Current induced on a pair of wires above earth by a vertical electric dipole for grazing angles of incidence

Exact expressions for the current induced on a pair of horizontal wires above the earth by a vertical electric dipole have been available for some time. It is well known that the wire currents can be expanded as a continuous spectrum current plus a sum of discrete modal currents. Each current consists of a monofilar and a bifilar component. In this paper, conditions for which the currents can be approximated either by the discrete modal currents or a simple approximation to the continuous spectrum current are found. For simplicity it is assumed that the earth is perfectly conducting and that the wires are thin and can be characterized by a surface impedance boundary condition. Using steepest descent integration, the case for grazing incidence (distance from source to observation point R greater than the perpendicular distance from the source to the center of the wire array r) is examined. It is found that either the monofilar or the bifilar component of current can be written as a single term which is proportional to 1/R if R is of the order of r or to 1/R^5/2 if R is ‘very large.’ In the intermediate range the discrete modal currents dominate the solution. Transition solutions valid between these ranges are given.