Introduction

Electrical methods can quickly provide estimates of the impurity content of an ice core with a resolution of a few millimeters. The electrical conductivity method (ECM; Reference HammerHammer, 1977; Reference HammerHammer and others, 1980) can detect volcanic events and measure acidity. Dielectric profiling (DEP) as a non-destructive method additionally yields estimates of salt and ammonia concentrations (Reference Moore, Paren and OerterMoore and others, 1992, 1994). We used the DEP method in the field to find well-known volcanic horizons and to estimate the age of ice being taken on a traverse in north Greenland in 1995.

ECM measures an ice core’s d.c. conductivity (Reference HammerHammer, 1980). The ice core is first microtomed, then two electrodes with a potential difference of 1000-2000 V arc dragged across its freshly cut surface. The resulting microampere current largely reflects the hydrogen ion concentration [H⁺]. We did not use this method during our traverse as we did not wish to cut up our ice cores.

The DEP method measures an ice cure’s a.c. capacitance and conductance (Reference Moore and ParenMoore and Pareil, 1987) at 12 frequencies between 20 Hz and 300 kHz. The core is placed between two curved electrodes which form a capacitor with the ice core as its dielectric. In our new device the electrodes are driven by a 250 kHz signal, and their a.c. capacitance and conductance are measured with an auto-balancing bridge. At this frequency the ice core’s conductivity and permittivity can be calculated immediately once the free air capacitance between the electrodes is known.

While trying to replicate the DEP instruments of Reference Moore and ParenMoore and Paren (1987) and Reference MooreMoore (1993), we were unable to obtain an exact solution of the instrument’s electrical properties, either its potential function or its free air capacitance, because its electrodes do not encircle the ice core (Reference WilhelmsWilhelms, 1996). Reference Moore and MaenoMoore and Maeno (1991) could only give a rough estimate of the free air capacitance of their DEP electrode geometry. By altering the electrode geometry, however, we obtain an exact solution using Green’s functions, and by modifying the guard electrodes we eliminate stray capacitances. Thus we are able to quantify precisely and improve

the device’s performance. Our DEP instrument is the consequence of the guarded capacitor method carefully applied to the ice core’s curved geometry

The Guarded Capacitor method and DEP

A DEP instrument is essentially a calibrated scanning capacitor that measures a section of ice core by having it serve as its dielectric. To measure just the bulk dielectric properties of an ice core, the design of a DEP instrument must circumvent three main sources of error.

Polar ice cores are normally measured at temperatures above -30°C, but should not be stored at temperatures above -10°C (Reynolds, 1985). Above -25°C an ice core’s surface conductivity becomes significant (Reference PetrenkoPetrenko, 1993). Reference Camp, Kiszenick, Arnold, Riehl, Bullemer and EngelhardtCamp and others (1969), for example, measured a surface conductivity that was 20% of the bulk conductivity in a polycrystalline ice sample at -11.6°C. A DEP instrument avoids surface currents using guard electrodes which force the electric field vector to enter and exit the sample perpendicular to its surface.

In a parallel-plate capacitor, guard electrodes are usually sufficient to avoid external stray capacitance. The curved electrodes of a DEP instrument, however, approach each other at the edges, so that a significant surface charge is influenced from the outside to some distance beyond the edges. A DEP instrument eliminates this exterior stray capacitance by external, electromagnetic shielding of the LO electrode (cf. Fig. 1).

When an ice sample contacts a metal electrode, the ice and metal partially exchange charges (Reference PetrenkoPetrenko, 1993). This exchange can be eliminated by inserting an insulating blocking layer between the sample and the electrodes (Reference Mounier, Sixou, Riehl, Bullemer and EngelhardtMounier and Sixou, 1969; Reference Gross, Wu and BryantGross and others, 1975), for example a thin film of Teflon (Reference Gross, Hayslip and HoyGross and others, 1980). Alternatively, in a modern DEP instrument, the blocking layer is achieved by anodizing the aluminum electrodes (Reference Wolff, Moore, Clausen, Hammer, Kipfstuhl and FuhrerWolff and others, 1995).

Fig. 1. Measurement of a guarded capacitor with blocking layers. The LO and H1 electrodes connect to the corresponding inputs of a Hewlett Packard 4284A Precision LCR Meter. The electrical shielding and the guard electrode connect to a physical ground, while the LO electrode connects to a virtual ground at ground potential.

Figure 1 shows a guarded, electrically shielded capacitor with blocking layers. Figures 2 and 3 show its realization as a DEP instrument with curved electrodes.

The first DEP instrument (Reference Moore and ParenMoore and Paren, 1987) had fixed lower and upper electrodes, a 108° HI electrode in which the ice core was placed and a 108° LO electrode, broken into 5 cm segments and scanned electrically using relays. A later version uses 2 cm segments (Reference Wolff, Moore, Clausen, Hammer, Kipfstuhl and FuhrerWolff and others, 1995). Curved guard plates were fitted at both ends, and flat guard plates were mounted alongside the HI and LO electrodes.

A second high-resolution 50 kHz DEP instrument had a fixed 108° HI electrode and a single, straight, guarded, 3 mm wide LO electrode which was moved by hand over the ice core (Reference MooreMoore, 1993). A later version, which inspired the present instrument, uses a curved EO electrode (Reference Friedmann, Moore, Thorsteinsson, Kipfstuhl and FischerFriedmann and others, 1995). Both instruments give a qualitative measure of changes in an ice core’s high-frequency conductivity. Because of their geometry, the electrical properties, such as the potential function or the free air capacitance, of the first four DEP instruments are inexactly known, even though the free air capacitance can be estimated (Reference Moore and MaenoMoore and Maeno, 1991).

Fig. 2. Schematic of the DEP instrument.

Fig. 3. Schematic of the electrode configuration.

The New Dep Instrument: Theory and Design

To know its electrical properties more precisely, we designed and tested a high-resolution instrument with an improved set of electrodes. Its potential distribution is easily calculated using Green’s functions, which allows substantially more accurate dielectric measurements of an ice core.

Proof of guarding

From the potential, Reference WilhelmsWilhelms (1996) calculated the components of the electrical field normal and tangential to the ice core’s surface. The ratio of the tangential to the normal component over the area scanned by the LO electrode is less than 0.03 if the diameter of the ice core is at least 0.98 electrode radians, our estimate of its minimum size. Assuming the ratio of the tangential and radial conductances is approximately 0.2 (Reference Camp, Kiszenick, Arnold, Riehl, Bullemer and EngelhardtCamp and others, 1969), the ratio of the corresponding currents will he less than 0.01. The guarding will thus reduce the surface currents to less than 1%, which is satisfactory.

Fig. 4. The portable DEP instrument in operation during the North Greenland Traverse, 1995.

Fig. 5. Calculated potential distribution both with and without an ice-cure sample. The electrodes and the upper (LO) electrode angle of 108° are drawn with a solid line. The upper (LO) and lower (HI) electrodes are at 1/2 unit positive and 1/2 unit negative potentials. The equipotential lines are in 1/10 unit potential steps from the horizontal zero line. The axes are in units of ice-core radians.

Results and Discussion

The improved DEP instrument obtains dielectric properties (Fig. 6) which agree very well with those calculated from the conductance value of σ _∞ = 1.9 ? 10^-5 S m^-1 for -20°C, the conductance value for Greenlandic glacial ice measured by Paren (1973, Fig. 1), with a parallel plate system.

The redesigned guard electrodes allow the measurement of precise conductivity values even at relatively high sample temperatures (here -10°C), temperatures at which surface currents would otherwise become excessive. Assuming the Reference LooyengaLooyenga (1965) mixing model and a permittivity for pure ice of 3.17, the instrument yields ice-core densities that agree with precise densities measured by γ absorption (Reference WilhelmsWilhelms, 1996; Fig. 7).

Despite its relatively broad width, the LO electrode’s improved geometry allows the instrument to reproduce many fine variations in the density (Fig. 8). Until now, such details could only be resolved by continuous γ-absorption measurements.

A calibration of the instrument’s HP 4284A LCR Meter suggests the high-frequency permittivity determined for an ice core has an error of 4.5%. The calibration suggests the conductivities have an error of 8-15% for core sections from below and above 30 m depth, respectively (Reference WilhelmsWilhelms, 1996).

Fig. 6. Measurements, with error bars of ice from a north Greenland ice core compared to the smooth electrical properties of pure glacier ice measured by Reference Paren, Whalley, Jones and GoldParen (1973) with a parallel plated capacitor set-up assuming the model of Reference JaccardJaccard (1959) and compensating for a density effect predicted by the Reference LooyengaLooyenga (1965) mixing model.

Fig. 7. Density predicted from permittivity by the Looyenga mixing model (shown with roughly 15% error bars) compared to density measured by γ absorption with an error of 0.006 Mg m³ (solid line).

A better bridge would increase the accuracy of the measurements, as would a longer LO electrode. Λ longer LO electrode, however, would decrease the resolution.

The much higher precision of our DEP instrument opens up new possibilities for analyzing the initial firn section of ice cores. We plan to extend the method to low frequencies through tight control of the blocking layers. Preliminary lests on a north Greenland core show improved fitting to the Looyenga density model.

Fig. 8. Density predicted from permittivity by the Looyenga mixing model, compared to density determined from γ absorption measurements. The difference at 62.1 m is due to a volcanic horizon.