Chapter 5

Electrical Properties of Rocks and Minerals

5.1. CLASSIFICATION OF ELECTRICAL METHODS

Electrical prospecting involves the detection of sur- face effects produced by electric current flow in the ground. There is a much greater variety of tech- niques available than in the other prospecting meth- ods, where one makes use of a single field of force or anomalous property - gravitation, magnetism, elas- ticity, radioactivity. Using electrical methods, one may measure potentials, currents, and electromag- netic fields that occur naturally- or are introduced artificially- in the earth. Furthermore, the measure- ments can be made in a variety of ways to determine a variety of results. Basically, however, it is the enormous variation in electrical conductivity found in different rocks and minerals that makes these techniques possible.

Electrical methods include self-potential (SP), tel- luric currents and magnetotellurics (MT), resistivity, including mise-h-la-masse, electromagnetic (EM), in- cluding AFMAG, and induced polarization (IP). They are often classified by the type of energy source involved, that is, natural or artificial. On this basis the first three and AFMAG above are grouped under natural sources and the remainder as artificial. Such a classification can be made for prospecting methods in general. Hence gravity, magnetics, and radioactiv- ity are included in the natural source methods, whereas seismic requires artificial energy.

In the following chapters we shall study the elec- trical methods in a slightly different sequence, group- ing three natural source methods together but considering AFMAG with EM, because the field techniques are quite similar. For the same reason IP will be considered immediately after resistivity.

5.2. ELECTRICAL PROPERTIES OF ROCKS AND MINERALS

5.2.1. Electrical Potentials

(a) General. Several electrical properties of rocks and minerals are significant in electrical prospecting. They are natural electrical potentials, electrical con- ductivity (or the inverse, electrical resistivity), and the dielectric constant. Magnetic permeability is also an indirect factor. Of these, electrical conductivity is by far the most important, whereas the others are of minor significance.

Certain natural or spontaneous potentials occur- ring in the subsurface are caused by electrochemical or mechanical activity. The controlling factor in all cases is underground water. These potentials are associated with weathering of sulfide mineral bodies, variation in rock properties (mineral content) at geo- logical contacts, bioelectric activity of organic mate- rial, corrosion, thermal and pressure gradients in underground fluids, and other phenomena of similar nature. There are four principal mechanisms produc- ing these potentials; the first is mechanical, the latter three chemical.

(b) Electrokinetic potential. Also known as streaming potential, this is observed when a solution of electrical resistivity p and viscosity 7 is forced through a capillary or porous medium. The resultant potential difference between the ends of the passage is

284 Electrical properties of rocks and minerals

where { is the adrorption (zeta) potential, A P is the pressure difference, and k is the solution dielectric constant.

The quantity { is the potential of a double layer (solid-liquid) between the solid and solution. Al- though generally of minor importance, the streaming effect may be the cause of occasional large anomalies associated with topography. It is also observed in self-potential well logging, where the drilling fluid penetrates porous formations (911.3.1).

(c) Liquid-junction (diffusion) potential. This is due to the difference in mobilities of various ions in solutions of different concentrations. The value is given by

where R is the gas constant (8.31 J/”C), F is the Faraday constant (9.65 X lo4 C/mol), 8 is the absa- lute temperature, n is the valence, I, and I, are the mobilities of anions and cations, and C, and C, are the solution concentrations. In NaCl solutions, Ia/Zc = 1.49, hence at 25OC,

Ed = - 11.6 log( C,/G) (5.2b)

E, is in millivolts.

(d) Shale (Nernst) potential. When two identical metal electrodes are immersed in a homogeneous solution, there is no potential difference between them. If, however, the concentrations at the two electrodes are different, there is a potential difference given by

R8 ’ Fn (:) E I ---In - (5.3a)

For n = 1, 8 = 298 K, this becomes (E, in milli- volts)

E, = - 59.1 log( CJC,) (5.3b)

The combined diffusion and Nernst potentials are known as the electrochemical, or static, self-potential. For NaCl at P C , the electrochemical self-potential (in millivolts) is

( T + 273) 273

E, = - 70.7 log( 2) (5.4)

When the concentrations are in the ratio 5 : 1, E, = f 50 mV at 25°C.

(e) Mineralization potential. When two dissimilar metal electrodes are immersed in a homogeneous solution, a potential difference exists between the electrodes. This electrolytic contact potential, along with the static self-potential, considered in Section 5.2.1 b, c, d is undoubtedly among the basic causes of the large potentials associated with certain min- eral zones and known as mineralization potentials. These potentials, which are especially pronounced in zones containing sulfides, graphite, and magnetite, are much larger than those described in the preced- ing sections; values of several hundred millivolts are common and potentials greater than 1 V have been observed in zones of graphite and alunite. Because of the large magnitude, mineralization potentials can- not be attributed solely to the electrochemical poten- tials described earlier. The presence of metallic con- ductors in appreciable concentrations appears to be a necessary condition; nevertheless, the exact mecha- nism is not entirely clear, as will be seen in the more detailed discussion of mineralization potentials in Section 6.1.1 in connection with the self-potential prospecting method.

Other sources of electrical potentials in the earth should be mentioned. From Equations (5.2a) and (5.3a) it can be seen that the magnitude of the static self-potential depends on temperature; this thermal effect is analogous to the pressure difference in streaming potential and is of minor importance. Ob- viously metal corrosion - of underground pipes, ca- bles, etc. - is a local source of electrochemical poten- tial. Large-scale earth currents (w.2.1) induced from the ionosphere, nuclear blasts, thunderstorms (see AFMAG, §7.4.2e), and the like create small, erratic earth potentials. Currents of bioelectric origin flow- ing, for instance, in plant roots are also a source of earth potentials. Negative potentials of 100 mV have been reported in this connection, in passing from cleared ground to wooded areas.

Most of the earth potentials discussed above are relatively permanent in time and place. Of the vari- able types, only telluric and AFMAG sources have been employed in prospecting. When measuring static potentials these fluctuations cause a back- ground noise and may be a nuisance.

5.2.2. Electrical Conductivities

(a) General. Electric current may be propagated in rocks and minerals in three ways: electronic (ohmic), electrolytic, and dielectric conduction. The first is the normal type of current flow in materials containing free electrons such as the metals. In an electrolyte the current is carried by ions at a comparatively slow rate. Dielectric conduction takes place in poor con- ductors or insulators, which have very few free carri-

Electrical properties 285

Table 5.1. Resistivities of minerals

Resistivity (Om)

Mineral Formula Range Average

Bismuthinite Covell i te Chalcocite Chalcopyrite Bornite Pyrite Pyrrhotite Cinnabar Mol ybdenite Galena Millerite Stannite Stibnite Sphalerite Cobalt i te Arsenopyrite Niccol ite Bauxite Cuprite Chromite Specularite Hematite Limonite Magnetite llmenite Wolframite Pyrolusite Quartz Cassiterite Rutile Uraninite

Anhydrite Calcite Fluorite Siderite Rock salt Sylvite Diamond Serpentine Hornblende Mica Biotite Bitum. coal Anthracite Lignite Fire clay Meteoric waters Surface waters

(ign. rocks) Surface waters

(sediments) Soil waters Natural waters

(ign. rocks) Natural waters

(sediments) Sea water Saline waters, 3% Saline waters, 20%

(pitchblende)

Biz53 c u s CYS

FeS, F e A HgS MoS, PbS NiS CyFeSnS,

ZnS CoAsS FeAsS NiAs A12Q . n H 2 0

FeCr204

2Fe2Q . 3H20

FeTiQ Fe, Mn, WO, Mn02 Si 0, Sn02 Ti02

CuFeS, Cu5FeS4

S&

C Y O

Fe2Q Fez03

Fe304

uo2 CaSO, CaCQ CaF2

NaCl KCI C

Fe*(C4)3

~

18-570 3 X 10-’-8 X lo-’ 3 X 10-5-0.6 1.2 X 10-5-0.3 2.5 X 10-5-0.5 2.9 X 10-s-1.5 6.5 X 10-6-5 X

10 - - lo6 3 X 10-5-3 X 10’

10-3-6 X lo3 lo5- lo1’ 1.5 - lo7 3.5 x 1 0 - ~ - 1 0 - ~

1 0 - ~ - 2 x I O - ~ 2 x io2-6 x lo3

1-106

3.5 x 1 0 - ~ - 1 0 ~ lo3-lo7

10-10’ 5 x 10-~-10 4 x 1o1O-2 x 1014 4 x 1 0 - ~ - 1 0 ~

2 X 10-’-15

- 300

5 X 10-’-5.7 X lo3 - 50

30-1000

1-200

2 X lo-’ lo-, 4 x lo-’ 3 x I O - ~ 3 x 10-1 I O - ~ 2 x lo7 10 2 x I O - ~ 3 x I O - ~

5 x 106 10’

I O - ~ 2 x I O - ~

30

6 X

0.2 500

1 o9 2 x 1012 8 X IOl3 70

30 - 1 013 101-1012 10-10l4 2 x io2-3 x lo3 2 x 102-106 9 x 1 0 ~ - 1 0 ~ ~ 2 x 102-106 0.6-10’ 1 0 - ~ - 2 x 10’ 9-200

30-lo3

0.1 -3 x 10’

10-100

0.5 - 150

1-100

30

100

9

3 0.2 0.1 5 0.05

286 Electrical properties of rocks and minerals

where + is the fractional pore volume (porosity), S is the fraction of the pores containing water, pw is the resistivity of water, n = 2, and a, rn are con- stants, 0.5 I a I 2.5, 1.3 I rn I 2.5. For example, suppose S = 1, a = 1.5, and rn = 2, then pJpW = lS/# and for values of + = 0.01, 0.1, 0.3, 0.5, pe/pw becomes 1.5 X lo4, 150, 17, and 6, respec- tively.

Water conductivity varies considerably (see Table 5.1), depending on the amount and conductivity of dissolved chlorides, sulfates, and other minerals pre- sent.

The geometrical arrangement of the interstices in the rock has a less pronounced effect, but may make the resistivity anisotropic, that is, having different magnitudes for current flow in different directions. Anisotropy is characteristic of stratified rock that is generally more conductive in the bedding plane. The anisotropy effect depends on the ratio of maximum to minimum resistivity, may be as large as 2 in some graphitic slates, and varies from 1 to 1.2 in rocks such as limestone, shale, and rhyolite.

As an example, consider the layered formation shown in Figure 5.1, having resistivities p1 and p2

whose respective fractional volumes are v and 1 - U.

Here the resistivity in the horizontal direction - a stack of beds effectively in parallel - is

ers or none at all. Under the influence of an external varying electric field, the atomic electrons are dis- placed slightly with respect to their nuclei; this slight relative separation of negative and positive charges is known as dielectric polarization of the material and it produces a current known as the displacement current.

(b) Electronic conduction. The electrical resistivity of a cylindrical solid of length L and cross section A, having resistance R between the end faces, is given by

p = RA/L (5.5)

If A is in square meters, L in meters, and R in ohms, the resistivity unit is the ohm-meter (Qm). For dimensions in centimeters the unit becomes the ohm-centimeter (Qcm): 1 Qm = 100 Qcm.

The resistance R is given in terms of the voltage V applied across the ends of the cylinder and the resultant current Z flowing through it, by Ohm's law :

R = V/Z

where R is in ohms and the units of V and I are volts and amperes.

The reciprocal of resistivity is the conductiviv u, where the units are siemens per meter (S/m). Then

u = l / p = L/RA = (Z/A)/( V/L) = J / E (5.6)

where J is the current density (A/&) and E is the electric field (v/m).

(c) Electrolytic conduction. Because most rocks are poor conductors, their resistivities would be ex- tremely large were it not for the fact that they are usually porous and the pores are filled with fluids, mainly water. As a result the rocks are electrolytic conductors, whose effective resistivity may be defined as in Equation (5.3, where the propagation of cur- rent is by ionic conduction - by molecules having an excess or deficiency of electrons. Hence the resistiv- ity varies with the mobility, concentration, and de- gree of dissociation of the ions; the latter depends on the dielectric constant of the solvent. As mentioned previously, the current flow is not only slow com- pared to ohmic conduction, but represents an actual transport of material, usually resulting in chemical transformation.

The conductivity of a porous rock varies with the volume and arrangement of the pores and even more with the conductivity and amount of contained wa- ter. According to the empirical formula due to Archie (19421,

pe = a+-"S-"p, (5.7)

In the vertical direction, the beds are in series so that

Pu = Pl* + P2(1 - (5 .9)

Then the ratio is

Pu - = ( 1 - 2 u + 22) + Ph

If v 1 and p2/p1 >> 1, this simplifies to

(5 . lo)

If the layer of resistivity p1 is for water-saturated beds, this ratio might be quite large.

(d) Dielectric conduction. The mechanism of di- electric conduction - the displacement current - was described briefly at the beginning of this section, where it was pointed out that the displacement cur- rent flows only in nonconductors when the external electric field changes with time. The significant pa- rameter in dielectric conduction is the dielectric constant k , sometimes called the specijic inductive

Electrical properties

Figure 5.1. Anisotropic resistivity as a result of horizontal bedding.

287

capacity of the medium. In analogy with magnetic quantities M, H, k , B, and p (53.2.1) we have an electrostatic set: electric polarization (electric dipole mornent/unit volume) P , electric field strength E , electric susceptibility q , electric displacement y l , / u n i t area) D , and dielectric constant k . In electrostatic units, the relations between these are

P = q E D = E + 4nP = E ( l + 4aq) = kE (5.11)

whereas in m k s units,

P = q E D = e O E + P = E ( e O + q ) = E E (5.12)

and the dielectric constant k = 1 + q/eo = e/eo. In electrostatic units, P , E and D are volts per

centimeter and q and k are dimensionless. In m k s units E, eo, and q are in farads per meter, P , D are in coulombs per square meter, E is in volts per meter, and k is again dimensionless and the same in either system.

The dielectric constant is similar to the conductiv- ity in porous formations in that it varies with the amount of water present (note that water has a very large dielectric constant; see Table 5.5). We shall see in Section 6.2.3 that displacement currents are of secondary importance in earth materials because electrical prospecting methods generally employ low frequencies.

5.2.3. Magnetic Permeability

Where EM sources are employed, the voltage in- duced in a subsurface conductor varies not only with the rate -of change of magnetic field, but also with the magnetic permeability of the conductor. From Maxwell’s equation,

aH V X E = -1.1-

at

we see that currents induced in the ground are enhanced by the factor p. Practically, however, the permeability rarely is appreciably greater than unity, except. for a few magnetic minerals (95.4.3); conse- quently it is of no particular significance in electrical work, except when F%03 is present in large concen- tration.

5.2.4. Polarization Potentials

Where a steady current is passed through an elec- trolytic conductor containing mineral particles it is possible, as described in Section 5.3.1, to determine the effective resistivity. If a current is suddenly switched on or off in a circuit containing an elec- trolyte, a finite time elapses before the potential increases to a fixed value or drops to zero. The delayed buildup or decay of current is characteristic of electrolytic conduction, and is due to accumula- tion of ions at interfaces between the electrolyte and mineral particles. As a result, a potential opposing

288 Electrkal properties of rocks and minerals

Area = A. Metal cap (mercury.

Wjre rings

High imbdance

Figure 5.2. Simplified schematic of equipment for measuring resistivity of core samples.

the normal current flow is developed across the interface. A similar effect is observed at the contact between electrolytes and clay particles. These are known as polarization potentials; the process is called the induced polarization effect. Induced polarization (IP) prospecting involves these interface potentials. They will be considered in more detail in Section 9.2.

5.3. MEASUREMENT OF ELECTRICAL PROPERTIES OF ROCKS AND MINERALS

5.3.1. laboratory Measurement of Resistivity

In order to measure directly the true resistivity of a rock, mineral, electrolyte, and so forth, it is neces- sary to shape the sample in some regular form, such as a cylinder, cube, or bar of regular cross section. An experimental arrangement is shown in Figure 5.2. The main difficulty is in making good electrical contact, particularly for the current electrodes. For this purpose tinfoil or mercury electrodes may be used and it is generally necessary to apply pressure to the current electrodes; sometimes the ends of the sample are dipped in soft solder. From Figure 5.2 and Equation (5.6) the resistivity is given by

p = AV/LI

The power source may be dc or preferably low frequency ac (400 Hz or less). The possibility of anisotropy can be checked by measuring the resistiv- ity in two directions, provided the shape is suitable for this.

Obviously one can make these measurements in the field as well, on drill core, grab samples, even outcrop, if the electrode contact is reasonably good. Estimates of resistivity, made on samples by using an ohmmeter and merely pressing or scraping the termi- nals of the leads against the surface however, are not very trustworthy.

5.3.2. Measurement of Dielectric Constant

An ac bridge may also be used to measure the resistivity of soils and electrolytes. At audio frequen- cies any reactive component - normally capaci- tive- must be accounted for in order to get a good bridge balance. Consequently the measurement de- termines the effective capacitance, as well as resistiv- ity, of the specimen. Since capacitance varies with the dielectric constant of the material, it is thus possible to determine the latter by substitution. The Schering capacitance bridge is suitable for this mea- surement in the laboratory (Hague, 1957).

Typical values of electrical constants

Table 5.2. Resistivities of various ores

289

Ore Other minerals Gangue P (am)

FeS 20%

CoAsS

Pyrite 18% 2% (chalco) 80% 300 60% 5% (ZnS) + 15% 20% 0.9 95 % 5% (ZnS) 1 .o

41 % 59% 2.2 x lo- , 79% 21 % 1.4 x I O - ~ 95 % 5% 1.4 x I O - ~

FeAsS 1 0 - ~ - 1 0 - ~ CusFeS, 3 x I O - ~ CusFeS, 40% 60% SiO, 7 x 10-2 Fe, Mn, WO, lo3 - 10’ PbS, near massive 0.8 Fe2Q 0.1 - 300 Fe,Q, massive 2.5 x lo3

Pyrrhotite

SbS, in quartz FeAsS 60% 20% SiO, 0.39

4 X lo3-3 X lo7

Iron Fe30, 60% 45 75% brown iron oxide Fe304

80% 1.7 x lo3

2 x 104-8 x los 5 x 103-8 x lo3

Zinc 30% 0.75

90% 130 Graphitic slate 0.1 3 Graphite, massive 10-,-5 X

MnO, colloidal ore

CuFeS, CuFeS, 90% 2% FeS 8% SiO, 0.65

2 x io2-4 x lo3 3 x 10-2 10-,-1

1.6 MoSz

CYS

FeCr,O, 1 o3

5% PbS, 15% FeS 10% PbS, 10% FeS 5% PbS

25 %

50%

5%

5.4. TYPICAL VALUES OF ELECTRICAL CONSTANTS OF ROCKS A N D MINERALS

5.4.1. Resistivities of Rocks and Minerals

Of all the physical properties of rocks and minerals, electrical resistivity shows the greatest variation. Whereas the range in density, elastic wave velocity, and radioactive content is quite small, in magnetic susceptibility it may be as large as lo5. However, the resistivity of metallic minerals may be as small as

Slm, that of dry, close-grained rocks, like gab- bro as large as lo7 Slm. The maximum possible range is even greater, from native silver (1.6 X lop8 Om) to pure sulfur (W am).

A conductor is usually defined as a material of resistivity less than Slm, whereas an insulator is one having a resistivity greater than lo7 Slm. Be- tween these limits lie the semiconductors. The metals and graphite are all conductors; they contain a large number of free electrons whose mobility is very great. The semiconductors also carry current by mo- bile electrons but have fewer of them. The insulators

are characterized by ionic bonding so that the va- lence electrons are not free to move; the charge carriers are ions that must overcome larger barrier potentials than exist either in the semiconductors or conductors.

A further difference between conductors and semiconductors is found in their respective variation with temperature. The former vary inversely with temperature and have their highest conductivities in the region of 0 K. The semiconductors, on the other hand, are practically insulators at low temperatures.

In a looser classification, rocks and minerals are considered to be good, intermediate, and poor con- ductors within the following ranges:

(a) Minerals of resistivity (b) Minerals and rocks of resistivity 1 to lo7 Slm. (c) Minerals and rocks of resistivity above lo7 Slm.

Group (a) includes the metals, graphite, the sul- fides except for sphalerite, cinnabar and stibnite, all the arsenides and sulfo-arsenides except SbAs,, the antimonides except for some lead compounds, the

to about 1 am.

290 Electrical properties of rocks and minerals

Table 5.4. Variation of rock resistivity with water content

Rock % H 2 0 P (Qm)

Table 5.3. Resistivities of various rocks and sediments

Rock type Resistivity range (am)

Granite porphyry Feldspar porphyry Syenite Diorite porphyry Porphyrite Carbonatized

Quartz diorite

Porphyry (various) Dacite Andesi te Diabase (various) Lavas Gabbro Basalt Olivine norite Peridotite Hornfels Schists

porphyry

(calcareous and mica)

Tuffs Graphite schist Slates (various) Gneiss (various) Marble Skarn Quartzites

(various) Consolidated

shales Argillites Conglomerates Sandstones Limestones Dolomite Unconsolidated

Mark Clays Oil sands

wet clay

4.5 x lo3 (wet)-1.3 x lo6 (dry) 4 x lo3 (wet) 102 - 106 1.9 X l o3 (wet)-2.8 X l o 4 (dry) 10-5 x lo4 (wet)-3.3 x lo3 (dry)

2.5 x lo3 (wet)-6 x l o4 (dry) 2 x l o 4 - 2 x l o 6 (wet)

2 x lo4 (wet) 4.5 X l o 4 (wet)-1.7 X l o2 (dry)

-1.8 X l o 5 (dry) 60-lo4

20-5 x lo7 i o 2 - 5 x l o4 lo3 - lo6 10-1.3 X l o7 (dry) l o 3 - 6 X l o4 (wet) 3 x l o 3 (wet)-6.5 x lo3 (dry) 8 X l o 3 (wet)-6 x lo7 (dry)

20-lo4 2 X lo3 (wet)-1OS (dry) 10-102 6 X l o 2 - 4 X l o7 6.8 X l o 4 (wet)-3 X lo6 (dry) 102-2.5 X 10' (dry) 2.5 X l o 2 (wet)-2.5 X 10' (dry)

10-2 x 10'

20-2 x l o 3

2 x lo3- lo4

3.5 x i o 2 - 5 x lo3

10.-8 X l o 2

1-6.4 X 10' 50-lo7

20 3 - 70 1-100 4-800

tellurides, and some oxides such as magnetite, man- ganite, pyrolusite, and ilmenite. Most oxides, ores, and porous rocks containing water are intermediate conductors. The common rock-forming minerals, sil- icates, phosphates and the carbonates, nitrates, sul- fates, borates, and so forth, are poor conductors.

The following tables list characteristic resistivities for various minerals and rocks. The data are from various sources, including Heiland (1940, Ch. lo), Jakosky (1950, Ch. 5), Parasnis (1956, 1966, Ch. 6), Keller (1966), and Parkhomenko (1967).

Resistivities of the various metals in pure form, from antimony to zinc, vary by only about 2 orders of magnitude. (Bi = 1.2 X Om, Ag = 1.6 X

Om). Two other elements of common occurrence are

Om). Tellurium is an exception (=

Si ltstone 0.54 1.5 x lo4

Coarse grain SS 0.39 9.6 x l o 5 Coarse grain SS 0.1 8 1 0' Medium grain SS 1 .o 4.2 x lo3

Graywacke SS 1.16 4.7 x lo3 Graywacke SS 0.45 5.8 x l o 4 Arkosic SS 1 .o 1.4 x lo3 Organic limestone 11 0.6 x lo3

Dolomite 0.96 a x lo3 Peridotite 0.1 3 x lo3 Peridotite 0 1.8 x l o 7

Pyrophyllite 0 1 on Granite 0.31 4.4 x l o 3

Granite 0 1 0'0 Diorite 0.02 5.8 x l o 5 Diorite 0 6 X lo6 Basalt 0.95 4 x l o 4 Basalt 0 1.3 X 10' Olivine-pyrox. 0.028 2 x lo4 Olivine-pyrox. 0 5.6 x lo7

Siltstone 0.38 5.6 X 10'

Medium grain SS 0.1 1.4 X 10'

Dolomite 1.3 6 X l o3

Pyrophyllite 0.76 6 X lo6

Granite 0.1 9 1.8 X l o 6

graphite (5 x lo-' to 10 Om range, = 10-~ Om average) and sulfur (107-10'6 Om range, = 1014 Om average).

The variation in resistivity of particular minerals is enormous, as can be seen from Table 5.1. Among the more common minerals, pyrrhotite and graphite appear to be the most consistent good conductors, whereas pyrite, galena, and magnetite are often poor conductors in bulk form, although the individual crystals have high conductivity. Hematite and spha- lerite, in pure form, are practically insulators, but when combined with impurities may have resistivi- ties as low as 0.1 Om. Graphite is often the connect- ing link in mineral zones, which makes them good conductors.

The range of resistivities of various waters is notably smaller than for solid minerals; the actual resistivities are also lower than those of a great many minerals.

Table 5.2 from Parkhomenko (1967) lists resistivi- ties for a variety of ores. In general it appears that pyrrhotite in massive form has the lowest resistivity, that the resistivity of zinc ores is surprisingly low (possibly due to the presence of lead and copper fractions), and that molybdenite, chromite, and iron ores have values in the range of many rocks.

Table 5.3 lists typical values for rocks and uncon- solidated sediments. The ranges are quite similar to that for water, which is the controlling factor in many rocks.

Typical values of electrical constants

Very roughly, igneous rocks have the highest re- sistivity, sediments the lowest, with metamorphic rocks intermediate. However, there is considerable overlapping, as in other physical properties. In addi- tion, the resistivities of particular rock types vary with age and lithology, because the porosity of the rock and salinity of the contained water are affected by both. For example, the resistivity range of Pre- cambrian volcanics is 200-5,OOO Om, whereas for Quaternary rocks of the same kind it is 10-200 am.

The effect of water content on the bulk resistivity of rocks is evident from Table 5.3. Further data are listed in Table 5.4, where samples with variable amounts of water are shown. In most cases a small change in the percentage of water affects the resistiv- ity enormously.

As the depth of penetration of electrical methods is increased with new and refined equipment, it is found that the significance of water in lowering bulk resistivity of crustal rocks gradually decreases with increasing depth, whereas that of temperature and pressure increases. Hermance (1973) carried out deep sounding resistivity and magnetotelluric surveys in Iceland that indicated crust resistivities decreasing from 100 to 10 a m in the depth range 2 to 12 km. Because this is a geothermal area straddling the Atlantic Ridge, one would expect anomalous low resistivities at shallow (< 2 km) depth. However, modeling of the data suggested that water persisted to 8 to 10 km depth, whereas solid conduction in dry crustal rocks at high temperatures (700 to 1,OOO"C) and pressures (1 to 4 kb) became dominant below this.

Subsequent laboratory studies on dry granites, basalts, and gabbros in the temperature range 500 to 1,OOO"C by Kariya and shankland (1983) provided rough agreement with the results of Hermance and showed a 2-order decrease in resistivity over the 500°C temperature change.

291

Table 5.5. Dielectric constants of rocks and minerals

Rock, mineral Dielectric const.

Galena Sphalerite Cassiterite Hematite Fluorite Calcite Apatite Barite Peridotite Norite Quartz porphyry Diabase Trap Dacite Obsidian Sulphur Rock salt Anthracite Gypsum Biotite Epidote Plagioclase feldspar Quartz Granite (dry) Gabbro Diorite Serpentine Gneiss Sandstone (dry to moist) Packed sand (dry t o moist) Soil (dry to moist) Basalt Clays (dry to moist) Petroleum Water (20°C) ice

18

23 25

7.9- 69.7

6.2 - 6.8 7.8- 8.5 7.4- 11.7 7-12.2 8.6 61 14 - 49.3 10.5 - 34.5 18.9 - 39.8 6.8 - 8.2 5.8- 10.4 3.6-4.7 5.6 5.6 - 6.3 5-11.5 4.7 - 9.3 7.6- 15.4 5.4- 7.1 4.2 - 5 4.8 - 18.9 8.5 - 40 6.0 6.6 8.5 4.7-12 2.9-105 3.9- 29.4 12 7-43 2.07 - 2.1 4 80.36 3 - 4.3

Table 5.6. Magnetic permeabilities

Mineral Permability

5.4.2. Dielectric Constants of Rocks and Minerals

As mentioned previously, the dielectric constant is a measure of the electrical polarization resulting from an applied electric field. This polarization may be electronic, ionic, or molecular. The first type is char- acteristic of all nonconductors. Ionic displacement occurs in many rock-forming minerals, whereas wa- ter and the hydrocarbons are the only common ma- terials that exhibit molecular polarization.

Because of the relatively slow mobilities of the charge carriers, molecular polarization - the largest of the three effects- and ionic polarization are in- significant at very high frequencies. Thus the dielec- tric constant, which is proportional to the degree of

Magnetite Pyrrhotite Titanomagnetite Hematite Pyrite Rutile Calcite Quartz Hornblende

5 2.55 1.55 1.05 1.0015 1.0000035 0.999987 0.999985 1.00015

polarization, varies inversely with frequency. It is also indicative of the amount of water present, be- cause water has a dielectric constant of 80 at low frequencies.

Table 5.5 lists dielectric constants for various minerals and rocks. Most of the measurements have been made at frequencies of 100 kHz and up. For very low frequencies the values would be generally

292 Electrical properties of rocks and minerals

REFERENCES Archie, G. E. 1942. The electric resistivity log as an aid in

determining some reservoir characteristics. Trans. AIME 146,54-62.

London: Pitman.

Prentice-Hall.

Icelandic crust. Geophysics 38, 3-13.

CA. Trija.

conductivity of dry lower crustal rocks. Geophysics 48,

Hague, B. 1957. Alternative Current Bridge Methods.

Heiland, C. A. 1940. Geophysical Exploration. New York:

Hermance, J. F. 1973. An electrical model for the sub-

Jakosky, J. J. 1950. Exploration Geophysics. Newport Beach,

Kariya, K. A., and Shankland, T. J. 1983. Electrical

52-61. Keller, G. V. 1966. In Handbook of Physical Constants,

Parasnis, D. S . 1956. The electrical resistivity of some S. P. Clark, Jr., ed. Geol. Soc. Am. Memoir 97,553-76.

sulphide and oxide minerals and their ores. Geophys. Prosp. 4,249-19.

Elsevier.

G. V. Keller, transl. New York: Plenum.

Parasnis, D. S. 1966. Mining Geophysics. Amsterdam:

Parkhomenko, E. I. 1961. Electrical Properties of Rocks,

higher by about 30%. In exceptional cases - one ex- ample being certain ice samples - the results have been larger by several orders of magnitude.

5.4.3. Magnetic Permeability of Minerals

The effect of p on electrical measurements is very slight except in the case of concentrated magnetite, pyrrhotite, and titanomagnetite. From Equation (3.9, magnetic permeability is related to susceptibility by the expression

p’ = 1 + 4sk‘ p - l + k inSIunits

in cgs units

p and p’ are dimensionless. Generally k is too small to change p appreciably from unity. Table 5.6 lists maximum permeabilities of some common minerals.