IKO is amplitude equivalent if the amplitude satisfies transport equation of the ray method (see equation (36), Chapter 4). It follows from the definition that equations (86) and (90) describe amplitude equivalent operators for homogeneous 3D and 2D media. And it is important to notice that the omitted terms (compare equations (85) and (86) as well (88) and (86)) do not influence the behavior of the senior discontinuity.

In order to construct the amplitude equivalent IKO for continuous inhomogeneous media, we may use the integral representation (82) of the solution of equation (81). It was mentioned above that the explicit expression of Green's function for inhomogeneous media is unknown. But it is sufficient to find the senior discontinuity of the Green's function by the ray method.

Ray approximation of Green's function for the equation (81) with mixed boundary conditions is

whereFinally one can receive that the weight function of the amplitude equivalent IKO is

where is the angle between the ray from to and the vertical axis.1/13/1998