n a t i o n of s u b s u r f a c e r e s i s t i v i t i e s , and t h e i n v e s t i g a t i o n o f inhomogeneous and a n i s o t r o p i c b o d i e s .  1.2  Early investigations The c o n t r a s t i n p h y s i c a l parameters o f t h e s u b s u r f a c e  r e g i o n s o f t h e E a r t h i s t h e b a s i c p r i n c i p l e used i n a l l  -2-  g e o p h y s i c a l methods f o r the e x p l o r a t i o n of s u b s u r f a c e One  bodies.  o f t h e most pronounced c o n t r a s t s i n r e s i s t i v i t y may be  observed i f r e s i s t i v i t y measurements a r e made by one of t h e e l e c t r i c a l methods over a s a l t dome or over a massive s u l p h i d e ore body.  The f i r s t method employed f o r the d e t e r m i n a t i o n of  such b odies made use of n a t u r a l e l e c t r i c f i e l d s i n t h e E a r t h (known as t e l l u r i c c u r r e n t s ) which were p o s t u l a t e d by Davy i n 1821. As a r e s u l t of s t u d i e s o f the d i s t u r b a n c e s  created  i n E n g l i s h t e l e g r a p h i c l i n e s , Barlow (1849) o b t a i n e d  convinc-  i n g evidence  t h a t such c u r r e n t s do i n f a c t flow i n t h e E a r t h .  These c u r r e n t s flow everywhere along the s u r f a c e of t h e E a r t h i n large sheets.  Since t h e l a s t war, t e l l u r i c  current  p r o s p e c t i n g has become t h e p r i n c i p a l e l e c t r i c a l method f o r o i l exploration. and North A f r i c a .  The widest  a p p l i c a t i o n has been i n Europe  Although t h e mechanism by which  these  c u r r e n t s a r e generated has not been p r e c i s e l y e s t a b l i s h e d i t i s g e n e r a l l y b e l i e v e d t h a t they a r e induced  i n the Earth's  s u r f a c e by i o n o s p h e r i c c u r r e n t s which c o r r e l a t e w i t h t h e d i u r n a l changes i n the E a r t h ' s magnetic f i e l d .  Several  workers have attempted t o c o n s t r u c t an e q u i v a l e n t system of c u r r e n t s i n t h e ionosphere  from a knowledge of the v a r i a t i o n s  i n t h e d i r e c t i o n of t h e e l e c t r i c v e c t o r observed at s e v e r a l s t a t i o n s .  Glsh  simultaneously  (1939) s t u d i e d the d i u r n a l v a r i a -  t i o n s of t e l l u r i c c u r r e n t s recorded  a t twelve worldwide  s t a t i o n s and c o n s t r u c t e d a worldwide c u r r e n t system.  However  ) I  -3-  the number of s t a t i o n s i n h i s i n v e s t i g a t i o n was  not  sufficient  to g i v e a t r u e p i c t u r e . T e l l u r i c c u r r e n t s can not be used f o r the  determination  of a b s o l u t e v a l u e s of the r e s i s t i v i t y of s u b s u r f a c e They are g e n e r a l l y used f o r the l o c a t i o n of inhomogeneities.  strata.  subsurface  The u s u a l method f o r the d e t e r m i n a t i o n  the r e s i s t i v i t y of d i f f e r e n t l a y e r s and b o d i e s  of  i n s i d e the  E a r t h i s t o apply a r t i f i c i a l generated c u r r e n t t o the E a r t h at  two  p o i n t s , and measure the p o t e n t i a l drop between  other p o i n t s .  An apparent r e s i s t i v i t y may  thus be  two  obtained  when the g e o m e t r i c a l r e l a t i o n s h i p between the f o u r e l e c t r o d e p o s i t i o n s i s known.  The  p e n e t r a t i o n depth obtained by  this  method i s approximately  p r o p o r t i o n a l t o the s e p a r a t i o n of  the c u r r e n t e l e c t r o d e s .  To determine the r e s i s t i v i t y at  depths of thousands of f e e t would r e q u i r e an l a r g e s e p a r a t i o n of the e l e c t r o d e s .  impracticabaly  Thus t o o b t a i n  t i o n on the r e s i s t i v i t y at depth i n the c r u s t and upper mantle i t i s necessary Determinations  i n the  to u t i l i s e other methods.  of the r e s i s t i v i t y of the E a r t h down to  the core-mantle boundary have been made by v a r i o u s u s i n g two  informa-  d i f f e r e n t methods - v a r i a t i o n s i n the  authors  Earth*s  magnetic f i e l d and a knowledge of the temperature d i s t r i b u t i o n i n s i d e the E a r t h .  The  possibility  of o b t a i n i n g  information  on the d i s t r i b u t i o n of r e s i s t i v i t y w i t h i n the E a r t h from the observed v a r i a t i o n s of the geomagnetic f i e l d was  first  -4-  c o n s i d e r e d by Schuster  (1889), i n h i s development of a  of the d a i l y magnetic v a r i a t i o n s .  theory  He showed t h a t i n the  absence of e l e c t r i c c u r r e n t s f l o w i n g through the  Earth's  s u r f a c e , i t i s p o s s i b l e t o a n a l y s e the magnetic f i e l d  observed  at  of  the s u r f a c e i n t o two  internal origin was  subsequently  p a r t s one  of e x t e r n a l and one  (Chapman and B a r t e l s 1940).  Such a method  developed by Chapman (1919) and by Chapman  and P r i c e (1930) who  derived e x p l i c i t expressions  f o r the  i n t e r n a l and e x t e r n a l p a r t s of the d a i l y magnetic v a r i a t i o n s , c o n s i d e r i n g the E a r t h as a s p h e r i c a l conductor.  Lahiri  Price  separations  (1939) d e r i v e d s i m i l a r e x p r e s s i o n s  f o r the  and  of the magnetic f i e l d u s i n g the storm time v a r i a t i o n s observed a l l over the world.  In a l l these methods the  i n t e r n a l p a r t has been i n t e r p r e t e d i n terms of a r e s i s t i v i t y d i s t r i b u t i o n i n s i d e the E a r t h .  I t may  be shown  mathematically  t h a t there i s no unique s o l u t i o n to the problem of  finding  the e l e c t r i c a l c u r r e n t d i s t r i b u t i o n i n the E a r t h which produces a g i v e n magnetic f i e l d  ( i n t e r n a l p a r t ) at the  s u r f a c e and from t h i s r e s u l t i t i s not d i f f i c u l t  Earth's  t o see t h a t  any attempt t o determine the r e s i s t i v i t y i n the E a r t h from the induced magnetic f i e l d at the s u r f a c e c o n t a i n s a s i m i l a r uncertainty. i t was  For t h i s reason,  necessary  i n a l l the above i n v e s t i g a t i o n s  t o use models of the E a r t h ' s i n t e r i o r , which  c o u l d e x p l a i n the i n t e r n a l p a r t of the magnetic  field.  Knowing the temperature d i s t r i b u t i o n i n s i d e the  Earth  -5-  it  i s p o s s i b l e t o f i n d the r e s i s t i v i t y d i s t r i b u t i o n i f c e r t a i n  assumptions a r e made r e g a r d i n g the c o m p o s i t i o n of the mantle and c o r e .  D i f f e r e n t E a r t h models c o r r e s p o n d i n g t o d i f f e r e n t  temperature d i s t r i b u t i o n s i n s i d e the E a r t h have been proposed by some authors (McDonald 1957, Hughes 1953, Tozer 1959) t o o b t a i n the r e s i s t i v i t y d i s t r i b u t i o n throughout t h e mantle and core.  Both these methods, v a r i a t i o n s i n the geomagnetic  field  and the temperature d i s t r i b u t i o n i n s i d e t h e E a r t h , a r e g e n e r a l l y used t o determine t h e r e s i s t i v i t y of v e r y deep r e g i o n s , i . e . a t depths exceeding 400 km.  They a r e not so  u s e f u l f o r d e t e r m i n i n g the r e s i s t i v i t y 6f the upper 100 km. I t was not u n t i l the  1950 t h a t the p o s s i b i l i t y  of e s t i m a t i n g  r e s i s t i v i t y d i s t r i b u t i o n i n s i d e the E a r t h from e l e c t r o -  magnetic o b s e r v a t i o n s a t one p l a c e was r e a l i s e d .  Tikhonov  (1950) i n R u s s i a suggested the method as a t o o l f o r e x p l o r a t i o n a t g r e a t depths w h i l e almost s i m u l t a n e o u s l y Kato and K i k u c h i (1950) i n Japan showed t h a t some measurements t h a t they had made on phase angles between the magnetic and t e l l u r i c f i e l d s c o u l d be i n t e r p r e t e d on the b a s i s of a two-layered Earth.  T h i s was a s i g n i f i c a n t advance on the q u a l i t a t i v e  t e l l u r i c f i e l d s t u d i e s of Schlumberger However i t was not u n t i l  and h i s co-workers.  1953, when C a g n i a r d p r e s e n t e d h i s  b a s i c paper, t h a t the f u l l p o t e n t i a l of the m a g n e t o t e l l u r i c method was r e a l i s e d .  The term " m a g n e t o t e l l u r i c s " was a s s i g n e d  by C a g n i a r d to the study of t h e v a r i a t i o n s i n the magnetic and  and e l e c t r i c f i e l d s of the E a r t h f o r the d e t e r m i n a t i o n o f resistivity.  1.3  The m a g n e t o t e l l u r i c method The b a s i s o f t h i s method i s the computation o f the wave  impedance from a p a i r of o r t h o g o n a l e l e c t r i c and magnetic f i e l d components measured s i m u l t a n e o u s l y over a homogeneous, i s o t r o p i c Earth. Schelkunoff  The concept  o f wave impedance i s due t o  (1938), and from i t t h e apparent r e s i s t i v i t y may  be c a l c u l a t e d from e i t h e r o f the f o l l o w i n g two e x p r e s s i o n s .  (1.1) or  where  P  the apparent r e s i s t i v i t y i n ohm meters  T » the p e r i o d o f the m a g n e t o t e l l u r i c  disturbance  i n seconds Ex » t h e north-south  component o f the e l e c t r i c  d i s t u r b a n c e i n mv/km Ey =• t h e east-west component of the e l e c t r i c d i s t u r b a n c e i n mv/km Hx = the north-south  component o f the magnetic  d i s t u r b a n c e i n "Y H  y  « t h e east-west component o f the magnetic disturbance i n V  -7-  If the r e s i s t i v i t y of the E a r t h were uniform, measurements of the t a n g e n t i a l e l e c t r i c  and magnetic f i e l d s ,  i n perpendicular  d i r e c t i o n s , would determine  the r e s i s t i v i t y  E a r t h where the r e s i s t i v i t y  i s not uniform i t i s p o s s i b l e t o  speak of an apparent  (eq. 1 . 1 ) .  In an  r e s i s t i v i t y as t h a t v a l u e which, f o r a  uniform E a r t h , would g i v e the same f i e l d In t h e i r papers, Tikhonov  ratios.  and Cagniard, assuming a plane  p o l a r i s e d e l e c t r o m a g n e t i c wave i n c i d e n t p e r p e n d i c u l a r t o the s u r f a c e , gave formulae p e r m i t t i n g a c a l c u l a t i o n of the phase d i f f e r e n c e between the h o r i z o n t a l components of the and magnetic f i e l d s sections.  and of the impedance of m u l t i l a y e r e d  I n t e r p r e t a t i o n of the experimental r e s u l t s  then be based models.  on the r e l a t i o n s d e r i v e d from  Cagniard  normalised so t h a t they may  mathematical  These master curves are  be used f o r d i f f e r e n t  The d e t e r m i n a t i o n of the r e s i s t i v i t y  geological  of the E a r t h ' s  s u b s u r f a c e depends on a comparison between the f i e l d and these master curves. be o b t a i n e d parameters,  such as r e s i s t i v i t i e s and  e s t i m a t e s of parameters i n the r e a l E a r t h .  data.  The  curves  I f a proper f i t between the two  depths, which are assumed f o r the model, may  suggested  may  (1953) gave a s e t of master curves f o r the  i n t e r p r e t a t i o n of f i e l d c u r v e s .  models.  electric  can  layer  be used Niblett  as (1960)  a d i r e c t method of i n t e r p r e t a t i o n of m a g n e t o t e l l u r i c inapplicability  shallow r e s i s t i v i t y  of such a method f o r i n t e r p r e t i n g  s t r a t a w i l l be shown i n subsequent c h a p t e r s .  -8-  B e r d i c h e v s k y and B r u n e l l i  (1959) have g i v e n a d i f f e r e n t  impedance r e l a t i o n s h i p ,  _  When  (1.2)  4 7 r 5 . Id  P , t h e r e s i s t i v i t y of t h e l a s t l a y e r , tends t o  I  where  P^ i s t h e r e s i s t i v i t y o f the i h^ t h e t h i c k n e s s of t h e i * *  1  t  h  Ex I  Hy j  l a y e r i n ohm meters and  l a y e r i n meters.  Such a r e l a t i o n -  s h i p may not be a p p l i c a b l e f o r s h o r t e r p e r i o d s i n those i n s t a n c e s where a decrease i n r e s i s t i v i t y o c c u r s .  More  r e c e n t papers by many R u s s i a n authors have shown t h a t t h e m a g n e t o t e l l u r i c method has great scope. Tikhonov  In p a r t i c u l a r .  (1956) and Kolmakov (1961) have shown t h a t the  method may be used t o study the g e o e l e c t r i c p r o f i l e of s t r a t a l y i n g beneath a l a y e r of p r a c t i c a l l y i n f i n i t e r e s i s t a n c e which cannot, f o r t h i s v e r y reason, be s t u d i e d by d i r e c t c u r r e n t methods.  The m a g n e t o t e l l u r i c method has been used  d u r i n g the l a s t few years t o determine s u b s u r f a c e r e s i s t i v i t i e s a t d i f f e r e n t depths i n R u s s i a by Tikhonov and Shakhsuvavov (1956), B e r d i c h e v s k y and B r u n e l l i  (1961), V l a d i m i r o v (1960),  -9-  B r u n e l l i e t a l (1959), Kovtuia (1961), V l a d i m i r o v and Nikiforova  (1961), V l a d i m i r o v (1961), R o k i t y a n s k i (1961);  and i n t h e U.S.A. and Canada by Garland (1960), C a n t w e l l and Madden (1960), N i b l e t t and S a y n - w i t t - g e n s t i e n (1960), Garland and Webster (1960), Smith and B o s t i c k Hoffman (1962), B o s t i c k and Smith and V o z o f f (1962).  (1961), Horton and  (1962) and E l l i s , Hasegawa  F i g u r e 1.1 shows some o f t h e r e s u l t s  o b t a i n e d i n the U S.A  and Canada.  I t may be seen from t h i s  f i g u r e t h a t a g r e a t s c a t t e r i n g o f p o i n t s i s o b t a i n e d by most investigators.  The authors assume t h a t i n s t r u m e n t a l or  s t a t i s t i c a l e r r o r s a r e the major causes o f t h i s  scattering.  Only r e c e n t l y has an attempt been made t o e x p l a i n i t by inhomogeneity, tion,  a n i s o t r o p i c c o n d u c t i v i t y , or s o u r c e c o n f i g u r a -  ( C a n t w e l l , I960; B o s t i c k and Smith, ,1961; B o s t i c k and  Smith, 1962; P r i c e , 1962).  In the p r e s e n t i n v e s t i g a t i o n  this  problem has been s t u d i e d i n g r e a t e r d e t a i l . In h i s model Cagniard assumed t h a t the f i e l d g i v i n g t o v a r i a t i o n s i n the magnetic and e l e c t r i c f i e l d uniform over a h o r i z o n t a l d i s t a n c e comparable  rise  remains  t o t h e depth at i  which r e s i s t i v i t y d e t e r m i n a t i o n s are> made and propagates as a plane e l e c t r o m a g n e t i c wave.  One of the e a r l i e s t observa-  t i o n s t h a t r a p i d v a r i a t i o n s i n t h e t e l l u r i c f i e l d c o u l d be c o r r e l a t e d over l a r g e d i s t a n c e s was made by Schlumberger and Kunetz  (1946) who found t h a t s e l e c t e d components and s i m u l -  taneous p o r t i o n s of E a r t h c u r r e n t r e c o r d s a t two l o c a t i o n s ,  « E  cr, = 2 5 x 10r  CO  d, = I 5 km Pole Mountain, Wyoming, U S A (Essentially No Overburden}  4  -6  035= 6 x 10 d > 2  A  5  2 0 km is Variable  10' x v ' ^  10  X  \  y  *  Garland and Webster data x , N O T E very deep highly C o n d u c tive Overburden A l b e r t a , Canada cr< I O - 5  x  \  10  ~  fr •>  2  d = 600 2  km  (assuming this trend) Cantwell and Madden o N O T E - very little O v e r burden, M a s s ,U S A  10 3 3 x I O ( w e l l log data) - 2  jd. = 1.8 km B o s t i c k and S m i t h , a ^ T e x a s , U S A  10 10 -4  10  Fig.  1 KT 10  1.1.  10' 10  -2  10 10"  10 10  10 »o  1  -3  FREQUENCY %  10  2  IO  Apparent r e s i s t i v i t y vs p e r i o d o b t a i n e d investigators i n different regions.  3  PERIOD SECONDS  by  different  -li-  near D i j o n i n France and Madagascar, a d i s t a n c e of mately 900 km  approxi-  a p a r t , c o u l d have a c o r r e l a t i o n as high as  0.85.  S i m i l a r h i g h c o r r e l a t i o n s have been found by Duffus (1959) between V i c t o r i a i n western Canada and Borrego Springs i n southern  C a l i f o r n i a f o r magnetic v a r i a t i o n s .  Such h i g h  c o r r e l a t i o n s between t e l l u r i c r e c o r d s over a d i s t a n c e of 900  km suggests t h a t the assumption of a plane wave may  justified.  The  be  a d m i s s i b i l i t y of such an i d e a l i z a t i o n has been  the s u b j e c t of a t h e o r e t i c a l d i s c u s s i o n between Cagniard Wait (1954). considered  Wait p o i n t e d out t h a t i f the sources  are t o be  as an a r b i t r a r y system of d i p o l e s then the  as measured on the s u r f a c e must be m o d i f i e d . t h e o r e t i c a l l y that i f H  x  over a d i s t a n c e of 35 km,  and H  y  and  fields  He showed  do not change a p p r e c i a b l y  when tine p e r i o d of the  oscillations  i s g r e a t e r than 10 seconds and the ground r e s i s t i v i t y i s of the order of 10  13  Wait showed l a t e r  ohm  meters, the c o r r e c t i o n i s not  (1960) t h a t the r a t i o s E / H y  should, f o r t u n a t e l y , remain constant compared to A/2,  x  f o r source  and Ex/Hy distances  where A i s the wave l e n g t h of the  An examination of the f i e l d equations  Important.  source.,  i n d i c a t e s that  source  d i s t a n c e s i n excess of 5 t o 10 s k i n depths may  be a l l t h a t  i s r e q u i r e d to o b t a i n v a l i d r e s u l t s .  i n h i s method  Cagniard  has assumed the presence of l a r g e i o n o s p h e r i c c u r r e n t g i v i n g r i s e to micropulsations. have found evidence  sheets  Akasofu and Chapman (1961)  f o r the presence of r i n g c u r r e n t s at  -12-  h e i g h t s of about 60,000 km, h e i g h t s of about 21,000 km.  and Rosen and F a r l e y (1961) at These r e s u l t s would i n d i c a t e t h a t  i  v a r i a t i o n s i n the geomagnetic f i e l d f o r f r e q u e n c i e s l e s s .01  than  cps propagate towards the E a r t h as plane waves and f o r  f r e q u e n c i e s higher than  .01 cps c u r r e n t sources a t l e s s e r  h e i g h t s p l a y an important developed  role.  However P r i c e (1962) has  a g e n e r a l theory of the m a g n e t o t e l l u r i c method f o r  any source f i e l d .  He has shown t h a t i f the r e s i s t i v i t y i s  assumed t o v a r y w i t h depth below the s u r f a c e , the dimensions and d i s t r i b u t i o n of the i n d u c i n g f i e l d cannot be i g n o r e d , even when the f i e l d  i s on a g l o b a l s c a l e and the depths b e i n g probed  are q u i t e moderate.  No doubt h i s theory i s c o r r e c t from a  t h e o r e t i c a l s t a n d p o i n t but whether i t holds under a c t u a l f i e l d conditions i s s t i l l  undecided.  Rapid v a r i a t i o n s of the geomagnetic f i e l d t i o n s ) have been s t u d i e d by many authors  (micropulsa-  i n the past i n an  attempt t o f i n d the source d i s t r i b u t i o n .  S e v e r a l t h e o r i e s of  the d i f f e r e n t types of m i c r o p u l s a t i o n s which have been c l a s s i f i e d a c c o r d i n g to t h e i r p e r i o d and nature of occurence have been put forward by v a r i o u s authors Watanabe 1956 1959,  and  1959,  D e s s l e r 1958,  Jacobs and Sinno 1960,  (e.g. Dungey  Maple 1959,  B e n i o f f 1960,  1954,  Campbell  Jacobs and  Watanable 1962), and summarised by Jacobs and Westphal (1963). Such m i c r o p u l s a t i o n s correspond  to narrow frequency bands i n  which the energy i s c o n s i d e r a b l y enhanced.  In the magneto-  -13-  t e l l u r i c method, however, a g e n e r a l d i s t r i b u t i o n of energy over a wide frequency band (.001  t o 1 cps) i s more  important.  Hence, so f a r as m a g n e t o t e l l u r i c a n a l y s e s are concerned,  these  d i f f e r e n t t h e o r i e s of the o r i g i n of m i c r o p u l s a t i o n s are not very s i g n i f i c a n t although they have r e c e i v e d a g r e a t d e a l of a t t e n t i o n i n the l i t e r a t u r e d e a l i n g w i t h geophysics.  "theoretical"  However, t h e r e e x i s t s g e n e r a l agreement, based  on a l a r g e amount of evidence, t h a t such geomagnetic v a r i a t i o n s may (the  be e x p l a i n e d i n terms of a s o l a r c o r p u s c u l a r  s o l a r wind).  stream  The s o l a r wind i s p r i m a r i l y composed of  e l e c t r o n s and protons which are c o n t i n u a l l y f l o w i n g out from the sun and Impinging  on the E a r t h ' s magnetic f i e l d .  These  p a r t i c l e s , which t r a v e l w i t h a v e l o c i t y of the order of 1000  k m / s e c , are d e f l e c t e d by the E a r t h ' s magnetic f i e l d ,  which i s c o n f i n e d t o a t e a r drop shaped c a v i t y c a l l e d magnetosphere.  P u l s a t i o n s of the s o l a r plasma are  the  propagated  i n s i d e the magnetosphere as magnetohydrodynamic waves.  These  waves t r a v e l t o the ionosphere w i t h v e l o c i t i e s which v a r y from a few hundred to a few ionosphere  thousand km/sec.  Below the  they can no longer propagate as magnetohydro-  dynamic waves.  The wave i s then observed  round the world  as  an e l e c t r o m a g n e t i c wave. The t h e o r e t i c a l aspect of the f e a s i b i l i t y of u t i l i z i n g n a t u r a l m a g n e t o t e l l u r i c f i e l d s has now investigated.  been f a i r l y w e l l  However because of the d i f f i c u l t y of  -14-  c o n s t r u c t i n g equipment t o r e c o r d s m a l l v a r i a t i o n s o f magnetic f i e l d , these t h e o r e t i c a l s t u d i e s have o n l y experimental c o n f i r m a t i o n 0.1 it  cps).  Few  at low frequency f i e l d s  audio and bodies.  received  (below  attempts have been made t o a s c e r t a i n whether  i s p o s s i b l e t o make p r a c t i c a l use  Ward (1958  the  and  1959)  of higher  frequencies.  has used n a t u r a l f i e l d v a r i a t i o n s i n the  sub-audio frequency (AFMAG) range t o d e l i n e a t e In the sub-audio and  audio frequency range, magnetic  f i e l d f l u c t u a t i o n s appear as r a p i d l y o c c u r r i n g p u l s e s short duration.  ore  of  I f t h e r e i s no h i g h l y conducting s t r u c t u r e  nearby these f i e l d s w i l l tend t o be a l i g n e d i n a h o r i z o n t a l plane w i t h a random azimuth of p o l a r i s a t i o n .  In the  vicinity  of a good conductor, however, the p l a n e of p o l a r i s a t i o n becomes t i l t e d out of the h o r i z o n t a l and p o l a r i s a t i o n more c l e a r l y d e f i n e d . l e s s than  1.4  The  the azimuth of tilt  i s generally  45°.  Difficulties Complications  i n the i n t e r p r e t a t i o n of m a g n e t o t e l l u r i c i n interpreting magnetotelluric  data a r i s e  o n l y when a wide range of impedance v a l u e s  i s observed f o r  same p e r i o d .  (a) t o the use  Such a wide range may  "noisy" records  be due  data  the of  i n the a n a l y s i s , (b) the e l l i p t i c a l p o l a r i s a -  t i o n of the f i e l d , (c) the presence of inhomogeneous and/or anisotropic r e s i s t i v i t y strata. (a) Noise.  Because of the s u p e r p o s i t i o n of n o i s e over  one  -15of the s i g n a l s , e i t h e r magnetic or e l e c t r i c , may  be c o n s i d e r a b l y  impedance v a l u e s  a f f e c t e d i f amplitudes of i n d i v i d u a l wave  t r a i n s are used i n the c a l c u l a t i o n s .  To minimise n o i s e  e f f e c t s , many impedance v a l u e s are u s u a l l y averaged.  In  a d d i t i o n , the presence of n o i s e makes i t d i f f i c u l t t o c o r r e l a t e one  r e c o r d w i t h another.  minimised by the use  However, such d i f f i c u l t i e s may  of power s p e c t r a l d e n s i t i e s i n  c a l c u l a t i o n of impedance v a l u e s . Davenport and for  Blackman and  Root (1954) and Bandat  Tukey (1958),  The  c a l c u l a t i o n of  power s p e c t r a from r e c o r d s i s o n l y j u s t i f i e d i f the  power s p e c t r a l a n a l y s i s ,  s t a t i o n a r y time s e r i e s .  signals  In the d e s c r i p t i o n  ( s e c t i o n 4.3),  s i g n a l s on the r e c o r d s may  the  (1958) have g i v e n methods  t r e a t i n g s i g n a l s c o r r u p t e d by n o i s e .  r e p r e s e n t a s t a t i o n a r y time s e r i e s .  be  of  i t i s shown t h a t  be c o n s i d e r e d as p a r t s of  C a n t w e l l (1960) has  the  a  used average  impedance v a l u e s o b t a i n e d from power s p e c t r a l a n a l y s e s f o r the c a l c u l a t i o n of v a l u e s of apparent r e s i s t i v i t y . i s g e n e r a l l y used i n the a n a l y s i s t o s t a b i l i s e t i o n s of e s t i m a t e s of apparent r e s i s t i v i t y . which an e s t i m a t e may  the f l u c t u a -  T&e  success w i t h  be s t a b i l i z e d depends upon the  of resemblance of the s e l e c t e d p a r t of the r e c o r d s t a t i o n a r y wave. may  not be  series.  On  Averaging  degree  to a  Thus the averaging of spectrum e s t i m a t e s  justified  i f the s i g n a l chosen i s a s t a t i o n a r y  time  the other hand, f l u c t u a t i o n s i n apparent r e s i s t i -  v i t y v a l u e s may  not be due  t o the absence of a  stationary  -16-  time s e r i e s but t o other causes such as e l l i p t i c a l p o l a r i s a t i o n of  the f i e l d or the presence of an inhomogeneity.  Bostick  (1961) has g i v e n good reasons f o r not u s i n g the average of spectrum e s t i m a t e s i n the computation of apparent  resistivity.  To quote, " i t i s d o u b t f u l that averaging the spectrum e s t i m a t e s i n an attempt t o produce the unique apparent  resistivity  e s t i m a t e s demanded by the simple l a y e r e d model i s a worthwhile endeavori" (b) E l l i p t i c a l l y p o l a r i s e d f i e l d s . that e l l i p t i c a l l y p o l a r i s e d f i e l d s t e l l u r i c interpretations.  C a n t w e l l (1960) s t a t e d do not c o m p l i c a t e magneto-  T h i s i s o n l y t r u e however i f  impedance v a l u e s o b t a i n e d a l o n g the major or minor a x i s o f the ellipse  a r e used i n the computation of apparent r e s i s t i v i t i e s .  V l a d i m i r o v and An  (1961) emphasize  that i t i s necessary to  a s c e r t a i n the p o l a r i s a t i o n of the wave t r a i n  used; i f i t i s  found t o be e l l i p t i c a l l y ( r a t h e r than l i n e a r l y ) p o l a r i s e d , the  measurement c o o r d i n a t e system must be p h y s i c a l l y or  m a t h e m a t i c a l l y o r i e n t e d a l o n g the major a x i s o f the (c)  ellipse.  Inhomogeneous and/or a n i s o t r o p i c r e s i s t i v i t y media.  The  s t r u c t u r e of the E a r t h ' s c r u s t i s extremely complex and although  resistivity  d e t e r m i n a t i o n s by m a g n e t o t e l l u r i c  methods r e q u i r e a s t r a t i f i e d media i t i s e q u a l l y important to determine whether the method can be a p p l i e d t o inhomogeneous media.  Neves (1957) and d ' E r c e v i l l e and Kunetz  have a t t a c k e d the problem of a v e r t i c a l  (1959 and  discontinuity  1962)  (i.e. a  -17-  f a u l t ) i n a l a y e r e d E a r t h f o r c e r t a i n s p e c i a l cases of d i r e c t i o n of the e l e c t r o m a g n e t i c  field.  The  the  theoretical  problem of a f a u l t belongs t o t h a t famous c l a s s known as "problem of a f i n i t e l y  c o n d u c t i n g wedge".  In the more g e n e r a l  case such problems have not o n l y remained unsolved have not even been a t t a c k e d e x p e r i m e n t a l l y . 1962)  the  but so f a r  Rankin (1960  and  has s o l v e d the problem of a dyke i n a homogeneous  i s o t r o p i c medium, and Cantwell  (1960) i n h i s Ph.D.  t h e s i s has  g i v e n s o l u t i o n s f o r i n t e r p r e t i n g inhomogeneous and a n i s o t r o p i c media when the m a g n e t o t e l l u r i c f i e l d cally polarised.  i s l i n e a r l y or  L a t e r B o s t i c k (1962) developed  ellipti-  Cantwell's  approach and gave a d e t a i l e d method f o r i n t e r p r e t i n g such cases.  S e v e r a l Russian workers (e.g. R o k i n t y a n s k i  Kovtun 1961,  Chetaev 1960)  have g i v e n d i f f e r e n t methods f o r  i n t e r p r e t i n g inhomogeneous and a n i s o t r o p i c media by m a g n e t o t e l l u r i c method.  1961,  The  the  d e t a i l s of a l l these methods  are summarised i n s e c t i o n 7.1.  A simpler method f o r i n t e r -  p r e t i n g a n i s o t r o p i c media by m a g n e t o t e l l u r i c methods i s developed i n t h i s  1.5  thesis.  O u t l i n e of the t h e s i s The  f o l l o w i n g f o u r p o i n t s have been c r i t i c a l l y  examined  i n the present i n v e s t i g a t i o n . (1) The  methods of a n a l y s i n g r e c o r d s ,  (2) The  v a l i d i t y of the d i f f e r e n t assumptions i n  -18-  C a g n i a r d s work w i t h a p a r t i c u l a r r e f e r e n c e t o the f i e l d T  work  c a r r i e d out i n A l b e r t a . (3)  The d i f f e r e n t methods used t o o b t a i n the r e s i s t i v i t y  d i s t r i b u t i o n i n s i d e the E a r t h by the m a g n e t o t e l l u r i c method. (4) The methods of i n t e r p r e t i n g inhomogeneous and/or a n i s o t r o p i c r e s i s t i v i t y media. The main p a r t of the t h e s i s has been d i v i d e d i n t o two p a r t s , the d e t e r m i n a t i o n of the r e s i s t i v i t y of deep s u b s u r f a c e s t r a t a and the i n t e r p r e t a t i o n of a n i s o t r o p i c strata.  resistivity  The f i r s t s i x c h a p t e r s d e a l w i t h the f i r s t  three  t o p i c s l i s t e d above w h i l e i n the seventh chapter a method i s suggested and used t o i n t e r p r e t a n i s o t r o p i c media. last  chapter the r e s u l t s obtained i n the present  are d i s c u s s e d i n the l i g h t of  In the  investigation  of the known g e o l o g i c a l s t r u c t u r e  the area and a comparison i s made w i t h s i m i l a r  o b t a i n e d by other i n v e s t i g a t o r s i n other r e g i o n s .  results  -19-  CHAPTER I I  FIELD OPERATIONS  2.1  Purpose In t h e past many r e s i s t i v i t y measurements have toeen made  u s i n g the m a g n e t o t e l l u r i c few  method ( s e c t i o n 1.3) but o n l y a  have been found t o be s u c c e s s f u l i n d e t e r m i n i n g the  r e s i s t i v i t y down t o a depth of 100 km.  In a l l these measure-  ments d i f f e r e n t assumptions have been used t o d e r i v e r e s i s t i v i t y f u n c t i o n s , d i f f e r e n t techniques used t o a n a l y s e records  and d i f f e r e n t p r e c a u t i o n s  inducing f i e l d  ( s e c t i o n 1.3).  taken t o ensure a u n i f o r m  As Wait (1954) and P r i c e  (1962)  have s t r e s s e d , the most s e r i o u s assumption that i s u s u a l l y made i s t h a t t h e f i e l d  i s u n i f o r m over a h o r i z o n t a l d i s t a n c e  comparable t o the depth a t which r e s i s t i v i t y are made. it  In order  determinations  to t e s t t h e v a l i d i t y of such an assumption  i s necessary t o make simultaneous m a g n e t o t e l l u r i c  measure-  ments over a l a r g e p a r t of the E a r t h - no attempt has been made i n t h e past One  t o make measurements on such a l a r g e s c a l e .  of the e a r l i e s t observations  that rapid v a r i a t i o n s i n  the t e l l u r i c f i e l d c o u l d be c o r r e l a t e d over l a r g e was  distances  made by Schlumberger and Kunetz (1946, s e c t i o n 1.2).  -20-  S e v e r a l other experimental i n v e s t i g a t i o n s  ( f o r d e t a i l s see  s e c t i o n 5.3) have r e s u l t e d i n n e g a t i v e as w e l l as p o s i t i v e results. For m a g n e t o t e l l u r i c i n v e s t i g a t i o n s i t i s e s s e n t i a l t o make e l e c t r i c and magnetic  measurements over a h o r i z o n t a l  d i s t a n c e comparable t o the h e i g h t o f the source i n order t o ensure u n i f o r m i t y of the source.  I t i s g e n e r a l l y considered  t h a t the source l i e s i n the ionosphere which may extend the D l a y e r , a t a height of perhaps a height of 400 km.  from  60 km t o the Fg l a y e r a t  I t i s thus e v i d e n t t h a t , when the nature  of the source i s t o be i n v e s t i g a t e d , the minimum s e p a r a t i o n of s t a t i o n s i s 60 km and an upper l i m i t t o the extent o f the s o b s e r v a t i o n s w i l l be determined  e n t i r e l y by l o g i s t i c  considerations. Moreover, i n order t o o b t a i n an e s t i m a t e of t h e l a t e r a l s c a l e of the source, along a p r e f e r r e d c o o r d i n a t e l i n e , a space harmonic a n a l y s i s of the v a r i a t i o n s i n the magnetic f i e l d along the l i n e must be c a r r i e d o u t . A minimum o f s i x s t a t i o n s i s necessary f o r such ait a n a l y s i s Thus an experiment  ( N i s h i d a 1962).  was c o n c e i v e d r e q u i r i n g the e s t a b l i s h -  ment of s i x s t a t i o n s i n a geographic n o r t h - s o u t h l i n e approximately 100 km a p a r t . chosen on the assumption  The n o r t h - s o u t h d i r e c t i o n was  that any i o n o s p h e r i c c u r r e n t f l o w  would l i e l a r g e l y i n an E-W sheet or l i n e s 1960).  each  (Jacobs and Slnno  To study the e f f e c t o f source c o n f i g u r a t i o n , i t i s  -21-  necessary t o minimise the v a r i a b l e s by s e l e c t i n g a h o r i z o n t a l l y s t r a t i f i e d uniform g e o l o g i c a l s t r u c t u r e and terrain*  Hence i n p l a n n i n g  s t r u c t u r e and  t o choose a f l a t  the programme the  geological  topography of the a r e a i n which the  were t o be e s t a b l i s h e d was  stations  a l s o taken i n t o c o n s i d e r a t i o n .  The  o n l y p l a c e f u l f i l l i n g these requirements i n western North America was  found t o be the p l a i n s of A l b e r t a and  the s i x s t a t i o n s shown i n F i g . 2.1 considerations  accordingly  were o c c u p i e d .  Subsidiary  l i s t e d below were a l s o borne i n mind when  choosing the l o c a t i o n s of the s t a t i o n s . (1) A major n o r t h - s o u t h highway l i n k i n g a l l s t a t i o n s . (2) Freedom from major power l i n e s and  other  electrical  disturbances. (3) A v a i l a b i l i t y of 2000 x 2000 f t . c l e a r e d a r e a in active agricultural  not  use.  (4) A v a i l a b i l i t y of 60 cps power. (5) P r o x i m i t y Edmonton was  of accommodation. made the base s t a t i o n from which the  s t a t i o n s c o u l d e a s i l y be c o n t a c t e d i f d e s i r e d . t i o n of s t a t i o n s v a r i e d between 110  2.2  Geology of the The  and  138  separa-  km.  area  s u b s u r f a c e geology of the a r e a under i n v e s t i g a t i o n  has been s t u d i e d e x t e n s i v e l y by many petroleum and  The  other  geologists  g e o p h y s i c i s t s w i t h the h e l p of w e l l l o g s and  geophysical  -22-  F i g . 2.1.  Map  showing the location of d i f f e r e n t stations.  the  -23-  data.  A d e t a i l e d account  has been g i v e n i n numerous papers  presented at the 'Western Canada Sedimentary B a s i n Symposium 1954'.  A b r i e f account of the geology of the area o b t a i n e d  from these papers  i s g i v e n below.  G e o l o g i c a l l y western quite d i s t i n c t units, dominantly  Canada may  be d i v i d e d i n t o t h r e e  (1) The Canadian S h i e l d , composed p r e -  of c r y s t a l l i n e igneous r o c k s and metamorphic r o c k s  of g r a n i t i c composition, w i t h l o c a l areas of sedimentary b a s i c v o l c a n i c r o c k s , (2) The d i p p i n g sedimentary  and  I n t e r i o r P l a i n s , where g e n t l y  s t r a t a , P a l a e o z o i c and  l a t e r i n age,  been s u b j e c t e d t o l i t t l e metamorphism or i n t r u s i o n , and  have (3)  The C o r d i l l e r a , a r e g i o n of complex f o l d i n g and f a u l t i n g w i t h sedimentary  r o c k s of Precambrian  i n t r u d e d by Mesozoic  and younger age e x t e n s i v e l y  and p l u t o n i c r o c k s of a wide range of  composition. The main t e c t o n i c u n i t s of western Canada are o r i e n t e d i n a n o r t h west d i r e c t i o n p a r a l l e l t o the Rocky Mountains, and c o n s i s t of a ' g e o s y n c l i n a l b e l t ' b o r d e r i n g the Rocky Mountains, and the e p i c o n t i n e n t a l r e g i o n l y i n g t o the east between the g e o s y n c l i n a l b e l t and the Canadian S h i e l d . F i g . 2.2  shows the d i f f e r e n t important  structural  elements.  I t i s thus e v i d e n t t h a t f o r m a g n e t o t e l l u r i c s t u d i e s the I n t e r i o r P l a i n s r e g i o n i s the most s u i t a b l e l o c a t i o n i n western  Canada.  In t h i s study a l l s t a t i o n s s h o u l d be  from any marked s u b s u r f a c e inhomogeneities  free  except f o r the  u. i. A. LEGEND P % PRE-CAMBRIAN OF ROCKY MTS. / • FAULT TRENDS / R E E F TRENDS u WESTERN BOUNDARY OF V PRE- CAMBRIAN OUTCROP FIG. 2.2 MAIN STRUCTURAL ELEMENTS OF  WESTERN CANADA.  -25-  southernmost  s t a t i o n , Cardston.  However s m a l l e r  resistivity  inhomogeneities such as the r e e f complex at s h a l l o w depths, do occur at some of the s t a t i o n s , e.g. #3,4,5.  Such  inhomogeneities do not a f f e c t the m a g n e t o t e l l u r i c  resistivity d a t a because  of t h e i r low r e s i s t i v i t y c o n t r a s t s compared t o the e n c l o s i n g beds. Recent e x p l o r a t i o n has shown t h a t most o f the I n t e r i o r P l a i n s i s u n d e r l a i n by r o c k s s i m i l a r t o those of the Canadian S h i e l d , and markedly d i f f e r e n t from the Precambrian r o c k s of the C o r d i l l e r a n r e g i o n . o i l f i e l d i n 1947,  Following  the d i s c o v e r y of the Leduc  e x t e n s i v e work has been done on the sub-  s u r f a c e Precambrian of C e n t r a l A l b e r t a . published  Burwash (1957) has  a v e r y comprehensive r e p o r t of such work.  H i s study  i s based mostly on core samples c o l l e c t e d from a l l over Central Alberta.  With the h e l p of aeromagnetic maps of p a r t  of C e n t r a l A l b e r t a and the a d j o i n i n g areas and from w e l l l o g data he concluded t h a t the Precambrian basement s l o p e s the south a t 25 f t . / m i l e . Fig.  2.3.  nature.  towards  Such a c h a r a c t e r i s t i c i s shown i n  The Precambrian r o c k s are mostly g r a n i t i c i n Garland and Burwash (1959) have shown t h a t the major  p a r t of the Bouguer g r a v i t y anomaly over C e n t r a l A l b e r t a must be a t t r i b u t e d t o l i t h o l o g i c a l  changes  i n the Precambrian  basement beneath the sedimentary s e c t i o n . a lithological  map  They have produced  of the basement, F i g . 2.4, by making use  of the p e t r o l o g i c a l and p h y s i c a l p r o p e r t i e s of samples  from  -26-  F i g . 2.3.  Precambrian subsurface map. (After Sikayobni, 1957.)  -27-  41  Fig.  2.4.  L i t h o l o g y o f t h e P r e c a m b r i a n basement as i n f e r r e d f r o m w e l l s a m p l e s and g r a v i t y anomalies. (After Garland and Burwash, 1959.)  -28-  w e l l s t h a t have reached  the Precambrian, together w i t h  the  g r a v i t y data. The sedimentary  r o c k s , o v e r l y i n g the Precambrian basement,  are mostly green and maroon s h a l e s , sandstones,  dolomites,  limestones, and a few c o a l and s a l t beds o c c u r r i n g i n d i f f e r e n t geological units.  A d e t a i l e d d e s c r i p t i o n of each of these rock  types b e l o n g i n g to d i f f e r e n t g e o l o g i c a l p e r i o d s w i l l not  be  g i v e n here because of t h e i r l e s s e r s i g n i f i c a n c e i n magnetot e l l u r i c investigations.  The m a g n e t o t e l l u r i c method, whose  r e s o l v i n g power depends upon the t h i c k n e s s and the c o n t r a s t s of the d i f f e r e n t  resistivity  l a y e r s , cannot be used t o d e l i n e a t e  d i f f e r e n t s u b s u r f a c e r e s i s t i v i t y s t r a t a o v e r l y i n g the Precambrian basement because of i n s u f f i c i e n t contrast.  resistivity  In the present I n v e s t i g a t i o n these r o c k  have been c o n s i d e r e d as one u n i t .  types  To a p p r e c i a t e the depths  to these s t r a t a a c r o s s s e c t i o n has been drawn, F i g .  2.5,  from the i s o p a c h maps g i v e n by Webb (1954).  does not  F i g . 2.5  show a t r u e g e o l o g i c a l c r o s s s e c t i o n although i t g i v e s the v a r i a t i o n of d i f f e r e n t s t r a t a b e l o n g i n g t o d i f f e r e n t  geolo-  g i c a l p e r i o d s along the s i x s t a t i o n s .  2.3  D e s c r i p t i o n of the f i e l d  operations  S i n c e the assembly of the l a r g e amount of equipment p e r s o n n e l r e q u i r e d f o r the i n v e s t i g a t i o n was of  and  beyond the means  a s i n g l e o r g a n i s a t i o n , a c o o p e r a t i v e programme was  under-  PIG.  2.5  GEOLOGICAL CROSS S E C T I O N ALONG T H E S I X S T A T I O N S  -30-  taken between the f o l l o w i n g  groups:  (1) The I n s t i t u t e of E a r t h S c i e n c e s , U n i v e r s i t y of B r i t i s h Columbia. (2) The Department of M i n e r a l Technology, of  California,  University  Berkeley.  (3) The P a c i f i c Naval L a b o r a t o r y , (4) The U n i v e r s i t y of A l b e r t a , Each of the s t a t i o n s was equipped  Esquimalt.  Edmonton.  t o r e c o r d north-south and  v e r t i c a l magnetic components together w i t h the east-west e l e c t r i c component.  I n a d d i t i o n an east-west  magnetic  component and a north-south e l e c t r i c component were r e c o r d e d throughout  the o p e r a t i o n at s t a t i o n #3 at B e i s e k e r .  one day a t a l l s t a t i o n s east-west  and north-south  For  electric  components and the v e r t i c a l magnetic component were r e c o r d e d . Normally  the two magnetic components IL^ and  and an e l e c t r i c  component Ey were r e c o r d e d s i m u l t a n e o u s l y on a r e c t i l i n e a r c h a r t , running a t a speed o f one i n c h per minute, except a t s t a t i o n #3, where the magnetic components were r e c o r d e d on E s t e r l i n e Angus r e c o r d e r s r u n n i n g a t a speed of 3/4"/min. Recordings of E^. and E , a t a l l s t a t i o n s were made i n order y  to  study the d i r e c t i o n of p o l a r i s a t i o n of the e l e c t r i c  at  the d i f f e r e n t s t a t i o n s .  Douglas (1962) has found  t i o n s of some inhomogeneities  field  indica-  i n the area a t shallow depths  from such a study of the d i r e c t i o n of p o l a r i s a t i o n of the electric  field.  -31-  Of the s i x s t a t i o n s , t h r e e were maintained by the U n i v e r s i t y of B r i t i s h Columbia,  one by the P a c i f i c  Laboratory and two by the U n i v e r s i t y of A l b e r t a .  Naval The U n i v e r -  s i t y of C a l i f o r n i a s u p p l i e d equipment f o r the r e c o r d i n g of E a r t h c u r r e n t s at a l l s t a t i o n s .  The d e t a i l s of the equipment  used by each group are g i v e n i n chapter I I I . ment of the s t a t i o n s was a l l o p e r a t i o n a l by August u n t i l August was  27th.  begun on August 15th.  The  establish-  7th and they were  Recordings were c o n t i n u e d  A continuous r e c o r d i n g f o r twelve days  made a t most of the s t a t i o n s except on a few o c c a s i o n s  when i t was  not p o s s i b l e t o run the equipment unattended at  n i g h t because of t h e i r extremely h i g h d r i f t .  GAL. AMP.  ATT POWER  co  CO  I  EARTH CURRENT  F I G , ' 3.1  BLOCK DIAGRAM SHOWING THE ARRANGEMENT OF DIFFERENT RECORDING UNITS  -33-  CHAPTER I I I  RECORDING OF MAGNETOTELLURIC SIGNALS  The  d e t e c t i o n of m a g n e t o t e l l u r i c  observation  signals involves  of v a r i a t i o n s i n the magnetic and  of the E a r t h .  Whitham (1960) and Garland  three d i f f e r e n t o r g a n i s a t i o n s f l u c t u a t i o n s w h i l e o n l y one  electric  field  (1960) have  summarised the d i f f e r e n t methods of r e c o r d i n g In the present i n v e s t i g a t i o n three  the  these v a r i a t i o n s .  types of equipment from  were used t o r e c o r d  type of equipment was  r e c o r d e l e c t r i c s i g n a l s at a l l s i x s t a t i o n s .  The  geomagnetic used t o present  chapter has been d i v i d e d i n t o f o u r s e c t i o n s d e s c r i b i n g d i f f e r e n t types of equipment used d u r i n g  the  the o p e r a t i o n .  The  d e s c r i p t i o n s are kept b r i e f t o a v o i d d u p l i c a t i o n s i n c e d e t a i l e d accounts have a l r e a d y  been p u b l i s h e d  in scientific  reports.  3.1  U n i v e r s i t y of B r i t i s h Columbia equipment Magnetic r e c o r d i n g s  w i t h the U n i v e r s i t y of B r i t i s h  Columbia equipment were made at t h r e e of the s t a t i o n s and  6).  and  5.  (#1,  In a d d i t i o n U.B.C. c o i l s were used at s t a t i o n s The  #4  arrangement of the d i f f e r e n t u n i t s i s shown i n  2,  25 LAYERS OF CO-NETtC A A STRIPS STRIP DIMENSIONS 30" LONG x f WIDE x .014" THICK STACKED IN STAGGERED LENGTHS TO FORM SINGLE CORE, 60" LONG  i  co  MEASURED RESISTANCE EACH COIL.  (NOMINAL)  COIL  30'  START  CAL. COIL 10 TURNS # 16 B 8 S GAUGE FORM EL WIRE  1  »  <i  2  =  H  a  3  =  66.0 64.4 65.5  M  it  ll  n  4 5  = =  66.6 66.2  II  n  6  =  64.0  «  NO  FINISH Fig.  Cross section of the magnetic detector.  OF OHMS u a M  a II  -35-  Fig.  3.1.  The d e t a i l s of each u n i t which were designed  by  D. A. C h r i s t o f f e l are g i v e n below, (a) D e t e c t o r s . formers  The d e t e c t o r c o i l s are wound on f i b r e g l a s s  i n the form of c y l i n d e r s of 1.5"  l e n g t h w i t h #20  diameter  formel i n s u l a t e d copper w i r e .  and  30"  Each c o i l  c o n s i s t s of 10,000 t u r n s wound i n 13 l a y e r s and has a c e n t r a l core of 0,014" s t r i p s of h i g h p e r m e a b i l i t y magnetic m a t e r i a l , laminated to form a bar 1" x 1/2" long.  The core i s f i x e d i n each c o i l  lengths p r o j e c t from each end and means of p i e c e s of cardboard to  i n c r o s s s e c t i o n and i n such a way  that  i s kept i n p o s i t i o n  tubing.  60" 15"  by  T h i s i s done p r i m a r i l y  i n c r e a s e the e f f e c t i v e p e r m e a b i l i t y of the core and  to  i n s u r e t h a t the f l u x d e n s i t y i n the c o i l due t o a s i g n a l i s uniform along i t s l e n g t h . In order t o p r o v i d e p r o t e c t i o n from moisture and  handling  and t o a v o i d any movement of the c o i l s which would produce s p u r i o u s s i g n a l s the c o i l s are encased i n p l a s t i c water p i p e s of  4" diameter.  The c o i l s are not s h i e l d e d w i t h any m a t e r i a l  as i t was. found t h a t t h i s was frequency  (0,01 - 10 cps) s i g n a l s .  c a p a c i t a n c e i s not h i g h enough important.  not necessary f o r r e c o r d i n g low  F i g . 3.2  In a d d i t i o n the  coil  t o make e l e c t r o s t a t i c  shows the d e s i g n of the c o i l .  measured r e s i s t a n c e s of each c o i l are g i v e n In inductance v a l u e of 96.25 h e n r i e s was  effects  The  F i g . 3.2.  found f o r each c o i l .  To o b t a i n the e f f e c t i v e p e r m e a b i l i t y of the c o r e the  An  1 2 3 4 5 6 7  Metal Reflector, # 566 Edmund Scientific Co. Ltd Lamp G - E # 1816 Aviation Rectangular Aparture, Slit size 5x 10 MM RC.X; Lens, # SN 1126, DIA 1.38", FL. 2.25", Edmund Scientific Co. Ltd. EYE Achromat # 6263 , DIA 29 MM, F L . 76 MM, •» .. .. Galvanometer # 41148, Cambridge Inst. Co. Ltd. R C A . 920 Gas filled twin Phototube F i g . 3.3.  Galvanometer amplifier layout.  -37-  demagnetising f a c t o r f o r the s p e c i f i c shape of the core body must be known. graphs.  T h i s may  e a s i l y be found from  demagnetising  Knowing the e f f e c t i v e diameter, the length/diameter  r a t i o may  be c a l c u l a t e d  and the c o r r e s p o n d i n g demagnetising  f a c t o r found from the graph netism' pp 848).  (Richard M. B o z o r t h 'Ferr©mag-  Making use of the e q u a t i o n N(B-H)  = o - -IT"  H  a few v a l u e s of H  Q  H  were c a l c u l a t e d  f o r the c o r r e s p o n d i n g  v a l u e s of B w i t h the h e l p of a B-H ( B e n f a c t i o n Min. Co. magnetic graph 44). giving  O.I)  graph f o r the m a t e r i a l used  s h i e l d d i v i s i o n manual 101-122,  A graph of B a g a i n s t H  Q  was  plotted,  the s l o p e  the e f f e c t i v e p e r m e a b i l i t y .  C r o s s s e c t i o n a l a r e a of the bar = 1" x 0.336" The e f f e c t i v e diameter  - 2 ^ 0.336/rr - 0.636"  Length of the bar  =  60"  Length/Diameter  »  94.3 —4  Demagnetising and  p.  stages.  (N/4-rr)  4 x  a  -  e f f  (b) A m p l i f i e r . galvanometer  factor  10  2710.  The s i g n a l from the d e t e c t o r i s f e d i n t o a  amplifier.  The f i r s t  The a m p l i f i c a t i o n  occurs m  stage i s i n the galvanometer  whose c i r c u i t diagram  i s shown i n F i g . 3.3.  and  two photocell  A beam of  light,  47 K  A / W  I MEG. 4  ANOD AN0DE 2O^ x  I MEG  PIN  BASE  PIN  NO. I • CATHODE I  PIN  NO. 2 « ANODE  I  PIN NO. 3 * ANODE  2  to  PIN NO. 4. « CATHODE 2  '  |  Fig.  I MEG  B-45V  >W I/I DPST  3.4.  Photocell a m p l i f i e r and impedance changer.  co  -39-  from an o p t i c a l d e v i c e as shown i n P i g . 3.3,  i s directed  towards the galvanometer which i n t u r n r e f l e c t s the beam i n t o a gas  filled  RCA  920  photocell*  The  a m p l i f i c a t i o n which  be obtained from the galvanometer depends upon the between the galvanometer and  p h o t o c e l l , w h i l e the  distance amplification  o b t a i n e d from the p h o t o c e l l depends upon the amount of f a l l i n g upon i t . noise,  However, i n c r e a s i n g  so t h a t a compromise must be made.  a m p l i f i c a t i o n i s achieved by a one (Fig.  distance  3.4),  which i s used t o f u r t h e r  increase  the The  in  the H-T  voltage.  beam i s s t a t i o n a r y cell, If  major p a r t One  i s necessary t o e l i m i n a t e  and  impedances of anodes one  two  and  5  The  By  observed.  t h i s method the .  are matched w i t h the  r e s i s t a n c e branch i n the c i r c u i t .  f i c a t i o n of the order of 1 0 - 1 0 galvanometer  photo-  be c e n t r e d by b a l a n c i n g w i t h the h e l p of i n F i g . 3.4.  ohm  drift  d i r e c t e d on t o the c e n t r e of the  a potentiometer shown by BAL  meg  required  When t h e r e i s no s i g n a l , i . e . when the  the t r a c e may  of the one  7  may  be  impedances An  ampli-  achieved from t h i s  amplifier.  output from the galvanometer a m p l i f i e r  Varian recorders.  of  triode  the  a t r a c e i n the c e n t r e of the r e c o r d e r s h o u l d be  not  amplifier  amplification  tube a m p l i f i e r alone would be s u f f i c i e n t t o o b t a i n a second one  increasing  second stage of  a m p l i f i c a t i o n i s achieved from t h i s a m p l i f i e r .  a m p l i f i c a t i o n but  light  stage d i f f e r e n t i a l  t o observe the s i g n a l s on a c h a r t r e c o r d e r . the  means  The  can  i s fed  When V a r i a n r e c o r d e r s are not used,  into the  -40-  -1000  X a Z  MAG  8  I00q  MEANOOK  6 L  4  -100 8 K6  L  > 5 o o  2  6 2 2 Variai  X  N  -10 8  H  Z  :  /  6  6 10 Varian  8  /  t and x /  V  Points from  O  /  u  II  Cal. Aug. 14.61 II  II  4-  26.61  I Volt Range  2  .001  6  INITIAL CALIBRATION  J  L__J  I  I  6  I  l_J_  8 .01 Frequency  F i g . 3.5.  J  2  '  '  4  J  I  '''I  6  8 .1  _L_  in cps  Frequency response of the horizontal and v e r t i c a l magnetic detectors (U.British Columbia) used at Meanook.  0.1  I L  -41-  s i g n a l i s f u r t h e r a m p l i f i e d w i t h the help of an o r d i n a r y A.C. a m p l i f i e r of 1 0  2  gain.  To vary the s t r e n g t h of the s i g n a l  b e f o r e f e e d i n g i t t o the V a r i a n r e c o r d e r an o r d i n a r y attenuator  i s used which can reduce the s t r e n g t h of the s i g n a l  in s i x d i f f e r e n t steps.  The frequency  i s shown i n F i g . 3.5 f o r two  3.2  response of the system  of the c o i l s  used at Meanook.  U n i v e r s i t y of A l b e r t a equipment The U n i v e r s i t y of A l b e r t a , Edmonton, p r o v i d e d  equipment  to r e c o r d magnetic v a r i a t i o n s a t two of the s t a t i o n s , C l i v e (#4) and Cooking Lake (#5).  Chopper a m p l i f i e r s together  U.B.C* d e t e c t o r s were used a t C l i v e t o r e c o r d H  x  with  and H . z  Galvanometer a m p l i f i e r s from t h e U n i v e r s i t y of A l b e r t a with one U.B.C. c o i l and one U n i v e r s i t y of A l b e r t a c o i l were used at Cooking Lake t o r e c o r d H  x  and H . z  A b r i e f d e s c r i p t i o n of  the U n i v e r s i t y of A l b e r t a equipment i s g i v e n below. (a) D e t e c t o r s .  Each d e t e c t o r was made of 20,000 turns of  enamelled copper wire wound about a 1" x 30" laminated AA c o r e .  The d e t e c t o r was covered  open c i r c u i t completely  on the o u t s i d e with one  l a y e r of windings f o r a s h i e l d .  enclosed  (b) A m p l i f i e r .  co-netic  The c o i l was  i n a wooden box approximately  9" x 9" x 30".  The galvanometer a m p l i f i e r s were of the s p l i t  beam-photocell-feedback type and were very s i m i l a r t o those used by U.B.C. S i l i c o n p h o t o r e s i s t o r c e l l s , depends upon the amount of l i g h t  whose r e s i s t a n c e  f a l l i n g upon them, were used  -42-  in  these  amplifiers.  g i v e n by  Hasegawa  amplifiers  and  i n the  those  used  of  phototubes they  the  of  one  Due  to the use  through the to allow  a gamma t o be  f e e d back  these  system  of p h o t o c e l l s i n s t e a d The  signal  amplifier.  i s f e d back to the  is sufficient  a m p l i f i e r s are  main d i f f e r e n c e between  t h r o u g h a D.C.  signal  t e n t h of  these  a r e more compact.  current flowing  obtained  The  of  o f U.B.C. i s t h a t no  latter.  i s sent  reamplified  details  (1962).  is  photocell  The  from  P a r t of  galvanometer  latter.  the  to  null  The a m p l i f i c a t i o n  a m i c r o p u l s a t i o n of  observed  the  a G  on  10  the  order  Varian  recorder,  3.3  Pacific The  Naval Laboratory  Pacific  equipment  Naval Laboratory  provided  geomagnetic v a r i a t i o n s at B e i s e k e r , of  the  short  equipment used are  Detectors.  No.  18  in  79  strips,  cross-section.  t u r n was  tight  end  (b) I n p u t  wire  wound on  e a c h 0.015" x A l l wire  enclosed  r e s i s t a n c e was  47  filter.  The  details  61-3,  a core  0.75"  c o n s i s t i n g of  x 72",  The  the  inductance  input f i l t e r  1/2 A  The  pipe with  35 inch  2  this water-  resulting  about  contained  of  copper  the winding w h i l e  cable connectors.  ohms and  about  s p l i c e s were w e l d e d .  i n a s e c t i o n of p l a s t i c  and  a  here.  insulated lap enclosed  fittings  to record  d e t e c t o r s were made o f 20,732 t u r n s  HF-insulated  s h i e l d v / i t h an in  The  s t a t i o n #3.  i n P.N.L. R e p r i n t  d e s c r i p t i o n of which i s g i v e n  (a)  Telcon  given  equipment  210  two  henries. bridged-T,  -43-  60 c y c l e r e j e c t i o n s e c t i o n s having a t o t a l DC r e s i s t a n c e of 18 ohms i n s e r t e d between t h e antenna and the a m p l i f i e r . The input f i l t e r i n c l u d e d c a p a c i t o r s f o r s e r i e s t u n i n g the d e t e c t o r s and a s e t of r e s i s t o r s which, i f r e q u i r e d , c o u l d reduce the "Q" v a l v e of t h e d e t e c t o r (c) DC A m p l i f i e r . 60 cps was used.  circuit,  A chopper type DC a m p l i f i e r o p e r a t i n g a t An e l e c t r o s t a t i c a l l y s h i e l d e d input t r a n s -  former was s p e c i a l l y b u i l t t o match the chopper t o t h e f i r s t stage of the a m p l i f i e r .  The chopper n o i s e was reduced by  l o w e r i n g t h e chopper-drive fed to  v o l t a g e and u s i n g a "bueking  coil",  by c u r r e n t which c o u l d be a d j u s t e d i n phase and amplitude, c a n c e l out pick-up  coil.  With a source  i n t h e c o n t a c t s i n t r o d u c e d by the d r i v e impedance of 40 ohms the maximum DC 7  v o l t a g e g a i n was about 10 .  An a t t e n u a t o r  to be reduced i n 10 db s t e p s t o -80 db.  allowed  the g a i n  The instrument had  a noise l e v e l of about 0.005 m i c r o v o l t rms i n t h e frequency band 0.02 t o 3 cps w i t h a 40 ohm source r e s i s t a n c e . frequency  responses of the H , H , and H  The  d e t e c t o r s a r e shown  i n F i g s . 3.6 and 3.7., 3.4  U n i v e r s i t y of C a l i f o r n i a equipment The  U n i v e r s i t y of C a l i f o r n i a , B e r k e l e y ,  ment t o r e c o r d the e l e c t r i c a l f i e l d a l l six stations.  provided  equip-  ( t e l l u r i c currents) at  The equipment c o n s i s t e d of two p a i r s of  n o n p o l a r i s i n g e l e c t r o d e s , one f i l t e r , one V a r i a n G 22  32-  MAG.  X  a  Y  BEISEKER  100  8 6 4  ^  Q  w O  o  >-  > Q  2  o  io  o  8 6 Gain 20 db  Fig. 3.6.  I 0.001  j  i  i  '  6  i  i  '  i  8 0.01  Frequency response of the horizontal (X and Y) magnetic detectors (Pacific Naval Laboratory) used at Beiseker. i  i  2 4 Frequency  )  in  i  6  i  i ii  8 0-1 cps —  j  i  i  6  i  0.1 8 l0 i  i  I I  -45-  Points from Calibration, Aug. 22.61 23.61 Gain  Fig.  3.7.  20 db  Frequency response of the v e r t i c a l magnetic d e t e c t o r used at B e i s e k e r .  Yz  0.1  .001  j  6  i ii  8 .01  2  Frequency  J  1—i—i—i i i 1  4  in cps  6  8 .1  =>  J  i  recorder  and l e a d s  recording The  electrodes  used  t o make c o n t a c t  copper-copper sulphate  porous ceramic pots.  added t o a warmed s a t u r a t e d to minimise the e f f e c t leakage.  This  Two  with  t o the  cells  the ground  contained  copper sulphate  Cadmium C h l o r i d e  in  s o l u t i o n i n order  o f t e m p e r a t u r e and t o e l i m i n a t e  t o other  cells  were  t o 5 % o f Knox g e l a t i n was  procedure r e s u l t e d i n remarkably  electrodes, superior  cross  connections  u n i t a t each s t a t i o n .  non-polarising standard  f o r the electrode  fluid  stable  s u c h a s g e l l e d Cadmium-  ( B o s t i c k and S m i t h 1 9 6 0 ) .  F i g . 3.8:; shows a  s e c t i o n o f an e l e c t r o d e i T h r e e e l e c t r o d e s were u s e d a t e a c h s t a t i o n t o r e c o r d t h e  electric of  field  i n two m u t u a l l y  the electrodes  ( t h e west e l e c t r o d e  u s e d a s a common e l e c t r o d e components  (E  separation  was  six in  x  perpendicular  for recording  t h e two  instability usually  A t most s t a t i o n s t h e e l e c t r o d e  2000 f t .  The e l e c t r o d e s were p l a c e d  was p o u r e d them.  since at t h i s  stable.  A small  i n the holes  T h i s was  o f t e m p e r a t u r e and  amount before  of copper lowering  sulphate  i n t o the holes,  is  solution  composition  the surroundings.  done  chemical  the electrodes  the chemical  i n t o equilibrium with  e l e c t r o d e s were l o w e r e d  i n holes  depth the moisture content  T h i s was done t o b r i n g  electrodes  electric  and E y ) .  t o minimise the e f f e c t  One  shov/n i n F i g . 3 . 1 ) , was  t o e i g h t f e e t deep, augered i n t h e s o i l . order  directions.  into of the  Once t h e  t h e impedance b e t w e e n  -47-  # 18 GAUGE INSULATED WIRE SOLDERED TO COPPER PIPE  CORK  PURE COPPER K PIPE K>  PLUG  PROTECTIVE LAYERING OF RUBBER  THIN WALL POROUS CUP  COPPER SULFATE GEL  I'I  1.1  i .i i > -i r-v /////////  /  ///////'////  SCALE  3  Fig.  3.8.  I'I  INCHES  Cross s e c t i o n of copper-copper electrode.  sulfate  -48-  a p a i r was measured. to  More copper s u l p h a t e s o l u t i o n was added  t h e holes i f r e q u i r e d u n t i l a value between 200 t o 2000  ohms ( g e n e r a l l y 600 ohms) was o b t a i n e d .  The h o l e s were then  f i l l e d w i t h l i g h t s o i l and the t o p covered w i t h plywood and a t h i c k l a y e r of s o i l .  A f t e r two t o three days the e l e c t r o d e s  reached, f o r a l l p r a c t i c a l purposes, chemical their  e q u i l i b r i u m with  surroundings. In a d d i t i o n , a f o u r t h e l e c t r o d e was a l s o p l a c e d a t a  d i s t a n c e of 6 f t . from the w e s t ' e l e c t r o d e  ( F i g . 3.1), i n order  to check t h e d r i f t between t h e e l e c t r o d e s from day t o day. To measure the d r i f t between two e l e c t r o d e s p l a c e d 2000 f e e t apart i s extremely d i f f i c u l t of d r i f t it  because of t h e s u p e r i m p o s i t i o n  and long p e r i o d f l u c t u a t i o n s .  On t h e other hand,  i s r e l a t i v e l y easy t o measure t h e d r i f t  electrodes only s i x feet apart.  between two  In a d d i t i o n , each p a i r of  e l e c t r o d e s was s h o r t c i r c u i t e d d u r i n g t h e n i g h t t o minimise drift. The  arrangement of the d i f f e r e n t u n i t s f o r r e c o r d i n g  the e l e c t r i c f i e l d  i s shown i n F i g . 3.1.  E l e c t r o d e connect  t i o n s t o t h e r e c o r d e r s through a f i l t e r box were of No. 18 l i g h t p l a s t i c coated wire t o ensure t h a t c o n t a c t w i t h t h e ground was made by the e l e c t r o d e s o n l y .  To t e s t whether the  wires were making c o n t a c t with t h e ground d u r i n g impedance v a l u e s were u s u a l l y checked.  operation,  Sudden decreases i n  impedance v a l u e s were g e n e r a l l y found t o be due t o breaks i n  -49-  the cable.  Testing impedances with an ohmmeter disturbs the  chemical equilibrium of the electrode pair so that t h i s test was carried out infrequently.  The junction between electrode  and wire was soldered and insulated at the electrode.  Thermal  junction potentials at t h i s point were n e g l i g i b l e because the temperature environment was constant  at a depth of 6-8 feet i n  the s o i l . The electrodes were d i r e c t l y connected to two low pass f i l t e r s i n order to remove power l i n e interference and to reject signals outside the chosen range of from 1 to 1000 second period. filter.  F i g . 3.9  shows the c i r c u i t diagram of the  The outputs from the f i l t e r s were passed through bias  steppers, which were inserted to cancel out any DC f i e l d and to step the recorder by a f i n i t e amount when a scale extension was required. of - 6.0 mv.  Each bias could be operated  i n two steps each  The bias steppers were manually operated.  Bias  was provided through a voltage divider as shown i n F i g . 3.9.:, The source of the bias voltage was a 1.34 volt mercury c e l l . The signals were f i n a l l y receorded on a G 22 Varian recorder.  The output impedance of a G 22 Varian recorder i s  e s s e n t i a l l y i n f i n i t e at balance, so that the 60 k i l o ohms impedance of the f i l t e r and electrode pair are n e g l i g i b l e i n comparison.  This i s necessary i f precise measurements of the  potential between an electrode pair are to be made.  The  frequency response of the f i l t e r and the recorder i s shown i n  1.34 V MALLORY MERC. CELL RM 4  25 K i\  (each)  33 K  SET FOR BIAS STEPS OF 6 X > MV  AAA/ <  50X1 t 1%  (each)  -VVAr-t-VVVf-VVVt-AAAr  NO FLOATING INPUT  -O  FLOATING OUTPUT o  1/i.F (each)  CO  o  -O  GNO.  -O  =~  Fig. 3.9.  Circuit  diagram f o r the E a r t h c u r r e n t  filter,  RECORDER CASE  -51-  Fig.  3.10.  A f l a t frequency response between 0.01 t o 0.1 cps,  which covers part of the magnetotelluric range, allows the signals to be read d i r e c t l y i n m i l l i v o l t s from the records.  3.5 F i e l d procedure In section 2.3 a short account of the f i e l d operations has been ifiven.  In the present section a b r i e f description i s  given of the d i f f e r e n t f i e l d procedures such as the orientation of the detectors, their c a l i b r a t i o n at the beginning and end of a day, and the time marking system and absolute c a l i b r a t i o n of some detectors. The detectors at a l l stations were oriented with respect to a geomagnetic coordinate system.  This system was also  adopted f o r the orientation of the earth current electrodes. To minimise noise the detectors were placed i n small trenches dug to s i z e and covered with soft s o i l on the top. The output from the detectors at each station was c a r r i e d by a shielded cable to a common junction box usually located 15 t o 30 feet from the c o i l s .  At the junction box the leads from each c o i l  were screw fastened to the leads of a shielded cable containing s i x conductors.  The s h i e l d o f t h i s cable was connected  with the detector lead at one end and to the ground o f the recording equipment at the other.  In t h i s way a l l detector  leads and shields were held at the same potential as the ground at the recording equipment.  10: 8 64  Response Filter Output  0.I— 0.01 1  across  Resistance from  J  470 f l 33  Oscillator  kft s  9.35  mV  J  I L_l_  8 0.1  2  Frequency  4  in  6  I I I  8 t  I  J  6  cps  F i g . 3 . 1 0 . Frequency response of the Earth current recording system.  I  I  I  8 10  -53-  Two methods of c a l i b r a t i n g detectors are i n general use. In one a c a l i b r a t i o n signal i s induced into the detector c i r c u i t from an a u x i l i a r y winding of a few turns.  In the  other a small measured voltage i s injected into the detector c i r c u i t by means of a series precision r e s i s t o r and dividing network. used. a known  In the present investigation the f i r s t method was  In order to use t h i s method i t i s necessary to create f i e l d r o u n d the d e t e c t o r and to compare i t with the  recorded f i e l d from the detector.  To accomplish  t h i s each  detector was placed coaxial and concentric with a c o i l of 5 turns, 20 meter i n diameter.  This was done by laying the  c i r c u l a r c o i l on the ground and f i x i n g the detector c o i l v e r t i c a l l y at i t s centre, half i n the ground and half above. As the length of the detector c o i l was much smaller than that of the c a l i b r a t i n g c o i l , an expression f o r the f i e l d at the centre of the c a l i b r a t i n g c o i l was used i n the c a l i b r a t i o n . Vozoff (1961) has shown t h e o r e t i c a l l y that the error due to the underlying earth i s less than one percent i f normal conductivities, frequencies below 100 cps and a c o i l radius of less than 100 meters are assumed.  It i s extremely d i f f i c u l t  to measure the current from an Ulta Low Frequency (U.L.F.) generator which i s of the order of 0.1 milliampere.  Thus the  U.L.F. output was calibrated i n terms of current with the help of a 1.5 v o l t battery and a Varian G 10 recorder.  Once the  output from the U.L.F. generator was calibrated, the  -54-  calibration current  o f t h e d e t e c t o r was c a r r i e d  input to the large c o i l  until  out by a d j u s t i n g t h e  a field  o f one gamma  was p r o d u c e d a t t h e c e n t r e where t h e d e t e c t o r was A graph of the output gave t h e c a l i b r a t i o n  from the d e t e c t o r versus curves.  as a b s o l u t e c a l i b r a t i o n , Operation tion  was c a r r i e d  t o time,  at different  w h i l e o p e r a t i n g , 10  potentiometer circuit.  this  f r o m t h e U.L.F. g e n e r a t o r  To check the c a l i b r a gain s e t t i n g s of the  internal coil  t o other  was s e n t  except  of c a l i b r a -  that a  o r g a n i s a t i o n s had s i m i l a r signal  i n terms of v o l t s  directly  to the i n t e r n a l  coils.  Time marks were p r o v i d e d operated  the Al&erta  The same p r o c e d u r e  A t some s t a t i o n s a f i x e d  calibrating  on t h e r e c o r d s f r o m  chronometers with e l e c t r i c  electrically  c o n t a c t s which a c t i v a t e d  t i m i n g pens t o g i v e m i n u t e a n d hour marks on t h e c h a r t The  c l o c k s were f r e q u e n t l y c h e c k e d b y means o f t i m e  f r o m WWV  signals.  An a c c u r a c y  the e l e c t r i c a l l y not  paper.  signals  Time marks a r e u s e d t o d e t e r m i n e t h e  commencement o f an e v e n t possible.  known  i n s t e a d o f a r e c o r d e r was u s e d i n t h e i n p u t  C o i l s belonging  windings.  then  t u r n s o f w i r e were wound r o u n d  t h e c e n t r e o f t h e U.B.C. c o i l s . t i o n was p e r f o r m e d w i t h  frequency  of c a l i b r a t i o n ,  out a f t e r  i n t h e l a b o r a t o r y a t U.B.C.  from time  amplifier  T h i s type  placed.  a n d h e n c e must be a s a c c u r a t e a s  o f ± 6 seconds c o u l d be o b t a i n e d  controlled  clocks.  p o s s i b l e t o put e x t r a time  from  A t a few s t a t i o n s i t was  p i p s on t h e r e c o r d s because of  -55-  the  type of r e c o r d e r s used.  In such i n s t a n c e s a r e l a y  operated by a d r y c e l l was used.  system,  The time p i p s were super-  imposed on the s i g n a l s and were marked a f t e r every minute and hour. to the  At some s t a t i o n s the s i g n a l s from t h e c l o c k were f e d  the c a l i b r a t i n g c o i l of the d e t e c t o r t o g i v e time p i p s on recorded s i g n a l s .  -56-  CHAPTER IV  METHODS OF ANALYSIS  4,1  General Few  g e o p h y s i c a l measurements a l l o w d i r e c t i n t e r p r e t a t i o n -  i n most i n s t a n c e s the data must be s u b j e c t e d t o a l e n g t h y analysis before i n t e r p r e t a t i o n i s p o s s i b l e .  In many geo-  p h y s i c a l problems t h e r e i s o n l y one v a r i a b l e i n t h e data and thus i t becomes simpler t o apply any c o r r e c t i o n s b e f o r e t h e analysis. two  In magnetotfelluric or t e l l u r i c measurements where  types of i n f o r m a t i o n , v i z . frequency  and magnitude, have  to be obtained from the same data, t h e problem becomes more difficult.  Because of t h e c o m p l e x i t i e s of t h e magnetic and  t e l l u r i c f i e l d s of the E a r t h i t i s d i f f i c u l t s e c t i o n of the r e c o r d s without u n d e s i r a b l e components. filtering way  first  t o analyse each  smoothing them t o remove  The best way t o achieve t h i s i s by  t h e r e c o r d s a t the d e s i r e d f r e q u e n c i e s .  The u s u a l  t o do t h i s i s by r e c o r d i n g t h e s i g n a l on magnetic tape  initially  and l a t e r f i l t e r i n g  the records.  I f the recording  i s made d i r e c t l y on c h a r t r e c o r d e r s , t h e s i g n a l s may be f i l t e r e d by numerical to f i l t e r  filtering  on f a s t computers.  the r e c o r d s u s i n g a c o n v o l u t i o n f i l t e r  Attempts  have been  -57-  made by  some w o r k e r s i n s i m i l a r  a visual  fields  analysis. be  Where f i l t e r i n g  used.  The  In the p r e s e n t t h e f o l l o w i n g two (1) V i s u a l  opened up  investigation  correlation  possible a statistical  and  o n l y a few  The  major cause o f  t o be  i n subsequent s e c t i o n s . t h e d a t a were a n a l y s e d  these  On  the other  magnetic  different  to  Most o f  On  component  (H )  found  component  (H ).  was  The low  gain setting  the  time  and  the  t o be more n o i s y t h a n  v e r t i c a l magnetic t h a t i t had  t o be  of the equipment.  Most o f  the  magnetic in  the  vertical the h o r i z o n t a l  intensity recorded  were  records.  noise present  the magnetic r e c o r d s  obtained.  records  the e l e c t r i c  between t h e e l e c t r i c  g i v e some i d e a o f  magnetic r e c o r d s .  the  station,  instrumentation  hand, t h e e l e c t r i c  less similar.  Hence a p o o r c o r r e l a t i o n  highest  The  q u i t e v a r i a b l e from s t a t i o n  m a g n e t i c r e c o r d s were more n o i s y t h a n  so  by  methods i t i s w o r t h -  of the r e c o r d s .  t h i s v a r i a t i o n was  t o be more o r  s t a t i o n s was  over  u s e f u l p o r t i o n s o f t h e r e c o r d s c o u l d be  at each s t a t i o n .  x  approach  method  method.  t o examine t h e n a t u r e  z  statistical  method,  describing in detail  records should  for  is  methods,  r e c o r d s were f o u n d  found  i s not  made c l e a r  (2) Power s p e c t r a l Before  be  advantages of a s t a t i s t i c a l  v i s u a l methods w i l l be  while  For  a n a l y s i s of t h e r e c o r d s a narrow band pass f i l t e r  e s s e n t i a l , w h i l e s u c h b a n d s may  may  ( G o l d s t e i n 1962).  a t most  with the  the instruments  were not very stable at their highest gain giving r i s e to noisy signals.  On the other hand, the east-west (H ) magnetic y  component at Beiseker (station #3)  had more harmonics than  the north-south (H^) component (Fig. 7 . 5 ) . more harmonics i n H  y  than i n IL^ i s probably due to l o c a l  sources at Beiseker (section 7.3). t e r i s t i c which was  The presence of  Another interesting charac-  found from an examination of the records i s  the change in the dominant period from s t a t i o n to s t a t i o n . Higher periods were: found to occur more frequently at northern stations than at southern stations.  Such a c h a r a c t e r i s t i c has  been reported by Jacobs and Sinno (1960). The analysis i n the present investigation has been divided into two parts.  The f i r s t part consists of an analysis  of the magnetic f i e l d data for two days from a l l s i x stations, while the second part consists of an analysis of magnetot e l l u r i c data at three stations, Meanook, Beiseker, and Cardston.  The magnetic analysis i s r e s t r i c t e d to periods  below 100 seconds while the magnetotelluric  analysis has-been  extended to periods up to 3000 seconds.  4.2  Visual c o r r e l a t i o n analysis Records from a l l stations were examined v i s u a l l y and  the  most coherent sections from each record selected for analysis. Processing  the records consists p r i m a r i l y o f determining the 1  frequency and amplitude of correlated o s c i l l a t i o n s which have  -59-  an approximately s i n u s o i d a l form*  The m i c r o v a r i a t i o n s p r e -  dominantly have the form o f t r a i n s of o s c i l l a t i o n s .  Because  of  the wide margin of e r r o r a s s o c i a t e d w i t h the d e t e r m i n a t i o n  of  the amplitude of s i n g l e i r r e g u l a r l y shaped p u l s e s , such  s i g n a l s are not u s u a l l y c o n s i d e r e d . electromagnetic f i e l d methods:  The amplitude of the  i s g e n e r a l l y determined by one of  two  1) the double amplitude of the h a l f p e r i o d of  c o r r e l a t e d o s c i l l a t i o n s , shown by  'a' i n P i g . 5.1  and i i ) the  a r i t h m e t i c mean of the double amplitude of two h a l f p e r i o d s , shown by 'b' i n F i g . 5.1. method was of  In the present a n a l y s i s the second  used s i n c e i t reduced t o some extent the i n f l u e n c e  the n a t u r a l n o i s e of the apparatus.  The magnetic r e c o r d s  were analysed i n the above manner a f t e r p i c k i n g out peak t o peak correspondences from the r e c o r d s at a l l s t a t i o n s In  ( F i g . 4.1),  the m a g n e t o t e l l u r i c method correspondences were p i c k e d out  between the magnetic  and e l e c t r i c r e c o r d s at each s t a t i o n .  The a c t u a l magnitudes of the m i c r o v a r i a t i o n s i n the e l e c t r i c and magnetic f i e l d s were determined from c a l i b r a t i o n curves drawn f o r the d e t e c t o r s at each s t a t i o n . b r a t i o n v a l u e was of  A new  cali-  o b t a i n e d f o r each s t a t i o n a t the b e g i n n i n g  each day and the amplitudes were thus c o r r e c t e d f o r any  day t o day v a r i a t i o n i n the c a l i b r a t i o n v a l u e s , which c o u l d be as l a r g e as - 10%.  The frequency of the v a r i a t i o n s  was  determined from the time marks t r a c e d on the r e c o r d s from the c l o c k a f t e r every minute.  The average p e r i o d of many c y c l e s  -600928  27  26  25  24  23  22  21  20  0928  27  26  25  24  23  22  21  20  FIG. 4-1  TYPICAL  EXAMPLES  AT  SIX  AUG. 18. 61 THE  OF NORTH-SOUTH  STATIONS  MAGNETIC  RECORDS  -61-  was taken as the r e p r e s e n t a t i v e p e r i o d f o r a p a r t i c u l a r  event.  Accuracy i n determining the p e r i o d was l i m i t e d by the accuracy of  the time marks (- 6 seconds over 24 h o u r s ) .  In the magneto—  t e l l u r i c method the r a t i o s of the amplitudes of o r t h o g o n a l f i e l d components were computed and i n s e r t e d i n equation 1.1 t o o b t a i n v a l u e s of apparent r e s i s t i v i t y a t d i f f e r e n t p e r i o d s .  4.3  Power  spectral  analysis  (a) G e n e r a l .  In the p r e v i o u s s e c t i o n a method f o r d e t e r -  mining the amplitude and frequency o f m a g n e t o t e l l u r i c s i g n a l s has been g i v e n .  The use of such a method i s l i m i t e d o n l y t o  noise free records.  In order t o o b t a i n the same i n f o r m a t i o n  from those r e c o r d s where t h e s i g n a l i s d i s t o r t e d due t o the presence of n o i s e , i t i s e s s e n t i a l t o c a l c u l a t e the energy d i s t r i b u t i o n w i t h i n narrow frequency bands by b r e a k i n g up the s i g n a l i n t o such narrow bands.  The use of F o u r i e r a n a l y s i s f o r  p e r i o d i c f u n c t i o n s and F o u r i e r i n t e g r a l s f o r non p e r i o d i c f u n c t i o n s together w i t h the transorm r e l a t i o n s h i p between the f u n c t i o n and i t s F o u r i e r spectrum have long been s t a n d a r d methods f o r a n a l y s i n g a time v a r y i n g s i g n a l d i s t o r t e d by noise.  A F o u r i e r a n a l y s i s i s g e n e r a l l y used f o r s t a t i o n a r y  time s e r i e s .  The  use of F o u r i e r a n a l y s i s i n m a g n e t o t e l l u r i c  i n v e s t i g a t i o n s i s j u s t i f i e d o n l y i f the s i g n a l s analysed possess the c h a r a c t e r i s t i c s of a s t a t i o n a r y time s e r i e s . Since the nature of the f i e l d  sources i s not known, i t has  -62-  b e e n assumed randomly  (Cantwell,  1960) f o r c o n v e n i e n c e t h a t t h e  occurring s i g n a l s of varying  of a s t a t i o n a r y time s e r i e s .  In a l l s t a t i s t i c a l  main o b j e c t i v e i s t o e l i m i n a t e n o i s e to obtain  an u n d i s t o r t e d  Ideally the F o u r i e r the  part  methods t h e  from the s i g n a l s i n order  picture.  t h e c a l c u l a t i o n o f a power s p e c t r u m  i s b a s e d on  a n a l y s i s o f a random t i m e s e r i e s w h i c h b r e a k s up  s i g n a l i n t o narrow  tion  a m p l i t u d e s do f o r m  f r e q u e n c y bands p e r m i t t i n g  o f t h e power i n t h e s e b a n d s .  the c a l c u l a -  M a t h e m a t i c a l l y i t may be  w r i t t e n as  F(w)  =  ff(t)e"  dt  J w t  (4.1)  -Vz where F(w) i s t h e F o u r i e r T r a n s f o r m o f f u n c t i o n f ( t ) , in  t h e r a n g e -T/2  the bandwidth the  ^  goes  t ^  to zero,  power s p e c t r a l d e n s i t y .  $  where  cb  -  spectral density  t h e power s p e c t r u m  c a s e , when  i s known a s  Hence, e q u a t i o n ( 4 . 1 ) r e d u c e s t o  Lim  *  W  I  * *  length  (4.2)  W  and F*(w) i s t h e  The computation  from a f i n i t e  c a r r i e d out using  and Root  In t h e l i m i t i n g  i s t h e power s p e c t r a l d e n s i t y ,  complex c o n j u g a t e o f F ( w ) .  not  T/2.  o f t h e power  of record  i s generally  a Fourier spectral analysis.  ( 1 9 5 8 ) , Bendat  defined  (1958), Robinson  Davenport  (1954) a n d B l a c k m a n  -63-  and  Tukey  Fourier  (1958) have summarised  the  disadvantages  s p e c t r a f o r such cases i n the  in  computation of  using power  spectra. A power s p e c t r u m may a n a l y s i s or  the  be  calculated using  autocorrelation function.,  spectrum i s r e l a t e d to the generally preferable  to c a l c u l a t e the  why  t r a n s f o r m s of  information  function. of man  and  each o t h e r ) .  the and  The  can  be  The  obtained  advantages of u s i n g  question  are  may  be  raised  power s p e c t r u m when from the  the  Tukey  (1958). do  not  In a l m o s t  autocorrelation  power s p e c t r u m  represent  a l l practical  the  instead  data w i l l  appreciably  i f not  by  of the  the  have b e e n  transmission  equipment employed t o o b t a i n  the  estimates of  the  e f f e c t s of  power s p e c t r a w i l l  this modification  power s p e c t r a  correlation  radically,  i s quite simple.  function  a Fourier  transformation,  f r e q u e n c y f u n c t i o n by inverse Fourier  however, t h e  of  the  modified, characterHence  have t o be  corrected  the  The  For  data.  the  c o r r e c t i o n procedure of the  The  for  correction  e s t i m a t e s of  division  the  random  data.  another frequency f u n c t i o n ,  transformation.  Black-  situations,  a c t u a l output of  In such c a s e s the  require  i t is  power s p e c t r u m i  processes.  of  power  a u t o c o r r e l a t i o n f u n c t i o n have b e e n summarised by  data analysed  istics  the  Fourier  power s p e c t r u m f r o m i t  the  i t i s necessary to c a l c u l a t e the  similar  As  autocorrelation function  (the a u t o c o r r e l a t i o n f u n c t i o n Fourier  either a  autowill  resulting and  autocorrelation  an function  -64-  a c t s as a p a s s i v e f i l t e r whose o n l y r e a l purpose i s t o d e t e c t p e r i o d i c components.  The d e t e c t a b i l i t y of a message from a  n o i s y s i g n a l depends on whether or not there i s a s p e c t r a l o v e r l a p of message and n o i s e .  The d e t a i l s of an o v e r l a p have  been w e l l i l l u s t r a t e d by G o l d s t e i n (1962) w i t h t h e h e l p few f i e l d examples.  In the case of a n o i s e f r e e r e c o r d one  would expect a f l a t spectrum. another  of a  B o s t i c k (1961) has suggested  method f o r c a l c u l a t i n g the power s p e c t r a l d e n s i t y by  d i r e c t l y f i l t e r i n g the data.. an analog  In h i s method he has made use of  computer.  In most cases, the n o i s e may be r e p r e s e n t e d , or approximated, by s t a t i o n a r y Gaussian random processes z e r o averages,  with  so t h a t a l l of t h e i r r e l e v a n t s t a t i s t i c a l  p r o p e r t i e s w i l l be contained by the autocovariance f u n c t i o n or the power spectrum.  In many cases, t h e s i g n a l s themselves may  a l s o be r e p r e s e n t e d , or approximated, by s t a t i o n a r y Gaussian random processes w i t h z e r o averages*  Noises, s i g n a l s , and  other ensembles of f u n c t i o n s which a r e approximately s t a t i o n a r y but not Gaussian  are o f t e n a l s o s t u d i e d i n terms of  autocovariance f u n c t i o n s or power s p e c t r a .  Although the  average and the spectrum a r e no longer the o n l y r e l e v a n t statistical (b)  p r o p e r t i e s , they a r e u s u a l l y the most u s e f u l .  B a s i s of the method.  The concept u n d e r l y i n g the  computation of power s p e c t r a a r e now d e s c r i b e d b r i e f l y .  The  e x p r e s s i o n s g i v e n r e l a t e t o the c a l c u l a t i o n o f the power s p e c t r a  -65of one time s e r i e s but s i m i l a r e x p r e s s i o n s may be used f o r the c a l c u l a t i o n of the power s p e c t r a of two time Let X j , Xg, Xg,  series.  X^...... .OXJJ r e p r e s e n t a time s e r i e s of  data obtained a t times t  t,  lf  2  tg,..  t^,........t.  The  a u t o c o r r e l a t i o n A(L) f o r such a s e r i e s i s g i v e n by TV  A ( L )  =  >V  (n3l)Z i- i X  LX  *  (n=E)  Z  X±  £ i-L X  ^\  The equation above and those which a r e g i v e n below a r e e v a l u a t e d f o r L and k having v a l u e s 0,1,2,3,  m,. where k i s the  l a g number and m the t o t a l number of l a g s . i n each case i s determined  The number of l a g s  when the d i g i t i s i n g  interval  A t C t j L + i - t i ) has been f i x e d , from the r e l a t i o n  f  where f ^ i s the frequency  k - 2 ^ A ¥  m  a  -  4 )  at l a g k.  The d i g i t i s i n g i n t e r v a l i s determined the maximum frequency f  ( 4  x  by the requirement  of  f o r the c a l c u l a t i o n of the power  s p e c t r a l d e n s i t y , g i v e n by  •max  2  A  t  where  A t i s i n seconds and f i n c p s . Equation ( 4 . 3 ) can o n l y max n be used f o r normalised data, i . e . 2— X -. 0. In the ±  1=1  present i n v e s t i g a t i o n where the data x^ were r e a d from one edge  -66-  of  the chart,  the value  o f Xj^ i s g i v e n by n  1=1 For  t h e c a l c u l a t i o n o f t h e power s p e c t r a l d e n s i t y  frequencies calculated  (equation  4.4) t h e a u t o c o r r e l a t i o n f u n c t i o n i s  a t e q u a l l y spaced  i n t e r v a l s (k = 0,1,2,3,.  In t h e c a s e o f two t i m e s e r i e s , b e t w e e n them i s g e n e r a l l y made.  negative  m).  a cross c o r r l e a t i o n  The c r o s s c o r r e l a t i o n i s  a l s o c a l c u l a t e d a t e q u a l l y spaced correlation  a t many  intervals.  The c r o s s  i s n o t an even f u n c t i o n and i t s p o s i t i v e and  parts  a r e c a l c u l a t e d r e s p e c t i v e l y from t h e f o l l o w i n g  expressions,  C ( L ) = ^ L  Z^=-L*i  -felL")  Z*i-L  Z  Y  i  <'> 4  6  and  (4.7)  From t h e a u t o c o r r e l a t i o n and c r o s s energy estimates be made u s i n g  of spectra,  thefollowing  correlation functions,  co-spectra, expressions.  and q u a - s p e c t r a  may  -67-  2. 2e(L)  X(k) = -Jp  cos  + A(o)  (4.8)  L'l  ~~ Z 2e(L) L £>k  Y(k) =  ' ~ yn  =/  6k  lrT  l  cos ^  B(L) + B(o)  (4.9)  ^  Z(k) - -=p-  272e(L) cos  E(L) + E(o)  (4.10)  W(k) - -|p  ^ 2 e ( L ) sin ^  F(L)  (4.11)  where X(k)  and Y(K) are the power s p e c t r a l densities of the  two time series. A(L) and B(L) are the auto-correlation functions of the two time series. Z(k)  and W(k)  are the in-phase (co-spectra) and out of  phase (qua-spectra) energy spectra. E(L) and F(L) are the in-phase and out of phase correlations between the two time s e r i e s . Sk=» 1/2 for k=»0 or k=m => 1 for a l l other values of k 2e(L) = 1 + cos ~  .  In addition, a r a t i o of the cross spectra to the product of the auto spectra i s used to estimate the coherency between the two time s e r i e s , i . e .  -68-  t h e coherency (R ) i s d e f i n e d as k  (4.12)  S i m i l a r l y the r a t i o of the qua-spectrum may  t o the co-spectrum  be used t o e s t i m a t e the phase l e a d of one s e r i e s over the  other. The apparent r e s i s t i v i t y may be c a l c u l a t e d from the formula g i v e n below p r o v i d e d the two s e r i e s r e p r e s e n t a p a i r of orthogonal e l e c t r i c  and magnetic f i e l d  components.  (4.13)  where X^(E) and  v k  (H)  are the power s p e c t r a l d e n s i t i e s of the  electric  and magnetic r e c o r d s at a p a r t i c u l a r frequency.  Cantwell  (1960) has shown t h a t the apparent  resistivity  should be m u l t i p l i e d by the square of the coherency between the e l e c t r i c resistivity.  and magnetic r e c o r d s to o b t a i n the a c t u a l Such a m u l t i p l i c a t i o n i s not necessary i f power  spectrum v a l u e s c o r r e s p o n d i n g t o h i g h coherency v a l u e s are used i n the apparent r e s i s t i v i t y (c) Method of computations.  calculations. The r e c o r d s from a l l  s t a t i o n s were examined v i s u a l l y and the most coherent s e c t i o n s of the e l e c t r i c  and magnetic r e c o r d s s e l e c t e d  for analysis.  S i m i l a r l y coherent magnetic r e c o r d s from each s t a t i o n were  -69-  also selected.  The r e c o r d s were hand d i g i t i s e d a t equally,  spaced i n t e r v a l s .  T a b l e 4.1 i l l u s t r a t e s the d i f f e r e n t  quency bands used, the time l a g &t f  m  a  v  fre-  and the maximum frequency  a t which estimates c o u l d be made.  TABLE 4.1  Frequency Band  At  max  0.001-0.003  24 sees  0.007-0.103  6 sees  0.083  0.018-0.023  6 sees  0.083  0.030-0.050  6 sees  0.083  0.0208  The d i g i t i s e d d a t a were r u n through an I.B.M. 704 computer at the U n i v e r s i t y of C a l i f o r n i a , B e r k e l e y , Center.  Computation  The program f o r the I.B.M. 704 was w r i t t e n by  P r o f e s s o r Ward and h i s c o l l e a g u e s u s i n g the Tukey spectrum estimation sub-routine. g i v e n i n Appendix  A.  The r e s u l t s of the computations are  The coherency between t h e e l e c t r i c and  magnetic r e c o r d s f o r a m a g n e t o t e l l u r i c a n a l y s i s and between t h e magnetic r e c o r d s f o r a magnetic puted.  In a d d i t i o n f o r the magnetic  a n a l y s i s were a l s o coma n a l y s i s the coherency  at each s t a t i o n w i t h r e s p e c t t o Meanook was computed  -70-  to i n v e s t i g a t e the source e f f e c t ( s e c t i o n  5.3).  A comparison between the two methods may now be made. The  advantages of u s i n g s p e c t r a l d e n s i t i e s i n an  of apparent r e s i s t i v i t i e s a r e many.  estimation  In the former method where  events a r e c o r r e l a t e d v i s u a l l y , p e r s o n a l e r r o r p l a y s tant r o l e .  In an e s t i m a t i o n  an impor-  o f s p e c t r a l d e n s i t i e s the coherency  between t h e e l e c t r i c and magnetic r e c o r d s i s c a l c u l a t e d at a l l f r e q u e n c i e s and only  those s p e c t r a l d e n s i t i e s where the maximum  coherency i s found, a r e used i n t h e c a l c u l a t i o n of  P  allows the data t o be handled i n an unbiased f a s h i o n .  A  . This Another  advantage i n u s i n g power s p e c t r a l d e n s i t i e s i n t h e present a n a l y s i s i s the detection extremely d i f f i c u l t  of v e r y low f r e q u e n c i e s  which are  t o observe by a v i s u a l c o r r e l a t i o n method  f o r v e r y weak events on h i g h speed magnetograms.  The g r e a t e s t  advantage of a power s p e c t r a l a n a l y s i s over a v i s u a l c o r r e l a t i o n i s the c a l c u l a t i o n of the coherency between t h e two series. any  The degree of coherency i s an important f a c t o r i n  study of m i c r o p u l s a t i o n s ,  g a t i o n s p l a y s an e q u a l l y  and i n m a g n e t o t e l l u r i c  important r o l e .  investi-  The coherency can  a l s o g i v e an i n d i c a t i o n of the amount of n o i s e present i n one time s e r i e s i f the other time s e r i e s i s presumed t o be n o i s e free.  4.6  Error  analysis  E r r o r s i n the present a n a l y s i s a r e of s e v e r a l  kinds.  -71-  Broadly speaking constant  t h e y may  e r r o r s and  be  d i v i d e d i n t o two  random e r r o r s .  Constant  w h i c h a r e i n h e r e n t i n t h e a n a l y s i s and easily. nature  On and  the other may  Constant tion  of  be  detectors.  be  and  t o dqy  not  calculated statistical  to incorrect  different  e r r o r s may  be  i n v e s t i g a t i o n p e r h a p s as h i g h a s 25-30%.  h e n c e any  c o u l d be  p o s s i b l e by  at the beginning  and  taken  i n t o account  ( F i g . 3.5).  p r e s e n t l y known methods.  from the c a l i b r a t i o n  Fig.  3.5,  and  3.7..  curves,  shown by  a t Meanook a t f r e q u e n c i e s l o w e e t h a n  than  f r o m o u r r e c o r d s were compared w i t h magnetograms a t t h a t s t a t i o n . justified  result  of the cps  obtained of t h i s  the e x t r a p o l a t i o n of the c a l i b r a t i o n  f r e q u e n c i e s b e l o w 0.01 c o u l d be  The  those  cps  a t Meanook.  made f o r c a l i b r a t i o n  Vladimirov  (1961) has  values  No  from  0.01  cps  extrapolalines  in  magnetic obtained from  normal  comparison  curves  such  at other  of  Calibration  0.01  -  Calibration  the dotted  Furthermore, values  the  The  end  change i n the c a l i b r a t i o n v a l u e s  tion  3.0  correlation  quite high  f a c t o r s f o r f r e q u e n c i e s b e l o w t h i s were o b t a i n e d by  field  calibra-  arrangements of  the magnetic d e t e c t o r s f o r f r e q u e n c i e s l e s s  was  those  v a r i o u s methods.  Constant  d e t e c t o r s were c a l i b r a t e d  e a c h day  of  c a l c u l a t e d by  e r r o r s i n t r o d u c e d by  the present  day  not  hand random e r r o r s a r e o f a  e r r o r s i n c l u d e e r r o r s due  electromagnetic  field  e r r o r s are  the d e t e c t o r s , p e r s o n a l e r r o r s i n the v i s u a l  a n a l y s i s and  in  can  categories,  for  comparison  stations.  shown t h a t i t i s n e c e s s a r y  to  apply  -72-  some corrections to the e l e c t r i c f i e l d i f i t i s measured over inhomogeneous ground.  The error i s not s i g n i f i c a n t for short  electrode separations but may become important as the separation i s increased.  Fig. 4 . 2 i l l u s t r a t e s this effect.  Estimation of such an error could not be made i n the present investigation because f i e l d data were not taken, but i t should not exceed 2 % .  From F i g . 4 . 2 i t i s clear however that the  relationship between the amplitude of microvariations i n the e l e c t r i c f i e l d and the length of the detector l i n e s may  be  important and should be estimated i n each area i f possible i n a l l directions i n which detector l i n e s are placed. Random errors introduced into the calculation of apparent r e s i s t i v i t i e s may be obtained from equation 1 . 1 .  viz.  4fk--*£ ra  T  +  2|H H  +  2 A E  (  4  <  1  4  )  E  It i s evident that i f the frequency can be found with s u f f i c i e n t accuracy, errors i n the c a l c u l a t i o n of apparent r e s i s t i v i t i e s are mainly due to errors i n determining the f i e l d amplitudes.  Averages of many amplitudes at the same  period were taken i n a l l r e s i s t i v i t y analyses, and standard errors of the mean calculated for i n d i v i d u a l periods. Fig.  6 . 6 and F i g . 6 . 1 2 show the standard errors of the mean  at different periods at Meanook and Cardston.  Although these  figures do not show the error i n i n d i v i d u a l measurements they  -73-  M, N, Fig. 4.2.  Relationship between the potential difference to be measured and the length of detector l i n e (MJNJ  => 1 0 0  m).  (After Vladimirov, 1 9 6 1 )  -74-  do g i v e an i n d i c a t i o n o f t h e r a n g e at  individual  of v a r i a t i o n  periods.  In the v i s u a l  correlation  a n a l y s i s , the f r e q u e n c i e s  i n d i v i d u a l e v e n t s were d e t e r m i n e d b y many c y c l e s . mination  5 s e c o n d s was  t a k e n f o r p e r i o d s up t o 200  f o r longer  from the  periods.  i n the  with which  seconds  and  the p e r i o d s  of the e r r o r s introduced  power s p e c t r a i s b a s e d  one  could  The  on t h e a s s u m p t i o n  i t may  records  ( F i g . 5.1)  possess p r o p e r t i e s s i m i l a r computation  i m p r a c t i c a l and  by B l a c k m a n and T u k e y  c o r r e c t i o n h a s t o be present during  infinitely  impossible  The  show t h a t a  a p p l i e d t o t h e power s p e c t r u m .  i n v e s t i g a t i o n s u c h a c o r r e c t i o n was the computation.  Another  a  computahas  been  smoothing In the  taken care  e r r o r w h i c h may  series. long  when o n l y  l e n g t h of r e c o r d  (1958) who  do  magnetotelluric  i s generally available.  t i o n o f power s p e c t r a f r o m a f i n i t e given  they  t o those of a s t a t i o n a r y time  u s e o f s u c h a method f o r a n a l y s i n g  length of r e c o r d  electric  be assumed t h a t  o f power s p e c t r a r e q u i r e s an  t h e n be  of  t h a t the s i g n a l s used  and m a g n e t i c  finite  be  computation  From t h e n a t u r e o f t h e  d a t a would  of  i n t h e power s p e c t r a l  form a s t a t i o n a r y time s e r i e s .  The  deter-  T h e s e foand w i d t h s were  a n a l y s i s were made i n a d i f f e r e n t way.  series.  of  records.  Estimates  The  of  b y s u c h a method, a b a n d w i d t h o f  d e t e r m i n e d by t h e a c c u r a c y read  t a k i n g an a v e r a g e  To c o m p e n s a t e f o r e r r o r s i n t r o d u c e d  of f r e q u e n c i e s  60 s e c o n d s  of amplitudes  become  of quite  -75-  s i g n i f i c a n t i n power spectral estimations i f data outside the truncated period are examined i s the truncation error. Bostick (1961) has given a method for estimating t h i s error. Such an error i s v i r t u a l l y nonexistent i f the data are truncated between clear cut events, as was done i n the present investigation.  If t h i s i s not possible the data should be pre-  whitened as much as possible. In the present investigation the e l e c t r i c and magnetic records were not p r e f i l t e r e d prior to the spectral analysis. This led to some s p i l l a g e of energy from the spectral peaks into adjacent frequencies, since the spectral analysis presupposes a "white" signal. end may  Some a l i a s i n g at the high frequency  also be present, but the energy density above the  Nyquist frequency was very low for the records studied. Despite these limitations of the a n a l y t i c a l techniques, the 80% range formula of Tukey was used to compute the probable errors of the power density estimates and was found to be adequate.  Higher range formulae were not used as they are  not j u s t i f i e d when the number of estimates i s very small. Eighty percent of the estimates f a l l in the range given below: 125  (80% range i n db)^ - ='no. ot\ /'lengthy /resolution records.| per ( j in cps pieces] [piece j ^  r 3  1  2  This equation applies to the records of a stationary time  (4.15)  -76-  s e r i e s whose s p e c t r u m i s r e a s o n a b l y  flat.  In o t h e r words t h e  r e c o r d s a r e s u p p o s e d t o be w h i t e i n t h e n a r r o w band u s e d f o r t h e power d e n s i t y c a l c u l a t i o n s . the estimated  frequency Table  gives  e r r o r s f o r t h e power s p e c t r a .  TABLE  4.2  Frequency range i n cps  Resolution i n cps  0.001-0.0025  0.0083  21600  0.007-0.012  0.0033  5400  "  XI.862  0.03 -0.05  0.0066  4200  "  XI.972  0.018-0.023  0.0033  5400  "  XI.862  Because of the l i m i t e d for  different  not  be c o n s i d e r e d  Length of Record  80%  sees  range  XI.212  s e t s o f v a l u e s o f power s p e c t r a  f r e q u e n c i e s average r e s i s t i v i t y i n the c a l c u l a t i o n  Tukey 80% range v a l u e s the probable  4.2  values  of probable  errors.  ( T a b l e 4.2) were c o n s i d e r e d  e r r o r s i n the apparent  resistivity  could  t o be  calculations.  M o r e o v e r i t has b e e n shown i n s e c t i o n 1.3 t h a t t a k i n g t h e a v e r a g e o f power s p e c t r u m e s t i m a t e s If  t h e m a g n e t i c and e l e c t r i c  errors be  i n the r e s i s t i v i t y  nullified  records  calculated  according to formula  i s not f u l l y  justified.  are e q u a l l y noisy the f r o m power s p e c t r a s h o u l d  4.13.  In t h e p r e s e n t  -77-  a n a l y s i s the e l e c t r i c  r e c o r d s were found t o be more or l e s s  white i n the narrow frequency bands used w h i l e the magnetic r e c o r d s were f a i r l y n o i s y .  Hence one would expect the e r r o r s  i n the c a l c u l a t i o n of apparent r e s i s t i v i t i e s  t o be as great  as those i n the computation of the power s p e c t r a of the magnetic r e c o r d s .  -78-  CHAPTER V  JUSTIFICATION OF THE ASSUMPTIONS IN THE MAGNETOTELLURIC METHOD  5.1  General In the c o n v e n t i o n a l m a g n e t o t e l l u r i c a n a l y s i s as developed  by Cagniard an apparent r e s i s t i v i t y  f^, a s c a l a r f u n c t i o n of  frequency, i s computed from experimental d a t a obtained from simultaneous measurements of the f l u c t u a t i o n s of the E a r t h ' s magnetic and t e l l u r i c f i e l d s .  The apparent r e s i s t i v i t y so  computed i s p l o t t e d as a f u n c t i o n of p e r i o d T and the r e s u l t ing  graph compared w i t h a s e t of t h e o r e t i c a l master curves  based upon simple models of a l a y e r e d E a r t h . t i o n i n the apparent r e s i s t i v i t y obtained by some authors  A great v a r i a -  thus computed has been  ( E l l i s 1962, Garland and Webster  1960) who e x p l a i n t h e i r r e s u l t s on the grounds that the assumptions u n d e r l y i n g the m a g n e t o t e l l u r i c method may not be realised.  Such a v a r i a t i o n i n apparent r e s i s t i v i t y  values  c o u l d be due t o the e f f e c t of the source or t o s u b s u r f a c e inhomogeneity.  To i n v e s t i g a t e these p o s s i b i l i t i e s i t i s  necessary t o make measurements s i m u l t a n e o u s l y over a homogeneous and an inhomogeneous media.  An attempt  t o study  -79-  such effects has ben made ( E l l i s 196X), but no conclusive r e s u l t s were obtained. In the present chapter no discussion i s given of the possible origins of micropulsations of the geomagnetic f i e l d , but  the v a l i d i t y of the d i f f e r e n t assumptions made by Cagniard  and followed i n the present work w i l l be reviewed.  Cagniard  and Tikhonov i n the development of their methods assume that, (1)  The f i e l d quantities involved vary harmonically and  may be represented by a factor  e *. JW  (2) The horizontal space variations of the magnetic f i e l d are  n e g l i g i b l e compared to v e r t i c a l variations, i . e . , a plane  electromagnetic wave i s incident upon the Earth. ( 3 ) The v e r t i c a l component of the magnetic f i e l d i s n e g l i g i b l e compared tp the horizontal component f o r a horizont a l l y s t r a t i f i e d Earth. The above assumptions are based on world wide characteri s t i c s of geomagnetic variations.  To judge the a d m i s s i b i l i t y  of these assumptions i t i s necessary to study the morphology of geomagnetic variations a l l over the world.  To carry out  and experiment on such a large scale i s beyond the scope of a single organisation (such as the University of B r i t i s h Columbia) and an analysis has to be made over a shorter distance.  Such an analysis does not provide an adequate basis  on which to judge the world wide v a l i d i t y of Cagniard's and Tikhonov's assumptions.  On the other hand i t i s possible to  -80-  judge their v a l i d i t y for a p a r t i c u l a r l o c a l i t y i f the v a r i a tions i n the l o c a l magnetic f i e l d are known over a horizontal distance comparable to the depth at which r e s i s t i v i t y determinations are made. Wait (1954) and Price (1962) have questioned the existence of plane electromagnetic waves giving r i s e to micropulsations in the geomagnetic f i e l d .  The following analysis i s no proof  of their existence on a world wide scale but does show the v a l i d i t y of the d i f f e r e n t assumptions at the stations where r e s i s t i v i t y determinations by Cagniard's method were made. The three assumptions mentioned above were tested i n the following manner.  5.2  Harmonically varying f i e l d s In the geophysical l i t e r a t u r e (e.g. Chapman and Bartels  1951) the assumption of harmonically varying f i e l d s i s commonly made.  To test the v a l i d i t y of t h i s assumption i n  the present investigation the records were examined for events which appeared more or less sinusoidal i n character and many such examples were found.  A v i s u a l correlation analysis i s  based s o l e l y on t h i s type (Fig. 5.1) of event.  Such a  c h a r a c t e r i s t i c of the events has also been shown i n section 4.2.  The computation of power spectra from f i n i t e lengths  of the records was made from such events forming a stationary time series (section 4.3).  It i s thus f e l t reasonable to  FIG. 5.1  TYPICAL  E  AND  H  SINUSOIDAL  M1CROPULSAliOUS  -82-  assume that the f i e l d i s harmonically varying.  5.3  Horizontal space variations of the geomagnetic f i e l d Because of the lack of geomagnetic data for the periods  generally used i n magnetotelluric investigations taken simultaneously a l l over the world, i t has not been possible i n the past to judge the v a l i d i t y of the existence of plane e l e c t r o magnetic waves.  Experimental investigations over short  distances have given positive as well as negative r e s u l t s (Duffus, Kinnear, Shand, and Wright 1962).  To study the s p a c i a l  d i s t r i b u t i o n of geomagnetic micropulsations i t i s e s s e n t i a l to make observations simultaneously at several stations located in a geologically undistrubed area.  In the past some observa-  tions have been made i n geologically disturbed regions by a few investigators.  Although a great v a r i a t i o n i n the  character of the geomagnetic variations was observed on comparing the r e s u l t s from a geologically disturbed region with those from an undisturbed region (1750 km apart, Duffus et a l 1962), the time of onset of d i f f e r e n t geomagnetic variations was found to be the same.  A uniform trend i n the power spectra  of the e l e c t r i c f i e l d has also been obtained between Ashkhabad and T b i l i s i i n the U.S.S.R., Ralston i n Canada and Austin and L i t t l e t o n i n the U.S.A., (Horton and Hoffman, 1962) from e l e c t r i c measurements  obtained  an i n t e r v a l of 2 1/2 years.  at the above stations over  This may indicate worldwide  -83-  characteristics  of the  geomagnetic v a r i a t i o n s .  a worldwide c h a r a c t e r i s t i c of  the  existence  can  be  explained  of e l e c t r o m a g n e t i c  1954,  these  waves b e c a u s e o f  to  Nishida  1962)  extremely  e x p l a i n s u c h phenomena.  l e n g t h of 3 x  10^  km  the magnetic f i e l d  regarding  present  has  b e e n j u d g e d by  given  4.3.  i n s e c t i o n s 4.2  and  north-south  components a t e a c h s t a t i o n period.  The  consistency  suggests a plane to  a first  at  an  approximation.  100  of required  s e c o n d s , a wave  Heirtzler  validity  (1962)  of  the  geomagnetic f i e l d  (KL^)  of the  and  o f s u c h an  this  short  analysis  shows a p l o t (H )  vertical  particular  of  are the  magnetic  z  second  components  events,  at  least  i n the c o n d u c t i v i t y  to t h i s  an  has  assumption  over  amplitude of b o t h  Data used  limited  of  s e v e r a l events at a l l  F i g . 5.2  a d d i t i o n a l c h e c k on  type  of  event.  a s s u m p t i o n power  interval  h o u r s d u r a t i o n on  August  (H  (H ) m a g n e t i c f i e l d  vertical  existence  f o r s e v e r a l e v e n t s o f 30  a l l s i x stations covering  ) and  subject  o f s u c h waves.  details  wave f o r t h e s e  a n a l y s i s were l a r g e l y As  Earth.  studying  The  the  been the  l o n g wave l e n g t h s  i n v e s t i g a t i o n the  stations simultaneously.  amplitude of  the  a p e r i o d of  the e x i s t e n c e  the u n i f o r m i t y of the  distances,  assumption  i s r e q u i r e d t o e x p l a i n the u n i f o r m i t y  a l l over the  shown s c h e m a t i c a l l y In the  For  such  Some i n v e s t i g a t o r s  have q u e s t i o n e d  the  the  waves, has  of d i s c u s s i o n between s e v e r a l a u t h o r s . (Wait  on  Whether  o f one  and  18 were computed f o r t h e components.  spectra a half  north-south The  -84-  1.5  2  FIG 5.2  3 4 STATION N U M B E R  LATITUDE  DISTRIBUTION  NORTH - SOUTH (H ) x  COMPONENTS  FOR  AND  OF  5  AMPLITUDES  VERTICAL ( H-)  EVENTS  OF  6 *  30  StC  OF  MAGNETIC PERiOD  85-  8 6 4 AUG  2  6 \  00' 8  18 61  TIME 1009 to 1106 5 5  6 4 2 108 6 4 2 I8 6 4 2 018 6 4 2 )0I8 6 4 2  '"T  1  2  1  I  4 6 8  POWER FOR  i I I I I | """I  I " 'I r_  001  DENSITY  2 Vs  NORTH-SOUTH  1 T l" I  4 6 8  I  :  01  I ""• 'I "' I T T T t " [  2  FREQUENCY AT THE  4 6 8 SIX  MAGNETIC COMPONENT  -861008; 6 :  0 000014  0001  1  1 —  2  4  1  i 6  8001  2  1—  FREQUENCY FIG  5 4  POWER FOR  DENSITY  VERTICAL  Vs  4 6 8 IN  FREQUENCY  MAGNETIC  1  01  2  CPS AT  1—i i  4 6 8 1  > THE  COMPONENT  SIX  STATIONS  -87  coherency of H  x  and H  z  f o r stations #1 through 5 r e l a t i v e to  station #6 were computed. are given i n Appendix A.  The r e s u l t s of such calculations F i g . 5.3 and F i g . 5.4 show the power  spectral density of HL^ and H  z  f o r the d i f f e r e n t stations.  power spectral density curves for H  x  The  (Fig. 5.3) have peak  values at about the same frequency at a l l s i x stations but for the v e r t i c a l magnetic f i e l d component (Fig. 5.4) their peak values are obtained at s l i g h t l y d i f f e r e n t frequencies. s h i f t of the peaks i n the H  z  The  s p e c t r a l density curves (Fig. 5.4)  i s probably due to the presence of more harmonics at the southern stations than at the northern.  Such a s h i f t could  have been eliminated i f the records had been f i l t e r e d at the desired frequency before the computation of power spectral density was made. stations both f o r H August 19th. H  x  and H  z  Similar power spectral computations at a l l x  and H  z  were made from the records of  Characteristics of the power spectral peaks for  were found to be similar to those shown i n F i g , 5.3,  and F i g . 5.4, except that their absolute values were d i f f e r e n t . The r e s u l t s of such computations are also given i n Appendix A, Peaks i n the coherency versus frequency plots generally coincided with peaks i n the spectral density plots as i s i l l u s t r a t e d i n F i g . 5.5.  The degree of coherency at these  peaks did change however from s t a t i o n to s t a t i o n .  These peaks  could s h i f t from hour to hour or from day to day.  Attention  was then limited to those frequencies showing spectral and  FIG. 5.5 POWER DENSITY 8 COHERENCY vs. FREQUENCY AT STATION #3 FOR NORTH-SOUTH MAGNETIC COMPONENT DATE: LOCAL TIME:  18 AUG., 1961 1009 - 1106.5  -89-  coherency peaks simultaneously at a l l stations.  The signal  giving r i s e to these universal peaks should then approximate to a plane wave. for both H  x  and H  To i l l u s t r a t e t h i s point, spectral densities z  were plotted at each s t a t i o n for coherency  peaks at 30 second period (Fig. 5.6).  The r e s u l t i n g curves  are very similar to a plot of amplitude against station (Fig.  5.2) and thus support a plane wave hypothesis for t h i s  frequency band on these occasions.  From F i g . 5.2 and F i g . 5.6  i t i s quite clear that the values of H  x  and H  z  for oscillations  of 30 second period do not change appreciably over a distance of 600 km.  H  z  i s f a i r l y constant from station #6 to 2, but  at #1 has a higher value.  Such a high value may be due to  the presence of an inhomogeneity, and as shown l a t e r , a high value of H  z  can be expected at t h i s s t a t i o n .  The plot of  spectral density versus stations (Fig. 5.6) shows a marked increase i n the values at station #1 although such a trend i s not so pronounced at t h i s s t a t i o n i n the plot of versus stations (Fig. 5.2).  amplitude  No s a t i s f a c t o r y explanation was  found for such a difference between the two curves. R e s t r i c t i n g the analysis to coherency peaks, the range of the spectrum which could be used for conductivity estimates by power density techniques was limited.  To examine the v a r i a t i o n  of the magnetic f i e l d for periods greater than 30 seconds, only the v i s u a l c o r r e l a t i o n method of analysis could be used.  Power  spectral values for periods longer than 30 seconds could not be  -90-  FIG. 5.6 LATITUDE DISTRIBUTION OF POWER DENSITY FOR H AND H FOR E V E N T S OF 3 0 SEC. PERIOD x  z  -91-  used s i n c e i t was extremely  difficult  t o o b t a i n the same l e n g t h  of u s a b l e r e c o r d at a l l s t a t i o n s s i m u l t a n e o u s l y .  The same -  technique as d e s c r i b e d i n s e c t i o n 4 . 2 t o o b t a i n peak t o peak v a l u e s of d i f f e r e n t events s i m u l t a n e o u s l y a t a l l s t a t i o n s , was F i g . 5 . 7 shows a p l o t of the amplitude  used.  and H  of  Z  at  each s t a t i o n f o r s e v e r a l events of 9 0 second p e r i o d , o b t a i n e d by a v i s u a l c o r r e l a t i o n a n a l y s i s .  Except  f o r the higher  values  of HJJ. on August 2 1 , a t 1 6 0 6 , a t s t a t i o n # 5 and on August 2 2 , a t 1514,  a t s t a t i o n # 3 , the f i g u r e shows a c o n s i s t e n c y i n ampli-  tude of both components f o r 9 0 second p e r i o d s .  Similar  analyses f o r p e r i o d s longer than 9 0 second c o u l d not be made because of the absence of these longer p e r i o d s at the southern stations. The e x i s t e n c e of a plane e l e c t r o m a g n e t i c wave g i v i n g to c o n s i s t e n t amplitudes  of geomagnetic m i c r o p u l s a t i o n s over  a d i s t a n c e of 6 0 0 km may be judged from a s l i g h t l y angle.  rise  The computation of apparent  from the r a t i o s of the amplitudes  resistivity  different  (eq. 1 . 1 )  of orthogonal p a i r s of  e l e c t r i c and magnetic f i e l d v a l u e s i s based s o l e l y on the assumption of the e x i s t e n c e o f plane e l e c t r o m a g n e t i c waves. Least s c a t t e r i n g of the p o i n t s i n a p l o t of apparent v i t y versus p e r i o d s h o u l d be o b t a i n e d when o n l y those which g i v e c o n s i s t e n c i e s i n amplitudes tance of 6 0 0 km or more are c o n s i d e r e d . f o r a homogeneous i s o t r o p i c medium.  resistievents  over a h o r i z o n t a l d i s This i s true only  In the present  - 9 2 -  21-8-61 1130 +-21-8-61  22-8-61 1 3 5 2  1606  — X ~  22-8-61 1514  - — 21-8 61  I  s fIG.5.7  21-8-61  1125  3 STATION  4 NUMBER  LATITUDE D I S T R I B U T I O N OP AMPLITUDES NORTH-SOUTH  2 2 - 8 - 6 1 1113  5  OF  (Hx) AND V E R T I C A L ( H z ) MAGNETIC  COMPONENTS FOR EVENTS  OF 90 S E C . PERIOD  1107  6  N  -93-  r  i n v e s t i g a t i o n such events were c o n s i d r e d i n the computation of apparent r e s i s t i v i t i e s f o r a few periods. i n the apparent r e s i s t i v i t y  Minimum  scattering  ( f ) v e r s u s p e r i o d (T) p l o t s , a  at s t a t i o n s #3 and 6 f o r these periods was o b t a i n e d .  At  s t a t i o n #3 where apparent r e s i s t i v i t i e s were c a l c u l a t e d  from  power s p e c t r a l e s t i m a t e s , p o i n t s of minimal s c a t t e r i n g i n the fa v e r s u s T p l o t correspond t o f r e q u e n c i e s where maximum coherency was o b t a i n e d a t a l l s t a t i o n s supports the assumption  ( s e c t i o n 6.2).  This  of the e x i s t e n c e of plane electromag-  n e t i c waves.  5.4  R e l a t i v e magnitudes of the v e r t i c a l and h o r i z o n t a l magnetic  f i e l d components  For a s t r a t i f i e d homogeneous i s o t r o p i c E a r t h i t can be shown t h e o r e t i c a l l y that the v e r t i c a l magnetic  component i s  z e r o when a p l a n e e l e c t r o m a g n e t i c wave impinges v e r t i c a l l y on it.  Workers i n the U.S.S.R. have r e c e n t l y r e p o r t e d very low  v e r t i c a l components over t h e s e a ( Z h i g a l o v 1961), c o n f i r m i n g this conclusion.  By o b s e r v i n g H  z  over l a n d and near the s e a  Duffus e t a l (1962) found higher v a l u e s of H  z  near the s e a  coast. F i g . 5.2 and F i g . 5.7 show the v a r i a t i o n s of H s i x s t a t i o n s f o r 30 second and 90 second p e r i o d s . be noted from these f i g u r e s t h a t H between s t a t i o n s #6 and 2.  z  z  along the  I t i s to  i s more or l e s s constant  In a d d i t i o n , the v a l u e of H / H z  x  -94-  does not exceed 0.25. Similar c h a r a c t e r i s t i c s are also obtained from F i g . 5.6. At Meanook and Beiseker where r e s i s t i v i t y determinations were made using Cagniard's method, the values of H  z  f o r periods longer than 90 second were computed  from d i f f e r e n t data f o r the magnetotelluric analysis. spectral densities were computed f o r H The r a t i o s of the power density of H  z  z  and H  x  Power  at Beiseker.  to that of KL^ f o r the  frequencies used i n the calculations of apparent  resistivity  are plotted i n F i g . 5.8. I t i s clear from t h i s figure that for  periods as high as 1000 seconds the value of the r a t i o  does not exceed 0.3. This suggests that the v e r t i c a l magnetic f i e l d at Beiseker i s n e g l i g i b l e compared to the horizontal f i e l d at a l l periods which have been used i n the r e s i s t i v i t y calculations.  An estimate of the v e r t i c a l magnetic f i e l d at  Meanook f o r periods greater than 90 seconds was made by a v i s u a l correlation analysis.  Values of the H /H r a t i o f o r z  periods up to 200 seconds d i d not exceed 0.3.  x  Tellurograms  and magnetograms from Meanook were used to obtain values of Ey/H f o r periods greater than 200 seconds. x  Recordings of H  were not made on rapid magnetograms, and hence values of H  z  z  for periods greater than 200 seconds could not be obtained f o r this station. H /H z  x  Niblett (1960) has given an average value of  f o r periods greater than 100 second as 0.56 f o r t h i s  station.  This value i s higher than that found at Beiseker.  It i s probably due to the location of Meanook i n the subauroral  ©  0.4  ©  © ©  © ©  0.3  Z_ X  © OG  0.2  i co  i ©  0.1 0 © ©  -J  1  6  10  _i  1 — I —  8 100  2  4  PERIOD Fig. 5-8  Ratio of as  vertical  a function  IN  ( H ) to horizontal ( H ) 7  of  period  v  at  Beiseker.  i  i  6  SECONDS magnetic  field  i i i L  8 1000 > components,  -96-  z o n e where m a g n e t i c variations  activity  is  subjected  to f a i r l y  rapid  along the magnetic m e r i d i a n .  From t h e  above  discussion i t  is  clear  made b y C a g n i a r d i n h i s method and f o l l o w e d investigation  are reasonable  for  that  the  i n the  assumptions present  the r e g i o n under c o n s i d e r a t i o n .  -97-  CHAPTER VI  INTERPRETATION OF THE MAGNETOTELLURIC DATA  6.1  General The g r e a t e s t problem encountered  i n a l l geophysical  methods i s the i n t e r p r e t a t i o n of the data.  Once the data have  been analysed and c o r r e c t e d f o r r e l e v a n t v a r i a b l e s , the p r o blem i s reduced t o the d e t e r m i n a t i o n of the d i f f e r e n t parameters  (or parameter) i n v o l v e d i n the method.  methods the i n t e r p r e t a t i o n of the d a t a i n v o l v e s a of  In most comparison  a f i e l d curve w i t h a s e t of master c u r v e s , both drawn t o  the same s c a l e . for  physical  These master curves a r e t h e o r e t i c a l curves  simple g e o l o g i c a l s t r u c t u r e s .  When the c l o s e s t f i t of  the f i e l d curve w i t h a master curve i s o b t a i n e d the parameters of  the mathematical  etc., of  model, such as r e s i s t i v i t y ,  layer  depths,  t h a t a r e assumed f o r the model may be used as e s t i m a t e s  the r e a l E a r t h parameters  t i o n s were made.  f o r the a r e a where the observa-  Such an i n d i r e c t approach  to the i n t e r p r e t a -  t i o n of g e o p h y s i c a l data has l e d t o some ambiguous r e s u l t s i n most g e o p h y s i c a l methods.  The degree of ambiguity  by u s i n g d i r e c t methods of i n t e r p r e t a t i o n .  i s reduced  Roy (1962) has  r e c e n t l y g i v e n a b r i e f account of the a m b i g u i t i e s i n v o l v e d i n  -98-  the  interpretation The  indirect  resistivity (  of geophysical  method i s u s e d t o d e t e r m i n e  from m a g n e t o t e l l u r i c data.  P ) and phase a n g l e  on a l o g a r i t h m i c s c a l e  nation of p r o f i l e  (Figs.  experimental  telluric (  Apparent  curves.  sounding  6.1a and b ) .  first  In p l o t t i n g  curves,  t o the thickness  layer.  resistivity  The d e t e r m i -  t h e o r e t i c a l master theoretical  the thickness  The r a t i o ( Pj)  (b^) and r e s i s t i v i t y  of apparent  of the f i r s t  resistivity  expressed (  resistivity  layer,  curves  magneto-  ( b ^ ) and  Pj^) o f t h e u n d e r l y i n g l a y e r s a r e c u s t o m a r i l y  relative  resistivity  parameters from m a g n e t o t e l l u r i c soundings i s  b a s e d on a c o m p a r i s o n between t h e s e and  subsurface  ( Q ) a r e drawn a s f u n c t i o n s o f t h e  a  period  data.  Pj)  of the  ( P^) t o t h e  i n the case  of a three-  l a y e r e d medium, f o r example, may b e w r i t t e n a s  i where A The  =  , V * A //>,and T i s t h e p e r i o d o f t h e o s c i l l a t i o n s . a  values of  unity  ?  1  and h  ±  i n the f i r s t  layer  are taken  as  i n t h e c o m p u t a t i o n o f t h e m a s t e r c u r v e s w h i c h makes i t  possible  t o u s e t h e same s e t o f c u r v e s  f o r the interpretation  of  curves  Vladimirov  field  discussed  i n different  regions.  (1961) h a s  the s i g n i f i c a n c e of the choice of o r i g i n  the master c u r v e s , versus T p l o t  and s u g g e s t e d  s h o u l d be t a k e n  that the o r i g i n  i n plotting  i n the  at the point T = l ,  P  a  P  =l.  a  Fig.  6.1(a).  Magnetotelluric two layer standard r e s i s t i v i t y curves. (After Yungul, 1961).  -100-  F i g . 6.1(b).  Magnetotelluric two layer standard phase angle curves. (After Cagniard, 1953.)  -101-  Such an o r i g i n should make i t p o s s i b l e t o determine ness o f the f i r s t  l a y e r d i r e c t l y from the curve as w i l l be  shown i n subsequent Cagniard  the t h i c k -  sections.  (1953) and Tikhonov  (1956) p u b l i s h e d a s e t of  master curves f o r a two l a y e r e d E a r t h w h i l e Yungul (1961) and Kolmakov (1961) have p u b l i s h e d a s e t f o r a t h r e e l a y e r e d E a r t h . These curves make i t p o s s i b l e t o determine t h i c k n e s s of s u b s u r f a c e s t r a t a .  Master  t h r e e l a y e r s have not been c o n s t r u c t e d .  the r e s i s t i v i t y and  curves f o r more than The experimental curve  ( p l o t t e d on the same s c a l e ) i s p l a c e d over the s e t of master curves and by means of t r a n s l a t i o n a l motions, the experimental curve  a match between  Pa(T) and a p a r t i c u l a r master curve  obtained, w h i l e m a i n t a i n i n g the p a r a l l e l i s m of the r e s p e c t i v e c o o r d i n a t e axes.  The o r d i n a t e  P  the experimental curve determines layer.  1 of t h e master curve on  3 a  the r e s i s t i v i t y o f the f i r s t  The v e r t i c a l l i n e T «* 1 ( F i g . 6.1a) g i v e s a p a r t i c u l a r  value of Ti on the experimental T - a x i s . first  l a y e r i s determined  The ,thickness of the  from the formula  (6.2)  or,  i f the v e r t i c a l l i n e T = 10 i s used,  J P  1  T /10 1 Q  (6.3)  -102-  The  parameters  of the second  ^2  M-l P i  =  layer  are  (6.4)  >  where p., t h e m o d u l u s o f t h e t h e o r e t i c a l  Thus t h e p r o c e d u r e f o r i n t e r p r e t i n g  P  curve i s defined  a  curves i s p r a c t i c a l l y  t h e same a s t h e w e l l d e v e l o p e d method f o r i n t e r p r e t i n g obtained  in direct  current  vertical  Cagniard  (1953) g a v e t h e f o l l o w i n g  mination of the depth to the second  as  electrical  curves  soundings.  e x p r e s s i o n f o r the  deter-  layer  (6.5)  when p o i n t bearing  A  ( F i g . 6.1b)  i s seen  t h r o u g h t r a n s p a r e n t paper  an e x p e r i m e n t a l c u r v e whose a b s c i s s a h a s  v a l u e o f T^ s e c o n d s .  E q u a t i o n (6.5) may  the numerical  be w r i t t e n  i n the  form  >  log \T^i  - log 2.53 - log  (6.6)  Since the curves are p l o t t e d  on a l o g a r i t h m i c  (6.6) shows t h e a d v i s a b i l i t y  of p l a c i n g  scale,  the o r i g i n  equation  at a  -103-  distance of log 2.53 to the l e f t of A (Vladimirov, 1961). Hence the v e r t i c a l l i n e mental T axis.  f - 1  should be read on the experi-  Phase curves i n magnetotelluric soundings are  interpreted i n a similar manner except that the motion of translation i s c a r r i e d out only along the horizontal axis with superposition  of the horizontal axes of the t h e o r e t i c a l and  experimental curves. P  a  Furthermore, the two translations (of the  and Q curves) which are to be executed p a r a l l e l to the  horizontal axis must be i d e n t i c a l . of the f i r s t layer must be known.  In addition, the r e s i s t i v i t y The dependence of the i n t e r -  pretation of phase measurements on the interpretation of amplitude measurements makes them less s i g n i f i c a n t i n an i n t e r pretation of magnetotelluric data, although geoelectric p r o f i l e may be determined more r e l i a b l y when both the the  0 curve are interpreted.  P  a  curve and  The parameters of a geoelectric  section may be determined from amplitude measurements alone but can not be determined from phase measurements only.  This  makes an interpretation possible from amplitude measurements only when phase measurements are not very r e l i a b l e .  Kolmakov  (1961) has also discussed the lesser importance of phase measurements i n an interpretation of magnetotelluric data for d i f f e r e n t geoelectric sections.  6.2  Determination of the d i s t r i b u t i o n of r e s i s t i v i t y In the present investigation r e s i s t i v i t y determinations  -104-  c o u l d be made a t the f o l l o w i n g three s t a t i o n s o n l y (1) Meanook, (2) B e i s e k e r , (3)  Cardston.  Because of i n s t r u m e n t a l d i f f i c u l t i e s and the l a c k of data f o r p e r i o d s longer than 100 seconds i t was not p o s s i b l e t o c a r r y out such an a n a l y s i s a t the other s t a t i o n s .  Moreover because  only l i m i t e d l e n g t h s of the r e c o r d s obtained from the 12 days r e c o r d i n g were u s a b l e the a n a l y s i s i s based on a r a t h e r s m a l l amount of data. (1)  Meanook.  At s t a t i o n #6, Meanook, the r e c o r d s were  analysed by the v i s u a l c o r r e l a t i o n method ( s e c t i o n 4.2). Apparent r e s i s t i v i t y  estimates were based s o l e l y on events  which c o u l d be c o r r e l a t e d v i s u a l l y on the east-west and north-south together of  magnetic r e c o r d s .  Values of E /H  a c c o r d i n g t o t h e i r p e r i o d and averaged.  were grouped Band widths  5 seconds f o r s h o r t e r p e r i o d s and 60 seconds f o r longer  p e r i o d s were used i n the a n a l y s i s ( s e c t i o n 4.6). of  x  electric  The number  o b s e r v a t i o n s w i t h i n a group v a r i e d , but u s u a l l y l a y between  10 and 15.  For some p e r i o d s i t was not p o s s i b l e t o o b t a i n more  than one v a l u e and hence o n l y s i n g l e v a l u e s f o r those  periods  were a v a i l a b l e f o r i n t e r p r e t a t i o n . Because of i n s t r u m e n t a l c h a r a c t e r i s t i c s and h i g h speed r e c o r d i n g i t was not p o s s i b l e t o p i c k up events w i t h longer than 200 seconds.  periods  Magnetograms and t e l l u r o g r a m s  -105-  TABLE 6.1  (Mv/Km.«y)  Mean values of P (ohms meter)  1.95 1.52 1.80 1.78 1.85 1.92 1.95 1.97 1.91 2.14 1.72 1.54 1.98 1.82 1.98 1.80 1.71 1.80 1.64 1.42 1.43 1.38 1.33 1.33 1.29 0.94 0.86 0.77 0.51 0.60 0.42  6.8 6.9 13.0 14.5 20.5 25.7 30.4 34.9 38.0 55.0 38.4 34.1 65.8 58.3 74.5 66.1 69.50 81.1 83.9 78.89 142.00 182.4 204.2 211.9 259.00 208.3 189.0 180.0 173.2 259.2 134.6  Mean values i period sees 9 15 20 23 30 35 40 45 52 60 65 72 84 88 95 102 119 125 156 195 348 480 580 652 780 1170 1260 1530 3330 3600 3960  Of  Ey/Hljj  a  S.D.M, of P a  ±1.2 ±0.0 ±0.4 ±1.6 ±3.5 ±1.1 ±0.1 ±0.0 ±0.0 ±8.7 ±1.1 ±0.0 ±0.0 ±6.3 ±3.2 ±10.0 ±3.5 ±0.0 ±0.0 ±0.0 ±26.6 ±2.7 ±45.5 ±46.1 ±0.0 ±0.0 0.0 0.0 0.0 0.0 0.0  -106-  -107-  recorded at the same time at the Dominion Observatory S t a t i o n at Meanook were used t o o b t a i n v a l u e s of E y / H p e r i o d s longer than 200 seconds.  x  ratios for  The use of t e l l u r o g r a m s i n  the present i n v e s t i g a t i o n i s not f u l l y j u s t i f i e d because of the d i f f e r e n c e i n e l e c t r o d e s e p a r a t i o n i n the two Our  e l e c t r o d e s e p a r a t i o n was  Observatory was  1.60  km.  0.61  installations.  km w h i l e t h a t of the Dominion  Hence the use of these  i n the present i n v e s t i g a t i o n i s o n l y j u s t i f i e d change i n r e s i s i t i v y t over 1.60 Observatory.  tellurograms  i f a marked  km does not e x i s t a t the  The r e c o r d s from the Dominion  Observatory  were  a l s o analysed by the v i s u a l c o r r e l a t i o n method. The s c a t t e r i n the i n d i v i d u a l v a l u e s of the r a t i o s w i t h i n a group i s expressed  as the standard e r r o r of the mean.  Averaged v a l u e s of Ey/IL^ r a t i o s f o r d i f f e r e n t p e r i o d s are g i v e n i n Table 6.1 versus  }  and the i n f o r m a t i o n d i s p l a y e d i n the Ey/IL^  p l o t i n F i g . 6.2.  According to N i b l e t t  (1960),  i t should be p o s s i b l e t o f i t such a p l o t by a s e t of s t r a i g h t lines.  I f the average or apparent  resistivity  P, a  s i d e r e d to be c o n s t a n t , then from the r e l a t i o n s h i p  P - 0.2T a  2 / x  i s con-  1  I  -108-  where  B  i s a constant and a plot of  versus -== x v^T  E„/H„  y  should  y i e l d a straight l i n e through the o r i g i n with slope B <*» J 5 P  &  In cases where i t i s d i f f i c u l t to f i t one straight  .  line,  through many points, a set of straight l i n e s with d i f f e r e n t P  values of  may be f i t t e d to the data.  A more general form  of equation (6.7) i s used i n such cases, v i z . E  ZJL x  2  A + —^— T  H  (6.8)  A and B are constants which are determined numerically f o r individual l i n e s .  In the present investigation  a f i t of three  straight l i n e s was found to be s t a t i s t i c a l l y j u s t i f i e d . Meanook, Ey/H was plotted against  For  (Fig. 6.2) i n order to  x  compare the r e s u l t s with those obtained by Niblett  (1960).  The  straight l i n e s i n t h i s figure have been drawn using a least square analysis f o r the equation E /YL^ - A  r  + B / r  v/T  where  and A where Y  i  " Ey/Hx  x. -  x  and  -4=  \p£  *4  Z i  - i  £ Yi  Y  x  r  =  Y - BX  (6.10)  >  Vi = Y  , '  u. - x. - x x i  ±  - Y  -109-  The  d e t a i l s of such an a n a l y s i s a r e given i n Appendix B.  equations  The  obtained a r e  f o r AB  H " l 7?" A  +  ^  (0,15  T  ^'> 0 4  f o r BC E„ _Z = A  2  B + — 1  -x  (.04 ^ T"^  ^.134)  \Tr"  and f o r CO E„ -£ . A H  3  B + — 2  x  (.134 ^ T"^  the c o n s t a n t s determined from equations A  1  ^ .264)  \TT  (6.9) and (6.10) a r e B  « +0.00  A  2  - +0.36  A  3  - +25.54  - +33.400  1  ,B - +7.264 2  B  3  - -3.776  I f an E a r t h c o n s i s t i n g of three homogeneous l a y e r s i s assumed then each s t r a i g h t l i n e i n F i g . 6.2 r e p r e s e n t s a l a y e r of different r e s i s t i v i t y  ( N i b l e t t , 1960).  To judge t h e v a l i d i t y  of t h i s statement t h e o r e t i c a l models w i t h d i f f e r e n t were c o n s i d e r e d .  The impedance ( E / H y  x  parameters  or E / H ) v a l u e s f o r a x  y  t h r e e l a y e r E a r t h model were computed u s i n g r e l a t i o n s g i v e n by Kolmakov  (1961).  -110-  w -y-2  2,T  2  (6.12)  Z  where  X  AU  Y  T  [jBR + [ B P  P ]  +  + R] +  S  R + Bpj -  Q  AU  AS  [ B R  +  P )  +  U  [ R  AT  [ B R  +  P ]  +  Q  [ B U  + SBj +  B P ]  +  A S ]  and S  277 A,, i/7fF  U  \  BGT  ferF  J  -  A  Q.T  -Ul-  an d  P. The  impedance v a l u e s  model h a v i n g  the  were computed f o r a t h r e e  layered  Earth  f o l l o w i n g parameters  100  10  and is  the r e s u l t s too small  (.001  to  .1  are  t o show any cps)  F i g . 6.4  frequency. three 0.62  The  straight  effect  g e n e r a l l y used  a n o t h e r f i g u r e on band.  shown i n F i g . 6.3.  shows a p l o t points lines.  of  in this  tellurics,  above  cps  The  l i n e s may  fitting  ratios  f i g u r e can  I f a l l the  a t t e n t i o n has  figure.  straight  .1  frequency  as can  best  p o i n t s up the be  thus  frequency  be  fitted  the p o i n t s  used  Since  i n magneto-  i n F i g . 6.4  a l a y e r i s not  of  straight  to frequencies  i n d i c a t e the p r e s e n c e of  by  to a frequency  s e e n i n F i g . 6.3.  been c o n f i n e d  whether each l i n e r e p r e s e n t s  and  a f u n c t i o n of  number o f  are g e n e r a l l y not  of  as  6.3  band  drawn f o r t h i s  (E/H)  c p s were p l o t t e d i n F i g . 6.4,  frequencies  the  s c a l e of F i g .  in magnetotellurics  a l a r g e r s c a l e was  l i n e s w o u l d have i n c r e a s e d  this  within  The  three  by  below three  layers  certain.  The  but  EARTH MODEL  -114-  points B  and  C  lines  and  BC.  AB  correspond occurs,  indicate To  sudden changes i n the s l o p e s of  determine whether these  t o depths at which a sudden change i n  t h e f o l l o w i n g e x p r e s s i o n was  ,  T^ Z - —  B are constants  period  i n seconds.  B =»  110  Z = 31.4 The  ,  the  A =» 0  the  C.  A  (AT + B)  g i v e n by  For  in fact  resistivity  used t o c a l c u l a t e  d e p t h o f p e n e t r a t i o n a t p o i n t s B and  A and  p o i n t s do  the  (6.13)  equation  (6.8)  and  line  AB  i n F i g . 6.4,  ,  T  =• 360  B  T i s the we  have  seconds  km.  a c t u a l v a l u e of Z = h  + h]_ = 30  2  v a l u e s of Z agree w i t h i n the order  + 1 = 31  km.  of accuracy  These  of  two  the measure-  ments. S i m i l a r l y by  using equation O  f The  actual value  these  two  values  the s t r a i g h t different Again  of of  lines  ( 6 . 7 ) , we  110 _____ oi 22 5  a a  i s lOJL'wv. 1°^  d  o  e  s  not  ohm The  meters d i f f e r e n c e between  a l l o w us  f o r the c a l c u l a t i o n  have  t o use  of r e s i s t i v i t y  depths. from  l i n e BC  i n F i g . 6.4,  we  the  have  slope at  of  »115  B -  =~  = 33.3 .  A - .155  ,  o  T  = 122.5 c  Z = 12.5 km. In the actual model t h i s depth corresponds to a plane i n the second layer.  Hence the change i n the slope of the l i n e BC  compared to that of the l i n e CD does not correspond to a new layer.  The use of the point C i n the interpretation of magneto-  t e l l u r i c data w i l l lead to ambiguous r e s u l t s . Impedance values at d i f f e r e n t periods were scaled o f f from Cagniard's master curves of apparent r e s i s t i v i t y versus period to judge the v a l i d i t y of Niblett's method f o r the determination of r e s i s t i v i t y at d i f f e r e n t depths. ing information i s plotted i n F i g . 6.5. points are f i t t e d by two straight l i n e s .  The r e s u l t -  In t h i s figure the The t h i r d l i n e  (dotted) shows similar e f f e c t s f o r frequencies higher than .1 cps as shown i n F i g . 6.3.  The point F i n F i g . 6.5 corres-  ponds to point B i n F i g . 6.4. From the straight l i n e EF we obtain A = 0  ,  B = 140  ,  T = 285 seconds and hence F  Z 2 i 31.5 km . No discontinuity i n the r e s i s t i v i t y ,  fg,  of the second layer  at a depth of 31.5 km was considered i n the actual model.  .6  h, = I km «  p  t  (  .4  -  IO m  X  E CM  •S  .3  Ui|x  -2fFig.  6.5.  (E/H)  v s f r e q u e n c y f o r a two  layered  Earth  model.  ift  .01  .02  .03  .04  f  in  .05  cps  .06  .07  .08  .09  117  Hence the computation of depths at which the r e s i s t i v i t y  changes  can not be made for a two layered Earth by N i b l e t t ' s method. Even though N i b l e t t ' s method can not be used to delineate shallow r e s i s t i v i t y s t r a t a i t may be used to delineate deeper r e s i s t i v i t y strata.  Such a c h a r a c t e r i s t i c of the method may be  seen i f we consider equation  (6.11).  The impedance values for  short periods, whose depths of penetration are less than the thickness of the top layer, are influenced by only two factors, the thickness and the r e s i s t i v i t y of the top s t r a t a .  In  contrast, the impedance values for longer periods, whose depths of penetration exceed the thickness of the top layer but are less than the combined  thickness of the top and second layers,  are influenced by the thicknesses and r e s i s t i v i t i e s of both the top and second layers.  For s t i l l longer periods where the  depth of penetration i s much greater than the depth of the t h i r d layer, the impedance values are influenced by the parameters of a l l three layers. evident from F i g . 6.14,  Such r e l a t i o n s h i p s are also  For extremely long periods the  impedance value (eq. 6.11) reduces to  z, (o)| 3  2  -  A 2  (  M T  where  Hence N i b l e t t ' s assumption that the impedance and period can be l i n e a r l y r e l a t e d i s only true f o r very long periods.  The  -118-  l i m i t i n g value of the p e r i o d when t h i s assumption  i s valid  may  be found f o r i n d i v i d u a l models by s u b s t i t u t i n g v a l u e s of the d i f f e r e n t parameters i n equation  (6.11).  To i n t e r p r e t  the  whole g e o l o g i c a l s e c t i o n i t i s e s s e n t i a l t o use a method which can d i s t i n g u i s h shallow as w e l l as deep s t r a t a . necessary t o use Cagniard's  T h i s makes i t  curve matching method.  Niblett's  method has no advantages over t h i s method. The depth t o the t h i r d l a y e r at Meanook from F i g . 6.2 c a l c u l a t e d u s i n g equation  (6.13) and was  T h i s v a l u e does not d i f f e r matching method (91.2 km,  found t o be 117.8  was km.  much from t h a t g i v e n by the curve section  6.3).  Values of the E„/H„ r a t i o s thus o b t a i n e d were i n s e r t e d i n equation  (6.7) and apparent  f u n c t i o n of p e r i o d .  resistivities  The apparent  P  a  computed as a  r e s i s t i v i t i e s so o b t a i n e d  were grouped together a c c o r d i n g t o t h e i r p e r i o d i n the same way  t h a t the E / H y  x  r a t i o s were grouped.  Standard e r r o r s of  the mean were c a l c u l a t e d t o show the s c a t t e r i n i n d i v i d u a l values.  Average v a l u e s of apparent  resistivity  together w i t h  the standard e r r o r s of the mean are g i v e n i n Table Average apparent  resistivities  p e r i o d i n F i g . 6.6.  6.1.  are p l o t t e d as a f u n c t i o n of  R e s i s t i v i t i e s and depths t o the d i f f e r e n t  f o r m a t i o n s were determined  by matching the experimental  curve  to the a p p r o p r i a t e master curve, F i g . 6.1(a), drawn by Yungul (1961). layer.  A resistivity  of 5.5  (The r e s i s t i v i t y  ohms was  o b t a i n e d f o r the top  of t h i s l a y e r o b t a i n e d from a s i n g l e  52 300  1  CD  +<L>  E i E  +  o 100 >> c/j CO LU cr  —  —  30 M I  10 o  LU  cr < Q_ Q_  <  10  1  30  100  RESISTIVITY  ALBERTA  OPERATION  +  MEANOOK  OBS.  I  300  PERIOD FIG. 6.6 APPARENT  o  vs. PERIOD  T ,  1  1000  DATA  DATA  i  3000  10,000  seconds  STATION # 6 ,  MEANOOK,  ALBERTA  -120-  well log i n the area l i e s between 5 and 10 ohms.) The experimental curve showed the best match with a master curve for p.-^ = 200.  The points  P-^ and T^ (shown by arrows i n F i g . 6.6)  were obtained by curve matching (section 6.1).  The r e s i s -  t i v i t y of the second layer and the thickness of the f i r s t  layer  were found to be 1100 ohm meter (5.5 x 200) and 2.1 km respectively.  Such a discontinuity i n r e s i s t i v i t y corresponds to the  Precambrian Niblett  basement.  (1960)j  No such discontinuity was observed by  Evidence for the existence of such a discon-  t i n u i t y i n t h i s area i s summarised i n section  8.2.  The curve matching method used to determine the constants of the f i r s t two layers uses short period events while for the constants of the t h i r d layer long period events are required. The determination of the constants of the t h i r d layer at Meanook are considered together with those at Beiseker (section 6.3). Phase measurements between E  y  and H  x  events for d i f f e r e n t  periods were not used i n the present investigation because of the d i f f i c u l t y i n obtaining t h e i r true values from a v i s u a l correlation analysis.  A few E  and  events of the same  period were analysed to f i n d their phases. i  A v a r i a t i o n up to  20° was observed and hence they could not be used i n the  r e s i s t i v i t y analysis. (2) Beiseker.  The values of the spectral density of the  e l e c t r i c and magnetic records together with the degree of coherency and phase differences between them i n narrow  -121-  TABLE  Record No.  A B B  A A B E E E E C C C  D C  D C  D D D D F F F F  Period (sees)  (E /H ) (mv/km.7)^  25 25 28.5 28.5 33.3 33.3 43.4 50.0 52.6 55.5 71.4 76.9 83.3 83.3 90.9 90.9 100.0 100.0 111.0 125.0 133.0 400.0 500.0 660.0 1000.0  2.1 2.8 3.3 1.2 1.4 2.8 4.1 3.8 3.8 3.8 4.2 4.7 4.5 2.4 3.9 2.5 3.2 2.3 2.2 2.1 2.1 0.7 0.4 0.3 0.2  2  y  x  P.  (ohm meters) 10.6 14.7 19.2 6.9 9.8 19.7 36.8 40.0 42.2 43.4 61,4 74.4 78.1 41.1 73.3 47.3 65.5 48.7 51.7 55.8 58.4 55.5 42.5 35.8 33.3  6.2  (Coh)' \R1 2  0.3 0.7 0.8 0.6 0.3 0.5 0.6 0.3 0.2 0.1 0.8 0.9 0.8 0.8 0.9 0.9 0.9 0.8 0.8 0.7 0.7 0.7 0.8 0.8 0.7  Modified (degrees) 38.5 -54.9 -71.2 74.0 103.0 -105.5 -107.9 -81.9 -81.2 -82.7 -69.8 -69.6 -69.5 -160.0 -67.3 -176.3 -65.1 165.0 150.0 140.3 97.8 9.2 9.6 5.8 11.1  &  38.5 125.1 108.8 74.0 103.0 74.5 72.1 98.1 98.8 97.3 110.2 110.4 110.5 20.0 112.7 3.7 114.9 165.0 150.0 140.3 97.8 9.2 9.6 5.8 11.1  -122-  TABLE 6.3  Record No. A A A A A E E E E C C C D C D C D D D D F F F F  Period (sees) 20.0 22.2 25.0 28.5 33.3 43.4 50.0 52.6 55.5 71.4 76.9 83.3 83.3 90.9 90.9 100.0 100.0 110.0 125.0 133.0 400.0 500.0 666.0 1000.0  < -/%f) E  12.5 10.2 9.3 8.1 6.0 5.2 4.4 3.8 3.4 27.8 23.9 20.2 26.0 17.4 24.0 16.8 23.7 20.4 17.1 16.1 2.7 2.1 1.7 1.3  < meters)  (Coh) \R\  51.7 47.0 48.3 47.5 41.6 46.8 45.7 42.0 39.8 411.0 380.0 348.0 448.0 328.0 451.0 346.0 490.0 468.0 442.0 444.0 224.0 218.0 232.0 275.0  0.8 0.8 0.4 0.2 0.7 0.4 0.3 0.3 0.3 0.8 0.9 0.9 0.8 0.9 0.8 0.9 0.8 0.8 0.8 0.8 0.9 0.9 0.8 0.6  o h m  2 9  (mv7km' y) ,  2  2  & (degrees) -104.2 -92.8 -84.1 -75.0 -94.9 36.4 48.3 61.0 62.4 -52.3 -43.4 -43.0 -125.5 -44.1 -166.0 -50.5 168.5 150.0 141.6 117.2 -80.4 -81.0 -80.1 -78.1  Modified 8 75.8 87.2 95.9 105.0 85.1 36.4 48.3 61.0 62.4 127.7 136.6 137.0 54.5 135.9 14.0 129.5 168.5 150.0 141.6 117.2 99.6 99.0 99.9 101.9  -123-  frequency bands are given i n Appendix A.  An examination of  these values shows a wide spread i n coherency within the pass band.  To examine more c a r e f u l l y such variations, spectral  density and the square of the coherency were plotted f o r (E , y  H ) and ( E , H ) pairs. x  x  y  Figs. 6.7 and 6.8.  Such variations are shown i n  It i s evident that peaks i n the coherency  versus frequency plots coincide with peaks i n the spectral density plot.  Hence r a t i o s of the spectral density of e l e c t r i c  and magnetic records can not be used for the computation of apparent r e s i s t i v i t y small.  at- frequencies where the coherency i s  Attention was then r e s t r i c t e d to the neighbouring  frequencies of spectral peaks.  Only those frequencies l y i n g  within the band widths of the spectral density curves were used to compute apparent r e s i s t i v i t i e s from values of the power spectra for orthogonal e l e c t r i c equation (4.11).  and magnetic pairs, using  The apparent r e s i s t i v i t i e s were divided into  three categories according to the degree of coherency between the  orthogonal magnetic and e l e c t r i c  calculation.  components used i n their  The f i r s t category indicates a degree of  coherency between 1.0 and 0.9, the second between 0.8 and and the t h i r d between 0.6 and 0.5.  0.7  Coherencies lower than  0.5 were not used since a great v a r i a t i o n i n r e s i s t i v i t y values for such coherencies was observed. are  given i n tables 6.2 and 6.3.  The calculated r e s i s t i v i t i e s Average values of apparent  r e s i s t i v i t y could not be calculated at Beiseker because of  -124-  FIG  67  POWER STATION  DENSITY No 3  COMPONENTS  S  FOR  COHERENCY E-W  Vs  MAGNETIC  FREQUENCY ft  N-S  AT ELECTRIC  -125-  FIG 6-8  POWER DENSITY 8 COHERENCY Vs FREQUENCY AT STATION No 3 FOR N - S MAGNETIC S E-W ELECTRIC COMPONENTS  -126-  i n s u f f i c i e n t data and actual values for i n d i v i d u a l periods were used.  The errors introduced i n the computation  of apparent  r e s i s t i v i t y from spectral density values were calculated using Tukey's 80% range formula. Table 4.1.  Estimated errors are given i n  Since i d e n t i c a l lengths of records were used for  both (Ey, E ) x  and (Ejj., Hy) pairs, the errors are the same i n  both cases. Apparent r e s i s t i v i t i e s divided into the above three categories are plotted against period i n F i g . 6.9(a) and F i g . 6.10(a). A scattering of points between periods of 70 to 100 seconds i s noticeable i n both figures.  A sudden jump i n r e s i s t i v i t y values  between periods of 50 to 70 seconds i s also noticeable i n F i g . 6.10(a) although no such jump i s found i n F i g . 6.9(a).  In  addition the apparent r e s i s t i v i t y values calculated from E / H x  y  r a t i o s were found to be higher than those calculated from Ey/H r a t i o s . x  This fact and the existence of a break i n the  r e s i s t i v i t y curve (Fig. 6.10(a)) suggest the presence of anisotropic conductivity i n t h i s region (section 7.4). In drawing the curves, F i g . 6.9(a) and 6.10(a),  the  greatest emphasis was given to those points which had a coherency i n the f i r s t category.  R e s i s t i v i t y determinations  at t h i s station could only be made along an east-west  profile  because of the extreme scatter of points along the north-south d i r e c t i o n (Fig. 6.10).  Curve matching (section 6.1) was  used  to determine r e s i s t i v i t i e s and depths to d i f f e r e n t interfaces.  100  1  i  1 oQo o J  a> E  i  I  +  30  /  *  V  s  t  J*  10  •  X  '  X  X  COHERENCY  r-  1  FIG.6.9a A P P A R E N T  10  30  PERIOD  T .  RESISTIVITY  vs. PERIOD  100  °  0.7  x  0.6  +  0.4  |R|  2  to L O to 0.5 to 0.3  300  _  1000  seconds STATION  #3,  B E I S E K E R ( FROM  4*  o  Q> <= PIG. 6 . 9 ( b )  PLOT OP PHASE ANGLE BETWEEN E AND H PERIOD AT BEISEKER * v  x  vs  A P P A R E N T RESISTIVITY  o ON  CD  CD  o  >  O O  p > ohm-meters cn  ro  T  co  T) I>  JO  m  ro  3J  m co co  <  "U  T)  m o o  m zo  co  o  CO  lc  k 1 \>° o  o —I o  co  H  CO  CD O O  ro  cn  CD  /8 +  X  O  pp  ZD  -  4± CT> CD  —+• —+• —+•  m co m  o  -c-r-  m  p  o  o  oo c n  o  p  -si  o O _E m  o -<  x |  o ro  \ \  co m  /  /  /  /  33 o  o V o »o O 1 o  J  O O  o  - 6 Z I  L  _ o  O O  ~e ©-  4  5  6  7  8  100  PERIOD IN Fig.  6.10(b),  2 SECONDS  P h a s e a n g l e betweem E^. and H  y  vs  period.  COHERENCY  |Rf  0 * 0.7  to  1.0  X = 0.6  to  05  + « 0.4  to  0.3  5  6  J  !  7  8  1_  1000  -131-  The  resistivity  of the f i r s t  m e t e r by c u r v e m a t c h i n g logs of nearby  wells.  (T =» 1,  P  obtained, tion  1) s e e n  o f 2.6  meter.  the depth  that km  ohm  meter  » 200  The  6.3  was  origin  from  obtained  of F i g . 6.1(a)  arrows  i n F i g . 6.9(a).  the second  layer  ( e q u a t i o n 6.2)  and  This  interpreta-  at Beiseker occurs at a has  a resistivity  of  1200  T h e s e v a l u e s a g r e e w e l l w i t h t h o s e a t Meanook again i s reasonably close  Precambrian  t o t h e known d e p t h  and  of  the  basement.  V a l u e s of spectral  10 ohm  best f i t f o r  F i g . 6.1(a).  t o be  t h r o u g h F i g . 6 . 9 ( a ) , when t h e b e s t f i t was  i s marked by  suggests  depth ohm  »  A  found  and between 5 and The  between F i g . 6 . 9 ( a ) and  l a y e r was  (Ey/IL^)  2  e s t i m a t e s and  and  (E /H ) x  used  o b t a i n e d from  2  y  i n the c a l c u l a t i o n  of  t h e power apparent  resistivity  values are p l o t t e d  as a f u n c t i o n o f f r e q u e n c y i n  Fig.  The  (E../H )  6.11.  p o i n t s f o r the  y by  three straight  of  the sudden  l i n e s but  r a t i o s may  t h o s e f o r (E / H )  cannot  2  v  jump i n ( E „ / H )  2  v  be  joined  x  v a l u e s between  .014  because  and..018 c p s .  y  x  o T h i s s u d d e n jump i n t h e presence  o f an  determined p o i n t B was  plot from  x  y  ratio  anisotropic r e s i s t i v i t y  body a t B e i s e k e r as was resistivity  (E /H )  also  indicated  ( F i g . 6.10(a)).  The  the s l o p e of the l i n e  found  t o be  25.3  i s p r o b a b l y due o r an from depth AB  the  inhomogeneous the  apparent  to the t h i r d  and  the p e r i o d  layer at  the  km.  P h a s e a n g l e s between o r t h o g o n a l e l e c t r i c records f o r the d i f f e r e n t  to  f r e q u e n c i e s at which  and  magnetic  resistivities  X  OA  .005  .010  .015  .020  >Fig.  6.11.  (E/fi)2  vs  .025  .030  .035  f in cps  frequency  at  station  #3,  Beiseker.  .040  .045  -133-  were c a l c u l a t e d , were a l s o o b t a i n e d analysis.  These phase a n g l e s  d u r i n g t h e power  are given  i n Tables  An e x a m i n a t i o n  o f them shows t h a t t h e y  within records  and v a r y g r e a t l y f r o m d a y t o d a y .  6.2  and  6.3.  are not c o n s i s t e n t  a n g l e s were computed b y t a k i n g t h e t a n g e n t qua-spectrum t o the co-spectrum,  spectral  The p h a s e  of the r a t i o s  of the  and h e n c e c a n v a r y b y 1 8 0 ° .  T h o s e p h a s e v a l u e s w h i c h were o u t b y 180° were c o r r e c t e d and these  corrected values are given  variation to  i n phase v a l u e s  i n the t a b l e s .  is still  the poor magnetic r e c o r d s .  found,  a n d may b e  A variation  not  e x p l a i n however t h e l a r g e v a r i a t i o n shown  and  6.10(b).  indicated  i n the present  Because of t h e i r  variability,  a quantitative resistivity  for Fig.  This s t i l l i n Figs.  qualitative  phase angles  striking.  c o u l d n o t be u s e d  i n t e r p r e t a t i o n b u t c o u l d be u s e d  interpretation.  The t r e n d s o f t h e c u r v e s i n  (between 20-40 s e c ) t h e n finally  o f more  A minimum and a maximum i n t h e two c u r v e s The p h a s e a n g l e s  decrease  w o u l d be e x p e c t e d  such  ( s e c t i o n 7.4).  6.9(b) a n d F i g . 6.10(b) show t h e p r e s e n c e  two l a y e r s .  o f an  i n this region,  investigation  does  6.9(b)  A p o s s i b l e e x p l a n a t i o n may be t h e p r e s e n c e  inhomogeneity or a n i s o t r o p i c r e s i s t i v i t y  in  attributed  o f 10° t o 15° was  o b t a i n e d by examining fewer magnetic r e c o r d s .  as was  A great  first  increase  decrease  with  than i s very  period  (between 40-100 s e c ) , and  to constant  values  at higher  periods.  (between 100-1000 s e c ) a s The s h a p e o f t h e c u r v e s  b e t w e e n 20-100 s e c i n d i c a t e s t h e p r e s e n c e  o f a bed of higher  -134-  TABLE 6.4  Mean period (sees)  Mean E / H (mv/km.«y? y  x  Mean values of  POL*  (ohm meters)  S.D.M. of E /H y  x  18.0  2.76  27.35  ±0.12  24.4  2.53  30.8  ±0.14  28.5  2.71  41.8  ±0.40  33.0  2.07  28.4  ±0.12  36.0  2.15  33.5  +0.20  43.0  2.00  43.0  ±0.02  48.0  1.60  24.7  ±0.00  57.0  2.23  56.7  ±0.09  63.0  1.95  48.1  ±0.05  68.0  1.89  48.7  ±0.06  75.0  1.87  52.9  ±0.13  84.0  2.04  70.4  ±0.02  95.0  1.92  70.4  ±0.19  1  -135-  r e s i s t i v i t y than t h a t of the top bed. was  a l s o found  i n the apparent  and F i g . 6.10(a). 400  and 1000  The  r e s i s t i v i t y c u r v e s , F i g . 6.9(a)  decrease  i n the phase angles between  sec shows the presence  l y i n g beneath a h i g h l y r e s i s t i v e The  Such a c h a r a c t e r i s t i c  of a l e s s r e s i s t i v e  bed.  t r e n d s of the curves i n F i g . 6.9(a) and  p e r i o d s g r e a t e r than 150 sec are remarkably decrease  i n apparent  The  r e s i s t i v i t y f o r periods greater  than  below the 1100-1260 ohm  of a l e s s r e s i s t i v e  meter r e s i s t i v i t y bed.  m i n a t i o n of the c o n s t a n t s f o r t h i s l a y e r and are g i v e n i n s e c t i o n  (3) Cardston.  The  bed  deter-  those f o r Meanook,  6.3.  The r e c o r d s were analysed by the v i s u a l c o r r e -  l a t i o n method ( s e c t i o n 4.2). between the east-west  Events which c o u l d be  y  were grouped  x  together a c c o r d i n g t o t h e i r p e r i o d and averaged. 5 seconds was  correlated  e l e c t r i c and n o r t h - s o u t h magnetic  r e c o r d s were c o n s i d e r e d and v a l u e s of E / H  of  6.10(a) f o r  similar.  150 sec a l s o i n d i c a t e s the presence  s t a t i o n #6,  bed  taken i n grouping the E /H  A band width  ratios.  x  The  number of o b s e r v a t i o n s w i t h i n a group v a r i e d , but u s u a l l y l a y between 10 and 15. for  each p e r i o d .  Standard e r r o r s of the mean were c a l c u l a t e d Average v a l u e s of the E / H y  x  ratios  together  w i t h the standard e r r o r s of the mean are g i v e n i n T a b l e The r e s u l t i n g i n f o r m a t i o n i s d i s p l a y e d i n F i g . 6.12,  6.4.  where  average Ey/EL^ r a t i o s are p l o t t e d a g a i n s t average p e r i o d s . The s c a t t e r i n the i n d i v i d u a l v a l u e s of the r a t i o s w i t h i n a  40 50 60 70 PERIOD T , seconds FIG.  6.12  H  vs  PERIOD  STATION  80  90  * l , CARDSTON  100  137-  g r o u p was f o u n d  t o be q u i t e  large  a n d i s shown i n F i g . 6.12  by  the standard error  of  s u b s u r f a c e s t r a t a c o u l d b e made b e c a u s e  variation  o f t h e mean.  No r e s i s t i v i t y  i n t h e Ey/Hx r a t i o s w i t h i n  l a c k of data a t p e r i o d s longer than ing  of the E /H v  ratios  i s perhaps  at Cardston.  of  were o b t a i n e d a t t h i s  Geologically Cardston l i e s of  a major  considered the  Ey/H  x  fault  belt  inhomogeneity  apparent r e s i s t i v i t i e s  points  100 s e c o n d s .  station  giving  (Figs.  zone.  rise  is  calculated  ( F i g . 6.13).  of period  inhomogeneity,  ( F i g . 6.13).  A resistivity  t h a n 100 s e c o n d s .  ence  x  A  ratios scatter  jump i n r e s i s t i v i t y  plot  i s obtained at  curve could  n o t be  of lack of data at periods  Although the e f f e c t  of  i n the apparent r e s i s t i v i t y  6.13) a s i n t h e Ey/EL^ r a t i o  study  from average Ey/H  i s n o t i c e a b l e b u t no s u d d e n  n o t s o w e l l marked  (Fig.  The p r e s e n c e  station.  o f s u c h an  drawn t h r o u g h t h e s e p o i n t s b e c u a s e longer  5.2 a n d 5 . 6 ) .  The p r e s e n c e o f s u c h an  (1962) a t t h i s  as a f u n c t i o n  scatter-  t o the s c a t t e r i n g i n  v a l u e s a s was f o u n d a t B e i s e k e r ( F i g . 6 . 1 0 ( a ) ) Cardston  This  and t h e  ( F i g . 2.2) may p e r h a p s b e  ( F i g . 6.12).  To e s t i m a t e t h e e f f e c t  of  groups,  has a l s o been i n d i c a t e d by a t e l l u r i c  undertaken by Douglass  were p l o t t e d  great  i s supported by the high values  at Cardston  versus T plot  individual  i n a disturbed  an i n h o m o g e n e i t y  of this  due t o t h e p r e s e n c e o f an  inhomogeneity Z/Hx w h i c h  This  estimations  plot  a t C a r d s t o n may b e i n f e r r e d f r o m  inhomogeneity plot  ( F i g . 6.12) i t s e x i s t these  figures.  -138-  ©0 0 0 0 0  _i  i_  i  8  0  ©  0  O  i 10  2  T in sees. F i g . G.13.  .0 03  Apparent r e s i s t i v i t y vs period, station #1, Cardston.  -i—i i i i 6 8 100  -139-  6.3  Combined a n a l y s i s o f Meanook and The  resistivity  (section  6.2)  were made by  and  6.9(a)) with  for  a two  confined portion it  estimates  a t Meanook and  The  interpretation  curves  200  and  curves  t h a t of  the  longer  Beiseker  than  900  respectively.  of the  The  To  decrease  must be values for  considered. (Figs.  a three  trasts  and  equations given  This  6 . 9 ( v ) and  bed  and  (6.11) and  by  The  seconds  6.6  at and  with i n -  resistive  phase  6 . 1 0 ( b ) , s e c t i o n 6.2).  (6.12).  the  Figs.  layered Earth  i s a l s o supported  the middle  was  layer i s  decreases  of r e s i s t i v i t y  a three  200  s e c o n d s a t Meanook  l a y e r e d E a r t h model f o r d i f f e r e n t t h i c k n e s s e s of  than  lowest  c r e a s i n g p e r i o d i n d i c a t e s t h e p r e s e n c e o f a low beneath a high r e s i s t i v e  6.1)  interpret  above i t .  apparent r e s i s t i v i t y 300  (Fig.  6.6  f o r a t h r e e o r more  l a y e r immediately  s e c o n d s and  (Figs.  i n s e c t i o n 6.2  for periods greater  t o m a t c h them w i t h  6 . 9 ( a ) show t h a t t h e  periods  curves  seconds.  l a y e r e d E a r t h i n which the r e s i s t i v i t y than  Beiseker  matching the f i e l d  to p e r i o d s s h o r t e r than of the f i e l d  smaller  data  a s e t of a p p r o p r i a t e master curves  layered Earth.  i s necessary  Beiseker  bed  model  angle  Master  curves  resistivity  l a y e r were computed  apparent r e s i s t i v i t y  conusing  P  a  is  by  (6.14) where  f*  i s i n ohm  meter.  -140-  INDEX  V  x  = 2/ h  V = z  h / 3  , 2 4  7^ = 3 0  h  = 0°  Mi = l 0 0 , M = I Q 0 0  h  ?  10'  to  £ 10 CD  ^=42.42,^ =00,^=200,  E i  B  E  ^,=28,7/2=00,  2  200,^=20  =00 /ii=IOO ^2 )  -  /i =IO  10  2.00,  o f  = 1  0  )  / W O O , /x = 5 2  V  2  = a>  /!, = 100 /l  2  =  l  OJ 1.0  10  10  10'  10'  >TT in (sec)' * 7  FIG 6 . 1 4 MASTER CURVES OF APPARENT RESISTIVITY FOR MAGNETOTELLURIC SOUNDINGS OVER A THREE LAYER EARTH  -141-  Values of apparent r e s i s t i v i t y are  computed from equation (6.14)  p l o t t e d as a f u n c t i o n of p e r i o d  Fig.  6.14.  (on l o g a r i t h m i c paper) i n  The d i f f e r e n t parameters  i n v o l v e d i n the computation  f o r the d i f f e r e n t  are shown on the c u r v e s .  shows the f o l l o w i n g c h a r a c t e r i s t i c  layers The  figure  features.  1) The form of the curves A and B remains the same d e s p i t e a d i f f e r e n c e of a f a c t o r of 50 i n the r e s i s t i v i t y  of the  third  layer. 2) In the c r i t i c a l case, Curve B, a decrease resistivity 1hat of a two a master  of the t h i r d  i n the  l a y e r has not a l t e r e d the shape from  l a y e r e d E a r t h model.  I n t e r p r e t a t i o n s based on such  curve w i l l l e a d t o ambiguous r e s u l t s .  3) The peak v a l u e s of the curves i n c r e a s e as the t h i c k n e s s of  the middle l a y e r i n c r e a s e s as may  be noted i n the d i f f e r e n c e  between curves G and E. 4) The p e r i o d c o r r e s p o n d i n g to the peak i n the apparent r e s i s t i v i t y plot shifts of  towards longer p e r i o d s as the t h i c k n e s s  the middle l a y e r i s i n c r e a s e d .  In other words, the t h i c k -  ness of the middle l a y e r i s analogous  t o damping i n  galvanometers. 5) The t r e n d of the curves at p e r i o d s s h o r t e r than those at which peak v a l u e s of the r e s i s t i v i t y are o b t a i n e d remains more or l e s s the same d e s p i t e g r e a t changes of  the t h i r d  i n the  resistivity  layer.  6) The t r e n d of the curves at p e r i o d s longer than those  -142-  at which peak values of the r e s i s t i v i t y are obtained i s governed by the value of the  f^/  ratio.  It has been shown by Kolmakov (1961) that a) when the r e s i s t i v i t y of the middle layer, from that of the enclosing  f^, does not d i f f e r  greatly  layers, only the thickness of a thin  layer can be determined p r e c i s e l y .  For thick layers, the deter-  mination of the thickness of the middle layer, hg, requires that the precise value of the r e s i s t i v i t y of the middle layer, and not merely i t s order of magnitude, be known; b) when the r e s i s t i v i t y of the middle layer d i f f e r s considerably of the containing  layers, hg can be determined very precisely  for thick as well as f o r thin layers. the order of magnitude of The  from that  fg ^  s  For t h i s purpose, only  required, not i t s precise value.  a p p l i c a b i l i t y of these two r e s u l t s to the present i n v e s t i -  gation w i l l be discussed i n subsequent paragraphs. In F i g . 6.15 apparent r e s i s t i v i t y values at Meanook and Beiseker are plotted as a function of period on the same scale as that of F i g . 6.14.  The two curves i n F i g . 6.15 are p a r a l l e l  up to a period of about 300 seconds i n d i c a t i n g the existence of a layer with the same r e s i s t i v i t y contrast compared to the top layer.  The existence of such a layer at Meanook and  Beiseker was shown i n section 6.2.  The s h i f t i n the peak values  of the two curves i n F i g . 6.15 i s probably due to changes i n the thickness of the middle layer and the r e s i s t i v i t y of the t h i r d layer at Meanook and Beiseker.  The apparent r e s i s t i v i t y f o r  IO  3  Fig.  6.15.  Apparent r e s i s t i v i t y vs period for Meanook and Beiseker,  -144-  periods longer than those at which the maximum values of are  /?  obtained, decreases more r a p i d l y at Beiseker than at  Meanook.  Such a rapid decrease i n r e s i s t i v i t y with period at  Beiseker indicates the presence of a bed at some depth whose r e s i s t i v i t y i s lower than at Meanook. Fig.  6.15 was placed over F i g . 6.14 to obtain a proper  match between the two sets.  The curve i n F i g . 6.15 f o r  Meanook f i t s well with curve C i n F i g . 6.14 except that i t has a s l i g h t l y higher peak value.  The curve i n F i g . 6.15 f o r  Beiseker, on the other hand, does not f i t well with any of the curves except to some extent with curve E.  Such an  interpretation reveals the following parameters f o r Meanook and Beiseker. Meanook  n  ,  Mr,  200 42.42 10  From section 6.2 we have 5.5 ohm  meters  2.1 km 1100 ohm meters 55 ohm meters h  42.42 x 2.1  2  89.1 km and  h  l  +  h  2  -  9  1  ,  2  k  m  -145-  Beiseker £ je,  -  200  z/h,  ^  24-30  h  ^  .-1-5  From section 6.2 we have (\ =  6.3 ohm meters  hj =  2.6 km  ^2 =  1260 ohm meters  t\ —  6.3 - 31.5 ohm meters  h and  hj + h  2  2  ^ 62.4 - 78 km =  65 - 80.6 km (mean 70 km)  The r e s i s t i v i t i e s of the top layers at Meanook and Beiseker obtained by matching the curves i n F i g . 6.14 with those i n F i g . 6.15 were found to be nearly the same as those given i n section 6.2. Comparing the values of the depth to the t h i r d layer obtained by curve matching with those obtained from Figs. 6.2 and 6.11 at Meanook and Beiseker, the values at Meanook are found to be closer  (117.8 km and 92 km) than the values at  Beiseker (25.3 km and 70 km).  The values found by curve  matching should be more r e l i a b l e than those found by the slope (Niblett's) method, section 6.2. From the above interpretation of magnetotelluric data at Meanook and Beiseker i t appears that a layer of very low r e s i s t i v i t y which exists at Beiseker at 70 km i s not found at  -146-  Meanook. at  This  does not prove t h a t  Meanook b u t t h a t b e c a u s e o f s m a l l e r  with the enclosing determination the  such a l a y e r does not e x i s t  thickness  contrasts  b e d s i t was n o t p o s s i b l e t o d e t e c t  of the depth t o such a l a y e r  precise value  On t h e o t h e r  resistivity  of the r e s i s t i v i t y  hand, t h e d e t e r m i n a t i o n  i s only  of t h i s  layer  i s known.  made and a g r e e f a i r l y w e l l w i t h e a c h o t h e r .  of  the considerable  This  difference i n the r e s i s t i v i t y beds  and  a n d Meanook c a n  be  of the enclosing  The  possible i f  of the r e s i s t i v i t y  of the middle layer both at Beiseker  l a y e r compared t o t h a t  i t .  i s because  of the middle  (section  6.2).  -147-  CHAPTER V I I  ANISOTROPY AND  7.1  INHOMOGENEITY  General The m a g n e t o t e l l u r i c method  used  developed  b y C a g n i a r d may b e  f o r the determination of subsurface r e s i s t i v i t y  t h e c a s e o f a homogeneous s t r a t i f i e d from  the t r u e r e s i s t i v i t y  used  t o determine  (Appendix  C).  may b e o b s e r v e d  the r e s i s t i v i t y  Great d i s p e r s i o n  impedance v a l u e s o b t a i n e d f r o m and m a g n e t i c similar  effect  giving  deviations  when t h e method i s  i s u s u a l l y observed a pair  i s a l s o observed  of orthogonal (Kovtun,  methods  i n the electric  1961).  A  i n the case of a n i s o t r o p i c  I n r e c e n t y e a r s a few p a p e r s different  Large  o f an inhomogeneous medium  r e c o r d s a t t h e same p e r i o d  conductivity. lished  Earth.  only i n  have been  pub-  of analysis f o r the  d e t e r m i n a t i o n o f s u c h s t r u c t u r e s b y m a g n e t o t e l l u r i c methods. Theoretical ities  and model s t u d i e s f o r two d i m e n s i o n a l  have b e e n made b y K u n e t z and d ' E r c e v i l l e  ( 1 9 6 0 ) , Neves are  (1957) and o t h e r s .  quite different  (1962),  Rankin  In g e n e r a l f i e l d c o n d i t i o n s  f r o m t h o s e o f t h e m o d e l and t h u s  cases i t i s extremely d i f f i c u l t model d a t a .  inhomogene-  t o compare  the f i e l d  i n many with  -148-  Most a u t h o r s ivities space  at a p a r t i c u l a r  over  l o c a l i t y without  subsurface  assuming i t t o  w h i c h r e s i s t i v i t y d e t e r m i n a t i o n s were made.  the presence  o f an  the present  studied  impedance  (E /H y  inhomogeneity  investigation  separately.  In t h i s  d e t e r m i n a t i o n of a n i s o t r o p i c o b t a i n e d by  x  resist-  a knowledge of  a h o r i z o n t a l d i s t a n c e comparable w i t h  the v a l u e s of the  In  to determine  v a r i a t i o n s of the magnetic f i e l d ,  uniform at  have t r i e d  o r E / H y ) was x  be  the  Any  the  depth  scatter  in  attributed  to  or a n i s o t r o p i c c o n d u c t i v i t y .  these  two  chapter  e f f e c t s have been  a method i s g i v e n f o r  c o n d u c t i v i t y and  a p p l y i n g i t t o the data obtained  the  the  results  at Beiseker  are  presented. In  the f o l l o w i n g s e c t i o n s the term  anisotropy refers  a n i s o t r o p i c r e s i s t i v i t y i n a homogeneous medium w h i l e inhomogeneity as a f a u l t dimensional  refers  t o a two  or a dyke.  The  dimensional  medium on  f e a t u r e i s c o n s i d e r e d t o be  the  inhomogeneity  either  term  such  s i d e of such  homogeneous  to  a  two  and  isotropic. The now  be  different  models proposed  described b r i e f l y .  dimensional  inhomogeneity,  breaking the mathematical magnetic f i e l d to  parallel  t h e c o n t a c t , and  a magnetic f i e l d  Neves such  various authors  (1957) has  treated a  as a v e r t i c a l  solution  t o and  by  an  into  two  electric  t h a t o f an e l e c t r i c  contact,  will two by  p a r t s ; t h a t of field  field  p e r p e n d i c u l a r t o the c o n t a c t .  a  perpendicular  parallel Field  to data  and  -149-  Fig. 7.1.  Theoretical magnetotelluric sounding across v e r t i c a l contact, H f i e l d p a r a l l e l to the strike. (After Cantwell, 1960).  -150-  T * 1.6 x IO~ secs. 5  o °o  / \  \  /  o  o  o  °P * {  \  IO  6  CM  / o o /  •o  —  r,-  x_ "o  /  /  I  X \  */> \  6  $M  /  •*  •jc  4  =8 x 10~  X  60  x(CM)  h 20crn s  Fig.  7.2.  P l o t o f E/H o v e r a h i g h l y c o n d u c t i n g and a p o o r l y c o n d u c t i n g dyke. ( A f t e r R a n k i n , 1960.)  -151-  may be analysed by f i r s t transforming i t along the major axes of the inhomogeneity and then using Neve's method f o r the interpretation i n those two d i r e c t i o n s .  For the f i n a l  analysis the two r e s u l t s may be combined.  Figure 7.1 shows  a t h e o r e t i c a l magnetotelluric sounding curve across a v e r t i c a l fault.  Similar mathematical solutions f o r dykes i n the case  when the magnetic f i e l d i s polarised p a r a l l e l to the structure have been given by Rankin (1960).  Theoretical and experimental  curves have been obtained by him f o r a number of d i f f e r e n t models and the agreement between them i s f a i r l y good. Figure 7.2 shows an experimental magnetotelluric sounding curve over a high r e s i s t i v i t y contrast dyke with deep overburden, Cheteav (1960) has given a method f o r the determination of the c o e f f i c i e n t of anisotropy ( i . e . the r a t i o of the impedance tensors i n the two p r i n c i p a l directions of anisotropy) and the i n c l i n a t i o n of a homogeneous anisotropic medium.  His approach necessitates r e s i s t i v i t y  determinations  by d i r e c t current methods i n addition to the magnetotelluric method.  where  Using the t o t a l impedance given by  -1522gj 0*G  or  1ZJ  e  - 1  1  Kovtun (1961) showed that i f Zj. i s plotted i n the d i r e c t i o n of the r e s u l t i n g figure i s an e l l i p s e with p r i n c i p a l axes Z and Z .  x  This i s of course evident from the above equation.  y  JZJJI  Thus when  has been calculated at the surface of an  inhomogeneous medium, an e l l i p s e may be drawn giving not only the directions of the p r i n c i p a l axes, but also the impedances |Z j x  | Zy j .  and  Rokityanski (1961) has given the r e l a t i o n -  ship between the directions of p o l a r i s a t i o n of the e l e c t r o magnetic f i e l d and the c o e f f i c i e n t of anisotropy ( k ) . For values of  k  greater than 5 the r e l a t i o n s h i p between the  d i r e c t i o n of p o l a r i s a t i o n ( 6 difference  f i  ) of the magnetic f i e l d and the  ( A(j>) between the directions of the p o l a r i s a t i o n  of the e l e c t r i c and magnetic f i e l d s i s approximately  linear.  Thus by f i t t i n g the best straight l i n e through a plot of A</> against © H  t  n  e  value of  K  may be obtained from i t s slope.  On the other hand, the method developed  i n the present  investigation may be used f o r a l l values of k . Cantwell  (1960) has given methods f o r interpreting  inhomogeneous and anisotropic structures using admittance tensors rather than scalar admittance.  His method  t h e o r e t i c a l l y j u s t i f i e d i s not very convenient  although  to use.  Bostick  and Smith (1962) have developed Cantwell's approach and given  -153-  a detailed method of analysis.  The basis of the method i s the  computation of the admittance i n d i f f e r e n t d i r e c t i o n s by a suitable transformation of coordinates.  For a homogeneous  Earth the admittance w i l l be constant i n a l l directions, but for an anisotropic and/or inhomogeneous Earth w i l l show minimum and maximum values.  The d i r e c t i o n corresponding  to the minimum  value of the admittance w i l l be the d i r e c t i o n of one of the axes of anisotropy.  Once t h i s d i r e c t i o n i s known the c o e f f i c i e n t  of anisotropy may e a s i l y be calculated.  7.2  Method of analysis For a plane wave incident on a homogeneous i s o t r o p i c or  horizontally layered Earth the r e l a t i o n s h i p between the horizont a l components of the e l e c t r i c and magnetic f i e l d s i s given by  B-  where f  n  ?[H ]  (7.1)  n  i s a unit vector directed v e r t i c a l l y downwards, and  i s the input or surface impedance of the body, which for  a given frequency  i s a constant at each point on the surface,  i . e . i t i s independent of the d i r e c t i o n i n which E and H are measured.  On the other hand, f o r an anisotropic or inhomogeneous  Earth the surface impedance i s a tensor quantity equation  (7.1) becomes  5*xy  a n c  *  -154-  (7.2)  where x and y are rectangular coordinates i n a horizontal plane (Fig. 7.3).  The components of the tensor  d i r e c t i o n of the x, y axes.  ~$  depend on the  xy  Suppose x, y are the axes along  which measurements are made and u, v the axes of anisotropy or inhomogeneity along which the r e s i s t i v i t y does not change. Then i n the u, v coordinate system equation (7.2) reduces to  (7.3)  where  ^> \ and  ^2  a r e  *  n e  p r i n c i p a l values of the tensor  f  x y  .  It i s here assumed that the constant geomagnetic f i e l d does not e s s e n t i a l l y d i s t o r t the symmetry of ^  x y  »  i . e . , under the  foregoing assumptions we can proceed from equation (7.2) to (7.3).  Thus from two independent measurements of the electro-  magnetic f i e l d components equation (7.2) can be used to calculate the four impedance tensor components.  Cantwell has  -155-  Fig.  7.3.  O r i e n t a t i o n of the a n i s o t r o p y respect to measuring axes.  axes  with  -156-  given such an interpretation for an anisotropic Earth. a method does not give the structure of anisotropy inhomogeneity.  Such  or  The p r i n c i p a l values of the subsurface imped-  ance tensor and the azimuth of the anisotropy axes are required to determine the structure. Let the anisotropy axes be i n c l i n e d at an angle  ©  to the  measuring axes (Fig. 7.3), then x => u cos Q  -  v  sin & (7.4)  y =» u s i n ©  •*• v cos ©  Solving Maxwell's equations f o r an anisotropic homogeneous half space, f o r electromagnetic f i e l d components along the u,v axes corresponding to the p r i n c i p a l values 6"^, 6 g of the conductivity tensor i n the horizontal plane we obtain  (7.5)  where Z  u  and Z  axes.  The d e t a i l s of the derivation of equation (7.5) are  y  are the impedance values along the u and v  given i n appendix D .  and thus  J G/oY  From equation (7.3) we have  =  % / S, (7.7)  -157-  Equation  (7.7), where  k  i s p o s i t i v e and r e a l ,  f o r a homogeneous a n i s o t r o p i c E a r t h . K  i s u s u a l l y complex.  i s true only  For inhomogeneous  In the f o l l o w i n g d e r i v a t i o n  bodies  K is  c o n s i d e r e d t o be r e a l or a t most w i t h a n e g l i g i b l y s m a l l argument. Thus knowing the impedance v a l u e s i n the u and v d i r e c t i o n s , the c o e f f i c i e n t of a n i s o t r o p y equation  (7.5).  IC may be c a l c u l a t e d u s i n g  In p r a c t i c e the u and v d i r e c t i o n s are not  known, and measurements a r e taken along x and y axes making an G  unknown angle s i o n s developed From equation  w i t h the u, v c o o r d i n a t e system.  below must then be used t o f i n d  k  (7.7)  z. which on u s i n g equation  (7*4) becomes  C o n s i d e r i n g a plane p o l a r i s e d e l e c t r o m a g n e t i c wave,  My  The  expres-  and &  .  -158-  so that  Law ©  U  (7.8)  - lav* c?  M  Similarly  Substituting equations ( 7 . 8 ) and ( 7 . 9 ) into (7.5), (  |< -  - ( f c ^ E -+ L f l ^ ® H ) t-Vw g -f  C? ^ e  (9fr  (7.10)  Denoting tan  S by  tan <9  E  ^  by x  tan 6 JJ by y  ] (7.11)  \ J  Equation ( 7 . 1 0 ) reduces to  f ( l - k x v ) - [ x y k C ^ + v ; ] ^ -+- ( x y - i c ) +  In t h i s equation  k. and  ^  geological section however x and y are variables. form,  are unknowns. R. and ^  =o  (7.12)  For a p a r t i c u l a r  are constants while  Equation ( 7 . 1 2 ) may be written  i n the  -159-  x + y + Axy + B  -  0  (7.13)  where ( 1 + K.) V and  (7.14)  k-  r  B  0+ If more than two v a l u e s o f x and y a r e o b t a i n e d equation  (7.13)  may be s o l v e d by a l e a s t squares method t o o b t a i n the v a l u e s of A and B .  Thus  and  ,  (7.15)  .  B - - -L ( 2 x + ^ y t f i s ^ y ; Eliminating  k  from the p a i r of equations  (aVofV-/ - K * - ^ ] T h i s equation has f o u r r o o t s , two a t rejected since  8  -  (7.14)  o '  » ± £  can never be imaginary.  (7.16)  which may  The other  be  two  r o o t s a r e g i v e n by  £  -  f\-S  ± v/^-8JV4  (7.17)  -160-  and are thus known when A and B are determined. of  ^  g i v e n by t h i s equation l e a d t o two  angles to one give  k  .  another.  another.  The  k  values  (7.14) then  are r e c i p r o c a l s of  one  I t must be s t r e s s e d t h a t the above d e r i v a t i o n i s t r u e  o n l y f o r a plane p o l a r i s e d e l e c t r o m a g n e t i c  7.3  two  d i r e c t i o n s at r i g h t  E i t h e r of the equations  two v a l u e s of  The  Determination  of  K  and  B  field.  at B e i s e k e r  Before a p p l y i n g the method t o the d e t e r m i n a t i o n of  k  and  (9 at B e i s e k e r , i t i s worthwhile t o see whether the s c a t t e r i n g of  p o i n t s i n F i g . 6.10  may  be e x p l a i n e d by other causes b e s i d e s  anisotropy. The sudden jump i n apparent 6.10(a) may (b) Presence tropy.  The  be due  resistivity  to three causes:  values i n F i g .  (a) Source e f f e c t ,  of a marked inhomogeneity,  (c) Presence  of a n i s o -  e f f e c t of each of these p o s s i b l e causes w i l l  be  considered i n turn. (a) In s e c t i o n 5.3  the assumption t h a t v a r i a t i o n s i n the  geomagnetic f i e l d are propagated  towards the E a r t h as a plane  e l e c t r o m a g n e t i c wave has been shown t o be v a l i d because of the constancy  of the amplitude  of the geomagnetic f i e l d  over a h o r i z o n t a l d i s t a n c e of 600 km. and the sudden jump i n the be due  components  The s c a t t e r of p o i n t s  PQ, VS T p l o t  ( F i g . 6.10(a))  may  to the c o r r u p t i o n of a plane wave by n o i s e from random  sources, w i t h the H and E v e c t o r s o r i e n t e d i n such a way  as to  -161-  give in  little  the  s c a t t e r i n t h e Ey/Hjj v a l u e s  E /H x  values.  y  F i g . 7.4  n o i s e f r o m some d i r e c t i o n t h a n Hy. exhibit cases H.  The  of  values  Df  t h a n 300  x  seconds.  7.4  may  y  7.5  same s o  y  that the  often apply.  x  and  Hy  may  source  t h a n i n Ey w h i l e in H Fig.  x  and  H . y  are  y  in  surface  anisotropy,  with  approximately  This explanation  i n v e s t i g a t e the  inhomogeneity at B e i s e k e r , were c o n s t r u c t e d .  of  the  whose  of  than  equal  values  s c a t t e r i n g i n F i g . 6.10.  producing  H  less  exemplified  value  would cause g r e a t e r  lower  Ey of  Thus  fluctuations in  E  x  equal f l u c t u a t i o n s  i s shown s c h e m a t i c a l l y  in  8.2. (b) To  all  An  case at Beiseker)  e x p l a i n the  changes i n the  generally  A n i s o t r o p i c s near vectors.  than  y  for periods  x  situation  axes are so o r i e n t e d t o g i v e a g r e a t e r (which i s u s u a l l y the  two  some h a r m o n i c s i n H by  Hx  to  illustrates  than f o r E / H  presumably c o n t r o l the E f i e l d  H  upon  However, t h e m a g n i t u d e s o f H^. and  the not  Figure  effect  where  were f o u n d  i s a l s o supported  coherence f o r E / H  u s u a l l y about Fig.  at Beiseker  predominance of  explanation  this point,  a much s m a l l e r  magnetic records  the g r e a t e r  a large scatter  illustrates  such a c h a r a c t e r i s t i c .  Such an  x  has  but  p o s s i b l e presence of p l o t s of  E v e n t s w h i c h c o u l d be  s i x stations simultaneously t h e Ey/H^. r a t i o s .  events of  22  t o 27  Ey/FL^.  The  were u s e d  results  s e c . p e r i o d and  are  any  versus  identified i n the  marked stations easily  computation  shown i n F i g . 7.6  i n F i g . 7.7  at  f o r those  for of  -162-  FIG 7.4  ADDITION  OF  SIGNAL  AND  RANDOMLY ORIENTED  NOISE  -164-  90 sec. p e r i o d . s t a t i o n #3  F i g u r e 7.6 shows a minimum v a l u e o f E / H y  (Beiseker) although such  i n F i g . 7.7 a t t h i s  station.  a minimum  Such a low v a l u e a t B e i s e k e r , a t  because of the u n i f o r m i t y o f H ( s e c t i o n 5.3).  over  A decrease  compared w i t h o t h e r s t a t i o n s telluric  s t u d i e s (Douglass  Beiseker  can give r i s e  lower  1962).  t o such  indicates  that  may b e  the depth However  still  Cardston  The major f a u l t  The p r e s e n c e  a l s o b e e n shown i n s e c t i o n at this  station  ( s t a t i o n #1)  are  of subsurface inhomogeneities at  ( F i g . 2.2) i s t h o u g h t  higher values.  Another  T h e h i g h e r v a l u e s o f Ey/Hj^  ( s t a t i o n #2) and C a r d s t o n  these s t a t i o n s .  belt  which lies very c l o s e t o  t o be r e s p o n s i b l e f o r t h e s e  o f inhomogeneity  a t C a r d s t o n has  6.2, a n d t e l l u r i c  have r e v e a l e d s i m i l a r  studies  (Douglass  characteristics.  n o t i c e a b l e f e a t u r e o f F i g . 7.6 i s t h e i n c r e a s e i n t h e  v a l u e a t s t a t i o n #4.  the depth that  t o the Precambrian  increases south of Beiseker.)  p r o b a b l y due t o t h e p r e s e n c e  x  in resistivity,  v a l u e s o f Ey/H^. s h o u l d be o b t a i n e d a t Champion a n d  a t Champion  Ey/H  from  No known g e o l o g i c s t r a t a a t  a decrease  Cardston, which i s not the case.  1962)  at Beiseker  has a l s o been o b s e r v e d  (Geological evidence  to the Precambrian  effects  a h o r i z o n t a l distance of  in resistivity  a l t h o u g h an i n c r e a s e i n t h e d e p t h responsible.  at  i s n o t s o marked  a p e r i o d o f 25 s e c , i s p r o b a b l y due t o s u b s u r f a c e  600 km  x  lower  Data  t o t h e Precambrian values of E / H y  x  from w e l l  logs indicate  that  i n c r e a s e s s o u t h o f Meanook, s o  s h o u l d be o b s e r v e d  at a l l stations  -165-  PERIOD  22-27sec. O -  1010  0.5h  1  2  S  3  4  5  STATION  PIG. 7.6  VARIATION OF E / H y  x  6 N  ALONG THE SIX STATIONS  -166-  F i g . 7.  Variation of E/H 90 sec period.  along the s i x stations, for  -167-  to the south.  Ignoring the r e s u l t s from station #4 (Clive)  such a c h a r a c t e r i s t i c i s obtained up to station #3. increase i n the value of E / H y  x  The  at station #4 i s probably due  to the presence of an inhomogeneity.  Figure 2.2. displaying  the location of the reef complexes, shows that t h i s station l i e s above the Bashaw reef complex which forms a peninsula extending into the shale basin and trending to the northeast. believed to be f a u l t controlled phenomena.  Reefs are  Extensive fracture  systems are known to extend underneath the sedimentary cover i n central Alberta forming tectonic b e l t s which appear to have largely controlled orientation of the shelf and basin.  Such a  reef complex may possibly be considered an inhomogeneity at Clive.  Except f o r a few i r r e g u l a r i t i e s , a lower value of E / H y  at station #5 i s noticeable i n F i g . 7.7.  x  Probably t h i s lower  value i s due to some inhomogeneity at t h i s station at great depth (10-15 km), but no corresponding geological structure was found which could account f o r i t .  On the other hand, E l l i s  (1962) has found evidence of anisotropy at t h i s station from the marked difference between the E / H x  y  and Ey/EL^ values  (Fig. 7.8). (c)  It i s clear from Figs. 7.6 and 7.7 that no marked  inhomogeneity exists at Beiseker which could give r i s e to the scatter i n the K^/Uy plot of F i g . 6.10(a), which can thus only be explained by assuming an anisotropic model.  The greater  magnitude of the wave impedance computed from one orthogonal  -168Theoretical E ,H x  Models  y  i > i)) /111 /11111111) / n >  6  2  3  1 0  8 0 1 0  E  y  /1!  ,H 11)  X  11  ) / / / ! 11)  11 ) I) I"  6  3  6 0 0 8 0  1 0  Observed Theoretical  interpretation Cooking Lake. (After E l l i s , 1962) I  I  10 Period  1 0 0 (seconds)  -169-  E-H pair (E /Hy) compared to that from the other orthogonal x  pair  (Ey/H ) i s consistent x  with the r e s u l t s obtained by other  workers (Bostick and Smith, 1962) and suggests the presence of an anisotropy. 7.2 to f i n d  In order to apply the method given i n section  l< and  © i t i s necessary to know the directions  of p o l a r i s a t i o n of the e l e c t r i c and magnetic f i e l d s for events of the same period.  Since no recordings were made on magnetic  tape at Beiseker, the only way  to determine the d i r e c t i o n of  p o l a r i s a t i o n was by p l o t t i n g the two components and finding the mean d i r e c t i o n from t h i s p l o t .  The directions of p o l a r i s a t i o n  of the e l e c t r i c and magnetic f i e l d s were found only f o r events with periods of 30 and 90 sec.  The records were searched f o r  events which were more or less sinusoidal, and each event cons i s t i n g of three to four cycles was read at 6 sec i n t e r v a l s . The amplitudes of the two e l e c t r i c and two magnetic components were plotted to f i n d the mean directions of p o l a r i s a t i o n . following expressions  The  were used to obtain the best f i t of an  e l l i p s e through the points on the p o l a r i s a t i o n diagram,  2  z~>  I**  and  zxVrv* 1  -  (7.18)  -  w  e  2  " r*7ry .(3~ <9 x  2  (7.19)  -170-  where  0  i s the angle which the major axis of the e l l i p s e  makes with the x axis (N-S), and a and b are the major and minor axes of the e l l i p s e .  Details of the derivation of  equations (7.8) and (7.19) are given i n Appendix B.  The r a t i o  a. A> was calculated from equation (7.19) i n order to f i n d the degree of e l l i p t i c i t y of the e l l i p s e . In a l l , 70 events were analysed to f i n d the directions of p o l a r i s a t i o n of the e l e c t r i c and magnetic f i e l d s .  Only 25  events were found when both the e l e c t r i c and magnetic were approximately l i n e a r l y polarised.  fields  However the e l e c t r i c  f i e l d was l i n e a r l y polarised i n a l l cases although a great v a r i a t i o n was found i n the magnetic f i e l d .  This v a r i a t i o n i s  probably due to noise e f f e c t s , as explained i n the beginning of t h i s section (Fig. 7.5). The computations were c a r r i e d out on an I.B.M. 1620 at the Computing Centre at the University of B r i t i s h Columbia.  The r e s u l t s of t h i s computation  including  errors i n the determination of the slope & are given i n Table 7.1. Figures 7.9 and 7.10 i l l u s t r a t e two t y p i c a l examples of the d i r e c t i o n s of p o l a r i s a t i o n f o r events of 90 and 25 sec. period.  After computing  the directions of p o l a r i s a t i o n of the  e l e c t r i c and magnetic f i e l d s , equations (7.15), (7.14) and (7.17) were used to calculate values of k and ® . The r e s u l t s of such a computation are given.-below.  PIG. 7 . 9  EXAMPLE OP THE DIRECTION OP POLARISATION OP ELECTRIC AND MAGNETIC FIELDS  Aug. H  x  and  H  17.  Time 1350  61 -  53  y  50+100  E  10 Fig.  20 7.10.  30  40  Example of the d i r e c t i o n 25 s e c p e r i o d .  20 of  polarisation  40 of  x  60  e l e c t r i c k y and  and  E  y  80 magnetic f i e l d s  100 for  -173-  For  90 sec. p e r i o d -  Gi/61  6 S  For  C=48.5°  '/&i ©  ^ ~  1.4 -41.5°  30 sec. p e r i o d Gi/^i.  C£  6  ~  'lGi  $ values f o r  k  ^  10.2  28.7° -  6  The  0.7  0.09  -61.3°  and £ of 1.4 and N 42° W a r e  g e o l o g i c a l l y r e a s o n a b l e a t B e i s e k e r and w i l l be d i s c u s s e d i n s e c t i o n 8.3. Impedance v a l u e s i n two m u t u a l l y p e r p e n d i c u l a r  directions  are needed t o c a r r y out such an a n a l y s i s t o i n v e s t i g a t e any possible anisotropy.  Only a t B e i s e k e r were measurements made  of two p a i r s of orthogonal e l e c t r i c ponents.  However t o i n v e s t i g a t e any p o s s i b l e  anisotropy  a t Meanook, E / H x  (1960) paper. from t h e E / H x  y  inhomogeneity or  d a t a were taken from N i b l e t t ' s  In F i g . 7.11 apparent r e s i s t i v i t i e s y  calculated  r a t i o s a r e p l o t t e d as a f u n c t i o n of p e r i o d T.  No s c a t t e r of p o i n t s any  and magnetic f i e l d com-  inhomogeneity.  i s o b t a i n e d s u g g e s t i n g the absence of On the other hand, the g r e a t e r  magnitude  -174-  F i g . 7.11.  Apparent r e s i s t i v i t y vs period f o r Meanook (from E /H ). (After N i b l e t t , 1960.) x y  -175-  of  t h e wave impedances computed from the E / H  to  those c a l c u l a t e d from t h e E / H  x  y  the presence  of a n i s o t r o p y .  x  data  y  data compared  ( N i b l e t t I960) suggests  No a n i s o t r o p y a n a l y s i s can be  made from impedance v a l u e s alone.  The data r e c o r d e d d u r i n g  the A l b e r t a Operation are p l o t t e d i n F i g . 7.12 which a l s o shows Niblett's results.  A shift  i n the two curves i s n o t i c e a b l e .  Such a d i f f e r e n c e i n the impedance v a l u e s obtained from r e c o r d i n g s made a t the same p l a c e on two d i f f e r e n t o c c a s i o n s has a l s o been r e p o r t e d by B o s t i c k and Smith (1962). p o s s i b l y be accounted  T h i s d i f f e r e n c e may  f o r by the d i f f e r e n c e i n the d i r e c t i o n of  p o l a r i s a t i o n of the e l e c t r o m a g n e t i c f i e l d .  I t i s shown i n  Appendix C t h a t f o r a n i s o t r o p i c and/or inhomogeneous masses the impedance measured a t t h e s u r f a c e depends not o n l y upon the s t r u c t u r a l parameters and or  inhomogeneity  0 (the i n c l i n a t i o n of the a n i s o t r o p y  axes w i t h the n o r t h d i r e c t i o n ) , but a l s o on  the d i r e c t i o n of p o l a r i s a t i o n of the e l e c t r o m a g n e t i c The decrease  field.  i n impedance v a l u e s a t p e r i o d s g r e a t e r than 600  sec. as obtained from the A l b e r t a Operation data i s not observable i n N i b l e t t ' s d a t a .  T h i s i s probably because  N i b l e t t ' s data i s r e s t r i c t e d t o p e r i o d s l e s s than'1000 s e c . w h i l e the A l b e r t a Operation data extends  t o p e r i o d s up t o  3000 s e c .  7.4  Error  analysis  E r r o r s i n the a n i s o t r o p y a n a l y s i s may be d i v i d e d  into  -176-  3 2  100 8 6 4 3-  E  2-  C| .£ 10 c£ 8  6  Alberta  4  Operation Data  Niblett's Data  3 2^  10  2  3  4  -I  u  6  Period Fig.  7.12.  8 100 T  3  4  -1  L  6  8 1000  Seconds  Change i n t h e a p p a r e n t r e s i s t i v i t y v a l u e a t Meanook o b t a i n e d f r o m d a t a t a k e n a t d i f f e r e n t , times.  -177-  two groups, those introduced during the computation  and those  which are inherent i n the method ( i . e . systematic e r r o r s ) . Errors which were introduced i n determining the d i r e c t i o n of p o l a r i s a t i o n of the e l e c t r i c and magnetic f i e l d s were calculated. The probable error i n determining the slope of the major axes of the e l l i p s e was calculated from the following expression.  n where  ^  -  T  J( V^)G P  ' j l  (7.20)  = the probable error  ' = the probable error of a hypothetical quantity of unit weight  CTI-Z)  V  p -  2 7 * ^  Q -  2  G -  2>>  -  Ci-h  -few* ©; 2  jy>  £xj  +  £y  v c  Details of the derivation of equation (7.20) are given i n Appendix B.  The probable error  Y^, , as shown i n Table  7.1  does not exceed 0.5 for most of the cases used i n the present analysis.  Hence the errors introduced i n f i n d i n g the  d i r e c t i o n of p o l a r i s a t i o n are n e g l i g i b l e . hand, systematic errors may be quite large.  On the other Some of these  errors (such as those due to incorrect c a l i b r a t i o n ) have been mentioned i n section 4.6.  An additional important systematic  -178-  TABLE 7.1  90 sec, p e r i o d E l e c t r i c a l Data  <9  Sample No.  i n degrees  a /b  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16  -35.5 -33.2 -49.6 -33.4 -35.7 -34.5 -34.6 -37.0 -39.1 -41.7 -33.9 -30.1 -39.0 -37.0 -40.1 -38.5  49.5 39.3 4.5 33.4 20.0 21.3 146.0 48.7 151.4 45.5 144.0 176.0 40.1 25.8 34.8 43.6  E 2  2  Magnetic Data  Jk  1 2 3 4 5 6  -24.6 -34.4 -38.9 -34.7 -32.1 -34.9  130.1 19.2 52.0 30.8 21.8 14.4  a2/b  30.8 27.5 26.3 8.7 4.8 2.6 8.18 38.6 25.4 0.0 27.8 31.4 32.1 20.3 37.9 34.6  3.0 1.6 25.1 5.0 11.7 5.1 2.5 4.7 21.9 2.6 129.4 17.1 3.2 11.3 16.3 10.6  0.85 1.47 0.11 0.12 0.07 0.11 0.42 2.51 0.11 0.36 0.05 1.01 0.96 0.11 0.99 0.54  2.5 4.0 5.5 11.1 3.0 27.9  0.49 0.65 1.07 0.45 1.42 0.56  0.26 0.19 11.31 0.22 .0.51 0.35 0.12 0.38 0.37 0.29 0.11 0.05 0.74 0.54 1.34 0.60  30 s e c .  JE  i n degrees  2  period  0.05 0.48 0.81 0.39 0.30 0.79  -1.0 48.6 72.2 71.9 59.0 44.8  -179-  (or c o n s t a n t ) e r r o r which may  a f f e c t the a n i s o t r o p y a n a l y s i s  i s any d e v i a t i o n i n o r t h o g o n a l i t y i n the c o o r d i n a t e system used f o r measuring if/2 - /S  E and H.  i n s t e a d of TT/2  i n e r r o r by an angle /3  I f the two axes are at an angle  then a l l E or H f i e l d d i r e c t i o n s are .  Because of t h i s , the azimuth of the  a n i s o t r o p y a x i s w i l l be determined w i t h an e r r o r which may c a l c u l a t e d by s u b s t i t u t i n g equations  (7.15) and  ( $H  (7.17).  ±  ) or ( # E ±  Without  ) in  a knowledge of  i s not p o s s i b l e t o c a l c u l a t e such an e r r o r .  be  /3  it  In the present  i n v e s t i g a t i o n the two c o o r d i n a t e systems were more or l e s s c o i n c i d e n t , and thus no e s t i m a t e of t h i s source of e r r o r  has  been made. Another  s y s t e m a t i c e r r o r which may  a f f e c t the  t i o n of the d i r e c t i o n of p o l a r i s a t i o n which was r e a d i n g the amplitudes of the N-S i '  and E-W  determina-  o b t a i n e d by  magnetic  components  at equal time i n t e r v a l s d i r e c t l y from the r e c o r d s may from the d i f f e r e n t response of the N-S  and E-W  arise  detectors.  I f the two d e t e c t o r s are not i d e n t i c a l , the d i r e c t i o n of p o l a r i s a t i o n of the magnetic few degrees  at every p e r i o d .  f i e l d w i l l be i n c o r r e c t by a To e l i m i n a t e t h i s e r r o r i t i s  necessary t o m u l t i p l y a l l amplitude r e a d i n g s of one of the components by a constant of the N-S  t o the E-W  (the r a t i o of the c a l i b r a t i o n  detectors).  factor  A similar correction i s  necessary f o r the e l e c t r i c f i e l d r e c o r d i n g s .  However because  of the c l o s e s i m i l a r i t y between the c a l i b r a t i o n curves of the  -180-  two magnetic d e t e c t o r s calculated  ( F i g . 3.9)  i n the present  such an e r r o r was  investigation.  not  -181-  CHAPTER V I I I  RESULTS AND CONCLUSIONS  8.1  General The r e s i s t i v i t y of d i f f e r e n t r e g i o n s w i t h i n the E a r t h  are determined  by the m a g n e t o t e l l u r i c method by matching f i e l d  curves w i t h r e s i s t i v i t y model c u r v e s .  There are many pro-  blems i n s c i e n t i f i c r e s e a r c h which r e q u i r e the f i t t i n g of data to an assumed p h y s i c a l system.  I f the data f i t t i n g i s s a t i s -  f a c t o r y then the system may be c o n s i d e r e d a p o s s i b l e model of the phenomenon s t u d i e d . w e l l approximated it  However, s i m p l y because the d a t a are  by the model proposed  i s no guarantee  that  i s a t r u e r e p r e s e n t a t i o n of the a c t u a l p h y s i c a l system.  To show t h a t the model c o n s i d e r e d i s c l o s e t o the a c t u a l p h y s i c a l system i t i s necessary t o compare the r e s u l t s o b t a i n e d by data f i t t i n g w i t h those o b t a i n e d by other methods.  In t h i s  chapter the r e s i s t i v i t y and a n i s o t r o p y r e s u l t s obtained by d a t a f i t t i n g are compared and d i s c u s s e d w i t h other known experimental and t h e o r e t i c a l r e s u l t s .  8.2  R e s i s t i v i t y r e s u l t s a t Meanook, B e i s e k e r and Cardston A t h r e e l a y e r e d E a r t h model was used t o i n t e r p r e t the  -182-  r e s i s t i v i t y curves at Meanook and B e i s e k e r  (section  Such an i n t e r p r e t a t i o n of the data i s not unique. four  or more l a y e r e d  6.3). Probably  E a r t h model would g i v e a b e t t e r  a  interpre-  t a t i o n but whether such a d e t a i l e d a n a l y s i s of the d a t a i s worthwhile (or even meaningful) i s very d o u b t f u l . i n g power, i . e . the a b i l i t y t o s e p a r a t e one of the m a g n e t o t e l l u r i c method has (1961).  I t depends upon two  t h i c k n e s s and not  possible  not  differ- appreciably  tors  to d i s t i n g u i s h two  (e.g. E l l i s 1962)  been d i s c u s s e d by  I t has  Vladimirov  layer,  the  been shown t h a t i t i s  l a y e r s whose r e s i s t i v i t i e s  ( s e c t i o n 6.3),  do  although some i n v e s t i g a -  have attempted t o do so  Such an i n t e r p r e t a t i o n of the data by  (Fig.  increasing  of l a y e r s w i t h very l i t t l e r e s i s t i v i t y c o n t r a s t to obtain  resolv-  l a y e r from another,  parameters of the  the r e s i s t i v i t y .  The  7.8).  the number does not  help  t h e i r t r u e r e s i s t i v i t y by the m a g n e t o t e l l u r i c method  because of i t s q u a l i t a t i v e nature. l a y e r s was  c o n s i d e r e d i n the  i n the present i n v e s t i g a t i o n . found t o be  Hence a maximum of  three  i n t e r p r e t a t i o n of the f i e l d Such an i n t e r p r e t a t i o n  data  was  satisfactory.  A l a y e r l y i n g at depths of 2.1 r e s i s t i v i t i e s of 1100 at Meanook and  ohm  meter and  km  and  1260  Beiseker r e s p e c t i v e l y .  2.6  ohm  km  and  with  meter was  found  At these s t a t i o n s  sedi-  mentary r o c k s o v e r l i e Precambrian igneous r o c k s at depths of 1.92  km  and  3.1  km.  The  agreement i n depth between these  s e t s of r e s u l t s i s q u i t e good and  suggests t h a t  the  two  resistivity  -183-  of  t h e P r e c a m b r i a n r o c k s l i e s b e t w e e n 1100-1260 ohm  E s t i m a t e s of the r e s i s t i v i t y well  logs  of Precambrian r o c k s o b t a i n e d from  i n c e n t r a l A l b e r t a a r e o f t h e o r d e r o f 500  However, r e s i s t i v i t y to  meter.  v a l u e s o b t a i n e d from w e l l  the top of the Precambrian w h i l e r e s i s t i v i t y  ohm  meter.  logs correspond values obtained  by t h e m a g n e t o t e l l u r i c method a r e a v e r a g e v a l u e s down t o a d e p t h of  about  70-90 km.  to  exist  between t h e two  55 ohm 92.1  meter  km.  large scatter  meter  P  a  a t B e i s e k e r gave  pair  6.9(b)) d e f i n i t e l y  resistivity  layer  justified  versus T plot  However t h e t r e n d angle curves  e s t i m a t e s t o a depth of about  1500  km  to their  mean r e s i s t i v i t y and t h a t  inducing f i e l d s *  and P r i c e  and  They  low layer.  (1939) made the induced  the storm  time  concluded that  o f t h e E a r t h down t o 600 km  i s about  i n some r e g i o n s n e a r t h e s u r f a c e  of  resistivity  by c o m p a r i n g  of the d a i l y magnetic v a r i a t i o n  variation  meter  Lahiri  of  (Figs.  show t h e p r e s e n c e o f a  100 km.  of  The  because  l y i n g beneath the h i g h l y r e s i s t i v e  d e p t h s b e t w e e n 10 and  fields  a layer  ( F i g . 6.10(a))  T h e r e have b e e n many p r e v i o u s e s t i m a t e s o f at  resistivity  of o r t h o g o n a l e l e c t r i c  n o t be  and t h e p h a s e  6.10(b) and  of  t o l i e a t a depth of  i n the other o r t h o g o n a l p a i r .  apparent r e s i s t i v i t y  layer  a t a d e p t h o f 65-80.6 km.  components may i n the  third  interpreted  a t B e i s e k e r f r o m one  and m a g n e t i c f i e l d  the  The  interpretation  6.3-31.5 ohm  interpretation  observed  results.  a t Meanook was  A similar  resistivity  the  Hence i t i s p o s s i b l e f o r s u c h a d i s c r e p a n c y  50  the ohm  t h e v a l u e must  -184-  be lower than t h i s .  However they account for their lower sur-  face values by treating the upper layer as a uniform ocean having a depth of about 1 km.  With t h i s model the r e s i s t i v i t y  of the s o l i d Earth below could not be lower than 10^ ohm meter down to depths of 200-300 km.  R e s i s t i v i t y measurements have  also been made by Coster (1948), Macdonald (1957) and Macdonald (1959) for several rock samples at various temperatures.  The aim of their work (andPrice's) was to attempt to  estimate the r e s i s t i v i t y d i s t r i b u t i o n i n the mantle and core, while magnetotelluric measurements on the other hand generally apply to depths between 0-200 km.  In order to compare the  r e s u l t s of the present investigation obtained by magnetot e l l u r i c methods with those obtained by other investigators, a l l r e s u l t s have been plotted on the same figure (8.1), the d i f f e r e n t models being taken from Cantwell (1960).  The i o n i c  r e s i s t i v i t y alone i s plotted for the d i f f e r e n t models.  It can  be seen from F i g . 8.1 that model 7 f i t s the data very well both at Beiseker and Meanook.  On the other hand no f i t i s  obtained with L a h i r i and Price's curve nor with Macdonald's curve.  According to the temperature  Macdonald*s model 7 a temperature expected at 80 km.  d i s t r i b u t i o n of  as high as 1600°K would be  At temperatures  greater than 1500° K the  electronic conductivity i s very small compared to the i o n i c conductivity (Tozer 1959).  Hence p l o t t i n g i o n i c r e s i s t i v i t y  in F i g . 8.1 for a comparison of r e s i s t i v i t y values at 70-100 km  -185-  DEPTH IN P I G . 8.1  km  R E S I S T I V I T Y v s DEPTH PLOT FOR DIFFERENT MODELS  -186-  depth i s j u s t i f i e d .  It i s not j u s t i f i a b l e , on the other hand,  to deduce anything regarding the chemical state of the mantle at a depth of 80 km from the present investigation, although a composition corresponding to Model 7 of Macdonald (1959) seems to be most l i k e l y . An explanation for the increase and decrease of r e s i s t i v i t y at d i f f e r e n t depths may be as follows.  At shallow depths the  porosity of the rocks decreases with depth because of the increase of hydrostatic pressure which the overlying mass of rocks exerts and which forces l i q u i d i n the pores upwards as pore space i s compressed (Angenheister, 1962). compression  With increased  of the pores, l i q u i d i n the rock matrix suffers an  increase i n hydrostatic pressure, while l i q u i d at lesser depths i s subjected to the increased hydrostatic pressure of the overlying water mass.  Thus the " e l e c t r i c conductivity of porous  l i q u i d s " loses i t s meaning at greater depths, where under high pressure new minerals are b u i l t and the content of the pore i s gradually b u i l t into a new g r i d .  With the decay of e l e c t r o -  lyte conductivity, the conductivity of the c r y s t a l considered as a semiconductor  begins to become important.  It i s worthwhile  to compare the present r e s u l t s with those  of other investigators who  also found a sudden decrease i n the  r e s i s t i v i t y at depths of 70-100 km by the magnetotelluric method.  Their r e s u l t s which were obtained at d i f f e r e n t  locations are l i s t e d below.  -187-  Resistivity (ohm meter)  Depth (km)  Present  30-60  80-90  Cantwell (1960)  80  70  Niblett (1960)  80-100  80  E l l i s (1962)  10  80  Investigation  The agreement between the f i r s t three i s quite good indicating that a value f o r the r e s i s t i v i t y of about 80 ohm meter may be expected at a depth of 80 km. Another s i g n i f i c a n t r e s u l t i s that no change of r e s i s t i v i t y has ever been observed at the Mohorovicic discontinuity. On the other hand, the "Moho" represents a boundary where the chemical composition of the rocks changes markedly or where phase changes take place. No d e f i n i t e r e s i s t i v i t y interpretation of the magnetot e l l u r i c data could be made at Cardston because of the large scatter of points i n the E / H y  versus T plot (Fig. 6.12).  x  Such a scatter has been attributed to the presence of an inhomogeneity, (Fig.  8.3  the major f a u l t which runs close to Cardston  2.2).  Anisotropy r e s u l t s at Beiseker It has been shown i n section 7.3 that the difference i n  magnitude between the r a t i o s E / H x  y  and Ey/H^ and the scatter  of points i n the r e s i s t i v i t y plots (Fig. 6.10(a)) can only  -188-  be explained on the assumption that a marked anisotropy exists at Beiseker.  Before discussing the detailed geological  structure at Beiseker  i t i s worthwhile to check that the  r e s u l t s obtained from the anisotropy analysis do in fact explain the difference i n magnitude between the Ex/H ratios.  a n ( i y  E  y/**  The following are the r e s u l t s obtained from the aniso-  tropy analysis: For 90 sec. period 0.73  6  * i 48.5 1.4  0 ? -41.5° For 30 sec. period 10.24  e  28.7° 0.089  & Two  0  2r  -61.3°  sets of values are given for each period, but they  represent  x  the same anisotropic structure since the value of  i n one set i s complementary to that i n the other.  The  -189-  analysis of anisotropy at a period of 90 sec. was made from 16 almost p e r f e c t l y linear polarised f i e l d components while that at a period of 30 sec was made from 6 f i e l d components whose p o l a r i t y was only approximately l i n e a r .  This makes the  r e s u l t s obtained i n the l a t t e r case less r e l i a b l e than those in the former.  Hence the r e s u l t s obtained from the events  with a period of 90 sec. only w i l l be considered here. In F i g . 8.2 6\ and <T are the directions of the con2  d u c t i v i t i e s , i . e . the axes of the anisotropy while E and H are the t o t a l e l e c t r i c and magnetic f i e l d s whose directions were obtained from p o l a r i s a t i o n diagrams.  For an anisotropic  medium the e l e c t r i c f i e l d i s not p a r a l l e l to the current density except along the conductivity axes and i s not perpendicular to the magnetic f i e l d .  "  °1 1  Jg =  ^2^2  J  and  where Since  and J  2  2  s  E  are the current densities along  ^0,^-1  6\ > 6* >  l  We have  o  t h a t  0""^ and 67).  w i l l be much larger than Eg. J  Moreover  l ^> 2* J  Hence the magnetic f i e l d w i l l be approximately perpendicular to the current density J^. perpendicular to J (^J^+Jg).  In F i g , 8.2 H i s drawn  The d i r e c t i o n of p o l a r i s a t i o n  -190-  Fig.  8.2.  Diagram showing t h e o r i e n t a t i o n of t h e a n i s o t r o p y a x e s and t h e d i r e c t i o n o f p o l a r i s a t i o n o f E and H f i e l d s .  -191-  of H was found to be N42°E from t h i s f i g u r e .  The average  d i r e c t i o n of H found from f i e l d records was about N 36° E. The close agreement between these two r e s u l t s makes the above interpretation plausible. that H  x  ~  H  y  and that E  the r e s u l t that E / H x  y  x  Moreover i t i s evident from F i g . 8.2 >  E  y  as was generally observed.  Thus  i s greater than Ey/EL^ at a l l periods makes  the above interpretation of anisotropy reasonable. Garland and Burwash (1959) carried out a detailed p e n o l o g i c a l study of the Precambrian of central Alberta.  F i g . 2.4  shows the l i t h o l o g i c a l map of the Precambrian basement obtained by them from studies of well log samples and gravity anomalies. The locations of a l l stations used i n the above magnetot e l l u r i c analysis are also shown i n F i g . 2.4.  Station #3,  Beiseker, i s located very close to the boundary between g r a n i t i c and gneissic type rocks, between which a conductivity contrast of 1.4 may be expected.  According to Garland and /  Burwash (1959) such a boundary should extend downwards to a depth of 8-9 km i n order to give a proper f i t to t h e i r gravity data.  From the present investigation i t follows that such a  boundary probably extends s t i l l further to cause a marked difference between the magnitude of the E / H x  y  and E / H y  x  r a t i o s at 100 sec. period. Nothing d e f i n i t e can be said about those agents which give r i s e to such differences at greater depths extending down to the mantle.  Angenheister (1962) suggests the following  -192-  three possible causes of conductivity anisotropy i n the mantle, (1) Convection  currents,  (2) P a r t i a l pressure release, (3) High pressure modifications. Of these three agents high pressure modifications play the most important r o l e at depths greater than 400 km.  Several  workers have suggested d i f f e r e n t chemical compositions  for the  deeper mantle on the basis of high pressure work.  8.4  Conclusions The following conclusions may be drawn from the r e s u l t s  obtained i n the present investigation, (1) The v i s u a l c o r r e l a t i o n method of analysing magnetot e l l u r i c data i s preferable to the power s p e c t r a l method when a large amount of noise free data i s a v a i l a b l e . (2) Phase angles, between pairs of orthogonal  electric  and magnetic f i e l d components, which do not give any addit i o n a l information to that obtained from apparent r e s i s t i v i t y values, may be used for q u a l i t a t i v e i n t e r p r e t a t i o n i n the magnetotelluric method. (3) The assumption that the geomagnetic f i e l d i s uniform over a horizontal distance comparable to the depth at which r e s i s t i v i t y determinations  are made i s j u s t i f i e d .  This  overcomes Price's objection to Cagniard's t h e o r e t i c a l approach. (4) With appropriate a n a l y t i c a l techniques  i t i s possible  -193-  to u t i l i s e the magnetotelluric method to determine the major e l e c t r i c a l d i s c o n t i n u i t i e s i n the crust and upper mantle. (5) The magnetotelluric method may be used to determine the physical parameters of anisotropic bodies,  provided  s u f f i c i e n t data i s available. (6) The magnetotelluric method appears to be of only semi-quantitative value when r e s i s t i v i t y inhomogeneities are present. ( 7 ) Magnetotelluric signals of frequencies higher than about 0.1 cps are usually of low coherence  over a distance  of 600 km and therefore are apt to be generated by rather l o c a l sources.  Such l o c a l sources invalidate the magneto-  t e l l u r i c method f o r frequencies higher than 0.1 cps, as Price has shown.  -194-  APPENDIX A  In the following pages the r e s u l t s of the power spectral computation, obtained from the IBM 704 Computer at the University of C a l i f o r n i a , are given.  The r e s u l t s have been  divided i n two sections. AI - Power spectral computation of two days' magnetic records from s i x stations, A l l - Power spectral computation of the magnetic and e l e c t r i c records at station #3, Beiseker. The following notation has been used i n the text f o r the records corresponding to d i f f e x t e n t days. A - corresponds to records obtained on 18.8.61 B  -  C D -  " 19.8.61 «» 9 i a «i (between ^l.B.bi 1428-1558) " 91 R 6i (between ^• ' 1900-2030) b  b l  E -  " 23.8.61  F -  " 24.8.61  Each set of power spectra i~esults gives f i r s t the types of records used, the date and time, followed by the r e s u l t s of the computation.  The power spectra (X,Y) f o r the two types  of records are given i n the same order as that of the records. The symbols used f o r each column correspond to the quantities  -195-  given  below.  K A X B Y E Z F W P Q R R*R PHIL  — L a g number - A u t o c o r r e l a t i o n of primary r e c o r d - Power s p e c t r a l d e n s i t y o f p r i m a r y r e c o r d - A u t o c o r r e l a t i o n of secondary r e c o r d - Power s p e c t r a l d e n s i t y o f s e c o n d a r y r e c o r d - I n p h a s e c o r r e l a t i o n b e t w e e n t h e two r e c o r d s - I n p h a s e power s p e c t r a l d e n s i t y ( c o - s p e c t r u m ) - Out o f p h a s e c o r r e l a t i o n b e t w e e n t h e two r e c o r d s - Out o f p h a s e power s p e c t r a l d e n s i t y ( q u a - s p e c t r u m ) - Normalised co-spectrum - Normalised quadrature spectrum - Coherence - Coherence squared — Phase l e a d o f s e c o n d a r y over p r i m a r y .  -196-  A I  The r e s u l t s magnetic  of  the  power  r e c o r d s at  all  six  f o l l o w i n g pages. (X,Y)  are given  converted  i n terms o f  calibration  stations  The r e s u l t s i n terms of  curves.  spectral  of  chart  the  computation of  are given power  in  the  the  spectral  density  d i v i s i o n s w h i c h may be  gamma w i t h t h e  help of  the  -197-  1 TUKEY SPECTRUM tSTlHATION  0  OJ  0 9 6 9 J A K  ALTA  HZ  A  STATION  X  v  r  OJ  3996  4~ 1 7 6 9  2  I B  1 8  1  TIME  il  1 0 0 9 1 1 0 6 5 LOGY E  V  2 3 . 2 5  4  9 6 4 3  4  r 2v: 2341  2 3 . 3 7  4  3 7 3 9  4  Z  F  W  1698  0 0 0 0  0000  ' . 8 3  P  0  R  . 0 0  . 8 3  R»R . 7 0  . 0 2  PHI1 1 8 0 . 0  1  4  3764  4  1856  2 3 . 2 7  4  5272  4  2496  2 3 . 4 0  4  3462  4  1743  3  1573  2  4 3 1 4  • . 8 1  . 8 1  . 6 6  4  3531  2  9 0 1 2  2 1 . 9 5  4  1386  3  2088  2 2 . 3 2  4  3257  2  4 7 4 9  2  8 9 1 1  1  8 4 1 6  • . 3 5  . 0 6  . 3 5  . 1 2  1 6 9 . 9  3  4  3633  8 2 6 3  2 0 . 9 2  4  4679  3  1032  2 2 . 0 1  4  3568  1  7 0 5 8  3  1875  2  1427  • . 2 4  • . 4 9  . 5 5  . 3 0  • 1 1 6 . 3  4  4  3742  1 1  2 0 . 9 9  4  7560  2  6 3 4 3  2 1 . 8 0  4  3 7 1 7  1  6 2 4 1  3  1855  1  5 3 6 7  5  4  3638  1  8 2 1 4  2 0 . 9 1  4  5307  2  2 9 7 9  2 1 . 4 7  4  3343  1  4 9 4 8  3  2 4 0 7  1  6  4  3558  2  1019  '21.01  4  2868  2  4 2 0 3  2 1 . 6 2  4  3124  1  3 7 3 3  3  1973  7  4  3 6 0 4  2  1556  2 1 . 1 9  4  3959  2  6 3 0 5  2 1 . 8 0  4  3482  1  4 0 6 4  3  1966  8  4  3579  2  2 1 1 5  2 1 . 3 3  4  5666  2  4 9 7 0  2 1 . 7 0  4  3 6 6 9  1  8 9 8 5  3  2781  9  4  345 7  2  2 2 7 4  2 1 . 3 6  4  5057  3  1298  2 2 . 11  4  3323  2  2 3 0 0  3  3265  2  10  4  342 8  2  2 3 6 7  2 1 . 3 7  4  3887  3  4 7 8 5  2 2 . 6 8  4  3152  2  2 7 8 5  2  6 2 6 2  2  9668  1  1 7 8 . 6  • . 2 5  - . 2 2  . 3 3  . 1 1  • 1 3 9 . 3  1467  ' . 3 2  • . 0 9  . 3 3  . 1 1  • 1 6 3 . 5  6 8 9 6  • . 1 8  . 0 3  . 1 8  . 0 3  1 6 9 . 5  2 4 7 6  . 1 3  . 0 8  . 1 5  . 0 2  3 1 . 4  6 6 1 2  . 2 8  • . 0 2  . 2 8  . 0 8  •4.2  1750  . 4 2  • . 3 2  . 5 3  . 2 8  • 3 7 . 3  5099  . 2 6  • . 4 8  . 5 5  . 3 0  •61.4 • 1 2 8 . 3  11  4  3473  2  2396  2 1 . 3 8  4  4032  3  7909  2 2 . 9 0  4  3368  2  2 5 5 9  3  1413  2  3240  • . 19  • . 2 4  . 3 0  . 0 9  12  4  341 7  2  3 2 1 7  2 1 . 5 1  4  4 4 1 0  3  8 8 7 7  2 2 . 9 5  4  3450  2  8660  3  2024  2  5 9 8 4  ' . 5 1  . 3 5  . 6 2  . 3 9  13  4  3308  2  4 3 9 6  2 1 . 6 4  4  4 3 0 5  3  8 2 6 4  2 2 . 9 2  4  3288  3  1003  3  3297  3  1134  • . 5 3  . 6 0  . 7 9  . 6 3  1 3 1 . 5  14  4  3 2 9 7  2  3268  2 1 . 5 1  4  4579  3  5180  2 2 . 7 1  4  3220  2  6 3 9 4  2  5143  2  6 9 4 2  • . 4 9  . 5 3  . 7 3  . 5 3  1 3 2 . 7  2  4 9 7 2  ••22  . 3 3  . 3 9 . 2 6  . 1 6 . 0 7  1 2 3 . 7  1 4 5 . 4  4  3307  2  1145  2 1 . 0 6  4  4752  3  2 2 9 8  2 2 . 3 6  4  3231  2  1124  2  1685  16  4  3 2 1 6  1  4 9 3 1  2 0 . 6 9  4  4064  3  1330  2 2 . 1 2  4  3222  1  4 7 5 7  3  1603  1  4 6 8 6  . 1 9  . 1 8  17  4  3135  1  3642  2 0 . 5 6  4  3552  2  9 1 8 4  2 1 . 9 6  4  3271  3994  3  2029  1  2 7 2 3  • . 0 2  ' . 1 5  . 1 5  . 0 2  ' 9 8 . 3  "18  4  3154  1  2088  2 0 . 3 2  4  4 1 5 0  2  6 0 1 7  2 1 . 7 8  4  3292  1  3037  2  6 5 3 0  1  5 9 1 8  • . 2 7  ' . 5 3  . 5 9  . 3 5  • 1 1 7 . 2  1590  1  15  4 4 . 6  19  4  3146  1  2 0 . 2 0  4  4796  2  3335  2 1 . 5 2  4  3150  1  3096  2  6 0 3 5  2 5 9 6  • . 4 3  • . 3 6  . 5 5  . 3 1  • 1 4 0 . 0  20  4  3060  1  1209  2 0 . 0 8  4  4 1 3 9  2  2 1 2 6  2 1 . 3 3  4  302 3  1  2 5 1 5  2  7 3 7 5  5678  • . 5 0  ' . 1 1  . 5 1  . 2 6  • 1 6 7 . 3  21  4  3011  9368  1 9 . 9 7  4  3284  2  1584  2 1 . 2 0  4  3 1 2 9  1  1672  I  2187  •1202  ••43  • . 0 3  . 4 4  . 1 9  ' 1 7 5 . 9  22  4  3018  8132  1 9 . 9 1  4  3654  1  9 8 6 5  2 0 . 9 9  4  3262  1837  2  5443  2 8 6 2  ••06  ' . 1 0  . 1 2  . 0 1  • 1 2 2 . 7  . 0 2  2 3  4  2 9 7 7  7837  1 9 . 8 9  4  2 4  4  2920"  7 0 3 6  1 9 . 8 5  " 4  25  4  2 9 1 2  3592  1 9 . 5 6  4  T--il  K  0 9 6 9 J A K  <;  E Y ALTA  P  HZ  A 4  h  4  T  R  U  STATION X  3996  C  6  1  7666  2 0 . 8 8  4  3108  3799"  1  8241  2 0 . 9 2  4  2 9 4 2  3272  1  4 1 4 8  2 0 . 6 2  4  3071  I  M  M  E  AND"  LOGX  1769  4 2 6 2  2  S 1 8  T  -a-  61  B 3  2 2 6 3  i  r JJWa i o  1  T I M  L  2 3 . 2 5  A  N  7 3 5 3  2 4 8 2  . 1 1  ••10  . 1 5  8 4 0 7  . 0 3  ' . 0 3  . 0 4  . 0 0  ' 5 3 . 0  6599  0 0 0 0  • . 1 2  . 0 0  . 12  . 0 1  1 8 0 . 0  F  M  P  Q  R  2 7 4 0  3  2 0 3 1  6 3 3 8  3  1346  1488  2  •1  ' 4 2 . 2  X L 0 6 5  LOGY 2 0 . 8 7  I  I  E 1  6 6 5 9  2  1  4  3764  4  1856  2 3 . 2 7  2  1105  2  1075  2 1 . 0 3  2  7845  2  2  4  3 5 3 1  2  9 0 1 2  2 1 . 9 5  3  1033  1  6 7 9 7  2 0 . 8 3  3  1679  4378  0 0 0 0  0 0 0 0  R»R  PHI1  . 3 8  . 0 0  . 3 8  . 1 5  4 5 5 6  2  7380  1  1440  . 3 2  . 0 1  . 3 2  . 1 0  1.8  6 2 2 2  2  1930  1  1808  • . 0 3  . 0 7  . 0 8  . 0 1  1 0 9 . 0  . 0  3  4  3633  1  8 2 6 3  2 0 . 9 2  2  6471  1  5992  2 0 . 7 8  2  9 3 6 8  3 2 5 8  2  6 6 3 9  4 5 6 5  • . 4 6  . 0 6  . 4 7  . 2 2  1 7 2 . 0  4  4  3742  1  9668  2 0 . 9 9  2  9 5 4 6  1  4 6 9 0  2 0 . 6 7  2  3070  8 2 5 6  2  3085  7 3 7 2  • . 1 2  ' . 11  . 1 6  . 0 3  • 1 3 8 . 2  5  4  3 6 3 8  I  8 2 1 4  2 0 . 9 1  2  4314  1  3972  2 0 . 6 0  2  9 8 7 0  3 1 1 9  2  5560  1181  ' . 0 5  ' . 2 1  . 2 1  . 0 5  • 1 0 4 . 8  6  4  3 5 5 8  2  1019  • 1 6 1 . 5  1  1  2 1 . 0 1  2  3883  1  3 1 5 6  2 0 . 5 0  3  1331  1  1424  2  2 4 1 2  4 7 5 4  ••25  ' . 0 8  . 2 6  . 0 7  7  4  3 6 0 4  2  1556  2 1 . 1 9  2  5 9 3 0  1  2 9 1 2  2 0 . 4 6  2  6 6 5 7  1  2 3 9 5  2  3564  3 2 9 7  • . 3 6  ' . 0 5  . 3 6  . 1 3  • 1 7 2 . 2  8  4  3579  2  2 1 1 5  2 1 . 3 3  2  3353  I  4555  2 0 . 6 6  2  6 8 5 0  1  3892  2  3530  9  4  3457  2  2 2 7 4  2 1 . 3 6  2  4 2 8 3  1  5961  2 0 . 7 8  3  1259  1  5743  2  3 5 2 9  10  4  3428  2  2 3 6 7  2 1 . 3 7  2  1210  1  6281  2 0 . 8 0  3  1059  1  7168  2  2672  11  4  3473  2  2396  2 1 . 3 8  2  5 0 2 4  1  7711  2 0 . 8 9  2  6 2 5 8  1  8 5 8 3  2  2 1 0 3  12  4  3417  2  3 2 1 7  2 1 . 5 1  2  2566  2  2 0 5 9  2 1 . 3 1  2  8184  2  1418  2  3699  13  4  3308  2  4 3 9 6  2 1 . 6 4  2  3054  2  3 9 4 9  2 1 . 6 0  3  1143  2  2 3 6 1  2  1600  14  4 "3297  2  3268  2 1 . 5 1  2  1354  2  3579  2 1 . 5 5  2  8 5 1 4  2  1972  2  4186  15  4  3307  2  1145  2 1 . 0 6  2  4 6 2 5  2  2 0 6 9  2 1 . 3 2  2  1  6 2 6 9  2  1514  4  3216  1  498 3  16  4 9 3 1  2 0 . 6 9  2  1889  2  1389  2 1 . 1 4  2  8 0 8 2  6 1 3 4  2  4 3 1 9  17  4  3135  1  3642  2 0 . 5 6  2  3551  1  7574  2 0 . 8 8  9560  8 3 5 9  1  7996  4  3154  1  2  18  2088  2 0 . 3 2  2  1721  1  3972  2 0 . 6 0  2  5618  1262  2  3719  19  4  3146  1  1590  2 0 . 2 0  2  5153  1  3668  2 0 . 5 6  2  5149  1965  1  2743  4 4 0 7  "20  4  3060  1  1209  2 0 . 0 8  1  8 7 1 6  1  2 6 3 4  2 0 . 4 2  2  8/384  4 1 8 3  2  1956  •1  1185  2 3 7 7  1  1  1318  • . 4 0  ' . 1 3  . 4 2  . 1 8  • 1 6 1 . 3  1701  • . 4 9  " . 0 1  . 4 9  . 2 4  • 1 7 8 . 3  1  1454  • . 5 9  . 1 2  . 6 0  . 3 6  1 6 8 . 5  1  2 5 3 8  ••63  . 1 9  . 6 6  . 4 3  1 6 3 . 5  2  1311  • . 5 5  . 5 1  . 7 5  . 5 6  1 3 7 . 2  2  2688  • . 5 7  . 6 5  . 8 6  . 7 4  1 3 1 . 3  2  2 0 2 9  ••58  . 5 9  . 8 3  . 6 8  1 3 4 . 2  1  6 4 6 6  • . 4 1  . 4 2  . 5 8  . 3 4  1 3 4 . 1  1  3 6 5 9  • . 0 7  . 4 4  . 4 5  . 2 0  9 9 . 5  1  2 1 9 3  . 1 6  . 4 2  . 4 5  . 2 0  6 9 . 1  6 0 0 4  . 4 4  . 2 1  . 4 9  . 2 4  . 0 8  . 1 8  . 2 0  . 0 4  6 6 . 0  • . 2 3  • . 0 1  . 2 3  . 0 6  • 1 7 8 . 4  2 5 . 4  21  4  3011  9 3 6 8  1 9 . 9 7  2  1  1854  2 0 . 2 7  2  816 5  1798  22  2  2 1 6 5  • 1  8585  ' . 1 4  ' . 0 7  . 1 5  . 0 2  • 1 5 4 . 5  4  3 0 1 8  8 1 3 2  1 9 . 9 1  2  3262  1  1801  2 0 . 2 6  2  4 2 6 5  1868  2  1656  • I  9 7 8 3  . 1 5  • . 0 8  . 1 7  . 0 3  • 2 7 . 6  2 3  4  2 9 7 7  7837  1 9 . 8 9  2  2961  1  1743  2 0 . 2 4  2  5347  2 4 6 9  2  1838  2 9 3 6  . 2 1  ' . 2 5  . 3 3  . 1 1  • 4 9 . 9  24  4  2 9 2 0  7036  1 9 . 8 5  2  2238  1  1617  2 0 . 2 1  2  8 0 6 8  3124  1  2 1 5 6  3 2 4 0  . 2 9  ' . 3 0  . 4 2  . 1 6  • 4 6 . 0  25  4  2 9 1 2  3592  1 9 . 5 6  1  5751  8194  1 9 . 9 1  2  6 6 3 4  1752  2  3298  0 0 0 0  . 3 2  . 0 0  . 3 2  . 1 0  . 0  E  Z  F  W  P  Q  R  3801  0000  0 0 0 0  ••77  . 0 0  . 7 7  . 6 0  1 8 0 . 0 1 7 5 . 7  T~ 0 9 6 9 J A T" U  K  E  0  OJ  AND  2  I 0  4  6  LUGX  K  ~s"  Y  ALTA  HZ  A 4  1  4  3 2 1 0  4  295~5  "  T  R  STATION X  3479  2"  P E C  M  U 6  S  T  I  18  8  6]  E  AND  LOGX  5  M  A  1  TIME  B  I  0  N  1 0 0 9 LOGY  4  1525  2 3 . 1 8  5  3303  5  1578  2 4 . 2 0  4  7556  4  4  R*R  PHI1  1588  2 3 . 2 0  5  3224  5  1608  2 4 . 2 1  4  7 5 5 1  4  3791  1  7760  3  2871  ••75  . 0 6  . 7 5  . 5 7  2" 6401  2 1 . 8 1  5  3178  3  3245  2 2 . 5 1  4  7585  1  9 5 2 9  3  1392  2  9922  . 0 7  . 6 9  . 6 9  . 4 8  8 4 . 5 ' 3 3 . 1  3  4  3106  1  7 6 1 5  2 0 . 8 8  5  3192  2  5871  2 1 . 7 7  4  7 6 4 1  1  3462  3  2 9 4 9  1  2 2 5 5  . 1 6  ' . 1 1  . 2 0  . 0 4  4  4  3231  2  1087  2 1 . 0 4  5  3198  2  5901  2 1 . 7 7  4  7 6 2 2  1  6 4 2 4  3  2 8 5 8  1  1268  . 2 5  . 0 5  . 2 6  . 0 7  1 1 . 2  5  4  3 0 7 7  2  1436  2 1 . 1 6  5  3181  2  4 3 1 3  2 1 . 6 3  4  7 5 3 0  1  1980  3  2751  2  1181  . 0 8  ' . 4 7  . 4 8  . 2 3  • 8 0 . 5  6  4  2 9 8 9  2  3  4 3 1 5  7  4  3085  8  4  3067  9  4  2 9 0 4  10  4  2878  «  2 1 8 7  2 1 . 3 4  5  3146  2  4 3 2 4  2 1 . 6 4  4  7558  4 1 5 1  . 0 2  . 0 1  . 0 2  . 0 0  3 6 . 4  2  2480  2 1 . 3 9  5  3138  2  6 1 3 7  2 1 . 7 9  4  7678  2  1346  3  5417  1  5982  . 3 5  . 1 5  . 3 8  . 1 4  2 4 . 0  "2  2 7 3 2  2"1.4"4  5  3 1 3 6  2  8352  2 1 . 9 2  4  7679  2  2 5 4 0  3  5 2 3 4  1  2 2 3 3  . 5 3  ' . 0 5  . 5 3  . 2 8  2  3636  2 1 . 5 6  5  3114  2  9 3 9 4  2 1 . 9 7  4  7 5 5 3  2  1346  3  4 6 8 7  2  2 4 1 3  . 2 3  ' . 4 1  . 4 7  . 2 2  • 6 0 . 8  2  5 9 4 0  2 1 . 7 7  5  3096  3  1024  2 2 . 0 1  4  752 8  2  1516  3  5222  2  3465  • . 1 9  • . 4 4  . 4 8  . 2 4  • 1 1 3 . 6  3 0 8 6  5 6 2 8  ' 5 . 0  2954  2  5 7 4 9  2 1 . 7 6  5  2  7 7 3 5  2 1 . 8 9  4  7656  2  2 1 4 9  3  6 4 2 2  2  1886  • - 3 2  • . 2 8  . 1 8  • 1 3 8 . 7  12  4  2891  2  2 3 5 7  2 1 . 3 7  5  3068  2  3971  2 1 . 6 0  4  7 6 7 5  1  3 1 3 4  3  6 5 3 4  1  2 9 5 0  • . 1 0  ' . 1 0  . 1 4  . 0 2  • 1 3 6 . 7  13  4  2762  1  6398  2 0 . 8 1  5  3041  2  3131  2 1 . 5 0  4  7609  1  2 0 9 4  3  6484  I  1875  . 1 5  ' . 1 3  . 2 0  . 0 4  • 4 1 . 8  14  4  2 7 7 7  1  4145  2 0 . 6 2 "  5  3024  2  3338  2 1 . 5 2  4  7645  1  1098  3  7196  1  1224  ' . 0 9  . 1 0  . 1 4  . 0 2  1 3 1 . 9  15  4  2 8 1 3  1  2 2 3 6  2 0 . 3 5  5  2  3349  2 1 . 5 2  4  7690  4 2 5 3  3  7 6 3 0  1  3190  . 0 5  16  4  2690  1  1865  2 0 . 2 7  5  3001  2  2 9 8 6  2 1 . 4 8  4  7 6 4 6  1  1234  3  7 1 2 6  1  17  4  2584  1  1221  2 0 . 0 9  5  2 9 7 5  2  2 0 9 0  2 1 . 3 2  4  7628  1  3 9 7 2  3  7070  18  4  2 6 3 6  1  5  2 9 5 9  2  1608  2 1 . 2 1  4  7 7 1 8  9 1 7 2  3  7778  1418  ' . 2 2  • . 3 5  4  2647  1  5  2948  2  1399  2 1 . 1 5  4  7 7 4 5  7206  3  7 8 4 6  6 0 1 4  ' . 1 9  ' . 1 6  5  2 9 2 8  1  6 2 0 0  2 0 . 7 9  4  7695  i3410  3  7343  0 0 0 0  ••19  . 0 0  11  19  2ff~-  4  "4  2539""  1047  2 0 . 0 2  1019  2 0 . 0 1  5 3 9 1 " 1 9 . 7 3  "  3022  1  . 4 3  . 3 7  . 3 7  1722  . 1 7  . 2 3  . 2 8  . 0 8  5 4 . 4  7320  . 0 1  ••14  . 1 5  . 0 2  . 1 4  • 8 6 . 9  . 4 1  . 1 7  • 1 2 2 . 9  . 2 5  . 0 6  • 1 4 0 . 2  . 19  . 0 3  ' 1 8 0 . 0  8 2 . 4  -198-  TUKEY SPtCTRUM ESTIMATION 0522JA ALA I M A G X 18 8 61 STAT O IN 6 AND 1 T M I E 1009 TO 11065 [ A F a R RR . i»1 31 4 1 9 9 0 5 5 6 1 2 2 7 . 5 5 1 0 2 1 3 3 5 2 2 . 1 2 3 4 2 6 5 2 7 5 4 0 0 0 0 0 0 0 0 0 . 2 8 . o o . 2 8 . 0 8 •22 •.0.8 14 18 22 49 6 6 02 40 42 2 7 ..8 36 5 97 42 35 19 59 9 21 27 2 .8 02 2 03 73 5 26 72 70 78 23 37 3 0 0 23 28 731•..2 51 «.i i ..2 71 ..0 7 2 3 6 5 5 2 1 7 4 4 7 1 9 7 9 2 . 3 7 1 3 5 7 7 2 1 7 0 ' . 31 3 1 0 • 9 2 .0 34 14 14 39 1 3 5 712 10 1 .5 34 2 0 1 7 2 6 0 3 5 2 17 7 .3 83 5 7 7 7 116 02 06 33 "7 4 7 3 5 50 25 3 .''.221 ••1.9 ..3 25 9 ..0 8 1 3 7 4 .. 4 4 1 3 1 1 2 2 1 . 4 5 5 0 4 2 5 3 7 8 2 1 . 3 5 0 3 2 " " 6 2 3 4 6 1 4 1 5 8 5 2 4 1 2 1 3 7 0 5 4 1 2 1 6 2 1 1 6 5 2 1 0 . 7 4 1 7 9 9 4 8 1 4 2 1 6 . 8 3 2 8 0 7 1 5 6 5 3 3 5 4 9 4 8 2 9 0 . ' 2 4 . ' 3 5 . 4 2 . 1 8 1 2 4 3 . 64 1 04 35 4 1 18 32 55 62 1 1 ..3 43 7 1 4 7 2 1 8 ..5 3 87 48 63 61 56 "'5 7 9 9 03 32 4 ••0.1 8.•'2134 ..1 27 9 .0 8 1 2 9 0 .. 7 4 1 0 21 15 2 64 11 760 921 12 3 1 14 72 92 22 21 0 73 34 1 4 29 88 13 3 52 03 80 7 21'"7 6 5 94 ..0 3 1 2 3 2 8 4 1 1 4 8 3 3 7 1 2 . 3 4 2 7 3 1 3 . 3 3 4 9 5 1 2 7 7 4 3 4 1 2 3 0 • . 0 . ' 1 8 . 1 9 0 4 1 0 2 7 9 41 1 4 7 4 8 72 61 18 6 .5 94 18 10 07 5 33 19 76 37 72 22 26 2 .0 42 53 62 86 92 28 17 76 08 3'2 9 6731 2 25 32 19 09 .'•19.52.'•3-324 .3 91 .3 .17 5"11418 89 8 .. 1 0 4 1 0 2 9 7 0 9 2 2 . 4 1 . 3 4 9 3 3 7 3 . 6 . 1 39 8 11 02 54 42 2 0 ..2 1 4 3241 4 37 7 1 02 8 93 9 2 32 0 7 5 '3 7 1 9 1>7 6 3 .793•.0 78 3 ..5 3 1 7 9 .1 13 21 4 4 1 094 661 1 29 1 2 29 0 54 4 12 62 12 50 29 9 22 31 ..38 22 6 22 92 63 2 4 22 73 3 14 55 65 33 3 14 4 5 01-•'.5 .33 5 ...6 4 7 1 47 95 . 1 1 0 1 9 7 2 1 . 6 4 1 8 4 2 2 3 . 4 2 3 6 9 3 1 5 3 3 2 2 9 4 3 4 . 6 5 7 4 . 5 4 1 1 7 . 1 4 3 9 7 7 0 6 9 4 9 1 8 .7 41 4 32 70 02 5 4 17 65 96 3 2 ..3 2 9 8 9 8 2 38 48 47 3 2 8 9 32 4 0 7 •.2.1 .7 01 ..5 781 ..5 0 91 84 1 5 3 9 21 47 02 51 06 99 02 2 16 .2 2 9 3 8 42 2 2 9 4 3 2 4 0 2 2 5 2 3""3 2 5 5 0 3 17 04 78 8 80 ..4 52 3 4 6 ...1 1 6 3 9 2 2 4 2 1 . 3 7 8 4 9 3 6 1 1 6 2 2 7 . 9 3 " 2 2 8 3 2 8 3 7 0 3 2 6 2 9 2 6 . 5 2 . 6 7 . 4 5 3 8 9 18 73 53 85 6 23 010612 21 12 4 84 1 94 59 03 38 9 812 23 5 92 23 36 31 69 42 5 0 7 91 23"'3 6 2 4 42 7 •.1 .28 0 ..3 571 ..1 23 62 9 . 1 39 9 8 13 7 ...3 32 11 9 32 04 06 22 2 ..0 0 2 1 8 8 3 4 4 42 2'2 11 04 45 1 ...3 '2 92 .0 1 9 3 9 0 6 0 I 9 5 3 2 0 9 7 4 3 5 3 1 2 2 1 . 3 2 3 2 8 1 3 3 7 1 3 1 3 9 9 6 7 2 2 1 0 . 0 2 . 1 0 . 0 1 1 1 3 .9 2 01 3 38 75 98 55 7 2 312 0 7 .7 61 4 31 12 36 69 26 8 5 5 2 17 8 .6 42 35 28 16 5 13 7 8 41 3 10 13 23 3 15 0 3 8 ••.1 9 .1 25 ..3 2 ..1 13 01 23 69 2 1 8 5 1 0 2 0 . 9 2 5 7 8 3 2 1 . 0 7 1 5 9 6 3 ' 4 1 7 1 8 3 5 . 0 3 6 1 6 ... 2 2 3 9 1 3 9 1 3 7 0 3 2 0 5 . 7 3 6 5 5 4 2 7 2 2 9 2 1 8 . 6 " 2 " 3 4 1 1 1 5 3 1 6 3 ' 1 2 0 3 2 2 0 9 • . 3 2 • 1 4 . 3 5 . 1 2 1 5 7 4 2 3 3 7 8 8 5 14 32 15872 06 5 .3 04 15 0 41 2 7 4 35 72 1 8 ..7 3 1 7 6 0 1 3 4 5 2 3 2 8 7 9 15 89 18 •'1203 .'1.021 ..2 5 ..0 61 1 5 2 2 .1 2 4 3 7 6 8 3 2 4 0 . 3 2 9 3 2 8 0 3 2 1 9 0 3 1 9 7 7 1 1 8 6 9 2' 2 2 4 5 2 9 . 1 0 0 1 7 2 25TU387K 82 04 .2RM 39 435 5T21 16 .4 N 21488 8631 3'3487 0000 .08 .00 .08 .01 1800 .. Y S26272T U t730 S2 ITM A C F M p Q R RR . L O G Y K  X  LOGX  B  3 3 2 2 2  Y  LOGY  I  E  M  P  PHU  1  2  2 2 2 2 2 3 3  1 1  3  2 2 1 1 1 1  EALIA  0522JA K  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25  K 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25  ALTA  3 3 2 2 2 2 2 2 2 2 2 3 3 2 2 2 2 2 2 1 1 1 1 1 1 1 S  1990 1246 6829 1139 1443 1216 1034 1045 1148 1147 1029 9896 1061 1041 9770 9240 9217 9586 9835 9060 7985 8518 9139 7885 7683 8782  LOGX  5561 60 44 5520 1357 1121 1165 1356 1825 3371 4876 7092 1054 1124 9197 6949 5090 4169 3001 1716 9353 5723 5101 3703 3158 4274 2627 PEC  MAG  3 3 2 2 2 2 2 2 2 2 2 3 3 2 2 2 2 2 2 1 1 1 1 1 1 1  22.75 22.78 21.74 21.13 21.05 21.07 21.13 21.26 21.53 21.69 21.85 22.02 22.05 21.96 21.84 21.71 21.62 21.48 21.23 20.97 20.76 20.71 20.57 20.50 20.63 20.42  E  B  4 4 4 3 4 4 4 3 3 4 3 2 1 3 3 3 2 3 3 4 3 3  6783 1126 2764 5707 2673 1793 1032 9880 9045 1457 5637 2347 3444 4565 7428 7985 3746 3842 6298 1289 6752 5723 £ 9702 3 8926 3 6665 2 6151 M E S  3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2  2724 3436 1354 1358 1514 1632 1353 1250 1646 3347 7651 9925 8517 6579 3862 1890 1432 1229 1138 1144 1071 8708 9094 9237 7455 3319 M A  22.44 22.54 22.13 22.13 22.18 22.21 2 2 . 13 22.10 22.22 22.52 22.88 23.00 22.93 22.82 22.59 22-28_ 22.16 22.09 22.06 2 212 . 0 6 22.03  2 3 4 3 2 3 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3  i?*_ TI N  3336 6185 1218 5961 8089 5571 1015 6280 1368 4491 8603 5998 3119 3648 5505 5897 5100 3986 3404 4590 5690 3790 1865 4466 6017 2826  5561 6044 5520 1357 1121 1165 1356 1825 3371 4876 7092 1054 1124 9197 6949 5090 4169 3001 1716 9353 5723 5101 3703 3158 4274 2627  I  LOGX 22.75 22.78 21.74 21.13 21.05 21.07 21.13 21.26 21.53 21.69 21.85 22.02 22.05 21.96 21.84 21.71 21.62 21.48 21.23 20.97 20.76 20.71 20.57 20.50 20.63 20.42  B 4 3 3 3 3 3 2 3 2 3 3 2 2 3 2 2 3 2 3 3 2 1 3 2 2 3  1863 2840 9173 2268 7094 6417 1117 3706 3857 4846 2501 9011 1039 1696 9446 7682 1023 7074 1422 1577 3085 9054 1425 5129 4187 1235  Y ,  c  2 2 2 2 2 2 2 2 2 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 1  21.96  LOGY  7106 o-«.l»J 2 1 . 8 5 9016 2 1 . 9 5 2927 2 1 . 4 7 1844 2 1 . 2 7 1518 2 1 . 1 8 " 1917 2 1 . 2 8 2352 2 1 . 3 7 2759 2 1 . 4 4 6586 2 1 . 8 2 1497 2 2 . 1 8 2508 2 2 . 4 0 2968 2 2 . 4 7 2365 2 2 . 3 7 1377 2 2 . 1 4 7689 2 1 . 8 9 6906 2 1 . 8 4 . 21.88 7571 2 1 . 7 4 5509 2 1 . 5 4 3490 2 1 . 4 1 2596 2 1 . 2 6 1800 2 1 . 2 0 1571 1587 2 1 . 2 0 1722 2 1 . 2 4 1790 2 1 . 2 5 8800 2 0 . 9 4  E 2 3 3 2 2 3 3 3 2 2 3 3 2 2 3 3 3 3 3 3 3 2 2 3 3 2  7269 3638 4242 4500 6017 3597 3986 2084 1399 9689 3745 3011 3774 7024 2082 1975 1387 1358 1344 1454 1592 6017 3121 1815 1783 1746  PHI1  2  3 3 2 1 1  1 1 1 2 3 3 3 2 2 1 2 2 1 1 1  1 21.97 21.87 21.52 T I 0 X 18 8R 61 U STATION 6 AND 3 TIME 1009 TO 11065  X  A 4 4 3 4 4 4 4 4 4 4 4 3 4 4 3 3 3 3 3 3 3 3 3 3 3 3  0 X 18 8 61 STATION 6 AND 2 TIME 1009 TO 11065  X  4 1990 4 1246 3 6829 4 1139 4 1443 4 1216 4 1034 4 1045 4 1148 4 1147 4 1029 3 9896 4 1061 4 1041 3 9770 3 9240 3 9217 3 9586 3 9835 3 9060 3 7985 3 8518 3 9139 3 7885 3 7683 3 8782 T U K E Y  1  PEC  MAG  A  0522JA  1 1' !•  2764 3027 2918 5724 1493 7707 1063 5411 7726 6022 1603 1221 1964 1661 8669 2137 7776 1166 1149 6250 1318 2861 5788 1046 5374 7533  I 3" 1033 3 ' 1220 2 ' 2267 1' 7005 1' 3613" 1" 3427 1' 408 3 1' 5194 2' 2191 2' 4485 2 ' 3641 2 2304 2 7445 2 6556 2 3275 2 2147 2 2995 2 2708 2 1462 1 5982 1 1703 1 1033 2842 5879 1 1918 1 1335  3 3 3 3 3 3 3 3 3 3 3 1 3 2 3 3 2 1 2 3 3 2 3 3 3  0000 2818 3446 1803 4777 1154 4965 1284 3060 1314 2457 2867 2483 2353 6779 2962 1006 5651 5457 3682 1213 1745 7012 1526 1112 3308  f 0000 3 5243 3 1251 3 3660 3 1538" 3 2142 3 2035 2 4876 3 1974 2 4128 3 2053 3 1103 2 9739 2 7348 2 3734 2 6538 1 6820 2 4737 2 1019 2 6987 2 1374 2 2009 2 3545 2 3250 2 8568 2 •2422  0000 2 2855 2 1208 2674 1 1277 5546 3294 1 8246 2 2105 2 6546 3 1535 3 1575 2 4840 2 3174 2 3860 2 3414 2 3694 2 1863 1 4318 I 6289 1 5303 5164 1 5322 I 3339 2923 0000  W 0000 1 6897 1 5443 1 2569 1 1832 1 5690 I 8795 1 6582 1 8823 2 3662 2 9597 3 1334 3 1024 2 5240 2 3277 2 2793 2 2260 1 9948 '6288 1 •1165 1916 6916 •1093 1 •1126 •4757 0000  • .71 • .66 • .34 • .13 • .04 .02 .00 .11 .10 •-05 .07 .38 .63 .68 .53 .22 .10 .19 .26 .19 •.05 ••14 • .03 .06 ••03 • .08  P • .52 '.52 ••56 '.44 •.28 '.23 '.23 '.23 •.46 ' .52 • .27 .13 .46 .58 .45 .36 .53 .67 .60 .38 .17 .12 .04 .08 .22 .28  .00 .06 .14 .01 .03 '.01 .01 .17 .28 .51 .66 .49 .16 '.13 '.24 '.35 •.48 '.31 •.10 '.19 •.21 .02 .29 .20 .02 .00  .71 .67 .37 . 13 .05 .02 .01 .21 .30 .51 ".66 .62 .65 .69 .58 .41 .49 .36 .28 .27 .22 .14 .29 .20 .03 .08  Q  R  .00 .03 .14 .16 .14 .38 .49 .29 .19 .43 .72 .75 .63 .47 .45 .47 .40 .24 '.03 •.07 .02 .08 •.01 '.15 '.05 .00  .52 .52 .58 .47 .31 .44 .54 .37 .50 .68 .77 .77 .78 .75 .63 .59 .67 .71 .60 .39 .17 .14 .04 .17 .23 .28  .50 .45 .13 .02  • 6b" .00 .00 .04 .09 .26 .44 .38 .43 .47 .34 .17 .24 .13 .08 .07 .05 .02 .09 .04 .00 .01  R«R  180.0 174.6 157.5 177.3 139.5 •35.7 72.1 56.7 69.8 95.3 84.6 52.2 13.8 •10.8 '24.0 •58.0 '78.1 •58.0 '20.6 •45.2 • 104.0 169.8 96.2 72.6 151.5 180.0  PHI1  . 2 7 •180.0 . 2 7 176.8 .34 166.5 .22 159.9 .10 153.1 . 2 0 121.1 .29 114.9 .14 128.3 .25 158.1 .46 140.8 .59 110.8 .59 80.2 .60 54.0 .56 38.6 .40 45.0 .35 52.4 .45 37.0 .50 20.2 .36 •2.5 .15 •11.0 .03 6.4 .02 33.8 .00 •21.0 .03 •62.4 .05 •13.9 .08 '.0  -199S  T U K f c i r ALTA  0522JA  H  A  K  c  C  MAG  T  R  X  X  U  M  L  STATION LOGX  6  S  T  1  B  4  1990  3  5561  22.75  5  1246 6829  3  6044  22.78  2  5520  21.74  113.9  2  1357 -21*13  2  1121  M  AND 4  A  T  TIME  I O N 1009T0  11065 8  Y LOGY [jjociL.'/VrVj  4251  5  5  3162  5  2453 3069 3361  18  61  t  2  F  M  0  R  1416  0000  0000  • .49  .00  .49  1511  24.18  4  2520  4  5  1566  24.19  4  2603  4  1395  4  1373  2  2926  • .45  '.01  3  6574  22.82 7/. *t  4  2  2034 077A  2  4  2973 3145  8348 7414  2 1  1799 9540  .11 -n?  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' 5 6 2 . 5 . 6 1 . 3 7 1 5 5 .. 1 2 4 3 4 1 7 2 3 2 1 7 2 1 5 . 1 3 2 5 9 2 2 2 0 5 4 2 1 3 . 1 3 3 3 4 1 1 5 0 0 3 2 74 66 41 75 84 12 .''6.632 .1 .33 ..6471..5 01 1 16 55 25 14 3 "443 3 0 8 "224 3 9 62 1 6 .5 41 "332 7 1 2 2 12 22 90 2 19 1 .21 3 3 32 85 62 2 1 0 1 4 3 2 9 1 2 4 6 4 9 .. 1 3 2 9 7 3 2 6 8 2 1 . 2 9 4 8 1 8 4 2 0 . 3 3 2 1 2 7 4 9 3 3 3 5 6 • 1 1 4 7 7 • . 4 1 . 0 0 . 4 1 . 1 7 1 7 9 7 1 5 4 3 3 0 7 2 1 1 4 5 2 1 0 . 6 3 2 7 3 8 1 3 9 3 0 2 0 5 . 9 3 3 1 2 6 83 4 B 0 • I2 0B 45 36 •.0.0 60 ..0 16 40 ..02 5 8 .54 17 64 3 2 1 6 I14 94 3212 0 6 ..9 3 2 6 7 5 2 6 2 0 4 ..0 33 24 46 7 4 15 74 1 6 33 3 3 9 5 13 7 .'•10 0•1 115 7.4 . 1 4 3 1 3 5 30 6 2 0 5 6 32 2 0 5 71 1 12 2 3 6 9 2 03 3 73 3 2 1 5 3 1 4 3 3 4 1 4 3 5 2 7 . 0 2 • 1 6 . 1 6 . 0 3 • 8 1 8 4 3 1 5 4 1 2 8 8 2 0 3 . 2 3 2 2 2 1 2 3 8 7 2 0 . 8 3 3 0 0 5 3 59 651•16 19 98 28 7 ••.05 151 1 ..211..0 11 54.293 10 94 3 4 6 1 5 2 00 2 03 2 25 521 1 1 99 10 42 0 ..8 2 10 18 73 63 3 3 7 .09.•'0•.0 061 11'•1 . 2 4 31 0 6 01 I19 13 29 00 9 2 0 ...8 3 1 8 1 1 3 2 02 1 43 3 39 29 68 7 19 2 4 7 0 3 3 9 1 5 • 1 7 3 0 6 . ' 2 3 7 . 2 4 . 0 6 3 5 . 2 1 4 3 0 1 6 8 1 9 9 7 3 1 4 7 1 1 1 2 6 7 2 0 1 . 0 3 3 2 0 3 14 11761 3 3 75 071••l12 00 86 3 '.11 .•'02.08 ..1 2 ..0 64 9.3 9 . 2 39 07 18 88 13 2 19 98 .91 3 1 4 5 5 11 2 8 9 2 0 ..1143 3 05041 12 3 3 4 8 6 .0.2 0 9 001 1••1•7 22 34 4 2 7 7 3 7 1 .9 3 1 5 1 8 1 1 3 7 0 2 01 3 3 0 1 3 9 8 0 3 3 5 6 7 • 1 5 7 0 0 • 0 4 ' 0 . 5 . 0 7 . 0 1 2 4 . 2 4 4 2 9 2 0 7 0 3 6 1 9 8 . 5 3 1 3 3 4 1 1 6 0 7 2 0 2 . 1 3 3 1 9 6 .9 25 42912 3592195 .6 31063 8742199 .4 33086 13652 33852 0000 • .07 .00 .07 .00•1BO0 _ -  • '4  3  .... -  2  5  .  2  0  U  .....  ......  9  2'  .00  1  K  A  B  .  L  0  G  Y  fc  -204-  TUKEY SPECTRUM ESTIMATION 0969JAALTA193 61 H YA N E D XSTAT O IN3 T M IE 1146500 J K A HX L O G X L O G Y fc 2 H "p "b R RR . PH1I 3 2 7 2 1 1 4 1 7 7 2 0 6 . 2 4 2 9 0 5 4 1 1 3 1 2 3 0 . 5 3 1 9 1 1 2 1 1 6 0 0 0 0 0 0 0 0 0 • 1 7 . 0 0 . 1 7 •14820.9 0 . 2 5 3 7 2 1 6 5 4 0 2 0 8 . 2 4 2 6 7 8 4 1 2 1 1 2 3 0 . 8 2 2 0 2 7 2 1 4 6 6 3 1 0 8 3 2 1 1 0 8 • . 1 6 • 1 2 . 2 1 . 0 4 1 ' 15 63 26 2. 116 9 35 4.220 08 .-944._44_.223.347.1 3_?1225728_-22J2 1 .1 31656 -J.7554 25 4325 50 1 6 9 6384. .03 .•'02.9 3 ..24 •J.0Q 68 '•136.8.1 J_.3 3 8 6 6 8 . . _ 2 .5L7._ . J 1 2 5 . . 18 10 07 41 5 392 70 ..3 42 4 2 22 25 3 912 12 7 32 23 4 3551 1 6 8 7741 2 9 4 87 101 ..4 .4 0 •40.0 53 5 1 2 6 776 2 07 4 3 2 3 5 9 1 87 03 2 1 ...6 11 32 1 3 59 2 4'2 27 76 0 6 8 50 1 .•'•10 03 .5 2 .20 7 ••1 6 2 4 5 0 1 1 3 8 1 2 0 5 . 9 4 2 2 0 2 2 1 7 5 2 1 2 4 2 6 3 1 5 2 5 2 5 2 0 6 1 2 3 7 7 . 6 4 2 9 . 7 0 . 5 2 4..6 .9 2 7 2 4 6 7 1 1 7 5 5 5 2 0 . B 8 4 2 1 0 B 2 2 1 0 5 2 1 3 . 2 2 6 9 5 1 2 1 0 0 4 2 1 3 1 8 1 4 3 8 7 . 8 0 . ' 3 5 . 8 7 7 . 5 • 2 3 82 1 2 2 8 2 1 2 3 4 2 1 0 . 9 4 2 1 0 1 2 2 7 3 2 2 1 4 . 4 2 2 8 1 5 2 1 4 8 2 1 3 3 0 4 1 7 2 0 8 . 8 1 . ' 3 9 . 9 0 • 2 5 . 9 2 2 1 9 2 11 71 98 42 > i25.494 2 1 0 0 2 3319783 U 02 15 76 99 16 86 28 02 19 91 52 1'0 6 •• ..4 .8 81 •.8 73 8 •29.91 12 8 9 0 8 24 3 2 1 4 2 0 7 6 2 62 2 16 6 .55 0 2 3 42 2 2 2 3 42 2 13 845 08 3 ..7 7 6 541..9 96 2 2 7 2 0 2 3 5 9 2 1 6 . 4 4 2 0 5 8 2 4 4 5 6 2 1 . 2 4 3 3 3 2 3 4 9 6 2 2 7 6 5 2 2 0 . 7 9 . ' 5 3 30 3..8 9 12 2 22 17 01 67 32 38 97 85 32 14 6 .6 04 42 0 7 S 22 30 35 31 12 1 5 .3 21 2 29 52 64 32 22 30 08 19 31 3 06 28 32 1 7 9 41 .8 .86 3 •• ..4 9 ..9 96 6 .92 •••2 3 2 2 2 1 . 2 1 2 4 2 2 1 . 1 8 1 1 6 2 1 0 4 4 3 6 . 5 14 2 2 9 7 2 12 989012 1 .1 21 11 45 2 19 35 96 42 20_9.101 .42 1 4 8 6 2 10i4 7 2-32J3A 73 6 7 4 0 .87 7 ..''4 0 96 6 ..9 25.0 1 16 72 73 3 2 1 2 13 .0 14 4 2 7 I14 7 2 1 1 0 3 1 8 f_4 6 6_-1 31 95 80 4 .8 38 9 ...9 9 92 2 •••24.3 1 7 6 i 7 3 1 4 2 0 8 . 6 4 2 0 9 2 3 5 2 2 0 6 . 4 2 1 9 5 9 1 4 8 9 1 2 1 3 1 6 1 2 . 8 7 . ' 3 5 2 .7 17 2 22 17 16 82 4 3 8 3 20 05 6 .5 44 2 0 9 5 1 28 4 912 20 04 .5 2 05 361 12 34 09 40 3 23 0 1 2 17 12 18 36 6 .8 .87 6 .•'2 .36 2 ..9 21 ••213 0 ..5 4 3 5 6 0 2 . 4 2 0 8 7 1 2 2 9 3 . 6 2 1 8 1 2 6 9 9 6 3 2 2 2 6 6 2 3 5 42 0 3 .0 71 4 2 0 2 0 11 6 3 2 2 0 2 .9 1 17 9 0 3 16 17 66 86 2' 3 37 82 4 •13 5 2 4 ..7 85 6 ..''0 17 8 ..7 85 8 ..7 7 •11.8 1 2 9 2 8 i 1 0 1 8 2 0 . 4 1 9 2 2 8 0 7 0 1 9 . 1 2 1 9 9 5 3 2 3 4 5 9 4 6 5 6 •5.0 2 11 47 63 6 4 40 75 0~11996 .4 41 8 5 6 3 8 6 7 94 5 9 22 6 18 17 92941 2 "1 16 77 27 3 ••116 30 02 17 ..4 ..4 8 14 3 0 .5 8~~4 1 8 1 9 2 8 0 51 1 9 ...5 73 15 7 2 2 4 38 0 ..0 271 .2 34 7 .1 3 389 4.6 6 2 1 5 8 4 2 2 9 7 1 9 3 . 6 4 1 7 5 4 1 8 3 5 1 9 2 6 5 5 0 7 1 3 2 5 1 2 " 3 5 6 0 ' 1 3 8 3 0 . 1 6 . 0 6 4 7 .. 3 8 6 8 2 3 1 6 1 9 3 . 6 4 1 6 6 6 7 3 6 4 1 8 8 . 7 2 1 0 6 1 2 4 4 0 2 2' 4 1 9 7 1 4 8 4 . 0 3 . 1 1 . 1 2 . 0 1 7 3 . 5 21660 1269191 .0 41609 '12218183 .5 21350 29541 2"2997 0000 .18 .00 .18 .03 TRUM ESTIMATION T U KSP EECY 0969JA ALTA 19 8 61 H XA N D EY STAT O IN 3 T M IE 1450 1600 I I , _ L H * J . . . »«.0 R1 1' 8P H 1 I 2 02 00 01•• 1 ..2 .0.0 08 .1 0203 0 1-4 21 8921 4''5 85 491 31'0 O G Y? 5 3 9 4L 811434 9 4 ..7 2 8 7 7 27 96 30 61 1 . 2 6 0 9 • 0 2 2 ' 4 6 1 4 4 5 5 5 1 9 6 8 5 1 9 9 4 0 . 0 1 2 3 7 . 3 5 .2 5 '45 265..4 15 7 --..1 8 2 -4521201511 -4157157 1 12 37 46 17852 12 9_.5 .64 0 7 9 36 4X 2 8 ..1 .061 1''47.2 36.9 2 2 32 7 .7 42 5 111026/3 4 . 5 A L O G X • 1 9 0 4 3 ? _ 9 1 2 5 2 _ 5 5 5 1 9 7 _ 1 2 1 3 4 4 7 . 0 _3K 2 . 5 1 4 2 4 .1 . 3 4 1 1 5 3 2 2 . 5 . 2 3 2 4 3 8 2 1 " ' 1 6 7 8 2 9 8 0 7 2 3 6 2 4 8 6 8 71 12 202 00 038_5 .20 1 -4.9 4 2 .7 l.546_- 1 1i09 93" 2 0 8 . . 6 3 1 5 5 3 8 • 2 . 0 . 6 0 1 1 ' 8 1 1 2 5 2 2 9 6 2 7 6 1 9 8 2 1 3 4 7 1 4 7 7 6 . 5 2 1 5 ~ " i 0 1 3 4 6 . 7 . 5 1 6 9 9 8 • 5 . 2 . 5 3 1 6 ' 9 0 3 2 4 ' 9 3 0 3 1 2 7 1 0 5 3 2 1 8 0 1 B 4 4 2 0 0 9 . 3 6 2 1 3 . 0 1 1 0 0 1 5 1 1 . . 8 1 1 4 5 B 5 ' . 7 1 . 3 9 1 8 ' 3 1 5 2 5 ' 6 0 9 2 3 8 6 7 1 3 9 9 19 72 5 111893912 71 10 0 0 1 7 1 13 .1 16 10 •'10759.5 9 . ..6 3 •12-1-24 204.''1.683•• .0 0 •!74'2 5 7 -73192061 2 7 6 1 5 11 14 27 22 13 2 ..87 08 75 1 2 1 6 9 1 7 . 6 7 7 1 4 2 5 6 4 5 2 8 6 1 1 3 0 3 0 2 1 4 . j _ 2 1 0 . 5 1 0 6 9 0 •85.86 ..8 7 1 2 5 --4 7 2 6 2 -'4232081 ..1 11 54 03 56 52 5 9 9 56 0 7251"2 2 13 6 .1 25 12'-37 54602 1 7 .8 81 1072_ 4 3 2 9 . ' 8 9 3 8 9 6 2 6 8 2 4 2 4 3 7 3 6 6 4 2 . 9 2 7 2 1 . _ 9 _ 4 . 8 • . 6 8 . 8 3 1 6 9 5 2 1 7 3 8 1 5 3 6 3 2 1 2 2 3 77 468 3 80 90 52 2 1 2 . 3 2' 1 5 4 0 21 12 5 .6 9 1 0 5 2 "lb 9 . 6 9 . ' 2 3 . 7 3 5 1 6 8 1 * 2 2 5 2 1 6 6 8 7 2 5 1 3 0 ' 0 9 1 8 2 0 . 7 1 1 6 0 1 6 . 10 04 43 3 2 u . 7 7 . 0 8 . 7 7 3 6 3 6 4 7 8 9 1 4 5 5 6 2 1 1 7 1 5 3 4437- 1976 49 2 0 5 . 6 2 1 0 0 1 2 0 9 . 9 1 1 2 7 . 2 . 1 3 . 7 3 8 6 7 5 2 2 8 1 3 0 0 3 2 5 0 9 9 3 0 . 0 2 1 . 2 0 4 . 6 2 1 8 6 9 20 06 7 .8 1 0418 40281 2512704 1 3 . 6 9 3 5 7 4 6 . 8 . 1 1 2 0 4 7 l " 4 0 2 2 2 5 1 8 9 2 3 3 5 7 1 2 1 6 4 . 0 " 2 . 0 5 1 0 1 4 7 . 8 7 8 9 6 . 7 4 . 2 4 2 65 43 91 4 63 82 6 I1 6 2 2 2 1 3 9 5 1 2 4 8 9 1 2 4 0 2 1 0 3 . 8 0 6 . 7 5 1 0 2 1 1 5 . 8 0 1 1 2 7 7 . 7 0 . 3 8 2 2 1 5 2 5 2 2 2 6 4 I 4 6 5 1 1 2 3 6 5 1 2 1 5 2 0 3 . 3 2 0 7 . 2 5 1 0 1 7 1 6 . 7 3 1 1 0 9 3 . 5 9 . 4 4 1 6 3 2 1 4 1 3 9 1 3 2 9 6 4 2 2 3 1 1 4 7 0 1 1 5 0 2 7 0 1 . 8 2 0 6 . 2 5 1 0 1 2 1 7 . 5 6 6 0 6 7 . 4 1 . 3 9 7 1 9 186526382 -93 2322 2879 1 3 431 2 18 02 02 08 0 .41 12-- 91817844 6 0 3 ..8 5 1808081I 69 19 8 1 431 1085 .18 .3 71 ..3 1 0 7 7 2 2 6 1 3 8 7 1 9 . 1 9 9 4 4 9 1 .359 1 4 3 8 • 7 0 . 3 1 7 ' 4 2 7 1 7 4 5 7 • 1 4 8 1 6 1 9 5 . 4 4 9 8 0 2 6 1 3 5 1 9 7 . 9 3 4 8 6 2 • 2 2 5 2 3 2 0 . 0 6 1 .. . 2 4 • . 1 8 . 1 7 • 1 7 5 2 8 1 3 2 2 2 1 8 8 6 4 • 1 7 7 8 0 1 9 5 . 1 4 9 7 3 4 6 1 0 0 1 9 7 . 9 3 2 3 4 2 3 • 4 1 3 5 1 . 1 6 . 0 3 1 6 7 9 . 1 6 . 0 3 2 1 ' 0 8 5 ' 1 1 5 4 2 1 9 5 . 1 4 9 6 4 9 6 3 0 5 2 2 0 2 3 • 1 7 2 0 7 1 9 8 . 0 3 2 2 2 2 4 2 1 6 5 .4 4 9540 3229195 .1 2-2265 • 1' 323122'738 0000 •14 .00 . 14 .02 1' 80.0 25 2032 1750192 - i i.  H ..  B~  1 2  F" " ~  E Y ;  ~ '  .03  2_  .asgo_ _z  2  .32  _JU3X_  4  .81  9 10 11  .91 .93  13 15 16  18 19 20 21 22 23 24 25  .16  2  I i I  1  •34.  .90 .84 .83  I  .23  •I  1  I  •1  .19  •.0  1  To";  a  21.15  T066  .12 .40 .56 .65 .40 .48 .75.80 .68 .54 .59 .54 .48 .61 .64 .54 .32 .17 "TTT  •83.3 •71.2 •54.9 • •18.6 6.0 9.9 9.4 17.6 28.4 36.6 43.7 64.3  -205-  TUKEV SPECTRUM ESTIMATION 3522JA ALTA M A GXA N D ELEC Y 21 8 61 STAT O IN 3 T M I E 1428 TO 1558 RR K 4A X 212 .5 4e 23053 0000 0000 .41 .00 ..41 .1.6 ••0 .0 5B 33582225 14 2 29 5 3 15 .91 5 16 0 5 71 4412 2 7 ..6 4 1 2 2 6 4 4 7 5 9 0 3 6 ••.54 .43 .6 0 3 7 4 18 582 31 185 771 3 9 2 7 2 4 10 26 73 92 23 3 8 2 .5 4 7 3 3 9 2 2 5 9 4 17 23 48 6 26 6 7 6 4 4 "1 3 04 05 62 2 6 72 08 9 .4 .5 5 .73 7 ...4 5 91 •••4 43 4...9 8 3 3 4 1 4 9 2 5 3 6 3 2 1 7 . 3 4 3 8 6 9 3 3 1 0 2 2 2 4 . 9 3 5 7 9 3 7 4 9 6 4 3 6 3 5 2 6 7 . 5 8 • . 5 2 . 7 8 6 4 1 4 3'4 4 5'1 9549442 1 7 ..7 32'6 4631 3 32 7 5 0 2 28 4 43 2 6 4 "2 35 B S 76 27 39 4 ..4 0 .'•5778 ..8774 .5 5 ••4 9 .5 5 4' 1 15 59 72 3 2 2 2 0 4 35 9 7 4 3 0 2 2 ..5 7 31 7 05 40 62 3 11 37 73 2 4' 8 9 43 2 4 0 .7 7 6 2 .9.1 6 4' 1 6 0 5 3 4 3 0 0 2 2 6 . 3 4 6 2 2 4 2 2 3 4 2 3 3 . 4 1 0 8 0 3 3 8 4 5 4' 1 7 0 8 3 8 2 6 6 . 3 9 . ' 8 4 . 9 3 . 8 7 • 6 5 7 "1 74361 3 5 8 4 8 2 26 7 74 7 5 4 0 33 30 30 62 3 5 ..2 1 2 4 8 5 0 3 19 26 05 7 ..3 32 6 .•'8 .86 6 .9 4 .8 69 7..5 3 84 4' 16 4 3 46 79 47 82 22 2 ..6 8 44 67 85 72 94 4 2 22 38 3 64 4 19 12 58 83 3 3 386 661 14 4«2 14 20 06 64 38 ..9 2 .88 4 •••6 9 3 8 0 5 3 2 4 . 4 3 7 0 5 3 2 . 5 3 7 3 1 3 2 2 8 3 3 3 7 6 2 . 3 1 • 8 3 8 9 . 7 9 6 9 . 88 1 01 3' 17 76 08 0 2"4 16 37 45 92 2 1 ..3 441 67 83 3 '24 17 43 53 2 2 1 ..6 3 3 0 7 5 2 5 3 4 3 4 2 78U3 1 0 3 7 ..3 81 .'•34. /4.8 31 .6 96 '•32. 1 3 4 2 1 6 7 . 1 6 3 2 1 6 8 3 1 7 9 3 2 2 3 8 6 4 2 6 6 5 2 1 5 8 5 5 . 6 . 3 7 3 . 6 1 2 39 1 3 6 2 1 7 40212 10 2 .4 44 45 9 81 2 22 3647812 12 3 .2 73 35 8 4 6 2 15 23 45 64 2 0 0041 1 3 4 8 2 .6 2 •17 ..3 65 4 ..1 421 ••1 5 ..6 1 3 4 1 0 8 7 2 1 1 2 1 . 4 6 5 1 1 2 1 . 8 4 2 9 1 4 4 1 0 1 1 2 3 7 . 3 3 • . 0 9 1 5 3 14 4 11 09 29 21 12 37 26 22 1 1 .1 21 4 46 75 11 50 02 21 16 52 90 02 21 2 .2 01 3 9 29871 1 2 7 6 0 4'27 74 821 9 98 45 34 6 .0 .19 9 .'0.077 .1 .22 0 ..0 41 •3168.4 9 . S I1 3 8 4 2 2 1 . 1 . 3 8 4 1 1 3 3 6 1 0 0 6 "3'34 9 9 5 2 16 65 15 62 14 .21 4 4 7 7 8 2 1S S 12 21 13 1 9 36 2 8 4 35 96 78 1'2 715033 27 5 4 7 ..2 58 4 ..6 22 96 '•620.2 1 7 1 1 7 0 2 2 2 1 ..2 4 2 3 4 9 2 2 2 7 9 ...6 3 2 6 41 9 54 4' 1 6 7 8 35 9 .« '•68.7.408...7 3 1 8 3 " 2 1 7 0 2 2 6 8 6 2 1 4 3 3 2 8 6 9 2 2 3 5 6 2 1 3 7 2 1 3 5 9 1 8 8 2 0 4 2 0 4 5 2 1 7 7 2 . 3 5 7 9 . 6 2 ••7 61 3...3 5 1 9 3 4 4 6 3 2 1 9 1 6 2 1 2 . 8 4 2 6 1 1 2 1 4 1 3 2 1 1 . 5 3 3 5 4 8 1 3 5 1 0 4 " 1 6 1 2 2 1 0 3 7 . 2 1 . ' 6 3 . 6 7 . 4 4 2 01 3 5 7 91132 2 0 0 52 1 3 ..7 04 44 47 15751 1 74 05 98 62 20 09 8 .3 53 36 03741 19 6 2 6 3'9 35571 1 62 80 09 5 ..0814••5.5 70 .5 .52 8 .2 .37 3 ••7 84 1..4 9 2 3 5 9 2 1 8 4 3 2 1 2 1 8 . 7 0 1 7 3 4 3 2 0 1 6 2 2 3' J1 2 52 42 1 1 ..0 4 36 65 51 90 17 68 2 0 .9 36 7 7 4 11 L1 29 72 53 53 18 41 14 6 9 4 .212•••4.414 ..4 42 5 ..1 181•1'07648 2 3 3 31 69 47 2 1 1 8 2 1 0 7 44 3 1 1 8 7 2 09 .6 13 5 5 0 0 1 34 9 2 38 93 59 9 .'•1 .. B 2 4 3 2 7 2 1 2 3 9 2 1 0 . 9 4 1 4 8 1 1 9 1 3 7 2 0 9 . 6 3 3 6 5 9 1 2 4 2 9 4 1 1 4 4 1 4 . 2 3 • 4 5 . 5 1 . 2 6 • 1 1 6 7 . 2 5 33 13 06 26 2 12 21 59 22 1 1 ..0 31 39 25 95 31 19 7 2 9 2 0 9 ..9863 12 43 30 01 12 38 04 85 4 17 17 56 0 14 02 75 9 .'•2.380 .•'1 .30 7 .3 .42 6 ..1 201••1 16 21 73 .1 2 6 2 5 2 1 2 1 0 9 4 7 3 0 7 2 0 2 8 4 3 9 9 6 . r19 2 73 19 77 53 0 ..7 3 1 1 5 1 5 6B 55 0 7 ..5 32 80 451 6 30 19631 3 6 7 31• 18 606768•.0.0 4.'1.031 ..0416 ..0 03 0 51 6^42 8 . 2 8 3"2 8 "6 74 22 96 82 2 09 8 64 4 3 6 0 0 1 5 7 82 2 0 7 6 3 4 3 3 2 65 28 8 9 ''5 2 9 3 3 7 7 0 3 8 9 2 0 9 . 2 4 3 3 6 3 1 5 3 8 7 2 0 7 . 3 3 4 7 9 5 4 8 1 5 3 ' 1 3 2 1 1 3 4 3 . 0 7 . 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B•109.6 •I •I 121.4 .1812 .03••130.7 . i ".O"l 41541..0 • 1 .09 3 106.5 .20 ..0 0 4 .00 125.0 180.0 19.75  3031  •4 3 4 2 3 2908 •1916 3 2149 3 1106 • i 4366 9657 1' 4837 3- 1123 • l 9689 3 ' 1930 8469 • 2 4367 3 ' 2331 3 ' 2274 • 1' 3299 3 ' 1774 • 1• 3010 2 •9 6 2 2 • 1 '1 5 9 8 1' 7739 2 6541 6363 • 1 1336 3 2525 3 1786 3 1216 9766 2 9334 3 7616 2 539 1 1010 2 1293 • 1 2" 2 6 0 1 6 3 2 4 1906 2" 2 ' 9610 ' 1 1414 1977 3" 1207 1511 3 130 7 4057 3 ' 1176 1168 2 ' 7815  LOGY  21.76 21.86  21.33 2 1.72 21.93 21.89 21.63 21.29 21.02 20.82  20.25 2 0 . 19  19.99 19.73 19.72 19.73 19.68 19.64 19.57 19.40 19.31 19.38 19.31 19.21 19.21 1 9 . 19 1 9 . 11 19.01 19.05 19.09  19.00 19.00 19.04 19.01 18.96 19.06 19.13 19.10 19.09 19.0719.07 19.09 19.15 19.16 19.09 18.74  E  3 3 3 3 2 3 3 3 3 3 3 2 2 3 3 3 3 3 3 2 2 2 2 3 3 3  4813 4323 3020 128 1 5145 2060 3124 3578 3421 2768 1 795 7015 3334 1182 1747 2000 195 8 " 1677 1227 6810 1026 4421 8774" 1131 1171 1014 7059. 2 3290 5036 2 3904 2 664 2 2 8395 2 9031 2 8556 2 7183 2 5098 2 2611 1 •1362 • 2776 2 •4920 2 •6218" 2 •6331 2 •5058 2 •2341 2 1100 2 4435 2 6799 " 2 7927 2 7918 2 7123 2 6056  I  F  R  W  0000 1456 0000 3293 3752 2 1350 6862 1 5075 2 1107 7630 2 2669 1 7906 2 1159 2 2588 2 5303 7 421 7443 2 1906 2 8616 2 1952 3 1249 1 5312 3 1101 2 0620 1 7793 2 7378 2 6089 2 1013 2 3227 2 5211 1 6914 2 1827 " 2 2588 8426 1 4386 2 1048 2618 4668 2 2001 1 1909 2 3301 1 2162 2 3673 1 1883 1 2031 2 3031 1 1720 1 1802 1251 2 1443 1 1241 5621 4729 1 7842 3296 5954 2 2966 4393 7189 2 4567 6257 4541 2 5492 4281 2 5773 4263 '3281 3451 2 5520 2610 • 1657 2 4905 • 1024 1750 2 39 39 •1193 1505 2 2765 ' 1 8981 1212 2 1587 ' 1 •6153 1 5 767 • 1 7476 8752 '4539 " 5232 6237 3089 • 1 1407 6274 3246 1 1470 • 1 1540 • I 1713 1 19 72 •2 • 7 3 0 2 •2 6 1 0 1 1 5689 •6 5 9 0 6 1 8847 •1 • 3 4 5 6 '1725 • 3 9530 2 1261 2 1587 •2 6 8 5 4 ' 2 3903 2 1654 •2 1 8 4 9 • 3• 7 9 5 6 2 1512 • 1• 1 1 4 4 • 2 8669 2 1307 •1 • 1 7 2 2 • 1 1476 •2 • 8 8 7 1 2 1168 •2 7 6 7 6 2 1145 ' 2 •8809 •2 • 6 4 5 7 2 1393 •1 • 1 2 7 6 •2 • 6 8 9 1 2 1642 • 1• 2 3 2 5 •2 ' 8 2 9 6 • 1586 •2599 2 1548 2 1060 • 1• 1 2 7 3 • 1• 1 0 9 4 9864 •2 •7 344 ' 2 •6975 "9154" • 1 0 2 9 - , 2 3 0 1 '" 1390 2 • 1995 • 1 1387 2 •2423 •1 1 7 4 3 •22• 5 1 5 9 2 •2243 • 1 1306 •2 • 9 1 3 6 2 • 1550 0000 •2 • 2 3 2 0 2  .06  • .04 .54 .83 .91 .95 .96 .92 .87 .86 .77 .65  .64 .58 .47 .56 .65 .63 .54 .55" .57 .50 .46  .29 .21" .31  • .05  • .04 • .01 .16  .00 .37 .77 .56 .37 .24 .15 .05  • .27 •".33 ' .36 ' .43 '.58 • .61 • .61 • .57 '.31 -.39  -.54 •.52 • .36 • .29 ••35 '.24  .06 .16 .11 '.06 •.31  .07 .02  K»R  .37 .14 . 77 .78 .91 .95 .96 .97 .93 .91 .83 .93 .86 .93 .88 .87 . .90 .81 .88 .77 " .81 .62 .65 .42 .76 .57 .78 .77 .76" " " . 5 7 .67 .58 .58 .48 .38 .28 .26 .35 .12 .17 .08 .31 .16 .08 .02 .00 .16 .25  '.19 • .09 ' .06 • .08 " .10 -.07 ••12 . 14 • .10 • .27 •.17 • .28 .33 ' .12 ••14 • .08 ' .08 "".02"' .09 .12 .12 .17 ' .05 .17 .17 • .11 .16 • .06 .00 .06  .02  91.4 93.3  15.0  2.8 •7.3 •17.4  •22.7 •29.3 7 •41.4 '42.8 •43.7 •44.8 •40.  •44.9  •30.3  •40.9 27.4  119.7 113.3  •49.4 •49. 1 '•"12672. •118.4  .11 .01  .03  1  •133.5  -209-  TUKEV SPECTRUM ESTIMATION 0522JA ALTA M A G X AND ELEC Y STAT O IN 3 T M I E 1116T0 1246 8 23 61 J K A X L O G X B Y L O G Y E I F W P 0 RR « R PH1 I 10 1 028 1 4 1 4 22 21 8 5 4 6 8 3 5 ..0 36 40 82 7 34 0 0 6 30 0 0 0 0 0 0.'0.070 ..6 6 ••171287 . 13 8 9 18 56 89 42 2 ...5 0 8 2 7 6 433 31 42 08 92 2 3.2 5 33 66 33 86 98 7 30 80 58 22 4 9 6 3 .'•5.23.6 50 3 ...3 2 9 .00 2 96 9. 3 2 3 4 2 8 4 2 2 2 1 4 6 7 7 1 8 2 7 2 6 44 36 8 6 8 2 2 5 1 1 2 3 1 7 4 7 • . 3 6 2 0 • 5 3 . 3 3 3 6 5 - 3.-3. 24' ? 1 15 11 7 75412 34 4S 55 77 6 3 7 6 .34 '.81 .88 .78 6 •' 757.1 .6 7 6 2 9 2 19 8 .5 8,6*46 9 6 2 32 28 471777. 2 24 .6 00 30 32 1 9 3 1 2 8 0 5 3 3 2 3 4 2 8 8 4 0 2 1 . 6 7 6 4 3 2 2 . 7 0 2 2 9 6 0 3 4 4 9 2 3 1 3 8 7 . 1 9 • . 8 7 . 8 9 . 7 9 • 7 8 . 0 6 3 51 2 24 77 68 71 12 21 16 8 8 6 63 54 50 43 19 5 2 52 2 ..9123 3 2 0 5 15 3 4 83 49 54 97 82 36 18 08 99 9 ••.17 .04••9 .99 0 ..7 8811'9 '02 7.3 3a.2 10 29 92 ...8 35 1 31 12 27 .37 70 65 74 02 17 38 03 8 33 8.70 74 .8 0..8 .2 7 8 1 2 8 2 2 2 0 9 2 1 3 4 6 1 5 2 2 9 2 6 1 . 7 8 I 6 3 2 9 7 6 2 2 6 9 1 • . 1 9 ' . 7 7 . 5 9 1 ' 0 4 9 1 4 .0 750- 21187210 38 3 0 9 l ?'2 064 4 31201 1 7 ..1 1 01 3 13 0 .3 7 45 8 1 5 2 2 19 12 71 3 ..3 8 6 7 9 1 085 15 17 91 14 0 .'•16.07..''2 12 2 ..4 2 0 08 41'•4130.779 1 2 2 7 3 2 2 1 4 4 2 1 3 . 5 7 1 6 2 4 8 2 9 1 6 9 3 9 1 9 6 1 2 2 1 2 1 5 6 4 1 7 0 7 2 . 2 3 . 0 5 . 1 2 2 2 1 1 4 2 3 5 0 5 2 1 5 . 4 5 7 4 7 2 6 7 6 2 7 1 8 . 3 3 9 4 9 3 1 3 3 7 0 1 6 7 3 2 2 3 5 7 . 0 7 . ' 4 8 . 4 9 . 2 4 • 8 1 . 9 1 3 1 3 1 6 2 4 2 0 0 2 1 6 . 2 5 9 1 2 2 6 4 0 2 9 1 8 . 1 3 9 4 2 9 1 5 8 4 0 2 6 7 6 2 3 7 7 8 . . 1 1 . ' 7 3 . 7 4 . 5 4 • 8 1 . 2 1 3 9 1 3 61 15 43 28 91 45 77 21!4 .7 131 2 5452 617 .4 3 198 17 39 86 27 83 2639 2 2 9993740 ..14 0 .'75 .75 ..5 7 86 2..6 7 6 3 5 455 97-. .222 1.3 3 -1 46 19 39 7 19 32 7 •••8 8 3 2 2 1 1 . 2 6 3 8 9 2 1 9 1 2 1 2 . 8 3 8 9 8 6 3 5 2 7 2 0 5 2 1 8 7 5 . 0 2 . ' 5 7 . 5 7 . 3 7 . 7 1 7 33 4 4 1 7 7 3 2 1 2 ..5 6 3 2 0 2 17 3 .61 3 8 5 2 1 3 61 2 8 3 0 1 3 0061 ..0 7 .68 ..7 68 9 ..4 •'85 4..0 1 8 3 3 5 263 21 2 2 1 7 8 6 2 1 2 5 6 39 75 12 2 1 85 22 31 2 .2 38 8 5 7 6 I1 1 16 98 12 2 7 05 92 2 12 47 0 71 ..•''7 8 67 18 1 9 3 2 2 1 8 9 0 2 1 2 . 8 6 3 4 3 2 1 6 0 2 7 1 . 1 3 8 2 2 3 1 1 8 3 2 1 9 0 2 1 2 . 1 7 3 . 7 4 . 5 4 • 8 175 .81. 7 2 0 3 2 9 2 4 2 3 0 6 4 2 1 4 . 9 6 3 0 9 2 2 1 7 2 0 1 3 . 4 3 7 9 1 6 1 4 5 1 6 2 2 2 2 8 2 1 7 7 0 1 . 8 . 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S P E C T R U M  E S T I M A T I O N  MAG Y ANO ELEC X STAT1UN 3 TIME 1116T0 1246 X :2515  LOGX  B  Y  21.40 4 4040 3 7901 2 2 3199 2 1 . 5 0 4 3615 3 9826 2 1514 2 1 . 1 8 4 2974 3 2691 2. 1787 2 1 . 2 5 4 7431 1 704S 2 1522 2 1 . 1 8 4 2056 3 2912 2 1244 2 1 . 0 9 4 1763 3 3014 2 1780 2 1 . 2 5 4 1511 3 2670 2 2097 2 1 . 3 2 4 1320 3 2080 2 1997 2 1 . 3 0 4 1164 3 1047 ? 1157 -2_ l o«n 71 . 3 0 4 l n37 2 3033 2 1 . 4 8 3 9751 2 3126 2 5804 2 1 . 7 6 3 9768 2 6379 2 6346 2 1 . 8 0 4 1058 2 8064 4 1242 2 4698 2 1 . 6 7 2 6723 2 4191 2 1 . 6 2 4 1470 2 4756 7 7A77 ? 31*8 21 , " 4 \ mo 2 2076 2 1 . 3 2 4 1742 2 2585 2 1917 2 1 . 2 8 4 1755 2 3112 2 1711 2 1 . 2 3 4 1662 2 2414 2 1495 2 1 . 1 7 4 1513 2 1698 2 1200 2 1 . 0 8 4 1372 2 1974 ? 1 988 1 8845 2 0 . 9 5 4 1 7RH 4 1282 1 7153 2 0 . 8 5 2 1489 1 7389 2 0 . 8 7 4 1318 2 1271 1 6842 2 0 . 8 4 4 1341 2 1064 1 5420 2 0 . 7 3 4 1334 1 8529 4 1291 ' 1 5392 2 0 . 7 3 I 7517 1 7307, 4 1 253 . 1 5583 7 0 . 7 5 1 5046 2 0 . 7 0 4 1246 1 8049 1 3615 2 0 . 5 6 4 1207 1 6396 4 1103 1 2907 2 0 . 4 6 I 4611 I 3121 2 0 . 4 9 3 9865 I 3893 3 8960 1 2851 2 0 . 4 5 1 24U3 1 1587 3 8530 .1 2 30.7. 2 0 O 6 1 1860 2 0 . 2 7 3 8364 1 2298 1 3263 1 1569 2 0 . 2 0 3 8082 1 1427 2 0 . 1 5 3 7321 1 3347 1 1226 2 0 . 0 9 3 6489 1 2800 9884 1 9 . 9 9 3 6281 1 2533 9088. 1 9 , 9 6 _ _3. 649.4... —1_ 25.77 8 342 1 9 . 9 2 3 6808 1 2432 6886 1 9 . 8 4 3 7406 I 2380 3 8380 6067 1 9 . 7 8 1 2547 3 9110 5893 1 9 . 7 7 1 2437 5462 1 9 . 7 4 3 9171 1 2225 6235 1 9 . 7 9 3 .8985 1 2.1J137857 1 9 . 9 0 3 8943 I 1967 8861 1 9 . 8 7 3 7490 I 1975 3 8503 6118 1 9 . 7 9 1 2141 4011 1 9 . 6 0 3 7886 I 2194 3 7317 1200 1 9 . 0 8 I 1087  LOGY  E  22.90 22.99 22.43 77.31 22.46 22.48 22.43 22.32 22.02 71 . 5 5 21.50 21.80 21.91 21.83 21.66  3 3 3 ? 2 3 3 2 2 7 2 3 3 2 2 i 1 1 2 2 2 7 3 3 2 2 2  ?1 t 4 f t  21.41 21.49 21.38 21.23 21.30 21 . 3 0  21.17 21.10 21.03 20.93 20.88 7 7H.R6 20.91 2 20.81 2 20.66 2 20.59 2 20.38 2 20.20 7 20.36 1 20.51 1 20.52 2 20.45 2 .2 20.40 2JI.A1— ? 20.39 2 2 0 . 38 2 20.41 2 20.39 2 20.35 2 20.32 2 20.29 2 2 20.30 20.33 2 20.34 2 20.04 2 :  2559 2532 2016  51 1 1  9353 1310 1028 5453 2970 3433  7531 1039 1027 7206 2800 57SK  5056 9519 2863 3696 5134 942 1 1280 1177 9159 7180 4464' 5074 2868 5058 5571 5494 4648 2431 5037 2054 1071 2847 5247 5831 4050 2760 2709 2222 1293 2J65 4788 6908 6316 5322 6781  Z 2 1 2 7 2 2 2 2 2 7 2 2 2 2 2 1 1 1 I 1 1 1 1 I 1 1 I 1 1 1  1294 1261 2754 7779  2327 2941 3820 3390 2095 1 306 1720 2791 2661 1657 1276  1150 6572 7424 5365 3330 3466 4432 5180 4058 2155 2211 374H 3172 1272 4506 1 1169 8910 •1 1013 3201 2887 1660 i ]2935 • I 1914 1228 3009 3372 3722 4449 4174 3315 2290 • 1 5840 1389 2737 1534  W  F 0000 3 1076 3 1503 ? 7473 2 5697 3 1459 3 1742 3 1483 2 9666 7 5106 2 2259 2 2886 2 4477 2 6782 2 7196 ? lasi 2 6074 2 7894 2 5373 2 3098 2 2554 ? 2740 1 8785 1 5268 1 1686 2 1190 2 1247 1 7661 2 1741 2 2180 2 1032 2 1355 2 2847 2'2845 1 9754 2 1113 2 2672 2 3648 2 2719 I 4538 2 1546 2 2084 2 1237 2 1041 2 5359 2 8298 2 8305 2 6968 2 6395 2 6783 2 6901  1 Z ? 2 2 I 2 2 ? 2 2 2 2 2 7 1 I 1 1 1 1 1 1  1 I 1  • • • •  1 1 1 1  • 1  p  0000 6120 1708 749R 2635 1263 4076 1104 1209 1 747 1214 2059 2989 2992 2446  • .09 • .01 .43  5757 3331 2904 5131 6809  • .05 • .27 ' .37 •.34 • .22 '.76 • .43 '.53 • .48 '.32 '.35 • .51 '.50 •.26 • .12 '.34 '.34 •.01 .15 .13 .08 .02 • .01 .08 .21 .26 .30 .37 .38 .29 .18 .05 ' .12 • .29 '.42  1 1<i7  33RR  1924 2835 5406 8620 8382 1930 1237 1924 1366 8206 1825 1755 2360 8610 9270 6261 3523 9870 7364 7605 2065 1021 2699 1778 3156 1181 2722 2633 0000  .46  .35 .48 .55 .51 .46 .49 .56 .46 .37 .29 .29  . 7A  Q .00 • .05 ' .27 • .41 • .40 • .21 .06 .17 .26 .47 .39 .34 .42 .53 .55 .4S  R  R.R  .09 .05 .51 .67 .53 .52 .56 .54 .53 .68 .68 .57 .56 .61 .62  .01 .00 .26 .38 .28 .27 .31 .29 .28 .46 .47 .32 .31 .37 .38 .77 .06 .09 .15 .22 .24 .13 .22 .37 .23 .12 .14 .26 .29 .23 .15 .17 .12 .01 .04 .16 .19 .11 .05 .01 .05 .07 .09 .15 , .20 .11 .03 .01 .07 .16 .18  .57  .25 .25 .14 .30 .14 .39 .32 .47 .44 .49 .26 .37 '.19 .47 •.29 .61 • .06 .48 .13 .34 . 13 " . 3 7 .03 .51 '.19 .53 .48 -.40 ' .37 .39 • .24 .41 '.07 .35 .09 .09 .19 '.11 '.38 .40 ' .42 .43 '.34 .34 '.22 .22 '.06 .10 .05 .22 .06 .27 '.02 .30 .09 .38 .24 .45 .15 .33 .19 .03 '.10 .11 •.24 .27 • .28 .40 .00 .42  PHI1 180.0 •98.8 •31.8 •47.0 •48.6 •23.2 6. 1 18.0 30.0 43.6 35.2 36.4 48.3 61.0 62.4 60.3 101.3 153.1 158.6 136.3 116. 1 135.7 '156.5 •151.3 • 172.4 157.7 159.2' 176,6 •158.7 • 123.5 • 108.3 • 144.9 • 168.4 93.3 •36.4 '71.5 •79.8 •87.3 '93.1 '38.8 13.8 12.7 •3.2 12.9 32.9 28.2 7.8 •63.7 •117.0 •136.1 • 180.0  -211-  S> P L- C T R U M 0969JA  ALTA 2 4 8 6 1  HX AND EY  A T 1 0 N STATION  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50  3 2 2 2 2 2 1 1 2 2 2 2 2 2 2 2 I 1 1 1 1 2 1 2 1 2 2 2 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2  0969JA  k" l  2 3 4 5 6 7 8 9 10 U 12 13 14 15 16 17 18 19 20 21 22 23 24 25  3 TIME  0032  0632  LOGY  K  3 1 8 808 22225 .08 33 32 13 32 .2 9 2 2 3 . 7 32 0 9 42 22 22 3 .2 3 1 9 4 7 . 9 3 115 94 052. 2222.21 36 .8 9. 2 8 0 5 2 1 8 . 3 2 1 5 23 1 22018 1 .98 1 7 6 8 . 143J4 206 .8 J_ 28 _1 Z3 1 3 3 8 2 2 0 5 3 1 2 6 8 8 2 0 4 ...3 1 3 3 8 7 2 0 5 3 1 94 50 25 6 .1 1017 .0 9 _ lIlA3 f3l67 6 .B .3 222 10 ^t65 J _ .7 1126 20281201 2 03 .6 . 0 176115005192.00 .0  1676 9605 7795 7149 4752 3212 9985 5724 '2357 '2974 '3479 '3828 '2840 '2730 '2541 ' 1678 '7136 •2770 1711 '5026 '6121 1051 '9232 ' 3900 '1231 '5181 ' 1076 '8537 ' 1342 '1238 . 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'256'4 '3807 '4791 ' 5441 '3724 '9435 '5699 3544 2985 5997 1118 1228 1570 2598 I E Y 1  .48 .69 .82 • B2  8.8  -^.8-9 .87 .83 . 70 .48 .46 .48  .32 ..3473 .23 . 16  1  19.98 20.06 20.22 20.29 20.14  12*.  19.91 20.03 20.08 20.10 20.05 19.98  1  ALTA 2 4 8 6 1 A  PHU  X  HY AND EX S T A I O N 3  l*°c'> ' 2 0 . 2 9  3 2090 1 1938 3 1442 1 5696 3 1185 2 1026 2 8672 2 1998 2 4533 2 3247 2 1233 2 3726 2 2906 2 1928 2 1374 2 •4915 1 3990 2 • 7430 1 2018 2 9412 ... „ 2299 2 "9268" 2 •8676 1 2483 2 '6678 1 1775 2 •5354 1 1243 1 1828 2 •3347 2 '1065 1 2508 1 2 540 1 540 5 2 2291 1 2131 1 1531 2 3692 1 1070 2 4243 7923 2 332 7 8083 2 3092 8747 2 1698 7147 1 8381 7563 1 3901 1 1043 1 •6233  B"  LOGX 20.76 21.01 21.30 21.51 21.57 21.46 21.14 20.60 20.30 20.36 20.39 20.25 20.09 20.26 20.40 2 0 . 40 20.33 2 0 . 19 20.03 19.90 19.91 "19.94" 19.85 19.88 20.02  4 4 4 4 4 3 3 3 3 4 4 4 4 3 3 3 2 3 3 3 3 3 3" 3 2 2  TIME Y  3622 3 1566 3372 3 3174 2949 3 3785 2363 3 5337 1668""" 3" 6 5 1 2 9419 3 6508 2329 3 4966 3939 3 2159 5245 2 9073 1238 2 2449 1 3 6 7 ' " 2"" 1 3 1 1 1330 1 9863 1159 1 6663 9091 1 6035 6010 1 7677 2647 - » 1 8265 3041"" 7 4 6 3" 1 7B32 2683 4322 1 7848 4916 1 5739 4980 1 3069 4225 1 1893 3151 1 1500 1727 1 1930 4099 1 2522 5123 1 2383  "i  0032  6044 7235 7538 4396 2700 3516 5 700 5402 2084  9895 4394 5263 7220 2224 5210 1 9549 I 7756 1 5774 1 6869 1 5368 •5511 6589 1'3777 2-1375 2-1987 2'2?87 2-2655 2-2761 2-3027 2-' 3 5 3 2  •2 3 2 1 7 1843 1825 1963 3405 4446 4008 2947 5012 5838 2176 •1'2296 1119 2479 1833 •1 9 1 6 3 •1 2 3 9 5 - 1 1139 •1 3 9 4 2 •2-5748 0000  .54 .52 .47 .47 .52 .54 .57 .45 .31 .47 .68 .68 .53 .58 .55 .42 .40 .51 .61 .59 .54  .00 .13 .11 .13 .25 .38 .38 .29 .42 .38 .12 ' .01 .10 .20 .13 .09 .04 .02 .04" -.01 .00  _.j>i .61 .59 .54  0632  LOGY 22.19 22.50 22.58 22.73 22.81 22.81 22.70 22.33 21.72 2 1.39 21.12 20.99 20.82 20.78 20.89 20.92 20.87 20.89 20.89 20.76 20.49 20.28 20.18 20.29 20.40 20.38  5710 7315 7536 7026 7050 .6328 59 38 4626 3694 7330 1271 1100  2'1597 2 ' 1702 1'8274 1'2340 1 1835 1 4755 1'1162 1"3067 2-1077 2* 1 4 1 4 2'2034 2-2105 2'2178 2'2244 1'9937 •6676 2 1611 2 3190 2 4192 " 2 5156 2 6366  .33 .27 .34 .39 .20 _.2.9— .39 .37 .36 .43 .49 •13_ . 54 .53 .48 .49 .58 _.66 .69" .53 .52 .60 .69 .68 .54 .61 .57 .43 .40  • .0 .23 '39.5 .48 •32.7 .67 •11.1 .67 5.8 .77 9.6 J.9.. 9.2 .76 5.5 .69 •3.0 .48 ' 2 .6 .24 •22.7 .21 _^23_ •43.4 •77.0 .10 •47.1 .03 •7.5 .19 •15.0 .14 •46.9 .05 _«.07_. . ' 5 1 . 3 . •58.7 .11 •54.0 .07 10.6 .12 19.5 .15 3 1.8 .04 _.08 _ 40. 1 22.2 .15 18.5 .14 14.1 .13 •13.1 .18 • 18.7 .24 •_7.9 -28 .3 .29 14.1 .28 13.6 .23 15.6 .24 25.8 .33 3 5.1 .44 34.0 .47 32.5 .29 53.6 .27 38.5 .36 9.7 .48 •1.2 _.46 10.5 .29 18.9 .38 13.7 .32 11.8 .18 5. 1 .16 1.9 .26 • 4.6" .37 • .6 .34 .0 .29  2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1  "t"  9914 9539 7602 4598 2150 1241 2597 468 8 6675 7S29 7761 7363 6367 4713 3725 33B4 1630 8940 1582 3796 5282 5303 4234 2755 3234 6204  i !• 4 0 4 2  1' 1 2 2 2 2 1 1 1 1  4785 5895 1865 2337" 2301 1899 9197 2893 2011 1106 1615 2531 4217 6513 1 1303 1 1554 7925 1778 1375 1592 2839 2015 1119 1719 1548  F 3 3 3 3 3 3 3 3 3 3 2 3 3 3 3 3 3 3 2 1 2 2 2 2 2  0000 1987 3448 4551 5157 5283 5089 4458 3509 2279 1056 1513 1056 1699 2109 2255 2066 1693 1174 6473 9497 3456 6218 7097 7209 5960  w" " p  "  2 2 2 .... 3 3 2 2 1 1 1 1 1 1 1 1 1 1 1 •1  0000 ••23 1959 '.11 4533 .09 8845 . 18 13 37 " '.'ii" 1458 .15 1119 .16 4936 .17 1135 .20 4441 .29 3515 .20 3437 .03 2 347 .07 1850 .15 2639 .17 3075 .29 2606 .36 2424 .19 1945 .05 1172 .06 63B7 .10 3195 .23 6630 .18 2314 .10 6131 .12 6464 • .10  0 .00 • .46 •.73 • .86 •".92 "" • .94 ••93 '.91 '.78 • .63 '.64 • .69 ' .68 • .68 '.70 '.68 • .60 '.59 •-56 ' .47 •.41 '.26 •.06 '.20 • .44 • .41  R .23 .47 .73 .88 .93' .95 .95 .92 .81 .69 .67 .69 .69 .69 .73 .73 .70 .62 .56 .48 .42 .35 .19 .22 .46 .42  R»R .05 .22 .54 .77 .87 .90 .89 .85 .66 .48 .45 .48 .47 .48 .53 .54 .49 .39 .32 .23 .18 .12 .03 .05 .21 .18  PHI1 180.0 •103.7 '82.6 •78.1 •80.1 •81.0 •80.4 •79.4 •75.7 •65.6 •72.5 •87.3 •83.6 '77.2 •76.1 '67.0 •59.2 '71.9 •84.8 •83.3 '76.0 •48.4 '18.2 •64.2 •74.3 •103.5  -212-  2 6 6 9 5 4 1 3 1 6 2 01 1 .5 23 1 0 6 3 2 8 1 4 2 0 4 ..5 6 1 8541 6 5 6 9 2 30 72 08 6 5'•60 552•• ..3 4 .•'29 .4 5 ..1 22 0••131975 .08 2 7 5 4 3 2 1 4 2 4 2 0 . 3 1 1 0 4 3 5 1 8 2 0 5 5 7 7 7 7 0 2 2 2 1 2 3 4 . 0 6 3 . 5 2 8 ••9 6 2 6 1 2 0 4 2'200.0 8" 28 5 7 91 l 2 82981"2 2003 4 .76"" 2 5 4 1 4 0 3 6 9 59 81 67 9 •3230116 5•'".2 2 .2 41 ..0 6 1 5335 .". 2 9 8 7 2 2 1 1 2 0 0 . 5 2 1 8 2 3 . 2 5 1 1 3 9 8 7 . 0 2 ' . 21 . 2 0 4 • 8 . 30 647194 7 8 18 00 88 0 0 ..4 42 6 392 60 ..8 86 791 9 2 1 63 09 2 ••6 67.•'34.39 .3 12 .86 3 1 3••'4 92 10 90 9 3 10 30 60 033li 2 2 1 7 2 2 03 3 4 8 10 6 10 09 33 7 2 1 5 43 60 32 9 ••.0.0 ..4 39 4 .1 1 ..16 2 '•1•8 1 0 . 3 2 4 8 7 1 2 4 0 2 . 9 3 2 2 2 1 5 6 2 0 3 . 3 2 9 9 3 9 2 9 2 1 6 0 6 • 5 3 0 5 . 2 4 . 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Y PG tR I OME 5l M f 1A| 0 N 0969JA ALTA 24 8 61 H YA N O HZ STAT O IN 3 T M I E 0032 0632 K A fX L O G X B Y L O G Y E Z F M P Q R R»R PH1I 0 9 01 15 16 99 36 82 0 2 ..9 3 9 0 3 2 5 3 18 1 4 6 5713 4 6 6 0 0 0 0 0 0 0 •.1.3 3 5 .12 2 11 86 00 ..1 13 32 1 4 4 2 2 0 7 61 3 3 3 3 9 3 2 70 28 32 2 8 1 ...70 61 3 3 1 4 0 2 5 6 42 2 0 80 4 10 7 3 9 3 375 ...0 00 4 ...7 12 3 .0 . 82 2 1 1 8 5 2 1 0 2 6 2 1 0 . 3 3 0 6 6 2 4 0 0 2 5 1 6 3 1 1 8 9 2 1 4 5 7 2 3 2 1 1 5 0 3 . 7 0 7 . 5 2 5 . 9 2 8 63732..221 949782 .1 .3032069 -22—3843 .21421116 .582 8 6 22302262 34 43 10 331 1 ..62 7 •1•46..5 4. 4 2 4 5 3 2 2 15 5 .71 ..3 2 5 3 7 4742 3 1•••1 94 51 57 6747..8 86 7 ••'2.3.0 666 ...8 92 1 .8 5 2 1 2 3 3 2 3 7 2 6 2 1 . 3 1 5 7 3 2 4 3 0 2 1 1 6 3 2 1 5 1 0 2 3 4 2 4 2 3 7 8 5 2 2 9 3 8 6 • 2 2 . 6 6 19 91 25 82 22 0672 2 11 4 6 3 17 01 94 62 3 4 6 2 7 12 5 42 0 5 7 2 2 2 34 22231 2 ••1 7 5 851 ••3.7 8 9 .7 90. ••2 26 4.3 .5 7 4 19 3 40 1 ..0 42 26 2 19 87 92 91 ...8 22 5 2 0 0 2 15 27 13 3 2 2 1 61 01 09 276..7 37 ...6 88 4 ..4 76 82 2 7 4 3 0 1 3 9 9 0 2 6 . 3 4 2 1 I 6 9 2 0 8 4 2 7 7 7 0 1 2 9 8 6 2 1 6 5 6 1 • . 5 7 • . 3 7 • 3 3 . 2 9 46182. 1 -222 091982 .20 03 .0 19663081 33 51 52 2 00 03 5 .6 5 8 95 841 9 107541 397R H ••7 41 55 86 4 ..3 30 4 •'.31 .17 .43 ..1 5 •'256.6 *56. 1 0 2 9 2 1 3 . 6 1 6 1 2 0 . 9 6 7 0 I 6 5 9 1 9 4 1 12 6 6 7 6 12 4 8 3 2 02 3 .5 92 19 8184 I121188482 0 3 ..4 9 2 2 7 4 5 42B 2 2 1 7 8 1••991 4702.0 .22 0 .•'5 .64 0 ..6 3 ..4 0 7 '8 2..0 0 1 2 2 6 6 7 8 1 7 7 5 2 0 . 1 B 8 2 0 0 2 7 7 9 5 2 • 1 3 4 7 2 2 7 0 5 2 5 4 3 0 8 ' 3 2 3 5 4 1 3 20 02 0 92 4 910 1 ..5 3 3 9 2 40 841 2 3 272 0n8 8 •••665 2 8 ..3 8 ...1 7 ..2 1 0 6 5 1 (8 1 T R0 7 n6 n ..0 .7 15 42 25 34 30 45 7_.~i7 152 804 2R 82 ..0 6 263 573 2749 11 11 1 3082 2 0« 1 4 6 4 5 7 48• 14 30 6 2 373 6 66 2 37 .•'•43.3 4 9 275 46 •••8 65 2.7 3 5 6 2 4 . 0 1 1 Jn.u 1 1 3 0 1 1 4 7 . 4 7 . 5 1 6 1 2 5 4 0 2 0 4 . 0 2 8 2 0 3 1 1 3 1 2 6 0 1 . 2 2 1 0 2 1 3 4 4 2 2 2 6 3 6 • 5 9 6 8 . 1 9 • . 3 3 . 3 8 . 1 4 • 6 0 . 0 1 72 2 29 921 2 1 3 1 2 01 3 .9 32 9 3 4 7 1 12 38 12 80 1 .1 21 19 32 99 50 4 • 12 64 52 22 2 0 0 6 ••231 4997.0 .16 6 •• .0 9 .17 8 .0 .00 31 •'249.7 .4 1 8 2 3 6 1 5 3 1 2 0 . 2 9 6 4 0 1 1 2 3 0 . 9 0 2 1 2 0 7 • 1 7 . 0 2 . 0 10 92 4 19 07 0 0 0 ..0 32 19 09 .01 2 4 2 3 13 61 78 41 I4 4 4 9 20285 •.0.13 ..2 12 6 .0 •1309.9 •71 2 24 32 3 293 72. 8 7 2 33.2 1 9 9 29 83 88 94 6 17 97 115 8021 .0 21 1 2 4 7 5 3 6 9 •1•31 3 •.1 .16 7 4 .03 5 4 . 2 1 3 0 0 8 1 9 9 . 1 7 9 5 2 7 4 1 9 8 . 7 1 0 4 9 3 3 1 9 1 0 0 4 1 8 3 8 . 0 0 . 2 4 . 2 4 . 0 6 91 A .8 2 2 2 1 6 9 8 8 7 4 7 1 9 9 . 4 2 7 1 5 9 7 2 6 8 1 9 8 . 6 6 3 8 6 • 1 8 8 8 5 2 1 1 6 2 1 0 5 0 . 1 1 . 1 3 . 1 7 . 0 3 4 9 . 2 3 1 8 3 8 1 7 1 4 7 1 9 8 ..5 2 6 16 70 0 6 3 1 6 1 9 8 ..6 02 16 3 3 6 1 3 9 5 2 11 24 56 3 ••219'•8882171 ..2 241 .''.101 .281 .0 .08 4 •2•49.0 2 4 1 3 9 0 1 7 5 6 3 1 9 8 8 2 5 2 5 7 0 6 1 9 7 1 2 5 0 1 5 7 9 2 1 3 . 2 .2 2 5 1 6 2 3 3 0 4 3 2 0 0 . 2 2 5 0 2 9 5 8 8 7 1 9 7 . 7 2 2 0 1 3 9 2 3 1 1 7 1 0 4 • 1 5 3 2 . 1 2 • . 2 0 . 2 3 . 0 5 • 5 8 .9 1 .1 4 2 4 . . 20, 1 . 5 . . 2 6 1 6 9 5 4 1 3 1 6 2 0 1 . 2 2 4 4 2 2 5 6 4 3 1 9 7 . 5 2 1 9 6 9 • 1 8 0 0 1 2 1 0 3 4 • 2 8 5 4 ' . 0 9 ' . 3 3 . 3 4 . 1 2 • 1 0 5 7 .. 204 08 4568 7354_198 2 7 1 5 4 3 2 . 7 2 2 1 3 1 9 1 6 1 9 2 5 6 1 ' 7 8 7 . ' 1 9 • 1 7 • 2 6 . 0 7 • 1 3 7 0 2 8 9 6 2 6 4 6 9 3 9 9 0 5 2 0 0 . 0 2 2 2 3 6 2 5 1 5 2 1 0 3 2 • 1 7 6 3 1 • 2 3 . 0 7 . 2 4 . 0 6 1 6 3 1 . 2 9 1 8 7 2 2 1 1 2 0 2 0 0 . 5 4 7 6 1 9 2 2 9 1 9 9 . 7 2 2 0 0 3 • 1 6 6 6 1 1 8 1 9 2 • 1 4 5 2 3 • . 0 7 . 0 4 . 0 8 . 0 1 1 4 5 8 . 3 01 1 6 18 00 88 2 0 0 ..4 5 02 15 3 8 2 7 3 1 9 9 ..2 1 88 341• 14 18 28 43 31 ••2 11 02271 ..0 16 3 •••2151 .1 7 .0 .07 3 ••3 3 1 37 49 17 4 8 9 10 90 9 42 2 5 2 7 9 5 8 1 98 9 02 2 1 6 14 31 88 96 2 .26 6 719 70.4 .1 3 2 1 4 4 8 7 1 2 4 0 2 . 9 2 5 7 2 6 7 3 2 4 1 9 . 6 2 1 7 8 6 4 5 7 0 8 8 6 4 • 2 4 4 8 • . 0 5 . ' 2 6 . 2 . 0 7 • 06 . 3 3 1 3 2 4 6 1 7 2 3 2 0 2 . 4 2 5 7 8 5 7 2 4 9 1 9 8 . 6 2 1 5 8 0 • 1 2 1 4 5 1 7 0 1 • 1 6 6 2 • 0 2 • 1 . 5 1 . 5 . 0 2 • 9 7 . 4 3 4 8 95761 i 9 11 44 04 52 ..5 2 5 61 13 7 9 78 91 1 9 ..0 2 B 23 9 2 8 17 20 86 2 ••221 .0.234.'•12.24 ..1 2 0 0 3 3 .6 3 5 15 5 10 91 9 6 2 59 5 313 4082 1 99 9 9 21 1 6 4 2 26 57 41 6 820 715.•''3 3 4 ...1 141 1•••1 1 3 4 .. 3 6 3 9 0 9 1 0 5 1 9 9 . 6 2 4 8 5 1 9 0 0 . 4 2 1 8 6 0 2 9 4 9 1 2 5 6 0 • 2 2 0 0 • . 2 2 . 3 7 1 4 3 3 38 71 17 2 4 0 ..9 24 5 3 9 2 2 8 ..7 25 11 13 6 ••119 53 09 0 •17 94 76 0 ••1I5 4 03 9 .0 .05 10 ..0 001 1 40 95 3 3 18 75 2517 1 1 43 25 62 2 00 1 52 3 7 96 6 7 76 37 87 41 19 99 8 72 2 2 2 9 9 4 346 463 42 4 •••2..0 0 3 ...0 4 143 .. 3 9 2 1 1 7 1 3 2 2 0 1 . 2 3 8 1 0 1 9 8 . 9 2 2 8 9 3 1 9 6 9 1 2 1 3 0 • 1 • 1 4 2 4 . 0 6 • 1 3 4 . 4 01 2 19 32 431 i 1 2 3 5 2 01 0 9 3 6 8 7 9 8 6 6 9 9 ..5 92 2 5 1 4 9 9 3 •1••1 8 5 ••1 6 4 7 .. 4 1 1 1 3 7 5 2 0 ..8 4 37 71 36 9 6 88 95 66 01 1 9 9 2 2 21 68 6 4 3 04 87 11 3 3 8 9 81 33 35 4 ••.1..3 2 8.'•'1.12.008 ..3 .29 9 .1 ..0 8 1•3 69 4.6 9 4 2 2 1 1 0 6 1 5 1 4 2 0 1 . 2 4 1 9 8 . 4 2 2 1 7 4 1 5 2 5 1 2 0 3 5 • 1 2 5 9 5 1 9 0 4 4 3 18 9 6 11 01 92 32 ..9 42 57 49 9 7 9 1 9 .9 21 7 9 2 80571 1 47 90 63 4 ••221 04440..1 33 0 ..''2 20 4 ..3 9 ..1 5 ••3 4 41 62 86 13 10 90 7 2 6 8 7 89 19 35 0 1 99 .0 12 19 20 82 9 •• 1 8 9 1 6 2 4 0 6 557 84..7 3 4 5 2 3 5 4 5 9 2 1 1 9 7 . 7 2 7 7 3 4 6 3 6 1 9 8 . 4 1 6 2 1 2 4 6 5 1 4 0 9 9 • 1 3 4 3 0 . 0 4 . 0 5 . 0 7 . 0 0 3 .. 4 6 i 2 6 2 4 7 2 5 3 1 9 8 . 6 2 8 7 4 B 6 1 6 3 1 9 7 . 9 1 1 7 2 0 • 1 1 0 1 8 1 4 9 0 8 • 1 4 1 6 9 • 0 2 . 0 6 . 0 6 . 0 0 1 0 3 7 4 6 6 9 5 10 99 2 9 6 9 2 6 3 1 0 1 98 8 02 15 0 1 9 ••114 7 1 9 14 14 62 07 9 1 11961•.0.0 6 .1 5 ..1 14 19 6 47 8 8 2 98 53 9 1 25 39 12 0 ...8 9 2 9 5 8 3 7 3 6 8 19 9 ..7 1 2 3 8 2 7 5 9 35 1 3 ..3 3 36 3 ..0 13 1 18 ... 4 9 1 2 2 1 1 6 9 2 0 0 7 2 9 5 5 7 7 5 3 9 1 8 . 8 2 1 4 7 3 • 1 4 0 5 7 3 2 0 0 2 5 2 . 0 4 2 7 . 2 8 . 0 8 8 1 0 50 1535 4902196 .9 29580 3609195 .6 21506 •22384 3530 0000 '.01 .00 .01 .00•1800 . 1 1  V 1 1 1 1 1  1  "i  1 1 1 1 1  2  1 1  i  i  1 1  2 2 2 2 2 2  I  "3  1 1 1  1 1 1  I  1 1 1  2 2 2 2 "2" 2 2 2 2  I  1 1  1  •1  '•".ii  ...  •".11  •1  y  7  2  9  7  •i 1 1 1 1 1 1  2  1 1 .1 1 1 1  ?  7 2 2 2 2 2 7  7  ?  2 2 2  2  1 1 1  1 1 1  1 1  %  ?  •1  1 1  1 1 2 2  .11  1  ">«<••'.!/!  1  1  •1  3  1  .11  1 1  1  1  I  s  3  • 1 • 1  "i  I  1 1  1  1 1  1 1  •1  ' 1  2 2 2  1  -213-  APPENDIX B  STATISTICAL ANALYSIS  Pearson (1901) gave a method f o r f i t t i n g a s t r a i g h t l i n e through a set of points i n a plane when both variables are subject to errors.  Similar r e s u l t s have also been derived  by several other workers.  The constants involved i n the  equation of the straight l i n e  y » A + Bx  (1)  are calculated from the expressions  B  -  £> - ^ L  W ^ - ^ v ^  qr~>;  z  (2)  and  A - Y - BX  (3)  In the present investigation Pearson's ideas have been developed to obtain expressions f o r f i t t i n g the best through N points.  ellipse  It i s also shown from the derivations  given  -214-  below that the r e s u l t s obtained by Pearson and others f o r f i n d i n g the slope of the best f i t t i n g straight l i n e may also be used f o r finding the slope of the major axis of an e l l i p s e provided the points are d i s t r i b u t e d at equal angles around the ellipse. The equation of an e l l i p s e i s given by / 2-  •+  _y_  (4)  If the axes of the e l l i p s e are rotated i n a clockwise sense through an angle  &  the above  equation becomes  ( x Cty3& -f-  V StU> G)  b2  ~  1  (5)  -215-  where x' = x c o s ©  + Y  sin©  y' = y cos<9  - x  sin©  By e x p a n d i n g e q u a t i o n  (5) we  have  -r  comparing  this  equation with Pearson's equation  x-  y  2  we  2  _  ^y ,xy K y  obtain  where  c  8=1  '  -  TJ-  *>  Z  x  A  • Zy  ,  -216-  P e a r s o n gave t h e f o l l o w i n g e x p r e s s i o n f o r t h e s l o p e o f the s t r a i g h t  Equation or  line:  (3) may a l s o be o b t a i n e d  by s o l v i n g  equations (7),  i n t h e f o l l o w i n g way. The c o o r d i n a t e s o f a p o i n t P a r e g i v e n b y  x =  a cos  UJ-'COS©  -  l> s i n LA>  •  sin©  (9) y =» a c o s tyo . s i n  By summing a l l p o i n t s o v e r  2.y^  and  by s o l v i n g  "  these  &  +  Wsin  the e l l i p s e  uo- • c o s <9  we  TTO^S^G  - i - TT (s^Coo^tS-  equations  for Q  have  (10)  217-  In d e r i v i n g equations  (10) i t i s assumed t h a t the p o i n t s on  the e l l i p s e are d i s t r i b u t e d at equal angles. Expanding equation  n  i-  Law  c?  -  (8) we have  z>* - z*>  ~~  By s o l v i n g equations  -r JCZ^-  -f- 4  ~ _  (10) f o r a /b  we  (Z~yf  "  obtain  a.  ( I D  L  ' *•* Lcvvv c3  where  Probable e r r o r i n the s l o p e Birge error  (1947) gave a method f o r f i n d i n g the probable  "Yp  (12)  where  T  i s the probable e r r o r of a h y p o t h e t i c a l  of u n i t weight, g i v e n by  quantity  -218-  and  P  the t o t a l  assigned weight  o f Z, g i v e n b y  d^ = t h e r e s i d u a l n « t h e number o f o b s e r v a t i o n s and  s «*• t h e number o f u n d e t e r m i n e d c o n s t a n t s polynomial  It  i s easier  tan 0  to find  (fora  o f d e g r e e J , S •» J + 1 ) . the probable  , and h e n c e e q u a t i o n  error  (8) i s u s e d  i n tan 2 &  than i n  i n the following  derivation. Let  us denote t a n 2 ©  b y S,  then  S - f (x,y)  Let will  t h e w e i g h t o f x and y be u n i t y . then  According  The p r o b a b l e  be  to equation  (8) S i s g i v e n by  error  of S  -219-  ax  Denoting  J^^-  T^  b  y  P  a  n  d  1*1  Similarly  Hence the probable error i s given by  where  «^ T ^  b  y  -220-  APPENDIX C  IMPEDANCE VALUE FOR AN INHOMOGENEOUS MEDIUM  Let the coordinate system Cx', y') refer to the axes of inhomogeneity and (x, y) to the measurement axes. The impedance values (Kovtun 1961) calculated  i n the directions  of inhomogeneity axes are given by  V  / H  x  where Ey', Hy', E ' and H^'are the components of the e l e c t r o x  magnetic f i e l d measured at the surface, are determined by the structure only, and are independent of the amplitude of the incident wave.  The impedance value calculated i n an  a r b i t r a r y d i r e c t i o n x i n c l i n e d at an angle © tion x', may be written i n the form £ V  Cos &  ~h Ey  y  St'yj (9  y ' Ccrs Q — Hy.' S-t-vv, 6  to the direc-  -221-  The impedance r a t i o Zy*/Z^  characterizes the magnitude of  the inhomogeneity i n the medium (for a homogeneously layered medium Zy7 = Z^'  and  Z / » Z ). x  The r a t i o H^'/Hy' may, i n the general case, be complex depending on the phase s h i f t and the amplitude of the components of the o r i g i n a l f i e l d . H  x  ' / H y  - Cot  For a l i n e a r l y polarised f i e l d ,  <9 . H  Thus the impedance Z , measured at the surface of an x  inhomogeneous structure i n any d i r e c t i o n , depends not only on the s t r u c t u r a l parameters and 0  , but also on the d i r e c t i o n  of p o l a r i s a t i o n of the incident electromagnetic  field.  -222-  APPENDIX 0  IMPEDANCE VALUE FOR AN ANISOTROPIC MEDIUM  Suppose the c o n d u c t i v i t y i s 6~i and perpendicular The  tT i n two mutually 2  d i r e c t i o n s i n an a n i s o t r o p i c medium ( F i g . 7 , 3 ) ,  c u r r e n t d e n s i t y along  these two c o n d u c t i v i t y axes w i l l  be  Maxwell's equation  _  G~2 Ev  Ju -  6*i Eu  gives  (Curl H )  or  Jv °  JL  u  - 4TT3^along the  =  Fu,  CT^ a x i s  s i n c e Hz - 0  OA  and ( C u r l E ) ^ •• — £L2Sfalong the  Replacing  ~  by  (C a x i s  where Z i s the depth of p e n e t r a t i o n  when the amplitude i s reduced t o h a l f i t s o r i g i n a l we have  value,  -223-  J_ t 2, " . c  and  Similarly  since  and  ~  - ju> H v  v  -224-  BIBLIOGRAPHY  Angenheister, tion  G.,  1962, The r e l a t i o n s h i p between t h e d i s t r i b u -  of e l e c t r i c a l  behavior  c o n d u c t i v i t y o f r o c k s and t h e i r  i n the crust  and upper mantle;  a symposium on M a g n e t i c  B a r l o w , W. 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