INTRODUCTION

Resistivities of earth materials vary by over forty orders of magnitude (powers of ten) from native metals at the low end to diamond at the high. First we’ll look at conduction mechanisms in (dry) minerals. Then we’ll discuss rocks and sediments in which most conduction is through the pore fluid.

METALLIC CONDUCTORS

In metallic conductors the electrical current takes the form of moving electrons flowing from regions of low potential to regions of high. Typically there is about one free electron per atom to participate in conduction. Resistivity increases with impurities and with temperature (about half a percent per degree C). At extremely low absolute temperatures metals become superconductors with even lower resistivity. Native metals such as copper, silver and gold as well as graphite are metallic conductors. They have the lowest resistivities of any earth material.

ELECTRONIC SEMICONDUCTORS

These materials have very low resistivities but not as low as metals. Conduction is by electrons and "holes". These are places where a valence electron is missing. Holes act as positive charges (?) and drift in the opposite direction with respect to the free electrons. For these materials resistivity decreases with temperature as more electrons are freed to carry the current. Sulfide, oxide and arsenide minerals are electronic semiconductors.

SOLID ELECTROLYTES

This group of minerals has higher average resistivity than the two previous groups. As the name implies, conduction is by ions. Small positive ions (cations) such as magnesium and iron are often the dominant charge carriers. These conduction ions may be impurity ions, interstitial ions and even missing ions; in other words not the stoichiometric ions of the ideal crystal lattice. Anions (negative ions) don’t play much of a role as they are about an order of magnitude larger than the cations and thus are too big the move easily through the crystal lattice.

Resistivities of these minerals drop with temperature. At low temperatures there is lots of sample to sample variation with conduction largely by impurities. At higher temperatures, as in the mantle, conduction is largely by cations freed from their lattice sites and there is much less sample to sample variation.

The common rock-forming silicate minerals such as olivine, feldspar and quartz are solid electrolytes.

"WET" ROCKS AND SEDIMENTS

In sediments and rocks in the (upper?) crust conduction is predominantly by ions in the pore fluids. The porosity may be between grains or take the form of joints, fault zones, microcracks and solution cavities.

Archie’s Law states that resistivity is directly proportional to pore fluid resistivity and inversely related to the porosity. We should be careful using this relationship as it is based on measurements of "clean" (without clay minerals) sandstones and limestones in oil fields and on a small range of porosities. A variety of theoretical formulae have been developed for specific idealized pore geometries; Maxwell’s formula is a typical example.

EFFECT OF PARTIAL SATURATION

Archie’s Law can be modified to account for partial saturation. With little pore fluid in a sedimentary rock, the fluid is isolated at separate grain contacts. There are no continuous connects throughout the rock and resistivity is very high, approaching that of the solid grains. For more pore fluid, continuous films on the grains begin to form a continuous fluid network and resistivity becomes very low. Adding more fluid now has little effect and resistivity only decreases a little.

Similar effects are seen in partially melted rocks where films and pockets of magma are much more conductive than the surrounding rock. The same effect is seen in silicate rocks with isolated or connected conductive minerals such as graphite, sulfides and oxides

RESISTIVITY AND THE WATER TABLE

In our field work we often see a difference between the water table depth estimated by seismic refraction and by resistivity sounding. The explanation is that resistivity decreases most noticeably for increase of saturation when the saturation is small. Compressional wave velocity is almost unchanged with respect to saturation until saturation is well over 90 percent. Thus the resistivity water table may correspond more closely with the top of the capillary fringe than with the true water table. For clay-rich sediments the resistivity may be very low and roughly constant regardless of saturation. In such materials resistivity soundings will not indicate any water table at all.

EFFECT OF FREEZING

As ocean water or pore water starts to freeze, the salinity of the pore water increases. Thus we are forming pure ice with a very high resistivity and residual pore water with lower resistivity than the original fluid phase. The result of these competing processes is that the increase of resistivity from freezing may occur over a substantial temperature range.

Resistivity profiles with tiny (mm) electrode spacings are used to find acid layers and cryptic volcanic ash layers in cores from ice sheets and glaciers. Typically the resistivity of cold polar ice is only one percent or less than values for pure laboratory ice.

EFFECT OF HUMID AND ARID CLIMATES

In humid climates there is generally an average downward flow of rain water and snow melt. The result is that ions are leached from the surficial layer and concentrated at depth. Thus the top layer resistivity may be quite high except for the zone of soil moisture.

In arid areas, in contrast, there is typically an upward flux of evaporated water. Ions are removed at depth and then precipitated out in pore spaces near the surface. The result may be near-surface cemented zones ("caliche") of high resistivity or low-resistivity zones of very salty soil moisture.

PERMEABILITY, POROSITY AND RESISTIVITY

In New England experience shows that permeability and hydraulic conductivity increase with resistivity. Clays have the lowest values of both properties and gravels have the highest. Some laboratory experiments, however, show that permeability drops as resistivity increases. How can we reconcile these contradictions?

Using a simplified model of pore geometry we discover that these relationships are a result of the distribution of pore sizes, not just the total porosity. If the pore radii are proportional to the porosity the permeability is inversely proportional to the resistivity. This situation may correspond to the lab experiments, which deal only with a small range of parameters. If the pore radii are inversely related to porosity, as in the field studies, then the permeability is directly proportional to the resistivity. These models ignore the possible systematic variation of pore fluid resistivity with pore size and also ignore surface conduction on clay minerals.

RESISTIVITY IN THE DEEP CRUST

Many sounding experiments indicate that in many places the deep crust has very, very low resistivity. At least three explanations have been advanced. One is that the pore water is extremely salty. Another is that there are conducting networks of minerals such as pyrite. The third is that there are networks of graphite. Locally, as along the mid-ocean ridges and near volcanoes, low resistivity may be caused by conducting networks of magma.