A refinement of the Kirchhoff approximation to the scattered elastic fields.

We study two canonical problems, diffraction of a plane elastic wave by a thin crack and diffraction of a plane elastic wave by a wedge, both in the high-frequency regime. In applications this regime is usually treated using the so-called Kirchhoff approximation. It is very easy to implement but there are situations when it is known to give distorted results. We discuss an easy correction procedure, which is applicable not only in geometrical regions but inside penumbras too. The procedure involves a version of the Physical Theory of Diffraction that relies on the Geometrical Theory of Diffraction rather than the full solution of the corresponding canonical problem.