A method to study the soil parameters’ frequency dependence of horizontally multilayered earth is developed. It is achieved by multifrequency inversion. Apparent resistivity can be obtained from the potential difference and the injecting current. Since the inversion is performed simultaneously at multiple frequencies and the inversion at each studied frequency is independent, parallel computing can be used to improve the efficiency of the inversion algorithm. The inverse problem in this study is an unconstrained optimization problem. So one of the central issues is the optimization of model parameters. Simulated annealing algorithm adopted in this study is an effective method to solve this kind of problem. The difference between the two calculation results based on the dynamic state field theory and quasi-static field theory is studied. The proposed method is validated by the interpretation of measurement data. The frequency dependence of soil parameters is studied by applying the method to interpret spectral-induced polarization data.

A mathematical model of the partial-element equivalent circuit method is developed in this paper that can be used to accurately calculate lightning current along a high-voltage alternating current substation grounding system buried in multilayered soil. Combined with the fast Fourier transform (FFT), the conduction effect of the components of the current harmonics is analyzed, and the effect of capacitance and induction between layers of soil are examined. Furthermore, the effects of the frequency-dependent conductivity and permittivity of the soil are considered. To speed-up calculation, the quasi-static complex image method and a closed form of Green’s function are used. Through the inverse FFT, the model can calculate the distribution of lightning current in any grounding system. This can be used to study the performance of the system’s response to transient lightning.

In this article, we propose a numerical method for accurately simulating the distribution of the lightning current along a grounding grid in a horizontal multilayered earth model. The mathematical model is based on the Galerkin's boundary element method where the quasi-static complex image method and the closed form of Green's function are used for calculations. Furthermore, the effects of the frequency-dependent conductivity and permittivity of the soil are considered. Analytical expressions are also derived for the mutual impedance and induction coefficient. The proposed model can calculate the distribution of the lightning current along a grounding system using the inverse fast Fourier transform and it can be employed to study the transient lightning response characteristics of a grounding grid.

A method to estimate frequency domain soil parameters of horizontally multilayered earth is developed. Cole–Cole model of complex conductivity form is adopted to describe the frequency dependence of soil parameters. The estimation of frequency domain soil parameters includes two stages. In the first stage, soil‐layered structure is determined under the DC field by the interpretation of resistivity sounding data. The obtained model parameters in this stage include the DC soil conductivity and thickness of soil layers. In the second stage, Cole–Cole model parameters are estimated based on the soil‐layered model obtained in the first stage. The theoretical formula of complex apparent resistivity is derived from Green's function with considering dynamic‐state field theory. Since dynamic‐state field is considered in the inversion algorithm, this method can be extended into high‐frequency domain. Discrete complex image method is used to calculate Sommerfeld integral quickly. In order to remove electromagnetic (EM) coupling between cables at high frequencies, a new electrode configuration method is proposed. Genetic algorithm is improved by combining with parallel computing. The parallel genetic algorithm is applied to the optimisation of model parameters.

A method to estimate soil parameters of horizontally multilayered earth model in frequency domain is developed with considering high‐frequency field. The theoretical formula of complex apparent resistivity with considering high‐frequency field is derived from Green's function. To avoid time‐consuming numerical integration, complex image method is introduced to solve Sommerfeld integral. Simulated annealing algorithm is applied to optimise soil parameters. The accuracy of this method is confirmed by interpreting field data under the DC field. As the inversion results of this method are different from other literature's results in a four‐layer model, the posterior analysis is made. Then this method is applied to the inversion of frequency domain soil parameters under both quasi‐static field and high‐frequency field. The differences of complex apparent resistivity distribution between quasi‐static field and high‐frequency field are compared at different frequencies.