Induced Polarization (IP) and Complex Resistivity

Basic Concept

The induced polarization (IP) effect is an electrical response of materials that was discovered during a direct-current (DC) resistivity survey (see Resistivity Method). After the current is injected into the subsurface, the measured voltage does not immediately go to zero but, instead, decays over time. This behavior occurs due to the capacitance of subsurface materials, which allows for the polarization of electrical charges during current injection and release of charge after current is shut off (Dobrin, 1960).

The capacitance of subsurface earth materials depends upon physical and electrochemical properties related to minerology/lithology, pore fluid chemistry, and fluid-grain boundary interactions. The IP method, though historically used primarily for prospecting disseminated ore, has become increasingly used in hydrogeophysics (Binley and Kemna, 2005).

The IP survey setup is nearly identical to that of DC resistivity, and IP data are often collected concurrently. However, specialized resistivity meters are required to make IP measurements, and quality data are more challenging to collect and interpret. The IP response can be measured in either the time domain or frequency domain.

Time domain IP responses are determined by measuring the voltage across the potential electrodes as it decays after shutting off a static (DC) current. Alternatively, frequency domain IP measurements involve injecting time-varying (AC) current at two or more frequencies. Spectral IP, which is an advanced frequency domain IP method also known as complex resistivity, compares the magnitudes and phase shifts of returning to injected signals for several frequencies.

General Theory of Induced Polarization and Complex Conductivity

The flow of electrical charge (i.e., current) is induced within subsurface earth materials when an external electrical field is applied to the environment. Subsurface charge is carried by (1) electrons that are conducted through metallic materials and/or (2) ions in the pore fluid and along mineral grain surfaces. For near surface environmental and hydrological applications, ionic conduction is typically the dominant mechanism for charge transport.

In ambient conditions, electrical charge distribution is relatively homogeneous and isotropic within a given subsurface body or formation. While under the influence of the external electric field, positive and negative charges become segregated according the electric field direction. During this bidirectional transport of positive and negative charges, polarization of the charges that occurs at fluid-mineral interfaces. This is known as interfacial polarization and is the primary driver for the IP effect. Though other polarization processes occur in the subsurface (e.g., Glover, 2015), they are generally insignificant in surface IP measurements.

Once the external electrical field is eliminated, the polarized charges resume their equilibrium positions over a measurable period of time. The behavior exhibited by these polarizable subsurface materials is similar to that of an electrical capacitor. As natural conditions are reestablished, the IP-affected materials produce a current as they discharge the electrical energy that was stored under the influence of the external field (see sketch below). The current generated during re-equilibration produces the decaying voltage signal received during an IP measurement.

Particle surface ions migration due to an applied external electric field

The sketch above shows particle surface ions movement or migration due to the application of an external electric field

Electrical impedance is the complex, frequency-dependent measure of ability to oppose alternating current (AC) flow. Similar to how resistivity is related to a measured resistance, complex resistivity, ρ*(ω) , or its reciprocal complex conductivity, σ*(ω), is the intrinsic material property related to impedance. The complex electrical behavior exhibited by earth materials (e.g., Vinegar and Waxman, 1984) is due to the combined influences of free-charge conductive mechanisms and capacitive mechanisms.

Complex conductivity can be defined in the following equation, which is composed of terms that are described in table below.

equation term	description
	real component of complex conductivity
	imaginary component of complex conductivity
	angular frequency

	bulk conductivity magnitude
	phase angle

The real component of complex conductivity represents electrical conductivity occurring by free charges, while the imaginary component represents capacitive properties that are primarily related to interfacial polarization. In other words, the real component of complex conductivity reflects both fluid and mineral surface properties, and the imaginary component reflects surface properties. Maps of the real and imaginary components of complex conductivity can highlight areas with significant surface polarization, which may be related to various subsurface properties/processes of interest (e.g., presence of clays, formation of biofilms, etc.).

The following sections include descriptions of how each sub-method is related to the real and/or imaginary components of complex conductivity.

Time Domain Induced Polarization

A time domain IP measurement involves the injection of a direct current into the subsurface via two current electrodes that are galvanically coupled to the ground. The current is transmitted for an amount of time that allows charge to sufficiently build up on surfaces within the earth materials. Sufficient charge buildup can be indicated by the stabilization of transmitted current and measured voltage at what are referred to as their primary values (I_P and V_P).

The current is turned off, and, after a short time that allows the transmitted current to dissipate, residual voltage is measured as it decays to zero. Data are collected during a relaxation time, which equal to the time allotted for current transmission and allows for the discharging of charged subsurface materials. Repeat measurements are collected with transmitted current polarity reversals to average out any constant potentials (see self-potential) and increase signal to noise (Mussett and Khan, 2005).

The curve of voltage decay over time is integrated over a defined time interval and then normalized by the primary voltage (V_P) to give apparent or integral chargeability (M_a) expressed as a percentage or in millivolts per volt (mV/V) (Binley and Kemna, 2005). The value of integral chargeability depends on the sampling period and is commonly converted and reported by the Newmont standard, which uses three second current on/off times and a one second integration interval (Sumner, 1976).

“Apparent” data are directly measured and assume a homogeneous earth, whereas “intrinsic” data are estimated using numerical inversion and account for the effects of heterogeneity. Maps of apparent chargeability can qualitatively indicate the subsurface capacitive properties, especially when chargeability is normalized by the measured conductivity (Slater and Lesmes, 2002). However, intrinsic chargeability inversions by fitting the apparent chargeability data to a 1D, 2D, or 3D spatial distribution has proven beneficial (Oldenburg and Li, 1994).

Binley (2015) reports that apparent chargeability and apparent phase angle are related by a constant approximately between 1 and 1.5. Thus, the phase angle may range from the apparent chargeability magnitude to one and a half times it (i.e., φ_a ≅ M_a to 1.5M_a). However, such a conversion factor may not be appropriate, and, ideally, an instrument configuration-specific empirical calibration is developed to relate the two parameters. Furthermore, Kemna and others (1997) describe a theoretical method for converting chargeability to phase angle.

The apparent phase angle is either estimated from the apparent chargeability or directly measured from a frequency domain IP measurement, which is discussed in the following section. Apparent resistivity and apparent phase angle can be processed and inverted (e.g., Kemna et al., 2004) to give spatial distributions of complex conductivity magnitude and intrinsic phase angle. Such inversion images can then be converted to the real and imaginary components of conductivity using the equation described above.

Frequency Domain Induced Polarization

Frequency domain IP requires the separate injection of two currents at different frequencies (e.g., typically between 0.1 and 10 hertz) and the determination of apparent resistivity for both. Apparent resistivity, which is defined as; ρ_a=k (injected current/measured current) = k (1/v^'), and is frequency dependent as a result of the frequency dependence of charge polarization. The lower frequency current allows more time for charge polarization with each cycle, and the apparent resistivity acquired with the lower frequency current (ρ_S) is larger than that acquired at the higher frequency (ρ_M).

The ratio of apparent resistivity measured by the two frequencies can be quantified by the percent frequency effect (PFE), which is computed by the normalized relation [ ( ρ_S- ρ_M) / ρ_M] x 100. The PFE can be interpreted as the percentage of charge in the system that becomes stored. The PFE does not require the injection of current extrema and can be used with various frequencies (Wightman and others, 2003).

Similar to integral chargeability, percent frequency effect can be normalized by the measured conductivity to indicate the capacitive properties of the subsurface (Slater and Lesmes, 2002). Furthermore, PFE data are expected to have some relationship to the apparent phase angle (φ_a ). For example, Scott (1971) reports a conversion that such that apparent phase angle ranges between 0.11 and 0.19 times the PFE. After this conversion, resistivity magnitude and phase angle can be inverted, and the results can be converted to real and imaginary conductivity.

Frequency domain IP measurements require significantly smaller source currents and are less sensitive to most common sources of noise. However, they are extremely susceptible to electromagnetic induction (EMI) coupling effects, particularly at higher frequencies, and data may be rendered unusable.

Spectral Induced Polarization

The spectral IP (SIP) method is a frequency domain (sometimes called “phase domain”) investigation of the IP effect that involves specialized equipment and a more in-depth analysis of the frequency-dependence of charge storage. Specifically, SIP examines how conductivity ( or resistivity) varies as a function of frequency by measuring and plotting frequency versus measured conductivity. Such plots are sensitive to the timescales of many electrical polarization processes that occur and can be related to properties (e.g., grain size distribution) (Lesmes and Friedman, 2005).

The SIP method injects an alternating current into the subsurface and compares the voltage signal measured across the potential electrodes to voltage signal transmitted via the current electrodes. Both transmitted and received signals are sinusoidal waves that oscillate continuously at the external AC field-specific frequency (f). See the sketch below showing the transmitted current and the received current with a phase angle shift due to the earth materials through with the transmitted current traveled.

Sketch showing the phase lag of the received current from the transmitted current

As shown above, due to IP effects, the received signal lags behind (i.e., is out of phase from) the transmitted signal. If the transmitted voltage is , V_Tx(t), and the received voltage is , V_Rx(t), then the signals can be related as follows:

SIP transmitted and received voltage formula

Thus, the apparent phase angle (φ_a ) determined by a SIP measurement is measured as the lag of the received signal behind the transmitted signal (in milliradians). Apparent resistivity magnitude can be calculated from maximum received voltage amplitude, injected current amplitude, and the geometric factor (Resistivity Method). Thus, data can be inverted for spatial distributions of intrinsic resistivity and phase angle and converted to real and imaginary conductivity as described in the sections above.

However, typically the value of SIP data is not in producing maps of real and imaginary conductivity, but rather in understanding the distribution of conductivity across a frequency spectrum. These distributions can be numerically fit (i.e., inverted) to various dielectric relaxation models, perhaps the most widely used being the Cole-Cole model (Cole and Cole, 1941). Pelton et al. (1978) formulated the model for SIP measurements as,

SIP resistivity as function of phase angle and low and high resistivity magnitude

equation term	description
	low frequency asymptotes of resistivity magnitude
	high frequency asymptotes of resistivity magnitude
	time or relaxation constant
	an exponent inversely related to the width of the frequency versus resistivity curve

Fitted Cole-Cole models can be linked to various subsurface properties such as pore geometry, specific surface area, and hydraulic permeability (Tong and Tao, 2008). SIP models can also be indicative of various geological materials, grain size distribution, and/or processes (e.g., contaminant biodegradation).

Summary and Applications

Induced polarization methods are extended from the electrical resistivity method and are primarily sensitive to capacitive properties and polarization processes that occur at fluid-grain interfaces. Capacitive processes are highly significant in areas with metallic minerals. Thus, IP methods are highly sensitive to disseminated ore due to the grain polarization that occurs at fluid-metallic mineral interfaces (Reynolds, 1997).

Though to a lesser extent, IP methods are also sensitive to regions with large particle surface area (e.g., high clay mineral content) and have proven useful in such environments. IP methods can image lithology or processes that reflect large differences in grain surface area such as those that differentiate clays from surrounding lithology (Slater and Lesmes, 2002). Another prominent application of IP is the monitoring of biodegradation processes occurring at the fluid-grain interfaces (Davis and others, 2006; Revil and others, 2012).

Induced polarization measurements can theoretically provide additional information about the subsurface and be collected using the electrode configurations used in resistivity surveys. Multielectrode surface systems can be used for rapid and noninvasive IP data collection and incorporate various electrode arrays, which are chosen based the survey objectives and spatial orientation-dependent resolution. The most commonly used arrays include the Wenner, Schlumberger, reverse-Schlumberger, and dipole-dipole. The Wenner array is best for delineating lateral variations, and vertical structure is better imaged with the dipole-dipole array.

However, relative to electrical resistivity, induced polarization data are rarely gathered in the field. Despite many advances in research, IP data remain challenging to collect, process, and interpret. Surveys must be carefully programmed to give both good coverage and have high signal to noise given the relatively small returning signals (microvolts to millivolts). To increase signal to noise, a higher transmission power may be needed. Source currents of up to 10 amps may be required, which may introduce the need for a generator and a heightened safety risk.

Additionally, performing and interpreting IP surveys can often be skill, cost, and/or time prohibitive. Data collection time multiplies with measurement stacking of multiple current cycles as well as longer current on/off times that may be needed to ensure voltage has sufficiently decayed before the next injection. Furthermore, like all electrical methods, models based on IP results bear a degree of inherent non-uniqueness because there is large overlap of electrical polarization values per different materials. Thus, careful analysis of data quality and uncertainty quantification is required to reduce ambiguity in interpretation (Binley and Kemna, 2005).

Nevertheless, the method is constantly advancing. IP methods may one day become more commonplace as the cost and complexity of implementation is reduced and tools for physical interpretation of data are developed. Induced polarization is a complex phenomenon resulting from several physio-chemical conditions and is not yet completely understood. However, there is a continually growing body of research attempting to link IP data to parameters of interest.

Abstracts of case studies are presented from research using IP to achieve various environmental characterization objectives. Some of which include the following:

Estimating water content/ soil moisture
Determining solute concentration/ salinity estimation
Mapping clays, contaminants, hydrogeological boundaries, fracture zones
Estimating microstructure and microgeometry of porous systems

Examples/Case studies

Attwa, M., Günther, T., Grinat, M., and Binot, F., 2011, Evaluation of DC, FDEM and IP resistivity methods for imaging perched saltwater and a shallow channel within coastal tidal flat sediments: Journal of Applied Geophysics, v. 75, no. 4, p. 656-670, doi:10.1016/j.jappgeo.2011.09.002.

Abstract: Presently, electrical resistivity methods are applied in a wide variety of geological and environmental site investigations. Geologically, the coastal tidal flat sediments formed shallow channel-like features at the northern part of Germany. Three geoelectrical methods are applied to image the near surface sediments including a shallow conductive zone within the tidal deposits at the North Sea coast. These methods, direct current (DC) resistivity, frequency domain electromagnetic (FDEM) and spectral induced polarization (SIP), are evaluated to show which one can provide the required spatial resolution under study area conditions. This evaluation also includes a synthetic modeling to assess the DC resistivity imaging technique. The results constitute an encouraging example using these geophysical methods in characterizing the coastal aquifers. The inversion results show that the subsurface resistivity distribution of tidal sediments can change rapidly within a short distance. A thin high conductive layer is observed above the peat and clay layers reflecting a perched saltwater. The 2D IP section shows that the perched saltwater is restricted to patched forms above an impermeable layer of clay. According to the IP images the boundaries of the clay layer are recognized with a good resolution due to the high membrane polarization of the clays. The EM and DC profiles show a shallow channel-like feature within tidal deposits. In this paper, the best FDEM field parameters and the role of EM in lithologic studies are emphasized. Two main limitations can be observed from DC synthetic modeling: (a) A smearing in the lower boundary of the perched saltwater; (b) an amplification of the lateral effect of the highly conductive layer. These limitations decrease the resolution of DC imaging for accurate defining our targets. Because the IP response depends on microgeometry, fluid chemistry and saturation, the 2D IP results demonstrate the suitability of this method to characterize the tidal deposits in the coastal area with a good resolution. In this study, the success of SIP method supports further investigations into studying the hydraulic parameters of tidal deposits in this area. The obtained results during this investigation provide an overview of the coastal aquifer and they can serve as a basis for refining the conceptual model of morphological elements and sedimentary sequences of the coastal tidal flat.

Binley, A., Slater, L.D., Fukes, M., and Cassiani, G., 2005, Relationship between spectral induced polarization and hydraulic properties of saturated and unsaturated sandstone: Water Resources Research, v. 41, no. 12, p. W12417, doi:10.1029/2005WR004202.

Abstract: There is growing interest in the use of geophysical methods for hydrological model parameterization. Empirical induced polarization (IP)–hydraulic conductivity (K) relationships have been developed, but these are only applicable to sediments in which the IP response shows limited variation with electrical current frequency. Here we examine the spectral IP response of samples taken from a UK sandstone aquifer and compare measured parameters with physical and hydraulic properties. We demonstrate the limited value of existing IP‐K models due to the inherent IP frequency dependence of these samples. Our results show how the mean relaxation time, τ, is a more appropriate measure of IP response for these sediments. A significant inverse correlation between the surface area to pore volume ratio and τ is observed, suggesting that τ is a measure of a characteristic hydraulic length scale. This is supported by a measured strong positive correlation between log τ and log K. Our measurements also reveal evidence of a relationship between τ and a dominant pore throat size, which leads to postulations about the parallelism between the spectral IP behavior and unsaturated hydraulic characteristics. Additional experiments show how the relaxation time is affected by degree of fluid saturation, indicating that saturation levels must be accounted for if our empirical relationships are applied to vadose zone studies. Our results show clear evidence of the potential value of frequency‐based IP measurements for parameterization of groundwater flow models.

Deceuster, J. and Kaufmann, O., 2012, Improving the delineation of hydrocarbon‐impacted soils and water through induced polarization (IP) tomographies: A field study at an industrial waste land: Journal of Contaminant Hydrology, v. 136-137, p. 25-42, doi:10.1016/j.jconhyd.2012.05.003.

Abstract: Without a good estimation of samples representativeness, the delineation of the contaminated plume extent and the evaluation of volumes of hydrocarbon-impacted soils may remain difficult. To contribute to this question, a time domain induced polarization (IP) field experiment was conducted on an industrial waste land. Boreholes were drilled to specify the local geological context. Cross-hole seismic tomographies were performed to extend borehole logs and to draw an interpreted geological cross-section. Soil samples taken during drillings were analysed in laboratory. A preliminary survey was conducted to locate the IP profile. The polarization signatures linked to the presence of clayey sediments were filtered out from the data set. Chargeability and resistivity depth soundings were computed and compared to mean concentrations of total organic products to overcome the data support issue between the geophysical models and the spot samples of soils. A logarithmic relation between chargeabilities and smoothed hydrocarbon concentrations in soils was found. Taking into account contaminant's concentration thresholds defined in local codes and regulations allows defining chargeability classes to delineate hotspots on this site. This showed that IP tomography can be an accurate screening methodology. A statistical methodology is proposed to assess the efficiency of the investigation strategy.

Gazoty, A., Fiandaca, G., Pedersen, J., Auken, E., and Christiansen, A.V., 2012, Mapping of landfills using time-domain spectral induced polarization data: the Eskelund case study: Near Surface Geophysics, v. 10, no. 6, p. 575-586, doi:10.3997/1873-0604.2012046.

Abstract: This study uses time-domain induced polarization data for the delineation and characterization of the former landfill site at Eskelund, Denmark. With optimized acquisition parameters combined with a new inversion algorithm, we use the full content of the decay curve and retrieve spectral information from time-domain IP data. Thirteen IP/DC profiles were collected in the area, supplemented by el-log drilling for accurate correlation between the geophysics and the lithology. The data were inverted using a laterally constrained 1D inversion considering the full decay curves to retrieve the four Cole-Cole parameters. For all profiles, the results reveal a highly chargeable unit that shows a very good agreement to the findings from 15 boreholes covering the area, where the extent of the waste deposits was measured. The thickness and depth of surface measurements were furthermore validated by el-log measurements giving in situ values, for which the Cole-Cole parameters were computed. The 3D shape of the waste body was pinpointed and well-defined. The inversion of the IP data also shows a strong correlation with the initial stage of the waste dump and its composition combining an aerial map with acquired results.

Lesmes, D.P. and Frye, K.M., 2001, Influence of pore fluid chemistry on the complex conductivity and induced polarization responses of Berea sandstone: Journal of Geophysical Research: Solid Earth, v. 106, no. B3, p. 4079-4090, doi:10.1029/2000JB900392.

Abstract: The spectral induced‐polarization (IP) response of rocks and soils is a complex function of pore solution chemistry, sample microgeometry, and surface chemical properties. We measure the complex conductivity and the time domain IP responses of Berea sandstone as a function of pore fluid ionic strength and pH. Complex conductivity is measured over the frequency range 10−3 to 106 Hz, and chargeability is computed using a time window of 0.16 to 1.74 s. The field IP parameters: phase, percent frequency effect, and chargeability are functions of both the surface and bulk electrical properties of the sample and are observed to decrease with increasing solution conductivity. Dividing these parameters by the sample resistivity yields normalized IP parameters (quadrature conductivity, metal factor, normalized chargeability) that are proportional to the imaginary component of the complex surface conductivity. Normalized IP parameters increase with ionic strength up to concentrations of 10−1 M NaCl and show a reduced response at pH 3, the point of zero charge for quartz‐dominated systems. For concentrations >10−1 M NaCl, the normalized parameters decrease with increasing concentration. This decrease in surface polarization may indicate a decrease in the effective mobility of polarizing charges at high solution concentration. Our data indicate that normalized IP parameters are directly related to the physiochemical parameters that control the surface conductivity responses of rocks and soils. Normalization of IP measurements in environmental investigations should increase the effectiveness of IP surveys, especially in high‐conductivity environments

Mwakanyamale, K.E., Slater, L.D., Ntarlagiannis, D., Binley, A., Day-Lewis, F.D., Ward, A.L., Heenan, J., and Placencia, E., 2010, Use of the time-domain induced polarization method to map the spatial distribution and depth of the Hanford-Ringold contact in the Hanford 300 Area–Results from 2D complex resistivity inversion, in Proceedings, AGU Fall Meeting: San Francisco, CA, American Geophysical Union, Abstract H23C-1199.

Abstract: The transport of Uranium [U(VI)] contaminated groundwater to the Columbia River in the Hanford 300 Area, Washington, is influenced by the depth and location of the Hanford-Ringold contact. Ringold Formation sediments have distinct physicochemical properties compared to the Hanford Formation sediments through which contaminated groundwater flows. Better definition of the spatial variability and the depth to the Hanford-Ringold contact across the site is crucial to improve understanding of contaminant transport between the aquifer and the Columbia River. In particular, there is only very limited information on the spatial variability of the contact between the river and the Hanford Integrated Field Research Challenge (IFRC) site where controlled experiments on U (VI) transport are being conducted. Data collected with land-based electrical resistivity, induced polarization (IP), and ground penetrating radar have only been of limited use for mapping this critical hydrological contact. However, recent waterborne IP imaging along the river corridor proved successful in characterizing the distribution of the Hanford-Ringold contact beneath the river due to the strong contrast in polarization between the Hanford and Ringold units. Therefore, a high-resolution IP survey was conducted along five 2D lines using static cables on the land, parallel to the shore; full resistivity and IP reciprocal datasets were collected. Here, linear IP error models that describe the increase in error with increase in measured chargeability are constructed to provide appropriate data weights in the inversion, and a 2D complex resistivity inversion of the resistivity and time domain IP data is performed to image the spatial distribution of electrical conductivity and normalized chargeability (proportional to the imaginary conductivity representing polarization) between the IFRC and the river. The Hanford-Ringold contact is clearly identified from the sharp contrast between the weakly polarizable Hanford Formation and the highly polarizable Ringold Formation. The results suggest that, given appropriate care to quantify and model measurement errors, IP is a very effective tool in mapping the key lithologic units at this site.

Ntarlagiannis, D., Robinson, J., Soupios, P., and Slater, L., 2016, Field-scale electrical geophysics over an olive oil mill waste deposition site: Evaluating the information content of resistivity versus induced polarization (IP) images for delineating the spatial extent of organic contamination: Journal of Applied Geophysics, v. 135, p. 418-426, doi:10.1016/j.jappgeo.2016.01.017.

Abstract: We performed 2D resistivity and IP measurements over a known olive oil mill waste plume at a site in western Crete, Greece. The objectives of the survey were: (1) to determine whether IP is more diagnostic in delineating the spatial extent of the plume relative to resistivity measurements alone; (2) to evaluate whether the additional information content obtained from IP is worth the effort given longer data acquisition times and higher measurement errors that inevitably characterize field IP data acquisition. Complex conductivity inversion of the field IP dataset revealed that the organic plume is characterized as a region of high electrical conductivity (real part of complex conductivity) consistent with the conceptual model for the electrical structure of a biodegraded LNAPL contaminant plume. The plume is also characterized by a region of high polarizability (imaginary part of complex conductivity) that is more localized to the known plume location (based on conventional monitoring) relative to the high conductivity region in the electrical conductivity image. This observation is attributed to the fact that electrical conductivity is more strongly controlled by hydrogeological and geological characteristics of the site that mask the response from the biodegraded plume. This result encourages the use of field IP to improve the spatial delineation of organic contamination in the subsurface. However, more laborious field procedures are required to acquire reliable field IP data and the inversion of field IP data remains more challenging than resistivity data alone.

Tong, M. and Tao, H., 2008, Permeability estimating from complex resistivity measurement of shaly sand reservoir: Geophysical Journal International, v. 173, no. 2, p. 733-739, doi:10.1111/j.1365-246X.2008.03730.x.

Abstract: Permeability is a key parameter associated with the subsurface production and injection. This paper introduces a new method which uses the complex resistivity of rock to estimate permeability in petroleum reservoirs. Complex resistivity measurements were carried out on 53 shaly sand samples from Daqing Oil Filed with a wide variation in permeability and porosity in the frequency range from 100 Hz to 20 MHz using a four-electrode technique. This paper investigates the relationship between the complex resistivity measurements and the permeabilities of the samples. The imaginary part of the complex impedance shows a power-law relation to the frequency ranges from 100 Hz to 1.5 kHz. The results show that permeability can be estimated well with expressions of the form of A · φB · βC, where β is the slope of the bilogarthmic plot of the imaginary part versus frequency, φ is the porosity, A, B and C are constants. The salinity of NaCl has little influence of the slope in the range of 1–10 g l−1. The isovalue maps of the error factor δ, which show substantial regions of near-minimum values of δ, are used to analyse the behaviour of δ with the change of the exponents B and C. The permeability estimation is more sensitive to the changes of the slopes than the porosity. The slope and the porosity are not completely independent. The slope is the decisive parameter for the estimation of the permeability. The additional use of the porosity improves the formula fit to the data significantly.

References

Attwa, M., Günther, T., Grinat, M., and Binot, F., 2011, Evaluation of DC, FDEM, and IP resistivity methods for imaging perched saltwater and a shallow channel within coastal tidal flat sediments: Journal of Applied Geophysics, v. 75, no. 4, p. 656-670, doi:10.1016/j.jappgeo.2011.09.002.

Binley, A. and Kemna, A., 2005, DC Resistivity and Induced Polarization Methods, in Rubin, Y. and Hubbard, S.S., ed., Hydrogeophysics: Springer, Dordrecht, v. 50, p. 129-156, doi:10.1007/1-4020-3102-5_5.

Binley, A., 2015, Tools and Techniques: Electrical Methods, in Schubert, G., ed., Treatise on Geophysics: Oxford, UK, Elsevier, v. 11, p. 233-259, doi:10.1016/B978-0-444-53802-4.00192-5.

Cole, K.S. and Cole, R.H., 1941, Dispersion and absorption in dielectrics: Journal of Chemical Physics, v. 9, no. 4, p. 341–351, doi:10.1063/1.1750906.

Davis, C.A., Atekwana, E., Atekwana, E., Slater, L.D., Rossbach, S., and Mormile, M.R., 2006, Microbial growth and biofilm formation in geologic media is detected with complex conductivity measurements: Geophysical Research Letters, v. 33, no. 18, p. L18403, doi:10.1029/2006GL027312.

Dobrin, M.B., 1960, Introduction to Geophysical Prospecting: New York,NY, McGraw-Hill Book Company Inc., 446 p.

Flores, C. and Peralta-Ortega, S.A., 2009, Induced polarization with in-loop transient electromagnetic soundings: A case study of mineral discrimination at El Arco porphyry copper, Mexico: Journal of Applied Geophysics, v. 68, n. 3, p. 423–436, doi:10.1016/j.jappgeo.2009.03.009.

Binley, A., 2015, Tools and Techniques: Electrical Methods, in Schubert, G., ed., Treatise on Geophysics: Oxford, UK, Elsevier, v. 11, p. 233-259, doi:10.1016/B978-0-444-53802-4.00192-5.

Glover, P., 2015. Geophysical properties of the near surface earth: Electrical properties, in Schubert, G., ed., Treatise on Geophysics: Oxford, UK, Elsevier, v. 11, p. 89–137, doi:10.1016/B978-0-444-53802-4.00189-5.

Kemna, A., Räkers, E., and Binley, A., 1997, Application of complex resistivity tomography to field data from a kerosene-contaminated site, in Proceedings, Environmental and Engineering Geophysics Society: Aarhus, Denmark, European Association of Geoscientists and Engineers, p. 151–154, doi:10.3997/2214-4609.201407300.

Kemna, A., Binley, A., and Slater, L., 2004, Cross-borehole IP imaging for engineering and environmental applications: Geophysics, v. 69, no. 1, p. 97-105, doi:10.1190/1.1649379.

Lesmes, D.P. and Friedman, S.P., 2005, Relationships between the electrical and hydrogeological properties of rocks and soils, in Rubin, Y. and Hubbard, S.S., eds., Hydrogeophysics: Dordrecht, The Netherlands, Springer, p. 87-128.

Macnae, J., 2016, Quantifying airborne induced polarization effects in helicopter time domain electromagnetics: Journal of Applied Geophysics, v. 135, p. 495-502, doi:10.1016/j.jappgeo.2015.10.016.

Mussett, A.E. and Khan, M.A., 2000, Looking Into The Earth: An Introduction to Geological Geophysics: New York, Cambridge University Press, 470 p.

Mwakanyamale, K.E., Slater, L.D., Binley, A., and Ntarlagiannis, D., 2012, Lithologic imaging using induced polarization: Lessons learned from the Hanford 300 area: Geophysics, v. 77, no. 6, p. 397–409, doi:10.1190/geo2011-0407.1.

Oldenburg, D.W. and Li, Y., 1994, Inversion of induced polarization data: Geophysics, v. 59, no. 9, p. 1327–1341, doi:10.1190/1.1443692.

Pelton, W.H., Ward, S.H., Hallof, P.G., Sill, W.R., and Nelson, P.H., 1978, Mineral discrimination and removal of inductive coupling with multifrequency IP: Geophysics, v. 43, no. 3, p. 497-638, doi:10.1190/1.1440839.

Revil, A., Atekwana, E., Zhang, C., Jardani, A., and Smith, S., 2012, A new model for the spectral induced polarization signature of bacterial growth in porous media: Water Resources Research, v. 48, no. 9, 20 p., doi:10.1029/2012WR011965.

Reynolds, J.M., 1997, An introduction to applied and environmental geophysics: Chichester, UK, John Wiley & Sons, Ltd., 681 p.

Scott, W.J., 1971, Phase Angle Measurements in the IP Method of Geophysical Prospecting [Ph.D. Thesis]: Montreal, McGill University.

Seigel, H.O., 1959, Mathematical Formulation and Type Curves for Induced Polarization: Geophysics, v. 24, no. 3, p. 547-565, doi:10.1190/1.1438625.

Semmlow, J., 2017, Circuits, Signals and Systems for Bioengineers (3^rd Edition): Hartford, CT, Academic Press, p. 782.

Slater, L.D. and Lesmes, D., 2002, IP interpretation in environmental investigations: Geophysics, v. 67, no. 1, p. 14-325, doi:10.1190/1.1451353.

Sumner, J.S., 1976, Principles of Induced Polarization for Geophysical Exploration: New York, Elsevier, 277 pp.

Vinegar, H.J. and Waxman, M.H., 1984, Induced polarization of shaly sands: Geophysics, v. 49, no. 8, p. 1140-1395, doi:10.1190/1.1441755.

Wightman, W.E., Jalinoos, F., Sirles, P., and Hanna, K., 2003, Application of Geophysical Methods to Highway Related Problems: Lakewood, CO, Federal Highway Administration, Office of Bridge Technology, 742 p.