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The theory of geophysical surveying by the high frequency electromagnetic method Brown, Christopher Ernest Gordon 1935

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I ACC: wot • ~UJ$-~  THE- THEORY  OF  GEOPtfYS J C A b ^ R V ^ BY  HIGH  FREQUENCY  T H E  E L E CTR0MAGNET1C  METHOD  BY  CHRISTOPHER ERNE5T  A  THESIS  S U B M I T T E D  M A S T E R  FOR  GORDON BROWAT  T H E D E G R E E  OF A P P L I E D I N  OF  S C I E N C E  T H E D E P A R T M E N T  E L E C T R I C A L  O F  ENGINEERING  7  T H E UNIVERSITY  OF BRITISH APRIL  -,  1935  COLUMBIA  CONTENTS. Pa^rt I . General P r i n c i p l e s of Electromasne t i c Surveying, General P r i n c i p l e s . E l l i p t i c a l Polarization.  3.  Single C o i l Method.  5.  T r i p l e C o i l Apparatus.  8.  Description of Apparatus.  JLJL ©  P i e l d Procedure.  17,  Choice of frequency.  2 0 .  E l e c t r i c a l Properties of Rocks and Minerals Interpretation of Results.  2 1 . 24.  Costs of Geophysical Exploration.  Mathematical Consideration of Electromagnetic F i e l d s in -the Region • of - -an Or ebod.y-.  -  General•Case'of Two F i e l d s d i f f e r i n g i n Direction and Time Phase,  -  30.  C r i t e r i a for complete Determination of the E l l i p s e .  32.  Calculation of the f i e l d f o r a simple case.  33.  The Nature of the F i e l d of the O s c i l l a t o r .  39.  Plane Electromagnetic Waves.  45.  The Magnetic Field. Strength  50.  Penetration of Electromagnetic Waves.  53  The Change i n Phase due to the Overburden.  64.  D i s t r i b u t i o n of C u r r e n t i n the Orebody. Sumraary o f Phase R e l a t i o n s h i p s ,  APPEH)IX. Apparatus,  L a b o r a t o r y Test o f the Three  THE THEORY 03? GEOPHYSICAL SURVEYING BY THE HIGH FREQUENCY ELECTROMAGNETIC METHOD. •• Part 1. General P r i n c i p l e s of Electromagnetic  Prospecting,  In the high frequency electromagnetic method of prospecting, an alternating magnetic f i e l d i s applied to an area by means of an o s c i l l a t o r and v e r t i c a l c o i l antenna.  The f i e l d from the antenna induces a cur-  rent i n any orebody, which may exist underneath the area being prospected, by reason of the greater cond u c t i v i t y of the ore as compared v/ith the country rock,  • This induced current, i n turn, produces a  secondary f i e l d at the surface which may be i n v e s t i gated by means of suitable  instruments..  • • Suppose, f o r instance, we consider the c o i l antenna shown i n f i g . 1, which carries a current,  Pig 1. i,«I, sin wt, where I, i s the instantaneous  current.  Then i f the mutual inductance between the antenna and the  circuit  i n the ..vein i s M  #  e * Instantaneous secondary e.m.  .—_..  t  r^i  m  A  and l - instantaneous secondary current x  where R * resistance of path i n t h e orebody 2  X = reactance of the orebody and tan  <fi -•  —  The secondary f i e l d w i l l he i n phase with the c u r r e n t i n - t h e orebody and, therefore, at the point P, we have two separate f i e l d s ; o s c i l l a t o r ,  the primary f i e l d from the  and the secondary field&s/«,/ t. w  T h i s - i s shown v e c t o r i & l l y i n f i g 2 f o r a j>olnt V,  t  situated to the - l e f t -of .J? (.gee-fig l b ) . instantaneous d i r e c t i o n o f t o  Assuming th©  be h o r i z o n t a l , the  secondary f i e l d , 4>, i s at an - angle, defending upon the a  position of JP.wifc*. respect t o P„  'If P i s t o the left'y  tip,  . ?igi2.•,,'^W'., of p (a«3 i n the diagrara)  9  :..V:  the f i e l d «£,will point d i a -  gonally upwards to the r i g h t , ??hile i f P, i s to the  right of P,  w i l l point downward to the l e f t .  \ •  Pig 3.  Pig  com! " •••  - -  shows the vectors i n varying positions i n a traverse of the conductor.  -  I f the plane, of t h e - c o i l antenna i s kept d i r ected towards the -points PjP^Pi e t c ^ the h o r i z o n t a l f i e l d ft, w i l l remain approximately  constant f o r one  traverse l i n e , providing PP^PjR.RP, remain small compared with the distanse away from the  transmitting loop  Thus a comparison -of the two components of the f i e l d i s p o s s i b l e . — T h i s -is- effected by-means of one or more--search ©oils-and--detecting-instruments. E l l i p t i c a l -Polarization ,of Resultant. - F i e l d . ••• Since there are two vectors^, a n d ,  -  which  d i f f e r both i n space and i n time phase, we cannot compound them by the parallelogram law.  They can  however, be compounded instantaneously, i . e . for Instantaneous values at a p a r t i c u l a r time of the cycle, when i t i s found that the resultant vector i s variable i n length and revolves with the angular v e l o c i t y u> of the primary and secondary fields,and that the path of i t s extremity traces.out an  ellipse.  As an example of this,, refer to f i g 4. have two vectors $ = / s/V,0  and 4>*  -  d i f f e r i n space by an angle ^ + 3°" .  Here we They  -3°°).  i  Values of and 4>*  if.  0  3o"  + OS  4\ o  Fig  3d" /2<f ISO  60°  -h + +• OJ4>O.S 0.26 ".+ •" 0.86  a 3oo" 330 zyo O.S I.O  Zio"  o  OS  0.86  o O.S~0.86 I.O0.86  4.  are given f o r various values of & . instantaneous values of  P l o t t i n g these  , and compounding corres-  ponding values by the parallelogram law, we f i n d the instantaneous values of the resultant flux vector, which traces out an-ellipse. Furthermore, i t w i l l be shov;n i n Part 11 that a l l out of phase f i e l d s of the same frequency can be compounded into one resultant f i e l d ;  so that there  i s a single plane e l l i p s e , and one only, at any point i n the f i e l d , due to any system of conductors,  A  f i e l d of t h i s nature i s said to be e l l i p t i c a l l y polarized. The Determination of the E l l i p s e . For the purposes of geophysical prospecting, i t i s unnecessary  completely to determine the e l l i p s e ;  we  need only obtain the d i r e c t i o n of i t s minor axis and an approximate idea of the e e c e n t r i c i t y .  The l a t t e r  can most e a s i l y be found by determining the r a t i o of lengths of the axes. use at present  The most successful method i n  simply finds the d i r e c t i o n of the  minor axis. The Single C o i l Method of Prospecting,, I t i s evident that, i n the event of there being no orebody i n the v i c i n i t y , the primary f i e l d i s the only f i e l d at the point under consideration;  in  this case a single search c o i l , rotated about an axis horizontal and i n the same plane as the antenna, w i l l be i n & horizontal plane when i t i s not threaded by any f l u x .  When an ore deposit i s present, the c o i l  w i l l also be horizontal d i r e c t l y above &he deposit,as at point A i n f i g 5., where  and <£_add d i r e c t l y to  Dit-echi'on of  '  '.•V  ••• /•. '  .  ^  \ v  i  .  i V  1  VI  '  \  'oil  • / . \ Conductor • . •••..../ ; ."// ' :  Pig .5.' form one u n i d i r e c t i o n a l resultant.  At points B and  B,, the p o s i t i o n of minimum pick up w i l l be at an angle as indicated.  I f the f i e l d i s e l l i p t i c a l l y  polarized, as i s usually the case, the minimum inten-  eity# i n the detecting unit w i l l toe d i f f i c u l t to determine.  This disadvantage i s inherent i n the single  c o i l method.  Sometimes i t i s possible to bring the  secondary f i e l d Into phase by a l t e r i n g the  frequency;  t h i s i s objectionable since i t gives non-uniform cond i t i o n s for: interpreting ••-a- set o f r e a d i n g ^ i f they are a l l taken at d i f f e r e n t frequencies. Thus i t w i l l be seen that the normal to the plane of-the c o i l points towards the buried conductor-.  F i g 6 shows the - o r i e n t a t i o n '-of the f i e l d ' e l l -  ipses i n the traverse across a buried conductor below  i i lined*cHct-  I ,  i >  Fig 7 . the uolnt P.  The dottedclinee represent the normals fci-j""""*  to the plane of the search c o i l , and the angles made hy these with the v e r t i c a l i s termed the dip of the coil  In f i g 7 . , the dips are shown plotted f o r a .  traverse from A to B.  -Note that the dip increases  at f i r s t and then rapidly decreases to aero over uhe orebody:  a f t e r crossing the orebody* the dip rap-  i d l y increases i n the opposite d i r e c t i o n , r i s e s to a maximum and f i n a l l y decreases as the secondary grows weaker with distance.  field  Outside the points A  and B , the f i e l d from the orebody i s too weak to have much e f f e c t compared with the primary f i e l d , -and the dip becomes zero again. The single c o i l apparatus.has been used very successfully and i s the basis of the methods used by the Radlore Oo and other geophysical concerns . operating.  now  . I t s chief advantage i e ease and r a p i d i t y  of manipulation.  The outstanding disadvantage would  seem to be that the e l l i p t i c a l character of the f i e l d i s completely ignored, and therefore, that an excell e n t source of information about she orebody i s neglected.  Again•in rough or h i l l y country ,.especially  with veins a.t- low angles, the method operates at a disadvantage since the plane of the e l l i p s e may depart greatly from the v e r t i c a l .  In t h i s case a aero  indication may be impossible to obtain..  For example,  consider a vein dipping at 4.5° as shown i n the block diagram f i g Sa.  The h i l l s i d e slopes at 45*and the  o s c i l l a t o r i s situated downhill i n the d i r e c t i o n AB. In f i g 8b,the oz- axis i s horizontal and p a r a l l e l with thelower edge M a b H  n  of the block diagram.  ab,a'b' and  are projections of the vector <$*_in the xy,xs and  d i f f i c u l t to draw the e l l i p s e c l e a r l y without complicating the diagram, hut i t can be-seen that'the e l l i p s e is•flat-lying  with the major axis,, depending on the  phase difference, i n the approximate d i r e c t i o n R, pointing diagonally•••downward to the right*  In t h i s case,  i t would be impossible to place a single search c o i l with i t s plane at right-angles to the plane o£5 the e l l i p s e , p a r a l l e l to  -, and-also with i t ' s fixed axis-  sighted-towards, and l y i n g i n , the-plane-of the antenna, a l l at the same time.  This means that a zero  indication would not be obtained i n any position of the c o i l * ' The T r i p l e C o l l  Apparatus.  I t i s evident from the above discussion that a single search c o i l can give the general d i r e c t i o n of the axes of the e l l i p s e , but that, i n order to have more d e f i n i t e information about the f i e l d , some other form of search c o i l i s necessary.  The t r i p l e  coil  apparatus i s an attempt to deal with, this matter;  it  has been experimented with i n the laboratory but i s s t i l l i n the experimental stage. -In t h i s m e t h o d t h r e e c o i l s , mutually at right angles,are used.  Since the e l l i p s e l i e s am one plane  only, a c o i l placed i n t h i s plane w i l l be threaded by no f l u x , and w i l l therefore give zero indication i n the detector.  This i s the sole purpose of one of  the c o i l s which i s used to placfe the other two at y  right angles-to the- plane of the e l l i p s e .  This i s  the f i r s t adjustment and may be understood by referring to f i g 9.  Here the e l l i p s e i s assumed to be i n  -3?ig 9-.~  the plane of the paper.  The "locating c o i l " i s  shown i n the plane of the e l l i p s e , i n which position i t i s threaded by no flux. The other two c o i l s , a and b, are shown i n section and are called the d i r e c t i o n finding c o i l s * They are mutually at right angles to the locating and have an equal number of turns.  coil  One of them, the  c o i l b, i s variable so that any percentage of the number of turns in c o i l a can be cut i n .  • •  • "10.. '  Suppose ,now, that the whole c o i l assembly be rotated, about the axis II, which i s perpendicular to the plane of the e l l i p s e , to the position bb' , a a ; 1  in this position, the, variable c o i l w i l l be perpendicular to the major axis, the fixed c o i l j v i l l be perpendicular to the minor axis and the locating c o i l w i l s t i l l be i n the plane of the e l l i p s e . Again, i n t h i s position, the voltages induced i n each d i r e c t i o n finding c o i l w i l l be proportional to the c o i l area, the number of turnsin the c o i l and the major or minor-axis of the e l l i p s e .  Thus, by-adjus-  ting the number of turns i n the variable c o i l , the voltages may be made equal and may be made to b a l ance each other out when connected i n a suitable way ;  to a detector.  In t h i s way ,the r a t i o of major to  minor axis can be found, using the number of turns and -  the area of the c o i l s i n the c a l c u l a t i o n . The scheme of connections -is shown diagrammat-  i c a l l y and i n simplified form i n f i g 10. FIXED COIL  VARMBt-f  Since the  Colt  TO <lf|--«i««f- -  Pig 10. phaoe. of the voltage i n the fixed c o i l d i f f e r s from that i n the variable c o i l b y H , a condenser i s  connected across the former and tuned to resonance. The voltage across the condenser C i s balanced against the voltage induced i n the turns i n c i r c u i t i n the var iable c o i l .  A detector i s connected  to the points  AB, where at balance, the voltage should be zero. The locating c o i l hascbeen omitted fron the diagram for simplicity;  i t i s cut i n across the points AB when  required by means of a two-way switch,, It i s evident fron the bare outline given here that-dip and s t r i k e of the plane of the e l l i p s e i s obtainable from readings taken with the locating c o i l ; also, that the dips and directions of major and minor axes i n the plane of the ellij>se, and the r a t i o of the axesj can be obtained from the setting of the d i r ection finding c o i l s . For - a complete determination of the e l l i p s e , the actual-, not relative,values of the axes are required.-  Fortunately,- this would not seem-to be nec-  essary:--  i t can .however, be obtained i n d i r e c t l y fsismi  the f i e l d strength of the primary f i e l d i f an assumption i s made as to the shape of the orebody.  The  subject of f i e l d strength i s taken up i n Part 11. Apparatus. A bare outlineof the p r i n c i p l e of the electromagnetic methods of prospecting has been given above. A detailed discussion w i l l follow i n part 11.• Meanwhile , l e t us consider the apparatus A. The Transmitter.  necessary.  The transmitting three units:  apparatus may be divided into  t h e o s c i l l a t o r , the c o i l antenna and the  power supply. (1) The O s c i l l a t o r . the need for p o r t a b i l i t y .  This varies according to In l e v e l country, where  transportation i s not a d i f f i c u l t y , a powerful i s possible.  outfit  Usually a single tube having 15 to 25  watts anode d i s s i p a t i o n i s employed, coupled d i r e c t l y to the antenna.  A 11X210 or, better, aW.E.212D, work-  ing on reduced anode voltage, i s s u f f i c i e n t . companies use two or more 46 s 1  Some  as a class B amplifier  of output from a small o s c i l l a t o r .  A pure wave form  i s a great advantage i n obtaining a balance at the receiving set, so that anything l i k e maximum output from the transmitter i s not possible.  Two  tubes,  working as a push-pull buffer amplifier, would eliminate even harmonics and would--appear- to be the best, In - addition- to-purity- of wave - form, it- is-necessary for the three - coil-method- , to-have-constant uency. case:  freq- •  The o s c i l l a t o r i s mounted i n a stout wooden i t can be constructed so thatvthe weight i s  about SO pounds. ( 2 ) The C o i l Antenna. of antennas have been t r i e d . i c a l Experimental  A number of patterns The Imperial Geophys-  Survey i n A u s t r a l i a used a loop con-  s i s t i n g of ten turns ow wire, 8 feet square, mounted on a pole about 15 feet long: collapsible.  the whole antenna  The Radiore Co uses a small c i r c u l a r  was  coi3., "doughnut" shape, having many turns, mounted on atripod withturntable.  Other companies use large t r i -  angular or i r r e g u l a r loops, supported on poles.  A  requirement f o r a large primary f i e l d i s that the c o i l which i s used as the tank inductance of the o s c i l l a t o r should have as large a n inductance and as low an e f f ective resistance as possible.  A compromise i s nec-  essary since i t i s an advantage to have a compact c o i l which i s rotatable on the mounting. (3) The Power Supply.  This i s the great d i f -  f i c u l t y v/hen transportation i s a problem.  A voltage  of 500-1000is used for the o s c i l l a t o r plate Rujjply. Hand-cranked generators have been successfully eiaployedfor the single c o i l method, but the requirement of constant f i e l d strength and frequency would seem to demand a steadier source of current f o r the three method.  coil  A l i g h t air-cooled gasoline motor, d r i v i n g  a - small 110 v o l t a . c generator-with•tube r e c t i f i e r , could be built- to weigh less than 100 l b s .  This i s  not unduly heavy, considering that one set up of the transmitter w i l l cover a radius of about 2500 f e e t or four f u l l s i z e d claims.  ;  The I.G.E.S. used a stor-  age battery and dynomotor, which would be s a t i s f a c t o r y .  "  .  «  '  •  j  Were  ftVVU  la.k/-C.  i f facilities,'were available for charging accumulators^ The whole transmitting o u t f i t would weigh i n the neighbourhood of 200 lbs and would require two pack horses to transport.  •14. B.  The Receiving Apparatus. ( l ) The Single C o i l Method.  The single c o i l  i s mounted on a tripod, having horizontal and v e r t i c a l graduated c i r c l e s , s i m i l a r to a t r a n s i t .  The  coil  i t s e l f has 50-100 turns of f i n e wire on a f i b r e hoop, up to 2 feet i n diameter.  Sights are set along  the  diametral axis about which the c o i l i s pivoted so that i t may enna.  be allgnedproperly with the transmitting antThe v e r t i c a l plate records degrees and minutes  of angle around t h i s axis: dip of c o i l .  t h i s i s used to indicate  The horizontal plate records azimuth  angles of the c o i l and i s operated i n the same way a transit.  as  These graduated c i r c l e s do not need the.  same degree of accuracy as those of the t r a n s i t : reading to ten minutes i s more accurate ting of the c o i l ,  -  a r  than the set-  -  - The detector-amplifier unit operates into a pair-of- headphones.  Unmodulated- transmission  was  employed by the I.G.E.S., with autodyne reception: i n t h i s case the received signal i n the phones i s proportional to the f i r s t power of the signal voltage. However, i t i s very doubtful whether i t i s advisable to introduce any o s c i l l a t i o n s into the receiving c i r cuits  Some American prospecting  the transmitter:  companies modulate  i n t h i s case, the received signal  i s proportional to the square of the signal voltage,so that an extra stage of amplification i s needed.  The  15, detector unit i s carried on the back of the operator or attached to the tripod. and l i g h t ,  The whole set i s compact  F i g 11 shows a t y p i c a l c i r c u i t , as used  F i g 11. by•the I.G.E.S.  -  The tapping i s taken 1/3  of the way  along the search c o i l -to produce o s c i l l a t i o n .  Tuned  transformer coupling in the f i r s t stage of amplification reduces harmonics^ and i s followed by a stage of resistance amplification. about  The t o t a l step-up r a t i o i s  200.  —  (2) The Three C o i l Met&od.  The three search  c o i l s a r e - f i x e d - r i g i d l y at right- angles to each other. The- axis of rotation, IM* , of the c o i l s i s perpendicular to the locating c o i l (see f i g 12): the sighting axis.  this i s also  Sighting i s done through the  hollow spindle MM% to which i s fixed the graduated  cir-  cle f o r finding the dip of the axes i n the plane of the e l l i p s e . spindle:  A U-shaped arm carries the ends of this  to the bottom of the U i s attached a hinge  with graduated  circle.  The hinge allows the U to  place the locating c o l l i n any plane normal to the D itself.  F i n a l l y , the wholecoil assembly i s rotatable  about a h o r i z o n t a l plate with graduated c i r c l e .  Thus  There are three c i r c l e s to be read i n any region near an orebody.  The whole system seems very  but study of the diagrams w i l l help.  comp!icated  /  Actually,when  the e l l i p t i c a l structure of the f i e l d i s thoroughly grasped, the adjustments should take very l i t t l e  time,  as the approximate orientation of the e l l i p s e i s known. Another point i n favour of the three c o i l method i s that the fixed d i r e c t i o n finding c o i l can be used as a single search c o i l for regions where there are no indications of an ore body.  It'would normally be  so used, and the other c o i l s would only come into play where the e l l i p t i c a l character of the f i e l d was marked. Thus the three c o i l method includes the single c o i l method. The selector switch panel can be made very compact and w i l l -pr-obably be mounted inside the c o i l assembly. • The panel contains two selector switches to a l t e r the number of tusns i n the variable c o i l , a reversing switch for the fixed c o i l and a switch to /  connect either the locating c o i l or the fixed direct i o n finding c o i l to the detector. The detector, which w i l l be mounted on one of the legs of the t r i p o d , w i l l be either a detectoramplifier head-phone set or a vacuum tube voltmeter. The l a t t e r would be preferable , i f s u f f i c i e n t sen-  1 s i t i v i t y can be Field  7  . '  combined with a rugged construction.  Procedure. The standard method of electromagnetic pros-  pecting, using a single search c o i l has been d e s c r i bed, together with a second method using three c o i l s . Since ray object has been to attempt  to develop the  l a t t e r form of apparatus, with a slew to the more complete determination of the f i e l d e l l i p s e , the f i e l d procedure w i l l be described from the standpoint of the three c o i l apparatus.  The procedure f o r a single  c o i l i s included, as the more complex apparatus i s used In this way  f o r preliminary investigation.  It i s assumed that i n indication of a possible orebody has been obtained by geological or mining work, and that the region i s to be examined geophysically to determine the location and course of the ore.  A  base l i n e Is f i r s t established along the strike of the probable vein system and-traverse l i n e s are run at suitable i n t e r v a l of say 100 feet.-  The c o i l .-ant-,  enna, i s then set up on the base l i n e inaa convenient •position to examine the area.. To examine the f i e l d with the fixed d i r e c t i o n finding c o i l , usedas a single c o i l , the receiving set  i s set up, l e v e l l e d and a sight taken through the /  hollow spindle back at the o s c i l l a t o r .  The  oscillate  i s then set i n operation and the c o i l antenna i s r o t ated by an assistant so that the axis of the c o i l  18.  assembly-coincides with the -vertical plane containing the c o i l antenna.  The switch on the selector panel  i s set so that the fixed d i r e c t i o n finding c o i l i s connected  to the detector.  Upon revolving  the c o i l  assembly round the sighting axis, a position of minimum i n d i c a t i o n i s given i n the headphones..  I f no  orebody i s present, the fixed d i r e c t i o n finding c o i l should be horizontal when t h i s adjustment has been made. If there i s an ore deposit present„ the direction finding c o i l w i l l not be horizontal, and, i n a l l p r o b a b i l i t y , the minimum i n d i c a t i o n i n the detector w i l l be very broad.  In t h i s case, the dip reading  of the fixed d i r e c t i o n finding c o i l i s entered i n the note book and the apparatus i s used to measure the elliptical  field.  To-measure the e l l i p t i c a l f i e l d , the switch i s f i r s t set to cut-in the locating c o i l .  The whole  assembly i s -then rocked about^the intermediate-axis toward or away from the dLaucection  of the o s c i l l a t o r  (in the plane of the c o i l antenna), u n t i l the zero position i s found.  I t i s possible that the lower  plate w i l l have to be undamped and the c o i l s  rotated  s l i g h t l y about the v e r t i c a l axis, i n conjunction with the rocking motion, to bring the locating c o i l accurately into the plane of the e l l i p s e .  When the plane  of zero indication has been found, the two lower c i r c l  are clamped.  The direction finding c o i l s are now  at right angles to the plane of the e l l i p s e . The next operation i s to determine the dips and r e l a t i v e lengths of the axes of the e l l i p s e .  T  The E w i t c h i s again set so that the fixed d i r e c t i o n finding c o i l only i s i n c i r c u i t , and the c o i l s are rotated around the sighting axis u n t i l a position of minimum i n t e n s i t y i s found.  The minor axis of the  e l l i p s e w i l l then he normal to the fixed c o i l .  The  second switch i s then set so that the fixed and variable c o i l s are balanced against each other, and f i n a l l y , the selector switches and reversing switch are manipulated u n t i l a balance i s obtained. The r e s u l t of t h i s operation i s that three angles and one r a t i o are obtained.  The reading of  the lower plate gives the azimuth angle of the s t r i k e of the plane of the e l l i p s e ;  the reading of the  intermediate- graduated c i r c l e gives i t s dip;  while  the upper c i r c l e gives the dips of - the major and minor axes i n the plane of the e l l i p s e .  Usually,  the plane of the e l l i p s e w i l l be p r a c t i c a l l y vert i c a l , and these l a t t e r readings may be used uncorrected;  i n the case of a f l a t l y i n g e l l i p s e ,  the actual azimuth and i n c l i n a t i o n of the axes may be e a s i l y computed.  • SO." The Choice of frequency. The voltage induced i n the orebody, and that induced i n the c o i l s of the receiver, are proportional to the frequency;  the f i r s t i s proportional to the  f i r s t power, and the second to the square*  Therefore,  a high frequency would appear to be of advantage i n inducing a large current i n the orebody, and hence, i n producing a large secondary f i e l d .  Unfortunately,  t h i s i s only p a r t i a l l y the case, since the higher the frequency,  the greater the absorption by eddy currents  in the overburden and overlying rocks.  A point i s  reached where an increase i n frequency produces a reduction i n inductive e f f e c t , owing to the low penet r a t i o n of the magnetic f i e l d .  This absorption  effect w i l l be discussed i n Part I I .  Prom experi-  mental r e s u l t s In caves and tunnels, i t xvas found that frequency of 20-30 k i l o c y c l e s gave the best res u i t s f o r penetration. *  I t would therefore appear  that some frequency i n t h i s band would be the best choice.  However, the design of the o s c i l l a t o r w i l l  enter into the problem, and i t w i l l probably be found that there i s d i f f i c u l t y i n obtaining enough inductance i n the antenna c i r c u i t for e f f i c i e n t operation  ;  and that a higher frequency w i l l give better r e s u l t s .  1.  Eve & Keys.  Eature, v o l . 124, page 178,  1929.  •  •  •  21.  .  E l e c t r i c a l Properties of Rocks and Minerals. It w i l l be evident from the foregoing d i s cussion, that i t i s the difference i n r e l a t i v e cond u c t i v i t y , between the ore minerals and the r o c i s and overburden surrounding them, which makes the geo~ e l e c t r i c a l methods possible.  7?e s h a l l no?/ examine  the r e s i s t i v i t y of these materials. The following table i s taken from the report of the Imperial Geophysical Experimental  Survey, and  i s the r e s u l t of measurements made on rock i n place. The values of r e s i s t i v i t i e s are given i n ohms per cm. cube. '  Material. A. . C r y s t a l l i n e Rocks.  Resistivity. Igneous rocks, .  B.  Consolidated Sedimentary Rocks.' Shalesj- Slates, Limestones, etc.  C.  Unconsolidated Formations. ' ' Clays, Sands, G l a c i a l Dejjosits, e t c  D.  Ore Minerals. (Selected Samples). Sphalerite, Hematite, S t i b n i t e , etc. . Chaloopyrite, Bornite, Chaleoeite,) P y r i t e , Galena, P y r r h o t i t e , etc. }  E.  Underground Water. normal Water, (potable). Saline Water. 1% KaCl. 10% 20%  « .  » .  •  2  *  / 0  ~'°  to -  sxio*  so - 10  . >° ~*_ . e  /0  t  • to - 10 s }  s  7  ?. 14  f.i  The importance  of r e s i s t i v i t y measurements being  made cn rock In p l a c e , l i e s i n the fact that the presence of water decreases the values considerably. Measurements made i n the laboratory on dry specimens/ usually show r e s i s t i v i t y v a l u . e s many hundreds of times those given i n the table.  This shows that  conduction i n rocks i s mainly of an e l e c t r o l y t i c character, whereas i n minerals, the reverse i s the case conduction being m e t a l l i c . Th£ •presence of soluble s a l t s i n the water ' permeating rocks and overburden Is l i k e l y to have very deleterious effects upon the success of t h i s method of prospecting.  F i r s t , i t diminishes the  r e s i s t i v i t y r a t i o between rocks, and ore:  secondly^  i t produces a screening action, which causes of the electromagnetic waves.  absorp-  In some d i s t r i c t s ,  as i n parts of A u s t r a l i a - where the underground t  waters are highly saline, prospecting by. geoelect r i c a l methods may be impossible. • In B r i t i s h Columbia, l i t t l e trouble should be experienced since the waters are,for the most part, fresh and of high resistivity.  Again, the presence of soluble s a l t s  may give r i s e to large out of phase f i e l d s owing to the r e l a t i v e l y low r e s i s t i v i t y :  these, however,  can usually be distinguished at once from orebodies, owing to their uniform quality. Upon starting to operate i n a new d i s t r i c t ,  P3 the average r e s i s t i v i t y of c o u n t r y r o c k s ana burdeB should be determined material i n place. system may  ovsr-  by measurements upon  Any s t a n d a r d e a r t h r e s i s t a n c e  be employed, as explained i n books on  geophysical s u r v e y i n g .  The average r e s i s t i v i t y  of  the orebodies cannot u s u a l l y be o b t a i n e d on ore i n p l a c e and must be made on s e l e c t e d samples. • In d e t e r m i n i n g the phase of thte secondary f i e l d , the r e s i s t a n c e and i n d u c t a n c e of the ore mate r i a l must be taken i n t o account.  On t h i s m a t t e r ,  t h e r e i s a pronounced d i f f e r e n c e o f o p i n i o n between l e a d i n g geophysicists.  J a k o s k y " c o n s i d e r s t h a t the  r e a c t a n c e of an orebody i s predominantly c a p a c i t a t i v e , e s p e c i a l l y i n the case of d i s s e m i n a t e d , f a u l t e d and broken o r e s .  I n t h i s e v e n t , the imped-  ance would decrease with f r e q u e n c y increase.  He'  s t a t e s t h a t i n h i s e x p e r i e n c e , many o r e s , which were p r a c t i c a l l y non-conductors - a t l o w - f r e q u e n c i e s w i t h d i r e c t c u r r e n t , show a v e r y low high frequency c u r r e n t s .  T h i s was  or  impedance to found  to be  the  case i n d e s e r t r e g i o n s , where no m o i s t u r e occurs i n the  orebodies. On the o t h e r hand, Sundberg* b e l i e v e s t h a t 0  1.  J.J.Jakosky  2.  Sundberg  Geo p h y s i c a l Prosuecting" A. I.M.E. 1929 " » *  • 24. • the opposite i s the case, and that the reactance, i f any,  i s predominantly inductive.  I f this i s so, the  impedance w i l l increase with frequency?  i t is in-  teresting to note that Sundberg uses low frequency cycles  •• ••  (500-1000,) methods, p r i n c i p a l l y , so that he may  be  said to have the courage of h i s convictions. The theory w i l l be advanced in Part II that the d i s t r i b u t i o n of high frequency currents (skin effect) alone determines the reactance of the orebody,which i e nearly constant e f f e c t i v e resistance.  and equal to the  I f this i s tru.e, the phase  angle of the secondary f i e l d due to the currents i n the o r e i s constant t  and equal to 45 lagging.  It  would be i n t e r e s t i n g to test t h i s theory out by measurements on an actual orebody at varying frequencies. Interpretation of Resuits. • Upon completion of the ..field work i n an area, :  the r e s u l t s are taken  to the o f f i c e and a set of  "index curves" f o r each traverse are The index curve i s a graphical way  constructed.  of finding the  approximate depth of a, conductor below the surface from a consideration of the minor axis of the ipse.  ell-  I t i s more or l e s s empirical, the assump-  tion being made that the primary vector i s h o r i z ontal and the secondary vector v e r t i c a l . struction i s as follows, f i g 13,  The con-  25.  "Tripod  Pig- i s  •-  The conducting-body is-assumed-to-be-below the point P, and,: since the d i p angles are the same on each side of P, i t i s v e r t i c a l .  Continue the d i p  vectors u n t i l they meet the l i n e P(£:  then draw the  horizontal to meet the v e r t i c a l l i n e through the point on the trax^erse where the dip was taken. This procedure gives one point on the curve. points are located by a s i m i l a r construction.  Other The  curve i n t h i s case, i s approximately a parabola, with axis v e r t i c a l .  The depth of the orebody does  not necessarily coincide with the apex of the curve owing to the refraction of the electromagnetic waves at the surface:  a c t u a l l y , i t w i l l he somewhat lower.  This construction i s of great value since, however shaky i t ' s mathematical foundation may be, i t has been found accurately to represent the actual state of affairs. Traverses and index curves are plottedvas shown i n f i g 14,  • Pig -14..  . •  By making these drawings f o r each part of the area surveyed, the strike and<pitch of underground ore* bodies may be calculated. A dipping orebody i s characterised by unequal dips on either side of; the apex. curve has the shape shown i n f i g 15.  The index I t i s evident  that diamond d r i l l i n g should be started on the side  -Fig 15  _ •V^-"-'.---^^-'^:':^v-^' ;  :  1  i  where the dip angles are smallest.; It i s usual-, --when starting work i n a d i s t r i c t to set up the •• apparatus-ever-a known orebody, and obtain index curves characteristic of the d i s t r i c t . These curves may than be compared with those from an unknown area. In rugged topography,the  form of the index  curve w i l l be d i f f e r e n t i n each cas ,depending on locai irregularities.  The d i r e c t i o n finding c o i l s  should show up to best advantage i n this kind of work where the observation stations are not necessarily at the same elevation.  The proximity of the orebody  28, can then he estimated e n t i r e l y by the degree of e l l i p t i c a l polarization of the f i e l d .  Vertical  out of phase components may be plotted along the traverse:  the magnitude of the vectors wlllincrease  as the orebody i s approached, rapidly decrease to zero over i t and increase i n the opposite sense as i t i s crossed.  Thus the point on the traverse , at  which the reversing switch to the fixed c o i l i s operated should indicate the apex of the conductor. (  This i s one of the advantages of the three c o i l apparatus which ought to make the interpretation of r e s u l t s easier i n a mountainous country , l i k e B r i t i s h Columbia, where l e v e l t e r r a i n i s the exception rather than the rule. In electromagnetic prospecting, the ratio of conductivity of d i f f e r e n t zones i s indicated by the instrument.,  • Hence a l l i n d i c a t i o n c obtained do not  necessarily indicate-orebodies.• Wet-shear zones or-schistose-graphitic rocks--will•often give i n d i c ations similar- to ore.  Geological evidence and  p r a c t i c a l experience i n the d i s t r i c t must be r e l i e d on fordistinguishing these features.  Further study  i s necessary, along t h i s l i n e , i n the f i e l d . The accurate interpretation of geophysical data can only be made i n conjunction with existing geological and mining data. Is usually very complex;  Underground structure ore shoots swell and pinch. JET . y  veins have i r r e g u l a r dips, and geological features are complicated by numerous f a u l t s .  The geophye-  29.. i c i s t must a l s o be a geologist and should be by the b e s t l o c a l knowledge a v a i l a b l e .  assisted  These methods  a r e no l o n g e r i n t h e i r i n f a n c y , but they must be i n t e l l i g e n t l y a p p l i e d t o g i v e satisfactory The  common b e l i e f - t h a t  resuite.  the ' e x i s t a n c e of m i n e r a l i s  i n d i c a t e d by a m y s t e r i o u s e l e c t r i c a l a p p l i a n c e i s erroneous.  Each i n d i c a t i o n of m i n e r a l must be exam-  inedon i t s  own m e r i t s and c o r r e l a t e d w i t h the geo-  l o g y of the  terrain.  f  - One  a p p l i c a t i o n of geophys-  i c a l work i s the e l i m i n a t i o n of b a r r e n a r e a s the expense of d r i l l i n g  before  or underground work i e i n -  curred.Costs ^fJjeo^hyBical E x p l o r a t i o n , Approximate c o s t s a r e not easy, t o e s t i m a t e . They v a r y with the n a t u r e of the ground, t h i c k n e s s of v e g e t a t i o n , , a c c e s s i b i l i t y f o r t r a n s p o r t a t i o n , e t c . An average p a r t y of-3  to 5 men  should cover from 3  to -35 • acres-per -day,- e x c l u s i v e of . p r e l i m i n a r y surveying , l a y i n g out-of base l i n e s and traverses.  The  1.0.1.8. g i v e s $3.25 p e r a c r e as the average c o s t under A u s t r a l i a n c o n d i t i o n s . She  In B r i t i s h eaiumhia, A few thousand  c o s t should be much the same.  d o l l a r s l a i d out i n t h i s way may i n l a t e r development. s i v e examination  save many thousands  "These methods are for i n t e n -  of areas suspected  of m i n e r a l i s a t i o n .  They a r e , i n g e n e r a l , not s u i t a b l e f o r r e c o n n a i s s a n c e p r o s p e c t i n g , a s t h e r e are cheaper methods f o r this work.  Part I I . Ma th ema t i c a l Consideration of the Electromagnetic F i e l d s i n th_e Region of an Orebody. General Case of Two F i e l d s d i f f e r i n g i n Direction and Time Phase,  Consider the ease shown i n f i g 16,  The vector ^sm(w+ -«*) makes an angle j + & with the vector H , s i n cut „  -  I y  • F i g 16.  Resolving these vectors along X and Y axes, we have  Sir\ ^to+ Cos & T - H , S i n tot - M S i n (tvf-J) Sin 0 X  =  H  2  2  x  Hext eliminate u>i  Stn(usf-c<)  cos  6  and  Substituting, Y=  H,  j S'ih — * 'Hi cos d  _  +-  x  gin 0  Cose  \-\ }S\n($i*~!2L— ) <^s*" y- cos/si^ ^— ) s/n «- ( CoS& — X t  X cos €>  - H,  md  squaring, «m <* r e a ^ ^ i ^  2 U°i <<  •2. CO*  This equation i s of the general type, Ax + 2Bxy + Cy = 1 2  r  which i s the equation of an e l l i p s e .  The semi-axes  are given hy the r e l a t i o n  The above discussion can be extended to cover any number of f i e l d s i n three dimensions b y adding the a x i a l components of the d i f f e r e n t f i e l d s . Thus the resultant a x i a l components are: X -  sm^tut  +  Y-•  Sm[uiH^  +-  where  M ^ sivt c  , H , H^H^ 2  t + <>('J + H ^ rjK^ujt+o< " J  SI.M (wt + oi') -h H ^ si>, (uif + ot "J  H £ , H^ H 2  ents of resultant f i e l d s H, H , oivc'oi"  and  y  H  2  ,  respectively, and  are the respective phase angles.  simplifying,  are compon-  Then  32. The c o e f f i c i e n t s of s i n ^ t  a n  d coBujt are constants,  and therefore, we obtain two further equations.  R, - Q, s i n co t R^ =  cos t^>+  where R,, Rj., are the resultant vectors from the compounding of the sine terms and the cosine terms respectively.  The vectors R, and R are 90°out of x  phase, so we obtain a single resultant vector, which rotates i n one plane and i s e l l i p t i c a l l y polarized. It i s therefore evident that, when many f i e l d s of l i k e frequency e x i s t , a l l d i f f e r i n g i n space and i n time phase, there i s always one plane through any point, which i s p a r a l l e l to the resultant f i e l d , and, furthermore, that the resultant f i e l d i s e l l i p t i c a l l y polarized i n that plane.  In  the three c o i l method, the locating c o i l finds t h i s . plane, while the d i r e c t i o n finding c o i l s determine the r a t i o of the axes of the e l l i p s e and t h e i r d i r ection. • • •:-  -  -  C r i t e r i a Xqr Complete Determination of the E l l i p s e . For a complete determination of the e l l i p s e , we need the following information. (l)  The d i r e c t i o n of one axis.  This i s  usually the minor axis and i s approximately given by the single c o i l method.  I t i s exactly defined  by three angles. (2)  The d i r e c t i o n of the other axis:  since the axes are mutually at right angles, this may he calculated. (3)  The magnitude of the axes.  The actual  magnitudes can only he obtained by assuming an approximate shape for the orebody, calculating the equation of the corresponding e l l i p s e and using the measurements obtained at the point.  The r a t i o of  the axes may be obtained as explained above, and i s sufficient. (4)  The phase of one of the axes with res-  pect to the primary f i e l d . ured.  This cannot be meas-  The problem requires further thought as the  information might prove very useful i f i t could be e a s i l y obtained.  •• • •  Calculation of -The F i e l d f o r aV Simple Case. .. .  Let us now  turn to the calculation of a very  simple case, i , e. that of a long straight conductor M, of small radius, at depth d. ordinates i s at 0.  The o r i g i n of co-  The return conductor i s con-  sidered to be at a.depth great enough that the f i e l d due to i t i s n e g l i g i b l e .  Consider the f i e l d at  point P.  Fig  17.  34. Let h, = H coswf and h (  z  - ^  cos(wt-^)  be  the primary and secondary f i e l d s at the point P, distant x from 0.  F i g 18 shows the vectors at the  point P.  Fig 18.  Resolving along axes,  or  v  -  •  -  2- • J * _____ Sim&  Cos  / (ujf  i J  V^-hd  1  X  -  H , C O _ Lot" -f  Then we have two  -  2  ^  COS©  Cos(co-t -<*)  r  Bcos  (T)  equations,  Y * - 4 s i m & cos (u> f--°<) X  /  Lot  Kext eliminate ut :  ASubstitute i n (3)  4-  A CoSQ cos(u>f - °t)  from  (2)  i -"in 0 Cos /u>+-«<J  © (3)  35© Again Oof  .  .  =  C<-o©s S •U> tT  I  Cos  --  —  V  —  V -f  d  CO S, d , TsjA \ih v  0 -V " • S•j n,e{ 7  t  Substitute i n (4) Br A  —;  -  .  0  -f  £©s  —  T  - •  fi  2  Squaring and dividing by s i n 0 S'»  &  J  (A  si^Q  ( A  J  A  1  How substitute i n the values. d  l~l  I  I  2.  n  1•  and we get, X + i X Y /- -U=— cos*< :  L  .  j^-  * * J  1  This equation i s of the type. AX 4  2BXY •+- CX^=- 1  2  •  and the lengths of the serai-axes are given by;  and the angle & between the major axis and the verti c a l i s defined by: A  -  C  Y/hen the appropriate values of A,B,and C, obtained from eqn, (6), are substituted i n eqne. (7) and (8), our information about the e l l i p s e i s complete.  Before we can use these equations, some r e l ationship between H,and I raust be found. 2  urate computation of I is  An acc-  not generally possible,  I  owing to the uncertainty regarding the e l a c t r i c a l properties of the c i r c u i t and absorption i n the overburden. assumption  However,we w i l l make the simplifying that the primary and secondary f i e l d s  are euual at the point 0:  then,  and substituting i n equation (6), we get,  We w i l l further assume that the reactance of the orebody-is n e g l i g i b l e .  I t was shown on page 1  that the secondary f i e l d lags the primary f i e l d by an angle £ + 4  s  _f> =.o - and «r-- £  , where .  <jt> = i  ;  i n this-case,  The expression, then, i s further  s i m p l i f i e d to  Applying eqn. (7), we find that the r a t i o of the axes i s  Again, applying eqn. ( 8 ) , the angle 0  i s given by  !  i  — .ri  !  I L  j  i " ...I..  1 -1~  —j—  j  —'— —-  i —I—  r —-i's' n  "«  —j—  U L  \j  1  _L.. -  :  -  -----  V  i  -----  • j—  -- j— 1  /  —i--  \  '  !  1  i 1" T "  /  /  -----  /  / " V  /;  -  •/ 1  \  —f-  ; J ~ T  / :  ; "  ""7  i  ...  U : 1  - f-----  :  i \/  \  :  -j -j—  \  —  I :  1  [  -i-  "1"  1.  ;  !  i i 1 :  :  !  1 _ j _ i j 1 —i— 1 Lev. d i  |  I /';  1  t - T _• i _  i :  J/iJ  |  I  —  \ r- —r-  y  ii  —  i  — i —  i  "":|"-'  i~-  \  -T-  -  —  .......  1  r  "i --  I  i 1  !~  "T " 1  1  i  i  |  —1-  --  i  „ C A l .COL  -T—  ... : ..  -  i  ;  \T.EC j1  .—p-ic  j  \  ..is.  —rC U R V  >_.  - —  IE —_\  i  -f-  ._;__  -  ,  !  p...  !  !  .j  I  J._.  i  i  In f i g 19 i s shown a calculated traverse of the conductor, with e l l i p s e s drawn to scale;  the  r a t i o of the axes i s given as a curve on a horizontal base of feet.  The conductor i s presumed to  be buried at a depth of 10 feet below the point 0. The index curve i s plotted by extending the minor axis to meet the v e r t i c a l through 0, and then talcing the corresponding ordinate on the v e r t i c a l l i n e through the observation station.  An examination of  the diagram shows that the ratio of the :_xes i s zero above the conductor, increases to a maximum at Zo  about ken feet to right or l e f t and decreases again at points farther removed.  Again, the dip of the  minor axis i s sero at 0, increases to a. maximum at . about ten feet to right or l e f t and decreases again at points further removed.  The index curve i s seen  to-be of complex form and - to-come to an apex, just above the conductor. - - T h i s - i s the type of curve given by the three c o i l apparatus. The single c o i l apparatus gives a d i f f e r e n t shape of curve.  By talcing eqn. (9) and l e t t i n g  oC-o j we get the following expression;  or, £x + Y / ^ V ^ j  -O  ©  Thus by ignoring the phase angle o( the e l l i p t i c a l t  polarization dissappears. hy,  The angle of dip i s given  ' . 38.  •  •  The index curve i s shown, p l o t t e d on t h i s bade in fig  20.  The curve conies to a much ©harper a^ex;  t h e r e i s d i f f i c u l t y i n d e t e r m i n i n g the e x a c t posi t i o n of the c o n d u c t o r . IJore c o m p l i c a t e d cases euch as d i p p i n g v e i n s and f l a t l y i n g deposits , can be treated, in the same manner and w i l l also give t h e o r e t i c a l solution©. A l l o w a n c e may also be made f o r the r e t u r n c o n d u c t o r . The object of calculation© o i this k i n d i e t o g e t an i d e a of the type o f o b s e r v a t i o n to expect i n the field.  Each d i f f e r e n t shape of c o n d u c t o r g i v e s  own t y p e of c u r v e ; the  it's  t h e r e f o r e , c a l c u l a t i o n e of a l l  eases s h o u l d be made b e f o r e g o i n g into the  field.  Much work has been done on models, p a r t i c -  u l a r l y i n the case of the sphere*}  T h i s i e an eaey  ease to c a l c u l a t e and the r e s u l t s have c o n f i r m e d the.  theoretical-work -by experiment.,  been done on d r a i n p i p e s ,  2  Work has  also  with good r e s u l t s .  The need f o r thie work l i e s in the zact  that,  w h i l e ii if easy to o b t a i n the solutions f o r the f i e l d g i v e n the shape of the c o n d u c t o r , the converse i s not eaey and in b e t t e r o b t a i n e d empirically.  (1) Kason, If ax. "Geophye. Prospecting" A . X . H . E . 1 9 2 9 (2) Report I.G.L.S. p.286 Comb. Univ Press. 1931  39.  •• '  '  Ike feature of the f i e l d from the O s c i l l a t o r . I t i s now necessary to consider the nature of the magnetic f i e l d which originates at the oscillator.  The argument follows Maxwell's fundam-  ental principles,and w i l l be followed throughout in detail,- i n order to obtain convenient .-  _  expressions  ......  for pra.cti.cal use l a t e r . Equations of the Electromagnetic F i e l d .  In consid-  ering the nature -of the electromagnetic f i e l d , we have two quantities to examine.  F i r s t , there i s  the magnetic c i r c u i t , which may be symbolized by, B  =  = H  + 4*7 I .  ©  where B - flux density, H* magnetic f i e l d intensi t y and I - i n t e n s i t y of magnetization i n the region, due to the-magnetizing of the medium.  force H  • . ^A. = permeability  These quantities, except  $  are  vectors, though they normally-operate i n the same d i r e c t i o n -in-an isotropic medium.  Also we have the  relationship, V. B This i s a statement  -o  •  (R)  of Gauss' Law, and. postulates  that as much magnetism leaves any region as enters i t . Secondly, we have the e l e c t r i c c i r c u i t , (1) The material f o r t h i s discussion was taken from the following sources: J.H.Jeans " E l e c t r i c i t y and Magnetism" C.U.P. Page. "Intro, to Theoretical Physics" Gibb and Wilson "Vector Analysis"  40, • where D_ e l e c t r i c displacement o r induction i n the region  }  £ = e l e c t r i c intensity which produces t h e  polarization  P i n the d i e l e c t r i c :  e c t r i c constant o f the medium.  lc i s the d i e l -  The l a t t e r i s only  times the d i e l e c t r i c constant as usually measured, but ids used here i n t h i s form to retain the symmetry between equations 15 and 17.  These quan-  t i t i e S j - a l s o a r e vectors though normally i n the same line-, i . e . i n vacuum or isotropic medium.  We  have also, Poissons equation,  where  density of free e l e c t r i c i t y i n the _?_?gion. Ampere•s r u l e states that the l i n e integral  of the magnetic force Hf, round any region, i s equal to 4TT times the surface integral of the current densityJf, taken over the same region.  f-H .dr =*n-fj:n  d<r  Therefore,  - ,# •  where n -is unit- vector in- d i r e c t i o n of vector-/<r . This can be transformed into the following, by Stokes Theorem, jH.df  = -4-n fsj.n d<r .- .7 V x R w tier  or, i n other words, CuH #  The following / denotes 7 denotes f denotes a  H  - 4n J  integral notation i s used. l i n e integral surface integral volume i n t e g r a l .  ®  - There are points to notice about t h i s result; f i r s t , that i t applies only for steady d i r e c t current:  i n magnetostatics,  Curl H = - V where  x V f B O  i s the magnetic potential. =- O  Secondly,  f o r steady d i r e c t current.  This l a t -  ter statement says that current does not c o l l e c t at any point, or that as much leaves a region as enters it.- ,  •- .  -  •- •  Let us-now passon to a region where the current density i s changing.  Consider the case of a  body which is-being charged by means of a current i  flowing through a wire AB , ~ l  (  <A  (see fig)„ -  Let charge  on body at any instant, be ^  q.  Describe a surface  around the body, and  call  the displacement thereon Then-, and  -  X  .  D-.-n-d<T - 4 - n ^  , differentiating,  But i » J ,integrated over the area of the wire =  The negative sign before the second integral i s on account of the inward flow of current, whereas tl  ,  the unit vector normal tornthe surface element d(T  ,  i s drawn with the positive d i r e c t i o n outward, this we  get,  Prom  y ^  + 4 - n J j . n d<r = o  and, by Gauss' vector theorem,  and, therefore,  V  f-4-n J ) = o  3 O'  •zrr i s called the "displacement current*': it Of. . • .. produces a l l the e f f e c t s of a true current i n regions where the e l e c t r i c displacement  i s changing.  We  may  therefore write the t o t a l current, actual and d i s placement , into eqn. 19.  We then get, f o r regions  where the current density i s changing,  Here ~ H  i s i n electromagnetic u n i t s , while J and  are i n e l e c t r o s t a t i c s units;  O  the constant" c i s  the - r a t i o between -the unite, which • i s 3 * 10  •  The  curl-of H i s not necessarily zero as i n magnStostatiCB-, because, while the -current density J  may  zero -,- as- i n - the region outside a wire carrying current j the -displacement - current may have a value, i f the current i s changing. We have now got the equations of the e l e c t r i c and magnetic c i r c u i t s themselves, and also a cross r e l a t i o n between the magnetic intensity H and the displacement  D.  We now proceed to develop another  cross r e l a t i o n s h i p between the e l e c t r i c intensity E and the magnetic flux density B. Paradays law states that the l i n e integral of the e l e c t r i c intensity,round any closed circmit,  i s numerically equal to the time rate of decrease of magnetic flux through i t : S.ffi.I . = e -  where N i s the number of  5  l i n e linkages.  and by Stokes  Therefore  Theorem  5  ..fE.dr.*  i n other words,  fs7x£.n  d<r * - ~  h  d  <  r  and, therefore, Curl E  = - c ~df  Wave Prouagation-,of  (E5  Electrical Effects,  In eqns. 21 and 22, we have obtained the necessary information to proceed.  Since we are p r i -  marily interested . i n .the region outside the wisse carrying the current, we may p u t J = o .  .  Then.  r...-iM.,r.H%g  '.Gtri.E.  Substituting eqn. 22a i n 21a,  hut  \7xVxH--W.H  —- V. Js7 H  • v v  • ' Similarly V  V  6 I N C E  H  -  n  W E  =  ^  .c* c>-P  Slhee V . £ = 0 '  V.H-c v-e = o  wAcre Ho free charge  These are extensions of Laplace*s equation to cover regions i n the v i c i n i t y of moving e l e c t r i c charges.  They do not hold for regions containing  any free charges.  In a gas free charges are neg-  ligible.  -  These equations, by the following transformations ca be jMt i n another form,  Let  1^ E  2  be  scalar magnitudes of the vector E along the axes of a right handed coordinate system: unit vectors along the axes.  also letij  K be  Then  therefore we have f o r the x component  Similar equations hold for y and z components;  also  We have then, six equations as f o l -  for H . x  a, Ex  lows a+*.  h3  -  b t* "  f*K L OX* £-\ /uk  tk £»•  L  c  a t *  4-  +  3x  v  If] 2*.£"* 4  V  2  _LT  J*. K C__ ^ K  Dz\J 2;^ These are the general d i f f e r e n t i a l equations of an e f f e c t similar to a wave motion, propagated the medium with a v e l o c i t y ^==—  .  through  In a i r or vacuum,  the values of pi and K are both unity:  i n this case,  the wave travels with v e l o c i t y c, which i s the same  as the T e l o c i t y of l i g h t . Plane Electromagnetic Waves. Consider the foregoing ecitations applied to a plane wave advancing along the x axis:  take  the e l e c t r i c i n t e n s i t y vector, then t* A"f doc*and the solution of this equation i s  This equation-states thet the instantaneous value of the e l e c t r i c force describes {sinusoidal variations both .with respect to time and with respect to space: that, i n the periodic tirae T, the wave has travelled .  tii&t-e-foi-e  a distance equal to th e wave length  and aieo that  the v e l o c i t y of propagation of the wave i s =~ . Now-in the case•of a plane wave moving i n any d i r e c t i o n , equation 28 can be written_ e *..E,si* .Z-a.fa.-^)  .kr-e  ^  where s- i s the distance measured along the l i n e of propagation-of- the-wave-. --• Let ti be unit vector along t h i s same l i n e , then ^7 --• ifc •* J ^ f  *-to.  and by eqn. 21a,  9Q  Curl H = ^ - H - n g x H and therefore,  h  x  *H  - i Qt  =±  ®  S i m i l a r l y , by eqn. 22a, These are the wave equations, and can be solved by substituting f o r the operators -| and £ .  By eqn. 29  46 a de _  P /  z n i /—  x  2s "  ~ _3_ _ Z-JIJ  and, s i m i l a r l y ,  7)t ~  T  Substituting these results i n eons. 30 and '61,  and l e t t i n g v  Telocity  of wave  c The negative sign i s eliminated by changing the order of the cross product,.  h  x E - ^  Similarly,  B  dD  I t w i l l be e a s i l y seen from these equations that the vectors D,B and n a r e - a l l at  .right-•angles.--  For i n s -  tance, dotting both sides with n i n eqn, 32,  H x  n  .n =  zD.n  = H. n —  -  ==.. O-  •Similarly B,r>  since tlxn- « 0-always. -  is-always -zero. --This-shows that the  vectors D and B are at right angles to n . —, D.6  * H xn  .nx  E = Hxnxn.  E  Again.  =o  c showing that D and B are at right angles to each other. The diagram, f i g 21, shows how and magnetic vectors are related.  the e l e c t r i c  B and B form a  right handed system with n, and are i n the wave front.  Note that E i s not coincident with D unless  the medium i s i s o t r o p i c .  47  e  AO  _Dt reckon  F i g 21. Energy of the Ware.•  Po  Theorem.  The energy passing any surfaae may be shown to be the vector product of B and H as follows:  ^  u 9H  c  also  subtracting  df Again  W  £  x H ) ~ V.(EXH)  +  = - E.S7 x H  ?here£QF®.~ ±X ?f l E  V./EXH)  +• H.V  MhlK  x E V,/£XH).  Integrating f o r the-whole-of the volume under consideration, and d i v i d i n g by 4-n , we get =O  and changing by Gauss' Theorem to surface integral  ^ft*"-"  fom  This theorem i s r e a l l y a statement of the law of conser vation of energy, and states that the rate of change of energy , integrated over the whole regional volume, i s equal to the energy passing the surface.  In an anisotropic medium, the Poynting  energy v e c t o r ^ |t A- H) I  b  not necessarily i n the  d i r e c t i o n perpendicular to the ware front, owing  ' • l?igv 22. to E not being coincident with £ ( f i g 22.). .. The wave then sidesteps'through the medium ( f i g 25).  Fig-23 being always-perpendicular -to - n.The energy per unit volume i s ^ ; ^ h ^ J , +  By taking -the- scalar-product of H with both sides of eqn. 33, and l e t t i n g ^ be unity,  ^H.H Hence----  = n Y E.H = -f O.E  H --.-K-jE  -  -  Therefore energy per unit volume ' / ^ / r \ l j *") JL This shows that magnetic and e l e c t r i c energy per cm* are' equal. The Vector P o t e n t i a l . We have seen by eqn. 16, V. B 0 z  m  Now l e t A  be a vector such that Curl A = B Also ^7.8 = V:  *  which i s i d e n t i c a l l y zero.  49. Again,  VxB  How V.^=0  (  -  V x  A  since A i s a vector depending on J and  Div 3 i s zero.  Also  VxH  Therefore,  Hence  5 and i n free space  = 4"J  x B =. - V . V A  V  X7 \Z ,4^,.. ~ - 4. n J V  r  H = B,  ^ r> J  =  *  Next we draw an analogy -from Laplace's equation, where V. V^> ? -4-nf>  where - -- volume density of  t  {  e l e c t r i c i t y and <p - potential = C^ifr p  .  In this case,  corresponds to J , a vector, and <^> corresponds  to A, another vector.  Hencewe can write  and multiplying by s j % and adding -  ..A  =  jMr  .  (g)  where-A i s called the-''vector-potential" of-the current J .  The vector potential at any point i n a  current carrying region i s found from the current density J by exactly the same process that the elect r i c scalar potential, cj> , i s found from the v o l ume density, ^>  t  except that the integration i n the  former case, i s a vector integration, Whereas, i n the l a t t e r case i t i s a vee4©T integration. magnetic f i e l d vector  s  The  then, i s found from the  vector potential by the r e l a t i o n ,  B = Curl A .  The iSagnetic F i e l d from the - O s c i l l a t o r , Ve w i l l now  t r y to find an expression f o r the  magnitude of the f i e l d from the o s c i l l a t o r .  The  following treatment-is adapted from Dellinger"^ •The'radiation from an antenna i s - u s u a l l y ' calculated by taking the e l e c t r i c and magnetic f i e l d equations f o r a Hersian doublet, modified according to the type of antenna, under consideration.  In this  case, we are primarily interested i n the magnetic Induction f i e l d ;  • - we-are • only-interested-in the r a d -  i a t i o n effect i n so far as we wish to avoid the soc a l l e d • •" a e r i a l -effect" • i n our search c o i l s . will  w"e  therefore, calculate, the magnetic f i e l d direc-  t l y from-the vector p o t e n t i a l , The Instantaneous  value of the-vector -pot-  e n t i a l , -due-to the current density J i n the v e r t i c a l conductor, i s ..... A  .  /  // ^  .  ,  /". /  ^  /  ^  .  since ••««/=-^ - , and a as =d-v-, where a-= area of wire, de =element of length.  Thereof ore at the point P  A ~  (see f i g 24),  since h i s small compared with d. Since we are dealing with a rapidly a l t e r nating current, we cannot assume that the electromagnetic effects are propagated instantaneously: it .a requires a time ~- for the effect to be transmitted c to the point P.  How  the current i n the c o i l i s  assumed to be everywhere the same and equal to (l) J. H  .  J>e II ln'ge  tr  (  V.  S. 6  ur.  -Sf efs  f  Vol  If,  '9I*>.  "Ri<*l«ti'°*  fro**.;  51.  i -  - i * S/'n t o t  then i n our expression f o r vector potential, we must take the current as i t was an instant of time % beforeand therefore, •'•  d  •  1  where A, i s the vector potential due to the l e f t hand wire, and .... . ^ - f e - a . due- to the right hand wire.-  Therefore the t o t a l  vector potential at the point P i s d  low by eqn,--85,  .  d - -i.  1  ^  C  u  k  |  4  ^ J—  •-  • •  since we are considering-a straight conductor, having no vector potential i n any other plane than that containing the coil,-and-perpendicular- to the d i r ection of-d.  The factor l / l O was introduced to  convert to amperes.- -•• -How d i f f e r e n t i a t i n g A , p a r t i a l l y with resu T  pect tod H  , -  cos (t-*) u  -  f  ,  ^  "  W  -  £  J  and writing d f o r d-1. since 1 i s very small compared .j  v  with d  lo cd  tod 7  (•  ,  c  I f the c o i l contains H turns, H w i l l be increased IT times: also substituting effective values f o r I ,  but ^ =  and  ^(  with the wave length.  H -- The  ±2*  ^  i f 1 i s small compared  The complete expression i s  A/4 U  z/r  +  A/A  f i r s t term represents the radiation f i e l d and  the second, -the induction f i e l d  The former var-  e  inversely with-the f i r s t power of d, while the l a t t e r varies inversely as d squared.  Therefore the ind-  uction f i e l d - f a l l s -off sapidly as the distance the o s c i l l a t o r i s increased. fields,we  I f we equate the two  f i n d that, at a distance  f i e l d s are equal. l i m i t i n g distance may be -done.  from  ~-  , the two  Theoretically , this i s tha from t h e - o s c i l l a t o r at which work  - In practice, the - search c o i l s act as  an a e r i a l before this-distance i s reached, and produce a signal loud-enough to drown the response from an orebody.  At 50K.C., ^= 6000 meters,  or approximately 3000 f t .  d- ^ = -~~ C  I e should l i m i t our  observations to a dis tance of 2500 f t . from the aeri a l , and l e s s i f possible.  Four f u l l sized claims  can thus be covered from one set up i n t h i s way, i f the o s c i l l a t o r i s located at a central point. For an o s c i l l a t o r having an anode d i s s i p a t i o n of 25 watts with 500 v o l t s on the plate, the c i r u l a t i n g current i n the c o i l antenna would be about 4© ra.amps.  I f the areal had h=6 f t , I = 6ft and 1 = 10  turns, then substituting these values i n eqn. 37, we  53 » f i n d that the induction f i e l d at 50 K . C . would be given by  H =  ^—r ~^ ef = /.5"2 x /o x  / o  x  g«.wss  gauss at 100 f t . 200  This gives an idea of the email f i e l d strength to be measured.  This i s the direct f i e l d , the second-  ary f i e l d would, i n general, be much smaller.  Since  the f i e l d strength i s d i r e c t l y proportional to the current i n the-antenna, i t i s important to make this' current as lagge as possible:  for t h i s reason,  a large tank inductance i s desirable as forming the antenna c o i l .  The c o i l must be-air spaced to  keep the effective' resistance and charging low.  current  - The-Radiore "doughnut* c o i l should be very  good i t this respect.  Limitations are placed  on  the number of turns-in the c o i l by the factors just mentioned, so they cannot- be-increased  indefinitely.  Pene trat-i on - of E l e c t r omapqi dA i c Waves.We w i l l now  turn to the question ofthe pen-  etration of waves through rock and overburden. Jeans has indicated a way 1  i n which the problem of  wave propagation through a medium with conduction may  be tackled.  The conduction current must be  included i n Man?.'ells equation for the c u r l of H. (1)  J.H.Jeans " E l e c t r i c i t y And Magnetism"  Ch 18  In the vector notation  The medium has conduction currents and displacement currents.  Now l e t  g - £  and.•..!..._  0  £  (  c  '  .__/__ £>„g  Substitute i n above eqn, c  L  <?f-  ^ w Df- J  This i s the same equation as f o r space, where the d i e l e c t r i c constant k , i s replaced hy a new constant K.r K-  .  -  The wave equations may be worked out i n . t h i s manner, and complex expressions obtained f o r wave slowness.-  In t h i s way, the attenuation and  phase change can be calculated t h e o r e t i c a l l y . following treatment i s due to Zenneck"^  The  but has-  been altered to conform to the right handed axes of modern convention.  I t affords a useful picture of  what happens to a wave t r a v e l l i n g over a conducting medium./' In f i g 25, l e t the d i r e c t i o n of propagation be the x axis , which i s taken i n the surface of the earth.  The z axis i s positive i n the upward d i r -  ection to conform with the right handed convention.  (l) J. "Ze/tiectr 'Uber d i-e Fot-tp'fi* zu»>j -ebsner Elek+t-e luaynel-tsche tH/ellCu. U'utjS erne Tel*1t-«pk,'-e  Lei'ra-flache  " Ann^U*  Jer  < fi>--e BezielinMj z.uhrfr<i<.t' b c m PAys.c vol 2i p Jo7 und  ffig- 25- • Let  F i g 26  3£=dielectric constant-in e.s.u. JA. x magnetic-permeability i n e.m.u. f>- r e s i s t i v i t y i n ohms/cm.cube. s «• s p e c i f i c conductivity =  e*.w.  f = frequency — =  c = 3 / i p ' % wave v e l o c i t y A-wave-length • -  q = wave slowness.  Again l e t the a x i a l components of e l e c t r i c intens i t y be X-Y-Z.  Referring to f i g 25, i t i s e v i -  dent that, i f - t h e magnetic-vector H be considered as along the Y axis, i t will-have no component along the X and Z axes.  Similarly, the e l e c t r i c vector  w i l l have no component along the Y axis, see f i g 26. low, ceferring to the discussion which has gone before, we have the following relations: these are repeated here fvv convenience.  56. Applying these to the element of volume l y d x x d z i n f i g 26,. we find that there i s an induced current -Zdx „ through the ease area l * d x , owing to the magnetic force H:  and, also a disp-  lacement current -jwkZdx, through the same area due to component -Z of the e l e c t r i c intensity.  Total  current i s therefore - ^ s - t - ^ K j ~z. „ Taking the l i n e integral of K round t h i s area  and-"by eqn. 19, t h i s i s egual th 4^ rent enclosed by t h i s area.  How  Y^H  times the cur-  Therefore  7 -  ^  •  l e t H vary einusoidally with space and  <s>  time  H - A <? M" "***)1  and substituting i n eqn. 38.  ~-  ^.[&±.i-M^-=.±vh.  S i m i l a r l y taking the area Ix dz . . .  Next take the area dxxds, Curl t -  --  -  By eqn. 22, we have c  3  f  In t h i s case the magnitudes of the scalar components are X,Y and Z.  Curl  therefore i d dx  J D  H d  X  T  --Z-  57. and , since there i s no component along the Y axis  r, i F - '\[ - + HI - _ i d  ^  The same result can he reached another way £". = Vefac + f- 2 g Acjclx - (A- ^ fdZ  , 3V  r  -  -,  [-2ct*J  9(PC dT.  Since E and H vary sinusoidally, *r cWe have now three equations , numbers 39, 40 and41 7)2  r  between X, Z and H.  H= €  Sz  f  Elirainesting X and Z from these  i s a solution of this equation, where  Asva complete solution of the three equations,  4/7  i 8 z J-  Y  _  4 /7^S ^ to f<] - Mext appljr-these- equations to a second parall-  elopiped 1 dx * & , i n the a i r above the interface z  x  F i g 27. The same equations hold on either side of the interface, except that s and 2c are d i f f e r e n t : also, the constants B and A are d i f f e r e n t .  Let values i n  06. a i r be s k A B and i n d i e l e c t r i c be s'k'A'B' Then by eqn  We  43,  next insert  the boundary conditions at the  inter-  face, -where x and a are zero and t Is zero. t i t u t i n g i n eqn. 44, we find  that  A=A*  .  SubsAgain,  when X = X, at the inter-face B,  .  e _  =  &  Writing T and • T, f o r the denominators i n eqn. 48, J> f o r 4 Z L ^  ,  _B  T Hence  _  a  "  X  B'-iPT--  T>  8,'-^^  T  Again from eqns. 45 and 46 2  "  %  ~  —  / T; ' "  /  s, +z w IT,  In the case of a i r s Is zero  z.  Now  l e t TA*  (/  (/  —then  7 7 7 ^  and  Thus X and Z d i f f e r i n phase by an angle <p , where M  '  resultant ©lli$ggu  ;  TNQ  e l e c t r i c i n t e n s i t y E i s the  of these two components,and traces out an . the .-ma^orVe^^  /•Thi  magnetic vector It, being p a r a l l e l to the i n t e r f a c e , is-.©till' plane ;poli»ize.$,v  int#r.''"'fa©©'  w»i5©-in0lined^'aB- i i i ' M l l y ©iiuntry It..'.would;.- »ot\ beV-., :  so; any longer. >  RocK  •'.'•V  1  < . • • • • • • V/e mary  •  ^ '; •-••;'• ' " "i '-:fig 28.'::  field  properties elling.  in f i g 28. surface.  -';V • " . • -' " -••  have seen that the wave f r o n t of the i s  -  ''/.'••'.  :  pri-  d i s t o r t e d , owing to the e l e c t r i c a l  of the earth over which the wave i s travThe d i s t o r t i o n i s shown diagraramatically  There in; a d i s c o n t i n u i t y a t the earth*s The expression,eqn. '62 d i f f e r o from  ;  60. that obtained by Zenneck i n that the sign of the exponent i s changed:  this i s because the Z axis was  taken upwards to-conform to  convention.  The p r i n c i p l e object of Zenneok's work on t h i s subject was  to f i n d the l o s s i n amplitude of a  radio wave, t r a v e l l i n g over a conducting medium. He found that, where the wave t r a v e l s over a good conductor,  such as sea water, there i s l i t t l e lose-  i n energy due to eddy currents below the i n t e r f a c e . If  , however, the medium conducts but poorly, as  i n rock and s o i l , there i s considerable penetration and consequent loss i n energy.  This phase of the  argument i s not of i n t e r e s t - i n geophysical  surveying  owing to the short-distances between the o s c i l l a t o r and the search c o i l .  We may,  however, proceed to  some interesting conclusions regarding the penetration of waves-into the- earth, Referring to eqn. 4-4  _  A  H  €  .  6  Since the Z axis i s positive upwards, i t i s evident that negative values of Z give decreasing amplitude of the wave as the distance from the surface increases At the surface  ;  /  w  t  n  X  )  Let B be a complex quantity B'  - -  (ft  We wish to find the depth at which the amplitude i s 2 of that at the surface. e  Accordingly, l e t  61. ,  :,'..-...=  Hence  h  0  e  e  i s the depth from the surface at which the  wave amplitude has decreased to ~ .  Notice that the  phase of the wave i s also altered.by  the factor  e  ?/e also know that from eqn. 51,  we have next to f i n d a complex expression f o r the wave slowness q i n the wave front,  JJOW  By eqn. 50  and•••5">*-/uj-if, .•..=••e'lfc^fitswhere  let ^ =  t**ic^ -j-'.  Therefore substituting i n eqn. 53 •  where  </>, ^  Again, since  4  ^  ^n/r = f f o r a i r and ^ = / f o r a i r and  rock, also since  where  and  =  ^  = = = r  —-—  Expanding the exponential term  Equating real and imaginarybparts,  Let- us-now-turn to a-practical example-of a wave- penetrating rock of f a i r l y high r e s i s t i v i t y (e.g Let ^>= /o ohms per ca. cube, K'£n  quartz d i o r i t e ) . for rock• and ^ ^  for air.  be •30,0000 cycles.  We then calculate the following  =  quantities  &  s  3  Slso l e t the frequency  >  * '° /0  •.••••••••  4" (vx"> )  o r  6  \//*> _• •  36"'o' TE"  9.2.*/©  e.  ••'Therefore the •••depth; at which the amplitude has decreased to ~p* of that at the surface is.aav/o'cm or 92 meters.  This i s a considerable depth due to  the comparatively low frequency of the-waves and the comparatively high r e s i s t i v i t y .  Actually orebodies  have been located to a depth of 400 f t .  However the  usual maximum depth i s 200 feet, so that the above r e s u l t may be said to agree with practice.  The we-  weakness of a l l theoretical methodsof treatment of t h i s problem l i e s i n the fact that the earth i s  . 63* . taken as being a homogeneous d i e l e c t r i c , having cond u c t i v i t y , which i s farvfrom being the case. and Keys  1  Eve  give the formula H  = H  D  €  v f  f o r f i e l d strength at a depth d.  This formula  r e s u l t s from following an argument similar to that of Steinmetz i n h i s treatment of the d i s t r i b u t i o n of alternating flux i n conductors  2  I t does not appear  to be correct i n t h i s instance as i t ignores the d i e l e c t r i c properties of the medium.  I f this f o r -  mula i s applied to the above example, the depth at which H =~ H i s found to be 492 meters, a considerably 6  different result.  The shove formula was meant to  apply to m e t a l l i c conduction and not to wave propagation through rock. Again, i t i s found i n practice that i t i s not possible to obtain any results i n a region of high ground conductivity, due to the screening action of the - overburden.  The - 1 .G-.1.S. - i n the course of  I t ' s work i n the Moonta d i s t r i c t of South A u s t r a l i a ^ met with highly- conducting overburden, saturated with saline water, which rendered attempts at elect r i c a l prospecting abortive.  The r e s i s t i v i t y of  (1) Eve and Keys "Applied Geophysics" Camb.Univ Pr (?) steinmetz*Transieht Phenomena and O s c i l l a t i o n s " i 3) l ) I.G.E.S.Report p.112.  this--overburden was 271 ohms/cm,cube*  Using the  previous method of calculation, i t i s found that, the f i e l d w i l l be reduced to -|of i t ' s value at the surface by passing through 1.54 meters of t h i s formation Furthermore, the eddycurrents induced i n this screening l a y e r of overburden,  WEES  found to give a uni-  form i n d i c a t i o n , similar to ore, over the whole territory. The change i n phase due to the overburden. We w i l l now proceed to apply Zenneck s reason?  ing to examine the change i n phase of the wave, due to the conductivity and capacitance of the over« burden,,  In eqn. 52 we saw that  and from eqn, 55, we found the value of <*+jb  Q  There-  fore equating reals, we find that  Applying-eqn. 57•to - the 4example of overburden^ with r e s i s t i v i t y of 1 0 stant of 3 .  5  olmis/cm. cube and d i e l e c t r i c con-  Then <?  •  Sappose we wish to  f i n d the change i n phase at a depth of 50 meters: Inserting a value of z =5000 cms  and § = 3/°/o'.  Therefore the phase difference of  H at a depth of 50 meters i s 3t°io' at the surface.  behind that of  This would be repeated when the  return wave comes back to the surface.  H  65.  It flux  mentioned above that the  ms  by the o s c i l l a t o r I s  produced  alternating  rapidly  reduced  as i t penetrates into the ore deposit, which may treated as a  eolid  conductor^.  The r e s u l t i s that the into  such  SO K,-G,  material  as  depth  of  pyrite is 8  Steinmets  elves  penetration of only  about  be 1  flux  1 cm at  Therefore the larger t h e surface area of  the deposit, t h e greater w i l l he the indication at .the receiver, Again,  the current  i s dependent on the The theory i s well  distribution  frequency known  due to  in t h e - d e p o s i t  "skin  effect*,  and w i l l not he given her©,  The e f f e c t i v e impedance, of a. conduct or i e -  Where  x=  d.c.  resistance  .  A = conductivity |-t •» permeability f = frequency 1= distance from centre of conductor to c i r -  Co that there i s no current at the centres  i t is  confined to a small skin on the outside of the conductor.  ]?or conductors of large dimensions such as  orebodies, and f o r high frequencies, the current only penetrates a f r a c t i o n of a centimeter.  In this case ft 362.  ei  66,-  the e f f e c t i v e resistance i s proportional to the diamc-ter of the conductor:  therefore narrow veins pro-  vide better indications than Passive bodies of greater t o t a l volume. Again, from eqn, 58, there Is an effective reactance  equal to the effective cesistance:  would seem, therefore  it  that the phase angle due to  t  the passage of current i n the conductor, i s always 45°and furthermore, that i t i s impossible for an orebody to show a capacitative reactance account.  Experimental work i n the f i e l d  v e r i f y or disprove  chis deduction.  on this should  I f this i s  correct, i t would seem that a l l the discussions on the subject of reactance  of deposits i n the pub-  l i s h e d art i c 1 e s, ar e - f r u i 11 e s s, Summary of Phase Relationships,• I f W/^iWtot  ...  i s the primary f i e l d , the sec-  ondary f i e l d w i l l foe given by ...  n  z  si* l^f-z.a  -4>-  - <k)  -  where <f> i s the phase angle due to the effective impedance of the deposit, while cj>^_ i e due to the transmission of the waves through the overburden.  For  the same orebody and setup of apparatus, MM f, therefore  "JT •=• I  d>. - zf =4*°+ (j>z  oc  d  for high frequencies, Again,  f f  so that the resultant f i e l d can be brought into  /  u  * «  -  phase "by increasing the frequency, since by this means IT +  Cp, t <f>i_  may be made equal to 180° or 360°  This accords with p r a c t i c a l knowledge. A further deduction of the approximate depth of an orebody might be made from the araount by which i t i s necessary.to raise the frequency at the osci l l a t o r to.bring the priaarj and secondary f i e l d s into r  phase.  Again this deduction must be checked i n •  the f i e l d . The whole question of the phase of the secondary f i e l d i s very complicated and depends on many unknown factors.  There i s nothing In the pub-  l i s h e d a r t i c l e s on geophysical prospecting which indicates that an attempt has been made to <5olve i t , possibly because those, who hare p r a c t i c a l experience, consider that i t cannot bo solved.  The anal-  vsis has onlv been attempted here i n order to show O"  *r  *~  the nature of the problem and-to get a better understanding of the mechanism of this geophysical method.  68. .APPMPIX, *3b3£2&2£2L  Ifist JD£ Three .Coil Apparatus.  In order to get data and experience f o r the construction and design of apparatus to he used i n . the f i e l d , i t was decided to constrict a model of the apparatus, and to attempt to measure an a r t i f i c i a l magnetic f i e l d with e l l i p t i c a l polarization, i n the laboratory. Search C o i l s .  I t was o r i g i n a l l y Intended to  take- the measurements through the whole frequency band from 500 cycles to 50 K.G.  However, i n the  design'of the model search c o i l s , no allowance was made f o r the distributed capacitance i n the type of winding adopted,  since the effect of this factor could  only be ascertained through experience;  i n con-  sequence, various disturbing factors were introduced into Jrhe 'experiment, which-rendered  the measurements  at the higher-, frequencies unsuccessful. ..  The -coils-,as-- constructed-, were -three i n number  and had diameters, l l - | , 12", 12£ ; n  tt  they were  wound on wooden frames and mounted at right angles to each other by means of pieces of ebonite, eut to the correct shape.  The inner c o i l was arranged as  the locating c o i l and had 600 turns.  The 12" c o i l  also had 600 turns, with 9 taps at 60 turns and 10 taps at 5 turns.  The outer c o i l acted as the fixed  d i r e c t i o n finding c o i l -and also had 600 turns.  The  9  i  <p  69. i n d u c t a n c e s , . c a l c u l a t e d by Kagaoka f o r m u l a , were ap1  p r o x i m a t e l y -200 t o 240 m i l l i h e n r i e s . t h e w i r e was #34, enamelled.  The size o f  The c o i l s -were placed  i n a wooden c r a d l e , shaped BO t h a t t h e y c o u l d be t u •turned .through any angle, Selector P a n e l . the f i g u r e .  The wiring diagram i s shown i n  The p a n e l i t s e l f was e b o n i t e , w i t h brass  s e l e c t o r s w i t c h e s and c o n t a c t s .  The r e v e r s i n g and  l o c a t i n g c o i l ••/switch was c o n v e n i e n t l y made from a 4-way telephone s w i t c h , taken from an o l d telephone switchboard.  I t was found t o be more c o n v e n i e n t  to mount t h e p a n e l s e p a r a t e l y , r a t h e r than  inside  the c o i l s , a l t h o u g h t h i s arrangement n e c e s s i t a t e d the use o f l o n g l e a d s from the t a p p i n g s t o t h e p a n e l , a f a c t o r w h i c h was l a t e r found t o i n t r o d u c e errors. The T e s t f i e l d .  The e l l i p t i c a l l y p o l a r i s e d  test  field-was produced-hy two l a r g e l o o p s , -9 f e e t having 10•turns-each;  square,  These were-wound- on a rough  lumber framework , e r e c t e d i n t h e l a b o r a t o r y .  The  c u r r e n t i n t h e l o o p s was supplied-by- various oscillators.  3?or audio f r e q u e n c i e s , a Cambridge I n s -  trument Co s o u r c e , c a l i b r a t e d on a mutual i n d u c t a n c e f r e q u e n c y b r i d g e , was t h e source 'of c u r r e n t . h i g h e r f r e q u e n c i e s , up t o 20 K.C.,a dynatron i l l a t o r , w i t h Campbell v a r i a b l e standard  Por osc-  inductanee  and-Tinling s t a n d a r d a i r condenser i n the o s c i l l a t o r y arm o f t h e c i r c u i t , was used.  -Above 20 K.C., a  70a a Hartley type oscillator,from the e l e c t r o s t a t i c sweep of a General E l e c t r i c cathode ray oscillograph was  employed:  t h i s instrument was  calibrated at the  factory. The current i n the two test f i e l d c o i l s  was  varied i n phase by a condenser i n the horizontal coil circuit;  the c i r c u i t i s shown i n f i g 29.  When f i r s t operated, the e l e c t r o s t a t i c coupling -between the test f i e l d c o i l s and the search c o i l s , was  found to be so great that no results could be  obtained at a l l .  - This d i f f i c u l t y was  partially  overcome by wrapping the c o i l s with aluminium f o i l and connecting the l a t t e r to earth.  The shielding  e f f e c t given i n this-way, was not complete owing to the d i f f i c u l t y of shielding the leads to the various instruments and -the c o i l s of the o s c i l l a t o r s . This d i f f i c u l t y persisted- throughout-the-experiment. The • inductance  of the-large-coils,-as meas-  ured and calculated- gave concordant results.  The  values of inductance and resistance were• Horizontal c o i l  1.340  mH  and 10.81  ohms  Vertical coil  1.365  mH  and 17.1-2 ohms.  The Detector-Amplifier Unit. This unit was b u i l t up from salvaged radio parts from several discarded sets.  At f i r s t , i t  took the form of a vacuum tube voltmeter-amplifier, resistance coupled, using the General Radio c i r c u i t ^ (1) Radio Engineer's Handbook,  p 161  71 „ The step up r a t i o of voltage was 200.  This appar-  atus was not successful owing to the d i f f i c u l t y of obtaining a s u f f i c i e n t l y sensitive voltmeter, f o r the output stage, from apparatus at hand i n the laboratory. The unit was then rearranged to be a 4-tube detector amplifier.  One tube gave amplification at  radio frequency, and was coupled to the autodyne detector by transformer, coupling.  The detector was  followed by two stages of transformer coupled audio amplification.  This arrangement was also aban-  doned, owing to d i f f i c u l t y with the radio frequency transformer at the comparatively low radio frequency of 20-50 K.C. f i n a l l y the unit was r e b u i l t to be a three tube detector amplifier unit with headphones. former audio coupling was used.  Trans  The tubes were  W.E.lOll? telephone-repeater tubes, with filament voltage of 4 v o l t s , and 6 v o l t s negative grid bias* I t worked well at audio frequencies and would probably have been satisfactory at higher frequencies, i f measurements had been possible at these frequencies. The general scheme of connections i s shown i n f i g 29.  72,  The Test Magnetic  ffleld.  Let Acos u>r ce f i e l d due to v e r t i c a l loop  " h o r i z o n t a l loop,  !Y i  —• j f i g 30  X - A cos ^ r  Resolving  Y  E l i m i n a t e <-o I'  8a  X /i  to r  cos  6 0 s tb  6  -f-  Squaring and rearranging v.* 1  7- Y /i.e.. . . . x  6'  r  A'  Si *  l i t i s - i s - t h e equation of the e l l i p s e .  The r a t i o of  the axes i s given by / 1  t  H  (A*  \  +  1/(4-  H..."  -^3-  How A and B are proportion?,! to the current i n the loops,  Therefore A -  *  /3  where c i s constant of p r o p o r t i o n a l i t y £ i s common voltage applied to both loops. R,R' are t o t a l resistances I>„L are inductances X  G  i s capacity added to h o r i z o n t a l loop.  By making the capacitative reactance i n horizontal loop c i r c u i t large compared v/ithioL, and «oL , 2  •and also waking R» as small as poe-ible, the current, and hence the magnetic f i e l d of the horizontal loop, may he made to have a phase difference of p r a c t i c a l l y  QOl  The terms R  w C  ,Z  and lA^may he neglected.  l  i s zero i f 4> = so°.  Also the terra J^-J  The  equation  A B  of the e l l i p s e i s then .4.*-  e1  and the majog axis i s either'horizontal or v e r t i c a l , according as A or B i s greatest.  I f these factors  are neglected the expression reduces to  Measurements-at Audio frequencies. The table-on the opposite page shows the various-resistances and-reactances  for frequencies  from 500-7000. cycles, together u i t h calculated and observed values of ^ terms  L, <Si-, and R  5  and £ ..  The smallnees of the  shows the j u s t i f i c a t i o n for neg-  l e c t i n g them. The angle © was measured with an Ahney Hand l e v e l , placed on the c o i l s *  The results show a  discrepancy with calculated values, at a l l frequencies. The balance setting was very broad at the lover frequencies and the results had.:-to be averaged i n these cases.  This somewhat dissappointing result can be  d i r e c t l y traced to the following causes.  74. ) Braadness of Balance Setting. The note i n the headphones couid never r e a l l y he made to dissappear.  This effect may he consid-  ered under the following subdivisions. (a)  The capacity coupling between the test  f i e l d c o i l s and the search c o i l s caused a continuous signal to be heard i n the phones.  The test f i e l d  were shielded with aluminium f o i l as described above; i t was  , however , not possible to shield a l l . l e a d s ,  nor to shield the output transformer l a t o r or buffer amplifier.  of the o s c i l -  The effect increases  with frequency, and makes this method of testing the apparatus impossible at radio frequencies. (b)  The leads to the selector panel are s i t -  uated i n the magnetic f i e l d , and so h.ad an eraf i n duced i n them.  These were made much longer than  necessary, since-this-effect was not anticipated when the apparatus was-designed. (c)  -  -  There was•considerable d i f f i c u l t y i n  tuning the fixed c o i l accurately. wound with too many turns of wire;  -  The c o i l s were a l l the signal was  extremely loud i n the phones, and the number of turns could havee been reduced by about SO^  with  advantage, considering the amplification employed. Coupling also probably occurred between turns of the  (&)  Capacitative coupling between the loops  and the wiring of the detector i t s e l f caused errors. I t was discovered at the end of the experiment, that the detector would give a small note i n the headphones, even i f unconnected with the c o i l s . (2)  Errors JLn the Angle of Inclination of the <Axes. In a l l probability, this was caused by dis-  t o r t i o n of the f i e l d i n the loop, due to lagge masses of i r o n , i n the form of e l e c t r i c a l machinery, i n the laboratory.  This machinery was a l l situated to the  north of the apparatus, since the l a t t e r was placed next to the south wall of the building. crepancy was about the same a t . a l l  The dis-  frequencies.  In addition to the above disturbing factors, the presence, of a slight 60 eyclehum may be mentioned. This was considered to be due to the transformers i n the transformer vault, and possibly-, to a s l i g h t leakage-between the a.o.-and d.c. c i r c u i t s of the laboratory , since the l a t t e r was used for B battery voltage for amplifier and o s c i l l a t o r . Work at High Frequency. An attempt was made to raise the frequency to 20- 39 K.C., and to make measurements i n this band. The  o s c i l l a t o r from the cathode ray oscillograph was  used f o r this purpose;  i t was connected to the loops  through a l i n e from the meter room at the other end of the laboratory.  76, Various systems were t r i e d to obtain an audi b l e note.  F i r s t , autodyne detection, with, tuned  plate and grid c o i l s i n the detector stage.coupled to the radio frequency transformer i n the preceding stage, was t r i e d .  This was abandoned owing to the  d i f f i c u l t y of constructing a suitable radio frequency transformer f o r such low freouenciee.  Second, the  vacuum tube voltmeter was used, and l a t e r , abandoned f o r reasons given above.  F i n a l l y , buzzer mod-  u l a t i o n i n the grid c i r c u i t of the o s c i l l a t o r gave an audible note i n the. phones* Measurements i n this frequency band f a i l e d f o r two reasons:  . f i r s t , owing to capacity coupling  between the c o i l s , as outlined above.  This was  especially bad because of the leng&h of l i n e  (about)  20 yards), from the o s c i l l a t o r and the test loops, and the h i g h frequency.  - Second, i t was found im-  possible -to-tune the fixed direction finding c o i l on account - of--the- large-natural -wavelength of the c o i l Thus, while measurements were not successful in t h i s hand, the reasons are not f a r to seek: therefore, we oannot assume that the method w i l l not be successful i n the f i e l d .  While the f i e l d s to be  measured in the f i e l d w i l l tend to be smaller than i n the laboratory, given correct design of the c o i l s , the disturbing factors w i l l be absent  Summary .of Conclusions. (1)  The fact that results were obtained on the low  frequencies, suggests that the principle of the apparatus; i s sound, but that careiul design i s essential. (2)  This method of testing the apparatus i s unsuit-  able for high frequencies.  A better method would  be to select a suitable underground conductor,  such  as an tbron pipe, and make actual measurements i n the f i e l d . (3)  .......  A considerable amount of information has been  gained about the design of the search c o i l s .  A com-  paratively few turns of wire, say 200, w i l l be used on the next o u t f i t .  This w i l l reduce the capacity  of the winding, since thay w i l l be space wound, and the c o i l w i l l have a small natural wave length.  The  d i f f i c u l t y of support for th'6 winding w i l l be i n creased*, able ,  -this, however, should not be insurmount-  - Again,,-the-leads  fron the tappings and-coils  to the selector panel w i l l be as short•as - possible.• the l a t t e r w i l l be mounted inside the c o i l assembly, as also w i l l be the tuning condenser. (4) set,  Radio frequency amplification, i n the detector i s not suitable for the comparatively  encies employed.  low frequ-  Autodyne detection, therefore, can-  not be used, owing to i n s t a b i l i t y when tuning the search c o i l s .  3?or t h i s reason  , i t w i l l be nec-  essary to modulate the transmitter.  Simple chopper  o r b u z z e r m o d u l a t i o n i n the g r i d c i r c u i t w i l l be sati s factory*  An e x t r a stage o f a m p l i f i c a t i o n can  be added i f n e c e s s a r y . (5)  V e r y c a r e f u l c o n t r o l o f the frequency i s nec-  e s s a r y a s the f i x e d d i r e c t i o n f i n d i n g c o i l must be tuned a c c u r a t e l y .  The o s c i l l a t o r should'be  calib-  r a t e d w i t h g r e a t care a g a i n s t a- -standard wayemeter. • There should, be f o u r • settings' t o g i v e say .20.,30/4.0, and 50 E.G.  The s e a r c h c o i l should have  condensers  • c o r r e s p o n d i n g t o these f r e q u e n c i e s , - w h i c h can be c u t i n by a s w i t c h on the s e l e c t o r p a n e l , a c c o r d i n g t o which f r e q u e n c y .is b e i n g used. . T h i s t u n i n g should be done permantly I n the l a b o r a t o r y , s i n c e i t cannot be done as a c c u r a t e l y i n the ' f i e l d * .  79. BIBLIOGRAPHY. Ambronn, "Elements "of Geophysics" McGraw-Hill 1928. B i e l e r , Can. Min. B u l l . #193 PS38  C.I.M.K.1928.  ££ake and ¥ilmotte»0n the Daylight Transmission Chara c t e r i s t i c s of Horizontally and V e r t i c a l l y Polarized Waves from Airplanes? Bellinger,J.H.  Proc.I.R.E. V o l 17 1929.  "Radiation from an Antenna?  U.S.  Bur.Stds. V o l 15, 1919-20. Il® and Keys, "Applied Geophysics* Cambridge University-Press, 1929, 3&S and Keys . TT  Bature V o l 124 p 178  e  A.I.M.E. Teoli. Publ. #316 1930.  Edge.A.B. Report of the Imperial Geophysical Experimental Surrey. Cambridge Univ. Press, 1931. Glob and Wilson. *Veotor Analysis'*. Jeans J..B. "Mathematical-Theory of E l e c t r i c i t y and t  Magnetism* Camb. Univ. Press.1916. Jakoaby-. J . "Geophysical Prospecting* A.I.M.E. 1929. Lundberg and ffordfitroia;- •**Geophysical Prospecting* A.I.M.E. Tech. Publ. 1929. Ha son. Maxff  *Geophysical Prospecting* A.I.M.E.1929.  Morecroft,J.H. *Principles of Radio Communication" Wiley and Sons 1927. Horecroft.J.H. "Hotes on Vacuum Tubes" Proc.I.R.E. Vol.8 #3 June 1920. Page. "Introduction to Theoretical Physics"  80, Bibliography  (eont.U  Steinmetz.CP.  "Transient Phenomena a.nd o s c i l l a t i o n  Mcgraw-Hill 1920 Sundberg. "Geophysical Prospecting? A.I,E.S. 1929, Thompson, J . J . ^ E l e c t r i c i t y and MagnetismS  CArah.  Univ. Press, 1903. • Fleming. J.A^  '"The P r i n c i p l e s of l l e G t r i c Wave  Telegraphy and Telephony* Longmans. 1916. Lahee„F.K,  " F i e l d Geology* Hcgraw-Hill 1931,  Zennec&T. "Tiber die • Portpflanzung ebener electromagnet ische V/ell en Isngs einer ebenen Leiterflasche und ihre Beziehung zur drahtloeen Telegraphies Annalen der Physik Vol,23 1907.  Translated by  Fleming "Engineering*- 3-une 1909,  Also i n the  book by Fleming see above.  

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