An integral equation method for low frequency electromagnetic fields in three-dimensional marine environments

Electromagnetic fields in three-dimensional marine environments are modelled in this paper. In particular, a volume integral equation method is used to calculate the electromagnetic fields from low frequency dipole sources in regions with varying bathymetry and sub-bottom structure. The horizontal variations are imbedded inhomogeneties in a horizontally stratified background model of the environment. A contracted (regularised) integral equation is derived and the resulting linear system of equations are preconditioned by the extended Born operator and solved by a conjugate-gradient algorithm. The solution to the extended Born approximation is chosen as the initial guess. Low frequency electromagnetic fields in conductive environments implay sparse system matrices, which makes this numerical method fast and memory efficient. A numerical example demonstrates the convergence of the solution as a function of the cell size in the discretisation of the volume. The convergence speed of the interative solver as well as the accuracy of the extended born approximation is shown. The example also demonstrates the effects on the electric field due to a range dependent bathymetry in a shallow marine environment.