Geophysical exploration to estimate conductivity and permittivity model of an excavated soil block

Abstract

An electrical model for a real stratified soil block is proposed in this paper. The model is suitable to estimate the physical properties of electrical conductivity and permittivity, as well as the thickness of each of the layers of the subsoil. For the estimation, we implement a methodology based on the efficient numerical solution of the Takahashi et al. infinite integrals for calculating the vector potentials at the soil surface. For the truncation of the infinite integrals, a new exponential based truncation criterion is proposed. Subsequently, to evaluate a more accurate fitting of the apparent resistivity curves obtained by measurements and by the Takahashi et al., integrals, two numerical optimization techniques based on genetic algorithms, and least squares method are implemented for accuracy assessment. Finally, a formal quantitative validation methodology is presented in this paper based on the comparison of the numerical optimization results with respect to a data set obtained by direct measurements of the electrical resistivity on the vertical excavation profiles on each subsurface layer down the experimental workstations named Site-1, 2, \ldots 4.