A Kirchhoff Integral approach to estimating propagation in an environment with nonhomogeneous atmosphere and complex boundaries

For terrestrial radio wave propagation, it has been previously demonstrated that second order effects, such as diffraction, can be estimated through a combination of geometric optics and Kirchhoff style integral relations. In the present paper, it is shown that the approach can also yield accurate estimates when refractive effects, such as atmospheric ducting, are present.