Geophysical Prospecting 30,942-944,1982.

C 0 MME NTS 0 N “RESISTIVITY P R 0 FILING WITH DIFFERENT ELECTRODE ARRAYS

OVER A GRAPHITE DEPOSIT” BY G. BRASS, H. FLATHE A N D R. SCHULZ*

A . R O Y * *

(1) The most obvious feature common to all the apparent resistivity profiles is that the anomalies are best developed for the smallest array length L in each case, without exception. These lengths are: L = 3a = 30 m for the Wenner array, L = a = 10 m for two-electrode array (called both “ single pole ” and “ half-Wenner ” by Keller and Frischknecht, 1966, pp. 100 and 180), L = 2a = 20 m for the three- electrode array “half-Wenner” of Brass et al. 1981, and L = a = 10 m for the half-Schlumberger array. The corresponding depths of investigation cannot exceed 10 m in any case; they are probably closer to 5 m. These array lengths are thus much too small for either the main graphite body, left of station 0, whose upper end is 40 m deep, or the “new discovery”, below station 60, whose average depth is 30 m. Without doubt, the anomalies are caused not by these deep bodies, as inter- preted by the authors, but by something much shallower and nearer to the ground surface. Note in passing that, for the same value of a in fig. 1, the array lengths can be entirely different in different electrode configurations.

(2) A second feature which also stands out prominently is that the half- Schlumberger profiles are the most noisy and susceptible to surfacial irregularities, as all gradient arrays must be. In contrast, the two-electrode profiles are by far the smoothest and most regular, one reason for which is the smaller (minimum) number of its active electrodes.

(3) The paper under discussion is an apt illustration of the pitfalls of using asymmetric arrays. The half-Schlumberger array, for instance, does not produce a simple high or a simple low centered over a target and can thus seriously mislead an unwary interpreter. For a resistive target of width less than the array length, its apparent resistivity response consists of a minor low, a major high, a broad low (blind zone) and a minor high (reflection peak)-a succession of four asymmetric and displaced peaks/troughs (see fig. 122 on p. 187 in Keller and Frischknecht (1966) or fig. 4.5 on p. 55 in Anon (1958)). Indeed, the three-electrode and the

* Received November 1981. ** Department of Geology, University of Ibadan, Ibadan, Nigeria.

942 001&8025/82/120&0942 $02.00 @ 1982 EAEG

COMMENT 943

half-Schlumberger lows over station 60 in figs 6 and 7-which the authors ascribe to a new graphite body-look suspiciously like a blind zone associated with the major high immediately to the left. This low is nongenuine in the sense that it is not caused by a buried conductor but is merely a part of the overall response of the resistive body below the high around stations 40-50. It is somewhat similar to the negative halo in the second derivative gravity map due to a heavy object. One is tempted to agree with the authors that this “must be regarded as one of the most remarkable results of this field study”.

(4) Figures 3 and 8 (left) depict the “new” graphite body as a plate of small vertical thickness and an average depth of 30 m. This has been mathematically modeled in fig. 8 (right) by a massive sphere of radius 14.3 m with center at 18.6 m. The wide discrepancy between the two models in regard to shape, size, and depth is glossed over by the authors with the following two statements: (i) “The sphere is the only 3-D body of arbitrary resistivity in a half-space for which an analytical solution can be derived, which is why this shape was used”; (ii) The shallowness of the center of the sphere “could be caused by small graphite intercalations above the graphite enrichment at station 60, which would influence the measured anomaly ”. If (ii) is correct, why was not the plate assigned a smaller depth to begin with? Alternatively, would it be true that a smaller sphere centered around 30 m does not reproduce the observed anomaly? How satisfactory the match really is in figs 10, 11, 12, and 13 is yet another matter. There is no reason, in fact, why there should be one.

(5) Another statement reads: “The increase in resistivity values (of the two electrode array) between -75 and 10 with increasing spacing and their decrease between 10 and 75 do not correspond to the geological situation”. This is not true between stations - 75 and - 25, where the two-electrode response in fig. 5 exhibits no systematic resistivity increases with array length. Nor is it true that, over the remaining stations, only the two-electrode configuration indulges in the alleged behavior. Apart from the gross factual inaccuracies in the above description of their own data, what baffles one most is the implication of the last part of the statement. One must realize that measurements, unless they happen to be unreliable, cannot but correspond to the geology as it actually is; no array can violate that. In fact, geology is never completely known and one uses the measured date to update it continuously, as the authors themselves have attempted by introducing a “ new ” graphite mineralization under station 60. Whether one is able to visualize or con- trive a geologic situation which reconciles and explains all observed data is a different question. That the actual geology would do so is, however, conceptually axiomatic.

(6) The data produced by Brass et al. (1981) suggest the following first-order interpretation. The two-electrode profile of array length 60 m defines the general background of resistivity; it maintains a remarkably steady value of about 100 Rm over the calcareous gneiss between stations -75 and 10, and then rises slowly over the gneiss to about 300 !&-I before falling again beyond station 65. Any genuine excursion of the apparent resistivity value above or below this general level in profiles using smaller array lengths relates to shallow and local variations of rock resistivity not deeper than about 10 m. Four significant variations of this kind are visible: two small highs around stations - 50 and - 30, a low between - 25 and 10,

944 A. ROY

and a rather prominent high around 30-40, as read from the symmetric array profiles. What these shallow variations are due to can be best guessed by the workers themselves. Leaching away of calcareous material, topographic effect, accu- mulation of water/moisture, hard or soft pocket and shallow graphitization are some of the possibilities. According to this interpretation, no graphite body is in- dicated below station 6 W x c e p t very superficially, if at all. This is corroborated by two independent lines of evidence : (i) earlier geophysical work by resistivity, induced polarization, Slingram, and Turam methods did not detect such a body, and (ii) this location falls within noncalcareous gneiss, while graphite “ is almost always found near limestone intercalations in the gneiss ”.

(7) Regardless of which interpretation is nearer reality, the conclusions of Brass et al. (1981) are premature until a drill locates the “new” graphite body below station 60 at an approximate depth of 30 m. Their data relate to measurements along a single line over one far-from-simple geologic environment, unsupported by systematic theoretical and laboratory studies under controlled conditions. One therefore hopes that they do not intend their conclusions to be a general pronounce- ment on the much wider question of relative performance of resistivity arrays.

(8) Apparao is barely mentioned in the Acknowledgements and the readers may not realize that he was one of the main participants in the field tests that the paper describes. In view of the persistently favorable experience of Apparao and Roy with the two-electrode array in India, it was suggested by the la t te r4ur ing Apparao’s deputation to BGR some years a g w t h a t some studies may be taken up in Ger- many on array comparison. The suggestion was accepted by BGR; indeed, Ap- parao’s stay in Germany was extended for this purpose. The paper could have included this background in less than 50 words.

REFERENCES ANON. 1958, Introduction to Schlumberger Well Logging, Document No. 8, x + 176 pp.

BRASS, G., FLATHE, H. and SCHULZ, R. 1981, Resistivity profiling with different electrode

KELLER, G.V. and FRISCHKNECHT, F.C. 1966, Electrical Methods in Geophysical Prospecting,

Schlumberger Well Surveying Corporation.

arrays over a graphite deposit, Geophysical Prospecting 30, 589-600.

vi + 523 pp. Pergamon Press, Oxford and New York.