Application of generalized impedance boundary conditions to sommerfeld half-space problem

摘要

Generalized impedance boundary conditions are employed to simplify the solution of the Sommerfeld half-space problem. An analytical expression is derived for the Hertz potential of a vertical electric dipole over the earths surface, in which the earth is assumed to be a layered media or homogeneous dissipative half-space. A Sommerfeld type integral in the potential function is expressed as the sum of two parts; a zeroth order Hankel function and an absolutely convergent series of Bessel functions. In addition, two expressiong in closed form are obtained as the far-field and near-field approximation of the present result.