Using the antenna impedance to estimate soil electrical parameters for the MIST global 21-cm experiment

Radio experiments trying to detect the global $21$~cm signal from the early Universe are very sensitive to the electrical properties of their environment. For ground-based experiments with the antenna above the soil it is critical to characterize the effect from the soil on the sky observations. This characterization requires estimating the soil's electrical conductivity and relative permittivity in the same frequency range as the observations. Here we present our initial effort to estimate the conductivity and relative permittivity of the soil using the impedance of an antenna mounted at a distance above the surface. In this technique, the antenna used for soil characterization is the same as the antenna used for sky observations. To demonstrate the technique we use the antenna of the MIST global $21$~cm experiment. We measured the antenna impedance at three sites in the Greater Concepci\'on area, Chile. The measurements were done between $25$ and $125$~MHz, matching the range used by MIST for sky observations. The soil parameters were estimated by fitting the impedance measurements with electromagnetic simulations of the antenna and soil. In this initial effort the soil was modeled as homogeneous. The conductivity at the three sites was found to be between $0.007$ and $0.049$~Sm$^{-1}$, and the relative permittivity between $1.6$ and $12.7$. The percent precision of the estimates at $68\%$ probability is, with one exception, better (lower) than $33\%$. The best-fit simulations have a better than $10\%$ agreement with the measurements relative to the peak values of the resistance and reactance across our frequency range. For MIST, these results represent a successful proof of concept of the use of the antenna impedance for soil characterization, and are expected to significantly improve in future implementations.