Wave propagation in air from a vertical magnetic dipole located in three rough-layered structures

Abstract

In this paper, the field scattered in the upper medium (air) by a system composed of three homogeneous media (air–sea–ground) that are separated by two rough interfaces is derived from a perturbation technique. The source is located in the inner medium (seawater), which is a vertical magnetic dipole. Then, by applying the boundary conditions at each interface, the scattered field in each medium is derived analytically and expressed using the Hankel transformation (integral over the radial distance r). This research assumes that the modulus of the sea permittivity () is much larger than that of the air and that the parameter (far field assumption), closed-form expressions of the involved integrals are found for the scattered field in the air by using an approximate method. No pole is considered and therefore the formulation is consistent with previous published results. Numerical results are given and represented graphically. In addition, this research presents a comparison of the results obtained here with those of one rough surface and two planar surfaces. This study will be useful for remote sensing of the ocean surface, especially when the transmitter is close to the surface.