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The theory of geophysical surveying by the high frequency electromagnetic method 1935
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Title | The theory of geophysical surveying by the high frequency electromagnetic method |
Creator |
Brown, Christopher Ernest Gordon |
Publisher | University of British Columbia |
Date Created | 2011-10-31 |
Date Issued | 2011-10-31 |
Date | 1935 |
Description | [No abstract available] |
Subject |
Electromagetism |
Genre |
Thesis/Dissertation |
Type |
Text |
Language | Eng |
Collection |
Retrospective Theses and Dissertations, 1919-2007 |
Series | UBC Retrospective Theses Digitization Project |
Date Available | 2011-10-31 |
Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
DOI | 10.14288/1.0105038 |
Degree |
Master of Applied Science - MASc |
Program |
Electrical and Computer Engineering |
Affiliation |
Applied Science, Faculty of |
Degree Grantor | University of British Columbia |
Campus |
UBCV |
Scholarly Level | Graduate |
URI | http://hdl.handle.net/2429/38474 |
Aggregated Source Repository | DSpace |
Digital Resource Original Record | https://open.library.ubc.ca/collections/831/items/1.0105038/source |
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I ACC: wot • ~UJ$-~ -, THE- THEORY OF GEOPtfYS J C A b ^ R V ^ BY T H E H I G H FREQUENCY E L E CTR0MAGNET1C METHOD BY CHRISTOPHER ERNE5T GORDON BROWAT A T H E S I S S U B M I T T E D F O R T H E D E G R E E OF M A S T E R O F A P P L I E D S C I E N C E I N T H E D E P A R T M E N T O F E L E C T R I C A L ENGINEERING 7 T H E UNIVERSITY OF BRITISH COLUMBIA APRIL 1935 CONTENTS. Pa^rt I . General Principles of Electromasne t i c Surveying, General Principles. E l l i p t i c a l Polarization. 3. Single Coil Method. 5. Triple Coil Apparatus. 8. Description of Apparatus. JLJL © Pield Procedure. 17, Choice of frequency. 2 0 . E l e c t r i c a l Properties of Rocks and Minerals 2 1 . Interpretation of Results. 24. Costs of Geophysical Exploration. Mathematical Consideration of Electromagnetic Fields in -the Region • of - -an Or ebod.y-. - General•Case'of Two Fields differing in Direction and Time Phase, - 30. Criteria for complete Determination of the Elli p s e . 32. Calculation of the f i e l d for a simple case. 33. The Nature of the Field of the Oscillator. 39. Plane Electromagnetic Waves. 45. The Magnetic Field. Strength 50. Penetration of Electromagnetic Waves. 53 The Change in Phase due to the Overburden. 64. D i s t r i b u t i o n of Current i n the Orebody. Sumraary of Phase R e l a t i o n s h i p s , APPEH)IX. Laboratory Test of the Three Apparatus, THE THEORY 03? GEOPHYSICAL SURVEYING BY THE HIGH FREQUENCY ELECTROMAGNETIC METHOD. • Part 1. General Principles 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 oscillator and vertical c o i l antenna. The f i e l d from the antenna induces a cur- rent in any orebody, which may exist underneath the area being prospected, by reason of the greater con- ductivity of the ore as compared v/ith the country rock, • This induced current, in turn, produces a secondary f i e l d at the surface which may be investi- gated by means of suitable instruments.. • • Suppose, for instance, we consider the c o i l antenna shown in 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 c i r c u i t in the ..vein i s M# et* Instantaneous secondary e.m. .—_.. m r^i A and lx- instantaneous secondary current where R2* resistance of path in the orebody 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 current in-the orebody and, therefore, at the point P, we have two separate fiel d s ; the primary f i e l d from the o s c i l l a t o r , and the secondary field&s/«,/ wt. This-is shown vectori&lly in f i g 2 for a j>olnt V, t situated to the - l e f t -of .J? (.gee-fig l b ) . Assuming th© instantaneous direction o f t o be horizontal, the secondary f i e l d , 4>a, i s at an - angle, defending upon the position of JP.wifc*. respect to P„ 'If P y i s to the left'- tip, . ?igi2.•,,'^W'., :..V: of p (a«3 in the diagrara) 9 the f i e l d «£,will point dia- gonally upwards to the right, ??hile i f P, i s to the right of P, w i l l point downward to the l e f t . Pig \ com! • Pig 3. " •• - - shows the vectors in varying positions in a traverse of the conductor. - If the plane, of the-coil antenna i s kept dir- ected towards the -points PjP^Pi etc^ the horizontal f i e l d ft, w i l l remain approximately constant for one traverse li n e , providing PP^PjR.RP, remain small com- pared 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. - Field. ••• - Since there are two vectors^, a n d , which differ both in space and in time phase, we cannot compound them by the parallelogram law. They can however, be compounded instantaneously, i.e. for Ins- tantaneous values at a particular time of the cycle, when i t i s found that the resultant vector i s variable in length and revolves with the angular velocity 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. Here we have two vectors $ = / s/V,0 and 4>* - i -3°°). They di f f e r in space by an angle ^ + 3°" . Values of and 4>* if. 0 3o" 60° 3d" /2<f ISO Zio" a zyo 3oo" 330 + OS + 0.26 +• OJ4> -h O.S o OS I.O O.S 4\ o ".+ •" 0.86 0.86 o O.S~ 0.86 I.O 0.86 Fig 4. are given for various values of & . Plotting these instantaneous values of , and compounding corres- ponding values by the parallelogram law, we find the instantaneous values of the resultant flux vector, which traces out an-ellipse. Furthermore, i t w i l l be shov;n in Part 11 that a l l out of phase fields of the same frequency can be compounded into one resultant f i e l d ; so that there i s a single plane ellipse, and one only, at any point in the f i e l d , due to any system of conductors, A fi e l d of this nature i s said to be e l l i p t i c a l l y pol- arized. The Determination of the Ellip s e. For the purposes of geophysical prospecting, i t is unnecessary completely to determine the ellipse; we need only obtain the direction of i t s minor axis and an approximate idea of the eecentricity. The latte r can most easily be found by determining the ratio of lengths of the axes. The most successful method in use at present simply finds the direction of the minor axis. The Single Coil Method of Prospecting,, It i s evident that, in the event of there be- ing no orebody in 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 in the same plane as the antenna, w i l l be in & horizontal plane when i t i s not threaded by any flux. When an ore deposit is present, the c o i l w i l l also be horizontal directly above &he deposit,as at point A in f i g 5., where and <£_add directly to Dit-echi'on of '.•V ' ••• /•. ' . i . i 1 V Conductor ; "// • / . ^ \ v \ V I ' 'oil \ • . ••../ . ': Pig .5.' form one unidirectional resultant. At points B and B,, the position of minimum pick up w i l l be at an angle as indicated. If the f i e l d i s e l l i p t i c a l l y polarized, as is usually the case, the minimum inten- eity# in the detecting unit w i l l toe d i f f i c u l t to det- ermine. 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 altering the frequency; this i s objectionable since i t gives non-uniform con- ditions for: interpreting ••-a- set of reading^ i f they are a l l taken at different 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 conduc- tor-. Fig 6 shows the - orientation '-of the field' 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 vertical i s termed the dip of the c o i l In f i g 7 . , the dips are shown plotted for 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: after crossing the orebody* the dip rap- idly increases in the opposite direction, rises to a maximum and f i n a l l y decreases as the secondary f i e l d grows weaker with distance. Outside the points A and B , the fi e l d from the orebody i s too weak to have much effect 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 now . operating. . Its chief advantage ie ease and rapidity 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 excel- lent source of information about she orebody i s neg- lected. 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 ellipse may dep- art greatly from the vertical. In this case a aero indication may be impossible to obtain.. For example, consider a vein dipping at 4.5° as shown in the block diagram f i g Sa. The h i l l s i d e slopes at 45*and the oscillator i s situated downhill in the direction AB. In f i g 8b,the oz- axis i s horizontal and parallel with thelower edge M of the block diagram. ab,a'b' and a Hb n are projections of the vector <$*_in the xy,xs and d i f f i c u l t to draw the ellipse clearly without compli- cating the diagram, hut i t can be-seen that'the ellipse i s • f l a t - l y i n g with the major axis,, depending on the phase difference, in the approximate direction R, poin- ting diagonally•••downward to the right* In this 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 ellipse, parallel to -, and-also with i t ' s fixed axis- sighted-towards, and lying in, the-plane-of the ant- enna, a l l at the same time. This means that a zero indication would not be obtained in any position of the c o i l * ' The Triple Coll Apparatus. It i s evident from the above discussion that a single search c o i l can give the general direction of the axes of the ellipse, but that, in order to have more definite information about the f i e l d , some other form of search c o i l i s necessary. The triple c o i l apparatus i s an attempt to deal with, this matter; i t has been experimented with in the laboratory but i s s t i l l in the experimental stage. -In this methodthree coils, mutually at right angles,are used. Since the ellipse l i e s am one plane only, a c o i l placed in this plane w i l l be threaded by no flux, and w i l l therefore give zero indication in the detector. This i s the sole purpose of one of the c o i l s y which i s used to placfe the other two at right angles-to the- plane of the ellipse. This is the f i r s t adjustment and may be understood by refer- ring to f i g 9. Here the ellipse i s assumed to be in -3?ig 9-.~ the plane of the paper. The "locating c o i l " i s shown in the plane of the ellipse, in which position i t i s threaded by no flux. The other two coils, a and b, are shown in section and are called the direction finding coils* They are mutually at right angles to the locating c o i l and have an equal number of turns. 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 in. • • • "10.. ' Suppose ,now, that the whole c o i l assembly be rotated, about the axis II, which is perpendicular to the plane of the ellipse, to the position bb' , aa 1; in this position, the, variable c o i l w i l l be perpen- dicular to the major axis, the fixed c o i l jv i l l be per- pendicular to the minor axis and the locating c o i l wil s t i l l be in the plane of the ellipse. Again, in this position, the voltages induced in each direction 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 ellipse. Thus, by-adjus- ting the number of turns in the variable c o i l , the voltages may be made equal and may be made to bal- ance each other out;when connected i n a suitable way to a detector. In this way ,the ratio of major to minor axis can be found, using the number of turns and the area of the coils in the calculation. - The scheme of connections -is shown diagrammat- i c a l l y and in simplified form in f i g 10. Since the F I X E D C O I L V A R M B t - f C o l t TO <lf|--«i««f- - Pig 10. phaoe. of the voltage in the fixed c o i l differs from that in the variable c o i l byH , a condenser is connected across the former and tuned to resonance. The voltage across the condenser C is balanced against the voltage induced in the turns in circuit in 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 in 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 strike of the plane of the ellipse i s obtainable from readings taken with the locating c o i l ; also, that the dips and directions of major and minor axes in the plane of the ellij>se, and the ratio of the axesj can be obtained from the setting of the dir- ection finding coils. For - a complete determination of the ellipse, the actual-, not relative,values of the axes are req- uired.- Fortunately,- this would not seem-to be nec- essary:-- i t can .however, be obtained indirectly fsismi the f i e l d strength of the primary f i e l d i f an ass- umption i s made as to the shape of the orebody. The subject of f i e l d strength i s taken up in Part 11. Apparatus. A bare outlineof the principle of the electro- magnetic methods of prospecting has been given above. A detailed discussion w i l l follow in part 11.• Mean- while , l e t us consider the apparatus necessary. A. The Transmitter. The transmitting apparatus may be divided into three units: theoscillator, the c o i l antenna and the power supply. (1) The Oscillator. This varies according to the need for portability. In level country, where transportation i s not a d i f f i c u l t y , a powerful outfit is possible. Usually a single tube having 15 to 25 watts anode dissipation i s employed, coupled directly to the antenna. A 11X210 or, better, aW.E.212D, work- ing on reduced anode voltage, i s sufficient. Some companies use two or more 46 1s as a class B amplifier of output from a small oscillator. A pure wave form i s a great advantage in obtaining a balance at the receiving set, so that anything like maximum output from the transmitter i s not possible. Two tubes, working as a push-pull buffer amplifier, would elim- inate 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 freq- • uency. The oscillator i s mounted in a stout wooden case: i t can be constructed so thatvthe weight i s about SO pounds. (2) The Coil Antenna. A number of patterns of antennas have been tried. The Imperial Geophys- ic a l Experimental Survey in Australia used a loop con- sisting of ten turns ow wire, 8 feet square, mounted on a pole about 15 feet long: the whole antenna was collapsible. The Radiore Co uses a small circular coi3., "doughnut" shape, having many turns, mounted on atripod withturntable. Other companies use large t r i - angular or irregular loops, supported on poles. A requirement for 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 oscillator should have as large an inductance and as low an eff- ective resistance as possible. A compromise i s nec- essary since i t is 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 oscillator plate Rujjply. Hand-cranked generators have been successfully eiaploy- edfor 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 for the three c o i l method. A light air-cooled gasoline motor, driving a - small 110 volt a .c generator-with•tube r e c t i f i e r , could be built- to weigh less than 100 lbs. This i s not unduly heavy, considering that one set up of the transmitter w i l l cover a radius of about 2500 feet ; or four fullsized claims. The I.G.E.S. used a stor- age battery and dynomotor, which would be satisfactory . " . « ' • j Were ftVVU l a . k / - C . i f facilities,'were available for charging accumulators^ The whole transmitting outfit would weigh in the neighbourhood of 200 lbs and would require two pack horses to transport. •14. B. The Receiving Apparatus. (l) The Single Coil Method. The single c o i l i s mounted on a tripod, having horizontal and vertical graduated circles, similar to a transit. The c o i l i t s e l f has 50-100 turns of fine wire on a fibre hoop, up to 2 feet in diameter. Sights are set along the diametral axis about which the c o i l is pivoted so that i t may be allgnedproperly with the transmitting ant- enna. The vertical plate records degrees and minutes of angle around this axis: this i s used to indicate dip of c o i l . The horizontal plate records azimuth angles of the coil and i s operated in the same way as a transit. These graduated circles do not need the. same degree of accuracy as those of the transit: a r reading to ten minutes is more accurate than the set- ting of the c o i l , - - - The detector-amplifier unit operates into a pair-of- headphones. Unmodulated- transmission was employed by the I.G.E.S., with autodyne reception: in this case the received signal in the phones is pro- portional 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 oscillations into the receiving c i r - cuits Some American prospecting companies modulate the transmitter: in this 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. The whole set i s compact and light, Fig 11 shows a typical ci r c u i t , as used Fig 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 oscillation. Tuned transformer coupling in the f i r s t stage of amplification reduces harmonics^ and i s followed by a stage of res- istance amplification. The total step-up ratio i s about 200. — (2) The Three Coil Met&od. The three search coils are-fixed-rigidly at right- angles to each other. The- axis of rotation, IM* , of the coils i s perpendic- ular to the locating c o i l (see f i g 12): this i s also the sighting axis. Sighting i s done through the hollow spindle MM% to which i s fixed the graduated c i r - cle for finding the dip of the axes in the plane of the ellipse. A U-shaped arm carries the ends of this spindle: to the bottom of the U i s attached a hinge with graduated c i r c l e . The hinge allows the U to place the locating coll in any plane normal to the D i t s e l f . Finally, the wholecoil assembly i s rotatable about a horizontal plate with graduated c i r c l e . Thus There are three circles to be read in any region near an orebody. The whole system seems very comp!icated/ but study of the diagrams w i l l help. Actually,when the e l l i p t i c a l structure of the f i e l d is thoroughly grasped, the adjustments should take very l i t t l e time, as the approximate orientation of the ellipse i s known. Another point in favour of the three c o i l method is that the fixed direction 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 coils 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 com- pact and w i l l -pr-obably be mounted inside the c o i l ass- embly. • The panel contains two selector switches to alter the number of tusns in the variable c o i l , a rev- ersing switch for the fixed c o i l / and a switch to connect either the locating c o i l or the fixed direc- tion finding c o i l to the detector. The detector, which w i l l be mounted on one of the legs of the tripod,will be either a detector- amplifier head-phone set or a vacuum tube voltmeter. The latter would be preferable , i f sufficient sen- 1 7 . ' s i t i v i t y can be combined with a rugged construction. Field Procedure. The standard method of electromagnetic pros- pecting, using a single search c o i l has been descri- bed, together with a second method using three coils. Since ray object has been to attempt to develop the latter form of apparatus, with a slew to the more com- plete determination of the f i e l d ellipse, 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 for a single co i l i s included, as the more complex apparatus i s used In this way for preliminary investigation. It i s assumed that in 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 line Is f i r s t established along the strike of the probable vein system and-traverse lines are run at suitable interval of say 100 feet.- The c o i l .-ant-, enna, i s then set up on the base line inaa convenient •position to examine the area.. To examine the f i e l d with the fixed direction finding c o i l , usedas a single c o i l , the receiving set i s set up, levelled / and a sight taken through the hollow spindle back at the oscillator. The o s c i l l a t e is then set in operation and the c o i l antenna i s rot- 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 direction finding c o i l i s connected to the detector. Upon revolving the co i l assembly round the sighting axis, a position of min- imum indication i s given in the headphones.. If no orebody i s present, the fixed direction finding c o i l should be horizontal when this adjustment has been made. If there i s an ore deposit present„ the direc- tion finding c o i l w i l l not be horizontal, and, in a l l probability , the minimum indicationin the detector w i l l be very broad. In this case, the dip reading of the fixed direction finding c o i l i s entered in the note book and the apparatus i s used to measure the e l l i p t i c a l f i e l d . To-measure the e l l i p t i c a l f i e l d , the switch is 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 oscillator (in the plane of the co i l antenna), until the zero position is found. It i s possible that the lower plate w i l l have to be undamped and the coils rotated slightly about the vertical axis, in conjunction with the rocking motion, to bring the locating c o i l accur- ately into the plane of the ellipse. When the plane of zero indication has been found, the two lower c i r c l are clamped. The direction finding coils are now at right angles to the plane of the ellipse. The next operation i s to determine the dips and relative lengths of the axes of the ellipse. T The Ewitch i s again set so that the fixed direction finding c o i l only i s in circuit, and the coils are rotated around the sighting axis until a position of minimum intensity i s found. The minor axis of the ellipse w i l l then he normal to the fixed c o i l . The second switch is then set so that the fixed and var- iable coils 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 result of this operation i s that three angles and one ratio are obtained. The reading of the lower plate gives the azimuth angle of the strike of the plane of the ellipse; the reading of the intermediate- graduated circle gives i t s dip; while the upper circle gives the dips of - the major and minor axes in the plane of the ellipse. Usually, the plane of the ellipse w i l l be practically ver- t i c a l , and these latter readings may be used un- corrected; in the case of a f l a t lying ellipse, the actual azimuth and inclination of the axes may be easily computed. • SO." The Choice of frequency. The voltage induced in the orebody, and that induced in the coils of the receiver, are proportional to the frequency; the f i r s t is 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 in inducing a large current in the orebody, and hence, in producing a large secondary f i e l d . Unfortunately, this i s only partially 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 in frequency produces a re- duction in inductive effect, owing to the low pene- tration of the magnetic f i e l d . This absorption effect w i l l be discussed in Part II. Prom experi- mental results In caves and tunnels, i t xvas found that frequency of 20-30 kilocycles gave the best re- suits for penetration. * It would therefore appear that some frequency in this band would be the best choice. However, the design of the oscillator 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 in obtaining enough induc- tance in the antenna circuit for efficient operation ; and that a higher frequency w i l l give better results. 1. Eve & Keys. Eature, vol. 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 dis- cussion, that i t i s the difference in relative con- ductivity, between the ore minerals and the rocis and overburden surrounding them, which makes the geo~ electrical methods possible. 7?e shall 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 is the result of measurements made on rock in place. The values of r e s i s t i v i t i e s are given in ohms per cm. cube. ' Material. Resistivity. A. . Crystalline Rocks. Igneous rocks, . 2 * / 0 ~'° B. Consolidated Sedimentary Rocks.' to - sxio* Shalesj- Slates, Limestones, etc. C. Unconsolidated Formations. ' ' Clays, Sands, Glacial Dejjosits, e t c so - 10 D. Ore Minerals. (Selected Samples). e. Sphalerite, Hematite, Stibnite, etc. >° . Chaloopyrite, Bornite, Chaleoeite,) /0~*_ t. Pyrite, Galena, Pyrrhotite, etc. } E. Underground Water. } • s normal Water, (potable). to - 10 Saline Water. 1% KaCl. 7s 10% « . • ?.14- 20% » . f.i The importance of re s i s t i v i t y measurements being made cn rock In place,lies in the fact that the pre- sence of water decreases the values considerably. Measurements made in the laboratory on dry speci- mens/ usually show resistivityvalu.es many hundreds of times those given in the table. This shows that conduction in rocks i s mainly of an electrolytic character, whereas in minerals, the reverse i s the case conduction being metallic. Th£ •presence of soluble salts in the water ' permeating rocks and overburden Is l i k e l y to have very deleterious effects upon the success of this method of prospecting. F i r s t , i t diminishes the re s i s t i v i t y ratio between rocks, and ore: secondly^ i t produces a screening action, which causes absorp- of the electromagnetic waves. In some di s t r i c t s , as in parts of Australia -t where the underground waters are highly saline, prospecting by. geoelec- t r i c a l methods may be impossible. • In Brit i s h Col- umbia, l i t t l e trouble should be experienced since the waters are,for the most part, fresh and of high r e s i s t i v i t y . Again, the presence of soluble salts may give rise to large out of phase fields owing to the relatively low res 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 in 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 country rocks ana ovsr- burdeB should be determined by measurements upon m a t e r i a l i n place. Any standard earth r e s i s t a n c e system may be employed, as explained in books on geophysical surveying. 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 obtained on ore i n place and must be made on s e l e c t e d samples. • In determining the phase of thte secondary f i e l d , the r e s i s t a n c e and inductance of the ore mat- e r i a l must be taken i n t o account. On t h i s matter, there i s a pronounced d i f f e r e n c e of opinion between l e a d i n g geophysicists. Jakosky" considers that the reactance of an orebody i s predominantly c a p a c i t - ative, e s p e c i a l l y i n the case of disseminated, f a u l t e d and broken ores. In t h i s event, the imped- ance would decrease with frequency increase. He' s t a t e s that in h i s experience, many ores, which were p r a c t i c a l l y non-conductors - at low-frequencies or w i t h d i r e c t c u r r e n t , show a very low impedance to high frequency c u r r e n t s . This was found to be the case i n desert regions, where no moisture occurs i n the orebodies. On the other hand, Sundberg*0 b e l i e v e s that 1. J.J.Jakosky Geo p h y s i c a l Prosuecting" A. I.M.E. 1929 2. Sundberg " » * • 24. • the opposite i s the case, and that the reactance, i f any, is predominantly inductive. If this i s so, the impedance w i l l increase with frequency? i t i s in- teresting to note that Sundberg uses low frequency cycles •• •• (500-1000,) methods, principally, so that he may be said to have the courage of his convictions. The theory w i l l be advanced in Part II that the distribution of high frequency currents (skin effect) alone determines the reactance of the ore- body,which ie nearly constant and equal to the effective resistance. If this i s tru.e, the phase angle of the secondary f i e l d due to the currents in the ore tis constant and equal to 45 lagging. It would be interesting to test this theory out by measurements on an actual orebody at varying freq- uencies. Interpretation of Resuits. • Upon completion of the:..field work in an area, the results are taken to the office and a set of "index curves" for each traverse are constructed. The index curve i s a graphical way of finding the approximate depth of a, conductor below the surface from a consideration of the minor axis of the e l l - ipse. It i s more or less empirical, the assump- tion being made that the primary vector i s horiz- ontal and the secondary vector vertical. The con- struction is as follows, f i g 13, 25. "Tripod Pig- i s • - The conducting-body is-assumed-to-be-below the point P, and,: since the dip angles are the same on each side of P, i t i s vertical. Continue the dip vectors unti l they meet the line P(£: then draw the horizontal to meet the vertical line through the point on the trax^erse where the dip was taken. This procedure gives one point on the curve. Other points are located by a similar construction. The curve in this case, i s approximately a parabola, with axis vertical. 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: actually,it 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 in f i g 14, • Pig -14.. . • By making these drawings for each part of the area surveyed, the strike and<pitch of underground ore* bodies may be calculated. A dipping orebody i s characterised by un- equal dips on either side of; the apex. The index curve has the shape shown in f i g 15. It i s evident that diamond d r i l l i n g should be started on the side -Fig 15 _ •;V̂ -"-'.---̂ -̂'̂ :'::̂ 1v-i '̂ where the dip angles are smallest.; It i s usual-, --when starting work in 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 different in each cas ,depending on locai irregularities. The direction finding coils should show up to best advantage in 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 entirely 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 in 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 oper- ated ( should indicate the apex of the conductor. This i s one of the advantages of the three c o i l app- aratus which ought to make the interpretation of results easier in a mountainous country , like Brit- ish Columbia, where level terrain i s the exception rather than the rule. In electromagnetic prospecting, the ratio of conductivity of different zones i s indicated by the instrument., • Hence allindicationc obtained do not necessarily indicate-orebodies.• Wet-shear zones or-schistose-graphitic rocks--will•often give indic- ations similar- to ore. Geological evidence and practical experience in the d i s t r i c t must be relied on fordistinguishing these features. Further study is necessary, along this line, in the f i e l d . The accurate interpretation of geophysical data can only be made in conjunction with existing geological and mining data. Underground structure Is usually very complex; ore shoots swell and pinch. JET . y veins have irregular dips, and geological features are complicated by numerous faults. The geophye- 29.. i c i s t must a l s o be a geologist and should be a s s i s t e d by the best l o c a l knowledge a v a i l a b l e . These methods are no longer 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 to give satisfactory resuite. The common belief-that the ' existance of m i n e r a l i s i n d i c a t e d by a mysterious e l e c t r i c a l appliance i s erroneous. Each i n d i c a t i o n of mineral must be exam- inedon i t f 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 t e r r a i n . - 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 barren areas before the expense of d r i l l i n g or underground work i e in- curred.- Costs ^fJjeo^hyBical E x p l o r a t i o n , Approximate costs are not easy, to estimate. They vary with the nature of the ground, thickness of vegetation,, 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 party 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 sur- veying , l a y i n g out-of base l i n e s and traverses. The 1.0.1.8. gives $3.25 per acre as the average cost under A u s t r a l i a n c o n d i t i o n s . In B r i t i s h eaiumhia, She cost should be much the same. A few thousand dollars l a i d out i n t h i s way may save many thousands i n later development. "These methods are for i n t e n - s i v e examination of areas suspected of m i n e r a l i s a t i o n . They are, i n g e n e r a l , not s u i t a b l e f o r reconnaissance prospecting,as there are cheaper methods f o r this work. Part II. Ma th ema t i c a l Consideration of the Electromagnetic Fields in th_e Region of an Orebody. General Case of Two Fields differing in Direction and Time Phase, Consider the ease shown in f i g 16, The vector ^sm(w+ -«*) makes an angle j + & with the I y vector H , s i n cut „ - • Fig 16. Resolving these vectors along X and Y axes, we have X = H 2 Sir\ ^to+ Cos & T - H , S i n to t - M 2 S i n (tvf-J) Sin 0 Hext eliminate u>i x Stn(usf-c<) cos 6 and Substituting, Y = H _ x gin 0 Cose , j S'ih — +- * 'Hi cos d \-\t}S\n($i*~!2L— ) <̂ s*" y- cos/si^ ^— ) s/n «- ( — X - H , X CoS& cos €> md squaring, «m <* r e a ^ ^ i ^ 2 U°i << •2. CO* This equation i s of the general type, Ax2 + 2Bxy + Cyr = 1 which is the equation of an ellipse. The semi-axes are given hy the relation The above discussion can be extended to cover any number of fields in three dimensions by adding the axial components of the different fields. Thus the resultant axial components are: X - sm^tut + M ^ c sivt t + <>('J + H ̂ rjK^ujt+o< " J Y-• Sm[uiH^ +- SI.M (wt + oi') -h H ̂ si>, (uif + ot "J where , H2, H^H^ H 2£, H^ H y H 2 , are compon- ents of resultant fields H, H , respectively, and oivc'oi" are the respective phase angles. Then and simplifying, 32. The coefficients of sin^t a n d coBujt are constants, and therefore, we obtain two further equations. R, - Q, sin co t R̂ = cos t^>+ where R,, Rj., are the resultant vectors from the com- pounding of the sine terms and the cosine terms res- pectively. The vectors R, and R x are 90°out of phase, so we obtain a single resultant vector, which rotates in 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 fields of l i k e frequency exist, a l l differing in space and in time phase, there i s always one plane through any point, which i s parallel to the resul- tant 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 in that plane. In the three c o i l method, the locating c o i l finds this . plane, while the direction finding coils determine the ratio of the axes of the ellipse and their di r - ection. • • •:- - - Criteria Xqr Complete Determination of the Ellip s e. For a complete determination of the ellipse, we need the following information. (l) The direction of one axis. This i s usually the minor axis and i s approximately given by the single c o i l method. It i s exactly defined by three angles. (2) The direction 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 app- roximate shape for the orebody, calculating the equation of the corresponding ellipse and using the measurements obtained at the point. The ratio 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 . This cannot be meas- ured. The problem requires further thought as the information might prove very useful i f i t could be easily obtained. • • • Calculation of -The Field for 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. The origin of co- ordinates i s at 0. The return conductor is con- sidered to be at a.depth great enough that the f i e l d due to i t i s negligible. 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 fields at the point P, distant x from 0. Fig 18 shows the vectors at the point P. Fig 18. Resolving along axes, o r v - - 2- • J * / i • - _____ Sim& Cos (ujf J V^-hd1 / (T) X - H , CO_ Lot" -f - 2 ^ COS© Cos(co-t -<*) Then we have two equations, Y * - 4 s i m & cos (u> f--°<) © X r B c o s Lot 4- A CoSQ cos(u>f - °t) (3) Kext eliminate ut : from (2) A- i -"in 0 Cos /u>+-«<J Substitute in (3) 3 5 © Again Oof = Cos I — V -f d C o s • t - V , , sjA \ih t0 -V7" • • , . . <- © S U> T - — CO S d T v Sjn e{ Substitute in (4) B r . 0 A - — ; £©s - f — T - • fi 2 Squaring and dividing by sin 0 S'» & (A J si^Q ( A1 A J How substitute in the values. d l~l I I n 2. 1 • and we get, X + i XY /-:-U=— cos*< L . j ^ - 1 * * J This equation is of the type. AX2 4 2BXY •+- CX̂ =- 1 • and the lengths of the serai-axes are given by; and the angle & between the major axis and the vert- i c a l is defined by: A - C Y/hen the appropriate values of A,B,and C, obtained from eqn, (6), are substituted in eqne. (7) and (8), our information about the ellipse i s complete. Before we can use these equations, some r e l - ationship between H,and I2raust be found. An acc- urate computation of IIis not generally possible, owing to the uncertainty regarding the elactrical properties of the circuit and absorption in the overburden. However,we w i l l make the simplifying assumption that the primary and secondary fields are euual at the point 0: then, and substituting in equation (6), we get, We w i l l further assume that the reactance of the orebody-is negligible. It was shown on page 1 that the secondary f i e l d lags the primary f i e l d by an angle £ + 4s , where <jt> = i ; in this-case, _f> =.o - and «r-- £ . The expression, then, is further simplified to Applying eqn. (7), we find that the ratio of the axes i s Again, applying eqn. ( 8 ) , the angle 0 i s given by ! i I j 1 ! — .r — i t 1 i " ! L - 1 ~ — j — —'— ...I.. r - T • _ i _ i 1 i _ j _ j i — - "« —-i's-' n ... j 1 — i — . d i i : ! —I— — j — \ j U L J / i J /' ; : ' : / i 1 | " T " 1 Lev I i i | " 1 " I 1 / 1 1 : I : — \ - - - - - • / 1 — f - i i ! ; 1. \ / \ i \ / : / ; J ~ T — ! ~ i 1 [ 1 : i -j - _ L . . — i - - U : 1 ; " 1 " T " 1 — i — - i - - : - ----- V i ""7 \ r - — r - i i " " : | " - ' i - j — - - - - - - f - / " V y i ~ - • j — - - j — - 1 - - - - - / - \ /; \ - T - - — ....... 1 "i r -- i - ... : .. - — I -- | —1- — r - i - T — „ C A l . C O L \T.EC >_. C U R V IE _ — \ - ; j 1 . — p - i c j ..is. . _ ; _ _ - f - i \ ! ! I , p . . . ! . j J._. i i In f i g 19 i s shown a calculated traverse of the conductor, with ellipses drawn to scale; the ratio of the axes i s given as a curve on a horiz- ontal 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 vertical through 0, and then talcing the corresponding ordinate on the vertical line 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 is 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. - - This-is the type of curve given by the three coil apparatus. - The single c o i l apparatus gives a different shape of curve. By talcing eqn. (9) and letting oC-o j we get the following expression; or, £x + Y / ^ V ^ j - O © Thus by ignoring the phase angle o( t the e l l i p t i c a l polarization dissappears. The angle of dip is given hy, ' . 38. • • The index curve i s shown, p l o t t e d on t h i s bade in f i g 20. The curve conies to a much ©harper a^ex; there i s d i f f i c u l t y i n determining the exact pos- iti o n of the conductor. IJore complicated 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©. Allowance may also be made f o r the r e t u r n conductor. The object of calculation© o i this kind i e to get an i d e a of the type of observation to expect i n the f i e l d . Each d i f f e r e n t shape of conductor gives i t ' s own type of curve; 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 the eases should be made before going into the f i e l d . 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*} This ie an eaey ease to c a l c u l a t e and the r e s u l t s have confirmed the. theoretical-work -by experiment., Work has a l s o been done on d r a i n p i p e s , 2 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 obtain the solutions f o r the f i e l d given the shape of the conductor, the converse i s not eaey and in b e t t e r obtained 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 Oscillator. It i s now necessary to consider the nature of the magnetic f i e l d which originates at the osc- i l l a t o r . The argument follows Maxwell's fundam- ental principles,and w i l l be followed throughout in detail,- in order to obtain convenient expressions .- _ . . . . . . for pra.cti.cal use later. Equations of the Electromagnetic Field. 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 cir 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 intens- i t y and I-intensity of magnetization in the region, due to the-magnetizing force H • . ^A. = permeability of the medium. These quantities, except $ are vectors, though they normally-operate in the same direction -in-an isotropic medium. Also we have the relationship, V. B - o • (R) This is a statement of Gauss' Law, and. postulates that as much magnetism leaves any region as enters i t . Secondly, we have the electric circuit, (1) The material for this discussion was taken from the following sources: J.H.Jeans "Electricity and Magnetism" C.U.P. Page. "Intro, to Theoretical Physics" Gibb and Wilson "Vector Analysis" 40, • - where D_ electric displacement or induction in the region } £ = electric intensity which produces the polarization P in the dielectric: lc i s the d i e l - ectric constant of the medium. The latter i s only times the dielectric constant as usually meas- ured, but ids used here in this 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 in the same line-, i.e. in vacuum or isotropic medium. We have also, Poissons equation, where density of free el e c t r i c i t y in the _?_?gion. Ampere•s r u l e states that the line 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. Therefore, f-H .dr =*n-fj:n d<r - ,# • where n -is unit- vector in- direction 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, in other words, C u H H - 4n J ® # The following integral notation is used. / denotes line integral 7 denotes surface integral af denotes volume integral. - There are points to notice about this result; f i r s t , that i t applies only for steady direct cur- rent: in magnetostatics, C u r l H = - V x V f B O where is the magnetic potential. Secondly, =- O for steady direct current. This l a t - ter statement says that current does not collect at any point, or that as much leaves a region as enters it. - , •- . - •- • Let us-now passon to a region where the cur- rent 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 (see fig)„ - Let charge , ~ - on body at any instant, be l ( <A ^ q. Describe a surface around the body, and c a l l X the displacement thereon . Then-, - D-.-n-d<T - 4 - n ^ and , 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 direction outward, Prom this we get, y ^ + 4-nJj.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*': i t Of- . . • . produces a l l the effects of a true current in regions where the electric displacement is changing. We may therefore write the total current, actual and dis- placement , into eqn. 19. We then get, for regions where the current density i s changing, Here ~ H i s in electromagnetic units, while J and O are in electrostatics units; the constant" c i s the - ratio between -the unite, which • i s 3 * 10 • The curl-of H is not necessarily zero as in magnSto- statiCB-, because, while the -current density J may zero -,- as- in - the region outside a wire carrying cur- rent j the -displacement - current may have a value, i f the current is changing. We have now got the equations of the electric and magnetic circuits themselves, and also a cross relation between the magnetic intensity H and the displacement D. We now proceed to develop another cross relationship between the electric intensity E and the magnetic flux density B. Paradays law states that the line integral of the electric intensity,round any closed circmit, i s numerically equal to the time rate of decrease of magnetic flux through i t : in other words, S.ffi.I5. = e - where N is the number of line linkages. Therefore and by Stokes5 Theorem ..fE.dr.* fs7x£.n d<r * - ~ h d < r and, therefore, Curl E = - c ~df (E5 Wave Prouagation-,of Electrical Effects, In eqns. 21 and 22, we have obtained the nec- essary information to proceed. Since we are p r i - marily interested . in .the region outside the wisse carrying the current, we may putJ = o . Then. . '.Gtri.E. r...-iM.,r.H%g Substituting eqn. 22a in 21a, hut \ 7 x V x H - - W . H —- V. Js7 H - 6 I N C E V.H-c v-e = o • v v H - ^ • ' V V n .c* c>-P Similarly Slhee V . £ = 0 wAcre Ho free charge ' W E = Let 1̂ E 2 be These are extensions of Laplace*s equation to cover regions in the vi c i n i t y of moving electric charges. They do not hold for regions containing any free charges. In a gas free charges are neg- l i g i b l e . - These equations, by the following transfor- mations ca be jMt in another form, scalar magnitudes of the vector E along the axes of a right handed coordinate system: also letij K be unit vectors along the axes. Then therefore we have for the x component Similar equations hold for y and z components; also We have then, six equations as f o l -for H x . lows a + * . tk £»• a t * h 3 - £-\ b t* " /uk L a, Ex f*K L OX* 4- + c J*. K C__ ^ K _ L - 3x v T 2*.£"* 4 I f ] V 2 2;^ Dz\J These are the general differential equations of an effect similar to a wave motion, propagated through the medium with a velocity ̂==— . In air or vacuum, the values of pi and K are both unity: in this case, the wave travels with velocity c, which i s the same as the Telocity of light. Plane Electromagnetic Waves. Consider the foregoing ecitations applied to a plane wave advancing along the x axis: take the electric intensity vector, then t* A"f doc*- and the solution of this equation i s This equation-states thet the instantaneous value of the electric force describes {sinusoidal variations both .with respect to time and with respect to space: that, in 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 velocity of propagation of the wave i s =~ . Now-in the case•of a plane wave moving in any direction, equation 28 can be written_ e *..E,si* .Z-a.fa.-^) .kr-e ^ where s- i s the distance measured along the line of propagation-of- the-wave-. --• Let ti be unit vector along this same line, then ^7 --• ifc •* J ̂ f *-to. and by eqn. 21a, 9Q Curl H = ̂ - H - n g x H - i Qt and therefore, h x *H = ± ® Similarly, by eqn. 22a, These are the wave equations, and can be solved by substituting for the operators -| and £ . By eqn. 29 46 a d e _ P / x z n i /— 2s " ~ and, similarly, _3_ _ Z-JIJ 7)t ~ T Substituting these results in eons. 30 and '61, and letting v T e l o c i t y of wave c The negative sign i s eliminated by changing the order of the cross product,. Similarly, It w i l l be easily seen from these equations that the vectors D,B and n are-all at .right-•angles.-- For ins- tance, dotting both sides with n in eqn, 32, H x n .n = zD.n = H. n — - ==.. O- since tlxn- « 0-always. - •Similarly B,r> is-always -zero. --This-shows that the vectors D and B are at right angles to n . Again. —, D.6 * H xn .nx E = Hxnxn. E =o c showing that D and B are at right angles to each other. The diagram, f i g 21, shows how the electric and magnetic vectors are related. B and B form a right handed system with n, and are in the wave front. Note that E i s not coincident with D unless the medium i s isotropic. h x E - ^ B dD 47e AO _Dt reckon Fig 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: ^ c u 9H also subtracting df Again W £ xH) ~ V.(EXH) + V./EXH) = - E.S7 x H +• H.V x E ?here£QF®.~ ±X ?fEl MhlK V , / £ X H ) . Integrating for the-whole-of the volume under con- sideration, and dividing by 4-n , we get = O and changing by Gauss' Theorem to surface integral fom ^ft*"-" This theorem i s really 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 in the direction perpendicular to the ware front, owing ' • l?igv 22. to E not being coincident with £ (fig 22.). .. The wave then sidesteps'through the medium (fig 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 letting ^ be unity, ^H.H = n Y E.H = -f O.E Hence---- H --.-K-jE - - Therefore energy per unit volume ' / ^ / r \ l j *") JL This shows that magnetic and electric energy per cm* are' equal. The Vector Potential. We have seen by eqn. 16, V. Bz0m Now let A be a vector such that Curl A = B - * Also 7̂.8 = V: which i s identically zero. 49. Again, VxB - V x A How V.^=0 ( since A i s a vector depending on J and Div 3 i s zero. Also V x H = 4 " J 5 and in free space H = B, Therefore, V x B =. - V . V A = ^ r> J Hence X7 V\Z ,4̂,.. ~ - 4. n J r * Next we draw an analogy -from Laplace's equation, where V. V^> ? -4-nf> t where -{-- volume density of el e c t r i c i t y and <p - potential = C^ifr . In this case, p 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 in a current carrying region is found from the current density J by exactly the same process that the elec- t r i c scalar potential, cj> , is found from the vol- ume density, >̂ t except that the integration in the former case, i s a vector integration, Whereas, in the latter case i t is a vee4©T integration. The magnetic f i e l d vector s then, is found from the vector potential by the relation, B = Curl A . The iSagnetic Field from the - Oscillator, Ve w i l l now try to find an expression for the magnitude of the f i e l d from the oscillator. The following treatment-is adapted from Dellinger"^ •The'radiation from an antenna is-usually' calculated by taking the electric and magnetic f i e l d equations for a Hersian doublet, modified according to the type of antenna, under consideration. In this case, we are primarily interested in the magnetic Induction f i e l d ; • - we-are • only-interested-in the rad- iation effect in so far as we wish to avoid the so- called • •" aerial -effect" • in our search coils. w"e w i l l therefore, calculate, the magnetic f i e l d direc- t l y from-the vector potential, The Instantaneous value of the-vector -pot- ential, -due-to the current density J in the vertical 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 (see f i g 24), A ~ since h i s small compared with d. Since we are dealing with a rapidly alter- nating current, we cannot assume that the electro- magnetic effects are propagated instantaneously: i t .a requires a time ~- for the effect to be transmitted c to the point P. How the current in the coil 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**.; 5 1 . i - - i * S/'n tot then in our expression for vector potential, we must take the current as i t was an instant of time % be- foreand 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 total vector potential at the point P i s d 1 d - -i. low by eqn,--85, ^ C u k | 4 . ^ J— • - • • since we are considering-a straight conductor, hav- ing no vector potential in any other plane than that containing the coil,-and-perpendicular- to the dir- ection of-d. The factor l/lO was introduced to convert to amperes.- -•• -- How differentiating A , partially with res- pect tod u T , H , - cos u(t-*) - f ^ " W - £ J and writing d for d-1. since 1 i s very small compared with d v . j (• , c lo cd tod7- If the c o i l contains H turns, H w i l l be increased IT times: also substituting effective values for I , but ^ = and ^ ( ^ i f 1 i s small compared with the wave length. The complete expression i s H -- - ±2* A/4 U + z / r A/A The f i r s t term represents the radiation f i e l d and the second, -the induction f i e l d e The former var- inversely with-the f i r s t power of d, while the latter varies inversely as d squared. Therefore the ind- uction f i e l d - f a l l s -off sapidly as the distance from the oscillator i s increased. If we equate the two fields,we find that, at a distance ~- , the two fie l d s are equal. Theoretically , this i s tha limiting distance from the-oscillator at which work may be -done. - In practice, the - search coils act as an aerial before this-distance i s reached, and pro- duce a signal loud-enough to drown the response from an orebody. At 50K.C., ̂= 6000 meters, d- ^ = C-~~ or approximately 3000 f t . Ie should limit our observations to a dis tance of 2500 f t . from the aer- i a l , and less i f possible. Four f u l l sized claims can thus be covered from one set up in this way, i f the oscillator i s located at a central point. For an oscillator having an anode dissipation of 25 watts with 500 volts on the plate, the c i r - ulating current in the co i l antenna would be about 4© ra.amps. If the areal had h=6 f t , I = 6ft and 1 = 10 turns, then substituting these values in eqn. 37, we 53 » find that the induction f i e l d at 50 K . C . would be given by H = ^—r x / o ~ ^ g«.wss efx- = /.5"2 x /o 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, in general, be much smaller. Since the f i e l d strength i s directly proportional to the current in the-antenna, i t i s important to make this' current as lagge as possible: for this 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 current low. - 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 Electr 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 1 has indicated a way in which the problem of wave propagation through a medium with conduction may be tackled. The conduction current must be included in Man?.'ells equation for the curl of H. (1) J.H.Jeans "Electricity And Magnetism" Ch 18 In the vector notation The medium has conduction currents and displacement currents. Now l e t g - £ 0 £ ( c ' and.•..!..._ .__/__ £>„g Substitute in above eqn, c L <?f- ^ w Df- J This i s the same equation as for space, where the dielectric constant k , i s replaced hy a new con- stant K.r K- . - The wave equations may be worked out in. this manner, and complex expressions obtained for wave slowness.- In this way, the attenuation and phase change can be calculated theoretically. The following treatment i s due to Zenneck"^ but has- been altered to conform to the right handed axes of modern convention. It affords a useful picture of what happens to a wave travelling over a conducting medium./' In f i g 25, let the direction of propagation be the x axis , which i s taken in the surface of the earth. The z axis i s positive in the upward dir- 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 t- H/ellCu. U'utjS erne Lei'ra-flache und < fi>--e BezielinMj z.uh rfr<i<.t 'bcm Tel*1t-«pk,'-e " Ann^U* Jer PAys.c vol 2i p Jo7 ffig- 25- • - Fig 26 Let 3£=dielectric constant-in e.s.u. JA. x magnetic-permeability in e.m.u. f>- r e s i s t i v i t y in ohms/cm.cube. s «• specific conductivity = e*.w. f = frequency = — c = 3 / i p ' % wave velocity A-wave-length • - q = wave slowness. Again l e t the axial components of electric inten- sity be X-Y-Z. Referring to f i g 25, i t i s evi- dent that, if-the magnetic-vector H be considered as along the Y axis, i t will-have no component along the X and Z axes. Similarly, the electric 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 dxxdz in f i g 26,. we find that there is an ind- uced 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 electric intensity. Total current i s therefore -^s-t-^Kj ~z. „ Taking the line integral of K round this area and-"by eqn. 19, this i s egual th 4^ times the cur- rent enclosed by this area. Therefore Y ^ H 7 - ^ • <s> How l e t H vary einusoidally with space and time H - A <? M"1"***)- and substituting in eqn. 38. ~- ^.[&±.i-M^-=.±vh. Similarly taking the area Ix dz . . . -- - Next take the area dxxds, By eqn. 22, we have Curl t - c 3 f In this case the magnitudes of the scalar components are X,Y and Z. therefore Curl i J H d D d dx X T --Z- 57. and , since there i s no component along the Y axis r, i F - '\[d- + HI - _ i - ^ The same result can he reached another way r -, £". = Vefac + f- 2 g Acjclx - (A- - ^ - [-2ct*J 9(PC dT. fdZ , 3V Since E and H vary sinusoidally, 7)2 r * r c- We have now three equations , numbers 39, 40 and41f between X, Z and H. Elirainesting X and Z from these Sz H= € is a solution of this equation, where Asva complete solution of the three equations, 4/7 Y i8z J- 4 /7̂S ̂ to f<] _ - Mext appljr-these- equations to a second parall- elopiped 1 x dx * &z, in the air above the interface Fig 27. The same equations hold on either side of the inter- face, except that s and 2c are different: also, the constants B and A are different. Let values in 06. air be s k A B and in dielectric be s'k'A'B' Then by eqn 43, We next insert the boundary conditions at the inter- face, -where x and a are zero and t Is zero. Subs- tituting in eqn. 44, we find that A = A * . Again, when X = X, at the inter-face B, . = e _ & Writing T and • T, for the denominators in eqn. 48, and J> for 4 Z L ^ , _B _ a T " X T > T Again from eqns. 45 and 46 — 2 " % ~ / T; ' " / s, +z w IT, In the case of air s Is zero z. (/ (/ 7 7 7 ^ Now l e t TA* — t h e n Hence B ' - i P T - - 8 , ' - ^ ^ Thus X and Z d i f f e r in phase by an angle <p , where M ' TNQ electric i n t e n s i t y E i s the resultant of these two components,and traces out an ©lli$ggu; . the .-mâ orVê ^ /•Thi magnetic vector It, being p a r a l l e l to the interface, is-.©till' plane ;poli»ize.$,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 • <.••• • - ^::'; •-••;'• ' " "i -';V • " . - ''/.'••'. ; '-:fig 28.'- • :-' " -•• V/e have seen that the wave front of the p r i - m a r y f i e l d i s distorted, owing to the e l e c t r i c a l properties of the earth over which the wave i s trav- e l l i n g . The distortion i s shown diagraramatically in f i g 28. There in; a discontinuity at the earth*s surface. The expression,eqn. '62 d i f f e r o from 60. that obtained by Zenneck in that the sign of the ex- ponent i s changed: this i s because the Z axis was taken upwards to-conform to convention. The principle object of Zenneok's work on this subject was to find the loss in amplitude of a radio wave, travelling over a conducting medium. He found that, where the wave travels over a good conductor, such as sea water, there i s l i t t l e lose- in energy due to eddy currents below the interface. If , however, the medium conducts but poorly, as in rock and s o i l , there is considerable penetration and consequent loss in energy. This phase of the argument is not of interest-in geophysical surveying owing to the short-distances between the oscillator and the search c o i l . We may, however, proceed to some interesting conclusions regarding the penetra- tion of waves-into the- earth, Referring to eqn. 4-4 . _ H A € 6 Since the Z axis is positive upwards, i t is 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. Accordingly, let e 61. , :,'..-...= h 0 e e Hence 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 find a complex expression for the wave slowness q in the wave front, By eqn. 50 JJOW l e t ̂ = and•••5">*-/uj-if, .•..=••e'lfĉ fitswhere t**ic^ -j-'. Therefore substituting in eqn. 53 • where </>, ^ and ^ Again, since ^n/r = f for air and ̂ = / for air and rock, also since ^ = = = r — - — where 4 = 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 quartz diorite). Let ^>= /o ohms per ca. cube, K'£n for rock• and ^ = ̂ for a i r . Slso l e t the frequency be •30,0000 cycles. We then calculate the following quantities & s> 4" (vx">6) o r 3* /0'° \//*> 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 resi 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 result may be said to agree with practice. The we- weakness of a l l theoretical methodsof treatment of this problem l i e s in the fact that the earth is . 63* . taken as being a homogeneous dielectric, having con- ductivity, which i s farvfrom being the case. Eve and Keys 1 give the formula H = H D € v f for f i e l d strength at a depth d. This formula results from following an argument similar to that of Steinmetz in his treatment of the distribution of alternating flux in conductors 2 It does not appear to be correct in this instance as i t ignores the dielectric properties of the medium. If this for- mula is applied to the above example, the depth at which H =~ H 6 i s found to be 492 meters, a considerably different result. The shove formula was meant to apply to metallic conduction and not to wave prop- agation through rock. Again, i t i s found in 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. - in the course of It's work in the Moonta di s t r i c t of South Australia^ met with highly- conducting overburden, saturated with saline water, which rendered attempts at elec- t r i c a l prospecting abortive. The re s i s t i v i t y of (1) Eve and Keys "Applied Geophysics" Camb.Univ Pr (?) steinmetz*Transieht Phenomena and Oscillations" i l ) 3) 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 sur- face by passing through 1.54 meters of this formation Furthermore, the eddycurrents induced in this screen- ing layer of overburden, WEES found to give a uni- form indication, similar to ore, over the whole ter- ritory. The change in phase due to the overburden. We w i l l now proceed to apply Zenneck? s reason- ing to examine the change in 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 10 5 olmis/cm. cube and dielectric con- stant of 3 . Then <? • Sappose we wish to find the change in 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' behind that of H at the surface. This would be repeated when the return wave comes back to the surface. 65. It m s mentioned above that the a l t e r n a t i n g flux p r o d u c e d by the oscillator Is r a p i d l y reduced as i t penetrates into the ore deposit, which may be treated as a e o l i d conductor^. Steinmets e l v e s 1 The result i s that the d e p t h o f penetration of f l u x into s u c h material a s p y r i t e 8 i s only a b o u t 1 cm at SO K,-G, 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, A g a i n , the current d i s t r i b u t i o n in t h e - d e p o s i t i s dependent on the f r e q u e n c y due to " s k i n e f f e c t * , The theory i s well known and w i l l not he given her©, The effective impedance, of a. conduct or i e - Where x= d . c . r e s i s t a n c e . 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 i s confined to a small skin on the outside of the con- ductor. ]?or conductors of large dimensions such as orebodies, and for high frequencies, the current only penetrates a fraction of a centimeter. In this case ft 362. ei 66,- the effective resistance i s proportional to the dia- mc-ter of the conductor: therefore narrow veins pro- vide better indications than Passive bodies of greater total volume. Again, from eqn, 58, there Is an effective reactance equal to the effective cesistance: i t would seem, therefore t that the phase angle due to the passage of current in the conductor, i s always 45°and furthermore, that i t i s impossible for an orebody to show a capacitative reactance on this account. Experimental work in the f i e l d should verify or disprove chis deduction. If this i s correct, i t would seem that a l l the discussions on the subject of reactance of deposits in the pub- lished art i c 1 e s, ar e - f rui 11 e s s, Summary of Phase Relationships,• . . . If W/^iWtot is 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 imp- edance of the deposit, while cj>^_ ie due to the trans- mission of the waves through the overburden. For the same orebody and setup of apparatus, MM f, - "JT •=• I for high frequencies, therefore d>. - zf =4*°+ Again, (j>z oc d 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 practical 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 osc- i l l a t o r to.bring the priaarj r and secondary fields into phase. Again this deduction must be checked in • the f i e l d . The whole question of the phase of the sec- ondary f i e l d i s very complicated and depends on many unknown factors. There i s nothing In the pub- lished articles on geophysical prospecting which indicates that an attempt has been made to <5olve i t , possibly because those, who hare practical exper- ience, consider that i t cannot bo solved. The anal- vsis has onlv been attempted here in order to show O" *r *~ the nature of the problem and-to get a better under- standing 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 for the construction and design of apparatus to he used in . 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, in the laboratory. Search Coils. It was originally Intended to take- the measurements through the whole frequency band from 500 cycles to 50 K.G. However, in the design'of the model search coils, no allowance was made for the distributed capacitance in the type of winding adopted, since the effect of this factor could only be ascertained through experience; in 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 in number and had diameters, l l - | n , 12", 12£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 direction finding c o i l -and also had 600 turns. The 9 i <p 69. inductances, .calculated by Kagaoka f o r m u l a 1 , were ap- proximately -200 to 240 m i l l i h e n r i e s . The size of the wire was #34, enamelled. The coils -were placed i n a wooden cradle , shaped BO that they could be t u •turned .through any angle, Selector Panel. The wiring diagram i s shown i n the f i g u r e . The panel i t s e l f was ebonite, w i t h brass s e l e c t o r switches and contacts. 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 conveniently made from a 4-way telephone switch, taken from an old telephone switchboard. I t was found to be more convenient to mount the panel separately, r a t h e r than i n s i d e the c o i l s , although t h i s arrangement n e c e s s i t a t e d the use of long leads from the tappings to the panel, a f a c t o r which was l a t e r found to introduce e r r o r s . The Test 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 t e s t field-was produced-hy two la r g e loops, -9 fee t square, having 10•turns-each; These were-wound- on a rough lumber framework , erected i n the l a b o r a t o r y . The current i n the loops was supplied-by- various osc- i l l a t o r s . 3?or audio frequencies, a Cambridge Ins- trument Co source, c a l i b r a t e d on a mutual inductance frequency bridge , was the source 'of current. Por h i g h e r frequencies, up to 20 K.C.,a dynatron osc- i l l a t o r , w i t h Campbell v a r i a b l e standard inductanee and-Tinling standard air condenser i n the o s c i l l a t o r y arm of the c i r c u i t , was used. -Above 20 K.C., a 70a a Hartley type oscillator,from the electrostatic sweep of a General Electric cathode ray oscillograph was employed: this instrument was calibrated at the factory. The current in the two test f i e l d coils was varied in phase by a condenser in the horizontal c o i l circuit; the circuit i s shown in f i g 29. When f i r s t operated, the electrostatic coupling -be- tween the test f i e l d coils and the search coils, 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 coils with aluminium f o i l and connecting the latter to earth. The shielding effect given in this-way, was not complete owing to the d i f f i c u l t y of shielding the leads to the var- ious instruments and -the coils of the oscillators. 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 c o i l 1.365 mH and 17.1-2 ohms. The Detector-Amplifier Unit. This unit was built 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 circuit^ (1) Radio Engineer's Handbook, p 161 71 „ The step up ratio 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 sufficiently sensitive voltmeter, for the output stage, from apparatus at hand in the lab- oratory. 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 det- ector 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 rebuilt to be a three tube detector amplifier unit with headphones. Trans former audio coupling was used. The tubes were W.E.lOll? telephone-repeater tubes, with filament voltage of 4 volts, and 6 volts negative grid bias* It worked well at audio frequencies and would prob- ably have been satisfactory at higher frequencies, i f measurements had been possible at these frequencies. The general scheme of connections is shown in f i g 29. 72, The Test Magnetic ffleld. Let Acos u>r ce f i e l d due to vertical loop !Y i " horizontal loop, — • j f i g 30 Resolving X - A cos ^ r cos to r Y Eliminate <-o I' X /i 8 a 60s tb -f- 6 Squaring and rearranging v.* 1 7- x Y 6' /i .e. . . 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 \ (A* H + 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 proportionality £ i s common voltage applied to both loops. R,R' are t o t a l resistances I>„LX are inductances G i s capacity added to horizontal loop. By making the capacitative reactance in horiz- ontal loop circuit large compared v/ithioL, and «oL2, •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 practically QOl The terms R , Z w lC and lA^may he neglected. Also the terra J^-J i s zero i f 4> = so°. The equation A B of the ellipse i s then .4.*- e1- and the majog axis i s either'horizontal or vertical, according as A or B i s greatest. If 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 uith calculated and observed values of ^ and £ .. The smallnees of the terms L, <Si-, and R5 shows the justification for neg- lecting them. The angle © was measured with an Ahney Hand lev e l , placed on the coils* The results show a discrepancy with calculated values, at a l l frequencies. The balance setting was very broad at the lover freq- uencies and the results had.:-to be averaged in these cases. This somewhat dissappointing result can be directly traced to the following causes. 74. ) Braadness of Balance Setting. The note in the headphones couid never really 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 coils and the search coils caused a continuous signal to be heard in 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 all.leads, nor to shield the output transformer of the o s c i l - lator or buffer amplifier. 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 in the magnetic f i e l d , and so h.ad an eraf in- duced in 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 in - tuning the fixed coil accurately. The coils were a l l wound with too many turns of wire; the signal was extremely loud in 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. It was discovered at the end of the experiment, that the detector would give a small note in the head- phones, even i f unconnected with the coils. (2) Errors JLn the Angle of Inclination of the <Axes. In a l l probability, this was caused by dis- tortion of the f i e l d in the loop, due to lagge masses of iron, in the form of electrical machinery, in the laboratory. This machinery was a l l situated to the north of the apparatus, since the latter was placed next to the south wall of the building. The dis- crepancy was about the same a t . a l l 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 in the transformer vault, and possibly-, to a slight leakage-between the a.o.-and d.c. circuits of the laboratory , since the latter was used for B battery voltage for amplifier and oscillator. Work at High Frequency. An attempt was made to raise the frequency to 20- 39 K.C., and to make measurements in this band. The oscillator from the cathode ray oscillograph was used for this purpose; i t was connected to the loops through a line from the meter room at the other end of the laboratory. 76, Various systems were tried to obtain an aud- ible note. F i r s t , autodyne detection, with, tuned plate and grid coils in the detector stage.coupled to the radio frequency transformer in the preceding stage, was tried. This was abandoned owing to the d i f f i c u l t y of constructing a suitable radio frequency transformer for such low freouenciee. Second, the vacuum tube voltmeter was used, and later, abandoned for reasons given above. Finally, buzzer mod- ulation in the grid circuit of the oscillator gave an audible note in the. phones* Measurements in this frequency band failed for two reasons: .first, owing to capacity coupling between the coils , as outlined above. This was especially bad because of the leng&h of line (about) 20 yards), from the oscillator and the test loops, and the high 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 coil Thus, while measurements were not successful in this hand, the reasons are not far to seek: therefore, we oannot assume that the method wi l l not be successful in the f i e l d . While the fields to be measured in the f i e l d w i l l tend to be smaller than in the laboratory, given correct design of the coils, 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 app- aratus; i s sound, but that careiul design i s essential. (2) This method of testing the apparatus is 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 in the f i e l d . ....... (3) A considerable amount of information has been gained about the design of the search coils. A com- paratively few turns of wire, say 200, w i l l be used on the next outfit. 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 in- creased*, -this, however, should not be insurmount- able , - Again,,-the-leads fron the tappings and-coils to the selector panel w i l l be as short•as - possible.• the latter w i l l be mounted inside the co i l assembly, as also w i l l be the tuning condenser. (4) Radio frequency amplification, in the detector set, i s not suitable for the comparatively low frequ- encies employed. Autodyne detection, therefore, can- not be used, owing to instability when tuning the search coils. 3?or this reason , i t w i l l be nec- essary to modulate the transmitter. Simple chopper or buzzer modulation i n the g r i d c i r c u i t w i l l be sat- i s f a c t o r y * An e x t r a stage of a m p l i f i c a t i o n can be added i f necessary. (5) Very c a r e f u l c o n t r o l of the frequency i s nec- essaryas 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 c a l i b - r a t e d w i t h great care against a- -standard wayemeter. • There should, be f o u r • settings' to give say .20.,30/4.0, and 50 E.G. The search c o i l should have condensers • corresponding to these frequencies,-which can be cut i n by a switch on the s e l e c t o r panel, according to which frequency .is being used. . This tuning should be done permantly In the l a b o r a t o r y , since 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. Bieler, Can. Min. Bull. #193 PS38 C.I.M.K.1928. ££ake and ¥ilmotte»0n the Daylight Transmission Char- acteristics of Horizontally and Vertically Polarized Waves from Airplanes? Proc.I.R.E. Vol 17 1929. Bellinger,J.H. "Radiation from an Antenna? U.S. Bur.Stds. Vol 15, 1919-20. Il® and Keys, "Applied Geophysics* Cambridge Univer- sity-Press, 1929, 3&S and Keys . Bature Vol 124 p 178e TT A.I.M.E. Teoli. Publ. #316 1930. Edge.A.B. Report of the Imperial Geophysical Exper- imental Surrey. Cambridge Univ. Press, 1931. Glob and Wilson. *Veotor Analysis'*. JeanstJ..B. "Mathematical-Theory of Elect r i c i t y and 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 oscillation Mcgraw-Hill 1920 Sundberg. "Geophysical Prospecting? A.I,E.S. 1929, Thompson, J.J. ^Electricity and MagnetismS CArah. Univ. Press, 1903. • Fleming. J.A^ '"The Principles of l l e G t r i c Wave Telegraphy and Telephony* Longmans. 1916. Lahee„F.K, "Field Geology* Hcgraw-Hill 1931, Zennec&T. "Tiber die • Portpflanzung ebener electro- magnet 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 in the book by Fleming see above.
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