Three‐Dimensional Numerical Modeling of a Capacitance Probe

In this study, a three‐dimensional model represents a capacitance probe measurement. It is based on Laplace's equation, which is solved using the Finite Element Method. A three‐dimensional model can accurately represent both the probe geometry and nonaxisymmetric components of soil heterogeneity. As a result we have obtained a three‐dimensional‐cartography of electrical potential V ( x , y , z ) in the medium surrounding the electrodes and the effective dielectric constant of the media observed. The model was implemented to address such questions as the influence of the air/soil boundary when making measurements near the surface and the probe's volume of influence. It is shown that the volume of influence of the probe can be derived from a weighting function based on the density of electromagnetic energy and can be computed for a homogeneous medium. It is numerically observed that the probe's volume of influence is quite independent of the permittivity of the medium in which the probe is embedded. It is then verified that dielectric perturbations located outside the so defined volume of influence have little effect on the calculation of the effective dielectric constant seen by the capacitance probe.