Two-and-one-half dimensional in-plane wave propagation

The purpose of this paper is to collect certain wave propagation results in two-and-one-half dimensions - defined as three dimensional propagation in a medium that has variations in two dimensions only. The results of interest are for sources and receivers in the plane determined by the two directions of parameter variation. The objective of this work is to reduce the analysis of the in-plane propagation to two dimensional analysis while retaining - at least asymptotically - the proper three dimensional geometrical spreading. We do this for the free space Green's function and for the Kirchhoff approximate upward scattered field from a single reflector. In both cases, we carry out a derivation under the assumption of a background velocity with two dimensional - c(x,z) - variation; we specialize the results to a constant background velocity and a depth dependent background velocity. For the convenience of the user we have included a glossary and two tables of equation numbers to help in finding specific results. Keywords include: Ray method; Geometrical optics; Wave propagation; Green's function; Jacobian; Travel time; and WKB.