An analytical four-layer horizontal electric current dipole model for analysing underwater electric potential in shallow seawater

The paper presents a new analytical four-layer (air–water–bottom–non-conductive layer) horizontal electric dipole model which allows an accurate approximation of ship's Underwater Electric Potential (UEP) from a sufficient depth in shallow coastal marine waters. The numerical methods, usually Finite Element Method (FEM) or Boundary Elements Method (BEM), are typically used to estimate the electric field and the distribution of static electric components of UEP around the ship. These methods enable analyses with high accuracy but, compared to other point-electrode methods and the proposed analytical model, they are relatively complex and need high computational time. The developed analytical model proposed in this paper allows real-time calculations without significant loss of accuracy of the UEP estimations. In the model, the problem of boundary values at the borders of individual layers is solved using the reflection/image method and applying the idea of continuity of electric potential at a given boundary between two adjacent layers. Its accuracy is verified based on the synthetic data provided by specialised software packages making use of FEM and BEM numerical methods. A dimensionless quantitative analysis of the relationships between basic parameters of the proposed four-layer analytical model and their impact on the accuracy of representation of individual electric field strength components is also delivered. The relationships between water and bottom conductivity and between water depth and bottom thickness are investigated and described. The obtained results show that the developed model allows detailed and reliable analysis of the electric field, especially in shallow coastal waters.