Analytical representation of the surface wave generated by an antenna at the interface between two homogeneous media

Theoretical approach to the solution of georadiolocation (inverse) problem of reconstructing the antenna current and the permittivity of the underlying surface, based on the measurements of the field propagating along the Earth℉s surface, is proposed. An expression for the tangential component of the electric field of the surface wave from a transmitting antenna lying in the plane of discontinuity of two homogeneous media is expressed in terms of the Laplace function Ŵ(q, ζ) of two complex arguments for any discontinuity parameters. The function Ŵ(q, ζ) is presented as series, which make it possible to calculate rapidly the values of Ŵ(q, ζ) and investigate its analytic properties. The inverse Laplace transform is performed by integrating the function Ŵ(q, ζ) over closed contours. The corresponding integrals are proper in this case, due to which the calculation time greatly decreases in comparison with the Fourier transform. When the permittivity dispersion can be neglected, the tangential component of the surface wave is algebraically expressed in terms of the function Ŵ(q, ζ). This circumstance allows one to decrease the time for calculating the surface wave at a specified point to several milliseconds and determine both the current through the transmitting antenna and the permittivity of the underlying surface for a few seconds.