In this talk, we introduce a two-dimensional first-kind integral model used in applied geophysics to investigate subsoil properties in a non-invasive way. The model describes the interaction between the soil and an electromagnetic device. The aim is to reconstruct the electrical conductivity of the soil from electromagnetic data. The definition of the two-dimensional model is derived, and a numerical study of the forward model based on Gauss-Legendre quadrature formulae is presented. To solve the inverse problem, a linear system obtained from the discretization of the integral equation in the model is considered. The main difficulty is the severe ill-conditioning of the system, so a regularization strategy is applied to obtain good solutions. Some numerical tests show the effectiveness of the proposed approach.