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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,Sc.(Hons), Indian I n s t i t u t e of Technology, Kharagpur, 1958 M.Tech., Indian I n s t i t u t e of Technology, Kharagpur, 1960 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of P h y s i c s We accept t h i s t h e s i s as conforming t o the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA November, 1962 i i i I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r a n a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a . , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d b y t h e H e a d o f my D e p a r t m e n t o r b y h i s r e p r e s e n t a t i v e . I t i s u n d e r s t o o d t h a t p u b l i c a t i o n o f t h i s t h e s i s s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f Z o o l o g y T h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , V a n c o u v e r 8, C a n a d a D a t e October 9, 1964 ABSTRACT The magnetotelluric method, which depends upon the determination of impedance values over a wide frequency range (0.001-1 cps) from a pair of orthogonal e l e c t r i c and magnetic f i e l d components, has been used i n the past by several investigators to determine the r e s i s t i v i t y of the crust and upper mantle. Because of the d i v e r s i t y of the r e s u l t s obtained by the magnetotelluric method i t was f e l t necessary to examine the method c r i t i c a l l y i n order to obtain useful and unambiguous r e s u l t s . To carry t h i s out an investigation was made of the magnetotelluric f i e l d recorded simultaneously at s i x stations i n cen t r a l Alberta during August 1961. The investigation i s divided into f i v e main sections; the record-ing of the magnetotelluric f i e l d , the analysis of the f i e l d records by various methods, the evaluation of the v a l i d i t y of the d i f f e r e n t assumptions made i n the magnetotelluric method, the determination of subsurface r e s i s t i v i t i e s , and the inves t i g a t i o n of inhomogeneous and anisotropic bodies. Continuous recordings of Ey, H x and H z were made during August 1961 for two weeks at s i x stations, each approximately 100 km apart and oriented i n a north-south d i r e c t i o n (113 .5° W longitude). In addition two extra components E x > Hy were recorded at the central station, Beiseker. Estimates of the wave impedance E y/H 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 in the plot of E y/H x against period T, Subsurface inhomogeneities near Cardston are believed to be the main cause of this scattering. At Beiseker, power spectra of selected lengths of records were computed and from them the ratios E y/H x and E x/H y were obtained in order to estimate subsurface resis-t i v i t i e s . In addition a method for interpreting anisotropic bodies has been suggested and used at Beiseker to explain the differences which exist between the ratios EV/HL and E x/H y. A comparison between the various methods suggested by different investigators to interpret magnetotelluric data has been made and i t has been shown with the help of theoretical 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 results i f applied to the interpretation of high frequency ( > 0.005 cps) magnetotelluric data. In order to judge the validity of the basic assumption - i v -of Cagniard's method, v i z . that the horizontal gradients of the f i e l d vectors are n e g l i g i b l e compared to v e r t i c a l gradients, power spectra of corresponding lengths of records, used for the estimation of the r e s i s t i v i t i e s , were computed at a l l s i x stations for the components Hx and Hz. Micro-pulsation a c t i v i t y which exhibited high coherence of Hx at a l l s i x stations yielded the least scatter i n the P vs T plot as was expected. By c a r e f u l l y selecting data on the basis of t h i s and other coherence 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 obtained of a marked decrease i n the r e s i s t i v i t y i n the uppfer part of the Earth's mantle. xiv ACKNOWLEDGEMENTS It is 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 c r i t i c a l l y . I would also like to thank Professor S. H. Ward, Depart-ment of Mineral Technology, University of California, Berkeley, for allowing me to work with him for a short time and without whose help a part of this 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 California, for help with the computations. I gratefully acknowledge the help received from the staffs of the Computation Centers of the University of British Columbia and the University of California. The constant interest shown by Dr. T. Watanabe and others in the Institute of Earth Sciences during this invesgigation i s appreciated. I also thank V. M. Brawn for reading my manuscript. This work was financially supported by the office of Naval Research under Contract No. 3116(00). - V -TABLE OF CONTENTS CHAPTER I INTRODUCTION 1.1 Aim of the thesis 1 1.2 Early investigations 1 1.3 The magnetotelluric method 6 1.4 D i f f i c u l t i e s i n the interpretation of magnetotelluric data 14 1.5 Outline of the thesis 17 II FIELD OPERATIONS 19 2.1 Purpose 19 2.2 Geology of the area 21 2.3 Description of the f i e l d operations 28 III RECORDING OF MAGNETOTELLURIC SIGNALS 33 3.1 University of B r i t i s h Columbia equipment 33 3.2 University of Alberta equipment 41 3.3 P a c i f i c Naval Laboratory equipment 42 3.4 University of C a l i f o r n i a equipment 43 3.5 F i e l d procedure 51 - v i -IV METHODS OF ANALYSIS 56 4.1 General 56 4.2 Vis u a l c o r r e l a t i o n analysis 58 4.3 Power spectral analysis 61 4.4 Error analysis 70 V JUSTIFICATION OF THE ASSUMPTIONS IN THE y MAGNETOTELLURIC METHOD 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 of the magnetic f i e l d 82 5.4 Relative magnitudes of the v e r t i c a l and horizontal magnetic f i e l d components 93 VI INTERPRETATION OF THE MAGNETOTELLURIC DATA 97 6.1. General 97 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 103 6.3 Combined analysis of Meanook and Beiseker data 139 VII ANISOTROPY AND INHOMOGENEITY 147 7.1 General 147 7.2 Method of analysis 153 7.3 Determination of k and 9 at Beiseker 160 7.4 Error analysis 175 - v i i -VIII RESULTS AND CONCLUSIONS 181 8.1 General 181 8.2 R e s i s t i v i t y r e s u l t s at Meanook, 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 194 A-I Magnetic 196 A-II Magnetotelluric 202 B STATISTICAL ANALYSIS 213 C IMPEDANCE VALUE FOR AN INHOMOGENEOUS MEDIUM 220 D IMPEDANCE VALUE FOR AN ANISOTROPIC MEDIUM 222 BIBLIOGRAPHY 224 - v i i i -LIST OF ILLUSTRATIONS Figure 1.1 Apparent r e s i s t i v i t y vs period obtained by d i f f e r e n t investigators i n d i f f e r e n t regions 10 2.1 Map showing the location of 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 subsurface map 26 2.4 Lithology of the Precambrian basement as infer r e d from well samples and gravity anomalies 27 2.5 Geological cross section along the s i x stations 29 3.1 Block diagram showing the arrangement of the d i f f e r e n t recording units 32 3.2 Cross section of the magnetic detector 34 3.3 Galvanometer amplifier layout 36 3.4 Photocell amplifier and impedance changer 38 3.5 Frequency response of the horizontal and v e r t i c a l magnetic detectors (University of B r i t i s h Columbia) used at Meanook 40 3.6 Frequency response of the horizontal (X and Y) magnetic detectors ( P a c i f i c Naval Laboratory) used at Beiseker 44 X X 3.7 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 45 3.8 Cross s e c t i o n of copper-copper s u l f a t e e l e c t r o d e 47 3.9 C i r c u i t diagram f o r the E a r t h c u r r e n t f i l t e r 50 3.10 Frequency response of the E a r t h c u r r e n t r e c o r d i n g system 52 4.1 T y p i c a l example of north- s o u t h magnetic r e c o r d s at the s i x s t a t i o n s 60 4.2 R e l a t i o n s h i p between the p o t e n t i a l d i f f e r e n c e to be measured and the l e n g t h of d e t e c t o r l i n e (M 1N 1 - 100 m) - 73 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 81 5.2 L a t i t u d e d i s t r i b u t i o n of amplitudes of nor t h - s o u t h ( H X ) and v e r t i c a l ( H Z ) magnetic components f o r events of 30 sec p e r i o d 84 5.3 Power d e n s i t y vs frequency f o r the north-south magnetic omponent at the s i x s t a t i o n s 85 5.4 Power d e n s i t y vs frequency f o r v e r t i c a l magnetic component at the s i x s t a t i o n s 86 5.5 Power d e n s i t y and coherency vs frequency at s t a t i o n #3 f o r north- s o u t h magnetic component 88 5.6 L a t i t u d e d i s t r i b u t i o n of power d e n s i t y f o r R, and HL f o r events of 30 sec p e r i o d 90 5.7 L a t i t u d e d i s t r i b u t i o n of amplitude of north-south (HJJ) and v e r t i c a l ( H Z ) magnetic components f o r events of 90 sec p e r i o d 92 -X-5.8 Ratio of v e r t i c a l (H z) to horizontal (Hjj.) magnetic f i e l d components as a function of period at Beiseker 95 6.1(a) Magnetotelluric two layer standard r e s i s t i v i t y curves 99 6.1(b) Magnetotelluric two layer standard phase angle curves 100 6.2 E / H vs l/v/~T for st a t i o n #6, Meanook 106 y x o 6.3 (E/H) vs frequency (0-.64 cps) for a three layered Earth model 112 6.4 (E/H) 2 vs frequency (0-.03 cps) for a three layered Earth model 113 o 6.5 (E/H) vs frequency for a two layered Earth model 116 6.6 Apparent r e s i s t i v i t y vs period, s t a t i o n #6, Meanook 119 6.7 Power density and coherency vs frequency at st a t i o n #3 for E-W magnetic and N-S e l e c t r i c components 124 6.8 Power density and coherency vs frequency at st a t i o n #3 for N-S magnetic and E-W e l e c t r i c components 125 6.9(a) Apparent r e s i s t i v i t y vs period, s t a t i o n #3, Beiseker (from E /H ) 127 y x 6.9(b) Phase angle between E y and H x vs period 128 6.10(a) Apparent r e s i s t i v i t y vs period, s t a t i o n #3, Beiseker (from ^/Hy) 129 - x i -6.10(b) Phase angle between Ex and H y vs p e r i o d 130 6.11 ( E / H ) 2 vs frequency at s t a t i o n #3, B e i s e k e r 132 6.12 E y / H x vs p e r i o d , s t a t i o n #1, Cardston 136 6.13 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 #1, Cardston 138 6.14 Master curves of apparent r e s i s t i v i t y f o r m a g n e t o t e l l u r i c soundings over a th r e e l a y e r E a r t h 140 6.15 Apparent r e s i s t i v i t y vs p e r i o d f o r Meanook and B e i s e k e r 143 7.1 T h e o r e t i c a l m a g n e t o t e l l u r i c sounding a c r o s s v e r t i c a l c o n t a c t , H f i e l d p a r a l l e l t o the s t r i k e 149 7.2 P l o t of E/H over a h i g h l y conducting and a p o o r l y c o n ducting dyke 150 7.3 O r i e n t a t i o n of the a n i s b t r o p y axes w i t h r e s p e c t t o measuring axes 155 7.4 A d d i t i o n of s i g n a l and randomly o r i e n t e d n o i s e 162 7.5 T y p i c a l example of north - s o u t h and east-west magnetic components at B e i s e k e r 163 7.6 V a r i a t i o n of E/H along the s i x s t a t i o n s 165 7.7 V a r i a t i o n of E/H along the s i x s t a t i o n s f o r 90 sec p e r i o d 166 7.8 R e s i s t i v i t y i n t e r p r e t a t i o n - Cooking Lake 168 7.9 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 of e l e c t r i c and magnetic f i e l d s 171 - x i i -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 of e l e c t r i c and magnetic f i e l d s , for 25 sec period 172 7.11 Apparent r e s i s t i v i t y vs period for Meanook (from Ej/Hy) 174 7.12 Change i n the apparent r e s i s t i v i t y values at Meanook obtained 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 plot for d i f f e r e n t models 185 8.2 Diagram showing the orientation of the anisotropy axes and the d i r e c t i o n of p o l a r i s a t i o n of E and H f i e l d s 190 - x i i i -LIST OF TABLES Table 4.1 Table c o n t a i n i n g the d i f f e r e n t frequency bauds, time l a g and the maximum frequency at which power spectrum es t i m a t e s c o u l d be made 69 4.2 80% range of the power s p e c t r a l d e n s i t y estimates 76 6.1 Apparent r e s i s t i v i t y , Ey/H x and standar d d e v i a t i o n of the mean of P at d i f f e r e n t p e r i o d s at Meanook 105 6.2 Apparent r e s i s t i v i t y , coherency and phase angle between E v and H„ at d i f f e r e n t p e r i o d s at B e i s e k e r 121 6.3 Apparent r e s i s t i v i t y , coherency and phase angle between E x and H y at d i f f e r e n t p e r i o d s at B e i s e k e r 122 6.4 Apparent r e s i s t i v i t y , Ey/H x and standard d e v i a t i o n of i t s mean at d i f f e r e n t p e r i o d s at Cardston 134 7.1 D i r e c t i o n of p o l a r i s a t i o n of e l e c t r i c and magnetic f i e l d s 178 CHAPTER I INTRODUCTION 1.1 Aim of the thesis Because of the d i v e r s i t y of the r e s i s t i v i t y r e s u l t s obtained i n the past by the magnetotelluric method, i t was f e l t necessary to examine t h i s method c r i t i c a l l y i n order to obtain useful and unambiguous r e s u l t s . This i s the main aim of the research described i n t h i s t h e s i s . To carry i t out an investigation has been made of the magnetotelluric f i e l d recorded simultaneously at s i x stations i n Central Alberta during August 1961. The investigation i s divided into f i v e main sections; the recording of the magnetotelluric f i e l d , the analysis of f i e l d records by various methods, the evaluation of the v a l i d i t y of the d i f f e r e n t assumptions made i n the magnetotelluric method, the determination of subsurface r e s i s t i v i t i e s , and the investigation of inhomo-geneous and anisotropic bodies. 1.2 Early investigations The contrast i n physical parameters of the subsurface regions of the Earth i s the basic p r i n c i p l e used i n a l l -2-geophysical methods for the exploration of subsurface bodies. One of the most pronounced contrasts 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 are made by one of the e l e c t r i c a l methods over a s a l t dome or over a massive sulphide ore body. The f i r s t method employed for the determination of such bodies made use of natural e l e c t r i c f i e l d s in the Earth (known as t e l l u r i c currents) which were postulated by Davy i n 1821. As a r e s u l t of studies of the disturbances created i n English telegraphic l i n e s , Barlow (1849) obtained convinc-ing evidence that such currents do i n f a c t flow in the Earth. These currents flow everywhere along the surface of the Earth i n large sheets. Since the l a s t war, t e l l u r i c current prospecting has become the p r i n c i p a l e l e c t r i c a l method for o i l exploration. The widest a p p l i c a t i o n has been in Europe and North A f r i c a . Although the mechanism by which these currents are generated has not been p r e c i s e l y established i t i s generally believed that they are induced i n the Earth's surface by ionospheric currents which correlate with the diurnal changes i n the Earth's magnetic f i e l d . Several workers have attempted to construct an equivalent system of currents i n the ionosphere from a knowledge of the variations i n the d i r e c t i o n of the e l e c t r i c vector observed simultaneously at several s t a t i o n s . Glsh (1939) studied the diurnal v a r i a -tions of t e l l u r i c currents recorded at twelve worldwide stations and constructed a worldwide current system. However ) I -3-the number of stations i n his investigation was not s u f f i c i e n t to give a true picture. T e l l u r i c currents can not be used for the determination of absolute values of the r e s i s t i v i t y of subsurface s t r a t a . They are generally used for the location of subsurface inhomogeneities. The usual method fo r the determination of the r e s i s t i v i t y of d i f f e r e n t layers and bodies inside the Earth i s to apply a r t i f i c i a l generated current to the Earth at two points, and measure the p o t e n t i a l drop between two other points. An apparent r e s i s t i v i t y may thus be obtained when the geometrical r e l a t i o n s h i p between the four electrode positions i s known. The penetration depth obtained by t h i s method i s approximately proportional to the separation of the current electrodes. To determine the r e s i s t i v i t y at depths of thousands of feet would require an impracticabaly large separation of the electrodes. Thus to obtain informa-t i o n on the r e s i s t i v i t y at depth i n the crust and i n the upper mantle i t i s necessary to u t i l i s e other methods. Determinations of the r e s i s t i v i t y of the Earth down to the core-mantle boundary have been made by various authors using two d i f f e r e n t methods - varia t i o n s i n the 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 inside the Earth. The p o s s i b i l i t y of obtaining 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 within the Earth from the observed variat i o n s of the geomagnetic f i e l d was f i r s t - 4 -considered by Schuster (1889), i n his development of a theory of the d a i l y magnetic va r i a t i o n s . He showed that i n the absence of e l e c t r i c currents flowing through the Earth's surface, i t i s possible to analyse the magnetic f i e l d observed at the surface into two parts one of external and one of i n t e r n a l o r i g i n (Chapman and Bartels 1940). Such a method was subsequently developed by Chapman (1919) and by Chapman and Price (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 external parts of the d a i l y magnetic v a r i a t i o n s , considering the Earth as a spherical conductor. L a h i r i and P r i c e (1939) derived s i m i l a r expressions for the separations of the magnetic f i e l d using the storm time variat 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 part has been interpreted 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 inside the Earth. It may be shown mathematically that there i s no unique solu t i o n to the problem of f i n d i n g the e l e c t r i c a l current d i s t r i b u t i o n i n the Earth which pro-duces a given magnetic f i e l d ( i n t e r n a l part) at the Earth's surface 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 to see that any attempt to determine the r e s i s t i v i t y i n the Earth from the induced magnetic f i e l d at the surface contains a s i m i l a r uncertainty. For t h i s reason, i n a l l the above investigations i t was necessary to use models of the Earth's i n t e r i o r , which could explain the i n t e r n a l part of the magnetic f i e l d . Knowing the temperature d i s t r i b u t i o n inside the Earth -5-i t i s possible to 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 certa i n assumptions are made regarding the composition of the mantle and core. Different Earth models corresponding to d i f f e r e n t temperature d i s t r i b u t i o n s inside the Earth have been proposed by some authors (McDonald 1957, Hughes 1953, Tozer 1959) to obtain 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 the mantle and core. Both these methods, variati o n s i n the geomagnetic f i e l d and the temperature d i s t r i b u t i o n inside the Earth, are generally used to determine the r e s i s t i v i t y of very deep regions, i . e . at depths exceeding 400 km. They are not so useful for determining the r e s i s t i v i t y 6f the upper 100 km. It was not u n t i l 1950 that the p o s s i b i l i t y of estimating the r e s i s t i v i t y d i s t r i b u t i o n inside the Earth from e l e c t r o -magnetic observations at one place was r e a l i s e d . Tikhonov (1950) i n Russia suggested the method as a t o o l for explora-t i o n at great depths while almost simultaneously Kato and Kikuchi (1950) i n Japan showed that some measurements that they had made on phase angles between the magnetic and t e l l u r i c f i e l d s could be interpreted on the basis of a two-layered Earth. This 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 studies of Schlumberger and h i s co-workers. However i t was not u n t i l 1953, when Cagniard presented his basic paper, that the f u l l p o t e n t i a l of the magnetotelluric method was r e a l i s e d . The term "magnetotellurics" was assigned by Cagniard to the study of the variatio n s i n the magnetic and and e l e c t r i c f i e l d s of the Earth for the determination of r e s i s t i v i t y . 1.3 The magnetotelluric method The basis of t h i s method i s the computation of the wave impedance from a pair of orthogonal e l e c t r i c and magnetic f i e l d components measured simultaneously over a homogeneous, i s o t r o p i c Earth. The concept of wave impedance i s due to Schelkunoff (1938), and from i t the apparent r e s i s t i v i t y may be calculated from either of the following two expressions. T » the period of the magnetotelluric disturbance in seconds Ex » the north-south component of the e l e c t r i c disturbance i n mv/km Ey =• the east-west component of the e l e c t r i c disturbance i n mv/km Hx = the north-south component of the magnetic disturbance i n "Y H y « the east-west component of the magnetic disturbance i n V (1.1) or where P the apparent r e s i s t i v i t y i n ohm meters - 7 -If the r e s i s t i v i t y of the Earth were uniform, measurements of the tangential 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 (eq. 1.1). In an Earth where the r e s i s t i v i t y i s not uniform i t i s possible to speak of an apparent r e s i s t i v i t y as that value which, for a uniform Earth, would give the same f i e l d r a t i o s . In t h e i r papers, Tikhonov and Cagniard, assuming a plane polarised electromagnetic wave incident perpendicular to the surface, gave formulae permitting a c a l c u l a t i o n of the phase difference between the horizontal components of the e l e c t r i c and magnetic f i e l d s and of the impedance of multilayered sections. Interpretation of the experimental r e s u l t s may then be based on the r e l a t i o n s derived from mathematical models. Cagniard (1953) gave a set of master curves for the inte r p r e t a t i o n of f i e l d curves. These master curves are normalised so that they may be used for d i f f e r e n t geological models. The determination of the r e s i s t i v i t y of the Earth's subsurface depends on a comparison between the f i e l d curves and these master curves. If a proper f i t between the two can be obtained parameters, such as r e s i s t i v i t i e s and layer depths, which are assumed for the model, may be used as estimates of parameters i n the r e a l Earth. N i b l e t t (1960) suggested a d i r e c t method of in t e r p r e t a t i o n of magnetotelluric data. The i n a p p l i c a b i l i t y of such a method for interpreting shallow r e s i s t i v i t y s t r a t a w i l l be shown i n subsequent chapters. - 8 -Berdichevsky and B r u n e l l i (1959) have given a d i f f e r e n t impedance r e l a t i o n s h i p , _ 4 7 r 5 . Id (1.2) When P , the r e s i s t i v i t y of the l a s t layer, tends to I Ex I Hy j where P^ i s the r e s i s t i v i t y of the i t h layer i n ohm meters and h^ the thickness of the i * * 1 layer i n meters. Such a r e l a t i o n -ship may not be applicable for shorter periods i n those instances where a decrease i n r e s i s t i v i t y occurs. More recent papers by many Russian authors have shown that the magnetotelluric method has great scope. In p a r t i c u l a r . Tikhonov (1956) and Kolmakov (1961) have shown that the method may be used to study the geoelectric p r o f i l e of s t r a t a l y i n g beneath a layer of p r a c t i c a l l y i n f i n i t e resistance which cannot, f o r t h i s very reason, be studied by d i r e c t current methods. The magnetotelluric method has been used during the l a s t few years to determine subsurface r e s i s t i v i -t i e s at d i f f e r e n t depths i n Russia by Tikhonov and Shakhsuvavov (1956), Berdichevsky and B r u n e l l i (1961), Vladimirov (1960), -9-B r u n e l l i et a l (1959), Kovtuia (1961), Vladimirov and Nikiforova (1961), Vladimirov (1961), Rokityanski (1961); and i n the U.S.A. and Canada by Garland (1960), Cantwell and Madden (1960), Ni b l e t t and Sayn-witt-genstien (1960), Garland and Webster (1960), Smith and Bostick (1961), Horton and Hoffman (1962), Bostick and Smith (1962) and E l l i s , Hasegawa and Vozoff (1962). Figure 1.1 shows some of the r e s u l t s obtained i n the U S.A and Canada. It may be seen from t h i s f i g u r e that a great sc a t t e r i n g of points i s obtained by most investigators. The authors assume that instrumental or s t a t i s t i c a l errors are the major causes of t h i s scattering. Only recently has an attempt been made to explain i t by inhomogeneity, anisotropic conductivity, or source configura-t i o n , (Cantwell, I960; Bostick and Smith, ,1961; Bostick and Smith, 1962; Price, 1962). In the present investigation t h i s problem has been studied i n greater d e t a i l . In his model Cagniard assumed that the f i e l d giving r i s e to va 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 remains uniform over a horizontal distance comparable to the depth at i which r e s i s t i v i t y determinations are> made and propagates as a plane electromagnetic wave. One of the e a r l i e s t observa-tions that rapid variations i n the t e l l u r i c f i e l d could be correlated over large distances was made by Schlumberger and Kunetz (1946) who found that selected components and simul-taneous portions of Earth current records at two locations, « E CO 10' 10 10 10 Pole Mountain, Wyoming, U S A (Essentially No Overburden} 4 A cr, = 2 5 x 10 d, = I 5 km 035= 6 x 10 d 2 > 20 km is Variable r 5 - 6 Garland and Webster x v ' data x, NOTE very ^ y deep highly Conduc-* tive Overburden \ X x Alberta , Canada cr< I O - 5 \ ~2 r (assuming this trend) f •> d 2 = 6 0 0 km 3 3 x IO - 2 (we l l log data) jd. = 1.8 km 10 Cantwell and Madden o N O T E - very little Over-burden, Mass ,U S A Bost ick and Smi th , a ^ T e x a s , U S A 1 1 10 10 - 4 KT 10 10' 10 - 2 10 10" 10 10 10 »o2 - 3 10 FREQUENCY % IO3 PERIOD SECONDS F i g . 1.1. 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 by d i f f e r e n t i n v e s t i g a t o r s i n d i f f e r e n t r e g i o n s . - l i -near Dijon i n France and Madagascar, a distance of approxi-mately 900 km apart, could have a c o r r e l a t i o n as high as 0.85. Similar high correlations 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 for magnetic v a r i a t i o n s . Such high co r r e l a t i o n s between t e l l u r i c records over a distance of 900 km suggests that the assumption of a plane wave may be j u s t i f i e d . The 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 subject of a t h e o r e t i c a l discussion between Cagniard and Wait (1954). Wait pointed out that i f the sources are to be considered as an a r b i t r a r y system of dipoles then the f i e l d s as measured on the surface must be modified. He showed t h e o r e t i c a l l y that i f H x and H y do not change appreciably over a distance of 35 km, when tine period of the o s c i l l a t i o n s i s greater than 10 seconds and the ground r e s i s t i v i t y i s of the order of 1013 ohm meters, the correction i s not Important. Wait showed l a t e r (1960) that the r a t i o s E y/H x and Ex/Hy should, fortunately, remain constant for source distances compared to A/2, where A i s the wave length of the source., An examination of the f i e l d equations indicates that source distances i n excess of 5 to 10 skin depths may be a l l that i s required to obtain v a l i d r e s u l t s . Cagniard i n h i s method has assumed the presence of large ionospheric current sheets giving r i s e to micropulsations. Akasofu and Chapman (1961) have found evidence for the presence of r i n g currents at -12-heights of about 60,000 km, and Rosen and Farley (1961) at heights of about 21,000 km. These r e s u l t s would indicate that i v a r i a t i o n s i n the geomagnetic f i e l d for frequencies less than .01 cps propagate towards the Earth as plane waves and f o r frequencies higher than .01 cps current sources at lesser heights play an important r o l e . However Price (1962) has developed a general theory of the magnetotelluric method for any source f i e l d . He has shown that i f the r e s i s t i v i t y i s assumed to vary with depth below the surface, the dimensions and d i s t r i b u t i o n of the inducing f i e l d cannot be ignored, even when the f i e l d i s on a global scale and the depths being probed are quite moderate. No doubt h i s theory i s correct from a t h e o r e t i c a l standpoint but whether i t holds under actual 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 (micropulsa-tions) have been studied by many authors i n the past i n an attempt to f i n d the source d i s t r i b u t i o n . Several theories of the d i f f e r e n t types of micropulsations which have been c l a s s i f i e d according to t h e i r period and nature of occurence have been put forward by various authors (e.g. Dungey 1954, Watanabe 1956 and 1959, Dessler 1958, Maple 1959, Campbell 1959, Jacobs and Sinno 1960, Benioff 1960, Jacobs and Watanable 1962), and summarised by Jacobs and Westphal (1963). Such micropulsations correspond to narrow frequency bands i n which the energy i s considerably enhanced. In the magneto--13-t e l l u r i c method, however, a general d i s t r i b u t i o n of energy over a wide frequency band (.001 to 1 cps) i s more important. Hence, so f a r as magnetotelluric analyses are concerned, these d i f f e r e n t theories of the o r i g i n of micropulsations are not very s i g n i f i c a n t although they have received a great deal of attention i n the l i t e r a t u r e dealing with " t h e o r e t i c a l " geophysics. However, there e x i s t s general agreement, based on a large amount of evidence, that such geomagnetic v a r i a -tions may be explained i n terms of a solar corpuscular stream (the solar wind). The solar wind i s primarily composed of electrons and protons which are continually flowing out from the sun and Impinging on the Earth's magnetic f i e l d . These p a r t i c l e s , which t r a v e l with a v e l o c i t y of the order of 1000 km/sec, are deflected by the Earth's magnetic f i e l d , which i s confined to a tear drop shaped cavity c a l l e d the magnetosphere. Pulsations of the solar plasma are propagated inside the magnetosphere as magnetohydrodynamic waves. These waves t r a v e l to the ionosphere with v e l o c i t i e s which vary from a few hundred to a few thousand km/sec. Below the ionosphere they can no longer propagate as magnetohydro-dynamic waves. The wave i s then observed round the world as an electromagnetic 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 natural magnetotelluric f i e l d s has now been f a i r l y well investigated. However because of the d i f f i c u l t y of -14-constructing equipment to record small variations of the magnetic f i e l d , these t h e o r e t i c a l studies have only received experimental confirmation at low frequency f i e l d s (below 0.1 cps). Few attempts have been made to ascertain whether i t i s possible to make p r a c t i c a l use of higher frequencies. Ward (1958 and 1959) has used natural f i e l d v ariations i n the audio and sub-audio frequency (AFMAG) range to delineate ore bodies. 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 occurring pulses of short duration. If there i s no highly conducting structure nearby these f i e l d s w i l l tend to be aligned i n a horizontal plane with a random azimuth of p o l a r i s a t i o n . In the v i c i n i t y of a good conductor, however, the plane of p o l a r i s a t i o n becomes t i l t e d out of the horizontal and the azimuth of p o l a r i s a t i o n more c l e a r l y defined. The t i l t i s generally less than 45°. 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 data Complications i n interpreting magnetotelluric data ar i s e only when a wide range of impedance values i s observed for the same period. Such a wide range may be due (a) to the use of "noisy" records i n the analysis, (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 s t r a t a . (a) Noise. Because of the superposition of noise over one -15-of the s i g n a l s , either magnetic or e l e c t r i c , impedance values may be considerably affected i f amplitudes of i n d i v i d u a l wave tr a i n s are used i n the c a l c u l a t i o n s . To minimise noise e f f e c t s , many impedance values are usually averaged. In addition, the presence of noise makes i t d i f f i c u l t to correlate one record with another. However, such d i f f i c u l t i e s may be minimised by the use of power sp e c t r a l densities i n the c a l c u l a t i o n of impedance values. Blackman and Tukey (1958), Davenport and Root (1954) and Bandat (1958) have given methods for t reating signals corrupted by noise. The c a l c u l a t i o n of power spectra from records i s only j u s t i f i e d i f the signals represent a stationary time s e r i e s . In the description of power s p e c t r a l analysis, (section 4.3), i t i s shown that the signals on the records may be considered as parts of a stationary time s e r i e s . Cantwell (1960) has used average impedance values obtained from power sp e c t r a l analyses for the c a l c u l a t i o n of values of apparent r e s i s t i v i t y . Averaging i s generally used i n the analysis to s t a b i l i s e the f l u c t u a -tions of estimates of apparent r e s i s t i v i t y . T&e success with which an estimate may be s t a b i l i z e d depends upon the degree of resemblance of the selected part of the record to a stationary wave. Thus the averaging of spectrum estimates may not be j u s t i f i e d i f the s i g n a l chosen i s a stationary time s e r i e s . On the other hand, flu c t u a t i o n s i n apparent r e s i s t i -v i t y values may not be due to the absence of a stationary -16-time s e r i e s but to 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 given good reasons for not using the average of spectrum estimates i n the computation of apparent r e s i s t i v i t y . To quote, " i t i s doubtful that averaging the spectrum estimates in an attempt to produce the unique apparent r e s i s t i v i t y estimates demanded by the simple layered model i s a worthwhile endeavori" (b) E l l i p t i c a l l y polarised f i e l d s . Cantwell (1960) stated that e l l i p t i c a l l y polarised f i e l d s do not complicate magneto-t e l l u r i c i nterpretations. This i s only true however i f impedance values obtained along the major or minor axis of the e l l i p s e are used i n the computation of apparent r e s i s t i v i t i e s . Vladimirov and An (1961) emphasize that i t i s necessary to ascertain 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 to be e l l i p t i c a l l y (rather than l i n e a r l y ) polarised, the measurement coordinate system must be p h y s i c a l l y or mathematically oriented along the major axis of the e l l i p s e . (c) Inhomogeneous and/or anisotropic r e s i s t i v i t y media. The structure of the Earth's crust i s extremely complex and although r e s i s t i v i t y determinations by magnetotelluric methods require a s t r a t i f i e d media i t i s equally important to determine whether the method can be applied to inhomogeneous media. Neves (1957) and d ' E r c e v i l l e and Kunetz (1959 and 1962) have attacked the problem of a v e r t i c a l d i s c o n t i n u i t y ( i . e . a -17-f a u l t ) i n a layered Earth for c e r t a i n s p e c i a l cases of the d i r e c t i o n of the electromagnetic f i e l d . The t h e o r e t i c a l problem of a f a u l t belongs to that famous class known as the "problem of a f i n i t e l y conducting wedge". In the more general case such problems have not only remained unsolved but so f a r have not even been attacked experimentally. Rankin (1960 and 1962) has solved the problem of a dyke i n a homogeneous i s o t r o p i c medium, and Cantwell (1960) i n his Ph.D. thesis has given solutions for interpreting inhomogeneous and anisotropic media when the magnetotelluric f i e l d i s l i n e a r l y or e l l i p t i -c a l l y polarised. Later Bostick (1962) developed Cantwell's approach and gave a detailed method fo r interpreting such cases. Several Russian workers (e.g. Rokintyanski 1961, Kovtun 1961, Chetaev 1960) have given d i f f e r e n t methods for i n t e r p r e t i n g inhomogeneous and anisotropic media by the magnetotelluric method. The d e t a i l s of a l l these methods are summarised i n section 7.1. A simpler method for i n t e r -preting anisotropic media by magnetotelluric methods i s developed i n t h i s thesis. 1 . 5 Outline of the thesis The following four points 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 analysing records, (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-Cagniard Ts work with a p a r t i c u l a r reference to the f i e l d work car r i e d out i n Alberta. (3) The d i f f e r e n t methods used to obtain the r e s i s t i v i t y d i s t r i b u t i o n inside the Earth by the magnetotelluric method. (4) The methods of inte r p r e t i n g inhomogeneous and/or anisotropic r e s i s t i v i t y media. The main part of the thesis has been divided into two parts, the determination of the r e s i s t i v i t y of deep subsurface s t r a t a and the inte r p r e t a t i o n of anisotropic r e s i s t i v i t y s t r a t a . The f i r s t s i x chapters deal with the f i r s t three topics l i s t e d above while i n the seventh chapter a method i s suggested and used to interpret anisotropic media. In the l a s t chapter the r e s u l t s obtained i n the present investigation are discussed i n the l i g h t of the known geological structure of the area and a comparison i s made with s i m i l a r r e s u l t s obtained by other investigators i n other regions. -19-CHAPTER II FIELD OPERATIONS 2.1 Purpose In the past many r e s i s t i v i t y measurements have toeen made using the magnetotelluric method (section 1.3) but only a few have been found to be successful i n determining the r e s i s t i v i t y down to 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 to derive r e s i s t i v i t y functions, d i f f e r e n t techniques used to analyse records and d i f f e r e n t precautions taken to ensure a uniform inducing f i e l d (section 1.3). As Wait (1954) and Price (1962) have stressed, the most serious assumption that i s usually made i s that the 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. In order to test the v a l i d i t y of such an assumption i t i s necessary to make simultaneous magnetotelluric measure-ments over a large part of the Earth - no attempt has been made i n the past to make measurements on such a large scale. One of the e a r l i e s t observations that rapid variations i n the t e l l u r i c f i e l d could be correlated over large distances was made by Schlumberger and Kunetz (1946, section 1.2). -20-Several other experimental investigations (for d e t a i l s see section 5.3) have resulted i n negative as well as p o s i t i v e r e s u l t s . For magnetotelluric investigations i t i s e s s e n t i a l to make e l e c t r i c and magnetic measurements over a horizontal distance comparable to the height of the source i n order to ensure uniformity of the source. It i s generally considered that the source l i e s i n the ionosphere which may extend from the D layer, at a height of perhaps 60 km to the Fg layer at a height of 400 km. It i s thus evident that, when the nature of the source i s to be investigated, the minimum separation of stations i s 60 km and an upper l i m i t to the extent of the s observations 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 to obtain an estimate of the l a t e r a l scale of the source, along a preferred coordinate l i n e , a space harmonic analysis of the variations i n the magnetic f i e l d along the l i n e must be c a r r i e d out. A minimum of s i x stations i s necessary f o r such ait analysis (Nishida 1962). Thus an experiment was conceived requiring the establish-ment of s i x stations i n a geographic north-south l i n e each approximately 100 km apart. The north-south d i r e c t i o n was chosen on the assumption that any ionospheric current flow would l i e l a r g e l y i n an E-W sheet or l i n e s (Jacobs and Slnno 1960). To study the e f f e c t of source configuration, i t i s -21-necessary to minimise the variables 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 geological structure and to choose a f l a t t e r r a i n * Hence i n planning the programme the geological structure and topography of the area i n which the stations were to be established was also taken into consideration. The only place f u l f i l l i n g these requirements i n western North America was found to be the plains of Alberta and accordingly the s i x stations shown i n F i g . 2.1 were occupied. Subsidiary considerations l i s t e d below were also borne i n mind when choosing the locations of the stations. (1) A major north-south highway l i n k i n g a l l stations. (2) Freedom from major power l i n e s and other e l e c t r i c a l disturbances. (3) A v a i l a b i l i t y of 2000 x 2000 f t . cleared area not i n active a g r i c u l t u r a l use. (4) A v a i l a b i l i t y of 60 cps power. (5) Proximity of accommodation. Edmonton was made the base s t a t i o n from which the other stations could e a s i l y be contacted i f desired. The separa-ti o n of stations varied between 110 and 138 km. 2.2 Geology of the area The subsurface geology of the area under investigation has been studied extensively by many petroleum geologists and geophysicists with the help of well logs and geophysical -22-Fig. 2.1. Map showing the location of the different stations. -23-data. A detailed account has been given i n numerous papers presented at the 'Western Canada Sedimentary Basin Symposium 1954'. A b r i e f account of the geology of the area obtained from these papers i s given below. Geologically western Canada may be divided i n t o three quite d i s t i n c t units, (1) The Canadian Shield, composed pre-dominantly of c r y s t a l l i n e igneous rocks and metamorphic rocks of g r a n i t i c composition, with l o c a l areas of sedimentary and basic volcanic rocks, (2) The Interior Plains, where gently dipping sedimentary s t r a t a , Palaeozoic and l a t e r i n age, have been subjected to l i t t l e metamorphism or intrusion, and (3) The C o r d i l l e r a , a region of complex f o l d i n g and f a u l t i n g with sedimentary rocks of Precambrian and younger age extensively intruded by Mesozoic and plutonic rocks of a wide range of composition. The main tectonic units of western Canada are oriented in a north west d i r e c t i o n p a r a l l e l to the Rocky Mountains, and consist of a 'geosynclinal b e l t ' bordering the Rocky Mountains, and the epicontinental region l y i n g to the east between the geosynclinal b e l t and the Canadian Shield. F i g . 2.2 shows the d i f f e r e n t important s t r u c t u r a l elements. It i s thus evident that f o r magnetotelluric studies the Interior Plains region i s the most su i t a b l e location i n western Canada. In t h i s study a l l stations should be free from any marked subsurface inhomogeneities 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 st a t i o n , Cardston. However smaller r e s i s t i v i t y inhomogeneities such as the reef complex at shallow depths, do occur at some of the stations, e.g. #3,4,5. Such r e s i s t i v i t y inhomogeneities do not a f f e c t the magnetotelluric data because of t h e i r low r e s i s t i v i t y contrasts compared to the enclosing beds. Recent exploration has shown that most of the Interior Plains i s underlain by rocks s i m i l a r to those of the Canadian Shield, and markedly d i f f e r e n t from the Precambrian rocks of the C o r d i l l e r a n region. Following the discovery of the Leduc o i l f i e l d i n 1947, extensive work has been done on the sub-surface Precambrian of Central Alberta. Burwash (1957) has published a very comprehensive report of such work. His 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 help of aeromagnetic maps of part of Central Alberta and the adjoining areas and from well log data he concluded that the Precambrian basement slopes towards the south at 25 f t . / m i l e . Such a c h a r a c t e r i s t i c i s shown in F i g . 2.3. The Precambrian rocks are mostly g r a n i t i c i n nature. Garland and Burwash (1959) have shown that the major part of the Bouguer gravity anomaly over Central Alberta must be attributed to l i t h o l o g i c a l changes i n the Precambrian basement beneath the sedimentary section. They have produced a l i t h o l o g i c a l map 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 physical properties of samples from -26-Fig. 2.3. Precambrian subsurface map. (After Sikayobni, 1957.) -27-41 F i g . 2.4. L i t h o l o g y 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. ( A f t e r Garland and Burwash, 1959.) -28-wells that have reached the Precambrian, together with the gra v i t y data. The sedimentary rocks, overlying the Precambrian basement, are mostly green and maroon shales, sandstones, dolomites, limestones, and a few coal and s a l t beds occurring i n d i f f e r e n t geological u n i t s . A detailed description of each of these rock types belonging to d i f f e r e n t geological periods w i l l not be given here because of th e i r lesser s i g n i f i c a n c e i n magneto-t e l l u r i c investigations. The magnetotelluric method, whose resolving power depends upon the thickness and the r e s i s t i v i t y contrasts of the d i f f e r e n t layers, cannot be used to delineate d i f f e r e n t subsurface r e s i s t i v i t y s t r a t a overlying the Precambrian basement because of i n s u f f i c i e n t r e s i s t i v i t y contrast. In the present Investigation these rock types have been considered as one u n i t . To appreciate the depths to these s t r a t a a cross section has been drawn, F i g . 2.5, from the isopach maps given by Webb (1954). F i g . 2.5 does not show a true geological cross section although i t gives 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 belonging to d i f f e r e n t geolo-g i c a l periods along the s i x sta t i o n s . 2.3 Description of the f i e l d operations Since the assembly of the large amount of equipment and personnel required for the inves t i g a t i o n was beyond the means of a s i n g l e organisation, a cooperative programme was under-P I G . 2.5 GEOLOGICAL CROSS SEC T I O N ALONG THE S I X ST A T I O N S -30-taken between the following groups: (1) The Inst i t u t e of Earth Sciences, University of B r i t i s h Columbia. (2) The Department of Mineral Technology, University of C a l i f o r n i a , Berkeley. (3) The P a c i f i c Naval Laboratory, Esquimalt. (4) The University of Alberta, Edmonton. Each of the stations was equipped to record north-south and v e r t i c a l magnetic components together with the east-west e l e c t r i c component. In addition an east-west magnetic component and a north-south e l e c t r i c component were recorded throughout the operation at s t a t i o n #3 at Beiseker. For one day at a l l stations east-west and north-south e l e c t r i c components and the v e r t i c a l magnetic component were recorded. Normally the two magnetic components IL^  and and an e l e c t r i c component Ey were recorded simultaneously on a r e c t i l i n e a r chart, running at a speed of one inch per minute, except at st a t i o n #3, where the magnetic components were recorded on E s t e r l i n e Angus recorders running at a speed of 3/4"/min. Recordings of E^ . and E y , at a l l stations were made i n order 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 f i e l d at the d i f f e r e n t stations. Douglas (1962) has found i n d i c a -tions of some inhomogeneities i n the area at 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 e l e c t r i c f i e l d . - 3 1 -Of the s i x stations, three were maintained by the University of B r i t i s h Columbia, one by the P a c i f i c Naval Laboratory and two by the University of Alberta. The Univer-s i t y of C a l i f o r n i a supplied equipment for the recording of Earth currents at a l l stations. The d e t a i l s of the equipment used by each group are given i n chapter I I I . The e s t a b l i s h -ment of the stations was begun on August 7th and they were a l l operational by August 15th. Recordings were continued u n t i l August 27th. A continuous recording for twelve days was made at most of the stations except on a few occasions when i t was not possible to run the equipment unattended at night because of t h e i r extremely high d r i f t . G A L . AMP. A T T POWER EARTH CURRENT co CO I FIG,' 3.1 BLOCK DIAGRAM SHOWING THE ARRANGEMENT OF DIFFERENT RECORDING UNITS -33-CHAPTER III RECORDING OF MAGNETOTELLURIC SIGNALS The detection of magnetotelluric signals involves the observation of variations i n the magnetic and e l e c t r i c f i e l d of the Earth. Whitham (1960) and Garland (1960) have summarised the d i f f e r e n t methods of recording these va r i a t i o n s . In the present investigation three types of equipment from three d i f f e r e n t organisations were used to record geomagnetic fluctuations while only one type of equipment was used to record e l e c t r i c signals at a l l s i x s t a t i o n s . The present chapter has been divided into four sections describing the d i f f e r e n t types of equipment used during the operation. The descriptions are kept b r i e f to avoid duplication since detailed accounts have already been published i n s c i e n t i f i c reports. 3.1 University of B r i t i s h Columbia equipment Magnetic recordings with the University of B r i t i s h Columbia equipment were made at three of the stations (#1, 2, and 6). In addition U.B.C. c o i l s were used at stations #4 and 5. The arrangement of the d i f f e r e n t units i s shown i n (NOMINAL) 30' START CAL. COIL 10 TURNS # 16 B 8 S GAUGE FORM EL WIRE FINISH Fig. 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 OF EACH COIL. COIL NO 1 » 66.0 OHMS « <i 2 = 64.4 u H a 3 = 65.5 a M it 4 = 66.6 M l l n 5 = 66.2 a II n 6 = 64.0 II Cross section of the magnetic detector. -35-F i g . 3.1. The d e t a i l s of each unit which were designed by D. A. C h r i s t o f f e l are given below, (a) Detectors. The detector c o i l s are wound on f i b r e glass formers i n the form of cylinders of 1.5" diameter and 30" length with #20 formel insulated copper wire. Each c o i l consists of 10,000 turns wound in 13 layers and has a c e n t r a l core of 0,014" s t r i p s of high permeability magnetic material, laminated to form a bar 1" x 1/2" i n cross section and 60" long. The core i s f i x e d i n each c o i l i n such a way that 15" lengths project from each end and i s kept i n position by means of pieces of cardboard tubing. This i s done primarily to increase the e f f e c t i v e permeability of the core and to insure that the f l u x density i n the c o i l due to a s i g n a l i s uniform along i t s length. In order to provide protection from moisture and handling and to avoid any movement of the c o i l s which would produce spurious signals the c o i l s are encased i n p l a s t i c water pipes of 4" diameter. The c o i l s are not shielded with any material as i t was. found that t h i s was not necessary for recording low frequency (0,01 - 10 cps) s i g n a l s . In addition the c o i l capacitance i s not high enough to make e l e c t r o s t a t i c e f f e c t s important. F i g . 3.2 shows the design of the c o i l . The measured resistances of each c o i l are given In F i g . 3.2. An inductance value of 96.25 henries was found for each c o i l . To obtain the e f f e c t i v e permeability of the core the 1 Metal Reflector, # 566 Edmund Scientific Co. Ltd 2 Lamp G - E # 1816 Aviation 3 Rectangular Aparture, Slit size 5x 10 MM 4 RC.X; Lens, # SN 1126, DIA 1.38", FL. 2.25", Edmund Scientific Co. Ltd. 5 EYE Achromat # 6263 , DIA 29 MM, FL. 76 MM, •» .. .. 6 Galvanometer # 41148, Cambridge Inst. Co. Ltd. 7 R C A . 920 Gas filled twin Phototube Fig. 3.3. Galvanometer amplifier layout. -37-demagnetising factor for the s p e c i f i c shape of the core body must be known. This may e a s i l y be found from demagnetising graphs. Knowing the e f f e c t i v e diameter, the length/diameter r a t i o may be calculated and the corresponding demagnetising factor found from the graph (Richard M. Bozorth 'Ferr©mag-netism' pp 848). Making use of the equation N(B-H) H = H o - - I T " O . I ) a few values of H Q were calculated for the corresponding values of B with the help of a B-H graph for the material used (Benfaction Min. Co. magnetic s h i e l d d i v i s i o n manual 101-122, graph 44). A graph of B against H Q was plotted, the slope giving the e f f e c t i v e permeability. Cross sec t i o n a l area 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 factor (N/4-rr) a 4 x 10 and p. e f f - 2710. (b) Amplifier. The s i g n a l from the detector i s fed into a galvanometer amplifier. The amplification occurs m two stages. The f i r s t stage i s i n the galvanometer and photocell whose c i r c u i t diagram i s shown i n F i g . 3.3. A beam of l i g h t , B - 4 5 V ANOD A N 0 D E x 2 O ^ | >W I/I DPST 47 K A / W I MEG. 4 PIN BASE PIN NO. I • CATHODE I PIN NO. 2 « ANODE I PIN NO. 3 * ANODE 2 to co I MEG PIN NO. 4. « CATHODE 2 ' F i g . 3 .4 . P h o t o c e l l a m p l i f i e r a n d i m p e d a n c e c h a n g e r . I MEG -39-from an o p t i c a l device as shown i n Pig. 3.3, i s directed towards the galvanometer which i n turn r e f l e c t s the beam into a gas f i l l e d RCA 920 photocell* The amplification which can be obtained from the galvanometer depends upon the distance between the galvanometer and photocell, while the amplification obtained from the photocell depends upon the amount of l i g h t f a l l i n g upon i t . However, increasing distance means increasing noise, so that a compromise must be made. The second stage of amplification i s achieved by a one stage d i f f e r e n t i a l amplifier (Fig. 3.4), which i s used to further increase the amplification to observe the signals on a chart recorder. The major part of the amplification i s achieved from t h i s amplifier. One triode tube amplifier alone would be s u f f i c i e n t to obtain the required amplification but a second one i s necessary to eliminate d r i f t in the H-T voltage. When there i s no s i g n a l , i . e . when the beam i s stationary and directed on to the centre of the photo-c e l l , a trace i n the centre of the recorder should be observed. If not the trace may be centred by balancing with the help of a potentiometer shown by BAL i n F i g . 3.4. By t h i s method the . impedances of anodes one and two are matched with the impedances of the one meg ohm resistance branch i n the c i r c u i t . An ampli-f i c a t i o n of the order of 10 5-10 7 may be achieved from t h i s galvanometer amplifier. The output from the galvanometer amplifier i s fed into Varian recorders. When Varian recorders are not used, the -40--1000 8 6 MAG X a Z MEANOOK L 4 -100 8 K6 > 5 o o N L 2 -10 : 8 6 / / 6 22 Variai X Z 6 10 Varian I00q / / V 2 t and x O INITIAL CALIBRATION Points from Cal. Aug. 14.61 II u II II 26.61 I Volt Range H 8 6 4-J L__J I I I l_J_ J ' ' J I ' ' ' I 0.1 _L_ I L .001 6 8 .01 2 4 Frequency in cps 6 8 .1 Fig. 3.5. Frequency response of the horizontal and vertical magnetic detectors (U.British Columbia) used at Meanook. -41-signal i s further amplified with the help of an ordinary A.C. amplifier of 10 2 gain. To vary the strength of the s i g n a l before feeding i t to the Varian recorder an ordinary attenuator i s used which can reduce the strength of the s i g n a l in s i x d i f f e r e n t steps. The frequency response of the system i s shown i n F i g . 3.5 for two of the c o i l s used at Meanook. 3.2 University of Alberta equipment The University of Alberta, Edmonton, provided equipment to record magnetic variations at two of the stations, C l i v e (#4) and Cooking Lake (#5). Chopper amplifiers together with U.B.C* detectors were used at C l i v e to record H x and H z. Galvanometer amplifiers from the University of Alberta with one U.B.C. c o i l and one University of Alberta c o i l were used at Cooking Lake to record H x and H z. A b r i e f description of the University of Alberta equipment i s given below. (a) Detectors. Each detector was made of 20,000 turns of enamelled copper wire wound about a 1" x 30" laminated co-netic AA core. The detector was covered on the outside with one open c i r c u i t layer of windings for a s h i e l d . The c o i l was completely enclosed i n a wooden box approximately 9" x 9" x 30". (b) Amplifier. The galvanometer amplifiers were of the s p l i t beam-photocell-feedback type and were very s i m i l a r to those used by U.B.C. S i l i c o n photoresistor c e l l s , whose resistance depends upon the amount of l i g h t f a l l i n g upon them, were used -42-i n these a m p l i f i e r s . The d e t a i l s of these a m p l i f i e r s are given by Hasegawa (1962). The main d i f f e r e n c e between these a m p l i f i e r s and those of U.B.C. i s t h a t no f e e d back system i s used i n the l a t t e r . Due to the use of p h o t o c e l l s i n s t e a d of phototubes they are more compact. The s i g n a l from the p h o t o c e l l i s sent through a D.C. a m p l i f i e r . P a r t of the r e a m p l i f i e d s i g n a l i s f e d back to the galvanometer to n u l l the c u r r e n t f l o w i n g through the l a t t e r . The a m p l i f i c a t i o n o b t a i n e d i s s u f f i c i e n t t o a l l o w a m i c r o p u l s a t i o n of the order of one t e n t h of a gamma to be observed on a G 10 V a r i a n r e c o r d e r , 3.3 P a c i f i c Naval L a b o r a t o r y equipment The P a c i f i c Naval Laboratory p r o v i d e d equipment to r e c o r d geomagnetic v a r i a t i o n s at B e i s e k e r , s t a t i o n #3. The d e t a i l s of the equipment used are g i v e n i n P.N.L. R e p r i n t 61-3, a s h o r t d e s c r i p t i o n of which i s g i v e n here. ( a ) D e t e c t o r s . The d e t e c t o r s were made of 20,732 turns of No. 18 H F - i n s u l a t e d wire wound on a core c o n s i s t i n g of 35 T e l c o n 79 s t r i p s , each 0.015" x 0.75" x 72", about 1/2 i n c h 2 i n c r o s s - s e c t i o n . A l l wire s p l i c e s were welded. A copper s h i e l d v/ith an i n s u l a t e d l a p e n c l o s e d the winding w h i l e t h i s i n t u r n was e n c l o s e d i n a s e c t i o n of p l a s t i c p i p e w i t h water-t i g h t end f i t t i n g s and c a b l e connectors. The r e s u l t i n g r e s i s t a n c e was 47 ohms and the inductance about 210 h e n r i e s . (b) Input f i l t e r . The input f i l t e r c o n t a i n e d two bridged-T, -43-60 cycle r e j e c t i o n sections having a t o t a l DC resistance of 18 ohms inserted between the antenna and the amplifier. The input f i l t e r included capacitors f o r s e r i e s tuning the detectors and a set of r e s i s t o r s which, i f required, could reduce the "Q" valve of the detector c i r c u i t , (c) DC Amplifier. A chopper type DC amplifier operating at 60 cps was used. An e l e c t r o s t a t i c a l l y shielded input trans-former was s p e c i a l l y b u i l t to match the chopper to the f i r s t stage of the amplifier. The chopper noise was reduced by lowering the chopper-drive voltage and using a "bueking c o i l " , fed by current which could be adjusted i n phase and amplitude, to cancel out pick-up i n the contacts introduced by the drive c o i l . With a source impedance of 40 ohms the maximum DC 7 voltage gain was about 10 . An attenuator allowed the gain to be reduced i n 10 db steps to -80 db. The instrument had a noise l e v e l of about 0.005 microvolt rms i n the frequency band 0.02 to 3 cps with a 40 ohm source resistance. The frequency responses of the H , H , and H detectors are shown in Figs. 3.6 and 3.7., 3.4 University of C a l i f o r n i a equipment The University of C a l i f o r n i a , Berkeley, provided equip-ment to record the e l e c t r i c a l f i e l d ( t e l l u r i c currents) at a l l s i x stations. The equipment consisted of two pairs of nonpolarising electrodes, one f i l t e r , one Varian G 22 3-2-100 8 6 4 ^ 2 Q w O o io 8 >-6 M A G . X a Y B E I S E K E R Gain 20 db Fig. 3 .6. Frequency response of the horizontal (X and Y) magnetic detectors (Pacific Naval Laboratory) used at Beiseker. I 0.001 j i i ' i i ' i i i ) i i i i i j i i i i i > Q o o I I 6 8 0.01 2 4 6 8 0-1 Frequency in cps — 6 8 l 0.1 0 - 4 5 -Yz Points from Calibration, Aug. 22.61 23.61 Gain 20 db F i g . 3 . 7 . F r e q u e n c y r e s p o n s e o f t h e v e r t i c a l m a g n e t i c d e t e c t o r u s e d a t B e i s e k e r . 0 . 1 j i i i J 1 — i — i — i i i 1 J i .001 6 8 .01 2 4 6 8 .1 Frequency in cps => r e c o r d e r and lead s f o r the e l e c t r o d e connections t o the r e c o r d i n g u n i t at each s t a t i o n . The e l e c t r o d e s used t o make c o n t a c t w i t h the ground were n o n - p o l a r i s i n g copper-copper s u l p h a t e c e l l s c o n t a i n e d i n standard porous ceramic pot s . Two to 5 % of Knox g e l a t i n was added t o a warmed s a t u r a t e d copper s u l p h a t e s o l u t i o n i n order to minimise the e f f e c t of temperature and t o e l i m i n a t e f l u i d leakage. T h i s procedure r e s u l t e d i n remarkably s t a b l e e l e c t r o d e s , s u p e r i o r t o other c e l l s such as g e l l e d Cadmium-Cadmium C h l o r i d e ( B o s t i c k and Smith 1960). F i g . 3.8:; shows a c r o s s s e c t i o n of an e l e c t r o d e i Three e l e c t r o d e s were used a t each s t a t i o n t o r e c o r d the e l e c t r i c f i e l d i n two mutually p e r p e n d i c u l a r d i r e c t i o n s . One of the e l e c t r o d e s (the west e l e c t r o d e shov/n i n F i g . 3.1), was used as a common e l e c t r o d e f o r r e c o r d i n g the two e l e c t r i c components ( E x and E y ) . At most s t a t i o n s the e l e c t r o d e s e p a r a t i o n was 2000 f t . The e l e c t r o d e s were p l a c e d i n h o l e s s i x to e i g h t f e e t deep, augered i n the s o i l . T h i s was done i n order t o minimise the e f f e c t of temperature and chemical i n s t a b i l i t y s i n c e at t h i s depth the moisture content i s u s u a l l y s t a b l e . A s m a l l amount of copper s u l p h a t e s o l u t i o n was poured i n the holes b e f o r e lowering the e l e c t r o d e s i n t o them. T h i s was done to b r i n g the chemical composition of the e l e c t r o d e s i n t o e q u i l i b r i u m w i t h the su r r o u n d i n g s . Once the e l e c t r o d e s were lowered i n t o the h o l e s , the impedance between - 4 7 -PURE COPPER K PIPE K> COPPER SULFATE GEL I ' I 1.1 i .i i > -i r-v # 18 GAUGE INSULATED WIRE SOLDERED TO COPPER PIPE CORK PLUG PROTECTIVE LAYERING OF RUBBER THIN WALL POROUS CUP ///////// / ///////'//// SCALE I'I 3 INCHES F i g . 3.8. Cross s e c t i o n of copper-copper s u l f a t e e l e c t r o d e . - 4 8 -a pair was measured. More copper sulphate solution was added to the holes i f required u n t i l a value between 200 to 2000 ohms (generally 600 ohms) was obtained. The holes were then f i l l e d with l i g h t s o i l and the top covered with plywood and a thick layer of s o i l . After two to three days the electrodes reached, for a l l p r a c t i c a l purposes, chemical equilibrium with t h e i r surroundings. In addition, a fourth electrode was also placed at a distance of 6 f t . from the west'electrode (Fig. 3.1), i n order to check the d r i f t between the electrodes from day to day. To measure the d r i f t between two electrodes placed 2000 feet apart i s extremely d i f f i c u l t because of the superimposition of d r i f t and long period f l u c t u a t i o n s . On the other hand, i t i s r e l a t i v e l y easy to measure the d r i f t between two electrodes only s i x feet apart. In addition, each pair of electrodes was short c i r c u i t e d during the night to minimise d r i f t . The arrangement of the d i f f e r e n t units for recording the e l e c t r i c f i e l d i s shown i n F i g . 3.1. Electrode connect tions to the recorders 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 to ensure that contact with the ground was made by the electrodes only. To test whether the wires were making contact with the ground during operation, impedance values were usually checked. Sudden decreases i n impedance values were generally found to be due to breaks i n - 4 9 -the cable. Testing impedances with an ohmmeter disturbs the chemical equilibrium of the electrode pair so that this test was carried out infrequently. The junction between electrode and wire was soldered and insulated at the electrode. Thermal junction potentials at this point were negligible because the temperature environment was constant at a depth of 6-8 feet in the s o i l . The electrodes were directly connected to two low pass f i l t e r s in order to remove power line interference and to reject signals outside the chosen range of from 1 to 1000 second period. Fig. 3.9 shows the circ u i t diagram of the f i l t e r . 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. Each bias could be operated in two steps each of - 6.0 mv. The bias steppers were manually operated. Bias was provided through a voltage divider as shown in Fig. 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 essentially 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 negligible in 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 in N O FLOATING INPUT C O 1.34 V MALLORY MERC. CELL RM 4 25 K AAA/ i\ < SET FOR BIAS STEPS OF 6 X > MV (each) 50X1 t 1% 33 K (each) -VVAr- t -VVVf-VVVt-AAAr 1/i.F (each) -O FLOATING OUTPUT o -O o GNO. -O RECORDER CASE =~ F i g . 3 . 9 . C i r c u i t diagram f o r the E a r t h c u r r e n t f i l t e r , -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 directly in mill i v o l t s from the records. 3.5 Field procedure In section 2.3 a short account of the f i e l d operations has been ifiven. In the present section a brief description i s given of the different f i e l d procedures such as the orientation of the detectors, their calibration at the beginning and end of a day, and the time marking system and absolute calibration of some detectors. The detectors at a l l stations were oriented with respect to a geomagnetic coordinate system. This system was also adopted for the orientation of the earth current electrodes. To minimise noise the detectors were placed in small trenches dug to size and covered with soft s o i l on the top. The output from the detectors at each station was carried by a shielded cable to a common junction box usually located 15 t o 30 feet from the coi l s . At the junction box the leads from each c o i l were screw fastened to the leads of a shielded cable contain-ing six conductors. The shield o f this cable was connected with the detector lead at one end and to the ground o f the recording equipment at the other. In this way a l l detector leads and shields were held at the same potential as the ground at the recording equipment. 10: 8 6-4 Response across 470 f l Filter Resistance 33 kft Output from Oscillator s 9.35 mV 0.I1— 0.01 J I L _ l _ J I I I I J I I I 8 0.1 2 Frequency in 4 6 cps 8 t 6 8 10 Fig. 3.10. Frequency response of the Earth current recording system. -53-Two methods of calibrating detectors are in general use. In one a calibration signal i s induced into the detector circuit from an auxiliary winding of a few turns. In the other a small measured voltage i s injected into the detector ci r c u i t by means of a series precision resistor and dividing network. In the present investigation the f i r s t method was used. In order to use this method i t is necessary to create a known f i e l d round 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 this each detector was placed coaxial and concentric with a c o i l of 5 turns, 20 meter in diameter. This was done by laying the circular c o i l on the ground and fixing the detector c o i l vertically at i t s centre, half in the ground and half above. As the length of the detector c o i l was much smaller than that of the calibrating c o i l , an expression for the f i e l d at the centre of the calibrating c o i l was used in the calibration. Vozoff (1961) has shown theoretically 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 is of the order of 0.1 milliampere. Thus the U.L.F. output was calibrated in terms of current with the help of a 1.5 volt battery and a Varian G 10 recorder. Once the output from the U.L.F. generator was calibrated, the - 5 4 -c a l i b r a t i o n of the d e t e c t o r was c a r r i e d out by a d j u s t i n g the c u r r e n t input t o the l a r g e c o i l u n t i l a f i e l d of one gamma was produced at the c e n t r e where the d e t e c t o r was p l a c e d . A graph of the output from the d e t e c t o r versus frequency then gave the c a l i b r a t i o n curves. T h i s type of c a l i b r a t i o n , known as a b s o l u t e c a l i b r a t i o n , was c a r r i e d out a f t e r the A l & e r t a Operation i n the l a b o r a t o r y at U.B.C. To check the c a l i b r a -t i o n from time t o time, at d i f f e r e n t g a i n s e t t i n g s of the a m p l i f i e r w h i l e o p e r a t i n g , 10 t u r n s of wire were wound round the c e n t r e of the U.B.C. c o i l s . The same procedure of c a l i b r a -t i o n was performed w i t h t h i s i n t e r n a l c o i l except t h a t a potentiometer i n s t e a d of a r e c o r d e r was used i n the input c i r c u i t . C o i l s b e l o n g i n g t o other o r g a n i s a t i o n s had s i m i l a r windings. At some s t a t i o n s a f i x e d s i g n a l i n terms of v o l t s from the U.L.F. generator was sent d i r e c t l y to the i n t e r n a l c a l i b r a t i n g c o i l s . Time marks were p r o v i d e d on the r e c o r d s from e l e c t r i c a l l y operated chronometers wi t h e l e c t r i c 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 minute and hour marks on the c h a r t paper. The c l o c k s were f r e q u e n t l y checked by means of time s i g n a l s from WWV s i g n a l s . Time marks are used t o determine the commencement of an event and hence must be as a c c u r a t e as p o s s i b l e . An accuracy of ± 6 seconds c o u l d be obtained from the e l e c t r i c a l l y c o n t r o l l e d c l o c k s . At a few s t a t i o n s i t was not p o s s i b l e t o put e x t r a time p i p s on the r e c o r d s because of -55-the type of recorders used. In such instances a re l a y system, operated by a dry c e l l was used. The time pips were super-imposed on the signals and were marked after every minute and hour. At some stations the signals from the clock were fed to the c a l i b r a t i n g c o i l of the detector to give time pips on the recorded s i g n a l s . - 5 6 -CHAPTER IV METHODS OF ANALYSIS 4,1 General Few geophysical measurements allow d i r e c t interpretation -in most instances the data must be subjected to a lengthy analysis before interpretation i s possible. In many geo-physical problems there i s only one variable i n the data and thus i t becomes simpler to apply any corrections before the analysis. In magnetotfelluric or t e l l u r i c measurements where two types of information, v i z . frequency and magnitude, have to be obtained from the same data, the problem becomes more d i f f i c u l t . Because of the complexities of the magnetic and t e l l u r i c f i e l d s of the Earth i t i s d i f f i c u l t to analyse each section of the records without f i r s t smoothing them to remove undesirable components. The best way to achieve t h i s i s by f i l t e r i n g the records at the desired frequencies. The usual way to do t h i s i s by recording the s i g n a l on magnetic tape i n i t i a l l y and la t e r f i l t e r i n g the records. If the recording i s made d i r e c t l y on chart recorders, the signals may be f i l t e r e d by numerical f i l t e r i n g on fa s t computers. Attempts to f i l t e r the records using a convolution f i l t e r have been - 5 7 -made by some workers i n s i m i l a r f i e l d s ( G o l d s t e i n 1962). For a v i s u a l a n a l y s i s of the r e c o r d s a narrow band pass f i l t e r i s e s s e n t i a l , w h i l e such bands may be opened up f o r s t a t i s t i c a l a n a l y s i s . Where f i l t e r i n g i s not p o s s i b l e a s t a t i s t i c a l method may be used. The advantages of a s t a t i s t i c a l approach over v i s u a l methods w i l l be made c l e a r i n subsequent s e c t i o n s . In the present i n v e s t i g a t i o n the data were analysed by the f o l l o w i n g two methods, (1) V i s u a l c o r r e l a t i o n method, (2) Power s p e c t r a l method. Before d e s c r i b i n g i n d e t a i l these methods i t i s worth-w h i l e t o examine the nature of the r e c o r d s . The magnetic r e c o r d s were found t o be q u i t e v a r i a b l e from s t a t i o n t o s t a t i o n , and o n l y a few u s e f u l p o r t i o n s of the r e c o r d s c o u l d be o b t a i n e d . The major cause of t h i s v a r i a t i o n was d i f f e r e n t i n s t r u m e n t a t i o n at each s t a t i o n . On the other hand, the e l e c t r i c r e c o r d s were found to be more or l e s s s i m i l a r . Most of the time the magnetic r e c o r d s were more n o i s y than the e l e c t r i c r e c o r d s . Hence a poor c o r r e l a t i o n between the e l e c t r i c and magnetic r e c o r d s should g i v e some i d e a of the n o i s e present i n the magnetic r e c o r d s . On the magnetic r e c o r d s the v e r t i c a l component (H z) was found t o be more n o i s y than the h o r i z o n t a l component ( H x ) . The v e r t i c a l magnetic i n t e n s i t y at most s t a t i o n s was so low t h a t i t had t o be r e c o r d e d w i t h the h i g h e s t g a i n s e t t i n g of the equipment. Most of the instruments were not very stable at their highest gain giving rise to noisy signals. On the other hand, the east-west (Hy) magnetic component at Beiseker (station #3) had more harmonics than the north-south (H^) component (Fig. 7 . 5 ) . The presence of more harmonics in H y than in IL^  i s probably due to local sources at Beiseker (section 7.3). Another interesting charac-t e r i s t i c which was found from an examination of the records is the change in the dominant period from station to station. Higher periods were: found to occur more frequently at northern stations than at southern stations. Such a characteristic has been reported by Jacobs and Sinno (1960). The analysis in 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 six stations, while the second part consists of an analysis of magneto-te l l u r i c data at three stations, Meanook, Beiseker, and Cardston. The magnetic analysis is restricted to periods below 100 seconds while the magnetotelluric analysis has-been extended to periods up to 3000 seconds. 4.2 Visual correlation analysis Records from a l l stations were examined visually and the most coherent sections from each record selected for analysis. Processing the records consists primarily 1of determining the frequency and amplitude of correlated oscillations which have - 5 9 -an approximately sinusoidal form* The microvariations pre-dominantly have the form of 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 error associated with the determination of the amplitude of single i r r e g u l a r l y shaped pulses, such signals are not usually considered. The amplitude of the electromagnetic f i e l d i s generally determined by one of two methods: 1) the double amplitude of the half period of correlated o s c i l l a t i o n s , shown by 'a' i n Pig. 5.1 and i i ) the arithmetic mean of the double amplitude of two half periods, shown by 'b' i n F i g . 5.1. In the present analysis the second method was used since i t reduced to some extent the influence of the natural noise of the apparatus. The magnetic records were analysed i n the above manner afte r picking out peak to peak correspondences from the records at a l l stations (Fig. 4.1), In the magnetotelluric method correspondences were picked out between the magnetic and e l e c t r i c records at each s t a t i o n . The actual magnitudes of the microvariations 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 for the detectors at each st a t i o n . A new c a l i -bration value was obtained for each st a t i o n at the beginning of each day and the amplitudes were thus corrected for any day to day v a r i a t i o n i n the c a l i b r a t i o n values, which could be as large as - 10%. The frequency of the variations was determined from the time marks traced on the records from the clock after every minute. The average period of many cycles -60-0928 27 26 25 24 23 22 21 20 0928 27 26 25 24 23 22 21 20 AUG. 18. 61 FIG. 4-1 TYPICAL EXAMPLES OF NORTH-SOUTH MAGNETIC RECORDS AT THE SIX STATIONS -61-was taken as the representative period for a p a r t i c u l a r event. Accuracy i n determining the period was limited by the accuracy of the time marks (- 6 seconds over 24 hours). In the magneto— t e l l u r i c method the r a t i o s of the amplitudes of orthogonal f i e l d components were computed and inserted i n equation 1.1 to obtain values of apparent r e s i s t i v i t y at d i f f e r e n t periods. 4.3 P o w e r s p e c t r a l a n a l y s i s (a) General. In the previous section a method for deter-mining the amplitude and frequency of magnetotelluric signals has been given. The use of such a method i s limited only to noise free records. In order to obtain the same information from those records where the sign a l i s distorted due to the presence of noise, i t i s es s e n t i a l to calculate the energy d i s t r i b u t i o n within narrow frequency bands by breaking up the sig n a l into such narrow bands. The use of Fourier analysis for periodic functions and Fourier int e g r a l s for non periodic functions together with the transorm r e l a t i o n s h i p between the function and i t s Fourier spectrum have long been standard methods for analysing a time varying s i g n a l distorted by noise. A Fourier analysis i s generally used for stationary time s e r i e s . The use of Fourier analysis i n magnetotelluric investigations i s j u s t i f i e d only i f the signals analysed possess the c h a r a c t e r i s t i c s of a stationary 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-been assumed (Cantwell, 1960) f o r convenience t h a t the randomly o c c u r r i n g s i g n a l s of v a r y i n g amplitudes do form p a r t 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 methods the 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 from the s i g n a l s i n order to o b t a i n an u n d i s t o r t e d p i c t u r e . I d e a l l y the c a l c u l a t i o n of a power spectrum i s based on the F o u r i e r a n a l y s i s of a random time s e r i e s which breaks up the s i g n a l i n t o narrow frequency bands p e r m i t t i n g the c a l c u l a -t i o n of the power i n these bands. 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) = f f ( t ) e " J w t dt (4.1) -Vz where F(w) i s the F o u r i e r Transform of f u n c t i o n f ( t ) , d e f i n e d i n the range -T/2 ^ t ^ T/2. In the l i m i t i n g case, when the bandwidth goes t o zero, the power spectrum i s known as the power s p e c t r a l d e n s i t y . Hence, equation (4.1)reduces t o $ - Lim * W I * * W (4.2) where cb i s the power s p e c t r a l d e n s i t y , and F*(w) i s the complex conjugate of F(w). The computation of the power s p e c t r a l d e n s i t y from a f i n i t e l e n g t h of r e c o r d i s g e n e r a l l y not c a r r i e d out u s i n g a F o u r i e r s p e c t r a l a n a l y s i s . Davenport and Root (1958), Bendat (1958), Robinson (1954) and Blackman -63-and Tukey (1958) have summarised the disadvantages i n u s i n g F o u r i e r s p e c t r a f o r such cases i n the computation of power s p e c t r a . A power spectrum may be c a l c u l a t e d u s i n g e i t h e r a F o u r i e r a n a l y s i s or the a u t o c o r r e l a t i o n f u n c t i o n . , As the power spectrum i s r e l a t e d to the a u t o c o r r e l a t i o n f u n c t i o n i t i s g e n e r a l l y p r e f e r a b l e to c a l c u l a t e the power spectrum from i t (the a u t o c o r r e l a t i o n f u n c t i o n and the power spectrum are i F o u r i e r transforms of each o t h e r ) . The q u e s t i o n may be r a i s e d why i t i s necessary to c a l c u l a t e the power spectrum when s i m i l a r i n f o r m a t i o n can be obtained from the a u t o c o r r e l a t i o n f u n c t i o n . The advantages of u s i n g the power spectrum i n s t e a d of the a u t o c o r r e l a t i o n f u n c t i o n have been summarised by B l a c k -man and Tukey (1958). In almost a l l p r a c t i c a l s i t u a t i o n s , the data analysed do not r e p r e s e n t the a c t u a l output of random processes. In such cases the data w i l l have been m o d i f i e d , a p p r e c i a b l y i f not r a d i c a l l y , by the t r a n s m i s s i o n c h a r a c t e r -i s t i c s of the equipment employed t o o b t a i n the data. Hence the estimates of power s p e c t r a w i l l have to be c o r r e c t e d f o r the e f f e c t s of t h i s m o d i f i c a t i o n of the data. The c o r r e c t i o n of power s p e c t r a i s q u i t e simple. For e s t i m a t e s of the auto-c o r r e l a t i o n f u n c t i o n however, the c o r r e c t i o n procedure w i l l r e q u i r e a F o u r i e r t r a n s f o r m a t i o n , d i v i s i o n of the r e s u l t i n g frequency f u n c t i o n by another frequency f u n c t i o n , and an i n v e r s e F o u r i e r t r a n s f o r m a t i o n . The a u t o c o r r e l a t i o n f u n c t i o n -64-acts as a passive f i l t e r whose only r e a l purpose i s to detect periodic components. The d e t e c t a b i l i t y of a message from a noisy s i g n a l depends on whether or not there i s a spectral overlap of message and noise. The d e t a i l s of an overlap have been well i l l u s t r a t e d by Goldstein (1962) with the help of a few f i e l d examples. In the case of a noise free record one would expect a f l a t spectrum. Bostick (1961) has suggested another method for c a l c u l a t i n g the power spectral density by d i r e c t l y f i l t e r i n g the data.. In his method he has made use of an analog computer. In most cases, the noise may be represented, or approximated, by stationary Gaussian random processes with zero averages, so that a l l of the i r relevant s t a t i s t i c a l properties w i l l be contained by the autocovariance function or the power spectrum. In many cases, the signals themselves may also be represented, or approximated, by stationary Gaussian random processes with zero averages* Noises, signals, and other ensembles of functions which are approximately stationary but not Gaussian are often also studied i n terms of autocovariance functions or power spectra. Although the average and the spectrum are no longer the only relevant s t a t i s t i c a l properties, they are usually the most useful. (b) Basis of the method. The concept underlying the computation of power spectra are now described b r i e f l y . The expressions given r e l a t e to the c a l c u l a t i o n of the power spectra -65-of one time seri e s but s i m i l a r expressions may be used for the c a l c u l a t i o n of the power spectra of two time s e r i e s . Let Xj, Xg, Xg, X^...... .OXJJ represent a time series of data obtained at times tlf t2, tg,.. t ^ , . . . . . . . . t . The autocorrelation A(L) for such a se r i e s i s given by TV >V A ( L ) =(n3l)Z Xi- L Xi * (n=E) £ X i - L ZX± ^\ The equation above and those which are given below are evaluated for L and k having values 0,1,2,3, m,. where k i s the lag number and m the t o t a l number of lags. The number of lags in each case i s determined when the d i g i t i s i n g i n t e r v a l AtCtjL+i-ti) has been fi x e d , from the r e l a t i o n f k - 2 ^ A ¥ ( 4 - 4 ) where f ^ i s the frequency at lag k. The d i g i t i s i n g i n t e r v a l i s determined by the requirement of the maximum frequency f m a x for the c a l c u l a t i o n of the power spectral density, given by •max 2 A t where A t i s i n seconds and f i n cps. Equation (4.3) can only max n be used for normalised data, i . e . 2— X± -. 0. In the 1=1 present investigation where the data x^ were read from one edge -66-of the c h a r t , the value of Xj^  i s g i v e n by n 1=1 For 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 at many f r e q u e n c i e s (equation 4.4) the 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 c a l c u l a t e d at e q u a l l y spaced i n t e r v a l s (k = 0,1,2,3,. m). In the case of two time s e r i e s , a c r o s s c o r r l e a t i o n between them i s g e n e r a l l y made. 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 at e q u a l l y spaced i n t e r v a l s . The c r o s s c o r r e l a t i o n i s not an even f u n c t i o n and i t s p o s i t i v e and negative p a r t s are c a l c u l a t e d r e s p e c t i v e l y from the f o l l o w i n g e x p r e s s i o n s , C ( L ) = ^ L Z ^ = - L * i -felL") Z * i - L Z Y i <4'6> and (4.7) From the a u t o c o r r e l a t i o n and c r o s s c o r r e l a t i o n f u n c t i o n s , energy est i m a t e s of s p e c t r a , c o - s p e c t r a , and qua-spectra may be made u s i n g the f o l l o w i n g e x p r e s s i o n s . -67-X(k) = -Jp 2. 2e(L) cos + A(o) (4.8) L'l £>k ' y n~ l lrT Y(k) = ~~ Z 2e(L) cos ^ B(L) + B(o) (4.9) L =/ 6 k ^ 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 spectral 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 correla-tions between the two time series. 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 ratio of the cross spectra to the product of the auto spectra is used to estimate the coherency between the two time series, i.e. -68-th e coherency (R k) i s defined as (4.12) Si m i l a r l y the r a t i o of the qua-spectrum to the co-spectrum may be used to estimate the phase lead 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 calculated from the formula given below provided the two seri e s represent a pair 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 spectral densities of the e l e c t r i c and magnetic records at a p a r t i c u l a r frequency. Cantwell (1960) has shown that the apparent r e s i s t i v i t y should be multiplied by the square of the coherency between the e l e c t r i c and magnetic records to obtain the actual r e s i s t i v i t y . Such a m u l t i p l i c a t i o n i s not necessary i f power spectrum values corresponding to high coherency values are used i n the apparent r e s i s t i v i t y c a l c u l a t i o n s . (c) Method of computations. The records from a l l stations were examined v i s u a l l y and the most coherent sections of the e l e c t r i c and magnetic records selected for analysis. S i m i l a r l y coherent magnetic records from each s t a t i o n were -69-also selected. The records were hand d i g i t i s e d at equally, spaced i n t e r v a l s . Table 4.1 i l l u s t r a t e s the d i f f e r e n t f r e -quency bands used, the time lag &t and the maximum frequency f m a v at which estimates could be made. TABLE 4.1 Frequency Band 0.001-0.003 0.007-0.103 0.018-0.023 0.030-0.050 A t 24 sees 6 sees 6 sees 6 sees max 0.0208 0.083 0.083 0.083 The d i g i t i s e d data were run through an I.B.M. 704 computer at the University of C a l i f o r n i a , Berkeley, Computation Center. The program for the I.B.M. 704 was written by Professor Ward and his colleagues using the Tukey spectrum estimation sub-routine. The r e s u l t s of the computations are given i n Appendix A. The coherency between the e l e c t r i c and magnetic records for a magnetotelluric analysis and between the magnetic records for a magnetic analysis were also com-puted. In addition for the magnetic analysis the coherency at each s t a t i o n with respect to Meanook was computed -70-to investigate the source e f f e c t (section 5.3). A comparison between the two methods may now be made. The advantages of using spectral densities i n an estimation of apparent r e s i s t i v i t i e s are many. In the former method where events are correlated v i s u a l l y , personal error plays an impor-tant r o l e . In an estimation of spectral densities the coherency between the e l e c t r i c and magnetic records i s calculated at a l l f r e q u e n c i e s and only those spectral d e n s i t i e s where the maximum coherency i s found, are used i n the c a l c u l a t i o n of P A . This allows the data to be handled i n an unbiased fashion. Another advantage i n using power spectral densities i n the present analysis i s the detection of very low frequencies which are extremely d i f f i c u l t to observe by a v i s u a l c o r r e l a t i o n method for very weak events on high speed magnetograms. The greatest advantage of a power spectral analysis 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 the two ser i e s . The degree of coherency i s an important factor i n any study of micropulsations, and i n magnetotelluric i n v e s t i -gations plays an equally important r o l e . The coherency can also give an ind i c a t i o n of the amount of noise present i n one time series i f the other time series i s presumed to be noise free. 4 .6 Error analysis Errors i n the present analysis are of several kinds. -71-B r o a d l y speaking they may be d i v i d e d i n t o two c a t e g o r i e s , constant e r r o r s and random e r r o r s . Constant e r r o r s are those which are i n h e r e n t i n the a n a l y s i s and can not be c a l c u l a t e d e a s i l y . On the other hand random e r r o r s are of a s t a t i s t i c a l nature and may be c a l c u l a t e d by v a r i o u s methods. Constant e r r o r s i n c l u d e e r r o r s due to i n c o r r e c t c a l i b r a -t i o n of 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 c o r r e l a t i o n a n a l y s i s and e r r o r s i n t r o d u c e d by d i f f e r e n t arrangements of the e l e c t r o m a g n e t i c d e t e c t o r s . Constant e r r o r s may be q u i t e h i g h -i n the present i n v e s t i g a t i o n perhaps as h i g h as 25-30%. The f i e l d d e t e c t o r s were c a l i b r a t e d at the b e g i n n i n g and end of each day and hence any change i n the c a l i b r a t i o n v a l u e s from day t o dqy c o u l d be taken i n t o account ( F i g . 3.5). C a l i b r a t i o n 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 than 0.01 cps was not p o s s i b l e by p r e s e n t l y known methods. C a l i b r a t i o n f a c t o r s f o r f r e q u e n c i e s below t h i s were ob t a i n e d by e x t r a p o l a -t i o n from the c a l i b r a t i o n curves, shown by the d o t t e d l i n e s i n F i g . 3.5, 3.0 and 3.7.. Furthermore, values of the magnetic f i e l d at Meanook at f r e q u e n c i e s lowee than 0.01 cps obtained from our r e c o r d s were compared w i t h those obtained from normal magnetograms at t h a t s t a t i o n . The r e s u l t of t h i s comparison j u s t i f i e d 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 curves f o r f r e q u e n c i e s below 0.01 cps at Meanook. No such comparison c o u l d be made f o r c a l i b r a t i o n v a l u e s at other s t a t i o n s . V l a d i m i r o v (1961) has shown t h a t i t i s necessary to apply - 7 2 -some corrections to the electric f i e l d i f i t i s measured over inhomogeneous ground. The error i s not significant for short electrode separations but may become important as the separa-tion is increased. Fig. 4 . 2 illustrates this effect. Estimation of such an error could not be made in the present investigation because f i e l d data were not taken, but i t should not exceed 2 % . From Fig. 4 . 2 i t i s clear however that the relationship between the amplitude of microvariations in the electric f i e l d and the length of the detector lines may be important and should be estimated in each area i f possible in a l l directions in which detector lines 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. 4 f k - - *£ + 2 | H + 2 A E ( 4 < 1 4 ) r a T H E It is evident that i f the frequency can be found with sufficient accuracy, errors in the calculation of apparent r e s i s t i v i t i e s are mainly due to errors in determining the f i e l d amplitudes. Averages of many amplitudes at the same period were taken in a l l r e s i s t i v i t y analyses, and standard errors of the mean calculated for individual periods. Fig. 6 . 6 and Fig. 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 in individual measurements they -73-M, N, Fig. 4.2. Relationship between the potential difference to be measured and the length of detector line ( M J N J => 1 0 0 m). (After Vladimirov, 1 9 6 1 ) - 7 4 -do g i v e an i n d i c a t i o n of the range of v a r i a t i o n of amplitudes at i n d i v i d u a l p e r i o d s . In the 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 , the f r e q u e n c i e s of i n d i v i d u a l events were determined by t a k i n g an average of many c y c l e s . To compensate f o r e r r o r s i n t r o d u c e d i n the d e t e r -mination of f r e q u e n c i e s by such a method, a band width of 5 seconds was taken f o r p e r i o d s up t o 200 seconds and one of 60 seconds f o r longer p e r i o d s . These foand widths were determined by the accuracy w i t h which the p e r i o d s c o u l d be read from the r e c o r d s . Estimates of the e r r o r s i n t r o d u c e d i n the power s p e c t r a l a n a l y s i s were made i n a d i f f e r e n t way. The computation of power s p e c t r a i s based on the assumption t h a t the s i g n a l s used form a s t a t i o n a r y time s e r i e s . From the nature of the e l e c t r i c and magnetic r e c o r d s ( F i g . 5.1) i t may be assumed t h a t they do possess p r o p e r t i e s s i m i l a r t o those of a s t a t i o n a r y time s e r i e s . The computation of power s p e c t r a r e q u i r e s an i n f i n i t e l y long s e r i e s . The use of such a method f o r a n a l y s i n g m a g n e t o t e l l u r i c data would then be i m p r a c t i c a l and i m p o s s i b l e when o n l y a f i n i t e l e n g t h of r e c o r d i s g e n e r a l l y a v a i l a b l e . The computa-t i o n of power s p e c t r a from a f i n i t e l e n g t h of r e c o r d has been giv e n by Blackman and Tukey (1958) who show t h a t a smoothing c o r r e c t i o n has t o be a p p l i e d t o the power spectrum. In the present i n v e s t i g a t i o n such a c o r r e c t i o n was taken care of d u r i n g the computation. Another e r r o r which may become q u i t e -75-significant in power spectral estimations i f data outside the truncated period are examined is the truncation error. Such an error is virtually nonexistent i f the data are truncated between clear cut events, as was done in the present investigation. If this is not possible the data should be pre-whitened as much as possible. In the present investigation the electric and magnetic records were not prefiltered prior to the spectral analysis. This led to some spillage of energy from the spectral peaks into adjacent frequencies, since the spectral analysis pre-supposes a "white" signal. Some aliasing at the high frequency end may also be present, but the energy density above the Nyquist frequency was very low for the records studied. Despite these limitations of the analytical 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 justified when the number of estimates is very small. Eighty percent of the estimates f a l l in the range given below: Bostick (1961) has given a method for estimating this error. 125 (80% range in db)^ - = 'no. ot\ /'lengthy /resolution records.| per ( j in cps pieces] [piece j ^  r 3 1 2 (4.15) This equation applies to the records of a stationary time -76-s e r i e s whose spectrum i s rea s o n a b l y f l a t . In other words the r e c o r d s are supposed t o be white i n the narrow frequency band used f o r the power d e n s i t y c a l c u l a t i o n s . T a b l e 4.2 g i v e s the estimated e r r o r s f o r the power s p e c t r a . TABLE 4.2 Frequency range i n cps 0.001-0.0025 0.007-0.012 0.03 -0.05 0.018-0.023 R e s o l u t i o n i n cps 0.0083 0.0033 0.0066 0.0033 Length of Record 21600 sees 5400 " 4200 " 5400 " 80% range XI.212 XI.862 XI.972 XI.862 Because of the l i m i t e d s e t s of v a l u e s of power s p e c t r a f o r d i f f e r e n t f r e q u e n c i e s average r e s i s t i v i t y v a l u e s c o u l d not be c o n s i d e r e d i n the c a l c u l a t i o n of probable e r r o r s . Tukey 80% range v a l u e s (Table 4.2) were c o n s i d e r e d t o be the probable e r r o r s i n the apparent r e s i s t i v i t y c a l c u l a t i o n s . Moreover i t has been shown i n s e c t i o n 1.3 that t a k i n g the average of power spectrum estimates i s not f u l l y j u s t i f i e d . I f the magnetic and e l e c t r i c r e c o r d s are e q u a l l y n o i s y the e r r o r s i n the r e s i s t i v i t y c a l c u l a t e d from power s p e c t r a should be n u l l i f i e d a c c o r d i n g t o formula 4.13. In the present -77-analysis the e l e c t r i c records were found to be more or less white i n the narrow frequency bands used while the magnetic records were f a i r l y noisy. Hence one would expect the errors in 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 to be as great as those i n the computation of the power spectra of the magnetic records. -78-CHAPTER V JUSTIFICATION OF THE ASSUMPTIONS IN THE MAGNETOTELLURIC METHOD 5.1 General In the conventional magnetotelluric analysis as developed by Cagniard an apparent r e s i s t i v i t y f^, a scalar function of frequency, i s computed from experimental data obtained from simultaneous measurements of the fluctuations of the Earth'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 plotted as a function of period T and the r e s u l t -ing graph compared with a set of t h e o r e t i c a l master curves based upon simple models of a layered Earth. A great v a r i a -tion i n the apparent r e s i s t i v i t y thus computed has been obtained by some authors ( E l l i s 1962, Garland and Webster 1960) who explain their r e s u l t s on the grounds that the assumptions underlying the magnetotelluric method may not be r e a l i s e d . 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 could be due to the e f f e c t of the source or to subsurface inhomogeneity. To investigate these p o s s i b i l i t i e s i t i s necessary to make measurements simultaneously over a homogeneous and an inhomogeneous media. An attempt to study - 7 9 -such effects has ben made ( E l l i s 196X), but no conclusive results were obtained. In the present chapter no discussion is given of the possible origins of micropulsations of the geomagnetic f i e l d , but the validity of the different assumptions made by Cagniard and followed in the present work w i l l be reviewed. Cagniard and Tikhonov in 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 J W*. (2) The horizontal space variations of the magnetic f i e l d are negligible compared to vertical variations, i.e., a plane electromagnetic wave is incident upon the Earth. ( 3 ) The vertical component of the magnetic f i e l d is negligible compared tp the horizontal component for a horizon-t a l l y s t r a t i f i e d Earth. The above assumptions are based on world wide character-i s t i c s of geomagnetic variations. To judge the admissibility of these assumptions i t is 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 British 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 validity of Cagniard's and Tikhonov's assumptions. On the other hand i t is possible to -80-judge their validity for a particular locality i f the varia-tions in the local 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 deter-minations are made. Wait (1954) and Price (1962) have questioned the existence of plane electromagnetic waves giving rise 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 validity of the different assumptions at the stations where re s i s t i v i t y determinations by Cagniard's method were made. The three assumptions mentioned above were tested in the following manner. 5.2 Harmonically varying fields In the geophysical literature (e.g. Chapman and Bartels 1951) the assumption of harmonically varying fields i s commonly made. To test the validity of this assumption in the present investigation the records were examined for events which appeared more or less sinusoidal in character and many such examples were found. A visual correlation analysis i s based solely on this type (Fig. 5.1) of event. Such a characteristic of the events has also been shown in 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 is thus f e l t reasonable to FIG. 5.1 TYPICAL E AND H SINUSOIDAL M 1 C R O P U L S A l i O U S -82-assume that the f i e l d is 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 in magnetotelluric investigations taken simul-taneously a l l over the world, i t has not been possible in the past to judge the validity of the existence of plane electro-magnetic waves. Experimental investigations over short distances have given positive as well as negative results (Duffus, Kinnear, Shand, and Wright 1962). To study the spacial distribution of geomagnetic micropulsations i t i s essential to make observations simultaneously at several stations located in a geologically undistrubed area. In the past some observa-tions have been made in geologically disturbed regions by a few investigators. Although a great variation in the character of the geomagnetic variations was observed on com-paring the results from a geologically disturbed region with those from an undisturbed region (1750 km apart, Duffus et al 1962), the time of onset of different geomagnetic variations was found to be the same. A uniform trend in the power spectra of the electric f i e l d has also been obtained between Ashkhabad and T b i l i s i in the U.S.S.R., Ralston in Canada and Austin and Littleton in the U.S.A., (Horton and Hoffman, 1962) from electric measurements obtained at the above stations over an interval of 2 1/2 years. This may indicate worldwide -83-c h a r a c t e r i s t i c s of the geomagnetic v a r i a t i o n s . Whether such a worldwide c h a r a c t e r i s t i c can be e x p l a i n e d on the assumption of the e x i s t e n c e of e l e c t r o m a g n e t i c waves, has been the s u b j e c t of d i s c u s s i o n between s e v e r a l authors. Some i n v e s t i g a t o r s (Wait 1954, N i s h i d a 1962) have questioned the e x i s t e n c e of these waves because of the extremely long wave len g t h s r e q u i r e d to e x p l a i n such phenomena. For a p e r i o d of 100 seconds, a wave l e n g t h of 3 x 10^ km 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 of the magnetic f i e l d a l l over the E a r t h . H e i r t z l e r (1962) has shown s c h e m a t i c a l l y the e x i s t e n c e of such waves. In the present i n v e s t i g a t i o n the v a l i d i t y of the assumption r e g a r d i n g the u n i f o r m i t y of the geomagnetic f i e l d over s h o r t d i s t a n c e s , has been judged by s t u d y i n g s e v e r a l events 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 d e t a i l s of such an a n a l y s i s are g i v e n i n s e c t i o n s 4.2 and 4.3. F i g . 5.2 shows a p l o t of the amplitude of the n o r t h - s o u t h (KL^) and v e r t i c a l (Hz) magnetic components at each s t a t i o n f o r s e v e r a l events of 30 second p e r i o d . The c o n s i s t e n c y of the amplitude of both components suggests a plane wave f o r these p a r t i c u l a r events, at l e a s t to a f i r s t approximation. Data used i n the c o n d u c t i v i t y a n a l y s i s were l a r g e l y l i m i t e d t o t h i s type of event. As an a d d i t i o n a l check on t h i s assumption power s p e c t r a at a l l s i x s t a t i o n s c o v e r i n g an i n t e r v a l of one and a h a l f hours d u r a t i o n on August 18 were computed f o r the north-south (H ) and v e r t i c a l (H ) magnetic f i e l d components. The - 8 4 -1.5 2 3 4 5 6 STATION N U M B E R * FIG 5.2 L A T I T U D E DISTRIBUTION OF AMPLITUDES OF NORTH - SOUTH (H x ) AND VERTICAL ( H-) MAGNETIC COMPONENTS FOR E V E N T S OF 30 S t C PERiOD 8 6 4 2 00' 8 6 4 2 10-8 6 4 2 I-8 6 4 2 01-8 6 4 2 )0I-8 6 4 2 8 5 -AUG 18 61 6 TIME 1009 to 1106 5 \ 5 '"T 1 1 I i I I I I | """I I "r_' I 1 T: l" I I I ""• 'I "' I T T T t " [ 2 4 6 8 001 2 4 6 8 01 2 4 6 8 POWER DENSITY Vs FREQUENCY AT THE SIX FOR N O R T H - S O U T H MAGNETIC COMPONENT - 8 6 -100-8; 6 : 0 000014 1 1 — i 1 1 — 1 1 — i i 0001 2 4 6 8001 2 4 6 8 01 2 4 6 8 1 FREQUENCY IN CPS > FIG 5 4 POWER DENSITY Vs FREQUENCY AT THE SIX STATIONS FOR VERTICAL MAGNETIC COMPONENT -87 coherency of H x and H z for stations #1 through 5 relative to station #6 were computed. The results of such calculations are given in Appendix A. Fig. 5.3 and Fig. 5.4 show the power spectral density of HL^  and H z for the different stations. The power spectral density curves for H x (Fig. 5.3) have peak values at about the same frequency at a l l six stations but for the vertical magnetic f i e l d component (Fig. 5.4) their peak values are obtained at slightly different frequencies. The shift of the peaks in the H z spectral density curves (Fig. 5.4) is probably due to the presence of more harmonics at the southern stations than at the northern. Such a shift 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. Similar power spectral computations at a l l stations both for H x and H z were made from the records of August 19th. Characteristics of the power spectral peaks for H x and H z were found to be similar to those shown in Fig, 5.3, and Fig. 5.4, except that their absolute values were different. The results of such computations are also given in Appendix A, Peaks in the coherency versus frequency plots generally coincided with peaks in the spectral density plots as i s illustrated in Fig. 5.5. The degree of coherency at these peaks did change however from station to station. These peaks could shift 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: 18 AUG., 1961 LOCAL TIME: 1009 - 1106.5 -89-coherency peaks simultaneously at a l l stations. The signal giving rise to these universal peaks should then approximate to a plane wave. To il l u s t r a t e this point, spectral densities for both H x and H z were plotted at each station for coherency peaks at 30 second period (Fig. 5.6). The resulting curves are very similar to a plot of amplitude against station (Fig. 5.2) and thus support a plane wave hypothesis for this frequency band on these occasions. From Fig. 5.2 and Fig. 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 is 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 later, a high value of H z can be expected at this station. The plot of spectral density versus stations (Fig. 5.6) shows a marked increase in the values at station #1 although such a trend is not so pronounced at this station in the plot of amplitude versus stations (Fig. 5.2). No satisfactory explanation was found for such a difference between the two curves. Restricting 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 variation of the magnetic f i e l d for periods greater than 30 seconds, only the visual correlation method of analysis could be used. Power spectral values for periods longer than 30 seconds could not be - 9 0 -FIG. 5.6 LATITUDE DISTRIBUTION OF POWER DENSITY FOR H x AND H z FOR EVENTS OF 30 SEC. PERIOD - 9 1 -used since i t was extremely d i f f i c u l t to obtain the same length of usable record at a l l stations simultaneously. The same -technique as described i n section 4 . 2 to obtain peak to peak values of d i f f e r e n t events simultaneously at a l l stations, was used. F i g . 5 . 7 shows a plot of the amplitude of and H Z at each s t a t i o n for several events of 9 0 second period, obtained by a v i s u a l c o r r e l a t i o n analysis. Except for the higher values of HJJ. on August 2 1 , at 1 6 0 6 , at st a t i o n #5 and on August 2 2 , at 1 5 1 4 , at st a t i o n # 3 , the fi g u r e shows a consistency i n ampli-tude of both components for 9 0 second periods. Similar analyses for periods longer than 9 0 second could not be made because of the absence of these longer periods at the southern stations. The existence of a plane electromagnetic wave giving r i s e to consistent amplitudes of geomagnetic micropulsations over a distance of 6 0 0 km may be judged from a s l i g h t l y d i f f e r e n t angle. The computation of apparent r e s i s t i v i t y (eq. 1 . 1 ) from the r a t i o s of the amplitudes of orthogonal pairs of e l e c t r i c and magnetic f i e l d values i s based s o l e l y on the assumption of the existence of plane electromagnetic waves. Least scattering of the points i n a plot of apparent r e s i s t i -v i t y versus period should be obtained when only those events which give consistencies i n amplitudes over a horizontal d i s -tance of 6 0 0 km or more are considered. This i s true only for a homogeneous i s o t r o p i c medium. In the present - 9 2 -21-8-61 1130 + - 2 1 - 8 - 6 1 1606 22-8-61 1514 - — 21-8 61 1125 22-8 -61 1 3 5 2 — X ~ 22-8-61 1113 21-8-61 1107 I s 3 4 5 STATION NUMBER 6 N f I G . 5 . 7 LATITUDE DISTRIBUTION OP AMPLITUDES OF NORTH-SOUTH (Hx) AND VERTICAL (Hz) MAGNETIC COMPONENTS FOR EVENTS OF 90 SEC. PERIOD -93-r investigation such events were considred 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. Minimum scattering in the apparent r e s i s t i v i t y ( f a ) versus period (T) p l o t s , at stations #3 and 6 for these periods was obtained. At station #3 where apparent r e s i s t i v i t i e s were calculated from power spectral estimates, points of minimal scattering i n the fa versus T plot correspond to frequencies where maximum coherency was obtained at a l l stations (section 6.2). This supports the assumption of the existence of plane electromag-netic waves. 5.4 Relative magnitudes of the v e r t i c a l and horizontal  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 Earth 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 zero when a plane electromagnetic wave impinges v e r t i c a l l y on i t . Workers i n the U.S.S.R. have recently reported very low v e r t i c a l components over the sea (Zhigalov 1961), confirming t h i s conclusion. By observing H z over land and near the sea Duffus et a l (1962) found higher values of H z near the sea coast. F i g . 5.2 and F i g . 5.7 show the variations of H z along the si x stations for 30 second and 90 second periods. It i s to be noted from these figures that H z i s more or les s constant between stations #6 and 2. In addition, the value of H z/H x -94-does not exceed 0.25. Similar characteristics are also obtained from Fig. 5.6. At Meanook and Beiseker where resis-t i v i t y determinations were made using Cagniard's method, the values of H z for periods longer than 90 second were computed from different data for the magnetotelluric analysis. Power spectral densities were computed for H z and H x at Beiseker. The ratios of the power density of H z to that of KL^  for the frequencies used in the calculations of apparent r e s i s t i v i t y are plotted in Fig. 5.8. It i s clear from this figure that for periods as high as 1000 seconds the value of the ratio does not exceed 0.3. This suggests that the vertical magnetic f i e l d at Beiseker is negligible compared to the horizontal f i e l d at a l l periods which have been used in the r e s i s t i v i t y calculations. An estimate of the vertical magnetic f i e l d at Meanook for periods greater than 90 seconds was made by a visual correlation analysis. Values of the Hz/Hx ratio for periods up to 200 seconds did not exceed 0.3. Tellurograms and magnetograms from Meanook were used to obtain values of Ey/Hx for periods greater than 200 seconds. Recordings of H z were not made on rapid magnetograms, and hence values of H z for periods greater than 200 seconds could not be obtained for this station. Niblett (1960) has given an average value of Hz/Hx for periods greater than 100 second as 0.56 for this station. This value is higher than that found at Beiseker. It is probably due to the location of Meanook in the subauroral 0.4 © 0.3 © © © © © Z_ X 0.2 © OG 0.1 0 © © © i co i 10 - J 1 1 — I — _i i i i i i L 6 8 100 2 4 6 8 1000 PERIOD IN SECONDS > Fig. 5-8 Ratio of vertical ( H 7 ) to horizontal ( H v ) magnetic field components, as a function of period at Beiseker. - 9 6 -zone where m a g n e t i c a c t i v i t y i s s u b j e c t e d t o f a i r l y r a p i d v a r i a t i o n s a l o n g t h e m a g n e t i c m e r i d i a n . From t h e above d i s c u s s i o n i t i s c l e a r t h a t t h e a s s u m p t i o n s made by C a g n i a r d i n h i s method and f o l l o w e d i n t h e p r e s e n t i n v e s t i g a t i o n a r e r e a s o n a b l e f o r t h e 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 greatest problem encountered i n a l l geophysical methods i s the interpretation of the data. Once the data have been analysed and corrected f o r relevant variables, the pro-blem i s reduced to the determination of the d i f f e r e n t physical parameters (or parameter) involved i n the method. In most methods the interpretation of the data involves a comparison of a f i e l d curve with a set of master curves, both drawn to the same scale. These master curves are th e o r e t i c a l curves for simple geological structures. When the closest f i t of the f i e l d curve with a master curve i s obtained the parameters of the mathematical model, such as r e s i s t i v i t y , layer depths, etc., that are assumed f o r the model may be used as estimates of the r e a l Earth parameters for the area where the observa-tions were made. Such an i n d i r e c t approach to the interpreta-t i o n of geophysical data has led to some ambiguous r e s u l t s i n most geophysical methods. The degree of ambiguity i s reduced by using d i r e c t methods of int e r p r e t a t i o n . Roy (1962) has recently given a b r i e f account of the ambiguities involved i n - 9 8 -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 d a t a . The i n d i r e c t method i s used t o determine s u b s u r f a c e r e s i s t i v i t y from m a g n e t o t e l l u r i c data. Apparent r e s i s t i v i t y ( P a) and phase angle ( Q ) are drawn as f u n c t i o n s of the p e r i o d on a l o g a r i t h m i c s c a l e ( F i g s . 6.1a and b ) . The determi-n a t i o n of p r o f i l e parameters from m a g n e t o t e l l u r i c soundings i s based on a comparison between these t h e o r e t i c a l master curves and experimental curves. In p l o t t i n g t h e o r e t i c a l magneto-t e l l u r i c sounding curves, the t h i c k n e s s (b^) and r e s i s t i v i t y ( Pj^ ) of the u n d e r l y i n g l a y e r s are c u s t o m a r i l y expressed r e l a t i v e t o the t h i c k n e s s (b^) and r e s i s t i v i t y ( Pj) of the f i r s t l a y e r . The r a t i o of apparent r e s i s t i v i t y ( P^) t o the r e s i s t i v i t y ( Pj) of the f i r s t l a y e r , i n the case of a t h r e e -l a y e r e d medium, f o r example, may be w r i t t e n as i where A = , V * Aa//>,and T i s the p e r i o d of the o s c i l l a t i o n s . The v a l u e s of ? 1 and h± i n the f i r s t l a y e r are taken as u n i t y i n the computation of the master curves which makes i t p o s s i b l e t o use the same s e t of 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 urves i n d i f f e r e n t r e g i o n s . V l a d i m i r o v (1961) has d i s c u s s e d the s i g n i f i c a n c e of the c h o i c e of o r i g i n i n p l o t t i n g the master curves, and suggested t h a t the o r i g i n i n the P a versus T p l o t should be taken at the p o i n t T = l , P a = l . Fig. 6.1(a). Magnetotelluric two layer standard r e s i s t i v i t y curves. (After Yungul, 1961). -100-Fig. 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 possible to determine the thick-ness of the f i r s t layer d i r e c t l y from the curve as w i l l be shown i n subsequent sections. Cagniard (1953) and Tikhonov (1956) published a set of master curves for a two layered Earth while Yungul (1961) and Kolmakov (1961) have published a set for a three layered Earth. These curves make i t possible to determine the r e s i s t i v i t y and thickness of subsurface s t r a t a . Master curves for more than three layers have not been constructed. The experimental curve (plotted on the same scale) i s placed over the set of master curves and by means of t r a n s l a t i o n a l motions, a match between the experimental curve Pa(T) and a p a r t i c u l a r master curve obtained, while maintaining the p a r a l l e l i s m of the respective coordinate axes. The ordinate P a 3 1 of the master curve on the experimental curve determines the r e s i s t i v i t y of the f i r s t layer. The v e r t i c a l l i n e T «* 1 (Fig. 6.1a) gives a p a r t i c u l a r value of Ti on the experimental T-axis. The ,thickness of the f i r s t layer i s determined 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 P1 T 1 Q/10 (6.3) -102-The parameters of the second l a y e r are ^2 = M-l P i > (6.4) where p., the modulus of the t h e o r e t i c a l curve i s d e f i n e d as Thus the procedure f o r i n t e r p r e t i n g P a curves i s p r a c t i c a l l y the same as the w e l l developed method f o r i n t e r p r e t i n g curves o b t a i n e d i n d i r e c t c u r r e n t v e r t i c a l e l e c t r i c a l soundings. Cagniard (1953) gave the f o l l o w i n g e x p r e s s i o n f o r the d e t e r -m i n a t i o n of the depth to the second l a y e r when p o i n t A ( F i g . 6.1b) i s seen through t r a n s p a r e n t paper b e a r i n g an experimental curve whose a b s c i s s a has the numerical v a l u e of T^ seconds. Equation (6.5) may be w r i t t e n i n the form (6.5) 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 s c a l e , e quation (6.6) shows the a d v i s a b i l i t y of p l a c i n g the o r i g i n at a -103-distance of log 2.53 to the l e f t of A (Vladimirov, 1961). Hence the vertical line f - 1 should be read on the experi-mental T axis. Phase curves in magnetotelluric soundings are interpreted in a similar manner except that the motion of translation is carried out only along the horizontal axis with superposition of the horizontal axes of the theoretical and experimental curves. Furthermore, the two translations (of the Pa and Q curves) which are to be executed parallel to the horizontal axis must be identical. In addition, the r e s i s t i v i t y of the f i r s t layer must be known. The dependence of the inter-pretation of phase measurements on the interpretation of amplitude measurements makes them less significant in an inter-pretation of magnetotelluric data, although geoelectric profile may be determined more reliably when both the P a curve and the 0 curve are interpreted. 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 reliable. Kolmakov (1961) has also discussed the lesser importance of phase measurements in an interpretation of magnetotelluric data for different geoelectric sections. 6.2 Determination of the distribution 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-could be made at the following three stations only (1) Meanook, (2) Beiseker, (3) Cardston. Because of instrumental d i f f i c u l t i e s and the lack of data for periods longer than 100 seconds i t was not possible to carry out such an analysis at the other stations. Moreover because only li m i t e d lengths of the records obtained from the 12 days recording were usable the analysis i s based on a rather small amount of data. (1) Meanook. At st a t i o n #6, Meanook, the records were analysed by the v i s u a l c o r r e l a t i o n method (section 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 could be correlated v i s u a l l y on the east-west e l e c t r i c and north-south magnetic records. Values of E /H x were grouped together according to the i r period and averaged. Band widths of 5 seconds f o r shorter periods and 60 seconds for longer periods were used i n the analysis (section 4.6). The number of observations within a group varied, but usually lay between 10 and 15. For some periods i t was not possible to obtain more than one value and hence only s i n g l e values for those periods were available for interpretation. Because of instrumental c h a r a c t e r i s t i c s and high speed recording i t was not possible to pick up events with periods longer than 200 seconds. Magnetograms and tellurograms -105-TABLE 6.1 i period Mean values O f Ey/Hljj (Mv/Km.«y) Mean values of P a (ohms meter) S.D.M, of Pa sees 9 1.95 6.8 ±1.2 15 1.52 6.9 ±0.0 20 1.80 13.0 ±0.4 23 1.78 14.5 ±1.6 30 1.85 20.5 ±3.5 35 1.92 25.7 ±1.1 40 1.95 30.4 ±0.1 45 1.97 34.9 ±0.0 52 1.91 38.0 ±0.0 60 2.14 55.0 ±8.7 65 1.72 38.4 ±1.1 72 1.54 34.1 ±0.0 84 1.98 65.8 ±0.0 88 1.82 58.3 ±6.3 95 1.98 74.5 ±3.2 102 1.80 66.1 ±10.0 119 1.71 69.50 ±3.5 125 1.80 81.1 ±0.0 156 1.64 83.9 ±0.0 195 1.42 78.89 ±0.0 348 1.43 142.00 ±26.6 480 1.38 182.4 ±2.7 580 1.33 204.2 ±45.5 652 1.33 211.9 ±46.1 780 1.29 259.00 ±0.0 1170 0.94 208.3 ±0.0 1260 0.86 189.0 0.0 1530 0.77 180.0 0.0 3330 0.51 173.2 0.0 3600 0.60 259.2 0.0 3960 0.42 134.6 0.0 -106--107-recorded at the same time at the Dominion Observatory Station at Meanook were used to obtain values of Ey/H x r a t i o s for periods longer than 200 seconds. The use of tellurograms i n the present investigation i s not f u l l y j u s t i f i e d because of the difference i n electrode separation i n the two i n s t a l l a t i o n s . Our electrode separation was 0.61 km while that of the Dominion Observatory was 1.60 km. Hence the use of these tellurograms in the present investigation i s only j u s t i f i e d i f a marked change i n r e s i s i t i v y t over 1.60 km does not e x i s t at the Observatory. The records from the Dominion Observatory were also analysed by the v i s u a l c o r r e l a t i o n method. The scatter i n the i n d i v i d u a l values of the r a t i o s within a group i s expressed as the standard error of the mean. Averaged values of Ey/IL^ r a t i o s f o r d i f f e r e n t periods are given i n Table 6.1 and the information displayed i n the Ey/IL^ versus } plot i n F i g . 6.2. According to N i b l e t t (1960), i t should be possible to f i t such a plo t by a set of straight l i n e s . If the average or apparent r e s i s t i v i t y Pa, i s con-sidered to be constant, then from the r e l a t i o n s h i p 2 Pa - 0.2T / x 1 I -108-where B is a constant and a plot of E „ / H „ versus -== should y x v^T yield a straight line through the origin with slope B <*» J 5 P& . In cases where i t is d i f f i c u l t to f i t one straight line, through many points, a set of straight lines with different values of P may be f i t t e d to the data. A more general form of equation (6.7) i s used in such cases, viz. 2 E ZJL Hx A + —^— (6.8) T A and B are constants which are determined numerically for individual lines. In the present investigation a f i t of three straight lines was found to be s t a t i s t i c a l l y j u s tified. For Meanook, Ey/Hx was plotted against (Fig. 6.2) in order to compare the results with those obtained by Niblett (1960). The straight lines in this figure have been drawn using a least square analysis for the equation E /YL^ - A r + B r/ v/T where and where A r = Y - B X (6.10) Y i " Ey/Hx > Vi = Y ± - Y x. - -4= , u. - x. - x x \p£ ' x i * 4 Z xi and Y - i £ Yi -109-The d e t a i l s of such an analysis are given i n Appendix B. The equations obtained are for AB for BC E„ B H " Al +7?" ( 0 , 1 5 ^ T '^04> - x \ T r " and for CO E„ B _ Z = A 2 + — 1 (.04 ^ T"^ ^.134) -£ . A 3 + — 2 (.134 ^ T"^ ^ .264) H x \ T T the constants determined from equations (6.9) and (6.10) are A1 « +0.00 B1 - +33.400 A 2 - +0.36 ,B2 - +7.264 A 3 - +25.54 B 3 - -3.776 If an Earth consisting of three homogeneous layers i s assumed then each straight l i n e i n F i g . 6.2 represents a layer of di f f e r e n t r e s i s t i v i t y (Niblett, 1960). To judge the 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 with d i f f e r e n t parameters were considered. The impedance (E y/H x or E x/H y) values f o r a three layer Earth model were computed using r e l a t i o n s given by Kolmakov (1961). -110-2,T w 2 - y - 2 Z (6.12) w h e r e and X Y S U A U [jBR + P ] + S T [ B P + R] + Q R + Bpj - BGT A U + SBj A S [ B R + P ) + U [ R + B P ] - A Q . T A T [ B R + P ] + Q [ B U + A S ] 277 A,, i/7fF \ ferF J - U l -an d P. The impedance v a l u e s were computed f o r a t h r e e l a y e r e d E a r t h model having the f o l l o w i n g parameters 100 10 and the r e s u l t s are shown i n F i g . 6.3. The s c a l e of F i g . 6.3 i s too s m a l l t o show any e f f e c t w i t h i n the frequency band (.001 t o .1 cps) g e n e r a l l y used i n m a g n e t o t e l l u r i c s and thus another f i g u r e on a l a r g e r s c a l e was drawn f o r t h i s frequency band. F i g . 6.4 shows a p l o t of (E/H) r a t i o s as a f u n c t i o n of frequency. The p o i n t s i n t h i s f i g u r e can b e s t be f i t t e d by t h r e e s t r a i g h t l i n e s . I f a l l the p o i n t s up t o a frequency of 0.62 cps were p l o t t e d i n F i g . 6.4, the number of s t r a i g h t l i n e s would have i n c r e a s e d as can be seen i n F i g . 6.3. Since f r e q u e n c i e s above .1 cps are g e n e r a l l y not used i n magneto-t e l l u r i c s , a t t e n t i o n has been c o n f i n e d t o f r e q u e n c i e s below t h i s f i g u r e . The f i t t i n g of the p o i n t s i n F i g . 6.4 by t h r e e s t r a i g h t l i n e s may i n d i c a t e the presence of three l a y e r s but whether each l i n e r e p r e s e n t s a l a y e r i s not c e r t a i n . The EARTH MODEL -114-p o i n t s B and C i n d i c a t e sudden changes i n the s l o p e s of the l i n e s AB and BC. To determine whether these p o i n t s do i n f a c t correspond t o depths at which a sudden change i n r e s i s t i v i t y o c c u r s , the f o l l o w i n g e x p r e s s i o n was used t o c a l c u l a t e the depth of p e n e t r a t i o n at p o i n t s B and C. T^ , A Z - — (AT + B) (6.13) A and B are c o n s t a n t s g i v e n by equation (6.8) and T i s the p e r i o d i n seconds. For the l i n e AB i n F i g . 6.4, we have B =» 110 , A =» 0 , T B =• 360 seconds Z = 31.4 km. The a c t u a l v a l u e of Z = h 2 + h]_ = 30 + 1 = 31 km. These two v a l u e s of Z agree w i t h i n the order of accuracy of the measure-ments. S i m i l a r l y by u s i n g equation (6.7), we have O 110 f a _____ oi 22 ohm meters a 5 The a c t u a l value of i s lOJL'wv. The d i f f e r e n c e between these two v a l u e s of 1°^ d o e s not a l l o w us to use the s l o p e of the s t r a i g h t l i n e s f o r the c a l c u l a t i o n of r e s i s t i v i t y at d i f f e r e n t depths. Again from l i n e BC i n F i g . 6.4, we have »115 B - = ~ = 33.3 . A - .155 , T = 122.5 o c Z = 12.5 km. In the actual model this depth corresponds to a plane in the second layer. Hence the change in the slope of the line BC compared to that of the line CD does not correspond to a new layer. The use of the point C in the interpretation of magneto-t e l l u r i c data w i l l lead to ambiguous results. Impedance values at different periods were scaled off from Cagniard's master curves of apparent r e s i s t i v i t y versus period to judge the validity of Niblett's method for the determination of r e s i s t i v i t y at different depths. The result-ing information is plotted in Fig. 6.5. In this figure the points are f i t t e d by two straight lines. The third line (dotted) shows similar effects for frequencies higher than .1 cps as shown in Fig. 6.3. The point F in Fig. 6.5 corres-ponds to point B in Fig. 6.4. From the straight line EF we obtain A = 0 , B = 140 , TF = 285 seconds and hence Z 2i 31.5 km . No discontinuity in 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 in the actual model. .6 « .4 X E •S .3 CM Ui|x -2f-ift h, = I km pt - IO ( m F i g . 6.5. (E/H) v s frequency f o r a two l a y e r e d E a r t h model. .01 .02 .03 .04 .05 f in 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 Niblett's method. Even though Niblett's method can not be used to delineate shallow r e s i s t i v i t y strata i t may be used to delineate deeper r e s i s t i v i t y strata. Such a characteristic 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 strata. 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 third layer, the impedance values are influenced by the parameters of a l l three layers. Such relationships are also evident from Fig. 6.14, For extremely long periods the impedance value (eq. 6.11) reduces to z , (o ) | 2 - A ( M 3 2 T where Hence Niblett's assumption that the impedance and period can be linearly related is only true for very long periods. The -118-l i m i t i n g value of the period when t h i s assumption i s v a l i d may be found for i n d i v i d u a l models by s u b s t i t u t i n g values of the d i f f e r e n t parameters i n equation (6.11). To interpret the whole geological section i t i s e s s e n t i a l to use a method which can d i s t i n g u i s h shallow as well as deep s t r a t a . This makes i t necessary to use Cagniard's curve matching method. Ni b l e t t ' s method has no advantages over t h i s method. The depth to the t h i r d layer at Meanook from F i g . 6.2 was calculated using equation (6.13) and was found to be 117.8 km. This value does not d i f f e r much from that given by the curve matching method (91.2 km, section 6.3). Values of the E„/H„ r a t i o s thus obtained were inserted i n equation (6.7) and apparent r e s i s t i v i t i e s P a computed as a function of period. The apparent r e s i s t i v i t i e s so obtained were grouped together according to th e i r period i n the same way that the E y/H x r a t i o s were grouped. Standard errors of the mean were calculated to show the scatter i n i n d i v i d u a l values. Average values of apparent r e s i s t i v i t y together with the standard errors of the mean are given i n Table 6.1. Average apparent r e s i s t i v i t i e s are plotted as a function of period i n F i g . 6.6. R e s i s t i v i t i e s and depths to the d i f f e r e n t formations were determined by matching the experimental curve to the appropriate master curve, F i g . 6.1(a), drawn by Yungul (1961). A r e s i s t i v i t y of 5.5 ohms was obtained for the top layer. (The r e s i s t i v i t y of t h i s layer obtained from a single 52 300 CD +-<L> E i E o 100 >-> c/j 30 CO LU c r 10 L U cr < Q_ Q_ < 1 + — — o 1 o A L B E R T A O P E R A T I O N D A T A + M E A N O O K O B S . D A T A I 1 i M I 10 30 100 300 1000 3000 10,000 PERIOD T , seconds FIG. 6.6 APPARENT RESISTIVITY vs. PERIOD STATION #6 , MEANOOK, ALBERTA -120-well log in the area l i e s between 5 and 10 ohms.) The experi-mental curve showed the best match with a master curve for p.-^  = 200. The points P-^  and T^ (shown by arrows in Fig. 6.6) were obtained by curve matching (section 6.1). The resis-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 respec-tively. Such a discontinuity in r e s i s t i v i t y corresponds to the Precambrian basement. No such discontinuity was observed by Niblett (1960)j Evidence for the existence of such a discon-tinuity in this area i s summarised in 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 third layer long period events are required. The determination of the constants of the third layer at Meanook are considered together with those at Beiseker (section 6.3). Phase measurements between E y and H x events for different periods were not used in the present investigation because of the d i f f i c u l t y in obtaining their true values from a visual correlation analysis. A few E and events of the same period were analysed to find their phases. A variation up to i 20° was observed and hence they could not be used in the r e s i s t i v i t y analysis. (2) Beiseker. The values of the spectral density of the electric and magnetic records together with the degree of coherency and phase differences between them in narrow -121-TABLE 6.2 Record P e r i o d No. (sees) ( E y / H x ) 2 (mv/km.7)^ P. (ohm meters) (Coh)' \R1 2 (degrees) M o d i f i e d & A 25 2.1 10.6 0.3 38.5 38.5 B 25 2.8 14.7 0.7 -54.9 125.1 B 28.5 3.3 19.2 0.8 -71.2 108.8 A 28.5 1.2 6.9 0.6 74.0 74.0 A 33.3 1.4 9.8 0.3 103.0 103.0 B 33.3 2.8 19.7 0.5 -105.5 74.5 E 43.4 4.1 36.8 0.6 -107.9 72.1 E 50.0 3.8 40.0 0.3 -81.9 98.1 E 52.6 3.8 42.2 0.2 -81.2 98.8 E 55.5 3.8 43.4 0.1 -82.7 97.3 C 71.4 4.2 61,4 0.8 -69.8 110.2 C 76.9 4.7 74.4 0.9 -69.6 110.4 C 83.3 4.5 78.1 0.8 -69.5 110.5 D 83.3 2.4 41.1 0.8 -160.0 20.0 C 90.9 3.9 73.3 0.9 -67.3 112.7 D 90.9 2.5 47.3 0.9 -176.3 3.7 C 100.0 3.2 65.5 0.9 -65.1 114.9 D 100.0 2.3 48.7 0.8 165.0 165.0 D 111.0 2.2 51.7 0.8 150.0 150.0 D 125.0 2.1 55.8 0.7 140.3 140.3 D 133.0 2.1 58.4 0.7 97.8 97.8 F 400.0 0.7 55.5 0.7 9.2 9.2 F 500.0 0.4 42.5 0.8 9.6 9.6 F 660.0 0.3 35.8 0.8 5.8 5.8 F 1000.0 0.2 33.3 0.7 11.1 11.1 -122-TABLE 6.3 Record Period < E - / % f ) 2 9 < o h m (Coh) 2 & Modified No. (sees) (mv7km',y) meters) \R\2 (degrees) 8 A 20.0 12.5 51.7 0.8 -104.2 75.8 A 22.2 10.2 47.0 0.8 -92.8 87.2 A 25.0 9.3 48.3 0.4 -84.1 95.9 A 28.5 8.1 47.5 0.2 -75.0 105.0 A 33.3 6.0 41.6 0.7 -94.9 85.1 E 43.4 5.2 46.8 0.4 36.4 36.4 E 50.0 4.4 45.7 0.3 48.3 48.3 E 52.6 3.8 42.0 0.3 61.0 61.0 E 55.5 3.4 39.8 0.3 62.4 62.4 C 71.4 27.8 411.0 0.8 -52.3 127.7 C 76.9 23.9 380.0 0.9 -43.4 136.6 C 83.3 20.2 348.0 0.9 -43.0 137.0 D 83.3 26.0 448.0 0.8 -125.5 54.5 C 90.9 17.4 328.0 0.9 -44.1 135.9 D 90.9 24.0 451.0 0.8 -166.0 14.0 C 100.0 16.8 346.0 0.9 -50.5 129.5 D 100.0 23.7 490.0 0.8 168.5 168.5 D 110.0 20.4 468.0 0.8 150.0 150.0 D 125.0 17.1 442.0 0.8 141.6 141.6 D 133.0 16.1 444.0 0.8 117.2 117.2 F 400.0 2.7 224.0 0.9 -80.4 99.6 F 500.0 2.1 218.0 0.9 -81.0 99.0 F 666.0 1.7 232.0 0.8 -80.1 99.9 F 1000.0 1.3 275.0 0.6 -78.1 101.9 -123-frequency bands are given in Appendix A. An examination of these values shows a wide spread in coherency within the pass band. To examine more carefully such variations, spectral density and the square of the coherency were plotted for (E y, H x) and (E x, Hy) pairs. Such variations are shown in Figs. 6.7 and 6.8. It i s evident that peaks in the coherency versus frequency plots coincide with peaks in the spectral density plot. Hence ratios of the spectral density of electric and magnetic records can not be used for the computation of apparent r e s i s t i v i t y at- frequencies where the coherency i s small. Attention was then restricted to the neighbouring frequencies of spectral peaks. Only those frequencies lying 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 electric and magnetic pairs, using equation (4.11). 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 electric components used in their calculation. The f i r s t category indicates a degree of coherency between 1.0 and 0.9, the second between 0.8 and 0.7 and the third between 0.6 and 0.5. Coherencies lower than 0.5 were not used since a great variation in r e s i s t i v i t y values for such coherencies was observed. The calculated r e s i s t i v i t i e s are given in tables 6.2 and 6.3. 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 6 7 POWER DENSITY S COHERENCY Vs STATION No 3 FOR E - W MAGNETIC COMPONENTS FREQUENCY AT ft N - S ELECTRIC - 1 2 5 -FIG 6-8 POWER DENSITY 8 COHERENCY Vs FREQUENCY AT STATION No 3 FOR N - S MAGNETIC S E-W ELECTRIC COMPONENTS -126-insufficient data and actual values for individual periods were used. The errors introduced in 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. Estimated errors are given in Table 4.1. Since identical lengths of records were used for both (Ey, Ex) and (Ejj., Hy) pairs, the errors are the same in both cases. Apparent r e s i s t i v i t i e s divided into the above three cate-gories are plotted against period in Fig. 6.9(a) and Fig. 6.10(a). A scattering of points between periods of 70 to 100 seconds is noticeable in both figures. A sudden jump in r e s i s t i v i t y values between periods of 50 to 70 seconds i s also noticeable in Fig. 6.10(a) although no such jump is found in Fig. 6.9(a). In addition the apparent r e s i s t i v i t y values calculated from E x/H y ratios were found to be higher than those calculated from Ey/Hx ratios. This fact and the existence of a break in the r e s i s t i v i t y curve (Fig. 6.10(a)) suggest the presence of anisotropic conductivity in this region (section 7.4). In drawing the curves, Fig. 6.9(a) and 6.10(a), the greatest emphasis was given to those points which had a coherency in the f i r s t category. Resistivity determinations at this station could only be made along an east-west profile because of the extreme scatter of points along the north-south direction (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 different interfaces. 100 a> E i I 30 t 1 0 1 i oQo o J + / s J * X 1 * V r- 1 • ' X X C O H E R E N C Y | R | 2 ° 0.7 to LO _ x 0.6 to 0.5 + 0.4 to 0.3 10 30 PERIOD T . 100 seconds 300 1000 FIG.6.9a A P P A R E N T RESISTIVITY vs. PERIOD STATION # 3 , BEISEKER ( FROM 4* o Q> <= PIG. 6 . 9(b) PLOT OP PHASE ANGLE BETWEEN E v AND H x v s PERIOD AT BEISEKER * o ON > T ) I > JO m 3J m co co < T) m o o co H CD m co m m 33 o x | m CO CD O O ZD c n A P P A R E N T RESISTIVITY p > ohm-meters _ o o ro " U m zo o o —I o co CO r o -c-r-co O O o CD O CD O ro cn O co O T lc k 1 \>° o V o o » o O 1 o /8 + X O pp -4± CT> CD —+• —+• —+• o o o p o p oo c n -si o O _E m o -< / / / / ro o \ \ J L - 6 Z I ~e ©-COHERENCY |Rf 0 * 0.7 to 1.0 X = 0.6 to 05 + « 0.4 to 0.3 J ! 1_ 4 5 6 7 8 100 2 PERIOD IN SECONDS 5 6 7 8 1000 F i g . 6.10(b), Phase angle betweem E^. and H y vs p e r i o d . -131-The r e s i s t i v i t y of the f i r s t l a y e r was found t o be 6.3 ohm meter by curve matching and between 5 and 10 ohm meter from lo g s of nearby w e l l s . The b e s t f i t f o r » 200 was obtained between F i g . 6.9(a) and F i g . 6.1(a). The o r i g i n of F i g . 6.1(a) (T =» 1, P A » 1) seen through F i g . 6.9(a), when the best f i t was obtained, i s marked by arrows i n F i g . 6.9(a). T h i s i n t e r p r e t a -t i o n suggests t h a t the second l a y e r at B e i s e k e r occurs at a depth of 2.6 km (equation 6.2) and has a r e s i s t i v i t y of 1200 ohm meter. These val u e s agree w e l l w i t h those at Meanook and the depth again i s r e a s o n a b l y c l o s e t o the known depth of the Precambrian basement. Va l u e s of (Ey/IL^) 2 and ( E x / H y ) 2 o b t a i n e d from the power s p e c t r a l e s t i m a t e s and used 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 y v a l u e s are p l o t t e d as a f u n c t i o n of frequency i n F i g . 6.11. The p o i n t s f o r the (E../H ) r a t i o s may be j o i n e d y x by t h r e e s t r a i g h t l i n e s but those f o r (E / H v ) 2 cannot because of the sudden jump i n ( E „ / H v ) 2 v a l u e s between .014 and..018 cps. x y o T h i s sudden jump i n the ( E x/H y) r a t i o i s p r o b a b l y due to the presence of an a n i s o t r o p i c r e s i s t i v i t y or an inhomogeneous body at B e i s e k e r as was a l s o i n d i c a t e d from the apparent r e s i s t i v i t y p l o t ( F i g . 6.10(a)). The depth to the t h i r d l a y e r determined from the s l o p e of the l i n e AB and the p e r i o d at the p o i n t B was found t o be 25.3 km. Phase angles between o r t h o g o n a l e l e c t r i c and magnetic r e c o r d s f o r the d i f f e r e n t f r e q u e n c i e s at which r e s i s t i v i t i e s X OA .005 .010 .015 .020 .025 .030 .035 .040 .045 >- f in cps F i g . 6 . 1 1 . ( E / f i ) 2 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 . -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 d u r i n g the power s p e c t r a l a n a l y s i s . These phase angles are g i v e n i n T a b l e s 6.2 and 6.3. An examination of them shows t h a t they are not c o n s i s t e n t w i t h i n r e c o r d s and vary g r e a t l y from day to day. The phase angles were computed by t a k i n g the tangent of the r a t i o s of the qua-spectrum to the co-spectrum, and hence can vary by 180°. Those phase v a l u e s which were out by 180° were c o r r e c t e d and these c o r r e c t e d v a l u e s are gi v e n i n the t a b l e s . A g r e a t v a r i a t i o n i n phase v a l u e s i s s t i l l found, and may be a t t r i b u t e d t o the poor magnetic r e c o r d s . A v a r i a t i o n of 10° t o 15° was obt a i n e d by examining fewer magnetic r e c o r d s . T h i s s t i l l does not e x p l a i n however the l a r g e v a r i a t i o n shown i n F i g s . 6.9(b) and 6.10(b). A p o s s i b l e e x p l a n a t i o n may be the presence of an inhomogeneity or a n i s o t r o p i c r e s i s t i v i t y i n t h i s r e g i o n , such as was i n d i c a t e d i n the present i n v e s t i g a t i o n ( s e c t i o n 7.4). Because of t h e i r v a r i a b i l i t y , phase angles c o u l d not be used i n a q u a n t i t a t i v e r e s i s t i v i t y i n t e r p r e t a t i o n but c o u l d be used f o r 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 . The trends of the curves i n F i g . 6.9(b) and F i g . 6.10(b) show the presence of more than two l a y e r s . A minimum and a maximum i n the two curves i s very s t r i k i n g . The phase angles f i r s t decrease w i t h p e r i o d (between 20-40 sec) then i n c r e a s e (between 40-100 s e c ) , and f i n a l l y decrease t o constant v a l u e s (between 100-1000 sec) as would be expected at higher p e r i o d s . The shape of the curves between 20-100 sec i n d i c a t e s the presence of a bed of higher -134-TABLE 6.4 Mean values of Mean period (sees) Mean E y/H x (mv/km.«y? POL* (ohm meters) S.D.M. of E y/H 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 that of the top bed. Such a c h a r a c t e r i s t i c was also found i n the apparent r e s i s t i v i t y curves, F i g . 6.9(a) and F i g . 6.10(a). The decrease i n the phase angles between 400 and 1000 sec shows the presence of a less r e s i s t i v e bed l y i n g beneath a highly r e s i s t i v e bed. The trends of the curves i n F i g . 6.9(a) and 6.10(a) for periods greater than 150 sec are remarkably s i m i l a r . The decrease i n apparent r e s i s t i v i t y for periods greater than 150 sec also indicates the presence of a less r e s i s t i v e bed below the 1100-1260 ohm meter r e s i s t i v i t y bed. The deter-mination of the constants for t h i s layer and those for Meanook, sta t i o n #6, are given i n section 6.3. (3) Cardston. The records were analysed by the v i s u a l corre-l a t i o n method (section 4.2). Events which could be correlated between the east-west e l e c t r i c and north-south magnetic records were considered and values of E y/H x were grouped together according to their period and averaged. A band width of 5 seconds was taken i n grouping the E /H x r a t i o s . The number of observations within a group varied, but usually lay between 10 and 15. Standard errors of the mean were calculated for each period. Average values of the E y/H x r a t i o s together with the standard errors of the mean are given i n Table 6.4. The r e s u l t i n g information i s displayed i n F i g . 6.12, where average Ey/EL^ r a t i o s are plotted against average periods. The scatter i n the i n d i v i d u a l values of the r a t i o s within a 40 50 6 0 70 PERIOD T , seconds 80 90 100 FIG. 6.12 H vs PERIOD STATION * l , CARDSTON 137-group was found to be q u i t e l a r g e and i s shown i n F i g . 6.12 by the standard e r r o r of the mean. No r e s i s t i v i t y e s t i m a t i o n s of s u b s u rface s t r a t a c o u l d be made because of t h i s g r e a t v a r i a t i o n i n the Ey/Hx r a t i o s w i t h i n i n d i v i d u a l groups, and the l a c k of data at p e r i o d s longer than 100 seconds. T h i s s c a t t e r -i n g of the E v/H r a t i o s i s perhaps due to the presence of an inhomogeneity a t Cardston. T h i s i s supported by the hig h v a l u e s of Z/Hx which were obtained at t h i s s t a t i o n ( F i g s . 5.2 and 5.6). G e o l o g i c a l l y Cardston l i e s i n a d i s t u r b e d zone. The presence of a major f a u l t b e l t at Cardston ( F i g . 2.2) may perhaps be co n s i d e r e d an inhomogeneity g i v i n g r i s e t o the s c a t t e r i n g i n the Ey/H x versus T p l o t ( F i g . 6.12). The presence of such an inhomogeneity 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 study undertaken by Douglass (1962) at t h i s s t a t i o n . To e s t i m a t e the e f f e c t of such an inhomogeneity, apparent r e s i s t i v i t i e s c a l c u l a t e d from average Ey/H x r a t i o s were p l o t t e d as a f u n c t i o n of p e r i o d ( F i g . 6.13). A s c a t t e r of p o i n t s i s n o t i c e a b l e but no sudden jump i n r e s i s t i v i t y v a l u e s as was found at B e i s e k e r ( F i g . 6.10(a)) i s obtained at Cardston ( F i g . 6.13). A r e s i s t i v i t y p l o t curve c o u l d not be drawn through these p o i n t s becuase of l a c k of data at p e r i o d s longer than 100 seconds. Although the e f f e c t of inhomogeneity i s not so w e l l marked i n the apparent r e s i s t i v i t y p l o t ( F i g . 6.13) as i n the Ey/EL^ r a t i o p l o t ( F i g . 6.12) i t s e x i s t -ence at Cardston may be i n f e r r e d from these f i g u r e s . -138-© 0 0 0 0 0 © 0 0 O .0 03 _i i_ i i -i—i i i i 8 10 2 T in sees. 6 8 100 Fig. G.13. Apparent r e s i s t i v i t y vs period, station #1, Cardston. -139-6.3 Combined a n a l y s i s of Meanook and B e i s e k e r data The r e s i s t i v i t y e s t i m a t e s a t Meanook and B e i s e k e r ( s e c t i o n 6.2) were made by matching the f i e l d curves ( F i g s . 6.6 and 6.9(a)) w i t h a s e t of a p p r o p r i a t e master curves ( F i g . 6.1) f o r a two l a y e r e d E a r t h . The i n t e r p r e t a t i o n i n s e c t i o n 6.2 was c o n f i n e d to p e r i o d s s h o r t e r than 200 seconds. To i n t e r p r e t the p o r t i o n of the f i e l d c u r v es f o r p e r i o d s g r e a t e r than 200 seconds i t i s necessary t o match them w i t h curves f o r a t h r e e or more 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 of the lowest l a y e r i s s m a l l e r than t h a t of the l a y e r immediately above i t . F i g s . 6.6 and 6.9(a) show t h a t the apparent r e s i s t i v i t y decreases at p e r i o d s longer than 900 seconds and 300 seconds at Meanook and B e i s e k e r r e s p e c t i v e l y . The decrease of r e s i s t i v i t y w i t h i n -c r e a s i n g p e r i o d i n d i c a t e s the presence of a low r e s i s t i v e bed beneath a h i g h r e s i s t i v e bed and a t h r e e l a y e r e d E a r t h model must be c o n s i d e r e d . T h i s i s a l s o supported by phase angle v a l u e s ( F i g s . 6.9(v) and 6.10(b), s e c t i o n 6.2). Master curves f o r a t h r e e 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 r e s i s t i v i t y con-t r a s t s and t h i c k n e s s e s of the middle l a y e r were computed u s i n g equations (6.11) and (6.12). The apparent r e s i s t i v i t y P a i s g i v e n by (6.14) where f* i s i n ohm meter. - 1 4 0 -10' to £ 10 CD E i E - 10 o f OJ 1.0 INDEX Vx = h2/ h Vz = h 3/ h 7^  = 30 ,24 = 0 ° M i = l 0 0 , M ? = I Q 0 0 ^ = 4 2 . 4 2 , ^ = 0 0 , ^ = 2 0 0 , /i2=IO B ^,=28,7/2=00, 2 0 0 , ^ = 2 0 =00 )/i i=IOO )^2 = 1 0 2 .00, / W O O , /x2= 5 V 2 = a> /!, = 100 / l 2 = l 10 1 0 ' >TT in (sec)'7* 10 10' FIG 6 .14 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 computed from equation (6.14) are plotted as a function of period (on logarithmic paper) i n F i g . 6.14. The d i f f e r e n t parameters for the d i f f e r e n t layers involved i n the computation are shown on the curves. The figure shows the following c h a r a c t e r i s t i c features. 1) The form of the curves A and B remains the same despite a difference of a factor of 50 i n the r e s i s t i v i t y of the t h i r d layer. 2) In the c r i t i c a l case, Curve B, a decrease i n the r e s i s t i v i t y of the t h i r d layer has not altered the shape from 1hat of a two layered Earth model. Interpretations based on such a master curve w i l l lead to ambiguous r e s u l t s . 3) The peak values of the curves increase as the thickness of the middle layer increases as may be noted i n the difference between curves G and E. 4) The period corresponding to the peak i n the apparent r e s i s t i v i t y plot s h i f t s towards longer periods as the thickness of the middle layer i s increased. In other words, the thick-ness of the middle layer i s analogous to damping i n galvanometers. 5) The trend of the curves at periods shorter than those at which peak values of the r e s i s t i v i t y are obtained remains more or less the same despite great changes i n the r e s i s t i v i t y of the t h i r d layer. 6) The trend of the curves at periods 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 re s i s t i v i t y of the middle layer, f^, does not differ greatly from that of the enclosing layers, only the thickness of a thin layer can be determined precisely. 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 re s i s t i v i t y of the middle layer differs considerably from that of the containing layers, hg can be determined very precisely for thick as well as for thin layers. For this purpose, only the order of magnitude of fg ^ s required, not i t s precise value. The applicability of these two results to the present investi-gation w i l l be discussed in subsequent paragraphs. In Fig. 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 Fig. 6.14. The two curves in Fig. 6.15 are parallel up to a period of about 300 seconds indicating 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 in section 6.2. The shift in the peak values of the two curves in Fig. 6.15 i s probably due to changes in the thickness of the middle layer and the r e s i s t i v i t y of the third layer at Meanook and Beiseker. The apparent r e s i s t i v i t y for IO3 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 rapidly at Beiseker than at Meanook. Such a rapid decrease in 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 Fig. 6.14 to obtain a proper match between the two sets. The curve in Fig. 6.15 for Meanook f i t s well with curve C in Fig. 6.14 except that i t has a slightly higher peak value. The curve in Fig. 6.15 for 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 for Meanook and Beiseker. Meanook n , Mr, 42.42 200 10 From section 6.2 we have 5.5 ohm meters 55 ohm meters 2.1 km 1100 ohm meters h 2 42.42 x 2.1 89.1 km and h l + h2 - 9 1 , 2 k m -145-Beiseker £ je, - 200 hz/h, ^ 24-30 ^ . - 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 2 ^ 62.4 - 78 km and hj + h 2 = 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 in Fig. 6.14 with those in Fig. 6.15 were found to be nearly the same as those given in section 6.2. Comparing the values of the depth to the third 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 reliable 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 is not found at -146-Meanook. T h i s does not prove t h a t such a l a y e r does not e x i s t at Meanook but t h a t because of s m a l l e r r e s i s t i v i t y c o n t r a s t s w i t h the e n c l o s i n g beds i t was not p o s s i b l e t o d e t e c t i t . The de t e r m i n a t i o n of the depth t o such a l a y e r i s o n l y p o s s i b l e i f the p r e c i s e v a l u e of the r e s i s t i v i t y of t h i s l a y e r i s known. On the other hand, 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 and t h i c k n e s s of the middle l a y e r both at B e i s e k e r and Meanook can be made and agree f a i r l y w e l l w i t h each o t h e r . T h i s i s because of the c o n s i d e r a b l e d i f f e r e n c e i n the r e s i s t i v i t y of the middle l a y e r compared t o t h a t of the e n c l o s i n g beds ( s e c t i o n 6 .2). -147-CHAPTER V I I ANISOTROPY AND INHOMOGENEITY 7.1 General The m a g n e t o t e l l u r i c method developed by C a g n i a r d may be used f o r the d e t e r m i n a t i o n of su b s u r f a c e r e s i s t i v i t y o n l y i n the case of a homogeneous s t r a t i f i e d E a r t h . Large d e v i a t i o n s from the t r u e r e s i s t i v i t y may be observed when the method i s used t o determine the r e s i s t i v i t y of an inhomogeneous medium (Appendix C ) . Great d i s p e r s i o n i s u s u a l l y observed i n the impedance v a l u e s o b t a i n e d from a p a i r of orth o g o n a l e l e c t r i c and magnetic r e c o r d s at the same p e r i o d (Kovtun, 1961). A s i m i l a r e f f e c t i s a l s o observed i n the case of a n i s o t r o p i c c o n d u c t i v i t y . In r e c e n t years a few papers have been pub-l i s h e d g i v i n g d i f f e r e n t methods of a n a l y s i s f o r the det e r m i n a t i o n of such s t r u c t u r e s by m a g n e t o t e l l u r i c methods. T h e o r e t i c a l and model s t u d i e s f o r two dimensional inhomogene-i t i e s have been made by Kunetz and d ' E r c e v i l l e (1962), Rankin (1960), Neves (1957) and o t h e r s . In g e n e r a l f i e l d c o n d i t i o n s are q u i t e d i f f e r e n t from those of the model and thus i n many cases i t i s extremely d i f f i c u l t t o compare the f i e l d w i t h model data. -148-Most authors have t r i e d t o determine subsurface r e s i s t -i v i t i e s at a p a r t i c u l a r l o c a l i t y without a knowledge of the space v a r i a t i o n s of the magnetic f i e l d , assuming i t t o be uniform over 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 depth at 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 were made. Any s c a t t e r i n the v a l u e s of the impedance ( E y / H x or E x/Hy) was a t t r i b u t e d t o the presence of an inhomogeneity or a n i s o t r o p i c c o n d u c t i v i t y . In the present i n v e s t i g a t i o n these two e f f e c t s have been s t u d i e d s e p a r a t e l y . In t h i s chapter a method i s g i v e n f o r the 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 c o n d u c t i v i t y and the r e s u l t s o b t ained by a p p l y i n g i t t o the d a t a obtained at B e i s e k e r are presented. In the f o l l o w i n g s e c t i o n s the term a n i s o t r o p y r e f e r s to 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 the term inhomogeneity r e f e r s t o a two dimensional inhomogeneity such as a f a u l t or a dyke. The medium on e i t h e r s i d e of such a two dimensional f e a t u r e i s c o n s i d e r e d t o be homogeneous and i s o t r o p i c . The d i f f e r e n t models proposed by v a r i o u s authors w i l l now be d e s c r i b e d b r i e f l y . Neves (1957) has t r e a t e d a two dimensional inhomogeneity, such as a v e r t i c a l c o n t a c t , by b r e a k i n g the mathematical s o l u t i o n i n t o two p a r t s ; t h a t of a magnetic f i e l d p a r a l l e l t o and an e l e c t r i c f i e l d p e r p e n d i c u l a r to the c o n t a c t , and t h a t of an e l e c t r i c f i e l d p a r a l l e l t o and a magnetic f i e l d p e r p e n d i c u l a r t o the c o n t a c t . F i e l d d ata -149-Fig. 7.1. Theoretical magnetotelluric sounding across vertical contact, H f i e l d parallel to the strike. (After Cantwell, 1960). -150-T * 1.6 x IO~5secs. o °o / \ / \ ° P{ * IO6 CM 4 o o o \ X \ / / o o •o — r,- x_ "o / / I \ / •jc •* X */> =8 x 10~6 $M 60 x(CM) h s20crn F i g . 7.2. P l o t of E/H over a h i g h l y conducting and a p o o r l y c o nducting dyke. ( A f t e r Rankin, 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 for the interpretation in those two directions. For the f i n a l analysis the two results may be combined. Figure 7.1 shows a theoretical magnetotelluric sounding curve across a vertical fault. Similar mathematical solutions for dykes in the case when the magnetic f i e l d i s polarised parallel to the structure have been given by Rankin (1960). Theoretical and experimental curves have been obtained by him for a number of different 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 over-burden, Cheteav (1960) has given a method for the determination of the coefficient of anisotropy (i.e. the ratio of the impedance tensors in the two principal directions of anisotropy) and the inclination of a homogeneous anisotropic medium. His approach necessitates r e s i s t i v i t y determinations by direct current methods in addition to the magnetotelluric method. Using the total impedance given by where -152-or 2gj 0*Ge 1 Z J 1 - 1 Kovtun (1961) showed that i f Zj. i s plotted in the direction of the resulting figure i s an ellipse with principal axes Z x and Z y. This i s of course evident from the above equation. Thus when JZJJI has been calculated at the surface of an inhomogeneous medium, an ellipse may be drawn giving not only the directions of the principal axes, but also the impedances |Z x j and | Zy j . Rokityanski (1961) has given the relation-ship between the directions of polarisation of the electro-magnetic f i e l d and the coefficient of anisotropy ( k ) . For values of k greater than 5 the relationship between the direction of polarisation ( 6 f i ) of the magnetic f i e l d and the difference ( A(j>) between the directions of the polarisation of the electric and magnetic field s i s approximately linear. Thus by f i t t i n g the best straight line 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 in the present investigation may be used for a l l values of k . Cantwell (1960) has given methods for interpreting inhomogeneous and anisotropic structures using admittance tensors rather than scalar admittance. His method although theoretically justified is not very convenient to use. Bostick and Smith (1962) have developed Cantwell's approach and given -153-a detailed method of analysis. The basis of the method is the computation of the admittance in different directions by a suitable transformation of coordinates. For a homogeneous Earth the admittance w i l l be constant in a l l directions, but for an anisotropic and/or inhomogeneous Earth w i l l show minimum and maximum values. The direction corresponding to the minimum value of the admittance w i l l be the direction of one of the axes of anisotropy. Once this direction i s known the coefficient of anisotropy may easily be calculated. 7.2 Method of analysis For a plane wave incident on a homogeneous isotropic or horizontally layered Earth the relationship between the horizon-ta l components of the electric and magnetic fields i s given by B - ? [ H n ] (7.1) where n is a unit vector directed vertically downwards, and f i s the input or surface impedance of the body, which for a given frequency is a constant at each point on the surface, i.e. i t i s independent of the direction in which E and H are measured. On the other hand, for an anisotropic or inhomogeneous Earth the surface impedance i s a tensor quantity 5*xy a n c* equation (7.1) becomes - 1 5 4 -where x and y are rectangular coordinates in a horizontal plane (Fig. 7.3). The components of the tensor ~$ x y depend on the direction of the x, y axes. 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 in the u, v coordinate system equation (7.2) reduces to (7.3) (7.2) where >^ \ and ^2 a r e * n e principal values of the tensor f x y . It is here assumed that the constant geomagnetic f i e l d does not essentially distort 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-F i g . 7.3. O r i e n t a t i o n o f t h e a n i s o t r o p y axes w i t h r e s p e c t t o m e a s u r i n g a x e s . -156-given such an interpretation for an anisotropic Earth. Such a method does not give the structure of anisotropy or inhomogeneity. The principal 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 inclined at an angle © to the measuring axes (Fig. 7.3), then x => u cos Q - v sin & (7.4) y =» u sin © •*• v cos © Solving Maxwell's equations for an anisotropic homogeneous half space, for electromagnetic f i e l d components along the u,v axes corresponding to the principal values 6"^, 6g of the conductivity tensor in the horizontal plane we obtain (7.5) where Z u and Z y are the impedance values along the u and v axes. The details of the derivation of equation (7.5) are given in appendix D . From equation (7.3) we have and thus J G / o Y = % / S, (7.7) -157-Equation (7.7), where k i s p o s i t i v e and r e a l , i s true only for a homogeneous anisotropic Earth. For inhomogeneous bodies K i s usually complex. In the following derivation K i s considered to be r e a l or at most with a n e g l i g i b l y small argument. Thus knowing the impedance values i n the u and v direct i o n s , the c o e f f i c i e n t of anisotropy IC may be calculated using equation (7.5). In practice the u and v d i r e c t i o n s are not known, and measurements are taken along x and y axes making an unknown angle G with the u, v coordinate system. The expres-sions developed below must then be used to f i n d k and & . From equation (7.7) z. -which on using equation (7*4) becomes Considering a plane polarised electromagnetic wave, M y -158-so that U Law © M - lav* c? ( 7 . 8 ) 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 . 1 0 ) Denoting tan S b y ^ ] tan <9E by x \ ( 7 . 1 1 ) tan 6 JJ by y J Equation ( 7 . 1 0 ) reduces to f ( l - k x v ) -[xy + k C^+v;]^ -+- ( x y - i c ) = o ( 7 . 1 2 ) In this equation k. and ^ are unknowns. For a particular geological section however R. and ^ are constants while x and y are variables. Equation ( 7 . 1 2 ) may be written in the form, -159-x + y + Axy + B - 0 (7.13) where ( 1 + K.) V and (7.14) k - r 0 + B If more than two values of x and y are obtained equation (7.13) may be solved by a least squares method to obtain the values of A and B . Thus and , . (7.15) B - - -L ( 2 x + ^ y t f i s ^ y ; Eliminating k from the pair of equations (7.14) (aVofV-/ - K * - ^ ] - o ' ( 7 . 1 6 ) This equation has four roots, two at » ± £ which may be rejected since 8 can never be imaginary. The other two roots are given by £ - f\-S ± v/^-8JV4 (7.17) -160-and are thus known when A and B are determined. The two values of ^ given by t h i s equation lead to two directions at r i g h t angles to one another. Either of the equations (7.14) then give k . The two values of k are r e c i p r o c a l s of one another. It must be stressed that the above derivation i s true only for a plane polarised electromagnetic f i e l d . 7.3 Determination of K and B at Beiseker Before applying the method to the determination of k and (9 at Beiseker, i t i s worthwhile to see whether the scattering of points i n F i g . 6.10 may be explained by other causes besides anisotropy. The sudden jump i n apparent r e s i s t i v i t y values i n F i g . 6.10(a) may be due to three causes: (a) Source e f f e c t , (b) Presence of a marked inhomogeneity, (c) Presence of aniso-tropy. The e f f e c t of each of these possible causes w i l l be considered i n turn. (a) In section 5.3 the assumption that variations i n the geomagnetic f i e l d are propagated towards the Earth as a plane electromagnetic wave has been shown to be v a l i d because of the constancy of the amplitude of the geomagnetic f i e l d components over a horizontal distance of 600 km. The scatter of points and the sudden jump i n the PQ, VS T plot (Fig. 6.10(a)) may be due to the corruption of a plane wave by noise from random sources, with the H and E vectors oriented i n such a way as to -161-g i v e l i t t l e s c a t t e r i n the Ey/Hjj v a l u e s but a l a r g e s c a t t e r i n the E x / H y v a l u e s . F i g . 7.4 i l l u s t r a t e s t h i s p o i n t , where n o i s e from some d i r e c t i o n has a much s m a l l e r e f f e c t upon Hx than Hy. The magnetic r e c o r d s a t B e i s e k e r were found to e x h i b i t such a c h a r a c t e r i s t i c . F i g u r e 7.5 i l l u s t r a t e s two cases of the g r e a t e r predominance of some harmonics i n H y than H x. Such an e x p l a n a t i o n i s a l s o supported by g e n e r a l l y lower v a l u e s D f coherence f o r E x / H y than f o r E y / H x f o r p e r i o d s l e s s than 300 seconds. However, the magnitudes of H^ . and H y are u s u a l l y about the same so t h a t the s i t u a t i o n e x e m p l i f i e d i n F i g . 7.4 may not o f t e n apply. A n i s o t r o p i c s near the s u r f a c e presumably c o n t r o l the E f i e l d v e c t o r s . An a n i s o t r o p y , whose 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 value of than Ey (which i s u s u a l l y the case at B e i s e k e r ) w i t h equal v a l u e s of H x and Hy may e x p l a i n the s c a t t e r i n g i n F i g . 6.10. Thus changes i n the source would cause g r e a t e r f l u c t u a t i o n s i n E x than i n Ey w h i l e producing approximately equal f l u c t u a t i o n s i n H x and H y. T h i s e x p l a n a t i o n i s shown s c h e m a t i c a l l y i n F i g . 8.2. (b) To i n v e s t i g a t e the p o s s i b l e presence of any marked inhomogeneity at B e i s e k e r , p l o t s of Ey/FL^. versus s t a t i o n s were c o n s t r u c t e d . Events which c o u l d be i d e n t i f i e d e a s i l y at a l l s i x s t a t i o n s s i m u l t a n e o u s l y were used i n the computation of the Ey/H^. r a t i o s . The r e s u l t s are shown i n F i g . 7.6 f o r events of 22 to 27 sec. p e r i o d and i n F i g . 7.7 f o r those of -162-FIG 7 .4 ADDITION OF SIGNAL AND RANDOMLY ORIENTED NOISE -164-90 sec. p e r i o d . F i g u r e 7.6 shows a minimum va l u e of E y / H x at s t a t i o n #3 (B e i s e k e r ) although such a minimum i s not so marked i n F i g . 7.7 at t h i s s t a t i o n . Such a low va l u e at B e i s e k e r , at a p e r i o d of 25 sec, i s probably due to s u b s u r f a c e e f f e c t s because of the u n i f o r m i t y of H over a h o r i z o n t a l d i s t a n c e of 600 km ( s e c t i o n 5.3). A decrease i n r e s i s t i v i t y at B e i s e k e r compared w i t h other s t a t i o n s has a l s o been observed from t e l l u r i c s t u d i e s (Douglass 1962). No known g e o l o g i c s t r a t a at B e i s e k e r can g i v e r i s e t o such a decrease i n r e s i s t i v i t y , although an i n c r e a s e i n the depth t o the Precambrian may be r e s p o n s i b l e . ( G e o l o g i c a l evidence i n d i c a t e s t h a t the depth to the Precambrian i n c r e a s e s south of B e i s e k e r . ) However s t i l l lower v a l u e s of Ey/H^. should be o b t a i n e d a t Champion and Cardston, which i s not the case. The hig h e r v a l u e s of Ey/Hj^ at Champion ( s t a t i o n #2) and Cardston ( s t a t i o n #1) are probably due to the presence of s u b s u r f a c e inhomogeneities at these s t a t i o n s . The major f a u l t b e l t which l i e s v e r y c l o s e t o Cardston ( F i g . 2.2) i s thought t o be r e s p o n s i b l e f o r these higher v a l u e s . The presence of inhomogeneity at Cardston has a l s o been shown i n s e c t i o n 6.2, and t e l l u r i c s t u d i e s (Douglass 1962) at t h i s s t a t i o n have r e v e a l e d s i m i l a r c h a r a c t e r i s t i c s . Another n o t i c e a b l e f e a t u r e of F i g . 7.6 i s the i n c r e a s e i n the Ey/H x v a l u e at s t a t i o n #4. Data from w e l l l o g s i n d i c a t e t hat the depth t o the Precambrian i n c r e a s e s south of Meanook, so t h a t lower v a l u e s of E y / H x s h o u l d be observed at a l l s t a t i o n s -165-PERIOD 2 2 - 2 7 s e c . O - 1010 0.5h 1 2 3 4 5 6 S STATION N PIG. 7.6 VARIATION OF E y/H x ALONG THE SIX STATIONS - 1 6 6 -Fig. 7. Variation of E/H along the six stations, for 90 sec period. -167-to the south. Ignoring the results from station #4 (Clive) such a characteristic is obtained up to station #3. The increase in the value of E y/H x at station #4 is probably due to the presence of an inhomogeneity. Figure 2.2. displaying the location of the reef complexes, shows that this station l i e s above the Bashaw reef complex which forms a peninsula extending into the shale basin and trending to the northeast. Reefs are believed to be fault controlled phenomena. Extensive fracture systems are known to extend underneath the sedimentary cover in central Alberta forming tectonic belts 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 for a few irregularities, a lower value of E y/H x at station #5 i s noticeable in Fig. 7.7. Probably this lower value i s due to some inhomogeneity at this station at great depth (10-15 km), but no corresponding geological structure was found which could account for i t . On the other hand, E l l i s (1962) has found evidence of anisotropy at this station from the marked difference between the E x/H 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 rise to the scatter in the K^/Uy plot of Fig. 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 -168-Theoretical Models E x ,H y i > i)) /111 /11111111) / n > 6 2 3 1 0 8 0 1 0 3 8 0 E y ,H X /1! 11) 11 ) / / / ! 11) 11 ) I) I" 6 6 0 0 1 0 Observed Theoretical interpretation -Cooking Lake. (After E l l i s , 1962) I I 1 0 Period (seconds) 1 0 0 -169-E-H pair (Ex/Hy) compared to that from the other orthogonal pair (Ey/Hx) is consistent with the results obtained by other workers (Bostick and Smith, 1962) and suggests the presence of an anisotropy. In order to apply the method given in section 7.2 to find l< and © i t i s necessary to know the directions of polarisation of the electric and magnetic fields for events of the same period. Since no recordings were made on magnetic tape at Beiseker, the only way to determine the direction of polarisation was by plotting the two components and finding the mean direction from this plot. The directions of polarisation of the electric and magnetic fields were found only for events with periods of 30 and 90 sec. The records were searched for events which were more or less sinusoidal, and each event con-sisting of three to four cycles was read at 6 sec intervals. The amplitudes of the two electric and two magnetic components were plotted to find the mean directions of polarisation. The following expressions were used to obtain the best f i t of an ellipse through the points on the polarisation diagram, 2 z~> (7.18) I** -and z x V r v * - w 2 e 1 " r*7ryx.(3~2<9 (7.19) -170-where 0 i s the angle which the major axis of the ellipse makes with the x axis (N-S), and a and b are the major and minor axes of the ellipse. Details of the derivation of equations (7.8) and (7.19) are given in Appendix B. The ratio a. A> was calculated from equation (7.19) in order to find the degree of e l l i p t i c i t y of the ellipse. In a l l , 70 events were analysed to find the directions of polarisation of the electric and magnetic fi e l d s . Only 25 events were found when both the electric and magnetic fields were approximately linearly polarised. However the electric f i e l d was linearly polarised in a l l cases although a great variation was found in the magnetic f i e l d . This variation is probably due to noise effects, as explained in the beginning of this section (Fig. 7.5). The computations were carried out on an I.B.M. 1620 at the Computing Centre at the University of Briti s h Columbia. The results of this computation including errors in the determination of the slope & are given in Table 7.1. Figures 7.9 and 7.10 ill u s t r a t e two typical examples of the directions of polarisation for events of 90 and 25 sec. period. After computing the directions of polarisation of the electric and magnetic fi e l d s , equations (7.15), (7.14) and (7.17) were used to calculate values of k and ® . The results of such a computation are given.-below. PIG. 7 . 9 EXAMPLE OP THE DIRECTION OP POLARISATION OP ELECTRIC AND MAGNETIC FIELDS H x and H y Aug. 17. 61 Time 1350 - 53 50+100 E x and E y 10 20 30 40 20 40 60 80 100 F i g . 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 of e l e c t r i c k y and magnetic f i e l d s f o r 25 sec p e r i o d . -173-For 90 sec. period Gi/61 - 0.7 6 C=48.5° S'/&i ^ 1.4 © ~ -41.5° For 30 sec. period Gi/^i. C£ 10.2 6 ~ 28.7° 6'lGi - 0.09 $ ^ -61.3° The values f o r k and £ of 1.4 and N 42° W are geo l o g i c a l l y reasonable at Beiseker and w i l l be discussed i n section 8.3. Impedance values i n two mutually perpendicular directions are needed to carry out such an analysis to investigate any possible anisotropy. Only at Beiseker were measurements made of two pairs of orthogonal e l e c t r i c and magnetic f i e l d com-ponents. However to investigate any possible inhomogeneity or anisotropy at Meanook, E x/H y data were taken from N i b l e t t ' s (1960) paper. In F i g . 7.11 apparent r e s i s t i v i t i e s calculated from the E x/H y r a t i o s are plotted as a function of period T. No scatter of points i s obtained suggesting the absence of any inhomogeneity. On the other hand, the greater magnitude -174-Fig. 7.11. Apparent r e s i s t i v i t y vs period for Meanook (from E /H ). (After Niblett, 1960.) x y -175-of the wave impedances computed from the E x/H y data compared to those calculated from the E y/H x data (Niblett I960) suggests the presence of anisotropy. No anisotropy analysis can be made from impedance values alone. The data recorded during the Alberta Operation are plotted i n F i g . 7.12 which also shows Nib l e t t ' s r e s u l t s . A s h i f t i n the two curves i s noticeable. Such a difference i n the impedance values obtained from record-ings made at the same place on two d i f f e r e n t occasions has also been reported by Bostick and Smith (1962). This difference may possibly be accounted for by the difference i n the d i r e c t i o n of po l a r i s a t i o n of the electromagnetic f i e l d . It i s shown i n Appendix C that for anisotropic and/or inhomogeneous masses the impedance measured at the surface depends not only upon the st r u c t u r a l parameters and 0 (the i n c l i n a t i o n of the anisotropy or inhomogeneity axes with the north d i r e c t i o n ) , 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 electromagnetic f i e l d . The decrease i n impedance values at periods greater than 600 sec. as obtained from the Alberta Operation data i s not observable i n Nib l e t t ' s data. This i s probably because Nib l e t t ' s data i s r e s t r i c t e d to periods less than'1000 sec. while the Alberta Operation data extends to periods up to 3000 sec. 7.4 Error analysis Errors i n the anisotropy analysis may be divided into -176-3 2 100 8 6 4 3-2-E C| .£ 10 c £ 8 6 4 3 Alberta Operation Data Niblett's Data 2^ -I u -1 L 10 2 3 4 6 8 100 3 4 6 8 1000 Period T Seconds F i g . 7.12. Change i n the apparent r e s i s t i v i t y v a lue at Meanook obtained from data taken at d i f f e r e n t , times. -177-two groups, those introduced during the computation and those which are inherent in the method (i.e. systematic errors). Errors which were introduced in determining the direction of polarisation of the electric and magnetic fields were calculated. The probable error in determining the slope of the major axes of the ellipse was calculated from the following expression. n - T ' j l J ( P V ^ ) G (7.20) where ^ = the probable error ' = the probable error of a hypothetical quantity of unit weight V CTI-Z) Ci-h - f e w * 2 © ; p - 2 7 * ^ - j y > Q - 2 £ x j G - 2>> + £ y c v Details of the derivation of equation (7.20) are given in Appendix B. The probable error Y^, , as shown in Table 7.1 does not exceed 0.5 for most of the cases used in the present analysis. Hence the errors introduced in finding the direction of polarisation are negligible. On the other hand, systematic errors may be quite large. Some of these errors (such as those due to incorrect calibration) have been mentioned in section 4.6. An additional important systematic -178-TABLE 7.1 90 sec, period E l e c t r i c a l Data Magnetic Data Sample No. <9E i n degrees a 2 / b 2 Jk i n degrees a2/b 2 J E 1 -35.5 49.5 0.26 30.8 3.0 0.85 2 -33.2 39.3 0.19 27.5 1.6 1.47 3 -49.6 4.5 11.31 26.3 25.1 0.11 4 -33.4 33.4 0.22 8.7 5.0 0.12 5 -35.7 20.0 .0.51 4.8 11.7 0.07 6 -34.5 21.3 0.35 2.6 5.1 0.11 7 -34.6 146.0 0.12 8.18 2.5 0.42 8 -37.0 48.7 0.38 38.6 4.7 2.51 9 -39.1 151.4 0.37 25.4 21.9 0.11 10 -41.7 45.5 0.29 0.0 2.6 0.36 11 -33.9 144.0 0.11 27.8 129.4 0.05 12 -30.1 176.0 0.05 31.4 17.1 1.01 13 -39.0 40.1 0.74 32.1 3.2 0.96 14 -37.0 25.8 0.54 20.3 11.3 0.11 15 -40.1 34.8 1.34 37.9 16.3 0.99 16 -38.5 43.6 0.60 34.6 10.6 0.54 30 sec. period 1 -24.6 130.1 0.05 -1.0 2.5 0.49 2 -34.4 19.2 0.48 48.6 4.0 0.65 3 -38.9 52.0 0.81 72.2 5.5 1.07 4 -34.7 30.8 0.39 71.9 11.1 0.45 5 -32.1 21.8 0.30 59.0 3.0 1.42 6 -34.9 14.4 0.79 44.8 27.9 0.56 -179-(or constant) error which may a f f e c t the anisotropy analysis i s any deviation i n orthogonality i n the coordinate system used for measuring E and H. If the two axes are at an angle if/2 - /S instead of TT/2 then a l l E or H f i e l d d i rections are i n error by an angle /3 . Because of t h i s , the azimuth of the anisotropy axis w i l l be determined with an error which may be calculated by substituting ( $H ± ) or ( # E ± ) i n equations (7.15) and (7.17). Without a knowledge of /3 i t i s not possible to calculate such an error. In the present investigation the two coordinate systems were more or less coincident, and thus no estimate of t h i s source of error has been made. Another systematic error which may aff e c t the determina-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 obtained by reading the amplitudes of the N-S and E-W magnetic components i ' at equal time i n t e r v a l s d i r e c t l y from the records may ari s e from the d i f f e r e n t response of the N-S and E-W detectors. If the two detectors 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 f i e l d w i l l be incorrect by a few degrees at every period. To eliminate t h i s error i t i s necessary to multiply a l l amplitude readings of one of the components by a constant (the r a t i o of the c a l i b r a t i o n factor of the N-S to the E-W detectors). A si m i l a r correction i s necessary for the e l e c t r i c f i e l d recordings. However because of the close 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 detectors (Fig. 3.9) such an error was not calculated i n the present investigation. -181-CHAPTER VIII 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 regions within the Earth are determined by the magnetotelluric method by matching f i e l d curves with r e s i s t i v i t y model curves. There are many pro-blems i n s c i e n t i f i c research which require the f i t t i n g of data to an assumed physical system. If the data f i t t i n g i s s a t i s -factory then the system may be considered a possible model of the phenomenon studied. However, simply because the data are well approximated by the model proposed i s no guarantee that i t i s a true representation of the actual physical system. To show that the model considered i s close to the actual physical system i t i s necessary to compare the r e s u l t s obtained by data f i t t i n g with those obtained by other methods. In t h i s chapter the r e s i s t i v i t y and anisotropy r e s u l t s obtained by data f i t t i n g are compared and discussed with 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 at Meanook, Beiseker and Cardston A three layered Earth model was used to interpret the -182-r e s i s t i v i t y curves at Meanook and Beiseker (section 6.3). Such an interpretation of the data i s not unique. Probably a four or more layered Earth model would give a better interpre-t a t i o n but whether such a detailed analysis of the data i s worthwhile (or even meaningful) i s very doubtful. The resolv-ing power, i . e . the a b i l i t y to separate one layer from another, of the magnetotelluric method has been discussed by Vladimirov (1961). It depends upon two parameters of the layer, the thickness and the r e s i s t i v i t y . It has been shown that i t i s not possible to d i s t i n g u i s h two layers whose r e s i s t i v i t i e s do not d i f f e r - appreciably (section 6.3), although some investiga-tors (e.g. E l l i s 1962) have attempted to do so (Fig. 7.8). Such an i n t e r p r e t a t i o n of the data by increasing the number of layers with very l i t t l e r e s i s t i v i t y contrast does not help to obtain t h e i r true r e s i s t i v i t y by the magnetotelluric method because of i t s q u a l i t a t i v e nature. Hence a maximum of three layers was considered i n the i n t e r p r e t a t i o n of the f i e l d data i n the present investigation. Such an interpretation was found to be s a t i s f a c t o r y . A layer l y i n g at depths of 2.1 km and 2.6 km and with r e s i s t i v i t i e s of 1100 ohm meter and 1260 ohm meter was found at Meanook and Beiseker respectively. At these stations s e d i -mentary rocks o v e r l i e Precambrian igneous rocks at depths of 1.92 km and 3.1 km. The agreement i n depth between these two sets of r e s u l t s i s quite good and suggests that the r e s i s t i v i t y -183-of the Precambrian r o c k s l i e s between 1100-1260 ohm meter. Est i m a t e s of the r e s i s t i v i t y of Precambrian r o c k s obtained from w e l l l o g s i n c e n t r a l A l b e r t a are of the order of 500 ohm meter. However, r e s i s t i v i t y v a l u e s o b t a i n e d from w e l l l o g s correspond to the top of the Precambrian w h i l e r e s i s t i v i t y v a l u e s o b t a i n e d by the m a g n e t o t e l l u r i c method are average v a l u e s down to a depth of about 70-90 km. Hence i t i s p o s s i b l e f o r such a d i s c r e p a n c y to e x i s t between the two r e s u l t s . The t h i r d l a y e r of r e s i s t i v i t y 55 ohm meter at Meanook was i n t e r p r e t e d t o l i e at a depth of 92.1 km. A s i m i l a r i n t e r p r e t a t i o n at B e i s e k e r gave a l a y e r of r e s i s t i v i t y 6.3-31.5 ohm meter at a depth of 65-80.6 km. The i n t e r p r e t a t i o n at B e i s e k e r from one 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 may not be j u s t i f i e d because of the l a r g e s c a t t e r i n the P a versus T p l o t ( F i g . 6.10(a)) observed i n the other o r t h o g o n a l p a i r . However the t r e n d of the apparent r e s i s t i v i t y and the phase angle curves ( F i g s . 6.10(b) and 6.9(b)) d e f i n i t e l y show the presence of a low r e s i s t i v i t y l a y e r l y i n g beneath the h i g h l y r e s i s t i v e l a y e r . There have been many p r e v i o u s e s t i m a t e s of r e s i s t i v i t y at depths between 10 and 100 km. L a h i r i and P r i c e (1939) made estimates t o a depth of about 1500 km by comparing the induced f i e l d s of the d a i l y magnetic v a r i a t i o n and the storm time v a r i a t i o n t o t h e i r i n d u c i n g f i e l d s * They concluded t h a t the mean r e s i s t i v i t y of the E a r t h down to 600 km i s about 50 ohm meter and t h a t i n some r e g i o n s near the s u r f a c e the value must -184-be lower than this. 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 this model the r e s i s t i v i t y of the solid Earth below could not be lower than 10^ ohm meter down to depths of 200-300 km. Resistivity measurements have also been made by Coster (1948), Macdonald (1957) and Macdonald (1959) for several rock samples at various tempera-tures. The aim of their work (andPrice's) was to attempt to estimate the r e s i s t i v i t y distribution in the mantle and core, while magnetotelluric measurements on the other hand generally apply to depths between 0-200 km. In order to compare the results of the present investigation obtained by magneto-t e l l u r i c methods with those obtained by other investigators, a l l results have been plotted on the same figure (8.1), the different models being taken from Cantwell (1960). The ionic r e s i s t i v i t y alone is plotted for the different models. It can be seen from Fig. 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 is obtained with Lahiri and Price's curve nor with Macdonald's curve. According to the temperature distribution of Macdonald*s model 7 a temperature as high as 1600°K would be expected at 80 km. At temperatures greater than 1500° K the electronic conductivity i s very small compared to the ionic conductivity (Tozer 1959). Hence plotting ionic r e s i s t i v i t y in Fig. 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 km PIG. 8.1 RESISTIVITY vs DEPTH PLOT FOR DIFFERENT MODELS -186-depth i s justified. It is not justifiable, 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 likel y . An explanation for the increase and decrease of r e s i s t i v i t y at different 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 liquid in the pores upwards as pore space i s compressed (Angenheister, 1962). With increased compression of the pores, liquid in the rock matrix suffers an increase in hydrostatic pressure, while liquid at lesser depths is subjected to the increased hydrostatic pressure of the over-lying water mass. Thus the "electric conductivity of porous liquids" loses i t s meaning at greater depths, where under high pressure new minerals are built and the content of the pore i s gradually built into a new grid. With the decay of electro-lyte conductivity, the conductivity of the crystal considered as a semiconductor begins to become important. It is worthwhile to compare the present results with those of other investigators who also found a sudden decrease in the r e s i s t i v i t y at depths of 70-100 km by the magnetotelluric method. Their results which were obtained at different locations are listed below. -187-Resistivity Depth Investigation (ohm meter) (km) Present 30-60 80-90 Cantwell (1960) 80 70 Niblett (1960) 80-100 80 E l l i s (1962) 10 80 The agreement between the f i r s t three is quite good indicating that a value for 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 significant result i s that no change of resist-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 definite r e s i s t i v i t y interpretation of the magneto-t e l l u r i c data could be made at Cardston because of the large scatter of points in the E y/H x versus T plot (Fig. 6.12). Such a scatter has been attributed to the presence of an inhomogeneity, the major fault which runs close to Cardston (Fig. 2.2). 8.3 Anisotropy results at Beiseker It has been shown in section 7.3 that the difference in magnitude between the ratios E x/H y and Ey/H^ and the scatter of points in 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 is worthwhile to check that the results obtained from the anisotropy analysis do in fact explain the difference in magnitude between the Ex/Hy a n ( i Ey/**x ratios. The following are the results 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 & 2r -61.3° Two sets of values are given for each period, but they represent the same anisotropic structure since the value of 0 in one set i s complementary to that in the other. The -189-analysis of anisotropy at a period of 90 sec. was made from 16 almost perfectly 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 polarity was only approximately linear. This makes the results obtained in the latter case less reliable than those in the former. Hence the results obtained from the events with a period of 90 sec. only w i l l be considered here. In Fig. 8.2 6\ and <T2 are the directions of the con-ductivities, i.e. the axes of the anisotropy while E and H are the total electric and magnetic fields whose directions were obtained from polarisation diagrams. For an anisotropic medium the electric f i e l d i s not parallel to the current density except along the conductivity axes and is not perpen-dicular to the magnetic f i e l d . We have J l " °1 E1 and Jg = ^2^2 where and J 2 are the current densities along 0""^  and 67). Since ^0,^-1 w i l l be much larger than Eg. Moreover 6\ > 6*2> s o t h a t J l ^> J2* Hence the magnetic f i e l d w i l l be approximately perpendi-cular to the current density J^. In Fig, 8.2 H is drawn perpendicular to J (^J^+Jg). The direction of polarisation -190-F i g . 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 p o l a r i s a t i o n of E and H f i e l d s . -191-of H was found to be N42°E from this figure. The average direction of H found from f i e l d records was about N 36° E. The close agreement between these two results makes the above interpretation plausible. Moreover i t i s evident from Fig. 8.2 that H x ~ H y and that E x > E y as was generally observed. Thus the result that E x/H y 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 peno-logical study of the Precambrian of central Alberta. Fig. 2.4 shows the lithological 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 in the above magneto-t e l l u r i c analysis are also shown in Fig. 2.4. Station #3, Beiseker, i s located very close to the boundary between granitic 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 in order to give a proper f i t to their 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 x/H y and E y/H x ratios at 100 sec. period. Nothing definite can be said about those agents which give rise to such differences at greater depths extending down to the mantle. Angenheister (1962) suggests the following -192-three possible causes of conductivity anisotropy in the mantle, (1) Convection currents, (2) Partial pressure release, (3) High pressure modifications. Of these three agents high pressure modifications play the most important role at depths greater than 400 km. Several workers have suggested different chemical compositions for the deeper mantle on the basis of high pressure work. 8.4 Conclusions The following conclusions may be drawn from the results obtained in the present investigation, (1) The visual correlation method of analysing magneto-t e l l u r i c data i s preferable to the power spectral method when a large amount of noise free data i s available. (2) Phase angles, between pairs of orthogonal electric and magnetic f i e l d components, which do not give any addi-tional information to that obtained from apparent r e s i s t i v i t y values, may be used for qualitative interpretation in the magnetotelluric method. (3) The assumption that the geomagnetic f i e l d is 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 is justified. This overcomes Price's objection to Cagniard's theoretical approach. (4) With appropriate analytical techniques i t i s possible -193-to u t i l i s e the magnetotelluric method to determine the major electrical discontinuities in the crust and upper mantle. (5) The magnetotelluric method may be used to determine the physical parameters of anisotropic bodies, provided sufficient data is 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 local sources. Such local sources invalidate the magneto-te l l u r i c method for frequencies higher than 0.1 cps, as Price has shown. -194-APPENDIX A In the following pages the results of the power spectral computation, obtained from the IBM 704 Computer at the University of California, are given. The results have been divided in two sections. AI - Power spectral computation of two days' magnetic records from six stations, A l l - Power spectral computation of the magnetic and electric records at station #3, Beiseker. The following notation has been used in the text for the records corresponding to diff e x t e n t days. A - corresponds to records obtained on 18.8.61 B -C -D -E -F -" 19.8.61 «» 9 i a «i (between ^ l . B . b i 1428-1558) " 91 R 6i (between ^ • b ' b l 1900-2030) " 23.8.61 " 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 results of the computation. The power spectra (X,Y) for the two types of records are given in the same order as that of the records. The symbols used for each column correspond to the quantities - 1 9 5 -g i v e n below. K — Lag number A - A u t o c o r r e l a t i o n of primary r e c o r d X - Power s p e c t r a l d e n s i t y of primary r e c o r d B - A u t o c o r r e l a t i o n of secondary r e c o r d Y - Power s p e c t r a l d e n s i t y of secondary r e c o r d E - In phase c o r r e l a t i o n between the two r e c o r d s Z - In phase power s p e c t r a l d e n s i t y (co-spectrum) F - Out of phase c o r r e l a t i o n between the two r e c o r d s W - Out of phase power s p e c t r a l d e n s i t y (qua-spectrum) P - Normalised co-spectrum Q - Normalised quadrature spectrum R - Coherence R*R - Coherence squared PHIL — Phase l e a d of secondary over primary. - 1 9 6 -A I The r e s u l t s o f t h e power s p e c t r a l c o m p u t a t i o n o f t h e m a g n e t i c r e c o r d s a t a l l s i x s t a t i o n s a r e g i v e n i n t h e f o l l o w i n g p a g e s . The r e s u l t s of t h e power s p e c t r a l d e n s i t y ( X , Y ) a r e g i v e n i n terms o f c h a r t d i v i s i o n s w h i c h may be c o n v e r t e d i n terms o f gamma w i t h t h e h e l p o f t h e c a l i b r a t i o n c u r v e s . -197-1 TUKEY SPECTRUM tSTlHATION 0 0 9 6 9 J A A L T A H Z S T A T I O N 6 A N D I 1 8 1 i l T I M E 1 0 0 9 1 1 0 6 5 O J K A r X v 2 L U G X B V r 2v: L O G Y E 4 3 9 9 6 4 ~ 1 7 6 9 2 3 . 2 5 4 9 6 4 3 4 2 3 4 1 2 3 . 3 7 4 3 7 3 9 1 4 3 7 6 4 4 1 8 5 6 2 3 . 2 7 4 5 2 7 2 4 2 4 9 6 2 3 . 4 0 4 3 4 6 2 2 4 3 5 3 1 2 9 0 1 2 2 1 . 9 5 4 1 3 8 6 3 2 0 8 8 2 2 . 3 2 4 3 2 5 7 3 4 3 6 3 3 1 8 2 6 3 2 0 . 9 2 4 4 6 7 9 3 1 0 3 2 2 2 . 0 1 4 3 5 6 8 4 4 3 7 4 2 1 9 6 6 8 2 0 . 9 9 4 7 5 6 0 2 6 3 4 3 2 1 . 8 0 4 3 7 1 7 5 4 3 6 3 8 1 8 2 1 4 2 0 . 9 1 4 5 3 0 7 2 2 9 7 9 2 1 . 4 7 4 3 3 4 3 6 4 3 5 5 8 2 1 0 1 9 ' 2 1 . 0 1 4 2 8 6 8 2 4 2 0 3 2 1 . 6 2 4 3 1 2 4 7 4 3 6 0 4 2 1 5 5 6 2 1 . 1 9 4 3 9 5 9 2 6 3 0 5 2 1 . 8 0 4 3 4 8 2 8 4 3 5 7 9 2 2 1 1 5 2 1 . 3 3 4 5 6 6 6 2 4 9 7 0 2 1 . 7 0 4 3 6 6 9 9 4 3 4 5 7 2 2 2 7 4 2 1 . 3 6 4 5 0 5 7 3 1 2 9 8 2 2 . 1 1 4 3 3 2 3 1 0 4 3 4 2 8 2 2 3 6 7 2 1 . 3 7 4 3 8 8 7 3 4 7 8 5 2 2 . 6 8 4 3 1 5 2 1 1 4 3 4 7 3 2 2 3 9 6 2 1 . 3 8 4 4 0 3 2 3 7 9 0 9 2 2 . 9 0 4 3 3 6 8 1 2 4 3 4 1 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 3 4 5 0 1 3 4 3 3 0 8 2 4 3 9 6 2 1 . 6 4 4 4 3 0 5 3 8 2 6 4 2 2 . 9 2 4 3 2 8 8 1 4 4 3 2 9 7 2 3 2 6 8 2 1 . 5 1 4 4 5 7 9 3 5 1 8 0 2 2 . 7 1 4 3 2 2 0 1 5 4 3 3 0 7 2 1 1 4 5 2 1 . 0 6 4 4 7 5 2 3 2 2 9 8 2 2 . 3 6 4 3 2 3 1 1 6 4 3 2 1 6 1 4 9 3 1 2 0 . 6 9 4 4 0 6 4 3 1 3 3 0 2 2 . 1 2 4 3 2 2 2 1 7 4 3 1 3 5 1 3 6 4 2 2 0 . 5 6 4 3 5 5 2 2 9 1 8 4 2 1 . 9 6 4 3 2 7 1 " 1 8 4 3 1 5 4 1 2 0 8 8 2 0 . 3 2 4 4 1 5 0 2 6 0 1 7 2 1 . 7 8 4 3 2 9 2 1 9 4 3 1 4 6 1 1 5 9 0 2 0 . 2 0 4 4 7 9 6 2 3 3 3 5 2 1 . 5 2 4 3 1 5 0 2 0 4 3 0 6 0 1 1 2 0 9 2 0 . 0 8 4 4 1 3 9 2 2 1 2 6 2 1 . 3 3 4 3 0 2 3 2 1 4 3 0 1 1 9 3 6 8 1 9 . 9 7 4 3 2 8 4 2 1 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. 1 5 4 7 7 4 5 2ff~- " 4 2 5 3 9 " " 5 3 9 1 " 1 9 . 7 3 " 5 2 9 2 8 1 6 2 0 0 2 0 . 7 9 4 7 6 9 5 Z F W P 0 R R » R P H I 1 4 1 6 9 8 0 0 0 0 0 0 0 0 ' . 8 3 . 0 0 . 8 3 . 7 0 1 8 0 . 0 4 1 7 4 3 3 1 5 7 3 2 4 3 1 4 • . 8 1 . 0 2 . 8 1 . 6 6 1 7 8 . 6 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 1 7 0 5 8 3 1 8 7 5 2 1 4 2 7 • . 2 4 • . 4 9 . 5 5 . 3 0 • 1 1 6 . 3 1 6 2 4 1 3 1 8 5 5 1 5 3 6 7 • . 2 5 - . 2 2 . 3 3 . 1 1 • 1 3 9 . 3 1 4 9 4 8 3 2 4 0 7 1 1 4 6 7 ' . 3 2 • . 0 9 . 3 3 . 1 1 • 1 6 3 . 5 1 3 7 3 3 3 1 9 7 3 6 8 9 6 • . 1 8 . 0 3 . 1 8 . 0 3 1 6 9 . 5 1 4 0 6 4 3 1 9 6 6 1 2 4 7 6 . 1 3 . 0 8 . 1 5 . 0 2 3 1 . 4 1 8 9 8 5 3 2 7 8 1 6 6 1 2 . 2 8 • . 0 2 . 2 8 . 0 8 • 4 . 2 2 2 3 0 0 3 3 2 6 5 2 1 7 5 0 . 4 2 • . 3 2 . 5 3 . 2 8 • 3 7 . 3 2 2 7 8 5 2 6 2 6 2 2 5 0 9 9 . 2 6 • . 4 8 . 5 5 . 3 0 • 6 1 . 4 2 2 5 5 9 3 1 4 1 3 2 3 2 4 0 • . 1 9 • . 2 4 . 3 0 . 0 9 • 1 2 8 . 3 2 8 6 6 0 3 2 0 2 4 2 5 9 8 4 ' . 5 1 . 3 5 . 6 2 . 3 9 1 4 5 . 4 3 1 0 0 3 3 3 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9 3 0 1 1 8 0 8 • . 0 3 . 0 7 . 0 8 . 0 1 1 0 9 . 0 1 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 8 2 5 6 2 3 0 8 5 7 3 7 2 • . 1 2 ' . 1 1 . 1 6 . 0 3 • 1 3 8 . 2 3 1 1 9 2 5 5 6 0 1 1 1 8 1 ' . 0 5 ' . 2 1 . 2 1 . 0 5 • 1 0 4 . 8 1 1 4 2 4 2 2 4 1 2 4 7 5 4 • • 2 5 ' . 0 8 . 2 6 . 0 7 • 1 6 1 . 5 1 2 3 9 5 2 3 5 6 4 3 2 9 7 • . 3 6 ' . 0 5 . 3 6 . 1 3 • 1 7 2 . 2 1 3 8 9 2 2 3 5 3 0 1 1 3 1 8 • . 4 0 ' . 1 3 . 4 2 . 1 8 • 1 6 1 . 3 1 5 7 4 3 2 3 5 2 9 1 7 0 1 • . 4 9 " . 0 1 . 4 9 . 2 4 • 1 7 8 . 3 1 7 1 6 8 2 2 6 7 2 1 1 4 5 4 • . 5 9 . 1 2 . 6 0 . 3 6 1 6 8 . 5 1 8 5 8 3 2 2 1 0 3 1 2 5 3 8 • • 6 3 . 1 9 . 6 6 . 4 3 1 6 3 . 5 2 1 4 1 8 2 3 6 9 9 2 1 3 1 1 • . 5 5 . 5 1 . 7 5 . 5 6 1 3 7 . 2 2 2 3 6 1 2 1 6 0 0 2 2 6 8 8 • . 5 7 . 6 5 . 8 6 . 7 4 1 3 1 . 3 2 1 9 7 2 2 4 1 8 6 2 2 0 2 9 • • 5 8 . 5 9 . 8 3 . 6 8 1 3 4 . 2 1 6 2 6 9 2 1 5 1 4 1 6 4 6 6 • . 4 1 . 4 2 . 5 8 . 3 4 1 3 4 . 1 6 1 3 4 2 4 3 1 9 1 3 6 5 9 • . 0 7 . 4 4 . 4 5 . 2 0 9 9 . 5 8 3 5 9 1 7 9 9 6 1 2 1 9 3 . 1 6 . 4 2 . 4 5 . 2 0 6 9 . 1 1 1 2 6 2 2 3 7 1 9 6 0 0 4 . 4 4 . 2 1 . 4 9 . 2 4 2 5 . 4 1 9 6 5 1 2 7 4 3 4 4 0 7 . 0 8 . 1 8 . 2 0 . 0 4 6 6 . 0 4 1 8 3 2 1 9 5 6 • 1 1 1 8 5 • . 2 3 • . 0 1 . 2 3 . 0 6 • 1 7 8 . 4 1 7 9 8 2 2 1 6 5 • 1 8 5 8 5 ' . 1 4 ' . 0 7 . 1 5 . 0 2 • 1 5 4 . 5 1 8 6 8 2 1 6 5 6 • I 9 7 8 3 . 1 5 • . 0 8 . 1 7 . 0 3 • 2 7 . 6 2 4 6 9 2 1 8 3 8 2 9 3 6 . 2 1 ' . 2 5 . 3 3 . 1 1 • 4 9 . 9 3 1 2 4 1 2 1 5 6 3 2 4 0 . 2 9 ' . 3 0 . 4 2 . 1 6 • 4 6 . 0 1 7 5 2 2 3 2 9 8 0 0 0 0 . 3 2 . 0 0 . 3 2 . 1 0 . 0 Z F W P Q R R * R P H I 1 4 3 8 0 1 0 0 0 0 0 0 0 0 • • 7 7 . 0 0 . 7 7 . 6 0 1 8 0 . 0 4 3 7 9 1 1 7 7 6 0 3 2 8 7 1 • • 7 5 . 0 6 . 7 5 . 5 7 1 7 5 . 7 1 9 5 2 9 3 1 3 9 2 2 9 9 2 2 . 0 7 . 6 9 . 6 9 . 4 8 8 4 . 5 1 3 4 6 2 3 2 9 4 9 1 2 2 5 5 . 1 6 ' . 1 1 . 2 0 . 0 4 ' 3 3 . 1 1 6 4 2 4 3 2 8 5 8 1 1 2 6 8 . 2 5 . 0 5 . 2 6 . 0 7 1 1 . 2 1 1 9 8 0 3 2 7 5 1 2 1 1 8 1 . 0 8 ' . 4 7 . 4 8 . 2 3 • 8 0 . 5 5 6 2 8 3 4 3 1 5 4 1 5 1 . 0 2 . 0 1 . 0 2 . 0 0 3 6 . 4 2 1 3 4 6 3 5 4 1 7 1 5 9 8 2 . 3 5 . 1 5 . 3 8 . 1 4 2 4 . 0 2 2 5 4 0 3 5 2 3 4 1 2 2 3 3 . 5 3 ' . 0 5 . 5 3 . 2 8 ' 5 . 0 2 1 3 4 6 3 4 6 8 7 2 2 4 1 3 . 2 3 ' . 4 1 . 4 7 . 2 2 • 6 0 . 8 2 1 5 1 6 3 5 2 2 2 2 3 4 6 5 • . 1 9 • . 4 4 . 4 8 . 2 4 • 1 1 3 . 6 2 2 1 4 9 3 6 4 2 2 2 1 8 8 6 • - 3 2 • . 2 8 . 4 3 . 1 8 • 1 3 8 . 7 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 1 2 0 9 4 3 6 4 8 4 I 1 8 7 5 . 1 5 ' . 1 3 . 2 0 . 0 4 • 4 1 . 8 1 1 0 9 8 3 7 1 9 6 1 1 2 2 4 ' . 0 9 . 1 0 . 1 4 . 0 2 1 3 1 . 9 4 2 5 3 3 7 6 3 0 1 3 1 9 0 . 0 5 . 3 7 . 3 7 . 1 4 8 2 . 4 1 1 2 3 4 3 7 1 2 6 1 1 7 2 2 . 1 7 . 2 3 . 2 8 . 0 8 5 4 . 4 1 3 9 7 2 3 7 0 7 0 7 3 2 0 . 0 1 • • 1 4 . 1 5 . 0 2 • 8 6 . 9 9 1 7 2 3 7 7 7 8 1 1 4 1 8 ' . 2 2 • . 3 5 . 4 1 . 1 7 • 1 2 2 . 9 7 2 0 6 3 7 8 4 6 6 0 1 4 ' . 1 9 ' . 1 6 . 2 5 . 0 6 • 1 4 0 . 2 i 3 4 1 0 3 7 3 4 3 0 0 0 0 • • 1 9 . 0 0 . 1 9 . 0 3 ' 1 8 0 . 0 - 1 9 8 -TUKEY SPtCTRUM ESTIMATION 052JA ALIA MAG X 18 8 61 STATION 6 AND 1 TIME 1009 TO 11065 K A X LOGX B [ Y i»3 LOGY E I F M P a R R.  P H U 4 1990 3 5561 22.75 5 1021 3 1315 22. 12 3 4265 2 7540 0000 0000 .28 .-oo .28 .08 •.0 1 4 1246 3 6044 22.78 3 6594 3 1599 22.20 2 2075 2 7772 3 7300 2 3271 .25 «.ii .27 .07 •22.8 2 3 6829 2 5520 21.74 4 7197 2 5979 21.78 3 7133 6208 3 3577 2 1783 •.01 '.31 .31 .10 •92.0 3 4 139 2 1357 21.13 4 2017 2 6035 21.78 3 5777 1 6003 3" 7473 1 5523 '.21 •19 .29 .08 137.4 4 4 1443 2 1121 21.05 4 5504 2 5378 21.73 3 5032 " " 1 6226 3 4614 1 5805 '.25 • .24 .35 .12 137.0 5 4 1216 2 1165 21.07 4 1799  4814 21.68 3 2807 1 5653 3 5494 1 8290 '.24 '.35 .42 .18 124.3 6 4 1034 2 1356 21.13 4 3162 2 7147 21.85 3 8466 1 5698 3" 5799  7034 • .18 '.23 .29 .08 129.0 7 4 1045  1825 21.26 4 1791 3 1179 22.07 3 4783 1 4281 3' 5087 1' 6532 •09 •14 .17 .03 123.2 8 4 1148 2 3371 21.53 4 2701 3 1342 22.13 3 349 5 1 2774 3 4230 2" 1230 • .04 '.18 .19 .04 102.7 9 4 1147 2 48 76 21.69 4 1105 3 1737 22.24 2 5689 2 1708 3 2963 2 3109 '.19 •-34 .39 .15 118.8 10 4 1029 2 7092 21.85 4 1807  3967 22.60 3 4326 2 8769 3' 3771 2 5293 • .52 '.32 .61 .37 "148.9 11 3 9896 3 1054 22.02 4 1434 3 7710 22.89 3 2922 3 2075 3' 3719 1> 7463 ' .73 •.03 .73 .53 177.9 12 4 1061 3 1124 22.05 4 1621 4 1529 23.18 2 6296 3 2427 3 1563 3 1450 -.59 .35 .68 .47 149.1 13 4 1041 2 9197 21.96 4 1228 4 2209 2 3.34 2 3692 3 1532 3 2455 3 2941 •34 .65 .74 .54 117.5 14 3 9770 2 6949 21.84 3 7025 4 1696 23.23 2 9898 2 3447 3" 3289 3 2407 • .10 .70 .71 .50 98.1 15 3 9240  5090 21.71 4 2029 3 8754 22.94 3 2402 2 5882 3" 2550 3 1078 .28 .51 .58 .34 61.4 16 3 9217 2 4169 21.62 3 7849 3 6116 22.79 3" 2283 2 8370 3 2629 2 6748 .52 .42 .67 .45 38.9 17 3 9586 2 3001 21.48 4 1950 3 3898 22.59 2 3364 2 5079 2" 3624 2 2145 .47 .20 .51 .26 22.9 18 3 9835  1716 21.23 3 1949 3 2001 22.30 2 3619 2 1881 3' 3444 2' 1041 .32 •.18 .37 .13 '29.0 19 3 9060 I 9353 20.97 4 2135 3 1246 22.10 3 2328 1 3371 3 1399 6722 .10 .02 .10 .01 11.3 20 3 798 5 1 5723 20.76 3 1369 2 6855 21.84 3 2165 1 3784 3 1123 1 5038 •.19 .25 .32 .10 126.9 21 3 8518 1 5101 20.71 4 1269 2 5783 21.76 2 5807 1 5961 3' 4033 1 1718 •35 .10 .36 .13 163.9 22 3 9139 1 3703 20.57 3 6554 2 7229 21.86" 2" 3411 1 5316 3' 1203 ' 2209 •.32 •14 .35 .12 157.4 23 3 7885 1 3158 20.50 4 1504 2 7437 21.87 3 1760 1 3452 3 2879 ! • 1818 •23 '.12 .25 .06 152.2 24 3 7683  42 74 20.63 3 2931 2 8035 21.90 3 1977 1 1869 2' 2245 2599 '.10 .01 .10 .01 172.1 25 3 8782  2627 20.42 3 9730 2 4355 21.64 2 1488 8631 3' 3487 0000 1 .08 .00 .08 .01 180.0 T U K E Y S P E C T R U M t S T I MAT 1 0 N 0522JA ALIA MAG X 18 8 61 STATION 6 AND 2 TIME 1009 TO 11065 K A X LOGX B 4 1990 3 5561 2 2 . 7 5 4 6783 1 4 1246 3 60 44 2 2 . 7 8 4 1126 2 3 6829 2 5520 2 1 . 7 4 4 2764 3 4 1139 2 1357 2 1 . 1 3 3 5707 4 4 1443 2 1121 2 1 . 0 5 4 2673 5 4 1216 2 1165 2 1 . 0 7 4 1793 6 4 1034 2 1356 2 1 . 1 3 4 1032 7 4 1045 2 1825 2 1 . 2 6 3 9880 8 4 1148 2 3371 2 1 . 5 3 3 9045 9 4 1147 2 4876 2 1 . 6 9 4 1457 10 4 1029 2 7092 2 1 . 8 5 3 5637 11 3 9896 3 1054 2 2 . 0 2 2 2347 12 4 1061 3 1124 2 2 . 0 5 1 3444 13 4 1041 2 9197 2 1 . 9 6 3 4565 14 3 9770 2 6949 2 1 . 8 4 3 7428 15 3 9240 2 5090 2 1 . 7 1 3 7985 16 3 9217 2 4169 2 1 . 6 2 2 3746 17 3 9586 2 3001 2 1 . 4 8 3 3842 18 3 9835 2 1716 2 1 . 2 3 3 6298 19 3 9060 1 9353 2 0 . 9 7 4 1289 20 3 7985 1 5723 2 0 . 7 6 3 6752 21 3 8518 1 5101 2 0 . 7 1 3 5723 22 3 9139 1 3703 2 0 . 5 7 £ 9702 23 3 7885 1 3158 2 0 . 5 0 3 8926 24 3 7683 1 4274 2 0 . 6 3 3 6665 25 3 8782 1 2627 2 0 . 4 2 2 6151 T U K E Y S P E C I R U M E S 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 T I C 3 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 LOGY 2 2 . 4 4 2 2 . 5 4 2 2 . 1 3 2 2 . 1 3 2 2 . 1 8 2 2 . 2 1 2 2 . 13 2 2 . 1 0 2 2 . 2 2 2 2 . 5 2 22 .88 2 3 . 0 0 2 2 . 9 3 2 2 . 8 2 2 2 . 5 9 2 2 - 2 8 _ 2 2 . 1 6 2 2 . 0 9 2 2 . 0 6 2 2 . 0 6 2 2 . 0 3 21i?*_ 21.96 21.97 2 1 . 8 7 2 1 . 5 2 T I 0 N E 2 F M p Q R R.  PHI1 2 3336 3 2764 0000 0000 • . 7 1 . 0 0 . 7 1 . 5 0 180.0 3 6185 3 3027 3 2818 2 2855 • . 6 6 . 0 6 . 6 7 . 4 5 174.6 4 1218 2 2918 3 3446 2 1208 • . 3 4 . 1 4 . 3 7 . 1 3 157 .5 3 5961 1 5724 3 1803 2674 • . 1 3 . 0 1 . 13 . 0 2 177.3 2 8089 1 1493 3 4777 1 1277 • . 0 4 . 0 3 . 0 5 • 6b" 139.5 3 5571 7707 3 1154 5546 . 0 2 ' . 0 1 . 0 2 . 0 0 •35.7 4 1015 1063 3 4965 3294 . 0 0 . 0 1 . 0 1 . 0 0 72 .1 3 6280 1 5411 3 1284 1 8246 . 1 1 . 1 7 . 2 1 . 0 4 56 .7 3 1368 1 7726 3 3060 2 2105 . 1 0 . 2 8 . 3 0 . 0 9 6 9 . 8 3 4491 1 6022 3 1314 2 6546 • - 0 5 . 5 1 . 5 1 . 2 6 9 5 . 3 3 8603 2 1603 3 2457 3 1535 . 0 7 . 6 6 " . 6 6 . 4 4 8 4 . 6 3 5998 3 1221 3 2867 3 1575 . 3 8 . 4 9 . 6 2 . 3 8 5 2 . 2 3 3119 3 1964 1 2483 2 4840 . 6 3 . 1 6 . 6 5 . 4 3 13.8 3 3648 3 1661 3 2353 2 3174 . 6 8 ' . 1 3 . 6 9 . 4 7 •10.8 3 5505 2 8669 2 6779 2 3860 . 5 3 ' . 2 4 . 5 8 . 3 4 ' 2 4 . 0 3 5897 2 2137 3 2962 2 3414 . 2 2 ' . 3 5 . 4 1 . 1 7 •58.0 3 5100 1 7776 3 1006 2 3694 . 1 0 •.48 . 4 9 . 2 4 ' 7 8 . 1 3 3986 2 1166 2 5651 2 1863 . 1 9 ' . 3 1 . 3 6 . 1 3 •58.0 3 3404 2 1149 1 5457 1 4318 . 2 6 • . 1 0 . 2 8 . 0 8 ' 2 0 . 6 3 4590 1 6250 2 3682 I 6289 . 1 9 ' . 1 9 . 2 7 . 0 7 •45.2 3 5690 1 1318 3 1213 1 5303 • . 0 5 • . 2 1 . 2 2 . 0 5 • 104.0 3 3790 1 2861 3 1745 5164 ••14 . 0 2 . 1 4 . 0 2 169.8 3 1865 5788 2 7012 1 5322 • . 0 3 . 2 9 . 2 9 . 0 9 9 6 . 2 3 4466 1 1046 3 1526 I 3339 . 0 6 . 2 0 . 2 0 . 0 4 7 2 . 6 3 6017 5374 3 1112 2923 ••03 . 0 2 . 0 3 . 0 0 151.5 3 2826 7533 3 3308 0000 • . 0 8 . 0 0 . 0 8 . 0 1 1 8 0 . 0 0522JA ALTA MAG X 18 8 61 STATION 6 AND 3 TIME 1009 TO 11065 LOGY 2 1 . 8 5 2 1 . 9 5 2 1 . 4 7 2 1 . 2 7 2 1 . 1 8 " 2 1 . 2 8 2 1 . 3 7 21 .44 2 1 . 8 2 2 2 . 1 8 2 2 . 4 0 2 2 . 4 7 2 2 . 3 7 2 2 . 1 4 2 1 . 8 9 2 1 . 8 4 . 2 1 . 8 8 2 1 . 7 4 2 1 . 5 4 2 1 . 4 1 2 1 . 2 6 2 1 . 2 0 K A X LOGX B c Y , o-«.l»J 4 1990 3 5561 2 2 . 7 5 4 1863 2 7106 1 4 1246 3 6044 2 2 . 7 8 3 2840 2 9016 2 3 6829 2 5520 2 1 . 7 4 3 9173 2 2927 3 4 1139 2 1357 2 1 . 1 3 3 2268 2 1844 4 4 1443 2 1121 2 1 . 0 5 3 7094 2 1518 5 4 1216 2 1165 2 1 . 0 7 3 6417 2 1917 6 4 1034 2 1356 2 1 . 1 3 2 1117 2 2352 7 4 1045 2 1825 2 1 . 2 6 3 3706 2 2759 8 4 1148 2 3371 2 1 . 5 3 2 3857 2 6586 9 4 1147 2 4876 2 1 . 6 9 3 4846 3 1497 10 4 1029 2 7092 2 1 . 8 5 3 2501 3 2508 11 3 9896 3 1054 2 2 . 0 2 2 9011 3 2968 12 4 1061 3 1124 2 2 . 0 5 2 1039 3 2365 13 4 1041 2 9197 2 1 . 9 6 3 1696 3 1377 14 3 9770 2 6949 2 1 . 8 4 2 9446 2 7689 15 3 9240 2 5090 2 1 . 7 1 2 7682 2 6906 16 3 9217 2 4169 2 1 . 6 2 3 1023 2 7571 17 3 9586 2 3001 2 1 . 4 8 2 7074 2 5509 18 3 9835 2 1716 2 1 . 2 3 3 1422 2 3490 19 3 9060 1 9353 2 0 . 9 7 3 1577 2 2596 20 3 7985 1 5723 2 0 . 7 6 2 3085 2 1800 21 3 8518 1 5101 2 0 . 7 1 1 9054 2 1571 22 3 9139 1 3703 2 0 . 5 7 3 1425 2 1587 23 3 7885 1 3158 2 0 . 5 0 2 5129 2 1722 24 3 7683 1 4274 2 0 . 6 3 2 4187 2 1790 25 3 8782 1 2627 20 .42 3 1235 1 8800 2 1 . 2 0 2 1 . 2 4 2 1 . 2 5 2 0 . 9 4 E I f W P Q R R«R PHI1 2 7269 3" 1033 0000 0000 • . 5 2 . 0 0 . 5 2 . 2 7 •180.0 3 3638 3 ' 1220 3 5243 1 6897 ' . 5 2 . 0 3 . 5 2 . 2 7 176.8 3 4242 2 ' 2267 3 1251 1 5443 ••56 . 1 4 . 5 8 . 3 4 166.5 2 4500 1' 7005 3 3660 1 2569 ' . 4 4 . 1 6 . 4 7 . 2 2 159.9 2 6017 1' 3613" 3 1538" 1 1832 • .28 . 1 4 . 3 1 . 1 0 153.1 3 3597 1" 3427 3 2142 1 5690 ' . 2 3 . 3 8 . 4 4 . 2 0 121.1 3 3986 1' 408 3 3 2035 I 8795 ' . 2 3 . 4 9 . 5 4 . 2 9 114.9 3 2084 1' 5194 2 4876 1 6582 ' . 2 3 . 2 9 . 3 7 . 1 4 128.3 2 1399 2' 2191 3 1974 1 8823 • .46 . 1 9 . 5 0 . 2 5 158.1 2 9689 2' 4485 2 4128 2 3662 ' . 5 2 . 4 3 . 6 8 . 4 6 140.8 3 3745 2 ' 3641 3 2053 2 9597 • . 2 7 . 7 2 . 7 7 . 5 9 110.8 3 3011 2 2304 3 1103 3 1334 . 1 3 . 7 5 . 7 7 . 5 9 8 0 . 2 2 3774 2 7445 2 9739 3 1024 . 4 6 . 6 3 . 7 8 . 6 0 5 4 . 0 2 7024 2 6556 2 7348 2 5240 . 5 8 . 4 7 . 7 5 . 5 6 3 8 . 6 3 2082 2 3275 2 3734 2 3277 . 4 5 . 4 5 . 6 3 . 4 0 4 5 . 0 3 1975 2 2147 2 6538 2 2793 . 3 6 . 4 7 . 5 9 . 3 5 52 .4 3 1387 2 2995 1 6820 2 2260 . 5 3 . 4 0 . 6 7 . 4 5 3 7 . 0 3 1358 2 2708 2 4737 1 9948 . 6 7 . 2 4 . 7 1 . 5 0 2 0 . 2 3 1344 2 1462 2 1019 ' 6 2 8 8 . 6 0 ' . 0 3 . 6 0 . 3 6 •2.5 3 1454 1 5982 2 6987 1 •1165 . 3 8 •.07 . 3 9 . 1 5 •11.0 3 1592 1 1703 2 1374 1916 . 1 7 . 0 2 . 1 7 . 0 3 6 . 4 2 6017 1 1033 2 2009 6916 . 1 2 . 0 8 . 1 4 . 0 2 3 3 . 8 2 3121 2842 2 3545 •1093 . 0 4 • . 0 1 . 0 4 . 0 0 •21.0 3 1815 5879 2 3250 1 •1126 . 0 8 ' . 1 5 . 1 7 . 0 3 •62.4 3 1783 1 1918 2 8568 •4757 . 2 2 ' . 0 5 . 2 3 . 0 5 •13.9 2 1746 1 1335 2 •2422 0000 . 2 8 . 0 0 . 2 8 . 0 8 ' . 0 - 1 9 9 -T U K f c i r S H c C T R U M L S T 1 M A T I O N 0 5 2 2 J A A L T A M A G X S T A T I O N 6 A N D 4 T I M E 1 0 0 9 T 0 1 1 0 6 5 8 1 8 6 1 K A X L O G X B Y L O G Y [ j joc iL . 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4 1 . 1 3 . 4 3 . 1 9 1 6 2 . 7 1 9 3 2 1 5 ( I 4 2 10 2 0 . 6 3 5 4 7 8 3 2 3 7 4 2 2 1 . 5 7 4 1 2 8 4 1 3 6 3 2 1 1 0 7 9 1 1 9 3 4 • . 2 9 . 1 5 . 3 2 . 1 1 1 5 2 . 0 2 0 3 2 1 7 1 1 3 8 - 4 2 0 . 5 9 5 4 7 7 0 2 3 8 0 8 2 1 . 5 8 4 1 2 5 8 9 0 7 7 2 5 6 4 5 1 2 2 4 4 ' . 0 7 . 1 9 . 2 0 . 0 4 1 1 2 . 0 2 1 3 2 1 6 1 1 3 1 2 5 2 0 . 4 9 5 4 7 4 2 2 4 0 6 6 2 1 . 6 1 4 1 2 6 2 5 1 4 9 2 8 7 6 1 1 1 7 8 4 . 0 5 . 1 6 . 1 6 . 0 3 7 3 . 9 2 2 3 2 1 0 3 1 1 9 . 6 2 0 . 2 9 5 4 / 0 4 2 2 9 7 8 2 1 . 4 7 4 1 2 5 7 7 8 2 2 2 7 1 2 9 7 5 2 9 . 1 0 . 1 0 . 1 4 . 0 2 4 3 . 9 2 3 3 2 1 0 3 1 1 2 1 6 2 J . 0 9 5 4 6 8 7 2 2 1 7 5 2 1 . 3 4 4 1 1 9 2 3 8 8 5 2 5 0 9 5 •2 6 8 6 4 . 0 7 . 0 0 . 0 7 . 0 1 1 . 0 2 4 3 2 1 0 9 6 7 iO 1 9 . 9 4 5 4 6 8 9 2 3 0 6 9 2 1 . 4 9 4 1 1 0 3 6 6 0 7 2 8 5 6 8 1 4 6 6 . 1 3 • • 0 3 . 1 3 . 0 2 • 1 2 . 7 2 5 3 1 7 7 6 4 0 ( . 6 1 9 . 6 1 5 4 6 6 0 2 1 9 5 0 2 1 . 2 9 4 1 0 9 5 4 9 3 9 2 9 6 8 9 0 0 0 0 . 1 8 . 0 0 . 1 8 . 0 3 • . 0 -201-T U K L v Y SPhCTRUM t S T I M A I 1 0 N 0969JA ALTA 19 8 61 HZ STATION 6 AND 2 TIME 1450 1600 J K A X LOGX B Y LOGY b 4 1282 3 4190 22 62 4 281d 3 3458 22.54 3 5374 1 4 1160 3 50 iZ 27.71 4 1895 3 4432 22.65 3 4697 2 4 1020 3 1166 22.07 3 7122 i 1068 22.49 3 3414 -.3. .3 9560 _48JL6_J1^68_ J_ _7i>22. _ a All_6_ .22.61.. 3 2955 4 3 9473 2 3003 21.48 4 1284 3 2416 22.36 3 1262 5 3 9184 2 1679 21.22 3 9146 2 5 142 1. 73  2758 6 3 862? 2 1035 21.28 2 5489 2 2511 2 1.40 3 1414 7 3 799 7 2 1837 21.26 3 3941 2 3778 21.58 2 6425 H 3 7752 2 1566 21.19 5773 2 6067 21.78 3 1137 9 -.7549 2 1497 21.1.18 . . 3. 2432. 2 7634_ .21.8<L. 3 (610 10 3 699 1 2 1606 21.21 v2 3143 3 1608 22.21 3 1043 11 3 6671 2 1643 21.22 2 7964 3 2615 22.42 2 2412 12 3 6462 2 1156 21.06 3 3190 3 2002 22. 30 2 6223 13 1 6418 1 5858 20.77 3 8975 2 8561 21.93 3 1867 14 3 6303 1 36 16 20.56 4 1040 2 4413 21.64 3 2 14 6.Q6  . 1. .24 a 2CL,3J_ 3. IhJZ 2 1914 2X^2 8_ .3156 4 16 3 5689 I 2654 20.42 3 7075 1 7115 20.65 2 9112 17 3 5551 1 3656 20.56 4 1031 . J 6371 20.80 3 1276 18 3 5180 1 2766 20.44 4 1181 1 6227 20.79 3 1780 19 3 4649 1 1240 20.09 3 7925 I 5717 20.76 3 1339 20 3 4248 90 J2 19.96 3 3411 1 4224 20.63 2 3861 21 1_3SSL6_ .2JD9 liU9_9_ -.3 JOJ2. _J -3731 20.57 -2-10-3 3. 22  3826 l" 1654 20.22 3 3680 1 3521 20.55 2 3042 23 3 3670 1 2385 20.38 2 3713 1 30B6 20.49 1 6421 24 3 3288 1 18 39 20.26 3 3659 1 2613 20.42 ? 8686 25 3 2812 5694 19.76 3 3499 1 137  20.14 3 1256 T U K E Y S P t C T R U M t S T I A T I C N 0969JA ALTA 19 8 61 HZ S TAT I UN 6 AND 3 TIME 1450 1600 K " A X LOGX B Y (ndi) LOGY t 4 1282 1 4190 22.62 2 2777 3547 19.55 2 1586 1 4 1160 3 5092 22.71 1 8702 6606 19.82 1 4560 2 4 1020 3 1166 22.07 2 1271 5979 19.78 2 1376 3 . 3 9560. 2 4826 21.68 2 1078 5974 19.78 1 8051 4 3 9473 2 3003 21.48 1 4085 7365 19 87 2 1 142 5 3 9184 2 1679 21.22 1 8872 1 1101 20.04 2 1471 6 3 8622 2 1885 21.28 1 1023 1 1620 20.21 1 6118 7 3 7997 2 1837 21.26 1 6999 1 1 762 0.25 2 1803 8 3 7752 2 1566 21.19 1340 1 1703 20.23 2 1030 9 3 7549 2 14J7 21.18 1 7659 1 2506 20.40 6881 10 3 699 3 2 1606 21.21 1 3338 1 4217 20.62 1 1392 11 3 6671 2 1643 21.22 1 4972 1 4923 20.69 1 7597 12 3 6462 2 1156 21.06 1 5042 1 3072 20.49 1 125 1 13 3 6416 1 5658 20.77 1 1817 9830 19.99 1 917 / 14 3 630 3 I 3636 20.56 1 4094 4636 19.68 1 4791 15 3 606 6. 1 2459 20. 39 1447 4281 19.63 2 1111 16 3 568 9* 1 2654 20.42 I 2303 3531 19.55 2 1468" 17 3 5551 1 3656 20.56 3098 3214 19.51 I 5324 18 3 5180 1 2766 20.44 1 2215 2675 19.43 1 3321 19 3 4649 1 1240 20.09 9135 2294 19.36 1202 20 3 4246 9092 19.96 1 2274 1936 19.29 1 8314 21 3 3986 9839 19.99 2681 1776 19.25 I 9315 22 3 3826 ~'l 1654 20.2? 1 2931 1872 19.27 1* "4812 23 3 3670 I 2385 20.38 1 1223 1471 19.17 1 '6915 24 3 )2d8 1 1839 20.26 1 1529 •1 9671 18.99 2 1300 25 3 2812 5694 19. 76 •2 1446 ' I 4600 18.66 2 1316 T IJ K £ Y S P L C T R U ME 5 T I MAT I 0 N 0969JA ALTA 19 e 61 HZ STATION 6 ANC 5 TIME 1450 1600 J K A X LOGX B Y (Wl) LOGY t4 1282 3 4190 22.62 5 3616 5 1611 24.21 2' 8052 1 4 1160 3 5092 22.71 5 3346 5 1672 24.22 2' 9315 2 4 1020 3 1166 22.07 5 3310 3 6456 22.81 3' 128? 3 9560 2. 4626 .21.68 5 3300 3 1608 22.21 3' 1726 4 3 9473 2 3003 21.48 5 3277 3 1646 22.22 3' 1604 5 3 9184 2 1679 21.22 5 3262 3 1213 22.08 3' 1236 6 3 8622 2 1865 21.28 5 3260 3 1673 22.22 2' 6415 7 3 7997 2 1837 21.26 5 3217 3 1812 22.26 1' 4347 8 3 7752 2 1566 21.19 5 3221 3 1316 22.12 2 3411 JL 3. 7549 2 1497 21.18 5 3206__ 2 8656 21.94 2 3862 10 3_ 6993 2 1606 2 1.21 5 3164 3 1146 22.06 2 5181 11 3 66 71 2 1643 21.22 5 3124 3 1451 22.16 2 8440 12 3 6462 2 1 156 21 06 5 3095 3 1163 22.07 3 1098 13 3 6418 1 5 8 5 1 20.77 5 3130 2 8472 21.93 3 1403 14 3 6303 1 3636 20.56  3096 3 1034 22.01 3 1931 15 ._3_6flt6 .1 2459 ?0,A9 .. 5. 3058. . i 1317 22.12 2592 16 3 5689 1 2654 20.42 5 3025 1269 22.10 3 3079 17 3 5551 1 3656 20.56 5 2987 3 1079 22.03 3 346 3 18 3 5180 1 2766 20.44 5 2965 3 1083 22.03 3 3696 19 3 4649 1 1240 20.09 5 2920 3 1131 22.05 3 3808 20 3 4248 9092 19.96 5 2891 2 9318 2 1.97 3 3959 21_ 3 3986. 9839 19.99 5 2848 2 7779 21.89 3 4051 22 3 3826 r 1654 20.22 5 2819 2 9750 21.99 3 4254 23 3 3670 1 2385 20.38 5 2777 3 1084 22.04 3 4834 24 3 3288 1 1839 20.26 5 2758 2 9342 21.97 3 5644 25 3 2812 5694 19.76 5 2714 2 4270 21.63 3 5802 I F W P Q R R»R PHI1 3 1101 0000 0000 .29 .00 .29 .08 ' .0 3 1546 3 • 1025 2 •3212 .33 '.07 . 3  .11 •11.7 2 3004 2 •0985 2 •??14 .42 • .12 .44 .19 •15.5 2 6623 2 ' 2660 2 •2537 .47 '•18 . .,.50. .25^  •21.0 2 1645 2 '4604 ? • 1467 .43 '.17 .46 21 '21.9 1 8161 2 '9240 1 ' 1489 .27 ' .05 .28 .08 ' 10.3 I 5990 2 ' 8691 1 ">173 .28 • .24 .36 .13 '40.8 1 7760 2 ' 3651 1 •8903 .30 '.34 .45 20 '48.8 1 ?625 2 •3903 2 •1 195 .09 • .39 .40 .16 •77.6 9691 2 ' 7931 1 •4742 • .0.3 '•14__ _- 14 . - 02 • 101.5 2 19?3 t 6034 1 ' ?020 .38 • .04 .38 .14 •6.0 2 3596 2 2082 2 •1857 .55 '.28 .62 .38 •27.3 ? 1737 2 4249 2 ' 2 165 .16 ' .45 .58 .34 •51.5 '6009 2 •2721 1 '7209 • .03 • .32 .32 10 •94.8 1 1048 2 8681 '9698 ' .08 • .08 .11 01 •137.2 J. 1029 . 2 •6L54 '62i5. . '.03 . .18_ JJ.48.7 9735 2 •1586 • 3840 ' .2? ' .09 .24 .06 • 158.5 H171 2 5940 '4866 '.17 • . 10 .20 .04 •149.2 7354 3 1477 • 2065 • . 18 '.05 .18 .03 •164.3 4735 3 1790 2726 • . 18 .10 .21 .04 150.1 3 )07 3 1343 4906 • .20 .25 .32 10 128.5 4374 3 1070 442.6 '.J3 ..23 _-32 . .11._1J4.7 3275 3 ' 1257 6404 • .14 .27 .30 .09 117.1 1276 3 1419 8069 .05 .30 .30 .09 81.0 3402 3 1032 3872 .16 .18 .24 .06 48.7 1551 2 5726 0000 .18 .00 .18 .03 • 0 Z F W P Q ~R R«R PHI 1 8258 0000 0000 .07 .00 .07 .00 180.0 1' 3722 1' 1 142 1 1172 .00 .01 .01 .00 •107.6 1 1284 1 186  3107 .15 .04 . 16 .03 • 13.6 I 1324 1 1567 1' 1308 .25 .24 .35 12 •44. 7 1 116 1' 6226 1 1971 .24 .42 .48 .23 •60.5 6390 2' 1144 7691 • .15 .18 .23 .05 • 129.7 1' 2329 1' 6535 1 1438 .42 .26 .50 .25 148.3 1' 1103 1 3887 1 2289 • . 19 .40 .45 20 115.7 1 1345 1 7368 1 1455 .26 .28 .38 .15 47.2 1 2057 _ 1 4961 6229 .34 . 10 .35 .12 16.8 1 4047 1 3459 1251 .49 .02 ".49 .24 1.8 1 6197 1 3Rf 5 9996 .69 .11 .70 .49 •9.2 1 3826 1 1?46 1 167  .64 .28 .70 .49 '23.7 6266 1' 4850 8159 .26 .34 .43 .18 '52.5 1' 1595 1 • 6265 1175 • .01 .09 .09 .01 •97.7 .2 2159 1" 1001 < 1 354 .00 • 13. .13 02 '89.1 1658 1 2 369 •1 5968 • .17 .06 .18 .03 •160.2 1 2961 8273 '4 9337 ' .27 .00 .27 .07 180.0 1 ?016 1' 2723 • 1 4721 ' .?3 .05 .24 .06 • 166.8 1084 3008 • 1 4906 ' .20 .09 .22 .05 '155.7 I' 8227 7415 • 1 3066 • .20 .07 .21 .04 • 159.6 1' 1029 1' 1182 '2 3448 ' .02 .01 .03 00 161.5 ? 2560 1 • 2266 "• 1 4499' .00 ".08 .08" .01 8~6.7~ 1' 6950 1' 1365 • 1 5230 • .12 .09 . 15 .02 143.0 1 7039 1 2151 • I 2445 • .17 .06 .18 .03 160.8 1' 1217 1 2674 0000 ' .08 .00 .08 .01 180.0 Z F w p" Q R R«R PHI1 1 2317 0000 0000 .00 .00 .00 .00 .0 2' 7268 3 1190 3 3819 • .02 .13 .13 .02 100.8 2 7251 3 1998 3 1098 • .26 .40 .48 .23 123.4 1 2897 3 2237 2 1698 .03 ' . 19 .20 .04 •80.3 l" 2229 3 2778 2 1277 .03 .18 . 18 .03 60.1 2 1206 3 3523 1 9579 .27 .21 .34 12 38.5 2 2197 3 3944 2 1691 .39 .30 .49 .24 37.6 2 1642 3 4388 1 7633 .28 .13 .31 .10 24.9 1 8073 3 5174 1 1809 .18 .04 . 18 .03 12.6 1 _386? 3 6022 I 1543 .11 .04 .12 .01 21.8 1984 3 6883 1 5971 • .00 .14 .14 .02 91.9 1 1831 3 7478 1 7505 ' .04 .15 . 16 .03 103.7 2793 3 7768 1 6022 ' .01 .16 . 16 .03 92.7 1 1347 3 8106 1 2450 .06 11 .13 .02 61.2 1 4714 3 8573 1 1829 .00 .09 .09 01 88.5 jaoa J . .90 72 3622. • .io._ _• 02 _ _.U0_ 01 1685.7 1 2120 3 9394 ""l 1515 ' .12 • .08 .14 .02 •144.5 1' 1021 3 9896 1 2455 • .05 '.12 .13 .02 • 112.6 6169 4 1024 1 1747 ' .04 • .10 .11 .01 •109.5 1 4512 4 1045  1260 • .04 '.11 .11 .01 '109.7 2661 4 1048 4975 • .03 •.05 .06 .00 •118.1 2806 4 1056 • 1 2552 • .03 • .00 .03 .00 •174.8 1354 1083 '147 .1 '.03 .03 .00 '71.9 7469 1129 '6068 .5 ' 4 .06 .00 '39.1 9598 4 1188 '1 2991 .07 .00 .07 .01 1.8 4828 4 1233 0000 .10 .00 .10 .01 .0 - 2 0 2 -T h e r e s u l t s o f t h e p o w e r s p e c t r a l c o m p u t a t i o n o f t h e m a g n e t i c a n d e l e c t r i c r e c o r d s a t B e i s e k e r a r e g i v e n i n t h e f o l l o w i n g p a g e s . T h e r e s u l t s o f t h e p o w e r s p e c t r a l d e n s i t y f o r t h e m a g n e t i c f i e l d c o m p o n e n t s a r e g i v e n i n t e r m s o f c h a r t d i v i s i o n s w h i l e t h o s e o f t h e e l e c t r i c f i e l d c o m p o n e n t s a r e g i v e n i n t e r m s o f 10 M v . - 2 0 3 -1 TUKEY SPECTRUM ESTIMATION 0 0969JA ALTA 18 8 61 HY EX STATION 3 TIME 1009 1165 OJ K A X . LOGX B Y LOGY E 4 1096 2 2701 21.43 4 3399 4 1096 23.04 1 4564 r _ 3 -1301 "2 4423 21.65 • '4 "2 728 4' 1329 23.12 2 6146 2 3' 5689 2 2465 21.39 4 2180 3 2510 22.40 2 5909 3 2 5510 2 1229 21.09 4 2633 2 3176 21.50 2 1004 . 4 3 2595 1 9778 20.99 4 2772 2 1666 21.22 2 6609 5 1 5369 2 1074 21.03 4 2325 2 1171 21.07 2 8099 6 3 1793 2 1301 21.11 4 2254 2 1932 21.29 1 2707 3 2200 " 2" 3661 21.56 "  4 2459 2 3327 21.52 2 1953 8 3 1441 2 8432 21.93 4 2281 2 4574 21.66 2 8687 9 3' 1654 3 1053 22.02 4 1930 2 3691 21.57 2 5158 10 2 9602 2 8 7 72 21.94 4 1841 2 2605 21.42 1 4836 11 3 1427 2 6053 21.78 4 1926 2 3958 21.60 2 309 6 12 2 8687 2 6839 21.84 4 1881 2 8911 21.95 2 4386 13 "2-2202 . -j-1094 22.04 4 1646 3 1254 22.10 6510 14 2' 879 7 3 1185 22.07 4 1484 3 1000 22.00 2 2397 15 2 1256 3 1091 22.04 4 1496 2 6535 21.82 2 6061 16 2 5269 2 8525 21.93 4 1437 2 4190 21.62 2 1848 17 2' 8112 2 3962 21.60 4 1233 2 1839 21.26 2 4658 18 1 1682 2 1527 21.18 4 1167 1 7698 20.89 2 4075 19 "3 1588 " 1 9687 "20.99 4 1225 1 4130 20.62 2 2338 " 20 2' 2307 1 6917 20.84 4 1077 1 2845 20.45 2 5337 21 3-1696 1 5873 20.77 3 8491 1 2501 20.40 1 3969 22 1 864 5 1 3987 20.60 3 8518 1 1795 20.25 2 3632 23 2 8831 1 2713 20.43 3 9032 1 1199 20.08 2 2293 24 2' 2559 1 3253 20.51 3 7265 1 1116 20.05 2 363 7 .... - 2 5 . - . 1943 1 2008 20.30" "3 5732 5579 19.75 2 2027 1 T U K E Y S P E C T R U M E ST I M A T I 0 N 0 0969JA ALTA HX AND EY 18 8 6  STATION 3 TIME 1009 11065 OJ K A X ' LTJCi B Y LOGY E 186 3 2 7106 21.85 . . . . . "7460 4 3034 23.48 3 4907 1 3 2840 2 9016 21.95 4 6753 4 3261 23.51 3 5650 2 3' 9173 2 2927 21.47 4 6247 3 2698 22.43 3 6859 3 3' 2268 2 1844 21.27 4 6386 2 8651 2 1.94 3 649 3 4 3 7094 2 1518 21.18 4 6480 2 6864 21.84 3 4011 5 3 6417 2 1917 21.28 4 6254 2 4961 21.70 3 4607 6" . . . . . . Vl'17" 2 2352 21.37 "4 6068 2 4254 21.63 3 7314 7 ' 3 3706 2 2759 21.44 4 6045 2 3800 21.58 3 5939 8 2 3857 2 6586 21.82 4 5993 2 4417 21.65 3 3244 9 3 4846 3 1497 22.18 4 5890 2 5494 21.74 3 4462 10 3 2501 3 2508 22.40 4 5792 2 6134 21.79 3 6087 11 2" 9011 3 2968 22.47 4 5753 2 6471 21.81 3 5546 12 2 1039 3 2365 22.37 V'4' 5713 2 7509 21.88 3 4604 13 3 1696 3 1377 22. 14 4 5540 2 7779 21.89 3 4519 14 2 9446 2 7689 21.89 4 5442 2 5575 21.75 3 4517 15 2 7682 2 6906 21.84 4 5455 2 3705 21.57 3 4596 16 3 1023 2 7571 21.88 4 5372 2 3266 21.51 3 4663 17 2 7074 2 5509 21.74 4 5218 2 2371 21.37 3 4411 18 3 1422 2 3490 21.54 4 5163 2 1419 21.15 3 4618 19 3 1577 2 2596 21.41 4 5121 2 1179 21.07 3 4265 20 2' 308 5 2 1800 21.26 4 4995 2 1222 21.09 3 3831 21 1 9054 2 1571 21.20 4 4894 . 2 1196 21.08 3 4409 22 3 1425 2 1587 21.20 4 4843 2 1030 21.01 3 4322 23 2 5129 2 1722 21.24 4 4807 1 8795 20.94 3 3599 24 2 4187 2 1790 21.25 4 4705 1 8957 20.95 3 3689 25 3 1235 1 8800 20.94 4 4505 1 4628 20.67 3 4097 r U K E 1 S PEC T R U M E S T I M A T I 0 N 0969JA ALTA HZ 18 8 61 STATION 6 AD 3 II ME 1009 11065 OJ K A X LOGX B . L 0 G Y fc 4 3996 4 1769 23.25 3 6124 3 1797 22.25 3 2650 I 4 3764 4 1856 23.27 3 4695 3 2155 22.33 3 3183 2 4 3531 2 9012 21.95 3 3311 2 4055 21.61 3 3633 3 4 3633 1 8263 20.92 3 3643 1 9114 20.96 3 3068 4 4 3742 1 9668 20.99 3 4634 1 5457 20.74 3 2679 5 4 3638 1 8214 20.91 3 4546 1 3802 20.58 • 3 3300 6 4 3558 2 1019 21.01 3 3632 1 5374 20.73 3 3791 7 4 3604 2 1556 21.19 3 3140 1 5898 20.77 3 3366 8 4 3579 2 2115 21.33 3 3457 1 7304 20.86 3 2968 9 4 345 7 2 22 74 21.36 3 3695 2 1511 21.18 3 3169 10 4 3428 2 2367 21.37 3 3437 2 2982 21.47 3 3392 11 4 3473 2 2396 21.38 3 2920 2 3217 21.51 3 3350 12 4 3417 2 3217 21.51 3 2592 2 2054 21.31 3 3341 13 "4 3308 "2 4396 21.64 "3 2712 2 1290 21.11 3 3386 14 4 3297 2 3268 21.51 3 2948 1 8224 20.92 3 3225 15 4 3307 2 1145 21.06 3 2738 1 3930 20.59 3 3126 16 4 3216 I 4931 20.69 3 2267 1 2526 20.40 3 3247 17 4 3135 1 3642 20.56 3 2057 1 2369 20.37 3 3246 18 4 3154 1 2088 20.32 3 2221 1 2387 20.38 3 3005 19 4 3146 I 1590 20.20 3 2251 1 1914 20.28 3 2998 20 4 3060 1 1209 20.08 3 1852 1 1390 20.14 3 3267 21 4 3011 9368 19.97 3 1471 1 1267 20.10 3 3203 22 4 3018 8132 19.91 3 1455 1 1289 20.11 3 3001 23 4 2977 7837 19.89 3 1518 1 1370 20. 14 3 3054 24 4 2920 7036 19.85 3 1334 1 1607 20.21 3 3196 25 4 2912 3592 19.56 3 1063 8742 19.94 3 3086 Z F H P Q R R»R PHI! 2 1791 0000 0000 .10 .00 .10 .01 '.0 2 2444 3 5865 3 1176 .10 • .48 .50 .25 •78.3 1 4992 2 7180 2 6413 .06 ' .82 .82 .67 •85.5 1 2307 3 1694 2 1288 •.12 •65 .66 .44 •100.2 1 1107 3 2280 1 7477 •.09 '.59 .59 .35 •98.4 1 1224 3 1988 1 6738 '.11 •60 .61 .37 •100.3 6547 2 3031 2 1077 * .04 ' .68 .68 .46 •93.5 3418 3 2208 2 2803 .01 '.80 .80 .65 '89.3 1 2244 3 4428 2 5542 • .04 '.89 .89 .80 •92.3 1 4470 3 2199 2 523/ '.07 • .84 .84 .71 •94.9 5932 2 3438 2 2294 .01 '.48 .48 .23 •88.5 1 5806 3 1184 2 1001 .12 '.20 .24 .06 •59.9 1 5062 3 2927 2 4896 .06 '.63 .63 .40 •84.1 1 5569 3 3377 3 1002 .05 '.86 .86 .73 '86.8 1 4759 3 1895 2 9657 • .04 • .89 .89 .79 •92.8 2 1846 3 1212 2 7316 •.22 '.87 .89 .80 '104.2 2 1193 3 2359 2 5063 • .20 '.85 .87 .76 •103.3 1 4354 3" 2309 2 2037 •.16 •.75 . 7  .60 • 102.1 1' 3916 2< 9622 1 6029 ' .36 '.56 .66 .44 '123.0 1 1855 3 1776 1 3578 •29 '.57 .64 .41 •117.4 8624 3 3144 1 2850 • .19 • .64 .67 .45 •106.8 6361 3 1851 1 2162 '.17 '.56 .59 .35 • 106.4 3068 2 6215 7779 '.11 • .29 .31 .10 •111.5 2218 3 1684 ' 1 1491 • . 12 .01 .12 .02 1 76.2 4939 3' 2254 •1 6213 •.26 .03 .26 .07 172.8 3524 3' 34 000,. •.33 .00 .33 .11 •180.0 Z F w P 0 R R»R PHI1 3 2632 0000 0000 •.57 .00 .57 .32 180.0 3 2855 3 3/62 2 8675 •.53 .16 .55 .30 163.1 2 2648 3 1503 2 3773 '.30 .42 .52 .27 125.1 1 7930 3 1251 2 1126 '.20 .28 .34 .12 125.2 1 5693 2 9412 1 8338 '.18 .26 .31 .10 124.3 1 2227 3 1447 9B61 ' .07 .03 .08 .01 156.1 I 2775 3 3573 9103 .09 • .03 .09 .01 •18.2 1 3715 3 2287 1 1097 .11 '.03 .12 .01 •16.5 1 6657 2 6750 2 1416 • .12 .26 .29 .08 115.2 2 1210 2 1804 2 5175 • .13 .57 .59 .34 103.2 1 9467 3 2726 2 9334 .08 .75 .76 .57 84.2 2 4437 3 2493 2 9340 .32 .67 .75 .56 64.6 2 6104 2 9441 2 4855 .46 .36 .59 .34 38.5 2 4230 3 1147 1 5294 .41 .05 .41 .17 7.1 1 4761 3 1716 I 3105 .07 '.05 .09 .01 •33.1 2 1985 3 1864 2 1387 ' .39 .27 .48 .23 145.1 2 2412 3 1979 2 2394 • .49 .48 .68 .47 135.2 2 1269 3 2018 2 1557 '.35 .43 .56 .31 129.2 1 2050 3 1825 I 5452 • .09 .24 .26 .07 110.6 6438 3 2195 1 2577 .04 .15 .15 .02 76.0 1 2519 3 2432 1 2753 .17 .19 .25 .06 47.5 1 1788 3 2432 1 2790 .13 .20 .24 .06 57.3 2937 3 2368 1 1106 .02 .09 .09 .01 75.1 9820 3 2366 5519 .08 • .04 .09 .01 •29.3 1 1945 3 2904 2799 .15 -.02 .16 .02 •8.2 I 1105 3 3240 0000 .17 . 0  .17 .03 .0 2 F W P Q R R»R PHI1 3 1615 0000 0000 .29 .00 .29 .08 • .0 3 1608 2 5097 3 1454 .25 • .23 .34 .12 •42. 1 1 3957 2 8901 2 5015 • .07 •.83 .83 .69 '94.5 1 4153 2 9367 1 1798 '.48 .21 .52 .27 156.6 1 1168 2 8395 1 3569 '.16 • .49 .52 .27 • 108.1 1 1372 3 1236 3880 '.25 •.07 .26 .07 •164.2 1 1090 3 2040 1 1326 •.15 '.18 .23 .05 • 129.4 1 2380 3 2346 3186 .25 .03 .25 .06 7.6 1 5262 3 1982 1 3550 .42 '.29 .51 .26 •34.0 1 4013 3 1877 2 1081 .22 '.58 .62 .39 •69.6 1 2944 3 2487 2 1625 '.11 '.61 .62 .39 •100.3 2 1086 3 3126 1 6560 • .39 '.24 .46 .21 •148.9 2 1427 3 3063 1 6525 '.56 .25 .61 .37 155.4 2 1500 3 2764 1 7812 '.63 .33 . 71 .50 152.5 2 1014 3 2946 1 2544 ' .62 .16 .64 .41 165.9 1 2749 3 3356 •1 1477 • .41 .00 .41 .17 179.7 4548 3 34B0 2045 '.13 .06 .14 .02 155.8 1716 3 3395 • I 13B7 •06 • .00 .06 .00 • 175.4 1 5314 3 3414 3527 .02 •16 .16 .03 •81.4 1 9083 3 3561 1927 •.05 •11 .12 .01 '115.2 1176 3 3795 •1 6988 • .09 '.05 . 11 .01 • 149.3 2470 3 3915 • 1 7 306 '.23 .07 .24 .06 163.5 1171 3 3701 • 1 2083 '.11 '.02 .12 .01 •169.9 1 2416 3 3457 •l 8606 .02 • .08 .09 .01 •74.3 1 3980 3 3567 •1 5700 • .04 ' .05 .07 .00 • 124.9 1 3652 3 3852 0000 • .07 .00 .07 .00 •1BO.0 -204-TUKEY SPECTRUM ESTIMATION 0969JA ALTA 19 3 61 HY AND EXSTATION 3 TIME 1450 6  H .. - i i. J K A HX LOGX B~ E Y ; LOGY fc 2 F " " ~ ~ ' H "p "b R R.  PHI1 3 2721 1 4177 20.62 4 2905 4 1131 23.05 3 1911 2 1160 0000 0000 •17 .00 .17 .03 •180.0 1 2 5372 1 6540 20.82 4 2678 4 1211 23.08 2 2027 2 1466 3 1083 2 1108 •.16 •12 .21 .04 '142.9 2 3 1622 1 6934 20.84 4 2371 3 1278 22.11 3 1656 7554 2 4250 1 6968 .03 •23 .24 .06 '83.8 J_. _ 3536 . 1 8665 .20-94. _4_ .23.4.8.. _2_?252_ -2J.5L7._ -J. .asgo_ _z .535J 1 2.534. _JU3X_ '.0.9 . .32 •J.Q •16.1 3 1104 1 5 397 20.73 4 2422 2 5379 21.73 2 3435 1 6874 2 2769 4811 .40 •03 .40 .1  •4.0 5 2 5807 1 2676 20.43  2359 2 1801 21.26 2 1351 1 3571 2'4270 6870 .51 '.10 .52 .27 •10.9 6 2 4501 1 3871 20.59 4 2202 2 1753 21.24 2 6123 1 5295 2 5206 1 2377 .64 •29 .70 .50 •24.2 7 2 4671 1 7555 20. B8 4 210B 2 2105 21.32 2 6951 2 1004 2 1318 1 4387 .80 '.35 .87 .75 •23.6 8 2 128 2 1234 21.09 4 2101 2 2732 21.44 2 2815 2 1482 1 3304 1 7208 .81 '.39 .90 81 •25.9 9 2 2219 2 1794 2i>25 4 2100 23173 2U50 2 1799 2 1820 2 1952 2'1048 .76 • .44 .88 •78 •29.9 10 1 8908 2 3118 21 .49 4 2076 2 3986 21.60 2 3564 2 2668 2 3914 2 1803 .76 • .51 .91 .83 •34. 1 11 2 2720 2 4359 21.64 4 2058 2 4456 21.65 2 4333 2 3496 2 2765 2 2350 .79 '.53 .96 .91 •33.9 12 2 1063 2 3983 21.60 4 207S 2 3331 21.52 2 2563 2 3013 1 3023 2 1794 .83 • .49 .96 .9  •30.8 13 2 2717 2 2875 21.46 4 2124 2 2051 21.31 1 8924 2 2089 1 1668 2 1041 .86 • .43 .96 .92 •26.5 14 2 2973 2 1991 21.30 4 2145 2 1394 2 1.14 2 1486 2 1447 2 2373 1 6740 .87 '.40 .96 .92 •25.0 15 1 173 2 1280 21.11 4 2117 I 7956 20_.90 2 1103 1 8fi0_6 2 -3JA6_-1 3984 .87 '.39 .96 .92 •24.3 6 1 7626 i 7314 20.86 4 2092 1 4352 20.64 2 1959 1 4891 2 1316 1 2150 .87 '.38 .95 90 •23.7 17 2 1182 I 4383 20.64 4 2095 1 2849 20.45 2031 I 3043 3012 1 1136 .86 •.32 .92 .84 •20.5 18 2 2764 i 3560 20.55 4 2087 1 2291 20.36 2 1856 1 2490 2 1269 7286 .87 '.26 .91 .83 •16.3 9 2 2266 I 2354 20.37 4 2020 1 1632 20.21 1 7903 1 1686 2' 3384 3524 .86 '.18 .88 .77 •11.8 20 1 2928 i 1018 20.01 4 1922 8070 19.91 2 1995 6763 2 3472 •1 5946 .75 '.07 .75 .56 •5.0 21 2 1466 4470 19.65 4 1856 3867 19.59 2 2356 1991 2" 1723 •1 3017 .48 .07 .48 .23 8.6 22 1 4173 3005 ~19.48~ ~4 1819 2805 19.45 7172 1 8724 2 1677 • 1 6024 .30 .21 .37 .13 34.6 23 2 1584 2297 19.36 4 1754 1835 19.26 I 5507 1 3251 2" 3560 '1 3830 .16 .19 .24 .06 49.7 24  3868 2316 19.36 4 1666 •I 7364 18.87 2 1061 2 4402 2' 4197 •1 1484 .03 .11 .12 .01 73.5 25 2 1660 1269 19.10 4 1609 '1 2218 18.35 2 1350 2 9541 2" 2997 0000 .18 .00 .18 .03 •.0 T U K E Y SPECTRUM ESTIMATION 0969JA ALTA 19 8 61 HX AND EY STATION 3 TIME 1450 1600 I I , _ LH*J . .. K A 1 X LOGX 1 2 _3 4 5 6 7 a _9_ "lb u 12 13 14 15 16 17 18 19 20 21 2877 5199 2079 1213 868 7 1347 2180 175 1392 8611 599 5 3736 7748 '9096 5343 3047-204 7 2649 2253 1632 1719 1077 2936 4760 3428. 4647. 1 1200 1 42 7  1 B40 1 9917 183 3030 6075 6421 3895 1800 9749 1 .6021. l" 4022 1 4686 1 5235 1 4139 1 2382 8656 2 2 3 1 24 2 25 2 • 252 3 •435 165 032 3486 3234 3222 1750 19.47 19.68 19.54 19._67_ To";08 20.63 2.93 21.00 21.07 21j.48_ "21.78 21.81 21.59 21.26 20.99 0.78 "0.60 20.67 20.72 20.62 0.38 19.94 19.54 19.51 19.51 19.24 8 5 143 5 112/ 5 1106 _5 1099 5~"i i 03" 1100 1085 1071 1069 1072_ T 0 6 6 1052 1043 1043 1044 1018 4 5394 4 5552 3 1851 2_5557 2 3624 1982 2053 1399 1122 2147 4125 3896 1695 5168 3636 2867 LOGY 3.73 23.74 2.27 l.74_ 21.56-21.30 21.31 21.15 21.05 21.33 .62 2 1.59 21.23 20. 71 20.56 20.46 5 028 5 1021 5 1017 5 1012 5 1001 4 9888 4 9802 4 9734 4 9649 4 9540 1 2517 1 2401 1 2152 1 1507 I 1020 6987 20.40 20.38 0.33 20.18 20.01 19.84 6135 6100 6305 3229 19.79 19.79 19.80 19.51 ? 2182 2 '2469 2-4517 ?_1759 2 4382"' 1 6276 2'4930 2'5609 1-6739 2 1206 1'4841 1'4559 1 1346 1 2275 1 1678 1'811 1'6903 1'8315 !•7257 1'4714 0000 3'1023 2-4522 3 1015 0000 1-4261 1'452 • 1965 • .12 • .09 .17 .45 .00 • .08 -.18 -.04 .12 .12 .25 .45 2 9807 2- 5229 3- 1271 2-3867 2 7615 2 5645 1 1532 1 5538 1 6998 1 45B5 •1-1242 2- 1704 .25 • .20 • .52 ' .71 ' .63 '.18 .23 .60 .53 .39 • .00 • .67 .34 .63 .75 .81 .63 .69 1- 7560 2'374 2' 1540 1 6016 2 1001 2- 1869 1 5055 2 1436 2 1223 1 6687 1 4556 1 3003 2-4726 2-6824 1 5363 2 5130 2 1171 2-5099 2-4301 2'4228 2-1738 1*2252 4789 5228 .10 .29 .48 .69 .77 .72 • .86 '.85 • .68 '.23 .08 .13 .87 .89 .83 .73 .77 .73 2-3357 2-1395 I 4651 4223 1- 9874 2- 1184 1-7457 1- 8864 2- 2023 2-2265 1 2164 1 2489 1 2365 1 1470 6341 1383 2-5189 I- 1622 2 2264 1- 3296 2- 3222 2-2963 3574 7896 1 1277 1 1093 6067 2879 .68 .74 .70 .59 .41 .18 .11 .24 .38 .44 .39 .37 .69 .78 .80 .73 .56 .41 • 1-4816 •1-7780 • 1-7207 • 1' 3231 1'7427 1 3222 2'1085 2'738 1438 •1 7528 '1 1542 0000 •710 • .18 -.16 •14 .31 .17 .03 .00 .33 .24 .16 . 14 »«R PHI1 .01 '180.0 .01 '136.9 .06 '47.2 .20 -4.9 .12 .40 .56 .65 .40 .48 .75-.80 .68 .54 .59 .54 2.4 108.1 134.6 151.1 •179.9 '105.5 •83.3 •71.2 •54.9 • •18.6 6.0 9.9 .48 .61 .64 .54 .32 .17 9.4 17.6 28.4 36.6 43.7 64.3 "TTT 108.5 .06 135.9 .03 167.9 .02 '180.0 - 2 0 5 -TUKEV SPECTRUM ESTIMATION 352JA ALTA MAG X AND ELEC Y 21 8 61 STATION 3 TIME 1428 TO 1558 K 4 A 2743 X 2 1583 L o c r 21.20 5 B 1171 3 V 3582 LOGY 22.55 4 e 1927 2 z 3053 F 0000 w0000 P .41 Q .00 . R .41 R.  .16 PHU ••0 1 4 06   3253 21.51 5 05  3 5741 22.76 4 738 2 6264 4 1745 2 5903 .46 • .43 .63 .40 •43.3 2 4 1279  3898 21.59 4 768  3 3914 22.59 4 46 2 6764 4" 3006 2 6709 .55 •.54 .77 .59 •44.8 3 3 4149 2 5363 21.73 4 3869 3 3102 22.49 3 5793  7496 4 3635 2 6728 .58 •.52 .78 .61 •41.9 4 3' 4459 2 '5944 21.77 3'2643 3 2750 22.44 3 1250 2 6173 4" 35BS i 7234 .40 '.57 . 74 .55 •49.5 5 4' 1157 3 1594 22.20 4 3961 3 7430 22.87 3 7046 3 1372 4' 2894 3 2679 .40 •78 .87 .77 •62.9 6 4' 1605 3 4300 22.63 4 6522 4 2234 23.35 4 1080 3 3845 4' 1708 3 8266 .39 '.84 .93 .87 •65.1 7 4" 1731 3 5848 22.77 4 7540 4 3336 23.52 4 1248 3 5061 3« 2406 4 1207 .36 •.86 .94 .88 •67.3 8 4' 1446 3 4748 22.68 4 6879 4 2300 23.36 4 1158 3 3361 4 1206 3 8965 .32 '.86 .92 .84 •69.5 9 3-8605 3 2697 22.46 4 4752 3 7053 22.85 3 7928 3 1386 4 2283 3 3762 .31 •83 .89 .79 •69.8 10 3' 1700 " y 1349 22.13 4 1683 ' 3 1453 22.16 3 3075 2 5343 4 2 78U 3 1037 .38 • . /4 .83 .69 '62. 8 11 3 4768 2 4675 21.67 . 4 1673 2 4733 21.68 3 1793 2 2386 4 2665 2 1585 .51 '.34 .61 .37 •33.6 12 3 9136 2 1742 21.24 4 4598 2 2348 21.37 3 5846 2 1246 4 2004 1 3482 .62 •17 .64 .41 •15.6 13 4 1087 2 1101 21.04 4 6511 2 1671 21.22 3 8429 1 4535 4 1001 1 1237 .33 • .09 .35 .12 •15.3 14 4 1029 2 1322 21.12 4 7150 2 1590 21.20 3 9281 1 2760 2 7781 9436 .19 .07 .20 .04 18.9 IS 3 8194 2 1276 21.11 4 6510 2 1620 21.21 3 8497 1 1336 4' 1042 9854 .09 '.07 .12 .01 •36.4 16 "3' 4995 2 1616 21.21 4 4778 2 1SS1 21.19  6284  3978 4'1753 1 7547 .25 « .48 .54 .29 '62.2 17 3 1170 2 2655 21.42 4 2349 2 2279 21.36 3 3264 1 9565 4' 2103 2 1678 .39 '.68 .78 .62 •60.3 18 3" 2170 2 2686 21.43 3 2869 2 2356 21.37 2 1359 1 8820 4 2045 2 1772 .35 • .70 .79 .62 •63.5 19 3 446 3 2 1916 21.28 4 2611 2 1413 21.15 3 3548 1 3510 4" 1612 2 1037 .21 '.63 .67 .44 •71.3 20 3 579 3 2 2005 21.30 4 4171 1 7096 20.85 3 6071 9626 3 9351 1 6805 .08 •57 .58 .33 •81.9 21 3-5911 2 1843 21.27 4 4755 1 8458 20.93 3 7034 1 1734 3' 2057 1 6209 . 14 • .50 .52 .27 •74.4 22 3' s i r s J 1254 21.10 4 4365 1 9168 20.96 3 6774 1 L275 3 4514 1 4694 . 12 • .44 .45 .11 ' 74. B 23 3 3647 2 1182 21.07 4 3165 1 8077 20.91 3 5500 1 1192 3 9238 1 3959 '.12 ••41 .42 .18 •106.8 24 3 2197 2 1239 21.09 4 1481 1 9137 20.96 3 3659 1 2429 4 1144 1 4839 •.23 •45 .51 .26 •116.7 25 3 1026 2 1252 21.10 3 3293 1 9729 20.99 3 1430 1 3085 4 1150 1 4079 '.28 •.37 .46 .21 •127.1 26 2 3365 2 1219 21.09 4 1955 1 7307 20. 86 2 8230 1 2844 3 9776 9625 •.30 '.10 .32 .10 •161.3 27 3 1753 1 9426 20.97 4 3115 1 5655 20.75 3 2841 3161 3 6753 • 1 8606 • .04 .01 .04 .00 164.8 28 3" 2978 " r 7298 20.86 4 3600 1 57B8 20.76 3 4305 6093 3 2621 8 768 .09 '.13 . 16 .03 '55^2 29 3 3770 i 6389 20.92 4 3363 1 5387 20.73 3 4795 4815 3' 1328 1 1343 .07 '.20 .21 .05 '70.3 30 3 3615 i 9084 20.96 4 2552 1 4932 20.69 3 4386 9447 3 4570 1 1429 .14 '.21 .26 .07 •56.5 31 3 3005 i 9370 20.97 4 1424 1 4610 20.66 3 3454 1 1104 3 6473 1 1864 .17 '.28 .33 .11 •59.4 32 3 2279 2 1008 21.00 3 2255 1 4535 20.66 3 2257 1 2044 3" 7312 1 2183 .30 •32 .44 .20 •46.9 33 3 1632 1 9593 20.98 3 8185 1 5617 20.75 3 1087 1 2249 3' 7063 1 2243 .31 '.31 .43 .19 '44.9 34 3 1212 ~1 9 52 AT 2 0.98^  4 156B " 1 5056 20. 70 2 2189 1 1148 3 5H62 1 2156 .17 '.31 . 35 . 12 '62.0 35 2 1307 I 9171 20.96 4 1873 1 3715 20.57 3 1439 5324 3 3988 1 1441 .09 •25 .26 .07 •69.7 36 3 1810 1 7774 20.89 4 1708 1 2918 20.47 3 2120 1255 3 1653 2452 • .03 '.05 .06 .00 •117.1 37 3 2635 1 8089 20.91 4 1186 1 2084 20.32 3 2485 5326 2 5606 •1 7323 •.13 .02 . 13 .02 172.2 38 3 2963 1 8434 20.93 3 4084 1 2188 20.34 3 2716 ' 1 5996 3 2 376 6380 '.01 '.15 .15 .02 •95.4 39 3 2696 1 6621 20.82 3 4520 1 2524 20.40 3 2254 1286 3 3321 5462 .03 '.13 .14 .02 •76.8 40 3 2189 1 5609 20.75~~ •T116 7 1 2145 20.33 3 1301 1554 3 3176 1220 • .04 ' " .04 . U6 . U  '141.V 41 3 1530 1 6021 20.78 4 1615 1 2051 20.31 2 4815 1910 3 2344 1234 '.05 • .04 .06 .00 •147.1 42 2 7540 1 6166 20.79 4 1704 1 2221 20.35 2 1735 1398 2 9938 1596 .04 '.04 .06 .00 •48.8 43 2 4232 1 6445 20.81 4 1382 1 2204 20.34 2 5946 4140 2 4503 3186 .11 •.08 . 14 .02 •37.6 44 3 1488 1 6530 20.81 3 7402 1 2211 20.34 2 6177 2866 3 1929 1927 .08 •05 .09 .01 •33.9 45 3 1977 1 6191 20.79 2 7129 1 2349 20.37 1 639 5 1268 3 3325 • I 5601 .03 .01 .04 .00 23.8 46 3 1728 1 6446 20V81 3 '9T35 I 2261 20.35 I' 72 / •1 8366 3 3970 • 1 3408 • 02 • 01 • 02 • 00 -22.2 47 3 1241 1 6772 20.83 4 1625 1 2198 20.34 3 1634 1340 3 3804 •1 1786 .03 • .00 .04 .00 •7.6 48 2 6531 1 6712 20.83 4 2038 1 2353 20.37 3 2268 1034 3 2956 • 1 2115 .03 .01 .03 .00 11.6 49 2 2248 1 6339 20.80 4 2049 1 2305 20.36 3 2475 2647 3 1374 • 1 4725 • .07 .01 .07 .00 169.9 50 2. 3662 I 2991 20.48 4 1680 1 1072 20.03 3 2117 2608 2 3290 0000 • .15 .00 .15 .02 180.0 T U K E Y S P E C T R U M ESTI M A T 1 0 N 352JA ALTA MAG Y AND ELEC X 21 8 61 STATION 3 TIME 1428 TO 1558 K A r x "' LOGX B Y LOGY "T" " Z F w P 0 . -R — P B n 4 1628 L-2 1201 21.08 5 1902 3 3088 22.49 4 2834 2 1360 0000 0000 .22 .00 .22 .05 .0 1 4 1185 2 1672 21.22 5 1644 3 6089 22.78 4 2397 2 1820 4 1456 2 2646 .18 •26 .32 .10 •55.5 2 3 5694 2 1449 21.16 5 1138 3 6441 22.81 4 1457 2 1731 4 2459 2 5854 .18 •-6I .63 .40 •73.5 3 3 1520 2 1597 21.20 4 4779 3 5912 22.77 3 4466 2 1349 4 2890 2 7002 .14 •72 .73 .54 •79.1 4 3 2616 2 2485 21.40 "4 '2092 " 3' 4852 22:69' ~T58T6~ "2"~2<T2A 4'2748 2 7315 .IB '•67 " .-69— -74F • 74T5 5 3 6843 2 7323 21.86 4 7892 4 1098 23.04 4"1516 3 1160 4 2097 3 2154 .41 •76 .86 .74 •61.7 6 3 9233 3 2201 22.34 5 1143 4 2926 23.47 4'2121 3 4698 4 1066 3 5692 .59 ••71 .92 .85 •50.5 7 3 9228 3 3703 22.57 5 1206 4 4556 2 3.66 4'2271 3 8760 2 7232 3 8503 .67 •65 .94 .88 •44.1 8 3 7480 3 2895 22.46 4 9919 4 3902 23.59 4'1920 3 7172 4 1017 3 6784 .67 • .64 .93 .86 '43.4 9 3 4606 3 1189 22.08 4 5796 4 1970 23.29 4'1166 3 2590 4 1629 3 3354 .54 •69 .88 .77 •52.3 10 3 1320 2 5904 21.77' 3 8176" 3 7529 22.88 3T2822 2 "6785" 4 1B76 3'1577 .30' ' . 75 .81 .65 ~* 6B.3 11 3 2141 2 4083 21.61 4 3929 3 2632 22.42 3 6253 2 2506 4 1736 2 7346 .24 •71 .75 .56 •71.2 12 3 4944 2 2790 21.45 4 7473 2 9722 21.99 4 1400 2 1226 4 1256 2 3459 .24 '.66 .70 .50 •70.5 13 3 6892 2 2354 21.37 4 9155 2 5294 21.72 4 1823 2 1221 3 5639 2 2042 .35 •58 .67 .45 •59.1 14 3 7290 2 2417 21.38 4 8840 2 4600 2 1.68 4 1860 2 1464 3 1571 2 1923 .43 '.56 . 71 .50 •52.7 15 3 6017 2 2088 21.32 4 6838 2 3839 21.58 4 1522 2 1410 3 7742 2 1350 .50 •48 .69 .48 •43.7 16 3 3925 2 1393 21.14' 3768 2 '2W5' 21.45 3 "9140 _ 2 1124 4* 1163 I 5158 .56' •.26 .67 "."39-•24.6 17 3 1332 2 1336 21.13 3 3733 2 3687 21.57 3 1769 2 1275 4 1320 1 3747 .57 •17 .60 .36 •16.4 18 3 1267 2 1479 21.17 4 2664 2 3872 21.59 3>5182 2 1470 4 1226 1 4355 .61 •.18 .64 .41 •16.5 19 3 3378 2 1275 21.11 4 4847 2 2377 21.38 4'1062 2 1079 3 9195 1 2410 .62 • .14 .63 .40 •12.6 20 3 4646 2 1451 21.16  5881 2 2490 21.40 4'1357  186 3 5167 1 1842 .62 •10 .63 .40 •8.8 21 3 5 0 0 5 2 1940 21.29 4 5730 2 4159 21.62 4'1356 2 1710 2 7404 1 6094 .60 •.21 .64 .41 •19.6 22 3 4418 2 1965 2 1.2 9 4'4579"-~Ty<)oo-~2r.~5<) 4T-TO86 ~'2 1564 3 31B4 1 7442 .56 •27 .63 —."39" -'25.5 23 3 2848 2 1761 21.25 4 2814  2715 21.43 3'6177 2 1193 3 6208 1 6342 .55 •29 .62 .38 •28.0 24 3 1049 2 1658 21.22 3 8655 2 3002 21.48 2'8654 2 1094 3 7908 1 8279 .49 • .37 .61 .38 •37.1 25 2 7560 2 1607 21.21 3 8726 2 3298 21.52 3 3907 2 1011 3 8026 1 7766 .44 '.34 .55 .31 •37.5 -206-26 3 2504 2 1511 21.18 4 2072 2 2378 21.38 3 7769 1 7737 3 6934 1'3654 .41 •19 .45 .20 '25.3 27 3 3961 2 1203 21.08 4 3020 2 1819 21.26 3 9986 1 5620 3 4883 1'2169 .38 •15 .41 .17 •21.1 28 3 4349 2 U40 2 1.06 4 3156" 2 T9~79~ 21.30 3 99B1 1 4119 3 1 759 . l'252H .21 •17 .32 -.10" »31V5 29 3 3475 2 1246 21.10 4 2589 2 2131 21.33 3 7638 1 4253 3 ' 1304 1*1837 .26 •11 .28 .08 •23.4 30 3 2066 1 9887 21.00 4 1616 2 1631 21.21  3910 1 4340 ' 3283 '1414 .34 •01 .34 .12 •1.9 31 2 4906 1 7434 20.87 3 5806 2 1346 21.13 2* 1821 1 3928 3 ' 4068 1518 .39 .02 .39 .15 2.2 32 2 ' 9788 1 6095 20.78 3 ' 3011 2 1842 21.27 3 ' 3524 1 4334 3 ' 4183 •4886 .41 •05 .41 .17 •6.4 33 3 ' 2095 1 5021 20.70 3* 9390 2 1909 21.28 3 ' 5818 1 4236 3 ' 3500 1 9620 .43 .01 .43 .19 1 .3 34 3 ' 2544 1 4780 20.68 tfi I3TJ2 2" 1399 21.15 1' 682 1 1 3181 3' 212U 1'8352 .39 «.U1 .39 .15 TiS-35 3" 2709 1 4452 20.65 4 ' 1336 2 1273 21.10 3 ' 6596 1 1644 2' 2548 1'183 .22 • .16 .27 .07 •35.7 36 3 ' 2381 1 4040 20.61 3 ' 9956 2 1583 21.20 3 ' 4729 5081  1561 1'309 .06 •16 .18 .03 '66.8 37 3 ' 1224 1 3387 20.53 3 ' 3908 2 1523 21.18 3 ' 1770 2188 3 2876 •6869 .03 •10 .10 .01 •72.3 38 2 4693  2623 20.42 3 2714 2 1071 21.03 3 1486 1539 3 3349 1293 .03 .02 .04 . 0 0 40.0 39 3 1712 1 2000 20.30 3 8602 2 1088 21.04 3 4174 •1 8237 3 3343 1'6689 .02 •01 .02 . 0 0 '39.1 40 3 2578 1 1347 20.13 ~ - tt- 1361" 2 145T 21.16 ' 1' 1246 3 2449 •8446 * . U 0 •19 .19 ;04 •-90; 8 41 3 3326 1 1095 20.04 4 1552 2 1376 21.14 3 6656 2654 2 4685 1'089 .07 •.28 .29 .08 •76.3 42 3 3309 1 1412 20.15 4 1357 2 1006 21.00 3 6025 5455 ' 1950 •6874 .14 '.18 .23 .05 •51.6 43 3 2449  2125 20.33 3 8983 2 1105 21.04 3 4748 4336 3 ' 4269 1*5992 .09 •01 .09 .01 •7.9 44 3 1363 1 2394 20.38 3 1800 2 1446 21.16 3 2644 • 1 6134 3 ' 6197 2619 .01 .04 .05 . 0 0 76.8 45 1 8774 I 1860 20.27 3> 7800 2 1262 21.11 2' 2053 5436 3* 6990 1722 ' . 1 1 .04 .12 .01 162.4 46 3" 1409 1 1520 20.18 4 ' 1785 — r 9456" 20.'98- " r 5037 «5T9 '1272— -•VM ."14 -,X>2-' 165.8 47 3- 2803 1 1558 20. 19 4 ' 2574 2 1099 21.04 3« 542 3 • 1516 3- 4835 •5553 • .04 •.13 .14 .02 ' 105.3 48 3 ' 3580 1 1236 20.09 4 ' 2969 2 1373 21.14 3 ' 6439 • 1051 3" 1872 •4857 '.03 '.12 .12 .01 • 102.2 49 3 ' 3209 9565 19.98 4 ' 2919 2 1177 21.07- 3 ' 6118 5631 3 1547 1 8011 .17 .02 .17 .03 8.1 50 3 ' 2421 4855 19.69 4 ' 2389 1 4674 20.67 3 ' 4360 5779 3 4679 0000 .38 . 0 0 .38 .15 •.0 1 T U K E Y 'S P E t i R u M EST 1 M A T I 0 N '0 0969JA ALTA 21 8 61 HX AND HZSTATION 3 TIME 1428 1558 OJ K A X . LOGX B Y LOGY E I F W P 0 R R»R PHI1 4 2743 2 1583 21.20 4 2867~" "2 8745 21.94 4 2218 1 •1734 0000 oooo • .05 . 0 0 .05 .00 180.0 1 4 2063 2 3253 21.51 4 2514 3 1386 22.14 4 1938 I •7469 2 •5087 2 3001 •11 .45 .46 .21 104.0 2 4 1279 2 3898 21.59 4 1731 2 7798 21.89 4 1246 1 4047 2 •2613 2 3024 .07 .55 .55 .31 82.4 3 3 4149 2 5363 21.73 3 7155 2 4115 21.61 3 3590 2 2527 2 2832 2 2007 • S4 .43 .69 .47 38.5 4 3 •4459 2 5944 21.77 3 •3321 2 3499 21.54 3 •5525 2 3330 2 7393 2 1722 .73 .38 .82 .68 27.3 5 4 •1157 3 1594 22.20 4 •1220 3 1219 22.09 4 ' 1320 3 1248 3 1294 2 3664 .90 .26 .93 .87 16.4 6 4 •1605 3 4300 22.63 4 •1766 " 3 4273 22.63 4 ' 1776 3 4026 3 1993"* "2 6429 ".94" .15 .95 •" .90 "~"9'.T 7 4'1731 3 5848 22.77 4 •1846 3 742 7 22.87 4 • 1853 3 6259 3 2619 2 2880 .95 .04 .95 .90 2.6 8 4 • 1446 3 4748 22.68 4 •1468 3 6440 22.81 4 • 1536 3 5255 3 2613 2'4256 .95 •.08 .95 .91 •4.6 9 3 •8605 3 2897 22.46 3 •7714 3 3121 22.49 3 •9216 3 2803 3 1857 2*6297 .93 '.21 .96 .91 •12.7 10 3 '1700 3 1349 22.13 2 6776 3 1083 22.03 3 • 1744 3 1083 2 8190 2'3681 .90 •30 .95 .90 •18.8 11 3 4768 2 4675 21.67 3 8680 2 2748 21.44 3 5158 2 2869 2>2560 1'9936 .80 '.28 .85 .72 ' 19.1 12 3 9136 2 1742 21.24 4 1461 1 8702 20.94 4 1012 1 7756 3 •1181" "ITTOT "S3 '.12 ~.64 " .41" ner*" 13 4 1087 2 1101 21.04 4 1732 1 6712 20.B3 4 1241 1 3090 3 • 1763 •1'5639 .36 ' . 0 1 .36 .13 •1.0 14 4 1029 2 1322 21.12 4 1657 1 4345 20.64 4 '1196 1 1074 3 ' 1817 1 1347 .14 .IB .23 .05 51.4 15 3 8194 2 1276 21.11 4 1292 1 3757 20.57 3 9274 1 1249 3 • 1265 7219 .18 .10 .21 .04 30.0 16 3 4995 2 1616 21.21 3 7459 1 4062 20.61 3 5180 1 4173 2 •2515 •4802 .52 ' .06 .52 .27 •6.6 17 3 1170 2 2655 21.42 3 1395 1 5466 20.74 2 5836 1 7800 • 2 8599 '4876 .65 •.04 .65 .42 •3.6 18 3 '2170 2 2686 21.43 3 •4041 " l " 5256 20.72" 3'526 1 6966 3 1821 • IS69 . 5 9 ' .02 ".5<5 "."34" 19 3 •4463 2 1916 21.28 3 •7860 1 4736 20.68 3 •6337 1 4474 3 2405 •9412 .47 '.10 .48 .23 •11.9 20 3 '5793 2 2005 21.30 3 '9500 1 4718 20.67  •7743 I 5151 3 2591 1'2583 .53 • .27 .59 .35 •26.6 21 3 •5911 2 1843 21.27 3 '8950 1 4697 20.67 3 •7598 1 4892 3 2240 1*3886 .53 • .42 .67 .45 '38.5 22 3 '5178 2 1254 21.10 3 •6698 1 5245 20.72 3 '6030 1 2960  1692 1'4192 .37 •52 .63 .40 •54.8 23 3 •3647 2 1182 21.07 3 •3440 1 5571 20.75 3 •3668 1 1342 2 8224 1'4168 .17 ••51 .54 .29 •72.2 24 3 •2197 2 1239 21.09 1 7011 " 1" "4843 20.69 3 '1149 1 1286 1'7832 P35~2"l .'IT "• .45" . 4"B~" ".23 r6'<5.9_ 25 3 • 1026 2 1252 21.10 3 3163 1 3910 20.59 2 9475 1 2379 2 •7191 1'2600 .34 '.37 .50 .25 •47.5 26 2 3365 2 1219 21.09 3 5378 13058 20.49 3 2620 1 2066 3 •1109 1«1995 .34 •33 .47 .22 •44.0 27 3 1753 1 9426 20.97 3 6423 1 2276 20.36 3 3814 1 1131 3 •1143 1*1163 .24 •.25 .35 .12 •45.8 28 3 2978 1 7298 20.86 3 6334 1 1761 20.25 3 4361 92 36 2 •8566 •5910 .26 •16 .31 .09 •32.6 29 3 3770 1 8389 20.92 3 5215 1 1532 20.19 3 4217 1 1271 2 •4503 •6260 .35 •.17 .40 .16 •26.2 30 3 3615 1 9084 20.96 3 3403 1 1239 20.09 3 3429 1 1467 1 •5454 •5928" -~7KK — r - 1 - e — .47 .22 2 ."0 31 3 3005 I 9370 20.97 3 1233 1 1215 20.08 3 2343 I 1407 2 3307 •4728 .42 '.14 . 4 4 .19 •18.6 32 3 2279 2 1008 21.00 2 •9082 1 1283 20.11 3 1116 1 1191 2 5846 • 1438 . 3 3 • .04 . 3 3 .11 •6.9 33 3 1632 1 9593 20.98 3 •2608 1 1277 20.11 1 •5997 5862 2 7976 ' 1965 .17 '.06 .18 .03 •IB.5 34 3 1212 1 9528 20.98 3 •3571 1 1292 20.11 2 •9518 3532 2 8814 •8160 .10 •23 .25 .06 •66.6 35 2 ' 1307 1 9171 20.96 3 '3770 1 1326 20.12 3 ' 1600 4863 2 8711 •8456 .14 '.24 .28 .08 •60.1 36 3 ' lHl'J 1 7774 2U.89 3 • tiro 1 "12" 6 9 '20.11 3 •2007 417 7 2 6 142 ' • r n r r -TIT - ; T 7 — ".03 " T r .TT 37 3 •2635 1 6089 20.91 3 '2037 1 1207 20.08 3 '1932 5309 2 7500 •1922 .17 '.06 . 18 .03 • 1 9 38 3 •2963 1 8434 20.93 2 '4135 1 1207 20.08 3 '1449 2819 2 5208 •3890 .09 '.12 .15 .02 •54.1 9 3 •2696 1 6621 20.82  1293 1 1135 20.06 2 •5904 '2011 2 2048 '3887 •07 '.14 .16 .03 • 117.4 40 3 •2189 1 5609 20.75 3 2674 9514 19.98 2 3917 • 1 •8941 1 •4687 •1'2362 '.04 • .01 .04 . 0 0 •165.2 41 3 •1530 1 6021 20.78 3 3440 9218 19.96 3 1066 1943 2 •2967 2635 . 0B . 1 1 .14 .02 53.6 42 2 •7540 1 6166 2 0 . 7 4 3 3369 953? "19.96 3 1489 1651 2 '5482' 2081 .07 . 0 9 ' . IT .01 " 5T76" 43 2 4232 1 9445 20.81 3 2534 9337 19.97 3 1802 •1 •7809 2 •6994 •1'3272 •.03 ••01 .03 . 0 0 •157.3 4 3 14S8 I 6530 20.81 3 1222 8473 19.93 3 1793 •1243 2 •7073 • 1558 •05 •.07 .08 .01 '128.6 45 3 1977 1 6191 20.79 2 •3597 8079 19.91 3 1433 1005 2 •6532 ' 1 6558 .04 .03 .05 . 0 0 33 .1 46 3 1728 1 6446 2U.01 3 •1924 8819 19.95 2 665 3 2775 2 •4090 3226 .12 .14 • IB .03 49.3 47 3 1241 1 67 72 0.83 3 •3133 9112 19.96 2 •2030 3208 2 •1428 ' 1 7303 .13 .03 .13 .02 12.8 48 2 6531 1 6712 20.83 3'3602 8TJ7~R."W  •8537 4005 2 1002 " "'•TOT" • 17 —r;iD .19 ~ ~,o%- • 31.3" 49 2 2248 1 6339 20.80  '3194 9487 19.98 3 •1031 4609 2 2712 ' 197* .19 •08 .20 .04 '23.2 50 2 •3662 1 2991 20.48 3 •2067 _5164 19.71 2 •8637 2162 2 3454 0000 .17 . 0 0 .17 .03 •.0 -207-1 U K b V P il C I R U M L S 1 M A I 0 Ii 0969JA ALTA 21 8 61 HX AND CY STATION 3 TI Mel 900 20.10 J K A X LOGX B Y LOGY b I F M P 0 R R»R P H l T O o i / i 3 8876 2 1016 21.01 4 363/ 3 2297 22.36 3 7 784 2 2368 0000 0000 .49 .00 .49 .24 • .0 1 3 786S 2 1786 21.25 4 3300 3 3352 22.53 3 7165 2 4774 2 2768 2 1471 .62 • . 19 .65 .42 '17.1 2 3 5389 2 1196 21.08 4 2674 3 1456 22. 16 3 5296 2 3297 2 6217 1 4877 .79 • .12 .80 .64 •8.4 3 3 2270 2 1626 21.21 4 1792 3 1278 22.11 3 2439 2 1560 3 1151 2 2906 .34 .64 . 72 .52 61.8 4 2' 7724 I 4565 21.66 3 8L1J 3 3026 22.48 2 9694 2 1337 3 1667 2 9770 ' .11 .83 .84 . 70 97.6 5 3' 3257 3 1267 22.10 3 1061 3 6025 22.78 3 4407 3 1733 3 2657 3 1438 • .63 .52 .81 .66 140.3 6 3' 4867 3 2020 22.31 3 8436 3 7865 22.90 3 7379 3 3521 3 3343 2 89/5 • .88 .23 .91 .83 165. 7 7 3- 5464 3 1635 22.23 4 1323 3 5687 22.75 3 944 1 3 2848 3 37 45 2 1834 • .92 ' .06 .92 .85 •176.3 8 3' 5104 3 1017 22.01 4 1503 3 2302 22. 36 4 1019 3 1095 3 3644 2 7134 • .72 • .47 .85 .73 • 146.9 9 3' 397B 2 7013 21.85 4 1395 2 8751 21.94 3 9367 2 2024 3 2937 2 5405 ' .26 • .69 .74 .54 •110.5 10 " 3" 2391 2 4264 21.63 4 1048 2 4717 21.67 3 697 1 2 1956 3 1606 2 2131 .44 ••46 .64 .42* •47.4* 11 2' 7041 2 2250 21.35 3< 533/ 2 3566 21.55 3 3440 2 2590 2 1943 1 4013 .91 • . 14 .93 .86 •6.8 12 2 8054 2 1081 21.03 2 5728 2 1999 21.30 2' 4074 2 1204 3 2077 1 1601 .82 .11 .63 .68 7.6 13 3 196 7 1 6080 20.78 3 6321 2 1094 2 1.04 3 3755 1 3735 3 3586 1 4092 .46 .50 .68 .46 47.6 14 3 267'. 1 6188 20.79 4 1 115 I 9735 20.99 3 6090 6764 3 4434 I 3473 • .09 .45 .46 .21 101.1 15 3 2932 . I. 6350 2Q.80. 1469 .1. 7073 20.65 3. 7.03 7 1 5037 3 4 706 .1 1469 • .75 .22 .78 .61 163.5 16 3 2829 1 4851 20.69 4 162/ 1 6272 20.80 3 6855 1 4658 3 42 76 160B • . 84 .03 .84 . 71 178.6 17 3 2496 1 2586 20.41 4 1605 I 4925 20.69 3 5667 1 1852 3 3323 6.210 • .52 •-17 .55 .30 •161.5 18 3 2000 1 2123 20.33 4 1417 1 4271 20.63 3 3806 1044 3 2056 8509 • .03 ••28 .28 .08 •97.0 19 3 1385 1 2326 20.37 4 1105 1 3992 20.60 3 1617 8979 2 7003 8808 .29 • .29 .41 .17 '44.4 20 2 6626 1 2062 20.32 3 /240 1 3540 20.55 2 5610 1 1268 2 5177 4719 .47 • .17 .51 .26 •20. 1 21 2' 1376 1 14U9 20.15 3 3302 1 2641 20.42 3 2444 9834 3 1427 4069 .51 .21 .55 .30 22.5 22 2' 9048 I 1063 20.03 2 1255 i 2334 20. 37 3 3 794 5351 3 1960 7955 .34 .51 .61 .37 56. 1 23 3' 1488 84 3 7 19.93 3 2631 l 2244 20.35 3 4526 2721 3 2107 6679 .20 .49 .52 .27 67.8 24 3' 1797 5956 19.77 3 3924 l 2485 20.40 3 4643 1772 3 1906 3423 .15 .28 .32 .10 62.6 25 3' 1807 4926 19.69 3 4051 l 2 744 20.44 3 4190 2286 3 1423 •1 7580 .20 .07 .21 .04 18.3 26 3' 1568 4725 19.67 3 3163 l 2678 20.43 3 3308 1505 2 8058 1211 .13 ' .11 .17 .03 • 38. 8 27 3' 1155 4053 19.61 3 1619 l 2396 20.38 3 2136 '2 3086 2 2iei 2552 .00 '.26 .26 .07 •89.3 28 2' 6294 3725 19.57 2 2281 i 2064 20.31 2 7594 •2 2621 2 2548 1553 • .00 • . 18 .18 .03 •91.6 29 1' 3086 4028 19.61 3 2025 l I860 20.27 2 7130 • 1 1849 2 5641 1441 .02 .17 . 17 .03 82.7 30 2 5884 32 j9 19.51 3 3502 l 1983 20.30 3 2109 • I 1888 2 7577 38 33 .02 .48 .46 .23 87.2 31 3 1107 1826 19.26 3 4445 l 2286 20.36 3 3247 1241 2 8069 3837 .19 .59 .62 .39 72. 1 32 3 1436 11'. 3 19.06 3 4630 l 2581 20.41 3 393 1 2798 2 7755 1668 .52 .31 .60 .36 31. 1 33 3 1530 • 1 9.841 18.99 3 4614 i 2741 20.44 3 4005 3068 2 6862 • 1 2162 .59 •.04 .59 .35 •4.1 34 ' 3 1392 1016 19.01 3 3919 i 2639 2 0.42" "' 3 3472 • 1 8957 2 5964 1225 .17 " .24 .29 .09 •53.8 35 3 1034 • 1 9940 19.00 3 2312 l 2281 20.36 3 2470 1623 2 5181 1420 ' .34 '.30 .45 .21 • 138.8 36 2 5136 • 1 8489 18.93 3 1380 I 2007 20.30 3 1240 1832 2 4261 •2 6504 • .44 .02 .44 .20 178.0 37 1 • 8762 • 1 7256 16.66 2 2641 l 2033 20.31 1 5173 • I 7379 2 3474 1677 • .19 .44 .48 .23 113.8 38 2' 6851 • I 7858 16.90 3 1062 , l 2210 20. 34 2 9639 • 1 8465 2 2410 1407 .20 .34 .39 .16 59.0 39 3" 1190 •1 99/3 19.00 3 3126 I 2440 20.39 3 1664 24 76 2 1627 • I 3341 .50 .07 .51 .26 7.7 40 3' 1513 1083 19.03 3 3741 l 2567 20.41 3 2012 22 37 2 1469 • 1 9154 .42 • .17 .46 .21 •22.3 41 3' 1594 • 1 7896 18.90 3 3532 I 2363 20.37 3 2046 1106 2 2020 1726 .26 • .40 .47 .23 •57.4 42 3' 1396 '-1 5920 16. 77 3 2441 I 1970 20.29 3 1778 • 1 2912 2 20/0 • 1 9412 • .09 1 .28 .29 .08 • 101.2 43 2' 9325 • I 70o3 18.05 2 5399 I 1714 20.23 3 1298 1436 2 3703 • 1 4661 • .43 .13 .45 .20 162.6 44 2" 293y • I 7205 18.86 3 1604 i 1841 20.27 2 6388 • I 9025 2 4346 1436 • .25 .39 .47 .22 122. 1 45 2 3398 * 1 6591 18.82 3 4176 i 2167 20.34 2 1163 '1 7916 2 4963 1875 .21 .50 .54 .29 67. 1 — 46 * "2" 7956 • 1 8220 18.91 3 5991 I 2459 20.39 2 8713 2327 2 5530 1060 .52 .24 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'256'4 ' 3 8 0 7 ' 4 7 9 1 ' 5 4 4 1 ' 3 7 2 4 ' 9 4 3 5 ' 5 6 9 9 3544 2 9 8 5 5 9 9 7 1 1 1 8 1 2 2 8 1 5 7 0 2 5 9 8 I E Y 3 1888 22.28 3 3130 22.50 3 2329 22.37 3 2094 22.32 3 1947 22.29 3 1902. 22.28. 3 1545 22.19 2 6805 21.83 2 1521 21.18 1 7683 20.89 1 4813 20.68 J_43J2_Z 1 3382 20.53 1 2688 20.43 1 3387 20.53 1 4075 20.61 I 3911 20.59 l_Afl6.B. 21t^6J_ l 3673 20.57 1 2281 20.36 1 1260 20.10 1 1005 20.00 7615 19. 1 9 . 9 8 2 0 . 0 6 2 0 . 2 2 2 0 . 2 9 2 0 . 1 4 12*. . 4 8 . 6 9 . 8 2 • B2 .88 . 2 3 . 4 8 . 6 7 . 6 7 . 7 7 - ^ . 8 - 9 J . 9 . . . 8 7 . 7 6 . 8 3 . 70 . 4 8 . 4 6 . 4 8 . 6 9 . 4 8 . 2 4 . 2 1 _ ^ 2 3 _ .32 . 16 .43 .37 .23 1 9 . 9 1 2 0 . 0 3 2 0 . 0 8 2 0 . 1 0 2 0 . 0 5 1 9 . 9 8 2 ' 1 5 9 7 2 ' 1702 1 ' 8 2 7 4 1 ' 2 3 4 0 1 1 8 3 5 1 4 7 5 5 1 ' 1 1 6 2 1 " 3 0 6 7 2 - 1 0 7 7 2* 1 4 1 4 2 ' 2 0 3 4 2 - 2 1 0 5 5 7 1 0 7 3 1 5 7 5 3 6 7 0 2 6 7 0 5 0 . 6 3 2 8 59 38 4 6 2 6 3 6 9 4 7 3 3 0 1 2 7 1 1 1 0 0 9 8 9 5 4 3 9 4 5 2 6 3 7 2 2 0 2 2 2 4 5 2 1 0 •2 3 2 1 7 1 8 4 3 1 8 2 5 1 9 6 3 3 4 0 5 4 4 4 6 . 5 4 . 5 2 . 4 7 . 4 7 . 5 2 . 5 4 . 0 0 . 1 3 . 1 1 . 1 3 . 2 5 . 3 8 1 9 5 4 9 I 7 7 5 6 1 5 7 7 4 1 6 8 6 9 1 5 3 6 8 • 5 5 1 1 4 0 0 8 2 9 4 7 5 0 1 2 5 8 3 8 2 1 7 6 • 1 ' 2 2 9 6 . 5 7 . 4 5 . 3 1 . 4 7 . 6 8 . 6 8 . 3 8 . 2 9 . 4 2 . 3 8 . 1 2 ' . 0 1 2 ' 2 1 7 8 2 ' 2 2 4 4 1 ' 9 9 3 7 •6676 2 1 6 1 1 2 3 1 9 0 2 4 1 9 2 " 2 5 1 5 6 2 6 3 6 6 6 0 4 4 7 2 3 5 7 5 3 8 4 3 9 6 2 7 0 0 3 5 1 6 6 5 8 9 1 ' 3 7 7 7 2 - 1 3 7 5 2 - 1 9 8 7 2 ' 2 ? 8 7 2 - 2 6 5 5 5 700 5 4 0 2 2 0 8 4 2 - 2 7 6 1 2 - 3 0 2 7 2-' 3 5 3 2 1 1 1 9 2 4 7 9 1 8 3 3 •1 9 1 6 3 •1 2 3 9 5 - 1 1139 •1 3942 • 2 - 5 7 4 8 0 0 0 0 . 5 3 . 5 8 . 5 5 . 4 2 . 4 0 . 5 1 . 6 1 . 5 9 . 5 4 . 1 0 . 2 0 . 1 3 . 0 9 . 0 4 . 0 2 . 0 4 " - . 0 1 . 0 0 . 3 3 . 2 7 . 3 4 . 3 9 . 2 0 _ . 2 . 9 — . 3 9 . 3 7 . 3 6 . 4 3 . 4 9 • 1 3 _ . 54 . 5 3 . 4 8 . 4 9 . 5 8 _ . 6 6 . 6 9 " . 5 3 . 5 2 . 6 0 . 6 9 . 6 8 . 5 4 . 6 1 . 5 7 . 4 3 . 4 0 _.j>i . 6 1 . 5 9 . 5 4 . 1 0 . 0 3 . 1 9 . 1 4 . 0 5 _«.07_. . 1 1 . 0 7 . 1 2 . 1 5 . 0 4 _ . 0 8 . 1 5 . 1 4 . 1 3 . 1 8 . 2 4 - 2 8 . 2 9 . 2 8 . 2 3 . 2 4 . 3 3 . 4 4 . 4 7 . 2 9 . 2 7 . 3 6 . 4 8 _ . 4 6 . 2 9 . 3 8 . 3 2 . 1 8 . 1 6 . 2 6 . 3 7 . 3 4 . 2 9 P H U • . 0 ' 3 9 . 5 • 3 2 . 7 • 1 1 . 1 5 . 8 9 . 6 9 . 2 5 . 5 • 3 . 0 ' 2 . 6 • 2 2 . 7 • 4 3 . 4 • 7 7 . 0 • 4 7 . 1 • 7 . 5 • 1 5 . 0 • 4 6 . 9 . ' 5 1 . 3 . • 5 8 . 7 • 5 4 . 0 1 0 . 6 1 9 . 5 3 1 . 8 _ 4 0 . 1 2 2 . 2 1 8 . 5 1 4 . 1 • 1 3 . 1 • 1 8 . 7 •_7.9 . 3 1 4 . 1 1 3 . 6 1 5 . 6 2 5 . 8 3 5 . 1 3 4 . 0 3 2 . 5 5 3 . 6 3 8 . 5 9 . 7 • 1 . 2 1 0 . 5 1 8 . 9 1 3 . 7 1 1 . 8 5 . 1 1 . 9 • 4 . 6 " • . 6 . 0 0 9 6 9 J A ALTA 24 8 61 HY AND EX STAION 3 TIME 0 0 3 2 0 6 3 2 k" A X LOGX B" Y LOGY "t" i F w" " p " 0 R R » R PHI1 3 2 0 9 0 l*°c'> ' 1 1938 2 0 . 2 9 4 3622 3 1566 2 2 . 1 9 2 9 9 1 4 !• 4 0 4 2 0 0 0 0 0 0 0 0 ••23 . 0 0 . 2 3 . 0 5 1 8 0 . 0 l 3 1442 1 5 6 9 6 2 0 . 7 6 4 3372 3 3174 2 2 . 5 0 2 9 5 3 9 1 ' 4 7 8 5 3 1987 2 1959 ' . 1 1 • . 4 6 . 4 7 . 2 2 • 1 0 3 . 7 2 3 1185 2 1 0 2 6 2 1 . 0 1 4 2 9 4 9 3 3 7 8 5 2 2 . 5 8 2 7 6 0 2 1 5 8 9 5 3 3 4 4 8 2 4 5 3 3 . 0 9 • . 7 3 . 7 3 . 5 4 ' 8 2 . 6 3 2 8 6 7 2 2 1998 2 1 . 3 0 4 2 3 6 3 3 5 3 3 7 2 2 . 7 3 2 4 5 9 8 2 1 8 6 5 3 4 5 5 1 2 . . . . 8 8 4 5 . 18 • . 8 6 . 8 8 . 7 7 • 7 8 . 1 4 2 4 5 3 3 2 3 2 4 7 2 1 . 5 1 4 1668""" 3" 6 5 1 2 2 2 . 8 1 2 2 1 5 0 2 2 3 3 7 " 3 5 1 5 7 13 37 " '.'ii" •".92 "" . 9 3 ' . 8 7 • 8 0 . 1 5 2 1 2 3 3 2 3 7 2 6 2 1 . 5 7 3 9 4 1 9 3 6 5 0 8 2 2 . 8 1 1 1 2 4 1 2 2 3 0 1 3 5 2 8 3 3 1458 . 1 5 • . 9 4 . 9 5 . 9 0 • 8 1 . 0 6 2 1928 2 2 9 0 6 2 1 . 4 6 3 2 3 2 9 3 4 9 6 6 2 2 . 7 0 2 2 5 9 7 2 1 8 9 9 3 5 0 8 9 3 1 1 1 9 . 1 6 ••93 . 9 5 . 8 9 • 8 0 . 4 7 2 • 4 9 1 5 2 1374 2 1 . 1 4 3 3 9 3 9 3 2 1 5 9 2 2 . 3 3 2 468 8 1 9 1 9 7 3 4 4 5 8 2 4 9 3 6 . 1 7 ' . 9 1 . 9 2 . 8 5 • 7 9 . 4 8 2 • 7 4 3 0 1 3 9 9 0 2 0 . 6 0 3 9 0 7 3 2 5 2 4 5 2 1 . 7 2 2 6 6 7 5 1 2 8 9 3 3 3 5 0 9 2 1 1 3 5 . 2 0 ' . 7 8 . 8 1 . 6 6 • 7 5 . 7 9 2 9 4 1 2 1 2 0 1 8 2 0 . 3 0 4 1238 2 2 4 4 9 2 1 . 3 9 2 7 S 2 9 1 2 0 1 1 3 2 2 7 9 1 4 4 4 1 . 2 9 • . 6 3 . 6 9 . 4 8 • 6 5 . 6 10 2 " 9 2 6 8 " ... „ 2 2 9 9 2 0 . 3 6 4 1367 ' " 2" " 1 3 1 1 2 1 . 1 2 2 7 7 6 1 1 1 1 0 6 3 1056 1 3 5 1 5 . 2 0 ' . 6 4 . 6 7 . 4 5 • 7 2 . 5 U 2 •8676 1 2 4 8 3 2 0 . 3 9 4 1330 1 9 8 6 3 2 0 . 9 9 2 7 3 6 3 1 6 1 5 2 1 5 1 3 1 3 4 3 7 . 0 3 • . 6 9 . 6 9 . 4 8 • 8 7 . 3 12 2 ' 6 6 7 8 1 1 7 7 5 2 0 . 2 5 4 1 1 5 9 1 6 6 6 3 2 0 . 8 2 2 6 3 6 7 2 5 3 1 3 1 0 5 6 1 2 347 . 0 7 ' . 6 8 . 6 9 . 4 7 • 8 3 . 6 1 3 2 •5354 1 1243 2 0 . 0 9 3 9 0 9 1 1 6 0 3 5 2 0 . 7 8 2 4 7 1 3 4 2 1 7 3 1 6 9 9 1 1 8 5 0 . 1 5 • . 6 8 . 6 9 . 4 8 ' 7 7 . 2 14 2 •3347 1 1 8 2 8 2 0 . 2 6 3 6 0 1 0 1 7 6 7 7 2 0 . 8 9 2 3 7 2 5 6 5 1 3 3 2 1 0 9 1 2 6 3 9 . 1 7 ' . 7 0 . 7 3 . 5 3 • 7 6 . 1 15 2 ' 1 0 6 5 1 2 5 0 8 2 0 . 4 0 3 2 6 4 7 - » 1 8 2 6 5 2 0 . 9 2 2 33B4 1 1 3 0 3 3 2 2 5 5 1 3 0 7 5 . 2 9 ' . 6 8 . 7 3 . 5 4 ' 6 7 . 0 16 1 540 5 1 2 5 4 0 2 0 . 4 0 2 3041"" "i 7 4 6 3" 2 0 . 8 7 2 1 6 3 0 1 1 5 5 4 3 2 0 6 6 1 2 6 0 6 . 3 6 • . 6 0 . 7 0 . 4 9 • 5 9 . 2 17 2 2 2 9 1 1 2 1 3 1 2 0 . 3 3 3 2 6 8 3 1 7B32 2 0 . 8 9 1 8 9 4 0 7 9 2 5 3 1 6 9 3 1 2 4 2 4 . 1 9 ' . 5 9 . 6 2 . 3 9 ' 7 1 . 9 18 2 3 6 9 2 1 1 5 3 1 2 0 . 19 3 4 3 2 2 1 7 8 4 8 2 0 . 8 9 1 1582 1 7 7 8 3 1174 1 1 9 4 5 . 0 5 • - 5 6 . 5 6 . 3 2 • 8 4 . 8 19 2 4 2 4 3 1 1070 2 0 . 0 3 3 4 9 1 6 1 5 7 3 9 2 0 . 7 6 1 3 7 9 6 1 3 7 5 2 6 4 7 3 1 1172 . 0 6 ' . 4 7 . 4 8 . 2 3 • 8 3 . 3 2 0 2 332 7 7 9 2 3 1 9 . 9 0 3 4 9 8 0 1 3 0 6 9 2 0 . 4 9 1 5 2 8 2 1592 1 9 4 9 7 6 3 B 7 . 1 0 • . 4 1 . 4 2 . 1 8 ' 7 6 . 0 2 1 2 3 0 9 2 8 0 8 3 1 9 . 9 1 3 4 2 2 5 1 1 8 9 3 2 0 . 2 8 1 5 3 0 3 2 8 3 9 2 3 4 5 6 3 1 9 5 . 2 3 ' . 2 6 . 3 5 . 1 2 • 4 8 . 4 22 2 1 6 9 8 8 7 4 7 " 1 9 . 9 4 " 3" 3 1 5 1 1 1 5 0 0 2 0 . 1 8 1 4 2 3 4 2 0 1 5 2 6 2 1 8 •1 6 6 3 0 . 1 8 • . 0 6 . 1 9 . 0 3 ' 1 8 . 2 23 1 8 3 8 1 7 1 4 7 1 9 . 8 5 3 1727 1 1 9 3 0 2 0 . 2 9 1 2 7 5 5 1 1 1 9 2 7 0 9 7 2 3 1 4 . 1 0 ' . 2 0 . 2 2 . 0 5 • 6 4 . 2 2 4 1 3 9 0 1 7 5 6 3 1 9 . 8 8 2 4 0 9 9 1 2 5 2 2 2 0 . 4 0 1 3 2 3 4 1 7 1 9 2 7 2 0 9 6 1 3 1 . 1 2 • . 4 4 . 4 6 . 2 1 • 7 4 . 3 2 5 1 • 6 2 3 3 1 1 0 4 3 2 0 . 0 2 2 5 1 2 3 1 2 3 8 3 2 0 . 3 8 1 6 2 0 4 1548 2 5 9 6 0 6 4 6 4 • . 1 0 • . 4 1 . 4 2 . 1 8 • 1 0 3 . 5 -212-26 1 6954 1 1316 20.12 3 1063 1 2814 20.45 1 6184 6569 2 3706 '5605 • .34 '.29 .45 .20 •139.5 27 1 5432 1 1424 20.15 3 1104 1 3518 20.55 1 7751 7702 2 2028 • 1252 • .34 • .06 .35 .12 • 170.8 28 V •9626 1 1204 '20.08" 2 8579 i 2891 "20.46"" i 2541 4036 1 5869 2015 '•".22 . 1 1 .24 .06 153.5" 29 1 •8722 1 1120 20.05 2 2181 l 2328 20.37 1 2511 • 1 3987 1 9917 •3316 .02 '.21 .21 .04 •83. 1 30 1 •6797 1 1088 20.04 2 60 3  l 2 396 20.38 1 8871 • 1 9093 2 1602 •6302 .06 • .39 .39 .16 •81.8 31 1 '3414 8809 19.94 3 1360 i 2172 20.34 2 1669 1037 2 1539 •4639 • .07 '.34 .34 .12 ' 102.6 32 1 •4487 1 1240 20.09 3 2200 I 2156 20.33 2 2099 3929 2 1606 •5305 • .24 '.32 .40 .16 •126.5 33 1 3246 1 1723 20.24 3 2817 i 2495 20.40 . 2 2290 5052 1 5444 •8110 '.24 '.39 .46 .21 •121.9 34 '8971" " "l 1405 2o". 15 "' "3 2919 "~ i  2 307" 20.36 2 1733" 3328 "" 21196 "' "69 78 "•".18 •". 39 .43 .18 '115.5 35 1556 9144 19.96 3 2567 l 1689 20.23 21492 3239 2 3070 • 3088 • .26 '.25 .36 .13 •136.4 36 3590 9105 19.96 3 1864 l 1391 20.14 2 1153 2054 2 3891 •2485 • . 18 • .22 .29 .08 '129.6 37 I • 1757 1 1234 20.09 2 8790 I 1331 20. 12 1 5505 • 1 5896 2 4510 •2963 .05 ' .23 .24 .06 •78.8 38 1 •8721 1 1426 20.15 2 3716 l 1495 20. 17 1 5598 1549 2 4277 •2915 . 11 '.20 .23 .05 •62.0 39 2 •1175 1 1325 20.12 3 1648 l 2342 20.37 1 6389 1240 2 34 39 •3224 .07 '.18 .20 .04 •69.0 40" "i •9341" "l 1235 20.09 ~3" 2696 I 3085 "2 0.49" " i 9069 2222 ' "2 1377 •4116" ' • " . i i "'• .21" ~. 24 " .06" •"i"8;4 41 2 •1123 1 1375 20.14 3 3427 I 2489 20.40 1 8589 2538 1 8122 •4520 • .14 ' .24 .28 .08 •119.3 42 2 •1106 1 1514 20.18 3 3733 l 1457 20.16 21124 2598 2 2638 '2987 .17 '.20 .27 .07 •49.0 43 1 •8269 1 1093 20.04 3 3574 l 1442 20.16 2 1165 4080 2 5504 • 1836 .32 • .15 .36 .13 •24.2 44 I •8813 6112 19.79 3 2913 l 2023 20.31 2 1308 2078 2 8322 •1'6873 . 19 ' .06 .20 .04 •18.3 45 1 • 2354 5921 19.77 3 1864 I 2143 20.33 2 1626 • 1 2155 3 1022 •I 3737 .02 .03 .04 .00 60.0 46 1 '2624 725 3 19.86 2 4915" l T585" 2"0. 2"b "2" "161"l 1151 ~3 iisi" •1 "5326 •".11 .05" . 12 . . . ' 155.2 47 1 6698 9559 19.98 3 1127 l 1064 20.03 2 1591 • 1 9283 3 1213 2707 • .09 .27 .28 .08 108.9 48 1 8295 1 1231 20.09 3 2697 i 1129 20.05 2 1295 1057 3 198 4712 • .09 .40 .41 .17 102.6 49 2 1223 1 1169 20.07 3 4132 l 1582 20.20 2 1342 1745 3 1047 2978 '.13 .22 .25 .06 120.4 50 2 1535 4902 19.69 3 5304 9184 19.96 2 1272 • I 8586 2 9053 0000 • .13 .00 .13 .02 • 180.0 T U KEY s P t GIRO M E 5 f l M A 1 | 0 N 0969JA ALTA 24 8 61 HY ANO HZ STATION 3 TIME 0032 0632 K A f X ">«<••'.!/! LOGX B Y LOGY E Z F M P Q R R»R PHI1 3 2090 1 1938 20.29 3 3903 2 5083 21.71 3 1465 1 3466 0000 0000 • .35 .00 .35 .12 180.0 1 3 1442 1 5696 20.76 3 3393 2 7238 21.86 3 140 7 1 2564 2 2084 7393 .13 .04 .13 .02 16.1 2 3 1185 2 1026 21.01 3 3066 2 4005 21.60 3 189 2 1457 2 3210 1 1503 .72 .07 .72 .52 5.9 3 2 8672. .2 1998. 21 .30 -2—38.31 7 1 .58 2 8674 2 2263 y 4131 1 •1 747 87 • .06 .82 .67 •4.4. 4 2 4533 2 3247 21.51 3 2069 2 4241 2.63 2 5374 2 3230 2 4303 1 •9556 .87 •26 .91 .82 •16.5 5 2 1233 2 3726 21.57 3 1573 2 4301 2.63 2 1510 2 3424 2 3785 2 •1427 .86 ' .36 .93 .86 •22.6 6 2 1928 2 2906 21.46 3 1096 2 3467 21.54 2 2057 2 2573 2 3221 2 •1175 .81 •37 .89 .79 •24.5 7 2 4915 2 13 74 21.14 2 6714 2 1899 21.28 2 5200 2 1213 2 2423 1 •6002 .75 • .37 .84 .70. •26.3 8 2 7430 1 3990 20.60 2 3421 I 6997 20.84 2 7770 1 2986 2 1656 1 •1976 .57 •.37 .68 .46 •33.5 9 2 9412. 1 -2018. 20.30 7 1 308 1 3550 20.55 7 8981 91 54 1 39RH •4584 .34 • .17 .15 •26*6. 10 2 9268 1 2299 20.36 1 6966 1 2310 20.36  9654 7007 I 6759 •7156 .30 '.31 .43 .19 '45.6 11 2 6676 1 2483 20.39 1 9814 I 2184 20.34 2 9227 454B 2 2178 1 •1402 .20 •.60 .63 .40 '72.0 12 2 6678 • i 1775 20.25 2 1B8  1 1880 20.27 2 7952 • 1 3427 2 2705 •9927 .02 '.54 % .54 .30 '88.0 13 2 5354 1 1243 20.09 2 3348 1 1409 20.15 2 6339 • 1 2481 2 3208 • 5066 .02 • .38 .38 .15 •87.2 14 2 3347 1 1828 20.26 2 5291 1 1381 20.14 2 4574 3604 2 3328 •6666 .23 '.43 .49 .24 •62.3 56 2 10655405_.~i 750R 20.40 ? 677(  1 1 1«1 Jn.u 7 301 8 4014 7 T77n  R7nn 77 • .47 .51 76 •65.7 1 1 2540 20.40 2 8203 1 1316 20.12 2 1021 3442 2 2636 •5968 .19 •.33 .38 .14 •60.0 17 2 2291 1 2131 20.33 2 9347 1 1318 20.12 3954 2652 2 2006 • 1497 .16 • .09 .18 .03 •29.4 18 2 3692 1 1531 20.19 2 9640 1 1283 20.11 1 9290 • 1 9042 2 1207 •1 •2379 .06 • .02 .07 .00 '14.7 19 2 4243 1 1070 20.03 2 9384 1 1021 0.01 2 1423 1674 I 4449 •1 •3225 .16 •.03 .16 .03 •10.9 20 2 3327 7923 19.90 2 8896 7918 19.90 2 1247 1318 1 5369 1083 .17 .14 .22 .05 39.4 21 2 3092. 8083. 19.91 7 7952 7475 1 9.87 ? 1049 •7 3319 ? 1004 1838 • .00 .24 .24 .06 91.A 22 2 1698 8747 19.94 2 7159 7268 19.86 6386 • 1 8885 2 1162 1050 .11 .13 .17 .03 49.8 23 1 8381 7147 19.85 2 6170 6316 19.80 1 6336 1395 2 1253 •2 '9827 .21 '.01 .21 .04 •4.0 24 1 3901 7563 19.88 2 5260 5706 19.76 2 1250 1579 2 1146 •1 •8811 .24 '.13 .28 .08 •29.2 25 1 6233 1 1043 20.02 2 5029 5887 19.77 2 2013 • 1 9231 1 7104 •1532 .12 • .20 .23 .05 •58.9 26 1 6954 1 1316 20.12 2 4422 5643 19.75 2 1969 • 1 8001 2 1034 •2854 ' .09 ' .33 . 34 .12 •105.7 27 1 5432 .1 .42.4. 204 ,1.5.. 08  4568 7354_ 19.87 2 2213 1916 1 9256 '1787 '.19 •17 • 26 .07 •137.0 28  9626 1  4693 9905 20.00 2 2236 2515 2 1032 • 1 7631 •23 .07 .24 .06 163.1 29 1 8722 1 1120 20.05 2 4761 9229 19.97 2 2003 •1 6661 1 8192 •1 4523 • .07 .04 .08 .01 145.8 30 1 6797 1 1088 20.04 2 5013 8273 19.92 2 1831 1243 1 4186 •1021 .13 •11 .17 .03 •39.4 31 1 3414 8809 19.94 2 5225 7958 19.90 2 1684 • 1 4883 1 3892 •2127 .06 •25 .26 .07 •77.1 32 1 4487 1 1240 20.09 2 5726 7324 19.86 2 1786 • 1 4570 8864 •2448 •.05 '.26 .26 .07 • 100.6 33 1 3246 1 1723 20.24 2 5785 7249 19.86 2 1580 • 1 2145 1 1701 • 1662 •02 • .15 .15 .02 •97.4 34 8971 i 1405 20.15 2 5617 7913 19.90 2 1B29 ' 1 2867 1 1282 • 1215 •.03 '.12 .12 .01 •103.3 35 1556 9144 19.96 2 5513 9834 19.99 2 1643 2254 6706 •2287 ' .24 • .24 .34 .11 •134.6 36 3590 9105 19.96 2 4985 1 1089 20.04 2 1860 2949 1 2560 •2200 '.30 • .22 .37 .14 •143.3 37 1 175 7 1 1234 20.09 2 4536 9228 19.97 2 2116 • 1 9500 7970 •1 5634 • .09 .05 . 10 .01 149.3 38 1 8721 1 1426 20.15 2 3796 7384 19.87 2 2513 •1 2939 •1 9446 • I 3444 • .03 .03 .04 .00 130.5 39 2 175 1 1325 20.12 2 3810 7677 19.89 2 2893 1969 1 2130 •1462 •20 •14 .24 .06 •143.4 40 1 9341 i 1235 20.09  3687 9866 19.99 2 2518 4147 4993 •1135 • .38 ' .10 .39 .15 •164.7 41 2 1123 1 1375 20.14 2 3739 8960 19.95 2 2266 3081 1 3389 •1 •8334 • .28 • .08 .29 .08 •164.9 42 2 1106 1 1514 20.18 2 4716 6856 19.84 2 2174 1525 1 2035 •1259 .15 '.12 .19 .04 •39.6 43 1 8269 1 1093 20.04 2 5499 7995 19.90 2 1792 2851 1 4964 •2204 .30 '.24 .39 .15 •37.7 44 1 6813 6112 19.79 2 6787 8130 19.91 2 1289 • 1 8907 1 6703 • 1440 .13 '.20 .24 .06 •58.3 45 1 2354 5921 19.77 2 7734 6936 19.84 1 6902 • 1 2465 1 4099 •1 3430 .04 .05 .07 .00 54.3 46 i 2624 7253 19.86 2 874B 6163 19.79 1 1720 • 1 018 1 4908 •1 4169 •02 .06 .06 .00 103.7 47 1 6698 9559 19.98 2 9692 6310 19.80 1 5019 • 1 4719 1 1609 1191 • .06 .15 .16 .03 111.6 48 1 8295 1 1231 20.09 2 9583 7368 19.87 2 1238 •1 2759 4427 3116 .03 .33 .33 .11 84.9 49 2 12  3 1 1169 20.07 2 9557 7539 19.88 2 1473 • 1 4057 3200 2552 .04 .27 .28 .08 81.0 50 2 1535 4902 19.69 2 9580 3609 19.56 2 1506 •2 2384 3530 0000 '.01 .00 .01 .00 •180.0 -213-APPENDIX B STATISTICAL ANALYSIS Pearson (1901) gave a method for f i t t i n g a straight line through a set of points in a plane when both variables are subject to errors. Similar results have also been derived by several other workers. The constants involved in the equation of the straight line y » A + Bx (1) are calculated from the expressions B - £>L - ^ W ^ - ^ v ^ qr~>;z ( 2 ) and A - Y - B X (3) In the present investigation Pearson's ideas have been developed to obtain expressions for f i t t i n g the best ellipse through N points. It is also shown from the derivations given -214-below that the results obtained by Pearson and others for finding the slope of the best f i t t i n g straight line may also be used for finding the slope of the major axis of an ellipse provided the points are distributed at equal angles around the ellipse. The equation of an ellipse is given by •+ _y_ / 2- (4) If the axes of the ellipse are rotated in 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 s i n © By expanding equation (5) we have -r comparing t h i s equation w i t h Pearson's equation x2- y 2 _ ^ y K y , x y , we o b t a i n where c 8=1 - TJ- * > A ' Z x • Zy -216-Pearson gave the f o l l o w i n g e x p r e s s i o n f o r the s l o p e of the s t r a i g h t l i n e : (9) Equation (3) may a l s o be obtained by s o l v i n g equations (7), or i n the f o l l o w i n g way. The c o o r d i n a t e s of a p o i n t P are g i v e n by x = a cos U J - ' C O S © - l> s i n LA> • s i n © y =» a cos tyo . s i n & + W s i n uo- • cos <9 By summing a l l p o i n t s over the e l l i p s e we have 2.y^ " TTO^S^G - i - TT (s^Coo^tS- (10) and by s o l v i n g these equations f o r Q 217-In deriving equations (10) i t i s assumed that the points 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 (8) we have i - n z>* - z*> -r JCZ^- -f- 4 (Z~yf L a w c? - ~~ ~ _ " By solving equations (10) for a /b we obtain a. L ' *•* Lcvvv c3 where ( I D Probable error i n the slope Birge (1947) gave a method for fi n d i n g the probable error "Yp (12) where T i s the probable error of a hypothetical quantity of unit weight, given by -218-and P the t o t a l a s s i g n e d weight of Z, g i v e n by d^ = the r e s i d u a l n « the number of o b s e r v a t i o n s and s «*• the number of undetermined c o n s t a n t s ( f o r a pol y n o m i a l of degree J , S •» J + 1). I t i s e a s i e r t o f i n d the prob a b l e e r r o r i n tan 2 & than i n tan 0 , and hence equation (8) i s used i n the f o l l o w i n g d e r i v a t i o n . Let us denote tan 2 © by S, then S - f (x,y) Let the weight of x and y be u n i t y . The probable e r r o r of S w i l l then be According t o equation (8) S i s gi v e n by -219-ax Denoting J^^- T^ b y P a n d «^  T ^ b y 1*1 Similarly Hence the probable error is given by where -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 in the directions of inhomogeneity axes are given by where Ey', Hy', E x' and H^'are the components of the electro-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 in an arbitrary direction x inclined at an angle © to the direc-tion x', may be written in the form V / H x £ V Cos & ~h Eyy St'yj (9 y ' Ccrs Q — Hy.' S-t-vv, 6 -221-The impedance ratio Zy*/Z^ characterizes the magnitude of the inhomogeneity in the medium (for a homogeneously layered medium Zy7 = Z^' and Z/ » Z x ). The ratio H^'/Hy' may, in the general case, be complex depending on the phase shift and the amplitude of the components of the original f i e l d . For a linearly polarised f i e l d , H x ' / H y - Cot <9H. Thus the impedance Z x, measured at the surface of an inhomogeneous structure in any direction, depends not only on the structural parameters and 0 , but also on the direction of polarisation of the incident electromagnetic f i e l d . -222-APPENDIX 0 IMPEDANCE VALUE FOR AN ANISOTROPIC MEDIUM Suppose the conductivity i s 6~i and tT 2 i n two mutually perpendicular directions i n an anisotropic medium (Fig. 7,3), The current density along these two conductivity axes w i l l be Jv ° G~2 Ev Ju - 6*i Eu Maxwell's equation gives (Curl H ) u - 4TT3^along the CT^  axis or _ JL = Fu, since Hz - 0 OA and (Curl E)^ •• — £L2Sfalong the (C axis Replacing ~ by where Z i s the depth of penetration when the amplitude i s reduced to half i t s o r i g i n a l value, we have -223-J_ t ~ - ju> H v 2, c " . v since and and Similarly -224-BIBLIOGRAPHY Angenheister, G., 1962, The r e l a t i o n s h i p between the d i s t r i b u -t i o n of e l e c t r i c a l c o n d u c t i v i t y of rocks and t h e i r behavior i n the c r u s t and upper mantle; C o n t r i b u t i o n t o a symposium on Magnetic P r o s p e c t i n g . K a s s a l . Barlow, W. H., 1849, On the spontaneous e l e c t r i c c u r r e n t s observed i n the wires of the e l e c t r i c t e l e g r a p h : P h i l . Trans., 139, 61-72. Bendat, J. S., 1958, P r i n c i p l e s and a p p l i c a t i o n s of random n o i s e theory: John Wiley and Sons. B e n i o f f , H., 1960, Observations of geomagnetic f l u c t u a t i o n s i n the p e r i o d range 0.3 t o 120 seconds: J . Geophys. Res. 65, 1413-1422. Berdichevsky, M. N., and B. E. B r u n e l l i , 1959, T h e o r e t i c a l premises of m a g n e t o t e l l u r i c p r o f i l i n g : B u l l . (IZV). Akad. S c i . Geophys. Ser. 757-761. Berdichevsky, M. N., 1960, Fundamentals of the t h e o r y of m a g n e t o t e l l u r i c p r o f i l i n g : Appl. Geophys. (USSR) No. 28. B i r g e , R. T., 1947, Lease square f i t t i n g of data by means of po l y n o m i a l s : Rev. Mod. Phys., 19, 298-347. -225-Blackman, R. B., and J. W. Tukey, 1958; The measurement of power spectra: Dover Publication, New York, j Bossy, L., 1959, Relationship between the electric and magnetic fields of a wave of very long period induced in a medium of variable conductivity; Geofisica Pura e  Applicata, 44, 119-134. Bostick, F. X., Jr., and H. W. Smith, 1961, An analysis of the magnetotelluric method for determining subsurface r e s i s t i v i t i e s : ONR Report No. 120, Elect r i c a l Engineer-ing Research Laboratory, Univ. Texas. Bostick, F. X. Jr., and H. W. Smith, 1962, Investigation of large scale inhomogeneities in the Earth by magneto-t e l l u r i c method: ONR Report No. 127, Electrical  Engineering Laboratory, Univ. Texas. Brunelli, M. N., Berdichevsky, M. N. Alekseev, A. M., and Burdo, 0. A., 1959, Observations of short periodic variations in Earth's electromagnetic f i e l d ; Bull. (IZV) Akad. Sci. USSR, Geophys. Ser.. 864-871. Burwash, R. A., 1957, Reconnaissance of surface of Precambrian of Canada: Bull. Am. Ass. Pet. Geol., 41, 70-103. -226-Cagniard, L., 1953, Basic theory of the magnetotelluric method of geophysical prospecting: beophys. 18, 605-635. Cagniard, L, 1956, Ele c t r i c i t e Tellurique: Handbuch der  Physik, Vol. 47, 407-469. Campbell, W. H., 1959, Studies of magnetic f i e l d micropulsations with periods of 5 to 30 seconds: J. Geophys. Res., 64, 1819-1826. Cantwell, T., 1960, Detection and analysis of low frequency magnetotelluric signals: Ph.D. Thesis, M.I.T. Cantwell, T. , and T. R. Madden, 1960, Preliminary report on crustal magnetotelluric measurements: J. Geophys. Res., 65, 4202-4205. Carstoin, J., 1959, Induced electromagnetic fields in the earth: Proc. Nat. Acad. Sci., 45, 204-208. Chapman, S., 1919, The solar and lunar diurnal variations of terrestrial magnetism: Phil. Trans. Roy. Soc. A, 218, 1-118. Chapman, S., and Bartels, J,, 1940, Geomagnetism. Vol. 1 and 2: Oxford University Press. Chapman, S., and S Akasafu, 1961. The ring current geomagnetic disturbance and the Van Allen radiation belts: J. Geophys. Res., 66, 1321-1350. -227-Chapman, S., and P r i c e , A. T., 1930, The e l e c t r i c and magnetic s t a t e of the i n t e r i o r of the e a r t h as i n f e r r e d from t e r r e s t r i a l magnetic v a r i a t i o n s : P h i l . Trans. Roy, Soc. A, 229, 427-460. Chetaev, D. N., 1960, The d e t e r m i n a t i o n of the a n i s o t r o p y c o e f f i c i e n t and the angle of i n c l i n a t i o n of a homogeneous a n i s o t r o p i c medium, by measuring the impedance of the n a t u r a l e l e c t r o m a g n e t i c f i e l d : B u l l . Acad. S c i . USSR, Geophys. Ser. 4, 12, 407-408. Davenport, W. B. J r . , and Root, W. L., 1958, I n t r o d u c t i o n to the theory of random s i g n a l s and n o i s e : L i n c o l n Lab. Pub. d ' E r c e v i l l e , I . , and G. Kunetz, 1962, The e f f e c t of a f a u l t on the E a r t h ' s n a t u r a l e l e c t r o m a g n e t i c f i e l d : Geophys. 27, 651-665. D e s s l e r , A. J . , 1958, The p r o p a g a t i o n v e l o c i t y of worldwide sudden commencements of magnetic storms: J. Geophys. Res., 63, 405. Douglass, J. L., 1962, Upper c r u s t a l inhomogeneities and t h e i r e f f e c t on t e l l u r i c c u r r e n t s . M. S. T h e s i s , Dept. of  M i n e r a l Tech., Univ. C a l i f . , B e r k e l e y . Duffus, H. J . , J. K. Kinnear, J . A. Shand, and C. S. Wright, 1962, S p a t i a l v a r i a t i o n s i n geomagnetic m i c r o p u l s a t i o n s : Can. J. Phys. 40, 1133-1152. -228-Duffus, H. J, and J. A. Shand, 1958, Some o b s e r v a t i o n s of geomagnetic micropulsation": J. Phys. 36, 508-526. Dungey, J. W., 1954, The p r o p a g a t i o n of A l f v e n waves through the ionosphere: Penn. S t a t e Univ. Ionos. Res. Lab. S c i . Rep. No. 57. E l l i s , R. M., H. Hasegawa, and K. V o z o f f , 1962, R e s u l t s and l i m i t a t i o n s of m a g n e t o t e l l u r i c surveys i n simple g e o l o g i c s i t u a t i o n s : Paper pr e s e n t e d at 32nd S.E.G. Meeting, C a l g a r y . E n g l i s h , W. N., D. J. Evans, J . E. Lokken, J. A. Shand, and C. S. Wright, 1961, Equipment f o r o b s e r v a t i o n of the n a t u r a l e l e c t r o m a g n e t i c background i n the frequency range 0.01-30 cps: Pac. Nav. Lab. Rep. 61-3. Garland, G. D., and R. A. Burwash,' 1959, G e o p h y s i c a l and p e t r o l o g i c a l study of Precambrian of C e n t r a l A l b e r t a : B u l l . Am. Ass. Pet. Geol., 43, 790-806. Garland, G. D., and T. F. Webster, 1960, S t u d i e s of n a t u r a l e l e c t r i c and magnetic f i e l d s : Res., N.B.S. Radio Propagation, 64D, No. 4. Garland, G. D., 1960, E a r t h C u r r e n t s , Methods and techniques i n Geophysics: I n t e r s c i . Pub. Inc., New York, 1, 277-307. -229-Gish, 0. H., 1936, Ele c t r i c a l messages from the earthj their reception and interpretations J, Wash. Acad. Sci., 26, 267-289. Goldstein, N. E., 1962, Numerical f i l t e r i n g of potential f i e l d signals as applied to geophysical exploration: M.S. Thesis, Univ. Calif., Berkeley. Series No. 188. Hasegawa, H., 1962, Magnetotelluric studies in central Alberta: M.S. Thesis, Univ. of Alberta. Heirtzler, J. R., 1962, The longest electromagnetic waves: Sci. Am. 26, 128-317. Hide, R., 1961, The origin of the main geomagnetic f i e l d : Physics and Chemistry of the Earth, Vol. 4, Pergamon  Press: New York, 27-98. Horton, C. W., and Hoffman, 1962, Power spectrum analysis of t e l l u r i c f i e l d at T i b l i s i , USSR, for periods from 2.4 to 60 minutes: J. Geophys. Res., 67, 3369-3371. Horton, C. W., and Hoffman, 1962, Magnetotelluric fields in the frequency range .03 to 7 cy/k.sec. Part 1. Power spectra. Part II. Geophysical interpretation: J. Res., N.B.S., 66D, No. 4. Hugh, H., 1953, The elec t r i c a l conductivity of the Earth's interior: Ph.D. Thesis, Univ. Cambridge. -230-Jacobs, J. A., and K. Sinno, I960, Worldwide characteristics of geomagnetic micropulsations: Geophys. J. Roy. Ast. Soc, 3, 333-353. Jacobs, J. A., and K. Westphal, 1963, Geomagnetic micropulsa-tions. Physics and Chemistry of the Earth. Vol. V.  Pergamon Press. Jacobs, J. A., and Watanabe, T., 1962, Propagation of hydro-magnetic waves in the lower exosphere and the origin of short period geomagnetic pulsations. J. Atmosp. Terr. Phys. 24, 413-434. Karp, S., 1959, Two dimensional Green's functions for a right angle wedge under an impedance boundary condition: New York Univ. Rep. No. EM-129. Kato, Y., and T. Kikuchi, 1950, On the phase difference of Earth currents induced by the changes of the Earth's magnetic f i e l d . Parts I, II: Tohoku Univ. Sci. Rep., Ser. 5, Geophysics, 2., Kebuladze, A., 1953, Some data on the interrelation between t e l l u r i c currents and the geomagnetic f i e l d : Akad. Nauk. SSSR. Geophys. Ser. (IZV), 12,57-72. Kebuladze, A., 1956, On the relationship between regional t e l l u r i c currents and the geomagnetic f i e l d : Akad. Nauk. SSSR. Geophys. Ser. (IZV), 15.37-60. -231-Kolmakov, M. V., and N. P. Vladimirov, 1961, On the equivalence of magnetotelluric sounding curves: Bull. (IZV) Akad.  Sci. Geophys. Ser., 349-354. Kolmakov, M. V., 1961, An interesting property of theoretical magnetotelluric sounding curves: Bull. (IZV) Akad. Sci. Geophys. Ser. 376-378. Kovtun, A. A., 1961, The magnetotelluric investigation of structures inhomogeneous in layers: Bull. (IZV) Akad. Sci. Geophys. Ser., 1085^-1087. Kunetz, G. , 1953, Correlation et recurrance des variations des currants tellurique et du champ magnetique: Proc.  French Assoc. Advancement Sci., 72nd Session, 240-243. Lahiri, B. H., and A. T. Price, 1939, Electromagnetic Induction in non-uniform conductors and the determination of the conductivity of the Earth from te r r e s t r i a l magnetic variations: Phil. Trans. Roy. Soc. A, 237, 509-540. Maple, F., 1959, Geomagnetic oscillations at middle latitudes: J. Geophys. Rev., 64, 1395-1404. McDonald, K. L., 1957, Penetration of the geomagnetic f i e l d through a mantle with variable conductivity: J. Geophys. Res., 62, 117-141. -232-McDonald, G. J . F., 1959, C a l c u l a t i o n on the thermal h e a t i n g of the E a r t h ; J . Geophys. Rev., 64, 1967-2000. Neves, A. S., 1957, The m a g n e t o t e l l u r i c method i n two dimensional s t r u c t u r e s : Ph.D. T h e s i s , M.I.T. N i b l e t t , E. R., and C. S a y n - w i t t g e n s t e i n , 1960, V a r i a t i o n of e l e c t r i c a l c o n d u c t i v i t y with depth by the m a g n e t o t e l l u r i c method. Geophys. 25, 998-1008. N i s h i d a , A., 1961, The o b s e r v a t i o n and a n a l y s i s of micro-p u l s a t i o n s . Unpublished manuscript I n s t i t u t e of E a r t h  S c i e n c e s , Univ. B r i t i s h Columbia. No r i t o m i , K., 1961, The e l e c t r i c a l c o n d u c t i v i t y of rock and the d e t e r m i n a t i o n of the e l e c t r i c a l c o n d u c t i v i t y of the e a r t h i n t e r i o r : J. Min. C o l l e g e , A k i t a Univ., 1, 27-59. Pearson, K., 1901, L i n e s and planes of c l o s e s t f i t of system of p o i n t s i n space: P h i l . Mag. 2, 559-572. P r i c e , A. T., 1962, The theory of m a g n e t o t e l l u r i c method when the source f i e l d i s c o n s i d e r e d : J . Geophys. Res. 67, 1907-1918. Rankin, D., 1960, A t h e o r e t i c a l and experimental study of s t r u c t u r e i n the m a g n e t o t e l l u r i c f i e l d : Ph.D. T h e s i s , Univ. A l b e r t a . -233-Rankin, D., 1962, The magnetotelluric e f f e c t i n a dyke: Geophys. 27, 666-676. Rikitake, T., 1950, Electromagnetic induction within the Earth and i t s r e l a t i o n to the e l e c t r i c a l state of the Earth's i n t e r i o r : B u l l . Earthquake Res. Inst. Tokyo, 28, pp 45, 219, 263. Rikitake, T., 1951, Changes i n Earth current and their r e l a t i o n s to the e l e c t r i c a l state of the Earth's crust: B u l l . Earthquake Res. Inst. Tokyo, 29, 271. Rokityanski, I. I., 1961, On.the application of the magneto-t e l l u r i c method to anisotropic and inhomogeneous masses: B u l l . (IZV) Akad. S c i . Geophys. Ser. 1050-1053. Rosen, A., and T. Farley, 1961, C h a r a c t e r i s t i c s of the Van Allen r a d i a t i o n zones as measured by the s c i n t i l l a t i o n counter on Explorer VI: J.-Geophys. Res.. 66. 2013-2028. Roy, A., 1962, Ambiguity i n geophysical i n t e r p r e t a t i o n : Geophysics 27, 90-100. Schaub, Yu. B., 1960, The interpretation of the r e s u l t s obtained by measuring the angle of i n c l i n a t i o n of the plane of p o l a r i s a t i o n of the variable natural magnetic f i l e d : B u l l . (IZV) Akad. S c i . Geophys. Ser., 1184-1188. -234-Schuster, A., 1889, The diurnal variation of terr e s t r i a l magnetism: Phil. Trans. Roy. Soc, A, 180, 467-512. Sikayobni, L. A., 1957, Major tectonic trends in the prairie region of Canada: Alta. Soc. Pet. Geolog., 5, 23-28. Smith, H. W., L. D. Provazek, F. X. Bostick, Jr., 1961, Directional properties and phase relations of the magneto-t e l l u r i c fields at Austin, Texas: J. Geophys. Res. 66, 879-888. Tikhonov, A. N., 1950, The determination of the electrical properties of deep layers of the Earth's crust: Proc.  (Doklady) Akad. Sci. USSR, No. 2. Tikhonov, A. N., and D. N, Shakhsuvarov, 1956, The f e a s i b i l i t y of using the Earth's natural electromagnetic f i e l d to study i t s upper layers: Bull. (IZV) Akad. Sci. Geophys. Ser. 410-418. Tozer, D. C., 1959, The elec t r i c a l properties of the Earth's interior: Phys. Chem. Earth, 3, 414-436. Vladimirov, N. P., and M. V. Kolmakov, 1960, The resolving power of the magnetotelluric method: Bull. (IZV) Akad. Sci. Geophys. Ser. 1066-1068. Vladimirov, N. P., 1960, On the f e a s i b i l i t y of ut i l i s a t i o n of -235-th e Earth's natural electromagnetic f i e l d for geologic explor at ion: Akad. Nauk. SSSR Geophys, Ser. (IZV) 19, 89-90. Vladimirov, N. P., and N. N. Nikiforova, 1961, On the i n t e r - . pretation of magnetotelluric sounding curves: B u l l . (IZV)  Akad. S c i . Geophys. Ser., 67-69. magnetotelluric oscillograms: B u l l . (IZV) Akad, Sc i , Geophys. Ser., 1075-1178. Wait, J., 1954, On the r e l a t i o n between the t e l l u r i c currents and the Earth's magnetic f i e l d : Geophysics 19, 281-289. Wait, J,, 1960, Influence of source distance on the impedance c h a r a c t e r i s t i c s of ELF radio waves: Proc. IRE 48, 1338. Ward, S. H., et a l , 1958, Prospecting by use of natural alternating magnetic f i e l d s of audio and sub-audio f r e -quencies : Trans. CIMM 61, 261-268. Ward, S. H., 1959, AFMAG - Airborne and ground: Geophysics 24, 761-789. Watanabe, T., 1956, Further study on the cause of giant pulsations: Tohoku Univ. S c i . Rep. Ser. 5, Geophys. 8. Vladimirov, N. P and V. A. An, 1961, A method of processing Watanabe, T., 1959, Morphology of the geomagnetic pulsation: J. Geomag. Geoelec. 10, 177-184. -236-Webb, J. B. 1954, Geological history of plains of western Canada: Am. Ass. Pet. Geolog. West. Canada Sed. Basin. Symposium, 3-28. Whitham, K., 1960, Measurement of the geomagnetic element: Methods and techniques in geophysics, Vol. 1, 104-167. Interscience Publisher Inc., New York. Yungul, S. H., 1961, Time variations of the e l l i p t i c i t y and preferred d i r e c t i o n of the pc t e l l u r i c f i e l d : J. Geophys. Res. 66, 557-561. Yungul, S. H., 1961, Magnetotelluric sounding three layer in t e r p r e t a t i o n curves: Geophysics 26, 465-473. Zhigalov, L. N., 1961, Some features of the v a r i a t i o n of the geomagnetic v e r t i c a l component i n the A r c t i c Ocean: D.R.B. (Canada) Translation T358R. 

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