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An analysis of errors caused by leakage currents and unintentional potential groundings in the electrical resistivity method

Abstract:

A common error in the electrical resistivity method occurs when a cable connecting to a current or potential electrode is inadvertently grounded at a point other than the intended electrode, thus creating an extra electrode. In this paper, we derive expressions for the magnitude of the induced error of the inadvertent electrode as a function of the position for a homogeneous infinite half-space for a general four-electrode array. We also derive a general expression for the magnitude of the error in terms of the current densities for ground with a general resistivity distribution. We compare the theoretical results for homogeneous ground with small-scale field surveys and find them to be in good agreement.

We show that the error in the measured apparent resistivity has a value that is proportional to the apparent resistivity for an array made up of the inadvertent electrode and the electrode to which it is connected. We find that the induced error becomes very large if the additional electrode is a current electrode and it is placed near a potential electrode or if it is a potential electrode and it is placed near a current electrode. The magnitude of the error is the same whether the additional electrode is a current electrode or a potential electrode. The induced error approaches a constant non-zero value as the additional electrode is moved towards infinity. Resistivity heterogeneity in the ground can either increase or decrease the error depending on the sensitivity of the array formed by the inadvertent electrode and the electrode to which it is connected.

Authors: S.L. Butler a, , L. Pitka  , R.J. Spiteri

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