In this paper, we have derived a novel integral representation for the ground wave propagation over land-to-sea mixed-paths by applying the Helmholtz-Kirchhoff integral theorem. By using the method of stationary phase applicable uniformly as the stationary phase point approaches the endpoint of the integral, we have derived the asymptotic solution for the scattered fields consisting of the first-order and the second-order diffraction terms. We show that the asymptotic solution thus derived agrees with the asymptotic solution derived by applying the aperture field method (AFM) and the method of stationary phase. We have confirmed the validity and the utility of the novel integral representation and its asymptotic solution by comparing with the widely used mixed-path theorem and the experimental measurement performed in Kanto area and Tokyo bay.

Locality in high frequency diffraction is embodied in the Method of Moments (MoM) in view of the method of stationary phase. Local-domain basis functions accompanied with the phase detour, which are not entire domain but are much larger than the segment length in the usual MoM, are newly introduced to enhance the cancellation of mutual coupling over the local-domain; the off-diagonal elements in resultant reaction matrix evanesce rapidly. The Fresnel zone threshold is proposed for simple and effective truncation of the matrix into the sparse band matrix. Numerical examples for the 2-D strip and the 2-D corner reflector demonstrate the feasibility as well as difficulties of the concept; the way mitigating computational load of the MoM in high frequency problems is suggested.