Transient electromagnetic field of a vertical magnetic dipole above an atmospheric surface duct Hassan A. Zedan * , Adel Abo Selim Department of Mathematics, Faculty of Education, Kafr EL-Sheikh, Egypt Abstract The transient electromagnetic field generated by a vertical magnetic dipole above an atmospheric surface duct is investigated theoretically. The method used for the solution is essentially based on the application of which the two functions transform. Two in- tegral transforms of the wave equation of Fitzgerald vector – a Laplace transform in time and a two-dimensional Fourier transform in the horizontal coordinates in space – are applied. This leads to an integral representation of the solution of the wave equation in the transform space, considering initial, boundary and transition conditions. Saddle point and residue methods are used to compute the integral. Ó 2002 Published by Elsevier Science Inc. Keywords: Electromagnetic field; Vertical dipole; Laplace transform 1. Introduction Radiometeorologists have extensively studied the correlation between the propagation of electromagnetic waves in the atmosphere and meteorological conditions. Today, interest is mainly concerned with the effect of the atmo- sphere and target identification and imaging. Kahan and Eckart [1] studied the electromagnetic field due to a dipole placed within a uniform-height duct, and at arbitrary height from the conducting earth. The duct here is the middle medium of the three media (earth–air–ionosphere). The model assumes a Applied Mathematics and Computation 128 (2002) 141–148 www.elsevier.com/locate/amc * Corresponding author. E-mail address: zedan@edu-kaf.edu.eg (H.A. Zedan). 0096-3003/02/$ - see front matter Ó 2002 Published by Elsevier Science Inc. PII:S0096-3003(01)00025-X