Contact impedance of grounded and capacitive electrodes

Abstract

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 coupling may be superior to galvanic coupling. The standard equations for the impedance of capacitive electrodes assume 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, I review existing equations for the resistance of a galvanically coupled, spherical electrode in a fullspace. I extend the theory to the general case of a sphere in a spherically layered fullspace which may display both galvanic and capacitive coupling. 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. For very high resistivities around 1 M�, the transition frequency reduces to 100 Hz. Thus, in principle, one may determine electrical resistivity and permittivity by measuring magnitude and phase of the electrode contact impedance.