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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.

The time domain reflectometry (TDR) probe is a technique applied to soil moisture measurement. This probe is a waveguide composed of two or three parallel metallic rods inserted in the ground, between which one applies a step function of potential. The main objective of this paper is to contribute to the interpretation of the signals obtained at the entrance of the probe. The theoretical approach is formulated using two-dimensional Maxwell equations and we propose to take into account the transient polarization of the medium. We have simulated the waveguide in this medium, using the finite element method.