On asymptotics of a wave field near the origin of an interference head wave

Let an incident wave propagates in a medium with wave-speed c
₁
and illuminates a convex interface to a medium with propagation speed c
₂
, c
₂
> c
₁
. Let at some point O an incident ray meets an interface under critical reflection angle, then such a point looks like a source of an interference head wave which propagates in the first medium along the interface with the speed c
₂
. The wave field in a vicinity of O is rather complicated. In the paper, we discuss its high-frequency asymptotics.