An Integral Equation Approach to the Problem of Wave Propagation over an Irregular Surface
In this paper there is derived an approximate formulation of the problem of a scalar wave propagated over an irregular bounding surface. This formulation takes the form of a one-dimensional Volterra integral equation, which can, or so it appears, be very useful in numerical calculations of field intensities. In addition, analytical solutions of this equation are obtained in three special cases: an isotropic radiator (1) at the surface of a plane, homogeneous earth, (2) elevated above a plane earth, and (3) at the surface of a homogeneous sphere. The point to be made about these three special cases is that they all have been solved by the other, more exact methods; but the solutions presented here and obtained from the integral equation formulation are almost identical with these classical solutions.