Journal of Applied Geophysics 98 (2013) 44–53

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Journal of Applied Geophysics

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Time domain spectral induced polarization of disseminated electronicconductors: Laboratory data analysis through the Debyedecomposition approach

Grigory Gurin a,b,⁎, Andrey Tarasov a,c, Yuri Ilyin a, Konstantin Titov a

a St Petersburg State University, Department of Geophysics, Faculty of Geology, 7/9 Universitetskaya Naberezhnaya, 199034 St. Petersburg, Russiab “BGK” Ltd., 1 Petrovskaya Kosa Street, 197110 St. Petersburg, Russiac “VIRG-Rudgeofizika” JSC, 1 Petrovskaya Kosa Street, 197110 St. Petersburg, Russia

⁎ Corresponding author at: St Petersburg State UniversFaculty of Geology, 7/9 Universitetskaya Naberezhnaya,Tel.: +7 9500290861.

E-mail address: gurin-geo@mail.ru (G. Gurin).

0926-9851/$ – see front matter © 2013 Elsevier B.V. All rihttp://dx.doi.org/10.1016/j.jappgeo.2013.07.008

a b s t r a c t

a r t i c l e i n f o

Article history:Received 29 November 2012Accepted 27 July 2013Available online 6 August 2013

Keywords:Induced PolarizationDisseminated oreDebye decompositionRelaxation time distribution

Wemeasured Spectral Induced Polarization responses of 22models of disseminated orewith a time domain (TD)technique. The models were mixtures of calibrated sand (0.2–0.3 mm)with calibrated ore grains (average radii:0.045, 0.055, 0.13, 0.20, 0.38 and 0.55 mm). The grains represent a mixture of pyrrhotite (30%), pyrite (30%),magnetite (30%) and chalcopyrite (10%) coming from a natural ore. In the models, the grain concentration(by volume) varied between 0.6 and 30%.Weobtained IP decayswith a conventionalfield TDmeasuring technique and a lab low-current transmitter in thetime range from 0.3 ms to 64 s. The IP decaysmeasuredwith various current wavelength formswere inverted torelaxation time distributions (RTD) on the basis of the Debye decomposition approach.RTD parameters were found to be closely related to the ore volumetric content and the ore grain size. The totalchargeability is independent of the grain size, but is determined by the grain volume fraction. In contrast, themean IP relaxation time is related to the grain size. These facts make RTD attractive to use in ore prospectingand studying reactive permeable barriers.Moreover, for low salinity pore water used in this study, the relaxation times of disseminated ores are three tofour decades smaller than that of the insulating grains of the same size typical of common soils and sediments.This allows recover the relaxation times on the basis of relatively fast IP measurements with short time pulses(in TD) or high frequency values in the frequency domain; however attention should be paid to inductive andcapacitive couplings.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

In the last decades, there is a growing interest in the use of theInduced Polarization (IP) method mainly in hydrogeology and environ-mental geology. This produced strong development of field techniqueand data interpretation methodology, improved factual databases, aswell as stimulated development of a spectral IP (SIP) approach, whenIP parameters are investigated through large frequency (or time)ranges. One of the latest developmentswas a so-called Debye decompo-sition (DD) technique (Nordsiek and Weller, 2008; Tarasov and Titov,2007; Tong et al., 2006; Zisser et al., 2010), which allows obtaining a re-laxation time distribution (RTD). The relaxation time distribution char-acterizes polarization magnitude as a function of its characteristic

ity, Department of Geophysics,199034 St. Petersburg, Russia.

ghts reserved.

relaxation time. It was shown that SIP is a powerful tool for discriminat-ing the pore or grain size in soils and sediments, and, so, for predictingtheir texture parameters, like the specific surface (e.g., Slater et al.,2005, 2006;Weller et al., 2010) and, possibly, the hydraulic conductivity(e.g., Revil et al., 2012).

Recent experimental researches were mainly focused on soils andsediments. Only few datasets concerning disseminated electronicconductors or semiconductors (which we call thereafter as ‘metallicparticles’) were obtained in the framework of monitoring reactive per-meable barriers (Slater et al., 2005, 2006), environmental applications(Ntarlagiannis et al., 2010; Placencia-Gómez et al., 2013), and investiga-tions of archaeological objects (Florsch et al., 2011, 2012).

However IP is traditionally used in mining geology for disseminatedore prospecting (e.g., Nelson and Van Voorhis, 1983; Pelton et al., 1978;Scott andWest, 1969; Seigel et al., 1997; Vanhala and Peltoniemi, 1992).In the past decade the current prices of rare metals (precious or noble,and, especially, gold) have continuously increased. Gold is very fre-quently accompanied by disseminated sulfide minerals like pyrite and

Fig. 1. Induced polarization in the time domain. a—current pulses; b—electrical voltage re-sponse to the current; c—sketch of the time domain IP measurements.

45G. Gurin et al. / Journal of Applied Geophysics 98 (2013) 44–53

arsenopyrite, and IP anomalies are traditionally considered as gold de-posits indications (e.g., Andreev, 1992; Hofstra and Cline, 2000). How-ever to the best of our knowledge the DD technique has been used tostudy disseminated metallic particles in two recent papers only andhas been applied to limited datasets (Nordsiek and Weller, 2008;Placencia-Gómez et al., 2013).

In this paper we systematically apply the DD technique to newlaboratory data obtained in models of disseminated ore. The modelswere mixtures of sand and metallic particles of different mass contentand grain size. We compared RTD-derived parameters with traditionalIP parameters like the chargeability, and we show advantages in theuse of the RTD technique in study disseminated metallic particles.

2. Induced Polarization fundamentals

Induced Polarization of porous media is a synonym of the low-frequencydispersion of electrical conductivity. Thismeans that the elec-trical conductivity is a complex quantity, which depends on the value ofelectrical field frequency. This definition is directly used in a so calledFrequency Domain (FD)when the electrical conductivity (or its inverse,the resistivity) is measured in a wide frequency range (over 9 decades,from 1 mHz to 1 MHz, in laboratory conditions, and over 3 decades,from 0.1 to 100 Hz, in field conditions). In FD a couple of parameters(1) the real and imaginary components of electrical conductivity (resis-tivity) or (2) its absolute value and phase are used.

The imaginary conductivity value, σ″, represents the magnitude ofinduced polarization (e.g., Lesmes and Frye, 2001). The phase angle,

φ ¼ tan−1 σ ″

σ ′≈σ ″

σ ′; ð1Þ

depends on both the polarization magnitude and the conduction mag-nitude σ′. In field measurements the common FD parameter is alsothe frequency effect,

FE ¼ σ f 1ð Þ−σ f 0ð Þσ f 0ð Þ ; ð2Þ

which can be considered as a ‘local’ measure of the conductivity varia-tion in the frequency range from f0 to f1.

IP is also manifested by a specific behavior, when the electrical fieldis a sequence of rectangular impulses. An electrical voltage in responseto application of a rectangular current pulse is an increased function oftime (Fig. 1). After the pulse end (when the current is turned off, theoff-time) the voltage first decreases instantaneously, and, then decaysslowly. This IP manifestation is directly used in a so called Time Domain(TD) technique,which is frequently applied infield conditions especiallyinmining applications. In TD, the polarizability (see Fig. 1) calculated onthe basis of the voltages in the off-time, U(t), and at the end of the on-time, U0 (Komarov, 1980; Wait, 1982),

η tð Þ ¼ U tð ÞU0

; ð3Þ

is frequently used. Its average through the off-time between two pulses,the chargeability,

m ¼ 1t2−t1

Zt2t1

η tð Þdt; ð4Þ

is defined as IP field integral parameter (e.g., Lesmes and Frye, 2001).The proportionality between the complex conductivity phase, the fre-

quency effect and the chargeability is well established theoretically andexperimentally (Marshall and Madden, 1959; Seigel, 1959; Vinegar andWaxman, 1984; Wait, 1982). These parameters are measures of theratio of the capacitive to conductive properties of materials (Lesmes

and Frye, 2001). In contrast, σ″ is a direct measure of the capacitance ofmaterials. Its TD analogical parameter is a normalized chargeability,

mn ¼ mρ: ð5Þ

where ρ is the electrical resistivity value. Note, like the conductivity, thenormalized chargeability is measured in Siemens per meter, and in sed-iments it is tightly related to the surface conductivity (e.g., Lesmes andFrye, 2001; Slater and Lesmes, 2002).

Induced Polarization decays are not easy to compare because theyare monotonous decreasing function. This is because a differential po-larizability, a decay derivative with respect to the time logarithm,

ηd tð Þ ¼ dη tð Þd log tð Þð Þ ; ð6Þ

was proposed (Komarov, 1980) and frequently used in Russia (see, e.g.,Titov et al., 2002, 2005). In contrast tomonotonous decays, the differen-tial polarizability containsmaximum at the time value close to the valueinverse of the critical frequency in FD. A shape of differential polarizabil-ity vs. inverse of time is similar to that of the phase angle vs. frequencyin FD.

3. Induced Polarization of sand–ore mixtures

Last decade great progress was achieved in understanding IP of soilsand sediments. Existing models are mostly based on a theory of polari-zation of colloidal particle with electrical double (or triple) layer devel-oped in colloidal sciences (Schurr, 1964; Schwarz, 1962), and applied to

Fig. 2. Sketch of induced polarization of metallic particle in electrical field E = −gradΨ.The electrical behavior of the particle in the external field is determined by its effectiveconductivity. The effective conductivity is produced by the surface conductivity, σs, re-sponsible for tangential ionic flow and by the interfacial conductance, S, responsible thenormal Faraday current shown by arrows. The surface potential, Ψs is the overvoltage,which determines the rate of redox reaction.

46 G. Gurin et al. / Journal of Applied Geophysics 98 (2013) 44–53

IP of sand packs (Leroy et al., 2008). The theory is based on the balanceof tangential ionic flows produced by electrical field and diffusion alongthe grain surface. The link to sediments was obtained by convolution ofthe single grain response with a grain size distribution (Revil andFlorsch, 2010). However this model cannot be directly applied to thecase of metallic particles disseminated in sandymatrix because ore par-ticles are electronically conducting and the electrical current in the di-rection normal to the grain surface can exist (e.g., Placencia-Gómezet al., 2013). This current appears if a redox reaction occurs at the sur-face (e.g., Wong, 1979). A majority of ions in the pore solution (likeK+, Na+, Cl−, CO3

2−), which mostly determines the solution conductiv-ity, cannot participate in the reaction because they cannot enter to theore mineral framework. This is because Wong (1979) defined so-called specific ions, which can reduce or oxidize at the surface accordingto reaction,

Xnþ þ e− ↔ b Xn−1; ð7Þ

where the symbol b refers to the mineral framework.For the non-specific ions themetallic particle behaves as an insulator

and the theory developed for the colloidal particle should be applicableto ionic transport along the metallic surface. The theory predicts (Reviland Skold, 2011; Schurr, 1964; Schwarz, 1962) that the magnitude ofpolarization is related to the complex frequency dependent surface con-ductivity produced by surface excess of ions,Σ. Accordingly, without theredox reaction, in the external electrical field, the particle behaves as theconductive sphere with equivalent conductivity (O'Konski, 1960),

σ s ¼2Σr

; ð8Þ

where r is the particle radius.For the rate of redox reaction of specific ions, and the respective elec-

trical current density normal to the interface, ic, the Butler–Volmerequation can be applied (Bockris et al., 2000). For the case of small elec-trical field typical of IP measurements, the Butler–Volmer equation canbe simplified to a linear form:

ic ¼ i0ekT

ψ s; ð9Þ

where i0 in Am−1 is the exchange current determining electrochemicalproperties of the interface; e = 1.602 × 1019 is the electron charge in C;Ψs is the overvoltage at the interface in V, which determines themagni-tude of electrical current crossing the interface; k = 1.380 × 10−23 isthe Boltzmann constant in J K−1; and T is the absolute temperature in K.

The quantity S ¼ i0 ekT expressed in S m−2 is the equivalent conduc-

tance in the direction normal to the interface, and it is easy to showthat σc = Sr is the effective conductivity of the particle produced bythe redox reaction. This means that in absence of the surface conductiv-ity, in the external electrical field, the particle with the normal compo-nent of electrical current at the interface (according to Eq. (9))behaves like the sphere with the conductivity σc. Therefore, the electri-cal behavior of the particle, σp, is determined by the sum

σp ¼ σ s þ σ c; ð10Þ

which is finite even the sphere material can be considered of infiniteconductivity.

The ratio of the particle conductivity and that of the surroundingregion, σp/σ0, determines the electrical field near the particle (Fig. 2).The potential of applied field at the interface represents the overvoltagein Eq. (9). Because the potential varies along the interface as (e.g.,O'Konski, 1960)

ψs e 3σ0

2σ0 þ σ eE0 � r � cosϑ; ð11Þ

the overvoltage and the Faraday current arrive at maximum and mini-mum values at two poles of the sphere, and the overvoltage is zero atthe sphere equator. According to Eq. (9) the behavior of the normal cur-rent is exactly the same (see Fig. 2).

4. Material and methods

We used mixtures of sieved sand (0.2–0.3 mm) and crushed andsieved natural ore of different grain sizes. The commercial sand from aquarry in St. Petersburg region, Russia, consisted (by volume) of 73%of quartz, 26% of feldspar, and 1% of other minerals. The ore samplewas taken from Hautavaara deposit (Karelia, Russia), crushed andfractioned with sieving. Ore microscopic analysis showed (by volume)pyrrhotite (30%), pyrite (30%), magnetite (30%) and chalcopyrite (10%).

We used fresh water as the pore solution to model IP response inhumid climate conditions typical of e.g., Finland, Canada and Nord ofRussia. The solution was NaCl with electrical conductivity value20 mS m−1 at room temperature of 22 °C (the salinitywas 135 mg l−1).

The sand and the crushed ore were separately washed with distilledwater to extract the dust particles. The sand was then oven dried, andthe crushed ore was mixed with sand. The mixtures were filled withNaCl solution and were kept 48 h before measurements. In preliminaryexperiments we found that the chemical equilibrium cannot beachieved at the solution conductivity of 20 mS m−1. The mixture con-ductivity gradually increased, which we attributed to the sulfide min-erals dissolution and oxidation (e.g., Bonnissel-Gissinger et al., 1998;Placencia-Gómez et al., 2013). This is becausewe decided to fill themix-tures againwith the same solution½ h beforemeasurements just at themoment of the mixture deposition to the measurement cell. We filledthemixture by flushing about five pore volumes of 20 Sm−1 NaCl solu-tion.We believe that this approach is consistentwith natural conditionswhen ore is in contact with flowing groundwater. Considering that ourexperimental conditions are far from equilibrium we controlled themixture resistivity. The porosity value calculated for our models was0.5 ± 0.05. Twenty two models were prepared with this procedure(Table 1).

The measurement cell was a Plexiglas rectangular box, 104.3 cm3 involume (Fig. 3). Two current plate cupper electrodes were settled ateach end of the cell, which allowed one-dimensional distribution of themacroscopic electrical field within the studied model. The cell was cov-ered by a plate where two non-polarizing Cu/CuSO4 electrodes were

Table 1Summary of the experiments.

№ r, mm ξ, % m, mVV−1a M, mVV−1 τ, sb Sv, cm−1 ρ, Ωm

1 0.55 0.56 1.90 45 0.0063 30 1122 0.55 1.11 2.53 63 0.011 61 1093 0.55 2.23 7.40 151 0.0082 121 1044 0.55 4.45 11.68 184 0.0108 243 1085 0.55 8.90 23.80 387 0.0155 485 1066 0.55 17.80 32.52 651 0.011 971 987 0.55 26.70 51.20 921 0.0137 1456 818 0.125 0.65 0.16 23 – 156 1179 0.125 1.30 0.45 59 – 312 11510 0.125 2.60 0.53 97 – 624 10711 0.125 5.19 0.80 204 0.00035 1247 11312 0.125 10.39 1.48 358 0.0004 2494 11513 0.125 20.78 4.74 576 0.0006 4987 10014 0.045 0.71 0.37 32 – 477 11015 0.045 1.43 0.40 99 – 953 11116 0.045 2.86 0.32 144 – 1907 10917 0.045 5.72 0.32 257 0.00015 3813 11118 0.045 11.44 0.68 408 0.00019 7627 11219 0.045 22.88 1.43 771 0.00021 15,253 10620 0.055 5.51 0.33 154 0.00022 3006 11021 0.200 5.10 0.90 152 0.0017 766 10522 0.375 5.01 2.49 144 0.0037 400 107

a Wavelength form with 2 s pulse and pause duration.b Missing values of τ mean that in the experiment the relaxation time was very small

and cannot be properly resolved with given value of the total chargeability.

47G. Gurin et al. / Journal of Applied Geophysics 98 (2013) 44–53

installed. The electrolyte for the electrodes was prepared with agar gel,which prevented the model contamination by the electrolyte. Also theends of electrodes represented salt bridges 2 mm length installed flushwith the cover plate, which prevented electrical field distortion nearthe electrodes. Such cells are frequently used in laboratory IP measure-ments (e.g., Titov et al., 2002; Tong et al., 2006; Tong and Honggen,2007). To measure the model resistivity, prior to the measurements,

Fig. 3. Sketch of themeasurement setup. a—measurement cell: C are plate current electrodes, Pc and d—cross sections of the measurement cell.

we calibrated the cell using NaCl solutions with known electrical resis-tivity values (10, 20, 40, 50, and 100 Ωm). With this test we obtainedthe geometrical factor, which was 0.020 ± 0.001 m.

We carried out the resistivity and IP measurements based on the TDtechnique, and using a commercial receiver AIE-2 (www.elgeo.ru) and acustom made laboratory low current (10–500 μA) transmitter. Thestudied time range was from 0.3 ms to 64 s. A high impedancematching device was used to connect the receiver with the measure-ment cell. We used sequences of pulses of the opposite polarity withthe duration from 1 s to 64 s, and with equal on-time and off-time.We sampled IP signals by averaging the polarizability (Eq. (4)) in nar-row time windows in order to obtain an acceptable signal-to-noiseratio. At early times (from 0.3 to 100 ms), when the polarizability waslarge, the short time windows (0.3 ms) were used, and at late times(from 100 ms to 64 s), when IP strongly decayed, the long time win-dows (20 ms) were applied (see Fig. 1). To increase the signal-to-noise ratio we also accumulated the voltage responses of several pulses,and we calculated the average voltage values. For short wavelengthformswe accumulated up to 12 responses of couples of pulses (negativepulse–off-time–positive pulse–on-time), and for long wavelengthforms we accumulated four responses.

We kept the same current value, 50 μA, throughout the whole mea-surement series. Considering the cell geometry, this current producedthe current density value close to that obtained in field conditions(6.6 μA cm−2), which guarantees a linear IP character.

In order to estimate the ramp time after the current switch-off andthe noise level of the receiver channel we carried out tests with (1) ac-tive resistors, (2) the cell filled with NaCl solutions of different salinityvalues, and (3) RC circuits (Fig. 4). The results of the test with active re-sistor are shown in Fig. 4a. The rampof the current vanished after 0.3 ms.The electromagnetic noise level was found to be less than ±50 μV,which corresponds to the polarizability value of ±3.10−2 mVV−1. Thisvalue is much lower in magnitude than that we typically obtained inour experiments.

are non-polarizing copper/copper sulfatemeasuring electrodes; b—electrical connections;

Fig. 4. Results of the setup tests. a—measurements obtained with two active resistors (1 and 3 kΩ); b—measurements obtained with the sample cell filled with NaCl solution with theresistivity of 50 and 100 Ωm; c—RC circuit; d—measurements with RC circuits (see Fig. 3c).

48 G. Gurin et al. / Journal of Applied Geophysics 98 (2013) 44–53

The results of the test on the cell filled with NaCl solutions withknown electrical resistivity are shown in Fig. 4b. The electromagneticnoise level was found to be around ±100 μV, which corresponds tothe polarizability value of ±6.10−2 mVV−1. This level is a bit higherthan that in the previous test, but the corresponding polarizability isagain much lower in magnitude than that we typically observed inour experiments. In the both tests, the noise level increased with in-creasing of the load resistance values.

The signal deformations, possibly related to the voltage measuringwere tested using RC circuit (Fig. 4c) with known relaxation times.Fig. 4d shows a reasonable agreement between the theoretical and ex-perimental decays. Small deviations at the late time range can be relatedto imperfect character of the electrolytic condensers used in this test.Similar results were previously reported in Titov et al. (2010).

In the experiments, we obtained IP decays as arithmetic averagevalue of three independent measurements. Then we approximated de-cays by a set of exponential decays with various magnitude and

relaxation times. This approximation allowed us reducing the randomnoise, obtaining smoothed decays and interpolating the voltage valueson the logarithmic time scale. Then on the basis of the smoothed decaysobtained with different wavelength forms we calculated RTDsaccording to the Debye decomposition approach.

TheDebye decomposition (DD) approach (e.g., Nordsiek andWeller,2008) allows deconvolution of an IP signal to a sumof elementary polar-izing responses describing by the Debye relaxation model and withdifferent relaxation times. Distribution of magnitude of the Debye re-sponses as a function of the relaxation time is obtained with DD.Although this approach is phenomenological, recalling that an insulat-ing spherical grain polarization can be described based on the Debyemodel (Leroy et al., 2008; Schwarz, 1962), and that this model can bealso applied to an ensemble of grain with different radii (Revil andFlorsch, 2010) we should consider that DD can be linked to mechanisticmodels of IP. However this is only valid if the elementary polarizationprocess can be described by the Debye model.

Fig. 5.Chargeability vs. ore volumetric content for different currentwavelength forms and the grain radius 0.55 mm(a); and for different grain radii and the currentwavelength formwith2 s pulse and pause duration (b).

49G. Gurin et al. / Journal of Applied Geophysics 98 (2013) 44–53

Inversion of the decays to RTD is based on the equation relating thedimensionless polarizability, η(t), with the density of RTD, g(τ) (in s−1)(Tarasov and Titov, 2007):

η tð Þ ¼Z∞0

g τð ÞF t=τ; T ;NIð Þdτ; ð12Þ

where F(t/τ, T,NI) is the dimensionless theoretical IP decay, which is theconvolution of the presumed IP decay characteristic of a polarizing ele-ment of the rock texture, f(t/τ), with the current waveform, I(t0),

F t=τ; T ;NIð Þ ¼Zt0

I t0; T;NIð Þ � f t−t0τ

� �dt0; ð13Þ

where t0 is the integration variable; T is the pulse and pause duration;and NI is the number of the extra article accumulated pulses.

Eq. (12) is based on superposition of the responses of polarizing el-ements distributed with the probability density, g(τ). The elementshave a relaxation described by the f(t/τ) rule, and they are polarizedby the current with the wavelength form, I(t0,T,NI).

For the Debye relaxation model f(t/τ) is the damped exponential,

f t=τð Þ ¼ exp − tτ

� �: ð14Þ

Fig. 6. Total chargeability vs. ore volumetric content for two grain radii (a

By introducing a new variable, Z(s), instead of g(τ) on the basis ofnormalization (15), and the transformation of variables (16) and (17):

Z∞0

g τð Þdτ ¼Z∞−∞

Z sð Þds ¼ M: ð15Þ

s ¼ ln τð Þ; ð16Þ

p ¼ ln tð Þ; ð17Þ

Tarasov and Titov (2007) defined the new model function:

Φ p−s; T;NIð Þ ¼ F t=τ; T ;NIð Þ: ð18Þ

Using these new variables, they presented Eq. (12) in the form:

η pð Þ ¼Z∞−∞

Z sð ÞΦ p−s; T;NIð Þds: ð19Þ

Note that the density, g(τ), is expressed in seconds−1 (Eq. (12)),whileZ(s) is a dimensionless parameter (Eq. (15)). This parameter, characteriz-ing RTD, will be interpreted thereafter. Eq. (19) is the Fredholm equationof the first kind, which is an ill-posed problem. The Tikhonov regulariza-tion approach (Tikhonov and Arsenin, 1986) was applied to solve it. Formore details about the inversion procedure, see Tarasov and Titov (2007).

); different current wavelengths with the grain radius 0.55 mm (b).

Fig. 7.Relaxation timedistributions obtained for the sampleswith different grain radii (from0.045 mmto 0.55 mm) and constant volume content of the ore inclusions—5 ± 1%by volume(a); maximum value of RTDs vs. grain radius (b). In the panel (a) numbers show grain radii. The inset in panel (a) shows comparison of the measured IP decays and the decays (currentwavelength formwith 2, 4, 16, 64 s pulse) calculated on the basis of RTD for the sample with the ore grain radius 0.55 mm and ore volume content 4.45%. Note good agreement betweenthe measured and calculated data.

Fig. 8.Relaxation time distributions obtainedwith different ore content and the grain radii0.55 mm (a), and 0.125 mm (b). Numbers show the ore content by volume.

50 G. Gurin et al. / Journal of Applied Geophysics 98 (2013) 44–53

In this paperwe used two RTDparameters: the total chargeability, asdefined in Tarasov and Titov (2007) and Nordsiek and Weller (2008):

M ¼Zsmax

smin

Z sð Þds; ð20Þ

and the relaxation time determined from the largest peak in RTD, τmax.The inset in Fig. 7a shows comparison of themeasured IP decays and thedecays calculated on the basis of the recovered relaxation time distribu-tion. Themeasured and calculated decays are in good agreement, whichconfirms correctness of the used DD approach.

5. Results

Table 1 presents summary of the experiments. First we analyzed datain terms of the traditional IP parameter, the chargeability (see Eq. (4) andFig. 1). Fig. 5 shows the chargeability measured with different models.The chargeability is sensitive to the ore content. However it also dependson the current wavelength (Fig. 5a) and on the grain size (Fig. 5b). Theslope of the m–ξ relationships (which determines the sensitivity ofm to variations of ξ) decreases with increase of the rectangular pulse du-ration, and the chargeability magnitude increases with increase of themetallic inclusion radius. At low values of ξ (b10%), and for the smallestmetallic particles (0.045 mm) the chargeability found to be independentof the particle content and is determined by the sandy matrix.

Fig. 6 shows the total chargeability (Eq. (20)) as a function of the orecontent. The total chargeability also strongly depends on the ore con-tent, but in contrast to the chargeability, it was found to be independentof the grain size (Fig. 6a) and of the current wavelength form (Fig. 6b).

Fig. 7a shows RTDs for different sizes of themetallic inclusions.Withincrease of the grain radius, the RTD maximum position shifts rightalong the time axes. The magnitude of the maxima decreases with in-creased grain radii (Fig. 7b), which, in conjunction with increasedbroadness of the spectra, confirms the independency of the integralRTD parameter, the total chargeability (Eq. (20)), of the grain size (seeFig. 6).

Fig. 8 shows how RTDs vary with the ore concentration. The magni-tude of RTD monotonously increases with increased ore content, andthe maximum location is almost the same. Small variations of the max-imum position aswell as an appearance of smaller extra maxima are ef-fects of the second order. Possibly they are consequences of ambiguityof the data inversion because the Debye decomposition techniquesolves ill posed problem.

For comparison,we also plotted the relaxation times obtained in thiswork andpublished previously (Fig. 9). For the published data the relax-ation time was considered as an inverse of the critical angular frequen-cy. The data were fitted with a power law; however the determinationcoefficient is of moderate value. This might be explained by differentmineralogical composition of the grains, which was not accounted forin this work, and by different pore water salinity values (Mahan et al.,1986; Slater et al., 2005).

Fig. 9. Relaxation time vs. ore grain radius. 1—Wong (1979), different volume contents ofchalcopyrite; 2—Collett (1959), 3% of galena; 3—this work, 5%; 4—Grissemann (1971), 6.3%of chalcopyrite; 5—Ostrander and Zonge (1978) (see Zhdanov (2008)), 7.5% of chalcopyrite;6—Ostrander and Zonge (1978) (see Zhdanov (2008)), 7.5% of pyrite. Two best fits areshown: for all data (τ = 0.1 ⋅ r2) and for the data obtained in this paper (τ = 0.027 ⋅ r1.73).

51G. Gurin et al. / Journal of Applied Geophysics 98 (2013) 44–53

Fig. 10 shows relationships between the specific surface area, SV, ofthe ore grains and the normalized chargeability (Eq. (5)). In this workwe defined the specific surface area as the total surface of the grainsper unit volume. We calculated Sv assuming the grains are of sphericalshape, and on the basis of their radius and volumetric content,

SV ¼ 3rξ: ð21Þ

So, considering (a) the form of the particles can be not spherical, and(b) their surface can be rough, our estimation of Sv should be viewed as

Fig. 10. Relationships between the normalized chargeability and the specific surface areaof metallic particles. 1, 2, and 3 are the models with ore grain radii 0.55, 125 and0.045 mm, respectively, and various ore grain contents.

the lowermost limit. Slater et al. (2005) and Slater et al. (2006) arguedthat the normalized chargeability is a goodmeasure of themetallic par-ticles specific surface area (they determined the surface area per unitepore volume; however these two definitions differ by the porosityvalue,whichwas different but almost constant in the both datasets). Re-cently Weller et al. (2010) extended this result for the case of ionconducting sediments. We tested this hypothesis on the basis of thediscussed data. Fig. 10a shows that M–SV relationship does exist, but isnot universal: the power–laws relationships are well determined, andtheir exponents are almost the same, but their multipliers are differentdepending on the grain size.

6. Discussion

The resistivity measurements reveal small variations of the bulk re-sistivity (Table 1). For the volumetric content ofmetallic particles below30%, the resistivitywas 105 ± 7 Ωm. This confirms that thewater salin-ity values were very similar in different experiments, and the experi-mental results are comparables. Only one experiment with the largestcontent of metallic particles (30%) shows smaller resistivity value(81 Ωm), which can be related to additional current passages throughclusters of metallic grains.

The chargeability strongly varies with the ore content. However,Fig. 5 shows that the sensitivity ofm–ξ relationships decreases with in-creasing current pulse duration. This is explained by an integral charac-ter of the chargeability (Eq. (4)). In our experiments (Table 1), the timeconstant values were in the range from 1.5 × 10−4 to 1.6 × 10−2 s.Therefore the strongest impact of themetallic particles to IP signals cor-responds to this time range. In contrast, at late times the sandy matrixcharacterized by larger time constant (about 10 s (Titov et al., 2002))significantly contribute to the IP signals. With increase of the pulse du-ration and of the integration time (see Eq. (4)) the relative impact ofmetallic grain decreases and the impact of matrix increases, whichleads to decreased sensitivity of the chargeability to the ore content.

The magnitude of the chargeability measured with 2 s pulse dura-tion decreases with decrease of the grain size (Fig. 5b). This is explainedby the decrease of the time constant with decrease of the grain size (seeTable 1). With decrease of the time constant, the contribution of metal-lic particle to chargeability also decreases,which leads to decrease of thechargeability magnitude. Moreover, fine particles (0.045 mm), whosetime constant is about 2 × 10−4 s, at small concentration (above 10%)were not actually detected by the chargeability (Fig. 5b), because it isdetermined by the sandy matrix. Summarizing presented data we con-clude that the chargeability cannot be considered as a universal quantityto measure the ore content.

The total chargeability was found to be independent of the grain size(Fig. 6a), and strongly dependent on the ore volumetric content. Howev-er, in our experiments, at a constant value of ξ the specific surface of me-tallic particles should proportionally increase with decrease of the grainradius (Eq. (21)). Moreover, Fig. 10 shows that the normalizedchargeability does depend on the specific surface, but the relationshipsare specific for each grain size. (Note because in our experiments the re-sistivity values varied within very small range about the value of105 Ωm, the total chargeability and the normalized chargeability aresimply related asMn ¼ M

105.) In experiments with iron–sand and magne-tite–sand mixtures reported in Slater et al. (2005) and Slater et al.(2006), respectively, it was found that the normalized chargeability isproportional to the specific surface of inclusions of iron or magnetite.On the one hand, we should precise, that the results of Slater and co-workers were obtained with metallic particles of almost the same size(0.4 mm for the iron and 0.43 mm for the magnetite), and, so, their re-sults can also be interpreted in terms of relationshipMn–ξ, just becausethe increase of themetallic particles surface leads to increase of their vol-ume. On theother hand, considering IP as the interface phenomenon, theuniversal link between the IP magnitude and the volumetric propertyseems to be counterintuitive. To explain this apparent contradiction let

Fig. 11. RTD recovered with different wavelength forms and different pulse duration.

52 G. Gurin et al. / Journal of Applied Geophysics 98 (2013) 44–53

us consider the IP magnitude,Mn, to be proportional to the surface areaof a metallic particle, their number per unit volume, χ, and the magni-tude of polarization of individual particle, γ, whichmust be proportionalto the particle induced dipole moment. Let us further assume, γ is pro-portional to the particle radius, r,

γ e r; ð22Þ

Mn e r2 � χ � r ¼ r3 � χ: ð23Þ

With this assumption, it is straightforward the polarization magni-tude is proportional to the volumetric particle content. The proportion-ality γ ~ rmight be attributed to the overvoltage arising at the interfacebecause of the applied electricalfield (see Fig. 2). Note the overvoltage isproportional to the particle radius according to Eq. (11).With increasingparticle radius the overvoltage at two particle poles increases in magni-tude, and, consequently, the electrical current crossing the interface alsoincreases (Eq. (9)). Assuming that this normal current is responsible forstrong polarization typical of metallic particles, we argue that smallerparticles have smaller polarization magnitude.

Therefore according to our data the normalized chargeability is a di-rect measure of the ore volumetric content.

With increase of the grain radius, the RTD maximum position shiftsright along the time axes (Fig. 7a), which confirms that the main relaxa-tion time also increases. Our data are in accordancewith previously pub-lished results (Fig. 9). This behavior is in qualitative accordance withobservations on sand packs, where the relaxation time increaseswith in-crease of sand particle size (e.g., Leroy et al., 2008; Titov et al., 2002).

The data collected in Fig. 9 show a quadratic relationship,

τ ¼ r2

2D; ð24Þ

where r is the grain radius (inm), andD is the ion diffusion coefficient in(m2s−1). This is in agreementwith the diffusion kinetic typical of polar-ization of a single grain composed by dielectricmaterial and surroundedby the electrical double layer (e.g., Schwarz, 1962). However the diffu-sion coefficient value calculated according to Eq. (24) and the data plot-ted in Fig. 9 was found to be unrealistically large (5 × 10−6 m2s−1 vs.typical value for ions in aqueous solutions ~10−9 m2s−1). Thereforethe diffusion coefficient calculated from Eq. (24) should be consideredas an apparent value. The value ofD obtainedwhen our data were fittedalone was found to be even greater (Fig. 9). Certainly, this value of thecoefficient was obtained with single value of the water electrical con-ductivity (20 mSm−1), and should increase again with increased elec-trolyte conductivity (because the relaxation time decrease about oneorder of magnitude per one order of electrolyte activity increase(Mahan et al., 1986; Slater et al., 2005)). In the case of low salinitywater discussed here, the relaxation time for an ore grain is about103–104 times smaller than that of a silica grain with the same radius.Therefore our experimental data in conjunction with the data of Slateret al. (2005) suggest that IP must be governed by processes which aremuch faster than diffusion. Good candidate, which can accelerate the re-laxation, is the redox reactions on the particle boundary, which is stim-ulated by the overvoltage produced by external field (see, e.g., Wong,1979). However this discussion is out of scope of the present paper,and will be subject of a separate paper.

In our experiments we found that the RTD peaks breadth increaseswith increase of the particle size. Different breadths of the peak in IPspectra are usually associatedwith the extent of particle size distribution(e.g., Revil and Florsch, 2010). Thus, when experimental data are fittedwith the Cole–Cole type equations (e.g., Cole and Cole, 1941; Peltonet al., 1978) this is pronounced in various values of the Cole–Coleexponent. In the diffusion-related models the relaxation time is directlyrelated to the characteristic diffusion length, τ ~ l2. In our experiments,the diffusion length can be dependent not only on the grain radii, but

also on the grain surface roughness. Regarding the fact that differentminerals can have different kind of cleavability, the surface roughnessdegree can be different for different grain sizes. Also regarding our pro-cedure of the grain preparation, we cannot guarantee that the grainsize distributionwas exactly the samewithin each grain size class. How-ever our data are qualitatively in agreement with those of Grissemann(1971), who observed similar variation of the peak breadth on the con-ductivity phase distribution with the grain radius variation (see Fig. 4 inWong (1979)).

In our laboratory measurements according to themethodology pro-posed by Tarasov and Titov (2007) we used different current wave-lengths. The maximum current wavelength was 64 s, which wasextremely time-consuming. We recognize that practical application ofthe Debye decomposition approach is limited by time needed for fieldmeasurements. However in contrast to the case of insulating sand par-ticles treated in Tarasov and Titov (2007), the relaxation times in thediscussed cases of metallic particles are considerable smaller (seeFig. 9). This is because, we performed a numerical experiment to under-stand, is it possible to obtain RTD on the basis of measurements withshort wavelengths. Fig. 11 illustrates results of this experiment.

We consider the best RTD was obtained when we used severalwavelength forms simultaneously (2, 4, 16, and 64 s). However, the po-sition and magnitude of the largest maximum peak in the RTD distribu-tion were also well recovered when only short wavelengths were usedin the Debye decomposition (Fig. 11). In particular even the use of pulseand pause duration of 2 s gives satisfactory recovery of the RTD. Thisopens a perspective of use the Debye decomposition approach in min-ing geology. However regarding very small values of the time constantreported in this work attention should be paid to possible inductiveand capacitive coupling at high frequency (low time) range.

7. Conclusions

In this paper, we systematically investigated the applicability of theDebye decomposition approach to the case of rocks and sediments con-taining ore minerals. We found this approach to be very useful forpetrophysical data interpretation. Comparing the standard techniquebased on the use of the chargeability and normalized chargeability, it al-lows better assessing the metallic grain concentration. For the givenwater salinity value, the total chargeability is appropriate measure ofthe volumetric content of metallic particles, and the main relaxationtime is a measure of the grain size. However, actually the ‘τ–r’ relation-ship is only empiric, because even formally it corresponds to the diffusionkinetics, the corresponding diffusion coefficient value is unrealisticallylarge. For the case of fresh water discussed in this paper, this leads toshorter relaxation time values comparing the case of common soils andsediments, which, in turn, allows relatively fast IP measurements.However small time (high frequency) ranges can be contaminated by ca-pacitive and inductive couplings,which canhinder propermeasurements

53G. Gurin et al. / Journal of Applied Geophysics 98 (2013) 44–53

of IP signals. This also means that in reality the IP mechanism is not con-trolled by the ion diffusion only. However the theoretical description ofthe IP mechanism for disseminated metallic particles is the purpose of aseparate paper.

Finally we should recall that our data were based on a specific orecomposition, and, possibly, the relationships, we presented in thispaper, are specific to the mineralogical composition of the studiedmodels. However influence of the mineralogical composition is also thepurpose of a future paper.

Based on the presented datawe recommendusing the parameters ofrelaxation time distribution obtained with the Debye decompositionapproach in ore prospecting and also in studying permeable reactivebarriers.

Acknowledgments

Very constructive suggestions and comments of the reviewers LeeSlater and Nicolas Florsch are greatly appreciated. This work wassupported by St. Petersburg State University (Grant 3.0.114.2010, andthe PhD project of G. Gurin). Equipment of Core Facility RC “Geomodel”of St. Petersburg State University was used in this work.

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