Estimation of Errors Related to Usage of Low-Frequency Resistivity in Measurements of Complex Soil Permittivity

Frequency-dependent soil properties are important in calculations related to transmission line performance. In some cases, the properties are modeled using complex permittivity. In order to calculate the imaginary part of the permittivity, direct current resistivity should be known. There are some difficulties in measuring direct current resistivity and frequency-dependent soil properties with a single device. Therefore, low-frequency resistivity is sometimes used instead of direct current resistivity. The work estimates complex permittivity errors related to this approximation and the relevance of those errors to practical simulations. It was shown that using low-frequency resistivity might lead to significant errors in the imaginary part of permittivity. And to reduce those errors, low-frequency resistivity should be measured at a frequency much lower than the lowest frequency of the required frequency range. At the same time, in practice, to accurately model frequency-dependent resistivity for a certain frequency range, it is sufficient to use relatively high frequency values for the low-frequency resistivity. In other words, high accuracy is not always required for the imaginary part of permittivity. For example, the Debye model (often used in finite difference time domain simulations) accurately approximates soil properties even when the low-frequency resistivity is measured at a frequency only a few times lower than the lowest frequency of the required frequency range. In some cases, the lowest frequency of the required frequency range can be used for the low-frequency resistivity.