electrical for ore body

7/30/2019 Electrical for Ore Body

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ORE BOD Y SIZE DETERMINATIOK INELECTRICAL PROSPECTING*

HAROLD 0. SEIGELt

ABSTRACTA method of determination of the size of ore body associated with a mineralized intersection ispresented which utilizes the primary voltage disturbance created by the body and the variation ofthe disturbance with electrode spacing. The form of the disturbance function is compared with

theoretical curves based on the oblate spheroid.

introductionIt is not an uncomm on situation that a mineralized intersection of smallmagnitude is obtained near the end of a long and costly exploratory drill hole.

The question that naturally arises is whether this mineralization represe ntsthe fringe of a much larger m ass of the same or better grade, or is merely alocalized deposit, perhaps even a small fissure vein intersected by the hole at alow angle. The fate of further drilling often rests on a relatively arbitrary decisionas to wh at the possibilities of extension actually are.

4 very diagnostic physical property which distinguishes metallic sulphidemineralization from the usual country rock is electrical conductivity. A facto rof 1,000 fold contrast is not uncomm on. Through the use of one of severalsimple electrodal arrays it is possible to utilize this property contrast towardsgiving us an estimate of the size of the body associated with an intersection.

BASIS OF METHODFigures I and 2 illustrate two arrays that may be used for this purpose. The

former is simply the normal array as used in petroleum electric logging, andthe latter may be referred to as the equispaced three electrode array. Current_1is passed between C1, placed a small distance from the intersection, and C P,placed generally at so me convenient surface point at a large distance from Cl.The current may be dc, comm utated dc, or very low frequency ac. The resultantvoltages in the ground are measured between PI, placed on the opposite sideof the intersection from Cl, and an equal distance therefrom, and Pz, placed infigure I at a large distance from all the other electrodes and in figure 2 at a dis-tance below PI equal to CIP1.

The flow pattern and potential distribution will be altered by the presen ceof the mineralization from -wh at it would normally be in barren ro ck. Curren t

* Presented at the Los Ange!es meeting March ~7, 1952. Manuscript received by the EditorJulv I, 1952 .t Newmont Exploration, Ltd., Jerome, Arizona.


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90 8 HARO LD 0. SEIGEL------__

tIII

Li c i---A- --.


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ORE BODY SIZE DETERMINATION IN ELECTRICAL PROSPECTING 909will tend to crow d into the good conducting material near Cr and flow out theends of the conductor rem ote from Cr. The net result is generally a robbing ofcurrent from th e vicinity of PI and a lowering o f the potential difference betweenPI and Pz. The magnitude of this effect depends on a number of things, includingthe ratio of conductivities, shape, and inclination of the body, and ratio ofelectrode spacing to length and thickness of the body. When there is a highconductivity contrast the ratio of electrode spacing to the length of the conductoris most important.

FIG. 2. Size determination configuration, equispaced three electrode array.By varying the electrode spacing , i.e., by expanding about the intersection

as center of Cr PI, we can vary the length of the conductor which is affectingour readings. The rate at which the observed voltages, or apparent resistivitiescalculated therefrom, return with increase of spacing to what may be consideredcharacteristic o f normal rock materials will be diagnostic as to the actual exten-sion of the mineralization awa y from the intersection.

For quantitative interpretation a basis of comparison is required. M odelexperimental or theoretical cu rves drawn up for simple conventionalized bodieswill serve the purpose. As an example of a body of reasonably adaptable shapewhich is amenable to theoretical treatment we may consider the oblate spheroid.The mathematical solution proc eeds as follows:


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910 HAROLD 0. SEIGELPOINT SOURCE ON AXIS OP OBLATE SPHEROID

Refer to figure 3 for the geometric configuration and coordinate system. T heorigin of a Cartesian coordinate system is established at the center of the oblatespheroid. The z axis is taken along the axis of rotation of the spheroid and the

tt

FIG. 3. Ohlate spheroidproblem, coordinatesystem.x and y axes perpendicular to it. The length of the major axis of the spheroid istaken as b and of the minor axis as d. The conductivity of the ellipsoid is takenas ul, and that of the surrounding medium as (TV.The transformation from car-tesian to oblate spheroidal coordinates (r, 0, 4) is given by

for

m = [Y + cz]l/z sin 0 cos I$y = [9 + c2]1ie sin 0 sin +2 = r cos 0

where6 = +[b - #]2.

Laplaces equation in the oblate coordinate system is given by

(1 )

& (rZ + 2) g[ 1 +Since our configuration is axially symm etric the dependence on C#Janishes.

The well behaved axially sym metric solutions obtained by separation of vari-ables are given by

vo= &l,Q,(.>P,(cos 0) (exterior region),7L=O c (3 )


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ORE BODY SIZE DETERMINATION IN ELECTRICAL PROSPECTING 9=1

111 = 2&P,(.>P,(cos 19) (interior region).?t=O c (4)The reciprocal distance between two po ints (7, 0) and ~1, O,), one or both on

the axis of rotation is given by_I_= + z. 2?$ + I) [Q~G) , (5) P,(COS B)P,(cos b)]or > f-1.R (5 )

PFZ (x) and @ z (x) are the Legend re functions of the first and second kinds.Consider the current source C at a distance rl from the center of the spheroid

on the axis of rotation. The coordinates of the potential measuring point P are(Y, O), whe re rl is greater than r.

Ignoring a factor o f I,/4auo throughout, we set as our potential functions,interior and exterior to the spheroid,

VO = ;g(2?2 + I)[&(':-) Pn(I_)PJcmBl]

+ 2 BnQn7t="

-exterior solution, y1> Y, and

as interior solution.The boundary conditions that have to be satisfied at Y =d/z areV. = Vl and CTO :=CJI$,

(6 )

(7 )

(8 )Applying these we may obtain our coefficients An and Rn by equating coeffi-

cients of Pn(cos e).Writing 6=ao /al, and expressing all distances in units of d/2 we find, as

ratios of apparent to exterior resistivities./,JPo = I + 4 i(r - S)e BnQn (. ) P,(COS e)TL=O E

in the exterior region, andpa/p0 is2 X2, P,(COS e)e ?I=0 0

(9 )

(10)in the interior region.


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912 HAROLD 0. SEIGEL

and (12)where

OL a/d where a is the separation of the C and P.e=(b2-dL)1/2/d is a measure of the eccentricity of the spheroid. For large

ratios of b/d, t is very nearly equal to b/d.Tables of all the functions above are available (2) and formulae (9 ) and (IO)may be readily evaluated numerically for any specific exam ple.When the potential measuring point is also on the axis of rotation of the

spheroid and below the sph eroid the equation (9) is further simplified.Then

8=?T and P,,(cos 0) = (- I)~.BASIS OF INTERPRETATION

So called resistivity departure curves have been prepared on the basis ofequation (9) for the configurations of figures I and 2, for various values of t, 6being taken as 1/200. These curves are presented in Figures 4 and 5 on a log-logbasis. Points of interest are as follows:

(I) The curves for the equispaced three electrode array give more markeddepartures for the same disturbing body than the normal array.

(2) All cu rves return to normalcy, i.e., pa approximately equal to PO, orthe spacing slightly larger than the total lateral extent of the body . This qualita-tive rule will establish an uppe r limit to the average extent of the body-from thehole.

(3) Curves for bodies of very limited lateral extent show a rapid return tonormalcy with increased electrode spacing, and then an apparent increase inresistivity over PO, falling asymptotically to an undisturbed condition w ithincreasing spacing.

(4 ) Curves for bodies of more generous lateral extent show a slow rise andreturn to normalcy, with no marked excess over po.

(5) On the basis of these theoretical curves it appears possible to determinethe proper value of c within a factor of 2 withou t any difficulty. This value of E


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ORE BODY SIZE DETERMINATION IN ELECTRICAL PROSPECTING 913

I.5a(= a/d I I I3. 0 I.0 b.0 8.0 ( I

FIG. 4. Oblate spheroid resistivity departure curves, normal array.

will correspond to the oblate sphero id giving the same average potential disturb-ance as the actual ore body and will provide a reasonable estimate of the sizeof the body.The special usefulness of the log-log plots of Figures 4 and 5 lies in that theypermit one to match curve forms directly without entailing a knowledge of pror even d.

Matching the form of the observed curve with a double family of curves forvarious e and 6 values will permit adequate q uantitative interpretation to bemade. A rough estimate of extent may be made if desired from the value ofspacing at which the values first return to normalcy. This entails a knowledgeof the approximate value of pO.


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9'4 HAROLD 0. SEIGEL

FIG. 5. Oblate spheroid resistivity departure curves, equispaced three electrode array, 6= r/200.

ACKNOWLEDGMENTI wish to gratefully acknowledg e the permission granted by Kewm ont

Exploration Limited, of Jerom e, Arizona, for permission to publish the materialcontained in this paper.

REFERENCESI. T. M. MacRobert, Spherical Harmonics, Dover Publications, New York (1948), p. 218.2. e. g.. Tables of Associated Legendre Functions, Columbia University Press (1945).

electrical for ore body

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