Formulation of non‐ray acoustics

The resolvent Green's function technique of Marcuvitz (1951) is used to obtain a contour integral solution for the acoustic field due to a point source located in a vertically inhomogeneous ocean. The integrand of the contour integral is composed of the product of a depth‐dependent Green's function and a range‐dependent: Green's function. The contour must separate the singularities of the two Green's functions. Various representations are obtained by deforming the contour of the integration. The Fourier‐Bessel integral representation is derived from the contour integral, and this derivation is compared with the work of Freehafer (1951), Brekhovskikh (1957), and Wait (1962). Evaluation of the various integral representations is accomplished by using Cauchy's residue theorem, stationary phase methods, and numerical integration techniques. The residue and stationary phase evaluations are then interpreted in terms of modes and rays.