Wide-angle formulation of the Beilis-Tappert method

The theory and numerical examples are given for a wide-angle formulation of the Beilis-Tappert method for wave propagation over irregular terrain. The vertical wave number k in the Beilis-Tappert method is not a physical wave number. Consequently, an essential but previously unknown element of the Beilis-Tappert method is the need to use a slope-dependent k-space vertical wave number filter. The filter selects the physical vertical wave numbers in k-space integrals. The importance of the vertical wave number filter ("k-control") is demonstrated theoretically and numerically for propagation over a steep hill and over a shallow hill. For the steep hill, it is shown that k-control is as important as the extension to wide angles. For the shallow hill, k-control and the wide-angle extension are much less important, so that, for some applications, the original narrow-angle formulation gives acceptable accuracy.