Geometrical ray theory; edge-diffracted rays and their traveltimes (second-order approximation of the traveltimes)

The general laws presenting global properties of reflected and transmitted rays are extended to the edge-diffracted rays by the use of the law of edge diffraction. Similar to reflected and transmitted rays, edge-diffracted rays and their traveltimes are described by the same four 2 X 2 matrices that are submatrices of the symplectic ray transformation matrix. If the incident rays have no line and point focus in the reflector having edges, one cone of diffracted rays corresponds just to one diffraction point. Otherwise, there may be an infinite number of cones of diffracted rays that are from one and the same diffraction point, and there may be no diffracted ray if the incident rays have a point focus in the reflecting surface with edges. For some cases, edge diffractions are the same as those from point diffractors and all diffracted rays are focused on the point focus of the reflected rays in the earth's surface.