DOCTORAL DISSERTATION SERIES TITLE # V AUTHOR UNIVERSITY. » v \ p» r\- ISv I #4 i m i * fi J r . fr- j 1 t> ii: v. id ■< j *- ■- /j /l DATE PUBLICATION NO. DEGREE I1!1 989 Mill U UNIVERSITY MICROFILMS M A N N AR BOR • MICHIGAN INDUCED POLARIZATION: A METHOD OF GEOPHYSICAL PROSPECTING By David Franklin Bleil A THESIS ubmitted to the School of Graduate Studies of Michigan State College of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics and Astronomy 1948 T A B L E A. 1. 2. 4. 5. LABORATORY EXPERIMENTS THEORETICAL DISCUSSION A Uniformly Mineralized Earth A Buried Sphere The Ellipse of Induced Polarization Concerning the Interpretation of Measurements D. 1. 2. 3. INTRODUCTION Description of Apparatus Existence of Induced Polarization Induced Polarization and the Energizing Potential Induced Polarization and the Matrix Resistivity Decay Time of the Induced Polarization Behavior at Chemical Boundaries Concerning Ionic Concentrations Other Factors Influencing the Polarization Signal Other Tank Experiments Conclusions C. 1. 2. 3. 4. C O N T E N T S Statement of Problem Historical Development B. 1. 2. 3. 4. 5* 6. 7. 8. 9. 10. OF FIELD SURVEY RESULTS Description of Field Instruments Measurements Overan Amphibolite Dike Measurements Across a Manassas Sandstone and Wissahickon Fault Measurements Over a Pyrrhotite Outcrop Measurements Over a Magnetite Ore Body SUMMARY REFERENCES APPENDIX A. 1. INTRODUCTION Statement of Problem Geophysical prospecting is the fascinating game of unraveling the subterraneous character of a region from clues supplied by measurements which can be made at the surface of the earth. These measurements determine the true or apparent physical properties of the region below. The physical properties of the earth most fre­ quently studied are its elasticity, density, magnetic susceptibility and electrical resistivity. In general, the problem of determining what lies beneath the surface of the earth is so complex that measurements of one par­ ticular physical property alone cannot provide an unam­ biguous solution. Frequently however, information gathered from several related physical quantities may be pieced together into a reliable picture of the sub­ surface structure. It is axiomatic that the more inde­ pendent physical quantities which are measured the more will be known about the nature of the structure below. Thus it becomes highly desirable to add to our list of measurable physical properties of earth materials. Induced polarization (IP) of the metallic minerals of the earth is one such additional physical quantity which may be used to contribute to the overall picture. It has long been known that both the anode and cathode of an electrolytic cell become polarized upon the passage of a current. This polarization of the electrodes is generally regarded as a nuisance but it is an electrical property which, by its very existence, provideSj a useful tool for the detection of metallic minerals in the earth either in the form of solid ore bodies or as disseminated particles. The detection of electrically conducting minerals by this property, stripped of its many inherent difficulties (to be dis­ cussed later) consists essentially of the following procedure. The metallic mass M (Fig. 1) is surrounded by a rock matrix, the interstices of which are filled with an electrolyte. In general the more or less good electrical conductivity of a rock is due to the inclu­ ded electrolyte. The presence of the mass M will dis­ tort the current flow causing an increase or decrease of the current density in the body depending upon whether its resistivity is higher or lower than the the matrix. The region ri.ero the current filaments enter the I'ass T' corresponds to the cathode of an elec­ trolytic cell ond that region where they leave to the anode of th cell and the retol itself to tne ordinary external circuit. A d: rent cur ren t, flowing frorr elec­ trode A to el ectrode B, vu 11 polar: se the mass I. posi­ tive on the sice where the current enters and negative where it leaves. If ti.o current frov A to B h interrupted the dips le on the ms as p ’.'.si11 :|’asipa te it 1''-I■p iou r m u n d 2r.g ■■ed iurn. bv send:r-- a cu rrent thron gh the h The recorder R indicate t e o am-.ic dron between /■’i _ t o points O a ■!cWi due to this pol arization current. I" order to a vo id m e a s u r i t h e ohr.ic drop duo to th c energizing a>1'r ■ent. tl:e switch 5 *c} not closed until the current circuit i s interrupted. ’ FIG. I "L i.,: A vc '•ubul a i"-r sc lie; !s ■ecu 11 nr ^•• V..U-L. KJ_i_'0Ltrical '-et:•ods of '■'eon:'.vsicr t !-r . ray be used r r- r;>*1 terms which crofitobly in t re oor': to follow. 1 he used frequently ar- here brought to the read rs attention. In all electrical methods •‘ . ore current is delivered directly to the ground a pair of current electrodes is required. Acb-itional.pu a pair of poten­ tial electrodes is required. The manner of arranging the electrodes varies and the more popular systems 1 s~’T‘i acquired nr-os. Then the current electrodes are ''\idolT’ separated r t h e no to" tie. I is measure-" in the neighborhood or one c •r p.1 ec.trode the term "point electrode" is applied to the system. More frequently the four or more electrodes are arranged in a straight line with some scheme of spacing employed. A very com­ mon spacing scheme is that of separating the four elec­ trodes by an equal spacing "a". This system is referred to as the Wenner system. The method of measuring the resistivity employing a low frequency double commutator and the Wenner configuration is called the Gish-Rooney system. This basic principle, although proposed as far back as 19121 , has received little attention on the European Continent and practically no attention in this country. The definite lack of interest in the method probably stems from the confusion apparent in the literature and the cloud of mysticism which surrounds some of the ear­ lier works. Heiland2 has expressed a doubt that a new quantity had been measured by the method. It is the intent of this thesis to rectify some of the errors which have crept into the literature, remove some of the existing mystery and to bring out the advantages and limitations of the method with the hope that it will grow into a useful tool for geophysical prospecting. 2. Historical Development A brief summary of the pertinent literature is out­ lined in this section in chronological order. Comments and criticisms relating to this published material will be reserved until they can be made in the light of the present investigation. In the patent1 granted to Schlumberger in 1912 there is mentioned, in one claim, the discovery of an induced polarization potential. However, it was not until his book3 published in 1920 and later4 revised in 1930, that he explained this new method of geophysical prospecting and gave a clear account of the basic prin­ ciple of induced polarization. He was aware of the fact that the measured potentials decayed with time but nevertheless claimed to have measured them with an ordi­ nary potentiometer. Schlumberger admitted that his ex­ periments in the field were not successful and since the chapter on induced polarization remained unchanged when the book was revised in 1930 the difficulties he encountered apparently remained. Some of the conclu­ sions he drew are included here for later references a) that some deposits such as pyrite are spontaneously polarized and that the self-poten­ tials so developed concealed the effect of induced polarization. 3 b) that the resistivity of the rock, sur­ rounding the ore body, enters into the inducedpolarization effect not more than to a secondary measure. c) that there exists, in a region free of ore bodies, a "residual11 polarization potential which disappears with time in much the same man­ ner as the polarization of an ore body disappears. d) that the effect of c) is observed when pure water is used in place of wet soil. (He attributed this volume polarization to a transport of ions creating a dissymetry between the regions surrounding the current electrodes.) Schlumberger regarded observation a) as being highly interesting and may have abandoned his induced polar­ ization studies in favor of spontaneous (self) polar­ ization. Muller^ described apparatus which he claimed would measure "simultaneously" the activating potential and the oppositely directed polarization potential. A single pair of electrodes served both to send current into the ground and to measure the polarization potential. Pul­ sating unidirectional current was delivered to the elec­ trodes by the secondary of a transformer in series with a vacuum tube rectifier. A galvanometer in series with another vacuum tube rectifier and a high resistance, all connected across the electrodes, measured the acti­ vating potential. A similar circuit connected across the same electrodes but with the rectifier reversed, measured the polarization potential. The deflections of both galvanometers were photographed on a common film. The method proposed by Miiller was discussed in more detail by Weiss° under the name of the "Electro­ chemical Method". Muller and Weiss were aware of Schlumberger1s work but they chose to explain the cause of the polarization effect differently. They contended that the ore body came into equilibrium with the negative ions of the electrolyte by emitting positive ions and thus becoming negatively charged, all this long prior to passage of the energizing current. The energizing current was then supposed to upset this equilibrium causing a large current to flow simultaneously with and in the opposite direction to the energizing current. In addition, without making adequate explanation, they came to the conclusion that polarization effects are capable of being induced at "chemical" boundaries. The method of 4 measuring the effects has changed from time to time and the interpretation of the results? obtained has been entirely empirical. Their claims for the method are: a) that the maximum polarization current flows simultaneously with the energizing current and in the opposite direction and, therefore, their apparatus will measure larger polarization effects than that of Schlumberger. b) that, if one plots the measured polar­ ization effects against the electrode separation, the "breaks" on the resulting curve are indica­ tive of "chemical" boundaries. A one to one cor­ respondence between depth and electrode separation is deduced, c) that the "screening" effect which panies other ordinary electrical methods is in this method and. therefore, great depths penetration are obtained with small amounts pended power. (3000 to 6000 ft. for 1 to 2 accom­ absent of of ex­ watts). An enlightening bit of the discussion which fol­ lowed Weiss1s paper is quoted in part, "Prof. A. 0. Rankine confessed that, in spite of Mr. Weiss's descrip­ tion now, and of long talks he had had with him previ­ ously, the operation of the method he had been using remained a mystery to him, chiefly in relation to the measuring circuit." The work of Muller and Weiss was criticized by Belluigi°> 9 who pointed out that their greatest source of error arose from the deconcentration of their nonpolarizable electrodes due to the energizing current passing through these electrodes. Belluigi modified, somewhat, the equipment of Muller and in particular used two pair of electrodes such that the energizing current did not pass through and deconcentrate his potential electrodes. His measurements, which were more refined but again used the same empirical interpretation of Weiss and Muller, showed that great depths are not likely to be revealed because of large near-surface effects. A method of geophysical prospecting which measures the response of the earth to an electrical transient, called Eltran, was patented by B l a u ^ . This method consists simply of applying a step pulse to the earth through a pair of electrodes and measuring the response of the earth to the step pulse across a second pair of electrodes. It is the complex impedance of the earth 5 which is measured and although polarization is not explicitly mentioned, it must nave some effect on the capacitive reactance of the earth. In a r e p o r t ^ which discusses the measurements of resistivity when large electrode separations are employed it is pointed out that a finite time is required to establish steady state conditions. The rate of growth or decay of the potential, assumed to be exponential, has a time constant given by tiie expression T r cub^ seconds P where c = 2.32 x 10"6 (dimensionless constant), yx = 1, b r separation of the curr nt electrodes in cm and p the resistivity in ohm-cm. Although the above formula was not developed in connection with hltran, the constant given was obtained from measurements made on earth electrical transients, using similar electrode configurations and should, therefore, apply. Later, Hawleyl 2 observed that five years 'had elapsed after B l a u ’s original disclosure, and that several companies had intensively investigated hltran but no data had been published. It was his objective to study the effect and, with highly refined equipment and with corrections for the response of two instruments, he measured the transient response of the earth, both for currents and potentials, obtaining values which are not compatible with the equa tion above. The time constants measured for the potential decay were small, not exceeding 350 microseconds for a separation of the current electrodes of 12,000 ft. For distances which are near the upper limit of those anticipated for IP survey work, the time constant was about led microseconds. Tiie growth and development of apparatus, which in its final form is not too unlike in operation that described in this thesis, is traced by Fot aponko -^,14 et al in a series of patents. Although the apparatus is well described, the explanation of tne origin of the polarization effects is not clearly outlined, an analogy is drawn between the polarization effects at current carrying electrodes (first in an electrolyte and then in oil) and the polarization effects observed in the earth. They extend the analogy far enough to make the claim that the direct detection of oil may be accompli shed . In the later patents they stress the idea that formation contacts are revealed by the measurements. 6 In addition to.these patents there are several other American^-'? lo patents issued on geophysical prospecting methods which use induced polarization as the principle of operation. These methods are not capable of a detailed study of the polarization signal and are, therefore, not discussed. It is significant that, other than the patent disclosures cited in this section, the subject of induced polarization as applied to geophysical prospecting is not treated in the Ameri­ can literature. 7 B. 1. LABORATORY EXPERIMENTS Description of Apparatus It did not appear possible to arrive at an intel­ ligent approach to the problem of geophysical prospec­ ting by induced polarization without first investi­ gating the conflicting ideas contained in the liters turft Experiments, therefore, were designed to study the exist>ence of polarization, the "residual” volume polarization observed by Schlumberger, the large reversed currents of Mttller and Weiss and the decay time of the polariza­ tion potential with particular reference to its relation to Eltran. All work of these early investigators had been conducted in the earth. The results of such experiments are always confused by the lack of exact knowledge of the state of mineralization, the concen­ tration and amount of electrolyte present, the effective resistivity and the variation of all of these quanti­ ties both in the horizontal and vertical directions. In order to avoid the above complications the experi­ ments were conducted in the laboratory where these fac­ tors were under the control of the experimenter. This part of the thesis deals with the results of these experiments. To simulate earth conditions a wooden tank 6 ft. x 8 ft.x 3 ft. was filled with clean quartz sand. A second wooden tank 3 ft. x 5 ft. x 1 ft. was filled with water. At first the experiments were conducted in both the sand and water tanks. It soon became apparent that the same results were obtained in both tanks and because of the ease of operation the water was used almost to the exclusion of the sand tank. In both tanks the resistivity was adjusted by adding the proper amount of salt (NaCl) water. Therefore, the electrolyte in all these experiments was a solution of NaCl in concentra­ tions which varied from 0 to 3*6^ by weight. The electrical circuit employed to record the data was essentially that shown schematically in Plate 1, and will be described here. The energizing current ci3>cuit consisted of the current electrodes CC', the resistor RC, the pulsing switch SP, reversing switch SR, control rheostat KH, batteries B, ammeter A and equivalent meter resistance RM. The ammeter was used to adjust the energizing current to a predetermined value. The meter was then replaced by its equivalent resistance RM to keep the circuit reactance entirely resistive. The current actually employed was shown by 8 PLATE I RH C'tI B RM SP m BUCK. CAL. TANK BUCK ion CAL. RT G I DIAGRAM SHOWING T A R G E T AND W A T E R T ANK, ELECTRICAL CIRCUIT the galvanonutor Q1 which recorded the ootentiol across HC. KG was generally a l-obr’ precision resis­ tor. The record lor; o'! event G 2 v:e s connect od in series f ordinar" Ag/AgCl vii th the uls ing s■?Itch r-rin electrodes II', noun tec] i : glaz.-, tub'1 ..uu ’n rr. to Cor''" th.e circuit which > easurer tue polarization potential. This circuit r,e~ cured t .e potential chord resulted fro- the induced polarization (II), after the ourrent had been interrupted. A second pair cf electrode P!1 were connecto 1 di recti*/ across the recording element J"' t :> ;ndic:te continuous]/' the not-nntia] across the v;nif target jtJrreierre.: hereafter as the space potertia]. When the target I (described lat ..-r) vos used, it was inserted centra 11” bet ween tiie elec•redos T r* and : 1 - n.G v" s '•'O'lnecte' tv the recordin'" elereent Gl in parallel with KT. except for one set ol records, described in the section on resis­ tivity, the resistor KT was a 1-ohm precision WATER resistor. The inherent LEVEL electrode -otentials were never greater than 0.9 rv A fl WIRE but frequentI" a steady difference of potential W'3 prod”.cod when the target was immersed in A 9 / A 4 CI ELECTRODE the electrolyte. To null this difference of poten­ tial, a Ih-oh-' resistor was inserted in aeries TARGET with o • -:. no tent ini cir­ cuit such that a current through the resistor pr o ­ vided a bushing voltage. FIG.2 The circuit, rrran -cd to d e l ’vor current in either oirection across tlr resistor ana ea :ne bucking circuit, is diagramed only as a block. A similar ty-c "0 'ircult was used to introduce known voltages into tiie no ton -ial circuits -for calibration nu.r" oses. 7 7 7 7 7 Throughout the labora tory and field enperinentu special precautions were taken to shield tiie nonpolarizablo electrodes from the direct polarizing action of the energizing current. Tiie vet.106 of mount­ ing the Ag/AgCl' e.lectrodes, w s irrr glass tubing as a current shield, is shown in Figure 2 . A r.otor-d: van ca" used to open and close 9 r Itornptely the nolarizati on-notential circuit, and both sides' the enarriz' o.c circuit. The sequence q -* events executed v-v i ho ’ ■ echnnism viz.s : 1.) oner the rol arize tl on-roten to o 1 circuit, 2) close t] a current circuit, ") oren th current circuit rod •') close 1 circuit. The sr/itchi as •"■'cheriisn hat to th e r o t ~ e require- ents: a) that, the current eirsa ti sf v th ri or cot 'cl/: tot v.li'lo the rc1''U11a ] snitch cu t t ■us a! /■*> f* b) that the- closing of t; e nnto'-tisl oirW£ s rl] no’s ;no - , >u t p T*rp ' r> *• RANGE CONTROL RESISTORS Rs =50w Rq =23w F IG. 3 '< 0vj inc -r-»f.J f "> T‘■•an '■'V • - 'A - 11 - n 1em.ent She! 1 ii" cor ,t. jX U~G v \ ) . o ■ > o • c*0 t1 1 nenp ^ ~ y t -j» • b -1:v r- pa lva'c.o'-’:-''tcrs 7? ...i,>_/, xf■ »••>o0 \■' 7-,ps-■ > ' * ; > , a c » r- f ‘ r> - .Ivano1"-'tera j,1 X ' •4U. ± s*r^1 rxX prc: •ncv o> **'*\■■•v-7 a' ■ •'■'r"x-.- •' x i -• /-» . ’ 1 1 . 1U ■;« -* irr~ 'vir\'v’r> •r» ™-U , r*onr 'i. !-r-*-1tr '■ « v-.. .0r,-r*-f,'5 _ 1i v-|O y*, ■-’1 s lit' 7 * f" sovpx ,,r ]r. 0” 'ir ■ ' » v-u TOr.ic* ■1r<'? t;; ■-Ur V|^W..S'i >*>•» .;n •v*r-nt T*,0-'*■''-' ^ '*1'C[ ^ / t « V , T t . j r > " ; T ' O had t'' h'“ ’■ont c h ;" i ') ina tru- V,-,h.-.r,f - - T .u . r\ -n-, ■•v r r,r- ••?t X ;.. '’ •-,hU troa ' T’O S 2 s ta c o 1'T’ t^ f'vqc n Ir +; (0 i~. ^ ; con O •?sto-J 1 n r' a vr:-S O 7Tj-q I/' pc-rp i7 "]r-“vr-p 1' 3 n a d Tus ta b] -12}h■-e -co*' ti‘ol r e ”i <7f “ • Th-"'1 r- n -••O_ O p trol ro^-;st--'r r 11 J’ p'birio- .r* nm.n a o]inprjr a r\ "tens '-■j-C; mu’ 1 1 r l e^ e " T.o. O r e r a n " c s t a r t s a t. 1 niy nr-u e x t e n d : \r r■'t, covens t e •'nt cjmj-o i ro”~ mv t o CO v . Oho i n - tru u " -.n t riras a .l"Ta ’ 's 'xoops t e d a t o r ne-' a cr- N s ____ _ i! 4 . , TARGET PULSE TIME 0.15 SEC (c) PULSE TIME I.27SEC 1. CURRENT 2. INDUCED POLARIZATION 1.07 SEC 3. SPACE POTENTIAL 4 . TARGET CURRENT to be outlined. The instruments were arranged in the manner shown in Plate 1 and, with no target in the tank, several current pulses were delivered to the water through the electrodes C C 1. The target was then inserted between the electrodes (PP1 and W ‘) which previously had been located in the center of the tank and separated just enough to allow the target to slide between them. Current pulses were again delivered to the water. The traces obtained are shown in Plate 3 where (a) was obtained for the no-target run and (b) and (c) with the target in place. In (a), Trace 1 gives both the magnitude and the duration of the cur­ rent pulse and Trace 3 shows the magnitude and shape of the potential across the target space. The sensi­ tivity of the recorder element which produced Trace 2 was so adjusted that a potential of 25 Jiv would pro­ duce a deflection of 1 mm. However, no deflection of this element was obtained, even for a potential as large as 12 volts across the target space. The same results held when the medium employed was sand satu­ rated with salt water. An interesting aside occurred when the first Lank of sand was tested. Two rather large and well localized IP signals were obtained as the potential electrodes were moved about the surface. The signals were traced to two extraneous nails burled in the sand. After the nails had been removed a signal still persisted. The sand was then run over a magnetic chuck and a considerable amount of magnetic material was removed. After this treatment no signal was ob­ served. All sand used from then on was passed over a magnetic chuck. _It has not been -possible to obtain a •polarization potential which arises from clean quartz sand or water (salt or fresh). The situation, however, was greatly altered when a piece of metal was intro­ duced between the electrodes. The results obtained when the target, with iron plates, was placed between the electrodes, are shown in (b) and (c). Examination of these records reveals that the shape of the ener­ gizing current pulse is essentially the same as that in the no-target case but the similarity of records ends there. The most significant feature of these (b and c) records is the decaying potential curves of Trace 2. They were measured by the electrodes P P 1 and the measurements were obtained entirely after the ter­ mination of the current pulse. These potentials arise from polarization induced at the target boundary. That these potentials are truly the results of polari­ zation effects is further demonstrated by the record of the current which passes through the target (Trace 4). The faces of the target acted as electrodes (cathode and anode) at the initiation of the energiz­ ing pulse and current, therefore, passed through the target. However, polarization at the target faces began and as a result the target current was decreased. The longer the pulse endured (c), the more the prod­ ucts of polarization developed, which resulted in a further decrease of the target current, but the current through the target was never reduced to zero. An equi­ librium was established between the rate of formation and the escape of electromotively active material, which necessitated a small current to continue to flow through the target. When the energizing current was interrupted, the electrolytic cell, formed by the prod­ ucts of polarization, discharged itself through the surrounding medium. The discharge of these products is like the discharge of a battery where the surroun­ ding medium plays the role of the electrolyte and the target that of the external circuit. The current delivered to the medium by the discharge of the prod­ ucts of polarization is shown as the reverse current through the target. A little reflection on shape of the space potential curve (Trace 3) gives added veri­ fication of the interpretation that the effects ob­ served are due to polarization at the faces of the metal target. 3« Induced Polarization and the Energizing Potential The procedure described above for obtaining data was followed for a variety of conditions, which pro­ duced oscillograms like those shown in Plate 3* These conditions were varied in such a manner as to facili­ tate a study of the IP potential as a function of the energizing current and the resistivity of the medium. Although several metals were used as targets, the largest amount of data was obtained with targets of sheet iron. A discussion of the results obtained from measurements on other metals will be given later. No cleaning procedure was used on any of the metals other than to remove the excess grease. The relationship of the induced polarization to the energizing current was studied by holding the resistivity, the target metal and target size constant and varying the energizing current. The energizing current was varied from 0.5 ma to 12 amp., the upper limit of current being determined by that value which produced arcing at the pulsing switch. For every sequence of runs made with the target in place, a cor­ responding set of runs was made with an identical set­ up except that the target had been removed. The target was next changed and all records were repeated. After the desired data at one resistivity was obtained, 13 the solution was altered and all records were re-run for the new value of resistivity. From these data several curves have been plotted and are described below. Plate 4 shows the plot of the IP potential, the space potential for no-target and the space potential with-target in relationship to the energizing current. As it should be, (Ohm's law) the potential across the target space for no-target is a linear function of the driving current. The with-target space potential is larger than the value given by Ohm's law up to the cross-over point which is approximately 1.2 v. Beyond this it falls below that of the straight ohmic drop. It should be noted also that the IP potential remains linear with the energizing current up to 5.6 amperes at which value saturation begins. The current which produces the saturation of the IP curve is the same value which yields the cross-over of the potential curves. This suggests that the IP potentials might well be plotted as a function of the ohmic (no-target) potential. The curves shown in Plate 5a and 5b are curves of the IP potential plotted against the ohmic potential of the target space. The curves of 5b are merely scale enlargements of 5a in the neighborhood of the origin. Curve 1 was obtained by using tap water whose resistivity was 3630 ohm-cm. Salt water was used to obtain Curves 2, 3 and 4 where the resis­ tivities were 820, 57 and 22.4 ohm-cms. respectively. Although the slope of each curve is different the curves have three common features, namely: 1) they pass through the origin (see 5b), and 2) they are linear to a saturation potential which appears to be approximately 1,2 v. From these curves it has been concluded that: a) no threshold of energizing potential is required to establish polarization effects. Ener­ gizing potentials as small as 0.5 mv produced observable polarization potentials. b) the induced polarization potential is a linear function of the ohmic (no-target) space potential up to a point beyond which saturation is approached. In place of the ohmic space poten­ tial, the potential gradient may be substituted because the abscissa, Plate 5» is proportional to the gradient. c) a saturation of the polarization occurs which begins at approximately 1.2 v across the target space. (It is interesting to note, in this 14 PLATE 4 .0 SPACE P O T E N T I A L NO T ARGET NDUCED POLARIZATION vs .8 ENERGIZING CURRENT .6 SPACE P OT E N T I A L W I T H TARGET .4 2 .0 / ).8 / >.6 '.4 INDUCED POLARIZATION POTENTIAL 2 ol 4 6 ENERGIZING 8 CURRENT (AMP) 10 PLATE 5 (a) INDUCED P O L A R IZ A TIO N P O T E N T I A L SPACE P O T E N T I A L ( N O T A R G E T ) vs INDUCED P O LA R IZ A T IO N PQTE N T I AL (M V ) 500 (4) p = 22 .4 cm / 400 (2) p = 8 2 0 f t cm 300 (I) p - 3 6 3 0 & cm 200 I 00 SPACE P O T E N T IA L (b) (V O L T S ) IN D U C ED PO L A R IZ A T IO N P O T E N T I A L SPACE P O T E N T I A L ( N O T A R G E T ) vs R E G IO N N E A R O R IG IN A M P L IF IE D 60 (2) = o INDUCED PO LAR IZATIO N P O T E N T IA L (MV1 80 {Z)p- 82 0 XI cm 30 20 { I )p ~ 3 6 3 0 XI cm o 20 40 60 60 IOO ■20 140 SPAC E P O T E N T IA L O ' ------------------ 0 5 L 10 15 _ _ _ _ l ------------------------ 20 25 30 RA TI O OF R E S I S T I V I T I E S 35 ( 40 45 50 L .1 55 60 The initial current through the target and the induced polarization potential are plotted against the ratio of target resistivity to the resistivity of the medium, './hen the ratio of resistivities is zero, the current through the target and the polarization induced are also zero as is expected. A third satu­ ration effect is to be seen on this plate. It appears that tiie maximum induced polarization potential will be developed across a mineral when its resistivity is one tenth of its surroundings. That is to say if a mineral, say serpentine for which p = 2 • 1C>3 , is embedded in a matrix of resistivity 10 times this value, it will be strongly polarized, whereas if the matrix had. an equivalent or lesser resistivity than the serpentine, that mineral would be only slightly polarized. 5. Decay Time of the Induced Polarization In the preceding section it was pointed out that the dissipation rate of the polarization potential was a function of the resistivity and it was hinted that it may depend upon some other property of the elec­ trolyte. Four decay curves are clotted in Plate 7s showing the decay as a function of time for media of resistivities 3630, 820 , 6/ and 22.4 ohm-cm. The ordinates of all the curves are in arbitrary units and have been matched at t * CO milliseconds. This m atch­ ing point was chosen because it was a convenient 2 mm after the zero time for a tape speed of 2.5 cm/sec. Tri9rG 2.s 2.*t.L1 c ciiLa* o x*on c o in ’ t'no clgcoy x*g o oi? ilic three curves 2 , 3, and 4 . The fourth, (that for p o ohm-cm or tap water) however, decayed at a much slower rate than the others. The curves of the growth of the polarization potential follow the same tyoe of behavior; i.e., the higher the resistivity, the longer is the time required to produce saturation. A knowledge of the growth curve is important in the determination of the required pulse time. The minimum pulse time is that which permits the polarization to reach saturation. A pulse time which is longer than the minimum is ’wasteful of the power supply. — 3 30 One significant feature of the four curves of 7a is that t.iey are definitely not exponential. If the polarizing charge upon the metallic mass discharges solely as an electric currrnt through a resistive medium, the rate of decay would be proportional to the remaining charge and the decay curve would indeed have exponential form, hence, it becomes apparent that some additional factor contributes to the rate of dis­ charge of the polarization. Towden and h i d e a l ^-7 16 PLATE 7 DECAY RATE OF POLARIZED IRON vs RESISTIVITY OF MEDIUM (SALT WATER) 30 TAP WATER SALT WATER " " " " (2) 0< 25 (3) X- (4) A« p e J 6 3 0 ft cm ^ ^ 8 2 0 ft cm p = 6 7 f t cm p - 22.4 ft cm 20 _) Li. W O O 400 000 1200 1600 2000 2400 2000 3200 3600 4000 T IM E ( M illis e c o n d s ) DECAY CURVES 33 t- D in (f+ c) u SOi Es ■■ t +c TAP WATER 3 % SALT-WATER (5) Z O I— o Uj _» liUJ Q O 400 800 (ZOO 1600 2000 T IM E ( M illis e c o n d s ) 2400 2 000 3200 3600 4000 investigated the discharge of the polarization from the electrodes of an electrolytic cell. They found that the potential (E) exhibited by small quantities of electromotively active material deposited on an electrode is proportional to that quantity. "This quantity is very small indeed, the deposition of suf­ ficient hydrogen to form only l/3000th of an atomic layer raising the potential of the cathode 100 milli­ volts." They further found that the discharge rate on open circuit depends upon, among other things, the presence of oxygen in the electrolyte. An expression was obtained in which the rate of decrease of the polarization potential is directly proportional to e^E. They pointed out that this was contrary to the rate of decay usually assumed (proportional to E^) or that (proportional to E) proposed by Heyrovsky. The three equations are given in Table 1 . Table 1 Hate of decay Potential vs time a *E dE = -Ae’ dt E = B - 1 ln(t + c) k Bowden and Hideal b _ _w2 dE Z * dt E = Usually a s sumed dE = - * E dt E = E0 c A (t * c) .... ^ Ordinary Exponontial, heyrovsky According to Bowden and Piideal Equation a obtains only when the oxygen has been carefully excluded from the electrolyte. To effort was made in the laboratory to exclude the oxygen and the concentration of oxygen in the earth is known to be large. Therefore, the decay curves presented in this thesis should not follow Bow­ d e n ’s relation but should be more like the relations given by Equations b or c. However, still other condi­ tions for which Equation b and c are valid were not met in the laboratory either. The theoretical equations, including Bowden's, represent the discharge of the active electrode material when no electric current flows through an external circuit. The electrodes formed by the target faces in the study of induced polarization were always connected, thus violating the no-current condition. If any agreement with the actual discharge curves shown in Plate 7a and either Equations a or b above obtains, it must then mean that the resistivity of 17 the medium is less important in determining the form of the rate of decay than the open circuit process of dis­ charging the polarization products. A comparison of the curves resulting from the Equations a, b, and c and the actual decay curves for tap water and 3e salt water is shown in Plate 7b. Equation a is compared with the discharge curve for tap water and the fit has been forced at t r 8 0 , 120 , and 200 milliseconds. The agree­ ment is not good but it was not expected to be. loth Curve 2 and 3 have been forced to fit the decay curve for iron in 3e salt water at t a SO and. 200 milliseconds respectively. The exponential (Curve 2) fits the actual curve ( 5) only at the two forced points. On the other hand, Curve 3 covered the decay curve over the entire range of the data available. It is concluded that the decay of the induced polarization potential with time is not mainly governed by the resistivity of the surrounding medium because the decay curves are not exponential in form. It fol­ lows thatvariations in the resistivity of the earth from, place to place can have little influence on the form of the decs;/ curves obtained. On the other hand, the good agreement (in form) of the discharge curves obtained in the salt water tank and the curve calcu­ lated from Equation b is interpreted to mean that the primary factors which determine t h e shape of the dis­ charge curve are the diffusion ui tne products of polar­ ization into the electrolyte and chemical action between them. Although the composition of the electrolyte is o v\ n 4“ v/.'v.JVyW o o u e- w V r m -rt-r X j w*. a X v\ T w' U r\ rs J A IN / 4- o «** v * /-s + - V . _ y -L C U h - ^ I/* .,/ r\ -yt U ii'O +■ V i r \ -P n X C* ^ A O governing the discharge are not expected to vary appre­ ciably. hence, two discharge curves obtained at dif­ ferent places on the earth may be compared at corre­ sponding values of time. It seems appropriate at this time to compare the decay of the IF potentials with tnose of earth transient (Eltran) potentials. The curves shown in Plate 7 re­ quire at least 0.3 seconds to fall to 1/e of their orig­ inal value. In order to compare the decay of these curves with the decay curves associated with Eltran it is necessary to choose one of the time constants (see Part A -2 ) reported in the literature. The formula, which arose from the resistivity studies, gives a time constant of several milliseconds when laboratory values are inserted into the equation. Remembering that the delay time introduced into the pulsing cycle was about 10 milliseconds, the magnitude of the transient to be expected upon closing of the potential switch may be calculated. Energizing potentials as large as 2.0 v were not uncommon and, therefore, a 2 millisecond time 13 constant would have given approximately a 14 millivolt residual signal in the tank for the no-target case. However, no signal as large as 5 microvolts was ever observed when the tank did not contain a polarizable object. Thus it appears that the results obtained by Hawley must be used and, therefore, with the time con­ stants he reports, it is concluded that current elec­ trode separations as large as 3000 ft. (more than is anticipated for field survey) may bo employed without interference from Jltran potentials. 6. Behavior at Chemical Boundaries It is the expressed belief of I.liller, Teiss, Fotapenko and others that a polarization potential can be induced at chemical boundaries. The term chemical boundary, although not defined, apparently refers to boundaries separating regions of chemically different electrolytes. It Is further implied that a high cor­ relation is expected between the chemical boundaries and formation boundaries. The mechanism of inducing a polarization at a boundary which does not have elec­ trically conducting minerals on one side is not ex­ plainable in terms of the laboratory results so far de­ scribed. Therefore, in order to investigate the effect produced at a chemical boundary, a cell made of plastic tubing 20 cm long and having an effective cross-sec­ tional area of 20 cm^ was filled with a concentrated solution of OU3O4. The ends of the cell were closed wit., vegetsble-paper diaphragms on t ~ which a layer of bees wax had been condensed to reduce the rate of dif­ fusion through the membrane. The cell containing the CuSOu was placed in the water tank in place of the target. The C U 0O 4 target was first immersed in tap water and a. series of records were made which showed the signal, the space potential across the target and the energizing current as the current was varied. Similar records were obtained for the target immersed in 0 .1 , 1.0 and 3 *6 ;.' salt water. The CU3O4 was removed from the target end in its place a 3m salt solution was added. A complete set of records was obtained for th° KaCl target. Data were also obtained when this cell con­ tained the same solution inside and out and also for a lp salt solution inside surrounded by a 3k salt solu­ tion. Ho induced polarization potentials were observed for any of the solutions contained in the cell when im­ mersed" in a medium of low resistivity. Small potentials were observed for both the CUSO4 and NaCl targets in tap water and still smaller potentials for the CUSO4 cell in 0 .1/1 salt water. The results obtained are shown in Plate Sa. A comparison of the largest potentials meas ­ ured for the chemical cel].; i.e., CUSO4 in tap water, (a) PLATE 8 20 I NDUCED P O L A R I Z A T I O N vs SPACE P O T E N T I A L CHEMICAL B O UN DA R IE S NaCI p -8 2 0 Si c m 0 4 8 12 20 16 24 S P A C E P O TT E EN N TT IIA A L (V O L T S ) (b) 400 IND U CE D P O L A R I Z A T I O N vs C U R R E N T DENSI TY 300 M E D IU M T A P W ATER p =3630 SI cm > S 2 O N I- 5 zoo _l o O Hi o D O CL 2 o 40 80 120 CURRENT DENSITY ( ^ a / c m 2 ) 160 200 240 with the IP potentials for an iron target of the same dimensions, also in tap water, is made in Plate 8b, A potential which decays with time was observed at the non-metallic boundary separating two solutions, each containing different ions. This potential, whatever m ay be its origin, is seen from Plate 8b to be a second order effect in relation to the induced polarization potential of iron. It appears unlikely that M&ller and Weiss could have observed an effect due to such a boundary at all and by no stretch of the imagination is its detection at 3 0 0 0 feet a conceivable result. 7. Concerning Ionic Concentrations Because no polarization was measured in either sand or water except when metal was introduced and because Schluraberger stated that an effect would appear because of the transport of ions producing a dissym­ metry around the current electrodes, another experiment was designed to investigate this possibility. The appa­ ratus employed was quite different from that already described and was designed to enhance the "dissymmetry*' effect. A pair of current electrodes in the form of iron sheets 8 5/8 in. x 10 1/2 in. (same as previously used) were attached, as far apart as possible, to an axle in such a manner that they could be rotated in or out of the tank. Mounted at right, angles to the current electrodes were a pair of nonpolerizable potential elec­ trodes. These potential electrodes were so mounted on the axle that they entered the electrolyte almost imme­ diately after the curr Gil t electrodes departed. A com— mutator on the axle completed the current circuit the instant the current electrodes entered the electrolyte and broke the circuit when they left it. The potential electrodes were connected at all times to a Brown chopper-amplifier and an bsterline Angus recorder. The gain of the system was adjusted until 40 microvolts represented one small division (1/25 in.) on the recorder tape. The current electrodes were introduced into the electrolyte for a predetermined length of time. At the end of that time the axle was rotated rapidly, removing the current electrodes from the electrolyte (thus remov­ ing any possibility of measuring their polarization) and introducing the potential electrodes. In tag water and salt water (concentrations 0.1, 0.3 end 3»6y) a vari­ ety of potentials was applied for time intervals up to 1 minute without generating potentials measurable with the equipment used. It was concluded that an induced potential difference due to the dissymmetry of ion con­ centration arising from transport under the action of a current was either too small to measure or that it disappears too rapidly to be measured with the equipment 20 PLATE 9 (a) IN D U C ED 700 P O LA R IZA TIO N PO TEN TIA L I N DUCE D POLARIZATION POTENTIAL (MV) FOR S EV ER AL TARGET MET AL S 600 (4) B R A S S (3) Cu 500 400 (2 ) Fe 300 200 100 0 2 3 4 5 SPACE 7 6 POTENTIAL- 9 6 (0 12 NO TARGET (VOLTS} ( b ) eoo IN D U C E D P O L A R IZ A T IO N P O TE N TIA L FOR I RON BARS IN TAP WATER ( MV) 700 POTENTIAL (3) INDUCED POLARIZATION (4) (2 ) L E N G T H ( IN C H E S ) 200 (3) 12 ioo 50 300 ENERGIZING CURRENT 550 (MA| 600 employed• The l a t t e r c o n c l u s i o n seems t o be t h e more l i k e l y e x p la n a tio n in view o f the r e l a x a t i o n tim e f o r s a l t w a t e r w h i c h 3 t r a t t o n l c computes t o be 2 x 1 0 ” 10 seconds. C e r t a i n l y t h e e f f e c t measured by Schlumbergeij p a r t i c u l a r l y w i t h t h e i n s t r u m e n t s he u s e d , w a - mot t h a t o f an i n d u c e d i o n i c c o n c e n t r a t i o n g r a d i e n t , however, he r e p o r t e d p o t e n t i a l measurements w k i c h decayed s l o w l y and m u s t , t h e r e f o r e , have a r i s e n f ro m some o t h e r cause, p o s s ib ly a u n ifo rm d is s e m in a tio n o f conducting m in e ra l p a r t i c l e s . 1. Other F a c to rs In flu e n c in g the P o l a r i z a t i o n S ig n a l rrn~ icro nr o t h e r f a c t o r s such as t e m p e r a t u r e , i o n c o n c e n t r a t i o n and t h e p a s s i v i t y o f t h e m e t a l l i c bo d y w h i c h i n f l u r a c e t h e p o l a r i z a t i o n p o t e n t i a l and a r e o f p a r t i c u l a r i n t e r e s t t o t h e p h y s i c a l c h e m i s t b u t have l i t t l e b e a r i n g on t h e g e o p h y s i c a l p r o b l e m . One f a c t o r w h ic h i s o f i m p o r t a n c e i n p r o s p e c t i n g i s t h e m e t a l o f vouch t h e o r e body i s composed. A study o f the e f f e c t on t h e i n d u c e d p o l a r i z a t i o n pro duced by t h e t a r g e t m e t a l hr.s boon s t a r t e d b u t o n l y a s m a l l a r o u r h o f d a t a has been o b t a i n e d . A t a r g e t , s i m i l a r to t h a t d e s c rib e d i n P a r t B - l b u t o f s c a l i e r d i a m e t e r , was d e s i g n e d so t h a t th e t a r g e t •: e t a l wa- r e a d i l y i n t e r c h a n g e a b l e , k i t h t h i s t a r g e t , end e l a t e s wade o f b r a s s , l o a d , cop pe r and i r o n were used t o o b t a i n c u r v e s o f in d u c e d p o l a r i z a t i o n os a f u n c t i o n o f t h e e n e r g i z i n g ( n o ­ t a r g e t ) space p o t e n t i a l . The c a r v e s o b t a i n e d f o r . t h e f o u r : o t a l s , when t h e s u r r o u n d i n g medium was t a p '■>r>: h o l . u i ^ C 1 ' ; _u , U' i l _i r i J ■ 1 j—. 4 v O-m o A ^ c. * 4L. C_<. _1_ v. t m i V v_; o t r r ■(■ O - L .T, C C/ • was found t o be golarizr b i o i n ta p and s a l t (haCl) we t e r . ..owevor, several irregularities ha v e been o b be seen i n P l a t e fa. The served , two o f '.hie t i s not as r e g_ u l a r as t h e c u r v e fo r t h c- bra s s r\ y e-• Prom l i r . e e r i t near the o r i g i n . o t h e r s a Vpj 1 t. The hn-.c oI.o cur ve f o r t h e lo a d t a r g e t o c c u rs a t a Two o t .or c u r v e s ( n o t shown) v o t e , t t a 1 2 'Gs t an 1 . 2 v . o20 and 67*V»-cm f o r t h e 1 Gc; G t a r g e t i n s a l t w a t e r ( r e s w h i v e l y) d i d , h o w e v e r , s t h e kn«e o f t h e c u r v e to begin a t 1 . 2 v . d e v e r a l . t h e r d e p a r t u r e s from the c u r v e s o’o t a i n o d f o r i r o n . e v e boon o b s e rv e d b u t a d i s ­ c u s s i o n vk t i w e f f e c t s w i l l be - w it h h e ld u n t i l a f t e r f u r t h e r s t u d y has been -'ado. F o r t h e p r o b le m a t hand i t i s s u f f i c i e p i t o say t h a t 'ho c u r v e s o b t a i n e d f o r t h e m e t a l s i n v e s t i g a t e d a r e e s s e n t i a l l y t h e same as t h o s e o b t a i nod wi n i r o n t a r g e t - u l r t e s w ere u s e d . c:, x ■ p= A p i e c e o f p y r r h o t i t e fro m t h e B e t t y B a k e r mine ( s e e P a r t D - 0 and l a t e r a p i e c e o f m .a g n c t itc " f l o a t " fro-.-; Lebanon B o u n ty , P e n n s y l v a n i a ( s e e F a r t D - 5 ) were p l a c e d i n t h e w a t e r t a n k and each s u b j e c t e d t o p o l a r - izirg curren ts. These clumps were too irregular to justify quantitative meas ure me nts, but they both gave signals which were corn arable to those obtained with the iron target. A carbon rod v;as also inserted between the potential electrodes i.: place of the target and a large II signal v/as observed. A", induced polari­ zation notential lias been obtained for everv metal in­ vestigated and also for a carbon r o d . The magnitude of the measured ootcntials ‘s com arable v/it : those ob­ tained with iron. Another factor which can influence the polarisa­ tion signal is the tandem effect of small dissominated ^articles. It v/as concluded, in- Part L -3 j that the induced polarisation potential is proportional to the potential gr-dient. This means t. at the curr :nt den­ sity (and, therefore, energising current) required to r-roduco saturation is inversel" proportional to the length o f the mineral particle. That current •chi ch will saturate r particle of one length wl 11 not satu­ rate a shorter one and, therefore, the polarization notential (at saturation) measured across two short ■'■"•'rtides in tnv'or will be greater than that across one particle of equivalent length. The induced polar­ ization. potential ^ensured a cross several iron bars each of different length and across ono combinatio1'1 r'f two bars in tan den is simm: ;•lott "d iw I late fb -s a func­ tion on the mw'rgiziny current i n milliaw.gores, Curves I, 2 and 3 "'ere obtained for iron b-rs whose lengths v/ere 3 , 6 and 12 1mcu es respectively. Curve /’ was ob ­ tained b;' r-lneir- the 3 and 6 Inc}: bars ’n tandem sepa­ rated bp ! /3 inch gap. The potential across the pair is a g v'ro::i" atelg t. i a t to b : expected for a ( inch bar until sa tu.ra tion begins anA then the potential across the combination exceeds that across the 12 inch bar. The potential across t h e combination will continue to increase u n t i l t h a t current has bee1'’ reached which. v : i l l produce saturation across the shorter bar. This t a n d e m e f f e c t w i l l serve to emphasize t h e disseminated mineral, parties.]arlv if t h : particles are well aligned and not videI” separated. An increase in the separation of the particles reduces t..,e polarizatlo mot ntisl '"ensured across the combination. The induced polarization potential will, t .erefore, be sensitive to t c percent­ age of polorizablc mineral .contained in the rock. 1. Other Tan':. Experiments Several experiments, unrelated except for the fact that the "ediurn in each case vac sand wet with salt water, are described in this section and they conclude the la bora tor;' xporimenta t i o n . oo n) i- .3on:.: of D i s s e m i n a t e d mineral It v;ss suggested i. Psrt 3-7 that the "residual" potential effect observ cl 1:7 3 chlumberger might be explained by the i n d u c e d -polarization of elec­ trically conducting minerals which are ore or less uniformly disseminated in the earth. The tandem effect discussed .1o fart -3 adds weight to this hypothesis. In order to verify the assu . t i o n that a mineralized zone v/as •'/b i o t o account .lor t h e ''residual11 polariza­ tion a small v-s" . je of sand was mineralized and inves­ tigated. A volum of clean quartz sand, 11 x 6 x T inches, was mineralized by t h e a d d i t i o n o f i r o n grit (sand-blasting s h o t ) u n t i l the mineral content v/as a o n r o x t o t e l y 10/ by weight. The mixture v/as placed i n a clot., ba g and returned t o t h e h o l e i n t h e send. Trie point electrode arrangement v/as u se d t o measure the induced polarization potential. The return current electrode u s i n one corner o f t h e sane tank and t n e reference potential electrode v/as in the diagonally o p p o s ite c o rn e r. The point current electrode and the p r o b i n g ' o t e r i L l a l T.cctrode were h e p t 2.5 i n c h e s apart and were moved t o g e t h e r along t i n / opposite diagonal of the tank. The results obtained, shown in Plate 10a , n r o v o t h a t a z o n e o f disseminated mineral cam be polarized. . f i l e t h e z o n e of disseminated mineral was i n p l a c e , t h e I f potential was measured in various d i r e c t i o n s across t h e z o n e . ./enuer configuration of w _L. ' -X ^ U -A. n ^'Sn ^ -1 t*r *'*' r* V fc j n r« o L ri '•cVJl ^ r> w- J. t* r k ' u r> 1", f t *- M w ~| , _i_ t u -I. 'w> i. ^ c* v *w 3 t h e c e n t e r o f tin/' system v/as a t t h e c e n t e r o f t h e z o n e . The l i n e o f e l e c t r o d e s v/as f i r s t oriented along the l o n g dime:-: s i on o f t h e z o n e and k n n r o t a t e d t o o t h e r p o s i t i o n s m h c . made a n g l e s o f 3 0 ° , 6 0 ° , SO0 , 120°, arid 170° t o t h a t lino r c s p o r n ivcly. The r e s u l t s f r o m the sir. orients tioms of k.c f i n e a..e shown p l o t t e d i n t h e insert dlcte 10c and they a r e i ■ good a g r e e m e n t v / i t h t h e p r e d i c t i o n s if f a r t C-3 c o n c e r n i n g t h e e l l i p s e o f p o la riz a tio n . 1;) U n ifo rm ly m in e ra liz e d fa .rth Tiio theoretical d e v e l o p m e n t o f Part C-l predicts t.mit the i n d u c e d polarization potential of a uniformly mineralized homogeneous earth und m the in­ fluence o f a point electrode f a l l s o f f as 1/r. The con­ d i t i o n s required a r e d i f f i c u l t t o m e e t . T h e y may be s a t i s f i e d i n the earth o v e r a sufficiently large volume b u t there is no way to determine beforehand whether or n o t the conditions are satisfied at any given location. An a t t e m p t was made ' t h e l a b o r a t o r y t o c h e c k this 23 PLATE 10 (a) INDUCED POLARIZATION POTENTI AL OF A ZONE OF D I S S E M I N A T E D N METAL SAND ••• • I P * s O R I E N T A T I O N OF ELECTRODE LIN E DISTANCE ( IN CHES I £•,»:**>'.vf c v«*y.v ( b ) : 600i ------------------- • . . . . . .----------------------------------------- IN DUCED POLARIZATION OF U N I F O R M L Y M I N E R A L I Z E D SAND ~........... IN AN IRON HEM ISPH ERICAL SHELL POTENTIAL (Mv/AMP) 550 ip U N M IN E R A L I ZED R E F E R E N C E P O TE N TIA L ELECTRODE NORMALIZED R = 16 IN C H ES M IN E R A LIZE D (2 ) X R = 16 INCHES R= 10 INCHES DISTANCE FROM POINT E l ECTROOE (INCHES) theoretical relation. A hemispherical shell 40.2 inches in diameter was filled with sand and wet with salt water. The point current electrode was a 1/8 inch iron rod which extended into the sand at the cen­ ter of the air-sand plane. The hemisphere itself served as the return electrode and the two electrodes together provided a current density pattern which was essentially radial and yielded equipotential surfaces which were hemispheres, as required by the infinitely extended half-space. The reference potential elec­ trode had to be at a finite distance from the point electrode because of the limited radius of the hemi­ sphere. Its location, however, needed to be described only in terms of its distance from the center because the equipotential lines on the surface of the sand are circles. When the hemisphere contained only clean quartz sand and salt water a polarization potential, which fell off rapidly with distance from the current electrode, was measured. This background potential arises from a differential polarization of the current electrode. In order that a current of approximately 600 ma could be delivered to the sand, the rod had to be inserted nearly an inch into the sand and, there­ fore, contact of the current electrode with the sand was not a point but a cylinder. The background polar­ ization potential was just measurable when the hemi­ sphere was filled with tap water in place of sand. The sand in the hemisphere was next mineralized to about 10/ by weight by the addition of iron grit. Small batches of grit and sand were mixed bjr hand (in a wheelbarrow with a hoe) to attain a fairly uniform mixture. Water was added to the mixture until the water table was at the surface of the sand. The measured induced polarization potential is plotted in Plate 10b as a function of the position of the prob­ ing potential electrode from the center of the he mi ­ sphere. The relation of these results to the theory is discussed in Part C-l. c) Induced Polarization Potential of a Buried Sphere An attempt was made to obtain experi­ mental verification of the theoretical results devel­ oped in Part C-2 for the potential of a buried sphere. The conditions required by the theory, in the develop­ ment of the approximate formula, were never realized in the laboratory. One difficulty which thwarted every attempt at measurement was the size of the current electrode required. The largest iron sphere available at the time was only 3 inches in diameter. Vi/hen that 24 sphere wrs buried to a depth of five times its radius, the current required to produce suitable potential measurements at the surface of •he sand, was of the order of 1 ampere. The electrode ares required to de­ liver one ampere was prohibitively large* A compromise v/as reached ••.•hereby tire deptu to the center of the sphere and the size of current electrode were both de­ creased until a measurable signal was obtained. The form of the measured potential distribution v/as in agreement witm that predicted by the the o r y 5 i . e . , the potential rose to a maximum over the sphere and then decreased and finally became negative as the distance from the point electrode v/as increased. The magnitude of the measured potential v/as, ho w e v e r , much greater than that predicted by the simplified expression (Equa­ tion Ip) in hart C- 2 . The conditions required by the theory were not net and, therefore, no comparison of the experimental and theoretical results car. be made which can check the validity of the theory. 10 . Conclusions The problem of establishing a potential by induc­ ing electromotively active- materials on the surface of a metallic obj ve t in an electrolyte has been investi­ gated. The following facts have been established: a) that a polarization potential can be induced on the surfaces _'f a metallic object in an electrolyte. b) that the potential induced is a linear function of the potential gradient until a poten­ tial of 1.2 v has been established across the object. Teyord this potential a saturation effect begins. c) ‘L-at diffusion and chemical action of the products of polarization play the predominant role in the determination of the rate of growth and decay of the polarization potential. d) that to a first approximation, only metallic or metallic-like objects are polarizable. The polarization of the cell containing CU0O4 surrounded by tap water is an exception but it is a second order effect. e) that metallic particles disseminated throughout an unpolarizsble matrix are polarizable. 25 Fro* these facts It is conduced; a) that polarization products are induced on a boundary In an electrolyte only when there is e change in the mode of conduction; i.e., from ionic to electronic or vice versa. b) that the charge density induced on the boundary Is proportional to the current density crossing normal to the boundary and of such sign as to oppose the current v/hich generates It. c) that if a polarization is induced at all it Is induced upon an electrically conducting m i n e r a 1 v.iii ci: . is either in the for;; of a solid ore 'ody or a s a ci.;ssonina tod mineral. L'-lCtL the current r e m i r e d to produce d) '111 be greeter for Lire eisso; ; m toe soturoi ti TO-Oil mineral for In a solid ore, Further, that for i *-Ci current the induced polarisaa given -p -v_ia.'r«i- ,J— tion tob entia 1 of a minora 11 zed zone ’mill bo ot.id J_ 'h;a v/h.c-n the ini neral is encased in a love roslstiv . roc'; t ran r n a k i t.n.. r r e s i s t i v e one on tvro a c c o n n t s ; 1 ) t. .n p o t entiai g r a d i e n t ostablishod a cr o s s the m i n e r a 1 '.•"111 bo s m a l l e r and ^i^ ef th c r e s i s t i v i t y ef m a t r i x t o m i n 2) Lhoral •.,il 1 h r 0 n pp p s c d . -j i■ h ’'' SiiC-.P'-' -Jf the decay c u r v e s m i l l bo inner: - -p- > i. • r:hi a "I vs !, a v iv o ' ; i: r.t i;u i , of tin r o s i s t i v 1.ly f'tnc i :odiur. s u r r o u n d i n g the m i n e r a l . 11 -f- e r e f o r e , have a The c u r v OS .. 1 •*time constant - * ---’vmr'‘ii mr 1 1 e l .. t_ j o 0 o a p p r o m i n u t e l y C . f p soc. r. a ho ve conclusions tiU- b the It f 0 ilov;O j.ro r ■ .. j-✓ V “i *.-i;(j.( L>i_ ■.le­1 ■’ ; J.J.. 7j 4-i 'V;.;* ■’ki ly‘.n tim 1 _i_ Ij .- 'L,i1J .t :.berg 1 ir arcs O * V * fie-' ft or c ■:r -L O ... •.J..-L1U V*\ hiJ_O hributi.in of elo n trirri' cal .1, a j- - ■icti V ‘": mi •n era 1 s # po Lmitia Is .-Xi-i,C*U . ' — .4 ■ > < r £ n 1 7 j * haveren (..k i L.m . Oi Oi'i;ko clai ..o to q nrobably i .k , .11 - .. * c1'•> '"on,-.m O f th . claims e l eui.Lor and * eiss ori gi n • rn arc: tona i . ■3 J. . vi -■.r of th o ahove conclusion •y* rre y . t j_ C' • u .o 0 luck V O m e a s red a ■; y hi m g O tnO-r l. _ i G i i tliG polari z a tion ()g the ir ov;n current GlG c trod os "hich r/as many :tor hiI1.1]"i j.he ef fee t they sought. tim G s yr ,m;' • i j 1 i The conclusions mulch result from the laboratory eroerinontation establish sore requirements on the p r o ­ cedure to be followed in the field and also on the method of reducing the data obtained. Ifecsurenents of h.e apparent resistivity mill have to be taken in con­ junction v:ith the induced polarization data. The 26 resistivity factor must be renov-d froin the measure­ ments obta Ined •in the field before such rr.eesurements are compare d. because of the linear relation between tao energising current arc the induced potential the field measurements will have to bo normalized to a given current. The for- of the curve for the decay of the induced polarization potential requires an energizing-curront pulse which is not less than 0.3 sec. du ra­ tion in order to produce time-saturatio i for a giver* current, however, the pulse tine does rot have to emceed C .7 sec. It appears from a considerstion of the electrical transient effects that the delay V time in the switching cycle may be as s?call as 10 milliseconds without interference from the rapidly decaying ohmic potential. 27 C. THEORETICAL DISCUSSIOH It is not surprising that there have been no attempts at a theoretical development for the inter­ pretation of induced polarization as applied to geo­ physical prospecting. The lack of understanding of the fundamental principles involved must have precluded any efforts along those lines. Certainly the usefulness of this prospecting method, will be greatly enhanced as the theoretical interpretation is expanded. The results obtained from the laboratory investigations provide a beginning for a theoretical development. In this sec­ tion three problems are discussed and mathematical re ­ lations are obtained for two of them. The first problem (uniformly mineralized earth) is offered as an explanation of the "residual" potential observed by Schlumberger. In the second problem (the buried sphere) an ore body is represented by a sphere only because it simplifies the geometry. The solution obtained for the sphere is complete in an analytical sense but it is far from being satisfactory for com­ putational purposes. The fundamental relation employed in the mathematical development was established in Part B —35 i.e., the induced polarization potential is propor­ tional to the energizing potential gradient P = cp i In the earth the resistivity may well be a function of the three space coordinates. However, in the following work variations in the matrix resistivity are not treated analytically. 1. Uniformly Mineralized Earth It was demonstrated in the laboratory ( Part B-9) that a polarization potential can be induced into a region which contains disseminated metallic particles. Previous to that demonstration it had been shown that the sand itself is not polarizable and neither is water. It v/as then concluded that the "residual" effect (meas­ ured by Schlumberger and verified with the present equipment whenever used in tie field) v/as the potential resuiting from a uniform distribution of disseminated electrically-conducting mineral particles in the earth. Accordingly, assume the earth to be uniformly miner­ alized and of uniform resistivity. Under the action of 28 -o 1n + '-I**'rz.r \, . "r111 b-'-r-oro 2 - r '" ‘T ’! i n " ' f r> t V f^ /,onsit'r rt H (y,r,,z) end ," n i ±.!■J 7-| p • - O -f' 4* 4- •? ^ »• o 7* = c 4* b' ::V..V-:,L :IH-';n mrf.N --j tro'’c at th t i+ pi'” vo"1'i^G § / 1; ‘: T .: ; a r i ^ I ~-t;_i r v r n •'•■i — —’ ,1 '* P. •-Mnt d i’'r\ 'T\ S v j in t -T f r: . ^ ^ p r n 7 >-1 rl - rv p *1.p/■>bpO(" 9 . ' i o e ■ ^ 'y '] 'to V* p i ■) p P •■ P > y .r ■(“ 1-. (o 11 9 rri S r h r'-T‘ 0 jP b1 t ] 1r< ■ 'V f'V H X'1r 11T v''0 -i n . Si .[ •r,( ■•'rr rit a rth 1 t'"i Stx'yV) Q( x y z ) FIG. 4 P c o s Od\t v \ ' '■f'"r R* 1 ■ ii then =- P ’^ but h - n i d uov/evo: in •vher^ the prin.c indicate: -iV^ p«4Lj -.p: ^>.1 4 1L ^-v-C j-.i. b .-u IJ „..• ;4i^ ■ * ■;/•"''■*''"j'i4 -f" I' ■I -.' y •4 .! ■ ,,-u( . r-t Therefore , * f&Oe'.y'.z'h-J P -V ( g ) d V Applying Gauss' I theorem - i ,5# but since p = -^j therefore V *P sO an d V * I = 0 and Srf(*,,y,,z‘) = - J S s A ® _ Now the normal component of i (and therefore of P) is everywhere zero on the surface of the earth except on the hemisphere £ where P = -U; = n K la 27fa2 • However, the radius of the hemisphere can be chosen as small as we please and therefore R can be taken con­ stant and equal to over the integration which then gives (i) From this it is seen that the induced polarization potential for the uniformly mineralized earth falls off like 1/r from a point energizing electrode. A n experiment, designed to test the 1/r relation for a uniformly mineralized earth, v/as described in Part B - S . The earth was simulated by an iron hemis­ pherical shell filled with mineralized sand. The potentials measured are plotted, in Plate 10b, against the distance from the "point" current electrode at the center. Curve 1 represents the background obtained when the sand was unmineralized and that curve falls off more rapidly than Curve 2 or Curve 3. Both Curve 2 and Curve 3 decrease with distance at a rate which is like *l/ir but departs from this relation close to the point electrode. As it has been pointed out, it was not possible to remove the reference potential electrode a great distance from the point electrode and, therefore, the effect of the nearby reference electrode has to be considered. The expression for the induced polarization potential which includes the effect of the nearby reference electrode is the differ­ ence of the two electrode potentials each considered with respect to the potential at infinity. The math­ ematical form of this expression is 30 A $ (x'y'z1) - kl - kl where r is the r R distance from the point electrode to the probing potential electrode and R is the corresponding dis­ tance to the reference potential electrode. If this expression is multiplied by r/I and the difference of potential is written as just (f> the resultant equation - kr R becomes the slope-intercept form for a straight line when r/I is plotted as a function of r. The slope of the line is negative and equal k/R and obviously, the intercept is k. The data used to plot Curve 2 and Curve 3 in Plate 10b have been multiplied by r and replotted as Curve 1 and Curve 2 respectively in Plate 11. Neither curve appears to yield a straight line, particularly in the vicinity of the origin. On the other hand, the apparent curvature is different also in that it is concave for one and convex for the other. The departure of these curves from a linear relation is due to the influence of the current elec­ trode which, considering the dimensions involved, was definitely not a point electrode. However, beyond the value r = 8 the two curves become reasonably straight. A straight line has been drawn through each set of data such that those points beyond r = 8 deter­ mine the line. The slope and. the intercept of each line is different but it must be remembered that k is not necessarily constant becj iso its value (k ~ c (° ) The slope can be written varies with the resistivity. m = k R = c R . This equation i: olved for c and its values, obtained from the two lines are equated; i.e. ? = m.q R] - m_2 R 2 ■ P i ~p 7 For lurve 1 Rq = 16 nn ^121 U 7 t and the corresponding values for Curve 2 R 2 = 10 m 2 = .250 10775 which gives P/P* -- -56 31 0 .4 U N IF O R M M IN E R A L IZ A T IO N (r(f>/1 i i - I N C H E S ) 0.3 H E M I S P H E R I C A L SHELL R E F E R E N C E P OT EN TI AL E L E C T R O D E ( R= 16) x DISTANCE 0.2 NORMALI ZED IP POTENTIAL R E F E R E N C E POTENTI AL E L E C T R O D E ( R = 10) 4 -o.i S - 0.2 PLATE 03l________ I________I________I _______I________ I_______ I_________I ________ I________I 0 2 4 6 8 10 12 14 16 18 20 II DI STANCE FROM P O I N T ELECTRODE ( I N C H E S ) From the measured values o'.’ the ohr the current, the resistivity r' tie end several values ere tabulated: P" f t 6 0.58 8 0.63 potent *al and ; been c o m m ted 12 0.49 Because the sand in the hemisphere is not uniformly mineralized, as the ratios of the resistivities indi­ cate, the values obtained from the retie the slopes * * cf the linos and 1.£. tii resistivities .are con•* therefore yd m i for ony.j + - 4* V x FIG. 5 of Li .LIttl e in f . i 1 vr,i 'Ctor ..I i!a t n of the depth or physical ntita t T-r*,-j* q Ze and from trie magnitude of the 1x3 T)0 ■"> rtni ere-body t* • * rials obt- ino -T i Serve as a guide in tno interpre■>* b ta ti o n , t pot enti a 2 f a buried snhere is calculated. ., . . m, Cons lO Lir> p , k;[iiJ .ore of radius s and resistivity p z d o ritil 0 r z - h/2 in a homogeneous earth' * bur led to (see Figure 5). Take the v:h se res J.4w)f-« a. ’V 't ;-r is p. or 1gir: at th G C ente r o f p r * . " , jo X -el 'verin g a I, ,• ,a ■—1- ": " T’ %**0 era • ( r c , -a. carry-- b \ e s i t e ta' t t M l - t t h e ” M* P t i I ? ■? - :1a,—ad ;■o l a j. j Or; f ! a n ar_ 1 e ran-;'' ce c r r e 3 "■i I t i a a .-i u r». . A>• 1’ _'a'; d "a • ■■ T * , . cr i o generated by :.ap L~.a s y t e r w X r r: t I ~ 3 fle a ,a n y CliG M - - a r e a'. _M X . 0 ..re -ar;; ;l z ! " ' <" ;o r • r- ’ riz[tier loionX . I:' a It , r o • .! m * ■ T* c-aorcr ;t--d a t o t no; aa r e P * a Mat oai M . fxc .1c a a a . r o r e , t .. ■•■'irr a r t be-a •t ! n't e r r u y La > • ■ t a " G i r t a le c j \ •. ' v(j ■. t a t ' a a' U T . i :.r:K. e OP ir • ■ ■' -wv ►J ■■ fa 'a ' ' * x FI G. 6 JlJ .i V a * L:"'i t_ C" ana 1 1 ' a ~ c-' 5 ,aan a> rtr„e„V)* J w=o I f>’> , ) T f W e o s m(y-%) 8 ^ ) 1 ^ ,1 §j is the Kronecker ^ > c °s m if, £ J > V S-* f „"JV ,L ds R o w if oi p „ > ) m . is a term which arises from the point-electrode alone, d = 41 4-n ’ S n("’/ h E IWsO snd f ( 7,)"+'sn M n*o & in which a m . = cosm^+B^Sinm^P^f/i) m f n=o W k=m L mro (n+jOl A »>keos",J'+B m ksi" /a^n+k+, (The coordinates r' and ya' refer to the image of the point P with respect to the center of the image sphere. Therefore, by symmetry the substitution of r and for r' and yu' respectively will lead to the potential at the point P with respect to the center of the real s ph er e) . N o w rewriting the potential to give 35 from which (9)(|5 e ) = - B £ § (f)n L + f - c - ^ Vdr Jtz(x ro £ : 0 a Vro' o n eo fc0 a n ' ' co + J r o ^ £ o P" (^ am k n ( A m k c o s m ^ + B m k sf" which gives the charge density from equation (41) to be Substituting f o r ?+Bmksm n=o wi»o LaJsin <9d J The cross-product of the sums disappear because of the orthogonal properties of the zonal harmonics, leaving co (11) _ ptfi.2ir J r y ^ ) 0L „ L / s i n ^ ^ / vo w0 fffiZTr •n (n+l)Sn^u,f^Lna s in 0 d 0 d 0 *>0 ’ iTJ Q tfoZir oo 0 0 " E P.[>)E°„k„ M mk cos m / + B mk sin m ^ o nruo k Here there are three integrals to be evaluated; (a) JJ -I o (b) .L noL n d/ “ V iV2tr ztr n -i o i'r27T (c) JJ ■I O 36 Now to evaluate (a) write oo n s=m ,L„ = |t0Jm„ Pr > ' cos m (V - W 0L = f o Isn, P > * » C /- fg ) where Jmn= ( 2 - S ° J ^ , P nm^ . ) and • I S^ 2- 0 ^ i P n > o ) However, the orthogonal properties require that s must equal n which then gives for (a) 1m « K [cos?m^ C0S <"# cos m ) + s in 2 m ^ (,s'inm ^sin m pfj+sinm ^cosm 2 E ^ > k A m|1CoSm ^ i nso +B sinm ^ ] +2 ^ (h A n + K « (|)1 P ^ > 2£ ^ “| anA, mn + 'KJ r J ] C° sm H a n Bmn+ " > > |) The evaluation of the potential at the surface (Equation 13) requires the evaluation of the double infinite series (Equations 12). Webb^O has demon­ strated the existence of a solution but it is rather involved. The problem is complicated by the air-earth boundary which introduces an infinite but convergent series of images. A first approximation then is the problem of the buried sphere in a full space. The 38 solution of this problem is contained in the first two terms for the potential expressed by Equation (13) where the coefficients A mn and Bmn are altered. A simpler form of the expression for the potential ob­ tains if the z-axis (the azimuth) is the line joining the center of the sphere and the point electrode. With this change (see Appendix II) the potential becomes (14) ['-<"-')/ N ow if _ L > iqq , the expression for

^A, $f) = k l E (7 7 jn ? l n=o 3. Pr, (cos 6) Ellipse of Polarization F ro m the tank experiments it was shown that the charge density is proportional to the current density actually crossing normal to the boundary. The a b i l ­ ity to detect a dipole by its potential depends on its momentj i.e., upon both the charge and the separation of the charge. The inclusion of the length factor then provides additional information. Imagine a len­ ticular body buried beneath the surface and a survey technique which employs a Wenner electrode configur­ ation. Further assume that the current electrode separation is comparable with the longest dimension of the body. Then when the electrode line is in the direction of the longest dimension of the ore body, the maximum potential gradient is established across the ore body. This orientation not only produces the maximum charge density but also the greatest separa­ tion of the charges. Therefore, the dipole induced and also the potential measured at the surface will be greatest (on two accounts) along the longest direction 39 of the mass and smallest perpendicular to that direc­ tion. As the line of electrodes is rotated from a direction perpendicular to the long dimension of the body the signal will increase until the line of elec­ trodes is along the longest direction. Further rota­ tion will decrease the potential going through a m i n ­ imum again. The values of potential obtained as a function of position will then generate an ellipse whose major axis is along the strike of the body. Verification of this effect was obtained over the m a g ­ netite deposit,(Plate 39) and in the laboratory (see insert in Plate 10a) over the mineralized zone. 4. Concerning the Interpretation of Measurements The mathematical development carried out for the problem of the uniformly mineralized earth has suc­ ceeded in yielding an equation which enables an inter­ pretation of the field measurements. The basic equa­ tion, which may be applied to any electrode configura­ tion is Equation (1) Part C-l. However, Equation (1) can be rewritten, forgetting Figure 4, in more familar symbols by replacing ^ by r and introducing the resistivity back into the equation; then Nov; if a four electrode array is used the IP potential difference measured across the potential electrodes is given by where the meaning of r and E is the usual one. For the .Venner configuration the equation reduces to +•- c -i where 4>0 represents the maximum difference in poten­ tial (at t = 0) across the potential electrodes. From the theory developed for the resistivity of a uniform, extended half-space it is known that for the Wenner configuration £7Td— ° P~ Io 40 Substituting for f in the equation for the induced polarization potential and solving for the value of c (1) where the current flow IQ , which produced the ohmic potential Vg, is taken to be the same as the value of the energizing current I which produced the induced polarization potential ^ Q . Substituting S for 2TTc yields the expression (2 ) S = <£jO V0 mv volt The quantity S may be defined as the induced polariza­ tion susceptibility and regarded as a property of the volume under measurement. It is this quantity which is to be compared in a field survey. The ratio of these two potentials yields a dimensionless quantity but for convenience the values of <{> 0 have been ex­ pressed in millivolts whereas those of V 0 are in volts. It is to point out the discrepancy in the magnitudes of the two quantities that the pseudo-dimensions milli­ volt/volt have been appended to the susceptibility con­ stant S. The graphical portrayal of the polarization sus­ ceptibility of an area will depend upon the manner of applying the electrode configuration to the area. In general there are two applications for any given elec­ trode configuration. In the first of these the elec­ trode separation is maintained fixed and the whole con­ figuration is moved from point to point along a traverse. The process is repeated for each traverse selected until the area has been covered. Any one configuration of the electrodes i n this system is "•ailed a station. If the values of 3 obtained at the various stations are plot­ ted at the points representing the center of those sta­ tions, a curve of the polarization susceptibility along each traverse is obtained, from these curves an areal susceptibility map may be constructed. The second a p ­ plication holds the center of the electrode configura­ tion fixed and the electrode separation is varied. The measurements obtained come from larger and larger vo l ­ umes of earth as the electrode separation is expanded ; hence, this application is called vertical profiling. The values of S so obtained are plotted against the electrode separation. At the present time insuffi­ cient data nave been obtained to establish an exact correlation between the depth and the electrode sepaiatim. 41 The apparatus described in Part D-l could not, u n ­ fortunately, aIv.'s.ys measure both Q andV0 for the same current. In such a case it becomes necessary to return to Equation 1 of this section. One intentional feature in the design of the field apoaratus which p r e ­ cludes the direct application of Equation 2 or 1 is the delay time in the switching cycle. 'I'here is a choice available in the manner of handling the data in connection with the IP potential at zero time. A workable method would be to displace the zero on the IP decay curve by a fixed time interval from the true zero, treat the IP potential at that point as the Q and compute S from it. A second and perhaps more d e ­ sirable method, is to extrapolate back to zero time. It should be pointed out that extrapolation is justified on the grounds that two properties of the curve are used (i.e., magnitude and rate of decay) provided that the curves fit a fixed form. From a study of the decay curves obtained in the field it was found that their form fits the E2 relation for the rate of decay acceptably well and the values of <£0 will be obtained from the equation A t +• c where , the difference of potential measured at the surface o f the earth, has replaced the electrode potential 2 used in the equations of Part B-5* fxm-.. ,*lHf/ D. 1. FIRLD SURVEY RESULTS Description of Field Instruments A large amount of laboratory experimentation had been completed before the first field trip was undertaken. A n attempt was made at the beginning of the field work to adapt the laboratory measuring equipment to satisfy field requirements. The Shell oscillograph is a rather cumbersome field instrument but it has in its favor the small amounts of power required to operate the galvanometer lamps. However, with it the results of field work remained unknown until the photographic record had been developed. The serious limitation on the use of the instrument imposed by bad impedance matching between the electrodes and the galvanometer element added to the inconvenience of developing paper in the field. The resistance offered by the potential electrodes varied widely as the electrodes were oved from place to place. Coupled with the variable electrode resistance was the frequent need to operate the instrument on arange where its resistance was many times less than that of the elec­ trodes. Under this condition an appreciable amount of current could flow, temporarily polarizing the poten­ tial electrodes. Difficulties were also encountered with the mechanical pulsing switch. The operation of that switch had been excellent in the laboratory but failed in the field because it did not satisfy the re­ quirement of high insulation resistance between the current and potential circuits, particularly in the extremely high relative humidity encountered in the Washington, D. C. area. An entirely new assemblage of equipment was prepared. This equipment was used through­ out all the field work and is described now. Plates 12a, 12b and 12A, 12B are photographs of the equipment and Plate 13 shows its arrangement in block diagram form. The first concern in the design of the pulsing switch was to maintain the leakage resistance adequately high (in excess of one megohm). The simplest solution to the problem was to physically separate the current and potential switches which was easily accomplished by a system of three relays. The switching circuit is shown schematically in Plate 14. The relay LI is the master relay and its normal position is that which com­ pletes the L2 coil circuit. When the switch SI has been closed for a sufficient time to charge the condenser C the switching circuit is armed. A pulse is obtained 43 i-lafe 12 F IE L D E Q U IPM EN T GASOLINE GENERATOR CURRENT ELECTRODES DRIVING STAKE POTENTIAL ELECTRODES' 'B" BATTERY- CURRENT METER OHMMETER SWITCH MECHANISM AMPLIFIER P L A T E 12 B PLATE 13 A M M E TE R RHEOSTAT AM PLIFIER REVERSING SWITCH RECORDER / B SUPPLY SHUNTING SWITCH C U R R EN T ELECTRODES PULSING SWITCH PO TEN TIA L ELECTRODES BLOCK DIAGRAM OF F IE L D E Q U I P M E N T O H M M ETER by momentarily closing switch 32 which discharges the condenser through a 10-ohm resistor. The condenser then accepts current through the coil of relay LI breaking the L2 relay coil circuit which effects the opening of the potential electrode circuit. Further, the closing of the contacts of the LI relay completes the circuit through the coil of the relay L3 closing its contacts and thereby sending a pulse of current through the ground. As the condenser becomes charged the current through the coil of LI decreases until the clapper can not be held to the magnet. When the LI contacts open the current through the L3 coil is inter­ rupted to terminate the current pulse. When the clapper of LI has returned to its normal position the current again flows through the coil of L2 closing that relay and completing the switching cycle. The cycle may be repeated at will by momentarily closing the switch S2. The duration of the pulse is controlled by the time con­ stant of the condenser circuit and may be altered by changing its circuit resistance (selector switch S3). The time intervals of the various stages of the pulsing cycle depend upon the magnitude and duration of the current through the relays. The time intervals are, therefore, controlled by the resistors in these circuits. A heavy duty 45v 11B" battery serves to power the three relay circuits. The circuit constants employed provided an energizing current pulse time which was approximately 1.45 seconds. The time interval between the opening of the current switch and the closing of the potential switch (delay time) varied in length from 12 milliseconds to 50 milliseconds with the average, for ten or more observations, of about 25 milliseconds. The variations found in the closing time of the potential switch is one of the undesirable features which should be removed in any redesign of the equipment. It has been shown (Part B-4) that a knowledge of the apparent resistivity is required in conjunction with the induced polarization data. In order to make the resistivity measurements the ohmic potential must be measured while the energizing current flows. Since the pulsing mechanism was designed to avoid closing the potential circuit during the current pulse a toggle switch S7 had to be used to shunt the current relay con­ tacts. With the shunting switch S7 and the reversing switch S8 current could be delivered to the ground in either direction which enabled records of the ohmic potential and the current to be obtained simultaneously. From these measurements the so-called dc apparent resistivity is computed. 44 S H U N T IN G S W IT C H S7 "b " SWITCHING CIRCUIT s u p p ly CURRENT ELECTRODES L2 MEG 3 0 0 4 1 1W PLUG-IN TYPE PARALLEL T FILTER 2000.fi. 1: 50041 AMPLIFIER z r 2C 10041 - BUCKING CIRCUIT 50041 ';5,v, VAr S4 2 0 0 41 IOIL< IW CALIBRATION CIRCUIT S5 5V I, L2- SIGMA 6V RELAY S6 PLATE L3 5K : 24V ADVANCE RELAY NORMALLY OPEN 14 POTENTIAL ELECTRODES 'The recording equipment employed was a commercially available Brush dc amplifier and magnetic pen-motor r e ­ corder. The 3 inch pen is driven by a D'Arsonval type calvanometer element which moves in the field of a per­ manent magnet. The amplifier and recorder combined have an essentially flat frequency response from zero to ICO cps. The amplifier always operates at its maximum gain which is about 1000. Sensitivity control is accomplished by a potential divider at the grid of the input stage. It is arranged to divide incoming signals into ranges which are multiples of 10 and further permits continuous control within each range. The power required for the amplifier and recorder combined is lfi5 watts at llOv, 60 cps. A large size 500-watt gasoline driven ac generator was tised in spite of its weight be­ cause the regulation of smaller units was poor, which resulted in a considerable drift of the pen. The input impedance of the amplifier is 10 megohms which is safely higher than the maximum (5000 ohms; potential electrode resistance tolerated. Because of the high input impedance of the amplifier, difficulties were encountered whenever the input circuit was opened. The grid of the first tube alternately "looked" into very low and very high impedances. To combat this a 0.1 megohm resistor was placed across the input to the amplifier shielding it from the action of the input switch but not without the loss of some signal. Very early in the field measurements it was discovered that on occasion man-made disturbances were of sufficient amplitude to mask the polarization effect. In the vicinity of Beltsville, Maryland an electrified rail­ road two and one half miles away was the source of 25 cps background which at times produced potential gradients as large as a 30 pv/meter. The 60 cps power lines were a constant source of interference. The magnitude of the disturbances depended upon the proximity to the power line, the resistance of the potential electrodes and their separation. A filter was used to minimize these spurious potentials. The predominant background varied in frequency from one locality to another and, therefore, several different filters were required. Connections were provided ahead of the amplifier for plug-in type filters. Resistancecapacitance filters of the "parallel-T" type (shown schematically on the drawing of the switching circuit) were used. The 60 cps rejector was required more often than any other and rarely was there an area where no filter was needed. A typical attenuation curve for one of these filters is shown in Figure 7. The use of the filter further decreased the signal arriving at the amplifier. The insertion losses introduced by the 45 0. l-rncrohr’ s h i e l d i n r r e s i s t o r and two f i l t e r r e d u c e s too incor'i’!" cl g r o l G b o o t . G b . dov/ever, the d i s t o r t i o n i n trod n e e d by the f i l t e r s was fo u n d to bo i n s i g n i f i c a n t f or e x t o n e n t i a l l m d s e r v i n g t r a n s i e n t s v;h"■s.e tirre c o n stantr" v.-ere c o-oarahlo' to tivrsc- -"'h too If s i g n a l s . ii al ibro t.i o n c i r c u i t , s i m i l a r t o t. a i de scr e bes n h a r t h- 1 '. as u sou xo i n j e c t ’m o w n d 0 \r/*'^ t cljW,e s i j.-o*.tL<' f on n C . i a 1 evp it t Lhe pot n t :al cir colt. A ciir.il'.: r ci 1' V s te a dy bO S'Viili 1 -ir n huc hl ng volte to to n o u ' r el 1 oc a T o •i h’;t. etc •)* t i e earth. o t o n t i C.1. -v e n o c u n tcreo ’ a cross L._1G inr ut c i r c u i t wa s useo. to c j e c h bi iG re go1S~ r. t. ioe 'oo oo r ti a l e l e c t r o d e s f o r Gci C11 Get -U p • ance ' yi ^; ov/evor 9 t. h e r e " d ing s r;e r c u.s o c o n 1 v t a vc P ins t r u ­ V 7 bi fficu It I':.". ontati . V . JL. _ z o 3 > *<1 _l cc F R E Q U E N C Y (eptl FIG. 7 -. r*^ . 4-' 11) d s I .r :O ■' j■ ■ . av 11 ,a J - - 'y' l"ii L . ^ j r i > o': c u r r o i o l • res u ’eor ''.’ i"■'*. G If * o jb^1c u t h e ’ O' ■ r r o n t j"ul '"'ul'oj hr e ended • n ■:ncv;l c ■ f the* r O :!h. ' .jX .. ‘’g S r e q o ; r e f b :1a 1 c a.' vJ-G a 71 r i. a t :: c n. P ,, t -T...0 ...•• 1” 1 O ' * 1 r c u i ay 12. The t r o l ! . a .■o t u t ' • r < > . r ; _ * • ] t * p '"1 "h O ' . ! ': . h . f-jd P. . c r u r e r o cord ~'r G C -j-b 'mat iter t ■- on sot arc t c r r i n a t i o c b ‘ the c u r r e n t nulso. , .v . ... h - O -f ,, >o ■ lS_ v ,j_ 4- . c i (.• ; ■ ' . -• The c u r r e n t e l e e trod es w e r e suce t iro n l u u i s p h o r o s , b in ehes in - b a e e t e r and n.- 1.i-.led w i t h leod to p r o v i d e a go p r e s su.ro c o n t a c t to tin: g r o u n d . Th.o r.oni sp h e r i c s 1 *;O p o s s i b i l i tv o f f o r w i n g i'?r v: ’ s ohos m te- avoi d 1l_C_,'V'-,(•- c l r'oles Vir d i f f e r e n t n*:Crh x ^ P ^T U X _ (so h a r t B -'•) J. t i on - 1 o poo’c r o l o o t . r o d o i t s e l f . I t r r 'v -\~'r ■ o an ' i n n e c - j s a r y p r e c a u t i o n v.-Lenevor t h e &1 n s e p a r a t io n s 10 f t . o r r r e r t - T . S h o rt i r o n i n c h e s l e n y an d 7 / n i n c h i n d la n e t e r v/er e u s e s v i a 1 o h ;- o r re n t a s t l a i e id x c c p t 3 r* 1 t ; E r* o n v• o i l v ;e r e 1 yo ,- it', t h e t h e r t o ^y* o n ' t h e h o rr* i s r ih•tC r-* ]■»o ;-i d i r e o h o r e s ii o s e L v/as sin 1 e l u o : : ;r n e s i p n G Ci . 3 m h o T ■. e o n e r g i s i n • O ,-^t p .c v e r : J. s u c h e l o ' - t r o d o a ' s s r a '1 ■u n ; r _L 8 o ” t r e n e l o Zo d a r e a i s u n d r j. o u r o -* 4. ^ f3 - i -• ^ b.'i ■. v< s. 3 e l o e t r o d e VP e v e ii on.t p -U n t o e s i r a ■j. .r» • e a r l 1 T ;V ? to- n X. '.. ? o ^ t r o d e t o t o h o n s n ;; ..It.' d d r t 1 -^4r, .i o >T' ■o 1 to a v r> a 1 s o o r e a c ' i L S O l u l a z e d b n o t s • X n S u c c O S S f 1 - -s V/Il G D VO o d f l a t " u n : n ’ -i. • e o r t I i . A j. v> 1 *p h o t tor: t ! u t.l l O s h o u I d b" 1 o D o n g r c< In e* i O U l d n r * x e l e e t r t : o n o J u s t a t e r . c e r t d ’ d -L. 4-:. ' • p * * • vy ’ • > ;0 n 3 n i o h o r . r e 11 i ' o s i s t c T ;i L' . * O' p o r t h e t v . c* t i ;h X ‘ '3 • u / Coid G O o +■ C u r t- Y.’o r sc o b b r e s u I t s c u r r e n t • n t i o n o d d p r e c o u t i o n - '7 h o u S * ’V , o l e c t r o d e A s D O C y a l p i 3 i f i i* 1 c a l t n .bO n l c s t i n ; s t i n _ -i v. 4- r. 7 -.. y s o b t a s h i e l d t P t o v i 3 e t h o •* -L n o d e c t r o d e s e n e r g 1 z i n 5 'O o v: ' . ,3 n 3 S O e a r a t i o n s n h e ­ **T o n .1 u n d Cl e o n t". T h e p l a c e c l v i n t C*' o n ..1 o e d -* ’0 b u t t’ •'J t :; o +t..i s c o n v e n i e n t . PLASTIC P O R O U S CEMENT CuSO. PI G. 8 i*’Ci lU.:,.- ■}1■*,'i Iici3 b G iV T .0 an .O 4 hiu n ■1.iJ 'J ■a., d e - s i r ne c ~i p_ -•. It YV V . r p r i s i n cl 1 J n.4i tea ted o n I"'reli .inary 0 qh i p • b • • o s t p or •p- -)1■ti os 'ir* h (J L\n aba r:d nno v.i a rfh; j Z.OQ ced _ T tsvi p p *x r-— -* jLn 3 i;C'” ',‘ ,.x»ht T 5 -• ,J *. -j ► ii•■ I": 1 ii— e -> I aryl 3 “ • • T P ~ * / V P . h i , 1 r ■ ' s o :\ '1 -;d ' • f 4cJ.A oa V ci.1 t .*8 :r -4 to.-1. 'i7Cih i ' '..Q • X . "■'SO, ha S -- V.f‘7 ]'■inr| t oo. 9 i-p * *"■G n rorati o o 8 1 cha T'actor i s +L I +I-'.c•> oqui V'.-ent . Af t Yr 4. c f > fpp, ■ r s p o r \ 0 “ ' * > ■ * v f j 4 n L-n •' O'/'j nt i.»p ct -r it.r i. r s'TC t i n 3 c t _cS r , 1 7 , i • < T r . r p r * J. h \v; ’ that :'u.rth c-r to t n L c r the equi ••.'■nt ce ("■d a re n '33 Vr o r e t h e ;r '.•h-L3 rrT,T \va o bette Xr» h :-now:'.’. r r * f- ‘V o ■3bio-'■X t >1_L area 5 ’-hiQ >'■e t 1: re lo-o -V -i3 >Pr 4C>3-V1 -V i -^ 3 d o 1 e c ' !- t ■rl s’:a rp b ound P r 1 o s SO t r.; A t•-ir~>p 1 ppvy] u^ t y p " I ^ r * r > 0 "■rs, 's 1 oeral 3 fro r turned over t r) the u * > m Geolc 0 1 r»ftp Sxir^oy .-p' t.hp. 1o r . a '*c t t >-ore tl:a T—, ten P o s aJ opart ent of Inter • r*ibir: cireo s - ha ir f a ’i C o 11': p '3^p -C ...i -Triv' :'i d l a t e 1 7i r C X. Jrr '» i ,V.d . e -VPe i '"VOS t : y t'O <* i c e o l ’ thi ■>c c; n i .1. .J. V ■A ■ ^ 1 Ar - 2. Measurements Over an Amphibolite Dike About 14 miles out of Washington, D. C. along Route 7, Fairfax County, Virginia an amphibolite (meta base It) dike is exposed in a road cut. The dike comes up through a knoll of Wissahickon (mica schist) a little off the center of the knoll, dipping to the east at an angle of about 60° with its strike roughly N 20 E. The dike is about 50 feet wide on the north side of the road and nearly 60 feet wide on the south. The topography, other than the knoll at the road cut, fails to reveal the dike. This dike was chosen as the object of the first investigation. Two traverses parallel to the road were made. The term traverse in all of the following work will mean a line along which measurements are made. Measurements, for which the electrode separation remains constant, made along any traverse are referred to as a run. Wh en the electrode spacing is increased during the set of measurements with the same center maintained for all spacings, the name vertical or depth profile is used to describe the measurements. Unless otherwise indicated the distance moved along the traverse from station to station in a given run is to be taken as being equal to the electrode separation. The first run over Traverse 1 used a Wenner configuration for which the electrode separation f,a" was equal to 20 feet. At each station several current pulses were delivered to the earth in each direction and the resulting IP potential was recorded. A section of recorder tape showing a typical signature is given in Plate 15* The paper speed for this record was 2.5 cm/sec. Wi th the paper speed reduced the resistivity data was next ob­ tained. Six dc resistivity measurements were made; the polarity being reversed between successive measurements. Fo urteen stations were taken along the first traverse. For R u n 2 the electrode spacing was increased to 50 feet and the first traverse was again covered. A second traverse, parallel to the first and 50 feet away was run using only a 5 0 - f o o t separation. The measurements obtained from this preliminary investigation over the dike were treated in the manner outlined in Part C-4 using Equation 2 to compute S. However, in order to bring out the effect of the various factors involved in reducing the data several preliminary curves obtained from R u n 1, Traverse 1 have been plotted. In Plate 16a a comparison is made between the resis48 CURRENT OFF— ► CURRENT — ON © © CURRENT PULSE 416 MA 1 = 416 © TAPE SPEED - 5 m m /s ec © TAPE S P E E D - 2 5 m m / s e c TYPICAL SIGNATURE IN D U C E D P O LA R IZA TIO N R E S IS T IV IT Y I VOLT CALIBRATION SIGNAL P O T E N T IA L PLATE (Q) *00° 0.(500 IND U C ED P O L A R IZ A T IO N POTENTIAL o 1000 R E S IS T IV IT Y 60 40 20 (20 eo DISTANCE i20 EFT a m p h ib o l it e M IC A S C H IS T META BASALT M IC A S C H IS T 180 l b ) (2) INDUCED POLARIZATION \ SUSCEPTIBILITY AT t = 0 120 ZlSO (I) INDUCED POLARIZATION SUSCEPTIBILITY AT t =8 0 RESISTIVITY \ d is t a n c e (fe e t W IS SA H IC K O N M ic a SC H IST A M P H IB O L IT E DIKE M ETA W IS S A H IC K O N B A S A LT INDUCED P O L A R IZ A T IO N M IC A SCHIST PO TE N TIA L A N D R E S I S T I V I T Y vs D IS T A N C E AMPHIBOLITE DIKE tivity and the induced polarization potential (measured at t — 80 milliseconds and normalized for the cu rrent)• Just as the theory predicts, there is good correlation between the IP potential and the resistivity. The effect of removing the resistivity factor (computing the ratio 0 / V o ) is shown as Curve 1 in Plate 16b. The good correlation between the curves of induced polarization and resistivity no longer persists. Curve 2 in Plate 16b shows the effect of extrapolation of back to zero time. Comparing Curves 1 and 2 in Plate 16b it is seen that the shape of the curves, for this run, has not greatly changed because of the extrapolation process. This is not always the case. F r o m this point on, the plotted curves are curves of the induced polari­ zation susceptibility S computed for 4) extrapolated back to zero. Values of S for R u n 2 of Traverse 1 and R u n 1 of Traverse 2 are shown with the corresponding values of resistivity on Plate 17. It had been expected that the high polarization readings would appear over the dike. In an effort to learn more about the two rocks, a sample of the mica schist was taken from an area approximately 100 feet northwest of the dike and a sample of the dike material was taken from the center of the dike. Both samples were dug from the road cut and from holes deep enough to give fresh material. The samples were ground to pass a 100 mesh sieve and then passed over a magnetic chuck. It was surprising to find that the mica schist examined contained 3 * 3 % magnetite whereas the amphibolite con­ tained only O . 3670. The amount of nonmagnetic conduc­ ting mineral which may have been present is not known. The dike material contained a large amount of moisture and it was hygroscopic. It had to be dried repeatedly in order to pass it through the sieve. A n electron diffraction pattern of the dike material2! matched that given for Nontronite (Fe0Si02 * 2H 2 O ) • It was concluded that the lew resistivity of the dike material was due to electrolytic conduction rather than electronic con­ duction. This is reasonable in v iew of the large amount of moisture contained in it because of its hygroscopic nature. (The zone under measurement was well above the water table). The higher polarization potentials measured over the mica schist are interpreted to be due to the higher concentration of magnetite. The results of this preliminary investigation were reviewed with members of the Geophysics Section of the USGS. The opinion of the group was that more supporting data were required. As a result two more traverses, parallel 49 PLATE IN D U C E D P O L A R IZ A T IO N 17 SURVEY A M P H I B O L I T E DIKE HORIZONTAL T R A V E R S E ELECTRODE SEPARATION 5 0 FT T RAVERSE 2 POLARIZATION 160 TRAVERSE I RUN 2 I NDUCED o in 40 200 150 DISTANCE 100 (FEET) W IS S A H IC K O N M IC A SCHIST AMPHIBOLITE D IK E META BASALT w m s m A W ISSA H IC K O N M IC A SCHIST RESI STIVI TY o (10 tf c m) SUSCEPTIBILITY (MV/VOLT) RUN I to the first hut disp lac ed to the n o rth 1 7 5 feet and 350 feet r e s p e c t i v e l y were run. The el ect rod e s e p a r a ­ tion u s e d was a g a i n 20 feet. In addit ion to these i n ­ duced p o l a r i z a t i o n data, all the traverses were r e m e a s ­ ured for resisti vity , emplo yin ' the G i s h - H o o n e y system, and ve rtical m a g n e t i c field readings were taken over the first three traverses. The res i s t i v i t y as measured by the G i s h - R o o n e y and the dc met hod s we re in good agreement. A l l of the r e s i s t i v i t y values clotted for the amp h i b o l i t e surve, are those obtained by the GishRoo n e y system. The m a g n e t o m e t e r data for the first three tr averses have been plotte d in Plate lG. Plate 1 9 is a r r anged to di s p l a y the general area of the s u r ­ vey, the po r t i o n of the dike w hich is visi ble os w e l l as the induc ed p o l a r i z a t i o n susc eptibility and r e s i s ­ tivity data for Tr averses 1 (Run 1), 3 and 4 . The induced p o l a r i z a t i o n s u s c e p t i b i l i t y and the r e s i s t i v i t y bo th fai l to d e f i n i t e l y * r e v e a l the existence of the dike be yon d the second traverse. The m a g n e ­ tometer data do not indica te a n y large m a g netic anomalies other than the one on T r a verse 1 w h i c h occurs off the dike on its n o r t h w e s t side. These observa tion s force the con c l u s i o n that the dike tapers out and dis appears on the n o r t h side of the road. Its ex ist ence beyond Traverse 2 is questi o n a b l e In terms of the results of any of the three methods. unfor tun ate ly, the m a g n e ­ tometer data for Tr aver se 4 have not be en-obtained. One physic al feature of the area is brought to the support of this conclusion. The dike Is wider w here it is ex nosed on the south side of the road cut than on the north side. If str ai ght lines are d rawn across the road lining up v’ith the exposed edges of the dike they c o n ­ verge In the ne ighborhood of the third traverse; i.e., the one 1 7 5 feet n o r t h of the first traverse. The conclusions drawn fror the a m p h i bolite survey are; 1 ) that d i s s e m i n a t e d cond uct ing m i n erals may yield ra ther large values of po lariz ation s u s c e p t i ­ bilities and 2 ) that bodies w hich are good conductors by virtue of the e lectrolyte pre se nt rather than the conducting miner a l s are not polarizable. 3• R e a s u r e m e n t s Acr o s s a h a n as sas S andstone and .7i s sahi ckon F ault The c o r r e l a t i o n of the p o l a r i z a t i o n s u s c e p t i b i l i t y wit;-, the muygnetite analys is obtained on Tr averse 1 su-'-'osted i i? t the meth o d mi< Lt be used to detect faults 50 PLATE 18 VERTICAL MAGNETIC FIELD SURVEY AMPHIBOLITE DIKE 500 TRAVERSE 3 175 FT BACK -900 TRAVERSE 2 50 FT. BACK -IQOO GAMMA TRAVERSE I 240 200 160 120 60 60 DISTANCE (FEET) W IS S A H IC K O N M IC A SCHIST AMPHIBOLITE \ DIKE \ META BASALT V ) C W v V .W A W IS S A H IC K O N M ICA SC HIST 160 PLATE 19 TRAVERSE 4 RESISTIVITY INDUCED POLARIZATION SUSCEPTIBILITY . RESISTIVITY \ * / RESISTIVITY (10 / cm) TRAVERSE 3 INDUCED POLARIZATION SUSCEPTIBILITY (MV/VOLT) INDUCED POLARIZATION SUSCEPTIBILITY TRAVERSE I INDUCED POLARIZATION SUSCEPTIBILITY RESISTIVITY / _I60___________120___________80 _ D IS T A N C E (F E E T ) HIGHWAY 7, FAIRFAX CO., VIRGINIA m V 0- A ' V A nN . V . . . . V'^V, VM o . . W IS S A H IC K O N \ '-Vv MICA SCHIST \\ V. M P H IB O LIT E m . . W IS SA H IC K O N MICA SCHIST iA S A L T \\y v.\^\\'V-^V' . < \ , \ AY \ \ > A V \ IN D U C E D P O L A R IZ A T IO N SURVEY AMPHIBOLITE DIKE IN W IS S A H IC K O N ALONG HIGHWAY 7, FAIRFAX CO.,VIRGINIA where the change in resistivity is not pronounced and where a change in the amount of conducting minerals occurs. It was believed that a fault of this tyre exists near hanassas, 7irginia where the Tissahickon, known to contain variable amounts of magnetite, has pushed uu against the hanassas Sandstone. The fault (see Plate 20) is exposed along the Euck hall road about 1 1/2 miles east of hanassas. (Plate 20 is a composition of a portion of the U. 3. A rmy Engineers map of the Quantico quadrangle and a portion of the U3GS man of the Fair f ax Quadrangle. The two maps did not quite coincide, therefore, several roads have been "faked" in to provide continuity. The line of the fault whs located by h i l t o n , 2 2 ) The area selected for the measurements was a gently sloping corn field. In­ duced nolaris atio n and resistivity measurements were made along three traverses roughly perpendicular to the fault and each 200 feet apart. A Tenner system of electrodes in which "a" was equal to 2 0 feet was again employed. Samples of earth were taken from the road cut at 2 5 , 5 0 , 75*5 1 0 0 and 1 7 0 feet in each direction from, the .exposed fault. The material gathered, a p proxi­ mate!;’ 5 pounds per sample, was ground to pass a 1 0 0 mesh sieve. The magnetic materials were separated from all but the sandstone sample at 7 5 feet w hich net with an accident and was completely lost. The measured values of the IP susceptibility, the resistivity in ohm-cm and the results of the magnetic mineral analysis are shown plotted in Plate 21. The -4 i o rji j 4— -J --w -i 4— » - v l O; u y— 4- y— a. Kya I-* t*s onuw rh a. h -5 V-> «? 4- y-N u o i 1 m ou fy —S — > ^ I 4- -? /—» ^■•'i C O x-LV 5 xc3.uj.u ii 47*M, ^ i I ujh traverse to traverse. The change fr o m low to high r e ­ sistivity is along the probeble strike. There is little correlation from traverse to traverse in the IP suscepti­ bility curves. One relative high is maintained in the center cf the three traverses. The vary high peak of Traverse 1 diminishes until at Traverse 3 it has disO'peered whereas a slight hint of a poak on the other side of the center of Traverse 1 grows as one progresses bock to Traverse 3 , F r o m the mineral analysis it must be concluded that there is more variation in the m a g ­ netic mineral content within either the sandstone or mica schist than there is from one to the other. The magnetic materials which entered into the determination of the percentages shown contained, a substantial amount of weakly magnetic mineral wh ich was not identified. It is concluded from this survey that the IP sus­ ceptibility measurements do not locate this fault b e ­ cause a sufficient change in the conducting mineral 51 PLATE 21 200 200 TRAVERSE 2 INDUCED POLARI Z ATI ON RE S I S T I V I T Y (10 flcm ) SUSCEPTI BI LI TY ( MV/ VOLT) TRAVERSE 3 TRAVERSE I FEET ^■VISIBLE FA U LT R O A D -------------------------- 'I f! TIp',"'i TF7] ' 1,1,1, W IS S A H IC K O N I*M A N A S SA S S A N D S T O N E * IN D U C E D P O L A R I Z A T I O N MANASSAS t1 ,1! rlPPIP, SURVEY S A N D S T O N E - W IS S A H IC K O N FAULT M ANASSAS, VIRGINIA c o n t e n t fro m one f o r m a t io n t o th e o t h e r does n o t e x i s t . T h is c o n c lu s io n i s s u p p o rte d by th e m a g n e tic m in e r a l a n a ly s is . I'enuirerents Over a Pyrrhotite Outcrop The results obtained ^rorn the amphibolite dike and the Lhnassas Sand stone surveys are inconclusive and co n­ fused because of a lack of knowledge concerning the variation in the concentration of disseminated minerals. In order to avoid this confusion, measurements should be made over an area where the mineralized zone is definitely k n o w n to exist in quantities which approach those of an ore body. Information about two ore bodies, not far from Washington, D. C . , was obtained through USGS. The fi rst of these is described as the Gossan Les.d2^ , Carro ll County, Virginia. Plate 22 is a p h o t o ­ graph of a man (furnished by USGS) showing the Gossan Lead whi ch extends for 17 miles from near Galax, Virginia to the vicinit y of Sylvatus, Virginia. The Gossan Lead consists of a series of elongated sulphide ore bodies of w h ich the prima ry ore is pyrrhotite. The mineralized zone is incased in the pre -Cam bri an Lynch bur g eneiss. The ore in the Cranberry segment outcrops ( s o o E S i n Plate 22) along U. S. H i g h w a y 52 near Kill sville, Virginia for a distance of a p p r o x i ­ mately 200 feet. The le.ckgroimd in the photo gra ph of the instruments in Plates 12A and 12B (supplied by H. C. Spicer) is the outcropped pyrrhotite along U. S. H i g h w a y 52. The “ f l o a t ” found along the outcrop was rather massive nyrrhotite. (./hen a piece of ore with freshly exposed faces was connected to the leads of an ohmineter, the meter read zero on the 1 -ohm scale). Two traverses were run across this outcrop; one along the shoul der of the road and the second one p a r a l ­ lel to the first, 2 0 feet Lb of the road and about 12 feet above the road level. Tice second traverse ran only across the wes t contact of the mi neralized zone because tne hi llside wr s steep, covered wi t h the dump of an old nit and he avily overgrown. A lean er system for vi) ich " a ” was 2 0 feet was used to obtain the data of Irav rse 1 Hun 1 and Traverse 2 Ru n 1. The results of those f-o r u n s , nlotted i- Plate 23, sho^ t.*e induced polarization susceptibility increasing to a maximum as the contact .is a^nroached from the side of tne country rock. Once the contact is crossed the polarization suscep tib ili ty apcears to fall to zero, however, it is real]" the induced po lar iza tio n potential whxe n has fallen to zero (or at least below the lower limit of 52 PL A TE 22 UNITED STATES D EPARTM ENT GEOLOGICAL OF THE INTERIOR STRATEGIC SURVEY F ig . I I N D E X MAPoftheGOSSAN LEAD. CARROLL COUNTY, VIRGINIA Giving location of m ineralized segments and names applied to those northeast o f Chestnut Creek Outlined area shown in d e ta il by Fig. 2 F ederal highway Stote highway 0 1 MINERALS INVESTIGATIONS PRELIMINARY 2 3 4 Sc a l e in M il e s 5 6 S N OR R J.W LLSvl SSAN 36 4 0 GALAX NOKE GALAX HILLSVILLE D A N V I L LE MAPS PLATE 23 INDUCED P O L A R IZ A T IO N SURVEY PYRRHOTITE C R A N B E R R Y SEG M ENT ALONG U.S. HIGHWAY 5 2 , H ILLSVILLE , VIRGINIA TRAVERSE 2 2 0 FT. BACK TRAVERSE I LYNCHBURG GNEISS \ PYRRHOTITE LYNCHBURG GNEISS 400 E the i n s tr ument sens iti vit y). The fact that this p o t e n ­ tial falls to aero should m a k e the s u s c e p t i b i l i t y ' a l s o zero exce pt for the fact that the ohmic p o t e n t i a l also falls to_ zero over the p y r r h o t i t e zone. 'The s u s c e p t i b i l ­ ity is the r atio of these two potenti als and is, t h e r e ­ fore, i n d e t e r m i n a t e over the m i n e r a l i z e d zone. The zero value of the induced p o l a r i z a t i o n p o t e n t i a l is in e x c e l ­ lent a g r e e m e n t w i t h the e s t a b lished result (Part B-10) w h i c h states that the p o l a r i z a t i o n p o t e n t i a l is p r o ­ p o r t i o n a l to the p o t e n t i a l gradient'. H e r e the current was increased to 1 . 0 ampere, the sep a r a t i o n of the p o t e n t i a l el e c t r o d e s was 2 0 feet but the r e s i s t i v i t y ’"as zero as fa r as the field in str uments we re concern ed and, the refore, the p o t e n t i a l gr adient and c o n s e q u e n t l y the induced p o l a r i z a t i o n p o t e n t i a l r e m a i n e d zero. It has long been k n o w n that p y r r h o t i t e displays self ("s p o n t a n e o u s 1*) p o l a r i z a t i o n and becau se S e h l u m b e r g e r o stated that the " s p o n taneous" p o l a r i z a ­ tion of an ore bo dy w oul d co n c e a l the induced p o l a r i z a ­ tion p o t ential, rr.er.surements of trie s e l f p o t e n t i a l were made. The r e f e r e n c e e l e c t r o d e vias located 2 2 0 feet west of the center of the ore body and the p o t e n t i a l difference b e t w e e n it and the probe electrode w a s r e ­ corded as h.e probe e l e c t r o d e was moved ac ross the ore body ir 2 0 foot intervals. These data are plot ted in Plate 24 a long with re adin gs of the v e r t i c a l mag ne tic field m e a s u r e m e n t s t ak en a lon g the same traverse. The ore b o d y is d e f i n i t e l y s p o n t a n e o u s l y p o l a r i z e d but the self p o t e n t i a l s do not i n f l u e n c e tue induced p o l a r i z a ­ tion potenti al. The e n e r g i z i n g current wes pu lse d in both dire c t i o n ^ but no ch an ge in the m a g n i t u d e of the induced p o l a r i z a t i o n p o t e n t i a l was observed. It was necessary, however, tc use large b uck ing potentials to keep tlio r e c o r d e r pen in the center of the paper. There is a s e l f - p o t e n t i a l ’’well" at each in ter face of the p y r rhotite and a.-' a d d i t i o n a l one just w e s t of the center of the ore. An I n c l u s i o n of mica schist is vi sible in t. e road cut w hich cor r e s p o n d s in position to the extra, "".veil" In the self p o t e n t i a l curve. A smal l increas e in botli the induced p o l a r i z a t i o n poten t i a l and the r e s i s ­ tivi ty (both too small to a p p e a r In Plate 23) were ob-^ served at the same location. The extent of the i n c l u s i o n is not known. „ v e r t i c a l pr o f i l e was run over T r a v e r s e 1 starting with, an e l e c t r o d e s e p a r a t i o n of 400 feet and dec r easing the s e p a r a t i o n 1 0 0 feet at a time u n t i l the p o t e n t i a l el ectr ode s w e r e 100 feet apart. The center of the « VERTICAL MAGNETIC FIELD AND SELF POTENTIAL MEASUREMENTS PYRRHOTITE CRANBERRY SEGMENT 100 600 TRAVERSE I * VERTICAL MAGNETIC X _ p (G A M M A ) .LV- OjPy*°^o FIELD SELF POTENTIAL -100 -6 0 0 -200 -1200 V E R T IC A L SELF PO TE N TIA L (M V ) 9 -o , M A G N E TIC REFERENCE POTENTIAL ELECTRODE -3 0 0 250 W 200 150 100 50 50 150 200 250 DISTANCE (FEET) LYNCHBURG GNEISS PYRRHOTITE LYNCHBURG GNEISS 300 350 E 5 rn ro ■P sys t e m was the center of the ore body. Thus when the p o t e n t i a l ele ctr odes were 1 0 0 feet aoar t they were inside the zone whe r e a s at 2 0 0 feet t h e / we re outside. The results, sh own in Plate 2pb, are co nsisten t w i t h those a l r e a d y obtained. Inside of the zone the r e s i s ­ ti vity is zero and so is the IP pot ential and outside the zone t h e v are b o t h greate r the : zero. U n fortunately, the m e a s u r e m e n t s were not e x t e n d e d far en ough outw ard to d etermine the m a x i m u m s u s c e p t i b i l i t y value. 3 avers 1 ot ner ele ctrode con figur ati ons were tried in an effort to obtain a m e a s u r a b l e p o l a r i z a t i o n signal when trio e l e c t r o d e s were all within the m i n e r alized zone but the r e s i s t i v i t y was just too low. The pot ential el ectr ode s were intoincd at a 2 0 foot sep a r a t i o n from the current ele c t r o d e s (either on the inside or the o u t ­ side of the c urrent electrodes) and the sys tem wa s e x ­ panded. As long " s the e l ectrodes were s u f f i c i e n t l y remove d fror. the m i n e r a l i z e d zone so that a p o t e n t i a l gra di ent wes establish ed ( r esistivity no longer zero) a p o l a r i z a t i o n signal was measure d. P i n e co mbin ati ons of the four e l ectrodes are shown in Plate 25a a l ong wi t h the IF s u s c e p t i b i l i t y and r e s i s t i v i t y measure d at each po sit ion. The p y r r h o t i t e outcrop in the C r a n b e r r y segment had little or no cover alo ng ei the r T r a v e r s e 1 or 2. The p o t e n t i a l electr odes were in di rect contact w i t h the ore and since it v/rs such a good conduct or the potential ac ross two el ectrodes r em ai ned zero for all a lied c u r r e n t s . It w rwj decided to in v e s t i g a t e anothe r p ortion of the G o s s a n Lead w h e r e the ore was s u f f i ­ c ien tly -’a s s i v o to p rovide lor; r e s i s t i v i t y but where the cover wes rath e r thick. A site, In dic at ed by C D i i 1 --to 2 2 , near the outcr op of the B e t t y halier mine was selected. A n exp and ing el ect rod e syster was e m ­ ployed w h i c h had s center located a_ ..roxiu toly 3 5 0 feet K 6 5° A of DDL 1 (Buroru of l i n e s P r o j e c t 2902). The line of el ectrodes ran h 7ro - and the strike of the B e t t v F a k e r was a n o r o x i m a t e l y II 42° 1. The v e r t i c a l d epth o f - the ore of DDK 1 is from 196 feet to 207.8 feet, hich glows a thickness of ore of 1 1 . feet. Two dim in this a r e a is a b o u t 47°. It was o r i g i n a l l y planned that the line of e l e ctrod es would p a r a l l e l the strike, how­ ever, be c a u s e the area is h e a v i l y o v e r g r o w n the electro de line had. to ma ke aw ang le of about 3 9 ° to the strike. This m e a n t that at one end of two line both the current and p o t e n t i a l ele ctr ode s were near er to the ore than, the el ectrodes at t o o ther end were and the s i t u a t i o n b e ­ came worse as the electro de a r r a y was e x p a n d e d • becaus e PLATE 25 THE EFFECT OF ELECTRODE CONFIGURATION ON INDUCED P O L A R IZ A T IO N S U S C E P T I B I L I T Y PYRRHOTITE CRANBERRY SEGMENT INOUCED P O LA R IZ A T IO N S U S C E P T IB ILIT Y {M V /V O L T } (a) 20 ELECTRO DES 0 001 PYRRHOTITE CRANBERRY SEGMENT IN D U C E D 80 100 00 20 60 R E S IS T IV IT Y ( ! 0 5 f t cm ) LYNCHBURG GNEISS P O L A R IZ A T IO N S U S C E P T IB IL IT Y 120 140 160 100 (M V /V O L T ) 200 220 240 "a " { F E E T ) EXPANDING ELECTRODES ELECTRODE SEPARATION WENNER CONFIGURATION 220 .2 6 0 300 R E S IS T IV IT Y ( I 0 3XX cm ) 340 200 the several electrodes changed their positions with respect to t :.e ore tii.i s type of a survey -ay ot be used to d i s c o v e r e xp e r i m e n t a l l y the r e l a t i o n between the elec trode separation and the c-.opth of influence. The da ta obta ine d from the vertical* profiile over the j etty Baker mine nr s been po rtrayed in the usual manner in Plate 26. There ero.ears to be a one-to one c o r r e ­ lation between the depth to the ore and the electrode separation. At the 1^0 foot separation there is a sharp br eak in the curve. The vertical depth to the ore is lie feet: w h i c h places the shortest distance from the -nrface to the ore at about 150 feet. An appreci­ able amo unt of current wil l flow through the ore body for electrode separat ions greater than 1 5 0 feet, however, the break in the curve indicates a decrea se in the p o l a r i z a t i o n susceptibility. As an explan ati on of this inverse effort it is suggested that the o verb urd en is h i g h l y mi n e r a l i s e d and, as it can be seen in Plate 26, lias a h i g h resistivity. Therefore, a large ootential gradie nt is develop ed and all minerals contained in the ove rbur den w h i c h hav' r e s i s tivities of 2 0 x 1C3 ohm- cm or less ”rill be polarized. As a result, a h i g h "mlue of induced - olar ' • io s!'seept.ibi 1 i t*r i s e- sured. As the ele ctr ode arrey 's e x p a n d e d , more current reaches the ore body which, because of its low r e s i s ­ t i v i t y , robs the u p per reg ion of i ts share of the current and de creases the p oten tial gradient. The saturation effect prevents the ore from beco min g as Ad ghl" po larized as the di sse min ated m i n e r a l which is also closer to the surface and as a result the polariw 5 . .1 -_v V ./ - r\ > ” •J A U - • t -? I-n O _L. "1 * +•t.1.. W ^ ^ J. n ^ c o r* O • r r* - i. -h > • »r\ 'W n% *1 oot*woc! o W -i- N -r J. U U> V A— - system expends still f u r t h e r , a larger vo lu me of the overb urd en 1 s traversed by the current w hich again increases t::.e polar i z a t i o n susceptibility. It v/:" s mentioned earlier (Fart D-2) teat the e x ­ tra mo la tio v'1 b~ ck to Z'-ro tire occasional! " introduced c-anges in the nols ri cation cusc -wtibilitg- curve. The curve o b t - : iuod for **alv o s of

o and the changes introduced are a pusrent. 1. ieasur e n e n t s Over a magnet ite Ore Bod y informa tio n about a second ore body was obtained tnrou'-i UoGS. The ore, wedgod between, a lime stone and d 1 ab? sc con t - c t , v/^s one of the manTT small magnetite d e ­ cs its found in Le ban on County, i-ennsylvsnia• f o r t u ­ nately, the ares had been explored a>>d the data from six d iam ond-drill holes (DDI1) mer e available. fne p r o j e c ­ tion onto the ho r i z o n t a l plane of the pro bab le limit of 55 PLATE 26 V E R T IC A L P R O F IL E B E T T Y B AKE R Q. cm ) IN D U C ED POLARIZATION SUSCEPTIBILITY AT t = 8 0 m s (10 (2) INDUCED POLARIZATION S U S C E P T I B I L I T Y AT t = 0 RESISTIVITY 100 INDUCED POLARIZATION SUSCEPTIBILITY (M V/VO LT) (I) MINE 80 R E S IS TIV ITY 60 I00 2 00 ELECTRODE SEPARATION (F E E T ) 3 00 400 the ore body is^shown in Plate 27. Seven traverses were conducted in the areaj six of seven were over the probable ore body and the seventh was intentionally r e ­ moved therefrom. The location and direction of each of the seven traversed m a y be seen in Plate 27. The i n f o r ­ mation obtained fror the six D D E 1s was used to construct t .e probable outlines of the ore body and these outlines are shown in Plates 28, 22, 30 and 3 1 . I late 28 is a vertical sectio" through Traverse 1. Plate 29 shows a vertical section through Traverse 2 which arrears to be t .my thickest nart of h.o ore. Its maximum" t h i c k n e s s , rK-vh: 6 0 feet, occurs r 1 appr oximately >0 foot depth. Plates 30 and 31 are vertical sections through Traverses ^ and 9 respectively. Traverses 1, 2 and 3 were run roug hly parallel to one another in the north-s out h direction and spaced to pass over the existing drill holes. Along Traverse 1, two runs were c-.rui -teds H u n 1 for which ttp II g'r ri 50 fee ■■r,d Him- 2 for which " f wes 1 0 0 f e e . Th 0 station s for both of these runs were taken 0 1 2 p foot intervals • **" »' —ri2 “hv-,q olnri ^d"bion susce-;-tibili tv mr? the l i m e s t o n e a r r e a r s to be r a t h e r 5 me 11 -nd u n i f o r m l y a b o u t 20 wv / v o l t . As the m a g n e t i t e is a p u r o a c h e d fr om the l i n e n t o n e the s u s c e p t i b i l i t y c o n ­ stant in cr e a s e ? . The l a r g e s t v a l u m occurs a l o n g T r s v e m s 2 .were the ore shows it" thickest section. The double r'0 -.]■' -b'-orv. - l o n g Traversa 1 is of Inter es t. Tkw first am.’: occ r i w w r the top of the ore (rt its shr 1 low es t d e ” T h ) .d o second :rs just soot of ITih 3 w h e r e the ore m the ight to bo m o a t 121 Peat deem. The resis- ^ tiv~ b on •e""s a small r~2 n at the same m l a c o . In a d d i l ‘on to t;,c h susc eptibility .-and resistivi t:T sure- -ants, vortical .mg.a m tic field r w dir gs "ers also taken along Tr"versos 1, 2 -nd 3 (see Plate 3^) . An anom aly in the vertical fielm -.0 - ^'ire^ents which is c s large as the iargest value mo cured along Trav rse l occurs at the same location as the second peak in tne IF curve. There is certainly a well localized conducting b o d y located just south of DDh 1 ’ w hich is not revealed by the existing drill holes. It should be noted that the IF susceptibilitm curves and the vertical magnetic field dob: both woint to Traver se 2 as the location of the largest amount P L A T E 27 PROBABLE L IM IT OF ORE BODY HORIZONTAL PROJECTION M A G N ETITE LEBANON COUNTY, PEN NSYLVA N IA TR A VER SE 7 N7 TRAVERSE 3 TRAVERSE 2 TRAVERSE I D.D.H. 5 D.D.H. 4 D.D.H. 3 N5 T R A V E R S E /4 N4 TRAVER SE 5 D.D.H 6 N2 E2 0 1 D.om ond Hoi E4 E3 20 I 40 60 I I 80 SC ALE (feet) E5 100 I I • D.D.H. 2 E6 PLATE 28 VERTICAL CROSS SECTION T H R O U G H M I N E R A L I Z E D ZONE ALONG TRAVERSE I o S C A LE (F E E T ) D.D.H. 2 D.D. D.D.H. 99' 120' D. D. H. = DIAMOND DRILL HOLE SURFACE MAGNETITE DISINTEGRATED DIABASE LIMESTONE DIABASE SHALE PLATE 29 V E R T IC A L CROSS SECTION THROUGH MINERALIZED Z O N E ALONG I 0 TRAVERSE 2 --- 1 1 i i I 100 SC A LE(FEET) D.D.H. 6 D.D.H. 4 90— 141 ‘ l4 |,-^ S v § S :::: :: ::-f.-y.-jf.-.::::: '.V'— ■AVAV-.-V/: D.D H .= D I A M O N D D R I L L HOLE SURFACE f: f:::::: 88888< MAGNETITE DISINTEGRATED DIABASE LIMESTONE DIABASE SHALE PLATE 3 0 V E R T IC A L C R O S S S E C T IO N THROUGH MINERALIZED ZONE ALONG TRAVER SE 3 100 SCALE (FEET) D.D.H. 5 146 D .D .H .= D IA M O N D D R IL L H O LE SURFACE MAGNETITE DISINTEGRATED DIABASE LIMESTONE DIABASE SHALE P L A T E 31 V E R T IC A L CROSS S E C T IO N T H R O U G H MINERALIZED Z O N E ALONG TRAVERSE 5 I i i J L 100 SCALE (FEET) D.D.H. 5 D.D.H. 4 D.D.H. 3 99 v. 113 120 « D . D . H . = D IA M O N D : . I! D R I L L H O L E : SURFACE M A G N E T IT E D IS IN T E G R A T E D D IA B A S E L IM E S T O N E D IA B A S E SHALE PLATE 32 INDUCED POLARIZATION SURVEY MAGNETITE LEBANON COUNTY, PENNSYLVANIA HORIZONTAL TRAVERSES 0 = 5 0 FT RUN I TRAVERSE 3 TRAVERSE 2 D.DH.5 6c :^V zzz//z/zzz/szz, v/s o RESISTIVITY (IO! .n.cm ) 40 y / ' A / y INDUCED POLARIZATION SUSCEPTIBILITY (M V /V O LT ) / yyz///Z /// /S/ ' v/z/z/// -'/ /' // 't 'z z' //-' '/z // /z,tivzzzx,z/z/A. ...a ....z / ;A z /z a'zfz/-/Z''z/Z//^//z///z/A, D .D H .6 D.O.H. 4 TRAVERSE DISTANCE (F E E T ) 50' | of mineral. On the other hand, there appears to be little difference in the resistivity data from the three traverses. Run 2 of Traverses 1, 2 and 3 show (Plate 33) essentially the same information as is given in Plate 32. The double pea1: of Traverse 1 has practi­ cally disappeared and the peak along Traverse 3 has increased and broadened somewhat. The results^ other­ wise, appear much the same. The differentiation between the signals obtained over the ore body and those o b ­ tained from either side of it is not great. However, the ore is not very thick in this north-south direction. Better contrast can be obtained by plotting areal sus­ ceptibility maps. These maps have been plotted such that all signals 50 mv/volt or more are shaded black. The 5 mv/volt contour intervals are shaded such that each interval is lighter as the signal decreases. Two such maps have been plotted. The data of Run 1, Traver­ ses 1, 2 and 3 were used to prepare Plate 34 and the data from Run 2 of the same three traverses were used in the preparation of Plate 35/ Both maps show the greatest signals over the leading edge of the ore body and they both indicate the direction of the strike of the ore. Data from Traverse 4 was obtained with an expand­ ing electrode array which had its center 100 feet north of DDH 4 and its line of electrodes in the east-west direction. Traverses 5 and 6 were vertical profiles with their centers over DDH 4. Traverse 5 was parallel to Traverse 4 and Traverse 6 ran N 52° E. The results obtained from Traverses 4 and 5 are shown in Plate 37 along with fabricated vertical sections of the ore body corresponding to imaginary drill holes directly below the center of each electrode system. The results of these two traverses are to be disregarded for the large electrode separations because it was discovered, after the data had been taken, that the electrodes had been set near some cast iron drainage pipes which were in a horizontal position and along the line of the electrodes. However, neglecting the large separations there appears to be little correlation between depth of influence and electrode separation. The ore is nearer the surface under the electrode line of Traverse 4. The IP sus­ ceptibility is much larger for the small electrode sepa­ rations along Traverse 4 than along Traverse 5 which in­ dicates that the magnetite along Traverse 4 has been polarized. The results obtained along both traverses approach roughly the same value as the electrode separa­ tion increases. Traverse 6 was conducted in order to get away from the iron pipes, the effect of topography on the resistivity and still cross over the ore body. Only partial success was realized because the electrodes ended up against a metal fence at each end of the line. 57 PLATE 33 INDUCED POLARIZATION SURVEY MAGNETITE LEBANON COUNTY, PENNSYLVANIA HORIZONTAL TRAVERSES a = IOO FT RUN 2 0 TRAVERSE 3 6> 4t. lOO DDH 5 6 RESI ST IV IT Y (10 ft c m ) TRAVERSE 2 4 NOUCED POLARIZATION S'.'SGEPTlBlLlTY (MV/VOLT) s 0 ~r DDH 6 DDH 4 TRAVERSE I 2' i 50' INDUCED P O L A R I Z A T I O N SUSCEPTIBILITY ( M V / VOLT) TRAVERSE 3 TRAVERSE 2 TRAVERSE SCALE (feet) I d .d .h D.D.H. 3 .i I INDUCED P O L A R IZ A T IO N SU R VE Y MAGNETITE LEBANON COUNTY, PENNSYLVANIA AREAL SUSCEPTIBILITY 0 ; 5 0 FT MAP ^ m oj ■C> TRAVERSE 3 INDUCED POLARIZATION SUSCEPTIBILITY (MV/VOLT) TRAVERSE 2 SCALE (feet) TRAVERSE I INDUCED P O L A R IZ A T IO N SURVEY MAGNETITE LEBANON COUNTY, PENNSYLVANIA S U S C E P T IB IL I T Y MAP Q= 1 0 0 F T PLATE AREAL 35 PLATE 36 VERTICAL MAGNETIC FIELD SURVEY MAGNETITE LEBANON COUNTY, P E N N S Y L V A N IA 6000 TRAVERSE N0.3 4000 ZERO AT D.D.H. 5 2000 300 S 200 100 200 300 ii 00 200 300 Jk 400 N 100 200 300 400 N 100 400 N 2000 • 10000 OF F S C A L E T R A VE RS E NO. 2 ZERO AT D.D.H. 4 GAMMAS 8000 6000 4000 2000 300 S 200 100 12000 TR AV ER SE NO. I 10000 ZERO AT D.D.H. 3 8000 6000 4000 2000 300 S 200 100 0 DI STANCE D D H = DI AMOND D R I L L H OLE IN F E E T VERTICAL PROFILE MAGNETITE LEBANON COUNTY, PENNSYLVANIA RESISTIVITY POLARIZATION ( I0 2 i l c m ) SUSCEPTIBILITY (M V/VO LT) TRAVERSE 5 INDUCED TRAVERSE 4 O 20 40 60 60 100 120 140 160 160 ELECTRODE SEPARATION (FEET) 200 220 240 260 280 300 The results of this traverse are shown in Plate 38 . Once again there appears to be little correlation between the depth of influence and the electrode sepa­ ration. Rather, it appears that, as one of the poten­ tial electrodes approaches the ore, the IP signal in­ creases. As a chec1 * on the results obtained over the magnetite deposit a vertical profile was run in the east-west direction at a place well into the limestone and removed from the ore. The results (Plate 38 ) indicate the IP susceptibility to be small and quite uniform. The almost constant response is in agreement with the theory for the uniformly mineralized earth (Part C - l ) . The data obtained from the vertical profiles (Traverses 4, 5 and 6) are still useful even though the desired correlation of depth with electrode separa­ tion is not apparent. Over DDH 4, at an electrode separation of 100 feet, there ar e three values of the IP susceptibility? Traverse 2 Run 2 in the north-south direction, Traverse 5 and Traverse 6. When the results from these three stations are compared, it is found that the greatest value came from Traverse 5, the least from Traverse 2 and the value from Traverse 6 was intermediate. The discussion concerning the ellipse of p o l a r i z a t i o n (Part C-3) predicted that the greatest signal would appear in the direction of the strike. For this deposit the strike is in the east-west direc­ tion and the largest signal appeared in that direction. The results predicted by the discussion concerning the ellipse of polarization received additional verification from a survey conducted for that purpose. The results obtained everywhere over the limestone were consistently low and of the same magnitude. Those results obtained over the diabase were larger than the limestone measurements. Three more surveys were run in this area to check the predictions concerning the ellipse of polarization. For each survey a Wenner system was used. The electrodes were separated by 50 , 100 and 150 feet for each orientation of the elec­ trode line. The line was oriented first in the northsouth direction and then at 30°5 60°, 90°, 120° and 150° to the original direction. The first survey was conducted far removed fr om the ore and well over the limestone. The second survey had its center or rota­ tion somewhere near DDH 4. The results of these two surveys are plotted in Plate 39. The induced polar­ ization susceptibility for the limestone and the m ag­ netite are plotted in pairs according to the electrode separation used. It should be noted that the values for the limestone are quite uniform, both with respect 58 VERTICAL PROFILE LEBANON COUNTY, PENNSYLVANIA 1120 601 LIMESTONE TRAVERSE 7 18 0 (I0 3 i l c m ) 40l 201 40 MAGNETITE TRAVERSE 6 160 (lo z n c m ) 801 RESISTIVITY 0 "D r 3 m ELECTRODE SEPARATION “Q“ (FEET) $ PLATE 39 ELLIPSE OF POLARIZATION LEBANON COUNTY, PENNSYLVANIA i 20 M V / V O L T , MAGNETITE LIMESTONE I s Q=5 0 F T a = 100 F T a = 1 5 0 FT A to the orientation of the line and with the electrode separation. The dashed-circle is the average value of all the vectors for the particular electrode separa­ tion employed. The limestone has a resistivity of about 50 * 103 ohm-cm and, because the polarization susceptibility is low, the limestone must be weakly but u nifor mly mineralized. The three curves obtained over the magnitite changed considerably with electrode separation. Wh e n "a" is 50 feet the susceptibility is nearly constant which results in a circular pattern which is as it should be. The center of the*system is over DDH 4 and the ore is more than 50 feet from this point in any direction. Therefore, the ore is outside the influence of current density pattern and it is only the diabase which is polarized. For the 100 feet separation the IP susceptibility signal is 1.5 times as large in the direction of the strike as it is in the direction normal to the strike. The ratio of the largest to the smallest signal for the 1 5 0 foot separa­ tion has increased to roughly 2 • ’ 1 but the indicated direction of the strike has changed slightly. This rather preliminary investigation is considered to be in good agreement with the predictions of the theory. The third survey was conducted over the diabase at a place well removed from the ore. It is known that the diabase is more highly mineralized than the lime­ stone but it was expected that it would also be u n i ­ formly mineralized. Certainly no one direction was to be preferred over any other. However, an examination of the results, plotted in Plate 40, reveals that the induced polarization susceptibility is greater in the north-south direction than in any other direction. The measured value of the IP susceptibility in the northsouth direction is at least twice that measured in the east-west direction. The vectors Plotted for the elec­ trode separation of 50 feet show the IP susceptibility to be larger in the neighborhood of the north-south direction than it is in the east-''■rest direction, ^'he figure is more nearly an ellipse than a circle. However, for the electrode separation of 1 0 0 feet the vector pattern is more like*, except for the north-south direc­ tion, a circle than an ellipse and for the 1 5 0 foot electrode separation it is essentially a circle except for the north-south direction. The vector in the north-south direction increased as the electrode sepa­ ration increased. It was concluded that the source of the polarization potential was a long metallic object such as a water >'ipe or cable oriented in the northsouth direction because the side vectors decreased, and the north-south vector increased as the electrode array was expanded. A letter was sent to the owner of 59 ELLIPSE OF POLARIZATION 2 0 M V /V O L T DIABASE SCALE LEBANON COUNTY, PENNSYLVANIA Q* 5 0 FT a =150 FT PLATE 4 0 = 100 FT the land who in turn confirmed the existence of a water pipe in the place indicated by the measurements. It is concluded that the magnetite deposit was clearly located by the induced polarization suscepti­ bility. Other electrode arrangements or different types of traverses can be arranged such that the con­ trast between the induced polarization susceptibility measured over the ore and off the ore will be greater than it is now. However, that is a task for the future. The survey over the magnetite deposit con­ cludes the field work. 60 SUMMARY It is the intention of this thesis to correct some of the errors which have crept into the litera­ ture, to remove some of the existing mystery and to bring out the advantages and limitations of the method of induced polarization with the hope that it will grow into a useful tool for geophysical prospecting. To accomplish this purpose a series of laboratory experiments, designed to reveal the fundamental re­ lations involved, were conducted; a theoretical rerelation, based on the results of the laboratory ex­ perimentation, has been developed for the interpre­ tation of field data, and in addition to the preliminary field survey over an amphibolite dike, the method has been applied to three mineralized areas where the de­ tailed geology is quite well known. The results ob­ tained in the field are promising and in keeping with the experimental and theoretical developments. In the light of the results of this work the literature is briefly reviewed. The conclusions reached by Schlumberger^ concern­ ing geophysical prospecting by the method of induced polarization have been examined. He apparently under­ stood the elements of the fundamental process involved but he w a s lead to conclusions, either because of inadequate equipment or insufficient experimentation, which can not be supported by this work. His claims that the self-potentials generated by sulphide ores concealed the induced polarization effect are not sup­ ported by the present measurements over the pyrrhotite outcrop as reported in this thesis. At the east edge of the ore the self-potential generated was more than 300 mv, However, no evidence was found to support the contention that the induced polarization potential was concealed by that self potential. As a matter of fact, the largest value of the induced polarization potential was measured at this interface. The energizing current was made to flow in both directions across the boundary and the induced polarization for each direction of the current was measured. Within the limits of experimen­ tal error, the measurements were the same in both direc­ tions. If, because of chemical action, the interface of an ore body became saturated with electromotively t 1 active material, then additional current forced into the ground w o u l d _either deposit more material or remove some, all according to whether the energizing current aided or opposed the natural current. The addition of more electromotively active material can not in­ crease the potential of the saturated interface and, therefore, no induced polarization potential can be measured. If, on the other nand, the energizing cur­ rent opposed the natural current some material would be removed. If the amount of material removed reduces the concentration of the active material below satu­ ration, the return to saturation would be measured. The self potentials required to maintain the surfaces of an ore body in a saturated condition will be difficult to realize under the conditions of natural current flow. Schlumberger stated that the resistivity of the rock, surrounding the ore body, enters into the induced polarization effect not more than to a secondary measure. This statement is not far from correct if the form of the decay curve alone is considered. However, one of the results obtained in this thesis states that the induced polarization potential is proportional to the potential gradient established. This makes the induced polarization effect directly proportional tc the resistivity. Furthermore, the laboratory experiments have failed to bear out Schlumberger1s statement that the "residual” polarization potential was due to a transport of ions creating a dissymmetry between the regions surrounding the electrodes. Contrary to this statement, it was found that the only time polarization potentials were observed was when electrically conduct­ ing minerals were present. This observation lead to the theoretical development of the polarization potential of a uniformly mineralized earth which has been verified experimentally in the laboratory and in the field during the course of the work reported here, The publications of Kttller^*7 and .Zeiss6 concerning the "Electrochemical Ivlethod" contain so many errors that it is unfortunate that they were published at all. The work of Belluigi > might have succeeded except that he discarded only oart and not all of tne procedure estab­ lished by I/tiller. Although Belluigi improved the method of measurement he retained much of the interpre­ tation give-; by IKUller. Variations in the resistivity alone might well have accounted for the results Belluigi obtained. The present work has snown that polarization is induced only when electrically conducting minerals are present in the structure. Formation boundaries are not nolarizable unless a differential exists in the 62 concentration of electrically conducting mineral across such boundaries. Oil, as a non-electrolyte, should not generate electromotively active material against a boundary even though the boundary is mineralized. Fur­ thermore, the decay time of of the induced polarization potential is of sufficient duration to mask the differ­ ence in time required (as reported by F o t a p e n k o ^ ) to polarize an electrode first in an electrolyte and then in oil. It is concluded that oil cannot be directly located by the induced polarization method nor can oil be indirectly located unless it is very shallow. The method of induced polarization requires for its operation the existence of electrically conducting minerals in an electrolyte. This requirement confines the method to the location of electrically conducting minerals and other metallic objects. Its best appli­ cation should be to shallow mineral prospecting. It may, however, be used to locate pipe lines, rails, cables and other buried metallic objects. The method does differentiate between those aress where resistivity is low because of metallic conduction and those where resistivity is low because of good electrolytic con­ duction. The method is also capable of differentiating between two areas of equal resistivity but unequal mineralizations. It. should bo of use, therefore, in the location of disseminated minerals, such as the galena in the Missouri-Oklahoma-Kansas "Tri-state” region, where the resistivity change from a mineralized area to an unmineralized 'ne is insufficient to enable detection of the mineralized area by resistivity measure­ ments. The ellipse of polarization principle enhances the use of the method. This preliminary work has revealed certain d is ­ advantages in the IP method, several of which are in­ herent in the r cthod itself and others that may be eliminated by further development of the method. To begin with, the induced nolarization measurements cannot be divorced from resistivity measurements. This does not mean that separate equipment must be employed nor that the resistivity must be separately measured. H o w ­ ever, the two separate measurements will undoubtedly be desirable. A more serious limitation on the method and the one which confines it to shallow work is the "falloff” of the signal with depth. First, a current den­ sity must be established in order to polarize the earth minerals and then the signal must be returned to sur­ face which gives, at best, an inverse fourth power re­ lation. However, the magnitude of the potential in­ creases with the linear dimensions of the body and 63 thereby improves the relation of the signal vs death. An o t h e r lim itat ion at present is the polari zat ion’of di sseminated minerals which may mask the deeper lying ore bodies. The effect produced by changes in the con­ cen trat ion of the disseminated mineral is not known. There may be a saturation effect which depends upon the percentage conce ntra tio n of the mineral particles. Still another limitation, although not serious, is that pote n­ tials measured by the induced polarization method are u s u a l l y one order lower than those measured by the r esis­ tivity method. It is expected that the method of induced polar ­ ization will, w i t h improved instrumentation and a larger background ^f field results, find its place among the existing tools for geophysical prospecting for minerals. It must be remembered that the work reported here is only the initial phase. It is the author's hope that a us ef ul method of geophysical p r o s ­ pecting will be built upon the foundation established by this paper. 64 A CKN OKLhD GlLa^JJiMTS The author is indebted to the Naval Ordnance L a b o r a t o r y for the use of the equipment and facilities av ailable at the Laborat ory whic h have made this work possible. H e is deeply grateful for thm continued interest and tne many timely suggestions and criticisms of Dr. L. II. Humbaugji and Dr. V.r. G. Keck of the Lab o r a ­ tory staff. It is a pri vilege to acknowledge the as sist anc e of illustrators and photographers at the N aval Ordnance Laborat ory in the preparation of the plates and the assistance of kessrs. h. L. Sanderson and S. F. Haddad in the collection of the data. The author wishes to thank the Geophysics S e c ­ tion of the U. S. Geological Survey for services and facilities w hich were placed at his disposal and for the assist anc e given to hi m in the field work. Dr. J. H. Swa r t z supplied the verti cal magnetic field readings and hr. E. C. Spicer supplied the Gish-Iiooney r e s i s tivity measurements over the amphibolite dike. The author is indebted to them for these data and for their as sistance In the field work. H e also wishes to thank members of the Michigan State College faculty, pa rti cularly Dr. C. D. Hause for his interest and suggestions and Dr. C. P. Kells for the tedious lob of checking the mathematics. 65 * r> ,*i. r*jGjtao\—j. i-' i ,• 1. 2. 3. 4. p. 6. 7. 8. 5. 10. 11. 12. 13. 14. 19. 16. 17. 18. 19. 20. 21. 22. 23. C. Schlumberger,. German oat ant ;/-269 ,$20 (6 ,.:ov. IS 12) C. A. heilsnd, Geophysical AX' loration. F r o n t i c o - A a 11, ^ I n c ., How York (IS40), p 7 6 3 C, S c h l u m b e r g e r , Gtude 3ur La Prospection" Ylect riq ue Du Sous Sol. Gauthier-Villars et C's. Paris (1(20) Ch. S G. S c h l u x b e r g o r , loc. cit. revised (1S3G) Y. Yuller, Geits. f. Geophysik. 8, 423 (1S32) 0. V/eiss, Gorld Pet. Gongr. (London) Proc. 1 (p;?,2) : . I ulj.or, Gerlands Jsitr. z. Geophvsik. 4, 302 (IS 34); B e i t s . f. Geo-ohvsik 4, 330 (1834)5 ibid I6 ? 2 "4 (1040) A. R e l l u i g i , Yoitr. z. Angew. Geophysik* 5, l6s (IS34) A. Belluigi, Riv. Geoniner 2. ^6 (1941) L. Y. Plan U. 3. patent 1,(11,137 (1933) G. and Y. Schlumberger, A.I.Y.L. G eophys . Prosp. 32 (1(32); T. Y. Pearson, ibid 34 (1934) P. F. llavrley, Geophys. 3, 247 (1933) G. rotaoenko, U. 3. eatents ,•/ 2,190,320, >72,190,321, 772,190,322, #2,100?323 (1940) G. Peterson, Y. 3. patent ;/2, 190,324 (1940) A. Yatsubara, IT. 3. patent , 0 2 ,1 5 3 , 6 3 6 (1939) K. It. Lvjen, U. S. patent ,9 2 ,3 75,776, »2,379)777? ,/2 ,378,778 d i d ) F. P. Bowden and A. R. R i d e s 1, Aoy. Soc. i n c . , 1A 120, 59 :39 2 8) J. A. Stratton, Gleetromagnotic Theory, YcGrav-Yill, Bov York (1(41) p 15 G. Prasad, Spherical harmonics. Part I, Y e h a n a n o a 1 Press, Benares City, India (1(30) p 104 J . Y. V/ebb, Fhys. Rev. 37? 2 9 2 (1931) This wo rk was done at the POL- by Yr. C. Lufcy C. Yilton, Geologist at U S 33, Personal comwunication R. J. Bright and N . D. Raman, USuS Reports - Open File Series, The Gossan Lead, Carrol County, Virginia, Released lc February 1(48 66 Since there exists an unresolved difference between the -vork of hebb and the calculations in this caper the derivation of the constants employed is given here. This derivation is not intended to be completed in itself but must- be read in conjunction v/ith kebb's paper, '•/hrrover they fit, k e b b ’s ca l­ culations are used but tnere is an interchange in the summation indicies. V.lien reading V/obb1 s formulas read :n in place of n and -'ice versa. (1 ) ue a-B-L 4 rr c** b o w l/ro can be o••■ponded in ter< s of tno polar coordi­ he sr.-here by nates of the origin at the center the relation (2) i = i L ^ ) npn(cosot) nhich can be further exnanded by the biaxial expansion ■” r, » -) - r o p > * *•> p > > x cos m Substituting (2) and C ) the electrode becomes s (r'jj1(2-<£) in (1) the potential due to *•s,nm ,). n = o m = o v '' ' The subscript i refers to the coordinates of the point P ( r ,9, <* ) measured rith respect to the center of the image sphere instead of tne origin in the real sphere. The potential anyv/here outside the sphere is the sum of these throe potentials; i.e., = ue + us + u. - - I Z ( 7 0 )n ( ' X m n c° s m < P + \ rnnSln m c f ) < » + 2 I ( 7 ) nf,( A n,n 0 °s>nc<>4Bm n s ,nmc(i') fa) ,n+i fa) ■ + (AmnCOSrnCP; + B m n sinmcp.) ..‘ebb has given an expression for PnOO _ £ OnO!____ rlk t; n + i “ (rn+ k ) J ^ n + k + i kv / rhore r 1 and p.' are coordinates of the point Pp in terms a center at the imare srfnere. hn interchange of the indici.es n and k gives P* fa) ' - i l l (Amkcosm^ +BmkS,nmcf)^l-rPn> ‘) n=o m*o lf*»n ii A v/liere (depth of sphere = h/2), a mkn - ( n + fc )!__________ / \ n + '<+i ~ Cn+m) ! ( k - m ') ! \h 7 LQ O ho e since this is the potential at Pj_ (the image f P) due to S , it is also the potential at P due to ±. 7/e need only to interchange r 1 and r and p 1 and p. Tho notential inside the sphere is obviously I OO OO =■ 11 1 ( ^ ) n( C rnnC ° S m ^ + nso m-o DrnnS'n m<^ The boundary conditions require that |° r w n ic r o+ r= a g iv e s I l ( t ) n( K m n C0S m

w h ic h given ^ [lI-g r^ y '^ K rn n « » me?+9k’mn sio m«p)pJJ»f/<) +I I - (Amn « * mcp + Bmnsin me?) + I I I £ a mknCAmkcos m(9 + Bm|< s,n mc^P™ (A1)! mncosmfip + Dmn am mcp ) p m =\ ( . " O':: set ft Pa ::no equete s im ile r te s s e re l h o rm o n ic s . Then (1 ) (%) ^ m n + A mn+ i A m(, o (n|£n= c mn s nd a f Cf ) V,Q/ ^ ,nn 4-B mn + X Brrik a mkn ■= D m n. k Also " (% )" A mn+ n l A m k » m k n = n ^ C m0 g nd (2 ') n 0 " V mn - Cn+0 Bmn + n Z Bmka mkn = iv Dmft from which "(ff 'Knn-(nt0 A mn+nl A rnkamlCo=n^ [(if) ^mn4A'"n + Z A lnfca m |crvj- Cn + 0 A m n - n ^ A m n = f'@'k 'rrm(^)“ n ^ m n x ( i j + ^ l A mkOmkn- nI A mkamkn . [n(^.)+l]A mn = r,( 9 - , ) ' l< m n ( f - N) + n ( ^ - |) Z A m k a m l>(n-nfl! rrn, > {cos mCP.') . \ 1 " 'n r0' m'(n+m’)J nf AWlSin fTitPo J The value of E.-;n given by .'.'ebb i/ - K mn~ T~ p m { i* („ 4 > r0 ! H n W cos mcp. differs from that obtained above in the following points 1) it includes the term / a \ n (This is the most vr°y x ' serious discrepancy.) 2) there is a difference of sign between the value of K mn given here and that given by bebb 3) the Kronecher 8 ° is •'••issing which reduces m V coefficient of D in this paper to 1 v/hen m = 0. For vale.es of m ^ 0 the coefficient in ./ebb's formula is in agreement. 1) although ./ebb has specifically given only cos mCy for the value of K ,-n it arrears that the sin nCf v;as tahen care of by -.rental reservation. II The Induced lolarization Fotential of a Snhere _ln ci- Infinitely Intended bniform hediirr.. The problem of the buried sphere in a unilorm halfspace v:as corrplicrted by the air-earth boundary. As a first a p "roxira t i t ^ the problem consider the sphere to be at d i s t a n c e h be lor/ a horizontal plane in an infinitely c m u u e d uniform full-space. The radius of the sphere is a , its resistivity is P 2 and it is completely surrounded by a medium of resistivity Pp. Trie the origin of the coordinate system at the center of the sphere end the s axis to be the line ioininr the center -f the sphere end the currev.t el ec trode. The energizing c errant I produces a polarization charge density cr on the surface of the spncrc.ich accord!: g to the laboratory experiments Is given by t.:o re let Ion (1 ) 06 = -hip 1 co^-onort of the carzx.t ex: u YU.ore j p is uii or the surface of the sphere. vi The potential at the point 3( r!y’ z 1) rhoso radius vector is ot and viiose colatitude angl* is Qj is given b (2) crdS s R The charge doeshtpcr car be found fra. relation above and Oh 1 s Irrv. In order to "ind the current density at the surface ;f the sphere and uorual to it the potential .inside and outside the sphere due to the energizing current nust bo calcjIf tod. The poten­ tial outside is due in the first part to the ohmic drop in the o.oui,.; produced bp the energizing enrre-n.t and in the second part to I.he distortion of the field introduced b p the s .te r •. " h o potential at sor.-io point P outside the s-hera is >+_ ^ I Bn ?? Pn fco$0) 9 ~4inr % o The potential -on the .r* s. ! i a b r. -f- m+i i n s i d e v. ef the sphere rust be t-.o rG iO i-j f~- -J.u _ jr* _ . .'-j *.. i. .- bx_o x J x U j. t -Trt-nri AnrnPn(cos0) n=o .tt tin: s u r b o o ti.jns arc: b bn, s,.ho~-■ he-' bo ;.idnre conai- $+=r « r _r> n n 2 n+l -i ^ *'4 ^ L [ ^ r + 7 «♦'rnt,/3n] Pn(eos^ The radial component of the current density can now be computed from O h m ’s law w h ich gives i - 1 I r f < v'n~l, nag"*'(-n-l) , 1 . r~~P,i>r "4fffcb[9»+l r/n+|rn+* A>JPn(° ® r - - ° i ' a “ - 2 ^ t K n P „(co s4» ) Where K„= ^ r [ f - ( n t l ) ^ n] ■ l o w from Equ ati on 1 the charge density becomes a - & l 0W cos&) and the potential from Equation 2 is (3) t(*'>f,l>-^lL W c o s 0 ) ds s i;ow v:rit-e W f J S . f P ^ V ’ ) 5=0 and apply the biaxial expansion which gives k= a [ l (3 )Sr ( 2- O g ^ i Psm (cos^)Psm (cos 0 ) c o s m ^ ] Substituting for 1/R into Equation 3 gives * &■ JSL K"P"cos0dSli«)SS 2-s°J^ x F^m (cos #) m(cosO) cos m However, because of the orthogonal properties of the Legendre polynomials, m = 0 and s * n, which gives for the potential after integration over the sphere jt /y . . in ,k la 2 rK a (Q \npn (cos31 L K n (