Mathematical Modelling of Buried Electrode Resistivity Response from a Three-Layered Conductive Medium Containing Transitional Layers

Abstract In this work, we study the depth of a buried current electrode that constitutes an effect on the electric potential in a transition multilayer earth. A three-layered earth model is applied to simulate the data of electric potential. The model assumes that an overburden with the thickness has a constant conductivity over the layers of material having the feather of specific conductivity. The model is composed of a set of partial differential equations defined on the spatial domain. The Hankel transform is applied to derive equations defined on the wave number domain from the original problem. On the wave number domain, the analytic solution is determined by solving a boundary value problem. The achieved equations are then transformed back to get the equations defined on the spatial domain. The results of electric potential generated by the three-layered earth model are plotted and compared to indicate the behavior in response to different positions of current source while the parameters in the model are approximately assigned.