Normal Modes, Virtual Modes, and Alternative Representations in the Surface Duct Problem

Abstract

The surface duct model first proposed by W. H. Furry [D. E. Kerr, Propagation of Short Radio Waves (McGraw-Hill, New York, 1951), pp. 140–174] has formed the basis for most studies of surface duct transmission loss. Most recently, Pedersen and Gordon [J. Acoust. Soc. Amer. 47, 304–326 (1970)] have improved the accuracy of the computations necessary for the implementation of this model. At first sight, Furry's analysis appears very different from the virtual mode treatment of duct leakage [F. M. Labianca (to be published)]. The connection between the two approaches is established. Each treatment is shown to yield an alternative representation of the solution. The virtual mode results follow from an eigenfunction expansion of the solution, whereas Furry's treatment yields an alternative residue representation. The virtual mode theory of duct leakage is shown to be both conceptually more satisfying and computationally simpler than the theory of Furry. [Work supported by the Office of Naval Research under contract.]