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Chapter 5 Electrical Properties of Rocks and Minerals 5.1. CLASSIFICATION OF ELECTRICAL METHODS 5.2. ELECTRICAL PROPERTIES OF ROCKS AND MINERALS Electrical prospecting involves the detection of surface effects produced by electric current flow in the ground. There is a much greater variety of techniques available than in the other prospecting methods, where one makes use of a single field of force or anomalous property - gravitation, magnetism, elasticity, radioactivity. Using electrical methods, one may measure potentials, currents, and electromagnetic fields that occur naturally- or are introduced artificially- in the earth. Furthermore, the measurements 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), telluric currents and magnetotellurics (MT), resistivity, inincluding mise-h-la-masse, electromagnetic (EM), 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 radioactivity are included in the natural source methods, whereas seismic requires artificial energy. In the following chapters we shall study the electrical methods in a slightly different sequence, grouping 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. 5.2.1. Electrical Potentials (a) General. Several electrical properties of rocks and minerals are significant in electrical prospecting. They are natural electrical potentials, electrical conductivity (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 occurring 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 geological contacts, bioelectric activity of organic material, corrosion, thermal and pressure gradients in underground fluids, and other phenomena of similar nature. There are four principal mechanisms producing 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. Although 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). (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 mineral 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(c) Liquid-junction (diffusion) potential. This is ing sections; values of several hundred millivolts are due to the difference in mobilities of various ions in common and potentials greater than 1 V have been solutions of different concentrations. The value is observed in zones of graphite and alunite. Because of given by the large magnitude, mineralization potentials cannot be attributed solely to the electrochemical potentials described earlier. The presence of metallic conductors in appreciable concentrations appears to be a necessary condition; nevertheless, the exact mechanism is not entirely clear, as will be seen in the more where R is the gas constant (8.31 J/”C), F is the detailed discussion of mineralization potentials in Faraday constant (9.65 X lo4 C/mol), 8 is the absaSection 6.1.1 in connection with the self-potential lute temperature, n is the valence, I, and I, are the mobilities of anions and cations, and C, and C, are prospecting method. Other sources of electrical potentials in the earth the solution concentrations. In NaCl solutions, should be mentioned. From Equations (5.2a) and Ia/Zc = 1.49, hence at 25OC, (5.3a) it can be seen that the magnitude of the static Ed = - 11.6 log( C,/G) (5.2b) self-potential depends on temperature; this thermal effect is analogous to the pressure difference in streaming potential and is of minor importance. ObE, is in millivolts. viously metal corrosion - of underground pipes, ca(d) Shale (Nernst) potential. When two identical bles, etc. - is a local source of electrochemical potenmetal electrodes are immersed in a homogeneous tial. Large-scale earth currents (w.2.1) induced from solution, there is no potential difference between the ionosphere, nuclear blasts, thunderstorms (see them. If, however, the concentrations at the two AFMAG,§7.4.2e), and the like create small, erratic electrodes are different, there is a potential difference earth potentials. Currents of bioelectric origin flowing, for instance, in plant roots are also a source of given by earth potentials. Negative potentials of 100 mV have been reported in this connection, in passing from R8 E (5.3a) cleared ground to wooded areas. ’ ---InFn Most of the earth potentials discussed above are relatively permanent in time and place. Of the variFor n = 1, 8 = 298 K, this becomes (E, in milli- able types, only telluric and AFMAG sources have volts) been employed in prospecting. When measuring static potentials these fluctuations cause a backE, = - 59.1 log( CJC,) (5.3b) ground noise and may be a nuisance. ):( I 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 E, = - 70.7 ( T + 273) 273 log( 2) (5.4) When the concentrations are in the ratio 5 :1, E, = f 50 mV at 25°C. 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 conductors 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 ite Chalcocite Chalcopyrite Bornite Pyrite Pyrrhotite Cinnabar Molybdenite Galena Millerite Stannite Stibnite Sphalerite Cobalt ite Arsenopyrite Niccol ite Bauxite Cuprite Chromite Specularite Hematite Limonite Magnetite llmenite Wolframite Pyrolusite Quartz Cassiterite Rutile Uraninite (pitchblende) 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% Biz53 cus CYS CuFeS, Cu5FeS4 FeS, FeA HgS MoS, PbS NiS CyFeSnS, S& ZnS CoAsS FeAsS NiAs A12Q . n H 2 0 CYO FeCr204 Fe2Q Fez03 2Fe2Q . 3H20 Fe304 FeTiQ Fe, Mn, WO, 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’ 3.5 x 1 0 - ~ - 1 0 - ~ 2 X 10-’-15 1 0 - ~ - 2x I O - ~ 2 x io2-6 x lo3 - 300 1-106 Si 0, Sn02 Ti02 uo2 1-200 CaSO, CaCQ CaF2 Fe*(C4)3 NaCl KCI C lo-’ 4 x lo-’ 3xIO-~ 3 x 10-1 IO-~ 2 x lo7 10 2xIO-~ 3xIO-~ 10-3-6 X lo3 lo5- lo1’ 1.5 - lo7 3.5 x 1 0 - ~ - 1 0 ~ lo3-lo7 5 X 10-’-5.7 X lo3 - 50 10-10’ 5 x 10-~-10 4 x 1o1O-2 x 1014 4 x 10-~-10~ 30-1000 Mn02 2X lo-, 30 - 1013 101-1012 10-10l4 2 x io2-3 x lo3 2 x 102-106 9x10~-10~~ 2 x 102-106 0.6-10’ 1 0 - ~ - 2 x 10’ 9-200 5 x 106 10’ IO-~ 2xIO-~ 30 6X 0.2 500 1o9 2 x 1012 8 X IOl3 70 30 30-lo3 0.1 -3 x 10’ 10-100 100 0.5 - 150 9 1-100 3 0.2 0.15 0.05 286 Electrical properties of rocks and minerals ers or none at all. Under the influence of an external varying electric field, the atomic electrons are displaced 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): 1Qm = 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 + 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 constants, 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, respectively. Water conductivity varies considerably (see Table 5.1), depending on the amount and conductivity of dissolved chlorides, sulfates, and other minerals present. 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 + 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). In the vertical direction, the beds are in series so that Pu = (c) Electrolytic conduction. Because most rocks are poor conductors, their resistivities would be extremely 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 current is by ionic conduction - by molecules having an excess or deficiency of electrons. Hence the resistivity varies with the mobility, concentration, and degree 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 compared 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 water. According to the empirical formula due to Archie (19421, pe = a+-"S-"p, (5.7) Pl* + P2(1 - (5.9) Then the ratio is Pu - = (1 - 2u+ 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 dielectric conduction - the displacement current - was described briefly at the beginning of this section, where it was pointed out that the displacement current flows only in nonconductors when the external electric field changes with time. The significant parameter in dielectric conduction is the dielectric constant k , sometimes called the specijic inductive Electrical properties 287 Figure 5.1. Anisotropic resistivity as a result of horizontal bedding. 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 = qE D = E + 4nP = E ( l + 4aq) kE (5.11) = whereas in m k s units, P=qE 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 conductivity 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 induced 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, V aH X E = -1.1at 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); consequently it is of no particular significance in electrical work, except when F%03 is present in large concentration. 5.2.4. Polarization Potentials Where a steady current is passed through an electrolytic 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 electrolyte, 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 accumulation of ions at interfaces between the electrolyte and mineral particles. As a result, a potential opposing Electrkal properties of rocks a n d minerals 288 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 necessary 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 resistivity 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 terminals 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 frequencies any reactive component - normally capacitive- must be accounted for in order to get a good bridge balance. Consequently the measurement determines the effective capacitance, as well as resistivity, 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 measurement in the laboratory (Hague, 1957). Typical values of electrical constants 289 Table 5.2. Resistivities of various ores Ore Other minerals Gangue P (am) Pyrite 18% 60% 95% Pyrrhotite 41 % 79% 95% SbS, in quartz FeAsS 60% FeAsS CusFeS, CusFeS, 40% Fe, Mn, WO, PbS, near massive Fe2Q Fe,Q, massive Iron 2% (chalco) 5% (ZnS) + 15% 5% (ZnS) FeS 20% 80% 20% 300 0.9 1.o 59% 21 % 5% 2.2 x lo-, 1.4 x I O - ~ 1.4 x I O - ~ 4 X lo3-3 X lo7 0.39 10-~-10-~ 3x IO-~ 7 x 10-2 lo3- 10’ 0.8 0.1 - 300 2.5 x lo3 20% SiO, 60% SiO, CoAsS Fe30, 60% 75% brown iron oxide 25 % Fe304 Zinc 30% 80% 90% Graphitic slate Graphite, massive MoSz MnO, colloidal ore CYS CuFeS, CuFeS, 90% FeCr,O, 5% PbS, 15%FeS 10%PbS, 10%FeS 5% PbS 2% FeS 5.4. TYPICAL VALUES OF ELECTRICAL CONSTANTS OF ROCKS A N D MINERALS 50% 5% 8% SiO, 45 2 x 104-8 x los 5 x 103-8 x lo3 0.75 1.7 x lo3 130 0.13 10-,-5 X 2 x io2-4 x 1.6 3 x 10-2 10-,-1 0.65 1o3 lo3 are characterized by ionic bonding so that the valence electrons are not free to move; the charge carriers are ions that must overcome larger barrier 5.4.1. Resistivities of Rocks and Minerals potentials than exist either in the semiconductors or conductors. Of all the physical properties of rocks and minerals, A further difference between conductors and electrical resistivity shows the greatest variation. semiconductors is found in their respective variation Whereas the range in density, elastic wave velocity, with temperature. The former vary inversely with and radioactive content is quite small, in magnetic temperature and have their highest conductivities in susceptibility it may be as large as lo5.However, the the region of 0 K. The semiconductors, on the other resistivity of metallic minerals may be as small as hand, are practically insulators at low temperatures. Slm, that of dry, close-grained rocks, like gabIn a looser classification, rocks and minerals are bro as large as lo7 Slm. The maximum possible considered to be good, intermediate, and poor conrange is even greater, from native silver (1.6 X lop8 ductors within the following ranges: Om) to pure sulfur (Wam). A conductor is usually defined as a material of (a) Minerals of resistivity to about 1am. resistivity less than Slm, whereas an insulator is (b) Minerals and rocks of resistivity 1 to lo7 Slm. one having a resistivity greater than lo7 Slm. Be- (c) Minerals and rocks of resistivity above lo7 Slm. tween these limits lie the semiconductors. The metals and graphite are all conductors; they contain a large Group (a) includes the metals, graphite, the sulnumber of free electrons whose mobility is very fides except for sphalerite, cinnabar and stibnite, all great. The semiconductors also carry current by mo- the arsenides and sulfo-arsenides except SbAs,, the bile electrons but have fewer of them. The insulators antimonides except for some lead compounds, the Electrical properties of rocks and minerals 290 Table 5.3. Resistivities of various rocks and sediments Rock type Granite porphyry Feldspar porphyry Syenite Diorite porphyry Porphyrite Carbonatized porphyry Quartz diorite Porphyry (various) Dacite Andesi te Diabase (various) Lavas Gabbro Basalt Olivine norite Peridotite Hornfels Schists (calcareous and mica) Tuffs Graphite schist Slates (various) Gneiss (various) Marble Skarn Quartzites (various) Consolidated shales Argillites Conglomerates Sandstones Limestones Dolomite Unconsolidated wet clay Mark Clays Oil sands Resistivity range (am) 4.5 x lo3 (wet)-1.3 x lo6 (dry) 4 x lo3 (wet) 102 - 106 1.9 X lo3 (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 o 4 (dry) 2 x l o 4 - 2 x l o 6 (wet) -1.8 X l o 5 (dry) 60-lo4 2 x l o 4 (wet) 4.5 X l o 4 (wet)-1.7 X l o 2 (dry) 20-5 x lo7 io2-5 x lo4 lo3- lo6 10-1.3 X lo7 (dry) l o 3 - 6 X l o 4 (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 lo7 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) Table 5.4. Variation of rock resistivity with water content Rock Si ltstone Siltstone Coarse grain SS Coarse grain SS Medium grain SS Medium grain SS Graywacke SS Graywacke SS Arkosic SS Organic limestone Dolomite Dolomite Peridotite Peridotite Pyrophyllite Pyrophyllite Granite Granite Granite Diorite Diorite Basalt Basalt Olivine-pyrox. Olivine-pyrox. % H20 P (Qm) 0.54 0.38 0.39 0.18 1.5 x lo4 5.6 X 10' 9.6 x l o 5 10' 4.2 x lo3 1.4 X 10' 4.7 x lo3 5.8 x l o 4 1.4 x lo3 0.6 x lo3 6 X lo3 .o 1 0.1 1.16 0.45 1.o 11 1.3 0.96 0.1 0 0.76 0 0.31 0.19 0 0.02 0 0.95 0 0.028 0 a x lo3 3 x lo3 1.8 x l o 7 6 X lo6 on 1 4.4 x l o 3 1.8 X l o 6 10'0 5.8 x l o 5 6 X lo6 4 x lo4 1.3 X 10' 2 x lo4 5.6 x lo7 graphite (5 x lo-' to 10 Om range, = 1 0 - ~ Om average) and sulfur (107-10'6 Om range, = 1014 Om average). 20-2 x l o 3 The variation in resistivity of particular minerals 10.-8 X l o 2 2 x lo3-lo4 is enormous, as can be seen from Table 5.1. Among 1-6.4 X 10' the more common minerals, pyrrhotite and graphite 50-lo7 appear to be the most consistent good conductors, 3.5 x i o 2 - 5 x lo3 whereas pyrite, galena, and magnetite are often poor conductors in bulk form, although the individual 20 3 - 70 crystals have high conductivity. Hematite and spha1-100 lerite, in pure form, are practically insulators, but 4-800 when combined with impurities may have resistivities as low as 0.1 Om. Graphite is often the connecting link in mineral zones, which makes them good tellurides, and some oxides such as magnetite, man- conductors. ganite, pyrolusite, and ilmenite. Most oxides, ores, The range of resistivities of various waters is and porous rocks containing water are intermediate notably smaller than for solid minerals; the actual conductors. The common rock-forming minerals, sil- resistivities are also lower than those of a great many icates, phosphates and the carbonates, nitrates, sul- minerals. Table 5.2 from Parkhomenko (1967)lists resistivifates, borates, and so forth, are poor conductors. The following tables list characteristic resistivities ties for a variety of ores. In general it appears that for various minerals and rocks. The data are from pyrrhotite in massive form has the lowest resistivity, various sources, including Heiland (1940, Ch. lo), that the resistivity of zinc ores is surprisingly low Jakosky (1950,Ch. 5), Parasnis (1956,1966,Ch. 6), (possibly due to the presence of lead and copper Keller (1966), and Parkhomenko (1967). fractions), and that molybdenite, chromite, and iron Resistivities of the various metals in pure form, ores have values in the range of many rocks. from antimony to zinc, vary by only about 2 orders Table 5.3 lists typical values for rocks and unconof magnitude. (Bi = 1.2 X Om, Ag = 1.6 X solidated sediments. The ranges are quite similar to Om). Tellurium is an exception (= Om). that for water, which is the controlling factor in Two other elements of common occurrence are many rocks. 10-2 x 10' Typical values of electrical constants Very roughly, igneous rocks have the highest resistivity, sediments the lowest, with metamorphic rocks intermediate. However, there is considerable overlapping, as in other physical properties. In addition, 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 Precambrian 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 resistivity 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. 5.4.2. Dielectric Constants of Rocks and Minerals 291 Table 5.5. Dielectric constants of rocks and minerals Rock, mineral 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 t o moist) Basalt Clays (dry to moist) Petroleum Water (20°C) ice Dielectric const. 18 7.9- 69.7 23 25 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 Magnetite Pyrrhotite Titanomagnetite Hematite Pyrite Rutile Calcite Quartz Hornblende Permability 5 2.55 1.55 1.05 1.0015 1.0000035 0.999987 0.999985 1.00015 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 characteristic of all nonconductors. Ionic displacement occurs in many rock-forming minerals, whereas wa- polarization, varies inversely with frequency. It is ter and the hydrocarbons are the only common ma- also indicative of the amount of water present, beterials that exhibit molecular polarization. cause water has a dielectric constant of 80 at low Because of the relatively slow mobilities of the frequencies. charge carriers, molecular polarization - the largest Table 5.5 lists dielectric constants for various of the three effects- and ionic polarization are in- minerals and rocks. Most of the measurements have significant at very high frequencies. Thus the dielec- been made at frequencies of 100 kHz and up. For tric constant, which is proportional to the degree of very low frequencies the values would be generally Electrical properties of rocks and minerals 292 higher by about 30%. In exceptional cases - one example 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 in cgs units inSIunits 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. REFERENCES Archie, G. E. 1942.The electric resistivity log as an aid in determining some reservoir characteristics. Trans. AIME 146,54-62. Hague, B. 1957. Alternative Current Bridge Methods. London: Pitman. Heiland, C . A. 1940. Geophysical Exploration. New York: Prentice-Hall. Hermance, J. F. 1973. An electrical model for the subIcelandic crust. Geophysics 38, 3-13. Jakosky, J. J. 1950. Exploration Geophysics.Newport Beach, CA. Trija. Kariya, K. A., and Shankland, T. J. 1983.Electrical conductivity of dry lower crustal rocks. Geophysics 48, 52-61. Keller, G. V. 1966.In Handbook of Physical Constants, S. P. Clark, Jr., ed. Geol. Soc. Am. Memoir 97,553-76. Parasnis, D. S . 1956. The electrical resistivity of some sulphide and oxide minerals and their ores. Geophys. Prosp. 4,249-19. Parasnis, D. S. 1966. Mining Geophysics. Amsterdam: Elsevier. Parkhomenko, E. I. 1961. Electrical Properties of Rocks, G. V. Keller, transl. New York: Plenum.