gpy001020.pdf

GEOPHYSICS. VOL. 42, NO. 5 (AUGUST 1977): P. 1020-1036. 15 FIGS., 2 TABLES

A MODIFIED PSEUDOSECTION FOR RESISTIVITY AND IP

L. S. EDWARDS*

Dipole-dipole induced-polarization measurcment5 are commonly presented as pseudosections. but results using different dipole lenpths cannot be con- bined into a single pseudosection. By considering the theoretical results for simple earth models, a unique set of relative depth coefficients is empirically derived, such that measurements with different array parameters will mesh smoothly into a combined pseudosection. Application of these coefficients to a number of theoretical and field cases shows that the) give reasonable results when applied to more com- plicated models.

The empirical coefficients are compared with Roys theory of depth of investigation characteristic, and

support that theorq, if a modified definition of effective depth is accepted. This lead5 to an absolute depth scale for the modified pseudosection. It is shown that rough estimate5 of the depth to the top of an anomalous body can be made directly on the pseudosection, at true vertical scale.

This definition of effective depth is applied to other electrode arrays. It is shown, b) examples, that the resultins pseudosections give consistent estimates of depth to top. within the characteristic anomal) patterns of each array. The effective depths for various arrays are compared: the results agree with the traditional applications of each array.

INTRODUCTION The polar dipole-dipole electrode configuration is

the most popular array for frequency-domain induced- polarization (IP) measurements. The usual field procedure is to make a series of measurements with a fixed dipole length n, the dipoles being separated by a variable integral number of dipole lengths 110 (Figure la). Since the larger n-values are associated with greater depths of investigation, the data can be arranged in a 2-D pseudosection plot which gives a simultaneous display of both horizontal and vertical variations in apparent resistivity (or percent frequency effect, or metal factor). The conventional presentation. introduced by Hallof (1957). places each measured value at the intersection of two 4%degree lines through the centers of the dipoles (Figure 2). Each horizontal data line is then associated with a specific value of 17 and, by implication, with a given effe,ctive depth of investigation. The result is a

qualitative picture of vertical changes in apparent resistivity

For detail work, the measurements may be repeated using smaller or larger dipole lengths, yielding different pseudosections. There is no accepted method for combining measurements with different dipole lengths into a single pseudosection.

The term pseudosection recognizes that the plot is not to be viewed as assigning the data to these definite points in the vertical geologic section. The pattern of apparent resistivities associated with a given subsurface structure is complex, and in most cases does not correspond to the distribution of true resistivities. It is unlikely that any simple modifica- tion of the plotting procedure could produce a general improvement in this respect. for all structures. How- ever, the section is also pseudo in the sense that the plotting depths are not directly related to an) effective depth for the dipole-dipole array, and the

Manuscript received bq the Editor Ma) 7. 1976: revised manuscript received October I I, 1976 *U.N. Development Program, Rangoon. Burma. @ 1977 Society of Exploration Geophysicists. All rights reserved.

1020

Pseudosection for Resistivity and IP 1021

* I. >

(f) EOUATORIAL DIPOLE ( PLAN I (n=l FOR SOUARE ARRAY 1

FIG. 1, Geometry of electrode arrays

vertical scale of the pseudosection therefore has no precise meaning.

Two questions are considered here: (A) Is there a set of relutive plotting depths, for various values of n, which will aiiow &daczl obtair=d -with different dipoles lengths to mesh into a consistent sectional plot? (B) If so, is there an absoluw vertical scale which will place anomalous features at approximately the correct depth, in some recognizable way?

It should be noted that question (A) is peculiar to

the dipole-dipole array, as it is used in IP work. For other arrays, such as the Wenner. the Schlumberger, and the idcal polar dipole (II vcr) large). the internal geometry of the array is constant (or nearly so). and the depth of penetration is varied by changing a single parameter, which is esscntiall! the total length L of the array. As the effective depth of investigation is directly proportional to this parallicter, a vertical scale in units of L (or of some spacing factor (1) immediately produces a pseudoseciitrn with correct relative depths. The apparent resi\livity space\ of Habberjam and Jackson (1974) arc ,~n example fat the square array.

For the dipole-dipole array, the internal geometry is variable. For II = 1. it ii identical IO the Wenner- P configuration (Carpenter. 1955). For large 12, it approaches the true polar dipole gecltnctry. Although fractional values of n < 1 are not noI nially used in IP work, the geometry becomes identickll with the 2-pole array as II approaches zero. Both parameters. (I and n, are independently variable and must be involved in determining the effective depth of investigation. (The same considerations will apply IO the polc-dipole array if II is varied. as is sometime\ done in timc- domain IP work.)

The IP exploration literature is rather vague regarcl- ing the relative effects of changing II and a. It is USLI- ally implied that there is no sinlple relationship between the two parameters, and that quite different apparent resistivities will be obxcrvcd if. say, a large a, small II array is compared with a small (1. large II array. A positive answer to qucztion (A) cannot exist if this is the case. To have a sectional plot which meshes overlapping results obtained with different u-values, requires that a specific (dipole-dipole) result be associated with each definite point in the apparent resistivity space, and that tbcre are different equivalent combinations of n and t, which will give that measured result. It is one object of this paper to show that, within limits. this is true, and that only one

n=4 hd !d

FIG. 2. Conventional dipole-dipole pseudosection plot.

1022 Edwards

effective depth parameter is involved in the dipole- dipole array.

Conversely, it will be shown that these special properties of the dipole-dipole array afford an oppor- tunity to test certain concepts of the effective depth of investigation.

Question (B), relating to absolute plotting depths, can of course be asked about pseudosections for any resistivity array.

EMPIRICAL DETERMINATION OF RELATIVE PLOTTING DEPTHS

Each vertical line of data in a pseudosection repre- sents an expansion of the array about a fixed center, and constitutes a vertical sounding curve of the form p,, =f(z,), where zP is the effective depth at which each data point is plotted. The objective is to write

Zr = C,,a = Kc,,a, (1) where the coefficients c,, are the appropriate relative plotting depths for n = 1, 2, 6, which provide the answer to question (A); the constant K is the approprtate absolute scale factor which answers question (B).

The essential condition on the coefficients c,, is that they place any specified P,, of the sounding curve at a fixed depth zp, regardless of the (n, a) combination used. For a perfect solution, a single set of coefficients c,, should apply to all earth models, to all soundings in the section, to all depths in each sounding, and to all

true resistivity contrasts. Obviously this is not possible; the question is whether it is possible within limits which provide acceptable accuracy for the pseudosection presentation.

For any given earth model, the sounding curve can be written,

Pn =f(p,, P2, ., x~,x~. ., n, a), where the p, are the true resistivities, and the x, define the model dimensions and the array location. Assigning a value to p (,, setting n = 1, 2, 6, and solving for u will yield the exact relative values of the c,, of equation (I), for this model. (Selecting pI, is equivalent to selecting a depth in the sounding.)

The various earth models can be considered as perturbations from the case of a homogeneous earth of uniform resistivity. It is not possible to solve directly for the c,, for this case, since the sounding curve is simply pn = p, , and the c,, are indeterminate. However, any nonhomogeneous model can be made to approach the homogeneous case through smaller resistivity contrasts. If it can be shown that, for any given model, the sets of c,~ converge to a unique set for a homogeneous earth, this set can be taken to define the basic relative plotting depths for the dipole-dipole array. For practical, nonhomogeneous models, departures from this basic set can be treated as plotting errors.

Two simple earth models were selected as suitable for an empirical determination of the c,,: a sounding over a two-horizontal-layer earth, and a sounding

0.1 0.2 0.4 0.6 0.8 I Z./d+ 2 4 6 8 10

FIG. 3. Theoretical dipole-dipole two-layer resistivity soundings, plotted using the effective depths of column (5), Table 1. Discrete data points show a typical set of overlapping expansions from n = 1 to 6, for each a.

Pseudossction for Resistivity and IP 1023

FIG. 4. Theoretical dipole soundings expanded parallel to an outcropping vertical resistivity boundary, plotted as in Figure 3.

parallel to a vertical boundary, where the probes do not cross the contact (see insets, Figures 3 and 4.) For each model, p,, can be expressed as a function of pt, n, d/a, and the resistivity contract k (Ludwig, 1967). If the single dimension d is regarded as a scaling factor, we can write p,/pl =f(k, n, a),

A single determination of a coefficient set con- sisted of assigning values to pa/p, and k, and solving for a, for n = 1 to 6. Since this procedure gives no information on the absolute scale constant K of (I), these sets were arbitrarily normalized to cs = 1.000 for comparison.

A large number of these determinations were made for the horizontal layer model. A small but systematic variation was seen among the determinations, related to the k-values and the depth in the sounding. For

cl, these variations reached a maximum of about ?4 percent for k = 2 1.0; for cg < 22 percent, and for n 2 3 were negligible. To obtain a precise and objective set of coefficients, the soundings were matched at the depth where the maximum gradient occurs, and converged to k = 0 through positive and negative values of k. This basic coefficient set is listed in column (l), Table 1.

Determinations based on the vertical boundary model converged to the same basic coefficient set.

Column (2) in Table 1 lists these coefficients in terms of L , the distance between dipole centers, and shows the rapid approach to the ideal dipole-dipole arrangement, with increasing n.

Rather than show the details of the empirical derivation, it will be more useful to demonstrate the

Table 1. Empirically determined dipole-dipole depth coefficients, and comparison with two versiok of theoretical effective depth. *

(1) (2) (3) (4) (5) (6) (7) Cal. (1).

n e, = r, /_ = 3 &x a L (I normalized

to Cal. (3) +&d Cal. (I), Lmed

a normalized L to Cal. (5)

1 0.240 0.840 0.298 0.323 0.416 0.415 0.208

5 0.403 0.556 0.940 0.973 0.525 0.735 0.539 0.744 0.697 0.962 0.697 0.962 0.232 0.240 4 0.705 0.987 0.939 0.943 1.220 1.220 0.244

2 0.853 1.000 0.996 1.000 1.139 1.338 1.338 1.143 1.476 1.730 1.476 1.730 0.246 0.247

*Columns (1) and (2) are the empirical values, with arbitrary normalization. The values of Column (5) are accepted for the absolute coefficients C, = z,/a and used in the modified pseudosections.

1024

FIG. 5. The data of Figure 3, plotted using the depth scale of the conventional pseudosection

maximum plotting errors which can be expected if dipole soundings, using different a-values, are combined into a single sounding curve using the relative effective depths defined by these coefficients. (Here LP is taken = C,,a, using the coefficients of column (5), Table I; this is a different normalization, selected for reasons which will be discussed below.)

Figure 3 shows vertical sounding curves over a two-layer earth with a IO: I resistivity contrast. The data points represent six separate dipole expansions from n = I to n = 6, each using a different dipole length a. The a are chosen to provide some overlap, so that each n = 1 point falls between the n = 3 and n = 4 points of the previous expansion. The solid curves are for an ideal dipole array (n 2 20); the dotted curve is for an array with n = 1, and the difference between the two curves illustrates the maximum possible error for an n = 1 point in the plot. The curve for n = 2 lies between these curves; for n r 3, the curves are indistinguishable from the ideal curve.

If these soundings were presented in pseudosection form, it would be possible to have an apparent vertical misplacement of up to 4 or 5 percent of the depth to the boundary, for n = 1 readings at a couple of points in the pseudosection. This would hardly be noticeable in a pseudosection and would not cause any problems in contouring. For all other depths in the pseudosection, and all n 2 2, the errors would be insignificant. These curves define the maximum possible error; for larger values of k there is little change in the curves, and for smaller k the displace- ments for n = I would be much less.

Figure 4 shows similar sounding curves taken parallel to an outcropping vertical contact. The results are even better for this case, with a maximum possible vertical misplacement of

2 , / /lljll I I Illll 0.04 0.06 0.1 02 0.4 06 08

FIG. 6. Theoretical dipole resistivity soundings over an outcropping conductive dike, plotted as in Figure 3.

panded perpendicularly to the strike of the dike in both cases.

The plotting procedure works well, except at the discontinuities which occur when the probes cross a contact. For the shallow and deep parts of the soundings, the curiies for all n are identical, demon- strating the applicability of the basic coefficients. The n = 1 curve (dotted) departs considerably from the ideal case at each discontinuity. If these soundings were part of a pseudosection, it is evident that sizable vertical misplacements could occur for n = 1 readings, in the neighborhood of the cusps on the sounding curves. This difficulty is much exaggerated in Figure 6, since the perfectly outcropping model is not geologically realistic, and the sharp cusps of these sounding curves are never met in the field. It can be concluded that the plotting procedure should produce a consistent pseudosection over a real vertical dike

Percent frequency effects (PFE) are calculated as

the percentage change in a given sounding curve when the resistivity contrast is changed. Metal factor (MF) is merely the absolute change in apparent conductivity for the same case. Since PFE and MF are both controlled by the apparent resistivity curves, the same depth coefficients are valid for PFE and MF pseudosections. It can be shown that any vertical misplacements in PFE and MF pseudosections will be less than or equal to those in the resistivity pseudosection.

Since t is the only scaling factor involved in Figure 6, the curves are independent of the relationship between dike thickness and dipole length. A single theoretical pseudosection, plotted by this scheme, would be the master section for any dike with IO: 1 resistivity contrast. Figure 7 illustrates the MF pseudosection for this case. Ludwig (1967) presents dike pseudosections for eight values of t/u; if the proposed plot were used, the 321 cases of this catalog could be reduced to about 40, showing only the effects of

1026 Edwards

FIG. 7. Theoretical dipole-dipole MF modified pseudosection for a conductive, polarizable outcropping dike. Logarithmic contours intervals. (a) and (b) are the same section to different scales; (a) is appropriate to thin dikes, (b) to thick dikes. Data points with any (n, u) combination will match this section when plotted at effective depths, except for some error for n = 1 values at high-gradient points.

various resistivity contrasts and PFE distributions. It will be seen that the familiar 45-degree lines

of the conventional pseudosection are flattened out to about 30 degrees in Figure 7, due to the absolute vertical scale used. On the other hand, these are true straight lines, which converge precisely to the edges of the dike, due to the correct relative plotting depths. The vertical scale constant K could be in- creased so the plot looked more like the familiar dike pseudosection; this has not been done, for reasons discussed in the next section.

SIGNIFICANCE OF THE EMPIRICALLY DERIVED COEFFICIENTS

Roy and Apparao ( 197 1) introduced the concept of a depth of investigation characteristic (DIC) for resistivity arrays over a homogeneous earth. Rather than discussing subsurface distributions of current, they examined the contribution of each elementary volume of earth to the total signal (AV/Z) observed at the surface. Integrating this contribution over a thin horizontal layer, and normalizing so that the total signal equals unity, they constructed normalized depth of investigation characteristic (NDIC) curves for various arrays. In each case, the maximum con-

tribution is shown to arise from a layer at a definite depth, allowing a precise formulation of depth of investigation. Roy and Apparao defined this depth to be the depth of the maximum on the NDIC curve; for a polar dipole array (n = 9), they give - Cmax = 0.195 L = O.l95(n + 1)a.

Among field geophysicists, a common rule of thumb for non-outcropping bodies is: if the maximum IP effects occur for n = 3 or 4, the depth to the anomalous body is of the order of one dipole length a;ifforn= Ior2,thedepthisn. This rule is not inconsistent with Roy5 results, and this fact was the original stimulus for the present investigation.

Following the procedure of Roy and Apparao, the NDIC for the general dipole-dipole array can be written

NDIC = n(n + l)(n + 2)(2z&/aZ)

{[n + 4(z/n)2]-32 -2[(n + 1)2 + 4(z/a)2]-3*

+ [(n + 2)2 + 4(:/a)2]-32). (2)

The maximum NDIC of equation (2) occurs at depth zmaxr defined by


3u{2[(n + I) + u]-~ - [n + ~1~;~ P~/PI = 1 + ku [n(n + I)(n + 2)/21 - [(n + 2)2 + u]-} - {2[(n + I)2 + U]p* {[d + 4(ti/cr)]-2 -2 [(n + I)2 t 4@/a)2]-i

_ [n + U]-3/2 _ [(n + 2) + u]-2) = 0, (3)

where u = 4(~,,,/~)~. Solving numerically for zmax/u yields the vjalues listed in column (3) of Table I, When these are compared to column (4), which is column (I) normalized to the same value for n = 6, it is seen that there is still a systematic discrepancy at the low-n values.

This zrnaa is perhaps not the best choice for the effective depth, The NDIC curves are not symmetrical about the maximum, but are skewed toward greater depths. Intuitively, the median depth would seem preferable; that is, the effective depth could be defined to be the depth at which exactly one-half the total signal originates from above and one-half from below. Thus, defining zmcd as the solution of

+ [(n + 2)2 + 4(d/u)]~~}. (6)

The empirical procedure described above is equivalent to replacing d/u by ~~,/a, and solving for sets of (a, ~,/a) which give the same (arbitrary) value of p,/p,. Comparing with (5), wc see that for ir = ;mrd = d, (6) reduces to p,,/p, = I + k/2, independent of 12. Figure 4 confirms this; the curves for all II pass through the same point at z,/d = 1. For depths above or below this, the n = 1 curve diverges slightly, with opposite signs, giving an average difference near zero.

The equation for the two-layer case (Figure 3) can be written

I Zmtrl NDIC = l/2, (4) Z = 0

~urI~,=l+n(n+l)(n+2) ~F,,GL (7) o,= 1

where

leads to the equation,

n(n + l)(n + 2) {[n + ,I-12 - 2[(n + I)2 + u]-li2 + [(n + 2)2 + u]-12) = I, (5)

where u = 4 (~,,~~/a)~. The numerical solutions of (5) are listed in column (5), Table I. Column (6) shows the empirical coefficients normalized to column (5); within the limits of accuracy of the empirical determination, they are an exact match.

F,, = [n + (2md/a)2]-:2 - 2[(n + I) + (2md/a)z]-2

+ [(n + 2) + (2md/u)]~.

Again, for ze = imed = d, (5) shows that the coefli- cient of k is exactly unity. and (7) becomes

p,/p,=l+k+n(n+l)(n+2) 2 F,,,k. (8) This close agreement strongly suggests that the

NDIC concept of Roy has physical validity and practical application (particularly when the successful use of this plot on field data is considered). It also suggests that Zmed 1 as delined in (4), is the proper choice for the effective depth ir, thus defining the constant K of (I) and the absolute vertical scale of the pseudosection. The coefficients of column (5), therefore. have been chosen for the Cl, of equation ( i j and used in plotting all figures in this paper.

lli = 2

In this case, the various n-curves do not exactly coincide at 2,/d = I, but are independent of n to a first approximation. The differences due to the re- mainder of the summation average out over the range of k-values.

Column (7), Table I, lists the coefficients CL in terms of L instead of n. Calculation of zmrd for higher values of n shows that this coefficient approaches z, = 0.250 L for the ideal dipole array, which is exactly one-half the plotting depth used in the conventional pseudosection.

Relative plotting depths

The median depth concept can be directly related to the equations of apparent resistivity for the two models used in the empirical determination. The vertical boundary equation (Figure 4) can be written

The modified plotting procedure has been applied to some 50 case histories, both published and from the authors files, where careful observations have been made with two or more dipole lengths. In every case examined, the data meshed smoothly into a combined pseudosection.

Figure 8a shows metal factors measured over disseminated sulfides in volcanics in Upper Burma. The three sets of data for n = 1 to 6, using dipole

0) , ZN IN _ 0 2s I I I _ IS 3s L-O I I Y I Y I I I I

-t I 0 I Y METERS Ido

FEET n = I TO 6 ; a = 25 M, JO M, ( 100 M )

0 300 HORIZONTAL AND VERTICAL SCALE !a) DIPOLE-DIPOLE MF

or , 2N IN _ 0 _ IS 2s 3s L-O I I I Y 1 Y I Y r I I -OVERBURDEN

L = 1700 M ; 0 = 25, 75, (25, 175, 225 M

FIG. 8. (a) Dipole-dipole MF pseudosection from the Monywa porphyry copper area, Upper Burma. Data from three dipole lengths are plotted at effective depths ze (Table 2) and combined in a single section, with drill results to the same scale. (b) 2-pole array results over the same section; appropriate effective depths from Table 2. Frequencies 0.3 I and 2.5 Hz in both figures. Logarithmic contours at 100, 140, 190, 250, 350, 500, 700, 1000,


.

P

1030 Edwards

FIG. 10. Dipole-dipole modified pseudosections over a galena prospect in the Southern Shari State, Burma. Frequencies 0.31 and 5.0 Hz.

lengths of 100 m, 50 m, and 25 m, are contoured into one pseudosection without difficulty. The effective depths range from 8.3 m to 173 m. In this case, the observations were not even made in the same field season; the shallower data were taken a year later than the 100-m data, over a resurveyed line.

Figure 9 shows apparent resistivity and MF pseudosections over the Iso-Copperfields Magusi River ore body, Quebec (Fountain, 1974). In the original re- port, there are three pseudosections for a = 300 ft, a = 200 ft, and a = 100 ft, n = 1 to 4, separately discussed and interpreted. Figure 9 demonstrates that this is unnecessary, since they can be viewed in a single pseudosection.

Figure 10 illustrates a case where remarkable changes in apparent resistivity occur over short distances in the pseudosection. The PFE anomaly was located with 50 m dipoles at the end of a reconnais- sance line, and detailed with 40 m and 20 m dipoles on a resurveyed line. The target is a galena prospect in meta-sediments in the Southern Shan State, Burma. The wide range of resistivities is presumably due to the association of massive crystalline galena with wide quartz veins, silicified marbles. and clay zones typical of this area. It was pointed out, in connection with Figures 6 and 7, that there might be some difficulties with the n = 1 or n = 2 values in parts of a pseudosection where large apparent resistivity

gradients occur; nevertheless, there are no apparent contradictions among the three data sets shown.

Figure 1 I is compiled from data in Hallof (1967). There is a bit of scatter in the data. compared to the other examples. because these MFs are calculated from very low PFEs (maximum PI+E = 3.5 percent), with a large probable error. In the discussion of the separate pscudosections in the original. the statement is made concerning choice of dipole length and separation: The problem is complex; it is not merely a matter of the separation of the electrodes. Compare for instance the n = 3 measurements for u = 100 ft with the n = 1 measurements for tl = 300 ft. It is clear from Figure I I that there i\ no reason why these two lines of data should agree.

When this pseudosection plot was being developed, it was felt it would be mainly of acatlcmic interest, and that an exploration geophysicist familiar with the conventional plots would not find it worthwhile to change to a new plot. However. the author has a habit of compiling all detail IP work into a single section, because it provides an excellent check on the quality of the data. To date, in the few cams where there has been a serious mismatch between nearby values on the plot, checking of the data has shown either an error in field calculations or a bad orginal observation. In one frequency-domain survey in Burma, noise problems were so extreme, due to pre-monsoon thunder-


FIG. II. Dipole-dipole MF combined pseudosection, Broken Hill Area, NSW, Australia. I)ata from Hallof (1967).

storm activity, that the readings were considered quite unreliable. However, a composite pseudosection of several data sets showed consistent values and a weak but clear anomaly pattern.

Absolute depth scale The final vertical scale of the modified pseudo-

section has been fixed by theoretical considerations. According to Figure 3, a single horizontal boundary would be located in the area of maximum vertical gradient in a resistivity pseudosection (compare Figure 5). To determine whether this is a consistent feature for, other targets, IP results which included some drillhole information were examined. Some examples are shown in Figure 12, replotted from various published cases.

The general conclusion is drawn that the top of a buried anomalous body lies just above the maximum IP anomaly, in the area of maximum vertical gradient where the contour lines are crowded together. This rule, of course, is neither precise nor infallible. The depth to the top of mineralization is the only consistent feature of the pseudosections: the anomalies are relatively insensitive to the depth extent of the body.

Application to other arrays It is logical to extend the same concept of median

depth to other resistivity arrays, defining effective depth of investigation by (4). Some results are listed in Table 2.

Figure 13 illustrates application of the modified pseudosection to the pole-dipole array. Figures 13 a, b aretheoretical MPpseudosections. Figure l3c and d gives the only time-domain field data shown in this paper; the data points are reconstructed from profiles

of chargeability, and plotted as pzcudosectiona. It should be noted that 13 a and b arc calculated for a constant (I, variable n array. while 13 c and d were obtained with the three-electrode array (n = 1). with variable ~1. Using the appropriate effectiv*c depths from Table 2 makes the pseudosections directly comparable.

Figure Xb shows 2-pole results over the same section as the dipole-dipole results of Figure Xa. The effective depths are based on the actual positions ot the infinity electrodes, not on an ideal ?-pole array. It will be seen from Table 2 that the difference ix significant for the deepest reading\. Comparing the 2-pole results with the dipole-dipole. there is some loss of detail due to the weaker iresolution of the -pole array. but the main features of the anomaly are remarkably similar and occur at 111e same effective depths.

Figure l4a and b shows some xcalc model apparent resistivity results for the square array, which gives simple, straightfotward pseudosection patterns for these models. Use of the Schlumberger and Wennet arrays is usually restricted to vertical \oundings over horizontal layers, but Figure llc and d shows pseudosections over a sphere, as calculated by Scurtu (1972). In all four cases, the same general rule for the location of the upper boundary of the anomalous body is applicable.

COMPARISON OF ARRAYS A number of authors have discu\scd the relative

merits of various arrays in terms of depth penetration. Most of these discussions have been charac- terized by a rather arbitrary+ definition of array length, Roy and Apparao (I 97 I) make a sttmng case for the 2-pole array as much superior to all others, but they

1032

0

I

2

Edwards

- (a) VERTICAL DYKE (CALCULATED I I &GIN , 1973 ) (b) HoRlZONTAL SLA6 (MODELLED) c ALLOF. ,972)

( HALLOF, 1970) (d ) PINE POINT, CANADA c HALLOF, 1972)

(6) TIMMIN rassriE&/xs . &OESITE

r.n.1 TO 4 3:: t a.200FT.n.I TOS

9, ONTARIO V///l ( HALLOF, 1970) ( t) LINDEN, WISCONSIN ( HALLOF, 1970 I

0

100 1 FT

200 L

69N 90 92 93 94 95N 0 10 s 6 2 4N

I

(g ) NEWCASTLE, NEW SRUNSWICI? I HALLOF. 1970) (h 1 LINDEN. WISCONSIN ( HALLOF. 1967 I

( I) BACHELOR LIKE. GUEBEC~HENORlCK.FOUNTAIN, 1971) (j ) ARIZONA ( ROGERS. ,966)

- a 2OD FT. *I TO 3

( HALLOF. 19671 ( 1 ) YUTOORO, S. AUSTRALIA I HALLOF. 1970)

(m) BALLYVEROIN CU. IRELAND (HALLOF,SCHULTZ.BELL.1962) (n) MANITOBA NlCKiL BELT I ROTH. 1976 I

FIG. 12. Dipole-dipole metal factor pseudosections plotted by the modified method, with drill results to the same scale D-ata from various pubiished~ case hlstories.

Pseudosection for

define the length of the 2-pole array to be the u- parameter of Figure le. Both Roy ( 1972) and Dey et all (I 975) define the length of the pole-dipole array to be the distance BN = (n + 1)~ of Figure lb; and the usual definition of length of a Schlumberger array is the L/2 of Figure Id. Although the infinity

Table 2. Effective depths for various arrays, defining z p = z med [equation (4)].

Z,lU ZelL

Dipole-dipole n = 0.222 n = 0.5 ll= I

3 4

:

7 R 20 0~ (ideal array)

Schlumberger ideal, a + 0 L=40a L=20a L= 10n

7.66 3.82 1.90

0.192 0.192 0.191 0.190

Gradient L=40a.x=20a L = 40a; x = 15a

7.66 0.192 6.52 0.163

L=4ba,x= IOU 4.14 0.103

Pole-dipole (ideal, A at ~0) n = 1 (3-electrode)

2

Pole-dipole (practical, m = 20) n = 1 (3-electrode)

2 3 4

2

0.517 0.023 0.915 0.040 1.293 0.054 1.658 0.066 2.013 0.077 2.359 0.087

2-pole ideal (A, N, at co) 0.867 L=40a,x=20a 0.777 L = 20a, x = 100 0.724

j: L= 10a,x=5a 0.627 L=40a,x= IOU 0.758

Equatorial dipole n = 1 (square array)

z 4 10

$IdentiFal arrays

0.45 1 0.809 1.180 1.556 3.84

0.139 0.253 0.416 0.697 0.962 1.220 1.476 1.730 i ,983 2.236 5.25

0.519

0.519 0.925 1.318 1.706 2.093 2.478

0.063 0.101 0.139 0.174 0.192 0.203 0.211 0.216 0.220 0.224 0.239 0.250

0.173

-

-

-

0.019 0.036 0.063 0.019

0.319 0.362 0.373 0.377 0.383 0.384

Resistivity and IP 1033

electrodes conveniently do not appear in array did- grams, these electrodes are as real, and as difficult to lay in the field, as the other electrodes. Surely the only logical basis for comparison is to take the array length to be the total distance between the outer- most electrodes, that is, the L of Figure I.

Table 2 lists the effective depths for all these arrays, in terms of L, for realistic field arrays. Effective depths are of the same order of magnitude for the dipole-dipole, Schlumberger, and Wenner arrays, ranging from about L/6 to L/4, with the higher-n dipole-dipole arrays at the deeper end of the range. The pole-dipole and 2-pole arrays have significantly less depth penetration, in terms of overall array length. The 2-pole is, of course, simply a dipole-dipole array with n

(a) CONDUCTIVE DYKE (CALC.) c COOOON. 1973, lb) CONDUCTIVE HORIZONTAL SLAB t COGGON , ,973 I

(cl ALWIN DEPOSIT, B.C. I SEIGEL.ISTI, (d) LORNEX PORPHYRY C0PPER.B.C. f SEIOEL, ,971,

FIG. 13. Pole-dipole modified pseudosections, using effective depths from Table 2. (c) and (cl) are time-domain IP results. The metal factor of (c) is calculated as [chargeability (ms)/p, (ohm-m)] x 1000.

In fact, the results in Table 2 simply contirm that each array is well suited to its traditional applications. The dipole-dipole, Wenner, and Schlumberger configurations are best for detailed prospecting and horizontal-layer investigations, with large effective depths and good vertical resolution. For reconnais- sance prospecting of large areas, with minimum electrode movement, the pole-dipole and 2-pole arrays are more suitable; when an extremely large L is used, a shallower (relative) effective depth is desirable, to achieve some response from the upper earth. Naturally, the absolute vertical resolution is decreased when L is large. The gradient array has an effective depth which is almost too large for this purpose, resulting in the well-known small response

to compact shallow bodies, and almost complete lack of vertical resolution.

CONCLUDING REMARKS It is not claimed that this moditication leads to any

substantial improvement in the accuracy of depth interpretations for IP anomalies. For a horizontally stratified earth, the interpretation of sounding curves is more precise than any pseudosection procedure. For other models, any pseudosection plot will give equally good results, if used with an extensive catalog of appropriate master sections. The modified plot does have severalladvant~: (:t) it allows detail data, using different dipole lengths. to be assembled into a combined section for interpretation; (b) an

(Cl CONDCTlE SPHERE. SCHWYBFWER , SCURT, 19721 Id, CONDCTlYE OPIIERE. WENNER i SCURT. lP72i

FIG. 14. Apparent resistivity modifies pseudosections for some other arrays. (a) and (b) are scale model results, (c) and (d) are computer calculated.


I , 1, 0 I 1 I I I , A B 0 M N (01 DIPOLE-DIPOLE, n= I 0

I I I I I , 4 f A B M N

(b) DIPOLE- DIPOLE, n = 6

I I / I , I I 1 1

A M N B

(d) SCHLUMBERGER l GRADIENT), L =20 D

+A----_---- TO 40.5

0 I I I I

1, 1

B M N

(al POLE-DIPOLE.m=20, =I l3-ELECTRODE1

&_--__-__ TO 8.7 lI

I I 9 I I I I I B M N (11 POLE-DIPOLE,m=X),n=6

&.---____ _--_-__& TO 25.8

I

TO 25.8

0 I I I I

1 , I I ,

B I M

(91 Z-POLE, L=40 a

i -+ i PI M

(h) EPUATORIAL DIPOLE, n=lO (PLAN1

x/z, -

o.04 3 * I 0 I 2 3 4 I I I I I I I I

IO1 lb) (Cl (d.h) 10) (11 (0 7

FIG. 15. Electrode arrays which give the same (unit) effective depth for a homogeneous earth. The lower figure shows the depth interval which contributes 50 percent of the total signal at surface, as a measure of vertical

resolution.

1036 Edwards

approximate location for the top surface of the anomalous body can be quickly identified, if the data cover a sufficient range of depths; (c) this surface is located at true depth on the section, facilitating compilation of drillhole data, geologic inferences, and other geophysical data on the same section; and (d) it provides a check on the accuracy of the observations, by way of consistency in the plot.

The empirically derived depth relationships, within the dipole-dipole geometry, support the depth of investigation characteristic proposed by Roy, although the median DIC appears to be a more suitable measure of effective depth than the maximum DIC used by Roy. Although Roy extended his calculations in later papers (Roy, 1974) to show exact DIC curves for layered-earth models, it appears that the DIC for a homogeneous earth can be usefully applied to all practical cases.

Contrary to some statements made in the literature, there seems to be no essential relation between the dipole length, the size of the body to be detected, and the observed results, which are basically determined by the distance L between dipole centers. The dipole length can be selected by other considerations, such as the level of signal required, avoidance of EM coupling, reduction of noise levels, and convenience of survey locations. For easy interpretation, it would perhaps be best to use a single small dipole length, and achieve greater depth with large n-values. It is customary to restrict n to the range I to 4, or I to 6, increasing a to get greater depths. This is not done to match the dipole length to the dimensions of the supposed target, but to provide a sufficiently large signal at the receiver, and also to avoid an unnecessary density of data with the usual field procedures.

Application of this definition of effective depth to other arrays does not lead to startling conclusions, but confirms that each array is suited to its traditional use. The square and equatorial dipole arrays might merit more consideration as a standard IP array. The modified pseudosection plot can also be applied to the Wenner, Schlumberger, and 2-pole arrays, with comparable results, but the dipole-dipole and pole- dipole arrays allow simpler field procedures for 2-D profiling. Gradient array pseudosections would be pointless, since virtually no change in effective depth occurs when the receiver electrode separation is changed.

ACKNOWLEDGMENTS

The field measurements of Figures 8 and 10 were

made by U Kyaw Shwe and U San Lwin, Department of Geology, Rangoon University of Arts and Science.

I am indebted to Mr. F. A. Seward Jr., United Nations technical advisor, for his cooperation and encouragement of this work.

REFERENCES Alpin, L. M., 1966, The theory of dipole soundings, in

Dipole methods for measuring earth conductivity: Transl. by G. V. Keller, New York, Consultants Bureau, p. l-60.

Carpenter, E. W., 1955. Some note\ concerning the Wenner configuration: Geophys. Prosp., v. 3, p. 388- 402.

Coggon, .I. H., 1973, A comparison of IP electrode arrays: Geophysics, v. 38, p. 737-76 I.

Dev. A.. Mever. W. H., Morrison, H. F., and Dolan, W. M., 1975, Electric held response of two-dimensional inhomogeneities to unipolar and bipolar electrode configurations: Geophysics. v. 40, p. 630-640.

Fountain, D. K., 1974, Ground geophysical data over massive sulphide deposit, Noranda area, Quebec, Canada: Toronto, McPhar Geophysics Ltd.

Habberjam, G. M., and Jackson, A. A., 1974, Approximate rules for the composition of apparent resistivity sections: Geophys. Prosp., v. 22, p. 393-420.

Hallof, P. G., 1957, On the interpretation of resistivity and induced polarization measurements: Cambridge, MIT, Ph.D. thesis.

__ 1967, An appraisal of the variable frequency IP method after twelve years of application: Toronto, McPhar Geophysics Ltd.

~ 1970, The use of induced polarization measurements to locate massive sulphide mineralization in environments in which EM methods fail, in Mining and groundwater geophysics/ 1967: Ottawa, Queens Printer, p. 302-309.

__ 1972, The induced polarization method: Toronto, McPhar Geophysics Ltd.

Hallof, P. G., Schultz, R., and Bell, R. A., 1962, Induced polarization and geological investigation of the Bally- vergin copper deposit: SME Trans., v. 223, p. 312-318.

Hendrick, D. M., and Fountain, D. K., 1971, Induced polarization as an exploration tool, Nomnda area, Quebec: CIM Bull. Februarv.

Ludwig, C. S., 1967:Theoretical induced polarization and resistivity response for the dual frequency system collin- ear dipole-dipole array: Tucson, Heinrichs Geoexplora- tion Co. _

Roth, .I., 1975, Exploration of the southern extension of the Manitoba nickel belt: CIM Bull. September, p. 73-80.

Roeers. G. R.. 1966. An evaluation of the induced- Fol&ization method in the search for disseminated sulphides, in Mining geophysics, Vol. I: Tulsa, SEG, p. 350-356.

Roy, A., 1972, Depth of investigation in Wenner, three- electrode and diuole-dioole resistivitv methods: geophysFrosp., v. 20, p. 329-340. .

. _

~ 1974, Resistivity signal partition in layered media: Geophysics, v. 39, p. 190-204.

Roy, A., and Apparao, A., 1971, Depth of investigation in direct current methods: Geophysics, v. 36, p. 943-959.

Scurtu, E. F., 1972, Computer calculation of resistivity pseudosections of a buried spherical conductor body: geophys Proso.. v. 20. D. 605-625.

Seigel: H. O., 1971, Some comparative geophysical case histories of base metal discoveries: Geoexplor., v. 9, p. 81-97.