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Electrical Resistivity & Conductivity

Resistance, apparent resistivity & resistivity

The electrical resistivity of a material is the specific measure of it's resistance to the flow of electric current & has units OhmMetres. The conductivity is simply the inverse quantity. Geophysical survey measures the electrical resistance of the ground & from that an apparent resistivity can be calculated. The value of apparent resistivity is dependent upon the electrode configuration used & for surveys to be compared properly measured resistance values should be converted to apparent resistivity first. The general equation for calculating this is below, where AM, BM, AN & BN are the distances between the current probes A & B & the potential probes M & N. R is the measured resistance (as reported by the Geoscan Research RM15 for example).

rho_a = 2 pi R / [ (1 / AM) - ( 1 / BM) - (1 / AN) + ( 1 / BN) ]

This is especially important for surveys where data is collected at multiple probe spacings to sensitise it to different depths.

Variables

Variations in resistivity are caused by physical changes in the soil, e.g., differences in the quantity of stones, roots, voids etc. per unit volume. The voids, or pores, are the most important factor as they can contain water which, due to the presence of free ions, renders the relatively non-conductive mineral soil able to pass a current. Often the wetting of the pore surfaces will promote further ion exchange potentially raising the conductivity of the water further. Differences between the density of pores will affect the rate at which a soil can drain or become saturated & hence there are temporal differences between soils. The density of pores is dependent upon the formation of the soil & is increased through disturbance.

This is the basis of resistance survey for archaeological studies whereas for geological purposes the different resistivities of the minerals themselves are exploited.

Application

The greater the proportion of water within a soil relative to its neighbours the lower its resistivity will be & less pervious materials like stone will be more resistive than the surrounding soil. However, the technique is not only dependent upon the quantity of water in a soil but also the rate at which it varies & this can have a major effect upon the result. In addition, the simple relationship between soil moisture content & resistivity has to be viewed against the complex background of hydraulic potential & also the relationship between feature size & probe array geometry.

To consider a basic example, a ditch full of porous fill will hold water preferentially & thus appear as a low resistance anomaly. At the same time, the relatively greater depth of this porous soil will locally increase the hydraulic potential of the ground & lead to the upper regions drying faster than the surrounding soil. If the probe array used does not sample the electric potential due to the flow of current below this dry region, the ditch will appear as a high resistance anomaly not a low.

Other factors that need to be considered are:

wet conductive soils above less conductive ground will shield the deeper ground from current flow,
very dry surface soils will limit the injection of current & the detection of buried features,
very dry soil profiles will spread the current & reduce the spatial resolution,
impervious features trap moisture above them & the resulting decrease in resistivity can hide the resistive feature beneath,
porous soil both drains & saturates faster than less porous soil,
vegetation cover & hence the rate of evaporation from the surface can affect the data.