The contribution of the edge effects in the multiple high-frequency Kirchhoff diffraction by plane surfaces

In the context of wave propagation through a three-dimensional acoustic medium, we develop an analytical approach to evaluate the boundary edge effects in the high-frequency multiple diffraction by thin rigid obstacles. Starting from a multi-fold integral representation of Kirchhoff type, suitable asymptotic estimates are applied to the arising diffraction integrals so as to derive explicit formulas regarding two concrete examples of double reflection from plane surfaces. The corresponding results turn out to agree with those previously provided by a well-known theory of diffraction. The precision of the above formulas is finally controlled by comparison with the results from direct numerical treatments of the main integrals involved.