Publication Date:
2013-03-12
Description:
The contact impedance of electrodes determines how much current can be injected into the ground for a given voltage. If the ground is very resistive, capacitive electrodes may be an alternative to galvanic coupling. The impedance of capacitive electrodes is often estimated with the assumption that the halfspace is an ideal conductor. Over resistive ground at high frequencies, however, the contact impedance will depend on the electrical properties, i.e. electrical conductivity and permittivity, of the subsurface. Here, we review existing equations for the resistance of a galvanically coupled, spherical electrode in a fullspace, and extend the theory to the general case of a sphere in a spherically layered fullspace. We then develop a method to calculate the impedance of a spherical disc over a homogeneous halfspace. We carry out modelling studies to demonstrate the consistency of the algorithms and to assess under which conditions the determination of the electrical parameters from the impedance may be feasible. For a capacitively coupled electrode, the common assumption of an ideally conducting fullspace (or halfspace) breaks down if the displacement currents in the fullspace become as large as the conduction currents. For a moderately resistive medium with 1000 m this is the case for frequencies larger than 100 kHz. The transition from a galvanically coupled disc to a disc in the air is continuous as function of distance. However, depending on the electrical parameters and frequency, the impedance may vary by several orders of magnitude within a few nanometers distance or less. We derive a simple equation to assess under which conditions the impedance is independent of the electrode height, which may be important for determining subsurface permittivity and conductivity in cases where control on the exact geometry is difficult. Our theory is consistent with measured data obtained in a sandbox in the laboratory.
Print ISSN:
0956-540X
Electronic ISSN:
1365-246X
Topics:
Geosciences
Published by
Oxford University Press
on behalf of
The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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