Dome C station (74°39'S 124°10'E, East Antarctica)

The measured apparent resistivities ρ_a are shown in Figure 1(a), along with calculated ρ_a models. Figure 1(b) shows the actual resistivities ρ for each model. Model 1 was calculated taking variations of density and temperature only into account. Temperatures were calculated from a steady-state model with bottom temperature at the pressure-melting point, using an activation energy of 0.25 eV. The other models in Figure 1 use the same temperature and activation energy as model 1, but also include additional changes in ρ with depth in the ice that have been chosen to provide better fits to the observed data, and at the same time to accord in some way with other measured physical or chemical properties at Dome C. This requires further explanation.

Fig. 1 (a). Plot of apparent resistivities vs electrode separation for two profiles at Dome C. The height of each symbol represents the standard deviation calculated from linear fits to plots of potential difference vs current. Only data at separations greater than 50 m are shown. The solid curves show apparent resistivities calculated from the actual resistivity-depth models shown in Figure 1(b). The upper and lower branches of model 2 correspond to assumed resistivities in the bedrock of ZOO and 50 kΩ m, respectively. (b). Actual resistivity vs depth in the ice sheet according to three different models (explained in the text).

Our procedure was to examine first the variation of impurities with depth in the core. However, no model of ρ(Z) generated using resistivities inversely dependent on the concentration of impurities such as salts (Reference Petit, Briat and RoyerPetit and others 1981), sulfates and acids (M Legrand personal communication), microparticles (Reference Mosley-Thompson and ThompsonMosley-Thompson and Thompson 1980), and CO₂ (Reference Delmas, Ascendo and LegrandDelmas and others 1980) could produce ρ_a models that match the observed data, because those impurities all show an increase with depth in the Wisconsin ice. On the other hand, there would be no physical basis for assuming a direct correlation between conductive impurities and ρ(z).

We therefore looked next at the measured physical properties. The principal change is in the crystal size (Reference Duval and LoriusDuval and Lorius 1980). Crystals increase in size between 90 and 400 m, and below 540 m; in between there is a marked decrease. The abrupt decrease in crystal size between 400 and 540 m is associated with the Holocene-Wisconsin boundary as determined by the oxygen isotope ratios (Reference Lorius, Merlivat, Jouzel and PourchetLorius and others 1979). In this case, we found that the observed apparent resistivities could be fitted with models of ρ(z) that were qualitatively similar, i.e. that showed the same saw-tooth shape as the crystal-size variation in their deviation from the basic ρ(z) model (model 1). This is shown in Figure 1 by both model 2 and model 3, which do not differ at depths or separations less than 1500 m.

The lower curve, marked model 2 in Figure 1(a), clearly does not fit the observed apparent resistivities at separations greater than 2 or 3 km. To produce a fit, it is necessary to increase the resistivity somewhere at considerable depth, either in the ice (model 3 below a depth of 1 700 m) or in the underlying bedrock. The upper curve, marked model 2 in Figure 1(a), is based on the same resistivities in the ice as the lower (model 2) curve, but includes a very high resistivity of 200 kΩ m in the bedrock. Both the lower branch of model 2 and model 3 incorporate a bedrock resistivity of 50 kΩ m, still a high value (Reference Shabtaie, Thyssen and BentleyShabtaie and others 1982). Resistivities lower than 50 kΩ m in the bedrock can be accommodated by assuming still higher resistivites in the deep ice.

Although there is no obvious reason why resistivity should increase with crystal size, it is possible that variation may have been controlled by climatic change, i.e. that the history and age of polar ice influences its electrical properties. Regardless of the cause(s) of the resistivity changes, the correlation suggests that resistivity measurements could be used to estimate the depth to the climatic boundary.

Station J9 (82°21'S 168°39'W, Ross Ice Shelf, Antarctica)

Station J9 is the site of the Ross Ice Shelf (RISP) drill camp and is downstream from ice stream B. Limited information on isotopic ratios (δ¹⁸O) (P M Grootes personal communication), crystal cross-sections (I Zotikov and A J Gow personal communication), and ionic impurities (Reference Herron and LangwayHerron and Langway 1979) are available. Both the isotopic ratios and the crystal cross-sections reveal a distinct climatic boundary at about 275 m depth.

The measured ρ_a profile and four different models are shown in Figure 2(a). All models are based on temperature and density measured from the bore hole, with the activation energy of 0.25 eV for both snow and solid ice. The calculated ρ models are shown in Figure 2(b). Model 1 is calculated according to the temperature and density variations alone. The resulting ρ_a model is lower than the measured values at separations greater than 200 m. Next we considered the variation of salt impurities with depth reported by Reference Herron and LangwayHerron and Langway (1979). ρ is assumed to vary with concentration of impurity according to the relationship obtained by Reference Gross, Hayslip and HoyGross and others (1978) and discussed by Reference Shabtaie and BentleyShabtaie and Bentley (1979). The resulting model 2 does not match the measured values for separations greater than 50 m, so it seems unlikely that the reduction of impurities with depth in the J9 hole is responsible for the increase in resistivity.

Fig. 2 Plots of (a) apparent resistivity vs electrode separation, and (b) actual resistivity vs depth at station J9. Solid curves are calculated from models described in the text.

Models 3 and 4 both fit the observed data. For model 3, the resistivity is taken to vary with depth in accordance with changes in crystal cross-sections observed from the core hole. Model 4 shows a resistivity increase that takes place instead entirely in the Wisconsin-age ice. There are no impurity measurements at this depth to confirm or rule out this model, but we suspect that, as at Dome C, Byrd, and Camp Century stations, the impurities in the J9 core increase in the Wisconsin, causing a reduction rather than an increase in resistivity. Therefore, model 3 is preferred. Unfortunately, the strong effect on the apparent resistivities at large electrode separations of the highly-conductive sea-water beneath the relatively thin ice shelf makes it difficult to pin-point transitions deep within the ice.

Station R.I. (80°11'S 161°35'W, Ross Ice Shelf, Antarctica)

This station is located downstream from either ice stream D or ice stream E (the flow bands are not well-defined). The ice is thicker here than at J9, so resistivity variations within the ice column are more easily seen. The results of electrical soundings on two profiles perpendicular to each other are shown in Figure 3(a). The ρ_a values were combined statistically (Reference Shabtaie and BentleyShabtaie and Bentley 1979) beyond an electrode separation of 15 m where the effect of seasonal temperature changes and upper surface density inhomogeneities are absent. Five ρ and corresponding ρ_a models were chosen in this case (Figures 3(a) and (b)). As at the other stations, model 1 is based on density and temperature alone. (Temperatures were calculated assuming a steady-state ice shelf with zero bottom balance rate.) Model 2 Is the same as model 1, except that a bottom melt rate of 0.5 m a⁻¹ was used for the steady-state temperature calculation (this model could also be thought of as reflecting colder temperatures in a non-steady-state ice shelf. Clearly, the resistivities that result even from a large melt rate are not nearly high enough to match the measured data. Therefore, additional factors again must be taken into account.

Fig. 3 Plots of (a) apparent resistivity vs electrode separation, and (b) actual resistivity vs depth at station R.I. Solid curves are calculated from models described in the text.

Models 3, 4, and 5 all yield apparent resistivities that fit the data satisfactorily. All exhibit very high resistivities near the bottom of the ice shelf, as is required by the relatively high apparent resistivities at separations greater than 500 m. They differ substantially, however, in their characteristics at intermediate depths. Model 3 is the simplest, showing only a gradual monotonic increase in resistivity. This model satisfies the observations well. Model 4 was chosen to be similar to the variations fitted at Dome C and J9; it shows that that shape, with a Holocene/Wisconsin transition between 300 and 325 m deep, is also compatible with the apparent resistivities. Model 5 is a more extreme case, originally selected on a curve-fitting basis alone; it is included to give a sense of the range of models that can satisfy the observations. Because of its similarity to the models fit at Dome C and J9, where bore-hole data exist, we prefer model 4 for this site.