Scattering of high-frequency waves by surfaces in continuous media with allowance for rereflections

This study is devoted to the development of the ray theory of diffraction in application to arbitrary (nonconvex) smooth obstacles in the scalar case. A three-dimensional problem is considered. An asymptotic method of estimating the diffraction integrals is described. The method is based on the multidimensional stationary phase approach. The diffraction integrals are obtained on the basis of the generalization of the Kirchhoff physical theory of diffraction. Explicit expressions are derived for the pressure in the reflected wave in the cases of its single and double reflections.