Analytical interpretation of fixed source electromagnetic prospecting data

ANALYTICAL INTERPRETATION

OF FIXED SOURCE

ELECTROMAGNETIC PROSPECTING DATA

PROEFSCHRIFT

TER VERKRUGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAP-PEN AAN DE TECHNISCHE HOGESCHOOL TE DELFT OP GEZAG VAN DE RECTOR MAGNIFICUS IR. H. j. DE WIJS, HOOG-LERAAR IN DE AFDELING DER MIjNBOUW-KUNDE, VOOR EEN COMMISSIE UIT DE SENAAT TE VERDEDIGEN OP WOENSDAG 28 OKTOBER 1964 DES NAMIDDAGS TE 2 UUR

DOOR

ROBBERT

A.

BOSSCHART

geboren te Alblasserdam

1

Analytical interpretation of fixed source

electromagnetic prospecting data

DIT PROEFSCHRIFT IS GOEDGEKEURD DOOR DE PROMOTOR PROF. O. KOEFOED

TABLE OF CONTENTS

Samenvatting (Dutch summary) Introduction . Chapter 1 Chapter 2 A B Chapter 3 A B Chapter 4 A B C Chapter 5 A B C D Chapter 6 A B Chapter 7 Chapter 8 References

The TuraD1 D1ethod . Interpretation

Theoretical considerations Practical requirements. . Model experÏJnents . .' Dimensional considerations.

Model arrangements and data reductions

The response of a finite tabular conductor in the field of a fixed horizontal transll1Îtting loop

Changing geometrical relations . I Varia ti on of the strike

2 Varia ti on ofthe dip . . . . 3 Varia ti on of the depth 4 Position of the primary loop. Varying characteristics of the conductor

I Variation of the thickness. . 2 Variation of the resistivity . . 3 Variation of the permeability Varying dimensional relations

I Simultaneous variation of strike length and height 2 Independent variation of leng th and height . . 3 Variation of transmitting loop size . . . . . . . 4 Variation of the lateral position of the traverse. .

Application of the scale D10del results to the interpretation of field data. . . . .

Determination of the response parameter. . . . I Amplitude diagram for conductors of determinate size . 2 General response diagram for "thin" conductors . . . 3 "Thick" conductors and the relation between

e

and d. Permeability distortion . . . .

Determination of the geometrical relations I Strike

2 Dip . . . . 3 Depth . . . . Limits of applicability .

Strenght of the secondary field Effective depth of investigation . . Some remarks on field procedure .

ExaD1ples of the interpretation of field data I Turam survey in Strathy Township

2 Turam survey A in Isle'Dieu Township . 3 Turam survey B in Isle'Dieu Township 4 Turam survey in Comporté Township 5 Turam survey on the Murray Group SUD1D1ary and conclusions

5 lI 11 14 18 18 19 21 21 22 22 24 26 30 31 31 37 48 40 59 53 54 57 58 58 60 62 65 67 67 67 68 70 74 74 77 80 80 83 85 87 92 96 100 v

SAMENVATTING (DUTCH SUMMARY)

Systematische elektromagnetische ertsopsporing vindt in toenemende mate plaats in gebieden waar de kristallijnen formaties over grote uitgestrektheden

aan geologische waarneming zijn onttrokken door een bedekking van recente formaties of door verweringslagen.

Met het schaarser worden van directe geologische aanknopingspunten

neemt het belang van een quantitatieve interpretatie van de geofysische meet-resultaten toe. In veel gevallen zullen de langs deze weg bepaalde fysische

eigen-schappen van de ondergrond de enige basis vormen voor geologische

con-clusies.

Elektromagnetische methoden kunnen worden verdeeld in twee groepen, waarvan de eerste gekenmerkt wordt door een zich gelijktijdig en in vaste

configuratie voortbewegende bron en ontvanger, de tweede door de combi-natie van een stationaire bron en een bewegende ontvanger. Aan de quantita-tieve interpretatie van de eerste groep, de zgn. "Moving Source" methoden,

waartoe onder meer de meeste luchtprospectie-methoden behoren, is gedurende

de laatste jaren zeer veel aandacht gewijd.

Het voorliggende onderzoek heeft voornamelijk tot doel een analytisch

quantitatief interpretatiesysteem te vormen voor methoden van de tweede

groep, de zgn. "Fixed Source" methoden, en in het bijzonder voor de Turam-methode, welke de meest toegepaste van deze groep is.

Wanneer men vorm en afmetingen van stroomgeleidende ertsafzettingen

beschouwt, blijkt dat het grote merendeel lens- of plaatvormige lichamen zijn met strekkingslengten die variëren tussen 100 m en 1000 m, en die, voor zover is vastgesteld, meestal een diepgang hebben van dezelfde grootte orde. Der-gelijke lichamen doen zich, blijkens ons onderzoek, in de gebruikelijke "Fixed

Source" meetconfiguraties voor als eindige geleiders, waarvan het

storings-veld in het algemeen niet langs theoretische weg kan worden bepaald. Het onderzoek is daarom uitgevoerd met behulp van schaalmodellen.

Om een zo groot mogelijke analogie met de natuurlijke condities te bereiken, zijn de experimenten uitgevoerd met primaire velden van in de ertsprospectie

gebruikelijke frequenties en met plaatvormige modellen waarvan dikte en

ge-leidingsvermogen variëren, in tegenstelling tot de meestal toegepaste proce-dure, waarbij alleen de frequentie wordt gevarieerd.

De verschillende factoren welke de veldstoring bepalen, zijn verdeeld in drie

groepen, waarvan de eerste de geometrische factoren, de tweede de frequentie

alsmede weerstand en dikte van de geleider, en de derde de groep dimensionale verhoudingen omvat.

amplituden-verhouding van de reële en imaginaire componenten van de veld storing is

afzonderlijk onderzocht. Uit dit onderzoek blijkt, dat:

1. geometrische factoren de vorm van de storing, doch niet de

amplituden-verhouding beïnvloeden;

2. weerstand, dikte en frequentie de amplitudenverhouding beïnvloeden, doch niet d.e fundamentele vorm van de storing;

3. de dimensionele verhoudingen een belangrijke invloed hebben op de

abso-lute, zowel als de relatieve waarde van de amplituden.

Uit het onderzoek van de dimensionele verhoudingen blijkt dat hier een be-langrijk verschil bestaat tussen "Fixed Source" en "Moving Source" methoden.

In de laatste meetconfiguratie doen zich typische ertsgeleiders voornamelijk als

oneindige lichamen voor en dientengevolge hebben variaties in de strekkings-lengte of diepgang geen invloed op het karakter van de veldstoring.

Verder bevestigt en definieert het onderzoek de tweeduidigheid van de

storingsparameter A

=

l03

_e

/vd

(e

=

weerstand in ohmcm, d

=

dikte in m, v = frequentie) bij variatie van de geleiderdikte ofvan de frequentie, waaruit

volgt dat conclusies gebaseerd op frequentievariatie slechts in beperkte mate

van toepassing zijn op de resultaten van normale veldmetingen.

Andere belangrijke aspecten die zijn onderzocht betreffen de invloed van de magnetische permeabiliteit op de elektromagnetische veldstoring, het

effec-tieve dieptebereik van de Turam-methode en de werkwijze in de praktijk. Uit de resultaten van het modelonderzoek is een interpretatiesysteem

samen-gesteld, door middel waarvan de voor ertsopsporing belangrijkste gegevens quantitatief kunnen worden afgeleid uit de veldstoring. De praktische

toe-passing van dit systeem is gedemonstreerd aan de hand van een aantal

praktijk-voorbeelden welke een zo groot mogelijke variëteit van condities omvatten,

en waarbij de interpretatie is vergeleken met de resultaten van andere

INTRODUCTION

The fundamental principles of geo-electrical exploration methods are essentially

the same as those underlying magnetic, gravimetric and seismic methods, i.e.

the effect of the heterogeneous physical properties of the subsurface on applied

fields of force are investigated from the surface and the obtained results trans-lated into probable geologic structure. Where they notably differ, as a group, is in the much greater variety of procedures that can be followed in utilizing or applying fields offorce and in investigating the resulting distribution.

Natural fields, caused by telluric currents or spontaneous polarisation cur-rents, can be used as primary source, or the field can be created artifieially by means of direct, alternating or pulsed current. Artificial fields can be applied conductively, through eleetrödes, or inductively, by means of coils or large wire loops. Finally, different parameters of the eleetric or electromagnetic fields e.g. intensity, direction and velocity, or phenomena such as overvoltage

effects may be measured.

On the basis of the many possible combinations and permutations of

en-ergization and investigation procedures a prodigious number of prospecting

techniques have been coneeived, as witness the deseriptions th at ean be found in the litterature and in numerous patents [20, 21 J. However, in actual

practice only a relatively limited number of methods have proved adequate

to obtain useful information with sufficient speed and economy of operation to meet the requirements of mineral exploration. For the purpose of general orientation some of the techniques most commonly used in mining exploration

are shown in tabel 1.

Beeause of the great diversity any classification of geo-electrical methods is bound to be unsatisfactory from some point ofview. Even the generally adopted division in "Galvanic" (or Conductive) and "Inductive" methods, based on the type of energization, does not apply rigidly. Usually Inductive methods are further, classified according to the type of energizing source and receiving sys-tems employed, and the quantities measured. Actually these charaeteristics are, from the viewpoint of classifieation, relatively unessential, sinee they are subordinate to the geometrie transmitter-target-reeeiver relationship. Moving the transmitter and receiver in

a

fixed configuration over the target area gives rise to fundamentally different results than keeping the relation between the souree and the target area fixed and moving the receiver alone. The division in "Moving Source" and "Fixed Source" methods [12] is based on these

dif-Table 1 Geo-electrical ore prospecting Dlethods

Potential ElectroDlagnetic Transient Induced

polari-Dlethods Dlethods Dlethods zation Dlethods

Electrical field Magnetic field Decay of electrical Overvoitage effect

investigated investigated or magnetic field investigated

Source investigated

Natural

I

Spontaneous pola- Afmag [46]

I

rization [20,21,27]

Fixed Equipotential Turam (12,13, Induced

method 16,31,41,48] polarization

[20,21,35] Radio reference Transient type

method [12] "Gradient array"

Compensator [32,45]

method [12,35, 36,49]

Semi- Resistivity Verticalloop Induced

fixed "Drilling" [20, 21] E.M. (Dip Angle) polarization

[21,45,47] Transient &

Potential drop Frequency domain

ratio, T.T., [26,32,45]

Racom [15, 20,

21, 35]

Moving Resistivity Slingram (loop- Input pulse

"Trenching" frame) & system [2] [15,20,21] derived methods, Airborne &

ground-and air- ground borne [17, 18,27,

29,41,49,51] Rotary field method [18,19,39]

ferences and particularly helpful in eXplaining discrepancies between field data obtained with some of the most commonly used inductive methods. It

has therefore been adhered to in this context.

Moving source methods received their biggest impetus with the advent of airborne geophysics, both in direct application from the air and in subsequent ground follow-up, and have therefore in recent years been the object of inten-sive research. Fixed source methods have not e~oyed as much general interest and comparatively little has been published concerning their use and inter-pretation.

The present study was undertaken for immediate and practical purposes. The present trend to use electrical methods to investigate large, drift covered

. - - - -- - -- -- - - -- - -

-and geologically virtually blind are as has greatly aggravated the plight of the geophysical interpreter. Many subsurface features other than ore deposits may conduct electricity and cause distortion in applied fields. As aresult the average electromagnetic survey will yield anomalies far in excess of the number th at can be economically tested by means of direct methodsl such as diamond drilling or trenching. The responsibility for selecting one or more targets for further examination of ten rests wholly with the geophysicist and considering the usu al remoteness and inaccessibility ofthe ground and the interests at stake, such decisions de mand sound justification. Occasions where the interpre-tation can be comfortably extended, in a qualitative way, from known con-ditions (old mine works, trenches, mineralised outcrops etc.) into the un-known, have become rare indeed and it is increasingly necessary to assess conductors purelyon their specific characteristics and put the interpretation on a quantitative basis.

This necessity was, of course, evident at once in air borne electromagnetic prospecting and has been a major reason for the increased interest in moving source interpretation.

It might seem th at many of the results obtained in these recent studies could be applied in the interpretation of fixed source data as well. There are, how-ever, many fundamental differences. In moving source systems the distance, and therewith the free space coupling between source and conductor is variabie, giving rise to a varia bIe secondary current distribution and anomalies of a relatively complicated nature. On the other hand will identical conductors cause identical anomalies, because of the constant coupling between source and receiver. In fixed source systems the distance and the free space coupling are variabie between source and receiver, and constant between source and conductors. As aresult the secondary current distribution is stabie and the anomalies are of a less complicated nature, although some of their charact-eristics are dependent upon their location in the primary field. Further display the two systems, as a result of the difference in dimensional relations between source, receiver and conductor, a noticeably different sensitivity to conductor size variations.

Obviously, although many general conclusions will hold independent of the configuration, moving source interpretation can not be arbitrarily transposed to fixed source data.

The first object of the present work was to establish a quantitative inter-pretation system for the Turam method, the most widely used of the fixed source prospecting systems. The relevant phenomena to study for this purpose concern the secondary field and since the manner in which its components are being measured from the surface is a matter of convenience, the investigation has been given general applicability by expressing the results in complex 3

components (in-phase and out-of-phase or real and imaginary components)

besides the quantities measured by the Turam compensator. The former can

be readily transformed, if necessary, into the particular quantities measured by other methods using comparable energization with a different receiving procedure.

CHAPTER 1

THE TU RAM METHOD

Vnder average conditions, where the subsurface may be composed of materia1s of widely varying conductivity and configuration, the induced secondary fields have the same frequency as the primary field, but will generally differ in in-tensity, direction and phase, and the resulting field will be elliptically po1ar-ized [13]. A complete determination of the field ellipse [24, 35] would involve measuring field direction, amplitude and phase in two perpendicular planes,

which is time consuming and not of ten attempted in ore prospecting. Hence most methods aim at obtaining information of maximum diagnostic value from partial determinations of the field, some leaving more complete deter-minations to subsequent detailed surveys.

Most present moving- and fixed souree compensation methods were derived from the old (1925) Swedisch "Compensator Method" [12, 17, 35, 49], which

used a fixed transmitting source in the form of a long grounded cable or a

large rectangular or circular loop, and measured with a single receiving coil

the complex values of the vertical or the horizontal field relative to a reference

signal carried by cable from the transmitting source.

,SOURCE/ / . / / / '

----

. / . / . / . / . / . / /

---

. / . / / ~ ~---- . / . / / / '

---

~ . / / '

----

-

. / . / / ' ____ - TURA':/ . / S/ COMPENSATOR fn}2>

\)&

/

/,

or

sf,/ . / f,~

~~~

) /

Fig. I The Turam method. General layout

The Slingram or Loop-Frame method is a modification whereby the trans-mitting source has been made portable and is moved at a constant separation

with the receiving coil. The Turam method, developed in 1932 by E. H.

HED-STRÖM [16], employs the same type of energizing layout (fig. 1 and 2), but

measures the field strength ratio and the phase difference in two successive observation points by means of two receiving coils, th us eliminating the need for the reference signal and connection cabie.

The measured field streng th ratios are normalized through division by the

calculated free space ratios of the primary field. The phase differences are a

secondary phenomenon, generally independent of the primary field and

rarely need correction. The results are usually presented in the form of curves

PLAN ~ ~

'"

...,.

lil ~ ~ 1\ _<() ~

...

:!!

'"

...

ti > , Rt!DUC~D F. $. RATIO (' Fig. 2 Schema tic presentation of primary and secondary fields

I I

- - -

-showing, on some convenient scale, the values of the reduced field strength ratio and the phase difference at the midpoint between the two receiving coils. The presence of a subsurface conductor will be indicated by abnormal field strength ratios and phase differences. A typical anomaly over a secondary current will show a correspondance between high values of the field strength ratio and negative phase differences (fig. 2 and 3). The depth of burial of the current axis is reflected in the shape of the anomaly and the ratio of the maximum amplitudes offield strength and phase is a measure for the

conduct-ivity of the disturbing body, in the sense that good conductors will mainly

affect the field streng th and to alesser degree the phase displacement, whereas

poor conductors may cause considerable phase shifting without appreciably affecting the field strength.

In a non-conducting medium, where free space considerations apply, identical conductors wilt cause identical deflections in the ratio and phase curves, independent of their distance from the source, provided the direction of the primary flux is the same. This can be seen from the following consid-erations:

If we caU the primary field in two consecutive observation points Fn and

F

Fn+l, the normal ratio is _ n_. In the absence of secondary fields the observed

. . Fn+1 • (ObServed ratio)

ratlO IS the same, and the reduced ratlO l ' is 1,00. When a

sec-norma ratlO

. . Fn+in

ondary field occurs the observed ratlO can be wntten as and the

F

₊

+' F Fn+l +in+l d d · n Jn n re uce ratlO as F +' : F- or n+l +Jn+l n+l in+l

+

1 Fn+l . . . • . . . (1)

For an identical conductor m a different location the reduced ratio m a similar set of observation points mand

m+

1 is

im+l

+

1

Fm+l

. . . • . . . (2)

If the direction of the primary flux is the same, then

in im and in+l _ !m+l hence (1) and (2) are equal.

...

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lIOOm 3'0 3eo • • 0 "20 FIELD 08SE"VATlOHS F.$.IfATIO I I'HASE DIFF..

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I

~OUCED RATIO RATIO

...

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u,.

IJ? 5

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IN -I. OF RES1! j'H .,. OF FIRST on I'OINTS aBS. POIHT

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-2.5 "".5 - t.tI >. = 3.'

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+.:-- -T- --f(-:-~~, ---,

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I ... • • •

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----".-~""",- ,~

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tsto @

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o

CD , 1 h ., 1 . , L_.l. __ .=~=.51m a= ~ =21.!:5m 2

®

(9 a-n=3'm _-

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.=~=21m -20

Fig. 3 Data reduction and calculation of complex field components +20

VECTOR DIAGRAM '20

..

;;

..

...

..

40 ...

..

.0

~

\

40 '0 20 I'HASE AHGLE '0 +'0

-'0

-20

The phase shift is a secondary phenomenon, independent of the di stance

from the source, and for identical conductors proportional to the strength of

the secondary field. The phase difference curve of identical conductors is

therefore also identical.

These conclusions have later been verified in fig. 36. Anomalies can th

ere-fore compared directly, independent of their location, except close to the

source, where relations are complicated by the steepness 'of the primary field

gradient and the rapidly changing direction of the primary flux. In practice

conditions are often more complex; the normal field may be attenuated and

its direction changed because of the presence of other conductors (e.g.

over-burden) and mutual coupling may occur between acljacent conductors. The

effect of such distortions tends to vary with the distance from the primary

source.

For an exact examination of individu al anomalies it is necessary to calculate

the complex va lues of the field. The general procedure is illustrated in fig. 3.

The total field in any observation point is first expressed in percent ofits normal

value by consecutive multiplication of the inverse values of the reduced ratios,

starting from an undisturbed point between souree and anomaly values. The

obtained values are then multiplied with the eosine and the sine of the phase

angle to give the real and imaginary components in percent of the field in the

respective observation points. The shape of the anomalies (fig. 3, Rand I)

still depends to some extent on the primary field,

i.e.

the relative size of the

positive and negative deflections and the location of the inflextion points are

affected by the steepness of the primary field gradient. The total deflection is,

however, the same, independent of the distance from the sourçe or the choice

of the first "undisturbed" observation point and is therefore useçl for amplitude

companson.

If it is assumed that the secondary current is linear, its location can be

determined from the field curves as follows [35]:

dV - = 0 dx for

x=

a

d2_V - = 0 dx2 for

x=

O

dH - = 0 dx for

x=O

"Xhere V = vertical component of the secondary magnetic field

H = horizontal component of the secondary magnetic field

x = horizontal distance from the secondary current

a

=

depth of the secondary current below the surf ace

. Hence the current axis is located right below the inflexion point of the vertical

component and the maximum of the horizontal component. The depth a is

given by the horizontal distance from the maximum of the vertical component

to the current axis.

It has to be taken into consideration here, that the inflexion points of curves

Rand I may be displaced, and the determinations therefore inaccurate. The difference is negligible wh ere the primary field gradient is relatively flat, but in other cases the influence of the primary field has to removed entirely. This is done by expressing the secondary field in one unit, for instance in the

strength ofthe field in an arbitrarily chosen (undisturbed) point (fig. 3, R' and

I'). Since the scale of the obtained curves is determined by the choice of the

first point, their absolute amplitudes have no particular significance, but their

shape will indicate the exact location of the current axis, independent of the

distance from the source.

The relations betwe~n the different components and conductivity variations

can also be shown in vector diagrams of the type given in fig. 3, which trace

the variation of the secondary field when the receiver moves across the

con-ductor. The response of geological conductors varies between pure inductance

and pure resistance, capacitive reactance being negligible at normal pros

-pecting frequencies. Good conductors have a much greater inductance than resistance and the phase lag between the induced voltage and the secondary

current approaches - 90°. Po or conductors have a much greater resistance

than inductance and the phase lag between the induced voltage and the secondary current win be small. Since the inducted voltage is - 90 ° out of

phase with the primary field, the phase win vary between - 180 0 (or in-phase)

and - 90°, when the conductors vary from the inductive to the resistive limit.

In the diagram the secondary field vector of a good conductor win trace a

loop with its long axis close to the real component axis, i.e. the response displays predominantly field damping. The secondary field loop of a poor conductor

will have its long axis closer to the imaginary axis and indicate predominantly

CHAPTER

2

INTERPRETATION

A Theoretical considerations

The interpretation of geophysical observations can be considered to comprise

two phases, the first being the derivation of the spatial distribution of the field

of force and the physical properties from the measuring data, the second the

translation of the obtained solution into terms of probable geologic structure.

In the present context we will be primarily concerned with the physical

inter-pretation. The second phase, which has of necessity a more empirical

charac-ter, since it involves the many complex variations in composition and

con-figuration of the subsurface geology, we will revert to later, in connection

with the field examples.

Physical interpretation rests predominantly on basic theory and

mathemat-ical analyses. The usual procedure is indirect, i.e. the observations are

com-pared with calculated fields of assumed bodies or structures. Thus, theoretical

solutions of generalised prospecting problems play a major role in the

inter-pretation of magnetic, gravimetric and seismic surveys. In geo-electrical

inter-pretation the same approach has been used effectively for Potential methods

[15] (including transient I.P. [32]). Electromagnetic problems have proved to

be less amenable to mathematical treatment, but they lend themselves

partic-ularly well to laboratory sc ale model investigation.

The mathematical analyses of the response of conductors to applied

electro-magnetic fields usually consists in deriving from Maxwell's equations, which

embody the governing physical relations, a set of applicable differential

equations subject to the boundary conditions imposed by the involved media.

Solutions have been obtained for a number of relatively simple models,

such as a sphere [44], an infinite cylinder [42], infinite horizontal [43] and

vertical [51] (conducting half plane) sheets.

While these solutions are of fundamental importance, they are of little

immediate use to the interpreter, because most ore conductors form sheetlike,

lenticular or tabular bodies of limited size, which rarely have sufficient

sim-ilarity in shape with the sphere, the cylinder and the horizontal sheet, or in

physical properties with the half-plane model (the theoretical response of the

latter can only be determined for infinite conductivity [51]).

More important still, they appear in many prospecting configurations,

including those presently considered, as bodies with three finite dimensions,

Various attempts have nevertheless been made to use mathematical models

for direct interpretation. Because of the more favourable dimensional relations

(fig. 27) moving source data offer the best chances for success. In many cases

the half-plane model would, at least geometrically, apply and provide useful

information, if only on the in-phase response [28, 51].

To try and solve problems involving finite conductors spherical models

have been used, upon the assumption th at the response of the latter would be

essentially pertinent to bodies of other shapes [48]. For geometrical reasons the assumption appears too general and it can indeed easily be shown by

means of model experiments that it does not hold (chapter 4). In practice the

transposition wil! lead to erronous conclusions.

Discs would in many cases form applicable models and their response has

been the subject of several investigations [5, 9] which involved both theoretical

and model studies. A useful theoretical solution for the response has not resulted

from this work. The obvious difficulty is that, in order to be valid, the solution

has to take variabie radius as weU as variabie thickness into consideration,

besides finite conductivity. Contrary to a frequently expressed belief [8],

thickness and radius do not have an equivalent effect on the response (c

hap-ter 4) and a theoretical solution wil! therefore be no more easily obtainable

than for any finite tabular body.

For the present time at least, the direct applicability of theol'etical solutions,

even with the help of computers, appears to be limited, particularly in cases where fixed source measuring configurations are used and typical problems

concern bodies of finite dimensions. To investigate the response of finite

conductors we have to resort to scale model investigations. Mathematical

analyses forms, however, an indispensable basis for the determination of the

scale relations and a means to verify the validity of the experiments. A brief

summary of the relevant theoretical considerations is therefore given below:

In their basic form Maxwell's equations can be written as:

in which:

aD

curlH= - + ]

at

curl E =

aB

at

H

=

Magnetic field intensity

B

=

Magnetic induction

D = Electric displacement

Div. B = 0

Div. D = 1;

E = Electric field intensity

]

=

Electric current density

1; = Electric charge density

In homogeneous isotropic media without sources or sinks the following

eJ= E D

=

sE flH= B

e, s and fl are the resistivity, permittivity and permeability of the medium respectively.

Only harmonically time varying fields are considered, hence the equations

become:

curl H =

G

+

iws) E curl E = -iWflH

Div. H= 0 Div. E

=

0

A three dimensional equation which any of the field vectors will satisfy can

be obtained by taking the curl of the first equation and substituting for E:

(}2H (}2H (}2H

V2H= - + - + - = - k2H

(}x2

(}yz

(}Z2

In this equation the factor k

=

VSflw 2-(iflW/e) is called the propagation

constant. The first term sflW2 refers to displacement currents and the second

term iflW/e to conduction currents. When the relevant parameters for geologic materials are examined it appears that [47, 51] :

1. The dielectric constant may vary between 2.5 and 81.1 (water), giving the

permittivity s a range of 7.2 .108 _{to 2.2.10-}10 _farad/cm.

2. The relative permeability differs only appreciably from unity for ferro-magnetic materiais, where it may reach approximately 5. This gives the permeability fl a range of 4.10-7 _{(free space) to 20.10-}7 _{henrys per meter.} 3. The resistivity

e

may vary from 1010 _{to 10}4 _{ohmcm for crystalline rocks,}

from 105 _{to 10}3 _{ohmcm for overburden and from 10}4 _{to 10-}1 _{for sulphide}

ores, giving a total range of 1010 _{to 10-}1 _ohmcm.

For normal prospecting frequencies (audio frequency range) the term sflw2

will be very much smaller than the term iflW/e, except for very high resistivities,

in which case the response becomes immeasurably small and need not be

considered.

It can therefore be concluded th at displacement currents can be neglected in electromagnetic prospecting problems. Hence the field equation reduces to:

V2H = ZflW H

e

To determine the conditions under which the response of full scale conductors

can be duplicated on a laboratory sc ale, the equation is brought in dimension-less form. If we assume that the conductors can be characterized by any length

a and express the coordinates in th is length as follows:

x

=

~a Y

=

'YJa z = Ca

the equation in dimensionless form becomes:

a2

H

a2

H

a2

H iflwa

2

- + - + - = - -H

aÇl

arp

aC2

e

From this equation follows that the response is controlled by the parameter

iflwa/e. *) Thus, at a change of scale (involving all linear dimensions,

in-cluding those of the measuring configuration) the natural scale response can be retained by keeping the value of the response parameter constant.

B Practical requirem.ents

It has been mentioned above that the ave rage electromagnetic survey will very Iikely yield a far greater number of anomalies than can be examined

econom-ically by direct methods. The first problem the interpretation is required to

solve is therefore to differentiate between anomalies caused by metallic con-ductors and anomalies due to other causes, mainly electrolytic conductors such as overburden, weathered faults, etc.

Table 2 The Electrical Resistivity of Rocks and Sediments [3]

Material

Igneous and high grade metamorphic rocks Sedimentary rocks

Consolidate (slate, shale, sandstone, limestone etc.)

Unconsolidated (clay, silt, sand, gravel, soil etc.)

Resistivity (ohmcm)

103_-106

5 X 102_-10.

As a comparison of tabels 2 and 3 shows, ore deposits can be expected to be

better conductors than their surroundings. Graphitic slates, rarely considered

of economic interest, may in some cases show comparable conductivity, and

some overlapping between the ranges of electrolytic and metallic conductors is possible, but as a rule conductivity can be considered a satisfactory guide.

The vast majority of ore conductors appear to be bodies of lenticular,

sheetlike or tabular shape [1, 37], hence their response can be assumed to be

in first approximation determined by the parametere/vd [18] (as long as no ferromagnetic bodies are encountered fl

=

1). At a determinate frequency the response therefore reflects the ratio of the conductor properties

e

and d, and the first step in the interpretation will be to derive this ratio from the observed

anomalies. Since, as will be examined more extensively later, it is usually not

possible to determine

e

and d separately, the conductors have to be evaluated on the

e

/

d

ratio.

*) For convenience this parameter is usually expressed in the frequency v and used in inverted form as; y = e/f1va2 [18].

Table 3 The Electrical Resistivity of Ores and Minerals [26] Material Pyrite Chalcopyrite Pyrrhotite Arsenopyri te Löllingite Cobaltite Galena Zinc blende Heamatite Magnetite Psilomelane Hollandite Pyrolusite Bixbyite Braunite Hausmannite Manganite Piemontite Graphite

---Resistivity (ohmcm) Ore 10-2_-103 10-2_-10 10-3_-10-1 10-1_-10 1-3 X 10' 10-10' 1-1.1 x 103 1-10 10-1_-103 _(shales) Pure Mineral 5x 10-3_-5 10-2_{-7 X 10-'} 10-3_{-5 X 10-}3 3x 10-2 3x 10-3 1-5 3 X 10-3_{-3 X 10-'}

Insulator at ordin. temp. Insulator at ordin. temp. 10-2

Insulators

2 X 10-3 _{(polycrystalline)}

In blind terrain the eld-values form the most important and of ten the only

basis for discrimination between conductors. If other geophysical information

(e.g. a magnetic contour map) or geological information is available, the loc

a-ti on and pattern of the anomalies and sometimes even the dip or the depth of

burial may become important criteria. Usually, however, determination of the

exact location, position and shape of the conductor becomes worth while only

af ter it has been selected as a possible target for a further detailed survey or

for direct examination.

For moving source methods the relation between the response and the

eld-value is sufficiently constant, within a wide variation of geometrical relations,

to permit the use of the Real/lmaginary component ratio as a direct measure

for the conductor characteristics. Experience has shown however that in fixed

source configurations the relation between the response and the eld-value is

not constant, which means that one or more variabie factors are not accounted for in the response parameter. The reasons for this divergent behaviour have

to be sought in the different dimensional relations. In a moving source

con-figuration the average ore conductor *) will closely approximate the

mathe-matical model, i.e. as far as the measuring system can "see", alllinear

dimen-sions except d are infinite. The response win be near its asymptotic maximum

and variations in size will have little effect on the Ril-ratio.

In a fixed source measuring, configuration the same conductors appear as bodies of finite dimensions, a complication the theoretical solution does not cover. It may be expected' that variations in the finite dimensions (in the case of a tabular body the strike length and the depth extension) will affect the response and that the Ril ratio will have to be corrected for such variations before the

e

l

d

value can be derived from it. The Ril ratio will therefore further be called "apparent induction index".

Besides investigating the variation of the response in the normal way, i.e. by

varying the value of the response parameter y, it will be essential to find what other factors affect the apparent conductivity index and which corrections will have to be applied to the latter to arrive at the true

eld

value of the conductor. As far as the various geometrical factors are concerned, these determine to a large degree the size and shape of the response, but are less likely to have a marked effect on the apparent induction index. By using a standard combina-tion of energizing source and model conductor the effect of each individual geometrical factor on the response can be easily investigated and the results incorporated in diagrams to form a basis for the interpretation of the geometri-cal relationships.

This part of the interpretation superficially resem bles the interpretation of magnetic anomalies, but the process is not of comparable rigour. The source distribution of the electromagnetic field lacks the definition and the pronounced polarity of the magnetic field. The induced current will generally be of opposite sign in the upper and lower parts of a steeply dip ping body, but because of the greater distance from source and receiver and the relatively high rate of decline of the primary and secondary fields, the contribution of the return current to the field at the surface will be comparatively small and its presence will be-come apparent only with flatter dips. As a rule the shape" of the anomaly will be almost entirely due to the current distribution in the upper part ofthe body. In practice this has two consequences; firstly that the depth to the upper current axis can usually be determined without ambiguity, secondly that the prospects for an accurate determination of the dip of the body look rather dim.

Since the results ofthe model experiments are to be used in the interpretation offield surveys, the way they are compiled and the form ofthe system in which they are incorporated are of importance. Usually, because it is the simplest solution, an entirely indirect, or synhtetic interpretation, based on collections of type curves, is fàvoured. The practical merit of this approach is, however, limited, because it is virtually impossible to accumulate and classify enough curves to cover the variety of anomalies obtained in field surveys. Further is curve fitting by visual analogy a time consuming and tedious process, which easily reduces to a hit and miss routine. Particularly in view of the practical function of the interpretation, which, as outlined previously, is in the first

instance a process of elimination on the basis of amplitude relations, which does not require complete solutions, a predominantly analytical system is preferabie. In the restricted number of cases where a complete interpretation is desirable, the analytical solution can be verified and its accuracy improved by combining direct and indirect interpretation. Very good results can, for in-stance, be obtained with a procedure whereby the analytical solution is first modelled and the response of the model determined, whereafter possible discrepancies with the field anomaly are adjusted by means of a trial and error method and finally the initial solution is corrected accordingly. TÖRNQUIST has described this method for the interpretation of magnetic data [38], using mathematical models, and the author has shown solutions of moving source field data, obtained in a similar way, but based on scale model experiments [4]. The present experimental program will therefore chiefly aim at aquiring data which can be incorporated in an analytical interpretation system and less at the accumulation of type curves. For fixed source methods th is approach is even more desirable than for moving source methods, because of the greater number of variable factors involved. Fortunately it is also better feasible, since the invariable coupling between source and conductor gives rise to ano-malies of simpler shape, which are easier to analyse.

CHAPTER 3

MODEL EXPERIMENTS

A Dintensional considerations

The conditions under which the scale of electromagnetic systems can be changed while retaining thc field relations, follow, as has been shown from the principle of similitude and Maxwell's equations. The latter are linear and ad-mit of linear scaling in isotropic, linear media. Hence, in order to leave the field conditions unchanged during a change of scale, the response parameter

y

=

e

/

f-lvd2 _{has to be held constant. If the scale is multiplied by a certain factor}

and the frequency v left unchanged, it follows (assuming f-l = 1) that the resistivity

e

must be multiplied by the square of the same factor, and the transformation amounts to multiplying

e

/

d

with the scale factor [18, 27J.

Since the present investigation only concerns sheetlike or tabular conduc-tors, the parameter A = 103

_e

/

vd has been used to describe the conductor characteristics [18]. Thus, at a change of scale the new value of A is obtained by multiplication with the scale factor.

The model experiments were conducted at the reduced scale of 1: 1000,

which offers the convenience of permitting the use of metal plates hs conductors

in combination with measuring equipment normally used in field surveys. If with this scale change the frequency is left unchanged, the resistivity has to be decreased 106 _{times to obtain the same field relations. The change from}

ore-bodies, which have resistivities falling mainly in the range of lQL1Q2 ohmcm,

to metal bodies, which have resistivities in the range of 10-L _10-4 _ohmcm,

represents precisely the required decrease. Besides, the 1000 times reduction makes for a laboratory set-up of reasonable dimensions, yet large enough to obtain results with a high degree of accuracy and with a minimum of elaborate or expensive equipment.

To give the results the greatest practical utility, the shape and dimensions of the model will have to cause a current distribution representative of the average prospecting target. Considering the infinite variety of shapes ore de-posits may possess, no single configuration can be expected to cover all pos-sibilities. However, the majority of orebodies have two long and one short dimension and relatively straight upper edges, resulting from erosion, are common. The importance of analogy, moreover, rapidly decreases with dis-tance from the receiving system. Tabular models or sheets therefore form, as

extensive experience has indeed borne out, a very satisfactory compromise [4, 18, 51].

100

AR~A

(m2.10')

Fig. 4 Size histogram of fifty producing sulphide orebodies on the Canadian and Baltic shields

In choosing the dimensions of the models it wiU obviously be desirable to

cover a range comparable to natural scale bodies. For this purpose descriptions

of some 50 producing orebodies on the Canadian and Baltic shields have been

examined [1, 25, 37]. The large majority are lenticular or tabular bodies with

strike lengths between 200 and 600 mand depth extensions, where determined

or estimated, of the same order of magnitude (fig. 4). As has long been evident

from field experience, and further confirmed in the present investigation (see

fig. 27) the response of fixed source systems is particularly size sensitive in th is range. All results of the small scale experiments have therefore been related to

standard size bodies of H X L = 300 X 300 m.

B Model ar.rangeDlents and data reductions

The general layout employed in the experiments, which is basically the same

as described by SUNDBERG [35], is schematically represented in fig. 5. The primary field is created by means of an audio frequency signal generator

feeding rectangular tuned loops of dimensions comparable, on sc ale, to loops used in field work. Turam measurements were carried out with a set of minia-ture receiving coils, matc}led to a standard 220-660 cps type 2 S Turam

com-pensator. To investigate the field directly in complex values a procedure iden-tical to the "Compensator method", comprising a single receiving coil and a

reference circuit from the primary field connected to a standard 3600 cps

Boliden SL compensator, was employed. The models included metal sheets

and slabs of resistivities varying between 1.7 and 1200 X 10-6 _{ohmcm and}

thicknesses varying between .009 mm and 80 mmo The different components

geo-TURAM COMPENSATOR RECEIVING COILS

j

MODEL TRANSMITTING

I

LOOP /tEe. COIL ========================~~==~~======F==== L.F. COMPéNSATOR ! SIGNAL GENERATOR

Fig. 5 Schematic layout of model experiments

metrical relations. Linear dimensions, where critical, could be determined to .001 mm and the observations made with an accuracy of approximately 0.1

%

of the primary field. All profiles were measured outside, within a distance of twice the length of the short side of the primary loop.

The Turam results are shown in the form of reduced field strength ratios and phase differences (see fig. 3). In most cases the calculated complex values of the field are given as well. The "Compensator" measurements give the real and imaginary components of the field in percent of an arbitrarily chosen point,

which, in analogy with the procedure followed in calculating the complex

values from the Turam observations, is usually the same undisturbed point

between source and anomaly. These readings have to be corrected to give the field in percent of the primary field in the respective observation points, which is desirabie in order to obtain anomalies which are mutually comparable, as

well as identical to anomalies obtained by calculation from Turam

measure-. ments.

In all presented figures and diagrams the values of the linear dimensions and the various parameters refer to the natural scale.

CHAPTER 4

THE RESPONSE OF A FINITE TABULAR CONDUCTOR IN THE

FIELD OF A FIXED HORIZONTAL TRANSMITTING LOOP

It has been found expedient, in order to obtain data in a systematic and for interpretation accessible manner, to investigate the factors affecting the re-sponse in three groups, which embodied the effect of:

A. Changing geometrical relations between a transmitting source of fixed size and frequency, and a body offixed characteristics (/1-,

e

and d).

B. Variation of the response parameter y through variation of the exciting

frequency y or the parameters /1-,

e

and dof the body.

C. Changing dimensional relations, including variations of strike length and depth extent, of transmitting loop size and of the lateral location of the traverse in relation to the upper edge of the body.

The purpose of this division was to join factors determining primarily the shape of the anomalies in the first, factors affecting the amplitude relations in the "normal" way in the second and factors modifying the amplitude relations be-cause of finite conductor size in the third group. *)

A Changing geOlnetrical relations

When the eflects of changes in the geometrical configuration are investigated, it should not be lost sight of that within the range where observations are nor-mally taken, the free space field of the transmitting loop cannot be considered homogeneous. The field strength, as weU as the curvature of the flux lines, varies appreciably over this range.

The present set of experiments were carried out with a model of standard dimensions (300 X 300 m) and À

=

3.5 ohmcmsec/m, located at 500 m from the long side of a transmitting loop of 600 X 1200 m. For movements around the vertical axis of the body the field can by approximation be considered homoge-neous, but large variations of the dip will move the lower part of the body through an area of considerably varying field strength and direction. The results may therefore be expected to depart in some respects from the simple trigonometric relations that would apply in a homogeneous primary field.

*) Variation of the distance between source and conductor does not affect the response

(see p. 9 and fig. 36), except indirectly through the angle of incidence of the primary flux. This

,(0

0 . .

Fig. 6 Symbols used to describe geometrical and dimensional variations

1 Variation

of

the strike

In this context "strike" refers to the horizontal angle between the body and

the direction of traverse. As shown in fig. 7, the body was turned around its

vertical axis over an angle of 90°. In fig. 8 the maximum amplitudes of re al

and imaginary components, as well as the apparent induction index

Q,

(Rmax/lmax) have been plotted against the strike angle <P. The amplitudes

decrease approximately with the sine of the strike angle and cp remains

con-stant. The basic shape of the anomaly does not change in any characteristic way; it only shows the decreasing strength ofthe induced current.

I

2 Variation

of

the dip

With the source on the footwall side the acute angle between the body and the

plane containing the line of traverse and the nearest loop side has been called

the dip angle cp (fig. 6). Turam and complex field anomalies for different

values of cp are shown in fig. 9. With increasing cp the amplitudes decrease to a

point where the induced current revers es and the amplitudes become inverted.

The shape of the anomalies does not, except for the current reversal itself,

reflect the dip ofthe body in any marked way. Only with very flat dips does the

effect of the return current become noticeable in the slower recovery of the

real component. In fig. 10 the variation of Rmax, Imax and Q for different dip

angles are given in the form of a diagram. The field amplitudes vary, except

____ IIOOm TO SOURGE---,

I

_;

I

\

r R

-'0 "0

,.

FR '.20 +5 '.'0

/'~

\

R .~ ' . . :.---

-_.

----

.

_--/~ ---. P o 'OOI-._-__ -"~:'-'--:::.:==~-=-=._=__-~:...-:~='::,:~:'-~.-/-J, ~-.,.-!I;:.·~:..:-=-=·.~=-=-:.:.-=--=-:.::::..:~-l1.00

\i/

.

\'

.

___

.

-5 I ____ """--.--' +'0 gO ·gO BO

-'0

+5 '.'0 o '00 -_-_"'_=-_=_===::::..f.o;c-...;ft-.-,A;::-=-=-~-=-:;:-=-=-=-"',.-l '.00 r

·"--.

----

·

---rR

.gO -11

-'0

o +'0 gO -6

~ L _ _ ~,~.o ___ '~O~O _ _ ~f~Oft

>. .. ".11 L

=

"OOm .. H h • 201ft sP .. ISO· x .. 1100 m I> .. 90"

Fig. 7 Profiles showing field streng th ratio, phase difference and

complex components at different strike angles

.,.

1 R ~O 40 Q /S

..

---x---1!---Jr---x---x-- Q

--.---

R .~ .~

---0---0- ___

-<>- _

.~.

I

--"0-_"

---0.._

20 20 10 10 o <J - - - po.

Fig. 8 Variation of R, land Q with the strike angle

>. .. IJ./S L

=

IJOO ... = H

h

=

20m

sP

=

110·

x = /SOO ...

for very flat dips, with the sine of the angle of incidence of the primary flux

through the centre of the body. The deviations found when the dip becomes relatively flat are due to the influence of the return current along the lower part of the body and to the inhomogeneity of the primary, i.e. with large values

of fjJ the lower part of the body is located in an area of higher intensity of the primary field. The apparent induction index Q remains constaI).t, as far as can

be determined; close to the angle of minimum induction the amplitudes are

too small for a reliable determination. Approximately at fjJ

=

110 0 the

am-plitudes reverse, under the present conditions. They become relatively smalI, but at no time zero. In free space the value of fjJ for whiéh

f3

is zero (angle of minimum induction) depends on the height H of the body, the distance x

from the source and the depth h as follows:

sin

f3

=

cos (fjJ-a) t g a = - - - - -2h

+

Hsin q;

2x

+

HcosfjJ

In fig. 11 these values of fjJ are shown for different heights and depths of the body, as a function of the distance x from the source. In general the relations are simple. The angle of minimum induction increases with decreasing x,

in-creasing hand H; it decreases with increasing x, decreasing hand H.

3 Variation of the depth

The depth referred to here is the vertical distance h from the traverse to the upper edge ofthe body, as distinct from the depth a to the current axis (fig. 6).

- - - , s O t J f f C E _{À.3 ·0} P FR R IJ s 20m L = !JOOm = H R -20 +'0 1-20 120 ~' _ _ -'-'-'E"'"-=--:::~._._____ 0 _{o "00 100}

,.

·.0 +20 -Ia 80 P FR '·40 I R - 20 +'0 '·20 '20 ·.0 +20 -Ia 80 P FR ""0 1.40 1 R / " / \ .,.-.~. -20 +10 1.20 120

-

-! \

'-...

FR· - _ ) \ / ' , \ \ /""' '-...___... I . ___ .- I 'j ''/, - _ ,. -_._, Î " (.", /--::_---:::.-.----n _ 0

xrr

... _-:

1,00 50

.J

• 50 11 = 500m -:'~-:-.::::::..--:.:;.--\: ' _ . _ ·FR

\

~

~~

.

\

,

,.

.

Fig. 9 Profiles showing field strength ratio, phase difference and

complex components at different dip angles

", 50 40 30 20 '0 0 -'0 -20 Q

..

-30 ....

..

..

,. -40 ~ -50 R _Q

".

10 _IS 00 4 Q ~---)!---":.--::. --- --------Jt-- -- - -. - --11-- -- - ------ - - ---1"------- .. ----50 40 JO 2 20 - - - 0 - - - _ _ 0 _ '0 - - 0 _ _

-0-_

5 " - 20' 40' tJo· 100· '40· -'0 -20 -.0 -40 -'0 -00

-'0

À = '.5· L "" 300". = H h = 20", 11 "" ,00". '""-0... __ "",-_ --0... , ,

_,

, ,

_,

,

_, -- I ',.::-ya K.lnp R ux

Fig. JO Variation of R, 1 and Q with the dip of the conductor

Turam and complex field curves for different values of hare shown in fig. 12,

the variation of Rmax, Imax and Q with increasing h in fig. 13. The anomalies

accurately show the varying depth, i.e. the difference between hand the depth

to the current axis a *) determined from the curves is constant. For shallow

depths the rate of fall-off of the amplitudes is small, to increase to the inverse

lst and 2nd power of the depth.

In general the rate of decrease is higher for smaller bodies, lower for bodies larger than the present one.

Real and imaginary components decrease at the same rate and Q remains

virtually unchanged over the entire range.

4 Position of the primary loop

Appreciable variations in the position of the primary loop in relation to the

traverse and the target area are rare in practice. For the sake of completeness

examples of the three types of variation most likely to occur are shown in fig. 14.

Depending on the overall geometry the primary flux through the bod)' will

*) At this distance from the source the difference between a as determined from Rand lor

100· '20· ,~o • 1150· 120· 1000 lOOm

-X--

-_

---200m "OOm .. aam

----

---

---

-

---"":'" - - - -

---

---

--- -:- - -

-=-~:: ~

_---

--:..---H=300m .,0=00 h=20m iJ= 00

500m /SOOm 700m BOOm fJOOm

Fig. 11 Theoretical "extinction angles" for different values of the depth extension and the

depth of burial of a conductor as a function of the distance from the source

increase or decrease and so affect the amplitudes. In general the anomalies

remain the same as long as loop and traverse are in the same plane. Otherwise

they will be weaker. The basic shape of the anomalies and the ratio of the

amplitudes are not affected.

500 m TO SOURCE I 'P FR '.tsO 1.40 R -20' +10 t20 120 0 0 ~oo 100 • '0 +20 -10 .0 tsO +10 1·20 -10 ilO 0 0 ~oo 100 +10

_.'0

·10 .0 +10 1.20 -10 ilO' o o 1.00 100 +'0 .0

,.

'--':::'::':':"~~"./.'\/ _{'- -'- -'1'" .} . ~'R

\_.

_

.

..--

'

Ir."

I'

.

--

.

_

.

~

\

.

-

.

~,l

..-...

'

S

...

----

..

:

.

-

_..

...

-_.--_

.

_-_.,.

~=~-=-=~-

..

.

>.<]\.//

...

.

_-_

.

FR

I

\,

.

___

'R I _ ._ . _ " J - - ' - I ;=-~:~:;!~:~:~".,,:=

.

.

;

m

...

-:;~

I

--"-

'

_

.

-

.

_."

..

10' ,.0. I À

=

$.5 L

=

~OO m" H sP

=

tsO· 1/

=

500 m h=20m h =40m h = BOm

Fig. 12 Profiles showing field streng th ratio, phase difference and complex components at different depths of the conductor