Controls on induced polarization in sandy unconsolidated sediments and application to aquifer characterization

Transcription

1 GEOPHYSICS, VOL. 68, NO. 5 (SEPTEMBER-OCTOBER 2003); P , 8 FIGS., 1 TABLE / Controls on induced polarization in sandy unconsolidated sediments and application to aquifer characterization L. D. Slater and D. R. Glaser ABSTRACT Resistivity and induced polarization (IP) measurements ( Hz) were made on clay-free unconsolidated sediments from a sandy, alluvial aquifer in the Kansas River floodplain. The sensitivity of imaginary conductivity σ, a fundamental IP measurement, to lithological parameters, fluid conductivity, and degree of saturation was assessed. The previously reported power law dependence of IP on ace area and grain size is clearly observed despite the narrow lithologic range encountered in this unconsolidated sedimentary sequence. The grain-size σ relationship is effectively frequency independent between 0.1 and 100 Hz but depends on the representative grain diameter used. For the sediments examined here, d 90, the grain diameter of the coarsest sediments in a sample, is well correlated with σ. The distribution of the internal ace in the well-sorted, sandy sediments investigated here is such that most of the sample weight is likely required to account for the majority of the internal ace. We find the predictive capability of the Börner model for hydraulic conductivity (K ) estimation from IP measurements is limited when applied to this narrow lithologic range. The relatively weak dependence of σ on fluid conductivity (σ w ) observed for these sediments when saturated with an NaCl solution ( S/m) is consistent with competing effects of ace charge density and ace ionic mobility on σ as previously inferred for sandstone. Importantly, IP parameters are a function of saturation and exhibit hysteretic behavior over a drainage and imbibition cycle. However, σ is less dependent than the real conductivity σ on saturation. In the case of evaporative drying, the σ saturation exponent is approximately half of the σ exponent. Crosshole IP imaging illustrates the potential for lithologic discrimination of unconsolidated sediments. A fining-upward sequence correlates with an upward increase in normalized chargeability M n, a field IP parameter proportional to σ. The hydraulic conductivity distribution obtained from the Börner model discriminates a hydraulically conductive sand gravel from overlying medium sand. INTRODUCTION Improved interpretation of induced polarization (IP) surveys requires better understanding of the physicochemical controls on IP measurements and the significance of measured IP parameters. Induced polarization is attributed to the presence of interfaces at which local charge concentration gradients result in a delayed voltage response in earth materials upon current stimulation (for review, see Ward, 1990; Schön, 1996). Two distinct interfaces are commonly recognized and attributed to IP signals. Electrode (or metallic) polarization occurs at interfaces between zones of electronic and ionic conduction, such as the interface between a metallic mineral grain and electrolyte (for review, see Ward and Fraser, 1967). The large IP anomalies associated with electrode polarization have been utilized in mineral prospecting for disseminated sulfides. Membrane (or boundary layer) polarization occurs at interfaces between zones of unequal ionic transport properties associated with clays distributed through a rock matrix (Marshall and Madden, 1959). Induced polarization is hence a method for mapping clay content (Vacquier et al., 1957; Ogilvy and Kuzmina, 1972). The presence of organic contaminants, particularly in clays, may also generate significant IP anomalies (Olhoeft, 1985; Vanhala et al., 1992; Börner et al., 1993). Manuscript received by the Editor July 26, 2002; revised manuscript received April 12, Formerly University of Missouri Kansas City, Kansas City, Missouri 64110; presently Rutgers University, Department of Earth and Environmental Sciences, 195 University Avenue, Room 407, Newark, New Jersey Islater@andromeda.rutgers.edu. University of Missouri Kansas City, 420 Robert H. Flarshiem Hall, 5100 Rockhill Road, Kansas City, Missouri dannyglaser@ hotmail.com. c 2003 Society of Exploration Geophysicists. All rights reserved. 1547

2 1548 Slater and Glaser Small yet measurable IP signatures are also observed in the absence of metals, clay particles, or organic contaminants (Vanhala and Soininen, 1995; Schön, 1996; Vanhala, 1997). In this case, the interface causing the IP response is that between a silica mineral grain and electrolyte. The ace of silicate minerals carries a net negative charge, which is balanced by counter ions attracted to the ace. These counter ions form two layers: a fixed (Stern) layer chemically absorbed to the grain ace and a diffuse layer extending into the pore space. Upon application of an electric field, charges migrate tangentially (conduction) and are displaced normally/tangentially (polarization). This interface response depends on the frequency of the electric field, ionic mobility, temperature, and grain mobility (Revil and Glover, 1998). The significance of this polarization in relation to physical properties of clay-free, near-ace sediments is studied in this paper. Understanding induced polarization requires a model for the low-frequency electrical properties of earth materials. Theoretically based three-phase (dry mineral grain, pore fluid, and interface phase) effective medium theories are available (e.g., Bussian, 1983; Samstag and Morgan, 1991). A simpler approach that is easily adaptable to IP interpretation is based on modeling parallel ion transport paths through pore-filled fluids and at the grain fluid interface (Marshall and Madden, 1959; Waxman and Smits, 1968; Vinegar and Waxman, 1984; Börner et al., 1996; Schön, 1996; Lesmes and Frye, 2001). Lesmes and Frye (2001) review how standard measures of IP are related to such a parallel pathway model. In this paper we report low-frequency electrical measurements on clay-free unconsolidated sediments obtained from a sequence of alluvial deposits. We show that previously identified relationships between IP measurements and lithological parameters are discernible even when lithologic variability is restricted to a narrow range as encountered in a sequence of sandy deposits. However, results from this study suggest that the correlation between a representative grain diameter and IP parameters will depend on the particle-size characteristics of the material. We also show that IP parameters are a function of saturation and exhibit hysteretic behavior over a drainage and imbibition cycle. The results of a crosshole survey are included to illustrate how lithologic variability and hydraulic conductivity might be inferred from high-resolution IP surveys. LOW-FREQUENCY ELECTRICAL PROPERTIES Electrical model Measured complex conductivity σ is expressed in terms of conductivity phase shift φ and magnitude σ, or by the real σ and imaginary σ components, σ = σ e iφ = σ + iσ. (1) The real component is a representation of current flow in phase with the applied electric field, while the imaginary component is the displacement of current 90 out of phase with the applied field. There are two pathways for electric charge transfer within a medium: electrolytic (volumetric) conduction occurring through fluids in interconnected pore spaces and ace (interface) conduction occurring within an ionic double layer at the grain fluid interface. A simple model for the low-frequency electrical properties of earth materials is obtained by adding electrolytic and ace conduction pathways in parallel (e.g., Marshall and Madden, 1959; Vinegar and Waxman, 1984; Börner et al., 1996; Lesmes and Frye, 2001). At low frequencies (<1000 Hz), the complex conductivity is then σ = σ el + σ (ω) = [σ el + σ (ω)] + iσ (ω), (2) where σ el is the conductivity of the electrolytic path through the pore space and where σ and σ are frequency (ω) dependent real and imaginary components of the complex ace conductivity σ, respectively. Thus, σ represents interface current flow in phase with the applied electric field and σ represents diffusive interface polarization. This model assumes that measured imaginary conductivity is only a function of the ace (interface) conductivity, whereas the real conductivity is a function of both electrolytic and ace (interface) conductivity mechanisms. In clay-free sediments σ el σ such that σ σ el. The electrolytic conductivity σ el is considered independent of frequency when measured below 1000 Hz and given by σ el = ( 1 F ) σ w S n = σ w φ m eff Sn, (3) where σ w is the fluid conductivity, F is the formation factor related to the tortuosity of the electrolytic conduction path in a saturated medium, φ eff is the effective porosity for electrolytic current flow, m is a function of effective grain diameter (Sen et al., 1981), S is the degree of saturation, and n is a material specific saturation exponent quantifying the dependence of σ el on saturation (Archie, 1942; McNeill, 1990). Surface conduction The specific ace conductance s in a quartz-electrolyte system is a function of the ace area S 0, ace ionic charge density 0, and ace ionic mobility μ s : = eμ s 0 S 0, (4) s where e is the electronic charge. (Revil and Glover, 1998; Revil et al., 1998; Lesmes and Frye, 2001). Ionic charge density and ionic mobility generally depend on fluid chemistry. At low frequencies σ approaches the dc ace conductivity σ (dc), which is related to s via a geometric factor with units of length and is a characteristic of the geometry of the medium (Johnson et al., 1986; Pride, 1994; Revil and Glover, 1998). Johnson et al. (1986) define a geometric parameter, which they envisage as a weighted volume ace area ratio and a measure of the dynamically interconnected pore size such that lim σ = σ (dc) = 1 ( ) 2 s. (5) ω 0 F Revil and Cathles (1999) provide an expression for in natural earth materials as a function of a representative grain diameter R r : R r = m(f 1). (6) Consequently, in saturated earth materials σ is primarily determined by s, which is the product of o, μ s, and S 0 and is

3 Controls on induced polarization 1549 inversely related to a representative or average grain diameter R r through. Induced polarization parameters measured using field instruments include chargeability M, phase angle φ, and percent frequency effect (PFE). These equivalent parameters measure the ratio of interface polarization to the combined strength of electrolytic and ace conduction. The chargeability and PFE field parameters can be scaled by the conductivity magnitude to obtain normalized field parameters: normalized chargeability M n and metal factor M F, respectively (Keller, 1959; Marshall and Madden, 1959). These normalized field parameters are equivalent to σ and hence are sensitive to ace (interface) properties as in equations (4) (6). Lesmes and Frye (2001) review field IP and normalized IP parameters and their relationship to the model for low-frequency electrical properties described here. Previous experimental work Relationships between measures of the internal ace and imaginary conductivity terms have been shown in sandstone (e.g., Knight and Nur, 1987; Börner and Schön, 1991) and unconsolidated sediments (Börner et al., 1996; Slater and Lesmes, 2002). Börner and Schön (1991) identify a strong relationship between internal ace area normalized at total volume (S tot ) and ace conductivity. When porosity varies widely, the internal ace normalized to the pore volume (S por ) may correlate more closely with the ace conductivity (Börner et al., 1996). Schön (1996) reports an inverse relationship between median grain diameter (d 50 ) and σ in unconsolidated sediments. Slater and Lesmes (2002) illustrate an inverse relationship between grain size for which 10% of the sample is finer (d 10 ) and σ when applied to artificial sand clay mixtures and natural unconsolidated sediments. The dependence of σ on structural parameters encouraged the prediction of hydraulic conductivity K using IP measurements (Börner et al., 1996; De Lima and Niwas, 2000; Slater and Lesmes, 2002). These studies suggest that orderof-magnitude K estimates are obtainable for unconsolidated sediments and sandstone when K varies over three or more orders of magnitude. The Börner model, based on a modified (electrical) Kozeny-Carmen equation, is an attractive electrical approach to K estimation. It utilizes a complex conductivity measurement in conjunction with a fluid conductivity measurement to predict K. Estimates of formation factor F and S por are required in the electrical version of the Kozeny-Carmen model (Börner et al., 1996). When σ el σ, σ σ el and F of a saturated medium can be estimated if σ w is known [Equation (3)]. The measured imaginary conductivity σ provides an electrical estimate of S por.thebörner model is given as K = a FS c por[el] = a F ( ) 10 5 σ c, (7) [1Hz] where S por[el] is the electrically estimated S por, a = , and c ranges between 2.8 and 4.6, depending on material type. A general version of the model permitting different parameters for the relationship between specific ace and imaginary conductivity is K = A F ( ) σ c, (8) [1Hz] where A is a fitting parameter. Since ace charge density and ace ionic mobility are both modified by fluid chemistry, σ is observed to vary with σ w (Börner et al., 1993, 1996; Revil and Glover, 1998; Lesmes and Frye, 2001). Relative to σ el, ace conductivity exhibits weak σ w dependence (Vinegar and Waxman, 1984; Revil et al., 1998; Lesmes and Frye, 2001; Slater and Lesmes, 2002). Lesmes and Frye (2001) attribute the σ behavior of Berea Sandstone saturated with NaCl to the competing effects of ace charge density and ace ionic mobility with increasing pore solution concentration. Very few studies of the dependence of σ on degree of saturation are reported. Vinegar and Waxman (1984) investigate changes in σ with water saturation for an oil water system. They find that σ exhibits power law dependence on the degree of water saturation. However, the saturation exponent for σ is approximately half the exponent for σ. STUDY SITE The City of Olathe well field is located on the Kansas River floodplain near Desoto, Kansas. Installation of a horizontal collector well is planned to enhance yield and provide adequate water supply for the city. Limestone bedrock is overlain with a 14-m-thick sand aquifer (fining-upward sequence) capped by a 3 4-m-thick silt layer. The range of saturated aquifer thickness throughout the river valley is 0 30 m, averaging 13 m at the field site. Depth to the water table is approximately 10 m. Four wells were drilled in 2001 for sample retrieval and piezometer installation as part of an aquifer pump test to constrain horizontal well design. A Rotosonic vibratory drilling method was used to advance the core barrel and retrieve an unconsolidated sediment sample. This method was developed to obtain undisturbed core samples from unconsolidated aquifers. However, the coarse, granular matrix of this aquifer was of insufficient integrity to support a sample on removal. Consequently, only disturbed samples of aquifer material were obtainable for laboratory tests. Piezometers constructed from PVC tubing were screened over the full vertical distance of the aquifer and installed in the wells. Electrodes for crosshole electrical imaging were installed on piezometers in two wells spaced 10 m apart. Ideally, we would have used nonpolarizing electrodes, such as Pb-PbCl junctions or platinum electrodes (e.g., Weller et al., 1996). However, excessive cost and awkward implementation in boreholes ruled against this approach. Dahlin et al. (2002) show that, by using signal processing to correct for the electrode polarization at potential electrodes, stainless steel electrodes can give IP measurements of similar quality to that obtained with Pb-PbCl electrodes. This processing procedure is standard to the IRIS Syscal R1 instrument used in this study. Stainless steel mesh electrodes were wrapped around the outside of the piezometer at 0.64-m intervals between 4 and 18 m depth. Electrical contact in the unsaturated zone was achieved by grouting over the full length above the water table. Contact resistance between electrode and formation ranged from 0.1 to 10 k-ohm, with higher values in the unsaturated zone.

4 1550 Slater and Glaser Laboratory measurements EXPERIMENT The inherent difficulty in retrieving sandy unconsolidated sediments often limits laboratory electrical studies to repacked samples. The degree to which laboratory relationships apply at the field scale is a consideration. One can reasonably assume that grain-size distribution and ace area of the repacked sample will be representative of the in-situ material, given careful sample handling. These are the primary physical properties influencing the IP measurements discussed here. The total porosity, effective porosity, grain orientation, and possible anisotropy in grain orientation of repacked samples are unlikely to represent the in-situ condition because they will depend on the packing procedure. Laser particle-size analysis was used to determine the grainsize distribution for all samples. Twelve samples from the aquifer, six per well, were selected as representative of the range of grain-size characteristics encountered in this aquifer. Figure 1 shows the grain-size curves for four of the twelve FIG. 1. Grain-size distribution obtained from laser particle-size analysis for 4 of the 12 samples used in this study. The selected samples span the range of grain size encountered in these materials. samples used in this study. Selected samples shown in Figure 1 span the range of grain sizes in this study and illustrate that the aquifer is composed of well-sorted sands. Specific ace area was measured using a nitrogen BET method. Effective porosity φ eff is difficult to measure and was not determined in this study. However, total porosity φ tot, likely to be close to φ eff in these loosely packed sediments, was determined from wet and oven-dried weight measurements. Mineralogy was investigated using X-ray diffraction, and major/minor constituents were identified with the help of a computer program. Quartz was the only major mineral present in the twelve samples. Albite, microcline, and albide were detected as trace constituents in some samples. The results of laser particle-size analysis indicate that clay-size particles constitute negligible sample mass for all samples (Figure 1). Thus, the samples are considered effectively devoid of clay minerals and clay particles. Hydraulic conductivity K was measured using standard flow tests for sandy unconsolidated sediments (American, 1997). Measurements were made at four discharge velocities, and mean K and standard deviation σ dev were estimated. Electrical measurements were made for six NaCl solutions with σ w varying between 0.01 and 10 S/m. Formation factor F was estimated from the gradient of σ σ el versus σ w [Equation (3)]. This estimate assumes that σ is insignificant, deemed appropriate for these coarse, clay-free materials and verified by linearity in the plot of σ versus σ w. Table 1 summarizes sample physical properties and associated error estimates. A modified permeameter was used for simultaneous measurement of electrical and hydraulic properties on saturated, repacked samples (Figure 2). Four electrode electrical measurements were obtained with a National Instruments NI 4551 dynamic signal analyzer. Phase shift between current stimulusvoltage signal φ, i.e., between channel 1 and channel 2 in Figure 2, and conductivity magnitude σ were measured at 40 frequencies, spaced at equal logarithmic intervals, between 0.1 and 1000 Hz. Current was injected at silver coil electrodes located at sample ends. Sample voltage was measured using silver silver chloride point electrodes located just outside the current flow path. An AD620 preamplifer boosted the input impedance on the voltage channel and prevented current leakage into the circuitry (Figure 2a). The phase response of the Table 1. Measured physical properties of unconsolidated sediments from the Olathe study site, Kansas River floodplain: d 10 = grain diameter for which 10% of sample is finer by weight; d 90 = grain diameter for which 90% of sample is finer by weight; φtot = total porosity; Ss = specific ace area; F = formation factor (ND indicates not determined). d 10 d 90 S s Sample (m) (m) φ tot (m 2 /g) F N E E N E E N E E N E E ND N E E N E E N E E N E E N E E N E E N E E N E E error ±3.4% ±3.4% ±0.01 ±0.01 ±0.01

5 Controls on induced polarization 1551 preamplifier, which depends on frequency and sample resistance, was removed by obtaining a calibration on a precision resistor matching the sample resistance (Figure 2b). Real and imaginary conductivity were calculated from equation (1). Accuracy in the conductivity estimates was primarily determined by error in the phase measurement. Repeatibility tests indicate that relative errors are generally less than 5% and 1% for σ and σ, respectively (Slater and Lesmes, 2002). Prior to σ measurements, samples were flushed until outflow σ w matched inflow σ w, at which point pore σ w was considered known. Changes in pore σ w from ion exchange between the mineral ace and free electrolyte were not quantifiable but were assumed small because of the low cation exchange capacity (CEC) of coarse, clay-free sediments. Figure 3 shows the real and imaginary conductivity plotted as a function of frequency for all 12 samples. As σ σ el in these samples, σ is essentially frequency independent (Figure 3a). The frequency dependence of the imaginary conductivity (σ = σ ) is illustrated in Figure 3b. For most of the samples, σ is only weakly frequency dependent between 0.1 and 100 Hz. Some samples show power law dependence across the entire frequency range (e.g., N and N ) as previously reported for unconsolidated sediments and weakly consolidated sandstone (Börner et al., 1996). Other samples exhibit increased frequency dependence, with σ (ω) increasing more rapidly above 100 Hz (e.g., N and N ). These differences in σ (ω) may reflect differences in the grain/pore-size distribu- tion between samples. Lesmes and Morgan (2002) suggest that the relative proportion of grains with a certain radius determine the magnitude of σ (ω) at a particular frequency. Smaller repacked samples (length = 63 mm; radius = 25 mm) were constructed to investigate the dependence of σ on saturation in these materials. Degree of saturation was varied in two ways. Evaporative drying by exposure of the sample to air was one approach. Degree of saturation was determined from the weight loss associated with evaporative drying. These small samples were also interfaced with a high-precision syringe pump permitting accurate withdrawal and infusion of water. This allowed investigation of the dependence of σ on saturation over a drainage and imbibition cycle. Field measurements Crosshole electrical measurements were made between the two boreholes installed with electrodes at the Olathe well field. All measurements were made using an electrode configuration whereby voltage and current pairs were split between the two boreholes (bipole bipole configuration). Bing and Greenhalgh (2000) numerically illustrate that this electrode geometry provides good image resolution relative to other frequently used crosshole electrode configurations. The measurement sequence consisted of 1380 measurements and 1380 corresponding reciprocals (whereby the current and voltage pairs are exchanged), addressing 48 electrodes (24 per borehole). Relative reciprocal errors were generally less than 3% for the conductivity magnitude, with outliers discarded from the inversion. Chargeability error is better quantified by the absolute reciprocal error, as many low chargeability (<5 mv/v) measurements are obtained. Chargeability reciprocal errors were generally less than 1 mv/v, with outliers again discarded from the inversion. The data set was inverted by A. Binley using code developed at Lancaster University (see Kemna and Binley, 1996; Kemna et al., 1999). This 2D algorithm, based on an Occam s procedure (degroot-hedlin and Constable, 1990), implicitly assumes that the electrical structure in the third dimension is constant. The real world is rarely two dimensional. However, this approximation is relatively appropriate for such a sedimentary sequence, at least over the horizontal sensitivity of the electrical measurements (<10 m). Lithologic logs from four wells drilled over 20 m at the site, as well as ace resistivity measurements, support this assumption. The inversion requires measurements of σ and φ as input data. However, because of the equivalence between field and normalized IP parameters, we substituted measures of M for φ. The output from the algorithm is then the distribution of σ and a scaled phase angle, i.e., M. Similarly, the distribution of scaled measures of σ, simply defined as σ field, and σ, being the normalized chargeability M n (Lesmes and Frye, 2001), were obtained. RESULTS Laboratory results FIG. 2. (a) Schematic of instrumentation used to obtain low-frequency ( Hz) electrical measurements for sandy, unconsolidated sediments, (b) Example of measured phase φ for a sample calibration resistor and the corrected sample. In conductivity space, a positive phase is a capacitive effect. Figure 4 illustrates the dependence of measured electrical parameters on sample structural properties. Structural controls on electrolytic conductivity are assessed using F, which is the ratio of σ w to σ el [Equation (3)] and hence the ratio of σ w to σ when σ el σ (i.e. at high σ w ). Controls on magnitude of ace

6 1552 Slater and Glaser conductivity are assessed using σ (1Hz) to σ (1Hz) [equation (2)]. which is considered equal Formation factor versus φ tot (Figure 4a) follows an Archie relationship [equation (3)] with m = 1.6 ± 0.1, typical for unconsolidated sediments (e.g., Schön, 1996). The weak correlation coefficient reflects the limited φ tot range ( ) for these materials. The imaginary conductivity (i.e., σ ) approximates a linear dependence on S tot (Figure 4b) and also correlates with S por. For our samples σ is slightly better correlated with S tot than with S por. The correlation between grain size and σ depends on the percentage of the sample weight used to define the representative grain size. Figure 4c shows only a weak relationship between σ and d 10 for samples measured in this study. However, the σ dependence on grain diameter is clear when d 50 (the grain diameter for which 50% of the sample is finer by weight) or, better still, d 90 (the grain diameter for which 90% of the sample is finer by weight) is used as the representative grain-size parameter (Figures 4d and 4e). The correlation between representative grain-size parameter and σ is effectively frequency independent between 1 and 100 Hz, and R 2 (defining the strength of the correlation) increases smoothly from d 10 to d 90. Figure 5 illustrates the predictive capability of the Börner model for K estimation [equation (8)] when applied to these sediments. Least-squares regression of our data set yields c = 1.4 and A = with K in m/day and σ in S/m. Hydraulic conductivity predicted using the Börner model is plotted versus that measured with flow tests. The hydraulic conductivity of five of the eleven samples is well predicted. For the remaining six samples the predictive capability of the model is a little less than an order of magnitude. Note that the measured hydraulic conductivity spans only two orders of magnitude in these sediments. Figure 6 shows the dependence of measured σ and σ on σ w for four NaCl-saturated samples. The linear σ increase with increasing σ w reflects the dominance of σ el over σ in these samples and follows from equation (3). All four samples exhibit an increase in imaginary conductivity (σ = σ ) with increasing σ w at low σ w. An apex is observed, after which σ decreases with further increase in σ w. The position of the apex varies between samples but lies within S/m. Figure 6 illustrates that σ is much less σ w dependent than σ el. Within the σ w range of S/m, often typical of natural groundwater, σ is approximately constant for these samples. FIG. 3. Plots of (a) σ (ω) and (b) σ (ω) over the frequency range Hz for the 12 sandy unconsolidated sediments examined in this study. For these clay-free samples, σ σ el and is thus frequency independent to the first order.

7 Controls on induced polarization 1553 Figure 7 illustrates the dependence of σ and σ on saturation for sample N Figure 7a shows the change in the conductivity terms as the sample is dried by evaporation from S = 1toS = As a first approximation we fit single σ and σ saturation exponents to the entire saturation range. The σ σ el saturation exponent n [equation (3)] is 1.3 ± 0.1, and the saturation exponent for σ is 0.6 ± 0.1. Similar saturation dependence is also observed for two additional measured samples, with the σ saturation exponent consistently about half the σ saturation exponent. Figure 7b illustrates the dependence of σ and σ on saturation as water content in sample N is varied through a pressure drainage and imbibition cycle over the range S = 1toS = Hysteresis in both the σ and σ responses to saturation is observed, with higher values occurring during imbibition from S = The smaller sampling interval in saturation space achieved with the pressure drainage and imbibition experiments illustrates that saturation exponents vary over the saturation range. FIG. 4. Observed relationships between electrical measurements (1 Hz) and physical properties of unconsolidated sandy sediments. (a) Comparison of measured data (circles) and relationship given in equation (3), assuming φ tot φ eff (exponent m from least-squares minimization = 1.6 ± 0.1, R 2 = 0.58). (b) Squares: approximate linearity between σ and S tot, showing the best-fit relationship σ = (S tot ) 1.1±0.2 (R 2 = 0.66); triangles: relationship between σ and S por, showing best-fit relationship σ = (S por ) 1.2±0.3 (R 2 = 0.59). (c) Observed relationship between σ and d 10. (d) Observed correlation between σ and d 50, showing the best-fit relationship σ = 10 8 (d 50 ) 1±0.3 (R 2 = 0.54). (e) Observed correlation between σ and d 90, showing the best-fit relationship σ = 10 8 (d 90 ) 1.1±0.2 (R 2 = 0.65).

8 1554 Slater and Glaser FIELD RESULTS Figure 8 shows the results of electrical imaging correlated with summary lithologic logs. Sample locations and d 90 values obtained in the laboratory are also shown for comparison. The lithology consists of a general fining-upward sequence of sandy sediments overlain by silty clay. The groundwater ace falls within the fine medium sand unit at 10 m depth, approximately 2 m below the interface with the overlying fine sand. FIG. 5. Comparison of hydraulic conductivity predicted using the Börner model (K pred ) and that measured from flow tests on laboratory samples (K meas ). The straight line shows the 1:1 relation. The M n image shows a clear correlation with lithology in the sandy sediments and is consistent with the laboratory findings. There is an increase in M n throughout the fining-upward sequence and, given the difference in scale between laboratory and field measurements, a reasonable inverse correlation between M n and d 90 obtained from samples. Boundaries between major lithologic units at approximately 8 and 14 m correlate with shifts in the M n image. Note that M n is not strongly affected by the groundwater ace. The σ field image generally shows weaker correlation with lithology, although the interface between the fine sand and fine medium sand is well resolved. The overlying silty clay exhibits high σ field, presumably as a result of high σ. (Laboratory measurements of this material were not made.) High σ field in the fine sand may reflect high σ w of capillary-held pore fluid, supplied by ion-rich water percolating through the overlying silt/clay. The groundwater ace at 10 m affects σ el and hence σ field, causing an image structure within the fine medium sand that is unrelated to lithology. The interface between saturated and unsaturated fine medium sand causes a decrease in σ field above 10 m. Figure 8c is an image of the predicted hydraulic conductivity distribution based on the Börner model [equation (8)] using model parameters estimated from the laboratory measurements. The image is truncated above the groundwater ace as the model assumes saturation. The formation factor for each pixel in the image was estimated from the ratio of σ w measured in a well (0.09 ms/m) at the site to the pixel real conductivity (σ field ). This calculation assumes that measured σ w is representative of the pore fluid throughout the image zone and that σ field σ el. The validity of the first assumption is somewhat FIG. 6. Measured σ and σ (1 Hz) as a function of σ w for an NaCl solution: (a) N , (b) N , (c) N , (d) N ( =σ, =σ ).

9 Controls on induced polarization 1555 FIG. 7. (a) Measured σ and σ (1 Hz) as a function of saturation during evaporative drying of sample N The σ σ el saturation exponent n [equation (7)] is 1.3 ± 0.1 (R 2 = 0.98), and the saturation exponent for σ is 0.6 ± 0.1 (R 2 = 0.96). (b) Measured σ and σ (1 Hz) as a function of saturation during pressure drainage (triangles) and subsequent imbibition (circles) for sample N FIG. 8. Inversion result for 2D crosshole electrical survey at the Olathe field site correlated with site lithology, (a) M n with d 90 values obtained from laser particle-size analysis superimposed. (b) σ field. (c) Predicted hydraulic conductivity obtained with the Börner model. The M n color scale covers three orders of magnitude, whereas the σ field color scale covers only one order of magnitude. The groundwater ace falls within the fine medium sand unit at 10 m depth, approximately 2 m below the interface with the overlying fine sand.

10 1556 Slater and Glaser uncertain. The latter assumption is reasonable given the absence of clays and the relatively high fluid conductivity. Value M n was directly substituted for σ in the model. The basal sand and gravel layer is imaged as a hydraulically conductive zone, with K pred reaching 100 m/day. The overlying fine medium sand layer is imaged as a region with K pred 1 m/day. DISCUSSION Significance of laboratory measurements Our results illustrate the controls on induced polarization in sandy, unconsolidated sediments. The internal ace area is a fundamental lithological parameter controlling σ in these sediments. We find that σ is better correlated with the ace area normalized to the total volume S tot than with the ace area normalized to the pore volume S por.börner et al. (1996) find that using S por rather than S tot improves the correlation with σ when porosity varies considerably. Our result probably reflects the limited porosity range typical of sandy unconsolidated sediments (A. Weller, 2002, personal communication). Observed relationships between σ and representative grain-size parameters will vary, depending on how the ace area is distributed across the grain-size distribution. Consider first a material in which less than 10% of its weight accounts for most of its internal ace. In this case a strong correlation between σ and d 10 is expected. Sands with significant clay content fit this category because most of the ace area is associated with the finer clay particles (S o 1/R r ). The artificial sand clay mixtures and glacial till samples described in Slater and Lesmes (2002) match this description and illustrate a strong correlation between σ and d 10. In the case of coarse, well-sorted sandy samples described in our study, most of the sample weight is required to account for the majority of the internal ace. The imaginary conductivity then correlates with a representative grain diameter for which the majority of the sample is finer (d 90 ), as we observe. Relationships observed in Figures 4c 4e thus reflect the distribution of the specific ace across the grain size in these samples. Presumably, the strong correlation between σ and d 50 shown in Schön (1996) reflects the wide range of material type for which the median grain size accounts for most of the internal ace. Relationships between σ and effective grain diameter determined for natural materials thus depend on the grain-size distribution and how this controls the distribution of the internal ace. Consequently, any relationship between σ and effective grain diameter is site dependent. The predictive capability of the Börner model for K estimation from IP measurements is somewhat restricted by the limited K range typical of unconsolidated, sandy sediments. Börner et al. (1996) conclude that order-of-magnitude K estimates were achievable with this model when applied to a large range of material types. In our study, K varies by less than two orders of magnitude, and the predictive capability of the model when applied to these sediments is slightly better than an order of magnitude. The characteristic shape of the σ dependence on σ w observed for unconsolidated, sandy sediments is very similar to that observed by Lesmes and Frye (2001) for Berea Sandstone. They interpret this shape in terms of competing effects of ace charge density and ace ionic mobility on ace conductivity. Adopting this interpretation, we find that below about 0.5 S/m the increase in ace charge density with increasing σ w dominates the decrease in ace ionic mobility with increasing σ w. Consequently, σ increases with increasing σ w. Above about 1 S/m the effect of decreasing ace ionic mobility with σ w increase dominates, and the relationship between σ and σ w reverses. Fluid conductivity generally exerts a weak control on σ, relative to its control on σ σ el, in these clay-free unconsolidated sediments. Within a typical σ w range for natural groundwater, σ is approximately invariant in sandy, unconsolidated sediments. However, little is known about how the σ dependence on σ w varies with clay mineralogy, clay content, and clay distribution (addressed by Wildenschild et al., 2001) throughout the matrix. Clay is characterized by high CEC, which may enhance changes in ace chemistry with varying σ w. We thus recognize a need to expand studies of the controls of fluid chemistry on ace conductivity to a wider range of earth materials, particularly clay containing unconsolidated sediments. We show that ace conductivity is saturation dependent in sandy, unconsolidated sediments. During evaporative drying we observe that the saturation exponent for σ is approximately half that for σ, i.e., σ is much less dependent on saturation. Vinegar and Waxman (1984) report a similar relationship between real and imaginary saturation exponents for sandstone samples when oil is the nonconducting, porefilling medium. Hysteresis in the σ versus saturation curve (as observed in our data) is well documented and generally attributed to differing distributions of pore fluid resulting from drainage and imbibition processes (e.g., Longeron et al., 1989; Knight, 1991). To the best of our knowledge, we show the first results that illustrate hysteresis in the σ versus saturation response during drainage and imbibition. The cause of the σ dependence on saturation is uncertain and complicated by the fact that ace conduction may exist at the air fluid interface, as well as the solid fluid interface, in unsaturated sediments (Knight, 1991). A detailed discussion of mechanisms causing the dependence of σ our paper. Relevance to other applications on saturation is beyond the scope of Our laboratory studies indicate that ace conductivity in sandy, unconsolidated sediments is strongly dependent on lithological properties and is less dependent on fluid conductivity and saturation of the pore space. In contrast, σ measured in resistivity and electromagnetic surveys is highly dependent on fluid conductivity and saturation, which may limit successful interpretation of these geophysical measurements in terms of lithologic variability. Our discussion thus favors the use of IP for investigating lithologic variability in near-ace, unconsolidated sediments. Relationships between σ and lithologic parameters exist even when lithologic variability is relatively small, such as in the sandy aquifer studied here. Our field study provides an example of the potential significance of the current study to geophysical investigations. Fieldscale crosshole electrical imaging in this sandy aquifer demonstrates that subtle lithologic variability is resolvable from an IP image. Any dependence of IP on saturation, which would manifest itself as a decrease in M n above the groundwater ace, is minor relative to the influence of lithologic variability. In

11 Controls on induced polarization 1557 contrast, the conductivity image (i.e., σ field ) is less well correlated with the site lithology and is significantly influenced by the position of the groundwater ace. This field example also demonstrates how the Börner model might be used to depict order-of-magnitude or greater hydraulic conductivity variability from crosshole IP surveys in sandy sediments. The prediction of hydraulic conductivity from geophysical measurements continues to receive considerable attention. The Börner model is an attractive approach, as it has a semitheoretical basis and only requires an estimate of the groundwater conductivity in addition to the geophysical measurement. However, the predictive capability of this model in unconsolidated sandy aquifers is limited by the relatively narrow range of K in such materials. CONCLUSIONS This study illustrates that previously identified relationships between IP measurements and lithological parameters are discernible even when lithologic variability is restricted to a narrow range, as is typically encountered in a sequence of sandy deposits. However, the correlation between a representative grain diameter and IP measurements depends on the particlesize characteristics of the material. In the case of well-sorted, sandy sediments, IP measurements correlate most closely with measures of the coarsest fraction of the material. We find the predictive capability of the Börner model for K estimation from IP measurements is limited when applied to this narrow lithologic range of material type. Importantly, IP measurements are a function of saturation and exhibit hysteretic behavior over a drainage and imbibition cycle. Our results suggest that competing effects of ace charge density and ace ionic mobility on ace conductivity may explain the dependence of IP measurements on fluid conductivity in these materials. Results of crosshole electrical imaging of an alluvial sequence of sandy sediments illustrate how high-resolution IP measurements might be used to generate images of lithologic variability. The hydraulic conductivity distribution obtained from the Börner model successfully discriminates a hydraulically conductive sand/gravel from overlying medium sand. Further studies are required to better define the nature of ace conductivity in clay containing sediments as well as in unsaturated materials. ACKNOWLEDGMENTS This work was supported by National Science Foundation award EAR and American Chemical Society award PRF G2. Andrew Binley (Lancaster University, UK) performed the complex conductivity inversion using code developed at Lancaster. We thank D. Stous and C. 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