A Fredholm integral equation method for propagation predictions over small terrain irregularities

Two-dimensional propagation of vertical line source fields over lossy, irregular terrain is considered using the magnetic field integral equation. The terrain is characterized by its elevation profile and the local surface impedance, both of which may vary with distance. For treatment via the Fredholm integral equation, the domain under consideration is made finite by enclosing the terrain irregularity and the source within an arbitrary outer boundary. Absorbing boundary conditions are imposed on the outer boundary to reduce unwanted reflections from it. The integral equation is solved by the boundary element method with quadratic elements. Substantial comparison is made with specific canonical problems, with previously published results of other workers, and with measurements to validate the method