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UBC Theses and Dissertations

The search for intermodulation coupling in the ground Mitchell, Gerald George 1978

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The S e a r c h f o r I n t e r m o d u l a t i o n C o u p l i n g i n t h e G r o u n d b y G e r a l d G e o r g e M i t c h e l l B . S c , 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 1975 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE THE FACULTY OF GRADUATE STUDIES D e p a r t m e n t o f G e o p h y s i c s and A s t r o n o m y We a c c e p t t h i s t h e s i s as c o n f o r m i n g to t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA J u l y , 1978 G e r a l d G e o r g e M i t c h e l l 1978 In presenting th i s thes is in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Univers i ty of B r i t i s h Columbia, I agree that the L ibrary shal l make it f ree ly ava i lab le for reference and study. I further agree that permission for extensive copying of th is thesis for scholar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t ion of th is thesis for f inanc ia l gain sha l l not be allowed without my writ ten permission. Depa rtment The Univers i ty of B r i t i s h Columbia 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 Date T, ABSTRACT The assumption t h a t the ground behaves as a l i n e a r e l e c t r i c a l network i s t e s t e d w i t h a f i e l d experiment. Two s i n u s o i d s of c u r r e n t are t r a n s m i t t e d i n t o the ground s i m u l t a n e o u s l y . The p o t e n t i a l f i e l d i s measured and re c o r d e d on magnetic tape. Amplitude s p e c t r a are computed and searched f o r i n t e r m o d u l a t i o n c o u p l i n g terms, the presence of which i n d i c a t e n o n l i n e a r i t y . T e s t s on the UBC campus d i d not d e t e c t i n t e r m o d u l a t i o n c o u p l i n g . The f i r s t t e s t , at a v o l c a n o g e n i c massive s u l f i d e d e p o s i t , i n d i c a t e d s i g n i f i c e n t i n t e r m o d u l a t i o n c o u p l i n g . T h i s t e s t was r e p e a t e d with a d i f f e r e n t i n s t r u m e n t - e l e c t r o d e c o n f i g u r a t i o n . There was no c o u p l i n g d e t e c t e d i n the repeated t e s t . TABLE OF CONTENTS A b s t r a c t , 11 Table of Contents 1 1 1 Table of F i g u r e s i v Acknowledgment, Chapter 1 I n t r o d u c t i o n 1 Chapter 2 Theory 18 A T e s t f o r L i n e a r i t y 19 Chapter 3... I n s t r u m e n t a t i o n 29 Chapter 4 Experiments 37 T e s t s on the UBC Campus 42 Seneca T e s t 50 Chapter 4 Summary and C o n c l u s i o n s 57 B i b l i o i g r a p h y . . . 61 Appendix Diagram of the C o n t r o l C i r c u i t . . . 65 i i i Table of F i g u r e s F i g u r e 1 Schlumberger A r r a y f o r r e s i s t i v i t y F i g u r e 2 E l e c t r i c a l response of a m i n e r a l i z e d r o c k s F i g u r e 3 Decrease i n impedance of a s e r p e n t i n e sample at high charge d e n s i t y (Katsube 1973) F i g u r e 4 I n c r e a s e i n the d i s t o r t i o n c o e f f i c i e n t w i t h i n c r e a s i n g charge d e n s i t y f o r a g a l e n a sample (Katsube 1973) F i g u r e 5 Input-output of an e l e c t r i c a l network F i g u r e 6 Two p o s s i b l e r e l a t i o n s h i p s between V ( t ) & I ( t ) F i g u r e 7 The responce of v a r i o u s networks t o a s i n u s o i d a l input F i g u r e 8 The response of v a r i o u s networks to an i n p u t of two s i n u s o i d s F i g u r e 9 Block diagram of the i n s t r u m e n t a t i o n system F i g u r e 10 A. E l e c t r o d e a r r a y w i t h a common ground p o i n t f o r the i n p u t and output c i r c u i t s B. Separate ground p o i n t s F i g u r e 11 A. Output s i g n a l from a l i n e a r network B. Output s i g n a l from a n o n l i n e a r network F i g u r e 12 Amplitude s p e c t r a f o r the l i n e a r network o f f i g u r e 11 F i g u r e 13 Amplitude s p e c t r a f o r the t e s t i n f r o n t of the Geophysics and Astronomy B u i l d i n g UBC F i g u r e 14 A diode connected to the ground to induce n o n l i n e a r i t y F i g u r e 15 Amplitude s p e c t r a f o r the n o n l i n e a r network connected to the ground ( f i g u r e 14) F i g u r e 16 Amplitude s p e c t r a f o r the Seneca t e s t F i g u r e 17 Amplitude s p e c t r a f o r the t e s t at Seneca showing i n t e r m o d a t i o n c o u p l i n g i v ACKNOWLEDGEMENT I thank Dr. R.D. R u s s e l l f o r p r o p o s i n g the t o p i c and g u i d i n g my work. His a b i l i t y t o immediately see the h e a r t of a problem and the most l i k e l y p ath t o i t s s o l u t i o n was a g r e a t h e l p . Dr. R. Clowes loaned the D i g i t a l Marine Data Recording System to t h i s p r o j e c t . Mr. V. Ronka a s s i s t e d on one of the f i e l d t r i p s and c o n t r i b u t e d many u s e f u l s u g g e s t i o n s . The p r o j e c t was funded by the N a t i o n a l Research C o u n c i l g r a n t #A720. v CHAPTER 1 INTRODUCTION Many p h y s i c a l c h a r a c t e r i s t i c s o f the E a r t h may be i n -f e r r e d from a knowledge o f t h e E a r t h ' s e l e c t r i c a l p r o p e r t i e s , Measurement o f both n a t u r a l and man-made e l e c t r i c a l s i g n a l s p r o v i d e i n f o r m a t i o n on the l a r g e s c a l e s t r u c t u r e o f the Ea r t h ' s c r u s t and upper mantle, t o depths o f t e n s o f k i l o -meters. I t i s p o s s i b l e t o d e t e r m i n e the s t r u c t u r e and co m p o s i t i o n o f the r o c k s a t depths t o a few hundred meters. S t u d i e s o f the e l e c t r i c a l p r o p e r t i e s o f the s u b s u r f a c e i n v o l v e measurements o f the r e s i s t i v i t y o f the ground as a f u n c t i o n o f frequency and e l e c t r o d e c o n f i g u r a t i o n . These methods are d i s c u s s e d i n some d e t a i l i n most a p p l i e d geophy-s i c s t e x t b o o k s . Measurements o f the r e s i s t i v i t y o f the ground at s h a l l o w depths, w i t h i n a few hundred meters o f s u r f a c e , have 1 a p p l i c a t i o n s i n ground water i n v e s t i g a t i o n s and mining e x p l o r a t i o n . D.C. r e s i s t i v i t y methods have been used e x t e n s i v e l y s i n c e the 1920s i n ground water and mining e x p l o r a t i o n s u r v e y s . Four e l e c t r o d e s a r e connected t o the ground as i l l u s t r a t e d i n f i g u r e 1. A c u r r e n t I i s t r a n s m i t t e d between e l e c t r o d e s 1^ and I^- The r e s u l t a n t p o t e n t i a l d i f f e r e n c e between e l e c t r o d e s and P' i s measured and the apparent r e s i s t i v i t y o f the ground determined from the r e l a t i o n s h i p ( O a = TTML 2-! 2) v 1 2 1 1 yO i s c a l l e d the apparent r e s i s t i v i t y because i t i s the a r e s i s t i v i t y o f a h y p o t h e t i c a l homogeneous h a l f space which would produce the observed r e s u l t s . The a c t u a l d i s t r i b u t i o n of r e s i s t i v i t y v a l u e s i s u n l i k e l y t o be homogeneous. 2 Figure 1. Schlumberger A r r a y f o r R e s i s t i v i t y Soundings 3 From a knowledge o f the b e h a v i o r of the apparent r e s i s -t i v i t y as a f u n c t i o n of the e l e c t r o d e geometry and the p o s i -t i o n of the e n t i r e e l e c t r o d e a r r a y i t i s p o s s i b l e t o determine a probable d i s t r i b u t i o n of the a c t u a l r e s i s t i v i t y v a l u e s of the ground. T h i s i s the problem common to a l l types of s u r -face g eophysics t e c h n i q u e s . I t i s known as the i n v e r s i o n problem. Advances i n i n s t r u m e n t a t i o n have brought changes i n f i e l d equipment and procedures s i n c e the i n c e p t i o n of the r e s i s t i v i t y method. The g r e a t e s t advances i n the use of the method have been i n i n t e r p r e t a t i o n . D i g i t a l computers have per m i t t e d the development o f powerful t e c h n i q u e s o f one dimensional and two d i m e n s i o n a l i n v e r s i o n . Curve matching between f i e l d d a t a and computer generated c a t a l o g u e s o f r e s i s t i v i t y curves c a l c u l a t e d from l a y e r e d models c o n s t i t u t e d the f i r s t o f these i n t e r p r e t a t i o n 4 techniques. (Zohdy 1965, Orellana and Mooney 1966). This was followed by the development of automatic curve matching techniques. Recently methods have been developed for d i r e c t inversion of f i e l d data to probable models. Oldenberg (1978) applies the l i n e a r i z e d inverse theory of Backus and G i l b e r t (1968) to invert r e s i s t i v i t y data. This technique produces a one dimensional model of the v a r i a t i o n of r e s i s t i v i t y with depth. The data i s inverted automatically to a probable model without the necessity of p r i o r assumptions of r e s i s t i v i t y values or layers of homogeneous r e s i s t i v i t y . Pelton (1976) has developed a technique for the inversion of induced p o l a r i z a t i o n and r e s i s t i v i t y data to two dimensional models. This method compares the f i e l d data to a large l i b r a r y of forward problem s o l u t i o n s . The parameters of the model giving the c l o s e s t f i t to the f i e l d data are varied u n t i l a s a t i s f a c t o r y f i t between i t s forward problem s o l u t i o n and the data is achieved. The induced p o l a r i z a t i o n or o v e r v o l t a g e phenomena was observed i n a tank c o n t a i n i n g an aqueous s o l u t i o n and metal p a r t i c l e s at the Radio Frequency L a b o r a t o r i e s o f Boonton, N.J., U.S.A., i n 1946. A f t e r the c e s s a t i o n of an a p p l i e d c u r r e n t , a p o t e n t i a l d i s c h a r g e was observed i n the tank. H.O. S e i g a l and o t h e r s a p p l i e d t h i s knowledge t o the se a r c h f o r disseminated m e t a l l i c m i n e r a l d e p o s i t s i n the southwestern United S t a t e s i n 1949. A complete d i s c u s s i o n of the e a r l y h i s t o r y of I.P. i s a v a i l a b l e i n O v e r v o l t a g e Research and  Geophysical A p p l i c a t i o n s , Wait 1959. The I.P. phenomena i n r o c k s has been s t u d i e d both i n the f i e l d and i n the l a b o r a t o r y s i n c e the 1950s. R e c e n t l y P e l t o n (1972, 1978) has demonstrated t h a t the I.P. phenomena may be modelled by a r e l a x a t i o n model proposed by Cole and Cole (1941) t o p r e d i c t complex d i e l e c t i v e b e h a v i o r . The model and i t s frequency and time domain response are shown i n f i g u r e Figure 2 (a) A small s e c t i o n o f a m i n e r a l i z e d rock which has both blocked and unblocked pore passages. (b) An e q u i v a l e n t c i r c u i t f o r the m i n e r a l i z e d r ock. (c) T y p i c a l frequency domain response f o r the e q u i v a -l e n t c i r c u i t . (d) Time domain response c o r r e s p o n d i n g t o the frequency domain response p l o t t e d i n ( c ) . From P e l t o n 1978 7 The impedance of t h i s c i r c u i t i s Z(w) = R o d - m(l - 1 )) 1 + ( i w t ) c m = 1 1 + R i / R q t = X ( R 0 / m ) l / c P e l t o n (1977) has l a b o r a t o r y and f i e l d r e s u l t s which i n d i c a t e d e t e r m i n a t i o n s of m and t may be u s e f u l i n d i s -c r i m i n a t i n g between types of d e p o s i t s . He concludes the v a l u e s of m and t are a f u n c t i o n of m i n e r a l t e x t u r e r a t h e r than m i n e r a l type. As m i n e r a l texture... i s i n p a r t a f u n c t i o n -of m i n e r a l type, P e l t o n argues i t should be p o s s i b l e to d i s t i n g u i s h some types of d e p o s i t s from o t h e r s . His r e s u l t s i n d i c a t e i t may be p o s s i b l e to d i s t i n g u i s h between d e p o s i t s of g r a p h i t e and massive s u l p h i d e s by measuring complex impedance over a wide range of f r e q u e n c i e s and d e t e r m i n i n g m and t f o r each d e p o s i t . 8 R e c e n t l y developed i n s t r u m e n t a t i o n and i n t e r p r e t a t i o n techniques determine the frequency response of the ground over a wide range of f r e q u e n c i e s . The measurements are made si m u l t a n e o u s l y a t s e v e r a l harmonic f r e q u e n c i e s . The r e s u l t s are i n t e r p r e t e d with the assumption t h a t t h e r e i s no i n t e r -modulation c o u p l i n g due to e l e c t r i c a l n o n l i n e a r i t y o f the ground. T h i s assumption i s made i n v i r t u a l l y a l l work d e a l i n g with e l e c t r i c a l s i g n a l s i n the ground, the assumption being that at the s m a l l c u r r e n t d e n s i t i e s i n v o l v e d , the ground i s e l e c t r i c a l l y l i n e a r . Most of the experiments d e a l i n g with the e l e c t r i c a l l i n e a r i t y of r o c k s and m i n e r a l s have been l a b o r a t o r y experiments. The a p p l i c a t i o n of r e s u l t s o b t a i n e d i n the l a b o r a t o r y t o f i e l d s i t u a t i o n s i s always somewhat u n c e r t a i n . T h i s t h e s i s was undertaken t o t e s t , w i t h a f i e l d experiment, the assumption t h a t the ground behaves as a l i n e a r network, a t c u r r e n t d e n s i t i e s o f the same o r d e r as those used i n IP s u r v e y s . 9 Should some m i n e r a l s , rock t y p e s , or g e o l o g i c s t r u c -t u r e s conduct e l e c t r i c i t y i n a n o n l i n e a r manner i t i s c o n c e i v -a b l e that an a c c u r a t e d e s c r i p t i o n o f the n o n l i n e a r i t y might l e a d to a method of remote d e t e c t i o n of the element c a u s i n g the n o n l i n e a r i t y . T h i s p o s s i b i l i t y has been r e c o g n i z e d at l e a s t s i n c e 1950, when i t was the o b j e c t o f a United S t a t e s C patent a p p l i c a t i o n by Oscar Weiss and L u c i e n Masse. Russian G e o p h y s i c i s t s p u b l i s h e d the r e s u l t s of s e v e r a l s t u d i e s of e l e c t r i c a l n o n l i n e a r i t i e s i n r o c k s and m i n e r a l s i n the e a r l y 1970s. Ryss (1971, 1973) d e s c r i b e s a method c a l l e d the " P o l a r i z a t i o n Curve Contact Method". E l e c t r i c a l c o n t a c t i s made with a massive s u l p h i d e body and l a r g e c u r r e n t s are t r a n s m i t t e d between i t and an e l e c t r o d e i n the host r o c k s . The p o t e n t i a l a c r o s s the massive s u l p h i d e - h o s t rock i n t e r f a c e i s monitored. A s l o w l y v a r y i n g DC c u r r e n t i s t r a n s m i t t e d through the ore body and the c u r r e n t i s p l o t t e d a g a i n s t the p o t e n t i a l drop a c r o s s the i n t e r f a c e . D i f f e r e n t m e t a l l i c 10 minerals at the i n t e r f a c e may be i d e n t i f i e d from t h i s c u rve. At the orebody/host-rock i n t e r f a c e the c o n d u c t i o n mechanism changes from e l e c t r o n i c to i o n i c . The p o t e n t i a l drop across the i n t e r f a c e i s the p o t e n t i a l o f the e l e c t r o c h e m i c a l r e a c t i o n t a k i n g p l a c e t h e r e . K l e i n and Shuey (1976) have st u d i e d these r e a c t i o n s i n the l a b o r a t o r y u s i n g e l e c t r o d e s o f p y r i t e , c h a l c o p y r i t e , g a l e n a and g r a p h i t e . They conclude t h a t i t i s p o s s i b l e t o d e t e c t s u l p h i d e m i n e r a l s i n the presence of g r a p h i t e , and c h a l c o p y r i t e i n the presence o f p y r i t e , i n the l a b o r a t o r y . T h e y suggest that t h i s method c o u l d be used t o i d e n t i f y m i n e r a l s i n the w a l l o f a - d r i l l h o l e , but do not commit themselves on the s u b j e c t o f a p p l y i n g the method to e n t i r e ore b o d i e s . One o f the l i m i t i n g f a c t o r s of t h i s method i s the l a r g e c u r r e n t d e n s i t y r e q u i r e d t o d r i v e the e l e c t r o c h e m i c a l r e a c t i o n s observed by K l e i n and Shuey. T h e i r experiments 11 r e q u i r e d c u r r e n t d e n s i t i e s up t o 5mA/cm2. In h i s f i e l d t e s t s Ryss used a 30kW, 250A t r a n s m i t t e r . re In 1973 Katsube o f the G e o l o g i c a l Survey o f Canada p o r t e d the r e s u l t s o f some l a b o r a t o r y experiments on the e l e c t r i c a l n o n l i n e a r i t y o f s e r p e n t i n e , a s b e s t o s , p y r i t e , c u b a n i t e and g a l e n a . Of t h e s e he c o n c e n t r a t e d on the s e r p e n t i n e and g a l e n a , a n a l y s i n g t h e i r n o n l i n e a r c h a r a c t e r by th r e e d i f f e r e n t methods. The methods he used were the " d e s c r i b i n g f u n c t i o n a n a l y s i s method f o r n o n - l i n e a r systems f o r high and low impedance specimens", the " e l l i p s e a n a l y s i s method f o r n o n l i n e a r L i s s a j o u s f i g u r e s " , and the "double freq u e n c y a n a l y s i s method". For the d e s c r i b i n g f u n c t i o n a n a l y s i s , a n o n d i s t o r t e d s i n u s o i d a l waveform o f v o l t a g e , i n the case o f s e r p e n t i n e , and c u r r e n t , i n the case o f g a l e n a , was a p p l i e d t o the sample and 12 the r e s u l t i n g c u r r e n t or v o l t a g e monitored and r e c o r d e d . For an a p p l i e d s i n u s o i d a l v o l t a g e the r e s u l t a n t c u r r e n t may be expressed as I ( t ) = I Q y (I S i n (nwt) + I B Cos (nwt)) n=l n n a F o u r i e r s e r i e s . w and t are a n g u l a r frequency and time and I ^ n and iBn a r e determined to g i v e at l e a s t squares f i t between the e x p r e s s i o n and the s i g n a l . The t o t a l charge d e n s i t y i s d e f i n e d by Katsube as w q = 1 C ( I , S i n (wt) + I D Cos (wt)) dt coulombs/cm 2 A ) 1 o where A i s the area of the sample, For the S e r p e n t i n e sample the a p p l i e d v o l t a g e was v a r i e d between .3 and 30 v o l t s over a frequency range o f 1 0 - 1 Hz to 103 Hz. The impedence Z = V l 2 + i2 A B 1 1 was n o r m a l i z e d to i t s v a l u e at .3 v o l t s at each frequency. A v a r i a t i o n i n the normalized impedence. .as the a p p l i e d v o l t a g e 13 i n c r e a s e d was taken as e v i d e n c e of n o n l i n e a r t y . F i g u r e 3 i l l u s t r a t e s Katsube's r e s u l t s f o r the d e s c r i b i n g f u n c t i o n a n a l y s i s o f the s e r p e n t i n e sample. There i s a c r i t i c a l charge d e n s i t y , Q c r* o f 10~8 coulombs/cra 2 above which the sample becomes e l e c t r i c a l l y n o n l i n e a r . The c r i t i c a l c u r r e n t d e n s i t y , J c r i s For the g a l e n a sample the c u r r e n t d e n s i t y i s v a r i e d and the d i s t o r t i o n c o e f f i c e n t o f the r e s u l t a n t v o l t a g e , E, i s p l o t t e d a g a i n s t the charge d e n s i t y , F i g u r e 4. Katsube i d e n t i f i e s two c r i t i c a l charge d e n s i t i e s , 10~6 coulombs/cm and 10~4 coulombs/cm2 a s s o c i a t e d w i t h n o n l i n e a r phenomena i n the galena sample. J c r = Q TTf cr 125 F i g u r e 3. D e c r e a s e i n impedance o f a s e r p e n t i n e sample a t h i g h c h a r g e d e n s i t y . (Katsube 1973) io7 . id 6 id5 id 4 , io3 TOTAL CHARGE DENSITY (COULOMBS/cm ) F i g u r e 4. I n c r e a s e i n t h e d i s t o r t i o n c o e f f i c i e n t w i t h i n c r e a s i n g c h a r g e d e n s i t y f o r a g a l e n a sample. (Katsube 197 3) 15 The " e l l i p s e a n a l y s i s method f o r n o n l i n e a r l i s s a j o u s f i g u r e s " and the "double frequency a n a l y s i s method" used to analyze the specimens c o r r o b o r a t e d the r e s u l t s o b t a i n e d by the d e s c r i b i n g f u n c t i o n method. The double frequency method c o n s i s t s of a 10^ Hz s i g n a l at .3 v o l t s modulating a c a r r i e r of l e s s than 1 Hz. The v o l t a g e o f the c a r r i e r i s v a r i e d from .3 to 30 v o l t s . The waveform of the mo d u l a t i o n s i g n a l was observed i n the l i n e a r and n o n l i n e a r r e g i o n . The c r i t i c a l charge d e n s i t i e s f o r the onset of n o n l i n -e a r i t y , which Katsube observed i n the l a b , are e a s i l y a c h i eved i n the f i e l d . C u r r e n t s o f s e v e r a l amperes are commonly used i n I.P. Surveys. For the case o f s e r p e n t i n e , with a c r i t i c a l charge d e n s i t y of 10~? coulombs/cm 2, a c u r r e n t o f 1 ampere and a frequency of .1 Hz would p r o v i d e a charge d e n s i t y i n the n o n l i n e a r range t o a depth o f 70 meters. White made some l a b o r a t o r y measurements of e l e c t r i c a l 16 n o n l i n e a r i t i e s i n an M.Sc. T h e s i s at MacQuarie U n i v e r s i t y , A u s t r a l i a , i n 1974. The method used by White i s i n some r e s p e c t s s i m i l a r t o the method d e s c r i b e d i n t h i s t h e s i s . I t w i l l be d i s c u s s e d l a t e r . T h i s t h e s i s r e p r e s e n t s one o f the f i r s t s t u d i e s o f the e l e c t r i c a l p r o p e r t i e s of the ground made at the UBC Department of Geophysics and Astronomy and the f i r s t i n the f i e l d o f e l e c t r i c a l n o n l i n e a r i t i e s . One of the i n i t i a l o b j e c t i v e s of t h i s t h e s i s was the development o f a system c a p a b l e o f the d e t e c t i o n o f i n t e r -m o d u l a t i o n c o u p l i n g i n the ground. In terms of the time and e f f o r t r e q u i r e d t h i s q u i c k l y became the p r i n c i p a l o b j e c t i v e . I t i s hoped t h a t the e x p e r i e n c e g a i n e d and the r e s u l t s o b t a i n e d i n the course of t h i s work may form the s t a r t i n g p o i n t f o r f u t u r e i n v e s t i g a t i o n s i n t h i s a r e a . 17 CHAPTER 2 THEORY A l i n e a r system or network may be d e f i n e d as one i n which the p r i n c i p l e o f s u p e r p o s i t i o n a p p l i e s . The p r i n c i p l e of s u p e r p o s i t i o n may be d e f i n e d i n the f o l l o w i n g way. C o n s i d e r a f u n c t i o n F(x) such t h a t F ( X ] L ) = A F ( x 2 ) = B I f F ( X l + x ^ ) = A + B i e . F ( X l ) + F ( x 2 ) = F(x1 + x 2 ) the f u n c t i o n F(x) obeys the p r i n c i p l e o f s u p e r p o s i t i o n and i s t h e r e f o r e a l i n e a r f u n c t i o n o f x. 18 A Test For L i n e a r i t y An e l e c t r i c a l network may be determined t o be l i n e a r o r n o n l i n e a r by an experiment t h a t shows whether the p r i n c i p l e of s u p e r p o s i t i o n i s v i o l a t e d . One such experiment i n v o l v e s the input of a s i n u s o i d t o the network. C o n s i d e r f i g u r e 5. I ( t ) i s an input c u r r e n t and V ( t ) i s the r e s u l t a n t output v o l t a g e of the network. F i g u r e 6 i l l u s t r a t e s two p o s s i b l e r e l a t i o n s h i p s between V ( t ) and I ( t ) . The curve i n d i c a t e d by L i s f o r a l i n e a r network and a n o n l i n e a r network i s i n d i c a t e d by NL. The shape o f the curve NL may take any form f o r a n o n l i n e a r network. The s l o p e i s the o n l y a r b i t r a r y parameter f o r the s t r a i g h t l i n e L. We may r e p r e s e n t the r e l a t i o n s h i p between I ( t ) and V ( t ) by a power s e r i e s o f the form V ( t ) = a 1 I ( t ) + a 2 I 2 ( t ) + a 3 I 3 ( t ) + 3 19 L i t ) E l e c t r i c a l Network V(t) F i g u r e 5. The i n p u t and o u t p u t o f an e l e c t r i c a l network 20 For the case of the l i n e a r network a l l the c o e f f i c i e n t s of the s e r i e s except a^ are 0. For the n o n l i n e a r network t h i s i s not the case. Let the i n p u t , I ( t ) , be a s i n u s o i d o f amplitude equal to 1 and a frequency of I ( t ) = cos(wt) 2 3 V ( t ) = a-jcosfwt) + a 2 c o s (wt) + a ^ o s (wt) + T h i s may be transf o r m e d i n t o the f o l l o w i n g form through t r i g o n o m e t r i c i d e n t i t i e s V ( t ) = a 2/2 + 3a 4/8 + + cos(wt) {a1 + 3a 3/4 + 3a 4/4 + + cos(2wt) ( a 2 / 2 + 3a 4/8 + + cos(3wt) ( a 3 / 4 + ) + cos(4wt) ( a 4 / 9 + ) + 21 If the input to a network i s a sinusoid of current the output voltage can be described by equation 10. Whatever the shape of the output waveform, i f i t has no net DC term, i t s i n t e g r a l from -oo to +00 being zero, the even c o e f f i c i e n t s of equation 4 w i l l a l l be zero, or a l t e r n a t i v e l y 0 = a 2/2 + 3a 4/8 + The r e l a t i o n s h i p s between the inputs and the outputs of four networks are i l l u s t r a t e d in figure 7. Network 1 i s l i n e a r provided that the current amplitude does not become so great that i t causes heating problems in the r e s i s t o r . The other three networks are nonlinear. Of the three nonlinear networks, network 2, the s i n g l e diode i s the only one which produces an output with a net DC term. Equation 10 indicates that t h i s network w i l l have both odd and even harmonic's of the fundamental frequency i n i t s output. 22 Figure 7. The response of various networks to a s i n u s o i d a l input. The presence of components i n the o u t p u t amplitude s p e c t r a of networks 2, 3 and 4 which do not e x i s t i n t h e i r i n p u t amplitude spectrams, c o n s t i t u t e p r o o f t h a t the p r i n c i p l e of s u p e r p o s i t i o n i s v i o l a t e d and t h a t these networks are n o n l i n e a r . An e x p e r i m e n t a l problem w i t h the t e s t i l l u s t r a t e d i n f i g u r e 7 i s the d i f f i c u l t y o f t r a n s m i t t i n g a p e r f e c t s i n u s o i d . I f there are harmonic components p r e s e n t i n the input to the network they are g o i n g to be p r e s e n t i n the output. To account f o r a v a r i a t i o n i n t h e i r a m p l i t u d e s due t o n o n l i n e a r i t y of the network r e q u i r e s a knowledge of the t r a n s f e r f u n c t i o n o f the network. T h i s problem may be a v o i d e d by u s i n g an i n p u t s i g n a l which i s the sum of two s i n u s o i d s of d i f f e r e n t f r e q u e n c i e s and l o o k i n g f o r i n t e r m o d u l a t i o n c o u p l i n g terms i n the o u t p u t . C o n s i d e r the power s e r i e s e q u a t i o n 3. L e t I ( t ) = c o s ( w i t ) + cos(w2t) 5 ( i g n o r i n g phase r e l a t i o n s ) 24 S u b s t i t u t i n g e q u a t i o n 5 i n t o e q u a t i o n 3 and s i m p l i f y i n g g i v e s 6 V ( t ) = a 2 + 9a 4/4 + + c o s ( w 1 t ) ( a 1 + 9a 3/4 + ) + c o s ( w 2 t ) ( a ; L + 9a 3/4 + ) + cos(2w.t) (a_ / 2 + 2aA + ) 1 2 4 + c o s ( 2 w 2 t ) ( a 2 / 2 + 2 a 4 + ) + cos( (w_^  + w ^ ) t ) + + ) + c o s ( ( w 2 - w1)t) ( a 2 + 3 a 4 + ) + c o s ( 3 w 1 t ) ( a 3 / 4 + ) + c o s ( 3 w 2 t ) ( a 3 / 4 + .) + c o s ( ( 2 W l + w 2 ) t ) (3a 3/4 + ) + c o s ( ( 2 W l - w 2 ) t ) (3a /4 + ) + c o s ( ( 2 w 2 + w1)t) (3a 3/4 + .) + c o s ( ( 2 w 2 - w 1 ) t ) (3a 3/4 + ) + 25 Network Output Input versus Output Amplitude Spectra 2 8. The response of various networks to the simultaneous input of two sinusoids. The terms i n e q u a t i o n 6 which i n c l u d e both f r e q u e n c i e s ( i . e . (w^ + v ^ ) ) , are c a l l e d i n t e r m o d u l a t i o n c o u p l i n g terms. The presence of any o f these terms i n the output of a network which has two s i n u s o i d s as i t s i n p u t p r o v e s t h a t the network i s n o n l i n e a r . F i g u r e 8 i l l u s t r a t e s the i n p u t , o u t p u t , and amplitude s p e c t r a f o r the f o u r networks c o n s i d e r e d p r e v i o u s l y . T h i s i s the method t h a t i s used to determine whether the e l e c t r i c a l response of the ground obeys the p r i n c i p l e of s u p e r p o s i t i o n . A p o t e n t i a l advantage o f u s i n g the two-frequency method i s t h a t i f the ground i s e l e c t r i c a l l y n o n l i n e a r , and i f t h i s i s d e t e c t a b l e , the amplitude spectrum o f the two frequency method would p r o v i d e a b e t t e r d e s c r i p t i o n of the nature of the n o n l i n e a r i t y than would the s i n g l e f r e q u e n c y method. There 2 7 are p a i r s o f peaks which s h o u l d have i d e n t i c a l amplitudes i n the two-frequency spectrum ((w^ + w^) and (w^ - w^) e t c . ) which could s e r v e as a check on the v a l i d i t y of the r e s u l t s and the r e s o l u t i o n o f the system. A s i m i l a r method t o t h a t used i n t h i s work was used by White i n some l i n e a r i t y experiments w i t h rock samples at Macquarie U n i v e r s i t y i n 1974. White monitored the amplitude of the (w^ + w^) term i n an attempt t o determine the degree of e l e c t r i c a l n o n l i n e a r i t y o f h i s samples. Consequent-l y he o n l y observed i n t e r m o d u l a t i o n c o u p l i n g when the non-l i n e a r i t y was a s y m e t r i c a l , as i n the case o f the s i n g l e d i o d e of f i g u r e 8, or i f a DC o f f s e t were p r e s e n t . He d i s c o v e r e d i n f a c t t h a t the amplitude o f the (w^ + w^) term was dependent on the DC o f f s e t o f the i n p u t s i g n a l . White's method, a p p l i e d t o the o b v i o u s l y n o n l i n e a r network, network number 3 o f f i g u r e 8, would d e t e c t no i n t e r m o d u l a t ion c o u p l i n g u n l e s s t h e r e was a DC o f f s e t i n the i n p u t s i g n a l . 28 CHAPTER 3 INSTRUMENTATION The i n s t r u m e n t a t i o n was d e s i g n e d t o d e t e c t intermodu-l a t i o n c o u p l i n g i n the ground. T h i s r e q u i r e s the simultaneous t r a n s m i s s i o n o f two s i n u s o i d s o f c u r r e n t , the d e t e c t i o n o f the p o t e n t i a l f i e l d produced by the c u r r e n t , and the d e t e r m i n a t i o n of the amplitude s p e c t r a o f the p o t e n t i a l f i e l d . F i g u r e 9 i s a b l o c k diagram of the i n s t r u m e n t a t i o n developed t o perform t h i s experiment. C u r r e n t was s u p p l i e d t o t h e ground from two Kepco BOP 500 power s u p p l i e s which can be c o n n e c t e d as v o l t a g e - t o -c u r r e n t t r a n s d u c e r s . The i n p u t s i g n a l t o the two power s u p p l i e s was s u p p l i e d by two Wavetec f u n c t i o n g e n e r a t o r s . These were connected t o the i n p u t o f a summing a m p l i f i e r whose output went d i r e c t l y t o one o f the power s u p p l i e s . The o t h e r power su p p l y was d r i v e n by the same s i g n a l i n a n t i p h a s e . The two power s u p p l i e s were connected i n s e r i e s with the common 29 E V Io C V to C INPUT AMP LP OUTPUT AMP PS AMP PS E LP NULLED OUTPUT A TO _ J T A P E (~) Sine wave generator f l ] Invertor Summing a m p l i f i e r DA D i f f e r e n t i a l A m p l i f i e r V to C Voltage to Current Transducer PS Phase S h i f t e r L P Low Pass F i l t e r A to D Analogue to D i g i t a l Convertor Figure 9. Block diagram of the instrumentation system. 30 c o n n e c t i o n a l s o connected t o an e l e c t r o d e i n the ground. The c u r r e n t s were ba l a n c e d so t h a t t h i s ground w i r e c a r r i e d a v e r y s m a l l c u r r e n t and was o r i g i n a l l y i n t e n ded t o be the common ground f o r the whole system. The p o t e n t i a l c i r c u i t was l a t e r s e p a r a t e d due to problems a p p a r e n t l y r e l a t e d t o n o n - n e g l i g a b l e c u r r e n t i n t h i s ground w i r e , a l t h o u g h t h i s c u r r e n t was not d e t e c t e d . The p o t e n t i a l f i e l d was monitored wi t h a p a i r o f p o t e n t i a l e l e c t r o d e s connected t o a d i f f e r e n t i a l a m p l i f i e r with an in p u t impedance o f 100 megohms. The s i g n a l from the p o t e n t i a l e l e c t r o d e s was a m p l i f i e d t o between +_ 2 and + 8 v o l t s . T h i s s i g n a l was d i g i t i z e d and r e c o r d e d on magnetic tape. I t was a l s o i n p u t t o a summing a m p l i f i e r . The output from each o f the f u n c t i o n g e n e r a t o r s was put through a phase s h i f t e r and a v a r i a b l e g a i n a m p l i f i e r and i n p u t t o t h i s same summing a m p l i f i e r . The phase and amplitude o f each o f the s i n u s o i d s were a d j u s t e d i n d i v i d u a l l y t o produce a minimum 31 s i g n a l at the output o f the summing a m p l i f i e r . T h i s o p e r a t i o n o n l y n u l l s the fundamental f r e q u e n c i e s . Any harmonics produced i n the ground and any i n t e r m o d u l a t i o n c o u p l i n g terms are u n a f f e c t e d . The output from the summing a m p l i f i e r was a m p l i f i e d to between + 2 v o l t s and + 8 v o l t s , d i g i t i z e d , and recorded on magnetic tape. The n u l l i n g adjustments were ve r y t e d i o u s at the low f r e q u e n c i e s used. The output from the summing a m p l i f i e r was monitored on a Brush two-channel c h a r t recorded so t h a t the phases and amplitudes o f each o f the s i n u s o i d s c o u l d be a d j u s t e d to a minimum. At l e a s t 97 per cent o f the two primary s i g n a l s were n u l l e d out and the remaining s i g n a l a m p l i f i e d another 25 times. T h i s n u l l i n g procedure took about 30 minutes per t e s t . R e s u l t s of l a b o r a t o r y s t u d i e s o f the n o n l i n e a r e l e c t r i c a l p r o p e r t i e s o f g a l e n a and s e r p e n t i n e , by Katsube o f the G e o l o g i c a l Survey o f Canada, i n d i c a t e that n o n l i n e a r a f f e c t s , i f they are p r e s e n t , i n c r e a s e i n amplitude with 32 d e c r e a s i n g frequency. For t h i s reason i t was d e c i d e d to perform the t e s t s at very low f r e q u e n c i e s . In o r d e r to do t h i s i t was necessary to d i g i t i z e the s i g n a l s and r e c o r d them on magnetic tape. T h i s p e r m i t t e d the amplitude s p e c t r a of the s i g n a l s to be c a l c u l a t e d u s ing a F a s t F o u r i e r Transform computer a l g o r i t h m on the UBC IBM 370/168 computer. In order to achieve good r e s o l u t i o n o f the amplitude s p e c t r a s e v e r a l p e r i o d s of the lowest frequency had to be r e c o r d e d . The lowest frequency was s e l e c t e d to be 0.02 Hz. 24 p e r i o d s c o u l d be recorded i n 20 minutes p r o v i d i n g the r e q u i r e d r e s o l u t i o n . .065 Hz was s e l e c t e d as the frequency of the second s i n u s o i d . The c u r r e n t amplitudes used i n the experiment were determined to a degree by the equipment a v a i l a b l e . The BOP 500 power s u p p l i e s have a maximum output c u r r e n t of 80 m i l l i - A m p s (160 mA peak-to-peak). The c u r r e n t l e v e l s were s e t 33 at 120 mA peak-to-peak t o s t a y w e l l w i t h i n t h i s l i m i t . In order t o a c h i e v e c u r r e n t d e n s i t i e s o f the same o r d e r as those commonly o c c u r r i n g i n IP s u r v e y s the c u r r e n t e l e c t r o d e s were p l a c e d 8 meters a p a r t i n the f i e l d t e s t s . T h i s p r o v i d e s a -2 c u r r e n t d e n s i t y o f a p p r o x i m a t e l y 20 nA cm a t a p o i n t midway between the c u r r e n t e l e c t r o d e s . The e l e c t r o d e c o n f i g u r a t i o n used i n the f i e l d t e s t s are shown i n f i g u r e 10. The c u r r e n t e l e c t r o d e s were b r a s s rods which were hammered i n t o t h e ground. The p o t e n t i a l e l e c t r o d e s . and the ground e l e c t r o d e were porous p o t s , f i l l e d w i t h a s a t u r a t e d s o l u t i o n o f CuSO^ and water, wi t h a copper rod suspended i n the s o l u t i o n t o p r o v i d e the c o n n e c t i o n t o the e l e c t r o n i c system. C o n f i g u r a t i o n A of f i g u r e 9 was s u s p e c t e d of c a u s i n g erroneous r e s u l t s and c o n f i g u r a t i o n B was adopted f o r the f i n a l t e s t s . The tape r e c o r d i n g and d i g i t i z i n g system was the UBC 34 35 Department o f G e o p h y s i c s and Astronomy Marine S e i s m i c Data Recording System. I t c o n s i s t s o f an e i g h t c h a n n e l analogue t o d i g i t a l c o n v e r t o r , a b u f f e r f o r m a t t e r and a Kennedy n i n e t r a c k d i g i t a l tape r e c o r d e r . T h i s system produces tapes which are formatted t o be read by the UBC IBM 370/168 computing system. Three c h a n n e l s o f d a t a were r e c o r d e d . The i n p u t t o the power s u p p l i e s , the a m p l i f i e d output from the p o t e n t i a l e l e c t r o d e s and the a m p l i f i e d s i g n a l from the n u l l i n g c i r c u i t . The l a t t e r two of t h e s e s i g n a l s were passed through low pass f i l t e r s t o remove a l l s i g n a l s w i t h f r e q u e n c i e s above the N y q u i s t f r e q u e n c y o f the d i g i t i z e r . 36 CHAPTER 3 EXPERIMENTS F i e l d experiments were conducted at two s i t e s . The f i r s t was the lawn i n f r o n t o f the Geophysics B u i l d i n g at UBC. The second s i t e was i n a p i t a t a v o l c a n o g e n i c massive s u l p h i d e d e p o s i t near H a r r i s o n Lake B.C.. The d e p o s i t i s known as the Seneca d e p o s i t . In p r e p a r a t i o n f o r the f i e l d experiments the equipment was c a r e f u l l y t e s t e d i n the l a b o r a t o r y . A b l o c k diagram of the system i s shown i n the p r e v i o u s c h a p t e r , f i g u r e 8. Net-works o f l i n e a r r e s i s t o r s , r e s i s t o r s and d i o d e s , and r e s i s t o r s and l i g h t b u l b s were used t o t e s t the system. These networks and t h e i r a n t i c i p a t e d r e s p o n s e s are shown i n f i g u r e s 7 and 8. The f i r s t t e s t s were made with a network o f l i n e a r r e s i s t o r s . F i g u r e 11. N o n l i n e a r components i n the t r a n s m i t t i n g and r e c e i v i n g c i r c u i t s were d e t e c t e d by the 37 V ( w 2 ) to C ^ > 1 2 V Io C A A A V l o C IOO n 6 v 0 6 V to C 100 Kfi A A A 6 IKQ A A A 0 Figure 11 A. Output s i g n a l from a l i n e a r network. B. Output s i g n a l from a n o n l i n e a r network. 38 presence of i n t e r m o d u l a t i o n c o u p l i n g terms i n the output from the l i n e a r network. A f t e r much t r i a l and e r r o r a c i r c u i t was c o n s t r u c t e d which produced no i n t e r m o d u l a t i o n c o u p l i n g o f i t s own. Many o f the n o n l i n e a r problems were i n t e r m i t t e n t , making t h e i r d i a g n o s i s d i f f i c u l t . Due to the p o s s i b i l i t y o f an i n t e r m i t t e n t problem causing i n t e r m o d u l a t i o n c o u p l i n g i n the i n s t r u m e n t a t i o n , more confi d e n c e c o u l d be p l a c e d i n r e s u l t s which i n d i c a t e d a l i n e a r response than i n r e s u l t s which c o n t a i n e d i n t e r m o d u l a t i o n c o u p l i n g terms. Even a f t e r a f a i r degree of c o n f i d e n c e i n the c i r c u i t r y was e s t a b l i s h e d much time was spent on f i e l d r e s u l t s with i n t e r m o d u l a t i o n c o u p l i n g t h a t turned out most p r o b a b l y t o be due to the e l e c t r o d e a r r a y . E x p e r i m e n t a l l y determined amplitude s p e c t r a f o r network of r e s i s t o r s i s shown i n f i g u r e 12. Amplitude s p e c t r a o f the i n p u t , output and n u l l e d output are d i s p l a y e d f o r the 39 Input e (fl -H •H e Output N u l l e d Output UL i r ~ 1 1 0.05 0.1 0.15 0.2 FREQUENCY (HZ) i i 1 1 0.05 0.1 0.15 0.2 FREQUENCY (HZ) 1 1 0.D5 0.1 0.15 0 2 FREQUENCY (HZ) F i g u r e 12. A m p l i t u d e S p e c t r a f o r the l i n e a r network of f i g u r e 11. 40 network. The n u l l e d output has the fundamental f r e q u e n c i e s attenuated and the r e s t o f the spectrum a m p l i f i e d r e l a t i v e to the output. The v e r y low f r e q u e n c i e s used, .02 Hz and .065 Hz, r e q u i r e d a d i g i t a l r e c o r d o f at l e a s t 15 minutes f o r each t e s t . The output s i g n a l and the n u l l e d output s i g n a l were both passed through low pass f i l t e r s with an a t t e n u a t i o n o f 20 dB per decade above a c o r n e r frequency o f .2 Hz. The sampling frequency of the d i g i t i z e r was 2.44 Hz, g i v i n g a N y q u i s t frequency o f 1.22 Hz. A square wave at .02 Hz was i n p u t to the low pass f i l t e r and d i g i t i z i n g system under these c o n d i t i o n s and the e f f e c t s o f a l i a s i n g were not observed i n the amplitude s p e c t r a . 41 T e s t s on the UBC Campus Two experiments were conducted on the lawn i n f r o n t of the Geophysics B u i l d i n g at UBC. In the f i r s t , an e l e c t r o d e c o n f i g u r a t i o n i l l u s t r a t e d i n f i g u r e 10 was used. The r e s u l t s of t h i s t e s t are shown i n f i g u r e 13. Each power supply t r a n s m i t t e d a peak-to-peak c u r r e n t of 128 mA. T h i s was the sum of two s i n u s o i d s of 64 mA pk-pk. Si n c e the c u r r e n t from each e l e c t r o d e was always i n o p p o s i t e p o l a r i t y the peak c u r r e n t d e n s i t y at the p o i n t midway ...between them was a p p r o x i -2 mately 125 nA per cm . Two s i n u s o i d s , each .92 v o l t s peak-peak, were monitored a c r o s s the p o t e n t i a l e l e c t r o d e s . The r e s i s t i v i t y of the ground, from e q u a t i o n 1 i s 550 ^ M . Some t r o u b l e w i t h ground l o o p s i n t h e . i n s t r u m e n t a t i o n was encountered when the e l e c t r o d e a r r a y was f i r s t connected. Most of t h i s was e l i m i n a t e d by changes i n d e s i g n of the p o t e n t i a l c i r c u i t r y and the system ground p o i n t s . A f t e r 42 Input CD Cu E •f-\ e 20 -J D.O ' r 0-05 0.1 0.15 FREOUENCT (HZ) 0.2 46 -J Output o-23_| > 0.0 0.05 0.1 FREQUENCY (HZ) ~ ~ i — 0.15 ~1 0.2 N u l l e d Output CO -p 1 20" -H •rH E icH u 0.0 - r " 1— 0.05 0.1 0.15 FREQUENCY (HZ) 0.2 F i g u r e 13. A m p l i t u d e S p e c t r a f o r t h e t e s t i n f r o n t o f the G e o p h y s i c s b u i l d i n g , UBC. 43 c o n s i d e r a b l e t e s t i n g enough c o n f i d e n c e was e s t a b l i s h e d i n the e l e c t r o d e a r r a y and p o t e n t i a l d e t e c t i o n system t h a t s i g n a l s with amplitudes g r e a t e r than 1.0 mV peak-to-peak at the p o t e n t i a l e l e c t r o d e s were c o n s i d e r e d t o be the r e s u l t of i n t e r m o d u l a t i o n c o u p l i n g i n t h e ground. The amplitude spectrum o f the n u l l e d output o f f i g u r e 13 c o n t a i n s some v e r y s m a l l peaks at the i n t e r m o d u l a t i o n c o u p l i n g f r e q u e n c i e s . These peaks r e p r e s e n t a s i g n a l l e v e l o f about 0.5 mV peak-to-peak at the p o t e n t i a l e l e c t r o d e s , and are c o n s i d e r e d to be below the d e t e c t i o n l e v e l of the i n s t r u m e n t a -t i o n . These and s i m i l a r peaks i n f i g u r e 16 r e p r e s e n t no more than s t i m u l u s f o r f u r t h e r work w i t h more s e n s i t i v e equipment. The second experiment conducted i n f r o n t o f the Geophysics B u i l d i n g was p r o p o s e d by Mr. Vaino Ronka. T h i s i n v o l v e d c o n n e c t i n g a n o n l i n e a r element to the ground as a 44 Figure 14. A diode connected to the ground to induce n o n l i n e a r i t y . 45 t e s t t o see i f the systems were c a p a b l e of d e t e c t i n g i t . The e l e c t r o d e c o n f i g u r a t i o n and the p o s i t i o n o f the n o n l i n e a r network are i l l u s t r a t e d i n f i g u r e 14. The n o n l i n e a r element was a diode connected t o the ground by two e l e c t r o d e s , s e p a r a -ted by one metre. T h i s i n t r o d u c e d s i g n i f i c a n t i n t e r m o d u l a t i o n c o u p l i n g i n the o u t p u t . The diode was connected p a r a l l e l t o the l i n e of e l e c -t r o d e s , o f f s e t from the l i n e by 1 metre. Assuming homogeneous c o n d i t i o n s , the p o t e n t i a l a c r o s s the d i o d e would have been ap p r o x i m a t e l y the same as the p o t e n t i a l a c r o s s the p o t e n t i a l e l e c t r o d e s , 1.9 V, when the d i o d e was r e v e r s e b i a s e d . When the d i o d e was forward b i a s e d ( c o n d u c t i n g ) the p o t e n t i a l a c r o s s i t would not exceed .7 V. The r e s i s t a n c e o f the ground c o n t a c t s i n s e r i e s w i t h the d i o d e was not measured. A r e a s o n a b l e e s t i m a t e , based on measurements on o t h e r s e t s of e l e c t r o d e s , i n the same l o c a t i o n , i s 1000 46 Input Output N u l l e d Output n —, 1 , 0.05 0.1 0.15 0.2 FREQUENCY (HZ) 0.0 4 6 H o > •H 2 3-1 e u i r 0.D5 0.1 0.15 FREQUENCY (HZ) 4 -T 0.0 0.05 0.1 0 15 FREQUENCY (HZ) AA. . ~1 0.2 0.2 F i g u r e 15. A m p l i t u d e S p e c t r a f o r the n o n l i n e a r n e t w o r k c o n n e c t e d to t h e g r o u n d ( f i g u r e ] _ 4 ) 47 D i s r e g a r d i n g the d e c r e a s e i n the p o t e n t i a l caused by the c u r r e n t i n the d i o d e , as a f i r s t a p p r o x i m a t i o n , the c u r r e n t i n the d i o d e would be 1.2 mA. Two c u r r e n t e l e c t r o d e s t r a n s m i t t i n g 1.2 mA of c u r r e n t on a d j a c e n t c o r n e r s of a 1 meter by 1 meter square on the s u r f a c e o f a homogeneous h a l f - s p a c e with a r e s i s t i v i t y o f 550 ~H-M, would produce a p o t e n t i a l d i f f e r e n c e of 60 mV a c r o s s the o t h e r two c o r n e r s . The waveform i s i l l u s t r a t e d i n f i g u r e 7. Due t o ground c u r r e n t s and d r i f t i n g o f the zero i n the p o t e n t i a l c i r c u i t , the f=0 term i n the spectrum of the n u l l e d output f i g u r e 15 i s not a measure o f the i n t e g r a l of the c u r r e n t i n the d i o d e . The o t h e r terms i n the spectrum, the harmonics and the i n t e r m o d u l a t i o n c o u p l i n g terms, are caused by the p r e s e n c e o f the diode network. T h i s same experiment was performed w i t h a network o f back-to-back d i o d e s but d a t a was l o s t due t o a tape r e c o r d e r 48 problem. The problem was not r e c o g n i z e d u n t i l a f t e r the equipment had been d i s m a n t l e d . There was not s u f f i c i e n t time to repeat the t e s t . 49 Seneca Test The e l e c t r o d e a r r a y was s e t up i n a p i t at Seneca, a v o l c a n o g e n i c massive s u l p h i d e d e p o s i t 100 k i l o m e t e r s e a s t of Vancouver. H i g h l y a l t e r e d v o l c a n i c r o c k s are exposed i n the p i t . In the v i c i n i t y of the e l e c t r o d e a r r a y the r o c k s c o n t a i n 10% p y r i t e i n d i s s e m i n a t i o n s and s t r i n g e r s . The r e s t of the rock i s p r e d o m i n a n t l y secondary q u a r t z , s e r e c i t e and c l a y m i n e r a l s . Massive s p h a l e r i t e i s exposed i n t h i s p i t , 15 meters from the zone i n which the e l e c t r o d e a r r a y was s e t up. The d e p o s i t i s i n t e r p r e t e d t o have been p a r t of a submarine vent f o r m e t a l l i f e r o u s h y d r o t h e r m a l s o l u t i o n s , which caused d e p o s i t i o n o f m e t a l l i c m i n e r a l s i n the vent and on the s e a f l o o r o v e r l y i n g the v e n t . Seneca i s s i m i l a r to the Kuruko d e p o s i t s i n Japan. The r e l a t i v e p o s i t i o n s o f the e l e c t r o d e s were the same at Seneca as they were i n the t e s t a t UBC ( f i g u r e 10). The 50 amplitudes of the two s i n e waves of c u r r e n t were 64 mA pk-pk, g i v i n g a t o t a l s i g n a l of 128 mA pk-pk. The s i g n a l a c r o s s the p o t e n t i a l e l e c t r o d e s was two s i n e waves o f .64 V pk-pk. The r e s i s t i v i t y , from e q u a t i o n 1, i s 500 ^TL M. T h i s r e s i s t i v i t y appears t o be very h i g h f o r the amount o f a l t e r a t i o n and m i n e r a l i z a t i o n i n the r o c k . On another o c c a s i o n the r e s i s t i v i t y was determined t o be 400 ~ft,M i n the same l o c a t i o n so the measurement would appear t o be c o r r e c t . ' In o r d e r to a c h i e v e a p r o p e r n u l l the s i g n a l s i n the n u l l i n g c i r c u i t had t o be s h i f t e d i n phase. The s i g n a l s a c r o s s the p o t e n t i a l e l e c t r o d e s were r e t a r d e d i n phase r e l a -t i v e t o the input c u r r e n t . T h i s phenomenon has been w e l l documented i n areas of d i s s e m i n a t e d m i n e r a l i z a t i o n (Van V o o r h i s et a l 1973) and was a n t i c i p a t e d . The phase s h i f t s r e q u i r e d were 35 and 48 m i l l i r a d i o n s f o r the .02 Hz and .065 Hz s i g n a l s r e s p e c t i v e l y . These v a l u e s were c a l c u l a t e d from 51 the t r a n s f e r f u n c t i o n o f the phase s h i f t e r . The phase s h i f t e r was not c a l i b r a t e d . F i g u r e 16 shows t h a t t h e r e were no i n t e r m o d u l a t i o n c o u p l i n g terms with a m p l i t u d e s g r e a t e r than 0.5 mV peak-to-peak p r e s e n t i n the s i g n a l a c r o s s the p o t e n t i a l e l e c t r o d e s . As i n f i g u r e 13 t h e r e are some low amplitude peaks however t h e i r a m p l i t u d e s are too s m a l l t o be d e f i n a t e l y a t t r i b u t e d t o i n t e r m o d u l a t i o n c o u p l i n g i n the ground. I t i s tempting to p o i n t t o d i f f e r e n c e s i n the low amplitude peaks between the t e s t on campus and the t e s t a t Seneca but t h i s assessment should await more s e n s i t i v e i n s t r u m e n t a t i o n . The o n l y r e a l i s t i c c o n c l u s i o n which can be made from t h i s t e s t i s t h a t t h e r e are no i n t e r m o d u l a t i o n c o u p l i n g terms g r e a t e r than .3% of the amplitude or 10 p a r t s per m i l l i o n o f the power of the p r i m a r y s i g n a l s . 52 Input to Cu E <d •rH E 20A 0.0 0.05 0.1 0.15 FREQUENCY (HZ) Output 10 rH l.O-l o > o.o I 1 — 0.05 0.1 0.15 FREQUENCY (HZ) o. N u l l e d Output '2CH io -P rH O > -rH _ K M -rH E 0.0 I : i — 0.05 0.1 FREQUENCY (HZ) 0.15 F i g u r e 16. A m p l i t u d e S p e c t r a f o r the S e n e c a t e s t . 53 An e a r l i e r t e s t at Seneca i n d i c a t e d t h a t t h e r e was s i g n i f i c a n t i n t e r m o d u l a t i o n c o u p l i n g i n the ground. In t h i s t e s t the e l e c t r o d e c o n f i g u r a t i o n was s l i g h t l y d i f f e r e n t than i n the t e s t s j u s t d e s c r i b e d . I t i s shown i n f i g u r e 9a. The p o t e n t i a l f i e l d measurement was made r e l a t i v e t o the e l e c t r o d e which was the system ground. When t h i s was t r i e d on the UBC campus t h e r e was ve r y l i t t l e i n t e r m o d u l a t i o n c o u p l i n g . How-ever the t e s t at Seneca produced the r e s u l t s shown i n f i g u r e 17. T h i s caused c o n s i d e r a b l e i n t e r e s t i n the experiment. A repeat o f the experiment measuring the p o t e n t i a l f i e l d w i t h two p o t e n t i a l e l e c t r o d e s and a d i f f e r e n t i a l a m p l i f i e r as i n f i g u r e 9b, d e s c r i b e d i n the p r e v i o u s s e c t i o n , f a i l e d t o reproduce the n o n l i n e a r i t y . The t r o u b l e was suspected t o have been due t o c u r r e n t through the e l e c t r o d e which was a c t i n g as the common ground. No c u r r e n t was measured i n t h i s c i r c u i t when i t was checked p r i o r t o s t a r t i n g the tape r e c o r d e r . The d e t e c t i o n 54 Input Cu e 3 2 0 4 •h e o.o T 1 -I 1 0.05 0.1 0.15 0.2 FREQUENCY (HZ) Output N u l l e d Output o.o ~ - 1 — 0.05 0.1 0.15 FREQUENCY (HZ) 1 0.2 0.0 0.05 0.1 0.15 0.2 FREQUENCY (HZ) F i g u r e 17 . A m p l i t u d e s p e c t r a f r o m t e s t a t S e n e c a s h o w i n g i n t e r m o d u l a t i o n c o u p l i n g . 55 l i m i t of the m u l t i m e t e r used to measure t h i s c u r r e n t was 10 jJA so there c o u l d have been as much as 10JUh o f c u r r e n t i n the loop. I t i s p o s s i b l e t h a t the o u t p u t l e v e l o f one o f the c u r r e n t s u p p l i e s d r i f t e d d u r i n g the experiment. A f t e r o b t a i n i n g the r e s u l t s which i n d i c a t e d s t r o n g i n t e r m o d u l a t i o n c o u p l i n g , the experiment was examined f o r p o s s i b l e sources o f e r r o r . The common ground p o i n t appeared a prominent p o s s i b i l i t y f o r i n t r o d u c e d n o n l i n e a r i t i e s so the experiment was r e p e a t e d with t h i s p o s s i b l e source o f e r r o r removed. No s i g n i f i c a n t i n t e r m o d u l a t i o n c o u p l i n g was d e t e c t e d i n the second measurement. 56 CHAPTER 4 SUMMARY AND CONCLUSIONS An experiment to determine i f the ground's response t o e l e c t r i c a l s i g n a l s i s t h a t o f a l i n e a r network was performed at two l o c a t i o n s . One o f these l o c a t i o n s was on the lawn i n f r o n t o f the Geophysics B u i l d i n g at the U n i v e r s i t y o f B r i t i s h Columbia and the o t h e r was i n the b r e c c i a zone o f a vo l c a n o g e n i c massive s u l p h i d e d e p o s i t 100 k i l o m e t e r s east o f Vancouver. At both l o c a t i o n s the r e s u l t s i n d i c a t e d t h a t the response of the ground was l i n e a r w i t h i n the measuring c a p a b i l i t y o f the i n s t r u m e n t a t i o n , which c o u l d r e s o l v e a s i g n a l o f 1 mV peak-to-peak. The method used to determine the e l e c t r i c a l l i n e a r i t y of the ground was a t e s t which determined i f the p r i n c i p l e o f s u p e r p o s i t i o n a p p l i e d to e l e c t r i c a l s i g n a l s i n the ground. Two s i n u s o i d s o f c u r r e n t , with f r e q u e n c i e s o f .02 Hz and .065 Hz r e s p e c t i v e l y , were t r a n s m i t t e d i n t o the ground s i m u l t a n -57 e o u s l y and t h e r e s u l t i n g p o t e n t i a l f i e l d m o n i t o r e d , d i g i t i z e d , and r e c o r d e d on t a p e . The c u r r e n t a m p l i t u d e s were 64 mA peak-to-peak. The S c h l u m b e r g e r e l e c t r o d e a r r a y w i t h L=4M and 1=0.5M was used. A F o u r i e r t r a n s f o r m o f t h e t i m e s e r i e s on the tape was p e r f o r m e d u s i n g a f a s t F o u r i e r t r a n s f o r m r o u t i n e w i t h the UBC IBM 370/168 computer. The a m p l i t u d e s p e c t r a produced by t h i s r o u t i n e were s e a r c h e d f o r terms a t t h e i n t e r m o d u l a t i o n c o u p l i n g f r e q u e n c i e s . The absence o f i n t e r m o d u l a t i o n c o u p l i n g t erms was t a k e n as p r o o f t h a t t h e ground behaved as a l i n e a r n e t w o r k . The sy s t e m was c a p a b l e o f d e t e c t i n g i n t e r m o d u l a t i o n c o u p l i n g terms t h a t were g r e a t e r than 1 mV p e a k - t o - p e a k o r 0.3% o f t h e a m p l i t u d e o f t h e p r i m a r y s i g n a l . The e x p e r i m e n t s i n t h i s s t u d y were c a r r i e d o u t a t o n l y two s p e c i f i c l o c a t i o n s . There i s no e v i d e n c e t o assume t h a t s i m i l a r r e s u l t s would be o b t a i n e d a t o t h e r l o c a t i o n s o r w i t h d i f f e r e n t c u r r e n t d e n s i t i e s and f r e q u e n c i e s . 58 I f work c o n t i n u e s i n t h i s a r e a , I recommend t h a t a h i g h p r i o r i t y be p l a c e d on d e v e l o p i n g a compact, automated i n s t r u -ment which w i l l p r o v i d e o n - t h e - s p o t r e s u l t s . I f p o s s i b l e the s e n s i t i v i t y of the d e t e c t i o n c i r c u i t s h o u l d be capable of f a i t h f u l l y r e s o l v i n g s i g n a l s of 0.1 mV peak-to-peak t h a t are .03% of the amplitude of the p r i m a r y s i g n a l s . Future f i e l d measurements s h o u l d be d i r e c t e d toward d i f f e r e n t g e o l o g i c environments i n hopes t h a t a rock type or s t r u c t u r e with a i n t e r m o d u l a t i o n c o u p l i n g amplitude spectrum may be i d e n t i f i e d . I recommend the u l t r a - b a s i c r o c k s i n the Hope area as a t a r g e t f o r f u r t h e r work. Katsube d e t e c t e d n o n l i n e a r e f f e c t s i n s e r p e n t i n e a t low c u r r e n t d e n s i t i e s i n the l a b and these rock u n i t s are h i g h l y s e r p e n t i n i z e d . 59 B i b l i o g r a p h y Anderson, L.A. and K e l l e r , G.V., 1964, A study i n induced p o l a r i z a t i o n ; Geophysics, V 29, p 858-915 Backus, G. and G i l b e r t , F., 1968, The r e s o l v i n g power of gro s s e a r t h data; G e o p h y s i c a l J o u r n a l of the Royal A s t r o n o m i c a l S o c i e t y , V 16, p 169-205 DeWitt, G.W., S i l l , W.R., P a r a m e t r i c s t u d i e s of IP s p e c t r a ; presented at the annual meeting of the SEG, 1976 H a l l o f , P.G., 1974, The phase IP measurement and i n d u c t i v e c o u p l i n g ; Geophysics, V 39, p 650-665 Katsube, T.J. , Ahern, R.H. and C o l l e t t , L.S., 1973, E l e c t r i c a l n o n l i n e a r phenomena i n r o c k s ; Geophysics V 38, p 106-124 60 ion B i b l i o g r a p h y - cont'd K l e i n , J.D. and P e l t o n , W.H., 1976, A l a b o r a t o r y i n v e s t i g a t i of the complex impedance of m i n e r a l - e l e c t r o l y t e i n t e r f a c e s ; presented at the 46th annual i n t e r n a t i o n a l meeting of the SEG, Houston Texas, 1976 M a c M i l l i a n , R.H., N o n - l i n e a r c o n t r o l systems A n a l y s i s ; Pergamon P r e s s , New York Oldenburg, D.W., 1978, I n t e r p r e t a t i o n o f D i r e c t C u r r e n t R e s i s t i v i t y Measurements; G e o p h y s i c s , V 43, p 610-625 O r e l l a n a E., and Mooney, H.M., 1966. Master Tables and Curves  f o r v e r t i c a l E l e c t r i c a l Soundings Over Layered S t r u c t u r e s . Madrid, I n t e r s c i e n c i a 150 p 66 t a b l e s . 61 B i b l i o g r a p h y - cont'd P e l t o n , W.H., Ward, S.H., H a l l o f , P.G., S i l l , W.R. and Nelson, P.H., 1976, I n - s i t u Complex R e s i s t i v i t y s t u d i e s o f North American M i n e r a l D e p o s i t s : p r e s e n t e d a t the annual meeting o f the SEG 19 76. , 1978, M i n e r a l D i s c r i m i n a t i o n and Removal o f I n d u c t i o n c o u p l i n g w i t h M u l t i F r e q u e n c y IP; Geophysics, V 43, p 588-609 P e l t o n , W.H. , R i t j o , L. S w i f t , C M . J r . , 1976., I n v e r s i o n o f two dime n s i o n a l i n d u c e d p o l a r i z a t i o n and r e s i s t i v i t y d a t a ; p r e s e n t e d at the annual meeting o f the SEG 19 76. P e l t o n , W.H., Smith, B.D. and S i l l , W.R., 1974, I n v e r s i o n o f complex r e s i s t i v i t y and d i e l e c t r i c d a t a ; p r e s e n t e d a t the annual meeting o f the SEG 19 74. B i b l i o g r a p h y - cont'd Ryss, Y.S., 1971, Contact Method of P o l a r i z a t i o n Curves; i n  Borehole Mining Geophysics; G.K. Volosyuk and N.I. Safranov, e d i t o r s , L e n ingrad, Nedra. , 1973, The Search and E x p l o r a t i o n f o r Ore Bodies by the Contact Method of P o l a r i z a t i o n Curves; Leningrad, Nedra. S c o t t , W.J., and West, G.F., 1969, Induced p o l a r i z a t i o n of s y n t h e t i c high r e s i t i v i t y r o c k s c o n t a i n i n g d i s s e m i n a t e d s u l f i d e s ; Geophysics, V 34 p 87-100 Van V o o r h i s , G.D., Nelson, P.H., and Drake, T.L., 1973, Complex r e s i s t i v i t y s p e c t r a of porphyry copper m i n e r a l i z a t i o n ; Geophysics V 38, p 49-60. 63 B i b l i o g r a p h y - cont'd Wait, J.R., 1959, Ove r v o l t a g e Research and i t s G e o p h y s i c a l A p p l i a t i o n s ; New York, Pergman P r e s s . Weiss, 0., and Masse, L., E l e c t r i c a l method and apparatus f o r G e o l o g i c a l E x p l o r a t i o n ; 1954 U.S. p a t e n t number 2,690,537. White, R.M.S., 1974, A study o f n o n l i n e a r e l e c t r i c a l e f f e c t s i n m i n e r a l i z e d r o c k s ; M.S. t h e s i s , Macquarie U n i v e r s i t y , A u s t r a l i a . Wynn, J.C. and Zonge, K.L., EM c o u p l i n g , i t s i n t r i n s i c v a l u e , i t s removal and the c u l t u r a l c o u p l i n g problem; Geophysics, V 49, p 831-851. Zohdy, A.R., 1965, The a u x i l i a r y p o i n t method of e l e c t r i c a l sounding i n t e r p r e t a t i o n and i t s r e l a t i o n s h i p t o the Dar Zarrouk parameters; Geophysics, V 30 p 644-660 64 B i b l i o g r a p h y - cont'd Zonge, K.L., and Wynn, J.C. 1975, Recent advances and a p p l i c a t i o n s i n complex r e s i s t i v i t y measurements; Geophy V 40, p 851-864 65 Appendix Diagram of the C o n t r o l C i r c u i t r y 66 Output from the Buffer V( iv w2> Q t o V toC* 2 V( w,+ u»j) Q to V to C * l 5 x Nulled Output Nulled Output 0 ond A Io D Converter 25 x Nulled Output PHASE SHIFTER 9 - (180°+ 2tan -wRC) NULLING CIRCUIT IOK w 2 

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