An Analytical Solution of Electromagnetic Radiation of a Vertical Dipole Over a Layered Half-Space

An analytical solution for the wave scattering generated by a vertical dipole above horizontally stratified media is proposed. The solution to the problem is given in terms of 2-D Fourier transforms, which leads to Sommerfeld-type integrals. The solution is decomposed into three terms and an analytical closed-form solution as a function of physical layers specification for the electric field intensity is deduced from the results. Two terms are expressed with hyperbolic functions and the third term is presented using the Gauss error function. A numerical evaluation of the integrals that constitute the formal result of the problem validates the accuracy and efficiency of the proposed solution at various frequencies as well as at different distances from the source. The presented solution is also implemented for the particular case of surface ocean scattering in the high frequency (HF) band and the overall behavior of the solution, which consists of three terms, is evaluated by their distance from the antenna in the near field and far-field regions.